crate a list of steps, in order, that will solve the following equation. 2(x+3/4)^2 -5 =123
Answers
Answer:
x = -8.75; x = 7.25
Step-by-step explanation:
2(x + ¾)² - 5 = 123
Add 5 to each side: 2(x+ ¾)² = 128 Divide each side by 2: (x+ ¾)² = 64 Take the square root of each side: x + ¾ = 8 x + ¾ = -8 Subtract ¾ from each side: x = 8 - ¾ x = -8 - ¾ Convert to decimal fraction: x = 8 - 0.75 x = -8 – 0.75 Subtract: x = 7.25 x = -8.75The graph of your equation is a parabola with x-intercepts at x = -8.75
and x = 7.25.
The list of steps, in order, that will solve the equation is:
Addition of 5 to both sides to eliminate the value of -5Division of both sides of the equation by 2 to eliminate the coefficient of 2 from the left-hand sideTaking the square root of both sidessubtract 3/4 from each sideConvert the answer to decimalThe given expression is raised to a power of 2, so we can say that the given expression is a quadratic equation.
What is a quadratic equation?A quadratic equation is a form of an algebraic expression in which the variable is usually raised to the power of its second degree.
From the parameters given:
[tex]\mathbf{2(x + \dfrac{3}{4})^2 -5 = 123 }[/tex]
Addition of +5 to both sides[tex]\mathbf{2(x + \dfrac{3}{4})^2 -5 +5 = 123+5 }[/tex]
[tex]\mathbf{2(x + \dfrac{3}{4})^2 = 128}[/tex]
Division of both sides by 2[tex]\mathbf{\dfrac{2(x + \dfrac{3}{4})^2 }{2} =\dfrac{ 128}{2}}[/tex]
[tex]\mathbf{(x + \dfrac{3}{4})^2 = 64}[/tex]
Taking the square root of both sides[tex]\mathbf{\sqrt{(x + \dfrac{3}{4})^2} =\sqrt{ 64}}[/tex]
[tex]\mathbf{(x + \dfrac{3}{4})} =\pm8}[/tex]
Subtract 3/4 from both sides[tex]\mathbf{(x + \dfrac{3}{4} - \dfrac{3}{4}) }\mathbf{= \pm 8-\dfrac{3}{4}}[/tex]
[tex]\mathbf{x= \pm 8-\dfrac{3}{4}}[/tex]
[tex]\mathbf{x= +8-\dfrac{3}{4} \ \ OR \ \ x= -8-\dfrac{3}{4}} [/tex]
[tex]\mathbf{x=7.25 \ \ OR \ \ -8.75} [/tex]
Learn more about quadratic equations here:
https://brainly.com/question/17210919
Related Questions
the sum of the measures of the n interior angles of an n-gon is
Answers
Answer:
(n-2) * 180
Step-by-step explanation:
The sum of the measures of the interior angles of a polygon with n sides is
(n – 2)180
Ryan bought a guitar for $475.45. If he makes $9.25 per hour at his job, how many hours did he have to work to pay for the guitar? Explain how to find the answer and check it.
Answers
Answer: 51.4 hours
Step-by-step explanation: To figure out the answer to this equation you would divide the cost by how much you make, 475.45÷9.25=51.4
Ryan would need to work approximately 51.51 hours to earn enough money to pay for the guitar.
To find the number of hours Ryan had to work to pay for the guitar, we need to divide the cost of the guitar by his hourly wage.
Divide $475.45 (cost of the guitar) by $9.25 (Ryan's hourly wage):
$475.45 / $9.25
≈ 51.51
This calculation shows that Ryan would need to work approximately 51.51 hours to earn enough money to pay for the guitar.
To check the answer, multiply the number of hours (51.51) by Ryan's hourly wage ($9.25):
51.51 x $9.25 ≈ $476.33
The result is close to the cost of the guitar ($475.45), allowing for small discrepancies due to rounding or decimal approximations. Therefore, this confirms that Ryan would indeed need to work around 51.51 hours to cover the cost of the guitar.
To learn more about the division;
https://brainly.com/question/13263114
#SPJ2
a laptop computer is purchased for $950. after each year the resale decreases by 30%. what will the resale value be after 5 years?
Answers
Answer: 153
I think the answer is 153 because you have to do 950-30 and then divide it by 30 after you do that you multiply it by 5 and get 153.000000...
So you round it to the nearest whole number and that's 153
The resale value of a laptop after 5 years with a 30% decrease in value each year, follows the step-by-step calculation provided.
The resale value of a laptop after each year decreases by 30%. To calculate the resale value after 5 years, we need to consider the decreasing value each year:
After 1 year: $950 - $950 x 30% = $665
After 2 years: $665 - $665 x 30% = $465.50
After 3 years: $465.50 - $465.50 x 30% = $325.85
After 4 years: $325.85 - $325.85 x 30% = $228.10
After 5 years: $228.10 - $228.10 x 30% = $159.67
Find the total cost to the nearest cent. $25 pants; 20% off
Answers
Answer:
$20.00
Step-by-step explanation:
"$25 pants, 20% off" is equivalent to (1.00 - 0.20)($25), or:
0.80($25) = $20.00
This is the total cost to the nearest cent.
Answer:
$20
Step-by-step explanation:
Lets find the discount
25 * .2 = 5
You get $5 off
Price - discount = price you pay
25-5 = 20
HELP ASAP!!!!!!
What is the solution of the system below?
x=-3y-4
-3y=2x-7
z=-6x+y
a. x=-5, y=11, z=-71
b. x=11, y=-71, z=-5
c. x=-71, y=-5, z=11
d. x=11, y=-5, z=-71
Answers
d. x=11, y=-5, z= -71
To solve the given system of equations, we use the method of substitution. The solution is x = 11, y = -5, z = -71.
Explanation:To find the solution of the given system, we can use the method of substitution.
From the first equation, we have x = -3y - 4. Substituting this value for x in the second equation, we get -3y = 2(-3y - 4) - 7.
Solving this equation, we find y = -5. Substituting this value of y back into the first equation, we can solve for x. Plugging in y = -5, we get x = 11. Substituting these values for x and y in the third equation, we can find z. Plugging in x = 11 and y = -5, we get z = -71.
Therefore, the solution to the system is x = 11, y = -5, and z = -71.
Learn more about System of Equations here:https://brainly.com/question/21620502
#SPJ3
Select all that apply question! See picture
Answers
Lyle bought 3/8 of red grapes and 5/12 pound of green grapes how many pounds of grapes did he buy
Answers
Answer: 19/24
Step-by-step explanation:
3/8
+
5/12
=
(3 × 12) + (5 × 8)
8 × 12
=
76/96
=
76 ÷ 4
96 ÷ 4
=
19/24
I think the answer is is either B or C
Confused
Answers
Answer:C
Step-by-step explanation:If she studies for 10 munites and t equals munite t would go next tp 10 then d would go under it.
A reta que passa pelos pontos (2,-1) e (6,4) intersecta o eixo das abcissas no ponto (x,0) onde x é igual a:
a) -2,8
b) 2,8
c) 0,15
d) 1,8
e) 1,6
Answers
Answer:
[tex]x=2.8[/tex]
Step-by-step explanation:
we are given that
line passes through (2,-1) and (6,4)
Firstly, we will find equation of line
First point is (2,-1)
x1=2, y1=-1
second point is (6,4)
x2=6 , y2=4
now, we can find slope
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
now, we can plug values
[tex]m=\frac{4+1}{6-2}[/tex]
[tex]m=\frac{5}{4}[/tex]
now, we can use point slope form of line
[tex]y-y_1=m(x-x_1)[/tex]
now, we can plug values
[tex]y+1=\frac{5}{4}(x-2)[/tex]
since, we have to solve for x from (x,0)
so, we can set y=0
and then we can solve for x
[tex]0+1=\frac{5}{4}(x-2)[/tex]
[tex]5\left(x-2\right)=4[/tex]
[tex]x-2=\frac{4}{5}[/tex]
[tex]x=\frac{14}{5}[/tex]
[tex]x=2.8[/tex]
Solve for x in the equation?
a/(2x-c) = -1
Answers
Answer:
[tex]\frac{c-a}{2}[/tex]
Step-by-step explanation:
given [tex]\frac{a}{2x-c}[/tex] = - 1 ( cross- multiply )
- (2x - c ) = a ( distribute left side )
- 2x + c = a ( subtract c from both sides )
- 2x = a - c ( multiply both sides by - 1 )
2x = c - a ( divide both sides by 2 )
x = [tex]\frac{c-a}{2}[/tex]
Answer:
x = [tex]\frac{(a - c)}{-2}[/tex]
Step-by-step explanation:
a/(2x-c) = -1
The first step is to multiply both sides by (2x - c)
(2x - c)a/(2x-c) = -1(2x - c)
a = -2x + c
a - c = -2x + c - c
a - c = -2x
Divide both side by -2
(a - c)/-2 = x
∴ x = [tex]\frac{(a - c)}{-2}[/tex]
at first it increased by 25% and then decreased by 40%
Answers
Given question is incomplete; here is the complete question.
How did the temperature change if: at first it increased by 25 % and then decreased by 40% ?
Temperature will finally decrease by 25%.
Let the initial temperature is x° C,
If the temperature is increased by 25%,
Then the final temperature = x° + 25% of x°
= [tex]x+\frac{25x}{100}[/tex]
= [tex]x+0.25x[/tex]
= [tex]1.25x^\circ[/tex]
Followed by the decrease in temperature by 40%,
Then final temperature = 1.25x° - 40% of (1.25x°)
= 1.25x° - 0.5x°
= 0.75x°
Therefore, percentage decrease in temperature from initial temperature x°,
Percentage decrease = [tex]\frac{x^\circ-0.75x^\circ}{x^\circ}\times 100[/tex]
= 25%
Temperature will finally decrease by 25% when increased initially by 25% then decreased by 40%.
Learn more,
https://brainly.com/question/11708161
10 1/2 quarts if there were 7 groups doing the experiment and each group used the same amount of water,how many quarts
did each group use
Answers
Answer:
they each used 1.5 quarts PLEASE GIVE BRAINLIEST
Step-by-step explanation:
10.5 ÷ 7 = 1.5 QUARTS FOR EACH GROUP
To find out the amount of water each group used, the total quantity of water, 10 1/2 quarts, should be divided by the number of groups, which is 7. This gives the result of each group using around 1.5 quarts.
Explanation:To find out how many quarts each group used in the experiment, you would need to divide the total amount of water by the number of groups. In this case, you would divide 10 1/2 quarts by 7 groups.
First, you need to convert the mixed number 10 1/2 to an improper fraction or a decimal. 10 1/2 equals 21/2 or 10.5 in decimal form.
So, 10.5 quarts divided by 7 groups equals approximately 1.5 quarts.
Therefore, each group used 1.5 quarts of water for their experiment.
Learn more about division here:https://brainly.com/question/33969335
#SPJ2
identify an equation in point-slope form for the line parallel to y=5x+2 that passes through (-6,-1)
Answers
Answer:
y = 5x + 29
Step-by-step explanation:
y=5x+2
Given equation is in the form of y=mx+b
Where m is the slope = 5
and b is the y intercept = 2
When the lines are parallel then their slopes are equal
So the slope of parallel line is also 5 (m=5)
Given that the line passes through (-6,-1)
We use point slope formula
y-y1= m (x-x1)
m=5, x1= -6, y1=-1
Plug in all the values
y - (-1) = 5(x-(-6))
y + 1= 5 (x+6)
y + 1= 5x + 30
Subtract 1 on both sides
y = 5x + 29
HELP!!
a student finished 45 of her homework problems in class. if the ratio of problems she finished to problems she had left was 9:4, how many homework problems did she have total?
Answers
Answer:
60
Step-by-step explanation:
45 divided by 9 is 5. So you multiply 4 times 5. Which equals 20. So 20 plus 45 is 65. Hope you understand it.
Katherine is considering two new cell phone plans she doesn’t want to spend more for minutes she won’t use one plan allows up to 250 minutes per month for $49 and the other plan allows up to 350 minutes per month for $65 in the last six months she used 1470 minutes use estimating an exact answer to you to determine the best cell phone plan for Katherine
Answers
Answer: The plan with 250 minutes is best because she Maximus uses only 245 minutes per month so just 5 min to spare. Also i used mental math
Step-by-step explanation:
1470 divided by 6 equals= 245 minutes exactly unless Katherine had rounded her answer
Final answer:
To determine the best cell phone plan for Katherine, compare the cost per minute for each plan. The second plan, which allows up to 350 minutes per month for $65, has a lower cost per minute.
Explanation:
To determine the best cell phone plan for Katherine, we need to compare the cost per minute for each plan.
For the first plan, Katherine gets 250 minutes for $49, which means the cost per minute is $49/250 = $0.196 per minute.
For the second plan, Katherine gets 350 minutes for $65, which means the cost per minute is $65/350 = $0.1857 per minute.
Since the cost per minute is lower for the second plan, Katherine should choose the plan that allows up to 350 minutes per month for $65.
What is the value of x?
Answers
Answer:
D
Step-by-step explanation:
The diagonals of a rhombus intersect at right angles. So sneaky!!
So the third angle of the triangle containing the two base angles is 90 degrees.
2x + 3 + 3x + 2 + 90 = 180 Combine like terms5x + 95 = 180 Subtract 95 from both sides5x = 180 - 95 Combine the terms on the right.5x = 85 Divide by 5x = 85/5x = 17All the members of a construction crew work at the same pace. Six of them working together are able to pour foundation in 22 hours. c How many hours would this job take if the number of workers increased by factor of 4?All the members of a construction crew work at the same pace. Six of them working together are able to pour foundation in 22 hours. c How many hours would this job take if the number of workers increased by factor of 4?All the members of a construction crew work at the same pace. Six of them working together are able to pour foundation in 22 hours. c How many hours would this job take if the number of workers increased by factor of 4?All the members of a construction crew work at the same pace. Six of them working together are able to pour foundation in 22 hours. c How many hours would this job take if the number of workers increased by factor of 4?All the members of a construction crew work at the same pace. Six of them working together are able to pour foundation in 22 hours. c How many hours would this job take if the number of workers increased by factor of 4?All the members of a construction crew work at the same pace. Six of them working together are able to pour foundation in 22 hours. c How many hours would this job take if the number of workers increased by factor of 4?
Answers
Answer:
5.5 h
Step-by-step explanation:
There is an inverse relationship between the time (t) it takes to do a job and the number (n) of workers (the more workers. the faster the work gets done).
t = k/n Divide both sides by n
t/n = k
If we have two different numbers of workers, then
t₁/n₁ = t₂/n₂ Multiply each side by n₂
t₂ = t₁ × n₁/n₂
t₂ = 22 × 1/4
t₂ = 5.5 h
Which statement is true about PQ in relation to the circumscribed circle ?
Answers
check the picture below.
Answer:
The answer is PQ is the diameter
Step-by-step explanation:
Used paperback books are $0.25 and hardback books are $0.50. If you buy 3 paperback book and 5 hardback books, how much money do you spend
Answers
Answer:3.25$
Step-by-step explanation:
If one paperback book is 0.25 and you buy 3 of them, (0.25 x 3) is 0.75 and a hardcover is 0.50 per book, (0.50 x 5) is 2 dollars and 50 cents and if you add the two, you will get 3.25$
The amount of money to spend to buy 3 paperback books and 5 hardback books is,
⇒ $3.25
Given that,
The cost of Used paperback books is $0.25.
And, cost of hardback books is $0.50
Here, the cost to buy 3 paperback books is,
⇒ [tex]3 \times 0.25[/tex]
⇒ $0.75
And, the cost of 5 hardback books is,
⇒ [tex]5 \times 0.50[/tex]
⇒ $2.50
So, the total cost of 3 paperback books and 5 hardback books is,
⇒ $0.75 + $2.50
⇒ $3.25
To learn more about the addition visit:
https://brainly.com/question/25421984
#SPJ4
Boots: $59.00, discount: 10 percent sales tax 5.5 percent
Answers
Answer:
Total cost of boots = $56.02
Step-by-step explanation:
$59 x 0.90 = $53.10
$53.10 x 1.055 = $56.02
or
59 x 0.10 = 5.9
59 - 5.9 = $53.10
53.10 x 0.055 = $2.92 tax
$53.10 + $2.92 = $56.02
What is √9/14 in simplest radical form? Enter your answer in the box.
Answers
Answer: (3√14)/14
Step-by-step explanation: you should go buy a scientific calculator Casio or a TI calculator not much about $10 i will help a lot
Twenty five employees decide to chip in to buy a small refrigerator for the office. If the cost of the refrigerator is 275 how much does each person have to contribute
Answers
Answer:
Each employee will need to contribute $55.
Step-by-step explanation:
275 / 5 = 55
Answer:
275 / 25 = 11 25 goes into 275 11 times
Step-by-step explanation:
Solve equation for z
Answers
Answer:
z = 7
Step-by-step explanation:
9z + 4 / 5 - 8 = 5.4
Add 8 to both sides.
9z + 4 / 5 = 13.4
Multiply 5 by both sides.
9z + 4 = 67
Subtract 4 from both sides.
9z = 63
Divide both sides by 9.
z = 7
Answer:
7 (rounded up)
Step-by-step explanation:
9z+4/5=13.5
Multiply both sides by 5
9z+4=67.5
Subtract both sides by 4
9z=63.5
Divide both sides by 9
z=7 (rounded up)
Zayed is helping his classmates get ready for their math test by making them identical packages of pencils and calculators.
He has 7272 pencils and 2424 calculators and he must use all of the pencils and calculators.
If Zayed creates the greatest number of identical packages possible, how many pencils will be in each package?
Answers
Answer:
He should have 3 pencils in each package.
Step-by-step explanation:
you would do 7272 divided by 2424 so that there is a pencil for each calculater.
Answer:
The number of pencils in each package is 3.
Step-by-step explanation:
The total number of pencils = 7272
The number of calculators = 2424
He has to create greatest number of package and the condition is he has to use all the calculator and pencils.
The minimum number is 2424 which is number of calculators, So he can create maximum of 2424 packages. He must use all 7272 pencils.
So to find the number of pencils, we need to divide the number of pencils by the number of calculators.
The number of pencils in each package = [tex]\frac{7272}{2424}[/tex] = 3
The number of pencils in each package is 3.
Help with trig homework
Answers
Answer:
225 m
Step-by-step explanation:
Since we know they are similar triangles
8 15
---------- = -----------
120 bridge
Using cross products
8 * bridge = 15* 120
8* bridge = 1800
Divide each side by 8
8/8* bridge = 1800/8
bridge = 225
Answer:
225m
Step-by-step explanation:
the 2 triangles shown are similar by AAA
so their sides are in the same ratio
bridge/15 = 120/8
bridge length = 15*15 = 225m
plz somebody I need these and I'm failing math cause of these problems.
Answers
Answer:
1.A =113.04 cm^2
2.A =616 in^2
Step-by-step explanation:
To find the area of a circle we use the formula
A = pi * r^2 if we know the radius or
A = pi * (d^2/4) if we know the diameter
In problem 1 we know the radius
A = pi * r^2
A = pi * (6)^2
A = 36*pi
Using 3.14 for pi
A = 36* 3.14
A =113.04 cm^2
In problem 2 we know the diameter
A = pi * d^2/4
A = pi * (28)^2/4
A = pi 784/4
A = 196
Using 22/7 for pi
A = 196*22/7
A =616 in^2
Answer:
1. Area of the circle with 6 cm radius is [tex] 113.14 cm^2[/tex].
2. Area of the circle with 28 cm diameter is [tex] 616 cm^2[/tex].
Step-by-step explanation:
1. Radius of the circle ,r= 6 cm
Area of the circle , A= [tex]\pi r^2[/tex]
[tex]A=\pi (6 cm)^2=\frac{22}{7}\times 6 cm\times 6 cm=113.14 cm^2[/tex]
Area of the circle with 6 cm radius is [tex] 113.04 cm^2[/tex].
2. Diameter of the circle = d = 28 cm
Radius of the circle , r = [tex]\frac{28 cm}{2=14 cm[/tex]
Area of the circle , A= [tex]\pi r^2[/tex]
[tex]A=\pi (14 cm)^2=\frac{22}{7}\times 14 cm\times 14 cm=616cm^2[/tex]
Area of the circle with 28 cm diameter is [tex] 616cm^2[/tex].
what is an interger?
Answers
An integer is any whole number and it can be positive or negative. Integers cannot be fractions!
A few examples of integers are...
21, 4, -6666
can you use the sas congruence postulate to prove that the two triangles ate congruent? explain your reasoning
Answers
Answer:
diagram and the SAS Congruence Postulate to prove the two triangles are congruent. Explain Henry's mistake. LOGICAL REASONING Decide whether enough information is given to prove that the triangles are congruent. If there is enough information, tell which congruence postulate you would use.
Step-by-step explanation:
Either table C or Table D shows a proportional relationship. Plot all the points from the table that shows a proportional relationship. I'll post a picture of the graph. Table C is ( X= 2,4,6,8) and Y= ( 1,3,5,7). Table D is ( X= 2,6,8,10) and Y= ( 1,3,4,5).
Answers
Answer:
Step-by-step explanation:
A proportional relationship is a straight line through the origin that grows at a constant rate
For table C
The constant of proportionality is y/x
2/1 = 4/3 = 6/5 = 8/7 This is not true so this is not proportional
For table D
The constant of proportionality is y/x
1/2 = 3/6 = 4/8 = 5/10 This is true so this is proportional
Margo has a coin collection. She was given 1 coin as a gift, and she adds 3 coins per year. Which of the graphs below represents Margo's coin collection?
A) graph of line going through 1, 2 and 3, 4
B) graph of line going through 1, 1 and 3, 3
C) graph of line going through 1, 4 and 3, 10
D) graph of line going through 1, 2 and 2, 5
Answers
Answer:
Option C) graph of line going through 1, 4 and 3, 10
Step-by-step explanation:
Let y equal to Margo's coin collection
Let x equal to number of years
At the begining x=0, y=1 → Point=(x,y)→Point=(0,1)
She adds 3 coins per year, then y=1+3x
At x=1, y=1+3(1)=1+3→y=4→Point=(x,y)→Point=(1,4)
At x=3, y=1+3(3)=1+9→y=10→Point=(x,y)→Point=(3,10)
The graph of line going through (1, 4) and (3, 10), then the option C is the correct.