The graph of y = f ′(x), the derivative of f(x), is shown below. List the intervals where the graph of f is concave down.
(–4, –2) U (2, 4)
(–2, 2)
(–4, 0)
(0, 4)

Let the smaller number be x .

Then the larger number = 3x

Their sum = -10

This can be written in an equation as :-

[tex]x + 3x = - 10[/tex]

[tex]4x = - 10[/tex]

[tex]x = \frac{ - 10}{ \: \: \: 4} [/tex]

[tex]x = - 2.5[/tex]

Which means :-

The value of the first number = -2.5

The value of the second number = -2.5 × 3 = -7.5

Therefore , the smaller of the two numbers is = -7.5

Answer:

let a + b = -10

where a = 3b

substitute a into the equation: a + b = -10

3b + b = -10

b = -10 / 4

b = -2.5

a = 3b

a = 3(-2.5)

a = -7.5

check:

a + b = -10

-7.5 + (-2.5) = 10

-10 = 10

Answer:

[tex]\frac{4}7[/tex]

Step-by-step explanation:

Just as a reminder, to find the ratio of 2 numbers, you divide the first by the second, and to divide 2 fractions, you multiply the dividend by the reciprocal of the divisor.

In this case, that would be:

[tex]\frac{\frac{4}{5}}{\frac{7}{5}}[/tex]

[tex]= \frac{4}{5} \cdot\frac{5}{7}[/tex]

=[tex]\frac{4}7[/tex]

I hope this helped you.

Answer:

22/24 or 11/12

Step-by-step explanation:

Answer:

9/12, 2/12, 11/12

Step-by-step explanation:

The lowest common denominator of 3/4 and 1/6 is 12.

3/4 * 3/3 = 9/12

1/6 * 2/2 = 2/12

Now that both of the fractions have the same denominator, we can add them.

9/12 + 2/12 = 11/12

I hope this helps! Have a lovely day! :)

Answer:

Step-by-step explanation:

So,

We'll solve this using the Pythagorean Theorem.

Let

We know that,

[tex]{ \longrightarrow \bf \qquad (AC) {}^{2} = (AB) {}^{2} +( BC) {}^{2} }[/tex]

[tex]{ \longrightarrow \sf \qquad (AC) {}^{2} = (7) {}^{2} +( 6) {}^{2} }[/tex]

[tex]{ \longrightarrow \sf \qquad (AC) {}^{2} = 49 +36 }[/tex]

[tex]{ \longrightarrow \sf \qquad (AC) {}^{2} = 85 }[/tex]

[tex]{ \longrightarrow \sf \qquad AC = \sqrt{85} }[/tex]

[tex]{ \longrightarrow \sf \qquad AC \approx 9.21 }[/tex]

⠀

Therefore,

Answer:

Step-by-step explanation:

Formula

Time period

Calculation of penalty

Answer:

the answer is thirty three

Answer:

A) H you have to run before you can climb is what my teacher told me when looking at a graph so when reading the problem you have to run left for negative then climb for positive leaving the answer being a) h

Answer:

If you're multiplying then the answer would be  B.

Step-by-step explanation:

If you multiply two negative numbers, your product would be positive.

If you multiply 1 positive and 1 negative then your product will be negative.

Answer:

X=0

Step-by-step explanation:

Swap the side of the equation

8x=0 then divide both sides by eight

x=0

Answer:

(-4, -17), (-3, -10), (-2,5), (-1,2)

Step-by-step explanation:

All the coordinates are represent linear function.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The coordinates are,

⇒ (-4, -12), (-3,-10), (-2, -8), (-1,-6)

⇒ (-4, -17), (-3, -10), (-2,5), (-1,2)

⇒ (1, -7), (2, -10), (3, -13), (4, -16)

⇒ (1, 1), (2, 4), (3, 7), (4, 10)

Now,

We know that;

A relation between a set of inputs having exactly one output each is called a linear function.

Clearly, All the coordinate have exactly one output for every input.

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Answer:

Given:

1 mile = 1.6 km

So, to find how many miles are in 100 km, we need to divide 100km by 1.6km because one single mile contains 1.6km.

100km/1.6km = 62.5 miles

Answer:

Suppose that we have two line segments, AB and CD. We know that they have the same length.

I know that AB¯¯¯¯¯¯¯¯=CD¯¯¯¯¯¯¯¯ means AB is identical to CD (aka. They are the same lines), and also that AB¯¯¯¯¯¯¯¯≅CD¯¯¯¯¯¯¯¯ means that AB and CD have the same size, but what does AB=CD mean?

Step-by-step explanation:

Answer:

The explicit formula is [tex]a_n=15(\frac{4}{5})^{n-1}[/tex].

Step-by-step explanation:

First, we need to find the common ratio. We know this is a geometric sequence because the decrease from one term to the next is not a constant number.

To find the constant ratio, we can take the [tex]2^{nd}[/tex] term and divide by the [tex]1^{st}[/tex] term:

[tex]\frac{2nd}{1st}=\frac{12}{15}=\frac{4}{5}[/tex]

So, our common ratio is [tex]r=\frac{4}{5}[/tex].

We already know our initial term, [tex]a_0[/tex] is 15, so we get:

[tex]a_n=a_0(r)^{n-1}\\a_n=15(\frac{4}{5})^{n-1}[/tex]

Answer:

The total of the jeans is $40.80

She save $7.20

Step-by-step explanation:

The tax is 2.40

The sale took off 9.60

SO 48.0 + 2.40 - 9.60 = 40.80

pls mark brainliest

Step-by-step explanation:

1 yd = 3 ft

1 yd² = 2ft²

1 gallon covers: 15 · 9 = 135 ft²

955 : 135 ≈ 7.074 gal

7.1 gallons

# Jerry Don is here#

The quantity of paint required to paint the platform is 3 gallons.

The space occupied by any two-dimensional figure in a plane is called the area. Here we have three shapes a triangle, a rectangle and a parallelogram.

Given that the attached figure represents a platform in an auditorium. The crew needs to paint it green. One gallon of paint will cover 40 square yards. One gallon of paint will cover 40 square yards.

The area of the platform is,

Area = (3x2) + 2 ( 7x 2 ) + ( 4 x 2 )2 + 3(6) + ( 5 x 3 ) + ( 4 x 3 ) + ( 2 x 3 ) + ( 7 x 3 )

Area = 6 + 28 + 16 + 18 + 15 + 12 + 6 + 21

Area = 122 square yards.

The quantity of paint required will be calculated as,

Q = 122 / 40

Q = 3 gallons

Therefore, the quantity of paint is 3 gallons.

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Step-by-step explanation:

please mark me as brainlest

Answer:

u = 7\/10

Step-by-step explanation:

Step-by-step explanation:

2x + 4(x + 1) = 2x + 4x + 4 = 6x + 4

Answer:

[tex]6x+4[/tex]

Step-by-step explanation:

[tex]2x+4\left(x+1\right)[/tex]

[tex]Expand\;4(x+1):4x+4[/tex]

[tex]=2x+4x+4[/tex]

[tex]\mathrm{Add\:similar\:elements:}\:2x+4x=6x[/tex]

[tex]=6x+4[/tex]

Hence, 6x+4 expression is equivalent to 2x+4(x+1)

~Lenvy~

Answer:

d

Step-by-step explanation:

divide

Answer:X=3

Step-by-step explanation:

Answer:

(D) 36

Step-by-step explanation:

0.5%  = 0.5/100  =  0.005

It is given that the population (215) is predicted to increase by 0.5%. To know the value after increment, 215 has to be multiplied by (1 + 0.005) or 1.005.

In the equation P  =  215(1.005)t/3, the value of t/3 has to be equal to 1 for 0.5% increase.

t/3  =  1

t  =  3 years

Convert years to months.

n  =  3 ⋅ 12 months

n  =  36 months

The correct option is D.

Thanks!

Mark me brainliest!

Answer:

36

Step-by-step explanation:

Because t/3 means that 0.5% every 3 years. n will be 3 years which is 36 months

Point :

Parallel lines have same slopes.

_________________________________

[tex]6x + 5y = 11[/tex]

Subtract sides -6x

[tex] - 6x + 6x + 5y = - 6x + 11[/tex]

[tex]5y = - 6x + 11[/tex]

Divided sides by 5

[tex] \frac{5}{5}y = \frac{ - 6}{5}x + \frac{11}{5} \\ [/tex]

[tex]y = - \frac{6}{5}x + \frac{11}{5} \\ [/tex]

Look :

This is the slope-intercept of the given line. We know that the coefficient of x is the slope of the linear functions in slope-intercept form.

Thus the slope of the line which we want is :

[tex]slope = - \frac{6}{5} \\ [/tex]

_________________________________

We have following equation to find the point-slope form of the linear functions.

[tex]y - y(given \: point) = (slope) \times (x - x(g \: p) \: ) \\ [/tex]

Now just need to put the slope and the coordinates in the above equation.

[tex]y - ( - 8) = - \frac{6}{5} \times (x - ( - 2) \: ) \\ [/tex]

[tex]y + 8 = - \frac{6}{5}(x + 2) \\ [/tex]

To find the slope-intercept form of the above equation we need to take the y alone and then simplifies the equation.

Look :

[tex]y + 8 = - \frac{6}{5}x - \frac{12}{5} \\ [/tex]

Subtract sides by -8

[tex]y + 8 - 8 = - \frac{6}{5}x - \frac{12}{5} - 8 \\ [/tex]

[tex]y = - \frac{6}{5}x - \frac{12}{5} - \frac{40}{5} \\ [/tex]

[tex]y = - \frac{6}{5}x - \frac{52}{5} \\ [/tex]

This is what we want...

_________________________________

Now we must Check the equation by using the given point :

[tex]( - 8) = - \frac{6}{5}( - 2) - \frac{52}{5} \\ [/tex]

[tex] - 8 = \frac{12}{5} - \frac{52}{5} \\ [/tex]

[tex] - 8 = \frac{ - 52 + 12}{5} \\ [/tex]

[tex] - 8 = \frac{ - 40}{5} \\ [/tex]

[tex] - 8 = - 8[/tex]

So the equation is right.

_________________________________

And we're done.♥️♥️♥️♥️♥️

The volume of the rectangular prism is the amount of space in the prism

The volume of the rectangular prism is x^3+8x^2+19x+12 cubic inches

The given parameters are:

Base area = x^2+5x+4

Height = x + 3

The volume is then calculated as:

Volume = Base area * Height

So, we have:

Volume = (x^2+5x+4) * (x + 3)

Expand

Volume = x^3+5x^2+4x + 3x^2+15x+12

Collect like terms

Volume = x^3+5x^2+ 3x^2+4x +15x+12

Evaluate the sum

Volume = x^3+8x^2+19x+12

Hence, the volume of the rectangular prism is x^3+8x^2+19x+12 cubic inches

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Answer:

ok so first we have to find the total amount

4*5=20

5*2=10

10*3=30

24*1=24

0*3=0

now lets add up the total

20+10=30

30+24=74

104

then we have to divide by the amount of games to find the average or mean

104/14=7.43(aprox)

so she scores a average of about 7 points a game

Hope This Helps!!!

Answer:

a - 2b

Step-by-step explanation:

❖ Step 1: Distributive negative sign.

❖ Step 2: Combine like terms.

Therefore, the answer is a - 2b.

Have a lovely rest of your day/night, and good luck with your assignments! ♡

Answer:

a-2b

Step-by-step explanation:

(a-b+c)-(c+b)

Distribute the minus sign to the terms in the second parenthesis

a-b+c-c-b

Combine like terms

a-b+c-c-b

a-b-b+c-c

Cancel like terms

a-2b

Answer:

See below.

Step-by-step explanation:

1. 3 * 15 + 4 * 15 - 5 * 15

45 + 60 - 75

105 - 75

30

2. 3x + 4x - 5x

7x - 5x

2x

3. 3(x-2) + 4(x-2) - 5(x-2)

3x - 6 + 4x - 8 - 5x + 10

2x - 4

4. (I'm not typing that out)

7.5x + 19.5 + 10x + 26 - 12.5x - 32.5

5x+13

-hope it helps

Answer:   [tex]0.71 \le x \le 0.95[/tex]

Work Shown:

71% = 71/100 = 0.71

95% = 95/100 = 0.95

x represents the possible values of the scores. The compound inequality above shows that x is between 0.71 and 0.95, including both endpoints. Note the use of "or equal to" as part of each inequality sign.

You multiply (*) the pounds cost by the [tex]10[/tex] pounds when you get that amount you divide it by the cost of granola per pound that will give you [tex]4[/tex] dollars per pound.

Hope it helped!

[tex]\huge\boxed{Thanks,\;Plip.}[/tex]

We want to find and solve an equation that tells us the number of pounds of raisins that we need to add to a mixture to get to a desired price.

We will see that we need to add 3 pounds of raisins.

We know that:

If we mix M pounds of raisins with 10 pounds of granola, the total mass will be:

M + 10

The price of this will be:

M*$6.50 + (10)*$3.25

And we want the price of this mixture to e $4.00 per pound, then we have:

M*$6.50 + (10)*$3.25 = (M + 10)*$4.00

Now we need to solve the above equation for M.

M*$6.50 + $32.50 = M*$4.00 + $40.00

M*$6.50 - M*$4.00 = $40.00 - $32.50

M*($6.50 - $4.00) = $7.50

M*$2.50 = $7.50

M = ($7.50)/($2.50) = 3

M = 3

This means that we need to add 3 pounds of raisins.

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Answer:

A

Step-by-step explanation:

We know that this is the same as substituting a for x and multiplying the entire expression by -1.

[tex]f(a) = \frac{2a}{a - 1} [/tex]

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

Answer:

[tex]\displaystyle \boxed{y = -3} \\ \boxed{\pi} \\ \boxed{N/A} \\ f(x) = \boxed{-2cot\:(x + \frac{\pi}{2}) - 3}[/tex]

Step-by-step explanation:

[tex]\displaystyle f(x) = Acot(Bx - C) + D \\ \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{\pi}{B} \\ Amplitude \hookrightarrow |A| \\ \\ \\ Vertical\:Shift \hookrightarrow -3 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-\frac{\pi}{2}} \hookrightarrow \frac{-\frac{\pi}{2}}{1} \\ Wavelength\:[Period] \hookrightarrow \frac{\pi}{2} \\ Amplitude \hookrightarrow N/A[/tex]

OR

[tex]\displaystyle f(x) = \boxed{2tan\:x - 3} \\ \\ f(x) = Atan(Bx - C) + D \\ \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{\pi}{B} \\ Amplitude \hookrightarrow |A| \\ \\ \\ Vertical\:Shift \hookrightarrow -3 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{\pi}{2} \\ Amplitude \hookrightarrow N/A[/tex]

Here is all the information you will need. Now, what you need to know is that ALL tangent, secant, cosecant, and cotangent functions have NO amplitudes. Also, keep in mind that although this IS a tangent graph, if you plan on writing your equation as a function of cotangent, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle f(x) = 2cot\:x - 3,[/tex]in which you need to replase "tangent" with "cotangent", then figure the appropriate C-term out that will make the graph horisontally shift and map onto the tangent graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two graphs, we can tell that the cotangent graph [photograph on the right] is shifted [tex]\displaystyle \frac{\pi}{2}\:unit[/tex]to the right, which means that in order to match the tangent graph [photograph on the left], we need to shift the graph BACKWARD [tex]\displaystyle \frac{\pi}{2}\:unit,[/tex]which means the C-term will be negative, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{-\frac{\pi}{2}} = \frac{-\frac{\pi}{2}}{1},[/tex]but we are NOT YET DONE. Although we shifted the graph back into position, remember, cotangent is graphed in REVERCE, so we need to insert a negative in front of the amplitude term, and with that, the cotangent graph of the tangent graph, accourding to the horisontal shift, is [tex]\displaystyle f(x) = -2cot\:(x + \frac{\pi}{2}) - 3.[/tex]Now, with all that being said, we can move forward. To find the period in this case, you need to take a look at the distanse between each vertical asymptote. Now, accourding to this graph, the vertical asymptotes are at [tex]\displaystyle -\frac{\pi}{2} = x\:and\:\frac{\pi}{2} = x.[/tex]From here, you will then find the distanse between these asymptotes by simply perfourming the operation of Deduction, and doing that will give you [tex]\displaystyle \boxed{\pi} = \frac{\pi}{2} + \frac{\pi}{2}.[/tex]So, the period of this function is [tex]\displaystyle \pi.[/tex]Now, you will instantly get the jist of the horisontal shift by looking at the above formula. Just keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must pay cloce attention to what is given to you inside those parentheses. Finally, the midline is the centre of your graph, also known as the vertical shift, which in this case is at [tex]\displaystyle y = -3.[/tex]

Well, that just about wraps it up. Now that everything has been explained, you should understand it better. If you still have questions, do not hesitate to comment any you have.

I am delighted to assist you at any time.

Step-by-step explanation:

89 multiplied by negative 34 gives a negative answer, since positive multiplied by negative is negative hence,

(89) × (-34) = -3026