Complete the square: x2+7x+?=(x+?)2

Step-by-step explanation:

I assume the length that got cut off is 18.

Use Pythagorean theorem:

x² + 36² = (x + 18)²

x² + 1296 = x² + 36x + 324

972 = 36x

x = 27

Answer:

A  has the points plotted correctly

Step-by-step explanation:

We need to plot the data

A  has the points plotted correctly

B  has the point ( 10,5) plotted on (9,5)

C is missing (-6,-5)

D is missing (-6,-5) and has (-2,1) instead of (-2,-1)

Answer:

A.

Step-by-step explanation:

It would be very helpful to write the points individually from the data. Take the x value and place it with its corresponding y value:

(1,4) ; (2,2) ; (-2,-1) ; (-2,-6) ; (5,-4) ; (-6,-5) ; (10,5)

Now find the graph that has each of these points. You can write these down and cross them out if you find them on the graph, and once you find the graph where all of these points are crossed out, that's the correct graph.

The correct graph is A.

:Done

Answer:

Step-by-step explanation:

Given the inequality [tex]|z+4|>15[/tex], we are to find the solution set of the inequality. Since the the function is an absolute value, this means that the function will be positive and negative.

For the positive value of the function;

[tex]z+4>15\\\\subtract\ 4\ from \ both \ sides\\z+4-4 > 15 -4\\\\z>11[/tex]

For the negative value of the function we have;

[tex]-(z+4) > 15\\\\-z-4> 15\\add\ 4 \ to\ both \ sides\\\\-z-4+4> 15+4\\\\-z> 19\\\\[/tex]

Multiplying both sides of the inequality by -1 will change the sense of the inequality sign;'

[tex]-(-z)< -19\\\\z<-19[/tex]

Hence the solution sets are [tex]z> 11 \ and \ z< -19 \\[/tex] OR z less-than negative 19 or z greater-than 11

Answer:

z less-than negative 19 or z greater-than 11

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

Solution 1: At first, you might think that because there are 5 ways to choose the first store and 4 ways to choose the second store, the answer is 5 * 4 = 20 but this is over-counting by a factor of 2. Say that two of the stores are A and B. If she went to A then B, that's the same as going to B then A since you still go to the same stores, therefore, the answer is 20 / 2 = 10.

Solution 2: We need to find the number of ways to choose 2 stores from 5, we can do this by calculating ₅C₂ which equals:

5! / 2!  * 3!

= 5 * 4 * 3 * 2 * 1 / 2 * 1 * 3 * 2 * 1

= 5 * 4 / 2 * 1

= 10

Answer:

(y+10 ) years

Step-by-step explanation:

If Yiadom is y  years now.

Then after 10 years, his anew age will be = (y+10) yrs

Answer:

600

Step-by-step explanation:

first, 40% of 15000 is 6000,

10% of 6000, which is the number of students studying mathematics as well as science, 600

Answer:

•600 students studied both the subject.

Answer:

(d-4)(c-9)

Step-by-step explanation:

cd-9d-4c+36

d(c-9)-4(c-9)

pull out the (c-9),

(d-4)(c-9)

Answer:

A

Step-by-step explanation:

100fps=68.182mph

68.182/3.8=17.94

Mellissa's speed will be 17.94 mph.

Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance.

It is given that Melissa is able to Rollerblade 100 feet in 3.8 seconds.

We know that 100fps is equal to 68.182mph.

Mellissa's speed in meters per hour is calculated as:-

S = 68.182/3.8=17.94mph

Therefore, Mellissa's speed will be 17.94 mph.

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Answer:

9  3  -7  -13

4  -4  11  8

0  9  2  -4

Step-by-step explanation:

9  3  -7  -13

4  -4  11  8

0  9  2  -4

Answer: 9  3  -7  -13

4  -4  11  8

0  9  2  -4

Step-by-step explanation:

[tex]\sqrt{16}\times\sqrt{12}[/tex]

$=\sqrt{4^2}\times\sqrt{2^2\cdot3}$

$=4\times2\sqrt3=8\sqrt3$

Answer:

5 seconds

Step-by-step explanation:

Well we know that when the soccer ball is on the ground the height will be 0.

So we replace y with 0 and solve for x.

0=-12x²+60x

factor out and divide x, (this x is x=0, which is before he kicked it)

0=-12x+60

subtract 60 from both sides

-60=-12x

x=5

Answer:

√69 or 8.3 feets

Step-by-step explanation:

Hypotenuse=13

Therefore

13²=x²+10²

x²=169-100

x²=69

x=√69 feets

The distance from the base of the house is  8.3 feet.

The pythagoras theorem is used to obtain the sides of a right angled triangle.

Given that;

The hypotenues of the triangle is 13-foot

The length of the opposite side is 10 feet

Thus;

13^2 = 10^2 + a^2

a^2 = 13^2  -  10^2

a = √13^2  -  10^2

a = 8.3 feet

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Answer:

A is the appropriate option.

Step-by-step explanation:

The question given is a conditional statement.

With the condition that all master photographers are artist. This implies that any person who is a master photographer is automatically an artist.

A. Comparing the statement here, since Ansel Adam's is a master photographer, he is an artist.

B. Ansel Adams is an artist, but it is possible that not all artists are master photographer.

A is the correct option.

1. All master photographers are artists.

2. Ansel Adams is a master photographer.

Therefore, Ansel Adams is an artist.

Answer:

The correct answer is A.

Step-by-step explanation:

Answer:

(1) Therefore, a 90% confidence interval for the proportion of Americans who decide to not go to college because they cannot afford it is [0.4348, 0.5252].

(2) We can be 90% confident that the proportion of Americans who choose not to go to college because they cannot afford it is contained within our confidence interval

(3) A survey should include at least 3002 people if we wanted the margin of error for the 90% confidence level to be about 1.5%.

Step-by-step explanation:

We are given that a simple random sample of 331 American adults who do not have a four-year college degree and are not currently enrolled in school, 48% said they decided not to go to college because they could not afford school.

Firstly, the pivotal quantity for finding the confidence interval for the population proportion is given by;

                         P.Q.  =  [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]  ~ N(0,1)

where, [tex]\hat p[/tex] = sample proportion of Americans who decide to not go to college = 48%

           n = sample of American adults = 331

           p = population proportion of Americans who decide to not go to

                 college because they cannot afford it

Here for constructing a 90% confidence interval we have used a One-sample z-test for proportions.

So, 90% confidence interval for the population proportion, p is ;

P(-1.645 < N(0,1) < 1.645) = 0.90  {As the critical value of z at 5% level

                                                        of significance are -1.645 & 1.645}  

P(-1.645 < [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < 1.645) = 0.90

P( [tex]-1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < [tex]\hat p-p[/tex] < [tex]1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.90

P( [tex]\hat p-1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < p < [tex]\hat p+1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.90

90% confidence interval for p = [ [tex]\hat p-1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] , [tex]\hat p+1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ]

 = [ [tex]0.48 -1.96 \times {\sqrt{\frac{0.48(1-0.48)}{331} } }[/tex] , [tex]0.48 +1.96 \times {\sqrt{\frac{0.48(1-0.48)}{331} } }[/tex] ]

 = [0.4348, 0.5252]

(1) Therefore, a 90% confidence interval for the proportion of Americans who decide to not go to college because they cannot afford it is [0.4348, 0.5252].

(2) The interpretation of the above confidence interval is that we can be 90% confident that the proportion of Americans who choose not to go to college because they cannot afford it is contained within our confidence interval.

3) Now, it is given that we wanted the margin of error for the 90% confidence level to be about 1.5%.

So, the margin of error =  [tex]Z_(_\frac{\alpha}{2}_) \times \sqrt{\frac{\hat p(1-\hat p)}{n} }[/tex]

              [tex]0.015 = 1.645 \times \sqrt{\frac{0.48(1-0.48)}{n} }[/tex]

              [tex]\sqrt{n} = \frac{1.645 \times \sqrt{0.48 \times 0.52} }{0.015}[/tex]

              [tex]\sqrt{n}[/tex] = 54.79

               n = [tex]54.79^{2}[/tex]

               n = 3001.88 ≈ 3002

Hence, a survey should include at least 3002 people if we wanted the margin of error for the 90% confidence level to be about 1.5%.

[tex]f(x)=\sqrt{x+3}\\g(x)=8x-7\\\\f(g(x))=\sqrt{8x-7+3}=\sqrt{8x-4}[/tex]

0riginal break even point:

285000/ 60/35 = $166,250

New break even point = new fixed costs / ( selling price - variable cost/ selling price)

New break even point = 285,000 + 15,900. / ( 60-( 35-4.50)/60

300,900 / 60-30.50/60 = $612,000

The new break even point increases.

Answer:

g(x): 2(-5)+1= -10+1=-9

2(-1)+1= -2+1=-1

2(2)+1= 4+1=5

2(3)+1=6+1= 7

Hence, the range of [tex]g[/tex] using the set notation is [tex](-9,-1,5,7)[/tex].

What is the function?

Functions are often defined by a formula that describes a combination of arithmetic operations and previously defined functions; such a formula allows computing the value of the function from the value of any element of the domain.

Here given that,

The function g is defined as follows for the domain given.

[tex]g(x) = 2x+1,[/tex]  and domain [tex]= (-5, -1, 2, 3)[/tex]

So,

[tex]x=-5\\2(-5)+1\\= -10+1\\=-9\\\\x=-1\\2(-1)+1\\= -2+1\\=-1\\\\x=2\\2(2)+1\\= 4+1\\=5\\\\x=3\\2(3)+1\\=6+1\\= 7[/tex]

Hence, the range of [tex]g[/tex] using the set notation is [tex](-9,-1,5,7)[/tex].

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Answer:

a. 4

Step-by-step explanation:

-1(-4) = 4

Answer:

A 4

Step-by-step explanation:

opposite of –4 = 4

Answer:

work pictured and shown

Answer:

Last one

Step-by-step explanation:

● [ ( 3^2 × 5^0) / 4 ]^2

5^0 is 1 since any number that has a null power is equal to 1.

●[ (3^2 ×1 ) / 4 ]^2

● (9/4)^2

● 81 / 16

The probability that the 4 oldest people in the group were selected is based on combinatorics is 0.00303 or 0.303%.

Given that:

Find how many ways the 4 oldest people can be selected from the group.

Since the 4 oldest people are already determined, there is only 1 way to select them.

To calculate the probability, to determine the total number of ways to select 4 people from the group of 11. This can be found using the combination formula:

Number of ways to choose k items from n items :

C(n,k) = n! / (k!(n-k)!)

Calculate the total number of ways to select 4 people from the group:

Plugging n and k value from given data:

C(11,4 )= 11! / (4!(11-4)!)

On simplifications gives:

C(11, 4) = 330.

Calculate the probability:

Probability = Number of ways 4 oldest people selected / Total number of ways to select 4 people

Plugging the given data:

Probability = 1 / 330

Probability ≈ 0.00303 or 0.303%.

Therefore, the  probability that the 4 oldest people in the group were selected is based on combinatorics is 0.00303 or 0.303%.

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Answer:

15x - y = - 126

Step-by-step explanation:

will make it simple and short

first we need to find the slope (m) first in order to get the equation

given: (-8,6) (-9,-9)

                     y2 - y1         -9  -  6

Slope = m = -----------  =  ------------------ =  15

                      -x2 - x1        -9  -  (-8)

so the equation of the line using point (-8,6) and slope 15 is y - 6 = 15( x + 8)

y - 6 = 15x + 120

using the form equation Ax + By = C,  15x - y = -120-6

therefore... 15x - y = - 126       is the answer

Answer:

h(-4) = -2

Step-by-step explanation:

h(x)=-2x-10

Let x = -4

h(-4)=-2*-4-10

       =8-10

       = -2

Answer:

[tex]\huge \boxed{{-2}}[/tex]

Step-by-step explanation:

[tex]\sf The \ function \ is \ given:[/tex]

[tex]h(x)=-2x-10[/tex]

[tex]\sf To \ find \ h(-4), \ put \ x=-4.[/tex]

[tex]h(-4)=-2(-4)-10[/tex]

[tex]h(-4)=8-10[/tex]

[tex]h(-4)=-2[/tex]

Answer:

5x+4f-1(x)=3 this is short answer

the answer to your question is $75

Answer:

The passenger train is moving at 45 miles per hour

Step-by-step explanation:

Let the amount of time it took the two trains to travel the distance = t.

Since the two trains traveled the distance at the same time,

Rate of the passenger train =[tex]\frac{180}{t}[/tex]

Rate of the freight train = [tex]\frac{120}{t}[/tex]

Where t is in hours.

From the problem, we can see that the rate of the freight train was 15 miles per hour slower than the rate of the passenger train. Mathematically, we can represent this as

[tex]\frac{120}{t}= \frac{180}{t}-15[/tex]

from the above equation, we can now get our value for t  as

[tex]\frac{120-180}{t}=-15\\\frac{-60}{t}=-15\\t=4 hours[/tex]

We have our time of travel for the two trains as 4 hours.

The rate of the passenger train can now be calculated by 180/4 = 45 miles per hour

Answer:

1. add 1/2x to both sides

a. you want to combine the like terms. in this case, it is the x variable.

you are left with 7/6x = 5

2. multiply by 6/7

a. the reciprocal of 7/6 will cancel out the values

Answer:

yd^2

Step-by-step explanation:

I took the test :)

The farmer calculate surface area in unit of [tex]yd^{2}[/tex]

The surface area of any given object is the area or region occupied by the surface of the object.

Thus , The farmer calculate surface area in unit of [tex]yd^{2}[/tex]

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Answer: an equation that has one term which is nameless and squared also no term which gets raised to higher power.

Step-by-step explanation:

Answer:

5a³ - 40

Step-by-step:

The algebraic expression is:

5a³ - 40