Which method and additional information would prove δonp and δmnl similar by the aa similarity postulate? segments om and lp intersect at point n; triangles are formed by points lnm and onp; line k intersects with both triangles at point n. use a rigid transformation to prove that ∠opn ≅ ∠mln. use rigid and nonrigid transformations to prove segment pn over segment mn = segment ln over segment on. use a rigid transformation to prove that ∠npo ≅ ∠lnm. use rigid and nonrigid transformations to prove segment ln over segment on = segment pn over segment mn.

Answer:

a.

Equation 1: y = x + 1

Equation 2: y = 4x - 5

Substitute Equation 1 into Equation 2:

x + 1 = 4x - 5

Now, solve for x:

4x - x = 1 + 5

3x = 6

x = 2

So now we have x, lets solve for y:

y = x + 1

Substitute x:

y = 2 + 1

y = 3

So the point of intersection of line y = x + 1 and line y = 4x -5 is (2,3) as shown on the graph.

Lets do the other two now:

b.

Equation 1: x + 4y = 1

Equation 2: 2x - y = -7

For this one we cannot simply substitute we have to get rid of one variable to create another equation.

Lets get rid of x for equation 3. To do this we simply times Equation 1 by 2:

Equation 3: 2x + 8y = 2

With this we can minus Equation 2 and Equation 3 to get rid of x:

2x - y = -7

-

2x + 8y = 2

-9y = -9

y = 1

Now that we have the y value, we can now find x using any equations above, lets use Equation 1:

x + 4y = 1

x + 4(1) = 1

x + 4 = 1

x = 1 - 4

x = -3

So the point of intersection is (-3,1).

c.

Equation 1: 4x + y = 11

Equation 2: y = -2x + 3

For this question, we can just do what we did for question a.

Lets substitute Equation 2 into Equation 1:

4x + (-2x + 3) = 11

4x - 2x + 3 = 11

2x + 3 = 11

2x = 11 - 3

2x = 8

x = 4

So we got our x value, let get our y value. Lets use Equation 1 for that:

4x + y = 11

4(4) + y = 11

16 + y = 11

y = 11 - 16

y = -5

So, the point of intersection is (4,-5).

There were total 276 guests in the wedding that Joy organised.

Given,

fraction of the guest that chose beef = 1/3

fraction of the guest that chose chicken = 5/12

fraction of the guest that chose vegetarian = 1  - 1/3 - 5/12 = 1/4

we are asked to find the total number of guests in the wedding:

guests that chose vegetarian = 1/4

guests that chose vegetarian = 69

1/4 of the guest = 69

4/4 of the guest = 69 x 4 = 276

Hence there are total 276 guests in the wedding.

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Answer:

[tex]16x^4y^2 a^6[/tex]

Step-by-step explanation:

[tex](-4x^2ya^3)^2=(-4)^2(x^2)^2(y)^2(a^3)^2 \\ \\ =16x^4y^2 a^6[/tex]

Answer:

h = 9

Step-by-step explanation:

Step 1: Subtract 6h from both sides.

4h +3 −6h = 6h −15 −6h

−2h +3 = −15

Step 2: Subtract 3 from both sides.

−2h + 3 −3 = −15 −3

−2h = −18

Step 3: Divide both sides by -2.

(-2h/-2) = (-18/-2)

h = 9

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$500\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &5 \end{cases} \\\\\\ A=500\left(1+\frac{0.04}{4}\right)^{4\cdot 5} \implies A=500(1.01)^{20}\implies A \approx 610.10[/tex]

Answer:

the answer is either x= 4 , or it is   9[tex]x^{2} \\[/tex] - [tex]x[/tex] - 10

Step-by-step explanation:

Sorry dude, I'm confused a little bit on what to do, but i think one of these is right.

lmk if you get it right, and which one you used

Using the concepts of unitary method, we got that  $42.83 was the total for all of the food and drink. if me and my friend went to dinner together and ordered 4 hamburgers at $5.95 each, 3 baskets of fries at $4.25 each, and 4 sodas at $1.75 each

Since, we are given that cost price of one hamburger is $5.95,

so total cost of 4 hamburgers is =4×5.95=$23.08

Similarly, we are given that cost price of one baskets of fries which is $4.25,

so total cost of three baskets of fries is =3×4.25=$12.75

Similarly, we are given that cost price of one soda which is $1.75,

so total cost of 4 soda  is =4×1.75=$7.00

So, Total cost of my order is= 4 hamburger cost+3 baskets of fries cost +4 sodas cost =23.08+12.75+7.00=$42.83

Hence, if me and my friends went to dinner together and ordered 4 hamburgers at $5.95 each, 3 baskets of fries at $4.25 each, and 4 sodas at $1.75 each, the total for all of the food and drink was $42.83

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The angles found by the given figure are:

m∠5 = 97°

m∠7 = 97°

From the graph given we can get that the two parallel lines are cut by a transversal and:

m ∠4 = m∠2

m∠2 = 83°

hence, m∠2 + m∠5 = 180°

so,:

m∠5 = 180° - m∠2

= 180 - 83

= 97°

hence m∠5 = 97°

now, m∠7 = m∠5

since the vertical angles of two increasing lines are equal

so, m∠7 = 97°

Hence we get the two angles respectively.

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The mean length of time for each missed appointment in minutes will be 13.2 minutes per missed appointment.

The mean is the simple definition of the average of a large number. This actually implies one of the indicators of focused tendency in measurements. The statistic means is referred to as the normal. It is the ratio of the number of true judgments to the total number of impressions.

This sign was in a specialist's sitting area. 115 arrangements were missed a month ago. These missed arrangements were a sum of 25.3 hours.

The total number of minutes is given as,

⇒ 25.3 hours

⇒ 25.3 x 60 minutes

⇒ 1,518 minutes

The mean length of time for each missed appointment in minutes will be given as,

⇒ 1,518 / 115

⇒ 13.2 minutes per missed appointment

The mean length of time for each missed appointment in minutes will be 13.2 minutes per missed appointment.

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Step-by-step explanation:

item on sale costs 60 % of the original price

(sale price) = 60% of (original price)

(sale price) = 60% of $85

[given: (original price) = $85

(sale price) = $(60/100)*85

[60% may be written as 60/100 or 0.60 as needed by the problem]

(sale price) = $51.00

As per the given system of linear equation, the number of solution is infinite.

Linear equations:

An algebraic equation of the form

y = mx + b

Involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept is known as linear equation.

Given,

A system of three linear equations in three variables is consistent and dependent.

Here we need to find the number of solution for this system.

Here we know that the given system of three linear equations in three variables which is consistent and dependent.

We know that, the system is said to be consistent if it has at least one solution. Which means that the system which has no solution is said to be inconsistent.

Similarly, the system is has consistent solution is said to be independent if it has only one solution whereas it is said to be dependent if it has an infinitely many solutions.

Therefore, here the given system of three linear equations in three variables which is consistent and dependent, the system has an infinitely many solutions.

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Answer: x = 7

Step-by-step explanation: 6x = x^2 - 7

x^2 - 6x -7 =0

(x-7) (x+1) = 0

x = 7  

x = -1 ----> rejected

The positive solution of the required number is 7.

An expression is a grouping of one or more mathematical or logical operators, operands (values, variables, or other expressions), and brackets in mathematics and computer programming that denote a computation that can be evaluated to generate a value.

Let's start by translating the given sentence into an equation. Let "x" be the number we are trying to find. Then we can write:

6x = x² - 7

Now we need to solve for x. Let's rearrange the equation to get all the x terms on one side and all the constant terms on the other side:

x² - 6x - 7 = 0

We can solve this quadratic equation by factoring or using the quadratic formula, but let's use factoring for this problem. We need to find two numbers whose product is -7 and whose sum is -6. The two numbers are -7 and 1, so we can write:

(x - 7)(x + 1) = 0

This means that either x - 7 = 0 or x + 1 = 0. Solving for x, we get:

x = 7 or x = -1

Since we are looking for a positive solution, the answer is x = 7. Therefore, the positive solution is 7.

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Answer:

Step-by-step explanation:

(2/3)20

The probability that the sample proportion will be greater than 0.78 is:

78% of 400 is 0.78× 400 = 312.

So this probability is 1 subtracted by the p value of Z when x = 312

Z = (X - μ)/σ

We are going to approximate the binomial distribution to the normal.

Binomial probability distribution-

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

√V(X) = √np(1 - p)

Normal probability distribution-

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean and standard deviation o, the zscore of a measure X is given by:

Z = (X-μ)/σ

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z- score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that-

μ = E (X), σ = √V√(X).

In this problem, we have that:

n=400, p=0.8

So = E(X)=np=400-0.8=320

σ = √V(X) = √np(1-p)=√400×√0.8×√0.2=8

Hence, the probability that the sample proportion will be greater than 0.78 is:

78% of 400 is 0.78× 400 = 312.

So this probability is 1 subtracted by the p value of Z when x = 312

Z = (X - μ)/σ

Z = (312- 320)/8.

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When testing the difference between two population means, the sample variances are pooled to estimate the population variance when The population variances are assumed equal but unknown.

Population Mean:

The population mean can be calculated by the sum of all values in the given data/population divided by a total number of values in the given data/population.

In testing for the differences between the means of two independent populations where the variances in each population are unknown but assumed equal, the degrees of freedom are: n1 + n2 - 2.

population variance:

Population variance is a measure of how spread out a group of data points is. Specifically, it quantifies the average squared deviation from the mean.

Therefore When testing the difference between two population means, the sample variances are pooled to estimate the population variance when The population variances are assumed equal but unknown.

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Since they take prices rather than setting them, fully competitive enterprises must deal with a completely elastic demand curve.

What is competitive firm?

A perfectly competitive firm is a price taker, which means that it must accept the equilibrium price at which it sells goods. If a perfectly competitive firm attempts to charge even a tiny amount more than the market price, it will be unable to make any sales.

Since they take prices rather than setting them, fully competitive enterprises must deal with a completely elastic demand curve. They are so unable to alter the market selling price. In order to raise its income, a perfectly competitive firm will therefore increase output rather than pricing.

A totally competitive firm is unable to arbitrarily set its output price since it must accept the price set by the product's market demand and supply. As an alternative, the perfectly competitive firm can decide to sell any amount of output for the same price. Because customers are eager to purchase any quantity of the company's output at the market price, it follows that the firm must deal with a completely elastic demand curve for its product. The quantity that the perfectly competitive firm decides to produce, combined with the prices that are in effect on the market for inputs and outputs, will determine the firm's total revenue, total costs, and eventually the level of profits.

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Answer: 119 minutes

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Unit rates always compare quantities with different units

Ex. 10 km per 1 hour (10kph)

Answer:

729! Hope this helps :)

Step-by-step explanation:

Answer:

9^3 in standard form

Step-by-step explanation:

9 × 9 × 9

81 × 9

729

The amount of money that Richard will have when he turns 27 can be found to be $3, 474.26

Convert the interest rate to a periodic rate which will be in days as the interest is compounded daily:

= 7% / 365 days a year

= 0.019178%

The number of periods is:

= (27 - 15) years x 365 days a year

= 4, 380 days

The money that Richard will have when he turns 27 is:

= 1, 500 x ( 1 + 0.019178%) ⁴³⁸⁰

= $3, 474.26

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Answer:

cat = $30

dog = $45

Step-by-step explanation:

write the equation, assume cat = c, dog = d1

2c + 3d = 195 -> eq 1

4c + d = 165 -> eq 2

rewrite eq 2 so that dog is in term of cat

d = 165 - 4c -> eq 3

replace eq 3 into eq 1

2c + 3(165-4c) = 195

2c + 495 - 12c = 195

2c - 12c = 195 - 495

-10c = -300

c = -300/-10 = 30

replace c in eq 3

d = 165 - 4(30) = 165 - 120 = 45

The value of z such that 0.05 of the area lies to the right of z is 1.64.

Given:

0.05 = 5%

The z score is calculated:

z = x - μ / σ

from the t table the value of z is:

= 1.64

More details is in the image uploaded.

Therefore the value of z such that 0.05 of the area lies to the right of z is 1.64.

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The length of each side of the square is 4x - 1 while the area for the dimensions of the rectangle is (9x + 2y) by (9x - 2y) using the factorization methods of grouping and difference in two squares respectively.

Factorization is the process of breaking down a number in which when multiplied together will arrive at the original number.

Part A: Given the area of square as 16x² - 8x + 1, applying factorization by grouping;

16x² - 8x + 1 = 16x² - 4x - 4x + 1 (group terms with common factors)

16x² - 8x + 1 = 4x(x - 1) - (4x - 1) (factor out the common factor in each group)

16x² - 8x + 1 = (4x - 1) × (4x - 1) (factor the common factor from the expression)

16x² - 8x + 1 = (4x - 1)²

Part B: For the area or rectangle given as 81x² - 4y², factorizing by the method of difference in two squares;

81x² - 4y² = 9²x² - 2²y² (express as squares)

81x² - 4y² = (9x)² - (2y)²

81x² - 4y² = (9x + 2y) × (9x - 2y)

Therefore, 4x - 1 is the length of one side of the square as all sides of a square are equal and (9x + 2y) by (9x - 2y) is the dimension of the rectangle using the factorization methods of grouping and difference in two squares.

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Answer:

x=7/10

Step-by-step explanation:

Because this is a square, we know that all of the sides are equal.

Thus, we know that 6x-1=4x+6.

We can further use Algebra and subtract by 4x on both sides.

Now, we have 10x-1=6.

Then, we can add 1 to both sides, and get 10x=7.

Lastly, let's divide both sides by 10 to isolate x, getting x=7/10, or x=0.7

Answer: $14

Step-by-step explanation:

First, find the amount it will cost with one guest(x):

[tex]\frac{10}{5} =\frac{x}{1} \\\\10=5x\\\\x=\frac{10}{5} =2[/tex]

Then, use ratios to find the amount it will cost with seven guests(y):

[tex]\frac{2}{1} =\frac{y}{7} \\\\y=14[/tex]

Not sure if this is how you want it to be solved.

The ratio which compares to be a whole is:

2/9

Given,

Kenny has 2 red marbles and 4 black marbles.

we are asked to determine the ratio which compares a part to whole.

Based on the given conditions, formulate:

2 ÷ (4+2+3)

Calculate the sum

2/6+3

calculate the sum:

2/9

hence ratio is:

2/9

Hence we get the ratio as 2/9.

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The y-intercept of the equation means: D. It means the technician charges a fixed amount of $50 for the repair.

The y-intercept of an equation that models a situation is the initial or starting value. The y-intercept is represented in an equation that is expressed in slope-intercept form, y = mx + b, as "b". The value of "b" is the y-intercept.

Therefore, we are given that y = 20x + 50 represents the total amount the technician charges, in dollars, for a repair that takes specific hours. This implies that:

Therefore, y-intercept, b = 50, means: D. It means the technician charges a fixed amount of $50 for the repair.

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Answer:

XZ = 21 cm

Step-by-step explanation:

since the triangles are congruent then corresponding sides are congruent, so

LN = XZ , that is

5x - 19 = 2x + 5 ( subtract 2x from both sides )

3x - 19 = 5 ( add 19 to both sides )

3x = 24 ( divide both sides by 3 )\

x = 8

then

XZ = 2x + 5 = 2(8) + 5 = 16 + 5 = 21 cm

After factorizing we get the value as:

4sinαcosα

Given,

we have the expression as:

(sinα + cosα)² - (sinα - cosα)²

open the brackets using the identity of:

(a+b)² = a²+b²+2ab

(a-b)² = a²+b²-2ab

now evaluate:

⇒ sin²α + cos²α + 2sinαcosα - (sin²α + cos²α - 2sinαcosα)

⇒ sin²α + cos²α + 2sinαcosα - sin²α - cos²α + 2sinαcosα

⇒ cancel the like terms

⇒ 2sinαcosα  + 2sinαcosα

= 4sinαcosα

hence after factorization we get the value as 4sinαcosα

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The ordered pair P within the line segment AB is (- 1, 1 / 2).

In this question we have a segment whose endpoints are known: A(x, y) = (- 3, 2), B(x, y) = (5, - 4), and in which we need to determine the location of point P such that the following relationship is known:

k = AP / PB

[tex]\overrightarrow {AP} = k \cdot \overrightarrow {PB}[/tex]

P(x, y) - A(x, y) = k · [B(x, y) - P(x, y)]

(k + 1) · P(x, y) = A(x, y) + k · B(x, y)

P(x, y) = [1 / (k + 1)] · A(x, y) + [k / (k + 1)] · B(x, y)

Where:

If we know that A(x, y) = (- 3, 2), B(x, y) = (5, - 4) and k = 1 / 3, then the location of the ordered pair is:

P(x, y) = [1 / (4 / 3)] · (- 3, 2) + [(1 / 3) / (4 / 3)] · (5, - 4)

P(x, y) = (3 / 4) · (- 3, 2) + (1 / 4) · (5, - 4)

P(x, y) = (- 9 / 4, 6 / 4) + (5 / 4, - 1)

P(x, y) = (- 9 / 4, 3 / 2) + (5 / 4, - 1)

P(x, y) = (- 1, 1 / 2)

The ordered pair P is (- 1, 1 / 2).

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