Solving Square Root Worksheet (x - k)^2 Part 3
7. 4(x + 2)^2 + 320 = 0
8. 7(x - 4)^2 - 18 = 10
9. -2(x + 2)^2 - 5 = 8
10. 1/5(t + 3)^2 = 7
Answer:
7. x = -2 +/- [tex]4i\sqrt{5}[/tex]
8. x = 2 or x = 6
9. x = -2 +/- [tex]\frac{\sqrt{26} }{2} i[/tex]
10. t = -3 +/- [tex]\sqrt{35}[/tex]
Step-by-step explanation:
7. Subtract 320 from both sides: 4(x + 2)^2 = -320
Divide by 4: (x + 2)^2 = -80
Square root both sides: x + 2 = +/- [tex]\sqrt{-80}[/tex]. We need to add the imaginary i to this: +/- [tex]\sqrt{-80}[/tex] = +/- [tex]i\sqrt{80}[/tex] = +/- [tex]4i\sqrt{5}[/tex]
Subtract 2 from both sides: x = -2 +/- [tex]4i\sqrt{5}[/tex]
8. Add 18 to both sides: 7(x - 4)^2 = 28
Divide by 7: (x - 4)^2 = 4
Square root both sides: x - 4 = +/- 2
Add 4 to both sides: x = 4 +/- 2 ⇒ x = 2 or x = 6
9. Add 5 to both sides: -2(x + 2)^2 = 13
Divide by -2: (x + 2)^2 = -13/2
Square root both sides: x + 2 = +/- [tex]\sqrt{-13/2}[/tex]. We again need i: +/- [tex]\sqrt{-13/2}[/tex] = +/- [tex]i\sqrt{13/2} =[/tex] +/- [tex]\frac{\sqrt{26} }{2} i[/tex]
Subtract 2 from both sides: x = -2 +/- [tex]\frac{\sqrt{26} }{2} i[/tex]
10. Multiply by 5 on both sides: (t + 3)^2 = 35
Square root both sides: t + 3 = +/- [tex]\sqrt{35}[/tex]
Subtract 3: t = -3 +/- [tex]\sqrt{35}[/tex]
Hope this helps!
Answer:
7. -2 + 4sqrt(5) i, -2 - 4sqrt(5) i
8. x = 2, 6
9. x = -2 + sqrt(13/2) i, -2 - sqrt(13/2) i
10. t = -3 + sqrt(35), -3 - sqrt(35)
Step-by-step explanation:
7. 4(x + 2)² + 320 = 0
(x + 2)² = -80
x + 2 = +/- i × sqrt(80)
x + 2 = +/- i × 4sqrt(5)
x = -2 +/- i × 4sqrt(5)
8. 7(x - 4)² - 18 = 10
(x - 4)² = 4
x - 4 = +/- 2
x = 2, 6
9. -2(x + 2)² - 5 = 8
(x + 2)² = -13/2
(x + 2) = +/- i × sqrt(13/2)
x = -2 +/- i × sqrt(13/2)
10. 1/5(t + 3)² = 7
(t + 3)² = 35
t + 3 = +/- sqrt(35)
t = -3 +/- sqrt(35)
Complete each equivalent rate.
20 miles
1 gallon
180 miles
gallons
Answer:
20 gallons per 180 miles
Step-by-step explanation:
i need the steps for 29
I need electricity asap :):):):(:
Answer:
C
Step-by-step explanation:
You distribute the 11 with the numbers in the parenthesis
Special Triangles
Find the missing side lengths. Leave answers as radicals in the simplest form.
