What is the positive solution to the equation 0 = –x2 + 2x + 1? Quadratic formula: x = StartFraction negative b plus or minus StartRoot b squared minus 4 a c EndRoot Over 2 a EndFraction

Answers

Answer 1

Answer:

x = 2 + √2

x = 2 - √2

Step-by-step explanation:

- x² + 2x + 1 = 0

x² - 2x - 1 = 0

Here,

a = 1

b = - 2

c = - 1

Now,

Discriminant

D = b² - 4ac

= (-2)² - 4(1)(-1)

= 4 + 4

= 8

=2√2 > 0

Real and Distinct roots

x = - b +- √b² - 4ac/2a

= - (-2) +- √ = (-2)² - 4(1)(-1)/2(1)

= 2 +- √4 + 4/2

= 2 +- √8/2

= 2 +- 2√2/2

= 2 +- √2

x = 2 + √2 or x = 2 - √2

Answer 2

Answer:

x = 2 + √2 or x = 2 - √2

Step-by-step explanation:

Edge 2021


Related Questions

2(-n -3) - 7(5+2n)
Simplify to create an equivalent expression

Answers

[tex]\text{Simplify:}\\\\2(-n -3) - 7(5+2n)\\\\\text{Use the distributive property}\\\\-2n-6-35-14n\\\\\text{Combine like terms}\\\\-2n-6-35-14n\\\\-16n-6-35\\\\\boxed{-16n-41}[/tex]

what is the length of a diagonal of a cube with a side length of 1 cm?

Answers

Answer:

sqrt3 or about 1.7

Step-by-step explanation:

length^2 + Width^2 + Height^2 = Diagonal^2

so 1 + 1 + 1 = 3, which when square rooted equals

sqrt3 or about 1.7

Answer:

b

Step-by-step explanation:

edg

A savings account balance is compounded continuously.If the interest rate is 3.1% per year and the current balance is 1077.00 in how many years will the balance reach 1486.73?

Answers

Answer:13.8 is the best answer i could get

Step-by-step explanation:1,077 multiply that × 13.8 =14,862

Choose the formula for the volume of a rectangular prism V = lwh written in terms of h.

A. h = Vlw
B. h = lVw
C. h = lwV
D. h = Vwl
Part B
Find the height h of a rectangular prism with volume V = 96 cm3, l = 8 cm and w = 2 cm.

height =
cm

Answers

Answer:

h = V/lw and the height = 6cm

Step-by-step explanation:

h = V/lw

V= [tex]96cm^{3}[/tex]

l = 8 cm

w = 2cm

V/lw = 6

Thus, the height = 6cm

John's dog Fido is tied to a post in his backyard. Fido's leash is 8.5 feet long. Determine how much circular roaming area Fido has in the backyard to the nearest square foot. (Use 3.14 to represent π)

Answers

Answer:

227 ft^2

Step-by-step explanation:

Here, we are tasked with calculating the roaming area that Fido has

Calculating this is same as calculating the area of circle that has a radius which is equal to the length of the leash

Mathematically, the area would be

A = π * r^2

A = 3.14 * 8.5^2

A = 226.865 ft^2

To the nearest square foot, this is 227 ft^2

Please help me now plz I will mark you brainliest

Answers

Answer: C. Outside the circle.

Step-by-step explanation:

To find whether point M lies on the circle, first derive the equation of the circle from the radius and center given.

Equation of a circle:

[tex](x-h)^2 + (y-k)^2=r^2[/tex]

Substitute the coordinates (0, 0) for h and k, and 2 times the square root of 3 for r:

[tex]x^2 + y^2 = 12[/tex]

Now, substitute the points (-3, 2) for x and y:

[tex]9 + 4 = 12[/tex]

This equation is incorrect, as the (x, y) coordinates produce a greater value than the radius of the circle squared. When this occurs, the point given is outside of the circle.

(A point like (1, 1), when substituted into the equation and solved to get 1 + 1 = 12, would be inside the circle, as its (x, y) coordinates produce a smaller value than the radius of the circle squared.)

As such, the correct answer is C.

Find five rational numbers between 3/7 and 2/3

PLEASE HELP...... I NEED TO SUBMIT THIS NOW....

Answers

Answer:

First, you get both of them with same denominator:

3/7 and 2/3 => 9/21 and 14/21, however, there are only 4 rational numbers between 9/21 and 14/21.

The solution is that you can raise the denominator 2 times:

9/21 and 14/21 => 18/42 and 28/42

Now you can select : 19/42, 20/42, 21/42, 22/42, 23/42. They are a group of  5 rational numbers you are looking for.

Please help!! Due at 12 AM please!! Will help you !!! I do have another question that i posted
that has NOT been answered so if u can help with that also.

Answers

Answer:

Rocket A: The x-intercept= (0,0) and (7,0)

Maximum= (3.5, 220.5) *idk if your teacher wants x's or y's

Average Rate of Change over [0,2]= 90

Rocket B: The x-intercepts are=(0,0) and (4,0)

Maximum=(2,32)

Average Rate of Change over [0,2]= 16

Rocket A is faster

Step-by-step explanation:

Rocket A: graph on demos

when x is 2 y is 180 180/2=90

Rocket B: i graphed the points on demos and imagined maximun of the graph

(it also tell you the x-intercepts)

32/2=16

Hope this helps

solve system of linear equations by substitution -2x+9y=15
x+7=4 ​

Answers

Answer:

1

Step-by-step explanation:

-2x+9y=15

x+7=4 ​

Solve for X.

x +7=4

   -7.  -7

x = -3

Plug in X into the first equation

-2(-3) + 9y = 15

6 + 9y = 15

-6.           -6

9y = 9

Divide by 9 on both sides

9/9=1

Answer:

x = -3. | y = 1. | (-3,1)

Step-by-step explanation:

-2x+9y=15

x+7=4

-7. -7

x= -3

-2(-3) + 9y =15

6 + 9y= 15

-6. -6

9y = 9

÷9. ÷9

y = 1

Triangle A is a scaled version of triangle B. The dimensions of triangle B are three times the dimensions of triangle A. The area of triangle A is 24.5 sq cm. What is the area of triangle B?

Answers

Answer:

The  area of triangle B is [tex]2.72cm ^{2}[/tex]

Step-by-step explanation:

We will use the principle of similar triangles to solve the problem.

Since triangle A is just a scale version of triangle B, we can say that the two triangles are similar.

The area scale factor is the square of the length scale factor.

Given the length scale factor as 3,

The area scale factor will be 3 X 3 = 9 sq. cm

(Area of triangle A / Area of triangle B) =  (length of side A / Length of side B) square

[tex]\frac{24.5}{ area of B}= 3^{2}[/tex]

[tex]\frac{24.5}{Area of B}= 9\\Area of B = \frac{24.5}{9}= 2.72 cm ^{2}[/tex]

The  area of triangle B is [tex]2.72cm ^{2}[/tex]

Which property of equality could be used to solve -3x = 348? A. addition property B. subtraction property C. division property D. multiplication property

Answers

Answer:

B:subtraction property

Step-by-step explanation:

Alice has 1/6 of a bowl of cereal Allison her brother wants to split the cereal equally which expression represents the fraction of the box of cereal that Alice gets

Answers

Answer:

it would be 1/6 divided by 2, or the seond option.

Step-by-step explanation:

To split something equally, you'd divide it in half. In other words, you'd be dividing it by 2.

Therefore, it would be 1/6 divided by 2, or the seond option.

I hope this helped and have a good rest of your day!

Geometry Question!!!!

Answers

It is not tanget because you use the hypotenuse and adjacent which would be cosine

Answer:

D

Step-by-step explanation:

If AB is a tangent, then angle A must be a right angle.

If angle A is a right angle, then triangle ABC is a right triangle and will work in the Pythagorean theorem formula.

a^2 + b^2 = c^2

8^2 + 16^2 = 20^2

64 + 256 = 400

320 = 400

Since 320 = 400 is false, angle A is not a right angle, and AB is not a tangent to circle C.

Answer: D

Grace made a dot plot showing the distances she ran each day for two weeks. She says that she usually runs 7 miles each day because that is the distance that occurs most often. Do you agree with Grace's reasoning?

Answers

Answer: No

Step-by-step explanation:

Because Mode is not the best centre of tendency use for statistical data. And mode cannot be used for average.

Mean should be used for average values

Answer:

da ba dee da ba doo im blue

Step-by-step explanation:

Grace made a dot plot showing the distances she ran each day for two weeks.

She says that she usually runs 7 miles each day because that is the distance that occurs most often.

Do you agree with Grace’s reasoning?

Use the drop-down menus to explain and show your answer.

Dot plot named as ALTDCDistances RunALTDC has number line from 1 to 7. 1 dot on 1, 3 dots on 2, 3 dots on 3, 3 dots on 4 and 4 dots on 7 are given.

The mode, which is (3,4, or 7) ,(is or is not) a typical distance for the data. The median, which is (3.5,4, or 7),(is or is not) a typical distance for the data. The mean, which is (3,4, or 7) ,(is or is not) a typical distance for the data. So, Grace’s reasoning(is or is not ) correct.

A road bike has a wheel diameter of 622 mm. What is the circumference of the wheel? Use 3.14 for Pi.
976.24 mm
976.54 mm
1,852.08 mm
1,953.08 mm

Answers

Answer:

4th option: 1953.08 mm

Step-by-step explanation:

circumference of circle= [tex]\pi d[/tex]

Thus, circumference of wheel

[tex] = 3.14(622) \\ = 1953.08mm[/tex]

Answer:

D.

Step-by-step explanation:

Find the length of the third side to the nearest tenth.

Answers

Answer:

What’s the third length?..

Step-by-step explanation:

Solve 8.2ws 29.52. Which of the following must be true abo
OWS36
The arrow points left
The arrow points right
There is an open circle at 3.6.
There is a closed circle at 3.6.

Answers

Answer:

A B E

Step-by-step explanation:

A- w less-than-or-equal-to 3.6

B- The arrow points left.

E- There is a closed circle at 3.6.

Answer:

A B E

Step-by-step explanation:

Terry has 3 pairs of pants: black, khaki, and brown, and 4 shirts: yellow, red, blue, and white. He does not care which colors he wears together. If Terry chooses one pair of pants and one shirt at random, what is the probability that his outfit will be the black pants with the yellow shirt?

Answers

Answer:

1/12 my guy

Step-by-step explanation:

There really isn't one

Answer:

Would be 0.08333 or 1/12

Step-by-step explanation:

Sue invested $1,000 at an interest rate of 4% compounded semiannually. How much money

would she have in 3 years?

Answers

Answer:

She would have $1,126.16 in 3 years.

Step-by-step explanation:

Compound interest:

The compound interest formula is given by:

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit year and t is the time in years for which the money is invested or borrowed.

In this question:

Invested 1000, which means that [tex]P = 1000[/tex].

Interest of 4%, so [tex]r = 0.04[/tex]

Semianually is twice a year, so [tex]n = 2[/tex]

How much money would she have in 3 years?

This is A(3).

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

[tex]A(3) = 1000(1 + \frac{0.04}{2})^{6} = 1,126.16[/tex]

She would have $1,126.16 in 3 years.

PLEASE ANSWER I WILL MARK BRAINLIEST!!!!!!!!!!!!!!

Answers

Answer:

1.5 timesbottle Ythird bottle

Step-by-step explanation:

Insufficient dimensions are given to compute an exact volume of each geometry, so we have to assume that the volume is proportional to the product of base area and height. Then the relative volumes will be ...

  bottle X: (6 in)(2 in)(1 in) = 12 in^3

  bottle Y: (4 in)(3 in)(1.5 in) = 18 in^3

  3rd bottle: (3 in)(6 in^2) = 18 in^3

That is, the relative volumes are ...

  X : Y : 3rd = 12 : 18 : 18 = 1 : 1.5 : 1.5

The corresponding relative prices are ...

  X : Y : 3rd = 9.96 : 14.40 : 13:20 = 1 : 1.446 : 1.325

__

A. Bottle Y has 1.5 times as much lotion as Bottle X.

__

B. Bottle Y is a better buy than Bottle X. (The price relative to X is less than the volume relative to X.)

__

C. The 3rd bottle is the best buy. For the same volume, the price of the 3rd bottle is less than that of Bottle Y.

_____

Note that the relative volume and price ratios are found by dividing all the numbers in the ratio sequence by the first number:

  12 : 18 : 18 = (12/12) : (18/12) : (18/12)

  9.96 : 14.40 : 13.20 = (9.96/9.96) : (14.40/9.96) : (13.20/9.96)

Explain why you cannot use algebra tiles to model the multiplication of a linear polynomial by a quadratic polynomial.


As an added challenge develop a model similar to algebra tiles that will allow you to show this multiplication. Describe an example of your model for the product (x + 1)(x^2 + 2x +2)

Answers

Answer:

The product of (x + 1)(x² + 2x + 2) is

x³ + 3x² + 2x + 4

Step-by-step explanation:

The product of (x + 1)(x² + 2x + 2) is Given in the steps below.

(x + 1)(x² + 2x + 2) = x(x² + 2x + 2) + x² + 2x + 2

= x³ + 2x² + 2 + x² + 2x + 2

= x³ + 3x² + 2x + 4

Solve the equation.
-9x + 1 = -x + 17
X=-8
O X=-2
X = 2
X = 8

Answers

Answer:

-9x + x = 17 – 1  

8x = 16

X = 16/8  

X=2

The mean weight of females in a class is 60kg and that of the males is 72kg. If the mean

weight of the class is 68kg, what is the ratio of females to males in the class?​

Answers

Answer:

1:2

Step-by-step explanation:

Let's say there are x males and y females in the class.

The sum of all male weights will be 72x, and the sum of all female weights will be 60y.

If we get a class mean weight, we have:

(72x + 60y) / (x+y) = 68

72x + 60y = 68x + 68y

4x = 8y

y / x = 4/8 = 1/2

So the ratio of females to males is the class is 1:2

Sumara Kato's savings account has a balance of $1663. After 19 years, how much interest
will she have earned if her rate is 5.5% compounded annually?
(1) $3159.70 (2) $2936.27 (3) $2942.27
(4) $2925.27

Answers

Answer: $2936.27

Step-by-step explanation:

Present value = $1663

Rate = 5.5%

Time(n) = 19years

Future value= PV(1+r)^n

= 1663(1+5.5%)^19

= 1663(1.055)^19

=1663 × 2.766

=4599.86

Interest = Future value - Present value

= $4599 - $1663

= 2936

Trapezoid EFGH is inscribed in a circle, with [tex]EF \parallel GH[/tex]. If arc GH is 70 degrees, arc EH is x^2 - 2x degrees, and arc FG is 56 - 3x degrees, where x > 0, find arc EPF, in degrees.

Answers

Answer:

Arc EPF is 240°

Step-by-step explanation:

Since the quadrilateral, EFGH is a trapezoid and EF is parallel to GH, we have;

∠HGF + ∠GFE = 180°

∠GHE + ∠GFE = 180°

∠HGF + ∠HEF = 180°

∴∠HEF = ∠GFE

In ΔHEF and ΔGFE

∠EHF = ∠EGF (Angles subtending the same segment)

With side EF common to both triangles and ∠HEF = ∠GFE , we have;

ΔHEF ≅ ΔGFE (Angle Angle Side rule)

Hence, side FG = EH

For cyclic trapezoid side FG = EH

The base angles subtended by GH = 70

Arc EH = x² - 2·x

Arc FG = 56 - 3·x

Therefore;

70 + x² - 2·x + 56 - 3·x + arc EPF = 360 .............(1)

Also since the equation of a circle is (x-h)² + (y-k)² = r², where the center of the circle is (h, k), then as EF is a displacement of say z from GH, then arc EH = FG which gives;

x² - 2·x = 56 - 3·x

x² - 2·x - 56 + 3·x = 0

x² + x - 56 = 0

(x - 7)(x + 8) = 0

Therefore, since x > 0 we have x = 7

Plugging in the value of x into the equation (1), we have

70 + 7² - 2·7 + 56 - 3·7 + arc EPF = 360 .............(1)

70 + 70 + arc EPF = 360

arc EPF = 360 - 140 = 240°.

can you please help me with this thanks

Answers

Answer: 6

Step-by-step explanation:

in a 30 60 90 triangle the hypothenuse is [tex]2a[/tex], long side is [tex]a\sqrt{3}[/tex], and the short side is [tex]a[/tex]

)) A triangle has sides with lengths of 5 inches, 12 inches, and 13 inches. Is it a right
triangle?
yes
no​

Answers

Answer:Yes

Step-by-step explanation:

Given

Triangle has sides

length [tex]a=5\ in.[/tex]

[tex]b=12\ in.[/tex]

[tex]c=13\ in.[/tex]

If the triangle is Right angled then it must satisfy the Pythagoras rule

[tex](\text{Perpendicular})^2+(\text{base})^2=(\text{Hypotenuse})^2[/tex]

[tex](a)^2+(b)^2=(c)^2[/tex]

[tex]5^2+12^2=13^2[/tex]

[tex]25+144=13^2[/tex]

[tex]169=13^2[/tex]

[tex]13^2=13^2[/tex]

Therefore The given triangle is right angled

A circle is shown. 4 radii are drawn. Chords are drawn to connect the radii points on the circle to form 2 triangles. The triangles have base lengths of 6 centimeters and the other 2 sides have lengths of 5 centimeters. The distance between the base of the triangle to the outline of the circle is 1 centimeter. Everything around the triangles is shaded. What is the area of the shaded region? (25π – 48) cm2 (25π – 30) cm2 (25π – 24) cm2 (25π – 12) cm2

Answers

Answer:

Area of Shaded Region = (25π - 24) cm²

Step-by-step explanation:

See attachment

From the attached, the following observations are made;

Radius, r = 5cm

Base of triangles = 6cm.

Required

Area of shaded region.

If the distance between the base of the triangle to the outline of the circle is 1cm then the height of the triangle is 1cm less than the radius

Height = 5cm - 1cm

Height = 4cm

To calculate the area of the shaded region, we first calculate the area of the circle.

Area = πr²

Substitute 5 for r

Area = π * 5²

Area = π * 25

Area = 25π cm²

Then we calculate the area of both triangles

Area of 1 triangle is calculated as follows.

Area = ½ * base * height

Substitute 4 for height and 6 for base.

Area = ½ * 4 * 6

Area = 2 * 6

Area = 12cm²

Since both triangles are equal.

Area of two triangles = 2 * Area of 1 triangle

Area = 2 * 12cm²

Area = 24cm²

Having calculated the area of the circle and that of both triangles.

Area of shaded region = Area of Circle - Area of Triangles

Area of Shaded Region = 25π cm² - 24 cm²

Area of Shaded Region = (25π - 24) cm²

Answer:

The third one

Step-by-step explanation:

5x – (9x + 14) < 3(x + 10) - 2

Answers

Sorry I don’t know I just need points to ask my question

Answer:

5x-(9x+14)=−4x−14

3(x+10)-2=3x+28

So, 3(x+10)-2 is greater than 5x-(9x+14)

Suppose that the mean time that visitors stay at a museum is 94.2 minutes with a standard deviation of 15.5 minutes. The standard error of the mean,ox, is 3.1. A random sample of 25 of the times chosen. What interval captures 68% of the means for random samples of 25 scores?

Answers

Answer:

[tex] 94.2 -0.994*3.1 = 91.1186[/tex]

[tex] 94.2 +0.994*3.1 = 97.2814[/tex]

And the 68% confidence interval is given by (91.1186, 97.2814)

Step-by-step explanation:

For this case we know that mean time that visitors stay at a museum is given by:

[tex] \bar X = 94.2 [/tex]

The standard deviation is given by:

[tex] s= 15.5[/tex]

And the standard error is given by:

[tex] SE = \frac{s}{\sqrt{n}} =3.1 [/tex]

And we want to interval captures 68% of the means for random samples of 25 scores and for this case the critical value can be founded like this using the normal standard distribution or excel:

[tex] z_{\alpha/2}= \pm 0.994[/tex]

We can find the interval like this:

[tex] \bar X \pm ME[/tex]

And replacing we got:

[tex] 94.2 -0.994*3.1 = 91.1186[/tex]

[tex] 94.2 +0.994*3.1 = 97.2814[/tex]

And the 68% confidence interval is given by (91.1186, 97.2814)

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