700-175=525. 525/35=15
Need help!
What is the area of this triangle?
Enter your answer as a decimal in the box round only your final answer to the nearest tenth.
The answer is:
The area of the triangle is:
[tex]Area=13.2cm^{2}[/tex]
Why?We can solve the problem using the Side-Angle-Side (SAS) method, to calculate the area of a triangle given two sides and a single angle.
The SAS method to calculate the area of a triangle is given by the following the equation:
[tex]Area=\frac{abSinC}{2}[/tex]
Where,
a and b are the known sides.
C is the known angle
Now, we are given a triangle with the following dimension:
[tex]Side_{a}=7cm\\Side_{b}=8cm\\\alpha=28\°[/tex]
Then, using the information and solving we have:
[tex]Area=\frac{7cm*8cm*Sin(28\°)}{2}[/tex]
[tex]Area=\frac{56cm^{2}*Sin(28\°)}{2}\\\\Area=\frac{56cm^{2}*0.47}{2}\\\\Area=\frac{26.32cm^{2}}{2}\\\\Area=13.16cm^{2}[/tex]
Hence, the area of the triangle, rounded to the nearest tenth is:
[tex]Area=13.2cm^{2}[/tex]
Have a nice day!
Which of the sets of ordered pairs represents a function?
A = {(3, −5), (4, 6), (−3, 9), (2, 7)}
B = {(2, 4), (−1, −7), (5, 6), (4, 3)}
Only A
Only B
Both A and B
Neither A nor B
Answer:
Both A and B
Step-by-step explanation:
A = {(3, −5), (4, 6), (−3, 9), (2, 7)}
-Each x goes to a different y so this is a function
B = {(2, 4), (−1, −7), (5, 6), (4, 3)}
-Each x goes to a different y so this is a function
The population of a town is decreasing at a rate of 1% per year in 2000 there were 1300 people write an exponential decay function to model this situation then find the population in 2008.
A.) 1200 people
B.) 1300 people
C.) 1500 people
D.) 1100 people
Answer:
b
Step-by-step explanation:
Based on the rate at which the population is decreasing, we can calculate that population in 2008 is A. 1,200 people
The population after a certain number of years is:
= Population now x (1 - rate) ^ number of years
The number of years is:
= 2008 - 2000
= 8 years
The population in 2008 is therefore:
= 1,300 x ( 1 - 1%)⁸
= 1,199.57
= 1,200 people
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On a piece of paper, graph y-3>2x+2. Then determine which answer choice matches the graph you drew
ANSWER
Option C
EXPLANATION
The given inequality is
[tex]y - 3 \: > \: 2x + 2[/tex]
We add 3 to both sides to get,
[tex]y \: > \: 2x + 2 + 3[/tex]
[tex]y \: > \: 2x +5[/tex]
The corresponding linear equation is
[tex]y = 2x + 5[/tex]
This becomes the dashed boundary line of the inequality.
We test the origin to determine which half plane to shade.
[tex]0\: > \: 2(0)+5[/tex]
[tex]0\: > \: 5[/tex]
This is false.
Hence we shade the upper half plane.
The correct answer is C
Benito runs 1/10 of a mile each day. Which shows how to find the number of days it will take for Benito to run 3/5 of a mile?
A. divide 1/10 by 3/5
B. divide 1/10 by 5/3
C. divide 3/5 by 1/10
D. divide 3/5 by 10/1
D is most likely right. Basically, I would turn them into decimals and divide using a graphing calculator.
Answer:
D
Step-by-step explanation:
A contractor is building a set of stairs out of concrete. Each step is exactly the same length and width is the same and height from the last step.
A) Which solid figures can the staircase be broken into?
B) What are the dimensions of each solid figure?
C) How much concrete will be needed to form the staircase?
QA) Which solid figures can the staircase be broken into?
A) The staircase can be broken into 3 rectangular prisms.
QB) What are the dimensions of each solid figure?
A) We are given the height (2.5 ft) and the length (3 ft) of the entire staircase. To find the height and length of each step, just divide by 3:
2.5 / 3 = 5/6 ft high
3 / 3 = 1 ft long
Looking at the image given, we can see that the staircase is 6 ft wide.
Bottom prism: 3 ft long, 6 ft wide, and 5/6 ft high.
Middle prism: 2 ft long, 6 ft wide, and 5/6 ft high.
Top prism: 1 ft long, 6 ft wide, and 5/6 ft high.
QC) How much concrete will be needed to form the staircase?
A) To answer this question, we have to find the volume of each rectangular prism. The formula for the volume of a rectangular prism is
V = lwh; where l = length, w = width, and h = height.
We need to apply this formula to each prism. I'll go from the bottom up.
(1.) V = lwh; l = 3, w = 6, h = 5/6
V = (3)(6)(5/6)
V = 15 ft²
(2.) V = lwh; l = 2, w = 6, h = 5/6
V = (2)(6)(5/6)
V = 10 ft²
(3.) V = lwh; l = 1, w = 6, h = 5/6
V = (1)(6)(5/6)
V = 5 ft²
To find the amount of concrete needed to form the staircase, just add the volumes of the three rectangular prisms:
15 + 10 + 5 = 30 ft²
The contractor will need enough concrete to cover 30 ft² to form the staircase.
Hope this helps!
Final answer:
The staircase can be broken into rectangular prisms, each representing a step. The volume of each step is calculated using the given dimensions, which are then summed to find the total concrete needed.
Explanation:
To determine the amount of concrete needed to form a staircase, we need to calculate the volume of concrete required for each step and then sum them up. Since each step is of the same size, we can break down the staircase into a set of rectangular prisms, where each prism represents a step.
Dimensions of each solid figure (step): Given a stage height of 400 mm and 3 steps, the height of each step would be 400 mm / 3, which is around 133.33 mm or 13.33 cm. The length of the horizontal part of each step is 800 mm or 80 cm. Assuming a step width of 1,200 mm or 120 cm (since the steps must be wide enough for two people), we obtain the dimensions for each step.
To calculate the volume of each step, we use the formula for the volume of a rectangular prism: Volume = Length × Width × Height. Therefore, we have Volume = 80 cm × 120 cm × 13.33 cm for each step. To find the total volume for the staircase, we multiply the volume of one step by the number of steps (3 in this case).
Calculating the total concrete required: After finding the volume of one step, we multiply it by 3 (since there are 3 steps) to find the total concrete needed.
Find the distance between the points (3, -5) and (-6, -5).
ANSWER
9
EXPLANATION
We want to find the distance between the points (3, -5) and (-6, -5).
The given points have the same y-coordinates .
This means it is a horizontal line.
We use the absolute value method to find the distance between the two points.
We find the absolute value of the distance between the x-values.
The distance between the two points is
|3--6|=|3+6|=|9|=9
The radius of a right circular cylinder is increasing at the rate of 6 in./s, while the height is decreasing at the rateof 3 in./s. At what rate is the volume of the cylinder changing when the radius is 5 in. and the height is 11 in.?
The volume of a cylinder with radius [tex]r[/tex] and height [tex]h[/tex] is
[tex]V=\pi r^2h[/tex]
Differentiate both sides with respect to time:
[tex]\dfrac{\mathrm dV}{\mathrm dt}=2\pi rh\dfrac{\mathrm dr}{\mathrm dt}+\pi r^2\dfrac{\mathrm dh}{\mathrm dt}[/tex]
We're given that
[tex]\dfrac{\mathrm dr}{\mathrm dt}=6\dfrac{\rm in}{\rm s}[/tex]
[tex]\dfrac{\mathrm dh}{\mathrm dt}=-3\dfrac{\rm in}{\rm s}[/tex]
so that at the point when [tex]r=5\,\rm in[/tex] and [tex]h=11\,\rm in[/tex], the volume is undergoing a total change of
[tex]\dfrac{\mathrm dV}{\mathrm dt}=2\pi(5\,\mathrm{in})(11\,\mathrm{in})\left(6\dfrac{\rm in}{\rm s}\right)+\pi(5\,\mathrm{in})^2\left(-3\dfrac{\rm in}{\rm s}\right)[/tex]
[tex]\boxed{\dfrac{\mathrm dV}{\mathrm dt}=585\pi\dfrac{\mathrm{in}^3}{\rm s}}[/tex]
The volume of the right circular cylinder is changing at a rate of 255π cubic inches/sec with the radius increasing at 6 in./s and height decreasing at 3 in./s.
Explanation:The question involves the application of calculus concepts particularly related to volume flow rate. The volume (V) of a right circular cylinder is given by V = πr²h, where r is the radius and h is the height. We can take the derivative in respect to time (t) of both sides, which will result in dV/dt = πrh(dr/dt) + πr²(dh/dt).
According to the problem, dr/dt = 6 in./s and dh/dt = -3 in./s. The volume is changing when the radius (r) is 5 in. and the height (h) is 11 in. Substituting all these values into the formula, we get: dV/dt = π(5)(11)(6) + π(5)²(-3). This equals 330π - 75π = 255π cubic inches/sec.
Thus, the volume of the cylinder is changing at a rate of 255π cubic inches/sec.
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What is five ninths of 540? PLEASE HELP! lol
Answer:
three hundred
Step-by-step explanation:
Answer:
300
Step-by-step explanation:
5,9 times 540
*** PLEASE HELP ASAP
two cylinders have the same size base, but one is twice as tall. explain why the taller cylinder does not have double the surface area.
Answer:
The top isn't closed.
Step-by-step explanation:
The bottom is enclosed, creating more surface area, but the top is opened.
Answer:
The surface area of a cylinder is given by :
SA=[tex]2 \pi rh+2\pi r^{2}[/tex]
When the base is same but the height is doubled. Doubling the height replaces h with 2h:
New formula becomes:
SA=[tex]2 \pi r(2h)+2\pi r^{2}[/tex]
SA = [tex]4\pi rh+2\pi r^{2}[/tex]
We can see that only the height is doubled not the radius. The formula changes a little bit.
We can take an example-
Lets say the height of cylinder is 10 cm and radius is 4 cm
So, SA in 1st case :
SA=[tex]2\times3.14\times4\times10+ 2\times3.14\times (4)^{2}[/tex]
=[tex]251.2+100.48=351.68[/tex] cm square
SA in 2nd case:
[tex]4\times3.14\times4\times10+ 2\times3.14\times(4)^{2}[/tex]
= [tex]502.4+100.48=602.88[/tex] cm square
We can see that area of lateral surface doubles up in case 2 but the base area remains the same.
6. The pressure exerted on the walls of a container by a gas enclosed within it is directly proportional to
the temperature of the gas. If the pressure is 6 pounds per square inch when the temperature is 440° F,find
the pressure exerted when the temperature of the gas is 380°F.
(SHOW WORK)
Answer: 5.18 pounds
Step-by-step explanation:
Given: The pressure exerted on the walls of a container by a gas enclosed within it is directly proportional to the temperature of the gas.
Let 'p' denote the pressure exerted on the walls and 't' denotes temperature of the gas.
Then the equation is given by :-
[tex]p=ct[/tex], where c is the proportionality constant.
Also, the pressure is 6 pounds per square inch when the temperature is 440° F.
[tex]\Rightarrow\ 6=440c\\\\\Rightarrow\ c=\dfrac{6}{440}=\dfrac{3}{220}[/tex]
Then, the final equation to calculate pressure becomes :-
[tex]p=\dfrac{3}{220}t[/tex]
Now, the pressure exerted when the temperature of the gas is 380°F is given by :-
[tex]p=\dfrac{3}{220}\times380=5.181818\approx5.18\text{ pounds}[/tex]
If –1 is a root of f(x), which of the following must be true?
Answer:
(x + 1) is a factor of f(x).
Step-by-step explanation:
Please share the answer choices. Thank you.
If –1 is a root of f(x), which of the following must be true?
(x + 1) is a factor of f(x).
Please help me thank you
solution for #18 is C and for #19 is D
QUESTION 18
Use the Pythagorean Identity.
