Circle D is inscribed with triangle A B C. The measure of arc A B is 76 degrees. Point E is on the circle between points B and C.
What is the measure of arc BEC in circle D?

134°
150°
209°
210°

The total cost of 35 T-shirts, 45 pairs of shorts, and 25 windbreakers is $973.75.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Cost of 1 T-shirt = $7.50

Cost of 35 T-shirts = 7.50 x 35

                                = 262.5

Cost of 1 Shorts = $9.00

Cost of 45 T-shirt = 9.00 x 45

                             = 405

Cost of 1 windbreakers = $12.25

Cost of 25 windbreakers = 12.25 x 306.25

So, The total cost of 35 T-shirts, 45 pairs of shorts, and 25 windbreakers

= 262.5+405+306.25

=  $973.75

Hence Her total cost is $973.75.

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Answer:  [tex]8\sqrt{2}[/tex]

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

Work Shown:

x = length of each leg

Use the pythagorean theorem to get...

[tex]a^2+b^2 = c^2\\\\x^2+x^2 = 16^2\\\\2x^2 = 256\\\\x^2 = 256/2\\\\x^2 = 128\\\\x = \sqrt{128}\\\\x = \sqrt{64*2}\\\\x = \sqrt{64}*\sqrt{2}\\\\x = 8\sqrt{2}\\\\[/tex]

Or as an alternative path, you can divide the hypotenuse by [tex]\sqrt{2}[/tex] and then rationalize the denominator.

Both of these methods apply to 45-45-90 triangles only.

Answer:

[tex]8\sqrt{2}[/tex]

Step-by-step explanation:

We can sum the angles in a triangle to 180°:

m<D + m<E + m<F = 180°

m<D + 90° + 45° = 180°

m<D = 45°

Therefore, the triangle is an isosceles right triangle, since the base angles, <F and <D are the same measure. Because the triangle is isosceles, the legs are congruent, meaning that

DE = EF

We can use the Pythagorean Theorem([tex]a^{2} + b^{2} = c^{2}[/tex]) and plug in 16 as c, and DE and EF as a and b:

[tex]DE^{2} + EF^{2} = 16^{2}[/tex]

Since DE is the same as EF, we can substitute it in:

[tex]DE^{2} + DE^{2} = 256\\2DE^{2} = 256\\DE^{2} = 128\\DE = \sqrt{128}[/tex]

The square root of 128 is the same as [tex]8\sqrt{2}[/tex] since 128 can be factored into 64 x 2. So [tex]8\sqrt{2}[/tex] is the answer.

If you are looking for an easier way to do this, once you are able to recognize DEF is an isosceles triangle, you can say [tex]DE \times \sqrt{2} = 16[/tex] as this applies to all isosceles right triangles. This simplifies to:

[tex]DE = \frac{16}{\sqrt{2}} \\DE = \frac{16}{\sqrt{2} } \times \frac{\sqrt{2}}{\sqrt{2} } \\DE = \frac{16\sqrt{2} }{2} \\DE = 8\sqrt{2}[/tex]

[tex]~~(x^2 -3x)^2 -14(x^2 -3x) +40\\\\=u^2-14u+40~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~;[\text{Let}~ u = x^2 -3x]\\\\=u^2 - 10u-4u +40\\\\=u(u-10)-4(u-10)\\\\=(u-4)(u-10)\\\\=(x^2 -3x -4)(x^2 -3x -10)~~~~~~~~~~~~~;[\text{Substitute back}~ u = x^2 -3x]\\\\=(x^2 -4x+x-4)(x^2 -5x+2x-10)\\\\=\textbf{[}x(x-4) +(x-4) \textbf{]} \textbf{[}x(x-5) +2(x-5) \textbf{]} \\\\=(x+1)(x-4)(x+2)(x-5)[/tex]

Answer:  [tex]7\text{Ln}\left(e^{2x}+10\right)+C[/tex]

This is the same as writing 7*Ln( e^(2x) + 10) + C

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

Explanation:

Start with the equation [tex]u = e^{2x}+10[/tex]

Apply the derivative and multiply both sides by 7 like so

[tex]u = e^{2x}+10\\\\\frac{du}{dx} = 2e^{2x}\\\\7\frac{du}{dx} = 7*2e^{2x}\\\\7\frac{du}{dx} = 14e^{2x}\\\\7du = 14e^{2x}dx\\\\[/tex]

The "multiply both sides by 7" operation was done to turn the 2e^(2x) into 14e^(2x)

This way we can do the following substitutions:

[tex]\displaystyle \int \frac{14e^{2x}}{e^{2x}+10}dx\\\\\\\displaystyle \int \frac{1}{e^{2x}+10}14e^{2x}dx\\\\\\\displaystyle \int \frac{1}{u}7du\\\\\\\displaystyle 7\int \frac{1}{u}du\\\\\\[/tex]

Integrating leads to

[tex]\displaystyle 7\int \frac{1}{u}du\\\\\\7\text{Ln}\left(u\right)+C\\\\\\7\text{Ln}\left(e^{2x}+10\right)+C\\\\\\[/tex]

Be sure to replace 'u' with e^(2x)+10 since it's likely your teacher wants a function in terms of x. Also, do not forget to have the plus C at the end. This is a common mistake many students forget to do.

To verify the answer, you can apply the derivative to it and you should get back to the original integrand of [tex]\frac{14e^{2x}}{e^{2x}+10}[/tex]

Answer: (2,-2)

Step-by-step explanation:

Rotating 90 degrees counterclockwise (about the origin) maps (x,y) onto (-y,x), so the answer is N'(2,-2)

A function assigns the values. The function will move down by 3 units.

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

The graph of the function is given below. Now if 3 is replaced by a 0, then the y-intercept of the function will become zero while keeping the slope the same. Therefore, the function will move down by 3 units.

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Answer:

Step-by-step explanation:

Solution

The first step is to simplify the top of the fraction. Subtract 5.6 - 2.7

The numerator (top) and denominator(bottom) are decimal fractions. They are 2.9 for the top and 2.9 for the bottom.

The whole expression reduces down to 1, which is an integer.

Note

You have choices. If you want exact answers you will have to list those choices.

Answer: 1

Answer: C

Step-by-step explanation:

[tex]16x+8 \geq 12x+20\\ \\ 4x+8 \geq 20\\ \\ 4x \geq 12\\ \\ \boxed{x \geq 3}[/tex]

Answer:   [1, infinity)

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

Explanation:

Let's isolate x in the first inequality mentioned.

x + 7 ≥ 4

x + 7-7 ≥ 4-7

x ≥ -3

I subtracted 7 from both sides to undo the +7.

Now isolate x in the second inequality. We first add 8 to both sides, then divide both sides by 11.

11x - 8 ≥ 3

11x - 8+8 ≥ 3+8

11x ≥ 11

11x/11 ≥ 11/11

x ≥ 1

------------------

The two solutions we found were

x ≥ -3 and x ≥ 1

Next, draw out a number line with closed circles at -3 and 1. Shade to the right of each closed circle endpoint as you see below.

Notice that the two inequalities overlap for x ≥ 1

In other words, if a number is -3 or larger AND 1 or larger, then the number is 1 or larger.

The two solutions intersect to form x ≥ 1

The inequality x ≥ 1 is the same as 1 ≤ x which is the same as 1 ≤ x < infinity

Then that turns into the interval notation of [1, infinity)

The square bracket includes the endpoint 1.

If needed, use the infinity symbol in place of the word "infinity".

Answer:

[1, ∞)

Step-by-step explanation:

To solve a compound inequality, first separate it into two inequalities and solve them separately:

Solution of Inequality 1:

x + 7 ≥ 4

⇒ x ≥ 4 - 7

⇒ x ≥ -3

Solution of Inequality 2:

11x - 8 ≥ 3

⇒ 11x ≥ 3 + 8

⇒ 11x ≥ 11

⇒ x ≥ 1

As both graphs overlap for x ≥ 1, this is the solution.

Therefore, in interval notation:  [1, ∞)

[tex]15 \div 3( - 2) + | - 10| \\ 5( - 2) + 10 \\ - 10 + 10 \\ 0[/tex]

Hope it helps

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Following the 30% rule of thumb, Sally should only spend a maximum of $900 on her rent

Given Data

Let us find 30% of $3000

= 30/100* $3000

= 0.3*$3000

= $900

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Answer:

The prime factorization of 14 is 2 x 7.

Step-by-step explanation:

The prime factorization of 14 is 2 x 7.

Answer:

14 is a composite number

Step-by-step explanation:

Answer:

They would have $3 dollars left over.

Step-by-step explanation:

If you divide 187 by 4, you get 46.75. But if you look again, you can see that the remainder is 3 and it can confirm that it is the left over money that the club has now after buying as many ice cream cartons as possible.

Answer:

(3)+1. 12-2=9+1 so 9 is the answer

Answer:

6.5 x 10^7

Step-by-step explanation:

give brainliest, please!

hope this helps :)

If he is not eligible for Roth IRAs, then he cannot contribute to Roth IRAs. However, he can contribute $3,330 monthly under his company's Matching Program.

The Individual Retirement Account to which employees in the United States can contribute after-tax earnings is called the Roth IRA.

Under its governing principles, certain individuals whose annual income exceeds stipulated amounts are INELIGIBLE to contribute.

Recall that the question indicates that his company offers a matching program with a ratio 1:1 up to 3% of his annual salary.

Since his annual salary is $111, 000,

3% x 111,000 = 3,330.

This means that annually, the total matching contribution due to Adrian would be:

3,330 x 2 = 6, 660.

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The amount that the home will be worth after 7 years is  $457763.67

The geometric sequence is sometimes called the exponential sequence. The formula for calculating the nth term of an arithmetic sequence is expressed as:

Tn = ar^n-1

where

a is the first term = 120,000

r is the common ratio = 150000/120000 = 1.25

Required

7th term

Substitute

T7 = 120,000(1.25)^7-1
T7 = 120,000(1.25)^6

T7 = 120,000(3.8147)

T7 = $457763.67

Hence the amount that the home will be worth after 7 years is  $457763.67

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Answer:

(c) $457,763.67

Step-by-step explanation:

hope this helps:)

For the given function h(x), we have:

a) at x = -2 and x = 2.

b) y = 0 and y = 3.

First, we want to get the values of x at which we have maximums. To do that, we need to see the value in the horizontal axis at where we have maximums.

By looking at the horizontal axis, we can see that the maximums are at:

x = -2 and at x = 2.

Now we want to get the maximum values, to do that, we need to look at the values in the vertical axis.

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The limit of the given expression lim x → 0 [4eˣ/2 − 4 − 2x − 12x² +  x³] is determined as -2.

The limit of the given expression is calculated as follows;

lim x → 0 [4eˣ/2 − 4 − 2x − 12x² +  x³]

= (4e⁰)/2 - 4 - 2(0) - 12(0) + (0)

= (4)/2 - 4

= 2 - 4

= - 2

Thus, the limit of the given expression lim x → 0 [4eˣ/2 − 4 − 2x − 12x² +  x³] is determined as -2.

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Answer:

Graphs can be used to represent functions

The value of a is less than 0.

The function is given as:

The parent function of f(x) is:

So, by comparison:

The function becomes:

Next, we identify the vertex (in this case, the vertex is the minimum point on the graph)

So, we have:

Substitute these values in

So, the function becomes

From the graph, we have the following point;

So, the function becomes

Subtract 2 from both sides

Square both sides

Divide both sides by -9

So, we have:

-1 is less than 0.

Hence, the value of a is less than 0.

