Given the function f(x) = 4|x – 5| + 3, for what values of x is f(x) = 15?

Answer:

m∠LTE = 110

Step-by-step explanation:

1. add up all of the arcs.

2x+3x+4x-8+x-12

2. all of the arcs equal 360

2x+3x+4x-8+x-12=360

3. Find x

10x-20=360, x=38

4. angle LTE is equal to half of the sum of the intercepted arcs.

0.5(arc LE +GF)

5. plug in LE +GF with x

.5(76+144)

Answer:

m∠LTE = 110°

Step-by-step explanation:

We know that sum of all arcs of a circle is 360°

Therefore [tex]m(arcAL)+m(arcLG)+m(arcGF)+(mFE)=360[/tex]

Now we put the values of each arc

[tex](2x)+(3x)+(4x-8)+(x-12)=2x+3x+4x+x-8-12=10x-20=360[/tex]

10x = 360 + 20

10x = 380

[tex]x=\frac{380}{10}[/tex]

x = 38

Now from the theorem of intersecting chords in a circle

Measure of ∠LTE = [tex]\frac{1}{2}[m(arcEL)+m(arcGF)][/tex]

m(arc EL) = 2x = 2×38 = 76°

m(arc GF) = (4x - 8) = (4×38 - 8) = (152 - 8) = 144°

Now we can get the measure of ∠LTE

m∠LTE = [tex]\frac{1}{2}(76 + 144)=\frac{220}{2}=110[/tex]

Therefore m∠LTE = 110° is the answer.

The answer is b exponential

Answer:

v(0) = 32,000 . . . dollars

v(13) = 16,427 . . . dollars

Step-by-step explanation:

The initial value is the value of the function for t=0. Put that into the formula and evaluate.

v(0) = 32,000(0.95^0) = 32,000 . . . . dollars

__

The value after 13 years is the function value for t=13. Put that into the formula and evaluate.

v(13) = 32,000(0.95^13) ≈ 32,000·0.513342 ≈ 16,427 . . . . dollars

Answer: 23 - 6 = x

x = 17

Step-by-step explanation:

6 + x = 23

x = 23 - 6

23 - 6 = 17

x = 17

6 + 17 = 23

Hope this helps!

Answer:

6+x=23

Step-by-step explanation:

So, the number you need to find is x, so x plus 6 equals 23 (the sum of the two numbers).

Hope this helped :)

Answer:

  -57

Step-by-step explanation:

Put the value of x where x is and do the arithmetic.

  -7·9 +6 = -63 +6 = -57

x2 - 12x - 12 = 0

(x - 6)2 - 48 = 0

(x - 6)2 = 48

Hence, the answer is (B).

Answer:

B

Step-by-step explanation:

given

x² - 12x - 5 = 7 ( add 5 to both sides )

x² - 12x = 12

To complete the square

add (half the coefficient of the x- term )² to both sides

x² + 2(- 6)x + (- 6)² = 12 + (- 6)²

x² + 2(- 6)x + 36 = 12 + 36 ← complete the square on the left side

(x - 6)² = 48 → B

Answer:

The solution in the attached figure

Step-by-step explanation:

Let

x------> the numbers of boxes of popcorn sold

y-----> the number of boxes of pretzels sold

we know that

[tex]2x+5y\geq 500[/tex] ----> inequality that represent the situation

using a graphing tool

The solution is the shaded area above the solid line [tex]2x+5y=500[/tex] between the positive values of x and the positive values of y

see the attached figure

We aim to earn $500+, selling popcorn at $2/box and pretzels at $5/box. Equation: [tex]\( y \geq \frac{500 - 2x}{5} \)[/tex], where ( x ) is the number of popcorn boxes.

let's break down the problem step by step:

1. Let's define our variables:

  - ( x ): Number of boxes of popcorn sold

  - ( y ): Number of boxes of pretzels sold

2. We are given the following information:

  - The team earns $2 for every box of popcorn sold.

  - The team earns $5 for every box of pretzels sold.

  - The team wants to earn at least $500 from all sales.

3. We can express the total earnings from selling popcorn and pretzels using the given information:

  - Total earnings from popcorn sales: ( 2x )

  - Total earnings from pretzel sales: ( 5y )

4. Since the team wants to earn at least $500, we can write this as an inequality:

[tex]\[ 2x + 5y \geq 500 \][/tex]

Now, let's solve this inequality for \( y \):

[tex]\[ 2x + 5y \geq 500 \][/tex]

[tex]\[ 5y \geq 500 - 2x \][/tex]

[tex]\[ y \geq \frac{500 - 2x}{5} \][/tex]

So, the number of boxes of pretzels sold, ( y ), should be greater than or equal to[tex]\( \frac{500 - 2x}{5} \).[/tex]

Now, let's plot this inequality on a graph.

- Choose a few values of ( x ) and find the corresponding values of ( y ) using the inequality.

- Plot these points on the graph.

- Draw a line that passes through these points, and it should be a solid line because of the "greater than or equal to" sign.

- Shade the area above the line because ( y ) should be greater than or equal to[tex]\( \frac{500 - 2x}{5} \).[/tex]

Let's choose a few values of ( x ) to plot:

1. When ( x = 0):

[tex]\( y = \frac{500 - 2(0)}{5} = \frac{500}{5} = 100 \)[/tex]

2. When ( x = 100 ):

 [tex]\( y = \frac{500 - 2(100)}{5} = \frac{500 - 200}{5} = \frac{300}{5} = 60 \)[/tex]

3. When ( x = 200 ):

[tex]\( y = \frac{500 - 2(200)}{5} = \frac{500 - 400}{5} = \frac{100}{5} = 20 \)[/tex]

Answer:

(x - 6)(x + 5)

Step-by-step explanation:

You know that in order to get x^2 there has to be two x's so you get:

(x ...)(x...)

Then you also know that two numbers have to multiply together and equal 30 but also have a sume of -1. So you get:

(x - 6)(x + 5)

Answer: [tex](x+5)(x-6)[/tex]

Step-by-step explanation:

To solve the exercise you must keep on mind the following:

- You must find two numbers whose sum is -1 and whose product is -30.

- These numbers would be 5 and -6.

Therefore, you can factor the quadratic equation given in the problem above [tex]x^2-x-30[/tex], as you can see below:

[tex]x^2-x-30\\(x+5)(x-6)[/tex]

Answer:

  85

Step-by-step explanation:

0.350 L × n = 30 L . . . . . where n is the number of bottles.

Divide by 0.350:

  n = (30 L)/(0.350 L) ≈ 85.7

85 bottles can be filled, and one can be partially filled.

_____

Of course, you know the SI prefix milli- means 1/1000, so 350 mL = 350/1000 L = 0.350 L. When you do the division indicated above, ...

  (30 L)/(0.350 L)

the units of liters cancel, and you are left with the number of bottles.

Answer:

  The solids are similar.

Step-by-step explanation:

Every linear dimension of the larger solid is twice that of the smaller solid. Since the scale factor is the same in every direction, the figures are similar.

A) a positive correlation

Answer:

Part 1) [tex]m<OAD=60\°[/tex]

Part 2) [tex]m<DBA=30\°[/tex]

Step-by-step explanation:

Part 1) Find the measure of angle OAD

we know that

OA=OD=radius of the circle

If line AD≅ line AO

then

The triangle AOD is an equilateral triangle

Remember that

An equilateral triangle has the three equal sides and the three internal angles equal (60 degrees each one)

so

[tex]m<OAD=60\°[/tex]

Part 2) Find the measure of angle DBA

we know that

The inscribed angle measures half that of the arc comprising

so

[tex]m<DBA=\frac{1}{2}(arc\ AD)[/tex]

[tex]arc\ AD=m<AOD=60\°[/tex] ----> by central angle

substitute the value

[tex]m<DBA=\frac{1}{2}(60\°)=30\°[/tex]

Answer:

  54 square units

Step-by-step explanation:

A line (red in the attachment) can divide the figure into two triangles and a trapezoid. The formulas for the areas of these are ...

  area of a triangle = (1/2)bh . . . . . where b is the base and h is the height

The triangle on the upper left has a base of 3 and a height of 2, so an area of ...

  upper left triangle area = (1/2)(3)(2) = 3 square units . . . . area shown in red

The triangle on the upper right has a base of 6 and a height of 1, so an area of ...

  upper right triangle area = (1/2)(6)(1) = 3 square units . . . . area shown in yellow

___

The formula for the area of a trapezoid is ...

  area of a trapezoid = (1/2)(b1 +b2)h . . . . where b1 and b2 are the lengths of the parallel bases, and h is the height

The trapezoid has an upper base length of 9 and a lower base length of 7, and a height of 6, so its area is ...

  area of bottom trapezoid = (1/2)(9 + 7)(6) = 48 square units . . . . area shown in green

___

Then the total area of the figure is the sum of the areas of its non-overlapping parts:

  total area = upper left triangle area + upper right triangle area + trapezoid area

  = (3 + 3 + 48) square units = 54 square units

Answer:

104

Step-by-step explanation:

50+50-25*0+2+2

Order of operations....50+50-0+2+2

This equals to 100+2+2

Then you get the answer of 104.

I hope you understand..

Answer:

104

Step-by-step explanation:

Answer:

Wood family: 35 hours

Roberts family: 25 hours

Step-by-step explanation:

Let w represent the number of hours the Woods family ran their sprinkler. Then 60-w is the number of hours the Roberts family ran theirs. The total water usage (in liters) was ...

25w + 15(60-w) = 1250

10w = 350

w = 35 . . . . . . Wood family time (hours)

60-w = 25 . . . Roberts family time (hours)

___

Check

(35 h)·(25 L/h) + (25 h)·(15 L/h) = 875 L + 375 L = 1250 L . . . . answer checks OK

Answer:

C. $1246.82

Step-by-step explanation:

Using the factor shown in the table for a 25-year loan at 5.25%, the calculated payment is ...

5.992·(244.8·0.85) = 1246.82

The factor of 0.85 on the home price represents the effect of subtracting 15% from the price to get the loan value. Of course, the home price is the number of thousands, so is 244.8 thousand.

_____

If you do the calculation, rather than use a factor from a table, you get a mortgage payment value of $1246.91. This suggests that the numbers in the table need more significant digits for loan values this high.

Answer:

C is your answer

Answer:

  x = 1

Step-by-step explanation:

Subtract the right side of the equation and simplify:

  9x -4 -6x -2(x +1) +5 = 0

  9x -6x -2x -4 -2 +5 = 0 . . . . . eliminate parentheses

  x -1 = 0 . . . . . . . . . . . . . . . . . . collect terms

  x = 1 . . . . . . . . . . . . . . . . . . . . . add the opposite of the constant

_____

Check

Substitute the value of x where x is found in the equation.

  9·1 -4 -6·1 = 2(1 +1) -5

  9 - 4 - 6 = 2·2 -5

  -1 = 4 -5 . . . . . true. The answer checks OK.

It’s B. The boys were able to cut more than half the yard.

Answer:

A) Together the boys didn't even cut half the yard.

Step-by-step explanation:

The amount cut was ...

1/8 + 1/5 = 5/40 +8/40 = 13/40

This amount is less than half = 20/40, so choice A is appropriate.

_____

You can reason about these fractions several ways:

1. half is 2 1/2 fifths. 1/8 is less than 1/5, so 1/5+1/8 < (2 1/2)/5.

2. half is 4/8. 1/5 is more than 1/8 but is less than 2/8. 1/8 + 1/5 < 3/8 < 1/2

3. 1/5 < 1/4; 1/8 < 1/4; 1/2 = 2/4, so two amounts less than 1/4 cannot be more than 1/2.

Answer:

1) and 2)

Step-by-step explanation:

Let us see the correction in the rest of the statements.

3) p→q represent the original conditional statement.

4) ~q → ~p represents the contrapositive of the original conditional statement

5) contrapositive of the original conditional statement will be ~q → ~p

There is one more implication called Converse of the original conditional statement . It is represented as q→p

Answer:

(4, 4) is the solution to both lines A and B.

Step-by-step explanation:

The solution to a system of equations is the point at which the two lines intersect. Lines A and B intersect at point (4,4). This means (4,4) is the point which makes both equations true for the same values. The correct answer is     "(4, 4) is the solution to both lines A and B."

The MVT guarantees the existence of [tex]c\in(1,3)[/tex] such that

[tex]f(c)=\dfrac{f(3)-f(1)}{3-1}=\dfrac{f(3)-4}2[/tex]

Since [tex]f'(x)\le2[/tex] for all [tex]x\in[1,3][/tex], we have

[tex]\dfrac{f(3)-4}2\le2\implies f(3)-4\le4\implies f(3)\le8[/tex]

so that [tex]V=8[/tex].

The mean value theorem is used to link the average rate of change and the derivative of a function.

The value of V is 8.

The given parameters are:

[tex]\mathbf{f'(x) \le 2}[/tex]

[tex]\mathbf{f(1) = 4}[/tex]

[tex]\mathbf{f(3) \le V}[/tex]

[tex]\mathbf{x \in [1,3]}[/tex]

Mean value theorem states that:

If [tex]\mathbf{f(x)\ is\ continuous\ at }[/tex] [a,b] and

[tex]\mathbf{f(x)\ is\ differentiable\ on }[/tex] (a,b),

Then there is a point c in (a,b), such that:  

[tex]\mathbf{f'(c) = \frac{f(b) - f(a)}{b - a}}[/tex]

From the question, we understand that: f is differentiable

This means that:

[tex]\mathbf{f'(c) = \frac{f(b) - f(a)}{b - a}}[/tex]

So, we have:

[tex]\mathbf{f'(c) = \frac{f(3) - f(1)}{3 - 1}}[/tex]

[tex]\mathbf{f'(c) = \frac{f(3) - f(1)}{2}}[/tex]

Substitute 4 for f(1)

[tex]\mathbf{f'(c) = \frac{f(3) -4}{2}}[/tex]

Recall that: [tex]\mathbf{f'(x) \le 2}[/tex]

The equation becomes

[tex]\mathbf{\frac{f(3) -4}{2} \le 2}[/tex]

Cross multiply

[tex]\mathbf{f(3) -4 \le 4}[/tex]

Add 4 to both sides

[tex]\mathbf{f(3) \le 8}[/tex]

From the question, we have: [tex]\mathbf{f(3) \le V}[/tex]

By comparisons;

[tex]\mathbf{V = 8}[/tex]

Hence, the value of V is 8.

Read more about mean value theorems at:

brainly.com/question/3957181

The formula to calculate the perimeter of a regular hexagon is P = 6s, where 'P' is the perimeter and 's' is the length of one side. It's crucial to use consistent units when measuring and calculating.

In mathematics, the perimeter of a shape is the distance around its borders. For a regular hexagon, which is a six-sided polygon with all sides of equal length, the perimeter is calculated by simply multiplying the length of one side by the number of sides. Therefore, if you know the length of a side, you can calculate the perimeter of the regular hexagon using the formula:

P = 6s

Where 'P' is the perimeter and 's' is the length of a side of the hexagon. It's important to use consistent units when making these measurements and calculations to ensure accuracy.

https://brainly.com/question/14338151

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The perimeter of a regular hexagon can be calculated using the formula: P = 6 * S, where P represents the perimeter and S represents the length of a side.

In mathematics, the perimeter of a shape is the distance around its borders. For a regular hexagon, which is a six-sided polygon with all sides of equal length, the perimeter is calculated by simply multiplying the length of one side by the number of sides.  The formula that describes the perimeter of a regular hexagon as a function of the length of its side is:

P = 6 * S

Where P represents the perimeter and S represents the length of a side.

Since a regular hexagon has six equal sides, you can multiply the length of a side by 6 to find the total perimeter.

https://brainly.com/question/32101495

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so the difference is 300 - 230 = 70.

now, if we take 230 to be the 100%, what is 70 off of in percentage?

[tex]\bf \hspace{34em}|\\\\ \begin{array}{ccll} amount&\%\\ \cline{1-2} 230&100\\ 70&x \end{array}\implies \cfrac{230}{70}=\cfrac{100}{x}\implies \cfrac{23}{7}=\cfrac{100}{x} \\\\\\ 23x=700\implies x=\cfrac{700}{23}\implies x\approx 30.43[/tex]

Answer:23%

Step-by-step explanation:

300-230=70

70/300=0.23(3 goes on forever)

So 23%

subtract the original with the decreased value, then divide the answer you get with 300. That should equal 0.23 or 23%

First find the gradient of the perpendicular line. You do this by taking the negative reciprocal of the gradient of the first line (y= 1/4x +3):

Perpendicular gradient = negative reciprocal of [tex]\frac{1}{4}[/tex] = -4

Next, you substitute the x and y values into the following equation and solve:

y = -4x +c

-2 = -4(-4) +c

-2 = 16 + c

-18 = c

Substitute c back into the equation above to get the final answer:

y = -4x -18

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

Answer

y = -4x - 18

Whenever you can invert a function, you have that the graphs of [tex]f(x)[/tex] and its inverse [tex]f^{-1}(x)[/tex] are reflected with respect to the line [tex]y=x[/tex]

So, given any point on the graph of [tex]f^{-1}(x)[/tex], you can simply swap its coordinates to get the correspondent point on the original function [tex]f(x)[/tex]

As an example, all exponential functions pass through the point [tex](0,1)[/tex], while all the logarithmic functions pass through the point [tex](1,0)[/tex]

Answer: switch x and y coordinates

Step-by-step explanation:

Answer:

  B. 125

Step-by-step explanation:

If you compute the actual volume as the product of the area of the triangle and the length of the piece, you get ...

  V = Bh = (1/2)(14.4 mm)(2.1 mm)·(8.25 mm) = 124.74 mm

That is closest to choice B, 125 mm.

___

You can estimate the volume by rounding the dimensions. The triangle can be considered to be a rectangle of the same base width and half the height, so you are looking to estimate the product ...

  (8.25 mm)(14.4 mm)(1.05 mm)

That's about 8 × 15 × 1 = 120 . . . . mm³.

Certainly, this is an estimate sufficiently close to allow you to choose the correct answer.

Answer:

So, marta will sprint 225 yards.

Step-by-step explanation:

Area of parallelogram= b*h

Given: Area = 776.5 square yards

Base = 34.5 yards

Area = b* h

776.5 = 34.5 * h

776.5/34.5 =h

=> h = 22.5

Since sprint is the same distance as of height of park so,

Distance of  1 sprint = 22.5 yards

Distance of  10 sprints = 10 * 22.5 = 225 yards

Answer:

hi

Step-by-step explanation:

Answer:

See the attachment

Step-by-step explanation:

A slope of -3/5 means the line drops 3 units for each 5 units it goes to the right. Then you can find another point on the line by going 5 uints to the left (to x=-2) and 3 units up (to y=1).

Plot the given point and the one just computed and draw the line through them.

Alright, so here we have a cone and a cylinder. The cone has a height of 12. The cylinder has a height of 10.5. Both shapes, because they're on top of each other, have a diameter of 26 or a radius of 13.

Equation for a cylinder: [tex]V_{cylinder} = \pi r^{2} h[/tex]

Equation for a cone: [tex]V_{cone} = \frac{1}{3} \pi r^{2} h[/tex]

We're going to add both of the volumes of these shapes as soon as we find them.

Cylinder:

[tex]V_{cylinder} = \pi r^{2} h\\= \pi (13)^{2} (10.5)\\\approx 5574.756[/tex]

Cone:

[tex]V_{cone} = \frac{1}{3} \pi r^{2} h\\= \frac{1}{3} \pi (13)^{2} (12)\\\approx 2123.717[/tex]

Add both values: 2123.717 + 5574.756 = 7698.473 cm³.

Hope this was helpful, let me know if I missed anything!

Answer:

7698.473 cm³.

Step-by-step explanation:

I need to write a 5-paragraph eassy, so please help me it is base on an article name "Schools in Maryland Allow Elementary Students to Carry Cellphones, by Amanda Lenhart, The Washington Post" here are some pic. I just need help writing two paragraph. I already have my Introduction, Body Paragraph #1 and my Body paragraph #2 just need my Body paragraph #3 and my Conclusion I will give brainlis and 30 pnt.

Prompt:

Write an argumentative essay answering the questions: Should students be allowed to carry cellphones on campus? You must support your claim with evidence from the text. You may also use relevant examples from your own experience, observations, and other readings.

Directions:

Before you begin, read the text below, which presents information about the advantages and disadvantages of carrying a cell phone at school. Use the Student Writing Checklist on the back of this page to plan and write a multi-paragraph essay that addresses the prompt. Use your own words, except when quoting directly from the text.

Answer:

Ron: 6+2√5 days ≈ 10.47 days

Lee: 2+2√5 days ≈ 6.47 days

Step-by-step explanation:

Let L represent the number of days it takes Lee to frame a cabin. Then it take L+4 days for Ron to frame it. Working together, they take 4 days. Then their rates, in cabins per day, add up as ...

1/L + 1/(L+4) = 1/4

Multiplying by the product of denominators, we get ...

4(L+4) +4L = L(L+4)

Subtracting the left side gives ...

L^2 -4L -16 = 0

Completing the square, we can write this as ...

L^2 -4L +4 = 20

(L -2)^2 = 20

L = 2 + √20 = 2 +2√5 ≈ 6.47

Lee takes 2+2√5 ≈ 6.47 days to frame a cabin.

Ron takes 6+2√5 ≈ 10.47 days to frame a cabin.