Mathematics High School

Which of the following equations has only one solution?
x2 + 4x + 4 = 0
x2 + x = 0
x2 - 1 = 0

Answers

Answer 1
x^2 + 4x + 4 = 0
(x+2)^2 = 0
x+2 = 0
x = -2

answer
this one has only one solution
Answer 2
The answer is the first one. 

1) x = {-2}
2) x = {0, -1}
3) x = {1, -1}

The first one only has one solution

Related Questions

Given that WXYZ is a rhombus, find the value of x. A. 15 B. 20 C. 30 D. 45

Answers

In this problem, we are given the equations of the two sides of a rhombus.

Equation 1 is 4 x – 10

Equation 2 is 2 x + 20

Since the given shape is a rhombus, therefore the two sides have equal sides. Hence, we can simply equate equation 1 and equation 2:

4 x – 10 = 2 x + 20

2 x = 30

x = 15


Therefore the answer is:

A. 15

4 x – 10 = 2 x + 20

2 x = 30

x = 15

Using the Law of Cosines, in triangle DEF, if e=18yd, d=10yd, f=22yd, find measurement of angle D

Answers

check the picture below.

[tex]\bf \textit{Law of Cosines}\\ \quad \\ c^2 = {{ a}}^2+{{ b}}^2-(2{{ a}}{{ b}})cos(C)\implies c = \sqrt{{{ a}}^2+{{ b}}^2-(2{{ a}}{{ b}})cos(C)} \\\\\\ \cfrac{{{ a}}^2+{{ b}}^2-c^2}{2{{ a}}{{ b}}}=cos(C)\implies cos^{-1}\left(\cfrac{{{ a}}^2+{{ b}}^2-c^2}{2{{ a}}{{ b}}}\right)=\measuredangle C\\\\ -------------------------------\\\\ \begin{cases} d=10\\ e=18\\ f=22 \end{cases}\implies cos^{-1}\left(\cfrac{{{ 18}}^2+{{ 22}}^2-10^2}{2(18)(22)}\right)=\measuredangle D[/tex]

[tex]\bf \implies cos^{-1}\left(0.893\overline{93}\right)=\measuredangle D\implies 26.63^o\approx \measuredangle D[/tex]

How do you get rid of an exponent on a variable?

Answers

To get rid of an exponent to do the inverse function which is to take the root, or you can expand it. 
Final answer:

To get rid of an exponent on a variable, apply the inverse operation of the exponent such as division or root operations.

Explanation:

To get rid of an exponent on a variable, you need to apply the inverse operation of the exponent. If the exponent is multiplication, you use division, and if the exponent is an exponentiation, you use a root operation. For example, to get rid of a squared variable, you take the square root of the variable. If you have a variable raised to the third power, you take the cube root of the variable.

Learn more about Exponents on Variables here:

https://brainly.com/question/11920046

#SPJ5

Joyce is trying to solve the equation y = x2 − 8x + 7 using the quadratic formula. She has made an error in one of the steps below. Find the step where Joyce went wrong.

Step 1: x equals negative 8 plus or minus the square root of the quantity eight squared minus four times one times seven, end quantity, all over two times one.

Step 2: x equals negative 8 plus or minus the square root of sixty-four minus twenty-eight all over two times one.

Step 3: x equals negative 8 plus or minus the square root of thirty-six all over two times one.

Step 4: x equals negative 8 plus or minus six all over two.

Step 1
Step 2
Step 3
Step 4

Answers

Joyce is trying to solve the equation y = x2 − 8x + 7 using the quadratic formula. She has made an error in one of the steps below. Find the step where Joyce went wrong. FIRST OF ALL, Y MUST EQUAL 0 Step 1: x equals negative 8 plus or minus the square root of the quantity eight squared minus four times one times seven, end quantity, all over two times one. THIS IS WRONG. IT SHOULD BE POSITIVE 8 plus or minus the square root of the quantity eight squared minus four times one times seven, end quantity, all over two times one. Step 2: x equals POSITIVE 8 plus or minus the square root of sixty-four minus twenty-eight all over two times one. Step 3: x equals POSITIVE 8 plus or minus the square root of thirty-six all over two times one. Step 4: x equals POSITIVE 8 plus or minus six all over two. Step 5 X=(8±6)/2 Step 6 X=14/2 =7 or Step 7 X=2/2 =1 Answers {1,7}. So the answer is Step 1.

