If m<BEG = (19x + 3)° and m<EGC = (m<GCB + 4x)°, which of the following statements is true about quadrilateral BEGC? Select all that apply.

A. x=4
B. m<BEG = 72°
C. m<EGC = 120°
D. m<GCB + m<CBE = 180°
E. m<BEG + m<EGC = 230°
F. The sum of all exterior angles of BEGC is equal to 360°.​

subtract 17, not 22, from both sides. 17 – 17 = 0 and 22 – 17 = 5. The answer should be x = 5.

Step-by-step explanation:

An equation between two variables that gives a straight line when plotted on a graph.

Lester made mistake in first steps he subtract 22 from the equation.

The correct solution of the equation is x =5.

Lester was solving an equation but he made a mistake.

The given equation is;

[tex]\rm x + 17 = 22[/tex]

An equation between two variables that gives a straight line when plotted on a graph.

The equation represents the linear equation and to solve the equation following all the steps given below.

Then,

The correct way to solve the equation is,

[tex]\rm x + 17 = 22\\\\x+17-17 = 22-17\\\\x +0=5\\\\x=5[/tex]

Hence, the correct solution of the equation is x =5.

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Answer:

(x, y) → (−x, y)(x, y)

Step-by-step explanation:

To do a transformation over the Y-axis, you just have to change the sign on the x in order to create a matching point on the other side of the Y axis, for example if you wish to make a reflection of the point (8,9), the reflection over the Y axis would be (-8,9), the same with X and Y, if you wish to make a reflection of (x,y) you just change the sign of the x like this: (-x,y)

The correct answer is option 1. [tex](x,y) \rightarrow (-x,y)[/tex]

To determine which transformation represents a reflection over the y-axis, we examine the options provided:

A reflection over the y-axis transforms the x-coordinate of a point to its opposite while keeping the y-coordinate unchanged. Therefore, the correct transformation is [tex](x,y) \rightarrow (-x,y)[/tex].

Reflection over the y-axis results in the point (x, y) being mapped to (−x, y). This is because the x-coordinate is negated while the y-coordinate remains the same.

The complete question is:

Which transformation represents a reflection over the y-axis?

1. [tex](x,y) \rightarrow (-x,y)[/tex]

2. [tex](x,y) \rightarrow (x,-y)[/tex]

3. [tex](x,y) \rightarrow (y,x)[/tex]

4. [tex](x,y) \rightarrow (-y,x)[/tex]

Answer:

The answer is 31.5

Step-by-step explanation:

Similar triangles have their corresponding sides to be in equivalent ratios

The length of PR is 31.5 inches

△WKT∼△NRP  means that, the following sides are similar

So, we have the following equivalent ratio

[tex]WK : TK = NR : PR[/tex]

From the complete question, we have the following parameters:

So, the ratio becomes

[tex]14 : 18 = 24.5 : PR[/tex]

Express the ratio as fraction

[tex]\frac{18}{14}= \frac{PR}{24.5 }[/tex]

Multiply both sides by 24.5

[tex]\frac{18}{14} \times 24.5= PR[/tex]

This gives

[tex]\frac{441}{14} = PR[/tex]

Divide 441 by 14

[tex]31.5 = PR[/tex]

Rewrite the above equation as

[tex]PR = 31.5[/tex]

Hence, the length of PR is 31.5 inches

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Slope intercept formula: y = mx + b where m equals slope and b equals the y-intercept.

Answer: y = -6x + 3

Final answer:

The equation in slope-intercept form for a line with y-intercept 3 and slope -6 is y = -6x + 3, showing a line decreasing by 6 units in y for each unit increase in x.

Explanation:

To write an equation in slope-intercept form, which is y = mx + b, we need to know the slope (m) and the y-intercept (b). In this case, we have a y-intercept of 3 and a slope of -6. Plugging these values into the slope-intercept form, we get the equation of the line:

y = -6x + 3

This equation tells us that the line crosses the y-axis at (0, 3) and for each unit increase in x, the value of y decreases by 6 units, since the slope is negative. This is a direct application of the algebra of straight lines and the concepts of slope and y-intercept.

