In the figure below, if BE is the perpendicular bisector of AD , what is the value of x?

Answer:

sec theta = r/v

Step-by-step explanation:

sec theta  = 1 /  sin theta

We know that sin theta = opp/ hypotenuse

1 / sin theta = hypotenuse /  opp

sec theta = hypotenuse /  opp

sec theta = r/v

Answer:

the tank can hold 12.5 gallons when it is full

Step-by-step explanation:

Let's assume

tank can hold 'x' gallons when it is full

we are given

The gas gauge in a car shows it has 40% of a tank of gas

So, gas in car is

[tex]=\frac{40}{100}\times x[/tex]

and we have

the car has about 5 gallons

so, we can set it equal

and then we can solve for x

[tex]5=\frac{40}{100}\times x[/tex]

[tex]5=\frac{4}{10}\times x[/tex]

[tex]5=\frac{2}{5}\times x[/tex]

Multiply both sides 5

[tex]5\times 5=5\times \frac{2}{5}\times x[/tex]

[tex]5\times 5=2x[/tex]

[tex]25=2x[/tex]

we get

[tex]x=12.5[/tex]

So, the tank can hold 12.5 gallons when it is full

Answer:

B

Step-by-step explanation:

A recursive rule for a geometric sequence

[tex]a_1\\\\a_n=r\cdot a_{n-1}[/tex]

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

[tex]a_1=-64;\ a_2=-16;\ a_3=-4;\ a_4=-1;\ ...\\\\r=\dfrac{a_{n+1}}{a_n}\to r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=\dfrac{a_4}{a_3}\\\\r=\dfrac{-16}{-64}=\dfrac{1}{4}\\\\\boxed{a_1=-64;\qquad a_n=\dfrac{1}{4}\cdot a_{n-1}}[/tex]

18/12=  [tex]1\frac{1}{2}[/tex] and  [tex]1\frac{7}{8}[/tex] = 15/8 is the correct option,  [tex]1\frac{1}{2}[/tex] is mixed fraction of 18/12 and 15/8 is improper fraction of  [tex]1\frac{7}{8}[/tex].

A fraction represents a part of a whole.

If a fraction has a numerator that is less than the denominator then the fraction is proper.

An improper fraction has a numerator that is greater than the denominator.

A mixed number is an integer written with a fraction.

18/12 is a improper fraction, let us simplify it by dividing numerator and denominator by 6

18/12 is 3/2.

The mixed fraction of 3/2 is [tex]1\frac{1}{2}[/tex]

Now the given mixed fraction is [tex]1\frac{7}{8}[/tex]

When we convert to improper we get (8×1)+7/8 , which is 15/8

Hence, 18/12=  [tex]1\frac{1}{2}[/tex] and  [tex]1\frac{7}{8}[/tex] = 15/8 is the correct option,  [tex]1\frac{1}{2}[/tex] is mixed fraction of 18/12 and 15/8 is improper fraction of  [tex]1\frac{7}{8}[/tex].

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Answer:

R=6%

Step-by-step explanation:

Given:

Total money deposited = $ 520

Total years = 5

Total earned = $156

Simple interest

To Find:

interest rate=R=?

Solution:

We know the formula for calculating total amount earned by a simple interest rate and formula for it is

I = P(rT)                     ..................(i)

where I is total amount earned

P is total money invested

r is rate

and t is time

putting the values gives us

156 = 520 (r)(5)

156 = 2600 r

dividing both sides by 2600

r = [tex]\frac{156}{2600}[/tex]

r= 0.06

We have to find R

Now from simple rules of

we know that

R = r* 100 %

so putting the value of r

R = 0.06 * 100 %

R = 6%

which is the rate at which money was invested

Answer:

it would be SSS...

Step-by-step explanation:

Its meaning is "side side side''... so you see how the triangle, ABD has the dashed (same number of lines) through the lines of the triangle, it means the sides are all congruent meaning that the sides are the same

Answer:

The triangles are not congruent.

Step-by-step explanation:

The triangle ABD is an equilateral triangle, then all their sides are equal and all the angles are equal to 60º. Then x=60º and y=30º (because the sum of the internal angles of a triangle have to be 180º)

Then we can conclude that the triangles are not congruent because they share two sides, but does no have any angle in common, as we can see in the next list of the angles.

angle ADB= angle ABD= angle DAB=60º

angle BDC=30º

angle DCB=30º

angle CBD=120º

Answer:

see explanation

Step-by-step explanation:

the result 0 = 0

means the equation has an infinite number of solutions

Answer:

All values of x make the equation true... THIS  IS THE CORRECT ANSWER!

