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

Expand & simplify 3(y+5)-5(y-3)

Answers

Answer:

-2y + 30

Step-by-step explanation:

3(y+5)-5(y-3)

Distribute

3y+15 -5y +15

Combine like terms

-2y + 30

Is 25 x 10 to the power of 0 in scientific​ notation? If​ not, explain. Use pencil and paper. Explain why 10 is used as the base in the second scientific notation factor.

Answers

Answer:

a) Scientific notation is written as a unit digit, that can have other digits after the decimal place, multiplied by 10 to the power of n, where n can be any integer number.

Then 25x10^0 is not scientific notation, because there are two digits at the left of the decimal point.

The scientific notation would be:

2.5x10^1

b) Why is this useful?

Because we divide all our measures in powers of 10.

For example, you know that 1 meter  = 100c

But we can also write this as:

1m = 1.0*10^3 cm.

The use of scientific notation comes useful because we can have a fast read of the dimensions of our measure, and in another hand, is way easier work with the 10 as a base when we solve equations.

The amount of fuel remaining in a gas grill is a function of the number of hours, h that the grill has been used. This relationship can be expressed by the function below. F(h) = 100 - 2h Determine and represent the domain of this function for the problem situation using inequality notation.

Answers

Given:

The amount of fuel remaining in a gas grill is a function of the number of hours.

[tex]F(h)=100-2h[/tex]

To find:

The domain for this situation.

Solution:

Domain is the set of input values.

The amount of fuel remaining in a gas grill F(h) is

[tex]F(h)=100-2h[/tex]

where, h is the number of hours.

Here, domain is the set of all possible values of h.

We know that, time and remaining fuel cannot be negative. So,

[tex]h\geq 0[/tex]      ...(i)

[tex]F(h)\geq 0[/tex]

[tex]100-2h\geq 0[/tex]

[tex]100\geq 2h[/tex]

[tex]50\geq h[/tex]       ...(ii)

Using (i) and (ii), we get

[tex]0\leq h\leq 50[/tex]

Therefore, the domain of the given function is [tex]0\leq h\leq 50[/tex].

Give the digits in the tens place and the hundredths place.
14.67

Answers

The digit in the tens place is 1. The digit in the hundredths place is 7.

Answer:

1 is in the tens and 7 is in the hundredths place.

Step-by-step explanation:

14.67

1 is tens place

4 is ones place

then the . decimal

6 is the tenths place and 7 is the hundredths place

Samantha and Caden are planning an end-of-school party for the computer club at their school. They each suggest a recipe for punch to serve at the party.


Samantha's Recipe


3

1

2

parts cranapple juice


2

1

2

parts lemonade


Caden's Recipe


4

1

4

parts cranapple juice


3

3

4

parts lemonade


For each recipe, write a ratio that compares the number of parts of lemonade to the total number of parts.









Which recipe will have the stronger lemon taste? Explain how you determined your answer.

Answers

Answer and Step-by-step explanation:

Samantha's recipe has:

3 parts cranapple juice

2 parts lemonade

In total, this recipe has:

t = 3 + 2

t = 5

ratio = [tex]\frac{2}{5}[/tex]

Caden's recipe has

4 parts cranapple juice

3 parts lemonade

In total:

t = 4 + 3

t = 7

ratio = [tex]\frac{3}{7}[/tex]

The punch with stronger lemon taste will be the one whose recipe have a bigger proportion of lemon.

For Samantha's recipe, the proportion is 2 ÷ 5 = 0.4

For Caden's, 3 ÷ 7 = 0.43

Caden's punch will have a slightly stronger taste of lemon, because its proportion is slightly higher than Samantha's.

PARTA

It takes Mrs. Miklos 5 minutes to grade 7 quizzes. At this rate, how many quizzes can she grade in 15 minutes?

Answers

Answer:

21 quizzes

Step-by-step explanation:

Divide 15 by 5 to know how many 5 minutes are in 15 minutes.

[tex]15 \div 5 = 3[/tex]

5 minutes are spent for 7 quizzes.

5 × 3 minutes are spent for 7 × 3 quizzes.

[tex]7 \times 3 = 21[/tex]

Mrs. Miklos can grade 21 quizzes in 15 minutes.

solve for x 2x+ 20
66​

Answers

Answer:

x = 23

Step-by-step explanation:

Alternate exterior angles are congruent if a and b are parallel

2x + 20 = 66

2x = 46

x = 23

Hope this helped!

Miles
Minutes
Martin's running ability is measured by this proportion:
1 3
7 21
1
7
Use the proportion to identify the values of the variables
that complete the rate table
3
21
a =
7
a
b=
CE
b
70
15
c

Answers

Answer:

the answer is

a=49

b=10

c=105

How do you do this? It really confuses me.
The points (5, 5) and (4, 3) fall on a particular line. What is its equation in slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.

Answers

Answer:

you substitute 4x=34

Step-by-step explanation:

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]

Solve the following system of equations algebraically:

y = 4x^2 + 17x + 14
y = 2x + 5​

Answers

Answer:

When x = -3  y = -1

When x = -3/4  y = 7/2

Step-by-step explanation:

y = 4x^2 + 17x + 14

y = 2x + 5​

Set each equation equal to each other

4x^2 + 17x + 14  = 2x + 5​

Subtract 2x from each side

4x^2 + 17x-2x + 14  = 2x-2x + 5​

4x^2 + 15x + 14  =  5​

Subtract 5 from each side

4x^2 + 15x + 14-5  =  5​-5

4x^2 + 15x +9  = 0

Factor

(4x+3) ( x+3) =0

Using the zero product property

4x+3 =0    x+3 =0

4x = -3      x=-3

x = -3/4     x=-3

Now we need to find y for each x

x =-3   y = 2x+5  =2(-3)+5 = -6+5 = -1  

When x = -3  y = -1

x = -3/4   y = 2(-3/4) +5 = -3/2 +5 = 7/2

When x = -3/4  y = 7/2

Which of these is most likely to form a normal distribution?
10 dice rolled 100 times
10 dice rolled 1 times
10 dice rolled 1000 times
010 dice rolled 10 times

Answers

Answer: a distribution with a known shape and other properties.

Step-by-step explanation: 10 dice rolled 1000 times

Answer:is below

Step-by-step explanation:

10 dice rolled 100 times

20 points!!
(5x-19)^2 < (x-23)^2
please someone help me with this inequality :c​

Answers

Answer:

[tex]x (-1,7)[/tex]

Step-by-step explanation:

We need to square a binomial.

The following rule is applied:

[tex](5x)^2+2*5x(-19)+(-19)^2<x^2+2x(-23)+(-23)^2[/tex]

In our example,

[tex]A^2+2AB+B^2=(A+B)^2[/tex]

   A is equal to 5x,

    B is equal to -19 and

   N is equal to 2.

[tex]5^2*x^2-2*5x*19+19^2<x^2x-23+23^2[/tex]

what is the speed of an object that travels 210 miles in 7 hours ​

Answers

Answer:

30 miles per hour.

Step-by-step explanation:

Answer:

The speed of the object is 30 miles per hour.

Step-by-step explanation:

210÷7=30

Could I please have BRAINLIEST?

Should it matter if areas far from large cities lose population?

Answers

Answer:

It should.

Step-by-step explanation:

If a nearby city is losing people then the large city should try to help.  

(?)^2-3(?)=-2 can anyone solve this

Answers

Answer: x = 1 or x = 2

Sub in x for ?:

x^2-3x = -2 (Move all the terms to one side, and set the equation to equal 0)

x^2-3x+2 = 0 (Factor the simple trinomial by finding two numbers that multiply to 2 and add to -3)

x^2-x-2x+2 = 0 (Factor the expression)

x(x-1)-2(x-1) = 0 (Group like terms)

(x-1)(x-2) = 0 (Solve for x by setting each term equal to 0)

x-1 = 0

x = 1

x-2 = 0

x = 2

∴ x = 1 or x = 2.

Solve for X

?????????????,??????,?,,,,,,,??????

Answers

Answer:

X= 10°

Step-by-step explanation:

Those two angles equal the same, knowing this we make them equal each other to solve them in an equation.

6x+34=8x+14

Then you solve, add the x's together, and the numbers together.

34-14=8x-6x

20=2x

Then you divide to find X

20/2= 10°

X= 10°

Step-by-step explanation:

6x+34=8x+14

34-14=8x-6x

2x=20

x=20/2

x=10

A cargo helicopter delivers only 100100100-pound packages and 120120120-pound packages. For each delivery trip, the helicopter must carry at least 101010 packages, and the total weight of the packages can be at most 1{,}1001,1001, comma, 100 pounds. What is the maximum number of 120120120-pound packages that the helicopter can carry per trip?

Answers

Answer:

5

Step-by-step explanation:

Given that:

Weight of package delivered = 100 - 120 pounds

Number of packages carried per trip is atleast 10 = ≥ 10

Total weight of packages must be at most 1,100 ≤1,100

The maximum number of 120 pound packages the helicopter can carry:

Maximum capacity = 1100 pounds

Number of packages ≥ 10

Let number of 110 packages carried = x

Number of 120 packages carried = y

x + y ≥ 10 - - (1)

100x + 120y ≤ 1100 - - - (2)

From (1): x ≥ 10 - y

100(10 - y) + 120y ≤ 1100

1000 - 100y + 120y ≤ 1100

1000 + 20y ≤ 1100

20y ≤ 1100 - 1000

20y ≤ 100

y = 5

y = number of 120 pound packages carried

y = 5

Answer:

5

Step-by-step explanation:

Let

x = number of 100 pound packages

y = number of 120 pound packages.

For each delivery trip, the helicopter must carry at least 10 packages.

x + y ≥ 10

x ≥ 10 - y

Total weight of the packages the helicopter can deliver can be at most 1,100 pounds

100x + 120y ≤ 1100

Divide through by 20

5x + 6y ≤ 55

Substitute x ≥ 10 - y into the equation

5(10 - y ) + 6y ≤ 55

50 - 5y + 6y ≤ 55

y ≤ 55 - 50

y ≤ 5

Therefore, the maximum number of 120 pound packages helicopter can carry is 5.

Two different linear functions are shown below with two points given from each function Use slope-intercept form Function A has The equation of line A is or point-slope form to find the equation of each.

Linear Function A

Points : (-5, -2), (-5, 7)

Linear Function B

Points : (7, -5), (-2, -5)

Which is true about the following:

1. Function A has...

A: Slope of -7
B: Slope of 0
C: Slope of 9
D: No slope

2. The equation of line A is :

A: X= -5
B: Y= -5
C: X= -2
D Y= 7

Function B has...

A: Slope of -7
B: Slope of 0
C: Slope of 9
D: No slope

The equation of Line B is :

A: X= -5
B: Y= -5
C: X= -2
D: Y= 7

Answers

Answer:

This answer is option 1

Step-by-step explanation:

The awnser is No slope,x=-5,A slope of 0,and y=-5

A family travels to Bryce Canyon for three days. On the first day, they drove 140
miles. On the second day, they drove 200 miles. What is the least number of miles
they drove on the third day if their average number of miles per day was at least
180?

Answers

Q:

A family travels to Bryce Canyon for three days. On the first day, they drove 140  miles. On the second day, they drove 200 miles. What is the least number of miles  they drove on the third day if their average number of miles per day was at least  180?

A:

To find the average number of something, you would take all of the numbers you want to find the average of, add them together, and divide by the total number of items you added up.

For example: in this question, you have 140 miles, 200 miles, and x miles (the amount of miles they drove on the third day).

You would add all of these miles together and divide by 3, since you added 3 numbers together. This would equal the average.

Finding the average:  

Create an equation where all of the miles they drove are added together, divide this expression by 3, and set this greater than or equal to 180 (since they drove at least 180 miles on average).

(140 + 200 + x)/3 ≥ 180

Solve for x to find the least number of miles they drove on the third day. Multiply both sides by 3.

140 + 200 + x ≥ 540

Combine like terms on the left side of the equation.

340 + x ≥ 540

Subtract 340 from both sides of the equation.

x ≥ 200

The least number of miles the family drove on the third day was 200 miles, since x can't be anything less than 200.

Answer: x = 200 miles

Roberto has run the first 16 miles of a race, means he is 72% finished. How long is the race?

Answers

Answer:

22.22222222

Step-by-step explanation:

Answer:

the race is 22 miles long.

Step-by-step explanation:

p         %

~~  =  ~~

w        100

Regal Cinemas sold a total of 8500 movie tickets. Proceeds totaled $64,600. Tickets can be bought in one of 3 ways: a matinee admission cost $5, student's admission is $6 all day, and regular admission are $8.50. How many matinee tickets were sold if twice as many student tickets were sold as matinee tickets? * Only type the number of matinee tickets that were sold

Answers

Answer:

900

Step-by-step explanation:

From the information given you can write the following equations:

x+y+z=8500 (1)

5x+6y+8.50z=64600 (2)

y=2x (3)

First, you can replace (3) in (2) and (1):

x+2x+z=8500

3x+z= 8500 (4)

5x+6(2x)+8.50z=64600

5x+12x+8.50z=64600

17x+8.50z=64600 (5)

Now, you have two equations:

3x+z= 8500 (4)

17x+8.50z=64600 (5)

Then, you can isolate z in (4):

z=8500-3x (6)

Next, you can replace (6) in (5):

17x+8.50(8500-3x)=64600

17x+72250-25.5x=64600

7650=8.5x

x=7650/8.5

x=900

You can replace the value of x in (3) to find y:

y=2x

y=2*900

y=1800

Finally, you can replace the value of x in (6) to find z:

z=8500-3(900)

z=8500-2700

z=5800

According to this, the answer is that 900 matinee tickets were sold.

How do you write 6.5 × 10^-1 in standard form?

Answers

Since it is -1 you would move the decimal back one space. So .65

If it was a positive 1 it would be 65

FAST
Which expression is equivalent to rm ÷ rn? (4 points)

rm – n
rm + n
rm • n
rm ÷ n

Answers

it should be rm - n I THINK, i’m not sure

66°
OT 6
11
12/13
Find the measure of the angle

Answers

B g I gcm gzhzrdyzrabc Vega. BzdzdGvm

Can someone please help me I need help

Answers

Answer:

8 in

Step-by-step explanation:

Step 1: Define

A = 56

b = 7

A = bh

Step 2: Find h

h = A/b

h = 56/7

h = 8

Answer:

h= 8 inches

Step-by-step explanation:

A= bh;  b= 7 inches;    Area= 56 inches squared

56= 7h

56/7 = 7h/7

h= 8 inches

hope this helps!

8) On Tuesday Heather bought six hats. On
Wednesday half of all the hats that she had
were destroyed. On Thursday there were
only 19 left. How many did she have on
Monday?
PLS HELP

Answers

Answer: On Monday, Heather had 32 hats.

Step-by-step explanation: After Heather bought six hats on Tuesday, she had double the amount of 19, since half of her hats were destroyed on Wednesday resulting in 19 left. Double of 19 is 38 hats, meaning she had 38 after she bought six on Tuesday. That means on Monday she had 38 - 6 = 32.


Plz help me I’ll give brainliest

Answers

I think it is D ... I am very sorry if I am wrong :)

hi so I need help with my math the question says use the long division algorithm to find the decimal value of the fraction -1/4​

Answers

Answer:

uhm well I'm not sure what you mean by algorithm but just think it like this :

Step-by-step explanation:

think of 1/4 as a quarter and it says the negative

so -.25

Which ordered pairs make both inequalities true? Select two options.
15142
y 231+1


Answers

Answer: The points C(1,2) and E(2,2) make both inequalities true

Step-by-step explanation:

we have

-----> inequality A

The solution of the inequality A is the shaded area below the dashed line

------> inequality B

The solution of the inequality B is the shaded area above the solid line

The solution of the system of inequalities is the shaded area between the dashed line and the solid line

see the attached figure

Remember that

If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequalities and the point lie on the shaded area of the solution

Plot the points and verify if lie on the shaded area

Let

see the attached figure

The points C(1,2) and E(2,2) lie on the shaded area

The points A(-1,3) and B(0,2) satisfy inequality B but don't satisfy inequality A

The point D(2,-1) satisfy inequality A but don't satisfy inequality B

therefore

The points C(1,2) and E(2,2) make both inequalities true

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