Answer:
x = 13
Step-by-step explanation:
The area of a rectangle is found by A = l*w. Since the length here is x and the width is 2x - 8, substitute these values and A = 234 to solve for x.
[tex]A = l*w\\234 = x(2x-8)\\234 = 2x^2 - 8x[/tex]
To solve for x, move 234 to the other side by subtraction. Then remove the common factor between all three terms of 2. Factor and solve.
[tex]2x^2 - 8x - 234 = 0 \\2(x^2 - 4x - 117) = 0\\2(x - 13)(x+9) = 0\\[/tex]
Set each factor equal to 0 and solve.
x - 13 = 0 so x = 13
x + 9 = 0 so x = -9
Since x is a side length and length/distance cannot be negative, then x = 13 is the length of the rectangle.
If you buy 8 kilograms of apples and 2.5 kilograms of pears how many more grams of apples are there
Answer:
[tex]5,500\ g[/tex]
Step-by-step explanation:
we know that
[tex]1\ kg=1,000\ g[/tex]
step 1
Find the difference between the kilograms of apples and the kilograms of pears
[tex]8-2.5=5.5\ kg[/tex]
step 2
Convert to grams
[tex]5.5\ kg=5.5*1,000=5,500\ g[/tex]
Using the diagram, to what height can the crane raise building material? Round to the nearest foot.
A) 62 ft
B) 75 ft
C) 78 ft
D) 80 ft
Answer:
C) 78 ft
Step-by-step explanation:
The side opposite the angle has the ratio to the hypotenuse:
Sin = Opposite/Hypotenuse
Then the solution to this problem is found by substituting the given information and solving for the height.
sin(45°) = height/(110 ft)
(110 ft)·sin(45°) = height ≈ 77.7817 ft
Rounded to the nearest foot, the crane can raise material to a height of 78 ft.
HELPPPPP!! The formula gives the volume V of a right cylinder with radius r and height h.
V=πr²h Solve for r.
Explain your answer. Should either answer be discarded? Why or why not?
Answer:
see explanation
Step-by-step explanation:
Isolate r² by dividing both sides by πh
r² = [tex]\frac{V}{h\pi }[/tex]
Take the square root of both sides
r = ± [tex]\sqrt{\frac{V}{h\pi } }[/tex]
The negative part can be discarded as r > 0, hence
r = [tex]\sqrt{\frac{V}{h\pi } }[/tex]
HELP PLEASE 23 POINTS ASAP Hanna arranged financing for her bachelor’s degree. She borrowed $5,000 as a student loan backed by the federal government, and she also received a grant of $3,000 for books and supplies. Hanna is also in the top 3% of her high school class and was awarded a $15,000 scholarship for her academic achievements. Lastly, Hanna took out a private loan for $6,000.
Not counting any interest Hanna may have to pay, how much of her financing is she required to pay back?
Scholarships and grants do not need to be paid back.
Government loans and private loans do need to be paid back.
She has 2 loans. $5,000 and $6,000.
She needs to pay back $11,000
Use the grouping method to factor the polynomial below completely. X^3+2x^2+5x+10
(X^3+2x^2) +(5x+10)
X^2(x+2) +5(x+2)
(X^2+5)(x+2)
Answer:
[tex](x+2)\text{ and }(x^2+5)[/tex] are the factors of given polynomial,
Step-by-step explanation:
We are given the following information in the question:
We are given a polynomial:
[tex]x^3 + 2x^2 + 5x + 10[/tex]
We have to factor this polynomial with the help of grouping method.
Grouping can be dine with the help of taking the common factors.
Working:
[tex]\text{Taking } x^2 \text{ common from the first two terms and 5 from the other two terms, we have}\\\Rightarrow x^2(x + 2) +5(x + 2)\\\text{Aain taking the common term}\\\Rightarrow (x+2)(x^2+5)[/tex]
Hence, the two factors of the given polynomial are:
[tex](x+2)\text{ and }(x^2+5)[/tex]
Cabrera bought 4 baseballs for him and his friends to use during practice. Each baseball cost 3.42. What was the total cost of the 4 baseballs?
Answer:
$13.68
Step-by-step explanation:
3.42 x 4
Final answer:
To find the total cost of 4 baseballs, each costing $3.42, we multiply the cost of one baseball by the number of baseballs, resulting in a total cost of $13.68.
Explanation:
The question asks to calculate the total cost of 4 baseballs, provided that each costs $3.42. To find the total cost, we need to multiply the cost of one baseball by the number of baseballs that were purchased. Hence, the calculation of the total cost of baseball is given by $3.42 (cost of one baseball) × 4 (number of baseballs) = $13.68. Therefore, the total cost of the 4 baseballs is $13.68.
