−2z+10+7z=16z+7
How many solutions does the following equation have?

Answer:

[tex]y=2x^2+8x+8[/tex]

Step-by-step explanation:

Notice that we are looking for a quadratic function that has only one real solution for y=0, that is a unique point that touches the x-axis

We need therefore to look at the discriminant associated with all 4 equations constructed by equaling y to zero. We then try to find one that gives discriminant zero , corresponding to a unique real solution to the equation.

a) [tex]9x^2+6x+4=0[/tex]  has discriminant: [tex]6^2-4(9)(4)=-108[/tex]

b) [tex]6x^2-12x-6=0[/tex] has discriminant: [tex](-12)^2-4(6)(-6)=288[/tex]

c) [tex]3x^2+7x+5=0[/tex] has discriminant: [tex](7)^2-4(3)(5)=-11[/tex]

d) [tex]2x^2+8x+8=0[/tex] has discriminant: [tex](8)^2-4(2)(8)=0[/tex]

Therefore, the last function is the one that can have such graph

Answer:

d

Step-by-step explanation:

Answer:

P(X = 4) = 0.1876

Step-by-step explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

In this question:

[tex]n = 15, p = 0.2[/tex]

We want P(X = 4). So

[tex]P(X = 4) = C_{15,4}.(0.2)^{4}.(0.8)^{11} = 0.1876[/tex]

1. The volume under the surface [tex]f(x,y)=e^{x+y}[/tex] is given by the double integral,

[tex]\displaystyle\int_0^1\int_0^1e^{x+y}\,\mathrm dx\,\mathrm dy[/tex]

We split up the integration region into a 2x3 grid of rectangles whose upper right corners are determined by the right endpoints of the partition along either axis. That is, we split up the [tex]x[/tex] interval [0, 1] into 2 subintervals,

[0, 1/2], [1/2, 1]

with right endpoints given by the arithmetic sequence,

[tex]r_i=0+\dfrac{i(1-0)}2=\dfrac i2[/tex]

for [tex]i\in\{1,2\}[/tex], and the [tex]y[/tex] interval [0, 1] into 3 subintervals,

[0, 1/3], [1/3, 2/3], [2/3, 1]

with right endpoints

[tex]r_j=0+\dfrac{j(1-0)}3=\dfrac j3[/tex]

for [tex]j\in\{1,2,3\}[/tex].

Then the upper right corners of the 6 rectangles are the points

(1/2, 1/3), (1/2, 2/3), (1/2, 1), (1, 1/3), (1, 2/3), (1, 1)

generated by the sequence [tex](r_i,r_j)[/tex].

The integral is thus approximated by the sum

[tex]\displaystyle\sum_{j=1}^3\sum_{i=1}^2f(r_i,r_j)\dfrac{1-0}m\dfrac{1-0}n=\dfrac16\sum_{j=1}^3\sum_{i=1}^2f(r_i,r_j)=\frac{e^{5/6}+e^{7/6}+e^{4/3}+e^{5/3}}6[/tex]

or approximately 2.4334. (Compare to the actual value of the integral, which is close to 2.952.)

For the midpoint rule estimate, we replace the sampling points [tex](r_i,r_j)[/tex] with [tex](m_i,m_j)[/tex], i.e. the midpoints of each subinterval, so the set of sampling points is

(1/4, 1/6), (3/4, 1/6), (1/4, 1/2), (3/4, 1/2), (1/4, 5/6), (3/4, 5/6)

and the integral is approximately

[tex]\displaystyle\sum_{j=1}^3\sum_{i=1}^2f(m_i,m_j)\dfrac{1-0}m\dfrac{1-0}n=\frac{e^{5/12}+e^{3/4}+e^{11/12}+e^{13/12}+e^{5/4}+e^{19/12}}6[/tex]

or about 2.908.

2. We approach the second integral the same way. Split up the [tex]x[/tex] interval into 8 subintervals with left and right endpoints given respectively by

[tex]\ell_i=-2+\dfrac{(i-1)(2-(-2))}8=\dfrac{i-5}2[/tex]

[tex]r_i=-2+\dfrac{i(2-(-2))}8=\dfrac{i-4}2[/tex]

for [tex]i\in\{1,2,\ldots,8\}[/tex], and the [tex]y[/tex] interval into 2 subintervals with

[tex]\ell_j=0+\dfrac{(j-1)(2-0)}2=j-1[/tex]

[tex]r_j=0+\dfrac{j(2-0)}2=j[/tex]

for [tex]j\in\{1,2\}[/tex].

The upper left corners of the rectangles in this grid are given by the sequence [tex](\ell_i,r_j)[/tex]. So the integral is approximately

[tex]\displaystyle\sum_{j=1}^2\sum_{i=1}^8f(\ell_i,r_j)\frac{2-(-2)}m\frac{2-0}n=51[/tex]

(Compare to the actual value, 32.)

Answer: a to the power 13

Step-by-step explanation: identity: a^m × a^n= a^m+n

^ means 'to the power'

PLEASE RATE 5 STARS AND VOTE AS BRAINLIEST:)

(^o^)(^o^)(^o^)(^o^)(^o^)(^o^)(^o^)(^o^)(^o^)(^o^)(^o^)(^o^)

Answer:

she should use 2 cups of peanut butter

Step-by-step explanation:

to know the answer to that

use this equation (pb is peanut butter &o is oil)

1cup of pb=1/2 cup of o

?=1 cup of o

1×1÷1/2= 1×1×2/1=2co cups of pb

Answer:

5?

Step-by-step explanation:

I think you would count the middle point. But i don't completely know...

Answer:

[tex] \boxed{Height \: of \: cylinder = 9 \: centimeters} [/tex]

Given:

Volume of cylinder = 576π cubic centimeters

Radius of cylinder (r) = 8 centimeters

Step-by-step explanation:

Let the height of cylinder be 'h'

[tex] = > Volume \: of \: cylinder = \pi {r}^{2} h \\ \\ = > 576 \cancel{\pi} = \cancel{ \pi}( {8}^{2} )h \\ \\ = > 576 = 64h \\ \\ = > 64h = 576 \\ \\ = > h = \frac{576}{64} \\ \\ = > h = 9 \: centimeters [/tex]

Height of cylinder = 9 centimeters

Answer:

Step-by-step explanation:

Considering the store in your neighborhood, price per pound of chicken is $2.89. The cost of 3 pounds is

3 × 2.89 = $8.67

Distance = 2.1 miles

The car averages about 22 miles per gallon in the city. It means that the number of gallons needed is

2.1/22 = 0.095 gallons

Cost of gas = $1.98/gallon

Cost of 0.095 gallons =

1.98 × 0.095 = $0.1881

Total cost = 8.67 + 0.1881 = $8.86

Considering the store across town, price per pound of chicken is $1.59. The cost of 3 pounds is

3 × 1.59 = $4.77

Distance = 8.6 miles

The car averages about 22 miles per gallon in the city. It means that the number of gallons needed is

8.6/22 = 0.39 gallons

Cost of gas = $1.98/gallon

Cost of 0.39 gallons =

1.98 × 0.39 = $0.77

Total cost = 4.77 + 0.77 = $5.54

Therefore, it is cheaper going to the further store. The amount that the cheaper option saves is

8.86 - 5.54 = $3.32

Answer:

it is so simple lol

Step-by-step explanation:

just know that that angle is 90 degrees which means that you should do 90-41

Answer:

49

Step-by-step explanation:

90*-41*=49

Answer:

A

Step-by-step explanation:

Removal of greatest common multiple makes the equation easier to factor it.

The best reason for factoring out the greatest common​ factor is,

⇒ Factor out the greatest common factor first because it makes the trinomial easier to factor if the numerical and variable parts are simpler.

The highest number that divides exactly into two more numbers, is called  Greatest common factors.

Given that;

We have to choose the best reason for factoring out the greatest common​ factor, if there is​ one, before attempting to factor a trinomial.

Now, We know that;

When we factor out the greatest common factor first then it makes the trinomial easier to factor if the numerical and variable parts are simpler.

Thus, The best reason for factoring out the greatest common​ factor is,

⇒ Factor out the greatest common factor first because it makes the trinomial easier to factor if the numerical and variable parts are simpler.

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Answer:

Probably different. The average customer will want to buy toys to play with, to have fun with, unlike a collecters motif which is to display their items.

Celcius to fahrenheit conversion is just using this formula

(x°C × 9/5) + 32 = y°F

where x is the degrees in celcius and y is the degrees in fahrenheit.

Le'ts plug in 63 into the equation

63 x 9/5=113.4+32=145.4 degrees fahrenheit.

Answer:

On the positive Y-axis

Step-by-step explanation:

Answer:

Positive Y-axis

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

36 candy

6 different types

if I pick random I'll get 1 of 6

.................................

Answer:

y= 4x +16

Step-by-step explanation:

slope-intercept form:

y=mx+c, where m is the gradient and c is the y-intercept

Given that the slope is 4, m=4.

y= 4x+c

To find the value of c, substitute a coordinate.

When x= -5, y= -4,

-4= 4(-5) +c

-4= -20 +c

c= 20 -4

c=16

Thus, the equation of the line is y= 4x+16.

Answer:

17/2 pi

Step-by-step explanation:

Area of the whole circle is pi r², which is 9 pi

9 pi x 17/9 pi / 2 pi = 17/2 pi

Answer:

1/4

Step-by-step explanation:

To find the slope given two points

m = (y2-y1) / (x2-x1)

   = (4-3)/(5-1)

   = 1/4

Answer:

[tex] \frac{1}{4} [/tex]

Step-by-step explanation:

[tex] \frac{y1 - y2}{x1 - x2} \\ \frac{3 - 4}{1 - 5} \\ \frac{ - 1}{ - 4} \\ = \frac{1}{4} [/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer: False.

Step-by-step explanation:

False. Negative numbers have imaginary roots, represented by [tex]i[/tex].

For instance, the square root of negative 36 would be 6i.

Answer:angle hlm is bisected by Lj

Step-by-step explanation:

The true statement is ∠HLM is bisected by LI

Given that ∠KLH=120°

We know that angle of straight line is 180°

∴∠KLM=180°

∠KLH+∠HLM=180°

120°+∠HLM=180°

∠HLM=60°

From figure, ∠HLI=30° and ∠ILM=30°

Line LI cuts the angle HLM into two equal parts such as HLI and ILM.

Therefore, ∠HLM is bisected by LI

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Answer:

A. If Frank is on the toll road for 8.00 miles and then leaves the lane, how much will he have to pay total for the trip?

B. Each day, Susan has to pay a toll of $10.00 when she uses the toll lane to get to school. How many miles does Susan travel on the toll lane to get to school?

C. John started a carpool with his coworkers to save money. He and his three passengers split the cost of the toll. If each person pays about $2.31 (which includes their contribution to the toll lane entry fee), how many miles do they travel on the toll lane?

Step-by-step explanation:

the toll lane charges $0.25 fixed plus $0.75 per mile driven: fee = $0.25 + $0.75miles

a) Frank ⇒ $0.25 + (8 x $0.75) = $6.25

b) Susan ⇒ $10 - $0.25 = $9.75 / 0.75 = 13 miles

c) John ⇒ $2.31 x 3 = $6.93 - $0.25 = $6.68 / 0.75 = 8.91 ≈ 9 miles. Each passenger should pay $2.33 because the total toll lane fee is $7.

Answer:

He will have $39,750 at the end of five years.

Step-by-step explanation:

This is a simple interest problem.

The simple interest formula is given by:

[tex]E = P*I*t[/tex]

In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.

After t years, the total amount of money is:

[tex]T = E + P[/tex]

In this question:

[tex]P = 30000, I = 0.065, t = 5[/tex]

Interest earned:

[tex]E = P*I*t = 30000*0.065*5 = 9750[/tex]

Total amount:

[tex]T = E + P = 9750 + 30000 = 39750[/tex]

He will have $39,750 at the end of five years.

Answer:

69.08

Step-by-step explanation:

π×d

3.14×22=69.08

Answer:

x=9

Step-by-step explanation:

first you would distribute the -4 and the -12

-24x-12=-12x-120

Then you would add 120 to both sides

-24x+108=-12x

Then add 24x to both sides

108=12x

Then divide both sides by 12

x=9

Answer:

[tex]x = 9[/tex]

Step-by-step explanation:

[tex] - 4(6x + 3) = - 12(x + 10) \\ - 24x - 12 = - 12x - 120 \\ - 24x + 12x = 12 - 120 \\ - 12x = - 108 \\ \frac{ - 12x}{ - 12} = \frac{ - 108}{ - 12} \\ x = 9[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

[tex]x=\frac{7}{2} =3.5\\\\y=2[/tex]

Step-by-step explanation:

The addition method (elimination method) allows us to combine two equations in such a way that the resulting equation has only one variable. Then we can use simple algebraic methods to solve that variable

Let:

[tex]4x-6y=2\hspace{10}(1)\\\\and\\\\2x-y=5\hspace{15}(2)[/tex]

Let's multiply (2) by -2:

[tex]-2*(2):\\\\2x(-2)-y(-2)=5(-2)\\\\-4x+2y=-10\hspace{12}(-2*(2))[/tex]

Now, add (1) and (-2*(2)):

[tex](1)+(-2*(2)):\\\\4x+(-4x)-6y+(2y)=2+(-10)\\\\-4y=-8[/tex]

Hence, solving for y:

[tex]y=\frac{-8}{-4} =2[/tex]

Replacing y into (2):

[tex]2x-(2)=5[/tex]

Solving for x:

[tex]2x=5+2\\\\2x=7\\\\x=\frac{7}{2} =3.5[/tex]

Therefore:

[tex]x=\frac{7}{2} =3.5\\\\y=2[/tex]

The value of Mike's car at the start of 2017 is £4116.

Percentage is a ratio in the form of fraction of 100.

Percentage is defined by the "%" symbol.

At the start of the year 2014, Mike's car was worth £12000.

The value of the car decreased by 30% every year.

So, The value of the car at the start of 2015 = £12000×[tex](1-\frac{30}{100})[/tex]

                                                                         = £ 12000×[tex]\frac{7}{10}[/tex]

                                                                         = £ 8400

Again, The value of the car at the start of 2016 = £8400×[tex](1-\frac{30}{100})[/tex]

                                                                              = £8400×[tex]\frac{7}{10}[/tex]

                                                                              = £5880

∴ The value of the car at the start of 2017 = £5880×[tex](1-\frac{30}{100})[/tex]

                                                                     = £5880×[tex]\frac{7}{10}[/tex]

                                                                     = £4116

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Answer:

Null hypothesis:[tex]p\geq 0.25[/tex]  

Alternative hypothesis:[tex]p < 0.25[/tex]  

The statistic would be given by:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

Now we need to find the critical value for the rejection zone of the null hypothesis. Since we have a left tailed test we need to find in the normal standard distirbution a value who accumulate 0.05 of the area in the left tail and we got:

[tex] z_{crit}= -1.65[/tex]

And the best choice for this case would be:

z < − 1.65

Step-by-step explanation:

Information provided

n=2431 represent the random sample taken

[tex]\hat p=[/tex] estimated proportion of interest

[tex]p_o=0.25[/tex] is the value that we want to test

[tex]\alpha=0.05[/tex] represent the significance level

Confidence=95% or 0.95

z would represent the statistic

Hypothesis to test

We want to verify if the true proportion of Americans who reduced meat consumption last year is less than 0.25, then the system of hypothesis are :

Null hypothesis:[tex]p\geq 0.25[/tex]  

Alternative hypothesis:[tex]p < 0.25[/tex]  

The statistic would be given by:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

Now we need to find the critical value for the rejection zone of the null hypothesis. Since we have a left tailed test we need to find in the normal standard distirbution a value who accumulate 0.05 of the area in the left tail and we got:

[tex] z_{crit}= -1.65[/tex]

And the best choice for this case would be:

z < − 1.65

Answer:

gay

Step-by-step explanation:

hha

Answer:

a = -99

Step-by-step explanation:

(−−99) is equal to just 99 since a negative and a negative equals a positive.

If -a is equal to 99, a must equal -99.

Answer:

increasing

Step-by-step explanation:

y = 1/2x +2

This function is increasing because the slope is positive.

Answer:

Any percentage cam be written as a part of 100

0.05% = 0.05/100 = 0.0005

I hope this helps you

Answer: .0005

Step-by-step explanation:

Move 2 spaces to the left