Find the equation of the line: With a slope of − 1 2 through (4, 5)

let the no of sweets be 7x, 3x, and 1x

Colin gets 7x

Sara gets 3x

gordon gets 1x

7x = 1x+54  (given)

7x - 1x= 54

6x= 54

x=9

hece sara gets 3x= 3*9

                               =27

The difference between the graph of the function is

The graph of f(x) is stretched horizontally.

In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

We have two function,

f(x) = 5 cos ( 1/2 x ) - 2

g(x) = 5 cos (x) -2

The graph represented by red line is function f(x) and the graph represented by blue line is g(x).

As, seen from the f(x) is stretched by 2 units then g(x).

Learn more about Function here:

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Answer:

To find ? we use sine

sin ∅ = opposite / hypotenuse

From the question

The hypotenuse is 50

The opposite is 25

So we have

sin ? = 25 / 50

sin ? = 1/2

? = sin-¹ 1/2

To find ? we use tan

tan ∅ = opposite / adjacent

From the question

the opposite is 8

the adjacent is 33

So we have

tan ? = 8/33

? = tan-¹ 8/33

? = 13.62

Hope this helps you

Answer:

-95

Step-by-step explanation:

Answer:

Step-by-step explanation:

25p = (25)(p)

50q = (25)(2q)

therefore

25p + 50q = (25)(p) + (25)(2q) = (25)(p + 2q)

Answer:

p + 2q = 1

Step-by-step explanation:

25(p + 2q) = 25

p + 2q = 1

It's (8,-2), (5,-1), (2,0), (-1,1), (-4,2).  Just took it and suffered the fate of the wrong answer.

Answer:

C

Step-by-step explanation:

Answer:

243 m³

Step-by-step explanation:

The volume of a rectangular pyramid is given by:

[tex]V = \frac13lwh[/tex]

Where

l = length = 9m

w = width = 9m

h = height = 9m

so the volume is 1/3*9*9*9 = 243 m³

Answer:

243

Step-by-step explanation:

The formula for the volume of a square-based pyramid is

[tex]V=\frac{lwh}{3}[/tex]

[tex]l[/tex] = length

[tex]w[/tex] = width

[tex]h[/tex] = height

[tex]V=\frac{9 \times 9 \times 9}{3}[/tex]

[tex]V=\frac{729}{3}[/tex]

[tex]V=243[/tex]

The area is 243 cubic meters.

Answer:

X=3.5

Step-by-step explanation:

9=x2+2

9-2=x2

(9-2)÷2=x

Answer:

3x%x+1-5/5

3× 5x

Step-by-step explanation:

3x-5x

35yx 53yx

Answer:

B. Multiply both sides of the top equation by 3

Step-by-step explanation:

Given:

4x+2y = 4

12x+y = 22

For the equations to have equal x-coefficients, you'll multiply both sides of (1) by 3

4x+2y = 4 (1)

12x+y = 22 (2)

B. Multiply both sides of the top equation by 3

3(4x+2y=4)

We have,

12x+6y=12 (3)

12x+y=22 (2)

Subtract (2) from (3)

5y=12-22

5y=-10

y= -10/5

y=-2

Substitute y=-2 into (1)

4x+2y = 4

4x+2(-2)=4

4x-4=4

4x=4+4

4x=8

x=8/4

x=2

Therefore, y= -2 and x=2

Answer:

its B

Step-by-step explanation:

A pex:)

I'm sorry if it's wrong but i think it's C.

Answer:

C. The point lies 1 unit below the regression line.

Step-by-step explanation:

A residual is calculated by doing the true value minus the predicted value. For instance, if a point's true value is 5, but the predicted value is 3, the residual of the point will be 5 - 3 = 2.

The regression line is the line of predicted values. So, if a data point has a residual of -1, that means that the predicted value overpredicted the point's value. So, the point will lie C. 1 unit below the regression line.

Hope this helps!

Answer        

6B+7X-9Y+19

Step-by-step explanation:

[tex]\sqrt{3}x^2+10x+7\sqrt{3}=0\\\\\sqrt3(x^2+\dfrac{10x}{\sqrt{3}}+7)=0\\\\x^2+\dfrac{10x}{\sqrt{3}}+7=0\\\\x^2+\dfrac{10x}{\sqrt{3}}+\dfrac{25}{3}-\dfrac{25}{3} +7=0\\\\(x+\dfrac{5}{\sqrt{3}})^2 = \dfrac{4}{3}\\\\|x+\dfrac{5}{\sqrt{3}}| = \dfrac{2}{\sqrt{3}}\\\\x_1 = \dfrac{2}{\sqrt{3}}-\dfrac{5}{\sqrt{3}} = -\dfrac{3}{\sqrt{3}} = -\sqrt{3}\\\\x_2 = -\dfrac{2}{\sqrt{3}}-\dfrac{5}{\sqrt{3}} = \dfrac{-7}{\sqrt{3}} = -\dfrac{-7\sqrt{3}}{3}[/tex]

Complete question is;

A mechanic sells a brand of automobile tire that has a life expectancy that is normally​ distributed, with a mean life of 34,000 miles and a standard deviation of 2500 miles. He wants to give a guarantee for free replacement of tires that​ don't wear well. How should he word his guarantee if he is willing to replace approximately​ 10% of the​ tires?

Answer:

The mechanics worded guarantee that the tyre will be replaced if it lasts less than or equal to 30796 miles.

Step-by-step explanation:

Let X = Life expectancy of the automobile tire

For the normal distribution, we are given;

μ = 34000

σ = 2700

Let y miles be the minimum miles of the tyres which the mechanic guarantees that he will replace if it's last less than that.

Now, since the mechanic is willing to replace approximately 10% of the tires, y would be such that:

P(X ≤ y) = 0.1

Using the z formula, we have;

P[(X - μ)/σ) ≤ [(y - μ)/σ] = 0.1

Thus;

P(Z ≤ ([y - μ]/σ) = 0.1

From z-distribution table the Z-score at 0.1 is approximately -1.2816

This is P(Z ≤ -1.2816)

Thus;

[y - μ]/σ = -1.2816

(y - 34000)/2500 = -1.2816

y - 34000 = -1.2816 × 2500

y - 34000 = -3204

y = 34000 – 3204

y = 30796

So, we conclude that the mechanic will guarantee that the tyre will be replaced if it lasts less than or equal to 30796 miles.

Answer:

A

Step-by-step explanation:

We know that (15, 11) (which means x = 15, y = 11) is a solution to Line Q so therefore:

11 = 4/3 * 15 + (k + 1)

11 = 21 + k

k = -10

Answer:

-10 = k

Step-by-step explanation:

y = 4/3x + ( k+1)

We know a point on the line is ( 15,11)

Substitute this point into the equation

11 = 4/3(15) + (k+1)

11 = 20 + k+1

Combine terms

11 = 21+k

Subtract 21 from each side

11-21 = k

-10 = k

Answer:

the number of female teachers is 616

Step-by-step explanation:

male     2: 112

Female 11 : x

now you want to find x which is the number of female teachers

multiply 11 with 112 and 2 with x

11 x 112= 2x

divide 2

1 232 = 2x/2

616 =  x

Hope that help :)

Answer: 300 ways

Step-by-step explanation:

We have to calculate each pair of students. You do this by multiplying 25*24 and then dividing it by 2 because then you would count them 2 times. After solving, you get 300 ways. ( It is correct because I entered it. ).

Answer:

y =2x

Step-by-step explanation:

Slope intercept form is

y= mx+b where m is the slope and b is the y intercept

y = 2x+0

y = 2x

Answer:

Step-by-step explanation:

e

Answer:

x = 59

Step-by-step explanation:

x−2=57

Add 2 to each side

x−2+2=57+2

x = 59

Answer:

X=59

Step-by-step explanation:

x−2=57

to isolate X you would have to add 2 to each side. x-2(+2)=x and 57(+2)=59

Answer:

The bank offering simple interest at rate of 3% for four years

Step-by-step explanation:

Hello,

To find out which deal would be better, we have to find how much accrued on the simple and compound interest.

Data;

Principal (P) = $7,000

Time = 4 years

Simple interest rate = 3%

S.I = PRT / 100

S.I = (7000 × 3 × 4) / 100

S.I = $840

In four years, he would have $7000 + $840 = $7840.

For compound interest,

C.I = P(1 + r/n)^nt

Where n = number of time compounded = 1 (since it's annually)

rate = 2.5% = 2.5/ 100 = 0.025

C.I = 7000(1 + 0.025/1)⁽¹*⁴⁾

C.I = 7000 (1 + 0.025)⁴

C.I = 7000×(1.025)⁴

C.I = 7000 × 1.1038

C.I = $7726.6

In four years he would have $7,726.6

After calculating and evaluating both option, it's advisable for him to select the bank offering a simple interest of 3% for four years

Answer:

third option

Step-by-step explanation:

Given

[tex]\frac{x+5}{x-2}[/tex] + [tex]\frac{x+6}{x-4}[/tex]

Multiply the numerator/denominator of the first fraction by (x - 4)

Multiply the numerator/denominator of the second fraction by (x - 2)

=[tex]\frac{(x+5)(x-4)}{(x-2)(x-4)}[/tex] + [tex]\frac{(x+6)(x-2)}{(x-2)(x-4)}[/tex]

Express the 2 fractions over the common denominator

= [tex]\frac{(x+5)(x-4)+(x+6)(x-2)}{(x-2)(x-4)}[/tex] ← expand numerator/ denominator using FOIL

= [tex]\frac{x^2+x-20+x^2+4x-12}{x^2-6x+8}[/tex]

= [tex]\frac{2x^2+5x-32}{x^2-6x+8}[/tex]

Answer:

Step-by-step explanation:

Tom wanted to find the inverse of f(x)= 4x - 2 using the steps in the attached image.

Tom's first mistake was in Step 3.

To correct the mistake, he should not switch the variables.

The correct procedure is:

Step 1 : Given

f(x) = 4x - 2

Step 2 : Change f(x) to y

y = 4x - 2

Step 3 : Add 2 to both sides

[tex]4x=y+ 2[/tex]

Step 4:  Divide each side by 4

[tex]x=\dfrac{y+2}{4}[/tex]

Step 5: Change x to [tex]f^{-1}(x)[/tex]

[tex]f^{-1}(x)=\dfrac{y+2}{4}[/tex]

Answer: 0.28157

Step-by-step explanation:

Given, The proportion of the community favored building a police substation in their neighborhood: p= 0.75

Number of citizens are chosen: n= 10

Let x be the binomial variable that represents the number of citizens favor the building of the police substation.

Then, the probability that exactly 8 of them favor the building of the police substation will be :

[tex]P(x=8)=\ ^{10}C_8(0.75)^8(1-0.75)^2[/tex]

 [Using binomial probability function [tex]P(X=x)=^nC_xp^x(1-p)^{n-x}[/tex]]

[tex]=\dfrac{10!}{8!2!}(0.100113)(0.0625)\\\\=0.2815678125\approx0.28157[/tex]

Hence, the probability that exactly 8 of them favor the building of the police substation =0.28157

Answer:

Approximately 13.9 units.

Step-by-step explanation:

First, note that ΔTVW is a right triangle.

Since we are given that ∠UTV is 112°, this means that ∠WTV is 68° because 180-112 is 68°.

Now that we know ∠WTV is 68°, we can use the basic trigonometric ratios to solve for VW. VW is the side opposite ∠WTV. We also know the hypotenuse. So, we would use sine. Recall that:

[tex]\sin(\theta)=opp/hyp[/tex]

Plug in 68° for theta, VW for the opposite, and 15 for the hypotenuse:

[tex]\sin(68)=VW/15\\VW=15\sin(68)\\VW\approx13.9078\approx13.9[/tex]

Answer:

(2, 34 )

Step-by-step explanation:

Since the points vary inversely then half the x, means double the y, thus

(2, 34) or (1, 68 ) would also belong in this inverse variation

Answer:

Step-by-step explanation:

To solve this problem you have to complete the square. To do that, set the quadratic equal to 0, then move the constant over to the other side. That's 2 steps in one, but they're simple ones:

[tex]-5t^2+10t=-65[/tex]

The first picky rule that completing the square has to follow is that the coefficient on the squared term has to be a 1. Ours is a -5, so we factor it out:

[tex]-5(t^2-2t)=-65[/tex] . Now it gets even pickier. To create a perfect square binomial on the left, we take half the linear term, square it, and add it in to both sides. Our linear term is a -2. Half of -2 is -1, and -1 squared is 1, so we add 1 into the set of parenthesis. BUT the -5 out front is a multiplier and refuses to be ignored. To offset the addition of the 1 inside the parenthesis, we have to multiply it by the -5 out front to get -5:

[tex]-5(t^2-2t+1)=-65-5[/tex]

The perfect square binomial on the left side and simplifying the right:

[tex]-5(t-1)^2=-70[/tex] . Now we'll move the 70 over and set the quadratic back equal to y:

[tex]-5(t-1)^2+70=y[/tex]

That's the quadratic in vertex form. The vertex here is (1, 70) which serves to answer 2 questions for us: the max height of the ball along with the time it was at that max height. For us, the ball reached a max height of 70 m after 1 second in its travels.

You could also do it the "calculus way" which is to find the derivative of the position function, which is

-10t + 10 = 0 and solve for t:

-10t = -10 so

t = 1. That's the time that the ball is at its highest point, and to find the highest point, sub that value in for t in the position function:

[tex]h(t)=-5(1)+10(1)+65[/tex] which comes to 70 m. I'm not sure what class you're taking so I did both! Calculus is way easier.

Answers

B, D and E are proportional

A, C, and F are not proportional

y = 3+x .... not proportional

y = 1.6x .... proportional

y = 3/(4x) .... not proportional

y = x .... proportional

y = 12x .... proportional

y = 2x+1 ... not proportional

=================================================

Explanations:

Anything in the form y = k*x is a direct proportional equation. As x goes up, so does y. The same happens if x decreases, and we'll have y also decrease. They go up together or down together. This is where the "direct" comes from. Specifically they change the same amount each time (hence the term "proportional").

For something like y = 1.6x, we have k = 1.6

In the equation y = x, we have y = 1x in reality so k = 1 here.

Lastly, y = 12x has k = 12.

----------------------

The other equations are not in the form y = kx. Whenever we have y = mx+b, with b nonzero, then y = mx+b is not proportional. The value of b must be 0 for it to fit y = kx form. This rules out y = 2x+1 and y = 3+x or y = x+3.

The equation y = 3/(4x) is an inversely proportional equation in the form y = k/x. It cannot be written as y = kx. Note how x is in the denominator for y = 3/(4x) while the same can't be said for y = kx. Inversely proportional equations have x increase and y decrease, or vice versa. They go in opposite directions.

Answer:

-2

Step-by-step explanation:

when setting up the synthetic division

it starts with -1(2) = -2

Answer:

did you have more

Step-by-step explanation:

Answer: i’ll attach the tables that my quiz had and if they’re the same tables that your quiz has then you can use this answer! but the answer is C. x | y

1 | 2

2 | 6

3 | 18

4 | 54

5 | 162

Step-by-step explanation:

every y-value can be multiplied by 3 to get the next y-value. also this answer is reliable because i got a 100 on my quiz on this! but here are the tables that were on my quiz:

Answer:

$4

Step-by-step explanation:

2 Bracelets + 3 rings = $26

2 rings = $12

3 rings = x

To get the cost of 1 ring you divide 12 by 2 and the answer you get is 6.

The total cost of the 3 rings is $18( $6*3)

Then you subtract the cost of both 2 bracelets and 3 rings($26) from the cost of 3 rings($18). The answer is $8. ( THIS IS THE COST OF 2 BRACELETS)

1 BRACELET= $4( $8/2)