Step-by-step explanation:

Answer:

answer is 8

8+14x+6x+12=180

Step-by-step explanation:

Answer:

The answer is 63/10, 63/100, 63/1000

Answer:

(-4,1)

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

QUESTION 1

The given function is

[tex]h(x)=-4x-72[/tex]

If [tex]x[/tex] decreases by [tex]11[/tex], then the new value is [tex]x-11[/tex].

We need to find the value the function at [tex]x-11[/tex] which is

[tex]h(x-11)=-4(x-11)-72[/tex]

This simplifies to

[tex]h(x-11)=-4x+44-72[/tex]

The increment in [tex]h(x)[/tex] is given by;

[tex]h(x-11)-h(x)=-4x+44-72-(-4x-72)[/tex]

This simplifies to,

[tex]h(x-11)-h(x)=-4x+44-72+4x+72[/tex]

This further simplifies to

[tex]h(x-11)-h(x)=44[/tex]

Therefore the corresponding increment in [tex]h(x)[/tex] is [tex]44[/tex].

QUESTION 2

The given function is

[tex]f(x)=\frac{3}{17}x+2[/tex].

If [tex]x[/tex] increases by [tex]51[/tex], then the new value of [tex]x[/tex] is [tex]x+51[/tex].

The increment in [tex]f(x)[/tex] is given by

[tex]h(x+51)-h(x)=\frac{3}{17}(x+51)+2-(\frac{3}{17}x+2)[/tex]

We expand the brackets to get,

[tex]h(x+51)-h(x)=\frac{3}{17}x+9+2-\frac{3}{17}x-2[/tex]

We simplify further to obtain,

[tex]h(x+51)-h(x)=9[/tex]

Therefore the corresponding increment in [tex]f(x)[/tex] is [tex]9[/tex].

When x decreases by 11, function h(x) increases by -100. When x increases by 51, f(x) increases by 9.

To find how much Function h(x) increases when x decreases by 11, we can calculate h(x) for the original value of x and the new value of x and then find the difference.

Original h(x) for h(x) = -4x - 72:

h(x) = -4x - 72

For x decreased by 11, the new x is x - 11:

New h(x) for h(x) = -4x - 72:

h(x - 11) = -4(x - 11) - 72

Now, we calculate the difference in h(x) values:

Δh = h(x - 11) - h(x)

Δh = [-4(x - 11) - 72] - (-4x - 72)

Now, simplify:

Δh = -4x + 44 - 72 + 4x - 72

The -4x and +4x cancel out:

Δh = 44 - 72 - 72

Now, calculate the difference:

Δh = -100

So, when x decreases by 11, h(x) increases by -100.

For the second part, to find how much f(x) increases when x increases by 51, we can use a similar approach.

Original f(x) for f(x) = (3/17)x + 2:

f(x) = (3/17)x + 2

For x increased by 51, the new x is x + 51:

New f(x) for f(x) = (3/17)x + 2:

f(x + 51) = (3/17)(x + 51) + 2

Now, calculate the difference in f(x) values:

Δf = f(x + 51) - f(x)

Δf = [(3/17)(x + 51) + 2] - [(3/17)x + 2]

Now, simplify:

Δf = (3/17)x + (3/17)(51) + 2 - (3/17)x - 2

The (3/17)x and - (3/17)x cancel out, and 2 - 2 also cancels:

Δf = (3/17)(51)

Now, calculate the difference:

Δf = 3 * 3

Δf = 9

So, when x increases by 51, f(x) increases by 9.

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Answer:

154 square inches

Step-by-step explanation:

Watch the attached figure of the square pizza box and the largest pizza that can fit into it.

Let the each side of the square pizza box be a inches.

Radius of the largest pizza that can fit into it = Half of the side of the pizza box = [tex]\frac{a}{2}[/tex]

So, area of the square box = Side * Side

                                             = a * a

                                             = a² square inches

It has also been given that the large box has an area of 196 square inches.

So,

Area of the box = a²

=> 196 = a²

Flipping the sides of the equation, we get

=> a² = 196

Taking square root on both the sides,

√a² = √196

a = 14 inches

So,

Side of square box = 14 inches

Radius of the largest pizza that can fit into it = [tex]\frac{a}{2}[/tex]

                                                                          = [tex]\frac{14}{2}[/tex]

                                                                          = 7 inches

Area of the largest possible pizza that could be placed into the box

= π *radius²                                       [since pizza is circular in shape]

= [tex]\frac{22}{7}[/tex] * 7²

= [tex]\frac{22}{7}[/tex] * 7 * 7

Cancelling out a pair of 7's from the top and bottom, we have

= 22 * 7

= 154 square inches

Answer:

D)

Step-by-step explanation:

sec(x) = 1/cos(x)

You know cos(x) = 1 for x=0, so sec(0) = 1.

You also know that sec(x) has vertical asymptotes where cos(x) = 0, at odd multiples of π/2. Only selection D matchest these characteristics.

Answer:

There would be no solution im pretty sure but not 100%

Step-by-step explanation:

Answer:

(4,-3) and (-2,5)

Step-by-step explanation:

The inverse of a function, is the function or rule formed by reflecting the line over y=x. This means essentially that all (x,y) values from the original function switch to (y,x).

(x,y)--->(y,x) in the new function.

If the function has points (-3,4) and (5,-2) then the inverse has points (4,-3) and (-2, 5).

Answer:

PLATO users, use this order:

(-2,5) and (4,-3)

Step-by-step explanation:

Answer:

80 degrees.

Step-by-step explanation:

The real question was:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The angle measurements in the diagram are represented by the following expressions.

(angle)∠A= 8x −8 and (angle)∠B= 5x +25

Solve for x and then find the measure of (angle)∠B.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

x= 11 and then since both angles equal the same......we know that angle B equals 80 degrees!

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To qualify for the special summer camp for accelerated students, a student must score at least approximately 978 on the standardized test, considering a score within the top 16% of all scores, given a mean score of 800 and a standard deviation of 120.

In a bell-shaped or normal distribution, the mean [tex]\(\mu\)[/tex] represents the central tendency of the data, and the standard deviation [tex]\(\sigma\)[/tex] measures the dispersion or spread of the scores. To find the score required to qualify for the top 16%, we use the z-score formula: [tex]\(z = \frac{X - \mu}{\sigma}\)[/tex], where X is the score, [tex]\(\mu\)[/tex] is the mean, and [tex]\(\sigma\)[/tex] is the standard deviation.

Given the mean score [tex]\(\mu = 800\)[/tex] and standard deviation [tex]\(\sigma = 120\)[/tex], the z-score corresponding to the top 16% is found using a standard normal distribution table or statistical software. The z-score associated with the top 16% is approximately z = 1.04.

Next, use the z-score formula to solve for the score X required to be in the top 16%: [tex]\(z = \frac{X - \mu}{\sigma}\)\\[/tex]. Rearranging the formula to solve for X gives us [tex]\(X = z \cdot \sigma + \mu\)[/tex]. Substituting the z-score value and the given mean and standard deviation into the equation yields [tex]\(X = 1.04 \cdot 120 + 800 = 978\)[/tex]. Hence, a student needs to score at least approximately 978 to qualify for the special summer camp for accelerated students, given the distribution of scores on the standardized test.

Answer: Negative infinity

note: if your teacher won't allow negative infinity, then try DNE for "does not exist"

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

Explanation:

As x gets closer to x = 4 from the left side of this value, then x starts at something like x = 3 and moves to x = 3.5, then to x = 3.9, then to x = 3.99, then to x = 3.999, etc

We get closer to x = 4 but never actually get there. If you look at the table attached, then f(x) = 1/(x-4) will keep getting more negative with larger and larger negative values. This growth goes on forever without any bound. So the limit is equal to negative infinity.

As you can see on the graph below, the curve heads downward as you approach x = 4 from the left hand side. Imagine you are a point on the curve, or this point is on a rollercoaster (the curve being the track itself). As you get closer to 4 from the left side, you go downhill. There is on limit to how far downhill you can go.

note: the graph and table in the attachment below were made by the free graphing calculator program GeoGebra

Answer with explanation:

The given rational function is

      [tex]y= \lim_{x \to 4^{-}} \frac{1}{x-4}[/tex]

To find the vertical Asymptotes , put

→  Denominator =0

→ x-4=0

→x=4, is the Vertical Asymptote.

Final answer:

To find the scaled length of a line representing 5 feet on a scale drawing with a scale of 0.5 inches = 2 feet, set up a proportion and solve for x. The answer is 1.25 inches.

Explanation:

To calculate the length of a line on a scale drawing, you must use the scale provided and set up a proportion based on that scale. In this case, the scale is 0.5 inches = 2 feet. To find out what 5 feet would be on the drawing, we can set up a proportion where 0.5 inches/2 feet equals x inches/5 feet. Solving for x gives us:

0.5 inches / 2 feet = x inches / 5 feet

To keep the units consistent, we use cross-multiplication:

(0.5 inches) * 5 feet = 2 feet * x inches

2.5 inches = 2 feet * x inches

Now, divide both sides by 2 feet to solve for x:

x = 2.5 inches / 2 feet

x = 1.25 inches

Therefore, a line that represents an actual length of 5 feet would be 1.25 inches long on the scale drawing.

∠8=180°-92°=88°

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

Answer:

Step-by-step explanation:

The answer is 88 degrees i got that question right.

Answer:

Radical form of the  expression [tex]4^{\frac{3}{2} }[/tex] is, 8

Step-by-step explanation:

Given the expression: [tex]4^{\frac{3}{2} }[/tex]

Since,  [tex]\sqrt{4^3}[/tex] is same as [tex]4^{\frac{3}{2} }[/tex]

Now, to write an exponent in radical form,

then the  denominator or the index goes in front of the radical and

the numerator goes inside of the radical.

we raise the base to the power of the numerator then:

[tex]4^{\frac{3}{2} }[/tex] = [tex]\sqrt{64}[/tex] = [tex]\sqrt{8 \times 8}[/tex] = [tex]\sqrt{8^2} = 8[/tex]

therefore, the radical form of the given expression is, 8

Answer: 3

Step-by-step explanation:

The slope of a line passing through two points (a,b) and (c,d) is given by :-

[tex]\text{Slope}=\dfrac{d-b}{c-a}[/tex]

In the given graph , the line is passing through (0,0) and (1,3) .\

Then the slope of line  passing through (0,0) and (1,3) will be :-

[tex]\text{Slope}=\dfrac{3-0}{1-0}\\\\\Rightarrow\ \text{Slope}=3[/tex]

Hence, the slope of the given line= 3

Answer:

Yes (under certain conditions)

Step-by-step explanation:

Binomial probability formula can be used if there are success and failure been discussed in the question.

The formula is given by

P(X=x) = \binom{n}{x}p^{x}q^{n-x}

where n= no. trials

p  = success

q= failure

x= point at which we need to find the probability

Here, 85 customers are surveyed, then n= 85

we will take, p= live entertainment had increased the amount of money they spent (success)

q = live entertainment had not increased the amount of money they spent (failure)

x should be defined, then only we can use binomial probability formula

Example, x= 10 customers said that the money they spent increased if the live entertainment provided.

Answer:

Yes

Step-by-step explanation:

Binomial distribution is valid for trials which consist of only two outcomes, and each trial is independent of the other.

Here 85 mall customers were randomly surveyed.  We have that each customers is independent of the other for the state o determine if the live entertainment provided had increased the amount of money they spent

Hence probability for each person  to say yes  can be taken as p and q =1-p for no reply.

There are only two outcomes.  

Also n =85 is sufficiently large to have np or nq >5

Hence the probability can be found using binomial probability formula provided p = probability for success of a single trial is given.

[tex]\mathsf{We\;know\;that : Density = \frac{Mass\;of\;the\;Object}{Volume\;of\;the\;Object}}[/tex]

[tex]\mathsf{Given : Mass\;of\;the\;Object = 20\;Grams}[/tex]

[tex]\mathsf{Given : Volume\;of\;the\;Object = 3.5\;cm^3}[/tex]

[tex]\mathsf{\implies Density = \frac{20}{3.5}(\frac{g}{cm^3})}[/tex]

[tex]\mathsf{\implies Density = 5.71\;(\frac{g}{cm^3})}[/tex]

To find the density of an object, we will use the formula for density which is \( d = \frac{m}{v} \), where:
- \(d\) represents the density of the object,
- \(m\) is the mass of the object, and
- \(v\) is the volume of the object.

Substituting the given values into the formula:
\(m = 20 \, \text{g}\) (mass of the object),
\(v = 3.5 \, \text{cm}^3\) (volume of the object),

we get:
\(d = \frac{20 \, \text{g}}{3.5 \, \text{cm}^3}\).

Dividing 20 grams by 3.5 cubic centimeters, we obtain:
\(d ≈ 5.71 \, \text{g/cm}^3\).

Therefore, the correct answer is:

C.5.71 G/CM3

Answer: C: y = 250x + 2000; the independent variable, x, represents the number of months after buying the car and the dependent variable, y, represents the amount of money paid on the car.

Step-by-step explanation:

The equation representing the total cost of the car over time is C(t) = 2000 + 250t, where 't' (the number of months) is the independent variable and 'C(t)' (the total cost) is the dependent variable.

To write an equation for the financing offer of a car company where customers pay a $2000 down payment and then $250 a month, we use a linear equation to represent the total cost of the car (C) over time (t):

C(t) = 2000 + 250t

Here, the independent variable 't' represents the number of months, and the dependent variable 'C(t)' represents the total cost of the car at a particular time. The independent variable is the one we have control over or choose values for, and the dependent variable is the one that changes in response to the independent variable.

Answer:

(3, 7)

Step-by-step explanation:

The midpoint of a line joining the points  (x1, y1) and (x2, y2) has midpoint

[(x1 + x2)/ 2]. (y1 + y2)/2 ]

Substituting the given points:-

Midpoint of MN =  (-2 + 8)/2 ,  (4 + 10)/2

= 6/2 , 14/2

= (3, 7)   (answer)

Answer:

9.00

Step-by-step explanation:

Use proportion:-

20% is equivalent to 1.80

1%  is equivalent to 1.80 / 20

100% is equivalent to (1.80 / 20 ) * 100

= 180 / 20

= 9

=  9.00

Answer:  We can plot the graph with help of below explanation.

Step-by-step explanation:

Since, given equation of polynomial,

[tex]P(x) = x^4 - 3x^3 - 8x^2 + 12x + 16[/tex]

End behavior : Since, the leading coefficient of the polynomial is positive and even.

Therefore, the end behavior of the polynomial is,

[tex]f(x)\rightarrow -\infty[/tex] as [tex]x\rightarrow -\infty[/tex]

And, [tex]f(x)\rightarrow +\infty[/tex]  as  [tex]x\rightarrow +\infty[/tex]

Points of the curve : since, P(4) = 0

Therefore, (x-4) is the multiple of P(x),

And we can write,  [tex]x^4 - 3x^3 - 8x^2 + 12x + 16= (x-4)(x^3+x^2-4x-4)[/tex]

[tex]x^4 - 3x^3 - 8x^2 + 12x + 16=(x-4)(x+1)(x^2-4)[/tex]

[tex]x^4 - 3x^3 - 8x^2 + 12x + 16= (x-4)(x+1)(x+2)(x-2)[/tex]

Thus, the roots of equation are 4, 2, -1 and -2.

Therefore, x-intercepts of the polynomial are (4,0) (2,0) (-1,0) and (-2,0)

Also, the y-intercept of the polynomial is ( 0,16)

Thus, we can plot the graph with help of the above information.

Emery initially borrowed $608. Each week, she paid off $76. After 2 weeks she had $456 left to pay and after 5 weeks she owed $228.

To find out the original amount borrowed, we need to determine how much Emery is paying off each week. If we look at the information given, after 2 weeks Emery still owes $456, and after 5 weeks, she owes $228. That's a difference of $228 over the span of 3 weeks, which means she is paying off $76 each week ($228 / 3 weeks = $76 per week).

Knowing this, we can figure out that she owed $608 before she started making payments (that is, $456 + $76*2 weeks = $608). Therefore, the original amount Emery borrowed from her brother was $608.

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the complete Question is given below

Emery borrowed money from her brother to buy a new phone and is paying off a fixed amount each week. After 2 weeks, she will owe $456, and after 5 weeks, she will owe $228. a. What was the original amount Emery borrowediginal amount borrowed?