[tex] \cos^{2}( \theta) +\sin^{2}( \theta) = 1[/tex]
We substitute the given value into the formula,
[tex] \cos^{2}( \theta) +( { \frac{4}{7} })^{2} = 1[/tex]
[tex] \cos^{2}( \theta) + \frac{16}{49} = 1[/tex]
[tex] \cos^{2}( \theta) = 1 - \frac{16}{49} [/tex]
[tex]\cos^{2}( \theta) = \frac{33}{49} [/tex]
Since we are in the first quadrant, we take positive square root,
[tex]\cos( \theta) = \sqrt{\frac{33}{49} } [/tex]
[tex]\cos( \theta) = \frac{ \sqrt{33}}{7} [/tex]
The 3rd choice is correct.
QUESTION 19.
We want to simplify;
[tex]18 \sin( \theta) \sec( \theta) [/tex]
Recall the reciprocal identity
[tex] \sec( \theta) = \frac{1}{ \cos( \theta) } [/tex]
This implies that,
[tex]18 \sin( \theta) \sec( \theta) =18 \sin( \theta) \times \frac{1}{ \cos( \theta) } [/tex]
[tex]18 \sin( \theta) \sec( \theta) =18 \times \frac{\sin( \theta) }{ \cos( \theta) } [/tex]
This will give us:
[tex]18 \sin( \theta) \sec( \theta) =18 \tan( \theta) [/tex]
The correct choice is D.
The graphs of f(x) and g(x) are shown below:
graph of function f of x open upward and has its vertex at negative 7, 0. Graph of function g of x opens upward and has its vertex at negative 5, 0.
If f(x) = (x + 7)2, which of the following is g(x) based on the translation?
g(x) = (x + 9)2
g(x) = (x + 5)2
g(x) = (x − 9)2
g(x) = (x − 5)2
the translation should make the equation
g(x)= (x+5)2
Answer:
b
Step-by-step explanation:
Eli is filling up gift bags each bag will have a 3 baseball cards which number sentence would Eli use to find how many bags he can feel if he has 21 cards?
21-3=18
21÷3=7
21+3=24
21x3=63
If Eli has a total of 21 baseball cards, and wants each bag to have 3 cards, you would divide the number of total cards by the amount you want in each group. Dividing is like grouping.
So, the equation he'd use is: 21 / 3 = 7
I hope that helped.
Answer:
21÷3=7
Step-by-step explanation:
Dividing the number of available cards by the quantity in each bag will tell Eli how many bags he can fill.
___
Division can be thought of as "repeated subtraction" with the quotient telling you how many times the divisor can be subtracted from the dividend. One way Eli can do this repeated subtraction is to put the cards into piles of 3:
ccc . ccc . ccc . ccc . ccc . ccc . ccc
He will run out of cards when he has made 7 piles.
what is 5 1/4 in decimal form
5 1/4 in decimal form is 5.25 because 25 is 1/4 of 100.
The mixed fraction 5 1/4 is equivalent to 5.25 in decimal form. The fraction 1/4 is converted to decimal by dividing 1 by 4 to get 0.25 and then added to the whole number 5.
Explanation:To convert the mixed fraction 5 1/4 to decimal form, you need to divide the numerator by the denominator for the fractional part and then add that result to the whole number part. In this case, 1 divided by 4 equals 0.25. Adding this result to the whole number 5 gives you 5.25, which is 5 1/4 in decimal form.
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which are the correct reprsentives of the inequality -3(2x-5)<5(2-x)check all that apply x<5
Answer:
x > 5Step-by-step explanation:
[tex]-3(2x-5)<5(2-x)\qquad\text{use the distributive property}\\\\(-3)(2x)+(-3)(-5)<(5)(2)+(5)(-x)\\\\-6x+15<10-5x\qquad\text{subtract 15 from both sides}\\\\-6x<-5-5x\qquad\text{add 5x to both sides}\\\\-x<-5\qquad\text{change the signs}\\\\x>5[/tex]
Find the midpoint between A and C.
(1, 1)
(5, -7)
(-5, 7)
(0.5, 0.5)
Answer:
(0.5, 0.5)Step-by-step explanation:
The formula of a midpoint of a segment AB with endpoints at A(x₁, y₁) and B(x₂, y₂):
[tex]M_{AB}\left(\dfrac{x_1+x_2}{2},\ \dfrac{y_1+y_2}{2}\right)[/tex]
From the graph we have the points A(-2, 4) and C(3, -3).
Substitute:
[tex]M_{AC}(x,\ y)\\\\x=\dfrac{-2+3}{2}=\dfrac{1}{2}=0.5\\\\y=\dfrac{4+(-3)}{2}=\dfrac{1}{2}=0.5[/tex]
Answer:
0.5 0.5
Step-by-step explanation:
because it is logically correct now deal with it! hehehe have a grate day un like me!;)
Help me please i have been on this problem for a while and my teachers aren't really helping!
Answer:
106 m²
Step-by-step explanation:
Imagine this shape was a square, it's area would be 120 m².
Now imagine the little rectangle with 7 m as the side, you will have to work out the area of that so
Side = 7
4 + 4 + ? = 10
8 + ? = 10
? = 2
So the area of the little rectangle is 14 m²
Now we minus both of the areas : 120 - 14 = 106
What are the coordinates of p?
A.(0,5)
B.0,7
C.7,0
D.5,0
Answer:
(5,0)
Step-by-step explanation:
Count how many units are there on the x-axis first and in this case it is 5 the count how many on the y axis (going up or down) and that is 0 so then use this for the coordinate: (x,y)=(5,0)
Answer:
(5,0)
Step-by-step explanation:
Count how many units are there on the x-axis first and in this case it is 5 the count how many on the y axis (going up or down) and that is 0 so then use this for the coordinate: (x,y)=(5,0)
if you are trying to choose a committee which of the following is the best sampling method?
A. simple random sampling
B. systematic random sampling
C. stratified random sampling
D. Cluster sampling
Answer:
The best answer would be B. systematic random sampling
Step-by-step explanation:
The best sampling method for choosing a committee is Cluster Sampling.
What are different types of sampling?Simple random sampling - Simple random sampling is a sort of probability sampling in which a researcher selects a subset of a population at random.
Systematic random sampling A probability sampling approach in which a random sample of a bigger population is selected with a defined periodic interval.
Stratified random sampling A form of sampling known as stratified random sampling includes dividing a population into smaller sub-groups known as strata.
Cluster Sampling The population is divided into groups first. Every member of some of the groupings is included in the total sample. The teams are chosen at random.
If we are trying to choose a committee, cluster sampling method would be the best as there should be representatives of every group of the society in that committee and the representative from each group should be chosen completely randomly.
Hence the cluster sampling method is the best way to choose a committee.
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Which graph shows the solution set of
Answer:
Hence final answer is [tex](1,3)[/tex].
correct choice is D because both ends are open circles.
Step-by-step explanation:
Given inequality is [tex]\frac{x-1}{x-3}<0[/tex]
Setting both numerator and denominator =0 gives:
x-1=0, x-3=0
or x=1, x=3
Using these critical points, we can divide number line into three sets:
[tex](-\infty,1)[/tex], [tex](1,3)[/tex] and [tex](3,\infty)[/tex]
We pick one number from each interval and plug into original inequality to see if that number satisfies the inequality or not.
Test for [tex](-\infty,1)[/tex].
Clearly x=0 belongs to [tex](-\infty,1)[/tex] interval then plug x=1 into [tex]\frac{x-1}{x-3}<0[/tex]
[tex]\frac{0-1}{0-3}<0[/tex]
[tex]\frac{-1}{-3}<0[/tex]
[tex]\frac{1}{3}<0[/tex]
Which is False.
Hence [tex](-\infty,1)[/tex] desn't belongs to the answer.
Similarly testing other intervals, we get that only [tex](1,3)[/tex] satisfies the original inequality.
Hence final answer is [tex](1,3)[/tex].
correct choice is D because both ends are open circles.
show the first step when factoring 5a^2b- 5a^2c -5db +5dc by grouping?
Answer:
[tex]5(a^2b-a^2c-db+dc)[/tex]
Step-by-step explanation:
Given expression is [tex]5a^2b- 5a^2c -5db +5dc[/tex].
Now we need to show the first step of factoring.
