Sketch the angle in standard position and draw an arrow representing the correct amount of rotation. Find the measure of two other​ angles, one positive and one​ negative, that are coterminal with the given angle and closer to the given angle than any other coterminal angle. Give the quadrant of the​ angle, if applicable. -90°

The angle m∠D of the triangle is 78 degrees.

A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.

The ΔKDT and ΔKPQ are isosceles triangle.

Isosceles triangle is a triangle that has two sides and angles equal to each other.

Therefore,

∠D + ∠T + ∠k = 180

∠D  = 6x + 6

∠T = 6x + 6

∠K = 2x

Therefore,

6x + 6 + 6x + 6 + 2x = 180

14x + 12  = 180

14x = 180 - 12

14x = 168

divide both side by 14

x = 168 / 14

x = 12

Therefore,

m∠D = 6x + 6 = 6(12) + 6 = 72 + 6 = 78 degrees.

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Tee welding joints are formed when two members intersect at a 90-degree angle that makes the edges come together in the center of a plate or component

9514 1404 393

Answer:

  D.  0, 1, or 2 solutions

Step-by-step explanation:

The line represented by g(x) may intersect the parabola represented by f(x) in 0, 1, or 2 places, as illustrated in the attachment. The curves are different shapes, so cannot overlap to give infinite solutions.

The system may have 0, 1, or 2 solutions.

Answer:

12

Step-by-step explanation:

Answer:

10y^2-3xy+6x

Step-by-step explanation:

Answer:

Step-by-step explanation:

60

8x10x3/4

Alright I got it.

So first what I did was I made an equation that match did the word problem.

The equation was 15x=250+10x

When I solved it the answer was 50.

so they would need to sell 50 Tshirts (x=50)

Answer:

x=2, y=3. (2, 3).

Step-by-step explanation:

2x+4y=16

-2x-3y=-13

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

y=3

2x+4(3)=16

2x+12=16

2x=16-12

2x=4

x=4/2

x=2

Answer:

100

Step-by-step explanation:

Multiply two of the side lengths

10×10 = 100

Answer:

Interval: [0,∞), solution: x≥0.

Answer:

Domain: (0,+∞)

Step-by-step explanation:

negative numbers cannot have a square root taken unless your working with imaginary numbers.

h(x) = f(x) + 5 represents a vertical shift of 5 units down from the graph of f(x) = 3x. The slope of the two lines is the same, but the y-intercept of h(x) is different from f(x).

A graph of a function is a visual representation of the relationship between the input values (x-coordinates) and the output values (y-coordinates) of a function. It is a way to visualize the behavior of the function and its relation to the x and y axes.

Here,

We can draw the graph as

h(x) = 3x - 5 can be written in terms of f(x) by adding 5 to the output of f(x)

h(x) = f(x) + 5

The transformation from the graph of f(x) to the graph of h(x) is a vertical shift of 5 units down. This is because the original function f(x) is shifted down by 5 units to get h(x). The slope of the two lines is still the same, 3, but the y-intercept of f(x) is (0,0) and the y-intercept of h(x) is (-5/3,0). The transformation causes the graph of h(x) to be shifted down 5 units along the y-axis, while the slope and x-intercept of the graph remain the same.

Hence, h(x) = f(x) + 5 represents a vertical shift of 5 units down from the graph of f(x) = 3x. The slope of the two lines is the same, but the y-intercept of h(x) is different from f(x).

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Answer:

Answer: Gloria will need 14 cups of flour

Step-by-step explanation: 2 1/3 x 6 = 14

Answer: 2.25 grams

Step-by-step explanation:

In this problem, we are given the ratio of grams to weight. Since we are trying to find how many grams to give to a person with a specific weight, we can use proportions to solve.

[tex]\frac{150mg}{5kg} =\frac{x}{75kg}[/tex]               [cross multiply]

[tex]11250=5x[/tex]                  [divide both sides by 5]

[tex]x=2250mg[/tex]

We are almost done with the problem. The problem is asking for grams, not mg, so we can use unit conversions to change that.

[tex]\frac{1000mg}{1g}=\frac{2250mg}{y}[/tex]          [cross multiply]

[tex]1000y=2250[/tex]               [divide both sides by 1000]

[tex]y=2.25[/tex]

Therefore, we need to give 2.25 grams.

Answer:

m arc 1 = 65°, m arc 3 = 129°, m ∠9 = 25.5°, m ∠ 10 = 57.5°

Step-by-step explanation:

m arc 1 => 180 - 115 = 65°

m arc 3 => 180 - 51 = 129°

m ∠9 => 51 ÷ 2 = 25.5°

m ∠ 10 => 115 ÷ 2 = 57.5°

The linear equation can be written in point-slope form as:

y + 7 = (3/8)*(x - 15.2)

So the correct option is A.

A linear equation with a slope M and a known point (h, k), can be written in the point-slope form as:

y - k = m*(x - h)

Here we know that the slope of the line is 3/8, then we get:

y - k = (3/8)*(x - h)

And we also know that this line must pass through the point (15.2, -7), then we know that:

h = 15.2

k = -7

Replacing these values we get:

y + 7 = (3/8)*(x - 15.2)

Thus the correct option is the first one, A.

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Answer:

U add 1 then add 2 for each number

Answer:

+1 then +2

Step-by-step explanation:

We are given a sequence of 1, 2, 4, 5, 7, 8, 10 and are asked to find the pattern.

To solve, we need to see how much is being added into every single number.

1, 2

+1

2, 4

+2

4, 5

+1

5, 7

+2

We see that there is a repetition of +1 and then +2.

Therefore the pattern is +1 then +2

The Correct answer while simplifying the given algebraic expression is: 4a²+1/2a+7

The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it.

Method to simplify any algebraic Expressions are :

Given:

=3a²+1/4a+3+a²+4+1/4a

=(3a²+a²)+(1/4a+1/4a)+(3+4)

=4a²+1/2a+7

So the Answer is

=4a²+1/2a+7

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The probability that they include at least five persons having blood of type O is given as follows:

0.1075 = 10.75%.

The number of donors needed so that the probability of including at least one student donor of type O shall be 0.9 or more is of 184 donors.

The mass probability formula, giving the probability of x successes, is of:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are given by:

The values of the parameters for this problem are given as follows:

n = 200, p = 1/80 = 0.0125.

The probability of less than five is given as follows:

P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4).

Using a binomial distribution calculator, these probabilities are given as follows:

Hence the probability of less than five successes is given as follows:

P(X < 5) = 0.0808 + 0.2046 + 0.2576 + 0.2153 + 0.1342 = 0.8925.

Hence the probability of at least five is given as follows:

P(X >= 5) = 1 - P(X < 5) = 1 - 0.8925 = 0.1075.

The probability of at least one is given as follows:

P(X >= 1) = 1 - P(X = 0)

P(X >= 1) = 1 - (1 - 0.0125)^n.

This probability is of 0.9 when:

1 - (1 - 0.0125)^n = 0.9

(0.9875)^n = 0.1

log((0.9875)^n) = log(0.1)

nlog(0.9875) = log(0.1)

n = log(0.1)/log(0.9875)

n = 183.1.

Rounding up, at least 184 donors must be surveyed.

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Answer:

$7

Step-by-step explanation:

Answer:

pretty sure its 7

Step-by-step explanation:

Answer:

[tex]\frac{27}{1024}[/tex]

Step-by-step explanation:

So the chance of getting yellow is 0.25

Getting it once is 0.25

Getting it twice is 0.25 • 0.25

Not getting it is 0.75

So we have 0.25 • 0.25 • 0.75 • 0.75 • 0.75 = [tex]\frac{27}{1024}[/tex]

The speed of the carts after collision is  3 m/s.

We have to note that in this case, we would need to apply the principle of the conservation of linear momentum. This implies that the momentum before collision would have to be the same as the momentum after collision.

Then we have;

Momentum before collision = Momentum after collision thus;

(3 * 4) + ( 1 * 0) = (3 + 1) v

Note that the two carts are said to stick together and move with a common speed

Hence;

12 = 4v

v = 12/4

v = 3 m/s

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Answer:

line is negative, so -3/4

Step-by-step explanation:

If they leave the money from the first 8 years in the account and continue to contribute $200 at the end of each quarter for the next 19 years, the future value in the account to help with their child's college is $215,293.42.

