The age of a father is three times that of his son, but six years ago, the sum of their ages was 45. What is the present age of the son?
​

the solution of number line is all the options are correct.

A number line is an image of numbers plotted on a straight line, either horizontally or vertically. We can compare numbers and execute simple arithmetic operations on them easily by writing the numbers down on a number line. The starting point of a number line is often regarded as zero (0). These numbers to the left of zero are all negative while the numbers just on right of zero are all positive. As a result, we can argue that on a number line, the value of numbers grows as we approach the right. The numbers on the right are therefore larger than the ones on the left, according to this statement.

Here,

Kendra and Jamal are standing in line. The number line shows their positions in meters with positive numbers representing positions to the right.

The position of Kendra is -6 and Jamal is 0.

Kendra is 6 meters left of Jamal.

Kendra and Jamal are 1-6 meters apart.

Jamal is 6 meters right of Kendra.

Hence, all the options are correct.

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Answer:  Lily babysits for less than 4 hours.

Step-by-step explanation:

We can start by multiplying 4 hours by 7/8 to find out how many hours Lily spends babysitting.

4 * (7/8) = 7/2 = 3.5 hours

Since 3.5 is less than 4, Lily babysits for less than 4 hours.

Answer: Less than 4. (3 1/2 hours)

Step-by-step explanation:

When you multiply a number by a number smaller than 1, the answer gets smaller.

Lily babysits for 3 1/2 hours because 4 x 7/8 = 3 1/2

Answer:

Average speed = Total distance travelled / Total time taken

 = 170 miles / 2.34 hours

 = 72.65 miles per hour or 72.65 mph

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The division of the given polynomial would be (x^4) + 81.

What is the synthetic division?

Synthetic division is a method for dividing polynomials that allows you to divide a polynomial by a linear factor (a factor in the form of (x-c) where c is a constant) without actually performing the long division process. It is a short cut method that simplifies the process of dividing polynomials.

To divide the polynomials using polynomial division, we will use the following steps:

Write the polynomials in descending order of exponents.

(2x^3 + x^4 - 6x^2 + 11x - 10) (x^2 + 2 - x)

Create a grid with the dividend on the left and the divisor on the right.

2x^3 x^4 -6x^2 11x -10

x^2 2 -x  

Bring down the leading coefficient of the dividend, which is 2x^3 in this case. Write it in the next row of the grid.

2x^3 x^4 -6x^2 11x -10

2x^3 x^2 2 -x  

Multiply the divisor (x^2 + 2 - x) by the leading coefficient (2x^3) and write the result in the next row.

2x^3 x^4 -6x^2 11x -10

2x^3 x^2 2 -x  

2x^5 2x^4 4x^3 -2x^4  

Subtract the second row from the third row and write the result in the next row.

2x^3 x^4 -6x^2 11x -10

2x^3 x^2 2 -x  

2x^5 2x^4 4x^3 -2x^4  

0 -x^4 -2x^2 11x -10

Divide the new leading term by the leading term of the divisor, which is x^2, and write the result in the next row.

2x^3 x^4 -6x^2 11x -10

2x^3 x^2 2 -x  

2x^5 2x^4 4x^3 -2x^4  

0 -x^4 -2x^2 11x -10

-x^2

So the final answer would be (-x^2) + (x^4 + 2x^2 - 11x + 10).

Hence, the division of the given polynomial would be (x^4) + 81.

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Answer:

y(y-5) =750 squared-feet

Step-by-step explanation:

[tex] {y}^{2} - 5y = 750 \\ 750 - y(y - 5) = 0 \\ (y + 25)(y - 30) = 0[/tex]

The mean is of 0.15. The standard deviation is of 0.0326.0.1774 of incoming kindergarteners are nearsighted.

The central limit theorem and the normal distribution are used to determine that:

a) A 0.15 is the mean.

b) A standard deviation of 0.0326 is present.

c) There is a 0.063 = 6.3% chance that fewer than 10% of the kindergarten applicants have nearsightedness.

d) 0.1774 percent of kindergarten students have nearsightedness.

The mean is of 0.15.

Item b:

s = p (1-p)/n = 0.15(0.85)/120

=  0.0326.

The standard deviation is of 0.0326.

Item c:

The probability is the p-value of Z when X = 0.1.

By the Central Limit Theorem

Z=  0.1 -0.15/ 0.0326.

=  -1.53

Z = -1.53 has a p-value of 0.063.

There is a 0.063 = 6.3% probability that less than 10% of the incoming kindergarteners are nearsighted.

Item d:

X = 0. 1774

The proportion is X when Z has a p-value of 0.8, so X when Z = 0.84.

0.1774 of incoming kindergarteners are nearsighted.

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Step-by-step explanation:

fufj5655 and I hope that you will be able to help me with the following to help me with the application for the role of the temple and many other people in the forest and a small village known as change in indirect speech to be the oldest

Answer:

A. 2¾

Step-by-step explanation:

The person needs the difference. This is a subtraction problem.

3 1/2 - 3/4 =

3/4 is just a fraction, but you can think of 3/4 as a mixed numeral by writing 3/4 as 0 3/4. The whole part is 0 and the fractional part is 3/4.

= 3 1/2 - 0 3/4

Now we are subtracting two mixed numerals. You need to subtract the whole part, 0, from the whole part, 3, and the fractional part, 3/4, from the fractional part, 1/2.

For the fractional parts, we need a common denominator of 4.

= 3 2/4 - 0 3/4

Now we have both fractions with a common denominator of 4, but since we cannot subtract 3/4 from 2/4, we borrow 1 from 3 as 4/4.

3 goes down 1 to 2, and the 1 which is borrowed as 4/4 is added to the 2/4 to give you 2 6/4. 2 6/4 has the same value as 3 2/4. Now we have:

= 2 6/4 - 0 3/4

We subtract 0 from 2, and we subtract 3/4 from 6/4.

= 2 3/4

Answer: 2 3/4

The cost of a candy bar is equal to $1.61.

In order to write an equation that model this situation, we would assign variables to the cost of candy bars and the cost of soda respectively, and then translate the word problem into algebraic equation as follows:

Next, we would translate the word problem into an algebraic equation based on the fact that three (3) candy bars and one (1) soda costs $5.63 as follows;

3x + y = 5.63   ...equation 1.

Additionally, one candy bar and four sodas cost $4.81 at the same price;

x + 4y = 4.81 ...equation 2.

x + 4(5.63 - 3x) = 4.81

x + 22.52 - 12x = 4.81

11x = 22.52 - 4.81

x = 17.71/11

x = $1.61

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-1

8 is bigger than 0, so according to the function, we need to use the third one so it would be -1

Answer:

a₄ = 25

Step-by-step explanation:

using the recursive formula [tex]a_{n}[/tex] = 2[tex]a_{n-1}[/tex] and a₁ = 4 , then

a₂ = 2a₁ - 1 = 2(4) - 1 = 8 - 1 = 7

a₃ = 2a₂ - 1 = 2(7) - 1 = 14 - 1 = 13

a₄ = 2a₃ - 1 = 2(13) - 1 = 26 - 1 = 25

Answer:

[tex] \frac{2257}{2400} [/tex]

Step-by-step explanation:

2400 - (120+23)

=2400 - 143

=2257

Therefore,

2257

2400

After calculating The perimeter of rectangle is 46.52 in the given rectangle.

What is area of rectangle?

area of rectangle can be defined as the product of length and breadth.

Given ,

A rectangle has a length 20 5 /6 and

breadth = 2 3/7

The perimeter of rectangle  = 2 (l+b)

length = (120 + 5 ) / 6 = 125/ 6

breadth = (14+3) / 7  = 17/7

perimeter  = 2 (125/6 + 17/7 )

= 2 ( (125*7 + 17 * 6) / 42 )

= 2 (875+102) / 42

= 2 * 23.26

= 46.52

Hence, after calculating The perimeter of rectangle is 46.52 in the given rectangle.

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The diameter of the circle is 16.66 units.

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the center.

Given a circle,

and two segments intersect at a point and form a right angle,

the length of the segment to the point of intersection is 6 units and 8 units as given in the figure,

and a segment pass from the center of the circle,

let the distance from point of intersection to center be x

so radius of circle be 6 + x from figure,

it forms a right triangle as shown in the figure, with hypotenuse 6 + x, base x, and perpendicular 8 units,

using Pythagoras theorem

h² = b² + p²

(6 + x)² = x² + 8²

36 + x² + 12x = x² + 64

12x = 64 - 36

12x = 28

x = 28/12

x = 2.333

radius of circle = 6 + x = 6 + 2.33 = 8.33

diameter of circle = 2r = 2 x 8.33 = 16.66 units

Hence the diameter is 16.66 units.

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Answer: The perimeter of a rectangle is given by the formula P = 2L + 2W, where L is the length and W is the width of the rectangle.

We know that the rectangular school banner has a length of 44 inches and a perimeter of 156 inches. And we can use the formula above to find the width of the rectangular school banner:

P = 2L + 2W = 156 inches

P = 2(44) + 2W = 88 + 2W = 156 inches

So the width of the rectangular school banner is W = 156 inches - 88 inches = 68 inches

Now, we know that the cheerleaders make signs similar to the banner. the length of a sign is 11 inches, we can use the same formula to find the perimeter of the sign.

P = 2L + 2W = 2(11) + 2W

So the perimeter of the sign is P = 22 + 2W inches

Since we don't know the width of the sign (W) we can't find the perimeter of the sign.

Step-by-step explanation:

Answer:

1the answer for this is easy it is 4.4

Answer: No, it is not possible to have a 3/8-inch pipe with an inside diameter of 21/32 inches

Step-by-step explanation:

The inside diameter of a pipe is always smaller than the outside diameter. The outside diameter of a pipe is a measurement of the pipe's exterior, while the inside diameter is a measurement of the pipe's interior. Therefore, if the pipe is 3/8 inches in outside diameter, the inside diameter will be less than 3/8 inches.

In addition, 21/32 inches is greater than 3/8 inches, so it is not possible to have a 3/8 inches pipe with an inside diameter of 21/32 inches. This is because the inside diameter is always smaller than the outside diameter.

- C

Step-by-step explanation:

hope this helps!:).....

The value of expression is ,

10) 6

11) 18

12) 2

13) 4

14) [tex]\frac{1}{4}[/tex]

15) [tex]\frac{1}{3}[/tex]

What is expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.

Here the given expression

10) 7+x+(-3)

Put x=2 then

=> 7+2-3

=> 7-1 = 6

11) 4[tex]x^2[/tex]+2

put x=2 then

=> [tex]4*2^2+2[/tex]

=> 4*4+2

=> 16+2=18

12) Ix+10I

put x=-12 then

=> I-12+10I

=> I-2I = 2

13) |2x + 1|

put x= 3/2 then

=> I2*[tex]\frac{3}{2}[/tex]+1I

=> I3+1I

=> I4I = 4

14)(x - 3)/4

put x=4 then

=> [tex]\frac{4-3}{4}[/tex]

=> [tex]\frac{1}{4}[/tex]

15) (5 - x)/6

put x=3 then

=> [tex]\frac{5-3}{6}[/tex]

=> [tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex]

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The rate of change is $6 per hour while the initial value is $20

An equation is an expression composed of variables and numbers linked together by mathematical operations.

The slope intercept form of a linear equation is:

y = mx + b

Where m is the slope (rate of change) and b is the y intercept.

Let y represent the total amount of money that Larry would have after working x hours.

From the graph, the y intercept is at (0, 20). Using point (0, 20) and (5, 50):

Slope = (50 - 20)/(5 - 0) = 6

The slope is $6 per hour

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Answer:

  rhombus

  (b) The diagonals are perpendicular but not congruent.

Step-by-step explanation:

You want to know what sort of figure the parallelogram JKLM is, given the vertices J(-2,7), K(7, 2), L(-2,-3), M(-11,2).

The x-values of points J and L on diagonal JL are the same, so that diagonal is a vertical line. Its length is 7 -(-3) = 10.

The y-values of points K and M on diagonal KM are the same, so that diagonal is a horizontal line. Its length is 7 -(-11) = 18.

The diagonals are perpendicular and not congruent, so the parallelogram is a rhombus.

Answer:

A, B and E

Step-by-step explanation:

Answer:

6375 mcg

Step-by-step explanation:

hopes this helps :)

Answer:

-15,-14,-13

Step-by-step explanation:

Let x = the first integer

Let x + 1 = the second integer

Let x + 2 = the third integer

The addition of all three equal -42

x + x + 1 + x + 2 = -42  Combine like terms

3x + 3 = -42  subtract 3 from both sides

3x + 3 - 3 = -42 - 3

3x = -45  Divide both sides by 3

x  = -15

Check

-15 + -14 + -13 = -42

-42 = -42

Answer:

Since slope of line passing through two points (x

1

​

,y

1

​

) and (x

2

​

,y

2

​

) is m=

x

2

​

−x

1

​

y

2

​

−y

1

​

​

We now find the slope of the line passing through the points (2,3) and (4,6) as shown below:

m=

4−2

6−3

​

=

2

3

​

Therefore, the slope of the line is  

2

3

​

.

Now use the slope and point (2,3) to find the y-intercept.

y=mx+b

⇒3=(

2

3

​

×2)+b

⇒3=3+b

⇒b=3−3=0

Write the equation in slope intercept form as:

y=mx+b

⇒y=

2

3

​

x+0

⇒y=

2

3

​

x

Step-by-step explanation:

The solution is: Correct option is 3: Equally likely and unlikely.

We have,

Equally likely indicates the likelihood that the outcomes of each experiment will occur. For instance, if you roll a fair, six-sided die, there is an equal probability of getting any of the faces (1, 2, 3, 4, 5, or 6). The likelihood of a coin landing on its head (H) or tail (T) is equal (T).

What has equal and unequal likelihood?

Equally likely suggests that the event is fair and that all possible outcomes have an equal chance of happening. If two outcomes are not equally likely to occur, then the event would be unfair and one or more of the events would be more likely to do so.

Given that, P(terriers) is 50%

i.e., P(terriers) = 1/2

So, P(not terriers) = 1 - 1/2 = 1/2

This is an equally likely and unlikely event. i.e., The likeliness and unlikeliness of the event are equal and equal to 50%.

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Answer:

25

Step-by-step explanation:

5/9 x 45  Cross cancel the 9 and 45. 9 goes into 9 once and 9 goes into 45 5 times

5/1 x 5/1 = 25/1 = 25

The quadratic expression for the curves is written as

The curve opening up y = a(x + 4)² - 7

The curve opening down y = -1/8(x - 4)² + 3

The equation of the quadratic equation is written using the formula

y = a(x - h)² + k

where h and k are points of the vertex v(h, k)

The curve opening up

h = -4 and k = ?

using points C and B

-5 = a(0 + 4)² + k, -5 = 16a + k

1 = a(4 + 4)² + k, 1 = 64a + k

solving simultaneously

-5 = 16a + k

1 = 64a + k

subtraction

-6 = -48a

a = 1/8

solving for k

-5 = 16a + k

-5 = 16 * 1/8 + k

k = -7

substituting the values

y = a(x + 4)² - 7

The curve opening down

A is the vertex (4, 3)

y = a(x - 4)² + 3

using D (0, 1) to solve a

1 = a(0 - 4)² + 3

1 - 3 = 16a

a = -1/8

hence the equation is y = -1/8(x - 4)² + 3

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