Answer:
(a)
Given: A line passes through the points (3, -2) and (6, 2)
Point slope form: An equation of line passing through two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is given by:
[tex]y -y_1=m(x-x_1`)[/tex] .....[1] where m is the slope of the line.
Calculate first the slope of the line:
Slope(m) = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the given points;
[tex]m = \frac{2-(-2)}{6-3}=\frac{2+2}{3} =\frac{4}{3}[/tex]
Substitute the value of m in [1] ;
[tex]y - (-2) = \frac{4}{3}(x-3)[/tex]
[tex]y+2=\frac{4}{3}(x-3)[/tex] ......[1]
therefore, the equation of line in point slope form is, [tex]y+2=\frac{4}{3}(x-3)[/tex]
(b)
to find the standard form of the equation [1]
Multiply both sides by 3 in [1] we get;
[tex]3(y+2) = 4(x-3)[/tex]
using distributive property; [tex]a\cdot (b+c) = a\cdot b + a\cdot c[/tex]
3y + 6 = 4x -12
Subtract 3y to both sides we get;
3y + 6 -3y = 4x - 12 - 3y
Simplify:
6 = 4x - 3y -12
Subtract 6 from both sides we get;
0 = 4x - 3y -12-6
Simplify:
4x - 3y - 18 =0
Therefore, the standard form of the equation is; 4x - 3y - 18 =0
Which student solved problems at a rate of 28 per minute?
The student that solved at a rate of 28 per minutes was Logan
Answer:
Logan
Answer:
Logan solved problems at a rate of 28 problems per minute.
Step-by-step explanation:
To find the number of problems per minute that a person solved, you will divide the number of problems that they solved by the number of minutes that they took.
Murray:
58 problems in 2 minutes,
58 / 2 = 29
He solved problems at a rate of 29 problems per minute.
Kris:
78 problems in 3 minutes,
78 / 3 = 26
He solved problems at a rate of 26 problems per minute.
Logan:
84 problems in 3 minutes,
84 / 3 = 28
He solved problems at a rate of 28 problems per minute.
Since you found that Logan solved problems at a rate of 28 problems per minute, Logan is the student that solved problems at a rate of 28 per minute.
[tex] \frac{1}{3} \times 4\frac{1}{4} = [/tex]
simplify to get 1/3 times 17/4 which simplifies to 17/12 or 1 and 5/12.
Answer:
17/12
Step-by-step explanation:
1/3 x 4 1/4 change to
1/3 x 17/4
multiply the top and then the bottom : 17/12
I need help please. Must be correct. 10 points. Thanks
We have the supplementary angles.
The sum of the measures of the two Supplementary Angles is 180°.
Therefore we have the equation:
13x - 2 + 39 = 180
13x + 37 = 180 subtract 37 from both sides
13x = 143 divide both sides by 13
x = 11
Answer: 11What is the volume of a pyramid with base of 11cm and a hight of 12cm?
Answer:
The answer would be 484
Step-by-step explanation:
Step 1: Multiply the length, width, and height.
11x11x12=1452
Step 2: Divide by 3
1452/3=484
You go to a school dance. There is an entrance fee, and there are slices of pizza for sale. After having 1 slice of pizza, you have spent a total of $6. After having 2 more slices of pizza, you have spent a total of $10. Write an equation that represents the total cost y after buying x slices of pizza at the dance.
The equation representing the total cost after buying x slices of pizza
is [tex]\( C(x) = E + x \times P \)[/tex].
Let's denote the entrance fee as E (in dollars) and the cost of each slice of pizza as P (also in dollars). Given the problem, we can write the following equations based on the given information:
After having 1 slice of pizza, the total cost is $6:
[tex]\(E + 1 \times P = 6\)[/tex]
After having 2 more slices of pizza (total 3 slices), the total cost is $10:
[tex]\(E + 3 \times P = 10\)[/tex]
To find the equation that represents the total cost (y) after buying x slices of pizza (let's call it C(x), we need to generalize the pattern observed in the given equations.
