Help with Pre Calculus

Answers

Answer 1

Answer:

The first option

Step-by-step explanation:

The domain of a rational function should be all real numbers except for when the denominator is equal to 0. To find when the denominator is equal to 0 you simply need to find the zeroes of the denominator... but in this case you can do that through factoring and using the quadratic equation.

So first step is going to be to factor out the GCF, which in this case is x. This gives you the equation. [tex]x(2x^2-x-15)[/tex]. So one of the zeroes is when x=0. Now to find the other two zeroes you can use the quadratic equation which is [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\[/tex]. So to find the other zeroes you simply plug the values in. a=2, b=-1, c=-15

[tex]x=\frac{-(-1)\pm\sqrt{(-1)^2-4(2)(-15)}}{2(2)}\\\\x=\frac{1\pm\sqrt{1-4(2)(-15)}}{4}\\\\x=\frac{1\pm\sqrt{121)}}{4}\\\\x=\frac{1\pm11}{4}\\\\x=\frac{12}{4}\\x=3\\\\x=\frac{-10}{4}\\x=-\frac{5}{2}[/tex]

Related Questions

Linda purchased a birthday gift from Bed Bath and Beyond for her mother. After applying the
coupon below Linda received a $12.25 discount off her purchase. What was the price of the
gift before and after the discount?

PLS HELP SOLVE !!!

Answers

Answer:

Before discount = $61.25

After discount = $49.00

Step-by-step explanation:

Given information:

Discount = $12.25Coupon = 20%

The price of the gift before the discount is 100%.

If the $12.25 discount was 20% of the purchase price, then:

⇒ original price (before discount) = (12.25 / 20) × 100 = $61.25

To find the price after the discount, simply subtract the discount from the found original price:

⇒ $61.25 - $12.25 = $49.00

Conclusion

Before discount price = $61.25After discount price = $49.00

pls help
B (20,25) (12,9)
C (150,125) (96,64)
D ( 25, 150) (16,96) (9,54)
E (5,125) (4,64)

Answers

Answer:

Side Length and Perimeter of One Face

Step-by-step explanation:

See attached image.

If you can help with this I would be thankful

Answers

The inverse of the function will be [tex]f(x) ^{-1}= 2x - 12\\[/tex]. option C is correct.

What is the inverse of a function?

Suppose that the given function is

[tex]f:X\rightarrow Y[/tex]

Then, if function 'f' is one-to-one and onto function (a needed condition for inverses to exist),

then, the inverse of the considered function is

[tex]f^{-1}: Y \rightarrow X[/tex]

The function is given as

[tex]f(x) = \dfrac{1}{2} x - 6\\\\[/tex]

The inverse of the function will be

[tex]f(x) ^{-1}= 2x - 12\\[/tex]

Therefore, option C is correct.

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The surface area of the triangular prism is
.

Answers

Answer:

576 m

__________________________________________________________ The surface area of the triangular prism is (Perimeter of the base × Length of the prism) + (2 × Base Area) = (S1 + S2+ S3)L + bh

For this question,
you know that the perimeter of the base is 6+10+8 which is 24.
and the length of the prism is 22,
so (22x24) + Base Area which is (6x8)/2-> 24x2
(22x24)+(24x2)= 528 + 48 = 576
so your answer is 576
__________________________________________________________

Hope this helped!

You have a dog walking business. You charge based on the weight of the dogs. For a 45-minute walk your prices are:

For dogs that weight 0 up to 15 lbs. you charge $5.00.
For dogs between 15 lbs. and 45 lbs. you charge $7.00
Dogs over 45 lbs. you charge $9.00.

Answer the following questions:
1. If a customer has a 6 pound Chihuahua how much would you charge?
2. If a customer has a 65 pound Labrador how much would you charge?
3. Define the variables:
4. Write a piecewise function for dog walking business, including the conditional statement for the variables.
5. Graph the function.

PLEASE ANSWER ALL FIVE PLEASEEAAAA

Answers

1: $5
2:$9
3. Variables and letters and symbols that represent unknown values

What is the measure of x?
16
x=[?]
Give your answer in simplest form.

Answers

Answer: [tex]8\sqrt{5}[/tex]

Step-by-step explanation:

By the geometric mean theorem,

[tex]\frac{y}{16}=\frac{4}{y}\\\\y^{2}=64\\\\y=8[/tex]

Thus, by the Pythagorean thoerem,

[tex]8^2 +16^2=x^2\\\\320=x^2\\\\x=\boxed{8\sqrt{5}}[/tex]

Determine the relationship between the two triangles and whether or not they
can be
proven to be congruent.

Answers

Answer: These ARE congruent to each other.

Step-by-step explanation: Do you see the ''tick marks?'' They both have 1 set of 2, and 1 set of 1. If that makes sense. They also have a "angle" in one of their acute angles.

* GEOMETRY

please help me show the work for number 15!!

Answers

Answer: (-2, -4)

Step-by-step explanation:

The translation that maps point A onto point B must also map point D onto point C.

Point A maps onto point B after a translation 8 units right and 6 units up, so point C maps onto point D after a translation 8 units left and 6 units down.

Thus, D has coordinates (-2, -4)

Which two numbers does √√61 lie between on a number line? O 7.7 and 7.8 O 7.8 and 7.9 O 7.9 and 8.0 Stm O 8.0 and Which two numbers does √√61 lie between on a number line ? O 7.7 and 7.8 O 7.8 and 7.9 O 7.9 and 8.0 Stm O 8.0 and 8.1

Answers

Answer:

B) 7.8 and 7.9

Step-by-step explanation:

Taking the square root of 61, we can conclude that the decimal form is 7.810, which falls between the range of 7.8 and 7.9

Answer:

√61 lie between 7.8 and 7.9

probability of hitting the shaded area

Answers

The probability of hitting the shaded area is 0.64

How to determine the probability?

The diameters are given as:

D = 10

d = 6

The shaded area is calculated as:

Shaded = π((D/2)² - (d/2)²)

So, we have:

Shaded = π((10/2)² - (6/2)²)

Evaluate the exponents

Shaded = 16π

The area of the big circle is calculated as:

Area = π(D/2)²

So, we have:

Area = π(10/2)²

Evaluate the exponents

Area = 25π

The probability of hitting the shaded area is:

P = 16π/25π

Evaluate

P = 0.64

Hence, the probability of hitting the shaded area is 0.64

Answers

Answer:

D. 11

Step-by-step explanation:

Take the two horizontal line measurements and subtract them.

13-9=4

That is how much it changed between these two numbers. Since x is exactly halfway between, simply divide 4 and 2.

4/2=2

Now, add that to 9 or subtract it from 13.

9+2=11

13-2=11.

Hope this helps!

If not, I am sorry.

Answer:

D. 11

Step-by-step explanation:

Since segment AC bisects segments ED and BF, the length of AC is the average of the lengths of EB and DF.

AC = x = (EB + DF)/2 = (9 + 13)/2 = 22/2 = 11

Answer: D. 11

help please i need answer ASAP

Answers

If the result is reflected over x-axis and vertically stretched by a factor of 5, the result will be g(x) = -5(x - 1)²

Transformation of functions

Transformation is a way of changing the position of an object o the xy plane. Given the parent function expressed as

f(x) = x^2

If the function is shifted to the left by unit, then we will have h(x) = (x - 1)²

If the result is reflected over x-axis and vertically stretched by a factor of 5, the result will be g(x) = -5(x - 1)²

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Find the area of the shaded regions. Give your answer as a completely simplified exact value in terms of pi (no approximations)

Answers

Answer:

A = 27π cm²

Step-by-step explanation:

the area (A) of the sector is calculated as

A = area of circle × fraction of circle

the central angle of the shaded sector = 360° - 90° = 270° , then

A = πr² × [tex]\frac{270}{360}[/tex]

= π × 6² × [tex]\frac{3}{4}[/tex]

= 36π × [tex]\frac{3}{4}[/tex]

= 9π × 3

= 27π cm²

Hi! Hope you're having a good day. So, there's a problem I had gotten wrong while I was preparing for the ACT, however, I didn't know how to answer the question to begin with. Can someone give me a step-by-step explanation on how this problem is solved correctly? (Picture included). Inside of the picture I included the answer I chose and the correct answer, could you also explain what I had done wrong? I used the FOIL method, but now I think that was incorrect to begin with. I also reattempted to do what I had done before, but each time I get a different answer, if you can help that'd be fantastic! :)

Answers

Answer:

[tex]3a^2+12a+12[/tex]

Step-by-step explanation:

first, you have to plug in x = a+2 into the function, which would look like:

[tex]f(a+2) =3(a+2)^2[/tex]

then, you can first simplify [tex](a+2)^2[/tex]. to do this, use the rule [tex](a+b)^2 = a^2 +2ab + b^2[/tex], so it would be [tex]a^2+(2*a*2)+2^2 = a^2 + 4a + 4[/tex]

this means your new equation is:

[tex]3(a^2+4a+4)[/tex]

you can then distribute the 3:

[tex]3*a^2+3*4a + 3*4 = 3a^2+12a+12[/tex]

let me know if there's anything you want me to clarify!

According to the property
below?
√30
OA. 25
OB. -√5
O C. 5
OD. -5
OE. √5
Vo = √ which choice is equivalent to the quotient
4

Answers

Answer:

√30/6 = √5

The correct answer would be E

The value of the expression √30/√6 is √5, option E is correct.

What is Number system?

A number system is defined as a system of writing to express numbers.

The given property is √a/√b = √(a/b)

Now we have to find the equivalent to the quotient √30/√6

By the given property let us plug in a as 30 and b as 6

√30/√6

= √(30/6)

When we simplify the fraction inside the root we get 5

= √5

Hence, the value of the expression √30/√6 is √5, option E is correct.

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Identify the domain of the given function.

Answers

Answer:

choice C

Step-by-step explanation:

x could be any number except -1.

Cause for x=-1 the denominator becomes undefined.

Solve for x: √x + 3-4=7

Answers

Answer:

x = 64

Step-by-step explanation:

Solve for x: √x + 3-4=7

√x + 3-4=7

= √x + 1 = 7

= √x = 7 + 1

= √x = 8

= (√x)² = 8²

x = 64

A line segment has endpoints Q(-16, -12) and R(21, -8).
What is the midpoint of the line segment?
02¹-201

Answers

Answer:

(2.5, - 10 )

Step-by-step explanation:

given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )

here (x₁, y₁ ) = (- 16, - 12 ) and (x₂, y₂ ) = (21, - 8 ) , then

midpoint = ( [tex]\frac{-16+21}{2}[/tex] , [tex]\frac{-12-8}{2}[/tex] ) = ( [tex]\frac{5}{2}[/tex], [tex]\frac{-20}{2}[/tex] ) = (2.5, - 10 )

Answer: c - (2 1/2 - 10)

Step-by-step explanation:

The events "male” and "buys lunch” are not independent because
P(buys lunch | male) = P(male) = 0.4.
P(male | buys lunch) = P(male) = 0.3.
P(buys lunch | male) = 0.3 and P(male) = 0.4.
P(male | buys lunch) = 0.4 and P(male) = 0.3.

Answers

The events "male” and "buys lunch” are not independent because P(male | buys lunch) = 0.4 and P(male) = 0.3.

Complete question

James surveyed people at school and asked whether they bring their lunch to school or buy their lunch at school more often. The results are shown below.

Bring lunch: 46 males, 254 females

Buy lunch: 176 males, 264 females

The events "male" and "buys lunch" are not independent because

How to determine the probability?

The number of male students is:

Male = 46 + 176

Male = 222

The number of female students is:

Female = 254 + 264

Female = 518

The total student is:

Total = 222 + 518

Total = 740

Next, calculate the probability of selecting a male student

P(Male) = 222/740

P(Male) = 0.3

Of all the 440 that buy lunch, 176 are male,

So, we have:

P(male | buy lunch) = 176 / 440

P(male | buy lunch) = 0.4

Because

P(male | buy lunch) and P(male) are not equal.

Then, the events "male” and "buys lunch” are not independent

Answers

(a) 10% of x = 9

x = 9 ⋅ (100/10)

x = 90 kg

(b) 12% of x = 12/100 of 90

Weight she lost = 10.8

Her new weight = 90 - 10.8

= 79.2kg

a) 9x 10=90
b) 10%=9 so 2%= 1.8
Now add 9 and 1.8 to get 10.8kg as your answer

Instructions: Rewrite the equation in Slope-Intercept Form. y−2=−2/5(x−5)

Answers

The equation in Slope-Intercept Form is y = -2/5 x + 4.

We have given that,

y−2=−2/5(x−5)

We have to rewrite the equation in Slope-Intercept Form.

What is the slope-intercept form of the line?

slope-intercept form is y = mx + b

for equation y - 2 = -2/5 (x - 5) we need to simplify/rearrange

so y - 2 = -2/5 x + -2/5 (-5)

= -2/5 x + 2

=> y = -2/5 x + 4

This line has a gradient of -2/5 (goes down 2 units and across 5 units) and a y-intercept of 4 so passes through the point (0,4).

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(5+4) +10=5+(4+10)
A. True
B. False

Answers

Answer:

A. True

Step-by-step explanation:

One of the ways to check this is solving each side of the equation.

(5+4)+10=5+(4+10)

Remember PEMDAS.

Parenthesis first.

(9)+10=5+(14)

Now, you can drop the parenthesis and add the numbers together.

9+10=19

5+14=19

19=19

This is a true statement.

Hope this helps!

If not, I am sorry.

true as they both add up to 19

Find the value of x in each case:

Answers

x = 90°

2x = 180°

Step-by-step explanation:

angle VTS= angle TSR (alternate angle)

now in ∆TRS,

2x + x + x = 360° (angle sum property of ∆)

4x = 360°

x = 90°

What is the value for y?
Enter your answer in the box.

Answers

Answer:

angle A=angleB .…(समदिबाहु त्रिभुज भएर)

34°=(x-5)°

or, 34=34

angleA+angleB+angleC=180°

or, 34+34+4y=180

or, 68+4y=180

or, 4y=180-68

or, 4y=112

or, y=112÷4

or, y=28

which equation represents the line through (4,5) and (0,-3)

A. y = 2x + 3

B. y = 2x - 3

C. y = -2x - 3

D. y = -2x + 3

Answers

The linear equation that represents the line that passes through the points (4,5) and (0,-3) is given by:

B. y = 2x - 3

What is a linear function?

A linear function is modeled by:

y = mx + b

In which:

m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

The line passes through (0,-3), that is, when x = 0, y = -3, hence the y-intercept is of b = -3.

The slope is given by the change in y divided by the change in x, hence:

m = (5 - (-3))/(4 - 0) = 2

Hence the equation is:

y = 2x - 3.

Which means that option B is correct.

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These points are linear.
Find the slope.
x036912
y12345
[?]
slope =?/?

Answers

Answer:

slope = [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (6,3) and (x₂, y₂ ) = (9,4) ← 2 ordered pairs from the table

m = [tex]\frac{4-3}{9-6}[/tex] = [tex]\frac{1}{3}[/tex]

Identify the causes of immigration and emigration?

Answers

A person can immigrate to another country for educational purposes.

A person can emigrate to another country for work.

A person can emigrate to another country due to war in their own country.

What is emigration and migration?

Migration is when a person moves from one geographical location or another. Immigration and emigration are types of migration.

Immigration is when a person moves to a foreign country. For example, when a US citizen moved to Italy for work. Emigration is when a person lives his home country.

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The composite figure is made up of a parallelogram and a rectangle. Find the
area. (choices in picture)

Answers

Answer:

88 sq. units

Step-by-step explanation:

1st. BxH

12-4 = 8 is our Base

8x8=64 that is out 1st area

and 2nd area is LxW which is 12x2 = 24

64+24= 88 sq. units

What are the domain and range of the function

Answers

Option 3 !
x≠-4 (the denominator makes it so x≠4)
and y cannot be -11

Question 1(Multiple Choice Worth 4 points)
(02.02) The figure shows the letter Z and four of its transformed images-A, B, C, and D:
Z.
B
6-
5-
3-
2-
n

Answers

The figure that shows the reflection of the letter Z is C

Complete question

The figure shows the letter Z and four of its transformed images—A, B, C, and D

Which of the four images was formed by a reflection of the letter Z?

A B C D

How to determine the reflection of Z?

From the graph, see attachment, we have the following highlights:

The letter Z is in the second quadrant.

Also, B and D are letter Z.

So, they cannot represent the reflection

When reflected across the x-axis, the reflection is C

Hence, the figure that shows the reflection of the letter Z is C