A 6 ounce package of fruit snacks contains 45 pieces how many pieceswould would you expect in a10 ounce package
Answer:
75 pieces
Step-by-step explanation:
1. determine how many pieces per ounce by dividing 45 by 6 (# of pieces in a 6 oz bag)
45/6= 7.5 pieces per ounce
2. multiply 7.5 (for one ounce) by 10
7.5*10 = 75
Answer:
75
Step-by-step explanation:
just answer it
Just need help finding X and Y
Answer:
x = 8 and y= 12Step-by-step explanation:
For x use the Pythagorean theorem:
[tex]x^2+6^2=10^2[/tex]
[tex]x^2+36=100[/tex] subtract 36 from both sides
[tex]x^2=64\to x=\sqrt{64}\\\\x=8[/tex]
We know: x + y = 20. Substitute:
[tex]8+y=20[/tex] subtract 8 from both sides
[tex]y=12[/tex]
An experiment consists of rolling a die, flipping a coin, and spinning a spinner divided into 4 equal regions. The number of elements in the sample space of this experiment is
12
3
6
48
Answer:
48
Step-by-step explanation:
The sample space of the experiment contains all the possible outcomes of all events.
There are 3 events that are taking place.
Rolling a die which has 6 possible outcomes.
Flipping a coin which has 2 possible outcomes.
Spinning a spinner which has 4 possible outcomes.
Since the outcome of each event is independent of the other, the total possible outcomes will be equal to the product of outcomes of each event.
i.e.
Total outcomes = 6 x 2 x 4 = 48
The sample space of the experiment contains all the possible outcomes. so the number of elements in the sample space of this experiment will be 48
Answer:
48
Step-by-step explanation:
In the given experiment, three events take place which include rolling a die, flipping a coin and spinning a spinner.
The possible outcomes of each of these events are as follows:
Rolling a die - 6
Flipping a coin - 2
Spinning a spinner - 4
Therefore, by multiplying their possible outcomes, we can find the number of elements in the sample space of this environment.
Number of elements = 6 × 2 × 4 = 48
rational exponents: quotient rule
u^2/5 / u^1/2
[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{u^{\frac{2}{5}}}{r^{\frac{1}{2}}}\implies \cfrac{1}{u^{\frac{1}{2}}\cdot u^{-\frac{2}{5}}}\implies \cfrac{1}{u^{\frac{1}{2}-\frac{2}{5}}}\implies \cfrac{1}{u^{\frac{5-4}{10}}}\implies \cfrac{1}{u^{\frac{1}{10}}}\implies u^{-\frac{1}{10}}[/tex]
If 1 adult female is randomly selected, find the probability that her pulse rate is between 72 beats per minute and 80 beats per minute.
To calculate the probability of an adult female's pulse rate being between 72 and 80 bpm, additional information like mean and standard deviation is necessary if using a normal distribution or population data for a simple probability.
Explanation:To find the probability that an adult female's pulse rate is between 72 beats per minute and 80 beats per minute, we need additional information such as the mean and standard deviation if the pulse rates follow a normal distribution, or the percentage of females with pulse rates in that range if the data is available in simple probability form.
Without this information, it's not possible to provide an exact answer. However, we can reference typical heart rate data or use estimation techniques to provide a rough idea of the probability. Health organizations often provide guidelines on normal heart rates for adults that could be used as a proxy in the absence of specific data points.
Which statements describe one of the transformations performed on f(x)=x^2 to create g(x)=2(x+5)^2+5
Answer:
Translated to the left 5 units and up 5 units and compressed horizontally by 2 units.
Step-by-step explanation:
The parent function given is [tex]f(x)=x^2[/tex]
This function has its vertex at the origin.
If we move this function 5 units to the left and 5 units up, then its vertex will now be at [tex](-5,5)[/tex].
If the parent function is then compressed horizontal by a factor of 2, then the transformed function will now have equation.
[tex]g(x)=2(x+5)^2+5[/tex]
Which of these points does not change its location when it is reflected across the y-axis? A (2, 0) b (0, 6) c (3, 3) d (5, 5)
Answer:
B. (0,6)
Step-by-step explanation:
To solve this question, you'll need to figure out what the final point is after reflecting each point. A quick way to figure this out is by multiplying (-1) to the x-coordinate.
When you reflect A. (2,0) over the y-axis, the point becomes (-2,0).
When you reflect C. (3,3) over the y-axis, the point becomes (-3,3).
