The graph below shows a translation of preimage triangle CDE to image triangle C’D’E’. What are the coordinates of image vertex D’?

3/5 - 6/9:

3/5 = 3•9 / 5•9 = 27/45

6/9 = 6•5 / 9•5 = 30/45

3/5 - 6/9 = 27/45 - 30/45

               = 27-30 / 45

               = –3/45

               = –1/15

The scale factor and the value of x for each figure is given as follows:

A) Scale factor of 1/3, x = 7 m.

B) Scale factor 0.4747, x = 4.5 in.

For Figure A, we have that the ratio between the areas is given as follows:

510/4590 = 1/9.

As the area is measured in square units, while the side lengths are measured in units, the scale factor is the square root of 1/9, hence it is given as follows:

1/3.

Then the value of x is obtained as follows:

x = 21 x 1/3

x = 7 m.

For Figure B, we have that the ratio between the areas is given as follows:

16/71 = 0.22535.

The scale factor is then the square root of 0.22535, which is given as follows:

0.4747.

Then the value of x is given as follows:

x = 9.5 x 0.4747

x = 4.5 in.

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Answer:

y=-2x+4

Step-by-step explanation:

Since it is parallel, it has to have the same slope m=-2. Just use the equation y-y=m(x-x) to solve the equation of the line.

\(y-y_0=m(x-x_0)\\y-(-2)=-2(x-3)\\y+2=-2x+6\\y=-2x+4\)

Certainly! The problem can be solved using the Pythagorean theorem,

which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, the ladder acts as the hypotenuse, and we need to find the length of the vertical side (height) it reaches up the wall.

The ladder forms the hypotenuse, and its length is given as 12 meters. The distance from the foot of the ladder to the base of the wall represents one side of the triangle, which is 4.5 meters.

By substituting the given values into the Pythagorean theorem equation: (12m)^2 = h^2 + (4.5m)^2, we can solve for the unknown height 'h'.

Squaring 12m gives us 144m^2, and squaring 4.5m yields 20.25m^2. By subtracting 20.25m^2 from both sides of the equation, we isolate 'h^2'.

We then take the square root of both sides to find 'h'. The square root of 123.75m^2 is approximately 11.12m.

Therefore, the ladder reaches a height of approximately 11.12 meters up the wall.

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Step-by-step explanation:

ig its box B if it was wrong sorry! but yes ig its B

The correct statement regarding the measure of variability used to represent the data is given as follows:

The IQR of 10 is the most accurate to use, as the data is skewed.

The interquartile range of a data-set is given by the difference of the third quartile by the first quartile of the data-set.

It is the measure of variability to be used when a data-set contains outliers, or is skewed, as is the case for this problem.

The charity received 18 donations, hence the quartiles are given as follows:

Hence the IQR is given as follows:

IQR = 22.5 - 12.5

IQR = 10.

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Answer:

Debit Insurance expense for $3,000

Credit Prepaid insurance for $3,000

Step-by-step explanation:

Before the recording entry, the monthly insurance expense has to be calculated first as follows:

Monthly insurance expense = Prepaid insurance / n ............. (1)

Where;

Prepaid insurance = Insurance policy amount = $36,000

n = number of months = 12

Substituting the values into equation (1), we have:

Monthly insurance expense = $36,000 / 12 = $3,000

Since the monthly insurance expense is $3,000, it implies that the insurance expense for March is $3,000.

the entry to record the monthly insurance expense in March will therefore look as follows:

Month      Account Title                     DR ($)                CR ($)              

March      Insurance expense          3,000

                    Prepaid insurance                                    3,000

               (To record monthly insurance expense for March)              

Answer:

Step-by-step explanation:

We observe the pattern:

It can be put as:

or

The nth term is going to be:

The sum of the 31 terms will be:

or

Use the formula for sum of the first n squares:

The sum N equals:

And the value of N/31 is:

Answer: The two lines intersect at (-4,3)

Step-by-step explanation:

So our first step would be to turn both of these into standard slope-intercept form.

1.)

4y + 3x = 0

4y = -3x

y = -3/4x

2.)

4y - x = 16

4y = x + 16

y = 1/4x + 4

Now that we have our 2 equations, y = -3/4x and y = 1/4x + 4 we can graph them to get an intersection at (-4,3)

Answer:

29

Step-by-step explanation:

The problem is 5x + 6 = 150

I subtract 6 from each sides except the one with the variable.

6 - 6 = 0 and 150 - 6 = 144.

