4. Gilbert generated the shape below on a computer. The shape contains an isosceles triangle with a
height of 8 centimeters. Determine the area of the shape to the nearest tenth of a square centimeter.
10 cm
8 cm
12 cm
10 cm

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 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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[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{0}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{0}-\stackrel{y1}{(-3)}}}{\underset{\textit{\large run}} {\underset{x_2}{2}-\underset{x_1}{4}}} \implies \cfrac{0 +3}{-2} \implies \cfrac{ 3 }{ -2 } \implies - \cfrac{3}{2}[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-3)}=\stackrel{m}{- \cfrac{3}{2}}(x-\stackrel{x_1}{4}) \implies y +3 = - \cfrac{3}{2} ( x -4) \\\\\\ y+3=- \cfrac{3}{2}x+6\implies {\Large \begin{array}{llll} y=- \cfrac{3}{2}x+3 \end{array}}[/tex]

Answer:

y = -1.5x + 3

Step-by-step explanation:

gradient = (-3 - 0) / (4 - 2) = -3/2 = -1.5.

equation on line through two points is given by

y - y1 = m (x - x1)

where y1 and x1 are the coordinates of the point and m is the gradient.

we can choose either point to use in the equation.

y - 0 = -1.5 (x - 2) = -1.5x + 3

y = -1.5x + 3

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 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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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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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.

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 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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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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Answer:

Step-by-step explanation:

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

400 / 48 = .12 is 12%

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:

356.89$

Step-by-step explanation:

259.9 + 62.99 = 322.98, 8.25% + 2.25 = 10.5 tax rate... So 322.98 + 10.5% = 356.89$

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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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 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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Answer:

Step-by-step explanation:

Answer:

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

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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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Denis was  told  to write the first non-objective statement by the arising trend of Neotraditionism.            

As he explains in his composition" The description of Neotraditionism,"" The  thing of Neotraditionism is to make  commodity new that isn't a  dupe, nor a simple extension, nor a parody of the old"( Denis, 1911). He believed that this movement  needed a new language of art, one that wasn't tied to emblematic  forms.

Kandinsky's  appearance atnon-objective  oil was  told  by his spiritual beliefs and his desire to express the inner nature of  effects. As he writes in Concerning the Spiritual in Art," The artist must have  commodity to say, for mastery over form isn't his  thing but rather the adapting of form to its inner meaning"( Kandinsky, 1977,p. 10). He believed that art should be a spiritual expression and that the inner world of the artist should be  restated into visual language.  

Kandinsky wrote  considerably about color in Concerning the Spiritual in Art. He believed that color had its own language and could convey  feelings and ideas. As he writes," Color is a means of  plying direct influence upon the soul. Color is the keyboard. The eye is the hammer. The soul is the piano, with its  numerous strings"( Kandinsky, 1977,p. 43). He believed that colors could be arranged in a way that would produce a symphony of  feelings in the bystander.

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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

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: D. Parallelogram

Step-by-step explanation: Step 1. Input all the points on a graph, there's not really much to it, sorry if I didn't help but the answer is D

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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Answer:

9 - 5 (x + 4) = 12 (x + 1)

-5x - 11 = 12x + 12

-5x - 11 + 11 = 12x + 12 + 11

-5x = 12x + 23

-5x - 12x = 12x + 23 - 12x

x = -23/17

Answer:

x=−23/17

Step-by-step explanation:

Distribute: 9-5(x+4) = 12(x+1)

= 9+−5x+−20=12x+12

Combine like term 9&-220:

−5x+−11=12x+12

Subtract 12x:

−5x−11−12x=12x+12−12x

=−17x−11=12

Add 11:

−17x−11+11=12+11

=−17x=23

Divide by -17:

−17x/-17=23/-17

x=−23/17

.

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.