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Answer:

22) 119

24) 15

Step-by-step explanation:

22) 61 + b = 180              <-- supplementary because on the same line

      b = 119                     <-- subtracted 61 from both sides

24) 87 + (6x + 3) = 180        <-- supplementary because on the same line

     87 + 6x + 3 = 180          <-- take out parantheses

     90 + 6x = 180               <-- add like terms

     6x = 90                         <-- subtracted 90 from both sides

     x = 15                            <-- solve for x by dividing 6 from both sides

Answer:

The answer is "[tex]\frac{26}{7}[/tex]"

Step-by-step explanation:

The whole question can be found in the file attached.

[tex]\to x + \frac{5}{7} = \frac{31}{7}\\\\[/tex]

Subtracting the [tex]\frac{5}{7}[/tex] from both sides of the equations:

[tex]\to x +\frac{5}{7} - \frac{5}{7} = \frac{31}{7} - \frac{5}{7} \\\\[/tex]

                    [tex]= \frac{31-5}{7} \\\\= \frac{26}{7} \\\\[/tex]

Answer:

A

Step-by-step explanation:

The explicit formula for a geometric sequence is

f(n) = f(1) [tex](r)^{n-1}[/tex]

where f(1) is the first term and r the common ratio

Here f(1) = 64 and r = [tex]\frac{f(2)}{f(1)}[/tex] = [tex]\frac{16}{64}[/tex] = [tex]\frac{1}{4}[/tex] , then

f(n) = 64 [tex](\frac{1}{4}) ^{n-1}[/tex] → A

Answer:

x > -24

Step-by-step explanation:

-x/4 < 6

Multiply each side by -4, remembering to flip the inequality

-x/4  *-4> 6*-4

x > -24

[tex]\boxed{\large{\bold{\red{ANSWER~:) }}}}[/tex]

[tex]\bold{ Note - }[/tex]

Answer:

4x + 2x would be 6x

Step-by-step explanation:

Answer:

10 the next day

Step-by-step explanation:

Using the least common multiple

3, 6, 8

The least common multiple is 24

24 hours from 10 the next day

Answer:

[tex]4+2\sqrt{31}\text{ by } -4+2\sqrt{31}[/tex]

Or about 15.136 centimeters by 7.136 centimeters.

Step-by-step explanation:

Recall that the area of a rectangle is given by:

[tex]\displaystyle A = w\ell[/tex]

Where w is the width and l is the length.

We are given that the length is 8 centimeters longer than the width. In other words:

[tex]\ell = w+8[/tex]

And we are also given that the total area is 108 square centimeters.

Thus, substitute:

[tex](108)=w(w+8)[/tex]

Solve for w. Distribute:

[tex]w^2+8w=108[/tex]

Subtract 108 from both sides:

[tex]w^2+8w-108=0[/tex]

Since the equation is not factorable, we can use the quadratic formula:

[tex]\displaystyle x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

In this case, a = 1, b = 8, and c = -108. Substitute and evaluate:

[tex]\displaystyle \begin{aligned} w&= \frac{-(8)\pm\sqrt{(8)^2-4(1)(-108)}}{2(1)} \\ \\ &=\frac{-8\pm\sqrt{496}}{2}\\ \\ &=\frac{-8\pm4\sqrt{31}}{2} \\ \\ &=-4 \pm 2\sqrt{31} \end{aligned}[/tex]

So, our two solutions are:

[tex]w=-4+2\sqrt{31} \approx 7.136 \text{ or } w=-4-2\sqrt{31}\approx -15.136[/tex]

Since width cannot be negative, we can eliminate the second solution.

And since the length is eight centimeters longer than the width, the length is:

[tex]\ell =(-4+2\sqrt{31})+8=4+2\sqrt{31}\approx 15.136[/tex]

So, the dimensions of the rectangle are about 15.136 cm by 7.136 cm.

Answer:

56

Step-by-step explanation:

Zoe : hanna

3         7

Zoe got 24

3*8 = 24

so multiply each side by 8

Zoe : hanna

3*8         7*8

24           56

Hanna got 56

Answer: $600

Step-by-step explanation:

Given

Anual makes [tex]\$12.50[/tex] an hour

For 48 hours, he makes

[tex]\Rightarrow 48\times 12.5\\\Rightarrow \$600[/tex]

Thus, he will make $600 for 48 hours

Answer:

 x=26.11

SOH-CAH-TOA

TOA: Tan= OPP/ADJ = tan(43)=x/28

  .932=x/28          26.11

Step-by-step explanation:

Answer: B

Step-by-step explanation:

B is basically showing the Pythagorean theorem does not work on the triangle's side lengths.

