Katie wants to save at least $280 to go on the math team field trip. He currently has $112 saved.
If he has 8 weeks left to save, which inequality and graph represent the amount of money per week he needs to save to meet the goal?

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]

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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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]

Let's begin solving the problem by illustrating the problem using a diagram:

Let the height of building B be x

Re-drawing the triangles to show the unknown side:

Using trigonometric ratios and sine rule

Hence:

The height of the building B is 79 ft

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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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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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:

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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The simplified form of the expression 29 - ( 11 - 2³ ) + 6² ÷ 4 is 35

Given the expression in the question;

29 - ( 11 - 2³ ) + 6² ÷ 4

To simply, replace 2 raised to the power of 3 with 8 and 6 raised to the power of 2 by 36

29 - ( 11 - 2³ ) + 6² ÷ 4

29 - ( 11 - 8 ) + 36 ÷ 4

Now, remove the parenthesis by performing the operation inside the parenthesis.

29 - ( 11 - 8 ) + 36 ÷ 4

29 - 3 + 36 ÷ 4

Now, divide 36 by 4

29 - 3 + 36 ÷ 4

29 - 3 + 9

Next, add -3 and 9

29 + 6

Add 29 and 6

35

Therefore, 35 is the simplified form of the expression.

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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 solution to the given equation (2(-2) - 4 = 12) is -20 and its graphical solution is shown in the image attached below.

A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numerical values that are placed at equal intervals along its length.

Next, we would solve the given equation as follows:

2(-2) - 4 = 12

Let us introduce a variable x into the equation as follows:

x = 2(-2) - 4 - 12

x = -4 - 4 - 12

x = -20

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The base of Triangle B is 1 inches.

Given,

Triangle A has a height of 8 inches

and base of Triangle is 2 inches

Let's Find the Area of Triangle A

We know that the formula of Area of Triangle

Area of Triangle = [tex]\frac{1}{2}[/tex] × b × h

where, b is the base and h is the height of triangle.

Plug the values of base and height in above formula.

Area of Triangle A  = [tex]\frac{1}{2}[/tex] × 2 × 8

Hence, Area of Triangle A is 8 sq. inches

In this question, Some part is missing that is:

Triangle A is similar to Triangle B

Now, For Triangle B is given:

Triangle B has a height of 16 inches

and, to find the base of the triangle.

We know, Area of Triangle A is 8 sq. inches.

Area of Triangle B =  [tex]\frac{1}{2}[/tex] × b × h

8 =  [tex]\frac{1}{2}[/tex] × b × 16

8 = 8b

b = 1 inches

Hence, The base of Triangle B is 1 inches.

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We get 700,000 after rounding off to the place value of the underlined digit in the number 698,072.

According to the question,

We have the following number with 6 as the underlined digit:

698,072

When rounding off the number, please note that the digits to the right of the underlined digit would be zero. However, we need to be careful where we need to scale up the underlined number or it would remain the same.

For this, we need to check the number to the right of the underlined digit. If the number right next to the underlined digit is greater than 5 then the underlined digit has to be scaled up. And if it is less than 5 then the underlined digit remains the same.

So, after rounding off we will get:

700,000

Hence, the number after rounding off to 6 in 698,072 is 700,000.

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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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viven

t = time

function

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

rocedure

The probability would be 0.0016

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

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):

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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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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A triangle that has two sides of 10 and 6 with an area of 12 units will have the third side length of 4.

The triangle can be described as the the figure that has threes sides which can be equal or varies base on the type of the triangle it is, and the area of the triangle is given, we can use the formula for the are of triangle which i s (1/2  * b * h )

Then the Area of a triangle = (1/2  * b * h)

we were given the two sides already with the area , then we can input the values as :

12 =( 1/2 * 6 * x)

where x is the third sides that is needed

x = 4

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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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A. The graph is shifted up 2 units

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 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.

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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The distance between the point is 5.

The formula to find the distance between two points (x1, y1) and (x2, y2)

distance = [tex]\sqrt{(x2-x1)^{2} + (\\ y2-y1)^{2} }[/tex]

Substituting points A(2,9) and B(-2,6), we get

distance = [tex]\sqrt{(-2-2)^{2} + ( 6-9)^{2} }[/tex]

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

              = [tex]\sqrt{16 + 9}[/tex]

              =[tex]\sqrt{25}[/tex]

             = 5

Therefore the distance between the two points is 5.

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Answer:

The correct number is -27.

Step-by-step explanation:

-81 ÷ 3 = -27

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