How can the statement be written as a conditional statement in if-then form? Lines on a coordinate plane are perpendicular if they have opposite reciprocal slopes.
A) If lines on a coordinate plane have opposite reciprocal slopes, then they are perpendicular.
B) If lines are on a coordinate plane, then they are perpendicular.
C) If lines are on a coordinate plane, then they have opposite reciprocal slopes.
D) If lines have opposite reciprocal slopes and are perpendicular, then they are on a coordinate plane.

Answer:

100 boys at the concert

Step-by-step explanation:

At a country concert, the ratio of the number of boys to girls is 2:7

Let 'b' be the number of boys in the concert

there are 250 more girls than boys

so b+250 are the number of girls in the concert

the ratio of boys to girls is b: b+250

Now make a proportion using the ratio

[tex]\frac{2}{7} =\frac{b}{b+250}[/tex]

Now solve for b . cross multiply the fraction

[tex](b+250) \cdot 2= 7 \cdot b[/tex]

[tex]2b+500= 7b[/tex]

Subtract 2b from both sides

[tex]5b= 500[/tex]

Divide both sides by 5

b=100

So there are 100 boys at the concert

Answer:

There are 1000 millimeters in a meter.

Starting from lower scale that is, centimeter, decimeter and then meter

1 cm = 10 mm

1 dm = 10 cm

And 1 meter = 10 dm

So, when you go up to mm from meter, we will do [tex]10^{3}[/tex] to get the relation between meter and mm.

Hence, 1 meter = [tex]10\times10\times10=1000[/tex] millimeters.

Christian's home is 10 miles away from the airport. He paid for one mile at the initial fare and 60 sets of 1/6 mile at the per-set rate, totaling 10 miles including the first mile.

The taxi fare Christian paid was $12.50, including a $1.60 tip. The initial charge by the cab company is $1.90 for the first mile. Therefore, without the tip, the fare for the distance traveled is $12.50 - $1.60 = $10.90. The first mile costs $1.90, so the remaining $9.00 covers the additional miles. As the company charges $0.15 for each additional 1/6 of a mile, we need to calculate how many sets of 1/6 mile are covered by $9.00.

To find out how many 1/6 miles can be covered by $9.00, we divide $9.00 by $0.15, which gives us 60. This means Christian traveled 60 sets of 1/6 mile beyond the first mile. Therefore, the total distance is the first mile plus 60 times 1/6 mile, which equals 10 miles in total.

So, Christian's home is 10 miles away from the airport.

The answer would be B!

The required time that spent on the Act II in the rehearsal is 1 3/4 hours.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
The rehearsal for Acts I and II of the school play lasted 5 1⁄2 hours.
3 3⁄4 hours were spent rehearsing Act I,
let the time spent on the Act II be x,
According to the question,
x  = 5 1/2 - 3 3/4
x = 5 - 3 + 1/2 - 3/4
x = 2 -1/4
x = 1 3/4

Thus, the required time that spent on the Act II in the rehearsal is 1 3/4 hours.

Learn more about models here:
https://brainly.com/question/22591166
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Answer:

[tex]h=8\frac{1}{2}\text{ inch}[/tex]

Step-by-step explanation:

Let h represent height of prism.

We have been given that Tana fills the prism with base lengths [tex]3\frac{1}{4}[/tex] inch and [tex]4[/tex] inch with a [tex]110\frac{1}{2}\text{ inch}^3[/tex].

We know that volume of prism is area of base times height, so we can set an equation as:

[tex]\text{Volume of prism}=\text{Base length}\times\text{Base width}\times \text{Height of prism}[/tex]

[tex]110\frac{1}{2}\text{ inch}^3=3\frac{1}{4}\text{ inch}\times 4\text{ inch}\times h[/tex]

[tex]\frac{221}{2}\text{ inch}^3=\frac{13}{4}\text{ inch}\times 4\text{ inch}\times h[/tex]

[tex]\frac{221}{2}\text{ inch}^3=13\text{ inch}^2\times h[/tex]

[tex]\frac{221}{2*13\text{ inch}^2}\text{ inch}^3=\frac{13\text{ inch}^2\times h}{13\text{ inch}^2}[/tex]

[tex]\frac{221}{26}\text{ inch}=h[/tex]

[tex]8\frac{13}{26}\text{ inch}=h[/tex]

[tex]8\frac{1}{2}\text{ inch}=h[/tex]

Therefore, the height of the prism is [tex]8\frac{1}{2}\text{ inch}[/tex].

Answer:

[tex]x=\frac{w}{2h-11}[/tex]

Step-by-step explanation:

Given equation,

w = 2hx - 11x,

⇒ 2hx - 11x = w

The steps for solving this equation for x are as follows,

Step 1 : By the converse of distributive property,

x(2h-11) = w

Step 2 : Isolate x in the left side of the equation by dividing both sides by 2h - 11 ( Division property of equality )

[tex]x=\frac{w}{2h-11}[/tex]

Answer:

The correct statement is:

It is not symmetric and has a peak at 1.

Step-by-step explanation:

We may make a dot plot based on the given information.

The dot plot is attached to the answer.

We may clearly observe that the dot plot is not symmetric since, there is no such point such that the plot to its left and right are equal.

Also,the frequency corresponding to '1' is highest (i.e. there are 4 dots above 1)

Hence, the peak of the dot plot is at '1'.

Answer: x = 7

Step-by-step explanation: To solve for x in this equation, we need to get x by itself on the left sides of the equation. Since x is being multiplied by 6, to get x by itself, we need to divide by 6 on the left side of the equation.

If we divide by 6 on the left side,

we must also divide by 6 on the right side.

On the left side, the 6's cancel and we have x.

On the right, 42 divided by 6 is 7 so x  = 7.

Heather can type the fastest. Comparing the two rates, we can see that Heather's rate of 68 words per minute is higher than Carrie's rate of 65.5833 words per minute.

To determine who can type the fastest, we need to calculate the typing rate in words per minute for both Carrie and Heather.

First, let's calculate Carrie's typing rate:

Carrie can type 787 words in 12 minutes. To find out how many words she can type per minute, we divide the number of words by the number of minutes.

[tex]\[ \text{Carrie's rate} = \frac{787 \text{ words}}{12 \text{ minutes}} \] \[ \text{Carrie's rate} = 65.5833 \text{ words per minute} \][/tex]

Next, let's calculate Heather's typing rate:

Heather can type 1020 words in 15 minutes. Similarly, we divide the number of words by the number of minutes to find her rate.

[tex]\[ \text{Heather's rate} = \frac{1020 \text{ words}}{15 \text{ minutes}} \] \[ \text{Heather's rate} = 68 \text{ words per minute} \][/tex]

Therefore, Heather can type the fastest.

Answer:

5+4p ≥ 32

No

Step-by-step explanation:

I promise this is the answer