This question has two parts. First, answer Part A. Then, answer Part B.
Part A
USE EFFICIENT METHODS Determine whether Δ D E F P ≅ ΔP Q R.
D(-7,-3), E(-4,-1), F(-2,-5), P(2,-2), Q(5,-4), R(0,-5)

Find the side lengths of each triangle.

A) D E=√13, P Q=√13, E F=2 √5, Q R=√13, D F=√29, P R=√13
B) D E=√13, P Q=√13, E F=√5, Q R=√26, D F=√29, P R=√13
C) D E=√13, P Q=√13}, E F=2 √5, Q R=√26, D F=2 √29, P R=√13
D) D E=√13}, P Q=√13, E F=2 √5, Q R=√26, D F=√29, P R=√13

Answer:

Step-by-step explanation:

[tex]\tt 30-19+29+30-29-10[/tex]

[tex]\tt 11+29+30-29-10[/tex]

[tex]\tt 40+30-29-10[/tex]

[tex]\tt 70-29-10[/tex]

[tex]\tt 41-10[/tex]

[tex]\tt 31[/tex]

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The lakefront company should make the investment as in 5 years they'll have a profit of 10000.

We know simple interest (SI) is given by SI = (p×r×t)/100, where

p = principle, r = rate in percentage, and t = time in years.

Given, the lakefront company is considering investing in a new dock that will cost 560,000.

So, a Capital cost of 10% is (560000/10) = 56000

The company's borrowing rate is 8%.

∴ SI = (560000×8×5)/100.

SI = 5600×8×5.

SI = 224000.

So, The total cost is (560000 + 56000 + 224000) = 840000.

After 5 years they can sell it for 300000.

And has a cash flow of 110000, so in 5 years it is 550000.

So, total earnings is (300000 + 550000) = 850000.

Total profit is (850000 - 840000) = 10000 so it is profitable.

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The correct option is All real values of a.

What is the real number?

The positive and negative integers, as well as the fractions created from them (also known as rational numbers), as well as the irrational numbers, are all real numbers.

We have,

3x² + 2xy = 4    ...................(1)

x + y = a             ...................(2)

By converting the second equation equals to y:

y = a - x             .....................(3)

By substituting the (3)rd equation into (1), we get

3x² + 2xy = 4

3x² + 2x(a - x) = 4

3x² + 2ax - 2x² = 4

x² + 2ax = 4

x² + 2ax - 4 = 0

Discriminant  = 4a² + 16 >=  0

2 distinct solutions & is ok for all a.

hence, the correct option is All real values of a.

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Answer:

24 inches

Step-by-step explanation:

To find the longest possible length of the shorter pieces that Terri can saw, you need to find the greatest common factor (GCF) of the three original lengths: 30 inches, 48 inches, and 72 inches.

The GCF of 30, 48, and 72 can be found by finding the prime factorization of each number and taking the lowest exponent for each prime factor.

30 = 2 * 3 * 5

48 = 2^4 * 3

72 = 2^3 * 3^2

The GCF is 2^3 * 3 * 5, or 24 inches. Therefore, the longest possible length of the shorter pieces that Terri can saw is 24 inches.

Hello,

I hope you and your family are doing well!

To find the GCF is to use the Euclidean algorithm, which involves repeatedly dividing the larger of the two numbers by the smaller one until the remainder is 0. This can be a quicker method for finding the GCF of larger numbers.

For example:

72 / 30 = 2 with a remainder of 12

30 / 12 = 2 with a remainder of 6

12 / 6 = 2 with a remainder of 0

The last non-zero remainder is 6, so the GCF is 6.

Regardless of the method used, the GCF of 30, 48, and 72 is 6, so the longest possible length of the shorter pieces that Terri can saw is 6 inches.

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Answer:

55

Step-by-step explanation:

Because you would minus 180-125 to get angle 1 and they said that angle 2 is parallel so they would be the same anwser so the answer is 55.

Answer:

The last option is the correct answer.

Step-by-step explanation:

Eddie and Brad together shovel the snow in 1 hour 26 minutes.

Two or more expressions with an Equal sign is called as Equation.

Given that it takes Eddie 2 hours to shovel the snow from a driveway and sidewalk.

Brad can shovel the snow from the same driveway and sidewalk in 5 hours.

We now find how long would it take them working together to shovel the snow.

Eddie does 1/2 in 1 hour or x/2 in x hours

Brad does 1/5 in 1 hour or x/5 in x hours

the sum is 1 full job

(x/2)+(x/5)=1

multiply both sides by 10

7x=10

x=(10/7) hours or 600/7 minutes =86 minutes

As we know 1 hour has 60 minutes.

We can write 86 minutes as 1 hour and 26 minutes.

Hence, 1 hour 26 minutes is the time taken by Eddie and Brad to shovel the snow.

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Answer:

5 weeks

Step-by-step explanation:

20 inches  /  ( 4 inches/week ) = 5 weeks

The absolute value function that is represented in the graph is f(x) = |x + 1.5| So the correct option is D.

The general absolute value function is:f(x) = |x|This absolute value function has a vertex at the point (0, 0). We know that the graphed function has a vertex at the point (-1.5, 0).

So basically we had a horizontal translation of -1.5 units or 1.5 units to the left. That is written as: g(x) = f(x + 1.5)

Replacing the absolute value function we get:g(x) = |x + 1.5|

Then the correct option is D.

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The coordinates of the other vertices of the triangle are (2a, 0), (2a, b), and (a, b).

What are the coordinates of the vertices of the triangle?

The coordinates of the vertices of a triangle are (x1,y1), (x2,y2), and (x3,y3). The line joining the first two is divided in the ratio l:k and the line joining this point of division to the opposite angular point is then divided in the ratio m:k+l.

To find the coordinates of the other vertices of the triangle, you can use the fact that the midpoint of a line segment is located at the average of the coordinates of the endpoints of the segment.

If the midpoint of one side of the triangle is located at (a, 0), then the coordinates of the two endpoints of this side must be (a, 0) and (2a, 0). The coordinates of one of the vertices is (2a, 0), and since this vertex is not the one located at the origin, the coordinates of the other vertex must be the origin, or (0, 0).

If the midpoint of another side of the triangle is located at (2a, b), then the coordinates of the two endpoints of this side must be (2a, b) and (2a, 0). One of the endpoints is (2a, 0), which we already know is a vertex of the triangle. The other endpoint, (2a, b), is also a vertex of the triangle.

Finally, if the midpoint of the third side of the triangle is located at (a, b), then the coordinates of the two endpoints of this side must be (a, b) and (0, 0). One of the endpoints is (0, 0), which we already know is a vertex of the triangle. The other endpoint, (a, b), is also a vertex of the triangle.

Hence, the coordinates of the other vertices of the triangle are (2a, 0), (2a, b), and (a, b).

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The required length of the longest side will be 28/5 cm in the triangle.

The perimeter of a triangle is defined as the addition of the lengths of the triangle's three sides.

We have been given that the three sides of a triangle are in the ratio of 3:5:7

Let's assume the sides are 3x, 5x, 7x

Since the perimeter of the triangle is 12 cm.

So, 3x+5x+7x = 12

Apply the addition operation,

15x = 12

x = 12/15

Reduce the above fraction to the simplest form

x = 4/5

So, longest side = 7x = 28/5 cm

Thus, the required length of the longest side will be 28/5 cm in the triangle.

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Answer:

(a) Equation of parallel line is y = x + 4

(b) Equation of perpendicular line is y = - x + 8

Step-by-step explanation:

Given line is

x - y = 4

Rewrite this as

x - 4 = y

or

y = x - 4

This is the equation of a line in slope intercept form which is generally

y = mx + b

where m is the slope and b the y-intercept

Here m = 1, b = -4

(a) A parallel line will have the same slope but a different y-intercept
So for starters we can write the equation of the parallel line as
y = x + b

Since this passes through (2,6) sub 2 for x and 6 for y to get

6 = 2 + b

==> b = 4

Equation of the line is
y = x + 4

(b) A perpendicular line will have as slope -1/m where m is the slope of the original line

Here m = 1, so -1/m = -1/1 = -1

Equation will be of the form
y = -x + b

Since this also passes through (2,6)
6 = -2 + b

==> b = 6 + 2 = 8

Equation of perpendicular line is
y = -x + 8

Answer:

No real solutions.

Step-by-step explanation:

No real solutions.

Answer:

[tex]\triangle CRQ \cong \triangle CSU[/tex] by SAS

Step-by-step explanation:

[tex]\angle QCR \cong \angle SCU[/tex] because of vertical angles.

y = -2/5 x -11/5 is the equation of line with slope -2/5 that passes through the point (2, -3).