When you reflect D. (5,5) over the y-axis, the point becomes (-5,5).
The only answer that does not change location is B. (0,6) as it stays at (0,6). If you multiply 0 by any number, it will always stay 0.
Multiplying the x-coordinate by (-1) to find the reflection point only works if you are reflecting it over the y-axis. You would multiple the y-coordinate by (-1) if you were reflecting over the x-axis.
Is (–2n)^4 = –8n^4? Choose the best explanation for why or why not.
A. Yes; –2 times 4 makes –8, and the n becomes n^4.
B. Yes; for n = 1, (-2n)^4 = -8 x 1 not equal to -8n^4
C. No; for values other than 0, (–2n)^4 = 16n^4 not equal to –8n^4.
D. No; the negative in front of the 2 means –2n^4 needs to become 1/2n^4
Answer:
The answer would be C
Final answer:
No, (-2n)⁴ is not equal to -8n⁴ because when -2 is raised to the fourth power, it results in a positive 16, making the correct evaluation of the expression 16n⁴. The correct answer is option (C).
Explanation:
The question is whether (-2n)⁴ is equal to -8n⁴. To evaluate the expression (-2n)⁴, you must raise both -2 and n to the fourth power. Since the exponent is even, the negative sign in front of 2 will become positive after being raised to the fourth power: (-2n)⁴ = (-2)⁴ × n⁴ = 16n⁴
So, the correct statement is No; for values other than 0, (–2n)⁴ = 16n⁴ not equal to –8n⁴. When raising a negative number to an even power, the result is positive, and (-2)⁴ equates to 16, not -8. Therefore, the option C is correct.
As a result, the misconception that -2 times 4 makes -8 is incorrect when dealing with exponents, as the negative sign is squared, turning it positive.
In quadrilateral ABCD, diagonals AC and BD bisect one another:
Quadrilateral ABCD is shown with diagonals AC and BD intersecting at point P.
What statement is used to prove that quadrilateral ABCD is a parallelogram? (5 points)
Angles BAD and ADC are congruent.
Corresponding angles BCD and CDA are supplementary.
Sides CD and DA are congruent.
Triangles BPA and DPC are congruent.
Answer:
Triangles BPA and DPC are congruent.
Step-by-step explanation:
The statement above is the only one of the bunch that is true, so is the best selection.
You don't even need to worry too much about how you might make the proof. You just need to be concerned with which are plausible answers. There's only one.
A company offers you a job with an annual salary of $60 000 for the first year and a 5% raise every year after. Approximately how much money in total would you earn in 5 years of working there?
$76577
$331538
$315000
$75000
Answer:
$75000
Step-by-step explanation:
5% of $60000 is $3000 and $3000 x 5 is $15000 and $15000 + $60000 is $75000
To calculate the total salary over 5 years with an initial salary of $60,000 and a 5% annual raise, you add the salary of each year considering the raise. The salaries over 5 years will be $60,000; $63,000; $66,150; $69,457.50; $72,930.38 respectively, amounting to a total of $331,537.88, which is approximately $331,538.
The question asks how much money you would earn total after 5 years of working at a company starting with a $60,000 salary and receiving a 5% raise each year. This is a problem of geometric progression in mathematics. To calculate the total amount earned over 5 years, we have to apply the formula for the sum of a geometric series because the salary increases by a fixed percentage each year. The salary each year is as follows: Year 1 - $60,000, Year 2 - $60,000*1.05, Year 3 - $60,000*(1.05)^2, Year 4 - $60,000*(1.05)^3, and Year 5 - $60,000*(1.05)^4.
Here is the calculation step-by-step:
Year 1: $60,000Year 2: $60,000 * 1.05Year 3: $60,000 * (1.05)²Year 4: $60,000 * (1.05)³Year 5: $60,000 * (1.05)⁴Now, add up the salaries for each year to find the total earnings:
Year 1: $60,000Year 2: $63,000 (5% of $60,000 is $3,000, so $60,000 + $3,000)Year 3: $66,150Year 4: $69,457.50Year 5: $72,930.38Add up these amounts to get the total earnings after 5 years:
Total = $60,000 + $63,000 + $66,150 + $69,457.50 + $72,930.38 = $331,537.88, which can be rounded to approximately $331,538.
Therefore, the correct answer is: $331,538.
Jim wants to collect at least 25 coins for his coin collection. He has already collected 5 coins. The inequality shown can be used to find n, the number of coins Jim still needs to collect. N + 5 ? 25 Which inequality represents the solution set for this situation? A) n ? 20 B) n ? 20 Eliminate C) n ? 30 D) n ? 30
Answer:
The answer is A for sure
Step-by-step explanation:
And this is why
n ≥ 20
n + 5 ≥ 25
n + 5 − 5 ≥ 25 − 5
n ≥ 20
Inequality shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
The inequality that represents the solutions set is
n ≥ 20.