The future value for this investment is computed in two separate solutions.

We have used an online finance calculator to facilitate the process.

The future value denotes the present deposits compounded at an interest rate.

Initial Deposits:

N (# of periods) = 32 quarters (8 years x 4)

I/Y (Interest per year) = 7.6%

PV (Present Value) = $0

PMT (Periodic Deposit) = $1,000

Results:

FV = $43,489.87

Sum of all periodic payments = $32,000.00

Total Interest = $11,489.87

Subsequent Deposits:

N (# of periods) = 76 quarters (19 years x 4)

I/Y (Interest per year) = 7.6%

PV (Present Value) = $43,489.87

PMT (Periodic Payment) = $200

Results:

Future Value (FV) = $215,293.42

Sum of all periodic payments = $15,200 ($200 x 76 quarters)

Total Interest = $156,603.55

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Answer:

Option A:

y = 3*(x - 5)^2 - 4

Step-by-step explanation:

For a quadratic equation:

y = a*x^2 + b*x + c

with the vertex (h, k), we can rewrite the function as:

such that:

h = -b/2*a

y = a*(x - h)^2 + k

Here we have the function:

y = 3*x^2 - 30*x + 71

the x-value of the vertex will be:

h = -(-30)/(2*3) = 30/6 = 5

And k is given by:

k = y(5) = 3*(5)^2 - 30*5 + 71 = -4

Then the vertex is:

(5, - 4)

And we can rewrite the equation in the vertex form as:

y = 3*(x - 5)^2 + (-4)

y = 3*(x - 5)^2 - 4

Then the correct option is A.

Answer: 12x^3 y^3 (x − 4y)

(GCF is: 12x^3 y^3)

Step-by-step explanation:

This is the best I can do, sorry that I don't have an explanation.

Using the given function and the ordered pairs, we observed that Mr. Poppen pays more initially, to join the club

From the question, we are to determine who pays more initially to join the club between Mr. Poppen and Mrs. Zagorski  

From the given information,

"Mr. Poppen joins a fitness club which has a cost represented by the function y = 10x + 70"

The initial amount paid by Mr. Poppen is the value of y when x is 0

y = 10x + 70

y = 10(0) + 70

y = 0 + 70

y = 70

From the given ordered pairs

(0, 50)

(1, 60)

(2, 70)

(3, 80)

We can conclude that the initial amount paid by Mrs. Zagorski is 50

Hence, Mr. Poppen pays more initially

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The tax rate of an Item that costs $450 Before tax. and the sales tax is $31.50 is 7%

The tax rate is the percentage of an income or an amount of money that has to be paid as tax.

To find the tax rate of $31.50 from $450

The formula is

Amount taxed/Principal amount x 100

= $31.50/$450 x100

=$3150/450

=7%

Hence, the tax rate is 7%

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Each nested cart add to the length of the row is 1.5 feet long.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given that, the store measured a row of 13 nested carts to be 23.5 feet long, and a row of 18 nested carts to be 31 feet long.

Each row has a starting cart that is 4 feet long, and the nested carts are next to it.  

It is measured that a row of 13 nested carts has a length of 23.5 feet.

Therefore, the original length of 13 nested carts is (23.5 - 4) = 19.5 feet.

So, each nested cart add to the length of the row 19.5/13 =1.5 feet

Again, a row of 18 nested carts to be 31 feet long.

Therefore, the actual added length of 18 nested carts is (31 - 4) = 27 feet.

So, each nested cart add to the length of the row 27/18 =1.5 feet

Therefore, each nested cart add to the length of the row is 1.5 feet long.

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"Your question is incomplete, probably the complete question/missing part is:"

A store is designing the space for rows of nested shopping carts. Each row has a starting cart that is 4 feet long, followed by the nested carts (so 0 nested carts means there's just the starting cart). The store measured a row of 13 nested carts to be 23.5 feet long, and a row of 18 nested carts to be 31 feet long.

How much does each nested cart add to the length of the row?

The conditions of the line to be intersecting, parallel, and coincident are explained below.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The types of lines are as follows:

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