Notice that the entrance fee remains constant regardless of the number of slices of pizza bought. So, we can write the equation as:
[tex]\[ E + x \times P = C(x) \][/tex]
Substituting the values given in the problem:
[tex]\[ C(x) = E + x \times P \][/tex]
So, the equation representing the total cost after buying x slices of pizza
is [tex]\( C(x) = E + x \times P \)[/tex]. This equation gives the total cost (y) as a function of the number of slices of pizza bought (x).
I need help! I need to know how to do the work and what the answer is plzzz
Answer:
36 ft
Step-by-step explanation:
So the proportion of the big triangle is 48:4 or 12:1. So if the small triangle’s height is 3 feet, then 3*12 is 36 feet.
Answer: 36 ft
Step-by-step explanation:
Similar triangles means there is a constant proportion between the left legs, the base legs, and the hypotenuses.
[tex]\frac{LeftLeg(large)}{LeftLeg(small)}= \frac{BaseLeg(large)}{BaseLeg(small)}[/tex]
[tex]\frac{x}{3}= \frac{48}{4}[/tex]
Cross multiply: x(4) = 3(48)
solve for x: ÷4 ÷4
x = 3(12)
= 36
what is 2fifth times 6seventh
Answer:
12/35
Step-by-step explanation:
"2fifth" = 2/5
"6seventh" = 6/7
"times" = *
Multiply across:
(2/5) * (6/7) = 12/35
12/35 is your answer
~
Answer:
12/35
Step-by-step explanation:
2/5 times 6/7
First multiply the numerators.
2 x 6 = 12
Then multiply the denominators.
5 x 7 = 35
Your answer is 12/35
Integration of (3X(X^2+3)^4) dx
[tex] [/tex]
Answer:
Step-by-step explanation:
[tex]\int 3x(x^2+3)^4 \ dx[/tex].
It is apparently obvious we could expand the bracket and integrate term-by-term. This method would work but is very time consuming (and you could easily make a mistake) so we use a different method: integration by substitution.
Integration by substitution involves swapping the variable [tex]x[/tex] for another variable which depends on x: [tex]u(x)[/tex]. (We are going to choose [tex]u[/tex] for this question).
The very first step is to choose a suitable substitution. That is, an equation [tex]u=f(x)[/tex] which is going to make the integration easier. There is a trick for spotting this however: if an integral contains both a term and it's derivative then use the substitution [tex]u=\text{The Term}[/tex].
Your integral contains the term [tex]x^2 + 3[/tex]. The derivative is [tex]2x[/tex] and (ignoring the constants) we see [tex]x[/tex] is also in the integral and so the substitution [tex]u=x^2+3[/tex] will unravel this integral!
Step 2: We must now swap the variable of integration from x to u. That means interchanging all the x's in the integrand (the term being integrated) for u's and also swapping (dx" to "du").
[tex]u=x^2+3 \Rightarrow \frac{du}{dx}=2x \Rightarrow dx = \frac{1}{2x} du[/tex]
Then,
[tex]\int 3x(x^2+3)^4 \ dx = \int 3x \cdot u^4 \cdot \frac{1}{2x} du = \int \frac{3}{2}u^4\ du[/tex].
The substitution has made this integral is easy to solve!
[tex]\int \frac{3}{2}u^4\ du= \frac{3}{10}u^5 + C[/tex]
Finally we can substitute back to get the answer in terms of x:
[tex]\int 3x(x^2+3)^4 \ dx = \frac{3}{10}(x^2+3)^5+C[/tex]
Which of the functions below could have created this graph?
Answer:
The answer is C
Step-by-step explanation:
The correct option is A. (F(x)=-x^{7}+4x^{3}-2x^{2}). This function matches all the key properties observed in the graph.
Sure, I've analyzed the image you sent and I can help you determine the correct option.
Based on the graph, we can see that it has the following properties:
It has three turning points, one minimum point and two maximum points.
The end behavior as x approaches positive or negative infinity is that the function increases without bound.
It intersects the x-axis three times.
Let's analyze the answer choices based on these observations:
Option A: (F(x)=-x^{7}+4x^{3}-2x^{2})This function has an odd leading term, which aligns with the increasing end behavior.
It has three factors, matching the number of x-intercepts.
By graphing this function, we can see that it matches the shape of the given graph with a minimum point followed by two maximum points.
Option B: (F(x)=x^{8}+4x^{4}+20x^{2})This function has an even leading term, which does not align with the increasing end behavior.
Even though it has four factors, it intersects the x-axis only twice.
Option C: (F(x)=x^{9}+12x^{8}+x^{7})This function has an odd leading term, which aligns with the increasing end behavior.
However, it only has two factors, not matching the three x-intercepts of the graph.
Option D: (F(x)=-x^{6}+x^{3}-x^{2})This function has an even leading term, which does not align with the increasing end behavior.
It also only has two factors, not matching the three x-intercepts of the graph.
can you simplify this expression -2b - 6 + 3b -2
Answer: b - 8 is what i believe the answer is make sure tho im only in 6 th grade Step-by-step explanation:
The area of a rectangle is 108m^2 and its diagonal is 15m. Find the perimeter of the rectangle. Please without quadratics.
[tex]\text{l-length}\\\text{w-width}\\lw-area\\108\ m^2-area\\d-diagonal\\\\\text{The equation}\ \#1:\\\\lw=108\to l=\dfrac{108}{w}\\\\\text{The equation}\ \#2:\\\\\text{Use the Pythagorean theorem:}\\\\l^2+w^2=d^2\to l^2+w^2=15^2\to l^2+w^2=225\\\\\text{Subtitute from}\ \#1\ \text{to}\ \#2:[/tex]
[tex]\left(\dfrac{108}{w}\right)^2+w^2=225\\\\\dfrac{11,664}{w^2}+w^2=225\qquad\text{multiply both sides by }\ w^2\neq0\\\\11,664+w^4=225w^2\qquad\text{subtract}\ 225w^2\ \text{from both sides}\\\\w^4-225w^2+11,664=0\qquad\text{substitute}\ t=w^2 > 0\\\\t^2-225t+11,664=0\\\\\text{use the quadratic formula or solve by factoring}.\\\\t^2-144t-81t+11,664=0\\\\t(t-144)-81(t-144)=0\\\\(t-144)(t-81)=0\iff t-144=0\ or\ t-81=0\\\\\boxed{t=144}\ or\ \boxed{t=81}\to w^2=144\ or\ w^2=81\\\\w=\sqrt{144}\ or\ w=\sqrt{81}\\\\\boxed{w=12\ m}\ or\ \boxed{w=9\ m}[/tex]
[tex]\text{Put the values of}\ w\ \text{to the equation}\ \#1:\\\\l=\dfrac{108}{12}\to\boxed{l=9\ m}\ or\ l=\dfrac{108}{9}\to\boxed{l=12}\\\\\text{The formula of a perimeter of a rectangle:}\\\\P=2l+2w\\\\P=2(12)+2(9)=24+18=42\\\\Answer:\ \text{The perimeter of the rectangle is equal 42 m}.[/tex]
The perimeter of the rectangle is 42m.
Explanation:To find the perimeter of the rectangle, we need to know the lengths of its sides. From the given information, we know that the area of the rectangle is 108m^2 and its diagonal is 15m. We can use this information to find the lengths of the sides.
Let the length of the rectangle be 'l' and the width be 'w'.
Given, lw = 108 and sqrt(l^2 + w^2) = 15.
Squaring both sides of the second equation, we get l^2 + w^2 = 225.
Since lw = 108, we can solve the quadratic equation l^2 - 108l + 225 = 0 to find l. In this particular case, the quadratic factors as (l - 9)(l - 12) = 0, so l = 9 or l = 12.
Substituting the values of l in the equation lw = 108, we find w = 12 or w = 9.
Since the perimeter is the sum of all the sides, the perimeter of the rectangle is (2l + 2w) = (2 * 9 + 2 * 12) = 42m.