Answer:

[tex]\frac{\sqrt{51} }{10}[/tex]

Step-by-step explanation:

Using the Pythagorean identity

sin²x + cos²x = 1 ⇒ cosx = ± [tex]\sqrt{1-sin^2x}[/tex], hence

cosΘ = [tex]\sqrt{1-(7/10)^2}[/tex]

        = [tex]\sqrt{1-\frac{49}{100} }[/tex]

        = [tex]\sqrt{\frac{51}{100} }[/tex]

        = [tex]\frac{\sqrt{51} }{\sqrt{100} }[/tex] = [tex]\frac{\sqrt{51} }{10}[/tex]

ANSWER

[tex]f(x) =x^3-6x^2-13x+42[/tex]

EXPLANATION

The zeros of the cubic function is given as:

x=7,x=-3,x=2

This implies that, x-7,x+3,x-2 are factors of the given cubic polynomial function.

We can write the completely factored form as a function of x to get:

[tex]f(x) = (x - 7)(x + 3)(x - 2)[/tex]

We expand to get:

[tex]f(x) = (x - 7)(x^2+ x-6)[/tex]

[tex]f(x) =x^3-6x^2-13x+42[/tex]

This is a cubic function because the highest degree is 3.

Answer:

c. (3.75, 3.5)

Step-by-step explanation:

Let's call the given segment AB, and the dividing point P. Then you want AP:PB = 1:3.

There are a couple of ways you can get there.

1. Recognize that when you subtract the coordinates of A from P, the difference will be 1/4 of the result of subtracting A from B. That is, ...

P-A = (1/(1+3))·(B-A)

We can see that B-A = (6,8) -(3,2) = (3, 6), so 1/4 of that is (3/4, 3/2) = (0.75, 1.5). Adding these values to the coordinates of A gives ...

P = A + (.75, 1.5) = (3.75, 3.5)

__

2. Finish working out the equation above to solve for P:

4(P -A) = B -A

4P = B + 3A

P = (3A + B)/4 . . . . . note the multiplier for A is the relative length of PB and vice versa

P = (3(3, 2) +(6, 8))/4 = (15/4, 14/4) = (3.75, 3.5)

_____

Comment on choosing an answer

You only need to determine one of the coordinates in order to pick the correct answer. Finding both coordinates can help give you assurance that you have worked it out correctly.

15 hours is the answer to this

1.69×5+9.95

Answer:

15 hours.

Step-by-step explanation:

In order to solve this, we just have to create an inequality, for ti to be more convenient for us to work with the first company we shouldn´t be spending more than 19.95 a month, otherwise we would be better off with the second one, so the total would be 19.95, and the base fee is $9.95 for the first ten hours, so X would be the number of extra hours we will use:

[tex]Base+Extra,hours=Budget[/tex]

Now we just insert the values in to the formula:

[tex]10+1.68x=19.95\\[/tex]

We clear X:

[tex]10+1.68x=19.95\\[/tex]

[tex]1.68x=19.95-10\\[/tex]

[tex]1.68x=9.95\\[/tex]

[tex]x=\frac{9.95}{1.69}[/tex]

[tex]x=5.91\\[/tex]

So the as the number of extra hours that we could use without going over the budget is 5.91, and the company wouldn´t charge us the .91, the number of extra hours is 5, plus the base hours, the total number of hours would be 15.

Here is the set up:

We know the given dimensions are increased by the same number.

Let x be that number.

The garden is a rectangle.

Area = length times width.

5m = 5 meters

12m = 12 meters

Area is 120 meters^2.

Here is your equation:

120 = (5 + x)(12 + x)

Take it from here.

He can ask the student to raise their hands and pick them

the teacher can ask them to pick the closest number. the teacher can choose the students with the highest grades.

Answer: 76 child tickets were sold that day.

Step-by-step explanation:

You need to set up a system of equations.

Let be "c" the number of child tickets sold that Wednesday and "a" the number of adult tickets sold that Wednesday.

Then:

[tex]\left \{ {{a+c=173} \atop {9.40a+5.70c=1345.0}} \right.[/tex]

Using the Method of Elimination, you can multiply the first equation by -9.40, then add both equations and finally solve for "c":

[tex]\left \{ {{-9.40a-9.40c=-1626.2} \atop {9.40a+5.70=1345.0}} \right.\\..................................\\-3.7c=-281.2\\\\c=\frac{-281.2}{-3.7}\\\\c=76[/tex]

ANSWER

A.

EXPLANATION

The parent function is

[tex]f(x) = \sqrt[3]{x} [/tex]

This function is transformed to obtain

[tex]g(x) = \sqrt[3]{x + 2} - 4[/tex]

The +2 is a horizontal translation, that shifts the graph of the parent function to the left by 2 units.

The -4 is a vertical translation, that shifts the graph of the parent function down by 4 units.

