Use the quadratic formula to solve. SHOW ALL STEPS FOR FULL CREDIT. Make sure that the final answer has a simplified radical. 2x² -10x +3

Answers

Answer 1

Answer:

whats that

Step-by-step explanation:

Answer 2

Answer:

[tex]x=\frac{5+\sqrt{19}}{2}\text{ and } x=\frac{5-\sqrt{19}}{2}[/tex]

Step-by-step explanation:

If we have the standard form [tex]ax^2+bx+c[/tex], then we can use the quadratic formula:

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

First, let's identify our coefficients. We have [tex]2x^2-10x+3[/tex].

This can be rewritten as [tex](2)x^2+(-10)x+(3)[/tex].

Therefore, a=2, b=-10, and c=3.

Substitute these values into the quadratic formula. This yields:

[tex]x=\frac{-(-10)\pm\sqrt{(-10)^2-4(2)(3)}}{2(2)}[/tex]

From here, simplify. Evaluate the expression under the square root:

[tex]x=\frac{10\pm\sqrt{100-24}}{4}[/tex]

Evaluate:

[tex]x=\frac{10\pm\sqrt{76}}{4}[/tex]

Note that:

[tex]\sqrt{76}=\sqrt{4\cdot 19}=\sqrt{4}\cdot\sqrt{19}=2\sqrt{19}[/tex]

Therefore:

[tex]x=\frac{10\pm2\sqrt{19}}{4}[/tex]

We can factor out a 2 from both the numerator and the denominator:

[tex]x=\frac{2(5\pm\sqrt{19})}{2(2)}[/tex]

Simplify:

[tex]x=\frac{5\pm\sqrt{19}}{2}[/tex]

Therefore, our roots are:

[tex]x=\frac{5+\sqrt{19}}{2}\text{ and } x=\frac{5-\sqrt{19}}{2}[/tex]


Related Questions

find the cube of 2.9​

Answers

Step-by-step explanation:

[tex] {2.9}^{3} \\ 2.9 \times 2.9 \times 2.9 \\ 8.41 \times 2.9 \\ 24.389[/tex]

Answer:

The cube of [tex]2.9[/tex] is [tex]24.389[/tex].

A 5000 seat theater has tickets for sale at 26 and 40. How many tickets should be sold at each price for a sellout performance to generate a total revenue of 153800.

Answers

Answer:

The number of tickets for sale at $26 should be 3300

The number of tickets for sale at $40 should be 1700

Step-by-step explanation:

Use 2 equations to represent the modifiers within the problem:

[tex]5000 = a + b \\ 153800 = 26a + 40b[/tex]

Now you want to find the point at which the variables are changed to make both equations correct, this can be done by graphing and finding the intersection of both lines.

[tex]5000 = 3300 + 1700 \\ 153800 = 26(3300) + 40(1700)[/tex]

3/4 change 3/4 to a decimal show work

Answers

Answer:

0.75

Step-by-step explanation:

You just need to convert 3/4 into a decimal.

For example: If you get 3 out of 4 problems right on a quiz, in percent form it will be a 75%, in decimal form 0.75 because you'll move the percent sign 2 spaces to the left. That will then be a decimal if you're converting 75% to 0.75.

3 divided by 4 is also going to give you 0.75. Because, a "fraction slash" is the dividing point. So,

3/4 = 0.75

Alex bought 2 1/4 pounds of M&Ms and 1.6 pounds of gummy worms. If the M&Ms cost $2 per pound, and the gummy worms cost $ $2.75 per pound, how much did he spend?

Answers

Answer:

Alex paid $8.90 total. $4.50 for the M&Ms and $4.40 for the gummy worms.

Step-by-step explanation:

2 [tex]\frac{1}{4}[/tex] is equivalent to 2.25, and if each pound is worth $2, then you would multiply the cost by each pound bought, shown like this: $2 (2.25) = $4.50 (You are distributing the $2 to find the product).

$2.75 (1.6) = $4.40

$4.50 + $4.40  = $8.90

which algebraic expression represents the phrase "the quotient of negative eight and the sum of a number and three"

Answers

Answer:

Let x be that number.

[tex] - 8 \div (x + 3)[/tex]

The quotient is the result of dividing a number by another. In this case, the numbers are - 8 and x + 3.

The circle shown has a radius of 12 mm. What is the circumference of the circle?

Answers

Answer:

75.36

Step-by-step explanation:

First you would use the formula [tex]C=2\pi r[/tex] and the fill in your values, 2·3.14·12 and you will get 75.36.

If anyone answers, I love you.

Answers

Answer:

-5 7

6 -3

-9 1

Step-by-step explanation:

im so sorry if im wrong don't sew meh

Enter the correct answer in the box by replacing the values of m and b.

Answers

Answer:

f(x) = -2x + 5  Plato

Step-by-step explanation:

PLS ANSWER HELP
Thanks

Answers

Its congruent to ELG :)

How are lines KL and MN related?
O The lines intersect at point K.
O The lines are parallel.
O The lines are perpendicular.
O The lines do not have slopes,

Answers

The lines are perpendicular

The lines KL and MN perpendicular to each other.

What is slope?

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

here, we have,

If a line passes through two points, then the slope of the line is

m = y2-y1/x2-x1

From the given graph it is clear that coordinates of points on line KL are K(-8,2) and L(6,2).

The slope of line KL is

m = 0

The slope of line KL is 0, it means it is a horizontal line.

From the given graph it is clear that coordinates of points on line MN are M(-4,8) and N(-4,-6).

The slope of line MN is

m = 1/0

The slope of line MN is 1/0 or undefined, it means it is a vertical line.

We know that vertical and horizontal lines are perpendicular to each other.

Therefore the lines KL and MN perpendicular to each other.

To learn more on slope click:

brainly.com/question/3605446

#SPJ7

Solve: 3(g − 2) = 8

Answers

Answer:

g=4⅔

Step-by-step explanation:

3(g - 2)=8

3g -6 = 8

3g= 8+6

3g= 14

[tex] \frac{3g}{3} = \frac{14}{3} [/tex]

g=4⅔

hope this helps

Step-by-step explanation:

3(g - 2) = 8

3(g - 2) = 8

+ 2 +2

3g = 8

3÷3= 0 8÷3 = 4.6

so your answer will be g= 4.6 (5 if you round it up) or if you need it in fraction form it will be 4 and 2/3

How is quadrilateral ABCD related to quadrilateral A'B'C'D' shown below?

Answers

what you put is correct. A’B’C’D’ is what would be shown if you rotate ABCD 90 degrees clockwise

Answer:

i think its a

Step-by-step explanation:

question in picture.

Answers

Answer:

4,3,0.5 youre welcome, good Luckk : )

help me pleaseeeeeeeeeeeeeeeeeeeeeee

Answers

A they’re parallel because they have same slope

12 ft
8 ft
8 ft
Find the area of the kite.

Answers

Answer:

The area of the kite would be 48.

48 is the area of the kite

3x-100 what does x equal?

Answers

Yes it’s 33.33 repeating

An indoor water park has two giant buckets that slowly fill with 1000 gallons of water before dumping it on the people below. One bucket dumps water every 18 minutes. The other bucket dumps water every 16 minutes. It is currently 2:45 P.M. And both buckets dumped water 15 minutes ago. Find the next two times that both buckets dump water at the same time.

Answers

Answer:

The next two times both buckets dump water at the same time are 4:54 P.M and 7:18 P.M.

Step-by-step explanation:

From the question, one bucket dumps water every 18 minutes, say bucket A;

and the other bucket dumps water every 16 minutes, say bucket B.

Also, It is currently 2:45 P.M. and both buckets dumped water 15 minutes ago,

that is, both buckets dumped water at 2:30 P.M.

For bucket A, the next times it will dump water will be:

2:48 P.M, 3:06 P.M, 3:24 P.M, 3:42 P.M, 4:00 P.M, 4:18 P.M, 4:36 P.M, 4:54 P.M, 5:12 P.M, 5:30 P.M, 5:48 P.M, 6:06 P.M, 6:24 P.M, 6:42 P.M, 7:00 P.M, 7:18 P.M, 7:36 P.M, 7:54 P.M, 8:12 P.M, 8:30 P.M etc.

For bucket B, the next times it will dump water will be:

2:46 P.M, 3:02 P.M, 3:18 P.M, 3:34 P.M, 3:50 P.M, 4:06 P.M, 4:22 P.M, 4:38 P.M, 4:54 P.M, 5:10 P.M, 5:26 P.M, 5:42 P.M, 5:58 P.M, 6:14 P.M, 6:30 P.M, 6:46 P.M, 7:02 P.M, 7:18 P.M, 7:34 P.M, 7:50 P.M etc.

From above, we observe that the next two times both buckets dump water at the same time are 4:54 P.M and 7:18 P.M.

Hence, the next two times both buckets dump water at the same time are 4:54 P.M and 7:18 P.M.

PLEASE HELP ME! I am not sure how to answer this question.​

Answers

Answer:

yes

Step-by-step explanation:

the diagnols are congruent meaning that the diagnol lines in the middle are the same length. So theoretically the left and right lengths are the same, and the top and bottom lengths are the same. The triagles named both have the same base and they're hieght is sbviouysly the same so they would be SSS each of the sides on one triangle coresspondes to the other.

Multiply. −2⋅(4)⋅(−3)⋅(5) −120 −4 4 120

Answers

Answer:

-44120

Step-by-step explanation:

2) If 20 workers can build a house in 45 days, how many more workers are needed
to complete it in 30 days?
А
6
B
15
С
10
D
18

Answers

It’s D 18 if wrong I’m sorry but I took this test as well

Answer:

B

Step-by-step explanation:

What is the solution to the linear equation?

–12 + 3b – 1 = –5 – b

b = –2
b = –1.5
b = 1.5
b = 2

Answers

Step-by-step explanation:

If you have any questions about the way I solved it, don't hesitate to ask me in the comments below ;)

The solution to the linear equation –12 + 3b – 1 = –5 – b is:

b = 2

The linear equation is:

–12 + 3b – 1 = –5 – b

Collect like terms

-12  -  1 + 5  =  -b  -  3b

Simplify the rearranged equation

-8   =   -4b

Divide both sides by -4

[tex]\frac{-8}{-4} = \frac{-4b}{-4}[/tex]

The given expression, after dividing both sides by -4, will give:

2  =  b

Rewriting the resulting solution:

b  =  2

Therefore, the solution to the linear equation –12 + 3b – 1 = –5 – b is:

b = 2

Learn more here: https://brainly.com/question/2159099

Write the equation of the line that contains the given point and has the given slope.

(–8, –8), slope is 3

Answers

Answer:

y - 8 = 3(x - 8)

Step-by-step explanation:

Point-Slope Form: y + y₁ = m(x + x₁)

x₁ - x coordinate

y₁ - y coordinate

m - slope

Step 1: Define

Point (-8, -8)

Slope m = 3

Step 2: Write in point-slope form

y - 8 = 3(x - 8)

Suppose there is a 1.7f drop in temperature for every thousand feet that an airplane climbs into the sky. If the temperature on the ground is 49.9f what will be the temperature when the plane reaches am altitude of 4,000ft?? The temperature will be_____F (type an integer or a decimal)

Answers

Answer:

[tex]43.1 ^{\circ}F[/tex]

Step-by-step explanation:

Give that for every 1000 feet increase in the height there is a drop of [tex]1.7 ^{\circ}F[/tex] in temperature.

So, the rate of temperature drop with respect to height, R = 1.7/1000 [tex]^{\circ}F/\text{ft}[/tex].

If the change in height is [tex]\Deltah[/tex][tex]\Delta h[/tex] feet, the temperature drop,

[tex]\Delta T= \Delta h R \;^{\circ}F\cdots(i)[/tex]

The temperature on the ground is 49.9 [tex]^{\circ}F[/tex].

At the ground, the height is 0, so the change in height, \Delta h when the plane reaches an altitude of 4,000 feet, is

\Delta h =4000-0=4000 feet

Now, from equation (i), the temperature drop

[tex]\Delta T= 4000 \times \frac {1.7}{1000}=6.8\;^{\circ}F.[/tex]

Hence, the temperature at an altitude of 4000 feet [tex]= 49.9-6.8=43.1 \;^{\circ}F[/tex].

John buys two ties that each cost $19.99 he also buys a pair of dress pants that were originally $64 but a discounted by 30% more over he has a coupon for $10 off a purchase of $50 or more purchase finally sales tax is 6% in his state how much did John pay for the ties and pants

Answers

Answer:

Cost of ties and pants = $52.5

Step-by-step explanation:

Total cost of ties = $19.99

cost of dress pants = $64, discountted by 30%

discount on dress pants = 30% of 64 = 0.3 × 64 = $19.2

∴ Discounted price of dress pants = 64 - 19.2 = $44.8

Total cost of ties and dress pants = 19.99 + 44.8 = $64.79

Now, let us apply the coupon

coupon = $10 off every purchase of $50 or more

Purchase amount = $64.79 ;  therefore coupon applies.

Applying coupon

Purchase amount = 64.79 - 10 = $54.79

sale tax = 6% or purchase price

sale tax = 6% × 54.79

sale tax = 0.06 × 54.79 = $3.29

∴ Final cost of ties and dress pants = 54.79 - 3.29 = $52.5

which is the following solution to
x-13<18

Answers

Answer:

X < 31

Step-by-step explanation:

Answer: X<31

Hope this helps!

what is the value of r in the equation r+6=14?

Answers

Answer:

r = 8

Step-by-step explanation:

Given

r + 6 = 14 ( subtract 6 from both sides )

r = 8

You subtract 6 from 14 and you’ll get 8 so r=8

What’s the highest common multiple?

Answers

Answer:

HCF = 90

Step-by-Step explanation:

2 × 3⁴× 5 = 810

2³× 3²× 5²= 1800

Find the prime factorization of 810

810 = 2 × 3 × 3 × 3 × 3 × 5

Find the prime factorization of 1800

1800 = 2 × 2 × 2 × 3 × 3 × 5 × 5

To find the HCF, multiply all the prime factors common to both numbers:

Therefore, HCF = 2 × 3 × 3 × 5

HCF = 90

I’ll give you 10 points and brainley

Answers

Answer:

Srry bro this is way to blurry for me to read... Also dont show your password to randoms.

Step-by-step explanation:

Which expression is equal to 527.471?*
(5x100)+(2x10)+(7x1)+(4x10) + (7x100)+ (1x1,000)
(5x100,000)+(2x10,000)+(7x1,000)+(4x100) + (7x10)+ (1x1)
(5x100)+(2x10)+(7x1)+(4x1/1) + (7x1/10)+ (1x1/100)
(5x100)+(2x10)+(7x1)+(4x1/10) + (7x1/100)+ (1x1/1,000)

Answers

Answer:

Step-by-step explanation:

527.471 =(5 ×100.000) +(2 ×10.000) +(7 ×1.000) +(4 ×100) +(7 ×10) +(1×1)

Answer:

500029301.171

Step-by-step explanation:

how to factorise 15x-10x^3

Answers

The answer is 5x(3-2x^2)
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