Question 3 of 50
Line A in the given graph has what kind of slope?
-1/2
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The ratio of boys to girls (3:4) and girls to adults (5:7) leads to a combined ratio of children to adults at the holiday camp of 5:4 after aligning the ratios on the common term for girls and simplifying.

To determine the ratio of children to adults at the holiday camp, we can use the given ratios:

First, express both ratios with a common term for girls to combine them accurately:

Since the ratio of girls to adults is 5:7, we can align this with the boys to girls ratio by multiplying the boys to girls ratio by 5 (the common term for girls). This gives us:

So, we have 15 boys and 20 girls for every 28 adults. The total number of children (boys and girls) is 15 + 20 = 35.

Therefore, the ratio of children to adults at the camp is 35:28, which simplifies to 5:4 after dividing both terms by 7.

Step-by-step explanation:

Jose need at least 94 more points in order to get an A on this semester

Measure of the smaller angle is 75°

Step-by-step explanation:

Let angles be 5x and 7x.

⇒ 5x + 7x = 180

⇒ 12x = 180

⇒ x = 15

⇒5x = 5 [tex]\times[/tex] 15 = 75°

To find the measure of the smaller supplementary angle, when the ratio of the two angles is 5:7, you need to set up an equation with 5x and 7x as the angle measures. Solve this equation to find the value of 'x', and then use 'x' to calculate the measure of the smaller angle, which amounts to 75 degrees.

In this mathematics problem, we know that two angles are supplementary if their measures add up to 180 degrees. If the ratio of the two supplementary angles is 5:7, we can set up an equation to solve for the unknowns.

Let 5x represent the measure of the smaller angle and 7x represent the measure of the larger angle. We know that the sum of these two angles should be 180 degrees, thus:

5x + 7x = 180

Combining like terms, we get:

12x = 180

Now, we can solve for 'x' by dividing both sides of the equation by 12:

x = 180 / 12, which equals 15

Now that we know the value of 'x', we can plug it back in to find the measures of the two angles. The smaller angle, which is 5x, is then:

5x = 5 * 15, which equals 75 degrees

So the measure of the smaller angle is 75 degrees.

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Answer:

1   7/20   mixed= 27/20

Step-by-step explanation:

Answer:

he hit the slopes  

Step-by-step explanation:

;)

Answer:

$14

Step-by-step explanation:

if Gerald's coins have the same value as his brothers, then that means they have exactly the same amount

Answer:

Step-by-step explanation:

All equations where x=2 is a solution : a(x-2) = 0......a ≠ 0

Answer:

Mr. Smiths class has 12 students and Mrs. Brown's class has 10 students.

Step-by-step explanation:

if 1/3 of the class is absent and that amount is four you would multiply 4 by 3 and get 12. If 2/5 of the class are missing and there 4 students first you would divide 4 by 2 and get 2, then you would take the 2 and multiply it by 5 and get 10.

133 is the Answer bc that is a supplementary angle and supplementary angles always sum up to 180 hope this helps please mark brainliest

Step-by-step explanation:

Answer: 30 ft

Step-by-step explanation: bc 1/2 inch = 3 feet combined length = 2 + 5= 5 inches therefore (5.0/0.5)(3)= 10(3)=30

Answer:

4

Step-by-step explanation:

√10  is a irrational number

Final answer:

The square root of 10 is an irrational number because it is a non-terminating, non-repeating decimal that cannot be expressed as a simple fraction. It lies between the integers 3 and 4 on the number line.

Explanation:

The square root of 10 is an example of an irrational number. Unlike integers and whole numbers, which are exact and do not have an ending decimal or fraction, and unlike rational numbers which can be written as a ratio of two integers (like 1/2 or 3/4), an irrational number cannot be expressed as a simple fraction.

The square root of 10 cannot be precisely written as a fraction because it is a non-terminating, non-repeating decimal. In other words, if we were to write out the decimal form of the square root of 10, it would have an infinite number of digits after the decimal point without any repeating pattern.

For a real-world example, consider that knowing whether a number is rational or irrational can influence how we represent that number in various contexts, such as in engineering or architecture, where precision is paramount.

Answer:

30

Step-by-step explanation:

Answer: intersecting

Step-by-step explanation:

they cross each other

Answer:

Option A. one rectangle and two triangles

Option E. one triangle and one trapezoid

Step-by-step explanation:

step 1

we know that

The area of the polygon can be decomposed into one rectangle and two triangles

see the attached figure N 1

therefore

Te area of the composite figure is equal to the area of one rectangle plus the area of two triangles

so

[tex]A=(8)(4)+2[\frac{1}{2}((8)(4)]=32+32=64\ yd^2[/tex]

step 2

we know that

The area of the polygon can be decomposed into one triangle and one trapezoid

see the attached figure N 2

therefore

Te area of the composite figure is equal to the area of one triangle plus the area of one trapezoid

so

[tex]A=\frac{1}{2}(8)(4)+\frac{1}{2}((4+8)(8)=16+48=64\ yd^2[/tex]

Answer:

[tex]x = 6[/tex] and [tex]y = 236[/tex]

Step-by-step explanation:

[tex]y = 296 - 10x[/tex]

[tex]y = 200 + 6x[/tex]

By equating both equations, we get:

[tex]296 - 10x = 200+6x[/tex]

[tex]16x = 96[/tex]  [Separate variables and constants]

[tex]x = 6[/tex]

By substituting [tex]x = 6[/tex] to the above equation, we get:

[tex]y = 296 - 10(6)[/tex]

[tex]y = 296 - 60[/tex]

[tex]y = 236[/tex]

Hence, [tex]x = 6[/tex] and [tex]y = 236[/tex]

Answer:

[tex]Amount\ of\ sales=\$ 6000[/tex]

Step-by-step explanation:

[tex]Let\ total\ sales=x\\\\Commission=3\%\ of\ total\ sale\\\\Commission=3\%\ of\ x\\\\It\ is\ given\ that\ salesperson\ gets\ \$ 180\ as\ commission.\\\\3\%\ of\ x=180\\\\\frac{3}{100}x=180\\\\x=\frac{180\times 100}{3}\\\\x=60\times 100\\\\x=6000\$\\\\Amount\ of\ sales=\$ 6000[/tex]

Answer:

  120 mph

Step-by-step explanation:

To find miles per hour, divide miles by hours. ("Per" essentially means "divided by".)

  (24 miles)/(0.2 hour) = 24/0.2 miles/hour = 120 miles/hour

Answer:5/12

Step-by-step explanation:

If you cut 10 ( the numerator) in half you get 5 and if you cut 24(the denominator) in half you get 12

Answer:

Step-by-step explanation:

Answer:1

Step-by-step explanation:just divide numerator by denominator

Question:

How fast should the ant walk to go around the rectangle in 4 minutes if the sides are 12 inches and 16 inches

Answer:

The ant should walk 14 inches per minute

Solution:

Given that,

Dimensions of rectangle are 12 inches and 16 inches

Find the perimeter of rectangle

Perimeter = 2(length + width)

Perimeter = 2(12 + 16)

Perimeter = 2(28) = 56

Thus perimeter of rectangle is 56 inches

Time taken = 4 minutes

We have to find the speed at which ant covers 56 inches in 4 minutes

The speed is given by formula:

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

[tex]speed = \frac{56}{4} = 14[/tex]

Thus the ant should walk 14 inches per minute

Answer:

it's B

Step-by-step explanation:

a triangle cannot two obtuse angles

A traingle does not contain two obtuse angles. Option B is correct.

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°.

Here,
A triangle cannot contain two obtuse angles.

A triangle cannot have the two obtuse angle, becaue for a triangle sum of the iternal angle must not exceeds 180°

Thus, A traingle does not contain two obtuse angles. Option B is correct.

Learn more about triangles here:

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Step-by-step explanation:

[tex]5 \times 5= 25[/tex]

Answer:

The dimensions of the wall are 100 ft x 100 ft

Step-by-step explanation:

we know that

The perimeter of a rectangular wall is

[tex]P=2(x+y)[/tex]

where

x is the length

y is the width

we have

[tex]P=400\ ft[/tex]

so

[tex]400=2(x+y)[/tex]

simplify

[tex]200=x+y[/tex]

[tex]y=200-x[/tex] ----> equation A

The area of a rectangular wall is equal to

[tex]A=xy[/tex] ----> equation B

substitute equation A in equation B

[tex]A=x(200-x)\\A=-x^2+200x[/tex]

This is the equation of a vertical parabola open downward (because the leading coefficient is negative)

The vertex represent a maximum

Convert the quadratic equation in vertex form

[tex]A=-x^2+200x[/tex]

Factor -1

[tex]A=-(x^2-200x)[/tex]

Complete the square

[tex]A=-(x^2-200x+100^2)+100^2[/tex]

[tex]A=-(x^2-200x+10,000)+10,000[/tex]

Rewrite as perfect squares

[tex]A=-(x-100)^2+10,000[/tex] ----> equation in vertex form

The vertex is the point (100,10,000)

The x-coordinate of the vertex represent the length of the wall for a maximum area

so

[tex]x=100\ ft[/tex]

Find the value of y

equation A

[tex]y=200-(100)=100\ ft[/tex]

therefore

The dimensions of the wall are 100 ft x 100 ft

To find the dimensions of a rectangular wall that maximizes the area enclosed by 400 feet of brick, you can use the formula for the area of a rectangle and find where the derivative of the area equation equals zero. By solving the resulting equations, you can determine the dimensions of the wall that will maximize the enclosed area.

To find the dimensions of a rectangular wall that maximizes the enclosed area with 400 feet of brick, we need to use the formula for the area of a rectangle, which is length times width. So, let's represent the width of the wall as x and the length as y. Since we have 400 feet of brick, we can write the equation 2x + 2y = 400. We can rearrange this equation to solve for y: y = (400 - 2x)/2. Now we have the area equation A = x * y,

which becomes A = x * ((400 - 2x)/2). To find the maximum area, we can take the derivative of A with respect to x and set it equal to zero: (400 - 4x)/2 = 0. Solving for x, we get x = 100. Substituting this back into the y equation, we find y = 100 as well. Therefore, the dimensions of the rectangular wall that maximize the area enclosed by the brick are 100 feet by 100 feet.

Answer:

B. 52 beats/min

Step-by-step explanation:

while resting her heart beats : 36×2 = 72 beats/min

while running her heart beats : 1 860÷15 = 124 beats/min

difference = 124-72 = 52 beats/min

:)

Answer:

B. 52 beats/min

Step-by-step explanation:

To find the answer you have to find the bpm of each time that Chandra recorded her heart rate. So when she recorded her heart rate when running, you simply divide 1850 by 15, and you should get 123.333 (repeating) I am assuming by the answers that we are rounding, so we are going to round that answer up. Next to find her heart rate while resting, you take her heart rate in 30 seconds, which is 36, and multiply it by 2, because it was her heart rate in half of the time that we are measuring it in. So when you multiply 36 by 2 you should get 72. The next step is to subtract 124 from 72. You answer is 52.

Answer:

B

Step-by-step explanation:

Because, according to the graph, they are making the most sells.

Answer:

- 40, - 50, - 60

Step-by-step explanation:

Note the common difference d between consecutive terms of the sequence.

- 20 - (- 10) = - 20 + 10 = - 10

- 30 - (- 20) = - 30 + 20 = - 10

Thus the difference d = - 10

To obtain a term in the sequence subtract 10 from the previous term

- 30 - 10 = - 40

- 40 - 10 = - 50

- 50 - 10 = - 60

The next 3 terms are - 40, - 50, - 60

The given question have mistake.

Question:

Which expression is not a polynomial?

(1) x – 1

(2) 4 + p

(3) [tex]5x^2-\sqrt x[/tex]

(4) [tex]8x-z^3[/tex]

Answer:

[tex]5x^2-\sqrt x[/tex] : Not a polynomial

Solution:

Definition of polynomial:

A polynomial can have constants, variables and exponents.

Constants = 2, 5

Variables = x, y, z

Exponents = [tex]x^2[/tex]

Not a polynomial:

Roots, fractions in power, negative powers and dividing by a variable are not polynomials.

Given expressions:

(1) x – 1 : Polynomial

(2) 4 + p : Polynomial

(3) [tex]5x^2-\sqrt x[/tex] : Not a polynomial

(4) [tex]8x-z^3[/tex] : Polynomial

Hence in the given expressions [tex]5x^2-\sqrt x[/tex] is not a polynomial.

Answer:

4 hours is what they use

Step-by-step explanation:

If they use 1/6 of their time each day

A day = 24 hours

1/6 times of that day will be

1/6*24= 4 hours