Hair color. |. Clothing
Brown. I Dress
Black. I Jumpsuit
Blonde. I Pajamas
Red. I Jeans


The table above shows hair colors and clothing available at a doll shop. How many different combinations of hair color ND clothing are there?

Answer:

The maximum value of C is 15

Step-by-step explanation:

we have

[tex]x\geq 0[/tex] -----> constraint A

[tex]y\geq 0[/tex] -----> constraint B

[tex]2x+y\leq 10[/tex] -----> constraint C

[tex]3x+2y\leq 18[/tex] -----> constraint D

using a graphing tool

The solution area of the constraints in the attached figure

we have the vertices

(0,0),(0,9),(2,6),(5,0)

Substitute the value of x and the value of y  in the objective function

(0,0) -----> [tex]C=3(0)-2(0)=0[/tex]

(0,9) -----> [tex]C=3(0)-2(9)=-18[/tex]

(2,6) -----> [tex]C=3(2)-2(6)=-6[/tex]

(5,0) -----> [tex]C=3(5)-2(0)=15[/tex]

therefore

The maximum value of C is 15

To find the maximum value of the objective function $C = 3x - 2y$ subject to the given constraints, we can use the method of linear programming. We have the given constraints:
1. $x \geq 0$ (x is non-negative)
2. $y \geq 0$ (y is non-negative)
3. $2x + y \leq 10$
4. $3x + 2y \leq 18$
The first two constraints define that our solution must lie in the first quadrant of the Cartesian plane, as both x and y must be non-negative.
The third and fourth constraints define linear inequalities which we will represent graphically to find the feasible solution region.
Let's start by finding the intercepts of the lines represented by constraints 3 and 4:
For the third constraint, $2x + y = 10$:
- If $x = 0$, then $y = 10$.
- If $y = 0$, then $x = 5$.
For the fourth constraint, $3x + 2y = 18$:
- If $x = 0$, then $y = 9$.
- If $y = 0$, then $x = 6$.
Plotting these lines on a graph will give us two lines which intersect with the axes to form their intercepts and bound a certain area on the first quadrant.
The feasible region is the area that satisfies all the inequalities simultaneously, including the non-negativity constraints of x and y.
Next, we find the vertices of the feasible region. The vertices occur where the lines of the constraints intersect each other as well as with the axes. From the graph, we could find that the feasible region is a polygon formed by intersecting the lines corresponding to the constraints. The vertices are:
1. Where $2x + y = 10$ and $3x + 2y = 18$ intersect.
2. Where $2x + y = 10$ and the y-axis intersect.
3. Where $3x + 2y = 18$ and the x-axis intersect.
We solve for each vertex by solving the system of equations corresponding to the constraints that intersect:
For vertex 1, solving $2x + y = 10$ and $3x + 2y = 18$ simultaneously, we could do this by multiplying the first equation by 2 to eliminate y, and then subtract it from the second equation:
$4x + 2y = 20$
$3x + 2y = 18$
Subtracting the second equation from the first gives
$x = 2$
Plug this value of x into one of the original equations:
$2(2) + y = 10$
$4 + y = 10$
$y = 6$
So, vertex 1 is at (2, 6).
Vertex 2 is at the y-intercept of $2x + y = 10$ which is (0, 10).
Vertex 3 is at the x-intercept of $3x + 2y = 18$ which is (6, 0).
Now, we calculate the value of the objective function at each vertex:
For (2, 6):
$C = 3(2) - 2(6) = 6 - 12 = -6$
For (0, 10):
$C = 3(0) - 2(10) = 0 - 20 = -20$
For (6, 0):
$C = 3(6) - 2(0) = 18 - 0 = 18$
The maximum value of C within the feasible region is found at the intersection points of the constraints. Among the calculated values for the objective function $C$ at the vertices, the maximum value is $18$ at the point $(6, 0)$.
Therefore, the maximum value of the objective function $C = 3x - 2y$ given the constraints is 18.

If  angle θ is in quadrant 3 and the value of sin θ = -3/5, then we can say that; cos θ = -4/5

We are told that the angle θ is in quadrant 3.

Now, we are told that; sin θ = -3/5

In the third quadrant, only tan θ is positive.

Thus, cos θ will be negative.

Thus;

cos θ = -4/5

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Answer:

If  angle θ is in 3rd quadrant and the value of [tex]sin\theta =\frac{-3}{5}[/tex], then  [tex]cos\theta =\frac{-4}{5}[/tex]

Step-by-step explanation:

Given that , angle θ is in 3rd quadrant and the value of [tex]sin\theta =\frac{-3}{5}[/tex]

We know that ,

[tex]sin^2\theta + cos^2\theta =1[/tex]

[tex]cos^2\theta =1 - sin^2\theta[/tex]

By replacing the  value of [tex]sin\theta =\frac{-3}{5}[/tex] we get,

[tex]cos^2\theta =1 - (\frac{-3}{5})^2[/tex]

[tex]cos^2\theta =1 - \frac{9}{25} = \frac{16}{25}[/tex]

Taking roots at the end of both sides we get,

[tex]cos\theta = \frac{4}{5}[/tex]  or [tex]cos\theta = \frac{-4}{5}[/tex]

We know that , In third quadrant, only tan θ and cot θ are positive.

Thus, cos θ will be negative.

So [tex]cos\theta = \frac{-4}{5}[/tex]  

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[tex]\dfrac{15(15-1)}{2}=\dfrac{15\cdot14}{2}=15\cdot7=105[/tex]

Answer:

Domain: All Real Numbers

Range: All real numbers

Step-by-step explanation:

The given function is:

[tex]f(x) = 2(x-4)[/tex]

Domain:

The given function will not be undefined on any value of x as there is no denominator involved in the function.

So, the domain of the function is all real numbers

Range:

Similarly the range of the function is also all real numbers.

Answer:

4(x-7)^2-(x-7)+3 (Assuming t is f)

Step-by-step explanation:

Let s(x)=x-7 and t(x)=4x^2-x+3 .

(t o s)(x)=t(s(x))=t(x-7)

Before I continue this means replace the orginal x in t with x-7.

This will then give you

4(x-7)^2-(x-7)+3

Answer:

Step-by-step explanation:

A polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain or polygonal circuit.

Answer:

50-4h<32

Step-by-step explanation:

If the temperature starts at 50 and the temperature is decreased by 4 per each hour, then:

1) after the first hour, the temperature is 50-4 or 46

1) after the second hour, the temperature is 46-4 or (50-4)-4 or 50-4(2).

So what I'm trying to show you that if I continue this pattern our equation for what happens h hours later is: 50-4h.

We want to know when is the temperature below 32 so less than 32.

Temperature<32

Put in our variable expression for temperature.

50-4h<32

The question is about using algebra to solve a real-life problem of temperature decrease. The correct inequality for the given problem is '50 - 4h < 32', which shows the number of hours it takes for the temperature (50 and decreasing 4 every hour) to be less than 32 degrees.

The subject matter of this question is mathematics, specifically algebra and inequalities. The question provides that the temperature in degrees Fahrenheit is reducing by 4 each hour from a starting point of 50°F and seeks to find the number of hours (h) it takes for the temperature to decrease below 32°F.

We can represent this situation as an inequality: 50 - 4h < 32. In English, this states that the temperature (50, decreasing by 4 each hour) should be less than 32 degrees. So, to answer your question, option B with '50 - 4h < 32' is the correct inequality for this problem.

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Answer:

the answer is c glad i could help

Answer:

∠PRQ = 85°

Step-by-step explanation:

∠PRS and ∠TRQ are vertical angles and congruent, thus

4x + 15 = 3x + 35 ( subtract 3x from both sides )

x + 15 = 35 ( subtract 15 from both sides )

x = 20

Hence ∠PRS = (3 × 20) + 35 = 60 + 35 = 95°

∠PRQ and ∠PRS form a straight angle and are supplementary, hence

∠PRQ = 180° - 95° = 85°

Answer:

Angle QRP = 85

Step-by-step explanation:

Hopefully you can see QRS and TRP both equal 180 degrees, we will use this.  

QRS is the same as QRP and PRS added together.  Just like TRP is TRQ and QRP.  We will call QRP R for simplicities sake, and we are given a formula for PRS and TRQ.  PRS = 3x+35 and TRQ = 4x+15.

So now we have two equations.

180 = QRP + PRS = R + 3x + 35

180 = TRQ + QRP = 4x + 15 + R

So it's basically a system of equations.

180 = 35 + R + 3x

145 = R + 3x

R = 145 - 3x

180 = 4x + 15 + R

Replace R with what we found in the last  equation

180 = 4x + 15 + 145 - 3x

180 = x +160

x = 20

Now go back to the first equation and plug 20 in for x

R = 145 - 3x

R = 145 -3(20)

R = 145 - 60

R = 85

So Angle QRP = 85

Let em know if something doesn't make sense.  

Answer:

[tex]\sqrt[5]{y^{3} }[/tex]

Step-by-step explanation:

[tex]y^{\frac{3}{5} } = y^{\frac{1}{5} * 3}[/tex] = [tex]\sqrt[5]{y^{3} }[/tex]

This is true because of the fractional exponent rule.

Answer:

Step-by-step explanation:If  

n

is a positive integer that is greater than  

x

and  

a

is a real number or a factor, then  

a

x

n

=

n

√

a

x

.

a

x

n

=

n

√

a

x

Use the rule to convert  

y

3

5

to a radical, where  

a

=

,  

x

=

, and  

n

=

.

5

√

y

3

Check the picture below.

Answer:

i think its d

Step-by-step explanation:

Answer: [tex]8.0*10^{-4}[/tex]

Step-by-step explanation:

You need to remember the Quotient of powers property:

[tex]\frac{a^m}{a^n}=a^{(m-n)}[/tex]

Then, given the expression:

[tex]\frac{(4.0*10^6)}{(5.0*10^9)}[/tex]

You must divide the coefficients and subtract the exponents. Then:

[tex]=0.8*10^{-3}[/tex]

In order to write this result in Scientific notation form, you need to move the decimal point one place to the right. Therefore, you get:

[tex]=8.0*10^{-4}[/tex]

Check the picture below.

If sides SX=5,SY=10,XU=4,YT=x then the length of ST=18.

A triangle is a two dimensional figure having three sides, three angles, three vertex. Th sum of all the angles is equal to 180°.

We have been given SX=5, XU=4,SY=10 and we are required to find the length of ST. We can write the sides as under:

SX/SU=SY/T

SX=5,SU=5+4=9,SY=10,ST=10+x

5/9=10/(10+x)

Solving this for the value of x.

5(10+x)=10*9

50+5x=90

5x=90-50

x=40/5

x=8

We know that ST=10+x.

We have to put the value of x in ST.

ST=10+8

=18

Hence if sides are SX=5,SY=10,XU=4,YT=x then the length of ST=18.

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Answer:

[tex]a_n=5n[/tex]

Step-by-step explanation:

They gave us the first two terms in the sequence which is 5,10.

They then tell us the sequence is arithmetic which means all you need to do to get the next term is add/subtract.

To get from 5 to 10, you would need to add 5.

So that is what we are doing every time here.

5,10,15,20,25,... so on...

Now we want to make an equation for this.

When you see arithmetic sequence, you should think linear equations.

x   |    y

-----------

1        5

2       10

3       15

4       20

Can you see the relationship between y and x?

Slope is 5 because that is what the sequence is going up by.

y=5x+b

Maybe you can already see b is 0. If not, you can use a point on the line to find b.

Let's use (1,5).

5=5(1)+b

5=5+b

0=b

So b=0.

The equation is y=5x.

Our since we are talking about sequences maybe you prefer to say [tex]a_n=5n[/tex]

The standard equation of a parabola with vertex (0, 0) and focus (-2, 0) is y^2 = -8x. It opens to the left with the directrix x = 2.

To find the standard equation of a parabola with vertex (0, 0) and focus (-2, 0), we can use the definition of a parabola as the set of all points equidistant from a point (the focus) and a line (the directrix).

Since the focus is at (-2, 0), the directrix is a vertical line equidistant from the vertex on the opposite side of the focus, which is x = 2. The distance between the vertex and the focus (or the vertex and the directrix) is 2 units, so q = 2. This means that the parabola opens to the left.

The standard equation for a parabola that opens horizontally is of the form (y - k)^2 = 4p(x - h), where (h, k) is the vertex and p is the distance from the vertex to the focus. Here, p = -2 because the parabola opens to the left.

Therefore, the standard equation for the given parabola is y^2 = -4(2)x or y^2 = -8x.

Answer:

B A triangle in which no two sides are congruent is scalene

Step-by-step explanation:

A triangle that has 3 congruent sides is an equilateral triangle

A triangle in which no two sides are congruent ( no sides are the same) is a scalene triangle

A triangle that has at least two congruent sides is an isosceles triangle

Answer:

a triangle in which no two sides are congruent

Step-by-step explanation:

Answer:

The graph of [tex]f(x)=5\cos(\frac{1}{2}x)[/tex] is a vertical stretch of 5 units and a horizontal stretch by 2 units of the parent graph

Step-by-step explanation:

We want to find out how the graph of [tex]f(x)=5\cos(\frac{1}{2}x)[/tex] compare with the graph of the parent function [tex]g(x)=\cos (x)[/tex].

We can observe that the transformation applied to the basic cosine function is of the form:

[tex]y=A \cos Bx[/tex]

The [tex]A=5[/tex] is a vertical stretch by a factor of 5 units.

[tex]B=\frac{1}{2}[/tex] is a horizontal stretch by a factor of 2 units.

Therefore the graph of [tex]f(x)=5\cos(\frac{1}{2}x)[/tex]  will stretch vertically by a factor of 5 units and stretch horizontally by a factor of 2 units as compared to  [tex]g(x)=\cos (x)[/tex].

See attachment

Answer:

All real numbers

Step-by-step explanation:

we have

f(x) = 3x +9

The linear function  has a range of all real numbers -------> (-∞, ∞)

f(x) can take any real value.

Please see attached image below, for more information

Answer:

I think its B because K is = to Y

So if K is 9 then the asymptote would be 9

Limiting the Y to the to be only greater than 9

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\text{The average rate of change of function}\ f(x)\\\text{over the interval}\ a\leq x\leq b\ \text{is given by this expression:}\\\dfrac{f(b)-f(a)}{b-a}\\\\f(x)=2x^2-7x\\\\\text{Put the values of x = 2 and x = 6 to the equation of the function:}\\\\f(2)=2(2^2)-7(2)=2(4)-14=8-14=-6\\f(6)=2(6^2)-7(6)=2(36)-42=72-42=-30\\\\\dfrac{f(6)-f(2)}{6-2}=\dfrac{-30-(-6)}{4}=\dfrac{-24}{4}=-6[/tex]

Answer:

x  ≥ 9.2

Step-by-step explanation:

If in a gymnastics competition an athletes final score is calculated by taking 75% of the average technical score and adding 25% of the artistic score all scores are out of 10 and one gymnast has a 7.6 average technical score, the gymnast needs x  ≥ 9.2 to have a final score of at least 8.0.

7.6 x 75 / 100 = 5.7

Final answer:

The gymnast requires an artistic score of at least 9.2 to achieve a final score of at least 8.0, calculated by taking 75% of their average technical score and adding 25% of their artistic score.

Explanation:

To find out what artistic score the gymnast needs to achieve a final score of at least 8.0, we use the given information that the final score is composed of 75% of the average technical score plus 25% of the artistic score. Let's represent the artistic score as A.

First, calculate 75% of the average technical score:
0.75 × 7.6 = 5.7

Now, set up the equation using the required final score (8.0) and the known technical score (5.7):
5.7 + 0.25A ≥ 8.0

To find the minimum artistic score (A), we subtract 5.7 from both sides of the equation:
0.25A ≥ 8.0 - 5.7
0.25A ≥ 2.3

Finally, divide by 0.25 to solve for A:
A ≥ ÷ 0.25
A ≥ 9.2

So, the gymnast would need an artistic score of at least 9.2 to achieve a final score of at least 8.0.

Answer:

2

Step-by-step explanation:

So we are going to do

(sum of parts of the secant)(part on outside)=(sum of parts of the secant)(part on outside) .

This is what you get from doing that:

(1+x+4)(x+4)=(11+x+1)(x+1)

Simplifying:

(x+5)(x+4)=(x+12)(x+1)

We could see which value of x makes both side the same.

Choice 1: Plug in 2 for x:

(2+5)(2+4)=(2+12)(2+1)

(7    )(6    )=( 14   )(3)

      42    =  42

This equation is true.

Choice 2: Plug in 3 for x:

(3+5)(3+4)=(3+12)(3+1)

(    8)(    7)=(    15)(   4)

     56     =   60

This equation is not true.

Choice 3: Plug in 6 for x:

(6+5)(6+4)=(6+12)(6+1)

( 11   )(  10 )=( 18   )(7   )

110            =   126

This equation is not true.

Choice 4: Plug in 7 for x:

(7+5)(7+4)=(7+12)(7+1)

(12  )( 11   )=( 19   )(8)

132         =152

This equation is not true.

Answer:

The answer is A or "2"

Step-by-step explanation:

Answer:

i think the answer is choice H

Step-by-step explanation:

the number of girls to total number of members is 12:22, if you simplify this it's 6:11

Answer:

6:11

Step-by-step explanation:

There are 12 girls.

There are 12+10 member in all.

That means there are 22 members in all.

So the ratio of girls to total members is 12 to 22 or 12:22. To reduce this, look for a common factor. 12 and 22 both share 2 as a common factor so divide both by 2 gives you 6:11.

Answer:

11

Step-by-step explanation:

It is given that:

r = 14 & s = 8

Plug in the corresponding numbers to the corresponding variables:

(3/7)(14) + (5/8)(8)

Solve. Remember to simplify. Do multiplication & division first, then add:

(3/7)(14) + (5/8)(8)

(3 * 14)/7 + (5 * 8)/8

(3 * 2) + 5

(6) + 5

11

11 is your answer.

~

Answer:

x = 21

Step-by-step explanation:

x- 12 = 9

Add 12 to each side

x- 12+12 = 9+12

x = 21

Answer:

[tex]\huge \boxed{x=21}[/tex]

Step-by-step explanation:

[tex]\Huge\textnormal{Add 12 from both sides of the equation.}[/tex]

[tex]\displaystyle x-12+12=9+12[/tex]

[tex]\Huge \textnormal{Simplify and solve to find the answer.}[/tex]

[tex]\displaystyle 9+12=21[/tex]

[tex]\huge \boxed{x=21}[/tex], which is our answer.

Answer:

Step-by-step explanation:

y=√(-x-3) - 3

y exisit : - x -3 ≥ 0

- x  ≥ 3

x ≤ - 3    the domain is :  D=] -∞,-3 ]

y=√(-x-3) - 3

y + 3 = √(-x-3)

x exisit :  y + 3  ≥ 0   ; y ≥ -3

the range is : w = [- 3,+ ∞ [

look the graph

Answer:

It is A i believe.

Step-by-step explanation:

Because, 15/100 = 0.15 and y is your regular price so;

y - 0.15

Sorry had to rewrite what i did, but i hope my answer has helped you.

Answer:

$30

Step-by-step explanation:

Find the cost per marker.

Given: 8 markers = $20

Divide 8 from both sides.

Let x = amount of markers.

(8x)/8 = (20)/8

x = 2.5

Each marker costs $2.50

Now, multiply 12 with $2.50

2.50 x 12 = 30

$30 is the cost of 12 markers.

~

Answer:

180 in

Step-by-step explanation:

The perimeter is just the sum of the lengths of the sides of the shape.

So all we need to do here is:

40+10+(40-18)+(50-10)+18+50.

I got (40-18) for the bottom of the top rectangle, the part that is poking out.

I got (50-10) for the right side of the rectangle that is poking out towards the bottom.

40+10+(40-18)+(50-10)+18+50

40+10+22       +40       +18+50

50     +62                      +68

50+62+68

112+68

180

180 in

I'm going to post a drawing here to show the lengths I was talking about:

Let your age = X

Now you have 500 - 3x = 278

Subtract 500 from each side:

-3x = -222

Divide both sides by -3:

x = -222 / -3

x = 74

You are 74 years old.

The age of an old man is 74 years old.

A word problem is a verbal description of a problem situation. It consists of few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.

For the given situation,

Let the age of an old man be x.

500 reduced by 3 times my age is 278 can be expressed as

⇒ [tex]500-3x=278[/tex]

⇒ [tex]500-278=3x[/tex]

⇒ [tex]222=3x[/tex]

⇒ [tex]x=\frac{222}{3}[/tex]

⇒ [tex]x=74[/tex]

Hence we can conclude that the age of an old man is 74 years old.

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Answer:

[tex]x^{3} -12[/tex]

Step-by-step explanation:

[tex]y=\sqrt[3]{x+12}[/tex]

Replace x with y to get

[tex]x=\sqrt[3]{y+12}[/tex]

Cube both side

[tex]x^{3}=y+12[/tex]

Subract 12 from both sides

[tex]x^3-12=y[/tex]