A boy is flying a kite. The length of the string is 61 meters and the
horizontal distance between the boy and the kite is 60 meters. Assuming
there is no slack in the string, find the height of the kite from the ground.

Answer:

-5x+13 given (-x+3)-(4x-10)

Answer:-5x+13

Step-by-step explanation:

We are going to distribute to get rid of the ( ):

-x+3-4x+10

Pair up like terms:

-x-4x+3+10

Combine the like terms:

-5x+13

Answer:

-5x+13

Step-by-step explanation:

( - x + 3) - (4x - 10)

Distribute the minus sign

( - x + 3) - 4x + 10

Combine like terms

-5x +13

[tex]-1=\dfrac{5+x}{6}\\\\-6=5+x\\\\x=-11[/tex]

"Solve for x" means get an equation that says " X = something ".  It has nothing but X all alone on one side, and the other side tells exactly what X is equal to.

How do you get such an equation ?  

-- Take what they gave you in the question.

-- Do anything you want on one side of it, to get X all by itself on that side.

BUT . . .

-- Whatever you do to one side, you must immediately do the same thing on the other side.

Here's how that goes:

Given in the question:  -1 = (5 + X) / 6

Multiply each side by 6 :  -6 = 5 + X

Subtract 5 from each side:  -11 = X

And there you are.  It's over almost as soon as it started.

The sum of three positive integers given their product is 7, analyze the factors of the product and sum them up.

The sum of three positive integers whose product is 8 can be found by analyzing the factors of 8.

Given that the product of three different positive integers is 8, the three integers are 1, 2, and 4. Therefore, the sum of these integers is 1 + 2 + 4 = 7.

Answer:

XY=10 cm

Step-by-step explanation:

Answer: 34 miles

Step-by-step explanation:

First multiply the 2 miles she power walked by the 7 days. (14 miles)

Next, multiply the 5 miles by the 4 days. (20)

Add both numbers, 20+14=34 miles

Answer:

left 1 unit, reflection about the x-axis, up 1 unit

Step-by-step explanation:

This is a cubic that has been moved left 1 unit because of the (x+1)^3 part.

It also has been moved up one unit because of the plus 1 on the outside of the cube.

There has also been a reflection across the x-axis because of the -1 in front of the -(x+1)^3 part.

In general, g(x-h)+k means:

1) the function g has been moved right (if h is positive) or moved left (if h is negative).

2) the function g has been moved up (if k is positive) or down (if k is negative)

Answer:

the answer of this question is 3/5

Answer: the answer is

0.04444

Answer:

r = 4.2 cm; d = 8.4 cm

Step-by-step explanation:

The radius is the distance from the centre of the circle to the circumference.

r = 4.2 cm

The diameter is the length of a straight line that passes through the centre with each end at the circumference.

d = 2r = 2 × 4.2 cm = 8.4 cm

Answer:

radius=4.2

diameter=8.4

Step-by-step explanation:

Answer:

[tex]y=3x+8[/tex]

Step-by-step explanation:

Slope-intercept form is as follows:

[tex]y=mx+b[/tex]

In this equation, "m" represents your slope and "b" represents your y-intercept.

To convert your equation into slope-intercept form, distribute your 3 across your parentheses and then add 5 to both sides to isolate for y.

[tex]y-5=3(x+1)\\y-5=3x+3\\y=3x+8[/tex]

Answer:

[tex]\large\boxed{x=\dfrac{7}{8}}[/tex]

Step-by-step explanation:

[tex]4^{(4x-1)}=32\\\\(2^2)^{4x-1}=2^5\qquad\text{use}\ (a^n)^m=a^{nm}\\\\2^{2(4x-1)}=2^5\iff2(4x-1)=5\ \ \text{use the distributive property}\ a(b+c)=ab+ac\\\\(2)(4x)+(2)(-1)=5\\\\8x-2=5\qquad\text{add 2 to both sides}\\\\8x=7\qquad\text{divide both sides by 8}\\\\x=\dfrac{7}{8}[/tex]

Answer:

[tex]20x^{4}-39x^{3} +26x^{2}-6x\\[/tex]

Step-by-step explanation:

Multiply the two polynomials by multiplying each term

[tex](5x^{2} -6x+2)(4x^{2} -3x)\\5x^2*4x^2+5x^2(-3x)+(-6)*4x^2+(-6x)(-3x)+2*4x^2+2(-3x)\\20x^{4}-39x^{3}  +26x^{2} -6x\\[/tex]

To multiply the given expressions, use the distributive property and combine like terms. The final result is 20x⁴ - 39x³ + 26x² - 6x.

