what is the equation for a line that passes through the points (3,1) and (4,-1)

Answer: z = 3

Step-by-step explanation: To solve this equation for z, we can first combine our like terms on the left side of the equation. Since 12 and 7 both have z after their coefficient, we can subtract 12z - 7z to get 5z.

Now we have 5z - 2 = 13.

To solve from here, we add 2 to the left side of the equation in order to isolate 5z. If we add 2 to the left side, we must also add 2 to the right side. On the left side, the -2 and +2 cancel out. On the right, 13 + 2 simplifies to 15.

Now we have 5z = 15.

Solving from here, we divide both sides of the equation by 5 to get z alone. On the left side, the 5's cancel out and we are simply left with z. On the right side, 15 divided by 5 simplifies to 3 so we have z = 3.

Ribbon B is [tex]\frac{11}{15}[/tex] meters long

Solution:

Given that,

Ribbon A is 1/3 meter long. It is 2/5 meter shorter than ribbon B

To find: length of Ribbon B

From given information in question,

Length of Ribbon A = [tex]\frac{1}{3} \text{ meter }[/tex]

Length of Ribbon A is 2/5 meter shorter than ribbon B

Therefore we can say,

Length of Ribbon A = length of ribbon B - [tex]\frac{2}{5}[/tex]

[tex]\frac{1}{3} = \text{ length of ribbon B } -\frac{2}{5}\\\\\text{length of ribbon B } = \frac{1}{3} + \frac{2}{5}\\\\\text{length of ribbon B } = \frac{ 5 + 6}{15} = \frac{11}{15}[/tex]

Therefore ribbon B is [tex]\frac{11}{15}[/tex] meters long

Answer:

$986

I attempted to do the simple math. I feel brain dead right now.  

Answer:

-41/36

Step-by-step explanation:

-5/9 + -7/12

x4        x3

-20/36 + -21/36

Negative + Negative = Negative

-41/36

Simplfy - > Can't, it's in the simpliest form.

Answer:

Step-by-step explanation:

(n/4)-1

Divide total slices by 4 friends then subtract 1 to get Harrison’s amount

Answer:

15.7 years

Step-by-step explanation:

Use the formula for compound interest. A = P(1 + i)ⁿ

A is the total amount of money. A = 7200

P is the principal, starting money. P = 3000

i is the interest per compounding period in decimal form. Since interest is compounded annually, i = 0.0575

n is the number of compounding periods. n = ?

Substitute the information into the formula and isolate n.

A = P(1 + i)ⁿ

7200 = 3000(1 + 0.0575)ⁿ    Solve inside the brackets

7200 = 3000(1.0575)ⁿ

7200/3000 = 1.0575ⁿ       Divide both sides by 3000

2.4 = 1.0575ⁿ

n = (㏒ ans) / (㏒ base)

n = (㏒ (2.4)) / (㏒ (1.0575))

n = 15.659.....     Exact answer

n ≈ 15.7       Rounded to the nearest tenth of a year

Therefore the person must leave the money in the bank for 15.7 years until it reaches 7200 dollars.

Answer:

$7.56

Step-by-step explanation:

37%=0.37

0.37*12=4.44

12-4.44=7.56

Answer:

$7.56

37% of 12= 4.44

12-4.44

Answer:

[tex]h=\frac{SA}{2\pi r}-r[/tex]

Step-by-step explanation:

The surface area of a cylinder is equal to

[tex]SA=2\pi r^{2} +2\pi rh[/tex]

Solve for h

That means ----> isolate the variable h

subtract  2πr² both sides

[tex](SA-2\pi r^{2})=2\pi rh[/tex]

Divide by 2πr both sides

[tex]\frac{SA-2\pi r^{2}}{2\pi r}=h[/tex]

Rewrite

[tex]h=\frac{SA-2\pi r^{2}}{2\pi r}[/tex]

Simplify

[tex]h=\frac{SA}{2\pi r}-r[/tex]

Answer:

Step-by-step explanation:

Two pairs of jeans cost $32 dollars so multiply 32 x 2 and get $64.

Three shirts cost $18, multiply 18 x 3 to get $54.

One jacket costs $54 so just do 1 x 54 and you will get $54.

54 + 54 + 64 = $172.

I hope this helped!