The correct option is A.

Answer:

A)

Step-by-step explanation:

First we will graph th parent function which is a cube root and we can see it in the attachment #1.

In this excercise there are two types of transformations of the parent function:

[tex]f(x)=\sqrt[3]{x}[/tex]

First:

[tex]f(x+b)[/tex] shifts the function b units to the left.(Attachment #2 )

[tex]f(x)=\sqrt[3]{x+2}[/tex]

[tex]b=2[/tex]

Second:

[tex]f(x)-c[/tex] shifts the function c units downward. (Attachment #3)

[tex]f(x)=\sqrt[3]{x+2}+4[/tex]

[tex]c=4[/tex]

Answer:

Step-by-step explanation:

If we change those mixed fractions to improper we will have a much easier time with them:

[tex]\frac{\frac{10}{3} }{\frac{13}{5} }[/tex]

Now that looks horrible.  The rule for dividing fractions by fractions is a simple one, thankfully.  Bring the bottom fraction up next to the top fraction, then flip it upside down and change the sign to multiplication:

[tex]\frac{10}{3}[/tex]×[tex]\frac{5}{13}[/tex]

Multiply straight across the top and straight across the bottom to get

[tex]\frac{50}{39}[/tex]

Depending upon what your teacher calls "simplest form", this form may be the simplest, or the mixed fraction may be the simplest.  The mixed fraction equivalent to this improper is

[tex]1\frac{11}{39}[/tex]

Answer:

x = 5/16

Step-by-step explanation:

"Solving this equation" means determining the x value that makes the equation true.  Since it's a linear equation, there can be only one solution.

Starting with 32x – 1 = 16x + 4, subtract 16x from both sides, obtaining:

16x - 1 = 4

and then add 1 to both sides, obtaining 16x = 5.  Then x = 5/16.

For this case we have that by definition, the surface area of a cone is given by:

[tex]SA = \pi * r * s + \pi * r ^ 2[/tex]

Where:

A: It's the radio

s: It's the slant

Substituting according to the data we have:

[tex]SA = \pi * 2.1 * 5.6 + \pi * (2.1) ^ 2\\SA = 36.9264 + 13.8474\\SA = 50.7738 \ m ^ 2[/tex]

If we round:

[tex]SA = 50.8 \ m ^ 2[/tex]

Answer:

True

Answer:

B

Step-by-step explanation:

30 are unusable in 200. So how many are unusable in 17,000??

We can set up a ratio and figure out the answer right away! Let x be the number of unusable bolts in 17,000, so we can write:

[tex]\frac{30}{200}=\frac{x}{17,000}\\200x=30*17000\\200x=510,000\\x=\frac{510,000}{200}\\x=2550[/tex]

THus, number of unusable bolts is 2550. B is right.

Answer:

Perpendicular

Step-by-step explanation:

Think of a ladder.  It has 2 long sides that are parallel to each other.  If a step is perpendicular to one long side then it is perpendicular to the other long side BECAUSE the 2 long sides are parallel to each other.

In a plane, if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other.

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The answer to your question is B. 65

Answer:

b

Step-by-step explanation:

you add them all together and divide 11 because there are 11 numbers.

i used to have problem on mean, median, and mode too.

You must do pythagorean theorem:

a^2 + b^2 = c^2

a and b are the legs and c is the hypotenuse

In this triangle...

a = 16

b = x

c = 34

so...

16^2 + x^2 = 34^2

256 + x ^2 = 1156

x^2 = 900

Then to isolate x square root both sides. This will get rid of the square on the x value.

This will give you...

30

x is 30

Hope this helped!

Answer: second option

Step-by-step explanation:

You need to apply the Pythagorean theorem:

[tex]a^2=b^2+c^2[/tex]

Where "a"  is the hypotenuse and "b" and "c" are the legs of the right triangle.

In the figure you can observe the value the hypotenuse of the right triangle and the value of one of this leg. Then, you need to solve for the other leg from [tex]a^2=b^2+c^2[/tex]:

[tex]b^2=a^2-c^2[/tex]

[tex]b=\sqrt{a^2-c^2}[/tex]

Substituting values, you get that the value of "x" is:

 [tex]b=\sqrt{(34)^2-(16)^2}[/tex]

 [tex]b=30[/tex]

Answer:

He should have divided 4 by  [tex]\frac{1}{2}[/tex]:

[tex]shifts=\frac{4}{\frac{1}{2}}\\\\shifts=8[/tex]

Step-by-step explanation:

You know that the students work [tex]\frac{1}{2}[/tex]-hour shifts at the charity event and Zack worked in the event for four hours.

Then, to calculate the number of shifts he worked, he should not have divided [tex]\frac{1}{2}[/tex] by 4. He should have divided 4 by  [tex]\frac{1}{2}[/tex].

Let's make the correct procedure to calculate the number of shifts Zack worked  at the charity event. This is:

[tex]shifts=\frac{4}{\frac{1}{2}}\\\\shifts=8[/tex]

Therefore, he worked 8 shifts.

To calculate the number of shifts Zack worked, we need to follow these steps:
1. Determine the length of one shift. According to the information provided, one shift lasts 1/2 hour.
2. Determine the total amount of time Zack volunteered. Zack volunteered for 4 hours.
3. To find out the total number of shifts Zack worked, we need to divide the total number of hours he volunteered by the length of one shift.
So, we take the total volunteer time (4 hours) and divide it by the shift length (1/2 hour):
\[ \text{Number of shifts} = \frac{\text{Total volunteer time}}{\text{Shift length}} \]
\[ \text{Number of shifts} = \frac{4}{1/2} \]
Now, when dividing by a fraction, you can multiply by its reciprocal. The reciprocal of 1/2 is 2/1, or just 2.
\[ \text{Number of shifts} = 4 \times 2 \]
\[ \text{Number of shifts} = 8 \]
So Zack should have determined that he worked 8 shifts in total during his volunteer time.

Answer:

7

Step-by-step explanation:

3x - 6 = 15

+6 +6

____________

3x = 21

3x = 21/3

x = 7

The value of x that satisfies the equation 3x - 6 = 15 is x = 7. This was calculated by isolating x and solving the equation.

The equation provided is 3x - 6 = 15, and the value for x that satisfies this equation is what we are looking for. To solve for x, we can start by adding 6 to both sides of the equation to isolate 3x on one side which results in 3x = 21. Finally, we divide each side by 3 to find the solution which gives us x = 7. Therefore, the solution to the equation 3x - 6 = 15 is x = 7

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Answer:

Step-by-step explanation:

D=RT

10=1T

T=10 HOURS FOR THE TURTLE.

10=5(T-8)

10=5T-40

5T=10+40

5T=50

T=50/5

T=10 HOURS FOR THE RABBIT.

LOOKS LIKE A TIE .

Answer:

Price of sweatshirt = $24

Price of t-shirt=$8

Price of shorts= $12

Step-by-step explanation:

Let

w be the price of one sweat shirt

t be the price of t-shirt

h be the price of shorts

The first statement is:  

The price of a sweatshirt at a local shop is twice the price of a pair of shorts.

w=2h     Eqn 1

Then,

The price of a T-shirt at the shop is $4 less than the price of a pair of shorts.  

t=h-4    Eqn 2

And

Brad purchased 3 sweatshirts, 2 pairs of shorts, and 5 T-shirts for a total cost of $136.

3w+2h+5t=136   Eqn 3

Putting the value of w and t in equation 3

3w+2h+5t=136

3(2h)+2h+5(h-4)=136

6h+2h+5h-20=136

13h=136+20

h=156/13

h=12

So the price of pair of shorts is $12.

Putting the value of h in equation 1

w=2(12)

w=24

Price of sweatshirt is: $24

Putting the value of h in eqn 2:

t=12-4

t=8

Price of T-shirt is $8 ..  

[tex]\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=1.5\\ h=5 \end{cases}\implies V=\cfrac{\pi (1.5)^2(5)}{3}\implies V=\cfrac{11.25\pi }{3} \\\\\\ V= 3.75\pi \implies V\approx 11.78~cm^3\qquad \leftarrow \textit{for one candle} \\\\\\ \stackrel{\textit{how many times does 11.78 go into 301.59?}}{301.59\div 11.78\implies 26}\qquad \leftarrow \textit{rounded up}[/tex]

The volume of the cone is one-third of the product of its base area and its height. The maximum number of candles that can be made from the liquid wax is 25.

The volume of the cone is one-third of the product of its base area and its height. It is given by the formula,

The Volume of Cone = (1/3) × π × (d/2)² × h

The volume of wax that is needed to make a single candle with a diameter of 3 cm and height of 5 cm is,

The Volume of Cone = (1/3) × π × (d/2)² × h

The Volume of Candle = (1/3) × π × (3/2)² × 5 = 11.78 cm³

The total wax available is 301.59 cm³, while the amount of wax needed to make a candle is 11.78 cm³, therefore, the number of candles that can be made with the total wax is,

The Number of candles = (301.59 cm³/ 11.78 cm³) = 25.5999

Since a half candle can not be produced, therefore, the maximum number of candles that can be made from the liquid wax is 25.

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The two smallest positive solutions, with a < b, are approximately

x ≈ 0.384 and x ≈ 1.64.

We have,

Isolate the sine function by dividing both sides by 8.

sin(5x) = 3/8

The inverse sine function (also called arcsin) is on both sides of the equation.

5x = arcsin(3/8).

Divide both sides by 5.

x = (1/5) arcsin(3/8)

Now,

arcsin(3/8) is approximately 0.4115.

So,

x = (1/5) * 0.4115

x = 0.384.

Since the sine function repeats itself every 2π radians, we add multiples of 2π/5 to the solution to find other valid values of x.

The second smallest positive solution

x = 0.384 + (2π/5) = 1.64.

Therefore,

The two smallest positive solutions, with a < b, are approximately

x ≈ 0.384 and x ≈ 1.64.

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The equation 8 sin(5x) = 3 is solved by isolating the variable term, using inverse sine to get an angle, and considering the period of the sine function when finding additional solutions.

To solve the equation 8 sin (5x) = 3, we first isolate the term involving the variable 'x'. Start by dividing both sides by 8. We get sin(5x) = 3/8.

The inverse sine (also known as arcsin or sin^-1) is used to get the angle whose sine is 3/8. So we have 5x = sin^-1(3/8).

To solve for 'x', we then divide both sides by 5: x = sin^-1(3/8) / 5.

This value of 'x' is a solution, but sine function repeats every 2π intervals, so we add multiples of 2π/5 to 'x' to get additional solutions.

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Answer: He has 45.61

Step-by-step explanation:The answer is 45.61 because you add the decimals, 28.35+17.26, then you aline the decimal points and add, then get 45.61

1 1

28.35

+ 17.26

45.61

Total money John has now is 45.61.

On the first day of the month, John had $28.35 and received an additional $17.26.

To find out how much money John has now, you need to add the initial amount to the additional money he received. Therefore, John now has

28.35 + 17.26 = 45.61 money

Answer:

[tex]\dfrac{14}{75}[/tex]

Step-by-step explanation:

Gavin made 6 out of 15 shots, so the probability that Gavin's next shot will be  successful is

[tex]\dfrac{6}{15}=\dfrac{2}{5}[/tex]

Jack made 7 out of 15 shots, so the probability that Jack's next shot will be  successful is

[tex]\dfrac{7}{15}[/tex]

The probability that they both make their next shot successfully is

[tex]\dfrac{2}{5}\cdot \dfrac{7}{15}=\dfrac{14}{75}[/tex]

Answer:

1/7

Step-by-step explanation:

Answer:

i think it would be 1/7 also

Step-by-step explanation:

The answer is:

The correct option is:

D) [tex](3^{2})^{6}=3^{12}[/tex]

To solve the problem, we need to remember the power of a power property, it's defined by the following way:

[tex](a^{m})^{n}=a^{m*n}[/tex]

When we have a power of a power, we must keep the base and then, the new exponent will be the product between the two original exponents.

So, we are given the expression:

[tex](3^{2})^{6}[/tex]

Then, calculating we have:

[tex](3^{2})^{6}=3^{2*6}=3^{12}[/tex]

Hence, we have that the correct option is:

D) [tex](3^{2})^{6}=3^{12}[/tex]

Answer:

The correct answer is option D).  3^12

Step-by-step explanation:

Points to remember

Identities

(xᵃ)ᵇ = xᵃᵇ

xᵃ * xᵇ = x⁽ᵃ ⁺ ᵇ⁾

xᵃ/xᵇ = x⁽ᵃ ⁻ ᵇ⁾

It is given that (3^2)^6

To find the correct option

(3^2)^6 can be written as, (3²)⁶

By using above identities,  

(3²)⁶ = 3⁽² ˣ ⁶⁾

 = 3¹²

Therefore the correct answer is option D).  3^12

ANSWER

B) 43

EXPLANATION

The given arithmetic sequence is 23, 28, 33, 38, . . .

We can observe the following pattern,

23+5=28

28+5=33

33+5=38

To obtain the subsequent terms, we add 5.

Therefore the next term is

38+5=43