in
ABC, ABC is a right angle AB=3 units, and BC=2 units &ABC is dilated by a scale factor of 0.5 with point 8 as the center of dilation, resulting
in the image AABC. Which statement about AB is true?
OA AB is 15 units long but lies on a different line than AB
OB AB is 3 units long but lies on a different line than AB
OC AB is 3 units long and lies on the same line as AB
OD. AB is 1.5 units long and lies on the same line as AB?

The simplified form of 13√5 + 3√5 is option c 16√5

Given,

The expression : 13√5 + 3√5

We have to simplify the above given expression.

Lets see the simplification of numbers with square roots.

1. Addition: a√b + c√b = (a + c) √b

2. Subtraction: a√b - c√b = (a - c) √b

3. Multiplication: a√b × c√b = a × c × b

4. Division: a√b ÷ c√b = a ÷ c

So here,

We can use addition:

That is,

a√b + c√b = (a + c) √b

Where,

a = 13, b = 5 and c = 3

Now,

13√5 + 3√5 = (13 + 3) √5 = 16√5

Therefore, the simplified form of 13√5 + 3√5 is option c 16√5

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The measure of each angles a,b and c are 32°, 74°  and 74°  respectively.

What is triangle?
Three edges and three vertices define a triangle as a polygon. One of geometry's fundamental shapes is this one. The symbol for an ΔABC triangle is A, B, and C.
Any three points determine a distinct triangle and a distinct plane in Euclidean geometry when they are non-collinear (i.e. a two-dimensional Euclidean space). To put it another way, each triangle is contained in a plane, and there is only one plane that includes that particular triangle. All triangles are contained in one plane if and only if all geometry is the Euclidean plane, however this is no longer true in higher-dimensional Euclidean spaces. Except as otherwise specified, the subject of this article is triangles in Euclidean geometry, more specifically, the Euclidean plane.

Let angle b be x

Therefore angle c will also be  x [as given b and c are equal] and angle a will be x - 42°.
Now as we know that the sum of the measures of the angles of a triangle is 180° therefore,

x + x + x - 42° = 180°

=> 3x = 222°

=> x = 74°  which is angle b and c

and angle a is (74 - 42)°  =32°  

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The value of A in the digit is 6.

The 14 digit numbers are written in the boxes.

The sum of any three consecutive digits is 20.

Therefore, from the last three digits,

5 + 9 + x = 20

14 + x = 20

subtract 14 from both sides of the equation

14 - 14 + x = 20 -14

x = 6

There the value of A is 6.

If you notice the pattern, it follows the same pattern forward and backward as follows:

69569569569569

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Answer: 2x + 3y =  33

Based on the beginning inventory to Hoover Electronics and the units to be sold, the number of units that Hoover should produce is 43, 700 units

First, find the ending inventory that Hoover Electronics would prefer which is 40% of the beginning inventory:

= Percentage of beginning inventory

= 40% x 15, 500

= 6, 200 units

The amount that Hoover should produce in units is:
= Amount to be sold + Ending inventory - Beginning inventory

= 53, 000 + 6, 200 - 15, 500

= 43, 700 units

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The two numbers so that the exact answer is between 6×7381 are 28,000 and 48,000.

Given:

To find two numbers the exact answer is between 6×7381.

7,381 is between the numbers 7,000 and 8,000.

Rounding the number 7,381 down to 7000 and multiplying 6 by it.

6 × 7,000 is 28,000

Rounding the number 7,381 up to 8000 and multiplying 6 by it.

6 × 8,000 is 48,000

The two numbers so that the exact answer is between 6×7381 are 28,000 and 48,000 respectively.

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Answer:

difference = 6 feet 5 inches

Step-by-step explanation:

The longest shot put throw by a boy is given as 25 feet 8 inches . The longest shot put throw by a girl is given as 19 feet and 3 inches. The number of times the longest shot put throw by a boy is greater than by a girl can be computed as follow.

