For what value of c does x^2−2x−c=4 have exactly one real solution?
PLEASE HELP!!!!!!!

Answers

Answer 1

Answer:

-5

Step-by-step explanation:

Moving all terms of the quadratic to one side, we have

[tex]x^2-2x-(c+4)=0[/tex].

A quadratic has one real solution when the discriminant is equal to 0. In a quadratic [tex]ax^2+bx+d[/tex], the discriminant is [tex]\sqrt{b^2-4ad}[/tex].

(The discriminant is more commonly known as [tex]\sqrt{b^2-4ac}[/tex], but I changed the variable since we already have a [tex]c[/tex] in the quadratic given.)

In the quadratic above, we have [tex]a=1[/tex], [tex]b=-2[/tex], and [tex]d=-(c+4)[/tex]. Plugging this into the formula for the discriminant, we have

[tex]\sqrt{(-2)^2-4(1)(-(c+4))[/tex].

Using the distributive property to expand and simplifying, the expression becomes

[tex]\sqrt{4-4(-c-4)}=\sqrt{4+4c+16}\\~~~~~~~~~~~~~~~~~~~~~~=\sqrt{20+4c}\\~~~~~~~~~~~~~~~~~~~~~~=\sqrt{4}\cdot\sqrt{5+c}\\~~~~~~~~~~~~~~~~~~~~~~=2\sqrt{c+5}.[/tex]

Setting the discriminant equal to 0 gives

[tex]2\sqrt{c+5}=0[/tex].

We can then solve the equation as usual: first, divide by 2 on both sides:

[tex]\sqrt{c+5}=0[/tex].

Squaring both sides gives

[tex]c+5=0[/tex],

and subtracting 5 from both sides, we have

[tex]\boxed{c=-5}.[/tex]


Related Questions

1/3 (1632 + x) = 726 solve for x
pLS help please i beg i plea plssss​

Answers

[tex] \frac{1}{3} (1632 + x) = 726[/tex]

[tex] \frac{1}{3} (x + 1632) = 726[/tex]

[tex] \frac{1(x + 1632)}{3} = 726[/tex]

[tex] \frac{x + 1632}{3} = 726[/tex]

[tex]3· \frac{x + 1632}{3} = 3·726[/tex]

[tex]x + 1632 = 3·726[/tex]

[tex]x + 1632 = 2178[/tex]

[tex]x + 1632 - 1632 = 2178 - 1632[/tex]

[tex]x =546[/tex]

So, the value of x is 546.

What is the mean for the following set of data, to the nearest whole number?5, 9, 15, 18, 2213171415

Answers

sorry but the digits after 18 are unclear. are they singular or going together in 2s or is it one big number?

ABCD is a rectangle with diagonals and if AC= 7x-4 and BD= 10 find the value of x ?

Answers

Answer: x=2

Step-by-step explanation:

The diagonals of a rectangle are equal.

Therefore AC=BD,

7x-4=10

7x=10+4

7x=14

x=14÷7

x=2

Cherly paid $35.20 for a strawberry shortcake and 4 doughnuts. ria paid $50.80 for a strawberry shortcake and 10 doughnuts. how much does a strawberry shortcake cost

Answers

Answer:$24.80

Step-by-step explanation:

a=15 b=? c=39

The answers are either: 36, 27, and 3√ 194

Would you please give me the answer and an explanation on how to get the answer.

Answers

C=39 which is the phyotimues and A+b=c

Work out the values of 9x - бу​

Answers

Answer:

3(3x - 2y)

Step-by-step explanation:

9x - 6y

Factor out 3 from the expression

3(3x - 2y)

PLEASE MARK ME AS BRAINLIEST AND HAVE A NICE DAY

i’m confused can y’all help ?

Answers

2) The slopes and y intercepts should be the same. In other words, the system of equations should overlap infinitely (meaning the lines overlap as “one line”).

3) y=3x+1 and y=3x-1 can be used for a system with no solutions. No value of x can make the equations equal.

Feel free to ask any follow-up questions!

9. Determine the discriminant of 2x² - 6x + 7 = 0 and then state how many solutions there are; additionally,
state the nature of the solutions. Do not solve.

Answers

We need to find the nature of the roots of the quadratic equation 2x² - 6x + 7 = 0 , and need to find the Discriminant

Now ,as we know that the Discriminant of any quadratic equation of the form ax² + bx + c = 0 , is D = b² - 4ac

So now ;

[tex]{:\implies \quad \sf D=(-6)^{2}-4\times 2\times 7}[/tex]

[tex]{:\implies \quad \sf D=36-56}[/tex]

[tex]{:\implies \quad \bf \therefore \quad \underline{\underline{Discriminant=-20}}}[/tex]

Now , as D < 0 ,So nature of roots will be imaginary

Lena has 1.6kg of sugar.She uses 470g for a cake.
How much sugar does she have left?

Answers

Answer: 1130 grams.

Step-by-step explanation:

She has 1130 grams remaining after converting 1.6kg to grams (160 0grams).

Answer:

1.13kg

Step-by-step explanation:

=> 1 kilogram = 1000 grams

convert into grams

=> 1.6 × 1000

multiply 1000 by 1.6

=> 1600

Now substract 470g from it

=> 1600 - 470

subtract 470 from 1600

=> 1,130g

convert the g back into kg

=> 1130 ÷ 1000

divide 1130 by 1000

=> 1.13kg

Someone plsss help me with this
I honestly totally forgot cuz they kept shoving dif stuff in my head, shawtees
So pls help

Answers

Answer:

Question 1. You can find the area of the rectangle, by multiplying the length and width of the rectangle, where (x + 2) is the length and (x + 1) is the width.

[tex]\mathrm{Question\:\:2.\quad{(x + 1)(x + 2) = { x }^{ 2 } +x+2x+2}}[/tex]

[tex]\mathrm{Question\:\:3.\quad{{ x }^{ 2 } +3x+2}}[/tex]

Step-by-step explanation:

Steps for finding the area of the rectangle

[tex]\mathrm{(x + 1)(x + 2)}[/tex]

Apply the distributive property by multiplying each term of x+2 by each term of x + 1

[tex]{ x }^{ 2 } +x+2x+2}[/tex]

Combine x and 2x to get 3x

[tex]{ x }^{ 2 } +3x+2[/tex]

Please Help Me I Will Give You The Brain Crown And Extra Points! Pt2

A projectile’s maximum height is shown by the vertex of the parabola. When does the cannonball reach its maximum height? Round to the nearest whole number and remember to include units.

Answers

Answer:  2 seconds

=========================================================

Explanation:

I'll be using x in place of t

The equation given is y = -4.9x^2 + 19.8x + 58

It is of the form y = ax^2 + bx + c which is the standard form for quadratics.

We have,

a = -4.9b = 19.8c = 58

Plug the first two values into the equation below

h = -b/(2a)

h = -19.8/(2*(-4.9))

h = 2.0204081632653

That value is approximate.

Rounding to the nearest whole number gets us roughly h = 2

Recall that (h,k) is the vertex of the parabola. In this case, it's the highest point. The cannonball reaches the highest point at roughly 2 seconds.

-----------------

Extra side notes:

To find the maximum height, plug the h value into the original equation. This will yield the value of k.To find the cannonball's flight time, plug in y = 0 and solve for x. Ignore the negative x solution.

Find the value of x ???

Answers

Answer: 82

Step-by-step explanation:

what is the sum of 5 4/6 + 4 1/3

Answers

Answer:

10

Step-by-step explanation:

First convert them to improper fractions

5 4/6 = (5×6 + 4)/6= 34/6

4 1/3 = (4×3 + 1)/3=13/3

Now make them have the same denominator. In order to do this, you must multiple 13/3 by 2/2, so both the denominators equal 6.

13/3 × 2/2 = 26/6

34/6 + 26/6 = 60/6 = 10

HELLO THERE, "Math wizards" and others can you solve these tricky problems? 2 ÷ 14 and solve this -5 ÷12 I will mark BRAINILEST ON WHOEVER MAKES THIER ANSWER IF THIER IS NOT A EXACT COPY OFF OF SOME ELSE'S :] looks like your "math power level" won't be high enough to beat this problem.....

Answers

Answer:

2/14=0.143

-5/12= -0.417

Step-by-step explanation:

To help open up a wine bar, Jose borrowed money from a bank. He took out a personal, amortized loan for $49,000, at an interest rate of 6. 65%, with monthly payments for a term of 7 years

Answers

Using simple interest, it is found that the monthly payments are of $854.875.

Simple Interest

Simple interest is used when there is a single compounding per time period.

The amount of money after t years in is modeled by:

[tex]A(t) = A(0)(1 + rt)[/tex]

In which:

A(0) is the initial amount.r is the interest rate, as a decimal.

In this problem, the parameters are A(0) = 49000, r = 0.0665, t = 7, hence the total amount is of:

[tex]A(t) = A(0)(1 + rt)[/tex]

[tex]A(t) = 49000[1 + 0.0665(7)][/tex]

[tex]A(t) = 71809.5[/tex]

Payments over a period of 12 x 7 = 84 months, hence the monthly payments are of:

71809.5/84 = $854.875.

More can be learned about simple interest at https://brainly.com/question/25296782

Santiago’s car travels 120 miles with 10 gallons of gas. Gustavo’s car travels 25 miles with 4 gallons of gas. Whose car gets the best gas mileage (miles per gallon)?

Answers

Answer:

gutavas get the best gas mileage

Find the value of x.

Answers

Answer:

Your answer is right at the top of the trapizoid

Step-by-step explanation:

How many 4/5 cup servings are in 2/5 of a cup of ice cream (in simpleist form)

Answers

Answer:

There is 1/2  of 4/5 cup servings in a cup of ice cream.

Use the drawing tool(s) to form the correct answers on the provided graph.
Consider the given function.
h(x) = (x + 1)^2 - 4 plot the intercept

Answers

Answer:

The answers are in the images below.

Step-by-step explanation:

The graph of the function  h(x) = (x + 1)² - 4 is given in attachment and it is a parabola.

What is Graph?

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The given function is h(x) = (x + 1)² - 4

h of x equal to x plus one whole square minus four.

We have to draw the graph of function  h(x) = (x + 1)² - 4

Let us find some points of the graph by considering the function.

When x=0,

y=-3

When x=1

y=0

when x=2

y=5

when x=3

y=12

Now let us plot these points on the graph, we get a parabola as in attachment.

Hence, the graph of the function  h(x) = (x + 1)² - 4 is given in attachment and it is a parabola.

To learn more on Graph click:

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I NEED HELP ASAP
Annual Interest Rate: A = P+Prt
Solve for r.

Answers

Answer:

r = [tex]\frac{A-P}{Pt}[/tex]

Step-by-step explanation:

Step 1: Subtract P from both sides.

[tex]P+Prt-P=A-P[/tex] [tex]Prt= A - P[/tex]

Step 2: Divide both sides by Pt.

[tex]\frac{Prt}{Pt} = \frac{A-P}{Pt}[/tex] [tex]r= \frac{A-P}{Pt}[/tex]

How long is the arc intersected by a central angle of StartFraction 5 pi Over 3 EndFraction radians in a circle with a radius of 2 ft? Round your answer to the nearest tenth. Use 3. 14 for Pi. 2. 6 ft 7. 0 ft 10. 5 ft 31. 4 ft.

Answers

The length of the arc of the circle with a radius of 2 ft and the angle made at the centre equal to [tex]\dfrac{5\pi}{3}[/tex] is 10.5ft.

What is the length of the arc of a circle?

The length of the arc of a circle is equal to the product of the circumference of the circle and the ratio of the angle made by the arc of the circle to 2π. It is given by the formula,

[tex]\text{Length of the arc}= 2\pi r\times \dfrac{\theta}{2\pi}[/tex]

It is given that the radius of the circle is equal to 2 ft while the angle made by the arc at the centre of the circle is equal to [tex]\dfrac{5\pi}{3}[/tex]. And we know the formula for the length of the arc, therefore, the length of the arc,

[tex]\text{Length of the arc}= 2\pi r\times \dfrac{\theta}{2\pi}[/tex]

                            [tex]= 2\pi \times 2 \times \dfrac{\frac{5\pi}{3}}{2\pi}\\\\= 10.471 \approx 10.5\rm\ ft[/tex]

Hence, the length of the arc of the circle with a radius of 2 ft and the angle made at the centre equal to [tex]\dfrac{5\pi}{3}[/tex] is 10.5ft.

Learn more about the Length of the Arc of a Circle:

https://brainly.com/question/1577784

Answer:

C or 10.5 ft

Step-by-step explanation:

the diagram shows a prism whose cross-section is an equilateral triangle of lengths 10cm. the length of the prism is 20cm​

Answers

Answer:

[tex]686.6 cm^2[/tex]

Step-by-step explanation:

From the volume we can find the surface area of one of the triangle sides, by dividing it by its height. You find out that the surface of the triangle face is [tex]\frac {866}{20}=43.3 cm^2[/tex]. Let's pick two of them since we have two side faces (one close to us in the image, one far away), for a total area of [tex]86.6 cm^2[/tex]. At this point we need to add the area of the rectangular faces, which are three rectangles of length 20 and height 10, for a grand total of [tex]3\times10\times20 = 600 cm^2[/tex].

Adding everything together, we get [tex]600+86.6 = 686.6 cm^2[/tex]

Answer:

c = 686.6

Step-by-step explanation:

A=ah+bh+ch+1/2√﹣a⁴+2(ab)²+2(ac)²﹣b⁴+2(bc)²﹣c⁴

=10·20+10·20+10·20+1/2·√﹣10⁴+2·(10·10)²+2·(10·10)²﹣10⁴+2·(10·10)²﹣10⁴

=686.60254

Multiply: (x+2)(x+8) Simplify and write your answer in Standard Form.

Answers

Answer:

(x+2)(x+8)=0

therefore if x+2=0

x+2-2=0-2

x=-2

and in standard form -2×10ⁿ where n=0

can someone help me out please ?

Answers

Answer:

[tex]8 + x = 25 \\ x = 25 - 8 \\ 17[/tex]

What value of x is in the solution set of 3(x – 4) > 5x + 2?
EO
0-10
ООО
05
A
5

Answers

Answer:

What value of x is in the solution set of 3(x - 4) = 5x + 2?

Solution:

3(x - 4) = 5x + 2 [Given]

Using the distributive law of multiplication on LHS

3x - 12 = 5x + 2

By grouping the similar terms on either sides and solving for x, we get

3x - 5x = 2 + 12

- 2x = 14

Divide both sides by -2 (by division property of equality)

(- 2x/2 )= 14/2

-x = 7

Therefore, the value of x is -7.

i need help for this qus
x+7=10

Answers

Step-by-step explanation:

x+7=10

10-7= x

x = 3

3+7=10

Answer:

x = 3

Explanation:

Subtract 7 from 10.

10 - 7 = 3

Therefore, 3 + 7 = 10

Translate this sentence into an equation.
64 is the sum of 20 and Greg's score.
Use the variable g to represent Greg's score.

Answers

Answer:

64 = 20 + g

Step-by-step explanation:

Greg's score is g.

Greg's score plus 20 is equal to 64.

In equation form, this is 20 + g = 64

20 + G = 64
20 is the known constant and is a known variable and is a addend to the score while G is another addend but we just don’t know the value so when you put the equation together the 20 would stand for the known addend and the G would stand for the unknown addend which both equal to 64z

What is the mean of this data set?
THE PUPSTERS
THE PUPSTERS
n = 10
Number of animals placed in a home:
2, 4, 4, 5, 5, 5, 5, 6, 6, 8
Number of animals placed in a home
Mean: ?
Range:?

Answers

Mean
= sum of numbers in set /number(n)
Sum of numbers
= 2+4+4+5+5+5+5+6+6+8
= 50
n= 10
Mean=50/10= 5

Range is the difference between the greatest and least numbers
Range = 8-2=6

nathan mixes 5 parts water with 2 parts liquid plant food

Answers

Answer: what ARE you trying to ask?

Step-by-step explanation: ??

Match the part of the circle with the term that best describes it.​

Answers

GH: chord
M: point of tangency
MJ: diameter
J: center
MH: radius
GH: secant

The part of the circle with the term is given.

What is a diameter?

A straight line that runs through the sideways of a body or figure, particularly a circle or sphere, is called as a diameter of a circle or sphere.

The matches of the part of the circle with the respective term is given below:

GH ↔ chord

M ↔ point of tangency

MJ ↔ diameter

J ↔ center

MH ↔ radius

GH ↔ secant

Therefore, all the part of the circle are matched with the respective term.

To learn more about the diameter;

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