Option A is the correct answer.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
Jim wants to collect at least 25 coins for his coin collection. He has already collected 5 coins.
The inequality shows the above situation.
n + 5 ≥ 25
Subtract 5 on both sides.
n ≥ 25 - 5
n ≥ 20
Thus,
The inequality that represents the solutions set is
n ≥ 20.
Option A is the correct answer.
Learn more about inequalities here:
https://brainly.com/question/20383699
#SPJ5
in the circle below, f is the center, gi is the diameter and m
Answer:
Part a) [tex]m<HIG=40\°[/tex]
Part b) IHG is a semicircle and GJI is a semicircle
Part c) HIJ is a major arc and HIJG is a major arc
Part d) [tex]arc\ GH=80\°[/tex]
Part e) [tex]arc\ GJI=180\°[/tex]
Step-by-step explanation:
Part a) Give an inscribed angle
we know that
The inscribed angle measures half that of the arc comprising
so
in this problem m<HIG is an inscribed angle
[tex]m<HIG=\frac{1}{2}(arc\ HG)[/tex]
[tex]arc\ HG=80\°[/tex] ----> by central angle
substitute
[tex]m<HIG=\frac{1}{2}(80\°)=40\°[/tex]
Part b) Give a semicircle
we know that
The diameter divide the circle into two semicircles
so
GI is a diameter
therefore
IHG is a semicircle
GJI is a semicircle
Part c) Give a major arc
we know that
The measure of a major arc is greater than 180 degrees
therefore
HIJ is a major arc
HIJG is a major arc
Part d) Measure of arc GH
we know that
[tex]arc\ GH=m<HFG[/tex] ----> by central angle
so
[tex]arc\ GH=80\°[/tex]
Part e) Measure of arc GJI
we know that
[tex]arc\ GJI=180\°[/tex] ----> the arc represent a semicircle
Choose the function whose graph is given by:
Answer:
y = tan(x -π) -1
Step-by-step explanation:
It looks like a straight tangent function shifted down one unit. Since the tangent function has a period of π, ...
tan(x -π) = tan(x)
so you're only looking for the function that has a translation downward of 1 unit. Of course that translation is accomplished by adding -1 to the original function.
The appearance of the graph is of ...
y = tan(x) -1
The choice that is equivalent to this is ...
y = tan(x -π) -1
Answer:
y = tan (x-pi)-1
Step-by-step explanation:
The function in the graph is a periodic function with intervals of pi and having discontinuities at regular intervals.
Hence this must be a transformation of the original trignometric funciton
tan x. y intercept is at -1 which shows that there is a vertical shift of 1 unit down.
Hence the funciton is y = tanx-1
But tan x is not given in any of the options.
Let us check which is equivalent to tan x-1
We find that tan(x-pi) = -tan (pi-x) = -(-tanx) = tanx
Hence the option 3 is the right answer
Marvin says that all rhombuses are squares are Athena says that all squares are rhombuses who is correct explain
Answer:
Athena
Step-by-step explanation:
Squares are rhombuses but rhombuses are not squares
Subtract 8 y^2 − 5 y + 7 from 2 y^2 + 7 y + 1 1
The answer is: −6y ^2 +12y+4
Answer:
[tex]\large\boxed{-6y^2+12y+4}[/tex]
Step-by-step explanation:
[tex](2y^2+7y+11)-(8y^2-5y+7)\\\\=2y^2+7y+11-8y^2-(-5y)-7\\\\=2y^2+7y+11-8y^2+5y-7\qquad\text{combine like terms}\\\\=(2y^2-8y^2)+(7y+5y)+(11-7)\\\\=-6y^2+12y+4[/tex]
Identify the type of transformation in the following graphic and describe the change.
Answer: transformation 5 units right
Step-by-step explanation: the preimage mapped to the image is moved 5 units to the right.
the algebraic expression is (x,y)-->(x+5,y)
Answer: M.A.T.H was translated (-5, 0) units; or five units to the left
Step-by-step explanation:
Point A is moved to the left to become A'.
Similarly, Points M, H, and T have moved to the left to become M', H', and T', respectively.
This type of transformation, in which all the points in a figure move in the same direction and by the same amount, is called a translation (moving sideways).
Each point has moved five units to the left.
Tony plans to run a 5,000-meter fun run at a constant rate of 250 meters per minute. He uses function f to model his distance from the finish line x minutes after the start of the race.
x f(x)
0 5,000
1 4,750
2 4,500
3 4,250
4 4,000
5 3,750
6 3,500
A.
Tony's function is always decreasing.
B.
Tony's function is always negative.
C.
Tony's function is exponential.
D.
The domain of Tony's function is [0 , 5,000].
Answer:
Option A.
Step-by-step explanation:
Based on the information provided on the question
the function used to model Tony's run is:
f(x) = -250*x + 5000
This means that after x = 20 minutes, Tony will arrive to the finish line
f(20) = -250*(20) + 5000 = -5000 + 5000 = 0
The function is always decreasing, because we are dealing with a line with negative slope.
Option A.
What is the greatest common factor of 35b^2,15b^3 and 5b?
Write the slope-intercept form of the equation that passes through the point (2, 3) and is parallel to the line y = 5/8x - 7
Answer: [tex]y=\frac{5}{8}x+\frac{7}{4}}[/tex]
Step-by-step explanation:
The slope-intercept form of a equation of the line is:
[tex]y=mx+b[/tex]
Where m is the slope and b the y-intercept-
If the lines are parallel then they have the same slope:
[tex]m=\frac{5}{8}[/tex]
You can find the value of b by substituting the point given and the slope into the equation and solving for b:
[tex]3=\frac{5}{8}*2+b\\b=\frac{7}{4}[[/tex]
Then the equation is:
[tex]y=\frac{5}{8}x+\frac{7}{4}}[/tex]
Answer:
[tex]y = \frac{5}{8} x+\frac{7}{4}[/tex]
Step-by-step explanation:
We are to write the slope intercept form of the equation which passes through the point (2, 3) and is parallel to the line [tex]y = \frac{5}{8} x-7[/tex].
We know that the standard (slope-intercept) form of an equation of a line is given by: [tex]y=mx+c[/tex]
where [tex]m[/tex] is the slope and [tex]c[/tex] is the y-intercept.
Since we are to find the equation of the line parallel to the given equation so its slope will be same as of [tex]y = \frac{5}{8} x-7[/tex].
Finding the y-intercept:
[tex]y=mx+c[/tex]
[tex]3=\frac{5}{8}(2)+c[/tex]
[tex]c=\frac{7}{4}[/tex]
Therefore, the equation will be [tex]y = \frac{5}{8} x+\frac{7}{4}[/tex].
Simplify radical 20.
I know the answer but just quizzing.
The first correct answer will be marked brainliest!
Answer:
2√5
Step-by-step explanation:
Use a factor tree to break down 20 into it's prime roots.
20 = 2 x 10
20 = 2 x 2 x 5
These are the prime factors of 20, so we can rewrite √20 as
(√2)(√2)(√5)
(√2)(√2) = √(2x2) = √4 = 2, so we have
2√5
1 Geometry question!
First find the value of the two vertical angles which have x in them.
Vertical angles are the same so you have:
4x = x +36
subtract 1x from each side:
3x = 36
Divide both sides by 3:
x = 36/3
x = 12
Now replace x with 12 to solve for the angles:
4x = 4(12) = 48 degrees.
All 4 angles need to equal 360 degrees, so now subtract 48 +48 from 360:
360 - 96 = 264
Y and the angle above it are vertical angles, so you can divide 264 by 2 to find y:
Y = 264 /2
Y = 132 degrees.
How do I simply this 6(4m + 5)
(6•4m) + (6•5)= 24m + 30
The correct answer is 30
Here’s how you solve it!
First multiply what’s in the parentheses
6✖️4m➕6✖️5
Now calculate the produce
24m➕6✖️5
Now multiply 6 and 5 then add the number to 24m
Then you are left with your answer:
24m➕30
Hope this helps! :3
If you were to round off the measurement 2.33501 grams to three digits, you would get
Answer:
2.34 grams
Step-by-step explanation:
The first 3 digits of the number are 2, 3, 3. The next digit is 5, which is more than 4, so 1 is added to the digit to its left and all digits to the right of the first three are dropped.
2.33 becomes 2.34 because of the 5 in the thousandths place.
Your rounded measurement is 2.34 grams.
What is the value of y? 3y^2 − 6 = 42
Hey there!
Let's start by adding 6 to both sides of the equation to eliminate the -6.
3y^2 = 48
Next, let's divide both sides by 3 to eliminate the 3.
y^2 = 16
Find the square root of both sides.
y = ±4
It can be both positive or negative 4 because -4 x -4 and 4 x 4 both equal 16.
The value of y is ±4.
Hope this helps!