The question asked us to find the difference between the throw. The difference between the throw is the boy throw minus the girls throw. Mathematically,

The longest boys throw = 25 feet 8 inches

The longest girls throw =  19 feet 3 inches

difference = The longest boy throw  - The longest girl throw

difference =  25 feet 8 inches -   19 feet 3 inches

difference = 6 feet 5 inches

If Katie Pittman earns a $60,840 annual salary, her weekly gross salary is $1170.

What is  weekly gross salary?

The number of hours worked multiplied by the hourly wage of an employee is how gross wages are determined for hourly workers. For instance, an employee making $12 per hour and working 25 hours per week would earn a gross weekly salary of $300 (25 x 12 = 300).

What is annual salary?

The gross pay (before tax deductions) divided by the number of pay periods in a year yields the yearly salary. For instance, a worker making $1,500 each week would make $78,000 a year (1,500 multiplied by 52).

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Answer:

Step-by-step explanation:

17/25

Using the Factor Theorem, the polynomial with real coefficients that has zeros -1 and 2 - 3i is given by:

f(x) = x³ - 3x² + 9x + 13.

The Factor Theorem states that a polynomial function with roots(also called zeros) [tex]x_1, x_2, \codts, x_n[/tex] is given by the following rule.

[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]

In which a is the leading coefficient of the polynomial, determining if it is positive(a positive) or negative(a negative).

Considering a leading coefficient of a = 1, the zeros of the polynomial are given as follows:

Hence the polynomial is given by:

f(x) = (x + 1)(x - 2 + 3i)(x - 2 - 3i)

f(x) = (x + 1)[(x - 2)² - (3i)²]

f(x) = (x + 1)(x² - 4x + 13), as (3i)² = 9i² = 9(-1) = -9, -(-9) = 9.

f(x) = x³ - 3x² + 9x + 13.

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It is proved that 12n-n²+ (2n-1)(4n+ 3) - 4 is a multiple of 7 because on solving it results in 7(n² + 2n -1).

To prove that 12n-n²+ (2n-1)(4n+ 3) - 4 is a multiple of 7.

When an algebraic expression is a multiple of 7 it should be divisible by 7.

Now, solve the algebraic expression.

12n - n²+ 8n² + 6n - 4n -3 - 4 (combine the like terms)

7n² + 14n - 7 (take out the common factor 7)

7(n² + 2n -1)

Therefore, the algebraic expression has a factor of 7 and is always a multiple of 7 for all positive integer values of n.

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An equation or inequality to model the situation: The distance d to school is 1 1/2 miles more than the distance p to the park is  d = p + 3/2

a statement that the values of two mathematical expressions are equal indicated by the sign =, is known as equation.

A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions is known as inequality.

For this situation, we would assume that both the distances i.e 'd' and 'p' are in miles.

It is mentioned that the distance d is more than the distance p by 3/2 miles.

It means that if we add  3/2 miles to the distance 'p' the output will be distance 'd'

The equation for this is as follows :- d = p + 3/2

It also means that if we substract 3/2 miles from distance 'd', the output will be distance 'p'

The equation for this is as follows :- p = d - 3/2

But we are asked in the situation that distance d is more than than the distance 'p'.

Therefore , an equation or inequality to model the situation: The distance d to school is 1 1/2 miles more than the distance p to the park is d = p + 3/2.

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The converse of  t > r is r > t

A converse statement is determined when both the hypothesis and conclusion are reversed or interchanged.

In this condition, the hypothesis is written as the conclusion and the conclusion is changed to be the hypothesis.

If a conditional statement is written as: x → y

The converse is then written as y → x

Where;

Given the expression as;

t > r

We can see that;

The converse will be;

r > t

Hence, the converse is r > t

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Answer:

29

Step-by-step explanation:

=5+5×5–1(5÷5=1)

Multiplication

=5+25–1(5×5=25)

Addition

=30–1

(25+5=30)

Subtraction

=29

(30-1=29)

The total probability that a king and pawn are selected without replacement is  1 / 31 .

The area of mathematics known as probability primarily deals with numerical(fractions or decimals) representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Sample space = 32 (16 black and 16 white pieces)

number of kings in the set = 2

Probability that a king is selected first

P(king) = 2 ÷ 32 = 1 / 16

Now the total number of pieces left = 32 - 1 = 31

number of pawns = 8+8 =16

Probability that a pawn is selected = 16 ÷ 31

P(pawn) = 16/31

Now the total probability that a king and pawn are selected without replacement = P(king) × P(pawn) = 1/16 × 16/31 = 1 / 31

Therefore the required probability is 1 / 31 .

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The transformations are

Transformation 1

Here, we have

The coordinates are given as

P(-5, 4), Q(2, 8), R(6, 1) and S(-1, -3)

The transformation is given as

<2, -4>

This is represented as

(x, y) ⇒ (x + 2, y - 4)

This means that the translation is (x + 2, y - 4)

When this rule is applied on the coordinates, we have

P'(-3, 0), Q'(4, 4), R'(8, -4) and S'(1, -7)

Next, we plot the image of the transformation on a coordinate plane

See attachment for the image of the transformation

Transformation 2

Here, we have

The coordinates are given as

E(-7, -7), F(-2, -3), G(-1, -6)

The transformation is given as

<8, 3>

This is represented as

(x, y) ⇒ (x + 8, y + 3)

This means that the translation is (x + 8, y + 3)

When this rule is applied on the coordinates, we have

E'(1, -4), F'(6, 0) and G'(7, -4)

Next, we plot the image of the transformation on a coordinate plane

See attachment for the image of the transformation

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[tex]y=\stackrel{\stackrel{m}{\downarrow }}{3}x\stackrel{\stackrel{b}{\downarrow }}{-1}\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

Another way that people can look up how much they owe in tax is by looking it at IRS.gov/account.

A tax that you pay to the federal government in the US as opposed to a state government If income is used to pay for college, it could not be subject to federal taxes. Federal taxes are collected by the federal government.

The marginal tax rate should be used to calculate federal taxes. It only applies to taxable income. Make changes to gross revenue to arrive at a determinable Taxable income before computing Taxable income. Deductions must then be made. After deductions, taxable income is available. There is no tax due if there is no taxable income.

At IRS.gov/account, you can securely log in to access your federal tax account. Once you've logged into your account, you can see your balance and the amount you owe, as well as 18 months' worth of payment history, access Get Transcript, and see the most important data from your most recent tax return.

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The rectangular prism has the following dimensions;

The total surface area of

The total surface area of the rectangular prism is 114 square meters

Answer: 8 is actually the constant of proportionality, since it is the number that stays the same regardless of the change in x and y.  

Step-by-step explanation:

Let's say you want to know how many pounds of meat a male lion would eat in a month in order to purchase for the zoo the correct amount of food needed.   Let's assume the month was 30 days.  we know that 8 is the amount of food per day (that number will not change because it is a constant.  

so 30 x 8 = 240 which is what y is for the 30 days.  

if you needed two weeks, 14 days.  14 x 8 = 112 pounds for the 14 days.  

So you see 8 stays the same for each scenario, so it is the constant that is used for all values of x to find y.  

Using the t-distribution, the 98% confidence interval for the mean temperature is of:

(47.335, 65.624).

The confidence interval is given as follows:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which the parameters are:

Using a calculator, the parameters from this sample are given as follows:

[tex]\mu = 56.43, s = 10.198, n = 10[/tex]

The critical value, using a t-distribution calculator, for a two-tailed 98% confidence interval, with 10 - 1 = 9 df, is t = 2.82.

The lower bound of the interval is:

[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 56.43 - 2.82\frac{10.198}{\sqrt{10}} = 47.335[/tex]

The upper bound of the interval is:

[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 56.43 + 2.82\frac{10.198}{\sqrt{10}} = 65.524[/tex]

Hence the interval is:

(47.335, 65.624).

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The journal entries to record both the dividend declaration and its distribution is : Dr Retained earnings  $44,640, Cr Common stock dividend distributable $31,000, Cr Paid-in capital in excess of par value, Common stock $13,640 .

TVX Company Journal entries

Feb 05

Dr Retained earnings  $44,640

[ (62,000 shares × 2%) ×$36 ]

Cr Common stock dividend distributable $31,000

[ (62,000 shares × 2%) ×$25 ]

Cr Paid-in capital in excess of par value, Common stock $13,640

($44,640 - $31,000)

(To record dividend declaration)

Feb 28

Dr Common stock dividend distributable$31,000

[ (62,000 shares × 2%) ×$25 ]

Cr Common stock, $25 par value $31,000

(To record dividend distribution)

Therefore the entry is  Dr Retained earnings  $44,640, Cr Common stock $31,000, Cr Paid-in capital $13,640.

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In general, given a function g(x), a transa

In linear equation, 3464.1016 feet  is the shortest length of fence that the Ranch owner can use.

What is linear equation definition and example?

Let L represent the length of the field.

Let W represent the width of the field.

Let F represent the length of fence needed.

L*W=500000

2L+3W=F Both length sides+both width sides+ fence across the width.

Let's look at the first equation again:

L*W=500000

W=(500000/L)

Now we can substitute (500000/L) for W in the second equation.

2L+3(500000/L)=F

2L+1500000/L=F

Now we have a function. We can input any length, and we'll know length needed. But how can we find the length needed so that F is as small as it can be? If you know derivatives, there's an exact way. The next easiest way to do it is to graph.

Manner 1: Derivative

Set the derivative to zero...when the length stops going down and starts coming back up, it'll be at it's lowest point.

2L+1500000^-1=F

F'=2-1500000^-2

0=2-1500000^-2

1500000/(L^2)=2

1500000=2L^2

1500000=L^2

L=866.025

Now, we know that L=500000/W

so 866.025=500000/W

W=500000/866.025

W=577.35027 feet.

Now,

2L+3W=2(866.025)+3(577.35027)

Minimum fencing needed: 3464.1016 feet.

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Answer:

c = 0.95*p

Step-by-step explanation:

With p representing the number of pounds purchased, and each pound costing 0.95, the total cost c can be found by multiplying the cost per pound by the total number of pounds. Simply put, total cost = 0.95 * total pounds.

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The  inequality in which involves one or more rational expressions is Rational inequality.

What is inequality?

Using the terms greater than, larger than or equal to, less than, or less than or equal to as a declaration of the order connection between two integers or algebraic expressions is known as inequality. Economic inequality comes in many forms, most notably wealth inequality measured by the distribution of wealth and income inequality measured by the distribution of income (the amount of money people are paid) (the amount of wealth people own). There are significant forms of economic inequality amongst various groups of people in addition to economic disparity between nations or states.

An inequality with a rational expression is said to be rational. Inequalities with rational expressions, such as 32x>1, 2xx34, 2x3x6x, and 142x23x, are referred to as rational inequalities.

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The answer is d. Rational inequality, which includes fractions with polynomials. Other options involve exponential, linear, or logarithmic functions, without rational expressions as in inequalities.

The right choice is d. Rational inequality. An objective disparity includes at least one sane articulations, which are portions with polynomials in the numerator and denominator. These disparities can be settled by finding the basic places where the normal articulation is indistinct or changes sign.

The arrangement includes deciding the stretches where the disparity turns out as expected in view of the indication of the judicious articulation in those spans. Interestingly, dramatic, direct, and logarithmic disparities include various kinds of numerical capabilities.

Remarkable imbalances contain dramatic terms, direct disparities incorporate straight capabilities, and logarithmic imbalances contain logarithmic capabilities. Each kind of imbalance has its own qualities and strategies for settling, however just objective disparities straightforwardly manage levelheaded articulations including parts of polynomials.

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Answer: 3.

Step-by-step explanation:

[tex]\left \{ {{4x-3y=3 \ |[*(-4)]} \atop {5x-4y=3} \ |[*3]} \right. \ = > \ \left \{ {{-16x+12y=-12} \atop {15x-12y=9}} \right. \ = > \ \left \{ {{y=3} \atop {x=3}} \right.[/tex]