In ΔTUV, m∠T = 58° and m∠U = 97°. Which list has the sides of ΔTUV in order from longest to shortest?

The balance in Marie saving account in week 20 will be $408  .

In the question ,

it is given that

the amount in Marie's saving account in week 1 is $180 .

amount of money deposited every week is = $12 .

to find the balance in week 20 means , she deposited money for 19 weeks .

the amount deposited in 19 weeks = 19 × 12 = $228

the equation to represent the balance after w weeks = 180 + 12*w

putting w = 19 in the equation , we get

the balance in saving account in week 20 = 180 + 12*19

the balance in week 20 = 180 + 228

= $408

Therefore , The balance in Marie saving account in week 20 will be $408  .

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The missing angle is as follows:

When two triangles are congruent they will have exactly the same three sides and exactly the same three angles.

In other words, two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal.

Therefore, the triangle ABC is congruent to EDF.

Hence,

∠A = ∠D

∠B = E

∠C = ∠F

Therefore,

m∠C = x

m∠F = 2x - 30

Hence,

m∠C = m∠F

x = 2x - 30

x - 2x = -30

-x = -30

x = 30

m∠C = 30 degrees

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Since it is labeled that this triangle has two equal sides, it is isosceles. Isosceles triangles' acute angles are always congruent, so we can infer that there are two angles with a measurement of 29 degrees. Knowing that all of the angles in a triangle add up to 180 degrees, we can set up this equation:

2*29 + 11x - 65 = 180

58 + 11x - 65 = 180

-7 + 11x = 180

11x = 187

x = 17

Knowing that "x = 17" we can find the measurement of the obtuse angle:

11*17 - 65

= 187 - 65

= 122

Answer:In this item, I take it that we are to get  the cube root of the given expression, -64x6y9. First, we look into the numerical coefficient, this is the product when -4 is multiplied to itself three times as shown below.

   -64 = (-4)(-4)(-4)

Then,

  x6 = x2 (x2) (x2)

and,

   y9 = (y3)(y3)(y3)

If we take the cube root, we consider only one item per product. Thus, the answer is,

   -4x²y³

Step-by-step explanation:

Answer:

3/5

Step-by-step explanation:

Given problem,

→ (1/10) + (1/2)

Let's solve the problem,

→ (1/10) + (1/2)

→ (1/10) + (5/10)

→ 6/10

→ 3/5 {simplest form}

Thus, answer is 3/5.

The equation of a line in point- slope form, that passes through (1, -7) and has a slope of -2/3 is (y + 7) = -2/3 (x - 1)

Information gotten from the question include

a slope of -2/3

points (1, -7)

A linear function consists of functions where the variables has exponents of 1.

The equation of a line in point- slope form is expressed in the form.

(y - y₁) = m (x - x₁)

Definition of variables

(y and y₁) = refers to variables in the y direction

m = slope

x and  x₁ = refers to variables in the x direction

substituting into the slope and point (1, -7) equation gives

()y + 7) = -2/3 (x - 1)

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Answer:

1,070 g

Step-by-step explanation:

Half-life is the length of time it takes for half of the radioactive atoms of a radionuclide to decay. In this scenario, the amount of radioactive atoms is halved after 15 minutes. After 45 minutes, then, the amount of radioactive atoms is halved three times. Therefore:

1st half-life: 8,560 ÷ 2 = 4,280 g

2nd half-life: 4,280 ÷ 2 = 2,140 g

3rd half-life: 2,140 ÷ 2 = 1,070 g

Answer:

2-3/-6-(-8)

= -1/2

Answer:

182 minutes

Step-by-step explanation:

0.09x+5=21.38

         -5.   -5

0.09x=16.38

/0.09.   /0.09

  X=182

182 minutes

Hopes this helps please mark brainliest

Answer:

5/8 - 1/4 = 3/8

Step-by-step explanation:

1 x 2 = 2, 4 x 2 = 8, so we're left with 2/8

Answer:

3/8

Step-by-step explanation:

5/8 - 1/4

to be able to compare fractions or add/subtract them directly, we need to bring them all to the same denominator (the bottom part of the fractions).

it is usually easier to bring the smaller to a larger number than the other way around, because of the existing numerators (the top part of a fraction).

since we are dealing with fractions (divisions !), the best way to manipulate them is by multiplying or dividing them by a factor.

so, what do we need to multiply with 4 to get 8 (the other denominator) ?

2, as 4×2 = 8.

aha.

but now careful, we cannot just multiply the denominator by 2. that would change the value of the whole original fraction.

we have to multiply denominator AND numerator by the same factor. that way the original value of the fraction remains the same, because we are essentially multiplying the whole fraction just by 1.

so,

1/4 × 2/2 = 2/8

and now we can easily use it in a calculation with other 8ths :

5/8 - 2/8 = 3/8

The range of scores that Marjorie's can receive in the final exam to earn a C in the course is 67 to 82  .

in the question ,

it is given that

the Marjorie's score in the tests are 67 , 78 , 75 , 78 .

let the score in the final exam be "x"

it is given that the final exam score is worth 6 test scores , which means

the score in final exam is = 6x

and the total number of tests = 6+4 = 10

given that to get the grade C minimum average is = 70

that is  (67 + 78 + 75 + 78 + 6x)/10 = 70

67 + 78 + 75 + 78 + 6x = 700

298 + 6x = 700

6x = 700 - 298

6x = 402

x = 402/6

x = 67

given that to get the grade C maximum average is = 79

that is  (67 + 78 + 75 + 78 + 6x)/10 = 79

67 + 78 + 75 + 78 + 6x = 790

298 + 6x = 790

6x = 790 - 298

6x = 492

x = 492/6

x = 82

the range of scores is 67 to 82 .

Therefore , The range of scores that Marjorie's receive in the final exam to earn a C in the course is 67 to 82  .

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The simplified expressions for the questions will be, 1) 3w, 2) 8x, 3) 10p, 4) 8b.

The simplification of an algebraic expression generally means breaking the equation into a smaller form for easier calculation with the help of formulas or using the rule of BODMAS.

Here, all the questions can be solved by using the BODMAS rule.

1) 7w + 2w - 6w

= (7w + 2w) - 6w

= 9w - 6w

= 3w.

2) 9x - 3x + 2x

= (9x + 2x) -3x

= 11x - 3x

= 8x.

3) 8p + 3p - p

= (8p + 3p) - p

= 11p - p

= 10p.

4) 6b - 3b + 5b

= (6b +5b) - 3b

= 11b -3b

= 8b.

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Step-by-step explanation:

[tex]7w + 2w - 6w \\ 9w - 6w \\ = 3w[/tex]

[tex]9x - 3x + 2x \\ 6x + 2x \\ = 8x[/tex]

[tex]8p + 3p - p \\ 11p - p \\ = 10p[/tex]

[tex]6b - 3b + 5b \\ 3b + 5b \\ = 8b[/tex]

Answer:

b

Step-by-step explanation:

the right side base angle and 80° are vertically opposite angles and are congruent, both 80°

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

123° is an exterior angle of the triangle , then

x + 80 = 123 ( subtract 80 from both sides )

x = 43

A rectangle that maximize the enclosed area has a length 800 yards and width is 800 yards. The maximum area is 640,000 square yards.

In the given question we have to find the maximum area of the rectangular area.

Liana has 3200 yards of fencing to enclose a rectangle.

So we know that the perimeter of rectangle is

P= 2(l+b)

Let length of the rectangle is x yards and width is y yards.

So the equation should be

2(x+y) = 3200

Divide by 2 on both side we get

x+y = 1600................(1)

As we know the area of rectangle is

A = xy

From the equation the value of y is 1600-x.

Now putting the value of y

A = x(1600-x)

A = 1600x-x^2

On differentiating

dA/dx = 1600-2x

Putting dA/dx=0

1600-2x=0

Subtract 1600 on both side we get

-2x= -1600

Divide by -2 on both side we get

x = 800 yards

Now putting the value of x in the y=1600-x

y=1600-800

y=800 yards

So the maximum area is

A= 800*800

A= 640,000 square yards

Hence, a rectangle that maximize the enclosed area has a length 800 yards and width is 800 yards. The maximum area is 640,000 square yards.

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Step-by-step explanation:

The formula D = 401t + 5940 can be used to approximate the total average credit card debt in a U.S. household (in dollars) t years after 1995. Use this formula to predict what the total average credit card debt will be in the year 2028.

2028 - 1995 = 33 years, so t = 33

D = 401t + 5940

D = 401(33) + 5940

D = 13,233 + 5940  

D = 19,173

Answer: In the year 2028, the total average credit card debt for a U.S. household will be $19,173

Answer: 13,8 litres

Step-by-step explanation:

£1.45 ------------ 1 L

 £20 ------------- ?

?= [tex]\frac{20 *1}{1.45} = 13,79310345 L[/tex] = 13,8 L

the equation of the line passing through the given points is y = 3

What is an equation of the line?

An expression which is satisfied by every point on the line is known as equation of the line. generally it is given in y = mx + c form where m is the slope and c is the y-intercept

We are given two point (-7,3) and (5,3)

We first find the slope of the lines passing through the given points

Slope = [tex]\frac{3-3}{5+7}[/tex]

Slope = 0

Substituting the value in the equation we get

y = c

Now the value of y in both the cases is 3

Substituting that we get c = 3

Hence y = 3 is the required equation of the line

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This week 41 students showed up to the archery class that cannot be broken into multiple groups of equal sizes.

Prime numbers are numbers that cannot be divisible by any other numbers besides 1 and itself. Between 30 and 50, there are 4 prime numbers, which are 31, 37, 41, and 43. So, these prime numbers cannot be divided into equal sizes of multiple groups. But by adding 2 (If Betty and Wilma join the students) in 31, 37, and 43 we get composite numbers that can be divided into multiple groups of equal sizes.

So, 41 students showed up to the archery class this week and as 41 is a prime number, Betty and Wilma could not break the archers up into groups of equal size, and even if Betty and Wilma joined the students there will be 43 archers which even is a prime number and thus cannot be divided.

41 is the only possible number of students between 30 and 50 which cannot be broken into groups of equal sizes even if Betty and Wilma join the archers.

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The answer to be entered in the boxes for the area model is 17, 0 and 17

An area model is a rectangular diagram or model used for solving multiplication and division problems, in which the quotient and divisor define the length and width of the rectangle

Given:

    ....60.....1.............

36|2160 | 36 | 17

2160 ÷ 36 = 60 R 0

36 ÷ 36 = 1 R 0

17  ÷ 36 =  0 R 17

Note:  (0 x 36) + 17 = 17

Therefore, the answer to be entered in the boxes is 17, 0 and 17 respectively

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For the given accumulated value, principal money and interest rate compounded continuously the time t is equal to 5.8 years.

As given in the question,

The formula given to us is A = P[tex]e^{rt}[/tex] where

A = accumulation value

P = principal money

t = time period

r = interest rate compounded

P = 9500

A = 2*9500

r = 0.12

By applying it in the given formula we get

19000 = 9500 * [tex]e^{0.12t}[/tex]

2 =    [tex]e^{0.12t}[/tex]

Take natural log on both sides

㏑(2) = 0.12t

0.6931 = 0.12t

t = 5.775

Therefore , For the given accumulated value, principal money and interest rate compounded continuously the time t is equal to 5.8 years after rounding it off to one place after decimal.

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The type of function best models Mrs. Robinson’s data is A. exponential function.

The formula f(x) = a^x defines an exponential function, where x is the input variable as an exponent. The exponential curve is determined by the exponential function and the value of x. Where an is greater than zero and less than one. x can be any actual number.

Mrs. Robinson created the table, which shows the number of cells in a biology experiment after a certain number of days. The independent variable, or x-value, in an exponential function is the exponent, while the base is a constant.

In this case, we can see that:

2 days = 2² = 4

3 days = 2³ = 8

4 days = 2⁴ = 16

This is an exponential function.

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The solution of the system of equation by substitution is x = 3 and y = -1.

System of equation can be solved using different techniques such as substitution method, elimination method and graphical method.

Let's solve the system of equation by substitution method

Therefore,

3x + 2y = 7

x = 3y + 6

Substitute equation(ii) in equation(i)

3(3y + 6) + 2y = 7

9y + 18 + 2y = 7

9y + 2y + 18 = 7

11y = 7 - 18

11y = -11

y = -11 / 11

y = -1

Hence, let's find x

x = 3(-1) + 6

x = -3 + 6

x = 3

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The equation of the graph given in the diagram which represents an absolute value function is: y = |x - 3| + 5.

The equation, in vertex form, of a absolute value function is expressed as y = a|x – h| + k, where:

From the graph, we know that:

Vertex (h, k) = (3, 5)

Substitute h = 3 and k = 5 into the equation, y = a|x – h| + k:

y = a|x - 3| + 5

A point on the graph is (5, 7). To find the value of a, substitute x = 5 and y = 7 into the equation y = a|x - 3| + 5:

7 = a|5 - 3| + 5

7 = 2a + 5

7 - 5 = 2a + 5 - 5 [subtraction property of equality]

2 = 2a

Divide both sides by 2

2/2 = 2a/2 [division property of equality]

Substitute a = 1 into y = a|x - 3| + 5:

y = |x - 3| + 5 [equation of the absolute value function]

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The number of buttons A will be 11. And the number of buttons B will be 11.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

A container of buttons contains a similar number of each kind of button it contains 220g of buttons. The weight of the button is given as,

Let x be the number of each button. Then the equation is given as,

8x + 12x = 220

20x = 220

x = 11

The number of buttons A will be 11. And the number of buttons B will be 11.

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Answer:

Step-by-step explanation:

5 + 4 × 3 - 2

9 × 3– 2 =

27–2 = 25

The commission that thereal estate agency gets is $16885.

The commission that the agent gets is $76750

The selling price for a house = $ 307,000

The commission rate for real estate agency = 5.5 %

The commission rate for the agent = 25 %

So, the commission which real estate agency gets:

= 5.5 % of $307,000

= 0.055 × $ 307,000

= $16885

The commission which agent get:

= 25% of $ 382,000

= 0.25 × $ 307,000

= $76750

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154.5

Step-by-step explanation:

left triangle and right triangle has the same degree.

M to Q 107/2 = P to R 53.5

O to N 110/2 = R to Q 55

Find X

M to N 92/2 = P to Q 46

Perimeter- 53.5+ 55+ 46= 154.5

In a one-period binomial model of an option value, the probabilities of an up-move and a down-move are "calculated from the model inputs."

The number of survivors, x, in n independent tests is described by a binomial model. The number of tests must be predetermined, the results—success or failure—must be statistically independent for each test, and the survival probability—p—must be constant throughout the tests. When a process is repeated a certain number of times (for example, in a set of patients), the result for each patient can either be a success or a failure, the binomial distribution model enables us to calculate the probability of observing a specified number of "successes."

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