Answer:
see explanation
Step-by-step explanation:
Using the cosine and tangent trigonometric ratios and the exact values
cos30° = [tex]\frac{\sqrt{3} }{2}[/tex] and tan30° = [tex]\frac{1}{\sqrt{3} }[/tex] , then
cos30° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{6}{m}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )
[tex]\sqrt{3}[/tex] × m = 12 ( divide both sides by [tex]\sqrt{3}[/tex] )
m = [tex]\frac{12}{\sqrt{3} }[/tex] ← rationalise by multiplying numerator/ denominator by [tex]\sqrt{3}[/tex] )
m = [tex]\frac{12}{\sqrt{3} }[/tex] × [tex]\frac{\sqrt{3} }{\sqrt{3} }[/tex] = [tex]\frac{12\sqrt{3} }{3}[/tex] = 4[tex]\sqrt{3}[/tex]
-------------------------------------------------------------------------------
tan30° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{n}{6}[/tex] = [tex]\frac{1}{\sqrt{3} }[/tex] ( cross- multiply )
[tex]\sqrt{3}[/tex] × n = 6 ( divide both sides by [tex]\sqrt{3}[/tex] )
n = [tex]\frac{6}{\sqrt{3} }[/tex] ← rationalise the denominator
n = [tex]\frac{6}{\sqrt{3} }[/tex] × [tex]\frac{\sqrt{3} }{\sqrt{3} }[/tex] = [tex]\frac{6\sqrt{3} }{3}[/tex] = 2[tex]\sqrt{3}[/tex]
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Which of the following is the solution of One-fourth x + 5 = 7?
Answer:
x/4 + 5 = 7
-5 -5
x/4 = 2
*4 *4
x=8
Step-by-step explanation:
Answer:
its 8
Step-by-step explanation:
i know so big brains
ax + 3x = bx + 5
solve for x
Answer:
Step-by-step explanation:
hello :
Ax + 3x = bx + 5
Ax + 3x-bx = bx-bx + 5
x(A+3-b) =5
x= 5/(A+3-b)
If I have 196 points and then loose 227 points how many points do I have in total
Answer:
You would have -31 points left. :)
196 - 227 = -31
Hope this helped!!
Answer:
-31
Step-by-step explanation:
196 - 227 = -31
You deposit $1800 into a bank account that pays 5% annual interest. Find the balance after 7 years if the interest is compounded quarterly. Round to the nearest cent
Answer:
The balance after 7 years would be $2,548.79
Step-by-step explanation:
We are given the following in the question:
P = $1800
r = 5% = 0.05
t = 7 years
The compound interest is given by:
[tex]A = p\bigg(1+\dfrac{r}{n}\bigg)^{nt}[/tex]
where A is the amount, p is the principal, r is the interest rate, t is the time in years and n is the nature of compound interest.
When compounded quarterly, n = 4
Putting values, we get,
[tex]A = 1800\bigg(1+\dfrac{0.05}{4}\bigg)^{28}\\\\A = \$2,548.79[/tex]
Thus, the balance after 7 years would be $2,548.79
What is the slope of the line through the points (-4, 6) and (-3, -1)?
Answer:
m= -7
Step-by-step explanation:
using the slope formula, plug in the variables and solve
m=rise/run
m=y2-y1 / x2-x1
(x1, y1) = coordinates of first point in the line
(x2, y2) = coordinates of second point in the line
Answer:
[tex]slope=-7[/tex]
Step-by-step explanation:
Use the slope formula for when you have two points:
[tex]\frac{y(2)-y(1)}{x(2)-x(1)}[/tex]
It is y over x because slope is rise over run : the change in the y-axis over the change in the x-axis. Plug in values:
(-4,6) (-3,-1)
[tex]\frac{-1-6}{-3-(-4)}[/tex]
Simplify
[tex]\frac{-1-6}{-3+4}=\frac{-7}{1}[/tex]
Simplify
[tex]\frac{-7}{1}=-7[/tex]
Done.
Please help me with this question.
Answer:
y = 6
Step-by-step explanation:
if the triangles are congruent then the corresponding sides are equal.
so
4x + 1 = 13
4x = 13 -1
4x = 12
Therefore x = 3
Now
8x - 2y = 2x + y
y + 2y = 8x - 2x
3y = 6x
3y = 6 * 3
3y =18
Therefore y = 6
Answer:
y = 6
Step-by-step explanation:
Since the triangles are congruent then corresponding sides are congruent
4x + 1 = 13 ( hypotenuse are congruent )
Subtract 1 from both sides
4x = 12 ( divide both sides by 4 )
x = 3
Thus
8x - 2y = 2x + y ( substitute x = 3 )
8(3) - 2y = 2(3) + y, that is
24 - 2y = 6 + y ( subtract y from both sides )
24 - 3y = 6 ( subtract 24 from both sides )
- 3y = - 18 ( divide both sides by - 3 )
y = 6
You ride your bicycle 40 meters. How many complete revolutions does the front wheel make?
The front wheel of the bicycle makes approximately 18 complete revolutions.
Explanation:To find the number of complete revolutions the front wheel makes, we need to know the circumference of the wheel. Let's assume the diameter of the wheel is 0.7 meters. The circumference of the wheel can be calculated using the formula C = πd, where C is the circumference and d is the diameter. Substituting the given values, C = 3.14 * 0.7 = 2.198 meters.
Since the bicycle travels 40 meters, we can divide the distance traveled by the circumference of the wheel to find the number of complete revolutions. 40 / 2.198 = 18.19.
So, the front wheel of the bicycle makes approximately 18 complete revolutions.
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For the following set of data, find the sample standard deviation,
to the nearest hundredth.
34, 47, 16, 43, 73, 17, 56
Summary:
The sample standard deviation of the given data set is approximately 20.72.
Explanation:To find the sample standard deviation, we can use the following steps:
Calculate the mean of the data set by adding up all the numbers and dividing by the total number of values. In this case, (34+47+16+43+73+17+56) / 7 = 38.57.Subtract the mean from each value to get the deviations from the mean: 34-38.57 = -4.57, 47-38.57 = 8.43, 16-38.57 = -22.57, 43-38.57 = 4.43, 73-38.57 = 34.43, 17-38.57 = -21.57, 56-38.57 = 17.43.Square each deviation: (-4.57)^2 = 20.89, (8.43)^2 = 70.92, (-22.57)^2 = 509.94, (4.43)^2 = 19.60, (34.43)^2 = 1185.37, (-21.57)^2 = 465.28, (17.43)^2 = 303.88.Add up all the squared deviations: 20.89 + 70.92 + 509.94 + 19.60 + 1185.37 + 465.28 + 303.88 = 2576.88.Divide the sum of squared deviations by the sample size minus 1: 2576.88 / (7-1) = 429.48.Take the square root of the result from step 5 to get the sample standard deviation: sqrt(429.48) ≈ 20.72.Add 6x+2y=-2 and 3x-2y=-5
Answer:
[tex]6x+2y=-2\\3x-2y=-5\\-------\\9x=-7[/tex]
Which one is bigger 2.300 mg or 2 g
Answer:
2 grams is bigger than 2.300 mg.
Step-by-step explanation:
1 milligram is equal to 0.001 gram.
1 gram is equal to 1000 milligrams.
If this helped you, Brainliest is appreciated.
Answer:
2 grams is bigger
Step-by-step explanation:
Two grams is bigger than 2.3 milligram . This is because 1 gram is equivalent to 1000 milligrams. To work that out you would multiply 2 by 1000, which is 2000
1 gram=1000 milligram
1) Multiply 2 by 1000.
[tex]1000*2=2000 mg[/tex]
However if it was a misplaced decimal and it was meant to be 2300 milligrams, then 2300 milligrams would be bigger.
Plot the coordinates
A (1, 2), B (4, 5), C (4, –3), and D (1, –1).
If the points are connected, what polygon is formed?
Triangle
Quadrilateral
Pentagon
Hexagon
Answer:
Quadrilateral
Explanation:
there are only for points,
triangle= three points
hexagon= 6 points
pentagon= 5 points
The A(1, 2), B(4, 5), C(4, -3), and D(1, -1) forms a quadrilateral.
What is a quadrilateral?A quadrilateral is a closed object in geometry that is created by connecting four points, any three of which are not collinear. There are 4 sides, 4 angles, and 4 vertices in a quadrilateral.
The points A (1, 2), B (4, 5), C (4, -3), and D (1, -1) form a quadrilateral
as all four points are noncolinear.
These four points represent four vertices of a quadrilateral.
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The Pew Research Center interviewed a random sample of 1,546 adult Americans to determine the average time they spent sleeping per night. The sample mean was found to be 7.2 hours of sleep, with a sample standard deviation of 1.4 hours. Construct a 95% confidence interval for the true mean. Interpret your confidence interval in words.
Answer:
CI=[ 7.1302,7.2698]
we are 95% confident that the true mean sleeping time lies between the interval[ 7.1302,7.2698]
Step-by-step explanation:
-Given that the sample size, n=1546 the mean is 7.2 hrs and the standard deviation, [tex]\sigma=1.4[/tex]
-The 95% confidence interval can be calculated using the formula:
[tex]CI=\mu\pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}\\\\=\mu\pm z_{0.025}\times \frac{\sigma}{\sqrt{n}}\\\\=7.2\pm1.96\times \frac{1.4}{\sqrt{1546}}\\\\=7.2\pm 0.0698\\\\CI=[7.1302, \ 7.2698][/tex]
The confidence intervals is therefore 7.1302,7.2698]
Hence, we are 95% confident that the true mean sleeping time lies between the interval[ 7.1302,7.2698]
If a part represents 24% of a total then which of the following is the fraction of the total part this represents ?
A. 7/20
B.1/24
C. 3/5
D.6/25
Akira turns in a written lab report to his science teacher.
Answer:
communicating results
Step-by-step explanation:
hope this helps
Step 1: Subtract 3 from both sides of the inequality.
Step 2: __________
Step 3: Divide both sides of the inequality by the coefficient of x.
What is the missing step in solving the inequality 5 – 8x < 2x + 3?
Add 2x to both sides of the inequality.
Subtract 8x from both sides of the inequality.
Subtract 2x from both sides of the inequality.
Add 8x to both sides of the inequality.
Answer:
Add 8x to both sides of the inequality
Step-by-step explanation:
took the quiz
The function f(x)= 9√x gives the speed in feet per second (ft/s) of a free-falling object after it has fallen x feet (ignoring air resistance). FInd the speed of the object after it has fallen 26 feet. If necessary, round your answer to the nearest tenth.
Answer:
45.9ft/s
Step-by-step explanation:
Simply plug your given value into the function
[tex]f(26)=9\sqrt{26} = 45.9 (1.d.p.)[/tex]
I need help asap:):):):
Answer:
4
Step-by-step explanation:
As you only need the answer (•‿•)
Answer:
5 shirts
Step-by-step explanation:
First, subtract the shipping from her money. 45 - 2.50 = 42.50. Now divide this by the price of each shirt. 42.50 ÷ 8.50 = 5. The shipping fee only applies once because it is for the entire order.
Which statements best describe the motion of Car A and Car B? Check all that apply.
Answer:
Car A and Car B are moving in opposite directions.
Car A is moving faster than Car B.
Car A and Car B pass each other at the crossover point on the graph.
Step-by-step explanation:
Hope that helps!
Simplify each expression.
ln e3 =
ln e2y =
eln 1 =
eln 5x =
Answer:
Step-by-step explanation:
the answers for "in e^3" is 3
"in e^2y" is 2y
"e^in 1" is 1
"e^in 5x" is 5x
Answer: 3, 2y, 1, 5x.
We have to simplify the given expressions.
We use the formula: [tex]ln(e^a)=a[/tex].
So, [tex]ln(e^3)=3[/tex], here a = 3.
[tex]lne^{2y}=2y[/tex], here a = 2y.
We will use that: ln(1) = 0 and [tex]e^{ln(b)}=b[/tex]
[tex]e^{ln(1)}=e^0=1[/tex]
[tex]e^{ln(5x)}=5x[/tex], here b = 5x.
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(5w7)2
What is the simplified power of the product?
A. 5w9
B. 10w14
C. 25w9
D. 25w14
Answer:
Its D i did the question
Step-by-step explanation:
A sporting goods company has observed a decline in sales following the end of each of its advertising campaigns. The decline in
sales follows the formula S=42e -0.16t, where is the monthly sales in millions of dollars and is the number of months after the end
of the advertising campaign. What will the monthly sales be three months after the end of the current campaign, rounded to the
nearest hundred thousand dollars?
Answer:
$26.0 million
Step-by-step explanation:
Use t=3 and do the arithmetic.
S = 42e^(-0.16·3) = 42e^-0.48 ≈ 26.0
Three months after the end of the campaign, monthly sales are predicted to be $26.0 million.
Answer:
$26.0 million
Step-by-step explanation:
A bonsai tree is 18 inches wide and stands 2 feet tall. What is the ratio of the width of the bonsai to its height?
Answer:
3:4
Step-by-step explanation:
Before we start to deal with the ratio, we need all lengths in the same units.
The width is 18 inches.
The height is 2 feet.
Let's convert the height to inches. Then we will have both dimensions in the same units, inches.
2 ft * (12 in.)/ft = 24 in.
Now we have:
width = 18 in.
height = 24 in.
ratio of width to height = 18 in. to 24 in. = 18/24 = 3/4 = 3:4
Final answer:
The ratio of the width to the height of the bonsai tree is 3:4 after converting both measurements to inches and simplifying. For the scale of a flower garden with a 1:12 scale and a plan width of 6 inches, the actual width of the garden is 6 feet.
Explanation:
The student asked about the ratio of the width to the height of a bonsai tree. First, it's important to have both measurements in the same units. Since the height is given in feet and the width in inches, we need to convert the height from feet to inches. There are 12 inches in a foot, so the height is 2 feet x 12 inches/foot = 24 inches. The resulting ratio of the width to the height is therefore 18 inches (width) to 24 inches (height). To simplify the ratio, we can divide both numbers by their greatest common divisor, which is 6 in this case. This gives us a simplified ratio of 3 to 4.
When calculating a scale for a flower garden, based on the available information where the plan shows 6 inches wide and the scale is 1:12, setting up the proportion would look like this: 1 inch on the plan equals to 12 inches in the actual garden. Therefore, to find the actual width of the flower garden, we multiply 6 inches (on the plan) by 12, resulting in an actual width of 72 inches or 6 feet.
PLEASE HELP!!!!
Ms. Calcutta, the owner of a business park is adding a recycling station for every three office buildings. To make it easier for the tenants, she is going to to use the circumcenter of the three office buildings to place the recycling stations. By doing this, it will be easier to get to the station, because it is equidistant from the three office buildings.
Complete Question:
Justify the rationale behind Ms Calcutta's decision to use the circumcenter
Answer:
Check below for the answer and explanations.
Step-by-step explanation:
Ms Calcutta wants every occupant of the three office buildings to have equal easy access to the recycling station. The circumcenter of the three three office buildings, where the recycling station is located, has equal distance from the three offices, this means that all of Ms. Calcutta's workers in the three buildings can have to the recycling station equally without causing unnecessary inconvenience for occupants of any of the buildings.
A scale drawing of an office space uses a scale of 2 inches in 3 yards the scale drawing has an area of 16 in.² what is the area of the actual office space
Answer:
36 Square Yards
Step-by-step explanation:
The Scale Drawing uses a ratio
2 Inches : 3 Yards
Therefore,
1 Inch = 3/2 Yards
If the area of the scale drawing is 16 Inch²
To get the area of the actual office, we multiply by the square of the scale factor.
Scale Factor=3/2
Therefore:
The area of the actual office space
=16X(3/2)² Square Yards
=36 Square Yards
Answer:
36 square yards.
Step-by-step explanation:
This question is solved with rule of three and ratios
We know that 2 inches is equivalent to 3 yards, and the area in the drawing is 16 square inches.
so if
2 inches ---- 3 yards then 1 inch is 3/2 yards.
Let's say that the office is 8 inches x 2 inches = 16 squared inches
Then, if we convert it to yards,
8 inches would be: [tex]8(\frac{3}{2})=12[/tex] yards
and 2 inches would be: [tex]2(\frac{3}{2})=3[/tex] yards
Then, the area of the office would be 12 x 3 = 36 squared yards.
Find the following product if possible. Explain if it is not possible.
(See picture)
Answer:
The answer to your question is the letter a
Step-by-step explanation:
| 1 4 -1 | | 2 -1 |
| 3 2 2 | | 0 3 | Product = 2 x 3 and 3 x 2 = 2 x 2
| 5 2 | It is possible to do this product,
the result will be a 2 x 2 matrix
Process
1.- Multiply first row by first column and second row by second column.
2.- Multiply the second row by the first column and second row by the second column.
= (1 x 2) + (4 x 0) + (-1 x 5) = 2 + 0 - 5 = -3
= (1 x -1) + (4 x 3) + (-1 x 2) = -1 + 12 - 2 = 9
= (3 x 2) + (2 x 0) + (2 x 5) = 6 + 0 + 10 = 16
= (3 x -1) + (2 x 3) + (2 x 2) = -3 + 6 + 4 = 7
Result
| 3 9 |
| 16 7 |