The pythagorean theorem is supposed to work for all right triangles

The rabbit will jump on the train after the train moves 0.4km

The given parameters are:

[tex]d = 100m[/tex] -- distance between the puppy and the train

[tex]s_1 = 8km/hr[/tex] -- the speed of the train

[tex]s_2 = 10km/hr[/tex] --- the puppy's speed

Required

The distance where the puppy catch up with the train

First, we calculate the relative speed (rs) of the puppy to the train

[tex]rs =s_2 - s_1[/tex]

[tex]rs =10km/hr - 8km/hr[/tex]

[tex]rs =2km/hr[/tex]

Calculate the time to catch up with the train using:

[tex]Time = \frac{Distance}{Speed}[/tex]

[tex]t = \frac{100m}{2km/hr}[/tex]

Convert km to m

[tex]t = \frac{100m}{2*1000m/hr}[/tex]

[tex]t = \frac{100m}{2000m/hr}[/tex]

[tex]t = 0.05hr[/tex]

Calculate the distance to catch up with the train using:

[tex]Distance = Speed * Time[/tex]

[tex]d= s_2* t[/tex] --- speed of the train multiplied by the time

So, we have:

[tex]d = 8km/hr * 0.05hr[/tex]

[tex]d = 8km * 0.05[/tex]

[tex]d = 0.4km[/tex]

Read more at:

https://brainly.com/question/14667411

Answer:

angle bisector

Step-by-step explanation:

Since the line divided the top angle into two equal pieces we call this an angle bisector.

Answer:

Ishaan is currently 15 years old.

Step-by-step explanation:

Let B represent Ben's current age and I represent Ishann's current age.

Ben is four times as old as Ishaan. In other words:

[tex]B=4I[/tex]

Six years ago, Ben was six times as old as Ishaan. In other words:

[tex]B-6=6(I-6)[/tex]

Solve for I. Substitute:

[tex](4I)-6=6(I-6)[/tex]

Distribute:

[tex]4I-6=6I-36[/tex]

Subtract 4I from both sides and add 36 to both sides:

[tex]2I=30[/tex]

And divide both sides by two. Hence:

[tex]I=15[/tex]

Ishaan is currently 15 years old.

Answer:

Age of Ishaan = 15 years

Step-by-step explanation:

Let Ishaan's age = x years

Age of Ben = 4 * x = 4x years

6Years ago:

Age of Ishaan = x - 6

Age of Ben = 4x - 6

6 years ago, Ben was 6 times as old as Ishaan

So, Age of Ben = 6 * Ishaan's age

     4x - 6 = 6 *(x-6)

4x - 6 = 6x - 36

Add 36 to both sides

4x - 6 + 36  = 6x  

4x + 30 = 6x

Subtract '4x' from both sides

30 = 6x - 4x  

30 = 2x

2x = 30

Divide both by 2 sides

x = 30/2

x = 15

A graph of the image of ABC under a dilation whose center is P and scale factor is 1/3 is shown in the image below.

In Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric shape, but not its shape. This ultimately implies that, the size of the geometric shape would be increased (enlarged) or decreased (reduced) based on the scale factor applied.

In this exercise, we would use an online graphing calculator to plot the image of ABC after a dilation by a scale factor of 1/3 centered at P.

Based on the image (see attachment), we can logically deduce that each vertex is 1/3 times as far from center P as the original vertex and each segment is 1/3 times as long as the original:

AC = 6.7/3 = 2.2

AB = 12.4/3 = 4.1

CB = 12.7/3 = 4.2

Read more on dilation here: brainly.com/question/20482938

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Answer:

Sum = .5 Product = -3

Step-by-step explanation:

Answer:

I Will explained you youuuuuu<uuuuuuuuuu

Answer: u = [tex]\frac{7}{8}[/tex] or 0.875

Step-by-step explanation:

Let us convert this statement to a question

[tex]4^{2}[/tex]-8u-9 = 0

16-8u-9 = 0

-8u = 0+9-16

-8u = -7

u = -7 ÷ -8

u = [tex]\frac{7}{8}[/tex] or 0.875

2x + y = -4

slope = -2

perpendicular slope = 1/2

new equation = x - 2y = x

(1) (2)= 2

(-2) (-8)=16

2+16 =18

new equation = x - 2y = 18

Answer:

Take the gross amount of any sum (items you sell or buy) – that is, the total including any VAT – and divide it by 117.5, if the VAT rate is 17.5 per cent. (If the rate is different, add 100 to the VAT percentage rate and divide by that number.)

Answer:

divide by 117.5 if the rate different, add 100 to the percentage and divide by the number therefore multiply by 100 to get the total

Step-by-step explanation:

the formula to calculate vat percentage

Answer:

Step-by-step explanation:

If AB and DE are equidistant from the center, that means that they are the same length. We set the equations equal to one another and solve for x:

3x - 7 = 5(x - 5) and

3x - 7 = 5x - 25 and

18 = 2x so

x = 9. Now we sub that into the expression for AB (or DE since they're the same length):

3(9) - 7 = 20

Both AB and DE measure 20 units.

Answer:

E500

Step-by-step explanation:

Given x the original price of the coat

437.5 + 0.125x = x

437.5 = 0.875x

x = E500

Answer:

0

Step-by-step explanation:

LN is an horizontal segment. it means that the line is parallel to x axis so its slope is 0

Answer: £21007.22

Step-by-step explanation:

First, find the interest amount using the formula SI = (P × R × T) / 100.

SI = (P × R × T) / 100 = (18790 × 5.9 × 2)/100 = 221722/100 = £2217.22

The total amount = principle amount + interest amount

= £18790 + £2217.22 = £21007.22

Answer:

just divide i believe

162÷9

15÷5

84÷14

24÷12

Step-by-step explanation:

The real part (red) and imaginary part (blue) of the Riemann zeta function along the critical line Re(s) = 1/2. The first non-trivial zeros can be seen at Im(s) = ±14.135, ±21.022 and ±25.011. The Riemann hypothesis, a famous conjecture, says that all non-trivial zeros of the zeta function lie along the critical line.