We know that first step of factoring in any problem is to find the GCF that is find the greatest common factor. We see that 5 is the only largest number that can divide each term so 5 is the GCF.
Now we write 5 outside parenthesis and divide given terms by 5 to find the terms that goes inside parenthesis.
Hence first step of factoring is given by :
[tex]5a^2b- 5a^2c -5db +5dc[/tex]
[tex]=5(a^2b-a^2c-db+dc)[/tex]
The first step when factoring [tex]\(5a^2b - 5a^2c - 5db + 5dc\)[/tex] by grouping is to group the terms and then factor out the common terms from each group
Let's factor the expression [tex]\(5a^2b - 5a^2c - 5db + 5dc\)[/tex] by grouping.
First, let's group the terms:
[tex]\( (5a^2b - 5a^2c) + (-5db + 5dc) \)[/tex]
Now, let's factor out the common terms from each group:
[tex]\( 5a^2(b - c) + 5d(-b + c) \)[/tex]
Now, we can factor out the common factor of 5 from both terms:
[tex]\( 5(a^2(b - c) + d(-b + c)) \)[/tex]
So, the factored expression is [tex]\(5(a^2(b - c) + d(-b + c))\).[/tex]
In the given expression, we have four terms[tex]: \(5a^2b\), \(-5a^2c\), \(-5db\), and \(5dc\).[/tex]
The first step in factoring by grouping is to group the terms in pairs. Here, we pair [tex]\(5a^2b\)[/tex] with [tex]\(-5a^2c\)[/tex] and [tex]\(-5db\)[/tex] with [tex]\(5dc\).[/tex]
Next, we factor out the common terms from each group. From the first group, we factor out [tex]\(5a^2\)[/tex], and from the second group, we factor out [tex]\(5d\).[/tex] This leaves us with [tex]\(b - c\)[/tex] in the first group and [tex]\(-b + c\)[/tex] in the second group.
Finally, we factor out the common factor of 5 from both terms to get the final factored expression [tex]\(5(a^2(b - c) + d(-b + c))\).[/tex]
So, the first step when factoring [tex]\(5a^2b - 5a^2c - 5db + 5dc\)[/tex] by grouping is to group the terms and then factor out the common terms from each group.
Complete question:
show the first step when factoring [tex]5a^2b- 5a^2c -5db +5dc[/tex] by grouping?
Find the reference angle of 10pi/13
Answer:
3π/13
Step-by-step explanation:
In order to find the reference angle of a given angle, first of all, its quadrant is determined
In order to determine the quadrant,
10π/13=10(180)/13
=138.46
As the given angle belongs to 2nd quadrant, it will be subtracted from 180 degrees also denoted by pi.
So,
Reference angle for 10π/13= π-10π/13
=(13π-10π)/13
=3π/13
So the reference angle for 10π/13 is 3π/13 ..
Given the function f(x) = 4(2)x, Section A is from x = 1 to x = 2 and Section B is from x = 3 to x = 4.
Part A: Find the average rate of change of each section. (4 points)
Part B: How many times greater is the average rate of change of Section B than Section A? Explain why one rate of change is greater than the other. (6 points)
Answer:
Step-by-step explanation:
I'm sure you want your functions to appear as perfectly formed as possible so that others can help you. f(x) = 4(2)x should be written with the " ^ " sign to denote exponentation: f(x) = 4(2)^x
f(b) - f(a)
The formula for "average rate of change" is a.r.c. = --------------
b - a
change in function value
This is equivalent to ---------------------------------------
change in x value
For Section A: x changes from 1 to 2 and the function changes from 4(2)^1 to 4(2)^2: 8 to 16. Thus, "change in function value" is 8 for a 1-unit change in x from 1 to 2. Thus, in this Section, the a.r.c. is:
8
------ = 8 units (Section A)
1
Section B: x changes from 3 to 4, a net change of 1 unit: f(x) changes from
4(2)^3 to 4(2)^4, or 32 to 256, a net change of 224 units. Thus, the a.r.c. is
224 units
----------------- = 224 units (Section B)
1 unit
The a.r.c for Section B is 28 times greater than the a.r.c. for Section A.
This change in outcome is so great because the function f(x) is an exponential function; as x increases in unit steps, the function increases much faster (we say "exponentially").
Answer:
Part A: Section A- 8, Section B- 32.
Part B: 4 times.
Step-by-step explanation:
The function is given by .
Section A is from x = 1 to x = 2.
Now, f(1) = 4 × 2 = 8 and f(2) = 4 × 2 × 2 = 16
Again, section B is from x = 3 to x = 4.
Now, f(3) = 4 × 2 × 2 × 2 = 32 and f(4) = 4 × 2 × 2 × 2 × 2 = 64
Part A:
In section A, the average rate of change is = 8
And in section B, the average rate of change is = 32
Part B:
Therefore, the average rate of change of section B is greater than section A is (32 / 8 = 4)
twenty-five members of the eighth grade class at Park Center Middle School are going to a museum and then to lunch each student must pay an entrance fee to the museum and 7.25 for lunch the cost for the trip is for for 443.75 what is the entry fee for one student
Answer:
$10.50
Step-by-step explanation:
The first step is to determine the cost per student for the trip.
It cost $443.75 for 25 students, so
TS = 443.75 / 25 = $17.75 per student.
From that $17.75, we know we should remove $7.25 for the lunch in order to get the entrance fee:
EF = 17.75 - 7.25 = 10.50
The entrance fee for one student was $10.50
Which statement describes the graph of function g?
Answer:
The graph of G is 3 units to the left of graph F
Step-by-step explanation:
I used Desmos graphing calculator to check my answer, but generally you can use this formula.
a(x + or - h) + or - k = y
h is vertical movement and k is horizontal movement.
Answer: Never mind that answer was incorrect it is not B!!
Step-by-step explanation:
A model rocket is launched from a roof into a large field. The path of the rocket can be modeled by the equation y=-0.04x^2+9.1x+11.9, where x is the horizontal distance, in meters, from the starting point on the roof and y is the height, in meters, of the rocket above the ground. How far horizontally from it’s starting point will the rocket land?
Answer:
228.8 meters
Step-by-step explanation:
y = -0.04 x² + 9.1 x + 11.9
When the rocket lands, y = 0:
0 = -0.04 x² + 9.1 x + 11.9
Solving for x, start by multiplying by -1:
0 = 0.04 x² - 9.1 x - 11.9
Multiply by 100:
0 = 4x² - 910 x - 1190
Solve with quadratic formula:
x = [ -b ± √(b² - 4ac) ] / 2a
x = [ 910 ± √((-910)² - 4(4)(-1190)) ] / 2(4)
x = [ 910 ± √(847140) ] / 8
x ≈ -1.3, 228.8
Since x can't be negative, x = 228.8 meters.
Answer:
The rocket will land at 208.02 m. Hence, if you are on the same connexus assignment, your answer will be A.
Hope this helps! :D
1. Which statement is true about the solutions to
x^2 - 1 = 24
Hint:
Isolate the squared term.
Take the square root of both sides.
Is this number rational? (Can you simplify?) Or is it irrational? (Does a square root remain?)
A
There is only one irrational solution.
B
There are two distinct rational solutions.
C
There are two distinct irrational solutions.
2. Marcus wants to solve the quadratic equation 2x^2 - 7x+3=0 Which expression could be one of the factors that he writes in order to solve the equation?
a. 2x-1
b. x-6
c. 2x+1
3. True or False
The solutions to 5x^2 = -2x are x = - 2/5 and x = 0
Hint:
Get all the terms to one side so the equation equals zero.
Factor out the GCF.
Set each term equal to zero.
Solve.
Compare solutions to those given in the problem.
a. true
b. false
4. True or False
The solutions to ( x + 3 )^2 - 4 = 0 are x = - 1 and x = - 5
Hint:
Isolate the squared quantity.
Take the square root of both sides.
Don't forget the plus or minus.
Solve for x.
Determine the two solutions. Compare with those given in the question.
a. true
b. false
Step-by-step explanation:
(B).(x=5 or -5) is the homogeneous mixture
The first equation has two distinct rational solutions, the expression 2x - 1 can be one of the factors to solve the second equation, the solutions to the third equation are x = -2/5 and x = 0, and the solutions to the fourth equation are x = -1 and x = -5.
Explanation:1. To find the solutions to the equation x^2 - 1 = 24, we can start by isolating the squared term:
x^2 = 24 + 1
x^2 = 25
Next, we take the square root of both sides to find the values of x:
x = ±√25
Therefore, there are two distinct rational solutions to the equation.
2. In order to solve the quadratic equation 2x^2 - 7x + 3 = 0, Marcus can use the quadratic formula x = (-b ± √(b^2 - 4ac)) / (2a). One of the factors he can write is 2x - 1.
3. The solutions to the equation 5x^2 = -2x are found by getting all the terms to one side and setting the equation equal to zero:
5x^2 + 2x = 0
Next, we factor out the greatest common factor:
x(5x + 2) = 0
Setting each term equal to zero, we get two values for x:
x = 0 or x = -2/5
Therefore, the statement that the solutions are x = -2/5 and x = 0 is true.
4. To find the solutions to the equation (x + 3)^2 - 4 = 0, we isolate the squared quantity:
(x + 3)^2 = 4
Next, we take the square root of both sides, considering both the positive and negative square roots:
x + 3 = ±√4
x + 3 = ±2
Solving for x, we get two solutions:
x = -3 - 2 = -5
x = -3 + 2 = -1
Therefore, the statement that the solutions are x = -1 and x = -5 is true.
Learn more about Quadratic Equations here:https://brainly.com/question/30098550
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Bentley went into a bakery and bought 4 donuts and 10 cookies, costing a total of $23. Skylar went into the same bakery and bought 8 donuts and 6 cookies, costing a total of $25. Determine the price of each donut and the price of each cookie.
Answer:
Donuts cost $2.00 and Cookies cost $1.50
Step-by-step explanation:
D = cost of a donut
C = cost of a cookie
4D + 10C = $23.00
8D + 6C = $25.00
Eliminate a variable when subtracting the two equations. Change both values with C to 60 in order to eliminate the C variable and solve for D.
80D + 60C = $250.00 subtracted from 24D + 60C = $138
56D = $112.00 (Divide by 56 to single out the variable)
56D/56 = $112.00/56
D = $2.00
Use the D value to solve for C.
4(2) + 10C = $23.00
8 + 10C = $23.00
8 - 8 + 10C = $23.00 - 8
10C = $15.00
10C/10 = $15/10
C = $1.50
Check:
Bentley:
4D + 10C = $23
4(2) + 10(1.50) = $23
8 + 15 = $23
23 = 23
Skylar:
8D + 6C = $25
8(2) + 6(1.50) = $25
16 + 9 = $25
25 = 25
Answer:
Each donut costs $2 and each cookie costs $1.5
Step-by-step explanation:
1. Let´s name the variables as the following:
x = price of one donut
y = price of one cookie
2. Write in an equation form which Bentley bought:
[tex]4x+10y=23[/tex] (Eq.1)
3. Write in an equation form which Skylar bought:
[tex]8x+6y=25[/tex] (Eq.2)
4. Solve for x in Eq.1:
[tex]4x+10y=23[/tex]
[tex]4x=23-10y[/tex]
[tex]x=\frac{23-10y}{4}[/tex] (Eq.3)
5. Replace Eq.3 in Eq.2 and solve for y:
[tex]8*(\frac{23-10y}{4})+6y=25[/tex]
[tex]\frac{184-80y}{4}+6y=25[/tex]
[tex]\frac{184-80y+24y}{4}=25[/tex]
[tex]184-80y+24y=100[/tex]
[tex]-80y+24y=100-184[/tex]
[tex]-56y=-84[/tex]
[tex]y=\frac{84}{56}[/tex]
[tex]y=1.5[/tex]
6. Replacing the value of y in Eq.3:
[tex]x=\frac{23-10*(1.5)}{4}[/tex]
[tex]x=\frac{23-10*(1.5)}{4}[/tex]
[tex]x=\frac{23-15}{4}[/tex]
[tex]x=\frac{8}{4}[/tex]
[tex]x=2[/tex]
Therefore each donut costs $2 and each cookie costs $1.5