What is the product of (2p + 7)(3p2 + 4p – 3)?

In order to overtake Susie in the election, Calvin must obtain at least 59% of the votes still cast.

Let's assume that there are a total of 100 votes in the election. If Susie receives 53% of the first 80 votes, she gets:

0.53 x 80

= 42.4 votes

And if Calvin receives 47% of the first 80 votes, he gets:

0.47 x 80

= 37.6 votes

So, Susie is currently ahead by:

42.4 - 37.6

= 4.8 votes

Now, let's assume there are N remaining votes. We want to know what percentage of the remaining votes Calvin needs to win, so we can set up an equation:

0.47 × (80 + N)

= 0.53 × (80 + N) - 4.8

Simplifying this equation, we get:

0.06 x (80 + N)

= 4.8

Dividing both sides by 0.06, we get:

80 + N = 80

N = 80

So, there are 80 remaining votes. To find the percentage of these votes that Calvin needs to win, we can set up another equation:

0.47 x (80 + 80) + x/100 x 80

= 0.53 x (80 + 80)

Simplifying this equation, we get:

37.6 + 0.8x = 84.8

Subtracting 37.6 from both sides, we get:

0.8x = 47.2

Dividing both sides by 0.8, we get:

x = 59

So, Calvin needs to win at least 59% of the remaining votes to catch up to Susie in the election.

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Answer:

63%

Step-by-step explanation:

ik

Answer:

need this  anyone got it?

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\huge\text{Hey there!}[/tex]

[tex]\textsf{28 + 24p = 36}[/tex]

[tex]\textsf{24p + 28 = 36}[/tex]

[tex]\large\textsf{SUBTRACT 28 to BOTH SIDES}[/tex]

[tex]\textsf{24p + 28 - 28 = 36 - 28}[/tex]

[tex]\large\textsf{CANCEL out: 28 - 28 because that gives you 0}[/tex]

[tex]\large\textsf{KEEP: 36 - 28 because that helps solve for the p-value}[/tex]

[tex]\textsf{36 - 28 = \bf 8}[/tex]

[tex]\large\textsf{NEW EQUATION: 24p = 8}[/tex]

[tex]\large\textsf{DIVIDE 24 to BOTH SIDES}[/tex]

[tex]\mathsf{\dfrac{24p}{24}=\dfrac{8}{24}}[/tex]

[tex]\large\textsf{CANCEL out: }\mathsf{\dfrac{24}{24}}\large\textsf{ because that gives you 1}[/tex]

[tex]\large\textsf{KEEP: }\mathsf{\dfrac{8}{24}}\large\textsf{ because that helps you solve for the p-value any}\\\\\large\textsf{gives you the value of it}[/tex]

[tex]\mathsf{p= \dfrac{8}{24}}\\\\\\\mathsf{p = \dfrac{8\div8}{24\div8}}\\\\\\\mathsf{8\div8=\bf 1}\\\\\mathsf{24\div8=\bf 3}[/tex]

[tex]\boxed{\boxed{\large\textsf{Answer: }\mathsf{\bf p = \dfrac{1}{3}}}}\huge\checkmark[/tex]

[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

1/3

Step-by-step explanation:

Got a 100 on T4L

Answer:

B is the answer.

Step-by-step explanation:

Given equations y + x = 5 and 5x + 5y = 25.

These equations have infinetely many solutions because they are equivalent.

This can be proven by the multiplicative property of equality and the commutative property of addition.

y + x = 5 → y × 5 + x × 5 = 5 × 5 [multiplicative property of equality] → 5y + 5x = 25 → [commutative property of addition] 5x + 5y = 25.

Answer:

y = (-2) 2^(x+1)

Step-by-step explanation:

Whenever x increases from by 1, y decreases by doubling (the negative value), so the exponent is -2

When x = -1, y = -2.

So the exponential equation (NOT linear) is

y(x)   =  -2*2^(x+1)

Check:

y(-1) = -2*2^(-1+1) = -2*1 = -2

y(0) = -2*2^(1) = -2*2 = -4

...

y(2) = -2*2^(2+1) = -2*8 = -16

all good.

Answer:

a should be 45

b should be 90

c should also be 45

Step-by-step explanation:

I know this because 180-135=45 for a

since c is also 45, beside c should be 135.

which means those angles are congruent.

since a triangle equals 180 degrees all together 180-45-45=90

so b is 90

correct me if im wrong

Answer:

The vertex of the graph is at (-4,1) and thus leading  the axis of symmetry be at x=-4.

Step-by-step explanation:

Answer:

a=acceleration due to gravity=9.8m/s²

v=final velocity

u=initial velocity

t=time taken

Answer: 5

Step-by-step explanation:

Answer:

Mark a line or colors from the left of 2 on the x until arrive on the point of 2

Step-by-step explanation:

Answer:

[tex] \large{ \tt{❃ \: EXPLANATION}} : [/tex]

[tex] \large{ \tt{❁ \: LET'S \: START}} : [/tex]

[tex] \boxed{ \large{ \tt{❊ \: AREA \: OF \: TRAPEZIUM \: (A) = \frac{1}{2} h(a + b)}}}[/tex]

- Plug the values & then simplify!

[tex] \large{ \tt{↬ \frac{1}{2} \times 10(2 + 7)}}[/tex]

[tex] \large{ \tt{↬ \frac{1}{2} \times 10 \times 9 }}[/tex]

[tex]↬ \boxed{ \large{ \tt{45 \: {m}^{2} }}}[/tex]

✺ Karma says : If you feel like you are losing everything , remember that trees lose their leaves every year and still they stand tall and wait for better days to come! ♪

♡Hope I helped! ت

☼ Have a wonderful day / evening ! ☪

# StayInAndExplore ! ☂

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Answer:

Solution given;

angle =270°

radius [r]=8cm

we have

length of arc =270°/360°×2×π*r

=270°/360°×2×3.14*8=37.68cm

length of the arc is 37.68cm.

Answer:

[tex] \dfrac{2x}{x + 7} [/tex]

Step-by-step explanation:

[tex] \dfrac{4x^2 - 16x}{2x^2 + 6x - 56} = [/tex]

Factor the numerator and denominator.

[tex]= \dfrac{4x(x - 4)}{2(x^2 + 3x - 28)}[/tex]

[tex]= \dfrac{4x(x - 4)}{2(x + 7)(x - 4)}[/tex]

[tex] = \dfrac{2x}{x + 7} [/tex]

Answer:

Whole numbers or integers from 0 to 10

Step-by-step explanation:

Either 0 tickets can be sold, or 1, or 2, or 3, or 4, etc. up to a maximum of 10;

It is not possible to sell -1 tickets or ¹/₂ a ticket and we are told they don't sell more than 10 so 11 is not a possibility either;

Logically then, the only possibilities are whole numbers between 0 and 10

Answer:

a=90

b=45

c=45

d=90

e=45

f=45

Answer:

8 questions each for short answer questions and 8 questions of Multiple Choice Questions type.

A total of 16 questions.

Step-by-step explanation:

The number of multiple-choice questions and the number of short answer type questions are the same.

Let it be equal to [tex]x[/tex]

→Average time it takes to attempt multiple choice question = 2 minutes

→Total time it takes to attempt multiple choice question = [tex]2 * x[/tex] minutes

→Average time it takes to attempt short answer type question = 3.5 minutes

→Total Time it takes to attempt short answer type question = [tex]3.5 * x[/tex] minutes

Total time for the test should be less than 45 minutes.

Now finally, we can make an equation out of the information listed above:

[tex]2x +3.5x <45[/tex]

[tex]\\ 5.5x <45[/tex]

[tex]x < 8.18[/tex]

Hence the value of [tex]x = 8[/tex]

Answer:

m∠ABC = 150°

Step-by-step explanation:

180° - 90° = 90°

[tex](2x+14)+(x+7)=90[/tex]

[tex](2(23)+14)+(23+7)=90[/tex]

[tex]((46)+14)+(30)=90[/tex]

[tex](60)+(30)=90[/tex]

[tex]x=23[/tex]

90° + 60° = 150°

Step-by-step explanation:

[tex]\cos^{4} x - \sin^{4} x[/tex]

[tex]= ( \cos^{2} x + \sin^{2} x)( \cos^{2} x - \sin^{2} x)[/tex]

[tex] = (1 - \sin^{2} x + \sin^{2} x)( 1 - \sin^{2} x - \sin^{2} x)[/tex]

[tex] = 1 - 2\sin^{2} x[/tex]

Note: I replaced all cos^2x terms using the identity

[tex]\cos^{2} x = 1 - \sin^{2} x[/tex]

Answer:

Then 1/2 or  30 minutes is the required time for Tom to cover the exact distance that Linda one hour before.

Two hours after Tom began Tom would cover 12 miles and three hours after Linda started Linda would be 6 miles far away from the starting point

Step-by-step explanation:

Linda walks in a straight line at 2 miles/hour

then after t ( hours time) she is    2 (m/h) * t   = d (L)

for Tom running at 6 m/h starting one hour later to cover the same distance d(L)

d(L)  =  6 m/h * ( t - 1 )    then:

2 (m/h) * t   =   6 m/h * ( t - 1 )

2*t  =  6*t - 6

4*t = 6

t = 6/4

t =  1,5 h

Checking that result.

we see that in 1,5 hours Linda has covered  2* 1,5  = 3 miles

and  in 0.5 hours  Tom covered the same distance  0,5 * 6 = 3 miles

NOTE: Remember that tom started one hour later.

Then 1/2 or  30 minutes is the required time for Tom to cover the exact distance that Linda one hour before.

b)  In this case

d(T) = 6* ( t - 1 )       must be equal  to  twice of the Linda distance

d(L)  = 2 * 2 * t

6*t - 6  =  4*t

2*t  =  6

t  = 3

To check it

in 3 hours   Linda had covered  3 * 2  =  6 miles

in 2 hours   Tom had covered   2 * 6  =  12 miles

Answer:

[tex]y = \tan(x + \frac{x^2}{2})[/tex]

Step-by-step explanation:

Poorly formatted question; The complete question requires that we prove that [tex]y=\tan(x+\frac{x\²}{2})[/tex]

When

[tex]\frac{dy}{dx} =1+xy\²+x+y\²[/tex] and [tex]y(0)=0[/tex]  

We have:

[tex]\frac{dy}{dx} =1+xy\²+x+y\²[/tex]

Rewrite as:

[tex]\frac{dy}{dx} =1+x+xy\²+y\²[/tex]

Factorize

[tex]\frac{dy}{dx} = (1+x)+y\²(x+1)[/tex]

Rewrite as:

[tex]\frac{dy}{dx} = (1+x)+y\²(1+x)[/tex]

Factor out 1 + x

[tex]\frac{dy}{dx} = (1+y\²)(1+x)[/tex]

Multiply both sides by [tex]\frac{dx}{1 + y^2}[/tex]

[tex]\frac{dy}{1+y\²} = (1+x)dx[/tex]

Integrate both sides

[tex]\int \frac{dy}{1+y\²} = \int (1+x)dx[/tex]

Rewrite as:

[tex]\int \frac{1}{1+y\²} dy = \int (1+x)dx[/tex]

Integrate the left-hand side

[tex]\int \frac{1}{1+y\²} dy = \tan^{-1}y[/tex]

Integrate the right-hand side

[tex]\tan^{-1}y = x + \frac{x^2}{2} + c[/tex]

[tex]y(0)=0[/tex] implies that: [tex](x,y) = (0,0)[/tex]

So:

[tex]\tan^{-1}y = x + \frac{x^2}{2} + c[/tex] becomes

[tex]\tan^{-1}(0) = 0 + \frac{0^2}{2} + c[/tex]

This gives:

[tex]0 = 0 +0 + c[/tex]

[tex]0 =c[/tex]

[tex]c = 0[/tex]

The equation [tex]\tan^{-1}y = x + \frac{x^2}{2} + c[/tex] becomes

[tex]\tan^{-1}y = x + \frac{x^2}{2} + 0[/tex]

[tex]\tan^{-1}y = x + \frac{x^2}{2}[/tex]

Take tan of both sides

[tex]y = \tan(x + \frac{x^2}{2})[/tex] --- Proved

Answer:

7/2 or 3 1/2

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

7/2

Step-by-step explanation:

3/2 + 4/2 = 7/2

Hope this helps!!

Answer:

The answer that is C

Step-by-step explanation:

The equation would be y=1/2x + 8 because the line touches the y-intercept at +8. The others would be incorrect as the line does not increase by a slop of 8/1 and/or is the y-intercept at -8.

Answer:

408.4

Step-by-step explanation:

Answer:

[tex](a)\ 257 * [-1] =-257[/tex]

[tex](b)\ (-30) * [9] =-270[/tex]

(c) The additive inverse of -21 is 21

[tex](d)\ 918 *[0]=0[/tex]

[tex](e)\ (-56) * [(-9)+(-1)] = 560[/tex]

Step-by-step explanation:

Required

Fill in the blanks

Represent all blanks with x

[tex](a)\ 257 * x =-257[/tex]

Divide both sides by 257

[tex]x =\frac{-257}{257}[/tex]

[tex]x = -1[/tex]

So:

[tex](a)\ 257 * [-1] =-257[/tex]

[tex](b)\ (-30) * x =-270[/tex]

Divide both sides by -30

[tex]x =\frac{-270}{-30}[/tex]

[tex]x = 9[/tex]

So:

[tex](b)\ (-30) * [9] =-270[/tex]

(c)The complete question here is to determine the additive inverse of (-21)

The [tex]additive[/tex] [tex]inverse[/tex] of a [tex]number[/tex] x is -x

So:

[tex](-21) \to -(-21)[/tex]

[tex](-21) \to 21[/tex]

[tex](d)\ 918 *x=0[/tex]

Divide both sides by 918

[tex]x=\frac{0}{918}[/tex]

[tex]x = 0[/tex]

So:

[tex](d)\ 918 *[0]=0[/tex]

[tex](e)\ (-56) * [(-9)+(-1)] = x[/tex]

Solve the inner brackets

[tex](-56) * [-9-1] = x[/tex]

[tex](-56) * [-10] = x[/tex]

Multiply

[tex]560 = x[/tex]

So:

[tex](e)\ (-56) * [(-9)+(-1)] = 560[/tex]

A)  [tex]-\sqrt{5}[/tex]

D)  [tex]\pi[/tex]

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

Explanation:

Choices B and C are rational because we can simplify them to form a fraction of integers.

[tex]-\sqrt{49} = -7 = -\frac{7}{1}[/tex]

[tex]\sqrt{0} = 0 = \frac{0}{1}[/tex]

Any rational number is of the form P/Q where P,Q are integers and Q is nonzero.

So we can rule out choices B and C.

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

Choice A on the other hand cannot be written as a fraction of integers. The 5 isn't a perfect square, which makes [tex]-\sqrt{5}[/tex] irrational.

The same can be said about [tex]\pi[/tex] which is roughly equal to 3.14; the decimal digits go on forever without a known pattern.

Choice A and choice D are the two answers.

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

If we know the pattern of the decimal digits, then we can turn the decimal number into a fraction of integers

The number -0.777, where the 7s go on forever, converts to the fraction -7/9

That means we rule out choice E.

Answer:

B. capacity.

Step-by-step explanation:

In this scenario, Mahak is measuring the maximum space inside a watering can. Thus, this is a measure of capacity because it gives the exact information as to the quantity of water the watering can hold at any given time.

Basically, the capacity of a container is a measure of the volume of fluid or any other substance that it is able to hold, which is typically measured in litres or cubic centimeters.

For example, if the shape of the watering can is cylindrical; its capacity (volume) would be measured using a mathematical expression.

Mathematically, the volume of a cylinder is given by the formula;

V = πr²h

Where;

what do you mean? theres no math. we cant answer this.

x+x is equal to 0

Answer:

2x

Step-by-step explanation:

x + x = 2x

Answer:

616.8

Step-by-step explanation:

look it up

Answer:

616.8 quarts

Step-by-step explanation: