Sara, Jenna, and Julia are going on a trip and want to combine their income over the next few months to pay for it. Jenna and Julia both make $450 per week and Sara makes $750 per week. Jenna and Julia also receive a $100 bonus from their bosses. Which expression represents how much money all three women make together, given they work the same number of weeks?

Firslty, we need to find the function, whcih we can do by substituting one into the other:

Now, for the domain we have more complicated approach.

We first have to find the domain for both f(x) and g(x).

The domain of f(x) is all real number, because it is a quadratic polynomial.

The domain of g(x) is all the real numbers except the x values that makes the square root interior negative, so all real numbers so that:

Now, the domain of the composite function f(g(x)) is the set of all the values of x in the domain of g(x) such that the corresponding g(x) is in the domain of f(x).

Since the domain of f(x) is all real numbers and g(x) is a real number function, all the values of g(x) will be in the domain of f(x), so we just need to check the values of x that are in the domain of g(x).

The domain of g(x), as we saw, is:

And any value of x will give a g(x) that will be in the domain of f(x) so, the domain of f(g(x)) is:

So, the correct alternative is:

Answer:

35

Step-by-step explanation:

90-55= 35 degress

Answer:it’s (-1,8)

Step-by-step explanation:

Answer: Greater

Step-by-step explanation:

Answer:

179 is greater than 31

Answer: 2 3/7

Step-by-step explanation:

Answer:

Slope:

JK = (1/3)

LK = (-2)

ML = (2/5)

MJ = (-3/2)

Quadrilateral JKLM is not a parallelogram because the slopes don't match.

Step-by-step explanation:

Slope = m

JK = (-4, 1), (2, 3)

       (x₁, y₁)  (x₂, y₂)

        y₂ - y₁         3 - 1               2            2           1

m = ------------ = ------------- = ---------- = --------- = -------

        x₂ - x₁         2 - (-4)         2 + 4         6           3

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

LK = (5, -3), (2, 3)

       (x₁, y₁)  (x₂, y₂)

        y₂ - y₁         3 - (-3)        3 + 3          6

m = ------------ = ------------- = ---------- = --------- = -2

        x₂ - x₁         2 - 5              -3           -3

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

ML = (0, -5), (5, -3)

       (x₁, y₁)  (x₂, y₂)

        y₂ - y₁        -3 - (-5)      -3 + 5         2

m = ------------ = ------------- = ---------- = ---------

        x₂ - x₁         5 - 0              5            5

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

MJ = (0, -5), (-4, 1)

       (x₁, y₁)  (x₂, y₂)

        y₂ - y₁        1 - (-5)         1 + 5          6          -3

m = ------------ = ------------- = ---------- = --------- = -------

        x₂ - x₁         -4 - 0            -4            -4          2

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

I hope this helps!

Answer:

Complementary angles have a sum of 90°.

(x²-16x)+(3x) = 90

x² -13x - 90 = 0

(x-18)(x+5) = 0

x - 18 = 0 or x + 5 = 0

x = 18 or x = -5 (reject)

Substitute x into the angles.

18²-16(18) = 36

Smaller angle = 36°

3(18) = 54

Larger angle = 54°

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y= - {x}^{2} +12x - 27[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

The values of x where a parabola cuts the x - axis (y = 0) are the roots of the quadratic equation.

I.e 3 and 9 for the given problem.

and the equation can be represented as :

[tex]\qquad\displaystyle \tt \rightarrow \: y = a(x - x1)(x- x2)[/tex]

where, x1 and x2 are the roots of the quadratic equation, a is a constant value (depicting strech in curve)

Now, plug in the values :

[tex]\qquad\displaystyle \tt \rightarrow \: y= a(x- 3)(x - 9)[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y = a( {x}^{2} -9x - 3x +27)[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y= a( {x}^{2} -12 +27)[/tex]

Now, we need to find the value of a, for that let's use the coordinates of a point lying on the curve (10 , -7)

[tex]\qquad\displaystyle \tt \rightarrow \: - 7= a( {10}^{2} -12(10) +27)[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: - 7= a(100- 120+27)[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: - 7= a( 7)[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: a = ( - 7) \div ( 7)[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: a = -1[/tex]

Now, we got all required values. let's plug the value of a in equation, and we will get the required equation of parabola.

[tex]\qquad\displaystyle \tt \rightarrow \: y= -( {x}^{2} -12x +27)[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y= - {x}^{2} +12x - 27[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

[tex]y=-x^2+12x-27[/tex]

Step-by-step explanation:

Intercept form of a quadratic equation

[tex]\boxed{y=a(x-p)(x-q)}[/tex]

where:

Given x-intercepts:

Substitute the given x-intercepts into the formula:

[tex]\implies y=a(x-3)(x-9)[/tex]

To find a, substitute the given point (10, -7) into the equation and solve for a:

[tex]\implies a(10-3)(10-9)=-7[/tex]

[tex]\implies a(7)(1)=-7[/tex]

[tex]\implies 7a=-7[/tex]

[tex]\implies a=-1[/tex]

Therefore, the equation of the function in factored form is:

[tex]\implies y=-(x-3)(x-9)[/tex]

Expand the brackets:

[tex]\implies y=-(x^2-9x-3x+27)[/tex]

[tex]\implies y=-(x^2-12x+27)[/tex]

[tex]\implies y=-x^2+12x-27[/tex]

Therefore, the equation of the function in standard form is:

[tex]\boxed{y=-x^2+12x-27}[/tex]

least common mutiple of...

6 and 8: 24

8 and 12: 24

12 and 9: 36

6 and 9: 18

Answer:numbers that are equal to 4/8 would be 2/4 and 1/2 and are you multiplying up?

Step-by-step explanation:

The midpoint of the line segment given is (1, 4.5)

In geometry, the midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints. It bisects the segment equally into two halves.

The formula of midpoint of a line is given as

[tex]M_x_y = \frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}[/tex]

Substituting the given values;

[tex]M_x_y = \frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\\M_x_y = \frac{-2+4}{2}, \frac{7+2}{2} \\M_x_y = 1, \frac{9}{2} \\M_x_y = 1, 4.5[/tex]

The midpoint of the line AB is equal to (1, 4.5)

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The slope of the line shown in the figure having equation x + 2y = 0 is 1/2.

The point A is at ( -2 , 1 ), point B is at ( -4 , 2 ) and Point C is at ( -2 , 2 ).

Let point D be at ( -4 , 1 ).

Now the new triangle is ΔBDA and the corner points are A is at ( -2 , 1 ), point B is at ( -4 , 2 ) and  point D is at ( -4 , 1 ).

The equation of line passing through two points  is given by:

[tex](y-y_{1} ) = (\frac{y_{2}-y_{1} }{x_{2} - x_{1} })(x - x_{1} )[/tex]

The equation of line passing through two points A( -2 , 1 ) and B( -4 , 2 ) IS

y - 1 = ((2-1)/(-4-(-2)))  (x-(-2))

y - 1 = (1/(-2)) (x+2)

2y -2 = -x -2

x + 2y = 0

The equation of straight line is x + 2y = 0

The equation in slope intercept form can be written as,

y = x/2 + 0

Slope = m = 1/2

Intercept = c = 0

So, we can conclude that 1/2 is the slope of the line .

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out of 500 people 200 like baseball and 120 people like to play game baseball/softball

suppose 48 out of every 120 people like baseball/softball.

of the people who like baseball/softball, 3 out of 5 play the game.

if you ask 500 people,

how many would you expect play baseball/softball

it means 40% like baseball and 60% like to play game

if there are 500 people

then 500 *(40/100)=200

thus 200 people like baseball

and 200*(60/100)=120

Hence 120 people to play game

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Answer:24

Step-by-step explanation:4+2=6,6+3=9,9+4=13,13+5=18,18+6=24

Answer:

24

Step-by-step explanation:

because in first piggy bank has 4 coins and second has 6 . difference=6-4=2

second has 6 coins and third has 9 . difference= 9 - 6 = 3 third has 9 coins and fourth has 13 . difference=13-9=4

fourth has 13 and fifth has 18 coins difference is 18 -13 =5

then,sixth has 24 because all have 2 3 4 5 difference then six has 6

Answer:

sorry i don't know it to should have listened to your teacher

Step-by-step explanation:

Label the points,lines,and planes to show AB and line in perpendicular

to each other in plane R to point B, plane R

Using the average sales per restaurant, the sales manager should report the Lemon-roasted chicken sandwiches as recording better sales performance than the Barbecued chicken sandwiches.

The averages represent the total sales generated at the lemon-roasted and barbecued restaurants, respectively, divided by the number in each group.

The average is the same as the mean of a data set.  It is computed by the mathematical operations of addition and division.

                                                        Lemon-roasted   Barbecued

The number of restaurants                        3                      5

Total sales during the testing period  6,000             7,200

Average sales per restaurant              2,000              1,440

Based on the average sales, the sales manager should report that the lemon-roasted chicken sandwiches are outperforming the barbecued restaurants.

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Answer:

he has 556 pages in his book

The calculated answer after simplification in which Ryan has number of baseball cards is: 357 cards

How to simplify statement problems?

In mathematics, the statement based problems can be solved by forming the equations. And later, simplify those equation by equating to each other. This method is very common for the complicated problems to make the calculation easy.

According to the question, Ryan collected 2650 cards. In which, he has more baseball cards compared to football cards.

Now, let us assume, baseball cards be 'B'; football cards be 'F' and hockey cards be 'H'.

As per the question, the formed equation from the statement for the simplification is:

B + F + H = 2650

3B = F and H + 150 = F

Substituting above values in the formed equation to get the simplify answer,

B + 3B + 3B - 150 = 2650 ⇒ 7B = 2500 ⇒ B = 357

Now, the value of football cards is: F = 3(357) = 1071

And, the value of hockey cards is: H = 1071 - 150 = 921

Hence, after simplification Ryan has number of baseball cards is: 357 cards

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Answer:

see explanation

Step-by-step explanation:

given that V is directly proportional to h³ , then the equation relating them is

V = kh³ ← k is the constant of proportion

to find k use the condition V = 48 when h = 4 , then

48 = k × 4³ = 64k ( divide both sides by 64 )

[tex]\frac{48}{64}[/tex] = k , then k = 0.75

V = 0.75h³ ← equation of proportion

1

when h = 3 , then

V = 0.75 × 3³ = 0.75 × 27 = 20.25 cm³

2

when h = 6 , then

V = 0.75 × 6³ = 0.75 × 216 = 162 cm³

then

162 ÷ 20.25 = 8

the volume will be 8 times bigger

What is your answer?

Answer:

11

Step-by-step explanation:

[tex]3^{2}[/tex] + 2

9 + 2

11

     Trigonometry is the study of angles and the angular relationships between planar and three-dimensional shapes. The cosecant, cosine, cotangent, secant, sine, and tangent are among the trigonometric functions (also known as the circle functions) that make up trigonometry.

Examples of algebra. Discover the vertex of absolute value. The vertex in this instance for y=|x5|+4 y = | x - 5 | + 4 is (5,4). Set the interior of the absolute value x5 x - 5 equal to 0 0 to determine the vertex's x x coordinate.

Examples of Algebra The degree of variable y in this instance is 1, which means that the degrees of the variables in the equation violate the definition of a linear equation, indicating that the equation is not a linear equation.

Pick a few x values and look for some ordered pairings to graph an absolute value function. Connect the points by plotting them on a coordinate plane. The graph has a V form, as you can see. (1) The graph's vertex is (0,0).

Obtain the equation y = ax2 + bx + c.

Determine -b / 2A. The vertex's x-coordinate is given here.

Simply enter the value of -b / 2a into the equation for x and solve for y to obtain the vertex's y-coordinate. The vertex's y-coordinate is given here.

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Evaluating Algebraic Expressions

We are given the expression:

-6b + 2a

And it's required to find the value of the expression for a=-6.9 and b=1.9

Substituting the values:

-6(-1.9) + 2(-6.9)

= 11.4 - 13.8

Operating:

=-2.4

The value is -2.4

Delilah is correct; it is

Here, we want to check who was right

Mathematically, we can dilate a figure by reduction or enlargement by the use of a specific scale factor

When the scale factor is less than 1, it is a reduction

However, if the scale factor is greater than 1, it is an enlargement

The original point is (x,y)

From the image coordinates given, we see that the scale factor is 6/5 which is greater than 1

Thus, the dilation is an enlargement and Delilah was right

The equation representing the pool draining in slope-intercept form is y = -12x + 38000 and the time for the pool to fully drain is 3167 minutes.

It is described as the relationship between two variables, and a straight line results from plotting the graph of the linear equation.

The equation is referred to as a linear equation in one variable if just one variable is contained in the linear equation.

As we know,

The standard form of the straight line is:

y = mx + b

The slope in this case is m, and the y-intercept is b.

From the data given:

y = -12x + 38000

Plug y = 0 to find how long it will take for the pool to fully drain:

0 = -12x + 38000

x = 3167 minutes

To fill it back up, the y-intercept is 0.

The slope is given M = 16

y = 16x

Now plug y = 38000 to find how long it will take for the pool to fill back up

38000 = 16x

x = 2375 minutes

Thus, the equation representing the pool draining in slope-intercept form is y = -12x + 38000 and the time for the pool to fully drain is 3167 minutes.

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Answer:

[tex]\sqrt{5}[/tex]

Step-by-step explanation:

to simplify use the rule of radicals

[tex]\frac{\sqrt{x} }{\sqrt{y} }[/tex] ⇔ [tex]\sqrt{\frac{x}{y} }[/tex] , then

[tex]\frac{\sqrt{15} }{\sqrt{3} }[/tex] = [tex]\sqrt{\frac{15}{3} }[/tex] = [tex]\sqrt{5}[/tex]

Probability that 5 of 6 stolen cars will be recovered with insurance records a car with a certain protection system will be recovered 91% of the time is equal to P(x=5)=0.3369 (approximately).

As given,

Insurance protection system recovered of a car=91%

p=0.91

q=1-p

 =1-0.91

 =0.09

n=6

x=5

Using Binomial theorem ,probability of 5 of 6 stolen cars will be recovered is:

ⁿCₓ(p)ˣ(q)ⁿ⁻ˣ

=⁶C₅(0.91)⁵(0.09)⁶⁻⁵

=[6!/(6-5)!5!] × (0.91)⁵× (0.09)

=6×(0.91)⁵×0.09

=0.3369

Therefore, probability that 5 of 6 stolen cars will be recovered with insurance records a car with a certain protection system will be recovered 91% of the time is equal to P(x=5)=0.3369 (approximately).

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Answer:

the slope is 0 and  the equation is y = -2

Step-by-step explanation:

Answer:

30√2 cm

Step-by-step explanation:

Maximum length of the rod = Length of the diagonal of the cuboid

Length of diagonal of cuboid = [tex]\sqrt{l^2+w^2 + h^}[/tex]

where l = length, w =width and h = height

For this particular cuboid,

Diagonal length = [tex]\sqrt{30^2+24^2 + 18^2}[/tex]

[tex]\sqrt{800 + 576 + 324} \\\\\\= \sqrt{1500}\\\\= 30\sqrt{2} \text{ cm}[/tex]

Answer:

  AB, DC, ED, GA

Step-by-step explanation:

You want to identify the segments that are skew to edge FH of cuboid ABCDEFGH.

Two lines are skew when no plane exists that can contain them both. That is, skew lines are not parallel and do not intersect.

Cuboid ABCDEFGH has 12 edges. Of those, 3 are parallel to FH, and 4 intersect FH. The remaining edges are skew to FH:

  AB, DC, ED, GA . . . . . segments skew to FH