What is an acrostic poem for the word percent
Final answer:
An acrostic poem for the word 'percent' is crafted with each line pertaining to the process and concept of calculating percents, expressed as a part of 100, or ratios with a denominator of 100.
Explanation:
An acrostic poem for the word percent could be:
Perusing numbers, calculations at hand,
Every figure is neatly planned.
Ratios and fractions - they all fit,
Calculations to make you think a bit.
Each part of a hundred, clearly set,
Numerical values that we get,
Twenty, fifty, seventy-five, all to percent we convert and drive.
This acrostic poem takes the word percent and creates a line for each letter that relates to the concept of percentages, which are ratios with a denominator of 100. Calculating percents involves setting up equivalent fractions or converting to decimals and fractions for ease of use in various mathematical situations. An understanding of this concept is essential for mathematical proficiency.
Graph the system of linear inequalities. Then state two possible solutions to the system. y> 2x + 2 y(less than or equal to)-3/2x-5
Answer:
I graphed it and u can find the two solutions :)
Step-by-step explanation:
Identify this conic section.
9x 2 + 4y 2 = 36
Answer:
The correct answer on Odyssey is Ellipse
Step-by-step explanation:
I got it correct on Odyssey
What is the rule?: 12, 24, 72, 288,1440
Answer:
12 x 2 = 24
24 x 3 = 72
72 x 4 = 288
288 x 5 = 1440
The result of each multiplication is being multiplied by the next consecutive number so the pattern is = x2,x3,x4,x5.
Step-by-step explanation:
Boom
Which sides of the isosceles triangle are the legs?
What is the effect on the graph of the function f(x) = x when f(x) is replaced with −1/2f(x)?
A) vertical reflection over x-axis and vertical stretch
B) vertical reflection over x-axis and vertical compression
C) horizontal reflection over y-axis and horizontal stretch
D) horizontal reflection over y-axis and horizontal compression
Answer:
It would be C
Graph the function represented in the table on the coordinate plane.
x: −2, −1, 0, 1, 2
y: 8, 5, 2, −1 , −4
please make answer a picture, im a bit dumb
Step-by-step explanation:
We are given the co-ordinates,
x : -2, -1, 0, 1, 2
y : 8, 5, 2, -1, -4
According to the graph, we see that this function represents a straight line.
The general form of the straight line is y = mx + c, where m is the slope and c is the y-intercept.
So, taking any two points we will find the equation of the straight line.
Consider, (0,2) and (1, -1). Now, slope is given by,
m = [tex]\frac{-1-2}{1-0}[/tex]
i.e. m = -3
Now, we will find the y-intercept of this equation using (0,2) and m = -3,
i.e. y = -3x + c
i.e. 2 = c
Hence, the equation of the straight line is y = -3x + 2.
What is the slip of a line that is parallel to the line (0,3) (3,2)
Answer:
The slope is -1/3
Step-by-step explanation:
We can find the slope of a line using the formula
m = (y2-y1)/(x2-x1)
= (2-3)/(3-0)
= (-1/3)
=-1/3
Answer:
m= -1/3
Step-by-step explanation:
Slope is determined from the formula:
y2-y1/x2-x1
Input the corresponding numbers in the formula.
2-3/3-0
-1/3
m= -1/3
Translate the sentence into an equation. Five more than the quotient of a number and 7 is equal to 8 . Use the variable c for the unknown number .
Answer:
c ÷ 7 + 5 = 8
Step-by-step explanation:
The Translate the sentence into an equation is c/7 +5 =8.
What is Algebraic expression ?
Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.
given variable is given as c therefore, the translation of the given equation Five more than the quotient of a number and 7 is equal to 8 will be :
c/7 +5 =8
Therefore, the Translate the sentence into an equation is c/7 +5 =8.
Read more about equations at :
https://brainly.com/question/10413253
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What is the value of x?
a. 35 degrees
b. 25 degrees
c. 17 degrees
d. 8 degrees
A coin is tossed five times find the number of possible outcomes
Answer:
10 possible outcomes
Step-by-step explanation:
- One coin has two sides (heads and tails)
- It is tossed 5 times
- 2 times 5 is 10
Given: ABC is a right triangle with right angle C. AB=18 centimeters and m∠A=22∘ .
What is BC ?
Enter your answer, rounded to the nearest tenth, in the box.
Answer:
BC = 6.7 cm (rounded to nearest tenth)
Explanation:
Given: ABC is a right triangle with right angle C as shown below.
Side AB=18 cm and m∠A=22°.
Using Sine ratio in triangle ABC to find BC.
Sine ratio is defined as the ratio of the opposite side of a right triangle to the hypotenuse.
i.e
[tex]\sin A = \frac{Opposite side}{Hypotenuse side}[/tex]
Let BC = x (opposite side) and AB = 18 cm(Hypotenuse side)
then;
[tex]\sin 22^{\circ} = \frac{x}{18}[/tex]
[tex]0.37460659341 = \frac{x}{18}[/tex]
Multiply both sides by 18 we get;
[tex]x = 0.37460659341 \times 18 = 6.74291868[/tex]
therefore, value of BC (nearest tenth place) is, 6.7 cm
Answer: 6.7cm
Step-by-step explanation: I took the K12 test.
Becky created a graph to represent her distance away from home one afternoon . She left home and ran to the park , met some friends and stayed at the park , and then walked back home using the same route . Which graph could Becky have created ?
Answer:
A discrete graph
Step-by-step explanation:
It would make sense because you can track the distances on the coordinate plane
Answer:
The first graph or A.
Step-by-step explanation:
76-42+65/2. ONLY ANSWER IF YOU KNOW IT FOR SURE.
Answer:
49.5
Step-by-step explanation:
76-42+65 is 99, the you divide by 2, and that is 49.5
42 point question 3/5 (10+5x)−1/3(6x+3)=9
Answer:
x = 4
Step-by-step explanation:
distribute both parenthesis on the left side of the equation
6 + 3x - 2x - 1 = 9
x + 5 = 9 ( subtract 5 from both sides )
x = 4
The minimum monthly payment for Anita‘s credit card is 2% of her balance or $10 which ever is higher if I need is balance at the end of her last billing cycle was $360 what is her minimum monthly payment
balance = $360
2% of balance = 0.02*360 = 7.20
Since $10 is larger than $7.20, this means the min monthly payment is $10
Answer: 10
PLEASE HELP ME: if the equation of the regression line for the data set (3,6),(6,2),(9,10) is y=2/3x+2, what is the SSE for the data set?
The SSE for the data set is: 24
Step-by-step explanation:The data points are given by:
(3,6),(6,2),(9,10)
The data points are as follows:
when x=3 y=6
when x=6 y=2
and when x=9 y=10
Also, the line of best fit is as follows:
[tex]y=\dfrac{2}{3}x+2[/tex]
The SSE( sum of square for error ) is calculated as follows:
Firstly we find the y-values from the line of best fit corresponding to x-values as in the data points.Now we find the residual corresponding to each x.( i.e. difference between the actual y-value and y-value on the line of best fit)Square this difference quantities and add them up to get SSE of the data set.The y-values from the line of best fitwhen x=3
from the line of best fit we have: y=4
when x=6
then y=6
when x=9
then y=8
Hence, the residual value is:when x=3 6-4= -2
when x=6 2-6= -4
and when x=9 10-8=2
Hence, the square of these difference quantity is:
(-2)²=4
(-4)²=16
and (2)²=4
Hence, the sum of these square quantity is: 4+16+4=24
Hence, the SSE of data is: 24
12(10b+6)=12(7b-6) pls helpppp
10b+6=7b-6.
3b=-12
b=-4.
*Note that you can just divide by 12 on both sides to simplify the equation.
If $7800 is invested at 5.2% interest compounded monthly, how much will the investment be worth in 11 years?
Answer:
$4,461.60
Step-by-step explanation: