The ratio of the number of adults to the number of children at the resturant is 3:7. Identify the choices below that represent an equivalent ratio. Choices: A: 6:14 B: 8:12 C: 15:35 D: 21:9 E: 30:70

Answer:

3) x = 50, vertical angles.

4) x = 20, supplementary angles

5) x = 14, complimentary angles

Step-by-step explanation:

vertical angles.

vertical angles are equal.

so, you can make this equation:

67 = x + 17

subtract 17 from both sides of the equation

67 - 17 = x + 17 - 17

67 - 17 = x

50 = x

supplementary angles

supplementary angles add up to 180

so, you can make this equation:

7x + 40 = 180

subtract 40 from both sides of the equation

7x + 40 - 40 = 180 - 40

7x = 180 - 40

7x = 140

divide both sides by 7

7x/7 = 140/7

x = 140/7

x = 20

complimentary angles

complimentary angles add up to 90

so, you can make this equation:

4x + 34 = 90

subtract 34 from both sides of the equation

4x + 34 - 34 = 90 - 34

4x = 90 - 34

4x = 56

divide both sides by 4

4x/4 = 56/4

x = 56/4

x = 14

Answer: Your answer is 61.25cm hope this helps!

Answer:

103

Step-by-step explanation:

108+85+94+103+112+115+98+119+126+105+82+89=1236

1236/12=103

Answer:

103

Step-by-step explanation:

This is the answer because:

1)  The mean of a set of numbers is the sum divided by the number of terms:

108 + 85 + 94 + 103 + 112 + 115 + 98 + 119 + 126 + 105 + 82 + 89 = 1236

There are 12 numbers, so divide 1236 with 12:

1236 ÷ 12 = 103

Therefore, the answer is 103.

Hope this helps! :D

Answer:

you have to "convert" the one to be set up the same as 3/10:

you subtract fractions, by having a common denominator and then subtracting the numerators.

10/10 -3/10 = 7/10

Step-by-step explanation:

i hope this helped :)

Answer:

y > (x - 50) * 210

Step-by-step explanation:

Given :

Number of dead trees = 50

Number of oranges produced by each of the remaining trees > 210

Let total number of trees = x ; total number of oranges produced = y

Hence, number of oranges produced, y

y > number of remaining trees * number of oranges produced per tree

y > (x - 50) * 210

Answer:

JL = 8 m

KD = 8 m

Step-by-step explanation:

By 45° - 45° - 90° triangle theorem:

[tex]JK = \frac{1}{ \sqrt{2} } JD \\ \\JK = \frac{1}{ \sqrt{2} } \times 8 \sqrt{2} \\ \\ \red{JK = \boxed{8 }}\: m \\ \\ KD= \frac{1}{ \sqrt{2} } JD \\ \\KD = \frac{1}{ \sqrt{2} } \times 8 \sqrt{2} \\ \\ \purple{ KD = \boxed{8 } }\:m\\ \\[/tex]

The measure of Angle D is the same as Angle B which is 63 degrees.

An angle requires two straight line/ line segments/rays, such that they're connected on one of their endpoints. The point of their joint is called the vertex of that angle. Those two line segments forming it are called arms of that angle. One arm is fixed, and one arm rotates around that vertex to make angles of different measurements. The fixed arm is called the initial arm. The moving arm is called the terminal arm.

The angle is the degree of rotation that it will take for the moving side to go from the initial side to the position it is currently on.

We are given that m∠B = 63°

Since the lines BC and AD are parallel to each other, they form the quadrilateral ABCD and parallelogram.

Therefore, according to the parallelogram properties,

the measure of Angle D is the same as Angle B which is 63 degrees.

Learn more about angles here:

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Answer:

The slope is 1/2

Step-by-step explanation:

To get the slope, we select any two points on the line and apply the slope formula

The points are;

(5,4) and (9,6)

The formula for the slope is;

m = (y2-y1)/(x2-x1)

m = (6-4)/(9-5) = 2/4 = 1/2

Answer:

5545

Step-by-step explanation:

Answer:

Correct answer is 120

Answer:

6 -6 -4

Step-by-step explanation:

Step-by-step explanation:

It's a quadratic equation which simplifies to x²+2x-8

Now if you want to "solve" it then you must be a little more particular with your question because you can do many things with a quadratic equation, you can:

1. Factorise it

2. find the zeros

3. graph it

4. describe the nature of its roots,etc

but let me help you factorise it

x²+2x-8

x²+4x-2x-8

x(x+4)-2(x+4)

(x-2)(x+4)

Step-by-step explanation:

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

Answer:

x = 32

Step-by-step explanation:

∠BCA = ∠DBA (90 - ∠DBC)

∠A = ∠A

ΔABD similar to ΔACB

AC/AB = AB/AD

x / 8 = 8 / 2

x = 32

The length of AC if The right triangle ABC with altitude BD drawn to hypotenuse AC, AB = 8 and AD = 2, is 32.

Three straight lines coming together create a triangle. There are three sides and three corners on every triangle (angles). A triangle's vertex is the intersection of two of its sides. Any one of a triangle's three sides can serve as its base, however typically the bottom side is used.

Given:

The right triangle ABC with altitude BD drawn to hypotenuse AC,

AB = 8 and AD = 2,

Check if the triangle Δ ABD similar to Δ ACB

∠ BCA = ∠ DBA (90 - ∠ DBC)

∠ A = ∠ A

Thus, Δ ABD is similar to Δ ACB by AAS similarity,

Calculate the length of AC by using the similarity property,

AC/AB = AB/AD

x / 8 = 8 / 2

x = 32

Thus, the value of AC is 32.

To know more about Triangles:

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Answer:

A=16

Step-by-step explanation:

6=A/4+2

-2       -2

4=A/4

x4  x4

16=A

Question:

A charter bus travels 225 miles in  4.5 hours. Assume the  distance travelled is directly  proportional to the time spent.

Write a direct variation equation.

Answer:

[tex]y = 50x[/tex]

Step-by-step explanation:

Let:

y =  distance

x = time

So:

[tex]y = 225[/tex]  and [tex]x = 4.5[/tex]

Since, they are directly proportional: The following relationship exists

[tex]y = kx[/tex]

Where

k = constant of variation

Substitute values for y and x

[tex]225 = 4.5 * k[/tex]

Make x the subject

[tex]k = \frac{225}{4.5}[/tex]

[tex]k = 50[/tex]

Substitute 50 for k in [tex]y = kx[/tex]

[tex]y = 50x[/tex]

Answer:

Income tax is money the government takes from your paycheck when you have a job

The government automatically takes income tax out of your paycheck every month

Answer:

96.56 kilometers

Step-by-step explanation:

Find how many kilometers he will drive by multiplying 60 by 1.60934

60(1.60934)

= 96.56

So, John will drive 96.56 kilometers in one hour

Answer:

the answer is A.

Step-by-step explanation:

to get the you would use the distributive property to multiple the 4 by the two term in the parentheses.

Answer:

It would be A

Step-by-step explanation:

The Key Skill is: Distribution Property

1) We have the expression 4(6-2x)

2) We have to use distribution property to expand this.

The way distribution property works is that we need to multiply the 6 by the 4 on the outside, and also the -2x by the 4 on the outside.

4 x 6 = 24

4 x -2x = -8x

Therefore, the final expression is 24-8x.  

The only answer that matches this is A.

Hope you understood & have a nice DAY!! :D

Answer:

10

Step-by-step explanation:

[tex] \sqrt{100} = 10[/tex]

Hope it helps you in your learning process.

Answer:

conversion factor

Step-by-step explanation:

that is what I found on the internet

hope it helps :)

Answer:A

Step-by-step explanation:Product means to multiply and A is showing 3/4 is multiplying C.

Consider we need to find the first five terms of the given AP and the explicit formula.

Given:

[tex]a_n=a_{n-1}-3[/tex] when [tex]a_1=5[/tex]

To find:

First five terms of the given AP and the explicit formula.

Solution:

We have,

[tex]a_n=a_{n-1}-3[/tex]       ...(i)

[tex]a_1=5[/tex], it means first term is 5.

Putting n=2 in (i), we get

[tex]a_2=a_{2-1}-3[/tex]

[tex]a_2=a_{1}-3[/tex]

[tex]a_2=5-3[/tex]

[tex]a_2=2[/tex]

Second term is 2. So, common difference is

[tex]d=a_2-a_1[/tex]

[tex]d=2-5[/tex]

[tex]d=-3[/tex]

First terms is 5 and common difference is -3. So, the first five terms of the AP are 5, 2, -1, -4, -7.

The explicit formula of an AP is

[tex]a_n=a_1+(n-1)d[/tex]

[tex]a_n=5+(n-1)(-3)[/tex]

[tex]a_n=5-3n+3[/tex]

[tex]a_n=8-3n[/tex]

Therefore, the explicit formula of AP is [tex]a_n=8-3n[/tex].

Answer:

The equation of line in the form of Ax + By = C is: [tex]\mathbf{4x+y=-17}[/tex]

Step-by-step explanation:

We need to find the equation of line, having slope m = -4 and passes through point (-2,-9)

First we need to find slope and y-intercept of the line.

The slope is given i.e. m = -4

Now, we need to find the y-intercept

Using the point (-2,-9) and slope m = -4, y-intercept can be found using:

[tex]y=mx+b\\-9=-4(-2)+b\\-9=8+b\\b=-9-8\\b=-17[/tex]

Now, the equation of required line having slope m = -4 and y-intercept b = -17 is:

[tex]y=mx+b\\y=-4x-17[/tex]

Now writing in form of Ax + By = C

[tex]y=-4x-17\\4x+y=-17[/tex]

So, the equation of line in the form of Ax + By = C is: [tex]\mathbf{4x+y=-17}[/tex].

Answer:

65% of the beads were used to make the bracelet.

Step-by-step explanation:

40% of the beads were blue which means 60% of the beads were red. If all the blue beads were used that means 40% was used so you add the 25% of the red beads that were used which is why the answer is 65%.

Answer: The scale is 5cm/m  (5 cm in the drawing are equivalent to 1 meter on the actual pit)

Step-by-step explanation:

When we have an original measure M, and we redraw it with a new scale, where the new measure is m, the scale used is equal to:

scale = m/M.

In this case, we know that:

The pit is 3m, by 5m

and the drawing to scale is 15cm by 25cm

(15cm is the rescaled version of the 3m side, and 25cm is the rescaled version of the 5m side)

Using the equation above, we can find that the scale is:

Scale = 15cm/3m = 5cm/m

and, if we use the other side, we get:

Scale = 25cm/5m = 5cm/m

Both calculations give the same scale, as expected.

Then the scale is 5cm/m, which means that 5 centimeters in the drawing are equivalent to one meter in the real pit.