Amanda needs $172 to buy all the clothes she wants.

To calculate the total cost of the clothes Amanda wants to buy, we need to add up the cost of each item.

To find the total cost, we add up these amounts:

= $64 + $54 + $54

= $172.

Therefore, Amanda needs $172 to buy all the clothes she wants.

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Answer: [tex]x=105\°[/tex]

Step-by-step explanation:

You can identify from the given figure that the angle  that measures 70 degrees is formed by two intersecting Chords.

It is important to remembe that, by definition:

[tex]Angle\ Formed\ by\ Two\ Chords =\frac{1}{2}(Sum\ of\ Intercepted\ Arcs)[/tex]

Based on this, you know that:

[tex]70\°=\frac{35\°+x}{2}[/tex]

Having this equation, the final step is to solve for "x" in order to find its value. You get that this is:

[tex](70\°)(2)=35\°+x\\\\140\°=35\°+x\\\\140\°-35\°=x\\\\x=105\°[/tex]

m = 90 - 6d is the equation to determine m, the number of measures Harita still needs to  memorize, as a function of d, the number of days of practice since she began learning the piece

Solution:

Given that Harita must memorize 90 measures of music for her cello solo at a concert

To find: equation to determine m, the number of measures Harita still needs to  memorize, as a function of d, the number of days of practice since she began learning the piece

Let "m" be the number of measures Harita still needs to  memorize

Let "d" be the number of days of practice since she began learning the piece

Given that She plans on memorizing 18 new measures for  every 3 days of practice

Rate per day is given as:

[tex]\frac{18}{3} = 6[/tex]

Therefore she memorises 6 per day

Therefore, the equation that relates 'm' to 'd' is:

m = total measures of music she must memorise - (number of measures she memorises per day x d)

m = 90 - 6(d)

m = 90 - 6d

Thus the required equation is found

Answer:

m = 90 - 6d is the equation to determine m, the number of measures Harita still needs to  memorize, as a function of d, the number of days of practice since she began learning the piece

Step-by-step explanation:

Answer:

Admission fee charged = $3

Cost of each ride = $10

Step-by-step explanation:

Let admission fee charged by amusement park in dollars be =[tex]x[/tex]

Let cost of each ride in dollars be =[tex]y[/tex]

Given:

Admission plus four rides cost $22

If each ride cost in dollars = [tex]y[/tex]

Cost of 4 rides in dollars will be  = [tex]4y[/tex]

So, the total cost in dollars will be given as =[tex]x+4y[/tex]

So, we have

[tex]x+4y=22[/tex]

Admission plus seven ride cost $31.

If each ride cost in dollars = [tex]y[/tex]

Cost of 7 rides in dollars will be  = [tex]7y[/tex]

So, the total cost in dollars will be given as =[tex]x+7y[/tex]

So, we have

[tex]x+7y=31[/tex]

So, we have the system of equation as:

A) [tex]x+4y=22[/tex]

B) [tex]x+7y=31[/tex]

Solving the system by elimination method.

Eliminating [tex]x[/tex] by subtracting equation A from B.

   [tex]x+7y=31[/tex]

- [tex]x+4y=22[/tex]

   -       -      -  [Sign of each term of subtract-ant gets reversed]

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

      [tex]3y=9[/tex]

Dividing both sides by 3.

[tex]\frac{3y}{3}=\frac{9}{3}[/tex]

∴ [tex]y=3[/tex]

Plugging in [tex]y=3[/tex] in equation A.

[tex]x+4(3)=22[/tex]

[tex]x+12=22[/tex]

Subtracting both sides by 12.

[tex]x+12-12=22-12[/tex]

∴ [tex]x=10[/tex]

Thus, admission fee charged = $3

Cost of each ride = $10

It will take Eli 2.4 minutes to complete 6 laps

Step-by-step explanation:

Given

Speed = s = 1000 meters per minute

Length of one lap = 400 meters

We have to compute time for 6 laps,, so we have to find the length of 6 laps combined

[tex]Length\ of\ laps = Length\ of\ one\ lap * 6\\= 400 * 6\\= 2400\ meters[/tex]

So our total distance will be: 2400 meters

using the formula for speed

[tex]s = \frac{d}{t}\\1000 = \frac{2400}{t}\\t = \frac{2400}{1000}\\t = 2.4[/tex]

So

It will take Eli 2.4 minutes to complete 6 laps

Keywords: Speed, distance

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Answer:1Vertical angles theoram

Step-by-step explanation:2 coverse of alternate interior angles theoram

Answer:

1. Reason options for 3rd statement:

Alternate Interior Angles Theorem

2.Reason options for 9th statement:

Converse of Alternate Interior Angles Theorem

Step-by-step explanation:

Answer: Jamie is incorrect

Step-by-step explanation:

The same number 10 is subtracted from both numbers 19 and 20. There result will only be the same if both numbers are equal.

