Graph H(x) =|x+5| and t(x)=|2x+5|

viven

t = time

function

what is the probability that the machine will not need repairs within 12

rocedure

The probability would be 0.0016

The equation of the line that passes through the points (0, 3) and (2, - 1) in point-slope form is y - 3 = - 2 · x, that is equivalent to y = - 2 · x + 3 (m = - 2, b = 3).

According to Euclidean geometry, a line can be constructed by knowing the location of two distinct points on a plane. Then, we can determin the slope of the line from the two points. First, determine the slope of the line by using the secant line formula:

m = (- 1 - 3) / (2 - 0)

m = - 4 / 2

m = - 2

Second, substitute all the variables in the equation of the line in point-slope form:

y - 3 = - 2 · x (Point-slope form)

y = - 2 · x + 3 (Slope-intercept form)

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From the right triangle, and using the definitions of the tangent and the cosine functions, we have:

From the problem, we identify:

Finally, using these values, we can find b and c.

Using (1):

Using (2):

The measure of angle B in triangle ABC is 158°.

A triangle is a 2-dimensional closed shape with three sides, three angles, and three vertices. A triangle would be a category of polygon.

For the given angles of the triangle ABC.

∠BAC = 78° , ∠CAD = 46° and ∠ADB = 110°.

Now,

∠BAC = ∠BAD + ∠DAC

Put the values;

78° = ∠BAD + 46°

∠BAD = 78° - 46°

∠BAD = 32°

Now, in a triangle; the sum of all three angles is 180°.

In triangle ADB

∠ABD + ∠BAD + ∠BDA = 180°

Put the values;

∠ABD +  32° +  110°  =  180°

∠ABD = 180°  -  142°

∠ABD = 158°

Thus, the measure of angle B is 158°.

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Mrs. Parkow's 5-digit mystery number is 73248.

Ten thousand is the starting point for five-digit numbers, which go up to ninety-nine million, nine hundred and ninety-nine. Integers are present in the places of ones, tens, hundreds, thousands, and ten thousands in these numbers. Any positive number may be placed at these places, with the exception of 0 at the ten thousands place.

A general 5-digit number can be written as:

a×10000 + b×1000 + c×100 + d×10 + e where a, b, c, and d are single-digit numbers.

a is the ten thousands digit

b is the thousands digit

c is the hundreds digit

d is the tens digit

e is the units digit.

Let 8 be at one's place that is e

Now, it is given that 8 is in a place that is 10 times less than the place of the 4.

This implies 4 is at the ten's place that is d.

Next, it is given that 3 is in a place that is 100 times greater than the place of the 4.

That is 100×10 = 1000 place

So, 3 is at the place of b.

The 2 is in a place that is 10 times less than the place of the 3. So, 2 is at the place of c.

The 7 is in a place that is 100 times greater than the 2. That is 100×100 = 10,000 place.

Thus, 7 is at the place of a.

Thus, we obtain

a= 7

b= 3

c= 2

d= 4

e= 8

Therefore, the 5-digit mystery number is 73248.

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Answer:

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

Step-by-step explanation:

Given table:

[tex]\begin{array}{|c|c|c|c|c|}\cline{1-5} x & -3 & -2 & -1 & 0\\\cline{1-5} f(x) & 6 & 0 & -2 & 0\\\cline{1-5}\end{array}[/tex]

The x-intercepts of a quadratic function are when f(x) = 0.

Therefore, the x-intercepts are:  x = -2 and x = 0.

Intercept form of a quadratic equation

[tex]y=a(x-p)(x-q)[/tex]  

where:

Substitute the found x-intercepts and one of the points from the table into the formula and solve for a:

[tex]\begin{aligned} y&=a(x-p)(x-q)\\\\\implies6&=a(-3-(-2))(-3-0)\\6&=a(-1)(-3)\\6&=3a\\a&=\dfrac{6}{3}\\\implies a&=2\end{aligned}[/tex]

Substitute the x-intercepts and the found value of a into the formula:

[tex]\implies y=2(x+2)(x-0)[/tex]

Expand to standard form:

[tex]\implies y=2(x+2)(x-0)[/tex]

[tex]\implies y=2x(x+2)[/tex]

[tex]\implies y=2x^2+4x[/tex]

To get the percentile

Step 1: Write the formula

For the 38th percentile

This means that the 38th percentile is between the 5th and 6th number

P38 = 41.64This means that approximately 38% of the data lie below 43, when the data are ranked

For the 60th percentile,

6089

60

Calls greater than 400 would be more economical in plan 1 than plan 2 and the inequality is 29 < 17 + 0.03x

The given parameters are:

Plan 1

Plan 2

Let the number of months be x.

So, we have the following equation

Plan 1: 29

Plan 2: 17 + 0.03x

For plan 1 to be more economical plan than plan 2, then we have the following inequality

Plan 1 < Plan 2

This is represented as

29 < 17 + 0.03x

Subtract 0.03x from both sides of the inequality

So, we have

0.03x > 12

Divide both sides by 0.03

x > 400

In (a), we have

x > 400

This means that the number of calls for the plan 1 to be more economical than plan 2, then the number of calls must be greater than 400

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A method of notation in which digits are divided into groups of three by commas is known as the standard form of a number.

When a number has three digits, these groups are termed periods?

The periods are separated by commas.

Large numbers have three spots between each group of digits. Periods are the names of the groups.

The periods are typically separated by commas.

number follows 100000 and 100001

nonetheless, does not include decimals, negative integers, or fractions. Let's first express the quantity in numerical form, so 100,000 represents 100,000. The next whole number after 100,000 is the one obtained by adding 1 to the previous amount. As a result, 100000 + 1 Equals 100001, the following whole number.

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The cosine of the angle given is negative.

Cosine is negative in the second and third quadrant

In the second quadrant,

In the third quadrant,

Therefore, the values that satisfy the equation are 99.6 and 260.4 degrees.

Answer:

[tex]y=x^2-4x-2[/tex]

Step-by-step explanation:

Standard Form of Quadratic:

[tex]y=ax^2+bx+c[/tex]

Vertex Form of Quadratic:

[tex]y=a(x-h)^2+k[/tex]

h = vertex x

k = vertex y

Think of h and k as the ordered pair (h,k).

Match this ordered pair to the vertex ordered pair.

(h,k) = (2, -6)

Plug in (h,k) into vertex form:

[tex]y = a(x-2)^2-6[/tex]

Use other point to solve for a.

[tex]3 = a(5-2)^2-6[/tex]

[tex]3=a(3)^2-6[/tex]

[tex]3=9a-6[/tex]

[tex]9=9a[/tex]

[tex]a=1[/tex]

Plug a back into vertex form and expand the expression into standard form:

[tex]y=(x-2)^2-6[/tex]

[tex]y=(x-2)(x-2)-6[/tex]

Use F.O.I.L. method to expand (x-2)(x-2).

F(first):  [tex]x*x=x^2[/tex]

O(outer):  [tex]x*-2=-2x[/tex]

I(inner): [tex]-2*x =-2x[/tex]

L(last): [tex]-2*-2=4[/tex]

[tex]y=x^2-2x-2x+4-6[/tex]

Combine like terms:

[tex]y=x^2-4x-2[/tex]

A. The graph is shifted up 2 units

Answer:

-1

Step-by-step explanation:

Correct option is A)

Given,

f(x)=5x−1

To find: f(0)

Put x=0 in the given eqation.

Therefore, we get

f(0)=5(0)−1

=0−1

=−1

The statement quantity 8 minus one third times the square root of 9 end quantity squared plus the quantity 1 minus 5 end quantity squared is simplified to 65

Fractions are defined as parts of a whole element, set or number.

There are various types of fractions, which includes;

Based on the information provided, we have;

Now, substitute the values

(8 - 1/3(√9))² +  (1 - 5)²

Find the square root

(8 - 1/3(3))²+ (-4)²

Find the square

(8 - 1)² + 16

7² + 16

49 + 16

Add the values

65

Hence, the value of the expression is 65

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The 90% confidence interval for the mean score, μ, of all students taking the test is; CI = (28.36, 30.64)

The formula for confidence interval is;

CI = x' ± z(s/√n)

where;

CI = Confidence Interval

x' is sample mean

z is critical value at confidence level

s is standard deviation

n is sample size

We are given;

n = 59

x' = 29.5

s = 5.2

z at CL 0f 90% = 1.645

Thus;

CI = 29.5 ± 1.645(5.2/√59)

CI = 29.5 ± 1.136

CI = (28.36, 30.64)

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The graph for the function (y = -(1/4)x + 3) is given in the attached image. See the explanation below.

Step 1 Find (x,y) pairs
Step 2: plot the points

Step 3 Draw the line on the graph.