The slope of the line is the rise to run ratio, or the rise divided by the run. It expresses the slope of a line in the coordinate plane.

The standard form of an equation is y = mx+c.

Here given,

A line with a slope of -2/5 that passes through the point (2, -3).

Simplify y = mx+c with m=2/5 and (x, y)=(2, -3). That is to say,

-3 = -2/5 (2)+c

⇒ -3 = -4/5 +c

⇒ c = -3 + 4/5

⇒ c = (-15 + 4) / 5

=> c = -11/5

When m = -2/5  and c = -11 /5 are substituted in y = mx+c, we get

y = -2/5 x -11/5

As a result, an equation for a line with a slope of -2/5 that passes through the point (2,-3) is y = -2/5 x -11/5.

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Answer:

  C.  2x+ 5y = −11

Step-by-step explanation:

You want the equation of the line with slope -2/5 through point (2, -3).

The equation of a line with slope m through point (h, k) can be written as ...

  y -k = m(x -h)

Then the equation of the line with slope -2/5 through point (2, -3) will be ...

  y +3 = -2/5(x -2)

We can put this in standard form by ...

  5(y +3) = -2(x -2) . . . . . multiply by 5

  5y +15 = -2x +4 . . . . . . eliminate parentheses

  2x +5y = -11 . . . . . . . . . add 2x-15 to both sides

The desired equation is 2x +5y = -11.

Answer:

see explanation

Step-by-step explanation:

from the table we can obtain that

f(x ) = 6x³ + 8x - 12 ( 6  0  8  - 12 , being the coefficients of the polynomial )

f(x) is divided by (x + 7) , since evaluated at - 7

the quotient is

6x² - 42x + 302 ( 6  - 42  302, are the coefficients of the quotient )

with remainder - 2126

Answer:

:))

Step-by-step explanation:

The maximum value is 22 as the last small line (end of the "whisker") is marked at 22. Hope this helps!! Pls mark as brainliest and lots of points, help ya girl out!!!

does it want the answer in a specific form?

slope intercept form; y = mx + b

slope = 2

b = -1

plug the values in

y = 2x -1 or y = 2/1x -1

The formula for estimating the population variance from the sample involves taking the sum of squared deviations and dividing it by N - 1

Population variance is a measure of dispersion that determines how far each data point is from the population mean.

On the population, the population variance is calculated. When the number of observations grows, a few data points are chosen to represent the entire population.

The variance calculated on these specific data points is referred to as the sample variance. The population variance can be estimated using the sample variance.

When the population variance is unknown , we estimate the population variance by using sample variance

The formula for estimating the population variance from the sample involves taking the sum of squared deviations and dividing it by N-1

Formula of sample variance  = [tex]s^2 = \frac{\sum f_i(x_i - \bar{x})}{N-1}[/tex]

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The percentage of her students that ride the school bus every morning would be = 84%

A percentage expression is an representation of a data set to a fraction of 100.

The total number of students = 25 students

The number of students that ride the school bus = 21

To calculate the percentage of the students that ride the bus the following is done;

= 21/25 × 100

= 2100/25

= 84%

Therefore, the percentage of her students that ride the school bus every morning is 84%

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The circumference of the circle will be 56.52 m.

And, The area of a circle will be 254.34 m².

What is Circle?

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

The radius of circle = 9 m

Now,

Since, The area of circle = πr²

Hence, The area of circle = 3.14 × 9²

                                        = 3.14 × 81

                                        = 254.34 m²

And, The circumference of the circle = 2πr

                                                         = 2 × 3.14 × 9

                                                         = 56.52 m

Thus, The circumference of the circle will be 56.52 m.

And, The area of a circle will be 254.34 m².

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Assuming that the tips are approximately normally distributed, an interval to estimate the true average tip (as a percent of the bill) with 90% confidence is (10.47, 11.73).

Assuming that the tips are approximately normally distributed, we would determine both the lower limit and upper limit for the confidence interval where 90% of the sample means occur as follows;

Lower limit = μ - σ/√x

Lower limit = 11.1 - 2.8/√20

Lower limit = 11.1 - 0.63

Lower limit = 10.47

For the upper limit, we have:

Upper limit = μ - σ/√x

Upper limit = 11.1 + 2.8/√20

Upper limit = 11.1 + 0.63

Upper limit = 11.73

For 90% of the sample means to occur, the confidence interval is as follows;

Confidence interval = (10.47, 11.73)

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Both balls will strike the ground simultaneously, but the faster ball will do so farther away from the table.

The unit g stands for gravitational acceleration. At sea level, the standard value of g on earth's surface is 9.8 m/[tex]s^{2}[/tex]

They will strike the ground simultaneously if the table and the ground are both flat.

It is customary to divide an object's motion into a vertical component and a horizontal component. While they are on the table, neither of the balls is moving vertically. Both balls begin to accelerate downward as soon as they leave the table due to the effects of gravity. Given that both balls experience the same acceleration from gravity, they will fall at the same rate and with the same downward velocity.

Both balls will strike the ground simultaneously, but the faster ball will do so farther away from the table.

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[tex]\frac{\sin \theta}{300}=\frac{\sin 2\theta}{400} \\ \\ \frac{\sin \theta}{300}=\frac{2\sin \theta \cos \theta}{400} \\ \\ \frac{1}{300}=\frac{\cos \theta}{200} \\ \\ \cos \theta=\frac{2}{3} \\ \\ \theta=\arccos(2/3) \\ \\ \theta \approx \boxed{48^{\circ}}[/tex]

Length of the rectangle is 25 and width of the rectangle is 14.

What do you mean by algebraic expression?

A combination of terms through addition, subtraction, multiplication, division, and other operations is known as an algebraic expression (or variable expression). An algebraic expression is composed of various parts.

Any algebraic expression's variables, constants, terms, and coefficients.

A variable is a symbol that doesn't have a set value. Any value may be used.

It is given that the length of a rectangle is 3 less than twice the width and the perimeter of the rectangle is 78 inches.

Let the width of the rectangle be x

Length of the rectangle become  2x - 3

Perimeter of rectangle = 2(length + width)

78 = 2(2x - 3 + x)

78 = 2(3x - 3)

78 = 6x - 6

78 + 6 = 6x

84 = 6x

x = 84/6

x = 14

length of the rectanle is 2x - 3 = 2(14) - 3 = 28 - 3 = 25

Width of the rectangle is x = 14

Therefore, length of the rectangle is 25 and width of the rectangle is 14.

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By using the concept of vector, it can be calculated that

Direction of the sum is 10.87° below the horizontal.

What is vector?

Anything that has both magnitude and direction and follow the vector addition law is called vector.

A = 2.71 m

[tex]A_x = 2.71 cos 60 = 1.355 \ m\\A_y = -2.71 sin 60 = -2.35 \ m[/tex]

B = 3.14 m

[tex]B_x = 3.14 cos 30 = 2.71 \ m\\B_y = 3.14 sin 30 = 1.57 \ m[/tex]

Sum of A and B = (1.355  +2.71) i + (-2.35 + 1.57) j

                           = 4.065i - 0.78j

Let the angle be [tex]\theta[/tex]

[tex]tan\theta = \frac{0.78}{4.065}\\tan\theta = 0.192\\\theta = tan^{-1}(0.192)\\\theta = 10.87^{\circ}[/tex]

Direction of the sum is 10.87° below the horizontal.

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Answer: 2. 37.8%

3. 30% decrease

Step-by-step explanation:

Increase = New Number - Original Number

Then:  divide the increase by the original number and multiply the answer by 100.

% increase = Increase ÷ Original Number × 100.

36.99-22.99=14

100(14/36.99)

37.8%

First: work out the difference (decrease) between the two numbers you are comparing.

Decrease = Original Number - New Number

Then: divide the decrease by the original number and multiply the answer by 100.

% Decrease = Decrease ÷ Original Number × 100

2.50-1.75=0.75

100(0.75/2.5)

30%

Answer:

  (11, 3)

Step-by-step explanation:

You want the point 1/6 of the way from A(14, -1) to B(-4, 23).

The point P that divides AB into the fractional parts k and (1 -k) is ...

  P = (1-k)A +kB

For k = 1/6, the dividing point is ...

  P = (5/6)(14, -1) +(1/6)(-4, 23) = (5·14 -4, 5(-1) +23)/6 = (66, 18)/6

  P = (11, 3)

The point 1/6 of the way from A to B is (11, 3).