What are the solutions to the quadratic equation 3(x - 4)2 = 75?
O x = -9 and x = 1
O x = -5 and x = 5
O x = -4 and x = 4
O x = -1 and x = 9

What Are The Solutions To The Quadratic Equation 3(x - 4)2 = 75?O X = -9 And X = 1O X = -5 And X = 5O

Answers

Answer 1

Answer:

4th option, x = -1 and x = 9

Step-by-step explanation:

3(x-4)²=75

or, (x-4)²=25

or, x²-8x+16-25=0

or, x²-8x-9=0

or, x²-9x+x-9=0

or, x(x-9)+1(x-9)=0

or, (x-9)(x+1)=0

so, x-9=0 or, x=9

and x+1=0 or, x=-1

Answer 2

The two solutions of the quadratic equation are:

x = -1 and x = 9

How to solve the quadratic equation?

The quadratic equation is:

3*(x - 4)^2 = 75

We can expand it as:

3*x^2 - 3*2*4*x + 3*16 = 75

3x^2 - 24x  -27 = 0

Now, using Bhaskara's formula we get:

[tex]x = \frac{-(-24) \pm \sqrt{(-24)^2 - 4*3*(-27)} }{2*3} \\\\x = \frac{24 \pm 30 }{6}[/tex]

So the two solutions are:

x = (24 + 30)/6 = 9

x = (24 - 30)/6 = -1

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Related Questions

the diameter of a bicycle wheel is 71 cm. calculate the circumference of the wheel​

Answers

Answer:

233.05

Step-by-step explanation:

take the diameter and divide it by 2, that will give you the radius. Take the radius and multiply it by 2 then by pi. That will give you the circumference. So for the this question it would be:

71 divided by 2 = 35.5cm

35.5 x 2 x pi = 233.05

slove................

Answers

Angle 4 and Angle 2 are vertical angles, meaning that they are congruent. Therefore, the measure of angle 2 is 127 degrees.

Angle 4 and Angle 3 are a linear pair, meaning that they are supplementary and add up to 180 degrees. Therefore, the measure of angle 3 is 53 degrees.

Angle 3 and Angle 1 are vertical angles, meaning that they are congruent. Therefore, the measure of angle 1 is 53 degrees.

Hope this helps!

Answer:

<1 = 53

<2 =127

<3 = 53

Step-by-step explanation:

Angles 2 and 4 are vertical angles and vertical angles are equal

<2 = <4 = 127

<1 + <2 =180 since they form a straight line

<1 + 127 = 180

< 1 = 53

<1 and <3 are vertical angles so they are equal

<1 = <3 = 53

Which of the following represents the solution to the inequality

Answers

Answer:

the question?

Step-by-step explanation:

the numbers written in rectangles are the products of the numbers in connecting circle. Please solve it fast its urgent ​

Answers

Answer:

It is the third one

Step-by-step explanation:

c

Arturo's goal is to find a job that provides an income of at least $60,000 a year. Kristen's Furniture offers him a job paying a base salary of $14,000 a year, plus a commission of 7% of his sales. Determine what Arturo's total sales will need to be for him to have a yearly income greater than or equal to $60,000.

If Arturo takes the job with Kristen's Furniture, he will need to have at least
$
in total sales to have a yearly income greater than or equal to $60,000 per year.

Answers

Answer:

He will need at least 657,142.86

Step-by-step explanation:

Determine how much commission he needs

60000-14000

46000

Commission is 7%

Let x be the sales

x*7% = 46000

x*.07 = 46000

Divide each side by .07

x = 46000/.07

x =657142.85714

Rounding to the nearest cent

x = 657,142.86

In the diagram below, what is the approximate length of the minor arc AB?

Answers

Answer:

The answer is "Option C"

Step-by-step explanation:

Given:

[tex]r= 30 \ cm\\\\\theta =60^{\circ}[/tex]

Using formula:

[tex]\frac{A}{\theta}=\frac{\pi r^2}{2\pi}\\\\\frac{A}{\theta}=\frac{\pi r^2}{2}\\\\A=\frac{r^2\times \theta}{2}[/tex]

a)out of 300 students In a class 60% of the students took physics and 35 students took chemistry and 20% of the students did not take any of this subject. how many students take both the subject​

Answers

Answer:

25 students take both subjects.

Step-by-step explanation:

Solve for 60% of 300 students:

60/100 = x/300

Cross multiply:

60 × 300 = 100 × x

18000 = 100x

Divide both sides by 100:

180 = x

Solve for 20% of 300 students:

20/100 = x/300

20 × 300 = 100 × x

6000 = 100x

60 = x

Solve for the percentage of students in chemistry:

x/100 = 35/300

x × 300 = 100 × 35

300x = 3500

x = 11.66666...7

x = about 11.7%

Find the difference in percentages:

100 - 60 - 20 - 11.7

8.3

8.3% take both subjects

Solve for 8.3% of students:

8.3/100 = x/300

8.3 × 300 = 100 × x

2490 = 100x

24.9

About 25 students

Check your work by adding all the students together (to get to 300):

25 + 60 + 180 + 35

300 students total

This is correct!

A runner covers the last straight stretch of a race in 3 s. During that time, he speeds up from 5 m/s to 11 m/s.What is the runner's acceleration in this part of the race? ​

Answers

Answer:

From first Newton's equation of motion:

[tex]{ \bf{v = u + at}}[/tex]

Substitute the variables:

[tex]{ \tt{11 = 5 + (a \times 3)}} \\ { \tt{3a = 6}} \\ { \tt{a = 2 \: {ms}^{ - 2} }}[/tex]

Acceleration is 2 ms-²

F(x)=-x^2+2mx+2m-3 with x<0

Answers

Answer:

m<√-3 OR m<√3i

Step-by-step explanation:

f(x)=x²+2m(x+1)-3

with x<0

b²-4ac<0

(2m)²-4(1×-3)<0

4m²+12<0

4m²<-12

m²<-12/4

m²<-3

m<√-3 OR m<√3i

Independent Practice


Find the number of solutions of the equation.

0 = x2 + 2x + 9


A.
3


B.
2


C.
1


D.
0

Answers

Answer:

Option D

Step-by-step explanation:

There are no real solution for the given equation

Answered by GAUTHMATH

If the scale on the map is 1cm :112 km. If two places are 197 miles apart. How far apart are they on a map

Answers

Answer:

22.4 cm

100% 2021 on edge!

Step-by-step explanation:

If I take a 7 question multiple choice test, with 4 choices per question, what is the probability that I get 1 wrong

Answers

Answer:

The probability is [tex]\frac{3}{4^7}[/tex].

Step-by-step explanation:

Total questions = 7

Number of choices of each question = 4

Probability to give the correct answer = 1/4

Probability to give the wrong answer = 3/4

Probability to give 1 answer wrong

[tex]\frac{1}{4}\times \frac{1}{4}\times \frac{1}{4}\times \frac{1}{4}\times \frac{1}{4}\times \frac{1}{4}\times \frac{3}{4}\\\\= \frac{3}{4^7}[/tex]

25. A pizza shop offers 30% off the price of a large pizza every Tuesday
night. If the regular price is $25, what is the discounted price?

Answers

Answer:

25 -(.3*25)

25-7.50 = $17.50

Step-by-step explanation:

Answer:

17.50

Step-by-step explanation:

First find the amount of the discount

25 * 30%

25 * .3

7.5

Subtract this from the original amount

25 - 7.5

17.50

This trapezium is drawn on a centimetre grid.
Find the area of the trapezium.

Answers

Answer:

A = 18 units²

Step-by-step explanation:

The area (A) of a trapezium is calculated as

A = [tex]\frac{1}{2}[/tex] h ( b₁ + b₂ )

where h is the perpendicular height and b₁, b₂ the parallel bases

By counting squares

h = 3, b₁ = 3, b₂ = 9 , then

A = [tex]\frac{1}{2}[/tex] × 3 × (3 + 9) = 1.5 × 12 = 18 units²

The radius of the large sphere is times longer than the radius of the small sphere.
How many times the volume of the large sphere is the volume of the small sphere?
Help! Help! Help! Please!

Answers

Answer:

A. ¹/27

Step-by-step explanation:

✔️Volume of large sphere = ⁴/3πr³

r = 18.6 in.

Volume of large square = ⁴/3*π*18.6³ = 26954.26 in.³

✔️Volume of small sphere = ⁴/3πr³

r = 6.2 in.

Volume of small sphere = ⁴/3*π*6.2³ = 998.31 in.³

✔️Ratio of the volume of the smaller sphere to the larger sphere = 998.31 : 26954.26

= 1 : 27

Therefore, the volume of the large sphere is ¹/27 of the volume of the small sphere.

i need help on this please SHOW WORK

Answers

[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]

See this attachment

Find the measure of 2

Answers

Answer:

92

Step-by-step explanation:

Angle 2 and 92 are corresponding angles and corresponding angles are equal when the lines are parallel

Answer:

[tex]\angle 2=92^{\circ}[/tex]

Step-by-step explanation:

When two parallel lines are cut by a traversal, their corresponding angles are always equal. Corresponding angles can be found if you took each point of intersection and aligned them up with each other.

In this case, we see that [tex]\angle 2[/tex] and the angle marked as 92 degrees correspond with each other. Since all corresponding angles are equal, we have:

[tex]\angle 2=\boxed{92^{\circ}}[/tex]

Please help me answer this question​

Answers

Answer:

a, 14.13. b, 39.25

Step-by-step explanation:

so for a the diameter is 6 so the radius is 3. The equation for the area of the circle is πr2. So 3x3=9. then 9x3.14=28.26. But then we have to divide by two cause we are finding only the shaded area. 28.26/2=14.13.

A is 14.13

for b, its the same thing, so the radiu is 5 and 5x5=25. 25x3.14=78.5, and divide two, so 78.5/2=39.25.

B is 39.25

WARNING: I am not sure this is correct, so if this is wrong i'm sorry, i'm learning too :)

Type the correct answer in the box. Use numerals instead of words.
Consider this expression.
|m^2+n^2|

Answers

Answer:

34

Step-by-step explanation:

We are here given a modulus expression and we need to find out the value when m = -5 and n = 3 .

Modulus :- It always gives positive value . For example ,

[tex]\rm\implies |-a| = a [/tex]

[tex]\rm\implies |a| = a [/tex]

The given modulus expression is :-

[tex]\rm\implies |m^2+ n^2| [/tex]

As the number inside the modulus operator are already squared therefore they will always give positive value for real numbers . Here we can omit the modulus .

[tex]\rm\implies m^2 + n^2 [/tex]

Plug in the given values ,

[tex]\rm\implies (-5)^2 + 3^2 [/tex]

Solve 5² and 3² and add them ,

[tex]\rm\implies 25 + 9 [/tex]

On adding ,

[tex]\rm\implies 34 [/tex]

Therefore ,

[tex]\rm\implies \boxed{\blue{\rm |m^2+n^2| = 34 }}[/tex]

Hence the required answer is 34 .

write an example of a monomial of degrees 5​

Answers

Answer:

find the value of:Cos = 0.54

Solve for x.
x - 42 = 98 – 9x
x = [?]

Answers

Answer:

x=14

Step-by-step explanation:

x - 42 = 98 – 9x

x+9x=98+42

10x=140

x=14

Answer:

[tex]x - 42 = 98 - 9x \\ x + 9x = 98 + 42 \\ 10x = 140 \\ x = 14 \\ thank \: you[/tex]

The simple interest formula is I = Prt, where I represents simple interest on an amount, P, for t years at a rate of r, where r is expressed as a decimal.

What is the amount of money, P, that will generate $40 in interest at a 10% interest rate over 5 years?

$60
$80
$90
$100

Answers

Answer:

80

Step-by-step explanation:

I = Prt

I = 40  R = .10  T = 5

40 = P (.10)(5)

40 = P(.5)

Divide each side by .5

40/.5 = .5P/.5

80 = P

The interest over 5 years is $80.

The correct option is B.

What is the simple interest?

Simple interest is the borrowing amount added only to the principal amount.

The Formula to calculate the simple interest is;

                                                 S.I. = P x T x R / 100,

Where S.I. is simple interest, P is the principal amount, T is the time period and R is the interest rate in a year.

We can use the formula I = Prt to solve for P. We know that I = 40, r = 0.10, and t = 5. Substituting these values, we get:

40 = P(0.10)(5)

Simplifying:

40 = 0.5P

Dividing both sides by 0.5:

P = 80

Therefore, the amount of money, P, that will generate $40 in interest at a 10% interest rate over 5 years is $80.

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Given that x= –1/2 and y = 4 , evaluate 3x²y + xy²​

Answers

Answer:

-5

Step-by-step explanation:

3x²y + xy²​

Let x = -1/2 and y = 4

3(-1/2)^2 (4) + (-1/2) (4)^2

Exponents first

3(1/4) (4) + (-1/2) 16

Multiply

3 - 8

Subtract

-5

Answer:   [tex]\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\la\la\la\la\ddddddddddddddddddddddddddddddddcleverdddddd\ffffffffffffffffffffffffffffffffffffffff\pppppppppppppppppppppppppppppppppppp\ddddddddddddddddddd\huge \boldsymbol {-5}[/tex]

Step-by-step explanation:                                                                                                                                                                                                                     simplify it                                                                                                                  [tex]\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\la\la\la\la\ddddddddddddddddddddddddddddddddcleverdddddd\ffffffffffffffffffffffffffffffffffffffff\pppppppppppppppppppppppppppppppppppp\ddddddddddddddddddd \displaystyle\ \Large \boldsymbol{} 3x^2y+xy^2=xy(3x+y)[/tex]                                                                       evalute                                                                                                        [tex]\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\la\la\la\la\ddddddddddddddddddddddddddddddddcleverdddddd\ffffffffffffffffffffffffffffffffffffffff\pppppppppppppppppppppppppppppppppppp\ddddddddddddddddddd \displaystyle\ \Large \boldsymbol{} -\frac{1}{2} \cdot 4 (-3\cdot \frac{1}{2}+4)=-2\!\!\!\!\diagup\cdot\frac{5}{2\!\!\!\!\diagup} =\boxed{-5}[/tex]                                                                                                                                                                                                                                                              

Which expression is equivalent to (x^-6/x-2)^3

Answers

Answer:

= (6/x - 2)^3

simplify -8/2 ÷ 6/-3​

Answers

Answer: the answer is 2 or C

-8/2 x -3/6

*Always do the recipical*

(-8 x -3) / (2 x 6)

-8 x -3= +24

2 x 6= 12

24/12= 2

The solution of the given expression -8/2 x -3/6 is 2. The correct option is B.

What is an expression?

In mathematics, expression is defined as the relationship of numbers, variables, and functions using mathematical signs such as addition, subtraction, multiplication, and division.

Given that the expression is,

-8/2 x -3/6

The expression will be solved as below,

E = (-8 x -3) / (2 x 6)

The numerator will get reciprocal and multiplied to the denominator,

E = 24 / 12

Divide the number 24 by 12 and get the solution,

E = 2

Therefore, the solution of the expression will be 2. The correct option is B.

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Use the given conditions to write an equations for the line in slope- intercept form. passing through (1,-8) and (-7,8)

Answers

Answer:

y = -2x - 6

Step-by-step explanation:

Going from the first point to the second, we see x decreasing by 8 from 1 to -7 (this is the 'run') and y increasing by 16 from -8 to +8 (this is the 'rise').  Thus, the slope of the line through these two points is m = rise/run =  16/(-8) = -2.

Using the point-slope formula y - k = m(x - h) and the point (1, -8), we get:

y + 8 = -2(x - 1), or

y = -8 - 2x + 2, or

y = -2x - 6 (in slope-intercept form)

Please answer correctly and I will give brainliest and crown plus an extra 20 points

Answers

Answer:

30.28 yd²

Step-by-step explanation:

Area enclosed = area of trapezoid + area of semicircle

= ½(a + b)*h + ½(πr²)

Where,

a = 5 yd

b = 2 + 5 = 7 yd

h = 4 yd

r = ½(4) = 2 yd

Plug in the known values

Area enclosed = ½(5 + 7)*4 + ½(π*2²)

Area enclosed = ½(12)*4 + ½(π*4)

= 6*4 + π*2

= 24 + 2π

= 30.2831853

≈ 30.28 yd² (2 decimal places)

A piece of fabric is 1/3 yard by 3 5/8 yards.
Irma solves 1/3*3 5/8 to find the area of the fabric in square yards.

Enter numbers to complete Irma's calculation for the area. (TTM)

Answers

Answer:

favricis 1/3 yard bt 3 5/8 yards wich it will be 64

does this table represent a function? Why or why not?

X: 2 2 3 4 5
Y: 1 4 4 2 5

Please answer it ASAP

Answers

No, certain points on the plot line the share the same output

find the original price if the price was 420 after a 10% discount

Answers

Answer:

466.67

Step-by-step explanation:

Let p be the original price

p - 10 % p = 420

p - .10p = 420

.9p = 420

Divide each side by .9

.9p/.9 = 420/.9

p =466.666666

Rounding to the nearest cent

p = 466.67

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