In the figure below, TRS = RTU and SR = UT. Which of the following triangle congruence criteria proves that TRS = RTU

HELLP MMMEEE PLZ

Answer:

HL

Step-by-step explanation:

The two hypotenuses of these right triangles are marked congruent, and the leg QS is shared, hence congruent.

The HL theorem applies.

(-1/4)x + 2 = 8

Multiply all terms by 4.

(-1)x + 8 = 32

Simplify.

-x + 8 = 32

Subtract 8 from both sides.

-x = 24

Multiply both sides by -1.

x = -24.

-1/4(-24) + 2 = 8

Evaluating functions is the process of substituting a specific value in place of the variable in a function to compute a result. For example, given the function f(x) = x^2, if asked to find f(2), you would replace x with 2 resulting in 4.

Evaluating functions in mathematics involves inserting a specific numerical value or a variable into a function to compute a result. For example, if you're given the function f(x) = x^2, and you're asked to find f(2), you simply substitute 2 in place of x in the function, resulting in 2^2, which equals 4.

For instance, if we were to evaluate f(5) for the given function, it would give the result 25 because 5^2 = 25. Hence, simply put, to evaluate a function is to replace the variable with the input value, and compute the result.

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Answer:

y = -2.8x +69.4

Step-by-step explanation:

Let y represent units of inventory, and x represent days since the last replenishment. We are given points (x, y) = (3, 61) and (13, 33). The line through these points can be described using the 2-point form of the equation of a line:

... y -y1 = (y2-y1)/(x2 -x1)(x -x1)

Filling in the given point values, we have ...

... y -61 = (33 -61)/(13 -3)(x -3)

Simplifying and adding 61, we get ...

... y = -2.8x +69.4

Try this solution:

a) the property of the inscribed quadrilateral is: m∠A+m∠G=m∠H+m∠F=180°.

It means (for m∠A+m∠G=180°), 21x-2+38x+5=180°, ⇒ x=3, m∠G=63-2=61°.

b) m(arcFAH)=2m∠FGH=2m∠G=122°.

c) x²-2x+y²-4y=11; ⇔ (x²-2x+1)+(y²-4y+4)=16; ⇔ (x-1)²+(y-2)²=4², where (1;2) is the centre and 4 - radius of this circle.

Answer:

[tex]x=7.2\ units[/tex]

Step-by-step explanation:

we know that

In the right triangle of the figure

The tangent of angle of 67 degrees is equal to divide the opposite side to the angle of 67 degrees (17 units) by the adjacent side to angle of 67 degrees (x units)

[tex]tan(67\°)=17/x[/tex]

Solve for x

[tex]x=17/tan(67\°)[/tex]

[tex]x=7.2\ units[/tex]

If we let m represent the number of months, then the population increase of the first town is 100m and its decrease is 200m. The population decrease of the second town is 175 m.

We want to find m such that the increases and decreases make the towns' populations equal. We add the increases and subtract the decreases to the base population in each case.

... first town population = second town population

... 53075 -100m +200m = 55825 -175m . . . . . the model equation

Solution

... 100m = 2750 -175m . . . . . collect terms, subtract 53075

... 275m = 2750 . . . . . . . . . . add 175m

... m = 10 . . . . . . . . . . . . . . . . . divide by 275

The populations will be equal in 10 months.

Answer:

175m-125m+38,200=40,600-150m

Step-by-step explanation:

I just completed it on imagine math

We know that , According to Pythagorean Theorem :

In a Right Angled Triangle :

✿  (Hypotenuse)² = (First Leg)² + (Second Leg)²

In the Figure : AC is the Hypotenuse and AB and BC are Two Legs

Given : Length of AB = 4 and Length of BC = 6

⇒ (AC)² = (AB)² + (BC)²

⇒ (AC)² = 4² + 6²

⇒ (AC)² = 16 + 36

⇒ (AC)² = 52

[tex]\mathsf{\implies AC = \sqrt{52}}[/tex]

[tex]\mathsf{\implies AC = 2\sqrt{13}}[/tex]

3rd Option is the Answer

After 5 years, the resale value of the laptop will be approximately $592.

The resale value of the laptop after each year can be calculated by multiplying the previous year's value by 0.75. Starting with the initial value of $2500, the resale value after 5 years can be found by multiplying $2500 by 0.75 five times. Let's calculate:

Therefore, the resale value of the laptop after 5 years will be approximately $592.

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Answer:

5^(3m+10)

Step-by-step explanation:

There are several ways you can go at this. One is to do the division of fractions the way you often do division with fractions: multiply by the inverse of the denominator.

= (5^(m+4)) · (25^(m+3))

= (5^(m+4)) · ((5^2)^(m+3))

= (5^(m+4)) · (5^(2m+6))

= 5^(m+4+2m+6)

= 5^(3m+10)

For this case, we have that by definition:

Let "x" be an angle of any vertex of a right triangle.

[tex]tangent (x) = \frac {Cathet \ opposite} {Cathet \ adjacent}[/tex]

So, if we want to find the angle x of the triangle shown we have:

[tex]tangent (x) = \frac {13} {6}\\x = arc \ tangent (\frac {13} {6})\\x = 65.23[/tex]

Rounding:

[tex]x = 65\ degrees[/tex]

Answer:

65 degrees

Option d

Answer:

5.) 348 kg

6.) 20.7 lb

7.) 240

Step-by-step explanation:

5.) 48% of 725 kg

48 × 725 ÷ 100 = 348 kg

6.) 15% of 138 lb

15 × 138 ÷ 100 = 20.7 lb

7.) 45% of _____is 108.

100 × 108 ÷ 45 = 240

Thus, 5.) 348 kg; 6.) 20.7 lb; 7.) 240

-TheUnknownScientist

Answer:

(x, y) = (5, 1)

Step-by-step explanation:

To eliminate x, you can double the second equation and subtract the first.

... 2(x +4y) -(2x -3y) = 2(9) -(7)

...11y = 11 . . . . . simplify

... y = 1 . . . . . . divide by 11

Using the second equation to find x, we have ...

... x + 4·1 = 9

... x = 5 . . . . . subtract 4

_____

Check

2·5 -3·1 = 10 -3 = 7 . . . . agrees with the first equation

(Since we used the second equation to find x, we know it will check.)

Answer:

about 82%

Step-by-step explanation:

The distribution of sample means has a standard deviation that is the pipe standard deviation divided by the square root of the sample size. Thus, the standard deviation of the sample mean is 0.003/√9 = 0.001.

Then the limits on sample mean are 1.010 - 1×0.001 = 1.009 and 1.010 +2×0.001 = 1.012. The proportion of the normal distribution that lies between -1 and +2 standard deviations is about 81.9%.

The problem involves statistical calculation involving mean, standard deviation, and Z-scores of a normal distribution. We first calculate sample standard deviation, then the Z-scores for the given range. After finding probabilities for the Z-scores, we subtract to get the final probability of 0.8185.

The problem at hand involves the field of statistics, specifically, the normal distribution, sample mean, and standard deviation. We can use the following steps to solve the problem:

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Answer:

[tex]\dfrac{mn^5}{p^4}[/tex]

Step-by-step explanation:

As with dividing any fractions, invert the denominator and multiply. Use the rules of exponents to combine factors.

[tex]\dfrac{\dfrac{m^2n^3}{p^3}}{\dfrac{mp}{n^2}}=\dfrac{m^2n^3}{p^3}\cdot\dfrac{n^2}{mp}\\\\=\dfrac{m^2n^3n^2}{p^3mp}=\dfrac{m^{2-1}n^{3+2}}{p^{3+1}}=\dfrac{mn^5}{p^4}[/tex]

_____

The applicable rules are ...

[tex]a^ba^c=a^{b+c}\\\\\dfrac{a^b}{a^c}=a^{b-c}[/tex]

Answer:

   = -sqrt(2)

Step-by-step explanation:

tan theta = -1

we know tan = opposite/ adjacent

So opposite/adjacent = -1

Multiply by adjacent on each side

opposite = - adjacent

We also know from pythagorean theorem that

opposite ^2 + adjacent ^2 = hypotenuse ^2

Substituting in for adjacent

opposite ^2 + (-opposite ) ^2 = hypotenuse ^2

opposite ^2 + opposite ^2 = hypotenuse ^2

2 opposite ^2 = hypotenuse ^2

 Taking the square root on each side

sqrt(2 opposite ^2)   =  sqrt(hypotenuse ^2)

sqrt(2) opposite = hypotenuse

We are now set to find the sec

sec theta = hypotenuse / adjacent

               = sqrt(2) opposite/ adjacent

Replace the opposite = -adjacent

                 = sqrt(2) (-adjacent)/adjacent)

                 = -sqrt(2)

The value of secθ for 3π/ 2 < θ< 2π is √2. This is because tanθ is negative in Quadrant III and sec²θ = 1 + tan²θ. Therefore, secθ = √2.

Step 1: Determine the quadrant of θ

We know that 3π/ 2 < θ< 2π, which means that θ is in Quadrant III. In Quadrant III, tanθ is negative and secθ is positive.

Step 2: Use the identity sec²θ = 1 + tan²θ to solve for secθ

The identity sec²θ = 1 + tan²θ can be used to solve for secθ given tanθ. Substituting tanθ = -1 into the identity, we get:

sec²θ = 1 + (-1)² = 2

Taking the square root of both sides, we get:

secθ = √2

Therefore, the value of secθ for 3π/ 2 < θ< 2π is √2.

For more such information on: tan

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Answer:

Step-by-step explanation:

riders : walkers = 10 : 1

The ratio tells you that 10 students ride the bus for every 1 student that walks. Since 10 is more than 1, more students ride the bus.

We know more students are riders, because we know that 10 is more than 1.

Answer:

A. 18.25

Step-by-step explanation:

After you do the multiplications, the problem is

... (56 +90)/8 = 146/8 = 18.25

_____

The division bar is a grouping symbol, equivalent to parentheses around both numerator and denominator. You must evaluate the numerator before you can divide by the denominator, which also must be evaluated before that division.

Answer:

21 ft

Step-by-step explanation:

C = 2πr

Filling in the given values, we have ...

131.88 ft = 2·3.14·r . . . . we can find r by dividing by its coefficient

131.88 ft/6.28 = r = 21 ft

Answer:

This question is not as hard as it seems.

Let the first number = x.

The other number will be x - 16.

The sum of both the number is 52.

So, x+x-16 = 52

Which would simplify to 2x -16 = 52.

When I add 16 to both sides, it would give me 2x = 68.

Then, divide both sides by 2.

This leaves us with x = 34.

Since we have x, now x-16 would be 34-16 = 18.

The two numbers are 34 and 18, this answer is correct because both of them add up to give me 52.

HOPE THIS HELPS!

Question

The sum of two numbers is 52 . The smaller number is 16 less than the larger number.What are the numbers?

Answer:

18 and 34

Step-by-step explanation:

[(52 - 16) : 2] + 16 =

(36 : 2) + 16 =

18 + 16 =

34

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

Check

34 - 18 = 16

34 + 18 = 52

the answer is good

Answer:

4

Step-by-step explanation:

The derivative of a 5th-degree polynomial is a 4th-degree polynomial, so will have at most 4 real zeros. The zeros of the derivative correspond to the turning points of the function.

Answer:

The measure of angle B is positive

Step-by-step explanation:

we know that

Positive angles are those measured counterclockwise.

therefore

in this problem

The measure of angle B is positive

Answer:

x⁶ +30x⁵ +375x⁴ +2500x³ +9375x² +18750x +15625

Step-by-step explanation:

The expansion is the sum of C(6, k)·x^(6-k)·5^k for k=0–6, where ...

... C(6, k) = 6!/(k!(6-k)!)

For k = 0–6, C(6, k) = {1, 6, 15, 20, 15, 6, 1}

Then the expansion is ...

... x⁶ +6·5¹·x⁵ +15·5²·x⁴ +20·5³·x³ +15·5⁴·x² +6·5⁵·x +5⁶

Using binomial theorem to expand the power of a binomial (X+5) to the power 6 and the result is [tex]X^6 + 30 \times X^5 + 300 \times X^4 + 1500 \times X^3 + 3750 \times X^2 + 4500 \times X + 3125[/tex].

To expand the expression (X+5) to the power 6 using the binomial theorem, we can use the formula [tex](a + b)^n = nC_0 \times a^n + nC_1 \times a^{(n-1)} \times b^1 + nC_2 \times a^{(n-2)} \times b^2 + ... + nC_n * b^n[/tex].

In this case, a = X, b = 5, and n = 6.

Using the binomial coefficients, the expanded expression becomes:

[tex]X^6 + 6 \times X^5 \times 5 + 15 \timesX^4 \times 5^2 + 20 \times X^3 \times 5^3 + 15 \times X^2 \times 5^4 + 6 \times X \times 5^5 + 5^6[/tex]

Simplifying this expression gives

[tex]X^6 + 30 \times X^5 + 300 \times X^4 + 1500 \times X^3 + 3750 \times X^2 + 4500 \times X + 3125[/tex].

about 83%

Put the given value in the formula and do the arithmetic.

... P(66) = 90/(1 +271·e^(-0.122·66))

... = 90/(1 +271·e^-8.052)

... = 90/(1 +271·0.00031846)

... = 90/(1 +0.0863)

... = 90/1.0863

... = 82.8 . . . . percentage with some coronary heart disease

Answer:

x = −10 and x = 4

Step-by-step explanation:

x2 + 6x = 40

Subtract 40 from each side

x^2 + 6x -40 =0

Factor,  what 2 numbers multiply to -40 and add to 6

10 * -4 = -40    10+-4 = 6

(x+10) (x-4) = 0

Using the zero product property

x+10 =0     x-4=0

x=-10    x=4

Answer:

x = −10 and x = 4

Step-by-step explanation:

We are given the following quadratic equation and we are to solve it to find the two solution for the variable x:

[tex]x^2+6x=40[/tex]

Rearranging the equation by putting the constant on the same side as the variables to get:

[tex]x^{2} +6x-40=0[/tex]

Now factorizing it to get:

[tex]x^{2} -4x+10x-40=0\\\\x(x-4)+10(x-4)=0\\\\(x+10)(x-4)=0\\\\x= -10, x= 4[/tex]

Therefore, the solution to the given quadratic equation [tex]x^2+6x=40[/tex] are x = −10 and x = 4.

f(x) = 8·1.25^x

An exponential function has the form ...

... f(x) = a·b^x

Then f(0) = a. Your graph shows f(0) = 8.

The base "b" can be found from any other point on the graph. You have marked the point (1, 10), so we can find "b" from ...

... f(1) = 10 = 8·b^1 = 8b

... 10/8 = b = 1.25 . . . . . . . divide by the coeffiicient of b

Now, we know the exponential function is ...

... f(x) = 8·1.25^x

Answer:

The correct answer is f(x) = 8·1.25^x

Step-by-step explanation:

Answer:

Step-by-step explanation:

The circumference of a circle of radius r is given by

... C = 2πr

When r = 1 m, then

... C = 2π(1 m) = 2π m

The relation between time, distance, and speed is ...

... time = distance/speed

... time = (2π m)/(1 m/s) = 2π s

_____

Comment on the scenario

We have a hard time imagining what sort of scenario this is modeling, as it appears the "boat" is rotating in such a way as to place the barnacle above and below the water level. This problem may be nonsensical, but at least it is workable. (Some aren't.)

Answer:2 pi

Step-by-step explanation:

Answer:

x > 1

Step-by-step explanation:

Firstly, the +3 must be moved over to the other side, making it a -3:

2x > 5 - 3

2x > 2

Then, divide both sides by two to get 1x:

x > 1

Hi there!

Answer:

X>1

*The answer must have a positive sign and greater than symbol.*

Step-by-step explanation:

First, you subtract by 3 from both sides of an equation.

[tex]2x+3-3>5-3[/tex]

Then, you subtract by the numbers from left to right.

[tex]5-3=2[/tex]

[tex]2x>2[/tex]

You can also divide by 2 from both sides of an equation.

[tex]\frac{2x}{2}>\frac{2}{2}[/tex]

Finally, you divide by the numbers from left to right.

[tex]2/2=1[/tex]

Final answer is x>1

I hope this helps you!

Have a nice day! :)

:D

-Charlie

Thank you so much! :)

:D

Answer:

Step-by-step explanation:

We know:

The sum of the measures of the angles of the triangle is equal to 180 °.

Therefore we have the equation:

[tex]y+(y-12)+56=180[/tex]         combine like terms

[tex]2y+44=180[/tex]              subtract 44 from both sides

[tex]2y=136[/tex]           divide both sides by 2

[tex]y=68[/tex]

The coin is flipped 15 times and you get 10 heads, is written as 10/15.

10/15 = 0.66666  = 66.7%

Answer:

9.2%

Step-by-step explanation: