a car and a motorcycle leave at noon from the same location, heading in the same direction. the average speed of the car is mph slower than twice the speed of the motorcycle. in two hours, the car is miles ahead of the motorcycle. find the speed of both the car and the motorcycle, in miles per hour.

Function representing the sequence will be f(n) = (23 - 3n

The first five terms of an arithmetic sequence are as 20, 17, 14, 11, 8....

Let n represents the number of term and f(n) the the term in the sequence.

Then we have to find the function that represents the sequence.

As we know explicit formula of an arithmetic sequence is given by

Or the function representing the sequence will be

f(n) = a + (n-1)d

where a represents first term of the sequence a = 20

and common difference d = 17-20 = (-3).

Now the function which represents this sequence will be

f(n) = 20 + (n-1)(-3) = 20 - 3n + 3 = 23 - 3n

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The area of the rhombus is  49√6. Option B

The formula for calculating the area of a rhombus is expressed as;

Area = pq/2

Where;

p and q are the diagonals of the rhombus

From the diagram shown, let's determine the value of p

Using the trigonometric identity;

Tan θ = opposite/adjacent

Substitute the values into the formula, we have;

tan 60 = p/7

Find the value of tan 60 and then substitute

√3 = p/7

cross multiply

p = 7√3

But;

Area = 7√3 × 7√3/2

Area = 49√6

Hence, the value is 49√6

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The improper fraction 7/8 has no value in the options given

To do this, we must divide the dividend by the divisor in order to change an improper fraction to a mixed number. After division, the acquired quotient becomes the whole numerals, the remainder becomes the new numerator, and the denominator remains the same, resulting in a mixed number.

To convert 7/8 into decimal number;

7/8 = 0.875

2 1/2 = 2.5

1 5/8 = 1.625

4% = 0.04

5 5/8 = 5.625

In the given options, none of them has a value of 7/8

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Answer:

d.) 100

Step-by-step explanation:

To solve, first find the value of g(-2):

[tex]g(-2)=5(-2)\\g(-2)=-10[/tex]

Next, use this value to find f(-10):

[tex]f(-10)=(-10)^2\\f(-10)=100[/tex]

Answer:All I know is that it’s not < or > but It might be ≤

Step-by-step explanation: Bye the way, you can only give brainliest when there is two questions.

[tex]\leq[/tex]

Step-by-step explanation:

If the company has made 6732.16 in³ wax , Total number of candles made is 67

According to the question,

It is given that a wax candle is in cylindrical shape

Diameter of candle = 4 in

Radius will be = 4 / 2

=> 2 in

Height of each candles = 8 in

Company has used 6732.16 in³ of wax

We have to calculate number of candles company has made

Volume of cylinder = πr²h

Where r is radius and h is height

Substituting all the values,

Volume of candle = π (2)² (8)

=> V = 3.14 × 4 × 8   (putting π = 3.14)

=> V = 100.48

Therefore , Number of candles made = Total volume /volume of one candles

=> 6732.16 / 100.48

=> 67 candles are made by company

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The point estimate of the proportion of the population adults who think that today's children will be better off than their parents is 0.24.

The point estimate of P, is defined as the proportion of successes in the sample.

P' = X/N ; where X = number of successes; N = total trials.

Here, N = 1000

According to the Child outlook file, number of "yes" = 240.

Hence, P' = 240/1000

P' = 0.24

Therefore, the point estimate of the proportion of the population adults who think that today's children will be better off than their parents is 0.24.

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The missing statements and reasons to proof that ∠1 is supplementary to ∠3 are:

S1: Line m is parallel to line n.

S2: ∠1 = ∠2

R3:  Corresponding angles postulate

R5: Supplement Postulate

S7:  m∠1 + m∠3 = m∠2 + m∠3

What are Supplementary Angles?

Supplementary angles, when added together will give us a sum of 180°.

Linear pair angles and corresponding angles are supplementary.