Let's look at Step 1.

Using the graph as an example, our first pair of x,y is (0, 3)

This is obtained by substituting 0 in the equation y = -(1/4)x + 3

⇒ y = -(1/4)0 + 3

y = 0 +3

y = 3, where x = 0

If we repeat this process with x = 1, x = 2, x = 3, we will get the corresponding y for case.

Step 2: Plotting the x,y pairs will give us points on the graph.

Step 3: connecting the dots will give us the same line in the graph that is attached.

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The estimates  for [tex]6\frac{1}{9}. 1\frac{5}{7}[/tex] is [tex]10\frac{10}{21}[/tex]

The actual answer of [tex]6\frac{1}{9}. 1\frac{5}{7}[/tex] is [tex]10\frac{30}{63}[/tex]

The estimated answer of the fraction can be done as follows:

[tex]6\frac{1}{9}. 1\frac{5}{7}[/tex]

Hence,

[tex]6\frac{1}{9} = \frac{55}{9}[/tex]

[tex]1\frac{5}{7} = \frac{12}{7}[/tex]

Therefore, the actual answer of the fractions is as follows:

[tex]\frac{55}{9}.\frac{12}{7} = \frac{660}{63} = 10\frac{30}{63}[/tex]

Hence, the estimated answer of the fractions can be calculated as follows

[tex]\frac{55}{9}.\frac{12}{7} = \frac{660}{63} = \frac{220}{21} = 10\frac{10}{21}[/tex]

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Answer:

The line is parallel to y + x =3

=> y = -x+3

the slope = -1

passes (-12, 0)

the equation would be :

y-0 = -1(x+12)

y = -x -12 Y=-x+12

Turn into mx+b form.

Y=-x+3

Plug in (-12,0)

0=-12+b

b=12

y=-x+12

It is negative X, because the slope has to be the same since it is paralle

Step-by-step explanation:

Answer:

Explanation:

Here, we want to estimate the rabbit population after 5 years

From the question, there was an approximate increase in the rabbit population by 150 (from 150 to 300) in a space of 2 years

Let us have an exponential relationship for this:

Let us get the value of t

P is the current population at 300

I is the initial

a is ?

t is the number of years which is 2

Mathematically, we have it that:

Now, for the 5 years tenor, we substitute 5 for t

We have that as:

From the option, we have an approximate value of 800 rabbits

Long division gives the answer of 24 when 72 is divided by 3.

Long division in mathematics is a strategy for breaking down complicated division problems into a series of simpler steps. It is the approach that division-based issues are typically solved using. The dividend, the quotient, the remainder, and the divisor can all be seen in the following long division.

So as we know:

Start by arranging it so that the dividend 72 is on the right side and the divisor 3 is on the left:

 3 ⟌ 7 2  

Start by arranging it so that the dividend 72 is on the right side and the divisor 3 is on the left:

    2    

   3 ⟌ 7 2  

Write the result (3 x 2 = 6) underneath the dividend after multiplying the divisor by the outcome from the previous step.

     2    

   3 ⟌ 7 2  

       6    

Write the solution below after subtracting the result from the previous step from the dividend's first digit (7 - 6 = 1).

Reduce the dividend's second digit (2) as follows:

    2    

   3 ⟌ 7 2  

     - 6    

       1 2  

The bottom number (12) is multiplied by the divisor (3) four times (s). Put 4 thus on top

Subtract the result of the previous step (3 x 4) from the divisor to get the solution (12), which you should write at the bottom:

  2 4  

   3 ⟌ 7 2  

     - 6    

       1 2  

      1 2  

Take the number above it and deduct the outcome from the preceding calculation. Write the response at the bottom after calculating (12 - 12 = 0).

The top number is the solution, and the remaining value is the bottom one.

Therefore, the result of 72 divided by 3 using long division is 24.

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Answer: [tex](-16, -6) \cup (-2, 8)[/tex]

Step-by-step explanation:

[tex]||x+4|-7| < 5\\\\-5 < |x+4|-7 < 5\\\\2 < |x+4| < 12\\\\1. -2 < x+4 < 2 \implies -6 < x < -2\\\\2. -12 < x+4 < 12 \implies -16 < x < 8\\\\\therefore (-16, -6) \cup (-2, 8)[/tex]

A. The relationship between number of towers and number of customers is proportional.

B. 12 customers.

A proportional relationship between two variables, x and y, is a relationship whereby the ratio y/x is the same all through the table of values.

Thus, the value of y/x is constant, and is referred to as the unit rate or constant of proportionality, k.

Part A:

Given the table of values, we have:

Constant of proportionality (k) = y/x = 252/5.25 = 300/6.25 = 348/7.25 = 444/9.25 = 48.

Therefore, it is a proportional relationship because it has a constant of proportionality, k = 48.

Part B:

Substitute k = 48 into y = kx (proportional relationship)

y = 48x.

The equation for the relationship is, y = 48x. Substitute y = 576 into the equation to find the value of x, number of customers:

576 = 48x

Divide both sides by 48

576/48 = 48x/48 [division property of equality]

12 = x

x = 12

The number of customers is 12.

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The simplified representation of the complex number expression is

23 + 37i

a + bi, where a and b are real numbers, can be used to represent any complex number.

The complex number expression is (6-4i)(1+5i)-(3-i)

now let us simplify,

or, (6-4i)(1+5i)-(3-i)

or, 6 + 30i - 4i -20i² -3 + i

or, 6 + 36i + 20 - 3 + i (we know that i² = -1)

or, 23 + 37i

Therefore the simplified complex expression is 23 + 37i

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Buying 12 pack is better as it is cheaper than 4 pack.

A problem can be solved using the unitary method by first determining the value of a single unit, and then multiplying that value to determine the required value. The unitary method involves determining the value of a single unit before determining the value of the necessary quantity of units.

Given Data

Protein bars come in a 4 pack box or a 12 pack box

4 pack costs 7.68 and the 12 pack costs 22.32

In 4 pack

4 pack = 7.68

1 pack = 1.92

In 12 pack,

12 pack =  22.32

1 pack = 1.86

4 pack > 12 pack

Buying 12 pack is better as it is cheaper than 4 pack.

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The graph of the polynomial function x³ - 3x² - 4x = 0 is shown if figure.

What is Polynomial function?

A mathematical expression of algebraic terms each of which consists of a constant multiplied by one or more variables raised to a nonnegative integral power.

Given that;

The degree of the polynomial function f(x) is 3.

And, The roots of the equation f(x) = 0 are -1, 0, and 4.

Now, The polynomial function are calculated as;

f (x) = 0

(x + 1) (x - 0) (x - 4) = 0

x (x + 1) (x - 4) = 0

x (x² - 4x + x - 4) = 0

x (x² - 3x - 4) = 0

x³ - 3x² - 4x = 0

Thus, The polynomial function is;

x³ - 3x² - 4x = 0

Therefore, The graph of the polynomial function x³ - 3x² - 4x = 0 is shown if figure.

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Answer:

[tex]\textsf{A.} \quad f(x)=\dfrac{1}{x-4}[/tex]

Step-by-step explanation:

An asymptote is a line that the curve gets infinitely close to, but never touches.

A vertical asymptote occurs when the denominator of a rational function is zero.

From inspection of the given graph, there is a vertical asymptote at [tex]x=4[/tex] .  

Therefore, the denominator of the rational function must equal zero when [tex]x=4[/tex] .

Therefore, the only solution where the denominator is zero when [tex]x=4[/tex] is:

[tex]\boxed{f(x)=\dfrac{1}{x-4}}[/tex]

Answer:

8 - 3 = 5

5 divided by 2 = 2.5

i = 2.5

3 x 2.5 = 7.5

4 + 7.5 = 11.5

11.5 divided by 9 = 1.277

z = 1.277

Hope this helps!

AlphaFay

The cost of one hotdog based on the given situation is $5

The correct answer option is Option C

let

Family A:

3h + 5w = 20

Family B:

6h + 3w = 33

Solve the two equations simultaneously:

3h + 5w = 20

6h + 3w = 33

Multiply (1) by 2

6h + 10w = 40

6h + 3w = 33

Substract the equations to eliminate h

10w - 3w = 40 - 33

7w = 7

divide both sides by 7

w = 7/7

w = 1

Substitute w = 1 into

3h + 5w = 20

3h + 5(1) = 20

3h + 5 = 20

3h = 20 - 5

3h = 15

divide both sides by 3

h = 15/3

h = 5

So therefore, the cost of one hotdog and one bottle water is $5 and $1 respectively.

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Answer: the answer is 5 dollars

Step-by-step explanation:

The sum of complementary angles = 90°

The angle shown is a right angle

Therefore:

k + 54.3 = 90

k = 90 - 54.3

k = 35.7°