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Nora is writing statements as shown below to prove that if segment ST is parallel to segment RQ, then x = 45: Statement Reason
1. Segment ST is parallel to segment RQ. Given
2. Angle QRS is congruent to angle TSP. Corresponding angles formed by parallel lines and their transversal are congruent.
3. Angle SPT is congruent to angle RPQ. Reflexive property of angles
4. Triangle SPT is similar to triangle RPQ. Angle-Angle Similarity Postulate 5. ? Corresponding sides of similar triangles are in proportion.
Which equation can she use as statement 5?
60:x = 48:(48 + 36) 60 + x = 48 + 36 60 − x = 48 − 36 60:(60 + x) = 48:(48 + 36)

Answer:

The Large Box Weighs 18 kg, and the small box weighs 6.5 kg

Step-by-step explanation:

Let a= the weight in kg of a large box

Let b= the weight in kg of a small box

Multiply both sides of (1)  by 4 and subtract (2) from (1)

1. 20a+8b=412

2. -3a-8b= -106

17a=306

a=18

and

5*8+2b=103

90+2b=103

2b=13

b=6.5

Answer:

B. 642.22 units squared

Step-by-step explanation:

Knowing that QP ║ MN and ∠QLP = ∠MLN, then ΔQLP ~ ΔMLN.

That means corresponding sides and heights have the same ratios.

We know that QP = 25, which corresponds to MN = 34. Also, the height of ΔQLP, LS, corresponds to the height of ΔMLN, LR = LS + SR = LS + 10. Let's say LS = x.

We can now write:

QP / MN = LS / LR

25 / 34 = x / (x + 10)

Cross-multiply:

34 * x = 25 * (x + 10)

34x = 25x + 250

34x - 25x = 250

9x = 250

x = 250/9 ≈ 27.78 units

So, LS = 27.78 units and LR = LS + SR = 27.78 + 10 = 37.78 units.

The area of a triangle is denoted by A = (1/2) * b * h, where b is the base and h is the height.

Here, the base of ΔLMN is MN = 34, and the height is LR = 37.78. Plug these in:

A = (1/2) * b * h

A = (1/2) * 34 * 37.78 ≈ 642.22 units squared

The answer is thus B.

~ an aesthetics lover

Answer:

i think its -$2

Step-by-step explanation:

The expected value of profit or loss is ZERO

Picker Wheel is a wheel spinner for a random picker. Various functions & customization. Enter choices or names, spin the wheel to decide a random result.

We have

If the wheel lands on win, you win $5;

on lose, you win nothing.

It costs $2 to play.

According to the question

Win written four times and Lose written six times.

P (W) = 4/10 = 0.4

P (L) = 6/10  = 0.6

x                  net                p(x)         xP(x)

Win            5 - 2  = 3         0.4          1.2

Loose        0 - 2  = -2        0.6         -1.2

∑xP(x) = 1.2 - 1.2 = 0

Hence , expected value  of profit or loss is  ZERO

or

You can say expected value is 2  $ against 2$ cost

5(0.4) + 0(0.6) = 2    against 2 $ ticket.

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Answer:

Option B is the correct option.

Step-by-step explanation:

[tex] - \frac{1}{2} + x = - \frac{21}{4} [/tex]

Move constant to R.H.S and change its sign:

[tex]x = - \frac{21}{4} + \frac{1}{2} [/tex]

Take the L.C.M

[tex]x = \frac{ - 21 + 1 \times 2}{4} [/tex]

[tex]x = \frac{ - 21 + 2}{4} [/tex]

Calculate

[tex]x = - \frac{19}{4} [/tex]

Hope this helps...

Good luck on your assignment..

Step-by-step explanation:

-19/4 is the correct answer for your question

Answer:

Systems of linear equations

Infinite amount of solutions

Step-by-step explanation:

Step 1: Rearrange 1st equation

2y = -x + 10

6y = -3x + 30

Step 2: Multiply top equation by 3

6y = -3x + 30

6y = -3x + 30

Since they have the same slope and same y-intercept, they are both the same line. That means that the systems of linear equations has infinite amount of solutions.

Answer:

-3, 5/2

Step-by-step explanation:

What are the roots of the function y = 4x2 + 2x – 30?

To find the roots of the function, set y = 0. The equation is 0 = 4x2 + 2x – 30.

Factor out the GCF of : 2, so the equation becomes 0 = 2(2x2+x-15)

Next, factor the trinomial completely. The equation becomes: 0=2(x+3)(2x-5)

Use the zero product property and set each factor equal to zero and solve.

x+3=0      2x-5 = 0

x = -3, 5/2

The roots of the function are -3, 5/2.

Hope this helped!

The roots of the function y = 4x² + 2x - 30 are -3, 5/2 after using the zero product property.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have:

y = 4x² + 2x - 30

To find the roots of the quadratic equation plug y = 0

4x² + 2x - 30 = 0

4x² + 12x - 10x - 30 = 0

4x(x + 3) - 10(x + 3) = 0

(x + 3)(4x -10) = 0

x + 3 = 0  or  4x - 10 = 0

x = -3 or x = 10/4 = 5/2

Thus, the roots of the function y = 4x² + 2x - 30 are -3, 5/2 after using the zero product property.

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Answer: 42.7%

Step-by-step explanation:

A = p (1+r/n)^nt

1500 = 1000 (1 + r/4)^4x1

r = 42.673

The  interest rate would you need to have in order to reach this goal if the amount is compounded quarterly is 42.7%

Given that,

Based on the above information, the calculation is as follows:

[tex]A = p (1+r\div n)^{nt][/tex]

[tex]1500 = 1000 (1 + r\div4)^{4\times 1}[/tex]

So, r = 42.673

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Question:

The volume of a right circular cone with both diameter and height equal to h is 250/7 cm³.

What is the value of h?

Answer:

A. 5

Step-by-step explanation:

Given

Solid Shape: Cone

Volume = 250/7

Diameter = Height

Required

Find the height of the cone

Provided that the diameter (D) and the height (h) are equal; This implies that

D = h ------ (1)

Also, Diameter (D) = 2 * Radius (r)

D = 2r

Substitute 2r for D in (1)

2r = h

Multiply both sides by ½

½ * 2r = ½ * h

r = ½h

Volume of a cone is calculated by;

Volume = ⅓πr²h

⅓πr²h = 250/7

Substitute ½h for r

[tex]\frac{1}{3} * \pi * (\frac{1}{2}h)^2 * h = \frac{250}{7}[/tex]

Take π as 22/7, the expression becomes

[tex]\frac{1}{3} * \frac{22}{7} * (\frac{1}{2}h)^2 * h = \frac{250}{7}[/tex]

Open the bracket

[tex]\frac{1}{3} * \frac{22}{7} * \frac{1}{4}h^2 * h = \frac{250}{7}[/tex]

Multiply both sides by 7

[tex]7 * \frac{1}{3} * \frac{22}{7} * \frac{1}{4}h^2 * h = \frac{250}{7} * 7[/tex]

[tex]\frac{1}{3} * 22 * \frac{1}{4}h^2 * h = 250[/tex]

Multiply both sides by 3

[tex]3 * \frac{1}{3} * 22 * \frac{1}{4}h^2 * h = 250 * 3[/tex]

[tex]22 * \frac{1}{4}h^2 * h = 750[/tex]

Multiply both sides by 4

[tex]4 * 22 * \frac{1}{4}h^2 * h = 750 * 4[/tex]

[tex]22 * h^2 * h = 3000[/tex]

[tex]22 * h^3 = 3000[/tex]

Divide both sides by 22

[tex]h^3 = \frac{3000}{22}[/tex]

[tex]h^3 = 136.36[/tex]

Take cube root of both sides

[tex]h = \sqrt[3]{136.36}[/tex]

[tex]h = 5.15[/tex]

[tex]h = 5[/tex] (Approximated)

Answer:

651.

Step-by-step explanation:

Note: In the given series it should be -29 instead of 29 because 29 cannot be a term of AP whose first term is 91 and common difference is -6.

Consider the given series is

[tex]91+85+79+...+(-29)[/tex]

It is the sum of an AP. Here,

First term = 91

Common difference = 85 - 91 = -6

Last term = -29

nth term of an AP is

[tex]a_n=a+(n-1)d[/tex]

where, a is first term and d is common difference.

[tex]-29=91+(n-1)(-6)[/tex]

[tex]-29-91=(n-1)(-6)[/tex]

[tex]\dfrac{-120}{-6}=(n-1)[/tex]

[tex]20=(n-1)[/tex]

[tex]n=20+1=21[/tex]

Sum of AP is

[tex]Sum=\dfrac{n}{2}[\text{First term + Last term}][/tex]

[tex]Sum=\dfrac{21}{2}[91+(-29)][/tex]

[tex]Sum=\dfrac{21}{2}[62][/tex]

[tex]Sum=651[/tex]

Therefore, the sum of given series is 651.

Answer:

Length= 58

width= 26

Step-by-step explanation:

Answer:

( x-2)^2 + ( y+1) ^2 = 25

Step-by-step explanation:

The equation of a circle is

( x-h)^2 + ( y-k) ^2 = r^2  where ( h,k) is the center  and r is the radius

The center is ( 2,-1) and the radius is the difference from the center to a point on the circle

(2,4) and (2,-1)

 since x is the same the radius is (4- -1) = 5

( x-2)^2 + ( y--1) ^2 = 5^2

( x-2)^2 + ( y+1) ^2 = 25

Answer and Step-by-step explanation:

The domain of a function is the values the invariable can assume to result in a real value for the variable. In other words, it is all the values x can be.

Since it's related to area, the values of x has to be positive. The domain must be, then:

[tex]-6x^{2} + 105x - 294 = 0[/tex]

Solving the second degree equation:

[tex]\frac{-105+\sqrt{105^{2} - 4(-2)(-294)} }{2(-6)}[/tex]

x = 3.5 or x = 14

The domain of this function is 3.5 ≤ x ≤ 14

The maximum area is calculated by taking the first derivative of the function:

[tex]\frac{dA}{dx} = -6x^{2} + 105x - 294[/tex]

A'(x) = -12x + 105

-12x + 105 = 0

-12x = -105

x = 8.75

A(8.75) = [tex]-6.8.75^{2} + 105.8.75 - 294[/tex]

A(8.75) = 165.375

The maximum area of the garden is 165.375 square units.

The Range of a function is all the value the dependent variable can assume. So, the range of this function is: 0 ≤ y ≤ 165.375, since this value is the maximum it will reach.

A(x) = 100

[tex]100 = -6x^{2} + 105x-294[/tex]

[tex]-6x^{2} + 105x - 394 = 0[/tex]

Solving:

[tex]\frac{-105+\sqrt{105^{2}-4(-6)()-394} }{2(-6)}[/tex]

x = 5.45 or x = 12.05

The values of x that produces an area of 100 square units are 5.45 and 12.05

Answer:

A

Step-by-step explanation:

The answer is A because in the triangle, the two smaller sides added up have to be more than the bigger side, or equal, if it is a right triangle. so 4 is the smallest 4+6=10, so it does not work, but lets see if it is a right triangle

4^2+6^2=16+36=52. it would have to equal 100 to be a right triangle. Use Pythagorean thereon.

For a triangle, the any two sides must be greater than the third side.The measure of AC cannot be equal to 4

A triangle has three sides and angle. For a triangle, the any two sides must be greater than the third side.

Given the following parameters

AB = 10 and

BC = 6

The measure of AC must be 8 for the theorem above to be true

6 +8 > 10

6 +10 > 8

10 + 8 > 6

Hence the measure of AC cannot be equal to 4

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Answer: kindly check Explanation.

Step-by-step explanation:

The function f(x) = 3x + 4 is a linear regression model. Orion's prediction was obtained by Substituting 25 for x to obtain the predicted variable

f(25) = 3(25) + 4 = 75 + 4 = 79.

However, with a correlation Coefficient of 0.39, which is a numerical value of range - 1 to +1 and is used to measure the statistical relationship between the dependent variable (number of gallons of ice-cream sold per day) and the independent variable (temperature).

The closer the correlation Coefficient (r) value is to +1 or - 1, the stronger the degree of correlation. Positive r values depicts positive relationship while negative r values depicts negative relationship. The closer the r value is to 0. The weaker the relationship and a r value of means there is no Relationship exists between the two variables.

With a correlation Coefficient of 0.39, we can Infer that that only a moderate positive relationship exists between temperature and gallons of ice cream sold per day.

Answer:

the leanth of the track is 1/2 miles long.

Step-by-step explanation:

Im sorry that i couldn't complete all the questions, I had a family thing to go to so sorry.

Answer:

Step-by-step explanation:

The statement

Twice the difference of a number and 8 is written as

2( b - 8)

The expression is greater than - 21 so we represent it by the > sign

So we have

2( b - 8) > - 21

Expand

2b - 16 > - 21

2b > - 21 + 16

2b > - 5

Divide both sides by 2

Hope this helps you

Answer:

[1  26  7]

Step-by-step explanation:

[1  26  7]

one row three column

==========================================================

Explanation:

We have a 1x3 matrix multiplied with a 3x3 matrix. This is a valid operation since the number of columns in the first matrix matches with the number of rows in the second matrix.

The resulting answer matrix will be 1x3 as it takes the number of rows of matrix A and the number of columns from matrix B, helping forming the answer matrix C.

The answer matrix looks like

[tex]C = \begin{bmatrix}x & y & z\end{bmatrix}[/tex]

where x, y and z are placeholders for actual numbers.

To get the value of x, we apply the dot product of the left matrix with the first column of the right matrix

x = (-1)(3)+(2)(2)+4(0) = -3+4+0 = 1

We'll do a similar set of steps to find y

Apply the dot product on the second column this time

y = (-1)(6)+2(4)+4(6) = -6+8+24 = 26

and the third column as well

z = (-1)(1)+2(0)+4(2) = -1+0+8 = 7

Since x = 1, y = 26 and z = 7, we can say

[tex]C = \begin{bmatrix}x & y & z\end{bmatrix}[/tex]

becomes

[tex]C = \begin{bmatrix}1 & 26 & 7\end{bmatrix}[/tex]

Answer:

966.

Step-by-step explanation:

Think of the word "of" as a sign that you have to multiply.

Thus, you can divide 333.27 by 34.5%.

You derive 966.

- Hope this helped.

Answer: n=1.8

Step-by-step explanation:

6n+14=25

-14 on both sides

25-14=11

6n=11

divide 6 on both sides

n=1.83333..

Answer:

n=[tex]\frac{11}{6}[/tex] of 1.8333...

Step-by-step explanation:

6n+14=25

-14       -14

6n=11

÷6  ÷6

n=[tex]\frac{11}{6}[/tex]

DOUBLE CHECK

6([tex]\frac{11}{6}[/tex])+14=25

11+14=25

Answer:

21x + 1

Step-by-step explanation:

f[g(x)]

= f(7x + 2)

= 3(7x + 2) - 5

= 21x + 6 - 5

= 21x + 1

Answer:

I believe it's Area = 120cm^2

Step-by-step explanation:

Answer:

solution,

Given: A rhombus

To find: It's area.

Formula to find the area of rhombus:

[tex] = \frac{1}{2} \times d1 \times d2[/tex]

( half of product of diagonals)

Also, in a rhombus ,the diagonals bisects each other.

So,

D1=5*2=10

D2=12*2=24

Area of rhombus:

[tex] \frac{1}{2} \times d1 \times d2 \\ = \frac{1}{2} \times 10 \times 24 \\ = \frac{240}{2} \\ = 120 \: {cm}^{2} [/tex]

Hope this helps..

Good luck on your assignment..

Answer:

see below

Step-by-step explanation:

1.

1, H - 2, H - 3, H - 4, H - 5, H

1, T - 2, T - 3, T - 4, T - 5, T

2.

2,H is one out of 10 possible outcomes, so the probability is 1/10

============================================================

Explanation:

Pick two points on this diagonal line where (x,y) has whole number coordinates. Two such points that fit the description are (-3,2) and (1,-1)

Use the slope formula to find the slope through these points

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

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

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

m = -3/4 is the slope

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

Extra info:

It doesn't matter which two points you pick as you'll always get the same slope value. Of course, the points must be on the diagonal line.

The negative slope indicates the line goes downhill as you move from left to right.

slope = rise/run = -3/4

rise = -3, a negative rise means we go down 3 units

run = 4, we go to the right 4 units

so we go down 3 and over to the right 4. This will move us from (-3,2) to (1,-1)

Answer:

Slope of Anya's line is m = 3

Step-by-step explanation:

Explanation:-

Given Anya graphed the line

                              (y−2)=3(x−1)

we know that  slope intercept form is

                                y = mx +c

now given Anya line

                           y−2=3(x−1)

            ⇒            y - 2 = 3x - 3

          ⇒             y = 3x - 3 + 2

         ⇒              y = 3 x - 1

Comparing slope -intercept form

                        y = mx +c

slope of Anya's line is m = 3 and y-intercept C = -1

Answer:

M=3

Step-by-step explanation:

Hope this helps!

Answer:

Step-by-step explanation:

y = x + 1

y = 3x - 2

3x - 2 = x + 1

2x - 2 = 1

2x = 3

x = 3/2 or 1.5

y = 1.5 + 1

y = 2.5 or 2 1/2

(1.5, 2.5)

Answer:

(1.4,2.5)

Step-by-step explanation:

Graphing

As we can see from the attached graphe, the intersection of the two lines, namely the solution, is (1.5,2.5).

So the closest approximation from the list is (1.4,2.5)

Answer:

Step-by-step explanation:

This is not a triangle at all. You must have typed the angles incorrectly. A triangle's angles have to add up to 180 and yours only add up to 160...

Answer:

Option (C).

Step-by-step explanation:

Graphed function is,

f(x) = x² - 2x - 3

     = x² - 2x + 1 - 1 - 3

     = (x² - 2x + 1) - 4

     = (x - 1)² - 4

f(-2x) = (-2x)² - 2(-2x) - 3

        = 4x² + 4x - 3

        = 4(x² + x) - 3

        = 4[x² + 2(0.5)x + (0.5)²- (0.5)²] -3

        = 4(x + 0.5)² - 1 - 3

        = 4(x + 0.5)² - 4

        = 4[(x - 1) + 1.5]² - 4

Therefore, parent function 'f' will be a horizontal shrink by 4 units and  shifted 1.5 units to the left.

Option (C) will be the answer.

Answer:

  book 25; pen 8

Step-by-step explanation:

If we let b and p represent the cost of a book and a pen, respectively, then the two purchases can be written as ...

  7b +4p = 207

  5b +5p = 165

Multiply the second equation by 4/5 and subtract the result from the first equation:

  (7b +4p) -4/5(5b +5p) = (207) -4/5(165)

  3b = 75 . . . . simplify

  b = 25 . . . . . divide by 3

Dividing the second equation by 5 gives ...

  b + p = 33

Solving for p, we have ...

  p = 33 -b = 33 -25 = 8

The cost of an exercise book is 25; the cost of a pen is 8.