Thus, to prove that ∠1 is supplementary to ∠3:

We are given that lines m and n are parallel.

∠1 and ∠3 are corresponding angles.

So therefore, ∠1 = ∠3 by the corresponding angles postulate.

∠2 and ∠3 are linear pair, their sum therefore equals 180° based on the definition of supplementary angles.

Based on the substitution property, we have the following:

m∠2 + m∠3 = m∠1 + m∠3

m∠1+m∠3=180°

Therefore, ∠1 is supplementary to ∠3 based on the definition of supplementary.

The missing statements and reasons to proof that ∠1 is supplementary to ∠3 are:

S1: Line m is parallel to line n.

S2: ∠1 = ∠2

R3:  Corresponding angles postulate

R5: Supplement Postulate

S7:  m∠1 + m∠3 = m∠2 + m∠3

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Answer:

Step-by-step explanation:

The number of commercials and movies on which the songs were played are 5 and 2.respectively

From the question, we have the following parameters that can be used in our computation:

The number of commercials is x, and the number of movies is y

The above parameters when represented as an equation is as follows

40x + 120y = 440

x = y + 3

Substitute x = y + 3 in 40x + 120y = 440

40(y + 3) + 120y = 440

Expand

40y + 120 + 120y = 440

Evaluate the like terms

160y = 320

Divide by 160

y = 2

Recall that

x = y + 3

So, we have

x = 2 + 3

x = 5

Hence, the number of commercials is 5 times

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Answer:

See attached image

Step-by-step explanation:

You can graph lines on a website called desmos graphing calculator!

Answer:

Step-by-step explanation:

you replace x with anything you want I will do 0. Then the the first point is (0,-4). Now I am gonna replace x with something else like 4. The second point is (4,8), now connect the two points and you got a line.

To get a number point 1 is impossible for any of the team to reach at the end of the described tournament.

As given in the question,

Total number of footballs teams = 3

Each team plays once with other team

Let three teams are Team1, Team2, and Team3

Team1 plays with Team2 and Team3

Team2 will play with Team3

Winning points = 3

Losing team points = 0

Withdraw teams points = 1

To reach in finals suppose Team1 plays with Team2 and Team3 and win

Points of team1 = 3 + 3

                         = 6points

As team plays once with other team , Team1 is out of the game.

Team2 and Team3 play with each other

To reach at the end of the tournament one team has to win let it be Team2

Points of Team2 = 3

Points of Team3 = 0

No withdraw game is possible to reach into finale.

Therefore, point 1 is impossible for any team to reach at the end of the tournament.

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The formula to solve for height(h) is given as, if the volume of the cylinder is, V = π r² h, is h = V /  π r².

An object's volume is a measurement of the amount of space it occupies in three dimensions. This indicates that an elephant's volume is more than a mosquito's volume.

Given:

V = π r² h

Here, r is the radius of the cylinder, V is the volume, and h is the height of the cylinder. The value of π is 3.14.

Take the remaining term of the right side to the left as shown below,

V /  π r²  = h

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Answer: 19.71 Million.

Answer:

Given: △ABC, m∠A=120°, AB=AC=1 Find: The radius of circumscribed circle

Step-by-step explanation:

:]

Theres no point 'Z', so i'm gussing you want the angle of <KLJ?

<K and <M are the same, therefore <M = 130

<J + <K + <M + <L = 360

130 + 130 = 260,  360 - 260 = 100

<J and <L are the same

<MJK = 50 and <KLM = 50

<KLM/2 = <KLJ

50/2 = 25

Answer:

B

Step-by-step explanation:

Determine the equation of the line given by the table and compare with given options.

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (2, 9) and (x₂, y₂ ) = (7, 19) ← 2 ordered pairs from the table

m = [tex]\frac{19-9}{7-2}[/tex] = [tex]\frac{10}{5}[/tex] = 2 , then

y = 2x + c ← is the partial equation of the line

to find c substitute any ordered pair from the table into the partial equation.

using (6, 17 ), that is x = 6, y = 17 , then

17 = 12 + c ⇒ c = 17 - 12 = 5

y = 2x + 5 ← equation of line from table, with y- intercept c = 5

thus the function with a y- intercept greater than the table line is B

Answer:

x=8/9

Step-by-step explanation:

step one: move x to one side. to do this, we are going to use inverse operations which means adding 3x to both sides.

3x+-3x cancels itself out and 3x+6x=9x.

now, the equation looks like: 9x-7=1

step two: isolate the variable, x. we want to just get x to be by itself so we need to get rid of the -7 next to it by using inverse operations again. this means we're going to add 7 to both sides.

7+-7 cancels itself out and 7+1=8.

now, the equation looks like 9x=8

step three: divide to get x by itself. we want to know what x alone is, not 9x. to do this we are going to use inverse operations one last time. this means dividing each side by 9, because 9x means "9 times x".

9x/9= x, 8/9

so the answer is x=8/9

hope this helped!!

The angle that the line 3y = 2x + 6 makes with the [x] axis is (θ) = 33°69'.

Given is the equation -

3y = 2x + 6

The given equation is -

3y = 2x + 6

y = (2/3)x + (6/3)

y = (2/3)x + 2

Slope of the line -

m = 2/3.

We know slope is also given by -

m = tan(θ)

So -

tan(θ) = 2/3

(θ) = tan⁻¹(2/3)

(θ) = 33°69'

Therefore, the angle that the line makes with the [x] axis is (θ) = 33°69'.

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Answer:(x,y)=(1/3 , 4/3)

Step-by-step explanation:

ANSWER : -1 , 3 , (-1 - 2i) , (-1 + 2i)

steps

find the zeros JUST MEANS SOLVE FOR X

x⁴-2x²-16x-15=0

break it up

let u = x²

x⁴ = (x²)² = u²

-16x+u²-2u-15=0

hold off on -16x

u²-2u-15=0

what 2 numbers when multiplied give you -15 & when added give you -2?

-5 and 3

(u-5) (u+3)

-16x + (u-5) (u+3) = 0

go back x

-16x + (x²-5) (x²+3) = 0

factor -1 out

( looks horrible so far lol )

-1 ((- x²+ 5) (x²+3) + 16x) = 0

multiply (- x²+ 5) with ( x² + 3 )

-1 (( - x² ( x² + 3 ) + 5 ( x² + 3 ) ) + 16x ) = 0

-1 (( - x² ( x² + 3 ) + 5 ( x² + 3 ) ) + 16x ) = 0

-1 (( - x² ( x² + 3 ) + 5 ( x² + 3 ) ) + 16x ) = 0

-1 (( - x² * x² + -x² * 3 ) + 5x² + 15 ) + 16x ) = 0

-1 (( - x⁴ + -2x² + 15 ) + 16x ) = 0

The total pressure experienced by a diver working 15m below surface of sea is 150000 Pa.

Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed.

We need to find the total pressure experienced by a diver working 15m below surface of sea.

P = h·ρ·g

P = pressure

h = depth = 15 m

ρ = density = 1g/cm³=1000kg/m³

g = acceleration due to gravity = 10 m/s²

Substitute the values in the formula of total pressure.

P=1000×15×10

P=150000Pa

Hence, 150000Pa is the total pressure experienced by a diver working 15m below surface of sea.

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When 36 reindeer are chosen at random, the probability that the mean weight is less than 100 kg is 0.1492.

A standard error is the standard deviation of its sampling distribution or an interpretation of that standard deviation.

Given,

Mean of the weights = 102.4 kg

Standard deviation = 13.9 kg

To determine the probability that the mean weight of 36 reindeer will be less than 100 kg, first compute the standard error using the formula,standard error, [tex]\sigma_x=\frac{\sigma}{\sqrt{n}}[/tex]

Where, [tex]\sigma[/tex]=standard deviation

n= number of reindeer

substitute the values in the formula,

[tex]\sigma_x=\frac{13.9}{\sqrt{36}}\\\\\sigma_x=2.31667[/tex]

Now,

[tex]P(x < 100)=P(x < \frac{100-102.4}{2.316})\\\\=P(z < -1.04)[/tex]

from z-score table,

=0.1492

Thus, the probability the their mean weight is less than 100 kg is 0.1492.

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Your question is incomplete, here is the complete question.

The weight of male reindeer of the R. Santa Claus subspecies is normally distributed with mean 102.4 kg and standard deviation 13.9 kg

if 36 reindeer are randomly selected, what is the probability their mean weight is less than 100kg?

For the given congruent triangles, the values of x = -1 and y = 3.

Two triangles are congruent if all three corresponding sides are equal and all three corresponding angles are equal. These triangles can be moved, rotated, flipped, and flipped to look identical. When rearranged they match each other.

The congruence symbol is "≅".As both the triangles are congruent therefore their corresponding sides will be equal.

3y + x = y + 5 ...........(1)

y - x = x + 5 ..............(2)

Equation

1:3y + x = y + 5

3y - y = 5 - x

2y = 5 - x

x = 5 - 2y ..............(3)

Substitute this value of x in equation (2)

y - x = x + 5 y = x + x + 5y

= 2x + 5 y = 2(5 - 2y) + 5y

= 10 - 4y + 54y + y = 15

5y = 15 y = 15/ 5

y = 3

Substitute this value of y in equation (3) x = 5 - 2(3) = 5 - 6 = -1

Therefore, x = -1 and y = 3

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The values (-7.5)-21.04 and (-7.5)+21.04 are not the same

A decimal can be defined as a number consisting of a whole number and also a fractional part.

These numbers are separated by a dot known as the decimal point

The decimal numeral system is seen as a standard system that denotes integer and non-integer numbers.

It is important to note the following operations;

From the information given, we have;

(-7.5)-21.04

Multiply the operation

+ 157. 8

Then,

(-7.5)+21.04

Multiply the operation

- 157. 8

Hence, the values are either negative or positive.

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The value of (a) r that make sense is 6 in. and (b) the value of A that make sense is 113.1 in²

You should understand that the pizza is fit inside the square box making all circumference of the circle to touch all the sides of the square box

The quadratic function reads

A= πr²

Where A= Area of circle,

π = 22/7

and r= radius of the circle

A= (22/7)*6

Width of the box is 12

Therefore 12/2 = r=6

A= (22*6*6)/7

A=113.1 in²

In conclusion, he value of (a) r that make sense is 6 in. and (b) the value of A that make sense is 113.1 in²

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The coordinates of the vertices after a reflection over the line y = -5 is given as follows:

T'(-2,-5), U'(2,-7), V'(-2,-9), W'(-3,-7).

The vertices of the original quadrilateral are given as follows:

T(-2,-5), U(2,-3), V(-2,-1), W(-3,-3).

The reflection line y = -5 is an horizontal line, meaning that after the reflection:

For example, the distance of the y-coordinate of the vertex U from -2 is of:

2 units above.

Then the y-coordinate of the vertex U' will be also 2 units from -5, just two units below, hence:

U'(2,-7).

Applying this rule for all the other vertices, they will be given as follows:

T'(-2,-5), U'(2,-7), V'(-2,-9), W'(-3,-7).

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Answer: 8

Step-by-step explanation:

8 times 8 is 64

Step-by-step explanation:

SWT + TWU =180º therefore SWU must be a line. Aka SWU is linear. So SWT and TWU must be a linear pair.

SWT + SWT = 180º therefore 2SWT=180º deviding both sies by 2 we get SWT = 90º Therefore SWT is replacing TWU. SWT is substituted into TWU. So substitution.

SU | TV basically means the line that passes through both points S and U is perpendicular to the line that passes through both points T and V. Therefore it is the Defenition of perpendicular lines.

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