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The pair of triangle formed are congruent using the side-side-side congruency theorem.

Two triangles are said to be congruent if they have the same shape and their corresponding sides are congruent.

Since the opposite sides of a parallelogram are congruent, if the parallelogram is cut through the diagonal, the pair of triangle formed are congruent using the side-side-side congruency theorem.

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Answer:

pi/2 units to the left

Step-by-step explanation:

the formula is y = cos(x-b) so when b is negative, the formula will show a plus sign because minus negative is adding. this means the graph is shifted -pi/2 to the right which is really pi/2 to the left

In the imaged attached, the most precise name for ABCD  is known to be rhombus.

Looking at the shape attached, one can see that the diagonals of a parallelogram are said to be bisecting one other and if it cross at right angles, it is said to be a rhombus.

Using the Diagonal midpoints of AC and BD, the equation will be:

(A+C)/2

(B+D)/2

To find if the midpoints are similar, then:

A +C = (3, 5) +(6, 2) = (9, 7)

B +D = (7, 6) +(2, 1) = (9, 7)

Therefore, from the solution above, the midpoints of the diagonals are the same, making the shape to be a parallelogram.

In terms of Diagonal vectors, the shape will be perpendicular when the figure is a rhombus. So:

 AC = C -A = (6, 2) -(3, 5) = (3, -3)

BD = D -B = (2, 1) -(7, 6) = (-5, -5)

So the lengths will be (3√2 vs 5√2).

Note also that the dot-product of these values need to be zero if they are perpendicular and as such:

 AC·BD = x1·x2 +y1·y2 = (3)(-5) +(-3)(-5) = -15 +15 = 0

Therefore, one can say that the diagonals are known to different length and are perpendicular bisectors, so the shape above is regarded as rhombus.

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Answer:

1/4, 0.5, -4/6, 4.5, 1/3, 7/8

explanation: it is the ratio of two integers

a/b where b is not = to 0

Answer:

i. {1,2,3,4,5,6,7,9}

ii. {1,3,5}

iii. {1,2,3,4,5,6,8,10}

Step-by-step explanation:

U= {1,2,3,4,5,6,7,8,9,10}

A= {1,3,5,7,9}

B= {1,2,3,4,5,6}

A U B = {1,2,3,4,5,6,7,9}

A n B = { 1,3,5}

A (prime) U B =

A(prime)= {2,4,6,8,10}

Therefore A(prime)= {1,2,3,4,5,6,8,10}

Step-by-step explanation:

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Answer:

$90

Step-by-step explanation:

The quadratic equation  is y = -0.15x² + 2x + 5.5 , Option D is the correct answer.

The complete question is

If a person who is 5.5 feet tall throws a baseball into the air, the path can be modelled using the table of values, where x represents the time in seconds and y is the height of the ball in feet.

(table is in the photo below)

Which quadratic equation models the data in the table?

y= −0.25x2 + 2x + 5.5

y= −0.35x2 + 2x + 5.5

y= −0.27x2 + 3x + 5.5

y= −0.15x2 + 2x + 5.5

The quadratic equation represented by the table is y = -0.15x² + 2x + 5.5

When  two algebraic expressions are linked with an equal sign , the expression formed is called an Equation.

The standard form of the Quadratic equation is

y = ax² + bx + c

here a, b and c are constants.

From the given data in the table

at point (0, 5.5)

5.5 = a(0)² + b(0) + c          

at point (1, 7.35)

7.35 = a(1)² + b(1) + c    

at point (2, 8.9)

8.9 = a(2)² + b(2) + c    

The system of equations will be solved to determine the value of a,b and c

a= -0.15, b = 2, c = 5.5

Therefore , The quadratic equation  is y = -0.15x² + 2x + 5.5 .

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Answer:

B) y= -0.25x^2 + 2x + 5

Step-by-step explanation:

I got it correct on test

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Answer:

probability; ( of choosing a yellow marble)

7 yellow marbles + 10 orange marbles = 17 in total

if the no of yellow marbles is 7 therefore = ⁷/10

so that is the probability ⁷/10

Hope this helps

The required value of  value of cospheta = √2/3​, here correct option is d) √2/3​.

The given equation is a Trignomatric Equation,
cos2pheta+cos^2pheta = 1

These are the equation which contains trigonometric operators such as sin, cos.. etc.. In algebraic operation.



cos2pheta + cos^2pheta = 1
Now we know that,

[tex]cos2x[/tex] = [tex]cos^2x -1[/tex]

so, substituting  cos2pheta = 2cos^2pheta - 1
2cos^2pheta-1 + cos^2peta = 1
3cos^2peta = 2
cos^2pheta = 2/3
cospheta = √2/3​

Thus, the required value for the cospheta = √2/3​.

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Answer:

$ 1805

Step-by-step explanation:

2000 × 95%

= 1900

1900 × 95%

= 1805

=============================================

Work Shown:

[tex]\perp (q,r,s,t) = \frac{qr + s}{t}\\\\\perp (2,6,4,8) = \frac{2*6 + 4}{8}\\\\\perp (2,6,4,8) = \frac{12 + 4}{8}\\\\\perp (2,6,4,8) = \frac{16}{8}\\\\\perp (2,6,4,8) = 2\\\\[/tex]

Let m = 2 so we can use this result later.

[tex]\perp (q,r,s,t) = \frac{qr + s}{t}\\\\\perp (4,7,2,6) = \frac{4*7 + 2}{6}\\\\\perp (4,7,2,6) = \frac{28 + 2}{6}\\\\\perp (4,7,2,6) = \frac{30}{6}\\\\\perp (4,7,2,6) = 5\\\\[/tex]

Let n = 5 so we can use this result later.

Add the two results.

m+n = 2 + 5 = 7.0 is the final answer.

A graph which represents the solution set for the compound inequality is shown in the image attached below.

In order to determine the graph which represents the solution set for the compound inequality, we would evaluate the given inequalities as follows.

Given the following inequalities:

⅓x + 10 ≥ 7

x - 10 ≥ 7

For the first inequality, we have:

⅓x + 10 ≥ 7

Multiply all through by 3;

x + 30 ≥ 21

x ≥ 21 - 30

x ≥ -9  ⇒ x < 9.

For the first inequality, we have:

x - 10 ≥ 7

x ≥ 7 + 10

x ≥ 17.

In conclusion, a graph which represents the solution set for the compound inequality is shown by using the number line in the image attached below.

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Answer:  [tex]-\frac{1}{2}[/tex]

Step-by-step explanation:

[tex]y -3 = -\frac{1}{2}(x-2)[/tex]

Write as slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.

[tex]y-3=-\frac{1}{2}x + 1[/tex]

     [tex]y = -\frac{1}{2}x+4[/tex]

Therefore, the slope is [tex]-\frac{1}{2}[/tex].

Answer:

-104

Step-by-step explanation:

Completed by plugging 50 in the equation:

-2(50) - 4 =

-100 - 4 =

-104

Answer:

The factors are (x-7) and (x-4)

Step-by-step explanation:

We are finding the factors of a function from the zeros

The zeros are 7 and 4

We can use the zero product property which is

(x-b)(x-c) = 0  where b and c are the zeros

(x-7) (x-4) =0

The factors are (x-7) and (x-4)

Answer:

d. 93 [tex]m^{2}[/tex]

Step-by-step explanation:

4×3= 12, 12/2 =6, 6×4 = 24

5×3= 15, 15×4= 60

3×3=9,

24+60+9= 93

A function assigns the values. A function is a rule that assigns each value of the independent variable to exactly each value of the dependent variable.

A function assigns the value of each element of one set to the other specific element of another set.

The given statement can be completed as given below.

A function is a rule that assigns each value of the independent variable to exactly each value of the dependent variable.

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Step-by-step explanation:

x=66°

180-118=62°

180-52+62=66°

hope this helps

Answer:

see below

Step-by-step explanation:

2: letter at the vertex,  placing a letter or number inside .... , or by using 3 letters

3:

WXY

WXZ

YXZ

4: X

The measure of the angle EFD will be 68 degrees. The correct answer is option B.

The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet.

Given that:-

The arc angle is 68 degrees and we need to find the angle EFD.

As it is given in the question that the angle suspended by the arc is 68 degrees so the angle EFD will also be equal to 60 degrees.

Therefore the measure of the angle EFD will be 68 degrees. The correct answer is option B.

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The value of x in the equation is 59/5

The equation is given as:

5x = 59

Divide both sides by 5

x = 59/5

This means that the value of x in the equation is 59/5

To know if the value is accurate, we simply multiply 5 by 59/5 and we get 59 as in 5x = 59

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Answer: B and C

Step-by-step explanation:

Let's start off with some definitions.

Supplementary Angles: Two angles that add up to 180°.

Right Angle: One angle equal to 90°. Also identified with a square on the angle.

Complementary Angles: Two angles that add up to 90°.

Straight Angle: A straight line, which equals to 180°.

Right off the bad, we can knock off A and D because there is no proof of those being seen.

The angle <EFH is a right angle because it is equal to 90°. If you pay close attention, the angles <EFG and <GFH both add up to 90°, making them complementary angles.

Therefore, the correct answers are B and C.

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Answer:

-5 + 12 i

Step-by-step explanation:

(2 + 3i)^2   = 4  + 6i  + 6i  + 9i^2

                 =   4   + 12 i   + 9(-1)

                     = - 5 + 12 i

Answer:

132

Step-by-step explanation:

180-48=132

Answer: 132

Step-by-step explanation:

let x = unknown amount

48 + x = 180

————————————————————————

Solve for x by subtracting 48 from both sides

48 - 48 + x = 180 - 48

x = 132

Answer:

≈5.3 feet,63.6 inches

Step-by-step explanation:

36+b²=64

-36 -36

b²=28

if we square root both sides we can get the radical/exact answer or the rounded one

radical: 4√7

rounded to the nearest tenth: 5.3 feet

The incorrect rounding for 53.864 is 53.87

The decimal to be approximated is as follows;

53.864

The first option rounded the decimal to 2 significant figures or a whole number.

The second option is incorrect because they rounded it wrongly to 2 decimal places. The correct 2 decimal round is 53.86.

The third option is approximated rightly to one decimal place.

The last option is rounded to the closes tens term.

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A ratio shows us the number of times a number contains another number. The maximum amount of purple that Susan can make is 25 ml.

A ratio shows us the number of times a number contains another number.

Susan makes purple paint by mixing red and blue paint in a ratio of 2:3. Now, if Susan wants to use the complete red paint then,

Purple paint she can make = 2/3 × 6/6 = 12 ml of red paint / 18 ml of blue paint

If Susan wants to use the complete blue paint then,

Purple paint she can make = 2/3 × 5/5 = 10 ml of red paint / 15 ml of blue paint

As per the first condition 18ml of blue paint is needed which is not possible, therefore, the second case is possible.

Thus, Susan needs to mix 10 ml of red paint and 15 ml of blue paint. Therefore, the amount of paint that Susan will make is,

Total Paint = 10ml + 15ml = 25ml

Hence, the maximum amount of purple that Susan can make is 25 ml.

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ABC reports the liability on the balance sheet as a $1 million current liability, and a $4 million long-term liability.

A current liability is a liability that is payable within 12 months or one year.

On the other hand, a long-term liability is a liability that is payable after 12 months or one year.

Since $1 million is payable in each of the next five years, this implies $1 million is payable within one year while $4 million is payable after one year.

Therefore, ABC reports the liability on the balance sheet as a $1 million current liability, and a $4 million long-term liability.

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In the given diagram, the length of OQ is 11

From the question, we are to determine the length of OQ

From the given information,

OP = 17

QP = 6

In the diagram, we can observe that

OQ + QP = OP

∴ OQ + 6 = 17

Subtract 6 from both sides

OQ + 6 - 6 = 17 - 6

OQ = 11

Hence, the length of OQ is 11

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[tex]\huge \boxed{\sf 11}\\\\\\\displaystyle \sf OP=OQ+QP\\\\OQ=OP-QP\\\\OQ=17-6\\\\OQ=11[/tex]

Answer:

No

Step-by-step explanation:

To determine if a point is a solution to a system of equations, you need to determine if the point is a solution to both equations.

Is ( 2,10) a solution to -3x-4y = 4

Substitute into the equation and see if it is true

-3(2) -4(10) = 4

-6 -40 = 4

-46 =4

This is not true so it is not a solution

Answer:

No

Step-by-step explanation:

The solution(s) of a system is/are the point(s) (x, y) where the lines intersect.

The question asks if (2, 10) is a solution of the system. This means the "x" value is "2" and the "y" value is "10".

We can substitute those values into both of the equations.

[tex]-3x-4y=4\\-3(2)-4(10)=4\\-6-40=4\\-46=6 \Rightarrow Incorrect![/tex]

The "x" and "y" values must be true for both equations, therefore (2, 10) is not a solution of the system.