Write “$4,915 for 72 shares of stock” as a unit rate. Round to the nearest hundredth if necessary.

Answers

divide

4915/72 = 68.2638

 so $68.26 per stock is the unit rate

What is the missing step in this proof?

Answers

The answer is the third choice..
Statement: Angle 1 and angle 4 are congruent, and angle 3 and angle 5 are congruent.
Reason: Alternate Interior Angles Theorem

Hope this helps!

The missing step in the proof is;

Statement: ∠1 ≅ ∠4 and ∠3 ≅ ∠5Reason: Alternate interior angle theorem.

The correct answer choice is option C.

What is alternate interior angles theorem?

Alternate angle theorem states that when two parallel lines are cut by a transversal, the resulting alternate interior or exterior angles are congruent.

It is used to prove that alternate interior angles are equal if two parallel lines are cut by a transversal,

Hence, angle 1 is congruent to angle 4 and angle 3 is congruent to angle 5.

Read more on alternate interior angle:

https://brainly.com/question/20344743

#SPJ3

Determine the standard variation of the data below. (1, 2, 3, 4, 5)

Answers

Calculate for the mean/ average of the given numbers:
 
                             μ = (1 + 2 + 3 + 4 + 5) / 5 = 3

Then, we calculate for the summation of the squares of differences of these numbers from the mean, S
 
                             S  = (1 - 3)² + (2 - 3)² + (3 - 3)² + (4 - 3)² + (5 - 3)²
                                S = 10

Divide this summation by the number of items and take the square root of the result to get the standard deviation.

                              SD = sqrt (10 / 5) = sqrt 2  
                                    SD = 1.41

Thus, the standard deviation of the given is equal to 1.41. 
              
                            

Answer:

So basically sqrt of 2...

Step-by-step explanation:

In which case would it be best to use the “Factoring Method” to solve the trinomial equation?
x^2 + 4x = -­5
4.3x^2 + 2.4x -­ 3 = 0
x^2 ­ - 4x + 3 = 0

Answers

The best case would be to use factoring in the last equation because it has whole numbers that are "factorable," meaning that its c value has factors that evenly add up to its b value.
In this case, (x-3)(x-1). -1*-3=3 and -1+-3=-4

State the Midpoint formula?

How are the midpoint formula and the Distance formula alike? How are they different?

Give a real-world example that could be addressed using the distance formula.

Give a real-world example that could be addressed using the midpoint formula.

Answers

Let point A (x₁, y₁) and point B (x₂, y₂)

Mid-point formula is given by: [tex][ \frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}] [/tex]

The distance formula is given by: [tex] \sqrt{(x_1-x_2)^2+(y_1-y_2)^2} [/tex]

The two formula are alike because they both need the information of two coordinate points 

They are different because the mid point formula is adding up then divide by two, whereas the distance formula is subtracting then square the answer.

--------------------------------------------------------------------------------------------------------------
Real life problem involving distance formula:

Plane A is spotted on a radar with cartesian coordinate (450, 640).
Plane B is spotted on the same radar with cartesian coordinate (350, 540)

Work out the distance between plane A and plane B.
--------------------------------------------------------------------------------------------------------------
Real life problem involving mid point formula

Ms. Holland arranges a treasure hunt for a group of scouts. She marks two points, C and D, with cartesian coordinate (-5, 6) and (7, 10) respectively. The clue is that the treasure is buried in the middle point between C and D. Work out the coordinate where the treasure is buried.
 

