Can someone help me answer this question about area of trapezium

AAS = Angle , angle and one side of 2 congruent triangles

SSS = All 3 sides are measure same of the 2 triangles.

ASA = 2 angles and the side between them are same

HL = A right triangle is congruent if its hypotenuse and one of its legs are congruent with the hypotenuse and one of its other legs.

The dimensions of the triangles' sides and angles determine whether two or more triangles are congruent. A triangle's size is determined by its three sides, and its shape by its three angles. Pairs of corresponding sides and corresponding angles in two triangles are said to be equal if they are congruent. They share a similar size and shape. In triangles, there are numerous congruence conditions. For the two triangles to be congruent, they must be the same size and shape. It should be possible to superimpose the two triangles under examination. A triangle's position or appearance appears to change when we rotate, reflect, and/or translate it. In that situation, we must recognize the six components of a triangle.

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In the probability distribution  table x=76 and p(x) is 0.3.

Here X is a random variable. P(X) is its probabilities corresponding to the different values of X.

now according to the properties of probability theory we know that sum of probabilities is 1.

so here to find the value of the probability of X corresponding to the value 76 we should use the following steps:

Probability means possibility. It is a branch of mathematics that deals with the occurrence of  random events. The value is expressed from zero to one.  The calculus of probability is introduced in mathematics to predict the probability of events occurring. Probability basically means the degree to which something is likely to happen. It is a basic theory of probability that is also used in  probability distribution, where  the probability of the result of a random experiment is studied. To determine the probability of an event, we should first know the total number of possible outcomes.

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Answer: 260 is greater than 53.46 times X +.13×350

Step-by-step explanation: You know you have to stay under $260 because that’s all she has so that’s where you get to 260 is greater than

And she knows she’s going to go about 350 miles so 260 is greater than $.13 times 350+5346 times you don’t know how many days so that your variable X

Answer below and in attached graph Step by stepShow and explain:1) The rule for a rotation by 90° around the origin is (x,y)→(−y,x) so I moved the y to x and changed the sign, I moved x to y position. 2) to translate 5 units right and 2 units down, you add (+5, -2) to your current coordinates of D’ E’ and F’ giving D’’ E’’ F’’. Pre Image ➡️ D’ E’ F’ ➡️. D’’ E’’ F’’ (+5, -2)D (-5, -2) ➡️ (2, -5) ➡️ (7, -7)E (0, -2) ➡️ (2, 0). ➡️ (7, -2)F (-4, -6) ➡️ ( 6, -4). ➡️ (11, -6)Attached graph of pre image and transformations

Answer:

x = 15

Step-by-step explanation:

150+3x-15=180 because of same-side interior angles therorem.

Then, we solve the problem to get 15.

Hope this helped! :)

Answer: [tex]y=2 \left(x+\frac{5}{2} \right)^2 -\frac{25}{2}[/tex]

Step-by-step explanation:

[tex]y=2x^2 +10x\\\\y=2(x^2 + 5x)\\\\y=2 \left(x^2 +5x +\frac{25}{4} \right)-\frac{25}{2}\\\\y=2 \left(x+\frac{5}{2} \right)^2 -\frac{25}{2}[/tex]

The coordinates of G is (d+c, b)

This is because the opposite sides of any parallelogram are equal in length, and so the length of side HG is equal to the length of side EF.

a) The length of side HG is equal to the horizontal distance (x2 - x1): xG - 0

The length of side EF is equal to the horizontal distance (x2 - x1): d - (-c) = d +c

Thus:

xG - 0 = d + c

xG = d + c

Therefore the x-coordinate of G is d + c

b) To find the y-coordinate of G, we also apply the idea that sides GF and HE are equal.

The length of side GF is equal to the vertical distance (y2 - y1): yG - 0

The length of side HE is equal to the vertical distance (y2 - y1): b - 0

Thus:

yG - 0 = b -0

yG = b

Therefore the y-coordinate of G is b

Finally, the coordinates of G is (xG, yG) = (d+c, b)

The number of each type of coins are as follows:

q = 15 quarters.

d = 30 dimes.

n = 25 nickels.

In order to solve this word problem, we would assign a variables to the unknown numbers and then translate the word problem into algebraic equation as follows:

Let d represent the number of dimes.

Let q represent number of quarters.

Let n represent number of nickels.

Let T represent total number of coins.

Note: 1 quarter is equal to 0.25 dollar, 1 nickel is equal to 0.5 dollar, and 1 dime is equal to 0.1 dollar.

Translating the word problem into an algebraic equation, we have;

Dimes; d = 2q     .....equation 1.

Nickels; (70 - (q + 2q)) = (70 - 3q)     .....equation 2.

Total coins; T = n + d + q

0.5(70 - 3q) + 2q(0.1) + q(0.25) = 8.00

Multiplying all through by 100, we have:

5(70 - 3q) + 2q(10) + q(25) = 800

350 - 15q + 20q + 25q = 800

350 + 30q = 800

30q = 800 - 350

30q = 450

q = 450/30

q = 15 quarters.

For the number of dimes, we have:

Dimes, d = 2q

Dimes, d = 2(15)

Dimes, d = 30 dimes.

For the number of nickels, we have:

Nickels, n = (70 - 3q)

Nickels, n = (70 - 3(15))

Nickels, n = (70 - 45)

Nickels, n = 25 nickels.

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[tex]-4x-1=-y\\y[/tex]

Flip the equation:

[tex]-y=-4x-1[/tex]

Divide both sides by -1:

[tex]\frac{-y}{-1} =\frac{-4x-1}{-1}[/tex]

[tex]y=4x+1[/tex]

__________________________________________________________

[tex]-4y+20+3x=0\\y[/tex]

Add -3x to both sides of the equation:

[tex]3x-4y+20+-3x=0+-3x\\-4y+20=-3x[/tex]

Add -20 to both sides of the equation:

[tex]-4y+20+-20=-3x+-20\\-4y=-3x-20[/tex]

Divide both sides by -4:

[tex]\frac{-4y}{-4} =\frac{-3x-20}{-4}[/tex]

[tex]y=\frac{3}{4} x+5[/tex]

Answer:

plane CGF and ABC

Step-by-step explanation:

A null hypothesis is directly opposed by an alternative hypothesis. As a result, if either one of the two theories is accurate, the other is untrue.

In statistical hypothesis testing, null and alternate hypotheses are utilized. The null hypothesis of a test always predicts no effect or no association between variables, but the alternative hypothesis reflects the effect or relationship that your research predicts.

A null hypothesis is directly opposed by an alternative hypothesis. As a result, if either one of the two theories is accurate, the other is untrue.

Based on the study question or issue that they are attempting to solve, the analyst or researcher develops a null hypothesis. The null may be distinguished in many ways depending on the question.

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The value of the function h(2) for h(t) = -16t2 + 32t + 5 is h(2) = 5

From the question, the function definition is given as

h(t) = -16t2 + 32t + 5

First, we express the exponent in the function properly

This is represented as

h(t) = -16t² + 32t + 5

The function value to calculate is given as

h(2)

This means that we calculate h(t) when t = 2

So, we have

h(2) = -16(2)² + 32(2) + 5

Evaluate the exponents

h(2) = -16(4) + 32(2) + 5

So, we have

h(2) = 5

Hence, the function value is 5

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The student got the solution to the quadratic equation wrong at step 2

A quadratic equation is a mathematical equation in which it's higher power of unknown is 2.

A quadratic equation can be solved by using 4 different method of choice which are formula method, factorization method , completing the square and graphical method.

x^2+4x-12=0 is an example of quadratic equation.

using factorization method to solve the value of x

x^2+6x-2x-12=0

grouping the equation

(x^2+6x)(-2x-12)=0

x(x+6)-2(x+6)=0

(x+6)(x-2)=0

for the equation to be satisfied

(x+6)=0

or

(x-2)=0

Therefore x= -6 or+2

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The diagonals WY and XZ intersect at E, we must prove that WE ∼ = YE and XE ∼ = ZE. The converse exists also true: If the diagonals of a quadrilateral bisect each other, then the quadrilateral exists as a parallelogram.

WXYZ cannot be a parallelogram because the value of x that creates one pair of sides congruent does not create the other pair of sides congruent.

Given that WXYZ, let the diagonals WY and XZ intersect at E, we must prove that WE ∼ = YE and XE ∼ = ZE. The converse exists also true: If the diagonals of a quadrilateral bisect each other, then the quadrilateral exists as a parallelogram.

A rhombus, therefore, contains all the properties of a parallelogram: Its opposite sides exist parallel. Its opposite angles exist equally. Its diagonals bisect each other.

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1000 times three-fifths divided by Start Fraction 13 Over 2 End Fraction is the required expression.

An expression is a combination of numbers, variables and operators.

Given that,

Maria has already written Two-fifths of her 1,000 word essay.

It means she has completed 2/5 of essay.

She has 3/5 more to do.

she continues writing at the same pace of 6One-half words per minute

So Her speed is 13/2 words per minute.

So 1000*3/5 (600 words) at 13/2 words per minute

we need to divide the number of words by the speed to work out the time: 1000*3/5/(13/2),

Hence 1000 times three-fifths divided by Start Fraction 13 Over 2 End Fraction is the required expression.

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Answer:

c

Step-by-step explanation:

Using the function rule, the value of g(r +2)  is r-2

Given the function rule g(k) = k-4.

Then g(r + 2)  can be found by replacing k with r+2 in the function g(k):

g(r+2) = r + 2 - 4

           = r - 2

Therefore, g(r+2) gives r - 2 when evaluated using the function rule.

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Answer:

6

Step-by-step explanation:

Trust

A decimal is a number that is divided into two parts: a whole and a fraction. Between integers, decimal numbers are used to express the numerical value of complete and partially whole quantities.

n/37=236n=1111 /37 =0.2972972972972972972972972972972972972972

The accepted method for representing both integer and non-integer numbers is the decimal numeral system. It is the expansion of the Hindu-Arabic numeral system to non-integer values. Decimal notation is the term used to describe the method of representing numbers in the decimal system.

A decimal is a number that is divided into two parts: a whole and a fraction. Between integers, decimal numbers are used to express the numerical value of complete and partially whole quantities.

A fraction expressed in a particular way is called a decimal. As an alternative to expressing 1/2, you might write 0.5 instead, with the zero in the ones place and the five in the tenths position.

n/37=236n=1111 /37 =0.2972972972972972972972972972972972972972

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The money which is expected to spend on new word processors during this year is

The probability distribution is

x:          0            1             2            3

f(x)         [tex]\frac{1}{10}[/tex]           [tex]\frac{3}{10}[/tex]           [tex]\frac{2}{5}[/tex]              [tex]\frac{1}{5}[/tex]

If the cost of the desired model is $1200 per unit and at the end of the year a refund of 50x2 dollars

So total money spent in this year is [tex]1200x-50x^2[/tex]          

Then the equation of expenses will be

[tex]\text{Expenses}=E(1200x-50x^2)[/tex]

We can rewrite it as

[tex]\text{Expenses}=E(1200x)-E(50x^2)[/tex]  

  [tex]\text{Expenses}=1200E(x)-50E(x^2)[/tex]   -----------------(1)

Now the mean of the probability distribution is ,

[tex]E(x)=\sum_{ }^{ }((x_i)(f(x_i))\\=(0\times\frac{1}{10})+(1\times\frac{3}{10})+(2\times\frac{2}{5})+(3\times\frac{1}{5})\\=\frac{3}{10}+\frac{4}{5}+\frac{3}{5}\\\\=\frac{3+8+6}{10}\\\\=\frac{17}{10}\\\\=1.7[/tex]      

The variance of the function is

[tex]E(x)=\sum_{ }^{ }(x_i^2)(f(x_i)[/tex]

        [tex]=(0^2\times\frac{1}{10})+(1^2\times\frac{3}{10})+(2^2\times\frac{2}{5})+(3^2\times\frac{1}{5})[/tex]

        [tex]=\frac{3}{10}+\frac{8}{5}+\frac{9}{5}[/tex]

        [tex]=\frac{37}{10}[/tex]

        [tex]=3.7[/tex]

On substituting the values in equation (1)

[tex]\text{Expenses}=1200E(x)-50E(x^2)[/tex]

              [tex]=1200(1.7)-50(3.7)^2[/tex]

              [tex]=2040-684[/tex]

              [tex]=1855[/tex]

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Answer:

The three options you would pick is
y2 – 5y = 750
750 – y(y – 5) = 0
(y + 25)(y – 30) = 0

Step-by-step explanation:

Hope this helps! :))

EXPLANATION:

To solve the exercise we must make a rule of three.

The exercise is as follows:

The equation that have same solution to 3x-12=24 is 4x - 30 = 18.

A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

The equation given is illustrated as:

3x - 12 = 24

Collect like terms

3x = 24 + 12

3x = 36

Divide through by 3.

3x / 3 = 36 / 3

x = 12

In this case, 4x - 30 = 18 will be:

4x - 30 = 18.

Collect like terms

4x = 18 + 30.

4x = 48

Divide

x = 48/4

x = 12

Therefore, 4x - 30 = 18 has same solution.

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Answer:

The upper pound is 4.25 m and the lower bound is 4.15 m

4.15 m ≤ 4.2 m < 4.25 m

Step-by-step explanation:

Let us solve the question

∵ The length of the car corrected to 1 decimal place

→ 1 decimal place means tenth

∴ It corrected to the tenths place which is 0.1

→ Divide it by 2

∵ 0.1 ÷ 2 = 0.05

∴ The limit is 0.05 m

→ To get the lower bound subtract 0.05 from the length of the car

∵ The length of the care is 4.2 m

∴ The lower bound = 4.2 - 0.05

∴ The lower bound = 4.15 m

→ To get the upper bound add 0.05 to the length of the car

∵ The length of the care is 4.2 m

∴ The upper bound = 4.2 + 0.05

∴ The upper bound = 4.25 m

∴ 4.15 m ≤ 4.2 m < 4.25 m

∴ The upper pound is 4.25 m and the lower bound is 4.15 m

P.s hopes this helps

Answer:72

Step-by-step explanation:

Let's begin by identifying key information given to us:

A is a 3 x 2 matrix

B is a 2 x 3 matrix

AB is the product of 3 x 2 matrix & 2 x 3 matrix. We obtain a 3 x 3 matrix

Therefore, the size of the product of A & B (that is AB) is a 3 x 3 matrix whenever these products exist

The solution of 0.125x +1 -0.25x < -3 is x > 32

Difference between equality and inequality equations

Both mathematical phrases, equations and inequalities, are created   by connecting two expressions.The equal sign (=) indicates that two expressions in an equation are believed to be equivalent. The symbols show that the two expressions in an inequality are not always equal: >, <, ≤ or ≥. Or in simple words the equation which has '=' sign is an equality equation while the inequality equation has the signs are >, <, ≤ or ≥.

The given expression is,

0.125x +1 - 0.25x < -3

subract the x value,

0.125x  - 0.25x + 1 < -3

-0.125x + 1 < -3

-0.125x < -3 - 1

-0.125x < -4

Now, if on both the sides the signs are -ve then change the inequality sign, like this

x > 4 / 0.125

x > 32

Hence, The solution of 0.125x +1 -0.25x < -3 is x > 32

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Answer:

$8303.75

Step-by-step explanation:

(6000x1.025^2)+2000=8303.75

The measure of the bigger angle is 117°

What are Supplementary Angles?

Two angles are said to be supplementary if their sums total 180 degrees.

Let,  x be the angle

and, x + 54 other angle measure.

we know, sum of Supplementary angle is 180°

so, the equation will be

x + (x + 54) = 180°

2x + 54 = 180

2x = 180 - 54

2x = 126

x = 63°

x + 54 = 63 + 54 = 117°

Therefore, The measure of the bigger angle 117°

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