To multiply the expression (5x²-6x+2) (4x²-3x), we can use the distributive property. Multiply the first term in the first binomial (5x²) by each term in the second binomial (4x², -3x), and then multiply the second term in the first binomial (-6x) by each term in the second binomial. Finally, multiply the third term in the first binomial (2) by each term in the second binomial. Combine like terms and simplify as needed to get the final result.

Applying this process, we get:

5x² × 4x² = 20x⁴

5x² × -3x = -15x³

-6x × 4x² = -24x³

-6x × -3x = 18x²

2 × 4x² = 8x²

2 × -3x = -6x

Combining all the terms, we have:

20x⁴ - 15x³ - 24x³ + 18x² + 8x² - 6x

Simplifying further, we get:

20x⁴ - 39x³ + 26x² - 6x

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Your mouse pointer is covering the number at the hypotenuse, but I assume that it is 10.

We can test to see if the triangle is a right angled triangle by using Pythagoras' Theorem. This is because the Pythagorean Theorem only works with right angled triangles.

The theorem is:

[tex]a^{2} + b^{2} = c^{2}[/tex]

where:

a = length of one leg of the triangle

b = length of the other leg of the triangle

c = the length of the hypotenuse.

If triangle FGH is a right triangle then:

[tex]\sqrt{51}^ {2} + 7 ^{2} = 10^{2}[/tex]

[tex]\sqrt{51} ^{2}[/tex] is just 51

[tex]7^{2}[/tex] is 49

and [tex]10^{2}[/tex] is 100

if we add up 51 and 49 we get 100. And of course, 100 = 100,

Since the theorem works, then the FGH is a right triangle

______________________________________

Answer:

True: FGH is a right angled triangle

7v(4v2-8v+1)+8(4v2-8v+1)

28v3-56v2+7v+32v2-64v+8

Answer= 28v3 -24v2 -57v +8

Answer:

x-intercept (-8,0)

y-intercept (0,2)

Step-by-step explanation:

To find the x-intercept, you set y equal to 0.

Like this:

-2(0)+x=2(0)-8

  0  +x=0    -8

        x=   -8

So the x-intercept is (-8,0).

To find the y-intercept, you set x equal to 0.

Like this:

-2y+0=2y-8

  -2y =2y-8

Subtract 2y on both sides

 -4y=-8

Divide both sides by -4

   y=2

So the y-intercept is (0,2)

Answer:

O 30, 24, and 18

Step-by-step explanation:

18^2+24^2=30^2

324+576=900

Final answer:

Using the Pythagorean theorem, only the set of lengths 24, 7, and 26 satisfy the condition for a right triangle, as 24² + 7² equals 26².

Explanation:

The question seeks to determine which set of lengths can form a right triangle. When assessing whether a given set of three lengths can form a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides (the legs) is equal to the square of the length of the longest side (the hypotenuse). The formula for the Pythagorean theorem is a² + b² = c², where a and b are the lengths of the legs, and c is the length of the hypotenuse.

We will check each set of given lengths:

Therefore, the lengths that would form a right triangle are 24, 7, and 26.

Answer:it’s the number that appears most often,so the answer would be 2,4,and 0.

Step-by-step explanation:

The modes of the data set are 0, 2, and 4

In this question, it is asking you to find the mode of the given data set.

We would be using the data set in the question in order to find out what the mode is.

The mode would be the number that "occurs" the most. In other words, the number(s) that are more "frequent."

Data set:

2, 2, 1, 4, 4, 2, 3, 0, 0, 4, 1, 0, 4, 0, 2

Now, we could count how many of each numbers there are.

0 = 4 (Most)

1 = 2  

2 = 4 (Most)

3 = 1

4 = 4 (Most)

When you're done counting the numbers, you would notice that 0, 2, and 4 have the highest number of occurrence in the data set.

This means that the modes of the data set are 0, 2, and 4

Answer:

Angle 1 equals 90 degrees. Angle 2 equals 38 degrees.

Step-by-step explanation:

Angle 1 is at the cross of two perpendicular lines, making it 90 degrees. Angle 2 can be found by making the two equal side lengths and the middle line into one triangle. This means that two of the angles are 52 degrees. This leaves 76 degrees to be split in the triangle. The middle line cuts the angle in half, making it 38 degrees

The correct equation for the given graph will be option A that is

y=[tex]x^{2} +9x+18[/tex]

It is a relationship between two variables and having a equal to sign in between.

Firstly we need to find the points of the respective equations.

y=[tex]x^{2} +9x+18[/tex]

y=[tex]x^{2}[/tex]+6x+3x+18

y=x(x+6)+3(x+6)

y=(x+3)(x+6)

Put  this equal to 0 and we get x=-3 and x=-6

y=[tex]x^{2} -2x+4[/tex]

It is a wrong equation.

y=(x-3)(x-6)

put this equal to 0 we get x=3 and x=6

Now we have to check in the graph whether points (-3,0)(-6,0) satisfies or (3,0)(6,0)

We can easily see that (-3,0)(-6,0) satisfies the graph.

Hence the correct equation is y=x2+9x+18

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The graph that represents the given piecewise function is the one on the right. Therefore the correct answer is option b.

The piecewise function f(x) is defined as follows:

f(x) = -x if x ≤ 3

f(x) = 2 if x > 3

To graph this piecewise function, you would draw two separate segments:

For x values less than or equal to 3, you would graph the line y = -x, which has a negative slope and goes through the point (3, -3). This line represents the function f(x) = -x for x ≤ 3.

For x values greater than 3, you would graph the horizontal line y = 2. This line represents the function f(x) = 2 for x > 3.

The transition from the first segment to the second occurs at x = 3. At this point, you would typically draw an open circle to indicate that the function is defined separately for x ≤ 3 and x > 3.

The graph will consist of a line sloping downward to the left (y = -x) for x ≤ 3 and a horizontal line at y = 2 for x > 3.

Therefore, the correct answer is option b.

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Answer:

This system has one solution (-1,1)

Step-by-step explanation:

The attached picture shows the solutions for the system

If we equalize the eq. obtain the following

-x=2x+3

From we obtain that x= -1

Using the first equation y=-x, we obtain that y=1

so (-1,1)

Answer:

=3501 yards.

Step-by-step explanation:

The three ships form a triangle.  From the Voyager the angle between the Norman and the Gladstone=180-(55+48)=77°

Let the position of the Voyager be V that of Norman be N and that of the Gladstone be G

Then, the distance between Norman and voyager is g

g/sin G=v/ Sin V

4590/Sin 77=g/Sin 48

g=(4590 Sin 48)/Sin 77

=3500.8 yards

The distance between the Norman and the voyager= 3501 yards.

[tex]\large\boxed{\text{C}).\,15\,\text{cm}}[/tex]

In this question, we're trying to find what the radius of the circular pie is.

In this question, we know that the area of the pie is 706.5 cm²

We can use the area to find our radius.

We would use the formula [tex]r=\sqrt\frac{A}{\pi}[/tex] to find the radius.

R= radius

A = Area

Your equation should look like this:

[tex]r=\sqrt\frac{706.5}{\pi}[/tex]

Now, you will solve.

[tex]r=\sqrt\frac{706.5}{\pi}\\\\\text{You can make it simpler by turning}\, \pi\,\text{into} 3.14\\\\r=\sqrt\frac{706.5}{3.14}\\\\\text{Divide 706.5 by 3.14}\\\\r=\sqrt225\\\\\text{Now, get the square root of 225}\\\\r=15[/tex]

When you're done solving, you should get 15.

This means that the radius of the pie is 15 cm.

Final answer:

To find the radius of the pie given its area of 706.5 cm², we use the formula A = πr² and solve for r, yielding an approximate radius of 15 cm. This corresponds to option C) on the given list.

Explanation:

To find the radius of the pie given its area, we can use the area formula for a circle: A = πr². Since the area of the pie is given as 706.5 cm², we can rearrange the formula to solve for the radius (r).

The rearranged formula to solve for the radius is: r = √(A/π).

Substituting the given area, we have:
r = √(706.5 cm²/π)
r = √(706.5/3.14159265359)
r ≈ √(225)
r ≈ 15 cm

Therefore, the radius of the pie is approximately 15 cm, making option C) the correct answer.

Answer:

2) Yes, each x-coordinate is only used once.

3) {1,2,3,4}

4) {25,45,60,70}

5) (3,60)

6) No because (4,7) and (4,25) share the same x-coordinate.

Step-by-step explanation:

A relation is a function if there is no more than one y-value assigned to an x.

Any x used can only be used once in an order pair.

You that here.

(1,25)

(2,45)

(3,60)

(4,70)

So basically because all of the x-coordinates are different, this is a function.

The domain is the x-coordinate of each pair (the first of each pair):

{1,2,3,4}.

The range is the y-coordinate of each pair (the second number of each pair):

{25,45,60,70}.

One ordered pair that I see in the table is (3,60). There are 3 others you can choose and I named them above.

{(4,10),(3,15),(1,5),(2,25),(4,25)} is not a function because there are more than one pairs with the same x-coordinate,4.  

Answer:

im trying to find this answer too dont worry :(

Step-by-step explanation:

I dont know

Answer:

Option B, [tex]3.27[/tex]

Step-by-step explanation:

Given -

The submerged vessel travel horizontal distance above the shipwrecked hull

[tex]= 400[/tex]

[tex]= 0.4[/tex] kilometers

The vertical distance from the the shipwrecked hull to the ground is equal to [tex]7[/tex] kilometers

There forms a right angled triangle with

Base [tex]= 7[/tex] kilometer

Perpendicular [tex]=[/tex] 0.4 kilometer

Tan (angle) [tex]= \frac{Perpendicular}{Base}[/tex]

Substituting the given values we get -

Angle of depression

[tex]= tan^{-1}(\frac{0.4}{7})\\= 3.27[/tex]

Hence, option B is correct.

Answer:

278.9 units^3 to the nearest tenth.

Step-by-step explanation:

This is a cylinder on the bottom . resting on the cylinder is a prism.

Volume of the cylinder = π r^2 h  where r = 1/2 * 7 = 3.5 and h = 6.

V = π * 3.5^2 * 6 = 230.907 units^3.

Volume of the prism = l*w*h

= 4*4*3 = 48 units^3.

Volume of the composite figure = 230.907 + 48

= 278.9.

Answer:

C

Step-by-step explanation:

When both the numerator and denominator of a rational function have the same degree, you divide the highest powered term's coefficients. That is the horizontal asymptote.

Since this function has third degree in both the numerator and denominator, we divide the respective coefficients to find the horizontal asymptote.

So, y = 9/7

Correct answer is C

Note:  horizontal asymptote is always in the form y = a (where a is the constant)

[tex]3\sqrt5-2\sqrt7+\sqrt{45}-\sqrt{28}=\\3\sqrt5-2\sqrt7+\sqrt{9\cdot5}-\sqrt{4\cdot7}=\\3\sqrt5-2\sqrt7+3\sqrt{5}-2\sqrt{7}=\\6\sqrt5-4\sqrt7[/tex]

The correct equivalent expression for 3√x⁵y=3 is option c. x⁵/³y

Therefore, after simplification, the equivalent expression to 3√x⁵y is x⁵/³y.

The expression 3√x⁵y​ represents the cube root of x⁵y. To simplify this expression, let's break it down step by step.

First, we can express 3√x⁵y in exponential form:

3√x⁵y =(3x⁵y)¹/³

Using the property (ab)ⁿ=aⁿ⋅bⁿ, we can separate the terms inside the cube root:

(3x⁵y)¹/³ =3(x⁵/³, y¹/³)

Now, let's look at the options provided:

a. x⁵/³y

b. x⁵/³y¹/³

c. x⁵/³y

d.x⁵/³y³

Comparing the simplified expression 3√x⁵y=3(x⁵/³, y¹/³) to the given options: correct equivalent expression for 3√x⁵y=3 is option c. x⁵/³y.

Answer:

[tex]\large\boxed{\dfrac{4}{x}+6}[/tex]

Step-by-step explanation:

Six more than the quotient of four and a number x:

[tex]\dfrac{4}{x}+6[/tex]

Answer:

[tex]\frac{4}{x}+6[/tex]

Step-by-step explanation:

We have been given a  word phrase. We are supposed to represent our given word phrase into an algebraic expression.

The quotient of four and a number x will be 4 divided by x. We can represent this information in an expression as:

[tex]\text{Quotient of four and a number }x=\frac{4}{x}[/tex]

Six more than the quotient of four and a number x would be [tex]\frac{4}{x}+6[/tex]

Therefore, our required expression would be [tex]\frac{4}{x}+6[/tex].