the left and right page numbers of an open book are two consecutive integers whose sum is 169. find the numbers.

Answer:

x= 40°

Step-by-step explanation:

Please see attached picture for full solution.

Key concepts:

- Corresponding angles are equal to each other

- The sum of the angles in a triangle add up to 180°

Answer:

Step-by-step explanation:

It takes 9 minutes to fill a depth of [tex]\frac{3}{5}[/tex] meters.

Filling  [tex]\frac{3}{5}[/tex] meters take 9 minutes time.

Filling 3 meters of the aquarium takes [tex]5\times9[/tex] = 45 minutes time (Multiplying by 5 both the numbers).

In order to fill 1 meter of the aquarium it will take [tex]\frac{9\times5}{3} = 15[/tex] minutes (Dividing by 3 both the numerical values).

Answer:

The rate is 15 minutes per meter.

Step-by-step explanation: please give brainliest

Answer:

1 1/2 hours

Step-by-step explanation:

divide 3/2 and whatever you got is your answer

Answer:

x = 6

y = 0

Explanation:

−2x+y=−12;3y−2x=−12

Rewrite equations:

−2x+y=−12;−2x+3y=−12

Solve −2x+y=−12 for y

−2x+y=−12

−2x+y+2x=−12+2x(Add 2x to both sides)

y=2x−12

Substitute 2x−12 for y in −2x+3y=−12

−2x+3y=−12

−2x+3(2x−12)=−12

4x−36=−12 (Simplify both sides of the equation)

4x−36+36=−12+36 (Add 36 to both sides)

4x=24

Divide both sides by 4

4x / 4 = 24 / 4

x = 6

Substitute 6 for x in y=2x−12

y=2x−12

y=(2)(6)−12

y=0 (Simplify both sides of the equation)

Answer:

To find out the length of AB you are trying to figure out how long it is

If B is at 45, and A is at 16

You need to figure out how far it is from 16 to 45

In order to do this the easiest way, you would go 45-16

45-16=29

AB=29

Hope this helps ;)

Answer:

Step-by-step explanation:

Because 4 to the power of -3 divided by 4 to the power of -1 switched (Like when there is a negative exponent you move the number or variable to the other side of the fraction) and scince both have a negative number you switch both. and 1-3 is -2 so you switch it to the bottem and put a 1 at the top.

                                         ^^Hope this helps!

The expressions equivalent to 4^-3 / 4^-1 are 1/4^2 and (4^-1)^-3.

In the subject of mathematics, the given expression is 4^-3 / 4^-1. To simplify this expression, you need to understand two rules of exponents:

Applying these two rules, 4^-3 / 4^-1 = 4^-3 * 4^1 = 4^(1 - 3) = 1/4^2.

Another way to simplify the expression is to use the rules of exponents to rewrite each part independently. 4^-3 = 1/4^3 and 4^-1 = 1/4. Therefore, 4^-3 / 4^-1 = (1/4^3) / (1/4) = 4, which is equivalent to (4^-1)^-3.

Therefore, the equivalent expressions are (B) 1/4^2 and (D) (4^-1)^-3.

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Answer:

4u+16

Step-by-step explanation:

first multiply the outside bumber(in this case its 4) by each of the numbers and variables inside. (making u turn into 4u) and ( making 4 turn into 16 bcs 4x4=16

Answer:

The smallest amount is [tex]\£6,911[/tex]

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=3\ years\\ A=\£8,000\\ r=5\%=5/100=0.05\\n=1[/tex]  

substitute in the formula above

[tex]8,000=P(1+\frac{0.05}{1})^{1*3}[/tex]  

solve for P

[tex]8,000=P(1.05)^{3}[/tex]  

[tex]P=8,000/(1.05)^{3}[/tex]  

[tex]P=\£6,910.70[/tex]  

Round to the nearest pound she can invest

The smallest amount is [tex]\£6,911[/tex]

Measure of one of the vertical angle is 156°

Solution:

The measure of angles given are (x + 104)° and 3x°.

The given angles are vertical in order.

If two lines meet at a point, then the angle formed in vertical positions are equal.

That is vertically opposite angles are equal.

⇒ 3x° = (x + 104)°

⇒ 3x° = x° + 104°

Subtract x° on both sides of the equation to equal the expression,

⇒ 3x° – x° = x° + 104° – x°

⇒ 2x° – x° = 104°

⇒ 2x° = 104°

Divide both sides of the expression by 2, we get

⇒ x° = 52°

Substitute x° = 52° in one of the vertical angle.

3x° = 3 × 52° = 156° (or)

x° + 104° = 52°+ 104° = 156°

Hence the measure of one of the vertical angle is 156°.

Answer:

There are 8 more girls than boys.

Step-by-step explanation:

First, find how many girls and boys are in the class. Add the two parts of the ratio together, 3 and 5 to get 8. Then divide 32 by 8 to get 4. Since the total number of students in the class is 4 times the ratio of boys to girls, multiply both sides of the ratio by 4. You then get 12 boys : 20 girls. You can check this by adding 12 + 20 to get 32. Next, subtract the number of girls from the boys. 20 - 12 = 8. Therefore, there are 8 more girls than boys.

Therefore there are 8 girls more than boys

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Answer: -8z-40

Step-by-step explanation:

-4(2z+6) = -8z-24

-8z-24-12=-8z-36

-8z-36=4 (you have to move 4 to the other side of the equal sign so 4 becomes -4)

-8z-40

Answer:

z= - 5

Step-by-step explanation:

−4(2z+6)−12=4

Step 1: Simplify both sides of the equation.

−4(2z+6)−12=4(Distribute)

−8z+−24+−12=4

(−8z)+(−24+−12)=4(Combine Like Terms)

−8z−36=4

Step 2: Add 36 to both sides.

−8z−36=4

−8z=40

Step 3: Divide both sides by -8.

−8z=40

z=−5

I hope that this will help

Answer:

Slope= -3/4

Step-by-step explanation:

[tex]\bf (\stackrel{x_1}{-4}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{(-2)}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{(-4)}}}\implies \cfrac{-1+2}{3+4}\implies \cfrac{1}{7}[/tex]

[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-2)}=\stackrel{m}{\cfrac{1}{7}}[x-\stackrel{x_1}{(-4)}]\implies y+2=\cfrac{1}{7}(x+4) \\\\\\ y+2=\cfrac{1}{7}x+\cfrac{4}{7}\implies y=\cfrac{1}{7}x+\cfrac{4}{7}-2\implies y=\cfrac{1}{7}x-\cfrac{10}{7}[/tex]

Answer:

15

Step-by-step explanation:

Answer:

Step-by-step explanation:

8+?=19

19-8=11

Y=11

Final answer:

To solve the equation 19 = 8 + y for y, you subtract 8 from both sides which gives you y = 11.

Explanation:

The equation provided, 19 = 8 + y, is a simple linear equation where you are solving for the variable y. To find the value of y, you need to isolate y on one side of the equation.

Here is the step-by-step process:

Start with the original equation: 19 = 8 + y.

To isolate y, you need to get rid of the 8 on the right side of the equation. You can do this by subtracting 8 from both sides of the equation.

Subtracting 8 from both sides gives us: 19 - 8 = y.

Simplify the left side: 11 = y.

Therefore, y equals 11.

Answer:

first C then B

Step-by-step explanation:

The distance Raphael needs to travel goes down by time. Therefore the y-value (the amount of distance) will go down as the x-value (the amount of time) will go up. So C.

The speed of the rollercoaster is increasing as time goes by. Therefor the y-value (the speed) will go up and the x-value (the amount of time) will also go up. So B.

Time is almost always moving forward so you can almost always assume x will go up.

Step-by-step explanation:

Check out the pic, if it doesn't help you can ask me whichever part you don’t understand

Answer:

I believe the answer to this question is: X=5.

Each new term is found by multiplying the last term by 2

1*2 = 2

2*2 = 4

2*4 = 8

2*8 = 16

and so on

Therefore the common ratio is r = 2.

The starting term is a = 1

The general nth term is [tex]a*(r)^{n-1} = 1*(2)^{n-1} = 2^{n-1}[/tex] where n is an integer (aka whole number) and n starts at n = 1.

Juan and raj cut up a banana to put on cereal. juan puts 1/7 of the banana on his bowl of cereal, and raj puts 2/5 ​ of the banana on his bowl of cereal.

what fraction of the banana did juan and raj put on their cereal altogether?

a. 2/35 banana

b. 3/12 banana

c. 3/7 banana

d. 19/35 banana

Juan and Raj altogether put 19/35 banana

Given that, Juan and Raj cut up a banana to put on cereal

[tex]fraction\ of\ banana\ put\ by\ Juan = \frac{1}{7}\\\\fraction\ of\ banana\ put\ by\ Raj = \frac{2}{5}[/tex]

We have to find the fraction of banana put by Juan and Raj altogether

This means, we have to add both the fractions

[tex]fraction\ of\ banana\ put\ altogether = fraction\ of\ banana\ put\ by\ Juan + fraction\ of\ banana\ put\ by\ Raj[/tex]

[tex]fraction\ of\ banana\ put\ altogether = \frac{1}{7} + \frac{2}{5}\\\\\text{Cross multiply to simplify }\\\\fraction\ of\ banana\ put\ altogether = \frac{1 \times 5 + 2 \times 7}{7 \times 5}\\\\fraction\ of\ banana\ put\ altogether = \frac{5+14}{35}\\\\fraction\ of\ banana\ put\ altogether = \frac{19}{35}[/tex]

Thus they put [tex]\frac{19}{35}[/tex] of banana by Juan and Raj altogether

Answer:

132 ft squared

Step-by-step explanation:

One way is to divide the shape into a rectangle and a triangle, by drawing a vertical line.

This gives a rectangle that is 9 by 11, so has area 99.

The triangle has a base of 11 and height of 15 - 9 = 6.

So the area of the triangle = 1/2 x b x h = 1/2 x 11 x 6 = 33

So the total area is 99 + 33 = 132.

Step-by-step explanation:

A bag of calories=1,596

calories in each serving of corn chips=?

1,596/12=133

"133 calories are present in each serving of corn chips."

Each serving of corn chips contains 133 calories.

To find the number of calories in each serving of corn chips, we need to divide the total number of calories in the bag by the number of servings.

Calories per serving= Number of servings/Total calories in the bag

​Calories per serving= 12servings/1,596calories= 133

In conclusion each serving of the corn chips contributes 133 calories to the overall caloric content of the bag.

This calculation allows you to find the caloric content per serving, providing a helpful metric for individuals managing their calorie intake.

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The number 28 is divided by the number 3 in fraction form is  9 1/3.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, The number 28 is divided by the number 3.

This can be written in fraction form as 28/3.

Now, 3×9 = 27.

Therefore, 28/3.

= 9 1/3.

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Answer:

None of the answers are correct, because 12/15=4/5, it's equivalent to 12 divided by 15.

Step-by-step explanation:

Answer:

y = -21

Step-by-step explanation:

Answer:

- 12

Step-by-step explanation:

The rate of change is measured by the slope m of the data

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (3, - 2) and (x₂, y₁ ) = (5, - 26) ← 2 ordered pairs from the table

m = [tex]\frac{-26+2}{5-3}[/tex] = [tex]\frac{-24}{2}[/tex] = - 12

Rate of change = - 12

The velocity of plane is 379 kilometer per hour

Solution:

Given that, plane was traveling from Florida to Canada

It flew 5 hours and went 1895 km

To find: Velcoity

The velocity can be found by dividing the distance traveled by time taken

[tex]velocity = \frac{distance}{time}[/tex]

Here in this sum,

distance = 1895 km

time = 5 hours

Substituting the values in formula,

[tex]velocity = \frac{1895}{5}\\\\velocity = 379[/tex]

Thus velocity of plane is 379 kilometer per hour