A school director must randomly select 6 teachers to participate in a training session. There are 34 teachers at the school. In how many different ways can these teachers be selected, if the order of selection does not matter?

Answers

The selection of r object out of n, is carried out in C(n, r) many ways, 

where [tex]C(n, r)= \frac{n!}{r!(n-r!)} [/tex]

n! meaning 1*2*3*....*(n-1)*n


According to this, the selection of 6 teachers out of 34, can be carried out in C(34, 6) many different ways.

[tex]C(34, 6)= \frac{34!}{6!(34-6!)}=\frac{34!}{6!(28!)}= \frac{34*33*32*31*30*29*28!}{6!28!}= \frac{34*33*32*31*30*29}{6!}[/tex]

[tex]=\frac{34*33*32*31*30*29}{6*5*4*3*2*1}= 34*11*4*31*29=1,344,904[/tex]

An isosceles triangle with equal sides of 5 inches and a base of 6 inches is inscribed in a circle. What is the radius, in inches, of the circle? Express your answer as a mixed number.

Answers

Final answer:

To find the radius of the circle inscribed in the isosceles triangle, we can use the formula for the inradius of a triangle. The inradius is given by the formula: inradius = (area of the triangle) / (semiperimeter of the triangle). First, we need to find the area and semiperimeter of the triangle. Then, we can calculate the inradius and find the radius of the circle.

Explanation:

To find the radius of the circle inscribed in the isosceles triangle, we can use the formula for the inradius of a triangle. The inradius is given by the formula:

inradius = (area of the triangle) / (semiperimeter of the triangle)

First, we need to find the area of the triangle. Since it is an isosceles triangle with equal sides of 5 inches, we can split it into two congruent right triangles. The height of each right triangle can be found using the Pythagorean theorem:

height = sqrt(5^2 - (6/2)^2) = sqrt(25 - 9) = sqrt(16) = 4 inches

Now, we can find the area of the triangle:

area = (1/2) * base * height = (1/2) * 6 * 4 = 12 square inches

Next, we need to find the semiperimeter of the triangle:

semiperimeter = (5 + 5 + 6) / 2 = 16 inches

Finally, we can calculate the inradius:

inradius = 12 / 16 = 3/4 inches

Therefore, the radius of the circle is 3/4 inches.

Solve for 4/x+2 = 2/x  x and determine if the solution is extraneous or not.
x = −2, extraneous
x = −2, non-extraneous
x = 2, extraneous
x = 2, non-extraneous

Answers

The given equation is:

4/(x + 2) = 2/x

First we get the value of x by doing cross multiplication so that all variables are in the numerator side:

4 x = 2 (x + 2)

4 x = 2 x + 4

2 x = 4

x = 2

An extraneous solution is one in which if we plug in the value of x back into the equation, the resulting values would be wrong.

Plug x = 2 back into the original equation:

4 / (2 + 2) = 2 / 2

4 / 4 = 2 / 2

1 = 1       (TRUE!)

Since the value of x = 2 satisfies the equation, then the solution is non-extraneous.

Answer:

x = 2, non-extraneous

70 decreased by twice a number

Use The variable n to represent the unknown number

Answers

70 - 2n <=== ur expression

The required expression of the given statement is 70-2n.

Given that,
To determine the expression for the given statement 70 decreased by twice a number.

What is arithmetic?

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

What is simplification?

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Let the number be n,
According to the question,
Number = n
70 decreased by twice the number,
So
= 70 - 2n

Thus, the required expression of the given statement is 70-2n.

Learn more about arithmetic here:

https://brainly.com/question/11424589

#SPJ2

A farmer had 17 sheep. all but 9 died. how many live sheep were left

Answers

all but 9 have died so he has 9 alive.
9 all BUT 9 died. I have to write 20 character for it to be "explained well" These words are basically fluff. my answer is in the first sentence.

Solve the equation: h/9 = 7. A. h = 1 2/7 B. h = 63 C. h = –63 D. h = 7/9

Answers

 I did this on a calculator so i'm 100% sure it's correct.
 
The answer is:  B. h= 63
Well, just times 7 and 9 since if you times 9 on both side,  h will be alone. Then just times 7 and 9 and will get 63, which is B.

HELPPP Plzzzzzzzzzz ASAP
Use Addition of Composite Figures to find the total shaded regions.

1) Find the shaded area. Round your answer to the nearest tenth, if necessary.

Answers

12*6 = 72 - (3*4) = 60 - (4*5) = 40
Come on, Queen. You can do this. It's a square sitting on top of a long skinny rectangle. The rectangle is 12 wide and 2 high. It's area is 12x2=24. The only tough part is figuring out the width of the block sitting on it. The width of the block is what's left after you subtract the 5 and the 3 from the 12. That's (12-5-3)=4. Whaddaya know ! The block is 4 wide and 4 high ... It's a square ! Its area is 4x4=16. Add that to the area of the rectangle and you have the answer.

Ryan spent $3.25 on lunch every day, Monday through Friday. If he had $20 at the start of the week, how much money will he have left after Friday?

Answers

$3.75

it's pretty simple you multiply $3.25 times the amount of days he spent the money so 5 which gives you $16.25 then subtract that out of $20 and you'll have $3.75 (:

The amount of money left after Friday is $3.75.

What is unitary method?

The method in which first we find the value of one unit and then the value of the required number of units is known as the Unitary Method.

According to the given question.

Amount of money spent for the lunch every day is $3.25.

Total amount of money Ryan have is $20.

Now, number of total days from Monday to Friday is 5.

So,

The amount spent for lunch for 5 days by Ryan

= 5 × $ 3.25 = $16.25         (by unitary method)

Therefore,

The amount of money left after Friday

[tex]\$20 - \$16.25\\= \$3.75[/tex]

Hence, the amount of money left after Friday is $3.75.

Find out more information about unitary method here:

https://brainly.com/question/22056199

#SPJ2

For a fixed amount of a gas at a constant temperature, the volume of the gas is inversely proportional to its pressure. At a pressure of 30 pounds per square inch (psi), a gas has a volume of 600 in.3. Which function can be used to model the volume of the gas y, in cubic inches, when the pressure is x psi?

Answers

we know that

A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form [tex]y*x=k[/tex] or [tex]y=k/x[/tex]

Let

x-------> the pressure in PSI

y------> the volume of the gas in cubic inches

In this problem we have the point [tex](30,600)[/tex]

so

[tex]x=30\ psi\\y=600\ in^{3}[/tex]

Find the constant k

[tex]y*x=k[/tex]

substitute the values of x and y

[tex]600*30=k[/tex]

[tex]k=18,000\ lb*in[/tex]

the equation is

[tex]y=18,000/x[/tex]

therefore

the answer is

[tex]y=18,000/x[/tex]

Answer:

[tex]y=\frac{18000}{x}[/tex]

Step-by-step explanation:

Let the volume of gas be y

Let the pressure be x

Since we are given that the volume of the gas is inversely proportional to its pressure.

⇒[tex]y \propto \frac{1}{x}[/tex]

Let the proportionality be k

So, [tex]y=\frac{k}{x}[/tex]  ---A

Now we are given that At a pressure of 30 pounds per square inch (psi), a gas has a volume of 600 cubic inches

So, substitute x = 30

y = 600

[tex]600=\frac{k}{30}[/tex]

[tex]600 \times 30=k[/tex]

[tex]18000 =k[/tex]

Substitute the value of k in A

So,  [tex]y=\frac{18000}{x}[/tex]

Hence  function can be used to model the volume of the gas y, in cubic inches, when the pressure is x psi is    [tex]y=\frac{18000}{x}[/tex]

Find the value of angle M

Answers

opposite angels = 180

 so 6m+13 +4m+7 =180

combine like terms

10m+20=180

10m =160

m=160/10 = 16

Angle M = 6m = 6(16) = 96 degrees

Which rate is the lowest price?
$6.30 for 9
$5.50 for 5
$4.20 for 7
$0.80 each

Answers

Answer: $4.20 for 7
This problem can be solved by dividing the pay by the number of items.

$6.30 / 9 = $0.70
$5.50 / 5 = $1.10
$4.20 / 7 = $0.60
$0.80 / 1 = $0.80

This shows that for the third option, $4.20 for 7, the rate per item is the lowest.

Which is a sum of cubes? a3 + 18 a6 + 9 a9 + 16 a12 + 8
a3 + 18
a6 + 9
a9 + 16
a12 + 8

Answers

Answer: [tex]a^{12}+8[/tex]


Step-by-step explanation:

let's check all the expressions

1. [tex]a^3+18[/tex]

here 18 is not a perfect cube.

2. [tex]a^6+9[/tex]

here 9 is not a perfect cube.

3.[tex]a^9+16[/tex]

here 16 is not a perfect cube.

4.[tex]a^{12}+8[/tex]

here 8 is a perfect cube, thus we can write above expression by using laws of exponents as

[tex](a^4)^3+2^3[/tex]

Thus, [tex]a^{12}+8[/tex] is a sum of cubes.

Use the diagram of the right triangle above and round your answer to the nearest hundredth. If measure B= 60 degrees and a = 10 meters, find b.

Answers

Answer: A. 17.32m

Step-by-step explanation:

Just took edge test

Answer:A

Step-by-step explanation:

In triangle PQR, C is the centroid.

A. If CY = 10, find PC and PY
B. If QC = 10, find ZC and ZQ
C. If PX = 20, find PQ

Answers

Because point C is the centroid of the triangle, therefore:

Segments PZ = ZR;  RY = YQ; QX = XP

A.
If CY = 10, then

PC = 2*CY = 20
PY = PC + CY = 20 + 10 = 30
Answers:     

PC = 20     

PY = 30

B.
If QC = 10, then

ZC = QC/2 = 5
ZQ = ZC + QC = 5 + 10 = 15
Answers:     

ZC = 5       

ZQ = 15

C.
If PX = 20
because the median RX bisects side PQ, therefore PX = QX = 20
PQ = PX + QX = 40
Answer:      

PQ = 40

A wire is first bent into the shape of a rectangle with width
4in and length 14in. Then the wire is unbent and reshaped into a square. What is the length of a side of the square?

Answers

First find the perimeter of the rectangle: 2w+2l which is 8+28=36. Then find the square root of 36 which is 6 so that is the answer.
First you have to find the area of the wire
Area of a rectangle=L*W= 14*4=56
Then divide that by 4 since a square has 4 equal sides
56/4=14
The length of a side of a square is 14 in

a triangle has two sides of the lengths 8 and 10 what value could the length of the third side be

Answers

The last side could be 6 making it a right triangle.
Pythagorean theorem proof: 6^2+8^2=10^2, or 36+64=100

The sum of the digits of a certain number is 12. When you reverse its digits you decrease the number by 36. Find the number

Answers

x+y=12

x*y =36

8+4=12, so make the digits 84, reverse to make it 48

84-48=36

 the numbers are 8 & 4

Identify a semicircle that contains C.

A.ABC
B.AC
C.CB
D. ACB

Answers

A semicircle that contains C is ACB.

Answer:  The correct option is (D). ACB.

Step-by-step explanation:  We are given to identify a semi-circle that contains the point 'C'.

As shown in the figure, AB is the diameter of the circle with center 'O'.

So, there are two congruent semi-circles made by the diameter AB.

The point 'C' lies on the upper semi-circle made by the diameter AB.

Since the upper semi-circle contains the point 'C', so it is named as the semi-circle ACB.

Thus, the semi-circle ACB contains the point 'C'.

Option (D) is correct.

30 POINTS!!!!!!!
A training field is formed by joining a rectangle and two semicircles, as shown below. The rectangle is 99m long and 72m wide.
Find the area of the training field. Use the value 3.14 for π, and do not round your answer. Be sure to include the correct unit in your answer.

Answers

You need to add the area of a rectangle which is 99 by 72, and the area of a circle with a diameter of 72
99 * 72 = 7128
3.14 * (72/2)^2
3.14 * 36^2
3.14 * 1296
4069.44
7128 + 4069.44 = 11197.44

Answer:

1273 hola aaaaa oigan busco novia

If the solution to 4 - 2x > x + 16 is x < a, what is the value of a?
A) 6
B) 4
C) 2
D) -4
E) -6

Answers

4-2x>x+16
B)4
I believe 4 is the answer If i was wrong can I at least get a thanks.

The sum of three consecutive odd integers is 18 less than 5 times the middle number. Find the 3 integers. Use an algebraic solution

Answers

X +(x+2) + (x+4) = 5(x+2)-18

3x+6 = 5x+10-18

3x+6 = 5x-8

3x=5x-14

-2x=-14

x=7

(x+2) =9

(x+4) =11

7 + 9+ 11 =27

5(9)-18 =45-18 =27


3 numbers are 7, 9 & 11

Other Questions
A nurse is developing a teaching plan for a client diagnosed with osteoarthritis. to minimize injury to the osteoarthritic client, the nurse should instruct the client to: The sense of disorganization that prompts a person to change when new information conflicts with previously organized thought patterns is The first personnel recovery (PR) task is _____________. This task activates the execution portion of the PR system. What does a broken yellow center line on the roadway mean? What is the BEST description and explanation for the underlined words in this sentence?The teenager smiled and exclaimed, My two favorite activities are eating and sleeping" What should happen when iki solution contacts something that does not contain starch? The field of ________ is concerned with maintaining biological diversity. The graph and table shows the relationship between y, the number of words Jean has typed for her essay and x, the number of minutes she has been typing on the computer. According to the line of best fit, about how many words will Jean have typed when she completes 60 minutes of typing? 2,500 2,750 3,000 3,250 Recent changes in the medicare system have affected the quality of health care that arnold's elderly aunt receives. these changes do not affect arnold directly, but urie bronfenbrenner would say they affect arnold's development because they are part of arnold's __________. What is the climax of chapter IV of The Story of My Life?A.Helen lies in bed at night and, for the first time, is excited about what will happen tomorrowB.Helen receives a new doll that was made for her by the children at the Perkins Institution.C.Helen throws the new doll onto the floor in anger and frustration, smashing it into pieces.D.Helen feels water on her hands and makes a connection between objects and language. A semicircular plate ft in diameter sticks straight down into fresh water along the surface find the force exerted by the water on one side of the plate The population of a town in 2000 was 430. The population is increasing at a rate of 0.9% every year. What will be the projected population of the town in 2010? Round your answer to the nearest whole number Of the 240 shirts on a rack, 40 percent are size medium. How many shirts on the rack are size medium? What role did the Han dynasty have in creating the Great Wall? Suppose you roll two standard number cubes once. Find the probability. P(7 or even) -cz+6z=tz+83 solve for z A rectangular gasoline tank can hold 36.0 kg of gasoline when full. what is the depth of the tank (in m) if it is 0.450 m wide by 0.900 m long? m (b) what is the volume of the tank (in gal)? (it is suitable for a passenger car.) gal What factors caused american business to develop into a mixed economic system rather than some other type of economic system? Which of the following is considered the MOST expensive form of books? Determine the factors of 15x2 + 3xy + 10x + 2y. (4 points)(3x + 2)(5x + y)(5x + y)(2x + 3)(3x + y)(5x + 2)(5x + 3)(2x + y) Steam Workshop Downloader