Yosef drops a basketball from his bedroom window, which is 3m off the ground. After each bounce,
the basketball comes back to 75% of its previous height. If it keeps on bouncing forever, what
vertical distance, to the nearest metre, will it travel?

The equation of line is =1/2 x+1/2 .

A line equation is a straightforward mathematical formula that uses the slope, x-intercept, and y-intercept of the line to describe the relationship between the points on the line.

The formula for a straight line is y=mx+c where c is the height at which the line intersects the y-axis, often known as the y-intercept, and m is the gradient.

In order to put the equation in y-intercept (y=mx+b) form and determine the equation of a graphed line, first determine the slope and y-intercept. The slope is the ratio of the y-to-x change.

y=mx+b

According to graph, points are (-1,0) and (1,1)

Hence we get –m+b=0 and m+b=1

On solving m = ½ and b = ½

The equation of line is =1/2 x+1/2 .

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Answer: x = -9

Step-by-step explanation:1

Combine like terms

2 Add the numbers

3 Rearrange terms

4 Subtract 14 from both sides

5 Simplify

6 Add x to both sides

7 Simplify

8 Divide both sides by the same factor

9 Simplify

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Answer:

x= -9

Step-by-step explanation:

Simplify  3x+14 -6x to -3x +14

Simplify 25−x+7  to  32−x32−x.

Add 3x3x to both sides.

Simplify  32−x+3x32−x+3x  to  32+2x32+2x.

Divide both sides by 22.

Simplify  18/2 to  99.

x=−9 is your final answer

The missing numbers in the third level can be 10, 6 and 18

On the first level of the number tower, we have

First level = 40

On the second level, we have

Second level = 16 and 24

The numbers on the third level of the number tower are missing.

However, these numbers must add up to the sum of 16, while the other must add up to 24

So, we can make use of

10, 6 and 18

This is because

10 + 6 + 6 + 18 = 40

Here, we have

2x + y = 14 and x + 2y = 16

Multiply 2x + y = 14 by 2

4x + 2y = 28

Subtract x + 2y = 16 from 4x + 2y = 28

4x - x + 2y - 2y = 28 - 16

Evaluate

3x = 12

Divide

x = 4

Also, we have 2x + y = 14

This gives

y = 14 - 2x

y = 14 - 2 x 4

y = 6

So, the values of x and y for 2x + y = 14 and x + 2y = 16 are 4 and 6, respectively

This has the same step as part (b)

In (b), we have

x = 4

Which gives

2x + y = 14

Make y the subject

y = 14 - 2x

Substitute 4 for x

y = 14 - 2 x 4

Evaluate

y = 6

Hence, the values of x and y for 2x + y = 14 and x + 2y = 16 are 4 and 6, respectively

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Step-by-step explanation:

x = ml of the 60% solution

y = ml of the 45% solution

x + y = 600

and therefore

x = 600 - y

0.6x + 0.45y = 0.5×600

we use the above identity in this equation :

0.6(600 - y) + 0.45y = 300

360 - 0.6y + 0.45y = 300

60 - 0.15y = 0

60 = 0.15y

y = 400 ml

x = 600 - y = 600 - 400 = 200 ml

Answer: (7,11)

Step-by-step explanation:

The domain and range of this function f(x) = 4(∛8)ˣ are: A. {x| x is a real number}; {y| y > 0}.

A function simply refers to a mathematical expression which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for uniquely mapping an input variable to an output variable.

In this scenario, the function f(x) = 4(∛8)ˣ represents an exponential function. Generally speaking, an exponential function is defined by the set of all real numbers on the x-axis.

Additionally, the value of four (4) is greater than zero (0) and as such the range defined by the set of all real numbers on the y-axis that are greater than zero (0).

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Answer:

A. {x| x is a real number}; {y| y > 0}

Step-by-step explanation:

on edge

The measure of the third angle in the triangle is 152°.

It should be noted that a triangle has three sides and the sum of the total angles is 180°.

In this case, two of the angles in a triangle measure 20° and 8°. The third angle will be:

= 180° - (20° + 8°)

= 180° - 28°

= 152°

The angle is 152°.

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Answer:

No.

The square root of any number can never be negative/ -1

Answer: down here

Step-by-step explanation:

4−50

5−Y

6−150

​

Factor the expressions that are not already factored.

−46=−2×23

−144=−2

4

×3

2

Identify all the factors and their highest power in all expressions. Multiply the highest powers of these factors to get the least common multiple.

3312(Y−5)

Expand the expression.

3312Y−16560

Answer:

a)Figure C

b) Figure A, B, and C

c)Figure B and C

Step-by-step explanation:

Note squares are rectangles

Answer:

T: (-10,1)

S: (-10,-4)

U: (-5,1)

V:  (-5,-4)

Step-by-step explanation:

Translation means moving the object. Subtract 4 from each x value and add 1 to each y value.

Answer:

T' = (-10, 1)

S' = (-10, -4)

U' = (-5, 1)

V' = (-5, 4)

Step-by-step explanation:

      To do this, we will take each coordinate point, subtract four units from the x-value, and add one unit to the y-value.

T = (-6, 0) ➜ (-6 - 4, 0 + 1) ➜ T' = (-10, 1)

S = (-6, -5) ➜ (-6 - 4, -5 + 1) ➜ S' = (-10, -4)

U = (-1, 0) ➜ (-1 - 4, 0 + 1) ➜ U' = (-5, 1)

V = (-1, -5) ➜ (-1 - 4, -5 + 1) ➜ V' = (-5, 4)

Answer:

The original price of the watch was 260pounds

Step-by-step explanation:

let the reduced price be x

(100%-15%)/100 of x=221

85x/100=221

85x=22100

there fore x=260pounds

Option C correctly represents the function.

For the given question;

From the definition of the function, two values in the domain can not have the same image, thus option a and b are incorrect.

Only option c correctly described the function, as for every value of out put there is only one input.

Thus, option c correctly described the function.

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Answer:

360

Step-by-step explanation:

The length of the sides of equilateral triangles are as follows

5cm,  15m , 8cm , 300m , 12m , 90mm .  

The whole length of a shape's boundary is referred to in geometry as the perimeter of the shape. By multiplying the lengths of all the sides and edges that surround an object, the perimeter may be calculated. It is measured in measures of length that are linear, such as centimeters, meters, inches, or feet. A regular polygon's sides are all the same length, as far as we know.

Therefore,

A regular polygon's perimeter is equal to the product of all of its sides, which is equal to the number of sides divided by the length of a side.

The measurement of a shape's length along its outline is known as its perimeter. Simple addition of the lengths of the object's edges serves as the perimeter measurement method.

The perimeter of an equilateral triangle

= 3a      where a is each side

So,

(a) P = 15 cm

3a = 15

a = 5

each side = 5 cm

(b) 45 m

3a = 45

a = 15 m

each side = 15 m

(c) 24 m

3a = 24

a = 8 cm

each side =  8 cm

(d) 900 m

3a = 900

a = 300 m

each side = 300 m

(e) 36 cm

3a = 36

a = 12 cm

each side = 12 cm

(f) 270 mm

3a = 270

a = 90 mm

each side = 90 mm

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The ratio of the short leg to the hypotenuse in the right triangle is 1 : 2. the correct option is D. 1 : 2

From the question, we are to determine the ratio of the short leg to the hypotenuse in the given right triangle

Given an equilateral triangle with side lengths 2 units each and interior angle 60° each as shown in the diagram below. If the triangle is divided into 2 equal right triangles as shown in the given diagram, the length of the hypotenuse will be 2 units, the length of the short leg will be 1 unit, and the length of the long leg will be √3 units.

Thus,

The ratio of the short leg to the hypotenuse will be

1 unit / 2 units

= 1 : 2

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Answer: 3/2

Step-by-step explanation:

The scale factor is the same as the ratio of the length of a side of the image to the length of the corresponding side in the preimage.

We know that Y'X'=3 and YX=2, so the scale factor is 3/2.

The side length of the square is 2 units.

The area of square is equal to the square of its side. Mathematically -

Area = (side)²

Given is a square which is cut into 4 identical triangles such that each triangle has an area of 1 square unit.

Assume that the side of the square is 'x' units. Then we can say that -

The area of square of side 'x' units = 4 x area of an individual triangle.

Mathematically -

x² = 4 x 1

x² = 4

x = √4

x = ±2

Area cannot be negative, then we can write -

x = 2 units

Therefore, the side length of the square is 2 units.

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Answer:

a: -$4

b:45

Step-by-step explanation:

First, you just divide the total amount lost by the number of shares. because it is a loss it's going to be a negative number. For the second one, you want the total so you are going to multiply 45 by 9 and because it's an increase, the answer is a positive number.

