The functions f(x) and h(x) share a common x-intercept.

f(x) = x2+4x

The function equation for the graph above include the following: B. f(x) = -[x] + 3.

In Mathematics and Geometry, a greatest integer function can be defined as a type of function which returns the greatest integer that is less than or equal (≤) to the number.

Mathematically, the greatest integer that is less than or equal (≤) to a number (x) is represented as follows:

y = [x].

By critically observing the given graph, we can logically deduce that the parent function was reflected over the y-axis (negative slope) and it was vertically translated from the origin by 3 units up;

y = [x]

f(x) = -[x] + 3.

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Miles is the number of miles Martin has run, and Total Time is the total time in minutes that he has been running, which is 11Miles + 5.

To create a linear model, we need to find the equation of the line that best fits the data.

We can do this by finding the slope and y-intercept of the line.
First, we need to find the slope, which is the change in y divided by the change in x.

We can choose any two points on the line to calculate the slope.

Let's use the first and second data points:
Slope = (y2 - y1) / (x2 - x1)
Slope = (104 - 60) / (9 - 5)
Slope = 44 / 4
Slope = 11
Now we can use the point-slope form of the equation of a line to find the y-intercept.

We can use the first data point:
The linear model has the form y = mx + b, where y represents the total time (in minutes), x represents the miles run, m is the slope, and b is the y-intercept.

We can use the data points to find the slope (m) as follows: m = (change in total time) / (change in miles)

Using the first two data points, (5, 60) and (9, 104):

m = (104 - 60) / (9 - 5) = 44 / 4 = 11

Now that we have the slope, we can find the y-intercept (b) using one of the data points.

Let's use (5, 60): 60 = 11 * 5 + b 60 = 55 + b b = 5

So the linear model representing Martin's pace is: y = 11x + 5 In this model, x is the miles run, and y is the total time in minutes.
y - y1 = m(x - x1)
y - 60 = 11(x - 5)
y - 60 = 11x - 55
y = 11x + 5
So the linear model that shows the miles Martin has run as the input, and the total time, in minutes, he has been running as the output is
Total Time = 11Miles + 5

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It should be noted that the ratio between the lengths of the two legs is B. 1: ✓3.

It should be noted that the ratio between the lengths of the two legs will be equal to the tangent.

In this case, tan (30°) = ✓3/3

Tan (60°) = ✓3

Therefore, the ratio between the lengths of the two legs of a 30-60-90 triangle will be 1 : ✓3.

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The entries of the first row is 3,6. Option B

To add the entries of the first row in the two matrices, we need to first identify the first row of each matrix and then add the corresponding entries together.

Matrix A:

[1  4]

[7  1]

Matrix B:

[2  2]

[4  3]

To add the first rows of these matrices, we simply add the corresponding entries:

1+2      4+2

2          6

Hence, the entries of the first of the two matrices is 2,6

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Answer:

23/100 equals 23%.

Answer: 23%

Step-by-step explanation: When doing these problems, remember, 100 and a 100% are the same thing, so when you have a problem like this, divide 25 by 100, then multiply by a 100.

Answer:

Step-by-step explanation:

A:  V = πr²h

B:  V = 1/3π(2r)²(2h) = 1/3π(4r²)(2h) = 1/3π8r²h = 8/3πr²h

C:  V = π(2r)²(2h) = π(4r²)(2h) = π8r²h = 8πr²h

D:  V = 1/3πr²(2h) = 2/3πr²h

The 6 drawings are grouped to one another

Given data ,

Let the 6 drawings into be divided into two groups of 3 drawings each

And , drawings of each group is similar to one another in some way

where Group 1: ABD

On simplifying the equation , we get

Their curves and the points are in a same order

Group 2: CEF

On simplifying the equation , we get

Their curves and points are oppositely drawn

Hence , the drawings are solved

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The complete question is attached below :

Group the 6 drawings into two groups of 3 drawings each. The drawings of each group must be similar to one another in some way - they must belong together.

Answer:

6 cm³

Step-by-step explanation:

The figure is a triangular prism with a triangular base with side lengths 3 cm, 4 cm, 5 cm. The height of the prism is 1 cm.

The sides measuring 3 cm and 4 cm form a right angle.

V = BH

where B = area of the base, and

H = height of the prism.

The base is a triangle, so B = (1/2)bh,

where b = base of the triangle, and

h = height of the triangle

V = (1/2)bhH

V = (1/2)(3 cm)(4 cm)(1 cm)

V = 6 cm³

The height of the skyscraper is D. 156.26 ft

To determine the height of the skyscraper,  we need to consider the following trigonometric identities listed thus;

From the information given, we have that;

Angle, θ = 38 degrees

The shadow casted is the adjacent side of the angle and is 200 ft

The height off the skyscraper is the opposite side

Now, using the tangent identity, we have that;

tan θ = opposite/adjacent

tan 38 = h/200

cross multiply the values, we get;

h = 200(0.7812)

Multiply the values

h = 156. 26 ft

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The hotel charge in the first city before tax was $6000 and the hotel charge in the second city before tax was $7500.

Let x be the hotel charge before tax in the first city, and y be the hotel charge before tax in the second city. Then we have:
y = x + 1500   (the hotel charge before tax in the second city was $1500 higher than in the first)
0.075x + 0.05y = 825   (the total hotel tax paid for the two cities was $825)
We can use the first equation to solve for y in terms of x:
y = x + 1500
Then we can substitute this expression for y into the second equation:
0.075x + 0.05(x + 1500) = 825
Simplifying this equation, we get:
0.075x + 0.05x + 75 = 825
0.125x = 750
x = 6000
So the hotel charge before tax in the first city was $6000. Using the first equation, we can find the hotel charge before tax in the second city:
y = x + 1500
y = 6000 + 1500
y = 7500
So the hotel charge before tax in the second city was $7500.
Therefore, the answer is: The hotel charge in the first city before tax was $6000 and the hotel charge in the second city before tax was $7500.

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The SinL as a fraction in the simplest form is 12/13.

We are given

The side NM = 5,

The side LM = 12,

By using Pythagoras' theorem, we can say that;

NL² = NM² + LM²

Substitute the values of NM and LM;

NL² = 12² + 5²

NL = 13,

For Sin L = perpendicular side/hypotenuse side

Sin L = NM / NL,

Sin L = 12/13

Therefore, the SinL as a fraction in the simplest form is 12/13

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Answer:

side AC

Step-by-step explanation:

is the opposite angle B because it is the furthest you can get on the triangle to be away from point B.

Answer:

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

AB and AC are perpendicular since AB is tangent to circle at point A.

BC is the hypotenuse of ΔABC and it length is:

Find the length of AB using Pythagorean theorem:

The required, -x is also 13 units from 0, but to the right of 0 instead of to the left.

The statement about -x is that it is 13 units to the right of 0. This is because the original number, which is 13 units to the left of 0, is represented by a point on the number line to the left of 0. If we negate this number to get -x, then we are reflecting it across the origin (0) to the right side of the number line. This means that the distance of -x from 0 is the same as the distance of the original number from 0, which is 13 units.

Therefore, -x is also 13 units from 0, but to the right of 0 instead of to the left.

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Answer:

P(A and B) = P(A)P(B)

= (1/3)(1/2) = 1/6

= about .17 = about 17%

Answer:

To express the expression 2/5 - 4/y + 3 as a single fraction, we need to find a common denominator for the fractions involved.

The common denominator for 5 and y is 5y.

First, we'll rewrite 2/5 as an equivalent fraction with the denominator 5y:

2/5 = (2 * y)/(5 * y) = 2y/5y

Next, we'll rewrite 4/y as an equivalent fraction with the denominator 5y:

4/y = (4 * 5)/(y * 5) = 20/5y

Now, we can rewrite the expression with the common denominator 5y:

2y/5y - 20/5y + 3

Since the denominators are now the same, we can combine the numerators:

(2y - 20 + 3 * 5y)/(5y)

Simplifying further:

(2y - 20 + 15y)/(5y) = (17y - 20)/(5y)

(a) The probability that exactly 4 orders will arrive in 30 minutes is 0.1127

(b) The probability that at least 2 orders will arrive in an hour is 0.7586.

(a)  We need to adjust λ to reflect the 30-minute time interval:

λ = 5 orders per hour * 0.5 hours = 2.5 orders in 30 minutes

Now we can plug in the numbers and calculate the probability:

P(X = 4) = ([tex]e^{2.5}[/tex]) *) [tex]2.5^{4}[/tex]/ 4! = 0.1127

(b) We can use the Poisson probability formula again, with λ = 5 orders per hour and x = 0 or 1:

P(X < 2) = P(X = 0) + P(X = 1) = 0.0404 + 0.2010 = 0.2414

Then we can subtract this from 1 to get the probability that at least 2 orders will arrive in an hour:

P(X ≥ 2) = 1 - P(X < 2) = 1 - 0.2414 = 0.7586

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The solution to a system of two linear equations is x = 3; y = 9. the following response is form the solution

1. From the origin, move 3 units right and 9 units up

2. The point of intersection of the two lines

3.Yes, if both lines are the same exact line

4. Can you have exactly two solutions to a Linear system of equations?

5. No, because lines are straight

6. Yes, if the lines are parallel

Parallel lines refers to lines that has equal slopes, such lines do no intersect each other at any point.

Hence we say that no solution is obtained in when linear equations turns out to be parallel lines.

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Answer:

m = [tex]\frac{3}{2}[/tex]

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 3, - 1 ) and (x₂, y₂ ) = (3, 8 )

m = [tex]\frac{8-(-1)}{3-(-3)}[/tex] = [tex]\frac{8+1}{3+3}[/tex] = [tex]\frac{9}{6}[/tex] = [tex]\frac{3}{2}[/tex]

Answer:

3/2

Step-by-step explanation:

To find the slope, we use the slope formula

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

    = (8- -1)/( 3 - -3)

    = (8+1)/(3+3)

     = 9/6

    = 3/2

Little's prediction for the second tests median score  is 84

From the question, we have the following parameters that can be used in our computation:

The dot plot

The median is the middle number on the dot plot

From the dot plot, the middle number is

Middle = 70

This means that

Median = 70

For the new prediction, we have

New median = 70 * (1 + 20%)

Evaluate

New median = 84

Hence, Little's prediction for the second tests median score  is 84

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Answer:131

Step-by-step explanation:

Use BEDMAS

9x(7+7)+5

=9 x 14 + 5

= 126 + 5

= 131

Answer:

Solving the system of equations.

Point form: (3+√25,−3+√2),(3−√25,−3−√2)

Equation form:

x=3+√25,y=−3+√2x=3−√25,y=−3−√2

Step-by-step explanation:

Answer:

400π m3

Step-by-step explanation:

V = πr^2h

V = π(5^2)(16)

V = π(25)(16)

V = 400π

Investment B is an ordinary  subvention with$ 3,906.64 in the account after one time. The correct answer is option d.    

To determine which investment is an ordinary  subvention and the  unborn value after one time, we first need to understand that an ordinary  subvention is a series of equal payments made at the end of each period.

Given the table, we can see that Investment A has payments starting in January and ends in November( missing December), while Investment B starts in February and ends in December.

thus, Investment B is the ordinary  subvention since the payments are made at the end of each month.  Now let's calculate the  unborn value of Investment B after one time  

1. Convert the periodic interest rate to a yearly rate( 10.035)(1/12)- 1 ≈0.002867

2. Determine the number of payments made 11 months  3. Use the  unborn value of  subvention formula FV =  P *(( 1 r) n- 1)/ r  

Where P =  yearly payment($ 350),

r =  yearly interest rate(0.002867), and n =  number of payments( 11) . Plug in the values

FV =  350 *(( 10.002867) 11- 1)/0.002867 ≈3906.64  

So, Investment B is an ordinary  subvention with$ 3,906.64 in the account after one time. The correct answer is optiond.

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The value of x that satisfies the equation -1.5x - 2.7 = 20.1 + 4.5x is -3.8.

To solve this equation, we need to isolate the variable x on one side of the equation. We can do this by using basic algebraic operations, such as adding, subtracting, multiplying or dividing both sides of the equation by the same value.

The first step in solving this equation is to get rid of the constant terms on one side of the equation. We can do this by adding 2.7 to both sides of the equation:

-1.5x - 2.7 + 2.7 = 20.1 + 4.5x + 2.7

Simplifying the left-hand side of the equation, we get:

-1.5x = 20.1 + 4.5x + 2.7

Next, we can move the variable terms to the left side of the equation and the constant terms to the right side of the equation by subtracting 4.5x from both sides:

-1.5x - 4.5x = 20.1 + 2.7

Simplifying the left-hand side, we get:

-6x = 22.8

Finally, we can solve for x by dividing both sides of the equation by -6:

x = -3.8

Therefore, the value of x that satisfies the equation -1.5x - 2.7 = 20.1 + 4.5x is -3.8.

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Step 1: Add Equation 2 and Equation 3 to eliminate z.

(-x + y - z) + (x - 3y) = -1 + 3

y - 4y = 2

-3y = 2

y = -2/3

Step 2: Substitute the value of y (-2/3) into Equation 3 to find the value of x.

x - 3(-2/3) = 3

x + 2 = 3

x = 1

Step 3: Substitute the values of x and y into Equation 1 to find the value of z.

3(1) - 8(-2/3) + z = 8

3 + 16/3 + z = 8

9/3 + 16/3 + z = 8

25/3 + z = 8

z = 8 - 25/3

z = 24/3 - 25/3

z = -1/3

Therefore, the solution to the system of equations is:

x = 1

y = -2/3

z = -1/3

Answer:

5.52 million people with blood group O in KwaZulu-Natal.

Step-by-step explanation:

Multiple alleles refer to the existence of more than two possible alleles (or variations) of a gene within a population. In the case of blood groups, there are multiple alleles for the gene that controls blood type, resulting in the four possible blood groups: A, AB, B, and O.

The blood group AB is the least common in the human population, with only 3% of people having this blood type.

To calculate the number of people who will have blood group O in KwaZulu-Natal, we need to multiply the total population by the percentage of people with blood group O.

9.2 million x (60/100) = 5.52 million people with blood group O in KwaZulu-Natal.

The distance from point B to point A is given as follows:

15,893 ft

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

For each angle, we have that:

Hence the position A is obtained as follows:

tan(16º) = 7200/a

a = 7200/tangent of 16 degrees

a = 25109 ft.

The position B is obtained as follows:

tan(38º) = 7200/b

b = 7200/tangent of 38 degrees

b = 9216 ft.

Hence the distance is of:

25109 - 9216 = 15,893 ft.

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