Evaluate Square root b2 - 4ac when a = 1, b = -6, and c = 9.

Answers

Answer 1

Answer:

[tex]x=3[/tex]


Related Questions

Numbers from 1 to 50 Find the probability of choosing
numbers with 4 in tens places.

Answers

Answer: 1/5

Step-by-step explanation:


There are 10 numbers, out of 50, which have a 4 in their tens place: 40, 41, 42, 43, 44, 45, 46, 47, 48, and 49.

Therefore our desired probability is 10/50 or 1/5.

New topic really confused

Answers

The cost given shows that the amount left is £12.

How to illustrate the information?

From the information given, it was stated that the person saved £60 and spent £42 on coat and £6 on scarf

The amount that the person has left will be:

= £60 - £42 - £6

= £12

In conclusion, the person has £12 left.

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Someone please help I’m lost

Answers

It’s because it’s intersecting so WXY and ZYX are congruent

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

There is one angle and an adjacent side of the triangle given equal to corresponding angle and side of the other triangle and if we observe the figure we can see that there's also a adjacent side XY common in both the Triangles.

Hence, the two triangles are congruent by SAS congruency criteria.

[tex] \qquad \large \sf {Conclusion} : [/tex]

SAS criteria

can anyone help me solve these questions, please

Answers

Step-by-step explanation:

8.√128/√2

ans √64

10.3√81

3√3*3*3*3(find factor)

3 √3(this is cube root therefore we kept one out of three then we kept remaining inside of root.this is surds because one factor is inside the surds if factor is not remaining inside the surds then this is not surds)

Solve for m. 3/4m>−12 m>−16 m<−16 m>−9 m<−9

Answers

Answer: m > -16

Step-by-step explanation:

[tex]\frac{3}{4}m > -12\\\\m > -\frac{4}{3}(12)=-16[/tex]

The volume of a prism with side lengths measured in millimeters is 20. How could this measurement be written? Check all that apply.

Answers

The unit measurement of the a volume in mm is mm³(millimetres cube.)

How to find volume ?

Volume is is defined as the space occupied within the boundaries. The objects are usually solid objects.

The volume of a 3 dimensional figure is the product of the base area and the height.

Therefore, the units of volume is measured in cubic units.

The volume of a prism with side lengths measured in millimetres is 20.

Therefore, the measurement can be represented as follows:

20 mm³

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jerome wants to bake two batches of muffins. He can bake two batches of chocolate chip (C), two batches pumpkin, or one batch of each.

Answers

The situation presented can be represented using the following letters CC, CP, PC, and PP.

How many combinations are possible in this situation?

The possible combinations are:

Two batches of chocolate chip or CC.Two batches of pumpkin or PP.One batch of chocolate chip and another of pumpkin of CP.One batch of pumpkin and another of chocolate chip or PC.

Based on this, the option that represents the situation is:

CC, CP, PC, and PP.

Note: This question is incomplete; here is the missing section:

What is the sample space of the event described above?

Answer choices:

a. CC, CP, PC, PP

b. CC, PP

c. CC, CP, PC

d. C, P

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WILL GIVE BRAINLIEST!!! If [tex]\frac{a}{b} =2[/tex] what is the value of [tex]\frac{a}{a-b}[/tex]?


Could the answer be D) or is it C)?


A) -2

B) 1

C) 2

D) It cannot be determined from the given information

Answers

Considering the given proportion, the value of [tex]\frac{a}{a - b}[/tex] is:

C) 2

What is a proportion?

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The proportion between a and b is given by:

a/b = 2.

Then:

a = 2b.

The expression is:

[tex]\frac{a}{a - b} = \frac{2b}{2b - b} = \frac{2b}{b} = 2[/tex]

Hence option C is correct.

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Plot each point that is a horizontal distance of 6 and a vertical distance of 2 from the origin.

Answers

The points that are a horizontal distance of 6 and a vertical distance of 2 from the origin are (6, 2), (-6, 2), (6, -2), (-6, -2)

What are points?

Points are undefined terms in geometry, however they are used to represent the coordinate or location of items in a coordinate plane

How to plot the point?

The features of the point are given as:

Horizontal distance = 6

Vertical distance = 2

The above means that:

x = 6

y = 2

The points are then represented as:

(x, y) = ±(x. y)

So, we have

(x, y) = ±(6, 2)

When the above equation is expanded, we have

(x, y) = (6, 2), (-6, 2), (6, -2), (-6, -2)

Next, we plot the points on a coordinate plane

See attachment for the graph of the plane

Hence. the points that are a horizontal distance of 6 and a vertical distance of 2 from the origin are (6, 2), (-6, 2), (6, -2), (-6, -2)

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Which expression is equivalent to (z−3)4z−6 for all values of z where the expression is defined?

Answers

The equivalent of the expression [ (z−3)4z−6 ] is 4z² - 12z - 6.

What is the equivalent of the expression?

Given the expression; (z−3)4z−6

First, we apply distributive property.

(z−3)4z−6

(z−3)4z−6

z(4z) - 3(4z) - 6

We remove the parentheses

4z² - 12z - 6

Therefore, the equivalent of the expression [ (z−3)4z−6 ] is 4z² - 12z - 6.

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What is 72 decreased by 32%

Answers

Hello,

What is 72 decreased by 32%

72 × (1 - 32%)

= 72 × (1 - 32/100)

= 72 × (1 - 0,32)

= 72 × 0,68

= 48,96

Answer:225

Step-by-step explanation:

help me with this pls and ty

Answers

Answer:

It is the second answer.

Step-by-step explanation:

When numbers with the same base are multiplied, you add the bases.

1/2 + 3/4 is the same as

2/4 + 3/4 = 5/4

So now we have 2 ^5/4^2.  When we have a power raised to a power.  We multiply the powers.

5/4(2)

(5/4(2/1) = 10/4 = 5/2.  The second answer is the same way to describe

2^(5/2)

The earth travels around the sun at about 1,110 miles per minute.

About how many miles does the earth travel around the sun per second?

Drag and drop the answer into the box.

The earth travels around the sun about ___ Response area miles per second.

Answers

Answer:

18.5 miles

Step-by-step explanation:

the Sun at an average speed of 67,000 mph, or 18.5 miles a second.

what percentage was the price of the shirt reduced

Answers

6%, 15-9 is 6, use the difference

You deposit $400 each month into an account earning 8% interest compounded monthly. Round to the nearest cent as needed. a) How much will you have in the account in 35 years? $ b) How much total money will you put into the account? $ c) How much total interest will you earn? $

Answers

If I deposit $400 each month into an account earning 8% interest compounded monthly, I will have $6,517 in my account in 35 years. The total money that I will put into the account is $168,000. I will earn a total compound interest of $6,117.

Calculating the Sum of Money in 35 years

Given information is as follows,

Principal, P = $400

Rate = 8%

Time, T = 35 years

n = 12 (Compounded monthly)

The amount for compound interest is given as,

A = [tex]P\frac{(1+\frac{R}{n} )^{nT} -1}{R/n}[/tex]

A = [tex]400\frac{(1+\frac{0.08}{12} )^{12.35} -1}{0.08/12}[/tex]

A = 6,517.02

A = $6,517 (to the nearest cents)

Calculating the Amount Put in Account

Since, $400 is deposited every month for 35 years,

Amount Put in 35 years for this compound interest =$400 × 12 × 35

= $168,000

Calculating the Compound Interest

A = P + CI

Thus, the compound interest is given by,

CI = A - P

CI = 6517 - 400

CI = $6,117

I will earn a total interest of $6,117

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Two angles in a triangle have measures of 42 and 82. (Degrees)

What is the measure of the third angle?

Answers

Answer:

angles of the triangle are equal 180

so 42+82=124

180-124=56

so the answer is 56

Step-by-step explanation:

PLEASE HELP PLEASE I DONT KNOW THIS QUESTION AND IVE BEEN STUCK ON THIS FOR A DAY​

Answers

A is -5 and B is 1 so yeah

Answer:

A = -5

B = 1

Step-by-step explanation:

Hello!

You simply plug in the given x-value into the equation to find the missing y-value.

Solve for A

Plug in -1 for x into y = 2x - 3.

y = 2x - 3y = 2(-1) - 3y = -2 - 3y = -5

Solve for B

Plug in 2 for x into y = 2x - 3.

y = 2x - 3y = 2(2) - 3y = 4 - 3y = 1

Jenny's lunch account has $10 in it. She buys lunch three days in a row and spends $2.50, $2, and $2.75. On the fourth day, she
deposits $10 before buying lunch for $3. What is Jenny's balance after buying lunch on the fourth day?

Answers

10-(2.5+2+2.75)+10-3 = 9.75

$9.75

Given the information
, we know that for the first 3 days, she spends a total of $7.25. On the fourth day, she deposits $10 before buying lunch for $3.

This means she had $20, but spent $10.25. $20-$10.25=$9.75 is the amount she has in her account.

At the movie theater child admission is $5.20 and adult admission is $9.90.. On Friday 163 tickets were sold for a total sales of $1303.50. How many adult tickets were sold that day?

Answers

The number of tickets sold on Friday were 66 children tickets and 97 adult tickets.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the number of children and y represent the number of adult, hence:

5.2x + 9.9y = 1303.5     (1)

Also:

x + y = 163    (2)

From both equations:

x = 66, y = 97

The number of tickets sold on Friday were 66 children tickets and 97 adult tickets.

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George plans to cover his circular pool for the upcoming winter season. The pool has a diameter of 20 feet and the cover extends 12 inches beyond the edge of the pool. A rope runs along the edge of the cover to secure it in place.
A. What is the area of the pool cover?
B. What is the length of the rope?

Answers

For the circular cover we have:

A) The area is 379.94 ft²

B) The length of the rope must be 68.2 ft

How to get the area of the cover?

Remember that the area of a circle of radius R is given by the formula:

[tex]A = pi*R^2[/tex]

Where pi = 3.14

In this case, the diameter of the pool is 20ft, then the radius is:

R = 20ft/2 = 10ft

And it must extend 12 inches beyond, then the radius of the cover must be:

R = 10ft + 12in

Now, we know that 1ft = 12 in, then we can rewrite the radius as:

R = 10ft +1ft = 11ft

Then the area of the cover is:

[tex]A = 3.14*(11ft)^2 = 379.94 ft^2[/tex]

B) now we want to get the length of the rope, we know that the rope runs along the cover, then the length of the rope must be equal to the circumference of the cover.

Remember that the circumference of a circle of radius R is:

[tex]C = 2*pi*R[/tex]

Then the length of the rope will be:

[tex]C = 2*3.14*11ft = 68.2ft[/tex]

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If m<1=72 then find the value of m<2

A.18
B.108
C.72
D.144

Answers

U can use both of ways to solve this question

If f (7) = 22, then
f(f-1(22)) = [?]

Answers

Answer: 22

Step-by-step explanation:

[tex]f(f^{-1}(x))=f^{-1}(f(x))=x[/tex]

Need help ASAP
I will mark Brainleist

Need help part A, B and C

Roller Coaster Crew
Ray and Kelsey have summer internships at an engineering firm. As part of their internship, they get to assist in the planning of a brand new roller coaster. For this assignment, you help Ray and Kelsey as they tackle the math behind some simple curves in the coaster's track.

Part A
The first part of Ray and Kelsey's roller coaster is a curved pattern that can be represented by a polynomial function.
1. Ray and Kelsey are working to graph a third-degree polynomial function that represents the first pattern in the coaster plan. Ray says the third-degree polynomial has four intercepts. Kelsey argues the function can have as many as three zeros only. Is there a way for the both of them to be correct? Explain your answer.

2. Kelsey has a list of possible functions. Pick one of the g(x) functions below and then describe to Kelsey the key features of g(x), including the end behavior, y-intercept, and zeros.
g(x) = (x + 2)(x − 1)(x − 2)
g(x) = (x + 3)(x + 2)(x − 3)
g(x) = (x + 2)(x − 2)(x − 3)
g(x) = (x + 5)(x + 2)(x − 5)
g(x) = (x + 7)(x + 1)(x − 1)

3. Create a graph of the polynomial function you selected from Question 2.

Part B
The second part of the new coaster is a parabola.

4. Ray needs help creating the second part of the coaster. Create a unique parabola in the pattern f(x) = (x − a)(x − b). Describe the direction of the parabola and determine the y-intercept and zeros.

5. Create a graph of the polynomial function you created in Question 4.

Part C
6. Now that the curve pieces are determined, use those pieces as sections of a complete coaster. By hand or by using a drawing program, sketch a design of Ray and Kelsey's coaster that includes the shape of the g(x) and f(x) functions that you chose in the Parts A and B. You do not have to include the coordinate plane. You may arrange the functions in any order you choose, but label each section of the graph with the corresponding function for your instructor to view.

Answers

Answer:

Part A

1. A third degree polynomial has exactly three zeros. This is because its highest power (or degree) is 3. Ray would only be correct in saying that a polynomial can have 4 zeros if it is a 4th degree polynomial. Since in this case, a 4rd degree polynomial is being discussed, Kelsey is correct.

2. Function chosen: g(x) = (x + 2)(x - 1)(x - 2)

End behaviour: x —> ∞, g(x) —> ∞

                         x —> - ∞, g(x) —> -∞

Zeros/x intercepts of the function: -2, 1, 2

y intercept: g(x) = (x + 2)(x - 1)(x - 2)

                   g(x) = (0 + 2)(0 - 1)(0 - 2)

                   g(x) = (2)(-1)(-2)

                   g(x) = 4

3. See Graph 1

Part B

4. f(x) = (x + 5)(x + 3)

Direction: opens upward

Zeros/x intercepts: -5, -3

y intercept: 15

5. See graph 2

Part C

You can draw the roller coaster yourself using the graphs below

You make a scale drawing of a tree using the scale 5 inches. = 27 feet. If the tree is 67.5 feet tall, how tall is the scale drawing?

Answers

Answer:

12.5 inches

Step-by-step explanation:

We use proportion to calculate the scale drawing

27 feet = 5 inches, so

67.5 feet = more inches (we know that it would be bigger than 5 inches)

We then put the bigger number on top and crossmultiply by saying:

67.5 over 27 × 5

Your answer should come out as 12.5 inches.

3(1-5x)=2(3x+1) find the solution set

Answers

Answer:

1/21

Step-by-Step Explanation:

Let's solve your equation step-by-step.

3(1−5x)=2(3x+1)

Step 1: Simplify both sides of the equation.

3(1−5x)=2(3x+1)

(3)(1)+(3)(−5x)=(2)(3x)+(2)(1)(Distribute)

3+−15x=6x+2

−15x+3=6x+2

Step 2: Subtract 6x from both sides.

−15x+3−6x=6x+2−6x

−21x+3=2

Step 3: Subtract 3 from both sides.

−21x+3−3=2−3

−21x=−1

Step 4: Divide both sides by -21.

-21x/-21=-1/-21

x=1/21

[tex]\boldsymbol{\sf{3(1-5x)=2(3x+1)}}[/tex]

Reorder terms

[tex]\boldsymbol{\sf{3(-5x+1)=2(3x+1) }}[/tex]

Distribute

[tex]\boldsymbol{\sf{-15x+3=2(3x+1) }}[/tex][tex]\boldsymbol{\sf{-15x+3=6x+2 }}[/tex]

Subtract 3x from both sides.

[tex]\boldsymbol{\sf{-15x+3-3=6x+2-3 }}[/tex]

Simplify

[tex]\boldsymbol{\sf{-15x=6x+1}}[/tex]

Subtract 6x from both sides.

[tex]\boldsymbol{\sf{-15x-6x=6x-1-6x }}[/tex]

Simplify

[tex]\boldsymbol{\sf{-21x=-1 }}[/tex]

Divide both sides by the same factor

[tex]\boldsymbol{\sf{\dfrac{-21x}{-21}=\dfrac{-1}{-21} }}[/tex]

Simplify

[tex]\boxed{\boldsymbol{\sf{x=\frac{1}{21} }}}[/tex]

NO LINKS!! Please help me with this problem​

Answers

[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

The given vertex and Focus are of a vertical parabola having an opening downward as the focus is in downward direction as the vertex.

Focus of the parabola can be written as :

[tex]\qquad \sf  \dashrightarrow \: (h ,k+ a )[/tex]

where, h and k are coordinates of vertex

so,

k + a = -2

-1 + a = -2

a = -1

So, the equation of parabola can be written as :

[tex]\qquad \sf  \dashrightarrow \: (x - h) {}^{2} = 4a(y - k)[/tex]

plug in the values ~

[tex]\qquad \sf  \dashrightarrow \: (x - 1) {}^{2} = 4(- 1)(y + 1) {}^{} [/tex]

[tex]\qquad \sf  \dashrightarrow \: (x - 1) {}^{2} = - 4(y + 1)[/tex]

Answer:

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

Step-by-step explanation:

Standard form of a parabola with a vertical axis of symmetry:

[tex](x-h)^2=4p(y-k) \quad \textsf{where}\:p\neq 0[/tex]

Vertex = (h, k)Focus = (h, k+p)Directrix: y = (k-p)Axis of symmetry: h = kIf p > 0, the parabola opens upwards, and if p < 0, the parabola opens downwards.

Given:

vertex = (1, -1)focus = (1, -2)

Comparing with the formulas:

⇒ h = 1

⇒ k = -1

⇒ k + p = -2  ⇒ -1 + p = -2  ⇒ p = -1

Substituting the values into the formula:

[tex]\implies (x-1)^2=4(-1)(y-(-1))[/tex]

[tex]\implies (x-1)^2=-4(y+1)[/tex]

Which is true regarding the system of equations?

6 x + 2 y = 46. 3 x + y = 23.
The system results in a false statement.
The system results in an intersection at one point.
The system results in parallel lines.
The system results in a true statement because they are the same line.

Answers

Answer:

they are the same line

Step-by-step explanation:

if you divide the first line by 2 you'll get:

2(3x)+2y=2(23)===> 3x+y=23

waht is the x^2 + 10 = 0

Answers

Answer:

x = ±√10i (i outside the radical), or approximately ±3.62i, or no solution depending on your class.

Step-by-step explanation:

x^2 + 10 = 0

x^2 = -10

x = ±√-10

x = ±√10i (i outside the radical), or approximately ±3.62i.

The solution is not real.

If you meant x^2 - 10 = 0 then x = ±√10 or approximately ±3.62. This solution is real.

Solve the system of equations.
y = 2x+ 3
y=x^2+3x+3

Answers

Answer:

(0,3)

(-1,1)

Step-by-step explanation:

Hello!

Since both equations are equal to y, we can set the right-hand side of the equations equal to each other.

[tex]y = 2x + 3\\y = x^2 + 3x + 3[/tex][tex]y = y[/tex][tex]2x + 3 = x^2 + 3x + 3[/tex]

Solve for x[tex]2x + 3 = x^2 + 3x + 3[/tex][tex]0 = x^2 + x[/tex][tex]0 = x(x + 1)[/tex][tex]x = 0, x =-1[/tex]

X can either be 0 or -1. Remember, a solution to a system is not complete without a y-value. Plug in 0 and -1 for x in the first equation, and find the corresponding y-values.

[tex]y = 2(0) + 3\\y = 3[/tex]

And

[tex]y = 2(-1) + 3\\y = -2 + 3\\y = 1[/tex]

So the solutions to the system are (0,3) and (-1,1)

Complete the following table given this information: (Do not round intermediate calculations.) Cost of machine $ 94,000 Residual value $ 4,000 Useful life 5 years Estimated units machine will produce 100,000 Actual production: Year 1 60,000
Year 2 15,000 Use MACRS table.
Straight line method?
Units of production?
Declining balance?
MACRS (5-year class)

Answers

The completion of the following table under different depreciation methods is as follows:

Depreciation Expense:

Method                           Year 1                     Year 2

Straight line                   $18,000                 $18,000

Units of production      $54,000                 $13,500

Declining balance        $37,600                $22,560

MACRS (5-year class)   $18,800                $30,080

Data and Calculations:

Cost of machine = $94,000

Residual value = $4,000

Depreciable value = $90,000 ($94,000 - $4,000)

Estimated useful life = 5 years

Depreciation expense:

Straight-line method = $18,000 ($90,000/5)

Estimated units of produciton = 100,000

Unit depreciation rate = $0.90

Actual production   Depreciation

Year 1 = 60,000      $54,000 ($0.90 x 60,000)

Year 2 = 15,000      $13,500 ($0.90 x 15,000)

Declining Balance:

Year 1 = $37,600 ($94,000 x 40%)

Year 2 = $22,560 ($94,000 - $37,600) x 40%

MACRS:

Year 1 = $18,800 ($94,000 x 20%)

Year 2 = $30,080 ($94,000 x 32%)

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