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3 years ago

If the given figure is rotated 270° counterclockwise around the origin, what are the

1 answer:

8 0

Flipping it counterclockwise means the Y-coordinate goes into the X-coordinate slot and becomes its opposite sign, the X-coordinate stays the same but now the Y- coordinate slot.

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For the straight line defined by the points (3,57) and (5,87), determine the slope ( m ) and y-intercept ( ???? ). Do not round

Sphinxa [80]

Answer: The slope of the line is 15 and y-intercept is 12.

Step-by-step explanation: We are given to find the slope and y-intercept of the straight line defined by the points (3, 57) and (5, 87).

We know that

the slope of a line passing through the points (3, 57) and (5, 87) is given by

$m=\dfrac{87-57}{5-3}=\dfrac{30}{2}=15.$

Since the straight line passes through the point (3, 57), so its equation will be

$y-57=m(x-3)\\\\\Rightarrow y-57=15(x-3)\\\\\Rightarrow y-57=15x-45\\\\\Rightarrow y=15x-45+57\\\\\Rightarrow y=15x+12.$

So, the required equation of the straight line is $y=15x+12.$

Thus, the slope of the line is 15 and y-intercept is 12.

4 0

3 years ago

A movie theater charges $4.50 for children and $8.00 for adults. On a certain day, 1200 people enter the theater and $8375 is co

Lady bird [3.3K]

Answer:

The number of adults who attended=850

The number of children who attended=350

Step-by-step explanation:

a). Determine first expression

Let the number of each group be as follows;

adults=a

children=c

total number of people=1200

This can be expressed as;

number of people=number of children+number of adults

replacing;

a+c=1200...equation 1

b). Determine the second expression

Let the total cost be expressed as shown;

total cost=(cost per child×number of children)+(cost per adult×number of adults)

where;

total cost=$8,375

cost per child=$4.5

number of children=c

cost per adult=$8

number of adults=a

replacing;

(8×a)+(4.5×c)=1,200

8 a+4.5 c=8,375...equation 2

c). Combine equation 1 and 2 and solve simultaneously

1(8 a+4.5 c=8,375)

4.5(a+c=1,200)=4.5 a+4.5 c=5,400

(8 a-4.5 a)+(4.5 c-4.5 c)=(8,375-5,400)=2,975

3.5 a=2,975

a=2,975/3.5

a=850

replacing the value for a in equation 1

850+c=1200

c=1200-850=350

The number of adults who attended=850

The number of children who attended=350

4 0

3 years ago

Following data, what would be the value of x?

kirill115 [55]

Answer:

The answer is C. 10

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

What can you conclude about 3/5 and 60/100 if you know 3/5 is equivalent to 6/10 and 6/10 is equivalent to 60/100

labwork [276]

First we check whether $\frac{3}{5}$ is equivalent to $\frac{6}{10}$

$\frac{3*2}{5*2}$ = $\frac{6}{10}$

Both top and bottom are multiplied by 2 to get $\frac{6}{10}$

So they are equivalent fractions.

Now we check whether $\frac{6}{10}$ is equivalent to $\frac{60}{100}$

$\frac{6*10}{10*10}$ = $\frac{60}{100}$

Both top and bottom are multiplied by 10 to get $\frac{60}{100}$

So they are equivalent fractions.

$\frac{3}{5}$ = $\frac{6}{10}$ = $\frac{60}{100}$

Hence we conclude that they are equivalent fractions.

5 0

4 years ago

Solve for x 14 x square+7x-6

irina [24]

Answer:

x=0.450765 or x=−0.950765

Step-by-step explanation:

14x² + 7x - 6

→ Find the product, sum and factors

Product = -6

Sum = 7

Factors = No factors

→ Since there are no factors utilise the quadratic formula

$\frac{-b+-\sqrt{b^{2}-4ac } }{2a}$

→ List the values of a, b and c

a = 14

b = 7

c= -6

→ Substitute into the formula

$\frac{-7+-\sqrt{7^{2}-4*14*-6} }{2*14}$

→ Simplify

x=0.450765 or x=−0.950765

8 0

4 years ago

Read 2 more answers