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3 years ago

Triangle ABC with coordinates A (3,-2), B (5,5), and C (-4, 2) is reflected across

Mathematics

2 answers:

Helen [10]3 years ago

6 0

Coordinates of ∆ABC

A(3,-2)
B(5,5)
C(-4,2)

Now co-ordibates of ∆A'B'C'

$\\ \rm\longmapsto A'=(3,2)$

$\\ \rm\longmapsto B'=(5,-5)$

$\\ \rm\longmapsto C'=(-4,-2)$

son4ous [18]3 years ago

5 0

Step-by-step explanation:

the formula of coordinates (x, y) that reflected across the x-axis : (x, y) => (x, -y)

so,

A(3, -2) => A'(3, 2)

B(5, 5) => B'(5, -5)

C(-4, 2) => C'(-4, -2)

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15. Jim had 103 red and blue marbles. After giving of his blue marbles and 15 of his red marbles

sesenic [268]

This question above is incomplete

Complete Question

Jim had 103 red and blue marbles. After giving 2/5 of his blue marbles and 15 of his red marbles to Samantha, Jim had 3/7 as many red marbles as blue marbles. How many blue marbles did he have originally?

Answer:

70 Blue marbles

Step-by-step explanation:

Let red marbles = R

Blue marbles = B

Step 1

Jim had 103 red and blue marbles.

R + B = 103.......Equation 1

R = 103 - B

Step 2

After giving 2/5 of his blue marbles and 15 of his red marbles to Samantha, Jim had 3/7 as many red marbles as blue marbles

2/5 of B to Samantha

Jim has = B - 2/5B = 3/5B left

He also gave 15 red marbles to Samantha

= R - 15

The ratio of what Jim has left

= Red: Blue

= 3:7

= 3/7

Hence,

R - 15/(3/5)B = 3/7

Cross Multiply

7(R - 15) = 3(3/5B)

7R - 105 = 3(3B/5)

7R - 105 = 9B/5

Cross Multiply

5(7R - 105) = 9B

35R - 525 = 9B............ Equation 2

From Equation 1, we substitute 103 - B for R in Equation 2

35(103 - B) - 525 = 9B

3605 - 35B - 525 = 9B

Collect like terms

3605 - 525 = 9B + 35B

3080 = 44B

B = 3080/44

B = 70

Therefore, Jim originally had 70 Blue marbles.

4 0

3 years ago

Apply distributive property to produce an equivalent expression for 6(7 e + 3)

Orlov [11]

Answer:

42e+18

Step-by-step explanation:

6×7=42

6×3=18

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4 years ago

What equation can be written for 29 is 6 more then k? what is K?

ehidna [41]

Answer:

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Step-by-step explanation:

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3 years ago

he Wall Street Journal Corporate Perceptions Study 2011 surveyed readers and asked how each rated the Quality of Management and

sergejj [24]

Answer:

Following are the solution to the given question:

Step-by-step explanation:

$H_0:$ Management quality and corporate reputation are independent.

$H_1:$ Management quality and corporate reputation are not independent.

Test statistic:

$\to \chi^2 = \frac{\sum (O-E)^2}{E}$

$= 0.71429 + 0.0102 +2.8809+0.625+1.75 +0.3333 +0+3.2143+7.5\\\\= 17.02806$

The critical $\chi^2$ for $df = (r-1)(c-1) = (3-1)(3-1)= 4$ and $\alpha = 0.05$ is $\chi^2= 9.4877$

Test statistic:

$17.02806 > 9.4877$ therefore rejecting the null hypothesis $H_0$ .

p-value $= 0.001909$

Interpretation:

There is no internal governance quality as well as the reputation of the organization.

3 0

3 years ago

110 freshmen participated in sports or clubs or both. 55 are involved in sports and 68 are involved in clubs. How many students

Varvara68 [4.7K]

Answer: 42

Step-by-step explanation:

Let A represents the number of freshmen participated in sports and B represents the number of freshmen participated in clubs.

Then , we have given that

$n(A)=55\\\\n(B)=68\\\\n(A\cup B)=110$

Using formula

$n(A\cup B)=n(A)+n(B)-n(A\cap B)$

We have,

$110=55+68-n(A\cap B)\\\\\Rightarrow\ n(A\cap B)=123-110=13$

Now, the number of students are involved in just sports is given by :-

$n(A)-n(A\cap B)=55-13=42$

Hence, 42 students are involved in just sports.

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3 years ago