The line with equation a+2b=0 coincides with the terminal side of an angle 0 in standard position and cos 0 < 0. What is the value of sin0?

Answer:

true/ true/ false/ true

Step-by-step explanation:

4x² is a term in both the numerator and denominator → Correct

factorise numerator and denominator

4x² - 4 = 4(x² - 1) ← common factor of 4

x² - 1 ← is a difference of squares and factors as

(x - 1)(x + 1)

4x² - 3x - 1 = (4x + 1)(x - 1) ← in factored form

Hence (x - 1) is a common factor in the numerator and denominator → Correct

4 is only a common factor in the numerator not the denominator

the denominator has three terms → Correct

being 4x² , - 3x and - 1

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:

C

Step-by-step explanation:

We can find the surface area of the dumbbell by adding the surface areas of each part. We have two equal round ends of the dumbbell to count and the skinnier inside. Each is a cylinder and each can be found by finding the area of the base (times 2 for two bases) and adding it to the circumference times the height.

[tex]2(\pi r^{2} )+(\pi d)h[/tex]

Dumbbell Ends

There are two ends and so we will count this measurement twice. The diameter is 12.5. The radius is half of this and is 6.25. The height is 8.

[tex]2(\pi r^{2} )+(\pi d)h[/tex]

[tex]2(\pi (6.25)^{2} )+(\pi 12.5)8[/tex]

[tex]2(\pi 39.0625 )+(\pi 100[/tex]

245.4369+314= 559.43

But we must count is twice, so 559.43(2)=1118.87 cm squared.

Dumbbell Middle

The diameter is 2.50. Radius is 1.25. The height is 10.5. The ends actually don't show because they are attached. So we will only calculate the second part and add it to the other.

[tex](\pi 2.5)10.5[/tex]=82.47

82.47+1118.87=1201.33 cm squared.

Why is this too large? Why isn't it an answer choice? Because the ends of the middle don't show, they also take up that much area on other side. They are not part of the surface area and they make it smaller. So we will subtract that area now.

[tex]2(\pi 1.25^{2} )[/tex]=9.817

1201.33-9.817=1191.84 cm squared.

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:  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.

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: WZ

The sequence ABCD has AD as the first and last letters of that sequence, so this pattern applies to WXYZ as well to pull out WZ. Angle A pairs up with angle W because they are both the first letters of the sequences. These angles are congruent from the fact that the parallelograms are similar. The same can be said for angle D and angle Z.

note: WZ is the same as ZW. The order doesn't matter when it comes to labeling segments based on endpoints.

Answer:

The answer is 823,054,658,786.

Step-by-step explanation:

Add all of them together.

Answer:

Step-by-step explanation:

Answer:

11.33333...(keeps repeating)

Step-by-step explanation:

8.5 ÷ 3/4 = 11.33333...(keeps repeating)

[tex]f(x)=-\left(\dfrac{1}{3}\right)^{-x}=-\Bigg[\left(\dfrac{1}{3}\right)^{-1}\Bigg]^x=-(3)^x\\\\f(x)<0\ \text{for any real values of x}\ (III\ and\ IV\ quadrant)\\\\a^x\ \text{is increased for}\ a>1.\ \text{Therefore}\ 3^x\ \text{is increased}.\\\\\text{We have}\ -3^x,\ \text{therefore the graph is decreased}.[/tex]

Only bottom left graph satisfy the conditions of the end behaviour and y-intercept. The bottom left option is correct.

Given:

The given function is:

[tex]f(x)=-\left(\dfrac{1}{3}\right)^{-x}[/tex]

To find:

The graph of the given function.

Explanation:

The given function can be rewritten as:

[tex]f(x)=-\dfrac{1}{3^{-x}}[/tex]

[tex]f(x)=-3^{x}[/tex]

For [tex]x=0[/tex], we get

[tex]f(0)=-3^{0}[/tex]

[tex]f(0)=-1[/tex]

So, the y-intercept of the graph is [tex]-1[/tex].

End behaviour of the graph:

[tex]f(x)\to 0[/tex] as [tex]x\to -\infty[/tex]

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

Only bottom left graph satisfy the above conditions.

Therefore, the bottom left option is correct.

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[tex]f(x)=5x\\\\\text{The domain:}\ D=\{0,\ 1,\ 2,\ 3,\ 4,\ 5,\ 6\, ...\}=\text{Whole numbers}\\\\\text{The range:}\\\\f(0)=5(0)=0\\f(1)=5(1)=5\\f(2)=5(2)=10\\f(3)=5(3)=15\\f(4)=5(4)=20\\f(5)=5(5)=25\\\vdots\\R=\{0,\ 5,\ 10,\ 15,\ 20,\ 25,\ ...\}[/tex]

[tex]10e^{2x}-5=23e^x\qquad\text{subtract}\ 23e^x\ \text{from both sides}\\\\10e^{2x}-23e^x-5=0\\\\10(e^x)^2-23(e^x)-5=0\\\\\text{substitution:}\ e^x=t > 0\\\\10t^2-23t-5=0\\\\10t^2-25t+2t-5=0\\\\5t(2t-5)+1(2t-5)=0\\\\(2t-5)(5t+1)=0\iff2t-5=0\ \vee\ 5t+1=0\\\\2t=5\ \vee\ 5t=-1\\\\t=\dfrac{5}{2} > 0\ \vee\ t=-\dfrac{1}{5} < 0\\\\\text{therefore}\ e^x=\dfrac{5}{2}\to\ln e^x=\ln\left(\dfrac{5}{2}\right)\\\\\boxed{x=\ln\left(\dfrac{5}{2}\right)}[/tex]

Answer:

B is the correct option choice !

Can you please provide the diagram.

When the pack of 80 stickers is divided evenly among the three friends, each friend receives 26 stickers, with the remaining 2 stickers going to their teacher.

In order to find out how many stickers each friend will get from a pack of 80, we can divide the total number of stickers by the number of friends. In this case, that's 80 stickers ÷ 3 friends. This division gives us a result of 26 stickers with a remainder of 2.

However, the question states that the remainder is given to their teacher. So while the remainder division resulted in each friend getting 26 stickers with an extra 2 left over, those extra 2 stickers are given to the teacher. Therefore, each friend ends up with 26 stickers.

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q - number of quarters

2q - number of dimes

2q · $0.10 - Amount in dimes

q · $0.25 - Amount in quarters

$9.00 - Total amount

The equation:

[tex]2q(0.1)+q(0.25)=9\\\\0.2q+0.25q=9\\\\0.45q=9\qquad\text{divide both sides by 0.45}\\\\q=20[/tex]

Paul has 20 quarters.

To find quarters does Paul have.

The branch of mathematics dealing with the properties and manipulation of numbers.

Let the q - number of quarters

2q - number of dimes

2q · $0.10 - Amount in dimes

q · $0.25 - Amount in quarters

$9.00 - Total amount

The equation:

2q(0.1)+q(0.25)=9

0.45q=9

q=20

So, Paul has 20 quarters.

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Answer:

ok first get each corner make a line to the dot with each point

Step-by-step explanation:

Answer:

$1,250

Step-by-step explanation:

We can write a proportion to find the total amount using the information given. A proportion is two equivalent ratios set equal to each other. If 1200 is 4% less than last year, it's 96% of what he raised last year.

[tex]\frac{96}{100}=\frac{1200}{y}[/tex]

We will cross multiply the numerator of one ratio with denominator of the other. And then solve for y.

96(y)=100(1200)

96y=120000

y=1250

Answer:

Choice C --- It intersects the x-axis at the same angle as line m

Step-by-step explanation:

Check out the attached image below for an example. In this example, both lines form a 30 degree angle with the x-axis. These two angles are congruent due to the corresponding angle theorem. This is the idea where two parallel lines form congruent angles such that they are in the same corresponding position.

Answer:

the answer is c

Step-by-step explanation:

Answer:

The Rosita investment worth in 2025 is $83486.4 .

Step-by-step explanation:

The expontential increase function is given by.

[tex]y = a(1 + r)^{t}[/tex]

Where a is the initial value , r is the rate of interest in the decimal form and t is the time.

As given

Rosita invested in a precious mineral.

The value of the mineral tends to increase by about 12% per year.

She invests $24,000 in 2014.

As

a = 24000

12% is written in the decimal form.

[tex]= \frac{12}{100}[/tex]

= 0.12

r = 0.12

As Rosita invested from 2014 to 2025.

Than

t = 2025 - 2014

t = 11 years

Put in the expontential increase function.

[tex]y = 24000(1 + 0.12)^{11}[/tex]

[tex]y = 24000(1.12)^{11}[/tex]

y = 24000 × 3.4786 (Approx)

y = $83486.4

Therefore the Rosita investment worth in 2025 is $83486.4 .

Answer:

Well if you are trying to find the length of each side you Divide 24 by 4 so your answer would be 6

Step-by-step explanation:

Answer:

2√6 inches

Step-by-step explanation:

Since the picture is a square the lengths of each side are equal and their measure is √24

= √4*√6

= 2√6  in simplest form

Answer: 8 miles per hour

Step-by-step explanation:

30 + 30 = 60, 60 minuets in an hour  4 + 4 = 8. 8 miles per hour hope i helped :)

Answer:

8 miles!

Step-by-step explanation:

30 + 30 = 60, 60 minutes in an hour and  4 + 4 = 8. So the answer is 8 miles per hour

Hope this helps!

Answer:

⇒[tex]6b=95.94[/tex]    (equation to determine cost of one box)

cost of one box 'b' = $`15.99

⇒[tex]120t = 95.94[/tex]    (equation to determine cost of per tile)

cost of one tile t = $0.7995.

Step-by-step explanation:

Given :

Jorge bought a crate of floor tiles for $95.94.

The crate had 6 boxes of floor tiles.

Each box contained 20 floor tiles .

To Find :

Write and solve equation to determine the cost per box'b'.

Write and solve a second equation to determine the cost per tile't'

Solution :

Cost of one box = b

There are 6 boxes

So, cost of 6 boxes = $  6b

Since Jorge bought 1 crate( = 6 boxes) of cost $95.94

⇒[tex]6b=95.94[/tex]     (equation to determine cost of one box)

⇒[tex]b=\frac{95.94}{6}[/tex]

⇒[tex]b=15.99[/tex]

Thus cost of one box = $`15.99

Since 1 box 20 floor tiles

So, 6 boxes (=1 crate) contain tiles = 6*20 = 120 tiles

We are given that cost of 1 crate( = 6 boxes = 120 tiles) is $95.94

Cost of one tile = t

Cost of 120 tiles = $120t

⇒[tex]120t = 95.94[/tex] (equation to determine cost of per tile)

⇒[tex]t=\frac{95.94}{120}[/tex]

⇒[tex]t=0.7995[/tex]

Thus cost of one tile t = $0.7995.

Final answer:

The width of the rectangle is calculated using the formula for the perimeter of a rectangle, P = 2l + 2w. Given a perimeter of 66 cm and a length of 24 cm, the width is found to be 9 cm.

Explanation:

The question is asking to find the width of a rectangle given the perimeter and the length. The formula for the perimeter of a rectangle is P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.

To find the width, we can rearrange the formula: w = (P - 2l) / 2.

Substituting the given values into the formula:

w = (66 cm - 2 * 24 cm) / 2

w = (66 cm - 48 cm) / 2

w = 18 cm / 2

w = 9 cm

Therefore, the width of the rectangle is 9 cm.

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!

Hope that helps and maybe earns a brainliest! :)

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.

Answer:

-2-p

Step-by-step explanation:

(p-2)x=4-p^2

(4-p^2)/(p-2)

-2-p

The solution of the expression for the given condition would be, - (p + 2).

Used the concept of trigonometry formula which stated that,

[tex](a - b)^2 = a^2 - 2ab + b^2[/tex]

Let us assume that,

When we multiply by x in (p - 2) the solution is (4 - p²).

So, it can be written in mathematical form as,

[tex]x \times (p - 2) = (4 - p^2)\\[/tex]

[tex]x \times (p - 2) = (2^2 - p^2)\\[/tex]

[tex]x \times (p - 2) = (2 - p) (2 + p)[/tex]

[tex]x \times (p - 2) = - (p - 2) (2 + p)[/tex]

Divide both sides by (p - 2),

[tex]x = - (p + 2)[/tex]

So, we get;

[tex](p - 2) \times - (p + 2) = (4 - p^2)[/tex]

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Answer:

(12) A

(14) A

(15) E

hope this help

Step-by-step explanation:

Answer: 6 of the picks would be green

Step-by-step explanation: