I WILL GIVE BRAINLEST

To solve this, you can use the geometric mean theorem. The leg of a right triangle is the geometric mean between the hypotenuse and the portion of the hypotenuse adjacent to the leg.

So that means that 28/y = y/12. You can then use means and extremes of proportions to simplify, and you get y^2 = 336, a.k.a  y = 4 root 21.

Then you do the same thing but with x.

28/x = x/16

x^2 = 448

x = 8 root 7

Answer:

B. x = 8√7, y = 4√21

Step-by-step explanation:

Look at the largest right triangle so the hypotenuse equals 12 + 16 = 28

According to the Pythagorean Theorem: y^2 + x^2 = 28^2

Then for the 2 smaller right triangles, they all the the same side, just called it z

so y^2 = 12^2 + z^2 => z^2 = y^2 - 12^2

and x^2 = 16^2 + z^2 => z^2 = x^2 - 16^2

then y^2 - 12^2 = x^2 - 16^2

y^2 - 144 = x^2 - 256

y^2 = x^2 - 112

Using the first equation

y^2 + x^2 = 28^2 => x^2 = 784 - y^2

So we have y^2 = x^2 - 112

and x^2 = 784 - y^2

then y^2 = (784 - y^2) - 112

y^2 + y^2 = 784 - 112

2y^2 = 672

y^2 = 336

y = 4√21

x^2 = 784 - y^2 = 784 - 336 = 448

x = 8√7

The perimeter of the triangle is 16+8√2.

The sum of the lengths of the sides is the perimeter of any polygon.

Perimeter = Sum of the three sides

There is a general formula for the perimeter of a triangle:

P=a+b+c

There are three steps to calculate the perimeter of a triangle:

Step 1: write the measurements of all the sides, and check that all the sides should have the same unit.

Step 2: Now, calculate the sum of all the sides.

Step 3: Then, give the answer along with the unit.

The given information is the two sides of a triangle are a=b=8 and c=8√2.

Now substitute all the given values in the above formula we get:

P=8+8+8√2

P=16+8√2.

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Answer: £3136

Step-by-step explanation:

First you want to find 28% of 800 to find out how much it increases by every year.

So 800*0.28= 224

And then you want to multiply 224 to 14 years to see how much he has to pay in 14 years

224*14=3136

Your answer: £3136

The value of a and b are -179/171 and -20/171 respectively.

Rationalising surds is where we convert the denominator of a fraction from an irrational number to a rational number. In more complex cases, it is useful to multiply the denominator by its conjugate to cancel out the surds in the denominator.

(2+5√7)/(2-5√7)

by rationalization

(2+5√7)/(2-5√7) × (2+5√7)/(2+5√7)

=( 4+10√7 + 10√7 + 175)/4+10√7 - 10√7- 175

= (20√7+179)/-171

= -20/171 √7 -179/171

therefore the value of a = -179/171 and b = -20/171

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Answer:

Step-by-step explanation:

You want to find the slopes of the lines shown in the attached graphs.

The slope of a line is its "rise" divided by its "run":

  m = rise/run

To determine slope from a graph, start at an identified point on the left, and count the grid squares up (+) or down (-) to the same horizontal line as the identified point on the right. This is the "rise". Then count the grid squares horizontally to the identified point. This is the "run". The slope is the ratio of these numbers.

1. rise 4, run 6, slope 4/6 = 2/3

2. rise -3, run 4, slope -3/4

3. rise -6, run 3, slope -6/3 = -2

4. run = 0; division by 0 is "undefined", so the slope is "undefined"

5. rise 4, run 1, slope 4/1 = 4

6. rise 0, run (anything), slope 0/1 = 0

__

Additional comment

It is helpful to remember that a horizontal line has a slope of 0, and a vertical line has a slope that is "undefined." Slope is positive if the line goes up to the right. It is negative if the slope goes down to the right.

Because the slope of a vertical line is "undefined," its equation cannot be written in "slope-intercept" form.

Here, points are marked on the lines. When that is not the case, it usually works well to identify points where the line crosses an intersection of grid lines.

You can also use grid crossings to check your answer for the slope. For example, the line on graph 3 crosses grid intersections that are 2 down and 1 over from the marked points (and other grid intersections), confirming a slope of -2.

If the acceleration of the object becomes 2 m/s², the value of force is,

⇒ 18 N

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

For a moving object, the force acting on the object varies directly with the object's acceleration.

Hence, We get;

⇒ F = k × a

Where, F is force of the object and 'a' is acceleration of the object.

Here, When a force of 27 N acts on a certain object, the acceleration of the object is 3 m/s².

So, We get;

⇒ F = k × a

⇒ 27 = k × 3

⇒ k = 9

Thus, If the acceleration of the object becomes 2 m/s², the value of force is,

⇒ F = k × a

⇒ F = 9 × 2

⇒ F = 18 N

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Answer:

D. Has a slope of 3/4 and passes through the point (0,1)

Step-by-step explanation:

The y-intercept is (0, 1), so this line passes through (0, 1).

slope = m = rise/run

Start at (0, 1). Go up 3. That is a rise of 3. Now go right 4. That is a run of 4.

slope = rise/run = 3/4

Answer: D. Has a slope of 3/4 and passes through the point (0,1)

Answer:

Step-by-step explanation:

First you would take .75n = .75 * 12 shirts

.75 * 12 = 9

You then would take 9 + 9.99 which obviously is 18.99$

Answer = 18.99$ per 12 T-shirts

Answer:

Green

Step-by-step explanation:

All you have to do is retrace retrace Alison’s steps. Note that there are 10 beads in the pattern, the 10th bead black. 210, 200, 190, 180, 170, 160, 150, 140. The 140th bead is black, because it is a multiple of 10. The 139 bead is black as well, because the end of Alison’s pattern contained 2 black beads. The next bead, bead 138, is green. So your answer would be green.

Step-by-step explanation:

cot(θ) = 1/tan(θ)

tan(θ) = sin(θ) / cos(θ)

Given cos(θ) = 15/17, we can find sin(θ) using the Pythagorean identity:

sin(θ) = sqrt(1 - (cos(θ))^2) = sqrt(1 - (15/17)^2) = 4/17

So, tan(θ) = 4/15

And, cot(θ) = 1/tan(θ) = 15/4

Answer: 15/8

Step-by-step explanation: We know that sin(0) will equal 8 by the 8,15,17 triangle. We using the restricted domain value for theta and using the pythagorean identities to get cot(0) as cos(0)/sin(0) and substitute the values. The denominators cancel and the result is 15/8.

The average distance between the Earth and the Moon is about 238,855 miles or 1.28 light-seconds.

To convert miles to feet, multiply by 5,280, giving us approximately 1.27 million feet. A rocket traveling at a speed of 1,540,000 ft/min would take approximately 82.5 minutes to travel to the Moon. The round trip to the Moon and back would take approximately 165 minutes, or about 2 hours and 45 minutes.

It's important to note that this is an estimate and the actual time it takes may vary due to various factors such as the rocket's trajectory, speed, and other environmental conditions. Also, it's worth noting that this speed is significantly faster than current spacecraft speeds, so the actual time it would take a rocket to travel to the Moon and back is likely to be much longer.

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The midpoint between the endpoints (9, -1) and (1, 15) is equal to (5, 7).

In order to determine the midpoint of a line segment with two (2) endpoints, we would add each point together and divide by two (2).

Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]

Substituting the given parameters into the midpoint of a line segment formula, we have the following;

Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]

Midpoint = [(9 + 1)/2, ((-1) + 15)/2]

Midpoint = [(10)/2, (14)/2]

Midpoint = (5, 7).

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The values of the proportion will be calculated by standardizing the normal distribution and using the Z table to find the values.

Here we are given that the mean distance traveled is 50,000 miles

with a standard deviation of 10,000

Now we need to find the proportion of trucks expected to travel between 34,000 and 50,000

(a)

Now for this, we need to find the area under the given normal curve between 34,000 and 50,000

For this, we need to first find the standard value. Hence we get

(X - μ)/σ

where μ = mean = 50,000

σ = standard deviation = 10,000

Hence we get

(34000 - 50000)/10000

= -1.6

(50000-50000)/10000 = 0

Looking up the value we will get

0.4452

(b)

The percentage of trucks to travel less than 30,000 will be

Z(30,000 - 50,000)/10000

= Z(-2)

looking the value up we will get

0.02275

= 2.275 %

More than 60,00 will be

1 - Z(60000-50000)/10000

= 1 - Z(1)

= 1 - 0.84134

= 0.15866

= 15.866%

Since the question asks "or" it will be a union of the 2 values to get

18.141%

(c)

Now the miles traveled by at least 80% of trucks will have a Z score of  0.8

Now in the Z table, we get the closest to be 0.80234 which has a Z value of 0.85

Now the no. of trucks will be

0.85 X 10000 + 50000

= 8500 + 50000

= 58,500

d)

Now if the standard deviation was 7000 instead of 10,000

The proportion of trucks to travel between 34 and 50 would be

Z(-16000/7000) = Z(-2.29)

0.48713

Percentage of trucks to travel less than 30 or more than 60 thousand miles in a year

is 100[ Z(-20000/7000) + 1 - Z(10000/7000) ]

= 100[Z (-2.86) + 1 - Z(1.43)]

= 100[0.00212 + 1 - 0.92364]

= 100 X 0.07849

= 7.849%

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Yes, 12 refrigerators and 11 pianos overload the truck, because 12 refrigerators and 11 pianos weighs more than 7100 lb.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

Given that, a truck that can carry no more than 7100 lb is being used to transport refrigerators and upright pianos

Let the number of refrigerators be x and the number of pianos be y.

Each refrigerator weighs 250 lb and each piano weighs 425 lb.

Here, 250x+425y≤7100

Will 12 refrigerators and 11 pianos overload the truck

Now, put x=12 and y=11 in the inequality 250x+425y≤7100, we get

250×12+425×11≤7100

7675≤7100 not true

Therefore, the inequality represent the given scenario is 250x+425y≤7100.

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Answer:

y = 1500 * 0.9575^t

Step-by-step explanation:

Where 0.9575 is equal to 1 - 0.0425, which represents a decrease of 4.25% each year.

If there are 50 marbles in a bag and 35 of them are brown, and Otti takes one marble and put it back afterwards and does it 300 times, then the estimated number of brown marbles Otti takes is around 105.

The expected number of brown marbles Otti takes can be estimated by multiplying the probability of drawing a brown marble (35/50) by the number of times he draws (300).

(35/50) × 300 = 105

This gives an estimated result of 105 brown marbles. It's important to note that this is just an estimate and the actual number could be different. The variation in the actual number of brown marbles Otti takes can be attributed to the randomness of the process.

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Using simple mathematical operations, we know that the positive difference between the mass of the fish and fisherman is 26.25.

An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value.

The operation's arity is determined by the number of operands.

The addition, subtraction, multiplication, division, exponentiation, and modulus operations are carried out via the arithmetic operators.

So, we know that:

Fish: 75kg + 75/4

75 + 18.75

93.75

Fisherman: 100kg + 100/5

100 + 20

120

Positive difference: 120 - 93.75 = 26.25

Therefore, using simple mathematical operations, we know that the positive difference between the mass of the fish and fisherman is 26.25.

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Let's start by setting up a system of equations to represent the given information:

3r = m - 7

9r = m + 11

where r is the cost of one rose, and m is the total amount of money that Masha has.

We can solve this system of equations using the elimination method:

Multiplying the first equation by 3, we get:

9r = 3m - 21

Subtracting the second equation from this, we get:

0 = -4m - 32

Simplifying, we get:

m = -8

Therefore, Masha has $-8, which means she owes money. This indicates that there may be an error in the problem statement or data provided.

Answer:

Masha has 16 dollars.

Step-by-step explanation:

3x + 7 = Masha's total money

9x = Masha's total money + 11 (after borrowing)

We can use the first equation to find the value of 3x, which is Masha's total money if she buys three roses:

3x + 7 = Masha's total money

3x + 7 = Masha's total money

3x = Masha's total money - 7

We can substitute the second equation to solve for Masha's total money:

9x = Masha's total money + 11

9x = (3x + 7) + 11

9x = 3x + 18

6x = 18

x = 3

Now we know that one rose costs 3 dollars. We can use the first equation to find Masha's total money if she buys three roses:

3x + 7 = Masha's total money

3(3) + 7 = Masha's total money

9 + 7 = Masha's total money

Masha's total money = 16

The probability of more heads than tails is 1/2 since the number of tails is divisible by 3.

A fair coin is one that has equal chances of being heads or tails when it is tossed. When a fair coin is tossed four times, the probability of getting more heads than tails is 1/2. This is because for each toss, the probability of getting a head or a tail is equal (1/2). This means that the probability of getting more heads than tails is the same as the probability of getting more tails than heads, which is 1/2.

Since the number of tails is divisible by 3, this means that in the four tosses, there must either be 0, 3, or 6 tails. Since there are no other possibilities, the probability of more heads than tails is 1/2 since it is equally likely to get more heads than tails or more tails than heads.

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Answer:

60x

30x

after mixing (60+30)x=90x

sold for=70x

gain=(90x-70x)/90x×100

20x/90x×100%

=22.22%

Answer:

548km^2

Explanation:

if the surface area is 137 km, and then it has a dialation of 4, then all you need to do is multiply by 137 by 4, which equals 548. That means the surface area of cylinder B is 548 km^2. Hope that helps.

The direction of point P is (2.5, 3.3). In this way, the point P that separates the line fragment from K to L with a 1 to 5 proportion has the coordinate (2.5, 3.3).

Given a line segment from K to L, and the proportion of the division as 1 to 5, we can find the direction of point P that separates the line section into the predetermined proportion.

The direction of point P can be tracked down utilizing the accompanying recipe:

P = (1 - t) K + t L

where t is the relative separation from direct K toward point P. To fulfill the 1 to 5 proportion, we can set t = 1/6.

Subbing the qualities into the equation, we get:

P = (1 - 1/6) K + 1/6 L

= 5/6 K + 1/6 L

To find the genuine direction of point P, we want to substitute the directions of K and L into the equation. For instance, if K = (3, 4) and L = (7, 8), the direction of point P can be determined as:

P = (5/6)(3, 4) + (1/6)(7, 8)

= (15/6, 20/6)

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Answer:

m = -2

b = -3

Step-by-step explanation:

Point slope formula of a line = [tex]y-y_{1} = M(x-x_{1} )[/tex]

Where x1 and y1 are the coordinates of the point and M is the slope.

Given slope = -2

Point = (-7,11)

So x1 = -7 and y1 = 11

Substituting the values in the point-slope formula, we get:

[tex]y-11 = -2(x - (-7))[/tex]

[tex]= > y = -2x -14 + 11[/tex]

Or

[tex]y = -2x -3[/tex]

Thus, m = -2 and b = -3

The actual balance is $36,400.68 which lower than the goal of $150,000. The Option D is correct.

The Formula to use to derive the actual balance is: P[((1 + r/n)^(n*t)) - 1) / (r/n)] where: FV = future value, P = monthly deposits, r = interest rate, t = time in years, n = number of compound in a year

From the given:

P = 200

r = 2.85% 0.0285

t = 30 years

n = 12 (compounded monthly)

Future value = 200((1 + 0.0285/12)^(12(30)) - 1) / (0.0285 / 12)

Future value = $113,599.32

The difference between the actual balance and the employee's goal is:

= $150,000 - $113,599.32

= $36,400.86

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The difference in elevation between the height of mountain and height of valley measuring from sea level is equal to 6594 feet.

Since it is given that the height of mountain from the sea level is 6874 feet and the height of valley is 280 feet. Therefore to calculate the difference in elevation, the heights will be subtracted from one another to get a value which will show the elevation. Since both the heights are measured from the sea level which is taken as constant, so no extra calculations will be needed.

Elevation difference = Height of mountain - height of valley

Elevation difference = 6874 - 280 = 6594 feet

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Answer:

2[tex]\sqrt{13x^{2} }[/tex]

Step-by-step explanation:

To simplify the expression √52x^4, we can break it down as follows:

√(52x^4) = √(4 * 13 * x^4)

Since the square root of a product is equal to the product of the square roots, we can simplify further:

√(4 * 13 * x^4) = √4 * √13 * √(x^4)

The square root of 4 is 2, and the square root of x^4 is x^2:

2 * √13 * x^2

Therefore, the simplified expression is 2√13x^2.

Answer:

[tex]\large\text{$2\sqrt{13}\;x^2$}[/tex]

Step-by-step explanation:

Given expression:

[tex]\sqrt{52x^4}[/tex]

Prime factorization is the process of representing a positive integer as a product of its prime factors.

The prime factorization of 52 is 2² · 13. Therefore, rewrite 52 as 2² · 13:

[tex]\sqrt{2^2 \cdot 13 \cdot x^4}[/tex]

[tex]\textsf{Apply the radical rule:} \quad \sqrt{abc}=\sqrt{\vphantom{b}a}\sqrt{b}\sqrt{c}[/tex]

[tex]\sqrt{2^2} \sqrt{13} \sqrt{x^4}[/tex]

[tex]\textsf{Apply the radical rule:} \quad \sqrt{a^2}=a, \quad a \geq 0[/tex]

[tex]2\sqrt{13} \sqrt{x^4}[/tex]

[tex]\textsf{Apply the radical rule:} \quad \sqrt[n]{a^m}=a^{\frac{m}{n}},\quad \textsf{assuming} \;a\geq 0[/tex]

[tex]2\sqrt{13} \;x^{\frac{4}{2}}[/tex]

[tex]2\sqrt{13} \;x^2[/tex]

Therefore, the simplified expression is:

[tex]\large\boxed{2\sqrt{13}\;x^2}[/tex]

Answer:

-193

Step-by-step explanation:

x+52+67+75=1

x+119+75=1

x+194=1

-194.    -194

x=-193

By using Area Model of Multiplication and Division, it can be concluded that the missing number in the area model is 40.

Area Model of Multiplication and Division is a rectangular chart used to multiply and divide two numbers or expressions, where the quotient and divisor determine the length and width of the rectangle.

In this model, we split up a large rectangular area into several smaller rectangular, using number bounds, to make calculations easier.

Now we take a look at our area model 14 x 16 in size.

Area I = 10 x 10 = 100

Area II = 6 x 10 = 60

Area III = 6 x 4 = 24

Using the same way, the missing number, area IV, can be calculated as follows:

Area IV = 10 x 4 = 40

Thus, it can be concluded that the missing number in the area model is 40.

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The integral ∫₁/₁₀¹⁰[㏒₁₀(10x)/x]dx = 2㏑10

Integration is the process of finding the antiderivative of a fuinction.

Given the integral

[tex]\int\limits^{10}_{\frac{1}{10} } {\frac{log_{10}10x }{x} } \, dx[/tex]

We evaluate the integral as follows

[tex]\int\limits^{10}_{\frac{1}{10} } {\frac{log_{10}10x }{x} } \, dx[/tex]

Now, using the properties of the laws of logarithms, we have ㏒ab = ㏒a + ㏒b

So, [tex]\int\limits^{10}_{\frac{1}{10} } {\frac{log_{10}10x }{x} } \, dx = \int\limits^{10}_{\frac{1}{10} } {\frac{log_{10}10 + log_{10}x }{x} } \, dx \\= \int\limits^{10}_{\frac{1}{10} } {\frac{log_{10}10}{x} } \, dx + \int\limits^{10}_{\frac{1}{10} } {\frac{log_{10}x}{x} } \, dx \\= \int\limits^{10}_{\frac{1}{10} } {\frac{1}{x} } \, dx + \int\limits^{10}_{\frac{1}{10} } {\frac{log_{10}x}{x} } \, dx\\[/tex]

So, using the property of change of base of logarithm, we have that

logx = lnx/ln10

, [tex]\int\limits^{10}_{\frac{1}{10} } {\frac{log_{10}10x }{x} } \, dx = \int\limits^{10}_{\frac{1}{10} } {\frac{1}{x} } \, dx + \int\limits^{10}_{\frac{1}{10} } {\frac{\frac{lnx}{ln10} }{x} } \, dx\\= \int\limits^{10}_{\frac{1}{10} } {\frac{1}{x} } \, dx + \frac{1}{ln10}\int\limits^{10}_{\frac{1}{10} } {\frac{lnx}{x} } \, dx\\= \int\limits^{10}_{\frac{1}{10} } {\frac{1}{x} } \, dx + \frac{1}{ln10}\int\limits^{10}_{\frac{1}{10} } {{lnx} \, dlnx[/tex]

[tex]\int\limits^{10}_{\frac{1}{10} } {\frac{log_{10}10x }{x} } \, dx = {[lnx]_{\frac{1}{10}}^{10} } + {\frac{[lnx]^{2}}{2} }_{\frac{1}{10}}^{10} } \\= ln10 - ln\frac{1}{10} + \frac{1}{2}[[ln10]^{2} - [ln\frac{1}{10}]^{2} ] \\= ln10 + ln10 + \frac{1}{2}[[ln10]^{2} - [-ln10}]^{2} ]\\= ln10 + ln10 + \frac{1}{2}[[ln10]^{2} - [ln10}]^{2} ]\\= 2ln10 + 0\\= 2ln10[/tex]

So, the we see that the integral [tex]\int\limits^{10}_{\frac{1}{10} } {\frac{log_{10}10x }{x} } \, dx = 2ln10[/tex]

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