"1.Provide the reasons for the proof.
Given: m angle1 = m angle2
Prove:

Answer:
StatementsReasons
a. m angle 1 = m angle 2a. Given
b. angle 1 is supplementary to angle 2.b. Definition of supplementary angles.
c. m angle 1 + m angle 2 = 180 c.
d. m angle1 + m angle1 = 180
2(m angle1) = 180d.
e. m angle1 = 90e.
f. angle 1 is a right angle.f. GIVEN OR PROVE IF PROVE PUT REASON....EXAMPLE: SUPPLEMENTARY......"

Answer:

[tex]x=\frac{-2\pm \sqrt{(2)^{2}-4(4)(-1)}}{2(4)}[/tex] is the answer.

Step-by-step explanation:

Given quadratic equation is 4x²+ 2x - 1 = 0

To find the solution of the equation we use the quadratic formula

[tex]x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}[/tex]

Now we put the values of a = 4, b = 2 and c = (-1)

Therefore, quadratic formula for the equation given will be

[tex]x=\frac{-2\pm \sqrt{(2)^{2}-4(4)(-1)}}{2(4)}[/tex]

Answer:

D) 15

Step-by-step explanation:

The value of the function f(x) = 5x + 40 at x = -5 will be 15. Then the correct option is D.

A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.

The function is given below.

f(x) = 5x + 40

The value of the function f(x) = 5x + 40 at x = -5, then the value of the function will be

f(-5) = 5 (-5) + 40

f(-5) = - 25 + 40

f(-5) = 15

Then the value of the function f(x) = 5x + 40 at x = -5 will be 15.

Then the correct option is D.

More about the function link is given below.

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Sam and Jesse wash a total of 70 cars over two days, by washing five cars each hour for seven hours each day.

Sam and Jesse work together to wash cars. They can wash five cars each hour, and they work for seven hours each day. Since they do this over the course of two days, we need to calculate the total number of cars they wash in this period.

First, we find out how many cars they can wash in one day by multiplying the number of cars they can wash in an hour by the number of hours they work:

Next, since they work for two days, we multiply the number of cars washed in one day by two:

Sam and Jesse wash a total of 70 cars over the two days.

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Answer:  The required sum of first terms of the series is [tex]\dfrac{1705}{64}.[/tex]

Step-by-step explanation:  We are given to find the sum of the first five terms of a geometric series with first term and common ratio as follows :

[tex]a_1=20~~~~~\textup{and}~~~~~r=\dfrac{1}{4}.[/tex]

We know that

the sum of first n terms of a geometric series with first term [tex]a_1[/tex] and common ratio r is given by

[tex]S_n=\dfrac{a(1-r^n)}{1-r}.[/tex]

Therefore, the sum of first 5 terms of the given geometric series is given by

[tex]S_5\\\\\\=\dfrac{a(1-r^5)}{1-r}\\\\\\=\dfrac{20(1-(\frac{1}{4})^5)}{1-\frac{1}{4}}\\\\\\=\dfrac{20\left(1-\frac{1}{1024}\right)}{\frac{3}{4}}\\\\\\=20\times\dfrac{4}{3}\times\dfrac{1023}{1024}\\\\\\=20\times\dfrac{341}{256}\\\\\\=\dfrac{5\times 341}{64}\\\\\\=\dfrac{1705}{64}.[/tex]

Thus, the required sum of first terms of the given geometric series is [tex]\dfrac{1705}{64}.[/tex]

The set of all real numbers n that are less than -3 can be represented as: [tex]\[ \{ n \mid n < -3 \} \][/tex]

The set of real numbers less than -3 encompasses an infinite range of values extending to the left of -3 on the number line. These numbers are characterized by being smaller than -3, denoted as ( n < -3 ). In interval notation, this set is represented as (-∞, -3), indicating that it includes all real numbers from negative infinity up to, but not including, -3.

This set is unbounded, as there is no limit to how far left the numbers extend, encompassing an infinite continuum of values that are progressively smaller than -3.

To convert from pounds to ounces, multiply the number of pounds by the unit equivalence of 1 pound = 16 ounces.

Conversion from pounds to ounces:

First, find the unit equivalence: 1 pound = 16 ounces.

Next, multiply the number of pounds by the unit equivalence. Thus, 5 pounds x 16 equals 80 ounces.

Lee Wong's annual salary raise of $3,000 represents a 4.6% increase from his original salary of $65,000 when rounded to the nearest tenth of a percent.

To calculate the percentage increase of Lee Wong's salary, we use the formula for percentage change: Percentage Change = (Change in Quantity / Original Quantity) × 100%. In this case, the change in quantity is the raised amount of $3,000, and the original quantity is the original salary of $65,000.

Percentage Increase = ($3,000 / $65,000) × 100% = 0.04615 × 100% = 4.615%. Rounded to the nearest tenth of a percent, Lee Wong's salary increase is 4.6%.

The slope of the line that passes through the points (1, -19) and (-2, -7) is calculated to be -4.

The slope of the line through the pair of points (1, -19) and (-2, -7), you can use the slope formula: slope (m) = (y₂ - y₁) / (x₂ - x₁), where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.

