What is the domain and range of the function?

Answer:

It is a factor and a variable.

Step-by-step explanation:

Answer:

34 miles is the distance from point A will they meet.

Step-by-step explanation:

Proportion states that the two ratios or fractions are equal.

Given the statement:

Distance between point A and B (i.e AB) = 200 mi.

Let the cyclist speed be c, and motor- speed be m;

then;

c = 17 mph and m=83 mph

Let they meet at distance x miles from a point A.  

By definition of proportion, we have;

[tex]\frac{x}{17} =\frac{200-x}{83}[/tex]

By cross multiply;

[tex]83x = 17(200-x)[/tex]

Using distributive property, [tex]a\cdot(b+c) =a\cdot b+ a\cdot c[/tex]

[tex]83x = 3400 - 17x[/tex]

Add 17x both sides we get;

[tex]83x+ 17x= 3400 - 17x +17x[/tex]

Simplify:

100x = 3400

Divide by 100 on both sides we get;

x = 34 miles

Therefore, the distance from point A will they meet is, 34 miles.

Answer:

Image

Step-by-step explanation:

Image

The missing number can be found using Matrix rule. We have to apply addition and subtraction rule to find the missing number form given matrix.

The missing number is -5.

Given:

The given matrix is,

[tex]\left[\begin{array}{cccc}9&38&47&4\\6&35&42&x\\12&21&23&27\end{array}\right][/tex]

Let the missing number is [tex]x[/tex].

Apply the subtraction rule to subtract second row from first row.

[tex]\left[\begin{array}{cccc}9&38&47&4\\3&3&5&4-x\\12&21&23&27\end{array}\right][/tex]

The sum of first three number is equal to the sum of digits of the first three number in the third row,

[tex]1+2=3\\2+1=3\\2+3=5[/tex]

Now from the same pattern.

[tex]2+7=4-x\\x=-5[/tex]

Thus, the missing number is -5.

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Answer: [tex]\bold{\dfrac{8}{13}}[/tex]

Step-by-step explanation:

Red   or    Face   -  duplicates (both red & face)

[tex]\dfrac{26}{52}[/tex]     +       [tex]\dfrac{12}{52}[/tex]      -     [tex]\dfrac{6}{52}[/tex]

= [tex]\dfrac{32}{52}[/tex]

= [tex]\dfrac{8}{13}[/tex]   simplified

Final answer:

The probability of selecting a red or face card from a standard deck of cards is 8/13. This outcome is more likely than selecting a heart suit face card specifically, which has a probability of 3/52.

Explanation:

The problem can be solved by understanding that the deck has 26 red cards (hearts and diamonds) and 12 face cards (jacks, queens, and kings), with 6 face cards being red. The total number of unique choices that are either red cards or face cards is the number of red cards plus the number of black face cards. This avoids double-counting red face cards.

There are 26 red cards, but we need to exclude the 6 red face cards already counted, and add the 6 black face cards (from clubs and spades), giving us 26 + 6 = 32 unique cards that are either red or face cards. The probability, P, is then 32/52, which simplifies to 8/13.

To compare, the probability of drawing specifically a heart suit face card is 3/52 as there are only 3 face cards (jack, queen, and king) in the heart suit. Comparing probabilities, 8/13 is greater than 3/52, so it is more likely to draw a red or face card than a heart suit face card.

The answer is C. 3/5

20 girls, 3 boys. 23/40 is about 60 percent, or 3/5.

I wrote the wrong answer on accident for whatever reason when I first sent this, I apologize.

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points (-7, 2) and (9, 6). Substitute:

[tex]m=\dfrac{6-2}{9-(-7)}=\dfrac{4}{16}=\dfrac{1}{4}[/tex]

The slope of the line passing through the points (-7,2) and (9,6) is 1/4.

Point-slope formula

[tex]y-y_{1} = m(x-x_{1} )[/tex]

In the slope formula, m stands for slope which is calculated as the

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

= Δy/Δx

where, m = slope

[tex](x_1, y_1)=[/tex] coordinates of the first point in the line

[tex](x_2, y_2)=[/tex] coordinates of the second point in the line

We have the points (-7,2) and (9,6).

Substitute the values [tex]x_{1}}$$[/tex], [tex]{x_{2}[/tex] and [tex]y_{1}}[/tex], [tex]${y_{2}[/tex]  in the above equation, we get

[tex]$m=\frac{6-2}{9-(-7)}[/tex]

[tex]$=\frac{4}{16}=\frac{1}{4}$[/tex]

Therefore, the slope m = 1 / 4.

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Answer:

Your answer is B!

Step-by-step explanation:

Answer:

168

Step-by-step explanation:

2x45=90

6x13=78

78+90=168

Answer:  Since 1/3 can't be turned into a decimal, change .5 into 1/2. In order to subtract, the fractions need a common denominator. The least common denominator is 6. So 1/3 turns into 2/6, and 1/2 turns into 3/6. Now you need to take 9 3/6 minus 6 2/6. The answer is 3 1/6 gallons of water.

Step-by-step explanation:

Final answer:

To find the remaining water in Tank A after pouring out 6 1/3 gallons, subtract 6.333 from the tank's total capacity of 9.5 gallons, which leaves 3.167 gallons remaining in the tank.

Explanation:

The question involves determining the remaining quantity of water in a tank after a certain volume has been removed, which is a basic subtraction problem in mathematics. To solve it, subtract the volume of water that was poured out from the total capacity of the tank.

Tank A capacity: 9.5 gallons

Volume of water poured out: 6 1/3 gallons

To perform the subtraction, we first need to convert 1/3 of a gallon into a decimal. A third of a gallon is approximately 0.333 gallons. Adding this to 6 gallons gives us 6.333 gallons.

Now, subtract the volume poured out from the tank's capacity:

9.5 gallons (capacity) - 6.333 gallons (poured out) = 3.167 gallons (remaining in the tank)

Therefore, 3.167 gallons of water are left in the tank.

Answer:

Y-coordinate = y - 4

Step-by-step explanation:

In the given question point D coordinate is (x, y)

and D after translation

x goes to 6 unit to the right and y goes to 4 unit down.

Hence,

          Y-coordinate = y-4

Example:From graph

              Let point D coordinate (x , y) = (2 , 3)

After rotation

              D coordinates is (x+6 , y-4) = (2+6 , 3_4) = (8 , -1)

Answer:

On edge. the answer is 1

Step-by-step explanation:

i just took it

Answer:

(A)This set of data is a function because every input has an output.

(B) This set of data would not be a function if two inputs had the same output, for example, if the inputs were 3,4,4,11 and the outputs were 5,7,11,21 then the data set would not be a function because for input 4 it has two different outputs.

Step-by-step explanation:

Answer:

A. Distributive Property

Step-by-step explanation:

I'm taking the exam right now. :)

Exterior angles of triangles = 360°.

So by definition:

[tex]9x + 6 + 10x - 1 + 10x + 7 = 360\\29x + 12 = 360\\29x = 348\\x = 12[/tex]

The value of x is 12.

Answer: 12

Step-by-step explanation:

We know that the sum exterior angles of a polygons is [tex]360^{\circ}[/tex].

Therefore,according to the given picture , we have

[tex]\angle{GHJ}+\angle{HJG}+\angle{JGH}=360^{\circ}\\\\\Rightarrow\ (9x+6)^{\circ}+(10x-1)^{\circ}+(10x+7)^{\circ}=360\\\\\Rightarrow\ 9x+6+10x-1+10x+7=360\\\\\Rightarrow\ 29x+12=360\\\\\Rightarrow\ 29x=348\\\\\Rightarrow\ x=\dfrac{348}{29}\\\\\Rightarrow\ x =12[/tex]

Hence, the value of x = 12

Answer:

Seven

Step-by-step explanation:

We have the following list of people coming to the reunion,

A grandmother  = 1

A grandfather = 2

Two mothers = 1 and 3

Two fathers = 2 and 4

i.e. Up until here there are total 4 people - Grandmother, Grandfather, Mother, Father ( 1, 2, 3, 4)

Four children = 4, 6, 7, 8

Three grandchildren = 6, 7, 8

One brother = 6

Two sisters = 7, 8

Two sons = 4, 6

Two daughters = 7, 8

Therefore, in addition to the four people above, one of the child will be the father and so there are 3 grandchildren.

So, number of people added in this step is 3 and total number of people up until here becomes 7.

A mother-in-law = 1

A father-in-law = 2

A daughter-in-law = 3

So, no new family member is added in this step.

Hence, total  number of family members coming to reunion are 7 namely Grandmother, Grandfather, Mother, Father, Three children.

Answer:

c (0,-4)

Step-by-step explanation:

-5x+y = -4

4x - 4y =16

Solve the first equation for y since we are using substitution.

-5x+y = -4

Add 5x to each side

-5x+5x+y = -4+5x

y = 5x-4

Substitute this equation y = 5x-4 into the second equation.

4x -4(5x-4) = 16

Distribute the -4

4x - 4(5x) -4(-4) = 16

4x-20x +16 = 16

Combine like terms

-16x +16 =16

Subtract 16 from each side

-16x+16-16 = 16-16

-16x =0

Divide by -16

x=0

But we still need to find y

y = 5x-4

y = 5(0) -4

y = -4

Answer:

m<Q = 92 degrees

Step-by-step explanation:

Opposite angles of a quadrilateral inscribed in a circle are supplementary.

Angles O and Q are opposite angles, so they are supplementary, so their measures add up to 180 degrees.

m<O + m<Q = 180

2x + 2x + 4 = 180

4x + 4 = 180

4x = 176

x = 44

m<Q = 2x + 4 = 2(44) + 4 = 92

Answer:

Q =92

Step-by-step explanation:

Since the quadrilateral is inscribed in a circle, the opposite angles add to 180 degrees.

<O + <Q = 180

2x+ 2x+4 = 180

4x+4 =180

Subtract 4 from each side

4x= 180-4

4x= 176

Divide by 4

x = 44

Q = 2x+4

Q = 2(44)+4

Q = 88+4

Q = 92

Answer:

(x+1) is a factor with remainder 0.

Step-by-step explanation:

We divide (x+1) into the polynomial [tex]-3x^4+2x^3-x^2+6[/tex] through long division or synthetic. We choose long division and look for what will multiply with (x+1) to make the polynomial [tex]-3x^4+2x^3-x^2+6[/tex] .

[tex](x+1)(-3x^3)=-3x^4-3x^3[/tex]

We subtract this from the original [tex]-3x^4-(-3x^4)+2x^3-(-3x^3)-x^2+6[/tex].

This leaves [tex]5x^3-x^2+6[/tex]. We repeat the step above.

[tex](x+1)(5x^2)=5x^3+5x^2[/tex].

We subtract this from [tex]5x^3-(5x^3)-x^2-(5x^2)+6=-6x^2+6[/tex]. We repeat the step above.

[tex](x+1)(-6x)=-6x^2-6x[/tex].

We subtract this from [tex]-6x^2-(-6x^2)+0x-(-6x)+6=6x+6[/tex]. We repeat the step above.

[tex](x+1)(6)=-6x+1[/tex].

We subtract this from [tex]6x-(6x)+6-(6)=0[/tex]. There is no remainder. This means (x+1) is a factor.

Answer: x = 6

==============================================

Explanation:

The medians of a triangle meet up at the centroid in such a way that they cut each other at a ratio of 2:1, meaning that one part of the median is twice as long as the other. In this case, MO is two times longer than OP, so,

OP = 2*MO

and

MP = MO + OP

MP = MO + 2*MO .... replace OP with 2*MO

MP = 3*MO

9x-24 = 3*(x+4) ... plug in the given expressions

9x-24 = 3x+12

9x-3x = 12+24

6x = 36

x = 36/6

x = 6

Answer:

1/5 chance

Step-by-step explanation:

well their are 4 balls and 2 chosen

their is 1/2 chance or pulling a yellow

1/4 chance of pulling a black and green

 Y1 Y2,Y1 B,Y1 G,Y2 Y1,Y2 B,Y2 G,B Y1,B Y2,B G,G Y1,R Y2,G B

so their is a 1/5 chance of pulling it

If x = the first number (equal to 1x) then the second number is 75% more than this.

This means the value of the bigger number is 100 + 75 (because 100 is the starting number and 75 is the percent bigger)

This can be shown with the following equation:

Amount * [tex]\frac{percentage}{100}[/tex]

x *  [tex]\frac{175}{100}[/tex] = 1.75x

1.75x is the value of the bigger number.

Answer:

Option C is correct.

The answer for the given expression is 0.

Step-by-step explanation:

Given the statement: Two times the difference of one-third of a number and three. and also variable given is 9.

Let x be the variable or number.

"One-third of a number"  means [tex]\frac{1}{3}x[/tex]

Also, "difference of one third of a number and three " means [tex]\frac{1}{3}x-3[/tex]

Now, "Two times the difference of one-third of a number and three" means   [tex]2 \times (\frac{1}{3} x -3)[/tex]

Then, the expression for the given statement : [tex]2 \times (\frac{1}{3} x -3)[/tex]

Substitute the value of x =9 in above expression we have;

[tex]2 \times (\frac{1}{3}(9) -3)[/tex] = [tex]2 \times (3 -3)[/tex] = [tex]2 \times (0)[/tex] = 0

therefore, the answer for the given expression is, 0

The solution is Option B.

The recursive formula to calculate Marta's salary is given by the equation

f ( n ) = f ( n - 1 ) + 2700

The salary of Marta after 4 years will be $ 33,000

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the initial salary of Marta be f ( 0 ) = $ 24,900

The increment in Marta's salary every year = $ 2700

So , the equation will be

f ( n ) = f ( n - 1 ) + 2700

when n = 1

Substitute the value of n = 1 in the equation , we get

f ( 1 ) = f ( 1 - 1 ) + 2700

f ( 1 ) = f ( 0 ) + 2700

f ( 1 ) =  24,900 + 2700

f ( 1 ) = $ 27,600

when n = 2

Substitute the value of n = 2 in the equation , we get

f ( 2 ) = f ( 2 - 1 ) + 2700

f ( 2 ) = f ( 1 ) + 2700

f ( 2 ) =  27,600 + 2700

f ( 2 ) = $ 30,300

when n = 3

Substitute the value of n = 3 in the equation , we get

f ( 3 ) = f ( 3 - 1 ) + 2700

f ( 3 ) = f ( 2 ) + 2700

f ( 3 ) =  30,300 + 2700

f ( 3 ) = $ 33,000

Hence , after 4 years the salary of Marta will be $ 33,000

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Marta's annual salary increases by $2700 each year. Applying the recursive formula: f(n) = f(n-1) + 2700; f(4)=f(3)+2700=f(2)+2700+2700=f(1)+2700+2700+2700=f(0)+2700+2700+2700+2700=24900+4*2700=35500, we determine that Marta's salary in 4 years would be $35,500.

The subject of the question involves recursion, or constructing a sequence of numbers in a specific way. In Marta's case, her salary can be calculated using a recursive formula that builds upon her previous salary. This formula relies on the concept of numerical patterns and can be represented as follows: f(n) = f(n-1) + 2700; where f(n) is Marta's salary after n years and f(n-1) is her salary the previous year.

At the start, Marta's salary is 24,900, which serves as the base case for our recursive function. Therefore, her income increases by $2700 each year. To get Marta's salary in 4 years, we would use the recursive formula: f(4) = f(3) + 2700 = f(2) + 2700 + 2700 = f(1) + 2700 + 2700 + 2700 = f(0) + 2700 + 2700 + 2700 + 2700 = 24,900 + 4*2700 = 35,500. So, Marta's salary is $35,500 after 4 years.

Therefore, the correct option among choices provided is none from the given options.

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Given:

b1 = 17 ft

b2 = 20 ft

h = 13 ft

r = 17/2 = 8.5 ft

Area of the Semi-circle = 1/2 π r²

= 1/2 (22/7) (8.5²)

= (11/7) (72.25)

= 113.535 ft²

Area of the trapezium = (h) (b1 + b2) / 2

= (13)(17 + 20)/2

= 240.5 ft²

Total area of the amphitheater stage = Area of Semi-circle + Area of the trazezium = 113.535 + 240.5 = 354.035 ft²

Answer:

The sale price is $43.50.

Step-by-step explanation:

58 x .25 = 14.50 off the original price

58 - 14.50 = 43.50

Answer:

The answer is π

Step-by-step explanation:

Not really an explanation, but you can type this in wolframalpha: integrate (x^3 cos x/2 + 1/2) sqrt(4-x^2) dx from x=-2 to 2

The given integral can be solved using numerical calculation methods. The integral by part formula also would be applicable in the given integral.

The value of the given integral is [tex]3.14\rm\: or\: \pi[/tex].

Given:

Write the given integral.

[tex]\int_{-2}^{2}\sqrt{4-x^2}\left(\cos\left(\dfrac{x}{2}\right)x^3+\dfrac{1}{2}\right)\\[/tex]

Write the formula for the integration by part formula.

[tex]\int u.v=u\int vdx-\int u'(\int vdx)dx[/tex]

Let,

[tex]u=\sqrt{4-x^2}[/tex]

[tex]v=\left (x^3\cos\dfrac{x}{2} +\dfrac{1}{2} \right)[/tex]

Now put the value in above formula and integrate.

[tex]\begin{aligned}\int_{-2}^{2}\sqrt{4-x^2}\left(\cos\left(\dfrac{x}{2}\right)x^3+\dfrac{1}{2}\right)&=\left [\dfrac{\frac{x\sqrt{4-x^2}}{2}+2\arcsin\left(\frac{x}{2}\right)}{2}\right]_{-2}^{2}\\&=\left [\dfrac{x\sqrt{4-x^2}}{4}+\arcsin\left(\dfrac{x}{2}\right)\right]_{-2}^{2}\\\end[/tex]

Now, further simplify the expression.

[tex]\int_{-2}^{2}\sqrt{4-x^2}\left(\cos\left(\dfrac{x}{2}\right)x^3+\dfrac{1}{2}\right)\\=\left [\dfrac{2\sqrt{4-2^2}}{4}+\arcsin\left(\dfrac{2}{2}\right)\right]-\left [\dfrac{2\sqrt{4-(-2)^2}}{4}+\arcsin\left(\dfrac{-2}{2}\right)\right]\\=1.57-(-1.57)\\=3.14[/tex]

The value of the given integral is [tex]3.14\rm\: or\: \pi[/tex].

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Answer:

x   = 5 sqrt(6)/3

 y= 10 sqrt(6)/3

Step-by-step explanation:

We know sin 60 = opposite/hypotenuse

    sin 60 = 5 sqrt(2) /y

 Multiply each side by y

y sin 60 = 5 sqrt(2)

Divide each side by sin 60

y sin 60/ sin 60 = 5 sqrt(2)/ sin 60

y = 5 sqrt(2) / sin 60

y = 5 sqrt(2) / sqrt(3) /2)

y   = 10 sqrt(2)/ sqrt(3)

You cannot leave a sqrt in the denominator

 y=   10 sqrt(2)/ sqrt(3) * sqrt(3)/sqrt(3)

   y= 10 sqrt(6)/3

tan 60 = oppositve/ adjacent

tan 60 = 5 sqrt(2)/ x

Multiply each side by x

x tan 60 = 5 sqrt(2)

Divide by tan 60

x = 5 sqrt(2)/tan 60

x =5 sqrt(2)/sqrt(3)

You cannot leave a sqrt in the denominator

x = 5 sqrt(2)/sqrt(3) * sqrt(3)/sqrt(3)

x   = 5 sqrt(6)/3

Answer:

16 cans of corn

Step-by-step explanation: