For a quadratic equation of the form:

[tex]av^2+bv+c=0[/tex]The quadratic formula is:

[tex]v_{1,2}=\frac{-b\pm\sqrt[]{b^2-4\cdot a\cdot c}}{2\cdot a}[/tex]In this case, we have the eqaution:

[tex]11v^2+8v=4[/tex]First, let's rest 4 on both sides to get 0 in the right hand side:

[tex]11v^2+8v-4=0[/tex]Then we can use the quadratic formula:

[tex]v_{1,2}=\frac{-8\pm\sqrt[]{8^2-4\cdot11\cdot(-4)}}{2\cdot11}[/tex]And solve:

[tex]\begin{gathered} v_{1,2}=\frac{-8\pm\sqrt[]{64^{}+176}}{22} \\ v_{1,2}=\frac{-8\pm\sqrt[]{240}}{22} \\ v_{1,2}=\frac{-8\pm\sqrt[]{16}\sqrt[]{15}}{22} \\ v_{1,2}=\frac{-8\pm4\sqrt[]{15}}{22} \\ v_{1,2}=\frac{-4\pm2\sqrt[]{15}}{11} \end{gathered}[/tex]Then the two solutions are:

[tex]\begin{gathered} v_1=\frac{-4-2\sqrt[]{15}}{11} \\ v_2=\frac{-4+2\sqrt[]{15}}{11} \end{gathered}[/tex]help meeeeeee pleaseee !!!!

1) The **Linear equation** that models the average price of a new home is;

y = -800x + 294000.

2) The prediction of the average price of a new hom in the year 2014 is; $256000

How to solve the equation in slope intercept form?We are told that the **average price** in the year 2004 was $294000

We are told that y is the **average price** in a home in the year x, where x = 0 represents the year 2004. Thus, this means that the **y-intercept** is $294000.

Since the line must pass through the points (0, 294000) and (7, 288400), it means that;

**Slope** = (288400 - 294000)/(7 - 0)

Slope = -5600/7

Slope = -800

Now, we know that the general formula for equation in **slope intercept form** is; y = mx + c

where; m is slope and c is y-intercept.

Thus;

1) **Linear equation **is; y = -800x + 294000.

2) For the average price of a new home in the year 2014, this means that x = 2014 - 2004 = 10 years

Thus;

y = -800(10) + 294000

y = $256000

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y= 3x - 5 y= -6x + 4

The given system of equation:

**y = 3x - 5 (1)**

**y = -6x + 4 (2)**

We can solve the system of equation by using elimination method :

**Elimination Method:** *In the elimination method you either add or subtract the equations to get an equation in one variable. When the coefficients of one variable are opposites you add the equations to eliminate a variable and when the coefficients of one variable are equal you subtract the equations to eliminate a variable.*

Subtract the equation (1) & (2)

[tex]\begin{gathered} y-y=3x-5-(-6x+4) \\ 0=3x-5+6x-4 \\ 0=9x-9 \\ 9x=9 \\ x=\frac{9}{9} \\ x=1 \end{gathered}[/tex]So, we get **x = 1**

Substitute the value of x in the equation (1)

[tex]\begin{gathered} y=3x-5 \\ y=3(1)-5 \\ y=3-5 \\ y=(-2) \end{gathered}[/tex]**y = (-2)**

So, the solution of the system of equations are : **(x,y) = (1,-2)**

**Answer: (x,y) = (1,-2)**

usBelow, the two-way table is given for aclass of students.FreshmenSophomoreJuniorsSeniorsTotalMale4622Female3463TotalIf a student is selected at random, find theprobability the student is a female given that it'sa junior. Round to the nearest whole percent.[?]%

[tex]\text{probability}=\frac{\text{ number of favorable cases}}{\text{ total number of }cases}[/tex]

Total number of students = 4 + 6 + 2 + 2 + 3 + 4 + 6 + 3 = 30

The probability that a student is female given that it is a junior is computed as follows:

[tex]\text{ P(}female|junior\text{)=}\frac{P(female\cap junior)}{P(junior)}[/tex]The probability that a student is female and junior is:

[tex]P(female\cap junior)=\frac{6}{30}=\frac{1}{5}[/tex]The probability that a student is a junior is:

[tex]P(junior)=\frac{2+6}{30}=\frac{8}{30}=\frac{4}{15}[/tex]Finally, The probability that a student is female given that it is a junior is:

[tex]P(female|junior)=\frac{\frac{1}{5}}{\frac{4}{15}}=\frac{1}{5}\cdot\frac{15}{4}=\frac{3}{4}=0.75\text{ or 75\%}[/tex]Sophie records the total number of cans of cat food she uses after different numbers of days. She wants to know if the number of cans of cat food she uses is proportional to the number of days. After 3 days – 6 cans After 4 days - 8 cans After 9 days – 18 cans 1. Complete the table # of Days (x) 3 4 (fill in the questions marks) # of Cans (y) 6 8 18 # of Days (x) # of Cans (y) = 2 3 2 2 8-2 4 니 2. Is the number of cans of cat food used proportional to the number of days? Explain. 3. How many cans of cat food will Sophie use after 12 days?

The number of cans is proportional to the number of days, because each day it uses 2 c

A simple random sample of 5 months of sales data provided the following information:

Month: 1 2 3 4 5

Units Sold: 97 110 89 97 92

a. Develop a point estimate of the population mean number of units sold per month.

b. Develop a point estimate of the population standard deviation (to decimals).

Using it's concepts, the **point estimates **for the population are given as follows:

**a)** Mean: 97 units sold per month.

**b)** Standard deviation: 16.06 units sold per month.

In the context of this problem, the 5 **observations **are given as follows:

97, 110, 89, 97, 92.

Hence the **mean **is given by:

M = (97 + 110 + 89 + 97 + 92)/5 = 97.

Considering the mean of 97 found above, the **standard deviation** is given as follows:

[tex]S(X) = \sqrt{\frac{(97 - 97)^2 + (110 - 97)^2 + (89 - 97)^2 + (97 - 97)^2 + (92 - 97)^2}{5}} = 16.06[/tex]

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vector W has its initial point at (2,5) and its terminal point at (-4,-2)

For the given points, vector in **component** **form** equals -6i^ - 7j^ and its **magnitude** is **9.22**

A quantity or phenomena with independent **qualities** for both magnitude and direction is called a **vector**. The term can also refer to a quantity's **mathematical** or **geometrical **representation. Velocity, momentum, **force**, electromagnetic fields, and weight are a few examples of vectors in nature.

Examples of vectors include **displacement**, velocity, acceleration, force, and others that show both the **direction** and the size of a quantity. Vector: The displacement is -4 feet, while the velocity is -40 miles per hour. Negative **displacement** and **velocity** indicate that the object is travelling counterclockwise.

Vector in **component form **-

(-4 -2)i^ + (-2-5)j^

**= -6i^ - 7j^**

Magnitude of the vector equals =

**√(-6)² + (-7)² = √85 = 9.22**

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Complete Question -

Vector w has its initial point at (2, 5) and its terminal point at (-4, -2). Write the vector in component form and find its magnitude.

Write the given equation of a line that passes through two given points (-2,-1) and (0,-5)

**Answer:**

y2-y1 x2-x1

**Step-by-step explanation:**

-5-(-1)

--------

0-(-2)

-4

---

2

-2

----

1

I am stuck on what to do after graphing points A, B and C

Remember that the coordinates are written in the form **(x,y)**. Plot the points with the given coordinates: **A(1,6)**, **B(1,1)** and **C(5,1)**:

Draw a right triangle using the same measures for the legs in order to construct **ΔDEF**, as described below:

In baseball, Ken gets on base 60% of the time he bats. If Ken bats 5 times, how many times did he get on base?

Assuming Ken gets the same percentage as usuall in these 5 times, we can calculated how many times he did get on base by calculating 60% of 5.

To do this we transform 60% into decimal my dropping the percentage sign and dividing it by 100 and then we multiply the decimal by 5:

[tex]\frac{60}{100}\cdot5=0.6\cdot5=3[/tex]So, Ken got on base 3 times.

If ken gets on base 60%, and he bats 5 times then he got on base 3 times

In the game of euchre, the deck consists of the 9, 10, jack, queen, king and ace of each suit. Players are dealt a five card hand.

What is the probability that a player is dealt 4 hearts? =

The **probability** that a player dealt with four **hearts** = 0

**Probability** is defined as the prediction of the occurrence of an event in a stated set.

This can be expressed in proportions that range from **0 to 1**, and they can also be expressed as percentages ranging from 0% to 100%.

From the question given, the **6 sets** include the following;

9, 10, jack, queen, king and ace.

There are no hearts given in the set of the event that occurred, therefore, the **probability** that a player dealt with four hearts = 0.

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A wheel on Ivan's bicycle is 1.1 m in diameter. Ivan races the bicycle for 165 m. How many times does the wheel turn as the bicycle travels this distance?Use the value 3.14 forn. Round your answer to the nearest tenth. Do not round any intermediate steps.

The radius(r) of the wheel is;

[tex]r=\frac{diameter}{2}=\frac{1.1}{2}=0.55m[/tex]The perimeter(P) of the wheel is given by the formula below:

[tex]P=2\pi r=2\times3.14\times0.55=3.454m[/tex]The distance travelled by Ivan is 165m.

So, the number(n) of times the wheel is:

[tex]n=\frac{165}{3.454}=\text{ 47.77}\approx\text{ 47.8}[/tex]**Hence, the correct answer is 47.8 **

Using standard normal table if the area is 0.125 what would the probability be ?

The area under a standard normal distribution, which we get on a standard normal table, is the same as the probability on that area.

Thus if the area is 0.125, **the probability is 0.125, that is, 12.5%**.

joeita sees on her activity tracker that it took her 58 minutes to run 6.25 hours miles assuming she runs at the same pace how far can she run in 40 minutes? round to the nearest hundredth how far can she run in m minutes

In a case whereby joeita sees on her** activity tracker **that it took her 58 minutes to run 6.25 hours miles the** distance** she can she run in 40 minutes is 4.31 miles.

This can be solved by the **cross multiplication** using the rate that given in the question.

We were told that joeita took 58 minutes of her time to run 6.25 hours miles , then to know the distance she can cover within 40 minutes is

58 minutes = 6.25 miles

40 minutes = X miles

Let X be the number of miles she want to cover in 40 minutes

we ca cross multiply the expression above as :

( 40 minutes * 6.25 miles ) = (58 minutes * X miles)

the X = 4.31 miles

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A store sells cat food in 4-pound bags. The cat food cost 2 dollars per pound.

Here is the completed table:

**Number of bags purchased Total weight Total Cost **

1 4 8

2 8 16

3 12 24

4 16 32

5 20 40

What is the total weight and the total cost?One bag of **cat food **weighs 4 pounds. This means that as the bag increases by 1, the weight of the bag increases by 4.

Weight of 1 bag of **cat food = ** 4

Weight of 2 bags of **cat food = ** 4 x 2 = 8

Weight of 3 bags of **cat food = ** 4 x 3 = 12

Weight of 4 bags of **cat food = ** 4 x 4 = 16

Weight of 5 bags of **cat food = ** 4 x 5 = 20

The cost of **cat food **is $2 per pound.

Cost of a **bag **of **cat food **= number of bags bought x weight of one bag x cost per pound

Cost of 1 bag of cat food = 1 x 4 x 2 = 8

Cost of 2 bags of **cat food **= 2 x 4 x 2 = 16

Cost of 3 bags of **cat food **= 3 x 4 x 2 = 24

Cost of 4 bags of **cat food **= 4 x 4 x 2 = 32

Cost of 5 bags of **cat food **= 5 x 4 x 2 = 40

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Use point slope form to write the lines with the given slope and point in slope intercept form.m= -1(-5,-4)

The slope point form is

[tex]y-y1=m(x-x1)[/tex]m is the slope

x1, y1 are the coordinates of a point on the line

The slope of the line is -1

m = -1

point (-5, -4) lies on the line

x1 = -5 and y1 = -4

Let us substitute them in the form above

[tex]y-(-4)=-1(x-\lbrack-5\rbrack)[/tex]Remember (-)(-) = (+)

[tex]y+4=-1(x+5)[/tex]The equation of the line in the slope-point form is **y + 4 = -1(x + 5)**

What is the value of x?

4x=5x-12

Enter your answer in the box.

X=

**Answer:**

12

**Step-by-step explanation:**

First, get all of the x values to one side of the equation so that we can solve for x. One way to do this is subtract 5x from both sides.

Now we have this:

4x - 5x = -12.

Simplify:

-x = -12.

We need positive x, so divide both sides by -1.

x = 12.

Hope this helps! :)

An architect is designing a gazebo which base is a regular dodecagon. At what angle should he cut to frame the base?

**Answer:**

**15**

**Explanation:**

Note that a regular dodecagon is a 12 sided polygon with internal angles that are equal and sides of the same length.

So determine at what angle the architect should cut to frame the base, we have to divide 360 by 12 and divide the result by 2 as seen below;

[tex]\begin{gathered} \frac{360^{\circ}}{12}=30^{\circ}\text{ (degre}e\text{ per corner)} \\ \frac{30^{\circ}}{2}=15^{\circ\text{ }}(angle\text{ to be cut)} \end{gathered}[/tex]**The angle that the architect should cut to frame the base is 15 degrees**

In the lab, Jane has two solutions that contain alcohol and is mixing them with each other. She uses 400 milliliters less of Solution A than Solution B. Solution A is 12% alcohol and Solution B is 20% alcohol. How many milliliters of Solution B does she use, if the resulting mixture has 176 milliliters of pure alcohol?

Using the concept of **volume**, 700 **milliliters** of Solution B was used.

Each thing in **three dimensions **takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its** volume**. It is sometimes referred to as the **object's capacity**.

When dealing with unknowns, the first step is to represent the unknowns using **variables**, draw up **equations** based on the available data, and then solve those equations to account for the unknowns.

**Volumes** of solutions A and B are here which is unknown.

Put these factors in place for us

Let x = the amount of solution A that was mixed in milliliters.

Let y= the amount of solution B that was mixed in milliliters.

The **amount** of volume utilized for A is 400 ml less than the amount used

for B.

This can be expressed mathematically as y - x = 400.

Or,

- x + y = 400 [1]

The ratios of alcohol in A and B are provided to us.

A contains 12% alcohol, hence its real alcohol content is 12% of x ml.

= 0.12x (12% = 12/100 = 0.12)

Similar to A, B has an alcohol content of 0.20x.

If x of A and y of B are combined, the total alcohol by volume is 0.12x + 0.20y.

and it is said that this amount is 176 ml.

Our second equation is therefore set up as 0.12x + 0.20y = 176 [2].

We create an equation containing only the other term by using both equations and removing either the x or y terms.

We should remove the x term from both equations to create a single equation that just contains the y term because the question only asks us to compute the volume of Solution B that was used.

Review the equations now:

- x + y = 400 [1]

0.12x + 0.20y = 176 [2]

x's coefficients should all be the same:

Increase [1] by 0.12

=> -0.12x + 0.12y =

= 0.12 x 400

=> 0.12x + 0.12y = 48 [3]

By adding [2] and [3], the x word is removed.

0.12x + 0.20y = 176+( -0.12x) + 0.12y = 48

0x + 0.32 y = 224

=> 0,32y = 224

Subtract 0.32 from both sides to get[tex]\frac{0.32y}{0.32}[/tex] = [tex]\frac{224}{0.32}[/tex]

==> y = 700

Therefore, 700 cc of Solution B was utilized.

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Gerard compares the offers at two different banks to decide where he should open a savings account. A. Draw a representation to show how much would be in the first savings account if Gerard's initial deposit were d dollars.

**Explanations:**

**Given** the following parameters

An **initial deposit** of Gerard is **"d" dollars**

For the** savings with 5% interest**, the interest on** "d" dollars** will be expressed as;

Get the** total savings plus interest** in the first account

Hence the** $1.05d will be in the first savings account** if Gerard's **initial deposit were d dollars**

For the other account:

Initial deposit = "d" dollars

Interest = $100

Since the** interest will be added to the first deposit,** hence;

**In Tabulated form:**

4x + 6 <2x>-1 x<-1x<2x>2

The given equation is

[tex]4x+6<2[/tex]First, we subtract 6 on each side.

[tex]\begin{gathered} 4x+6-6<2-6 \\ 4x<-4 \end{gathered}[/tex]Then, we divide the inequality by 4.

[tex]\begin{gathered} \frac{4x}{4}<-\frac{4}{4} \\ x<-1 \end{gathered}[/tex]Therefore, the right answer is the second choice. x < -1Write and solve an equation. Do not forget to label your variable or your units

Mr. Thompson weighs 260 pounds and he loses 4 pounds each month.

The equation will be :

**w = 260 - 4m**

where **w** is the weight after **m** months

when w = 220 pounds, the number of months will be :

220 = 260 - 4m

4m = 260 - 220

4m = 40

m = 40/4

m = 10

The answer is **10 months**

The following two right triangles are similar.If side DE = 45, side HI = 36, and side DF = 30, what is the length of side HJ?A)21B)24C)20D)19

SOLUTION:

Step 1:

In this question, we are given the following:

The following two right triangles are similar.If side DE = 45, side HI = 36, and side DF = 30, what is the length of side HJ?

**Step 2:**

**The details of the solution are as follows:**

Since side DE = 45, side HI = 36, and side DF = 30.

Then, the length of side HJ =

[tex]\begin{gathered} Using\text{ Similar triangles, we have that:} \\ \frac{DF}{DE}=\frac{HJ}{HI} \\ Then,\text{ we have that:} \\ \frac{30}{45}=\frac{HJ}{36} \\ cross-multiply,\text{ we have that:} \\ 30\text{ x 36 = 45 x HJ} \\ Divide\text{ both sides by 45, we have that:} \end{gathered}[/tex][tex]HJ=\frac{30\text{ x 36}}{45}[/tex][tex]HJ\text{ = }\frac{1080}{45}[/tex][tex]HJ\text{ = 24 \lparen OPTION B \rparen}[/tex]HELPDetermine the equation of the line shown in the graph:y = −1y = 0x = −1x = 0

in this problem we have a vertical line

The equation of a vertical line is equal to the x-coordinate of the point that passes through it

so

in this case

the equation of the line is

x=-1

help me please......

There is the required **value **would be 6 in the **box**.

The **ratio **is defined as a relationship between two quantities, it is expressed as one **divided **by the other.

Arithmetic operations can also be specified by the subtract, **divide**, and **multiply **built-in functions.

If you are in the partition XY in the **ratio **3 to 4 from point X to point Y

To determine multiply the length of XY.

XY = 14 units then 3/7 of 14

= 3/7 × 14

Apply the **multiplication **operation,

= 42/7

Apply the **division **operation,

= 6

Hence, the required **value **would be 6 in the **box**.

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ERROR ANALYSIS In Exercise 30, describe and correct the error in finding the inverse of the functionf(x)=1/7x^2, x>=0y=1/7x^2x=1/7y^27x=y^2+-√7x=y

Given the function

[tex]\begin{gathered} f(x)=\frac{1}{7}x^2 \\ x\ge0 \end{gathered}[/tex]To find the inverse, we must recall that the domain of the function becomes the range of the inverse function and vice-versa.

We are already given the domain of f, all the real numbers equal or greater than zero.

The domain of the function is exactly the same because x squared is always positive or zero, thus the domain and range of the inverse should be x≥0.

Once we find the inverse function, we'll use this concept.

Step 1: Substitute f(x) for y:

[tex]y=\frac{1}{7}x^2[/tex]Step 2: Swap the variables:

[tex]x=\frac{1}{7}y^2[/tex]Step 3: Solve for y:

[tex]y=\pm\sqrt[]{7x}[/tex]But as said above, the range of this function cannot include the negative numbers, thus the inverse function is:

[tex]f^{-1}(x)=\sqrt[]{7x}[/tex]Which expression is equivalent to the given expression?2x^2 – 14r + 24A. (2x – 12) (x - 2)B. 2(x – 3)(x – 4)C. 2(x - 5)(x - 2)D. 2(x – 8) (x + 3)

Step 1: We have the following expression:

[tex]2x^2\text{ }-\text{ 14x + 24}[/tex]Step 2: Fon finding the equivalent expression, we have to factoring the polynomial, this way:

[tex]2(x^2\text{ - 7x + 12)}[/tex]Step 3: Now we have to find two integer numbers that the result of adding them is - 7 and the result of multipliying them is 12

First number: -4

Second number: -3

Therefore, we have now:

2 (x - 4) (x - 3)

Step 4

Complete the instructions to move from one point to another along the line

y = 2/3x + 1

___ ___ unit(s), then right 9 units.

**Answer:**

**Step-by-step explanation:**

the equation is written in slope intercept form

y= mx + b with m= slope and b= y-intercept

so in your equation

y=2/3x + 1,

the slope is 2/3 and the y-intercept is (0,1)

slope is also known as rise/run

so to move from one point to another, starting at (0,1) (since you know that point is on the line) you would move up 2 units and to the left 3 units.

hope this helped!

The cafeteria prepares 80 meals a day for students if 3/8 of the meals are vegetarian, how many meals are are not vegetarian?

Meal prepared a day = 80 meals

Vegetarian meals will be

[tex]\text{vegetarian}=\frac{3}{8}\times80=\frac{240}{8}=30[/tex]Non vegetarian meals = 80 - 30 = **50 meals**

Dm³ + n = rwhat does D equal?

[tex]Dm^3+n=r[/tex][tex]Dm^3=r-n[/tex][tex]D^{}=\frac{r-n}{m^3}[/tex]

A printer takes 5 seconds to print 3 pages. How many pages can it print in 125 seconds? Enter the answer in the box.

**Answer:**

75?

**Step-by-step explanation:**

**Answer:**

75

**Step-by-step explanation:**

3 divided by 5

0.6x125

PLEASE HELP!!!!! Answer two questions about Equations AAA and BBB:A. x/4 + 1 = -3B. x + 4 = -121) How can we get Equation BBB from Equation AAA?Choose 1 answer:(Choice A)Rewrite one side (or both) using the distributive property(Choice B)Rewrite one side (or both) by combining like terms(Choice C)Multiply/divide only one side by a non-zero constant(Choice D)Multiply/divide both sides by the same non-zero constantBased on the previous answer, are the equations equivalent? In other words, do they have the same solution?Choose 1 answer:(Choice A)Yes(Choice B)No
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