What is the sum of the 22 solutions of the equation x^2-4x-45=0x
2
−4x−45=0 ?

Answers

Answer 1

The solution for the equation x² – 4x – 45 = 0 is (x – 9) (x + 5)

Given,

Quadratic equation = x² – 4x – 45

We can solve this by using quadratic formula.

Equations of the form ax² + bx + c = 0 can be solved using quadratic formula.

Here the equation is in the form of above mentioned:

x² – 4x – 45 = 0

Quadratic formula = [tex]\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}[/tex]

Substitute the values in the formula,

x = [tex]\frac{-(-4)(+-)\sqrt{(-4)^{2}-4(-45) } }{2}[/tex]

x = [tex]\frac{4(+-)\sqrt{16 -4(-45)} }{2}[/tex]

x = [tex]\frac{4(+-)\sqrt{16+180} }{2}[/tex]

x = [tex]\frac{4(+-)\sqrt{196} }{2}[/tex]

x = [tex]\frac{4(+-)14}{2}[/tex]

Now, solve the equation for:

x = [tex]\frac{4+14}{2}[/tex] = [tex]\frac{18}{2}[/tex] = 9

Next, solve the equation for:

x = [tex]\frac{4-14}{2}[/tex] = [tex]\frac{-10}{2}[/tex] = -5

According to ax² + bx + c = a(x - x₁) (x - x₂),

Here, x₁ is 9 and x₂ is -5

So,

x² - 4x - 45 = ( x - 9) (x - (-5))

That is,

x² - 4x - 45 = (x - 9) (x + 5)

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Related Questions

136 divided by -10 - 7 need help fast

Answers

Answer:

136÷-10-7=-20.6

Step-by-step explanation:

.........

Answer is 136 divided -10 -7 = -20.6

I will give brainlist

Write 'five more than three times a number equals 21' as an equation.

3x + 5 = 21
5x + 3 = 21
3x(5) = 21
5x(3) = 21

Answers

Answer:

I think it's 3x + 5 = 21 because three times a number would be 3x so that would eliminate options 2 & 4, then it says five more than three which would be adding five so that would only leave option 1 so that should be your answer

Hope this helps and may God bless you<3

The wholesale cost of a bicycle is $98.75. The markup for the bicycle is 33.3%. Find the selling price of the bicycle to the nearest cent.

Answers

The selling price of the bicycle in discuss upon addition of the mark-up which is 33.3% as described in the task content is; $131.63.

What is the selling price of the bicycle whose mark-up is as described in the task content?

The wholesale cost price of the bicycle in discuss is $98.75 as described in the task content while the markup for the bicycle is as given in the task content.

On this note, it follows that the selling price of the bicycle is the sum of its cost price and it's mark-up. Hence, we have;

Selling price = $98.75 + (33.3% of $98.75)

= $98.75 + (0.333 × $98.75)

= 98.75 + 32.88

= $131.63.

Ultimately, selling price of the bicycle in discuss upon addition of the mark-up which is 33.3% as described in the task content is; $131.63.

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Andre is guaranteed a minimum weekly salary of $400 plus 3.5% of his total sales. If he
sold $5740 worth of merchandise one week, what is his gross pay for that week.

Answers

5740-3.5%=5539.1

5740-5539.1=200.9

400(weekly pay)+200.9(3.5 percent of sales)=600.9


His gross pay would be 600.9 for that week.

Find the average rate of change of the function f(x) = 8x from x₁ = 0 to X₂ = 3.

Answers

Answer:

Step-by-step explanation:

average rate = f(3) - f(0) / 3 - 0 = 24 - 0 / 3 - 0 = 24 / 3 = 8

25
x 120°
y = [? ]º???

Answers

Answer:

Step-by-step explanation:

Answer: the sum of one interior angle and one exterior angle is 180. x+120=180. x=180-120. x=60°. sum of angles in a triangle is 180.

2 Determine the area of the square ABCD with AB=3cm. A 3cm B D C​

Answers

The area of the given square is a 9.

According to the statement

We have to find that the area of the square.

So, For this purpose, we know that the

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

From the given information:

The square ABCD with the side AB=3cm. A 3cm B D C​

Then

we know that the all the sides of the square all equals.

Then

AB=3cm = BC=CD=DA

Then

Area of the square = side*side

Area of the square = 3*3

Now,

The value of the Area of the square = 9.

So, The area of the given square is a 9.

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Question
Write the inequality shown by the shaded region in the graph with the boundary line y = -3x - 4.
Provide your answer below:
-10 -5
10
-10
y
5
10
I

Answers

We get the inequality as:

y > -3x - 4y < -3x - 4y ≥  -3x - 4y ≤  -3x - 4

There is no image to refer. So, here answering in general way.

Given,

The boundary line, y = -3x - 4

We can have 4 cases:

1) A dashed line and the shaded part is above the line.

y > -3x - 4

2) A dashed line and the shaded part is below the line

y < -3x - 4

Here we have dashed lines because the values of the line are not solutions for the inequality.

3) A solid line and the shaded part is above the line.

y ≥  -3x - 4

4) A solid line and the shaded part is below the line.

y ≤  -3x - 4

Here we have solid lines because the values in the line itself are solutions.

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24 × (-2) × 5 ÷ (-6)

Answers

Answer:

40

Step-by-step explanation:

Work from left to right.

24* (-2)*5/(-6)= -48*5/(-6)

-48*5/(-6)=-240/(-6)

-240/(-6)=40

Fran the Fearless has a well-known act at a local zoo. As part of the act, Fran handles a scary animal that she picks at random out of the Box of Terror. The following animals are in the box: 6 poisonous snakes, 8 nonpoisonous snakes, 11 poisonous spiders, and 4 nonpoisonous spiders. What is the probability that the animal Fran picks is poisonous or is a snake?

Answers

0.620  is the probability that the animal Fran picks is poisonous or is a snake .

How does probability explain work?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about how probable an event is to happen, or its chance of happening.

Total animal = ( 6 + 8 + 11 + 4 ) =  29

Let,  p = Event of poisonous animal

        s = event of spider

     p U s = event of poisonous or spider

      p ∩ s = event of poisonous or spider

n(P)   =  No of poisonous = ( 6 + 11 ) = 17

n(S)    =  No of spider =   ( 8 + 4 ) = 12

n(P ∩ S)  No of poisonous spider = 11

Then ,    P [ P ] = 17/29       , P [S ] = 12/29     P [ P ∩ S ] = 11/29

   P [ poisonous or spider ]

 = P [ P ∪ S ] = P [P] + P [ S ] - P [ P ∩ S  ]

                     = 17/29  + 12/29 - 11/29

                      =  18/29  = 0.620

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For the following two numbers, find two factors of the first number such that their product is the first number and their sum is the second number.

60,19

Answers

4, 15. 4x15=60 4+15=19


Use the segment addition postulate to solve for the length of BC, if AC = 16, BC = x + 11, and AB = 3x-7.

Answers

Answer: Can u pls help me withe my question?

Step-by-step explanation:

(2,8) (-4,-7) 5:3 weighted average

Answers

The weighted average is -33.

given,(2,8)(-4.-7)and their weighted average is 3:5

Weighted average is a calculation that takes into account the varying degrees of importance of the numbers in a data set. In calculating a weighted average, each number in the data set is multiplied by a predetermined weight before the final calculation is made.

(2,8)x5=10+40

           =50

(-4,-7)x3=-12-21

            =-33

therefoe, the weighted average is -33.

The average is the sum of all individual observations divided by the number of observations. In contrast, the weighted average is observation multiplied by the weight and added to find a solution.

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I need help I don’t understand

Answers

Answer: use your brain you can do it

Step-by-step explanation:

anything is possable with the power of imagination

You can't remember how many rides you went on at the amusement park. But, you know that each ride cost $3 and it cost $20 to get into the park. How many rides did you go on if you spent a total of $41?​

Answers

Answer:

7 Rides

Step-by-step explanation:

Alright so you can already take out 20 bucks out of 41, so 21 bucks left. Then it's simple division, 21 / 3 = 7. You went on 7 rides. Hope this helps. Have a great night. :)

Answer:

7 rides!

Step-by-step explanation:

Our equation: 20+3x=41

x= the number of rides you went on

41-20= 21

21/3=7

Therefore, you went on 7 rides :))

Can someone help with this question?✨

Answers

Answer:

-3/4

Step-by-step explanation:

From a point on the graph, count down and count right until you get to a another point. For example, for this problem, you can use (0,-2) as a starting point. From here, if you go down 3 and go right 4, you get another point on the graph. So, the slope is -3/4.

5 is added to the cube of a number

Answers

Answer:

x^3 + 5

Explanation:

Adrian scored 40% of the goals by his soccer team. if his team scored a total of 60 goals during the season, how many did adrian score ? show your work

Answers

Answer:

24 goals

Step-by-step explanation:

40/100×60=Adrians goals(g)

g=2400/100

=24

Step-by-step explanation:

24 goals in total I think.

Giving point asap , please asnwer

Answers

Okay, the answer is 464

Pls help I suck at math

Answers

a) The first five terms of the sequence are 1, 3, 9, 27 and 81.

b) The first five terms of the sequence are 1, - 1, - 3, - 5 and - 7.

c) The first five terms of the sequence are 1, 3, 7, 15 and 31.

d) The first five terms of the sequence are 1, 2, 5, 26 and 677.

e) The first five terms of the sequence are 1, 3, 7, 13 and 21.

How to find the first five terms of a series by a recurrence formula

Recurrence formulas are expressions that generates an element of a sequence in terms of previous elements of the series. Now we proceed to calculate the first elements of each sequence:

Case A

n = 1

a(1) = 1

n = 2

a(2) = 3 · a(1)

a(2) = 3

n = 3

a(3) = 3 · a(2)

a(3) = 9

n = 4

a(4) = 3 · a(3)

a(4) = 27

n = 5

a(5) = 3 · a(4)

a(5) = 81

The first five terms of the sequence are 1, 3, 9, 27 and 81.

Case B

n = 1

b(1) = 1

n = 2

b(2) = - 2 + b(1)

b(2) = - 1

n = 3

b(3) = - 2 + b(2)

b(3) = - 3

n = 4

b(4) = - 2 + b(3)

b(4) = - 5

n = 5

b(5) = - 2 + b(4)

b(5) = - 7

The first five terms of the sequence are 1, - 1, - 3, - 5 and - 7.

Case C

n = 1

c(1) = 1

n = 2

c(2) = 2 · c(1) + 1

c(2) = 3

n = 3

c(3) = 2 · c(2) + 1

c(3) = 7

n = 4

c(4) = 2 · c(3) + 1

c(4) = 15

n = 5

c(5) = 2 · c(4) + 1

c(5) = 31

The first five terms of the sequence are 1, 3, 7, 15 and 31.

Case D

n = 1

d(1) = 1

n = 2

d(2) = [d(1)]² + 1

d(2) = 2

n = 3

d(3) = [d(2)]² + 1

d(3) = 5

n = 4

d(4) = [d(3)]² + 1

d(4) = 26

n = 5

d(5) = [d(4)]² + 1

d(5) = 677

The first five terms of the sequence are 1, 2, 5, 26 and 677.

Case E

n = 1

f(1) = 1

n = 2

f(2) = f(1) + 2 · 2 - 2

f(2) = 3

n = 3

f(3) = f(2) + 2 · 3 - 2

f(3) = 7

n = 4

f(4) = f(3) + 2 · 4 - 2

f(4) = 13

n = 5

f(5) = f(4) + 2 · 5 - 2

f(5) = 21

The first five terms of the sequence are 1, 3, 7, 13 and 21.

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I NEED HELP IM A 4th grader pls help

Answers

For 11:
The smaller side of the smaller rectangle is 2 on the larger is 12 so 12 divided by 2 is six
The side for the smaller one is 5 so five times 6 is 30…
The answer for X is 30

For 12:
16 divided by four is four
The other side is six so for the bigger Triangle decide would be 6×4 which is 24
X is 24

How many elements belong to set A but not set B?

Answers

According to the venn diagram 21 elements belong to set A but not set B.

A Venn diagram is a diagram that helps us visualize the logical relationship between sets and their elements and helps us solve examples based on these sets. A Venn diagram typically uses intersecting and non-intersecting circles (although other closed figures like squares may be used) to denote the relationship between sets.

The given information is U = 23, n(A)= 21+ 5= 25 and n(B)= 15+5 =20

We have to find how many elements belong to set A but not set B.

In the given Venn diagram , The elements belong to set A but not set B is 21

The elements belong to set A but not set B is 21

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solve for f f/5=-8 need help asap

Answers

Step-by-step explanation:

[tex] \frac{f}{5} = - 8[/tex]

[tex]f = - 8 \times 5[/tex]

[tex]f = - 40[/tex]

Trey is assembling furniture, and the table below shows the
length of parts A-D. Record the letter of the part that is the
longest.
PART
LENGTH (IN.)
A
277
B
1.3
C
1.15

D
21
20

Answers

The longest part is Part B, which is a little longer than Part A.

What is the length?

The length is the measure of distance or total time from one point to another.

For example, when measuring dimensions, the length also shows the longest side of an object, especially the rectangle.

Together with the width, the length can be used to determine the area of an object or its perimeter.

Part                         A          B          C          D

Length (IN.)          1²/₇        1.3         1.15      ²¹/₂₀

Convert all lengths (A and D) into decimals:

Part                         A                 B           C          D

Length (IN.)         1.29 (1²/₇)       1.3         1.15     1.05 (²¹/₂₀)

Part B's length is the most extended length, followed by Part A, Part C, and lastly, Part D.

Thus, the most extended length of the four parts is Part B.

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Question Completion:

Part                         A          B          C          D

Length (IN.)          1²/₇        1.3         1.15      ²¹/₂₀

find (f+g) (x) for f(x)=1/x and g(x)=x^4

Answers

Given the functions f(x) = 1/x and g(x) = x⁴, the function operation ( f + g )(x) is x⁴ + 1/x.

What is the function operation ( f + g )(x)?

Given the functions in the question;

f(x) = 1/xg(x) = x⁴( f + g )(x) = ?

To evaluate f + g, replace the function designators in f + g with the actual functions and simplify

( f + g )(x) = f(x) + g(x)

( f + g )(x) = ( 1/x ) + ( x⁴ )

Remove the parenthesis

( f + g )(x) = ( 1/x ) + ( x⁴ )

( f + g )(x) = 1/x + x⁴

Reorder 1/x and  x⁴

( f + g )(x) = 1/x + x⁴

( f + g )(x) = x⁴ + 1/x

Given the functions f(x) = 1/x and g(x) = x⁴, the function operation ( f + g )(x) is x⁴ + 1/x.

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Finding Values of Sum and Difference Functions:
Answer all 3 questions on the picture:

Answers

Answer:

5917

Step-by-step explanation:

Given functions h(x)=x²+1 and k(x)=x-2, you want the values of (h+k)(2), (h-k)(3) and 3h(2)+2k(3).

Function evaluation

The value of a function f(x) is found by substituting the argument value for x in the function definition, then doing the arithmetic.

The value of a sum or difference of functions is the sum or difference of the values of those functions for the given argument.

(h+k)(2)

  (h+k)(2) = h(2) +k(2) = (2²+1) +(2 -2) = 5 +0 = 5

(h-k)(3)

  (h-k)(3) = h(3) -k(3) = (3² +1) -(3 -2) = 10 -1 = 9

3h(2) +2k(3)

   3h(2) +2k(3) = 3(2² +1) +2(3 -2) = 3(5) +2(1) = 17

Find the value of x.
X
38°
75°

Answers

Answer:

67

Step-by-step explanation:

Angles in a triangle add to 180°.

If the observed (actual) y value is 10, and the predicted value is 14, what is the residual? ​

Answers

The residual value with an actual value of 10 and a predicted value of 14 will be 4. Then the correct option is D.

What is Algebra?

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

We know that the difference between the predicted value and to actual value is known as the residual value.

Residual value = Predicted value - Actual value

If the observed (actual) y value is 10, and the predicted value is 14. Then the residual value will be

Residual value = 14 - 10

Residual value = 4

The residual value will be 4. Then the correct option is D.

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9/14×7/6 in the simplest form

Answers

Answer:

3/4

Step-by-step explanation:

[tex]\frac{9}{14} \times \frac{7}{6} \\ \\ =\frac{3}{14} \times \frac{7}{2} \\ \\ =\frac{3}{2} \times \frac{1}{2} \\ \\ =\frac{3}{4}[/tex]

If the distance traveled is (4s3 - 6s² + 4s + 14) miles and the rate is (s + 1) mph, write an expression, in hours, for the time traveled.​

Answers

The equation for time is URM:

[tex]time = \frac{distance}{speed \: (rate)} [/tex]

[tex]t(s) = \frac{4s {}^{3} - 6s {}^{2} + 4s + 14}{s + 1} = \frac{2(s + 1)(2s {}^{2} - 5s + 7) }{s + 1} \\ t(s) = 2(2s {}^{2} - 5s + 7) \\ t(s) = 4s {}^{2} - 10s + 14[/tex]

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