HELP PLS


Functions f and g are defined by these equations:

f(x)=80−15x g(x)=25+10x


Select all the statements below that are true regarding these two functions.


f(2)=50f of 2 is equal to 50

g(2)=50g of 2 is equal to 50

g(5)=75g of 5 is equal to 75

f(5)=75f of 5 is equal to 75

f(3) > g(3)f(3) > g(3)

f(−1) > g(−1)

Answer:

m <1 = 64

m<2= 26

Step-by-step explanation:

the angle is 90 degree

therefore, <1 + <2 = 90

(x+51) + (2x) = 90

3x +51 = 90

3x = 39

x = 13

According to the solving the function the value of  h(-2) + g(-2) is 45.

function is a mathematical phrase, rule, or law that establishes the relationship between an independent variable and a dependent variable (the dependent variable). Functions are used frequently in mathematics and are crucial for constructing physical links in the sciences.

To find h(-2) + g(-2), we need to evaluate h(r) and g(r) when r = -2, and then add the results:

h(-2) = 11(-2)² - 6 = 44

g(-2) = (-2)² + 8(-2) + 9 = 1

So, h(-2) + g(-2) = 44 + 1 = 45.

Therefore, h(-2) + g(-2) = 45.

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Answer: -5

Step-by-step explanation: 2 + -11 = -9 and subtract -4 from it since it’s the sum of 2 + -6. -9 - -4 is -9 + 4 so -5

Answer:

-5

Step-by-step explanation:

2+-11=-9

2+-6=-4

-9- -4=-5

The scaled triangle will be larger than the initial size by a factor 2.

The scaled square will be smaller than the initial side by a factor 4.

Dilation refers to a transformation that changes the size of a geometric figure without altering its shape.

Dilation involves scaling an object by a certain factor, that might result in  enlarging or reducing its dimensions uniformly in all directions.

Based on the given diagram, the new length and size of the object is calculated as follows;

For the triangle, (measure the length with ruler)

For the square; (measure the length with ruler)

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The measure of each unknown angle is -

{1} - x = √160

{2} - x = √176

In geometry, the tangent line to a plane curve at a given point is the straight line that "just touches" the curve at that point

Given are the images as shown in the image.

{ 1 } -

We can write using the Pythagoras theorem -

BC² = 6² + x²

(BA + AC)² = 6² + x²

14² = 6² + x²

x² = 14² - 6²

x² = 20 x 8

x² = 160

x = √160

{ 2 } -

We can write using the Pythagoras theorem -

24² = 20² + x²

x² = 24² - 20²

x² = 44 x 4

x² = 176

x = √176

Therefore, the measure of each unknown angle is -

{1} - x = √160

{2} - x = √176

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To find all points on the x-axis that are 16 units away from the point (5, -8), we can use the distance formula. The distance between two points (x₁, y₁) and (x₂, y₂) is given by the formula:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

In this case, the y-coordinate of the point (5, -8) is -8, which lies on the x-axis. So, any point on the x-axis will have a y-coordinate of 0. Let's substitute the given values and solve for the x-coordinate.

d = √((x - 5)² + (0 - (-8))²)

Simplifying:

d = √((x - 5)² + 64)

Now, we want the distance d to be equal to 16 units. So, we set up the equation:

16 = √((x - 5)² + 64)

Squaring both sides of the equation to eliminate the square root:

16² = (x - 5)² + 64

256 = (x - 5)² + 64

Subtracting 64 from both sides:

192 = (x - 5)²

Taking the square root of both sides

√192 = x - 5

±√192 = x - 5

x = 5 ± √192

Therefore, the two points on the x-axis that are 16 units away from the point (5, -8) are:

Point 1: (5 + √192, 0)

Point 2: (5 - √192, 0)

In summary, the points on the x-axis that are 16 units away from the point (5, -8) are (5 + √192, 0) and (5 - √192, 0).

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The area of the square with a side length of 3.1 meters is 9.61 square meters.

To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.

Area of a square = side length × side length

Substituting the given side length into the formula:

Area = 3.1 m × 3.1 m

To perform the calculation:

Area = 9.61 m²

It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.

Remember, to find the area of any square, you simply need to multiply the length of one side by itself.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

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a. The distance is 0.829 meters.

b. The distance is 1.86735 meters.

c. The times the child's bicycle tire must rotate to travel 1 kilometer is 26.53 times

d. The number of rotation is 12.589.

a. Given that the radius of the child's bicycle tire is 6 inches, we can substitute the values into the formula:

Circumference = 2 * π * 6 inches

To convert inches to meters, we use the conversion factor: 1 inch = 0.022 meters

Distance = 2 * π * 6 inches * 0.022 meters/inch

= 0.829 meters.

b. Similarly, for the woman's ten-speed bicycle with 13.5-inch radius:

Distance = 2 * π * 13.5 inches * 0.022 meters/inch

=  1.86735 meters.

c. To calculate how many times the child's bicycle tire must rotate to travel 1 kilometer, we need to convert 1 kilometer to inches and then divide it by the circumference of the tire.

1 kilometer = 1000 meters

1 meter = 1/0.022 inches

So, 1 kilometer = 1000 * (1/0.022) inches

Number of rotations = (1000 * (1/0.022) inches) / (2 * π * 6 inches)

=  26.53

d. Similarly, for the woman's bicycle tire:

Number of rotations = (1000 * (1/0.022) inches) / (2 * π * 13.5 inches)

=  12.589.

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\( \qquad\longrightarrow \sf f(x) = sin^{-1} \bigg(\dfrac{x}{2}\bigg)\\\)

The Derivative of f(x) with respect to x-

\( \qquad\longrightarrow \sf \dfrac{d}{dx} \:sin^{-1} \bigg(\dfrac{x}{2}\bigg)\\\)

\( \qquad\longrightarrow \sf \dfrac{1}{\sqrt{1-\bigg(\dfrac{x}{2}\bigg)^2}}\;\times \dfrac{d}{dx}\:\dfrac{x}{2}\\\)

\(\qquad\sf\because\boxed{\sf{ \: \dfrac{d}{dx} sin^{-1}x = \dfrac{1}{\sqrt{1-x^2}}}}\\\)

\( \qquad\longrightarrow \sf \dfrac{1}{\sqrt{1-\bigg(\dfrac{x^2}{4}\bigg)}}\;\times\dfrac{1}{2} \:x^{1-1}\\\)

\(\qquad \sf\because\boxed{\sf{ \dfrac{d}{dx }x^n = nx^{n-1}}}\\\)

\( \qquad\longrightarrow \sf \dfrac{1}{\sqrt{1-\bigg(\dfrac{x^2}{4}\bigg)}}\;\times\dfrac{1}{2} \times 1\\\)

\( \qquad\longrightarrow \sf \dfrac{1}{\sqrt{1-\bigg(\dfrac{x^2}{4}\bigg)}}\;\times\dfrac{1}{2} \\\)

\( \qquad\longrightarrow \sf\dfrac{1}{2}\: \dfrac{1}{\sqrt{1-\bigg(\dfrac{x^2}{4}\bigg)}}\\\)

\( \qquad\longrightarrow \underline{\sf\: \dfrac{1}{2\:\sqrt{1-\bigg(\dfrac{x^2}{4}\bigg)}}}\\\)

Henceforth, Option C) is the correct answer.

The answer to the sum is: ∑ k⁴ (k  ranges from 1 to 6)

Express the sum in sigma notation :

According to the question,

1 = lower limit of summation

k = the index of summation

1 + 16 + 81 + 256 + 625 + 1296 = 1² + 4² + 9² + 16² + 25² + 36²

                                                 = 1⁴ + 2⁴ + 3⁴ + 4⁴ + 5⁴ + 6⁴ ( i.e 16 = 4²=(2²)²)

                                                 = ∑ k⁴ (k ranges from 1 to 6)

 So, The answer to the sum is - ∑ k⁴ (k ranges from 1 to 6).    

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The equation that represents the statement the product of 1/5 and a number is equal to 1 1/2 is n/5 = 1¹/₂.

Since the question says, the product of 1/5 and a number is equal to 1 1/2.

This is a word problem

Let n be the number.

Since it says the product of a number n and 1/5, we have n × 1/5 = n/5

It says this product equals 1¹/₂.

So, we equate both expressions.

So, n/5 = 1¹/₂.

So, the equation that represents the statement the product of 1/5 and a number is equal to 1 1/2 is n/5 = 1¹/₂.

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The answer is n/5 = 1¹/₂.

       Hope this helps! good luck :)

Answer:

490000

Step-by-step explanation:

Substituting \(x=40\),

\(I=-425(40)^2 + 45500(40) - 650000=490000\)

Using probability we know that we have full probability or 1 that we will draw a coin that will have ethe value of at least $0.10.

A probability is a numerical representation of the likelihood or chance that a specific occurrence will take place.

Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Simply put, probability is the likelihood that something will occur.

When we don't know how an occurrence will turn out, we can discuss the likelihood or likelihood of various outcomes.

So, we have the chart:

Penny = 2/5 = 0.4

Nickel = 1/5 = 0.2

Dime = 1/4 = 0.25

Then, the probability of getting a value of at least $0.10

P(E) = 3/3

P(E) = 1

Therefore, using probability we know that we have full probability or 1 that we will draw a coin that will have ethe value of at least $0.10.

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Answer:

w=2.5

Step-by-step explanation:

divide 12.5 by 5: 12.5/5=2.5, so w=2.5

Answer:

2.5

Step-by-step explanation:

To solve for something you want to get it alone on one side. To do this for this problem you want to divide both sides by 5. This comes out to 2.5

Answer: The slope is 0.

Step-by-step explanation:

y -2/3=0

+2/3. +2/3

y=2/3

Answer:

X= (-40, 0

Y=(0, 15)

Step-by-step explanation:

Answer:

29

Step-by-step explanation:

Ok so with there being an X beside the number you go ahead and multiply the X and the number its beside (12) so 12x3=36 then you subtract 7 from 36 which will get you 29 hope this helped!

We can Add 7 black beads to make ratio 3 : 1.

Since we can only change the number of black beads, decide how many black beads you will add based on how many white beads there are.

There are three white beads in the picture.

Total beads we will have (b meaning black)b : 3

Ratio black : white beads 3 : 1

Use the common ratio, which is a number that both sides of the original ratio multiply by to get to the new ratio.

Find common ratio by dividing total by ratio white beads: 3/1 = 3

Multiply ratio black beads by common ratio. 3 X 3 = 9

We need 9 black beads in total.

Check answer

9 : 3    

Both sides divisible by 3; reduce ratio

= 3 : 1        

Which is Correct ratio

Hence, There will be a total of 9 black beads, but we already have 2 black beads:

(9 total) - (2 original) = (7 to add)

Therefore , we need to add 7 black beads.

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We can think of the wind as a vector of velocity that adds or substract from the velocity of the plane.

When the plane flies downwind, the speed of the wind adds to the speed of the plane.

For a time t the plane can fly 255 miles in this condition. We then can express the average speed as 255/t.

If the speed is the sum of the speed of the plane and the speed of the wind, we can write:

Now, if the plane flies against the wind, the speed of the wind is substracted from the speed of the plane:

If we know tha the speed of the plane is vp = 230 mph, we can add both equations and then find t:

Now that we know the value of t we can use any of the two equations we have written to calculate the speed of the wind (vw):

Answer: the speed of the wind is 25 miles per hour.

Answer:

85

Step-by-step explanation:

Answer:

z1(z2 + z3) = z1 z2 + z1 z3 ⇒ verified down

Step-by-step explanation:

∵ z1 = 4 + 3i

∵ z2 = 3 - 2i

∵ z3 = i + 5

→ Find the left side

∵ z1(z2 + z3) = (4 + 3i)[3 - 2i + i + 5]

∴ z1(z2 + z3) = (4 + 3i)[(3 + 5) + (-2i + i)]

∴ z1(z2 + z3) = (4 + 3i)(8 - i)

∴ z1(z2 + z3) = (4)(8) + (4)(-i) + (3i)(8) + (3i)(-i)

∴ z1(z2 + z3) = 32 - 4i + 24i - 3i²

→ Remember that i² = -1

∴ z1(z2 + z3) = 32 - 4i + 24i - 3(-1)

∴ z1(z2 + z3) = 32 - 4i + 24i + 3

→ Add the like terms

∴ z1(z2 + z3) = (32 + 3) + (-4i + 24i)

∴ z1(z2 + z3) = 35 + 20i

→ Find the right side

∵ z1 z2 + z1 z3 = (4 + 3i)(3 - 2i) + (4 + 3i)(i + 5)

∴ z1 z2 + z1 z3 = [(4)(3)+(4)(-2i)+(3i)(3)+(3i)(-2i)] + [(4)(i)+(4)(5)+(3i)(i)+(3i)(5)]

∴ z1 z2 + z1 z3 = [12 -8i + 9i -6i²] + [4i + 20 + 3i² + 15i]

→ Replace i² by -1

∴ z1 z2 + z1 z3 = [12 -8i + 9i -6(-1)] + [4i + 20 + 3(-1) + 15i]

∴ z1 z2 + z1 z3 = [12 -8i + 9i + 6] + [4i + 20 - 3 + 15i]

→ Add the like terms

∴ z1 z2 + z1 z3 = [12 + 6 + 20 - 3] + [-8i + 9i + 4i + 15i]

∴ z1 z2 + z1 z3 = 35 + 20i

∵ The left side = 35 + 20i

∵ The right side = 35 + 20i

∴ The left side = the right side

∴ z1(z2 + z3) = z1 z2 + z1 z3

The result of multiplying 5u by the difference between 3v and 4w is the vector -240i + 70j + 10.

In linear algebra, we often use scalars and vectors to perform various operations. Scalars are just ordinary numbers that can be used to multiply or divide vectors. On the other hand, vectors are quantities that have both magnitude and direction.

In this problem, we are given three vectors, u, v, and w, and we are asked to find the result of multiplying 5u by the difference between 3v and 4w.

First, let's calculate 3v - 4w. Since v = 4i - 2j and w = -2j, we can substitute these values to get,

3v - 4w = 3(4i - 2j) - 4(-2j)

= 12i - 6j + 8j

= 12i + 2j

Next, we need to find the scalar product of 5u and 12i + 2j. To find the scalar product of two vectors, we need to multiply the corresponding components and add up the products.

Therefore: 5u(3v - 4w) = 5u(12i + 2j)

= 5(-4i + j)(12i + 2j)

= -20i(12i) + 5i(2j) + 60j(i) - 10j(j)

= -240i + 10j + 60j + 10

= -240i + 70j + 10

So, the result of multiplying 5u by the difference between 3v and 4w is the vector -240i + 70j + 10.

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Answer:

(B) v=p-10 1/10

Step-by-step explanation:

v does equal p if you take 10.1 away each time that's what the 1/10 is there for

\(\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}\)

Solution -

\(Area\: of \:equilateral \:triangle\: = \: \frac{ \sqrt{3} }{4} a {}^{2} \\ \\ \implies \frac{ \sqrt{3}}{4} \times 14^{2} \\ \\ \implies \: \frac{ \sqrt{3} }{\cancel4} \times \cancel{196} \\ \\ \implies \: \sqrt{3} \times 49 \\ \\ \implies \: \bold\blue{49 \sqrt{3} \:units {}^{2}} \)

Further ,

value of \(\bold\orange{\sqrt{3} = 1.732}\)

therefore ,

\(Area = 49 \times 1.732 \\ \\ \implies \: \bold\red{84.69 \: units {}^{2} \: (approx.)}\)

hope helpful :D

Answer:

Step-by-step explanation:

Therefore, the answer is A. {5, 5√3, 10}.

The set of values {5, 5√3, 10} could be the side lengths of a 30-60-90 triangle.

In a 30-60-90 triangle, the sides are in a specific ratio. The ratio is 1 : √3 : 2, where the shortest side (opposite the 30-degree angle) has length x, the side opposite the 60-degree angle has length x√3, and the hypotenuse (opposite the 90-degree angle) has length 2x.

Let's check if the given set of values satisfies this ratio:

   If x= 5, then the side opposite the 60-degree angle should be 5√3, and the hypotenuse should be 10. These values match the ratio, so the set {5, 5√3, 10} could be the side lengths of a 30-60-90 triangle.

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One example of a nonempty subset u of R^2 such that u is closed under scalar multiplication, but u is not a subspace of R^2, is the set u = {(x, y) | x, y are rational numbers}.

This set is closed under scalar multiplication as if a and (x,y) are in u, a*(x,y) will also be in u because rational numbers are closed under multiplication.

A subset can be described with different properties, one of them is closure, a subset U is closed under an operation if the operation is applied to any two elements of U, and the result is also an element of U.

In mathematics, a subset is a set that is completely contained within another set. It is defined as a set U that is a part of a set S, such that every element of U is also an element of S. The notation used to indicate that U is a subset of S is U ⊆ S.

However, this set u is not a subspace of R^2 because it doesn't contain the zero vector (0,0) and it doesn't close under addition, as the sum of two rational numbers may not be a rational number.

Therefore, One example of a nonempty subset u of R^2 such that u is closed under scalar multiplication, but u is not a subspace of R^2, is the set u = {(x, y) | x, y are rational numbers}.

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