The graph of a function is shown.

​What is the maximum value of the function?

Answer:

drawing a blue marble is a harder then the yellow but not as hard as the red.

Answer:

Step-by-step explanation:

The diagonal must be an angle bisector for a rhombus.

That means that both bisected angles are equal.

2x + 16 = 5x - 8            Add 8 to both sides

2x + 16 + 8 = 5x

2x + 24 = 5x                 Subtract 2x from both sides

24 = 5x - 2x

24 = 3x                         Divide by 3

24/3 = x

x = 8

Answer:

[tex]y = - \frac{1}{5} x + 7[/tex]

Step-by-step explanation:

Slope -intercept form:

y= mx +c, where m is the slope and c is the y- intercept.

Since the given equation is already in the slope-intercept form, we can identify its slope by looking at the coefficient of x.

Slope of given line= 5

The product of the gradients of two perpendicular lines is -1.

m(5)= -1

[tex]m = - \frac{1}{5} [/tex]

Substitute the value of m into the equation:

[tex]y = - \frac{1}{5} x + c[/tex]

Substitute a pair of coordinates to find the value of c.

when x= 0, y= 7,

[tex]7 = - \frac{1}{5} (0) + c[/tex]

c= 7

Thus, the equation of the line is y= -⅕x +7.

Answer:

1

Step-by-step explanation:

no exponent

Answer:

4

Step-by-step explanation:

Length of the y component is how far the vector reaches vertically, so in this case it's 4

Answer:

Step-by-step explanation:

Sum = -9

Product = 20

Factors = -5 , -4    {-4 * -5 = 20 & -5 + (-4) = -9}

x² - 9x + 20 = 0

x² - 5x  - 4x + 20 = 0     Rewrite middle term

(x² - 5x) - 4x + 20 = 0        Group terms

x(x - 5) - 4(x - 5) = 0         Factor terms

(x-5)(x -4)=0

x -5 = 0   ; x - 4 = 0

x = 5       ; x  = 4

Ans: x = 5 , 4

Answer:

A.) y = 3/4x + 1

Step-by-step explanation:

First let's find the slope using the slope formula, (y₂-y₁)/(x₂-x₁). The two points given are (0,1)₁ and (4,4)₂. We have to substitute those values.

y₂ = 4, y₁ = 1, x₂ = 4, x₁ = 0 --> (4 - 1)/(4 - 0) = 3/4

The slope is 3/4.

Now, we have to find the y-intercept, which is where the line meets the y-axis. It touches the y-axis at (0,1). The y-intercept is 1.

Finally, we build our equation in slope-intercept form.

y = mx + b

y = 3/4x + 1

Answer:

[tex] \displaystyle a = \frac{1+vh}{v}[/tex]

Step-by-step explanation:

we want to figure out a value of a for the following condition

[tex] \displaystyle va - vh = 1[/tex]

to do so factor out v;

[tex] \displaystyle v (a - h )= 1[/tex]

divide both sides by v which yields:

[tex] \displaystyle \frac{(a-h) \cancel{(v)}}{ \cancel{v}}= \frac{1}{v} [/tex]

therefore,

[tex] \displaystyle a-h = { \frac{1}{v}}[/tex]

now,add h to both sides:

[tex] \displaystyle a = \frac{1}{v}+h[/tex]

further simplification if necessary:

[tex] \displaystyle a =\boxed{ \frac{1+vh}{v}}[/tex]

factor out of v

Dividing both sides by (v)

cancel out (v)

add h in both sides

cancelout h

[tex]\sf{ }[/tex] [tex]\sf{ }[/tex]

the value of a if va- vh is equals to 1 is [tex]\bold{\dfrac{1+vh}{v} }[/tex]

Answer:

15

Step-by-step explanation:

The given parameters are represented by drawing the triangle with the details given using MS Visio

The point Q is located between points M and N in ΔMNP

The point R is located between points N and P in ΔMNP

The incenter of the triangle = H

Line HQ is perpendicular to side MN on ΔMNP

Line HR is perpendicular to side NP on ΔMNP

The length of the segment QN = 36

The length of the segment HN = 39

By Pythagoras' theorem, HQ = √((HN)² - (QN)²)

∴ HQ = √(39² - 36²)  = 15

HQ = 15

Given that H is the incenter of ΔMNP, the lengths of the perpendicular from H to the sides of the triangle are equal to the radius of the inscribed circle of the triangle

Therefore, the radius lengths are HQ, and HR

∴ HR = HQ = 15

HR = 15.

Using the Pythagorean theorem:

Hypotenuse = sqrt( 20^2 + 15^2)

Hypotenuse = sqrt( 400 + 225)

Hypotenuse = sqrt(625)

Hypotenuse = 25

Answer: 25 inches

Answer:

25 inches

Step-by-step explanation:

We can use the Pythagorean theorem

a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse

20^2 + 15^2 = c^2

400 +225 = c^2

625=c^2

Taking the square root of each side

sqrt(625) = sqrt(c^2)

25 = c

Answer:

-2/8

Step-by-step explanation:

All you need to do is to find the common denominator which is 8

so 4/8 is good to go and remains as it is

For 3/4 you have to multiply the fraction by 2, both numerator and denominator

you will get 6/8

so 4/8-6/8 would give you -2/8 or -1/4

Answer:

7^-22

Step-by-step explanation:

Exponent laws.

Answer:

36 units

Step-by-step explanation:

this is a walk around problem

the sides of the triangle will be 10, 13, and 13

so the perimeter = 10 + 13 + 13

p = 36 units

Answer:

perimeter = 36

Step-by-step explanation:

Tangents drawn to a circle from an external point are congruent, then

perimeter = (5 + 5) + (8 + 8) + (5 + 5)

                = 10 + 16 + 10

               = 36

Answer:

$0.25

Step-by-step explanation:

We can use System of Equations to find out how much a can of cat food costs.

Let's use variables to represent the cat food and dog food:

x = cost of 1 cat food can

y = cost of 1 dog food can

Here are our 2 equations based on the scenarios in the question:

4x + 3y = 1.99

4x + y = 1.33

Now let's set the second equation to y using basic algebra:

4x + y = 1.33

y = -4x+1.33

And we're going to plug that value of y, which is -4x+1.33 into the first equation and solve:

4x + 3y = 1.99

4x + 3(-4x+1.33) = 1.99

4x + -12x+3.99 = 1.99

-8x + 3.99 = 1.99

-8x = -2

x = 1/4

x = 0.25

1 can of cat food costs $0.25

Hope that helps (●'◡'●)

Answer:

.25

Step-by-step explanation:

set up equations

1)4c+3d=1.99

2)4c+d=1.33

Method of use:Elimination

          4c+3d=1.99

       - (4c+d)=-(1.33)

        ___________

=2d=.66

divide by two on both sides to get .33 for d.

plug in

4c+.33=1.33

subtract .33 on both sides

4c=1

divide by four on both sides to get c

c=1/4 or .25

Answer:

x = 17

Step-by-step explanation:

The angles are same side interior angles and they will add to 180 when the lines are parallel

6x+8  + 4x+2 = 180

10x+10 = 180

Subtract 10 from each side

10x+10-10 =180-10

10x = 170

Divide by 10

10x/10 = 170/10

x = 17

Answer:

x = 17

Step-by-step explanation:

Theorem:

If two lines are cut by a transversal such that same-side interior angles are supplementary, then the lines are parallel.

For the lines to be parallel, the sum of 6x + 8 and 4x + 2 must equal 180.

6x + 8 + 4x + 2 = 180

10x + 10 = 180

10x = 170

x = 17

Lets Do

[tex]\\ \sf\longmapsto p = 2(l + w) \\ \\ \sf\longmapsto l + w = \frac{p}{2} \\ \\ \sf\longmapsto w = \frac{p}{2} - l \\ \\ \sf\longmapsto \boxed{ \bf \: w = \frac{p - 2l}{2} }[/tex]

Step-by-step explanation:

= 1/2x^2.12x^2 - 1/2x^2.4x + 1/2x^2.2

= 6x^4 - 2x^2 + x

Answer:

$7 is his Hourly Wage.

Step-by-step explanation:

We can start by finding out how much money Jada started with by adding the amount of money he had after buying the cake with how much he spent on the cake, 86 + 12 = 98.

We now know how much money he had before buying anything. Now we can just divide the total amount of money by how long he worked.

98 ÷ 14 = 7

Answer: 4x + 0.5y

Step-by-step explanation:

Concept:

Here, we need to understand the idea of the mean (average).

The "mean" is the "average" you're used to, where you add up all the numbers and then divide by the number of numbers.

If you are still confused, please refer to the attachment below for a graphical explanation.

Solve:

**Disclaimer** I assume the question is asking for the arithmetic mean instead of geometric. If it was, then you can refer to my answers. If it was not, then you can point it out and I will redo the question.

Terms: 2x-5y, 5x+2y, 8x+6y, x-y

Number of terms: 4

 [(2x-5y) + (5x+2y) + (8x+6y) + (x-y)] / 4

=[2x + 5x + 8x + x + 2y - 5y + 6y - y] / 4

=[16x + 2y] / 4

=4x + 0.5y

Hope this helps!! :)

Please let me know if you have any questions

Answer:

[tex]162.07[/tex]

Step-by-step explanation:

An image that creates represents this situation has been attached to this answer. As one can see, the diagram models the situation, the angle of depression represents the angle between the horizon line and the line of sight. The horizon line and the tower form a right angle (a (90) degree angle). This means that the angle of depression is complementary to the angle of sight. Therefore, one can state the following:

[tex](angle\ of\ depression) + (angle\ of \ sight)=90[/tex]

Substitute,

[tex](angle\ of\ depression) + (angle\ of \ sight)=90[/tex]

[tex](m<ABD)+(m<DBC)=90[/tex]

[tex]42+(m<DBC)=90[/tex]

Inverse operations,

[tex]42+(m<DBC)=90[/tex]

[tex]m<DBC=48[/tex]

Now one can use the right angle trigonometric ratios to solve this problem. The right angle trigonometric ratios are a series of ratios that describe the relationship between the sides and angles in a right triangle. These ratios are as follows:

[tex]sin(\theta)=\frac{opposite}{hypotenuse}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}\\\\tan(\theta)=\frac{opposite}{adjacent}[/tex]

Bear in mind, the terms (opposite) and (adjacent) are subjective, and change depending on the reference angle. However, the term (hypotenuse) refers to the side opposite the right angle and is constant regardless of the reference angle.

In this case, one has found an angle in the triangle, one is given the measure of the side opposite this angle, and one is asked to find the side adjacent to this angle. Therefore, it would make the most sense to use the ratio tangent (tan).

[tex]tan(\theta)=\frac{opposite}{adjacnet}[/tex]

Substitute,

[tex]tan(48)=\frac{180}{adjacent}[/tex]

Inverse operations,

[tex]tan(48)=\frac{180}{adjacent}[/tex]

[tex]adjacent=\frac{180}{tan(48)}[/tex]

[tex]adjacent=162.07[/tex]

Step-by-step explanation:

The depth of the water is increasing by 2 feet each minute.

Answer:

[tex](x-\frac{1}{2})^2=\frac{81}{4}[/tex]

Step-by-step explanation:

Hi there!

[tex]x^2-x-20=0[/tex]

This equation is written in the form [tex]ax^2+bx+c=0[/tex]. First, use partial factoring:

[tex](x^2-x)-20=0[/tex]

For x^2-x, the b value is -1 in [tex]ax^2+bx+c[/tex]. To complete the square, take the square of half of 1 and add it in the parentheses as the c value:

[tex](x^2-x+\frac{1}{2}^2 )-20=0[/tex]

However, when adding values to one side of the equation, we must to the same to the other side:

[tex](x^2-x+\frac{1}{2}^2 )-20=\frac{1}{2}^2[/tex]

Complete the square:

[tex](x-\frac{1}{2})^2-20=\frac{1}{4}[/tex]

Move 20 to the other side

[tex](x-\frac{1}{4})^2=\frac{1}{4}+20\\(x-\frac{1}{2})^2=\frac{81}{4}[/tex]

I hope this helps!

Answer:

Sa / Va = time traveled by bus a

Sb  / Vb + 3/4  = time traveled by van b

Sa / Va = Sb  / Vb + 3/4      times traveled are the same

            = (220 - Sa) / Vb + 3/4

Sa ( 1 / Va + 1 / Vb) = 220 / 80 + 3/4

Sa (140 / 4800) = 3.5

Sa = 120 km

Check: 120 km / 60 km/hr = 2 hr = Ta

Sb = 1.25 * 80 = 100 km   traveling for 1.25 hrs

Given:

The endpoints of the latus rectum at (-2, 3) and (-2, 15).

The directrix at x = 4.

To find:

The equation of the parabola.

Solution:

The equation of the parabola is:

[tex](y-k)^2=4p(x-h)[/tex]                   ...(1)

Where, [tex]x=h-p[/tex] is directrix and [tex](h+p,k\pm |2p|),p<0[/tex] are the end point of the latus rectum.

The directrix at x = 4. So,

[tex]h-p=4[/tex]               ...(i)

The endpoints of the latus rectum at (-2, 3) and (-2, 15). So,

[tex](h+p,k-|2p|)=(-2,3)[/tex]

[tex](h+p,k+|2p|)=(-2,15)[/tex]

Now,

[tex]h+p=-2[/tex]              ...(ii)

[tex]k-2p=3[/tex]              ...(iii)

[tex]k+2p=15[/tex]           ...(iv)

Adding (i) and (ii), we get

[tex]2h=2[/tex]

[tex]h=1[/tex]

Putting [tex]h=1[/tex] in (i), we get

[tex]1-p=4[/tex]

[tex]-p=4-1[/tex]

[tex]-p=3[/tex]

[tex]p=-3[/tex]

Putting [tex]p=-3[/tex] in (iii), we get

[tex]k-|2(-3)|=3[/tex]

[tex]k-6=3[/tex]

[tex]k=3+6[/tex]

[tex]k=9[/tex]

Putting [tex]h=1,p=-3,k=9[/tex] in (1), we get

[tex](y-(9))^2=4(-3)(x-1)[/tex]

[tex](y-9)^2=-12(x-1)[/tex]

Therefore, the required equation of the parabola is [tex](y-9)^2=-12(x-1)[/tex].

Answer:

x = 29.5

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos x = adj side/ hypotenuse

cos x = 67/77

Taking the inverse cos of each side

cos^-1( cos x) = cos^-1 (67/77)

x = 29.52626525

To the nearest tenth

x = 29.5

Answer:

Step-by-step explanation:

a) 1200≥25x+45y

b) YES, because:

1200≥25(15)+45(15)

1200≥375+675

1200≥1050

Answer: 300

Step-by-step explanation:

Based on the information given in the question, the number of participants in the study will be calculated thus:

The number if letters in the set are 8 from A - H. This means that there are 8 ways to choose 3 letter when the ordering matters.

This will be:

= 8!/(8 - 3)!

= 8 × 7 × 6

= 336

Since 36 sequences were not assigned, therefore the numbers that were assigned will be:

= 336-36

= 300.

There were 300 participants.

Answer: [tex]\$100[/tex]

Step-by-step explanation:

Given

T-shirt cost 5 times as much as a singlet

Suppose the price of a singlet [tex]x[/tex]

Price of a T-shirt is [tex]5x[/tex]

According to the question, for $800, trader can buy 32 more singlet than T-shirt

[tex]\Rightarrow \dfrac{800}{x}=\dfrac{800}{5x}+32\\\\\Rightarrow \dfrac{800}{x}-\dfrac{160}{x}=32\\\\\Rightarrow 800-160=32x\\\\\Rightarrow x=20[/tex]

Thus, the price of a T-shirt is [tex]5x=\$100[/tex]