Feature Question What is the area of a parallelogram whose vertices are A(−12, 2), B(6, 2), C(−2, −3), and D(−20, −3)? Enter your answer in the box. units²

The length of each leg is 14.69  in the triangle

In an isosceles triangle, the median drawn from the vertex angle also acts as an altitude, dividing the triangle into two congruent right triangles.

Let the length of one of the legs of the triangle "x".

Using the Pythagorean theorem, we can write:

x²+ (15)² = (21)²

x² + 225 = 441

x² = 441 - 225

x² = 216

Taking the square root of both sides, we find:

x = √216

x =14.69

Therefore, the length of each leg is 14.69 in the triangle

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Answer:

Step-by-step explanation:

you have to find the mean of the two fractions, adding and then dividing by two

(1/5 + 1/9) : 2 =

14/45 : 2 =

7/45

Step-by-step explanation:

Part A

The equation that represents the number of chairs at each table in the library is: 48 = 8c

Part B

To find the correct value, we'll solve the equation from Part A:

48 = 8c

c = 48 ÷ 8

c = 6

So, each table at the library will have 6 chairs.

Step-by-step explanation:

70 x 68 = 4760 marks

# mrks / 70  papers =  68 marks/paper

# marks   =   70 papers * 68 marks/paper

The range of the equation y = |x| is

∞ > x ≥ 0

The absolute value function x returns the distance between x and 0 on the number line regardless of the sign of x

Plotting a graph of y = | x| also have it that the smallest possible value of |x| is 0 which occurs when x = 0

for any other value of x, the unction y = |x | will be positive

hence we can say that the range of |x| is [0, ∞).

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Answer:

The circumference of the circle is 12pi cm.

Answer:

The circumference of the circle is 12π cm.

that's the answer

There are 72 students in the school.

The number for Igbo language = 54

The number for Igbo language = 40

The Venn diagram is attached

Assuming that the total number of students in the school is x.

Information from the problem

3/4 of students credited Igbo language and

5/9 credited Agriculture.

every student in the school credited at least one of the two subjects. hence we have that

3/4x + 5/9x - 22 = x

Simplifying this equation gives

3/4x + 5/9x - x = 22

11x / 36 = 22

11x = 36 * 22

x = (36 * 22) / 11

x = 72

The number for Igbo language

= 3/4 * 72 = 54

The number for Igbo language

= 5/9* 72 = 40

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The height of the TV is approximately 52.3 inches when rounded to the nearest tenth of an inch.Hence, the TV is approximately 52.3 inches tall.

To find the height of the TV, we can use the Pythagorean theorem, which states that the square of the hypotenuse (the diagonal) of a right triangle is equal to the sum of the squares of the other two sides.

In this case, the width and height of the TV form the legs of a right triangle, with the diagonal as the hypotenuse.

Let's denote the height of the TV as h. According to the Pythagorean theorem:

h² + 67² = 85²

Simplifying the equation, we have:

h² + 4489 = 7225

Subtracting 4489 from both sides, we get:

h² = 2736

Taking the square root of both sides, we find:

h ≈ 52.3.

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Answer:

Step-by-step explanation:

The mean mass per bag is 99 kilograms.

The mode is the value that appears most frequently in a dataset. In the given dataset of bag masses, the mode would be the mass value that occurs most often. Let's find the mode.

The masses of the bags are:

90, 94, 96, 98, 99, 102, 105, 91, 102, 99, 105, 94, 99, 90, 94, 99, 98, 96, 102, and 105.

To find the mode, we can simply count the frequency of each mass value and identify the one that appears most often:

90 appears twice

94 appears three times

96 appears two times

98 appears two times

99 appears four times

102 appears three times

105 appears three times

91 appears once

Therefore, the mode in this dataset is 99, as it appears most frequently.

To calculate the mean mass per bag, we need to sum up all the masses and divide by the number of bags. Let's calculate it:

Sum of masses = 90 + 94 + 96 + 98 + 99 + 102 + 105 + 91 + 102 + 99 + 105 + 94 + 99 + 90 + 94 + 99 + 98 + 96 + 102 + 105

Sum of masses = 1980

Number of bags = 20

Mean mass per bag = Sum of masses / Number of bags

Mean mass per bag = 1980 / 20

Mean mass per bag = 99 kilograms

Therefore, the mean mass per bag is 99 kilograms.

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The value of the given fraction is 18.

Given is fraction, [tex]\frac{2+\sqrt{5} }{2-\sqrt{5}} +\frac{2-\sqrt{5} }{2+\sqrt{5}}[/tex], we need to show it in a+b√5 form,

So,

[tex]\frac{2+\sqrt{5} }{2-\sqrt{5}} +\frac{2-\sqrt{5} }{2+\sqrt{5}}\\\\\\= \frac{(2+\sqrt{5})^2+(2-\sqrt{5} )^2 }{(2+\sqrt{5})(2+\sqrt{5} ) } \\\\\\= \frac{4+5+4\sqrt{5}+4+5-4\sqrt{5} }{2^2-\sqrt{5}^2 } \\\\\\= 18[/tex]

Hence the value of the given fraction is 18.

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The volume of the rectangular prism is 168.7 cubic units.

The volume of a rectangular prism can be calculated using the following formula:

V = base area x height

A prism is a polyhedron in three dimensions with two identical ends.

In this case, the base area is 24.1 units² and the height is 7 units.
Let the base area can be represented as B and the height be described as H,

then volume can be rearranged as,

V = BH

Here:

B = 24.1 units²

H = 7 units

When these values are entered into the formula, we get:

V = 24.1 x 7

V = 168.7

Therefore, the volume of the rectangular prism is 168.7 cubic units.

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The smallest size that will allow this confidence interval to be built is given as follows:

n = 75.

The bounds of the confidence interval are given by the rule presented as follows:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

The margin of error is calculated as follows:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The desired margin of error is of M = 0.5, as we have the time in hours, with [tex]\sigma = 2.2[/tex], hence the sample size is obtained as follows:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]0.5 = 1.96\frac{2.2}{\sqrt{n}}[/tex]

[tex]0.5\sqrt{n} = 1.96 \times 2.2[/tex]

[tex]\sqrt{n} = \frac{1.96 \times 2.2}{0.5}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{1.96 \times 2.2}{0.5}\right)^2[/tex]

n = 75 -> rounded up.

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Answer:

It is 3y^3.

Step-by-step explanation:

We can simplify the expression as follows:

-15(y^2)^4/(-5y^3y^2)

= -15y^8/(-5y^5)

= 3y^3

So, the simplified expression is 3y^3.

Answer:

Step-by-step explanation:

Divide 400 by 48 people who wants to live in a city.

400 / 48 = .12 is 12%

Answer:

Total Increase in Population of India from 1961 to 2001 = 1028-439 million = 659 million

Answer:1.5

Step-by-step explanation:

Y=1/2 of x

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From the origin, move 3 units to the right, and then move 9 units up is the intersection of the graphs of the two equations be located on a coordinate grid

What is Equation?

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

Given that solution to a system of two linear equations is x = 3: y = 9.

We need to find how the intersection of the graphs of the two equations be located on a coordinate grid

As we know that the numbers on right side of zero are positive and number of upside of zero on y axis are positive.

As x=3 which is positive

y=9 which is positive.

So From the origin, move 3 units to the right, and then move 9 units up is the intersection of two equations

Hence, From the origin, move 3 units to the right, and then move 9 units up is the intersection of the graphs of the two equations be located on a coordinate grid

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Answer:

100.9 km/h

Step-by-step explanation:

We use the fraction

37 km      =    x km

22 min        60min

when we cross multiply, we get

2220=22x, which gives us

x=100.909090...

but since we're rounding, we simply give the answer

100.9 km/h

The correct relationship between the angles are:

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

The figures (see attachment)

Using the figures and the definition of angle relationships, we have the relationships of the angles to be:

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Here is the table for the function f(x) = 3 * (3/4) ˣ:

x f(x)

-3 16.000

-1 4.000

0 3.000

1 2.250

3 1.688

The function is an exponential decay function

f(x) = 3 * (3/4) ˣ, in the given exponential function the starting function is

3. The base is 3/4.

The base is what determines exponential decay or growth. The condition for determining exponential growth or exponential decay is

The base function here is a factor which is 3/4 = 0.75 and less than one and hence a decay function

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The measure of angle C is  13. 94 degrees

To determine the value of the angle, we need to know the six different trigonometric identities.