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textsf{Question \#1 reads \boxed{\downarrow}}[/tex]

[tex]\large\text{Ivanna owns \underline{6 shares} of a certain stock. Yesterday the total value of}\\\large\text{her shares went down by \underline{24 dollars}. \boxed{\text{What was the change in value}}}\\\large\text{\boxed{\text{for each share}} ?}[/tex]

[tex]\huge\textsf{What should the equation look like?}[/tex]

[tex]\mathsf{\dfrac{24}{6} = change\ in\ value\ for\ each \ share}}[/tex]

[tex]\huge\textsf{How are we going to solve for the answer?}[/tex]

[tex]\mathsf{\dfrac{24\ dollars}{6\ certain \ stock} = change\ in\ value\ for\ each \ share}}[/tex]

[tex]\mathsf{24\ dollars \ \div\ 6\ certain\ stock\ = change\ in\ value\ for\ each \ share}[/tex]

[tex]\mathsf{4 = change\ in\ value\ for\ each \ share}}[/tex]

[tex]\huge\textsf{So, what s the answer to the question?}[/tex]

[tex]\large\text{Therefore, your answer should be: \boxed{\mathsf{4\ dollars}}}\large\checkmark[/tex]

[tex]\huge\textsf{Question \#2 reads \boxed{\downarrow}}[/tex]

[tex]\large\text{A private club grew by \underline{9 members} each week for \underline{45 weeks}. \boxed{\text {What}}}\\\large\boxed{\text{was the total change in the clubs size}} \large\text{ ?}}[/tex]

[tex]\huge\textsf{What should the equation look like?}[/tex]

[tex]\mathsf{\dfrac{45\ weeks}{9\ members} = total\ change\ in \ the\ clubs \ size}[/tex]

[tex]\huge\textsf{How are we going to solve for the answer?}[/tex]

[tex]\mathsf{\dfrac{45\ weeks}{9\ members} = total\ change\ in \ the\ clubs \ size}[/tex]

[tex]\mathsf{45\ weeks\ \div \ 9\ members = total\ change\ in\ the\ clubs\ size}[/tex]

[tex]\mathsf{5 = total\ change\ in\ the\ clubs\ size}[/tex]

[tex]\huge\textsf{So, what s the answer to the question?}[/tex]
[tex]\large\text{Therefore, your answer should be: \boxed{\mathsf{5\ members}}}\large\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

x = 17

Step-by-step explanation:

Mean of a set of data values = Sum of the data values ÷ number of data values

Here we have data:
18,23,x,22, and 20

Sum = 18 + 23 + x + 22 + 20 = 83 + x

Number of data points = 5

Mean = (83 + x) / 5 = 20 (given)

Multiplying both sides by 5 gives
83 + x = 20 x 5
83 + x = 100

Subtract 83 from both sides to give
x = 100 -83 = 17

x = 17

Answer:

Step-by-step explanation:

if 20 is the mean of 18,23,x,22, and 20 find the value of x​

(18 + 23 + x + 22 + 20) : 5 = 20

18 + 23 + x + 22 + 20 = 20 * 5

83 + x = 100

x = 100 - 83

x = 17

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

check

( 18 + 23 + 17 + 22 + 20) : 5 =

100 : 5 =

20

the answer is good

Answer:

5.049 x 10^11

She'd done the entire equation wrong

3 x 10^8 would be 300000000 when instead 10 should be to the power of 11 and 3 should be 5.049

Step-by-step explanation:

To rewrite something in scientific notation you have to group the numbers that aren't zero (5049) and convert it into a decimal (5.049)

(Decimals for scientific notations will ALWAYS have one number in the 1st digit, no matter what)

Then we see what we have to multiply our decimal to make it into our original number. We count the numbers in the decimal and the rest of our zeros (8+3=11)

5.049 x 10^11 = 504900000000

Yes, because all linear equations have graphs that are straight lines. This statement explains Roxanne is correct.

The first order of equations is linear equations. For lines in the coordinate system, linear equations are defined. A linear equation in one variable is one in which there is a homogeneous variable of degree 1 (one variable) in the equation.

There may be several variables in a linear equation. Linear equations with two variables, and so forth, are what the equation is known as if it has two variables. When the unknown values are replaced for those produced by the solutions of linear equations, the equation is proved to be true. There is just one answer when there is just one variable.

Hence the correct option is A

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The domain of the function f(x)=1/(x-3) will be all the real numbers except 3.

The domain of the function is defined as the set of all the possible values of the function. The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x).

A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

Given function is f(x)=1/(x-3). The domain of the function will be all the real numbers. But at x = 3 the value of the function does not exist.

Therefore, the domain of the function f(x)=1/(x-3) will be all the real numbers except 3.

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Answer:

[tex]x=\dfrac{-3+\sqrt{37}}{2}, \quad x=\dfrac{-3-\sqrt{37}}{2}[/tex]

Step-by-step explanation:

Given quadratic equation:

[tex]x^2+3x-7=0[/tex]

Step 1

When completing the square for a quadratic equation in the form [tex]ax^2+bx+c=0[/tex] the first step is to move the constant to the right side of the equation:

[tex]\implies x^2+3x-7+7=0+7[/tex]

[tex]\implies x^2+3x=7[/tex]

Step 2

Add the square of half the coefficient of the term in x to both sides to form a perfect square trinomial on the left side:

[tex]\implies x^2+3x+\left(\dfrac{3}{2}\right)^2=7+\left(\dfrac{3}{2}\right)^2[/tex]

Simplify:

[tex]\implies x^2+3x+\left(\dfrac{3^2}{2^2}\right)=7+\left(\dfrac{3^2}{2^2}\right)[/tex]

[tex]\implies x^2+3x+\dfrac{9}{4}=7+\dfrac{9}{4}[/tex]

[tex]\implies x^2+3x+\dfrac{9}{4}=\dfrac{28}{4}+\dfrac{9}{4}[/tex]

[tex]\implies x^2+3x+\dfrac{9}{4}=\dfrac{28+9}{4}[/tex]

[tex]\implies x^2+3x+\dfrac{9}{4}=\dfrac{37}{4}[/tex]

Step 3

Factor the perfect square trinomial on the left side:

[tex]\implies \left(x+\dfrac{3}{2}\right)^2=\dfrac{37}{4}[/tex]

Step 4

Square root both sides:

[tex]\implies \sqrt{\left(x+\dfrac{3}{2}\right)^2}=\sqrt{\dfrac{37}{4}}[/tex]

[tex]\implies x+\dfrac{3}{2}=\pm\dfrac{\sqrt{37}}{\sqrt{4}}[/tex]

[tex]\implies x+\dfrac{3}{2}=\pm\dfrac{\sqrt{37}}{2}[/tex]

Step 5

Subtract ³/₂ from both sides:

[tex]\implies x+\dfrac{3}{2}-\dfrac{3}{2}=-\dfrac{3}{2}\pm\dfrac{\sqrt{37}}{2}[/tex]

[tex]\implies x=-\dfrac{3}{2}\pm\dfrac{\sqrt{37}}{2}[/tex]

[tex]\implies x=\dfrac{-3\pm\sqrt{37}}{2}[/tex]

Therefore, the solutions of the given quadratic equation are:

[tex]x=\dfrac{-3+\sqrt{37}}{2}, \quad x=\dfrac{-3-\sqrt{37}}{2}[/tex]

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Answer:

i d k

Step-by-step explanation:

Answer:

Step-by-step explanation:

Find The Edge Of The Cube Whose Leteral Surface Area Is 36cm^2

LSA of cube = x^2 + x^2 + x^2 + x^2 = 4x^2

so

4x^2 = 36

x^2 = 9

x = 3

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

check

4 * 3^2 =

4 * 9 =

36

the answer is good

Answer: 3 cm

Step-by-step explanation:

When the weights (in grams) of the contents of several small bottles are 4, 2, 5, 4, 5, 2 and 6, the sample variance is D. 2.33.

It should be noted that in Mathematics, the variance simply means the average squared deviation of the mean.

From the information, the weights of the contents of several small bottles are 4, 2, 5, 4, 5, 2 and 6. Therefore, the sample variance will be illustrated thus:

N = number =7

Sum of the numbers = 28

Mean = 28 / 7 = 4

Sample variance will be:

= (4 - 4)² + (2 - 4)² + (5 -4)² + (4 - 4)² +(5 - 4)² +(2 -4)² + (6 - 5)²

= 14 / 6

= 2.33

Therefore, the variance is 2.33.

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The equivalent expression for [tex](3.7)^{-5}*(3.7)^{9}[/tex] is [tex](3.7)^{4}[/tex].

This is a question of exponents and powers.

Exponents

The exponent of a number says how many times to use the number in a multiplication. In [tex]8^2[/tex] the "2" says to use 8 twice in a multiplication, so [tex]8^2[/tex] = 8 × 8 = 64.

Here, 2 is the exponent or power and 8 is the argument.

We can use exponents when we have to deal with very large numbers.

For example:-

The distance between the Earth and the Sun is measured to be 149,600,000 Km.

To write it in simple terms we will write,

[tex]1.496 * 10^8[/tex] km.

We know that:-

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

Here,

a = 3.7,

b = -5 and,

c = 9

Hence, we can write,

[tex](3.7)^{-5}*(3.7)^{9}=(3.7)^{-5+9}=(3.7)^{4}[/tex].

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Answer:

ABC

Step-by-step explanation:

BECAUSE THEY ARE OPPOSITE