Step-by-step explanation:

Answer:

The value of a in this function is 0

Step-by-step explanation:

The given function is

[tex]f(x) = a(x + k)^\frac{1}{n} + c.[/tex]

Here , f(x) is y = [tex]x^{\frac{1}{2} }[/tex] So , n = 2.

By substituting the value we get the function :

[tex]f(x) = a(x + k)^\frac{1}{2} + c.[/tex]

The vertex of the graphs are : (k, c) = (-5 ,2)

The function becomes:

[tex]f(x) = a(x + 5)^\frac{1}{2} + 2[/tex]

The following point on the graph shows : (x, y) = (-4 , 5)

The function becomes:

[tex]5 = a(-4+ 5)^\frac{1}{2} + 2\\5 = a(-9)^\frac{1}{2} + 2\\\\\3 = a(-9)^{\frac{1}{2} }(Subtract 2 from both side )\\\\9 = a (-9) ( Square both sides) \\\\-1 =a ( Divide both side by -9)\\[/tex]

a = -1

Here , -1 is less than zero

Hence , the value of a is less than o.

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Answer: The correct answer is A, [tex](-2)^{2}[/tex].

Step-by-step explanation:

A negative multiplied with another negative is a positive. Squaring is multiplying an integer by itself. Thus, it would look like -2×-2, which is equal to 4. I hope this helps!! :)

The midpoint theorem simply states that the line segment that joins the two sides of the triangle is parallel to the third side.

Your information is incomplete. Therefore, an overview of the theorem will be given. It should be noted that the midpoint theorem states that the line drawn through the mid point of one side of the triangle is parallel to another side.

To find the midpoint, one can measure the distance between the two end points and divide the results by 2.

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Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. The correct option is B.

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.

When the indicated operation 4R₁ → R₁ is applied then the matrix will be,

[tex]\left[\begin{array}{ccc}1&2&0\\-2&-1&3\end{array}\right] \rightarrow \left[\begin{array}{ccc}4&8&0\\-2&-1&3\end{array}\right][/tex]

Hence, the correct option is B.

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Answer:

B, I solved then used interval notion to convert it.

Answer:

the answer is b

Answer:

the answer is b

Answer:

y = 15/-4 + 2.5x

Step-by-step explanation:

10x - 4y = 15

-4y = 15 - 10x

y = 15/-4 + 2.5x

The area of the shaded region will be 46.17 ft.²The number of unit squares that cover the surface of a closed-form is the figure's area.

The space filled by a flat form or the surface of an item is known as the area.

The number of unit squares that cover the surface of a closed-form is the figure's area. Square centimeters and other similar units are used to measure area.

Given data;

Semicircle radius , r = 9 ft.

The height of the triangle, h=r=9 ft

The triangle is located where it is inscribed in the semicircle. The diameter of the semicircle is given as b, the base length of the triangle.

The diameter of the semicircle = 2 × The radius of the semicircle

D=2r

D= 2 × 9 ft

D= 18 ft.

Triangle base length,b = D= 18 ft.

The area of the triangle is found as;

[tex]\rm A= \frac{1}{2}bh \\\\ A = \frac{1}{2} \times 18 ft. \times 9 ft. \\\\ A = 81 \ ft^2[/tex]

[tex]A_{semi}={\rm \frac{A_{circle}}{2}} \\\\ A_{semi}= \frac{\pi \ r^2}{2}\\\\\ A_{semi}= \frac{3.14 \times 9^2}{2} \\\\ A_{semi} = 127.17 ft^2[/tex]

The area of the shaded region is;

a= 127.17 ft.² - 81 ft.²

a = 46.17 ft.²

Hence,the area of the shaded region will be 46.17 ft.²

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Answer:

here ....x = 2 and y = 3

[tex] = xy - y + x \times x[/tex]

[tex] = 2 \times 3 - 3 + 2 + 2 \times 2[/tex]

[tex] = 6 - 3 + 2 + 4[/tex]

[tex] = 12 - 3[/tex]

[tex] = 9[/tex]