We compare both numbers;

19 and 20

On the number line 19 comes before 20, which means 20 is greater than 19. Hence the result of subtracting the same number 10 from both of them cannot be the same.

So Jamie is incorrect.

Answer:

she is wrong 19-10 equals to 9

Step-by-step explanation:

you subtract 19 from 10 and get 9:)

Answer:

Step-by-step explanation:

Let us suppose r be the total number of meals eaten in a restaurant

Let us suppose c be the total number of meals eaten in a car

Let us suppose h be the total number of meals eaten in a home

Substituting Equation [B] into [A],

[tex]r + c + h = 171.....[A][/tex]

[tex]r + r + 11 = 171[/tex]

[tex]2r + 11 = 171[/tex]

[tex]2r = 160[/tex]

[tex]r = 80[/tex]

Putting [tex]r = 80[/tex] in [tex]r = h + 20.....[C][/tex]

[tex]80 = h + 20[/tex]

[tex]h = 60[/tex]

Putting [tex]r = 80[/tex] and [tex]h = 60[/tex] in [tex]r + c + h = 171.....[A][/tex]

[tex]80 + c + 60 = 171[/tex]

[tex]c = 171 - 60 - 80[/tex]

[tex]c = 31[/tex]

Therefore,

Verification:

[tex]r + c + h = 171[/tex]

Putting [tex]r = 80[/tex], [tex]c = 31[/tex] and [tex]h = 60[/tex] in [tex]r + c + h = 171[/tex]

[tex]80 + 31 + 60 = 171[/tex]

[tex]171 = 171[/tex]

Keywords: number, equation

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The correct answer is:

Jessica can wax approximately 34,533,185 square meters per hour at her constant rate of waxing the floor.

To find out how many square meters Jessica can wax per hour, we first need to convert the square miles to square meters, then divide by the time taken.

1. Convert square miles to square meters:

  Since 1 mile = 1609.34 meters, to convert square miles to square meters, we square this conversion factor:

[tex]\[ 1 \text{ mile}^2 = (1609.34)^2 \text{ meters}^2 \] \[ 1 \text{ mile}^2 = 2,589,988.36 \text{ meters}^2 \][/tex]

  So, 20 square miles would be:

[tex]\[ 20 \text{ miles}^2 \times 2,589,988.36 \text{ meters}^2/\text{mile}^2 = 51,799,767.2 \text{ meters}^2 \][/tex]

2. Calculate the rate per hour:

  Jessica waxes 20 square miles in [tex]\( \frac{3}{5} \)[/tex] of an hour.

  So, her rate per hour is:

 [tex]\[ \frac{20 \times 2,589,988.36}{\frac{3}{5}} \text{ meters}^2/\text{hour} \][/tex]

  To simplify the calculation, we'll first find the reciprocal of [tex]\( \frac{3}{5} \): \[ \frac{1}{\frac{3}{5}} = \frac{5}{3} \][/tex]

  Now, we multiply the reciprocal by 20 square miles:

 [tex]\[ 20 \times 2,589,988.36 \times \frac{5}{3} \text{ meters}^2/\text{hour} \] \[ \text{meters}^2/\text{hour} = 34,533,184.8 \][/tex]

So, Jessica can wax approximately [tex]\( 34,533,184.8 \)[/tex] square meters per hour at her constant rate.

Answer:

  9

Step-by-step explanation:

The first simplification we can make is to replace 6^0 with 1.

The first rules of exponents we can apply are ...

  (a·b)^c = a^c·b^c . . . . . . similar to the distributive property

  (a^b)^c = a^(b·c)

This reduces your expression to ...

