please show the steps​

Please Show The Steps

Answers

Answer 1

Answer:

  x = -3, 0, or 7

Step-by-step explanation:

After removing common factors, the remaining quadratic can be factored by comparison to the factored form of a quadratic.

__

Step 1

Write the equation in standard form.

  4x³ -16x² -84x = 0

Step 2

Factor out the common factor from all terms.

  = 4x(x² -4x -21) = 0

Step 3

Compare to the factored form of a quadratic:

  (x +a)(x +b) = x² +(a+b)x +ab

This tells you the constants 'a' and 'b' in the factors can be found by considering ...

  (a+b) = -4 . . . . the coefficient of the x term of the quadratic

  ab = -21 . . . . . the constant term of the quadratic

It is often helpful to list factor pairs of the constant:

  -21 = (-21)(1) = (-7)(3) . . . . integer pairs that have a negative sum

The sums of these pairs are -20 and -4. We are interested in the latter. We can choose ...

  a = -7, b = 3

Step 4

Put it all together.

  4x³ -16x² -84 = (4x)(x -7)(x +3) = 0 . . . . . factored form of the equation

Step 5

Apply the zero product rule. This rule tells you the product of factors will be zero when one or more of the factors is zero:

  4x = 0   ⇒   x = 0

  x -7 = 0   ⇒   x = 7

  x +3 = 0   ⇒   x = -3

Solutions to the equation are x ∈ {-3, 0, 7}.

_____

Additional comment

What we did in Step 3 is sometimes referred to as the X-method of factoring a quadratic. The constant (ab product) is put at the top of the X, and the sum (a+b) is put at the bottom. The sides of the X are filled in with values that match the product and sum: -7 and 3. The method is modified slightly if the coefficient of x² is not 1.

A graphing calculator often provides a quick and easy method of finding the real zeros of a polynomial.

Please Show The Steps

Related Questions

Mitch walks 30 meters in 20 seconds. How many meters does Mitch walk per second?

Answers

Distance =30m, Time= 20s
Speed= distance/time
So speed= 30/20 = 1.5 m/s

Answer:

1.5 meters per second

Step-by-step explanation:

30 ÷ 20 = 1.5

13 - 6(2 − 6)² +8 evaluate

Answers

Step-by-step explanation:

______________________

13 - 6 ( 2 - 6 )² + 8

= Solution

= 13 - 6 (- 4 ) ² + 8

Now...remove the negative number...because negative number raise to even powers are positive...

= 13 - 6 × 4² + 8

= 13 - 96 + 8

= 13 + 8 - 96

= 21 - 96

= - 75

Hence the answer is - 75....

[tex]..[/tex]

______________________

A shirt on sale for 25%off. Sandy paid 7.50 for the shirt. What was the shirts regular price

Answers

£10

Step-by-step explanation:

firstly what you have to do is

since the percentage is decreased

we will say 100 - 25% = 75%

then we say 7.50/75% = 10

So we know that the original price was

£10 pounds

As 10- 25%= 7.5

The shirt's regular price is 10.

Given,

A shirt on sale for 25%off.

Sandy paid 7.50 for the shirt.

We need to find the regular price.

The regular price is the same as the selling price.

We have,

Regular price = Paid price  + offer discount%

offer discount = 25%

Paid price = 7.50

If after 25% off Sandy paid 7.50 which means Sandy paid only 75% of the price.

The regular price is always 100%

= Paid price  + offer discount%

= 75% + 25%

So we have,

75% = 7.5

Multiplying 25/75 on both sides.

25/75 x 75% = 7.5 x 25/75

25% = 2.5

We see that the offer discount is 2.5.

We have,

Regular price = Paid price  + offer discount%

                       = 7.50 + 2.5

                       = 10

Thus the shirt's regular price is 10.

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Write a​ slope-intercept equation for a line that passes through (-2,3) and (2,-5)

The slope of the given line is m
​(Simplify your answer. Type an integer or a simplified​ fraction.)

Answers

Answer:

y - 3 = -2 * (x+2)

Step-by-step explanation:


Two cars, A and B, are travelling along a straight road and in the same direction. Car B is 20 km
ahead of Car A. Car A is travelling at 60 km · while Car B at 50 km 1. They both start at 12:00
hours. At what time Car A will overtake Car B?

Answers

Answer:

2 o'clock

Step-by-step explanation:

Their 'closing speed' is 60 - 50 = 10 km/hr

they have 20 km between them

 at closing speed this will take   20 km / 10 km/hr = 2 hours for the cars to meet....this would be at 14:00    or  2 oclock

Help. Please and thanks.

Answers

Answer:

D

Step-by-step explanation:

the other 3 options are all true.

the sum of all angles in a triangle is always 180°.

so, when T is 40°, that leaves 180-40 = 140° to the other 2 angles. in an isoceles triangle they must be equal to each other, so they are half of the remaining 140°, which is 70°.

and of course the 2 sides are equal (hence "isoceles").

Part 1: Complete the operations geometrically.
Use vector operations to draw the resultant vector.
⦁ Draw 2u + 4v.

Answers

Answer:

Step-by-step explanation:

The geometrically operations 2u + 4v is (2,12).

For immediately line graphs there is a linear relationship between the x and y values and so the line is instantly and should be drawn with a ruler. The gradient determines how steep the road is and the y-intercept tells us the vicinity wherein the immediate line intersects the y-axis.

Why is a graph a direct line?

It continually goes up in steps of equal length, so it is a straight line. that is first-class as a way because it goes. It identifies the defining assets of a linear feature—that it has a constant rate of exchange—and relates that property to a geometric feature of the graph.

What is a straight line graph?

The graph follows a straight line equation shows a straight line graph.

equation of a straight line is   y=mx+cy represents vertical line y-axis.

x represents the horizontal line x-axis.    

m is the slope of the line

           slope(m)=tan∅=y axis/x axis.

c represents y-intercepts (it is the point at which the line cuts on the y-axis)Straight line graphs show a linear relationship between the x and y values.

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Stephanie is helping a midwife weigh new-born babies. The scales are in pounds but the sheet she has to complete is in kilogrammes. The baby weighs 8.06 lbs. When she converts this on a calculator the display reads 3.65595152. What is this in kilogrammes to 3 decimal places?

Answers

The weight of baby in kg is, 3.659 kg.

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The baby weighs 8.06 lbs.

Now, We know that;

⇒ 1 pound = 0.454 kg

Hence, The weight of baby in kg is,

⇒ 8.06 pounds = 8.06 × 0.454 kg

                        = 3.659 kg

Thus, The weight of baby in kg is, 3.659 kg.

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f(x) = x² + 2x − 3
Find f (2)
f(2) is equal to type your answer...

Answers

Answer:

f(2) = 5

Step-by-step explanation:

Given: f(x) = x² + 2x - 3

We are asked to find the value of the function when x = 2.

In the function, substitute 2 as the value of x and simplify:

f(2) = (2)² + 2(2) - 3

f(2) = 4 + 4 - 3

f(2) = 8 - 3

f(2) = 5

When x is equal to 2, the value of the function is 5.

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Consider the line y=-2/3x+9 . Find the equation of the line that is parallel to this line and passes through the point (-8,3) . Find the equation of the line that is perpendicular to this line and passes through the point (-8,3) .

Answers

The equation of line which is parallel to line is y = (-2x-7)/3.

What is Gradient?

Gradient is the ratio between change in y-axis to change in x-axis.

Here, Given Equation of line is y = [tex]\frac{-2}{3}x+9[/tex]

gradient of line m₁ = -2/3

Equation of line passing through point (-8, 3) and gradient -2/3 (parallel to given line) is

(y - y₁) = m₂(x - x₁)

( y - 3) = -2/3(x+8)

3y - 9 = -2x -16

3y = -2x -16 + 9

3y = -2x -7

y = (-2x-7)/3

Thus, the equation of line which is parallel to line is y = (-2x-7)/3

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The circumference of a circular garden is 122.46 feet. What is the radius of the garden? Use 3.14 for π and do not round your answer. feet

Answers

The radius of the circular garden whose circumference is 122.46 feet is: 19.5 feet.

What is the Circumference of a Circle?

Circumference = 2πr, where r is the radius of the circle.

Given the following:

Circumference = 122.46 feetRadius (r) = ?π = 3.14

122.46 = 2(3.14)(r)

122.46/2(3.14) = r

r = 19.5 feet.

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Answer correctly for branliest!

Answers

Slope is rise/ run, or change in y/ change in x. the error was that the person out run/rise, so the correct answer is 4/6.

HELP ASAP PLEASE!!!!!!!

Answers

1st , and 3rd will be your answer

Select ALL the expressions that have a value of 2² – 3³ + 29.
1. (78 ÷ 3) – 24
2. 83 – 14 × 62 – 2
3. –|–6|
4. |–6|
5. 72 – 3.1 – 19 × 2.1

Answers

There is no expression that is the same as the value of 2² – 3³ + 29 which is = 2.

Simplification of the given expression

To simplify the expression 2² – 3³ + 29. is as follows:

2² – 3³ + 29 = 4- 9+29

= 29 -5

= 24

(78 ÷ 3) – 24. To simplify is = 78/3=26-24 = 2 (false)

83 – 14 × 62 – 2. To simplify is = 69- 60 = 9 (false)

–|–6|. To simplify is -(-6) = +6( false)

-6( false)

72 – 3.1 – 19 × 2.1: To simplify is = 49.9×2.1 = 104.79 (false)

Therefore, there is no expression that is the same as the value of 2² – 3³ + 29. which is 2.

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47/6m+n- 7/2m-6/5n
Simplify

Answers

Answer:

[tex]\frac{13m}{3}-\frac{n}{5}[/tex]

Step-by-step explanation:

1) Simplify [tex]\frac{47}{6}m[/tex] to  [tex]\frac{47m}{6}[/tex]

[tex]\frac{47m}{6}+n-\frac{7}{2}m-\frac{6}{5}n[/tex]

2) Simplify [tex]\frac{7}{2}m[/tex]  to [tex]\frac{7m}{2}[/tex]

[tex]\frac{47m}{6}+n-\frac{7m}{2}-\frac{6}{5}n[/tex]

3) Simplify  [tex]\frac{6}{5}n[/tex]  to[tex]\frac{6n}{5}[/tex]

[tex]\frac{47m}{6}+n-\frac{7m}{2}-\frac{6n}{5}[/tex]

4) Collect like terms.

[tex](\frac{47m}{6}-\frac{7m}{2})+(n-\frac{6n}{5})[/tex]

5) Simplify.

[tex]\frac{13m}{3}-\frac{n}{5}[/tex]

2. What is the measure of angle A?

Answers

Answer:

the answer is 63 degrees

Step-by-step explanation:

Adelle keeps track of the time her bus arrives at her stop. Since she has been keeping track, her bus has arrived on time 16 days and has been late on 4 days. Based on her data, what percentage of the time should Adele expect the bus to be late?

Answers

Answer:

25%

Step-by-step explanation:

4 days of 16 days is 25% or 1/4

Hope this helps! ;-)

T
yler wants to determine if an individual's age affects whether or not they like jazz, rock, or country music. Which type of inference test should Tyler use?

Answers

The appropriate test is the chi-squared test for association/independence.

What is an inference test?

A statistical inference involves hypothesis testing about a population using a sample.

In this case, Tyler wants to determine if an individual's age affects whether or not they like jazz, rock, or country music. The appropriate test is the chi-squared test for association/independence.

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Answer:

chi-squared test

Step-by-step explanation:

Got it right on the test.

4 divided by 5yards 1 foot

Answers

4 divided by 5yards and 1 foot is. 1 yard and 1 foot

PLEASE I NEED HELP ASAP!!!!!!!!
Note: please add the answer next to the number its from so I can know which question was answered

Answers

Question 1: Option BQuestion 2: [tex]k[/tex] ≤ [tex]1[/tex]

Answer:

B, B

Step-by-step explanation:

< less than

> Greater Than

If it has a line under it it is equal too as well as greater or less.

The close dot means equal too and the open mean not equal to

The ratio of cats to dogs at the veterinarian is 21:39. What percent of the total animals are cats?

Answers

Answer:

35%

Step-by-step explanation:

Assuming that there are no other animals in the vet other than dogs and cats, that means the total amount of animals is 21 + 39, which is 60 animals. To find the percent of cats, simply place the number of cats based on the ratio (21) over the total number of animals (60) and multiply by a 100:

21/60 = 0.35

0.35 x 100 = 35%

Hope this helps!!

Answer:

35%.

Step-by-step explanation:

Fraction that  are cats =  21 / (21+39)

= 21/60

= 100 * 21/60

= 35%.


Please help! I need the right answer : (

A cone with the height h radius r has volume v=1/3 m2h. if the cone has a height of 6 in. And volume of v=8♊︎(pie)x+24m♊︎(pie), what is the radius r in terms of x? A. r=3x+2. B. r=4x^2+12x+9. C. r=2x+3 D. r= (2x+3) (2x-3)

Answers

Answer:9514 1404 393

Answer:

 h = 3V/(πr²)

Step-by-step explanation:

The formula can be solved for h by multiplying both sides by the inverse of the coefficient of h.

 

_____

Additional comment

Whenever a variable has a coefficient you don't want, you can make that be 1 by multiplying the equation by the inverse of the coefficient. This is the same as dividing by the coefficient. This makes use of the fact that for any non-zero 'a', the ratio a/a has a value of 1. Anything multiplied by 1 is unchanged.

 V = ah   ⇒   V/a = (ah)/a = h(a/a) = h·1 = h

Note that we multiply the whole equation (both sides of the equal sign) by 1/a. The basic rule of equality is that you can do whatever you like to an equation, as long as you do it to both sides.

Step-by-step explanation:

Can you match the teacher's comments to the definitions?

Answers

Answer:

Daniel =Were you thinking of perpendicular lines?

Oris= It seems like you've got the basic idea, but your definition could be more precise.

Kaoris= Yes well done...

a) Let A x B = {(1, 5), (1, 6), (2, 5), (2, 6), (3, 5), (3, 6)} then, find A, B, n(A), n(B)​

Answers

Step-by-step explanation:

A={1,2,3}

B={5,6}

n(a)=3

n(b)=2

3 years ago, the residents of Planet X found a black hole leading to another galaxy. Since then, they have been leaving Planet X at a rate of 120 residents per year.
The following equation describes this situation:
\quad -120\cdot 3 = -360−120⋅3=−360minus, 120, dot, 3, equals, minus, 360
What does -360−360minus, 360 tell us?
Choose 1 answer:
Choose 1 answer:

(Choice A)
A
A total of 360360360 residents left Planet XXX in the past three years.

(Choice B)
B
360360360 residents left Planet XXX each year.

(Choice C)
C
None of the above

Answers

Answer:

A total of 360 residents left Planet X in the past 3 years.

Step-by-step explanation:

120 are the residents per year and the 3 represents the years so when you multiply them it would make how many residents that left Planet X in 3 years.

Answers

A total of 360 residents left Planet X in the past 3 years.

Step-by-step explanation:

120 are the residents per year and the 3 represents the years so when you multiply them it would make how many residents that left Planet X in 3 years.A total of 360 residents left Planet X in the past 3 years.

Samuel worked 1/4 of a day on Tuesday and 3/8 of a day on Wednesday. Which
of these represents the fraction of a day he spent working on both days?

Answers

Rewrite 1/4 to have 8 as the denominator: 1/4 = 2/8

Now add the two days together:

2/8 + 3/8 = 5/8

Answer: 5/8

use the information provided to write the equation of each circle. center: (3, -15) radius: 3

Answers

Equation of circle in general

(x-h)²+(y-k)²=r²

For centre at (h,k)

So our equation is

(x-3)²+(y+15)²=3²(x-3)²+(y+15)²=9

HELP PLEASE 100 POINTS!!!
Given that triangle PHT is a right triangle and Line HY is an altitude, what is the missing justification in the proof that (PH)^2 + (HT)^2 = (PT)^2?

Answers

The correct option is D.
Step-by-step explanation:
Given information: Triangle PHT is a right
triangle and Line HY is an altitude.
According to the reflexive property, a side or
an angle is congruent to itself.
If A is an angle of a triangle then using
reflexive property
LAN LA
¿PIT ~ LYT
(Both are right angles)
IT ~ LT
(Reflexive property)
APHT~ AHYT
(AA rule of similarity)
Other statements and reasons are present in
the table.
The missing reason is reflexive property.
Therefore the correct option is D.

The missing reason is reflexive property.

Therefore, the correct option is D.

What is a triangle?

A triangle is a type of polygon, which has three sides, and the two sides are joined end to end is called the vertex of the triangle.

Given that a triangle PHT is a right triangle and Line HY is an altitude.

According to the reflexive property, a side or an angle is congruent to itself.

If A is an angle of a triangle, then using reflexive property.

∠A ≅ ∠A

∠PHT ≅ ∠HYT (Both are right angles)

∠T ≅ ∠T (Reflexive property)

ΔPHT ~ ΔHYT (AA rule of similarity)

Other statements and reasons are already in the table.

Hence the correct option is D.

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5) Mary is taking a swimming lesson on a rectangular pool which is 9 meters wide and 12 meters long. Find the area of the swimming pool.


a. What is asked?

b. What are given?

c. What is/are the operation/s to be used?

d. What is the number sentence?

e. What is the answer?​

Answers

Answers:

a) The Area of the swimming pool.
b) 9 meters wide, 12 meters long.
c) 9, 12 & multiplication.
d) 9 • 12
e) 108

5. A rectangle whose length and width are 10 and 6, respectively, is shown below. The rectangle is continuously
rotated around a straight line to form an object whose volume is 150.
6
10
hich line could the rectangle be rotated around?
A. a long side
B. a short side
C. the vertical line of symmetry
D. the horizontal line of symmetry

Answers

TheThe line that the rectangle could be rotated around is: C. the vertical line of symmetry.

Vertical line of symmetry

Analysis

Volume=Base area×height

If the rectangle rotated around horizontal line of symmetry

V1=Ah=πr²h

=π×9×10

=90π

If the rectangle rotated around short line

V2=Ah=πr²h

=π×10²×6

=π×100×6

=600π

If the rectangle rotated around vertical line of symmetry

V3=Ah=πr²h

=π×5²×6

=π×25×6

=150π

Therefore the correct option is C.

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