Then I bring 5x down.

Then I divided 5x with 5 and 144 with 5.

I got 28.8 for x, which means the friends had 28.8 action figures each.

And I don't think it would be possible for them to have 28.8 action figures, so you round to a whole number which would give you the answer 29.

I think I that makes sense.

Answer: The team needs to win 15 more games to get 90% winning percentage.

Step-by-step explanation:

80%=4/5  divide 15 by 5 and you get 3, which is 1/5 of 15, so you must multiply it by 4 to get 80% of 15 which is 3*4=12

If you want 90%(or 9/10) of 30, you do the same thing, and you get 27.

27-12=15.

The team needs to win 15 more games to get 90% winning percentage

Need 1500 g of cornflakes

The cost

The cost

Option one is cheaper as £2.97 < £3.50

Answer:

a)  A: two 750g boxes.

b)  £2.97

Step-by-step explanation:

750g box:

500g box:

Cost of two 750g boxes:

\(\implies 1.98+\dfrac{1.98}{2}=1.98+0.99=2.97\)

Cost of three 500g boxes:

\(\implies 1.75+1.75+0=3.50\)

As 2.97 < 3.50, it is cheaper to buy two 750g boxes.

It costs £2.97 to buy 1500g of cornflakes using the cheapest way.

In conclusion  the value that correctly fills in the blank in the table is 0.69.

Why it is?

To find the relative frequency of boys, we need to use the information given in the frequency table. We know that the total number of boys is 120 - 37 = 83, since the total number of students is 120 and the number of girls is 37.

We can then calculate the relative frequency for boys by dividing the number of boys who prefer math or social studies (40 + 43 = 83) by the total number of students (120):

Relative frequency for boys = (40 + 43) / 120 ≈ 0.69

Rounding to the nearest hundredth, we get:

Relative frequency for boys ≈ 0.69

Therefore, the value that correctly fills in the blank in the table is 0.69.

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Answer:

(0,3) (1,4)

Step-by-step explanation:

The calculated length of the segment MN in the triangle is 20

From the question, we have the following parameters that can be used in our computation:

The triangle

The third angle in the triangle is calculated as

Third angle = 180 - 50 - 50

Evaluate

Third angle = 80

The length of the segment MN is then calculated as

MN/sin(50) = 20/sin(50)

This gives

MN = sin(50) * 20/sin(50)

Evaluate

MN = 20

Hence, the length of the segment MN in the triangle is 20

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The inverse of matrix A, if it exists, is:

A^(-1) = [7/43, 2/43; 10/43, 9/43]

To find the inverse of a matrix A, we need to determine if the matrix is invertible by calculating its determinant. If the determinant is non-zero, then the matrix has an inverse.

Given the matrix A = [9, -2; -10, 7], we can calculate its determinant as follows:

det(A) = (9 * 7) - (-2 * -10)

= 63 - 20

= 43

Since the determinant is non-zero (43 ≠ 0), we can proceed to find the inverse of matrix A.

The formula to calculate the inverse of a 2x2 matrix is:

A^(-1) = (1/det(A)) * [d, -b; -c, a]

Plugging in the values from matrix A and the determinant, we have:

A^(-1) = (1/43) * [7, 2; 10, 9]

Simplifying further, we get:

A^(-1) = [7/43, 2/43; 10/43, 9/43].

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Answer:

9x

Step-by-step explanation:

it the same just with numbers next to them

Answer:

A. this is a vector, so you need a bar on top (ie not D)

Step-by-step explanation:

Answer:

a=1/8

b=the same 1/8

Step-by-step explanation:

here you have to count the number of ticks between 0 and 1 and then count to where the variable is and then your fraction for both of these would be 2/16 and simplified that would be 1/8

hope this helps!

letter A - 1/8

letter B - 1 1/8

This is because there is 16 marks in between each number and both A and B are at the 2nd mark 2/16 = 1/8

letter B is 1 1/8 because it is in front of the one.

Answer:

4

Step-by-step explanation:

A mode is the number having the highest frequency, that is, the number which occurs the most times. (The number which occurs the most here is 4, there are two 4s. You only have one of the rest of the numbers.)

The total number of different ways in which the 10 swimmers can achieve 1st, 2nd, or 3rd place is 720 ways.

Given that:

There are one of ten people in a swimming race. Prizes are awarded to swimmers who finish in first, second, and third places only.

Let's assume that there is A to J swimmers counted as 10 in number.

Then A comes in first, or B comes in first, or ... or J comes in first. So, there are 10 possibilities that any swimmers can come in the first place.

For second place, it can't be the swimmers that arrived first, but it could be any of the remaining 9 swimmers.

For third place, it can't be the first or second swimmers but there are 8 others and one of them will be the third.

Using permutation we can find the total number of different ways in which the 10 swimmers can achieve 1st, 2nd, or 3rd place, because the order of places matters.

The permutation is considered an ordered combination. Objects are arranged from last to first in permutations. The general formula for this is:

P(n, r) = n! /(n-r)!

Therefore, the required number of ways is = 10 possible first swimmers x 9 possible 2nd swimmers x 8 possible third swimmers.

The required number of ways = 10 x 9 x 8 = 720 ways.

Hence, there are 720 ways swimmers can achieve 1st, 2nd, or 3rd place.

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Answer:

C

Step-by-step explanation:

x + y + 10 = 0 ( subtract x + 10 from both sides )

y = - x - 10 → (1)

x² + y - 2 = 0 → (2)

substitute y = - x - 10 into (2)

x² - x - 10 - 2 = 0

x² - x - 12 = 0 ← in standard form

(x - 4)(x + 3) = 0 ← in factored form

equate each factor to zero and solve for x

x + 3 = 0 ⇒ x = - 3

x - 4 = 0 ⇒ x = 4

Answer and Step-by-step explanation:

Prime numbers are numbered that can't be divided by whole numbers other than itself and 1.

7, 11, and 37 are prime numbers that add up to 55.

7 + 11 + 37 = 55

7 + 48 = 55

55 = 55

#teamtrees #PAW (Plant And Water)

Answer:

37+17+1

Step-by-step explanation:

I think

A prime number always has 2 factors:-)

1 and itself are its factors

I hope it helps

AS per the given confidence interval, the z score is 0.54

The term confidence interval refers a parameter will fall between a pair of values around the mean.

Here we have given that if the 90 percent confidence interval for u is from 34 to 50 then there is a 10 percent

And we need to find the z value.

While we looking into the given situation, we have identified the following values,

Confidence interval = 95%

Interval = 34 - 50

Mean = 10

Through the given interval we have identified the that sample size was calculated as,

=> 50 - 34

=> 16

Then the z score is

=> z = 10/√16

=> z = 10/4

=> z = 2.5

Then according to the confidence interval, the value from the z table is obtained as.

=> z = 1.96

Then the difference is

=> 2.5 - 1.96

=> 0.54

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The required equation for a line passing through point A and perpendicular to BC exists 2y + 5x = 31.

First, we must obtain the slope of the line perpendicular to BC

Given the coordinates B(7,5), and C(2,3)

Get the slope BC, exists

\($m_{BC} = \frac{3-5}{2-7}\)

= -2/-5 = 2/5

The slope of the line perpendicular to BC will be -5/2.

The slope of the required line in point-slope form exists expressed as;

\($y - y_0 = m(x - x_0)\)

m = -5/2

\((x_0, y_0) = (3, 8)\)

Substitute the values into the formula we get

y - 8 = (-5/2)(x - 3)

2(y - 8) = (-5)(x - 3)

2y - 16 = (-5x + 15)

2y + 5x = 15 + 16

2y + 5x = 31

Therefore the required equation for a line passing through point A and perpendicular to BC exists 2y + 5x = 31.

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Scores between 23 & 59 will give Paul a C for the semester (an average between 70 and 79).

The sum of the scores on the first three, hundred point tests

= 82 + 88 + 87 = 257.

The total score required in four 100-point tests to get an average score of 70 = 70X4= 280.

The total score required in four 100-point tests to get an average score of 79 = 79X4= 316.

Therefore, the score on the fourth test should be between (280-257) & (316-57) i.e, 23 & 59 to get an average score of 70 & 79.

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Answer:

Sarah has to invest $502,958.58 today.

Step-by-step explanation:

This is a simple interest problem.

The simple interest formula is given by:

\(E = P*I*t\)

In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.

After t years, the total amount of money is:

\(T = E + P\)

In this question:

\(t = 35, I = 0.07, T = 1700000\)

She has to invest P today.

\(T = E + P\)

\(1700000 = E + P\)

\(E = 1700000 - P\)

So

\(E = P*I*t\)

\(1700000 - P = P*0.07*34\)

\(3.38P = 1700000\)

\(P = \frac{1700000}{3.38}\)

\(P = 502958.58\)

Sarah has to invest $502,958.58 today.