What is the scale factor of the dilation?

The lengths of the rectangle for which the area will be less than 125 cm² is 5 < m < 25

In this question, we have been given the width of a rectangle is fixed at 5 cm.

We need to determine​ (in terms of an​ inequality) those lengths for which the area will be less than 125 cm²

Let 'm' be the length of the rectangle.

The area of the rectangle is:

A = length × width

The area of the rectangle should be less than 125 cm²

5 × m < 125

Divide both the sides of the inequality by 5

m < 25

This means, the length of rectangle should be less than 25 cm

But length is always greater than the width of the rectangle.

So, we get an inequality 5 < m < 25

Therefore, the lengths of the rectangle for which the area will be less than 125 cm² is 5 < m < 25

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Well, here is the answer . . .

£12 = 13.73€

Answer:

360ft

Step-by-step explanation:

Here,

Given,

→Area=57600ft²

→Width=160ft

Now,

→Length=Area/Width
→Length=57600ft²/160ft=360ft

The values of m that can fit into the equation m² = 16 will be m = ±4.

It should be noted that a equation is simply used to illustrate the relationship between the variables that are given. From the information, it should be noted that the equation is illustrated as m² = 16.

Since m² = 16, we need to find the square root. This will be illustrated as:

m² = 16

m = ✓16

m = 4

It should be noted that (-4) × (-4) = 16 and 4 × 4 = 16.

Therefore, the correct option is m = ±4

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Answer:

8

Step-by-step explanation:

To find the time the rocket is in the air, we can find the time when the height is 0 (remember this time is not 0).

[tex]-16t^2+128t=0 \\ \\ t^2-8t=0 \\ \\ t(t-8)=0 \\ \\ t=0,8 \\ \\ t \neq 0 \implies t=8[/tex]

C. add 6 from the previous term

To get the next term in the sequence, you subtract 6 from the previous term.

greater than 1. If its less than, it will be decreasing.

olution:

Recall the Fundamental Counting principle; if there are m ways to make a selection and n ways to make a second selection, then there are m x n number of ways in which two selection can be made.

ut of the provided digits, if the number ends with 3

ase 1: Tnumber of one digit numbers.

ut of the digits provided, only one way to fil;l the box that is with one.

Thus, there is one digit odd integer here.

Case 2: The number of two digits.

Out of the digits provided, only one way to fill the last box is with digit 3, and any one of the 4 digits can filled in it as 0 cannot filled in either of the box.

Thus, number of ways are;

Aase 3: The number of three digit numbers.

ut of the digits provided, only one way to flll the last box is with digit 3, and any one of the 5 digits can be filled in second box, and thus any one of the 4 digits can be filled in first box as 0 cannot be fixed in the box.

Thus, number of ways are;

Lastly;

: The numbver of four digit numbers.

he number of ways are;

Thus, the total number of ways to select are;

INAL ANSWER: 125

Total ticket = 675

Child tickrt sold = 243

percentage of child tickets sold

The equation for each line will be y=-x+2.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that,

The coordinate of the points are (2,0) and (0,2)

The slope of the line is,

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1} \\\\ m = \frac{2-0}{0-2} \\\\ m = -1[/tex]

The standard equation of the line is,

y-y₁ = m(x-x₁)

y-0=-1(x-2)

y=-x+2

Thus, the equation for each line will be y=-x+2.

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The expression equivalent to [-40 + (-20) + (-60)] is [−20 + (−40) + (−60)]

As per the question statement, we are provided with a linear expression of [-40 + (-20) + (-60)], and four options.

We are supposed to determine the one expression from the given options, that is equivalent to the question mentioned expression of [-40 + (-20) + (-60)].

To solve this question, we will first calculate the value of the question mentioned equation, and then, calculate and compare the values of individual expressions provided in the options, to obtain our desired answer.

Therefore, [-40 + (-20) + (-60)] = [-40 - 20 -60]

or, [-40 + (-20) + (-60)] = -( 40 + 20 + 60)

or, [-40 + (-20) + (-60)] = -120.

Now, coming to the first option, expression [−40 − (20 − 60)] equates to

[-40 - (-40)] = (-40 + 40) = (40 - 40) = 0,

And [0 ≠ (-120),

Hence, [−40 − (20 − 60)] is not the equivalent expression to

[-40 + (-20) + (-60)].

Now, coming to the second option, expression [-(40 − 20) + (-60)] equates to [-(20) + (-60)] = (-20 - 60) = -(20 + 60) = (-80),

But again, [(-80) ≠ (-120)],

Hence, [-(40 − 20) + (-60)]  is not the equivalent expression to

[-40 + (-20) + (-60)].

Coming to the third option, expression [40 + 20 + 60] equates to (120)

But again, [120 ≠ (-120)],

Hence, [40 + 20 + 60] is not the equivalent expression to

[-40 + (-20) + (-60)].

Finally, Coming to the last option, expression [−20 + (−40) + (−60)] equates to (-20 - 40 - 60) = -(20 + 40 + 60) = (-120).

