how do i graph this?? it doesnt make any sense to me :(

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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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

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]

The dimensions of the box that minimizes the total cost is side of the square base is 7.23 m and height of the box is 4.82 m   .

In the question ,

it is given that ,

the bottom of the box is =  square ,

let the side of the square bottom be = "s" ,

so , the base area [tex]=[/tex] s²

let the height of the box [tex]=[/tex] h ,

Volume of the box = height × (base area)

So , the Volume of the box [tex]=[/tex] s²h

given that the volume of the box is 252 m³ , that means

s²h = 252

h = 252/s²

given that the Cost of bottom = $40 per m²

and the Cost of sides = $30 per m²

So , the total cost = 40s² + 30×(4sh)

substituting the value of h= 252/s² , we get

C = 40s² + 120s×252/s²

C = 40s² + 30240/s

to minimize the cost we differentiate with respect to s , and equating it  to 0 ,

we get ,

80s - 30240/s² = 0

s³ = 30240/80

s³ = 378

s = 7.23
again differentiating C = 40s² + 30240/s with respect to s , and equating it  to 0 ,

we get ,

d²C/ds² = 80 + (30240*2)/s³

at s=7.23 , d²C/ds² > 0

So , the minimum is at s = 7.23 ,

we have h = 252/(7.23)²

h = 4.82 .

Therefore , The dimensions of the box that minimizes the total cost is side of the square base is 7.23 m and height of the box is 4.82 m   .  

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Step-by-step explanation:

d = number of dimes

n = number of nickels

one dime = $0.10

one nickel = $0.05

d = 3n

0.1×d + 0.05×n = 3.85

0.1×3n + 0.05×n = 3.85

0.3×n + 0.05×n = 3.85

0.35×n = 3.85

n = 3.85 / 0.35 = 11

d = 3n = 3×11 = 33

she has 33 dimes (and 11 nickels).

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 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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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:

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 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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The area of the composed rectangle and the semicircle is 92.56 square units.

Area of rectangle and semicircle

The formula for the Area of a Rectangle.

A = l × w.

where l refers length and w refers width of the rectangle

The area of a semicircle refers the half of the area of the circle. Therefore, the area of a semicircle is 1/2(πr²), where r is the radius.

Given,

Here we have the figure below composed of a rectangle and a semicircle And we need to find the area of this figure then round to the nearest tenth place.

Here we know the following values,

Length of the rectangle = 10

Width of the rectangle = 8

Diameter of the circle = 8

Through the given diameter we have identified the radius as 4.

Now, the area of the rectangle is calculated as,

A = 10 x 8

A = 80 square units.

Similarly, the area of the semicircle is

A = 1/2 (π x 4²)

A = 1/2 x π x 8

A = π x 4

We know the value of π = 3.14, then the area of the semicircle is,

A = 3.14 x 4

A = 12.56 square units.

Therefore, the are of the figure is,

Total area = area of rectangle + area of semicircle

Total area = 80 + 12.56

Therefore, the total area of the figure is 92.56 square units.

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Answer:

Step-by-step explanation:

(2/3)20

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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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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The value of (tanx+2cosx) = [tex]2\frac{7}{20}[/tex].

Given that

sinx = [tex]\frac{3}{5}[/tex]

sinx = [tex]\frac{opp}{hyp}[/tex]

Using the Pythagoras' theorem

[tex]hyp^{2} = opp^{2} + adj^{2} \\\\adj^{2} = 5^{2}- 3^{2} \\ \\= 25-9\\\\adj^{2} = 16\\ \\adj = \sqrt{16} \\[/tex]

adj = 4.

Now we have to find out tanx and cosx

[tex]tanx = \frac{opp}{adj}[/tex]

[tex]= \frac{3}{4}[/tex]

[tex]cosx = \frac{adj}{hyp}\\ \\= \frac{4}{5}[/tex]

Now we have to find out the given equation (tanx+2cox)

[tex]= \frac{3}{4} +2(\frac{4}{5})\\ \\= \frac{15+32}{20} \\\\= \frac{47}{20} \\\\or\\\\= 2\frac{7}{20}[/tex]

Hence the answer is the value of (tanx+2cosx) = [tex]2\frac{7}{20}[/tex].

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Answer: 119 minutes

Step-by-step explanation:

Answer:

at least 17 sales

Step-by-step explanation:

On Wednesday she wants to earn 128.

Per day value = 60

128-60=68

She still needs to earn 68.

68 divided by 4=The number of sales needed to get 68 dollars=17

Thus she needs to make at least 17 sales, at most means maximum but she wants to earn AT LEAST 128 which means she wants more thus, answer is 4th option.

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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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

Answer:

D

Step-by-step explanation:

Unit rates always compare quantities with different units

Ex. 10 km per 1 hour (10kph)

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

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 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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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:

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).

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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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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