These identities are;

From the information given, we have that;

The Hypotenuse side of the triangle ABC =  34

the adjacent side of the triangle = 33

Using the cosine identity, we have that;

cos C= adjacent/hypotenuse

cos C = 33/34

Divide the values

cos C = 0. 9706

Find the inverse

C = 13. 94 degrees

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a. In the integrand ∫[x/(6x² + 5)²]dx, we make the substitution u =  (6x² + 5)

b. Writing the integrand ∫[x/(6x² + 5)²]dx in the form ∫f(u)du, f(u) = u²/12

Integration is the reverse of differentiation

a. Since we want to find the substitution in order to evaluate the following integrand ∫[x/(6x² + 5)²]dx, we proceed as follows

In the integrand ∫[x/(6x² + 5)²]dx, we see that the other function is the polynomial in the denominator which is (6x² + 5). So, we make the substitution u =  (6x² + 5)

b. To rewrite the integrand in terms of u so that ∫[x/(6x² + 5)²]dx is int he form ∫f(u)du, we proceed as  follows

Since  integrand ∫[x/(6x² + 5)²]dx and u = 6x² + 5. Differentiation u with respect to x, we have that

du/dx = d(6x² + 5)/dx

= d(6x²)/dx + d5/dx

= 12x + 0

= 12x

So, du/dx = 12x

xdx = du/12

So, substituting this into the integrand, we have that

∫[x/(6x² + 5)²]dx = ∫[x/u²]dx

= ∫[xdx/u²]

= ∫[du/12/u²]

=  ∫[du/12u²]  

So, comparing  ∫[f(u)du]  = ∫[du/12u²]  

So, f(u) = u²/12

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Answer:

[tex]f(u)=\dfrac{1}{12u^5}[/tex]

Step-by-step explanation:

Integration by substitution is a technique used to simplify the integration of complex functions. It involves writing part of the function in terms of a new variable u, where u is some function of x.

Given integral:

[tex]\displaystyle \int \dfrac{x}{(6x^2+5)^5}\; \text{d}x[/tex]

Substitute u for 6x² + 5.

Differentiate u with respect to x and rearrange the equation to isolate dx:

[tex]\dfrac{\text{d}u}{\text{d}x}=12x \implies \text{d}x=\dfrac{1}{12x}\; \text{d}u[/tex]

Substitute the expressions for u and dx into the original expression to rewrite the original integral in terms of u and du:

[tex]\begin{aligned}\displaystyle \int \dfrac{x}{(6x^2+5)^5}\; \text{d}x &= \int \dfrac{x}{u^5} \cdot \dfrac{1}{12x}\; \text{d}u\\\\&= \int \dfrac{1}{12u^5}\; \text{d}u\\\\\end{aligned}[/tex]

Therefore:

[tex]f(u)=\dfrac{1}{12u^5}[/tex]

The interest paid for the loan is $1748

Given that there is a 6.1% interest rate for a loan of $28,654 in student loan debt pay in the first year,

We need to find the interest paid for the same.

So,

Simple Interest = principal × time × rate / 100

= 28654 × 1 × 6.1 / 100

= 28654 × 0.061

= 1747.894

= 1748

Hence the interest paid for the loan is $1748

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The runner for which there is a proportional relationship between the of training and the amount of time spent running is given as follows:

D. Waverley.

A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other.

The equation that defines the proportional relationship is given as follows:

y = kx.

In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.

Waverley is the only runner for which the situation is modeled by a proportional relationship, as for each input, the output is 30 times the input.

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The complete polynomial is f(x) = 2x⁴ - 3x² - 6 and the values are n = 4 and a = -3

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

This means that

f(1) = 7

f(-3) = 129

So, we have

f(1) = 2(1)ⁿ + a(1)² - 6

f(-3) = 2(-3)ⁿ + a(-3)² - 6

Evaluate

f(1) = 2 + a - 6

f(-3) = 2(-3)ⁿ + a(-3)² - 6

Recall that

f(1) = -7 and f(-3) = 129

So, we have

2 + a - 6 = -7

2(-3)ⁿ + 9a - 6 = 129

This gives

a = -3

Recall that

2(-3)ⁿ + 9a - 6 = 129

So, we have

2(-3)ⁿ + 9(-3) - 6 = 129

2(-3)ⁿ = 162

Divide by 2

(-3)ⁿ = 81

Solve for n

n = 4

So, the complete polynomial is f(x) = 2x⁴ - 3x² - 6

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Let's start by simplifying the left side of the inequality:

3(x+3) + 12 <= 3x + 28

3x + 9 + 12 <= 3x + 28

3x + 21 <= 3x + 28

Subtracting 3x from both sides, we get:

21 <= 28

This is a true statement, which means that the inequality is true for all values of x. In other words, there are infinitely many solutions.

To represent this graphically, we can draw a number line and shade in all values of x for which the inequality is true. Since it's true for all values of x, we shade in the entire number line:

<=======()------------------->

In this number line, the open circle () indicates that the inequality is not true for that particular value (in this case, there is no specific value for x that makes the inequality false). The arrow indicates that the inequality is true for all values of x to the left and right of the open circle.

In summary, the inequality 3(x+3)+12 <= 3x+28 is true for all values of x, and there are infinitely many solutions.

I'm 15 BTW