And [(-120) = (-120)],

Hence, [−20 + (−40) + (−60)]  is the required equivalent expression to

[-40 + (-20) + (-60)].

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Answer:

−20+(−40)+(−60)

Step-by-step explanation:

they add up to the same thing and the order doesn't matter I think.

We are given the quadratic function c(p) = p^2 - 28p + 250 and we need to rewrite this in such a way that the minimum value is easy to find.

Remember that the vertex

where (h, k) is the vertex or the minimum point.

We use completing the squares method to do this. We divide the second term, -28p, by 2p, then square it.

We add 196 to p^2 - 28p to make it equal to (p - 14)^2, but since it will change the value of the equation, we need to subtract the same value from 250 so that the net effect is zero.

The equation is c(p) = (p - 14)^2 + 54.

Answer:

Step-by-step explanation:

=−10.44−4.2−(−6.85)

=−14.64−(−6.85)

=−7.79

Answer:

-7.79

Step-by-step explanation:

Given problem,

→ -16.26 - (-5.82) - (4.20) - (-6.85)

Let's simplify the problem,

→ -16.26 - (-5.82) - (4.20) - (-6.85)

→ -16.26 + 5.82 - 4.20 + 6.85

→ -10.44 + 2.65 = -7.79

Hence, the answer is -7.79.

The most appropriate choice for combination will be given by-

Models can wear 112 different types of outfit.

What is combination?

Combination determines the number of ways of selecting some number of particular items from a group of given item, here the order of selection do not matter.

If there are n objects and from there, r objects are chosen, number of ways will be given by

                                  [tex]n \choose r[/tex] = [tex]\frac{n!}{(n - r)! \times r!}[/tex]

Here,

Number of tops = 7

Number of pants = 2

Number of jackets = 8

From 7 tops the designer can choose 1 top in [tex]7 \choose 1[/tex] ways

                                                                        = [tex]\frac{7!}{(7-1)!\times 1 !}[/tex]

                                                                        = [tex]\frac{7!}{6!}[/tex]

                                                                        = [tex]7[/tex]

From 2 pants the designer can choose 1 pant in [tex]2 \choose 1[/tex] ways

                                                                        = [tex]\frac{2!}{(2-1)!\times 1 !}[/tex]

                                                                        = [tex]\frac{2!}{1!}[/tex]

                                                                        = [tex]2[/tex]

From 8 jackets the designer can choose 1 jacket in [tex]8 \choose 1[/tex] ways

                                                                        = [tex]\frac{8!}{(8-1)!\times 1 !}[/tex]

                                                                        = [tex]\frac{8!}{7!}[/tex]

                                                                        = [tex]8[/tex]

Total number of different outfits models can wear = [tex]7 \times 2 \times 8[/tex]

                                                                             = 112

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Yes, there is enough information to prove m||n.

By using the Vertical Angles Theorem, Corresponding Angles Theorem, and Alternate Exterior Angles Theorem we can prove that line m is parallel to line n.

In the given figure,

Let the given angles formed by transversal r, adjacent to line m be angle 1, and to line n be angle 2.

Now, the vertically opposite angle to angle 1 will be equal to it as they both are congruent.

The vertically opposite angle equal to angle 1 would be corresponding to angle 2 and corresponding angles formed by a transversal are equal and congruent.

Moreover, angle 1 and angle 2 are alternate exterior angles and by Alternate Exterior Angles Theorem, they are congruent.

Hence, it is proved by the Vertical Angles Theorem, Corresponding Angles Theorem, and Alternate Exterior Angles Theorem that line m is parallel to line n (m||n).

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Answer:

5

Step-by-step explanation:

Let n be the unknown number.

The quotient is the result obtained by dividing one number by another.

Therefore, the quotient of a number and 8 is ⁿ/₈.

If the quotient of a number and 8 is added to 1/4 the result is 7/8:

[tex]\implies \dfrac{n}{8}+\dfrac{1}{4}=\dfrac{7}{8}[/tex]

To solve, make the denominators of all the fractions the same:

[tex]\implies \dfrac{n}{8}+\dfrac{1 \cdot 2}{4 \cdot 2}=\dfrac{7}{8}[/tex]

[tex]\implies \dfrac{n}{8}+\dfrac{2}{8}=\dfrac{7}{8}[/tex]

[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}+\dfrac{b}{c}=\dfrac{a+b}{c}:[/tex]

[tex]\implies \dfrac{n+2}{8}=\dfrac{7}{8}[/tex]

Multiply both sides by 8:

[tex]\implies \dfrac{8(n+2)}{8}=\dfrac{7 \cdot 8}{8}[/tex]

[tex]\implies n+2=7[/tex]

Subtract 2 from both sides:

[tex]\implies n+2-2=7-2[/tex]

[tex]\implies n=5[/tex]

Therefore, the number is 5.

Explanation:

The question involves dividing radicals

To resolve the question, we will follow the steps below

Step 1: Write the expression

Step 2: simplify the expression in parts and apply the laws

Thus

For the second part

simplifying further

Hence, we have

Finally, we will combine the simplified terms, so that we will have

Hence, we will have

By canceling out the common parts, we will have the answer to be

Answer:

Step-by-step explanation:

Multiply both sides by 14 to find the missing value:

The most appropriate choice for speed will be given by-

Speed of plane in still air = 610 miles/hour

Speed of wind = 20 miles/hour

What is speed?

Distance travelled by a body in unit time is called speed.

Let the speed of plane in still air be x miles/hour

Speed of wind be y miles/hour

A plane traveled 3465 miles with the wind in 5.5 hours

So,

x + y = [tex]\frac{3465}{5.5}[/tex]

x + y = 630.......(1)

The plane travelled 3245 miles against the wind in the same amount of time

so,

x - y = [tex]\frac{3245}{5.5}[/tex]

x - y = 590.......(2)

Adding (1) and (2),

2x = 1220

x = [tex]\frac{1220}{2}[/tex]

x = 610 miles/hour

Putting the value of x in (1),

610 + y = 630

y = 630 - 610

y = 20 miles/hour

Speed of plane in still air = 610 miles/hour

Speed of wind = 20 miles/hour

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Answer:

Side = 10 units

Step-by-step explanation:

Original square area = s x s =s^2    

       now change the sides  and this equals 6s^2

3s  *  ( s+10)  = 6 s^2

                         3s^2 -30s = 0

                              s ( 3s-30) = 0      so s = 0   or  10

(3x+5)-([tex]x^{2} - 3[/tex])=9

[tex]x^{2}[/tex]-3x-8=-9

[tex]x^{2}[/tex]-3x=-1

[tex]x^{2}[/tex]-3x+1=0

Considering the z-test formula, it is found that:

a) Increasing the difference between the sample mean and the original population mean increases the test statistic.

b) Increasing the population standard deviation decreases the test statistic.

c) Increasing the sample size increases the test statistic.

Considering a z-test, the formula for the test statistic is given by the following rule:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which the parameters are defined as follows:

In item a, increasing the difference between the sample mean and the original population mean is increasing the numerator [tex]\overline{x} - \mu[/tex], meaning that the test statistic z will be increased.

In item b, increasing the population standard deviation [tex]\sigma[/tex] means that the denominator of the formula will be increasing, hence the test statistic will be decreased.

In item c, increasing the sample size n means that the denominator will be decreased, as the denominator is a fraction which is inverse proportional to the sample size, hence the test statistic z will be increased.

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He will cover total 247.5  kilometers on day 30 of his programe .

When there are identical differences between every two next words, the series is known as an arithmetic progression (AP). There is a chance to find a formula for the nth term of the AP using this kind of development. The series 2, 6, 10, 14, etc., for instance, is an example of an arithmetic progression (AP) because it follows a pattern in which each number is acquired by adding 4 to the preceding word. Nth term in this series equals 4n-2.

Given that :Lerato begins a new cycling programme with 2 km on the first day. Each day, he will increase his cycling by 500 m.

The formula to find Sum of an arithmetic progression is

S = [tex]\frac{n}{2}[2a+(n-1)d][/tex]

here , a = 2km

n = 30

d = 0.5km

S =[tex]\frac{30}{2}[2(2)+(30-1)0.5][/tex]

S = 247.5 km

He will cover total 247.5  kilometers  on day 30 of his programe

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The percentage of these cars with a fuel efficiency less than 24 mpg is 50 %.

Percentage, a relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity.

Given data:

44, 19, 51, 12, 34, 21, 15, 24

fuel efficiency less than 24 mpg is 19, 12, 21, 15

So, the percentage is

=4 / 8 x 100

= 1/2 x 100

= 50%

Hence, the percentage of these cars with a fuel efficiency less than 24 mpg is 50 %.

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Answer:

B. If I don't eat pizza after midnight, then I won't have a stomach ache.

Given

Answer: 17 million

Step-by-step explanation:

      We will set up a proportion to solve. We also will divide 26% by 100 to get a decimal, 0.26. We know that 26% of college students was 4.4 million, but we want to find 100%.

     [tex]\displaystyle \frac{0.26}{4.4\text{ million}} =\frac{1}{x\text{ million}}[/tex]

      Now, we will cross-multiply.

0.26 * x = 1 * 4.4

0.26x  = 4.4

      Lastly, we will divide both sides of the equation by 0.26. Then, we will round to the nearest million.

x = 16.923

x ≈ 17 million

From the graph, we can determine that the function f(x) is quadratic. The function f(x) is defined as:

The graph of (a) 1/2 f(x):

This implies that f(x) is compressed vertically by a factor of 1/2.

Using the points:

(-4, 8) , (-2, 2), (0,0), (2,2), (4, 8)

The graph of the function using a graphing calculator is shown below:

The graph of (b) 2 f(x)

This implies that the original function was stretched vertically by a factor of 2

Using the points:

(-4, 32), (-2, 8), (0,0), (2,8), (4,32)

The graph using a graphing calculator is shown below:

The domain:

This is a set of allowable x-values

Using interval notation:

The range:

This is a set of allowable y-values:

Using interval notation: