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2 years ago

Which of the following steps were applied to ABCD to obtain A’B’C’D’?

Mathematics

2 answers:

devlian [24]2 years ago

6 0

Answer:

c- shifted 3 units right and 4 units up

Step-by-step explanation:

In this problem, we have a quadrilateral named as ABCD. Recall that a quadrilateral is a two-dimensional shape having four sides. So, we need to identify what transformation has been performed to get A'B'C'D', which is the same quadrilateral shifted certain units right and up. So take one point, say, B, so how do we need to do to obtain point B'? well, we need to move that point 3 units right and 4 units up, but how can we know this? just count the number of squares you need to move from B to B' horizontally and vertically, which is in fact 3 units right and 4 units up.

Murrr4er [49]2 years ago

4 0

Answer: The correct option is

(c) shifted 3 units right and 4 units up

Step-by-step explanation: We are given to select the correct steps that were applied o ABCD to obtain A'B'C'D' as shown in the figure.

From the graph, we note that

the co-ordinates of the vertices of quadrilateral ABCD are A(2, 3), B(4, 8), C(6, 8) and D(8, 3).

And, the co-ordinates of the vertices of quadrilateral A'B'C'D' are A'(5, 7), B'(7, 12), C'(9, 12) and D'(11, 7).

So, the transformations from the vertices of ABCD to the vertices of A'B'C'D' are as follows :

A(2, 3) ⇒ A'(5, 7) = (2+3, 3+4),

B(4, 8) ⇒ B'(7, 12) = (4+3, 8+4),

C(6, 8) ⇒ C'(9, 12) = (6+3, 8+4),

D(8, 3) ⇒ D'(11, 7) = (8+3, 3+4).

Therefore, the required rule of translation from ABCD to A'B'C'D' is

(x, y) ⇒ (x+3, y+4). That is, 3 units right and 4 units up.

Thus, the required steps applied to ABCD to obtain A'B'C'D' are

Shifted 3 units right and 4 units up.

Option (c) is CORRECT.

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A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is

anzhelika [568]

You need to solve for one variable in equation 1 and substitute it in equation 2 to solve.

Equation 1: x+y=24
x= number of 3 pt questions
y= number of 5 pt questions
24= Total number of questions

Equation 2: 3x+5y=100
100= Total point value possible on test
3x= point value of 3 pt questions
5y= point value of 5 pt questions

x+y=24
Subtract y from both sides
x=24-y

Substitute in equation 2:
3x+5y=100
3(24-y) +5y=100
72-3y+5y=100
72+2y=100
Subtract 72 from both sides
2y=28
Divide both sides by 2
y=14

Substitute y=14 back in to solve for x:
3x+5y=100
3x+5(14)=100
3x+70=100
Subtract 70 from both sides
3x=30
Divide both sides by 3
x=10

So there are 10 three point questions
There are 14 five point questions.

Hope this helped! :)

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2 years ago

Read 2 more answers

Brock is training for a Crossfit competition. He began the training completing pull-ups and box jumps origanally, his training p

siniylev [52]

If the adjusted ratio was 2:7, then

2x is the number of pull-ups

and

7x is the number of box jumps.

You can state that since he completed 63 box jumps at the end of his training, then

7x=63,

x=9

and

2x=18.

The total number of exercises performed is 2x+9x=18+63=81.

As at start the ratio was 5:4, then

5y was the number of pull-ups

and

4y was the number of box jumps.

Therefore, 5y+4y=81,

9y=81,

y=9

and 5y=45, 4y=36.

Answer: Initially: 45 pull-ups and 36 box jumps. At the end: 18 pull-ups and 63 box jumps.

8 0

2 years ago

What is f(x) = 8x2 + 4x written in vertex form?

Alinara [238K]

Answer:

Vertex form: f(x)=8(x+\frac{1}{4}

Step-by-step explanation:

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2 years ago

Imogen sees a design for a garden in a magazine. She changes the scale because she wants a smaller garden. The figure below show

faust18 [17]

Answer:

Length A of the magazine garden is 28 feet is true.

Length B of the Magazine garden is 17.5 feet is true.

Length C of the Magazine garden is 35 feet is true.

Step-by-step explanation:

Please refer the attached figure.

Given:-

Magazine Scale is 1 inch = 3.5 feet.

Imogen's scale is 2 inches = 6 feet,

Therefore Imogen's scale is 1 inch = 3 feet.

In Triangle ABC,

side a = 8 inches, side b= 5 inches, side c= 10 inches.

To find:- The correct 3 options(actual size of sides of triangle ABC).

Solution:-

In triangle ABC,

Let,

AB=side a =8 inches

BC=side b =5 inches

AC=side c= 10 inches

Now, as per the given scale's of Magazine and Imogen's we can find the actual sizes.

Length A as per Magazine scale (1 inch = 3.5 feet) is,

$\therefore Length\ A=8\times 3.5$ -------------(as per scale)

$\therefore Length A=28\ feet$

and Length A as per Imogen's scale(1 inch =3 feet) is,

AB = side a

$\therefore Length\ A=8\times 3$ -------------(as per scale)

$\therefore Length A=24\ feet$

Therefore Length A of the magazine garden is 28 feet is true.

Now, Length B as per Magazine scale (1 inch = 3.5 feet) is,

BC = side b

$\therefore Length\ B=5\times 3.5$

$\therefore Length B=17.5\ feet$

Length B as per Imogen's scale (1 inch = 3 feet) is,

BC = side b

$\therefore Length\ B=5\times 3$

$\therefore Length B=15\ feet$

Therefore Length B of the Magazine garden is 17.5 feet is true.

Now, Length C as per Magazine scale (1 inch = 3.5 feet) is,

AC = side c

$\therefore Length\ C=10\times 3.5$

$\therefore Length C=35\ feet$

Length B as per Imogen's scale (1 inch = 3 feet) is,

AC = side c

$\therefore Length\ C=10\times 3$

$\therefore Length B=30\ feet$

Therefore Length C of the Magazine garden is 35 feet is true.

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2 years ago

Read 2 more answers

A car insurance company suspects that the younger the driver is, the more reckless a driver he/she is. They take a survey and gr

erastovalidia [21]

Answer:

The confidence interval for the difference in proportions is

$-0.028\leq p_1-p_2 \leq 0.096$

No. As the 95% CI include both negative and positive values, no proportion is significantly different from the other to conclude there is a difference between them.

Step-by-step explanation:

We have to construct a confidence interval for the difference of proportions.

The difference in the sample proportions is:

$p_1-p_2=x_1/n_1-x_2/n_2=(183/217)-(322/398)=0.843-0.809\\\\p_1-p_2=0.034$

The estimated standard error is:

$\sigma_{p_1-p_2}=\sqrt{\frac{p_1(1-p_1)}{n_1}+\frac{p_2(1-p_2)}{n_2} } \\\\\sigma_{p_1-p_2}=\sqrt{\frac{0.843*0.157}{217}+\frac{0.809*0.191}{398} } \\\\\sigma_{p_1-p_2}=\sqrt{0.000609912+0.000388239}=\sqrt{0.000998151} \\\\ \sigma_{p_1-p_2}=0.0316$

The z-value for a 95% confidence interval is z=1.96.

Then, the lower and upper bounds are:

$LL=(p_1-p_2)-z*\sigma_p=0.034-1.96*0.0316=0.034-0.062=-0.028\\\\\\UL=(p_1-p_2)+z*\sigma_p=0.034+1.96*0.0316=0.034+0.062=0.096$

The confidence interval for the difference in proportions is

$-0.028\leq p_1-p_2 \leq 0.096$

<em>Can it be concluded that there is a difference in the proportion of drivers who wear a seat belt at all times based on age group?</em>

No. It can not be concluded that there is a difference in the proportion of drivers who wear a seat belt at all times based on age group, as the confidence interval include both positive and negative values.

This means that we are not confident that the actual difference of proportions is positive or negative. No proportion is significantly different from the other to conclude there is a difference.

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2 years ago