Using the points given:

x₁ = 1, y₁ = -19

x₂ = -2, y₂ = -7

Substitute these values into the formula:

m = (-7 - (-19)) / (-2 - 1)

m = (12) / (-3)

m = -4

Therefore, the slope of the line through the points (1, -19) and (-2, -7) is -4.

The correct answer is that there are 2000 people in the school.

To solve this problem, we can set up a proportion based on the information given. We know that 9% of the school's population is in the band, and the band has 180 members. We want to find the total population of the school, which we will denote as [tex]\( P \)[/tex].

The proportion can be written as:

[tex]\[ \frac{9}{100} = \frac{180}{P} \][/tex]

Now, we can solve for [tex]\( P \)[/tex] by cross-multiplying:

[tex]\[ 9P = 180 \times 100 \][/tex]

Divide both sides by 9 to isolate [tex]\( P \)[/tex]:

[tex]\[ P = \frac{180 \times 100}{9} \][/tex]

Simplify the right side of the equation:

[tex]\[ P = \frac{18000}{9} \][/tex]

[tex]\[ P = 2000 \][/tex]

Therefore, the total population of the school is 2000 people. This matches the correct answer given in the options.

An equation for a line in the plane allows you to find the x- and y-coordinates of any point on that line.

The statement is True.

An equation for a line in the plane, such as y = mx + b, allows you to find the x- and y-coordinates of any point on that line. The x-coordinate can be found by substituting a given y-value into the equation and solving for x. Similarly, the y-coordinate can be found by substituting a given x-value into the equation and solving for y.

Answer: TRUE!!!!!

Step-by-step explanation:

trust me

The new ratio of Elena’s hair ties to Melanie’s hair ties is 8 : 3.

Given that Elena has 32 hair ties and Melanie has 8 hair ties, let’s analyze the situation:

Initial Ratio:

The ratio of Elena’s hair ties to Melanie’s hair ties is: [ \text{Elena : Melanie} = 32 : 8 = 4 : 1 ]

Melanie Gets 4 More Hair Ties:

After Melanie receives 4 additional hair ties, her total becomes: [ \text{Melanie’s new total} = 8 + 4 = 12 ]

New Ratio:

Now, let’s find the new ratio of Elena’s hair ties to Melanie’s hair ties: [ \text{Elena : Melanie} = 32 : 12 = 8 : 3 ]

Therefore, the new ratio of Elena’s hair ties to Melanie’s hair ties is 8 : 3.

Complete question:

Elena has 32 hair ties. Melanie has 8 hair ties. The ratio of Elena’s hair ties to Melanie’s hair ties is : 1. If, Melanie gets 4 more hair ties, the new ratio of Elena’s hair ties to Melanie’s hair ties is 8 :

Answer:

We should use C. 1.25

Step-by-step explanation:

We know that the children's book dimensions are 20 cm x 24 cm

We need to find a scale factor (which is a number) that will turn the dimensions 20 cm x 24 cm ⇒ 25 cm x 30 cm

We can write :

(20 cm) . a = 25 cm

Where ''a'' is the scale factor.

Solving for a :

[tex](20cm).a=25cm\\a=\frac{25cm}{20cm}=1.25 \\a=1.25[/tex]

This result is reasonable because the scale factor won't have units

A scale factor of 1.25 turns 20 cm ⇒ 25 cm

We can use the another dimension to verify :

(24 cm) . a = 30 cm

(24 cm) . (1.25) = 30 cm

30 cm = 30 cm

The scale factor is option C. 1.25

Answer:

No, the answer is not $ 336

The interest that she will pay is $ 504.

Step-by-step explanation:

Given : Andrea borrowed 2,240 at 15% apr for 18 months.

We have to calculate  the interest will she pay.

Using formula for Simple interest.

[tex]SI =P\times r\times t[/tex]

Where P is principal amount

r is rate of interest

t is time period.

Given : P = $ 2240

t = 18 months

In years , [tex]\frac{18}{12}[/tex]

r = 15% = 0.15

Substitute, we have,

[tex]SI=2240\cdot0.15\cdot\frac{18}{12}[/tex]

Simplify, we have,

SI = 504

Thus, The interest that she will pay is $ 504.

No, the answer is not $ 336

Andrea will pay $504 in interest on a loan of $2,240 at 15% APR over 18 months, not $336. The calculation involves converting the loan duration into years and applying the formula for simple interest.

To determine how much interest Andrea will pay on a loan of $2,240 at 15% APR for 18 months, we first need to understand that APR (Annual Percentage Rate) is the interest rate for a whole year (annual), rather than just a monthly fee or rate. Since APR is annual but our loan term is in months, we convert the duration into years to match the APR's annual nature. 18 months is equivalent to 1.5 years. Therefore, the interest calculation would be as follows:

Principal (the amount borrowed) = $2,240

Rate (APR) = 15%

Time = 1.5 years

Interest = Principal × Rate × Time

Interest = $2,240 × 15% × 1.5 = $2,240 × 0.15 × 1.5

Interest = $504

Therefore, Andrea will pay $504 in interest, not $336 as presumed. It's essential to accurately convert the time to years when dealing with APR to ensure the calculation is correct.

Tarriq must use "2" as the Multiplication Property of equality.

The Multiplication Property of Equality for any numbers a, b, and c, If we multiply both sides of an equation by the identical number, we always have equivalency.

Rearrange unfamiliar terms to the left side of the equation then

2x = -190 - 50

Calculate the sum or difference

2x = -240

Divide both sides of the equation by the coefficient of variable 2, and we get

x = -240 [tex]$ \div[/tex] 2

Calculate the product or quotient then we get

x = -120

Therefore, the correct answer is option D) 2.

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Tarriq must use factor C) 1/2, as this represents dividing both sides of the equation by 2 to isolate x, resulting in x = –120.

To finish solving the equation 2x = –240 using the multiplication property of equality, Tarriq must divide both sides of the equation by 2, which is the coefficient of x.

This step can be shown as:

2x / 2 = –240 / 2

The division property of equality allows us to simplify by canceling out the 2s on the left, resulting in:

x = –240 / 2

Therefore, x equals:

x = –120

This shows that the factor Tarriq must use to finish solving the equation is C) 1/2 since that represents the inverse operation of multiplying by 2.

To optimize the dimensions of a rectangle with an area of 32 square cm such that the distance from one corner to the midpoint of a non-adjacent edge is minimized, one must use the Pythagorean theorem and calculus. The minimum distance occurs when the rectangle is a square with sides measuring 4√2 cm.

Assume the rectangle's dimensions are length L and width W, with the given area 32 cm2 such that LW = 32. To minimize the distance (D) from one corner to the midpoint of the non-adjacent edge, we can use the Pythagorean theorem, given by D = √(L2 + (W/2)²).

Since the area is fixed, W can be expressed as 32/L, and we can write D as a function of L. After substituting 32/L for W and differentiating with respect to L, we can find the minimum by setting the derivative equal to zero and solving for L.

The minimum distance is achieved when the rectangle is a square, with length and width both equal to √32, which simplifies to 4√2 cm, which is approximately 5.66 cm for both dimensions.

Answer:

d. 20

Step-by-step explanation:

Replace the x and y values in the equation

(y = 0.5x + 10) to (x = 0.5y + 10)

Now, solve for the y value in the new equation. You'll get y = 2x + 20.

So, the intercept of the inverse function is 20.

The average rate of change of the function f(x)=120(0.1)^x from x=0 to x=2 is calculated as (f(2) - f(0)) / (2 - 0), which gives -59.4.

Average Rate of Change

The average rate of change of a function over an interval is calculated by the difference in function values at the endpoints divided by the difference in input values. For the function f(x) = 120(0.1)^x, we want to find this rate from x = 0 to x = 2. First, we find the function values:

f(0) = 120(0.1)⁰ = 120

f(2) = 120(0.1)² = 120(0.01) = 1.2

Then we use the formula for average rate of change:

Average rate of change = (f(2) - f(0)) / (2 - 0) = (1.2 - 120) / 2 = -118.8 / 2 = -59.4

Therefore, the average rate of change of the function on the interval from x = 0 to x = 2 is -59.4.

Three equivalent fractions for [tex]\( \frac{80}{100} \) are \( \frac{4}{5} \), \( \frac{160}{200} \), and \( \frac{400}{500} \)[/tex].

To find three equivalent fractions for [tex]\( \frac{80}{100} \)[/tex], we can simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 20 in this case.

1. Divide both the numerator and denominator by 20:

[tex]\[ \frac{80 \div 20}{100 \div 20} = \frac{4}{5} \][/tex]

So, [tex]\( \frac{80}{100} \)[/tex] is equivalent to [tex]\( \frac{4}{5} \)[/tex].

2. Multiply both the numerator and denominator by the same non-zero integer:

[tex]\[ \frac{80 \times 2}{100 \times 2} = \frac{160}{200} \][/tex]

So, [tex]\( \frac{80}{100} \) is also equivalent to \( \frac{160}{200} \)[/tex].

3. Similarly, we can multiply both the numerator and denominator by another non-zero integer:

[tex]\[ \frac{80 \times 5}{100 \times 5} = \frac{400}{500} \][/tex]

So, [tex]\( \frac{80}{100} \) is also equivalent to \( \frac{400}{500} \)[/tex].

Answer:

they spend $ 5.88 to buy a gift but there is not enough money left to buy a card of $3.25

Step-by-step explanation:

The earnings form Wednesday of Samuel and Jason are:

   Samuel earnings = 12.5x0.40 = $5

   Jason earnings = 7.1x0.40 = $ 2.84

The combined earnings form Wednesday are:

   Combined earnings = Samuel earnings + Jason earnings

   Combined earnings= $5 + $ 2.84 = $ 7.84

The spended earnings are:

    Spended earnings = combined earnings x ¾

    Spended earnings = 7.84 x ¾ = $ 5.88

The left over is:

    Left over = combined earnings – spended earnings

    Left over = 7.84 – 5.88 = $ 1.96

So, they spend $ 5.88 to buy a gift but there is not enough money left to buy a card of $3.25

Invest in more than one type of investment.