  [tex](2^8\cdot 3^{-5})^{-2}\cdot\left(\dfrac{3^{-2}}{2^3}\right)^4\cdot 2^{28}=2^{8(-2)}\cdot 3^{-5(-2)}\cdot\dfrac{3^{-2(4)}}{2^{3(4)}}\cdot 2^{28}\\\\=2^{-16}\cdot 3^{10}\cdot\dfrac{3^{-8}}{2^{12}}\cdot 2^{28}[/tex]

Now we can apply another two rules of exponents:

  (a^b)(a^c) = a^(b+c)

  1/a^b = a^-b

Using these, we have ...

  [tex]=2^{-16-12+28}\cdot 3^{10-8}\\\\=2^0\cdot 3^2\\\\=1\cdot 9=9[/tex]

The value of the expression is 9.

Answer:

After evaluating the expression, the result is 2/3

Step-by-step explanation:

Let's evaluate the expression given to us:

-2 + 12 - 2³/ 2⁰ * 3

-2 + 12 - 8/ 1 * 3 ⇒ 2⁰ = 1 and 2³ = 8

-10 + 12/ 3

2/3

After evaluating the expression, the result is 2/3

Answer:

slope is undefined

Step-by-step explanation:

Using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

If x₂ - x₁ = 0

Since division by zero is undefined then the slope of the line is undefined

This applies to a vertical line parallel to the y- axis

Answer:

-7

Step-by-step explanation:

Lets assume the number Peggy is thinking of be "x".

Now as given, when twice the number is added to three times one more than the number. We can write it as

∴ [tex]2x+3(x+1)[/tex]--- Equation 1

Again, it is given that Peggy gets the same result as when she multiplies four times one less than the number.

∴ [tex]4(x-1)[/tex]-- equation 2

Next, we can equate both the equation 1 and 2 as it is given that result is same.

[tex]2x+3(x+1)= 4(x-1)[/tex]

Let´s distribute 3 into [tex](x+1)[/tex] and 4 into [tex](x-1)[/tex]

⇒ [tex]2x+3x+3=4x-4[/tex]

⇒ [tex]5x+3=4x-4[/tex]

Subtract both side by 4x and 3

∴ [tex]x=-7[/tex]

∴ Peggy was thinking of -7

Answer:

The area of the larger square is 20 [tex]cm^2[/tex]

Step-by-step explanation:

Given:

The area of the smaller square   =  [tex]10 cm^2[/tex]

To Find:

The are of the larger square = ?

Solution:

The diagonal of the smaller square = diameter of the circle = sides of the larger square

The diagonal of the smaller square is

=>[tex]\sqrt{2(10)}[/tex]

=>[tex]\sqrt{20}[/tex]

=>[tex]\sqrt{2\times 2 \times 5}[/tex]

=>[tex]2\sqrt{5}[/tex]

Now this diagonal is equal to the side of the larger square

so the are of the larger square is

=>[tex](2\sqrt{5})^2[/tex]

=>[tex](2\sqrt{5}) \times (2\sqrt{5}) [/tex]

=> 20 [tex]cm^2[/tex]

Answer:

- 1 2/3 < 1/4

Step-by-step explanation:

hope this helps!!

The relationship between the numbers -1 2/3 and -1/4 in an inequality is -1 2/3 > -1/4. This is because -1 2/3 is closer to zero than -1/4, meaning in the negative number line, -1 2/3 is greater than -1/4.

To create an inequality that describes the relationship between the given numbers, -1 2/3 and -1/4, first convert them into the same form. Both of these numbers are negative, but -1 2/3 is greater because it is closer to zero.

So the inequality which represents this relationship is -1 2/3 > -1/4.

Let's convert them into improper fractions to make it easier to understand.

So, -1 2/3 becomes -5/3 and -1/4 remains the same as -1/4. Hence our inequality becomes -5/3 > -1/4, which confirms that -1 2/3 is greater than -1/4.

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Step-by-step explanation:

4x + 10 = 32

4x = 32 - 10

4x = 22

x = 11/2

if we add 4 to both sides of the equation :

4x + 10 + 4 = 32 + 4 ➡ 4x + 14 = 36

4x = 36 - 14 ➡ 4x = 22 and x = 11/2

as you can see the value for x didn't change because when we add/subtract or multiple/divide same number from both sides of an equation the result won't change.

The other parallel side is 44 m

Step-by-step explanation:

Let us revise the formula of the area of a trapezium

[tex]A=\frac{1}{2}(b_{1}+b_{2})h[/tex] , where

∵ The area of a trapezium is shaped field is 480 m²

∴ A = 480 m²

∵ The distance between two parallel sides is 15 m

∴ h = 15 m

∵ One of the parallel side is 20 m

∴ [tex]b_{1}[/tex] = 20 m

We need to find [tex]b_{2}[/tex]

Substitute all these value in the rule of the area below

∵ [tex]A=\frac{1}{2}(b_{1}+b_{2})h[/tex]

∴ [tex]480=\frac{1}{2}(20+b_{2})(15)[/tex]

- Multiply the two sides by 2

∴ [tex]960=(20+b_{2})(15)[/tex]

- Divide both sides by 15

∴ [tex]64=20+b_{2}[/tex]

- Subtract 20 from both sides

∴ [tex]44=b_{2}[/tex]

The other parallel side is 44 m

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Answer:

30 or 52

I'm not sure. Sorry. I tried my best. Don't let the "Helping Hand" fool you. You see you said 6 forks and twice as many spoons which equals 12+6. Then "as" knives. I got confused there. I think there it's either 12 or twice as many knives as spoons. In other words, 12×2.

6 + (6 × 2) + (6 × 2) = 30

6 + (6 ×2) + (12 × 2) = 52

Answer:

(-4,2)

Step-by-step explanation:

Answer:

(-4,2)

Step-by-step explanation:

Answer:

-8 i think

Step-by-step explanation:

The y-intercept of the graph for the function y = (x - 2)(x + 4) is found by setting x to zero, which results in a y-intercept of -8.

The y-intercept on a graph represents the point where the curve or line crosses the y-axis.

To find the y-intercept of the graph of y = (x - 2)(x + 4), you need to determine the value of y when x is zero. By substituting x with 0 in the equation,

we calculate the y-intercept:

Therefore, the y-intercept of the graph is -8.

Step-by-step explanation:

[tex]\begin{array}{c|cc}12&2\\6&2\\3&3\\1\end{array}\qquad\qquad\begin{array}{c|cc}56&2\\28&2\\14&2\\7&7\\1\end{array}\\\\12=\boxed{2}\cdot\boxed{2}\cdot3\\\\56=\boxed{2}\cdot\boxed{2}\cdot2\cdot7\\\\GCF(12,\ 56)=\boxed{2}\cdot\boxed{2}=4\\\\LCM(12,\ 56)=\boxed{2}\cdot\boxed{2}\cdot3\cdot2\cdot7=168[/tex]

Answer:

m+n = 337

Step-by-step explanation:

Lets start from the first triangle, It is given to be as 30-60-90.

The hypotenous of first rectangle be 2x, then other sides are by default x and

[tex]\sqrt{3}(x)[/tex] , using laws of trigonometry.

(sin(30) = 0.5  and cos(30) = [tex]\frac{\sqrt{3}}{2}[/tex])

The perimeter of first triangle is ,

= [tex]2x + x + \sqrt{3}(x) = x(3+\sqrt{3}) = \sqrt{3}x(1+\sqrt{3})[/tex]

Now, for second triangle, the longer leg is 2x, and similarly again,

other 2 sides are [tex]\frac{2x}{\sqrt{3}}  and \frac{4x}{\sqrt{3}}[/tex].

Again the perimeter of triangle comes out as,

= [tex]\sqrt{3}(x)(1+\sqrt{3})(\frac{2}{\sqrt{3}})[/tex]

Thus, the repeating pattern is identified. The consecutive perimeters differ by, multiplying by factor [tex]\frac{2}{\sqrt{3}}[/tex]

Thus, we can say that perimeter of 4th triangle is,

= [tex](\frac{2}{\sqrt{3}})^{3}(X)[/tex], where X is the repeating constant.

And of 12th triangle is,

= [tex](\frac{2}{\sqrt{3}})^{11}(X)[/tex],

Evaluating the above ratio, we get,

= [tex]\frac{81}{256}[/tex]

Thus, m =256 and n=81.

Thus, m+n = 256+81 = 337.