(c) Solve by Completing the Square (Round answers to the nearest tenth)
x²+10 x+2=2 x+5
Answers
After solving the equation by Completing the square , the answer is x = 0.4 , x = -8.4 .
In the question ,
it is given that ,
the equation is x² + 10x + 2 = 2x + 5,
rewriting the equation ,
we get ,
x² + 8x - 3 = 0
adding 3 to both sides ,
we get ,
x² + 8x = 3 ,
For the method of completing the square ,
we take half of the second term's coefficient, and square it, then add it to both sides.
that is 8/2 = 4 .
the equation becomes ;
x² + 2*x*4 + 4² = 3 + 4²
(x + 4)² = 3 + 16
(x + 4)² = 19
taking root on both the sides ,
we get ,
x + 4 = ±√19
So , x = -4 + √19 or x = -4 - √19
Simplifying further ,
we get ,
x = 0.35889 or x = -8.35889
rounding to the nearest tenth we get
x = 0.4 or x = -8.4 .
Therefore , the solution of the given equation is x = 0.4 , x = -8.4 .
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Related Questions
Which of the following is another way to label Plane J?
Select one: Plane h Plane
ABD Plane EFG Plane ADF
Check
Answers
Plane ADF is another way to label Plane J.
In order to determine which of the given options is another way to label Plane J, we need to first identify the key characteristics of Plane J.
These characteristics are its points, lines, and planes that it contains. We can then use these characteristics to compare and match them with the given options.
Here are the key characteristics of Plane J: Points: J, A, D Lines: JA, JD, AD Planes: Plane J Now let's examine each option to see which one matches the characteristics of Plane J: Option A: Plane h This option is not a match since Plane h is not one of the planes that contain the points J, A, and D.
Option B: Plane ABD This option is not a match since Plane ABD contains points A, B, and D but not point J.
Option C: Plane EFG This option is not a match since Plane EFG contains points E, F, and G but not point J.
Option D: Plane ADF This option is a match since Plane ADF contains points A, D, and F which are all points that are contained in Plane J.
Therefore, Plane ADF is another way to label Plane J.
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Which expression has exactly two terms
4n
Ab2
5y2
3x5
Answers
Answer: 3x +5
Step-by-step explanation:
I did it
ITS THE FOURTH QUESTION
Answers
The surface areas of the figures are 336, 82 and 836
How to calculate the surface areasFrom the question, we have the following parameters that can be used in our computation:
The figures
For the triangular prism, we have
Surface area = 2 * 1/2 * 6 * 8 + 12 * 10 + 8 * 12 + 6 * 12
Surface area = 336
For the rectangular prism, we have
Surface area = 2 * (7 * 3 + 3 * 2 + 2 * 7)
Surface area = 82
For the cylinder, we have
Surface area = 2π * 7 * (7 + 12)
Surface area = 836
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The surface area of the prisms are
1. 336 cm²
2. 82 m²
3. 836 cm²
What is surface area?The area occupied by a three-dimensional object by its outer surface is called the surface area.
A prism is a solid shape that is bound on all its sides by plane faces.
The surface area of prism is expressed as;
SA = 2B +pH
where B is the base area , p is the perimeter and h is the height.
1. SA = 2B +ph
B = 1/2 × 6 × 8
= 24 m²
p = 6+8+10 = 24m
h = 12m
SA = 2 × 24 + 24 × 12
= 48 + 288
= 336 cm²
2. SA = 2( 3× 2) + 3× 7)+ 2 × 7)
= 2( 6+21+14)
= 2( 41)
= 82 m²
3. SA = 2πr( r +h)
= 2 × 3.14 × 7( 7 + 12)
= 44( 19)
= 836 cm²
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What is the inverse of the function f(x) = 2x + 1?
1
Oh(x) =
Ex-
2
2
O h(x)
1
2
1
2
h(x) =
Ex-
- 3x + 2
h(x) =
X
+
Save and Exit
Next
Mark this and return
Answers
Answer:
The inverse function is \(f^{-1}(x) = \frac{x-1}{2}\)
Step-by-step explanation:
We have the following function:
y = 2x + 1
Finding the inverse:
Exchange y and x, and then isolate y again. So
y = 2x + 1
Exchange y and x
x = 2y + 1
2y = x - 1
\(y = \frac{x-1}{2}\)
So
The inverse function is \(f^{-1}(x) = \frac{x-1}{2}\)
Archie bought 100 shares of stock in an ice cream company 2 years ago. He paid $60.65 per share. He just sold all of his shares for $67.68 per share. How much did he gain?
Answers
Answer:
Step-by-step explanation:
First, we need to find the difference between the price that he sold the shares for and the price that he bought them at: (67.68-60.65) = 7.03
That means that there was a gain of $7.03 per share for Archie.
That being said, since Archie bought 100 shares, we can multiply that number by 100 to find the total gain from selling the shares:
(7.03x100)= 703
The answer then is:
Archie gained $703 from selling all of his shares.
Help me please I beg if you can
Answers
Answer: The mean is 3780
Step-by-step explanation:
Mean is found by adding all values and dividing the sum by how many values were added.
4250+4019+3895+3739+3401+3376=22680
22680/6=3780
A national park has eighty thousand, nine-hundred twenty-three and eighty-six hundredths acres of land. Write in standard form
Answers
Hi :)
Eighty thousand nine hundred twenty three and eighty six hundredths
80,923.86
Which expression is always equivalent to sin x when 0° < x < 90°?
(1) cos (90°- x)
(3) cos (2x)
(2) cos (45° - x)
(4) cos x
Answers
The expression that is always equivalent to sin x when 0° < x < 90° is (1) cos (90° - x). Option 1
To understand why, let's analyze the trigonometric functions involved. In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. Since we are considering angles between 0° and 90°, we can guarantee that the side opposite the angle will always be the shortest side of the triangle, and the hypotenuse will be the longest side.
Now let's examine the expression cos (90° - x). The cosine of an angle is defined as the ratio of the length of the side adjacent to the angle to the length of the hypotenuse. In a right triangle, when we subtract an angle x from 90°, we are left with the complementary angle to x. This means that the remaining angle in the triangle is 90° - x.
Since the side adjacent to the angle 90° - x is the same as the side opposite the angle x, and the hypotenuse is the same, the ratio of the adjacent side to the hypotenuse remains the same. Therefore, cos (90° - x) is equivalent to sin x for angles between 0° and 90°.
On the other hand, options (2) cos (45° - x) and (3) cos (2x) do not always yield the same value as sin x for all angles between 0° and 90°. The expression cos x (option 4) is equivalent to sin (90° - x), not sin x.
Option 1 is correct.
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what is 5/8x+4=3/8x+12
Answers
Answer: It equals 32!
Step-by-step explanation: Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation
need help asap please help! 50 points!!!!!!!!!!!!!!!!!!!!!!!! Plese do all problems
Answers
Answer:
Step-by-step explanation:
8) a) In a parallelogram, opposite sides are equal and parallel.
BC = AD
12x - 1 = x + 21
12x = x + 21 + 1
12x = x + 22
12x - x = 22
11x = 22
x = 22 ÷ 11
x = 2
AD = x + 21
= 2 + 21
AD = 23
In a parallelogram, adjacent angles are supplementary.
∠A + ∠D = 180°
\(\sf y - 9 + \dfrac{y}{2}=180\\\\ \dfrac{2y}{2}+\dfrac{y}{2}=180+9\\\\\)
\(\dfrac{3y}{2}=189\\\\y =189*\dfrac{2}{3}\\\\y=63*2\\\\y = 126\)
∠D = 126 ÷2
= 63
In parallelogram, opposite angles are congruent.
∠B = ∠D
∠B = 63°
the dice was thrown 35 times and following numbers were obtained prepare frequency table51423266142545361526254132141626333
Answers
This table shows the frequency of each number obtained after throwing the die 35 times
How to prepare frequency tableTo prepare a frequency table based on the numbers obtained from throwing a die 35 times, we can list the numbers from 1 to 6 and count the frequency of each number.
Numbers: 1, 2, 3, 4, 5, 6
Frequency: 5, 14, 6, 4, 5, 1
Based on the given numbers, the frequency table would look like this:
Number | Frequency
1 5
2 14
3 6
4 4
5 5
6 1
This table shows the frequency of each number obtained after throwing the die 35 times.
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My checking account balance was $443 on February 1st and $872 on February 7th. Show the rate of change
Answers
Answer:
$61.29 per day.
Step-by-step explanation:
Checking account balance on February 1st: $443
Checking account balance on February 7th: $872
Difference in balances: $872 - $443 = $429
Number of days between February 1st and February 7th: 7 days
Rate of change = Difference in balances / Number of days
Rate of change = $429 / 7 days
To find the rate of change per day, divide the difference in balances by the number of days:
Rate of change = $429 / 7 days ≈ $61.29 per day
Therefore, the rate of change in your checking account balance during that period was approximately $61.29 per day.
Mr. Wilkins delivers newspapers to several houses on Maple Street. He delivers 27 papers every day, Monday through Saturday, and 32 papers on Sunday. How many newspapers does Mr. Wilkins deliver to the homes on Maple Street in 4 weeks?
A.128 newspapers
B.236 newspapers
C.540 newspapers
D.776 newspapers
Answers
Answer: B.236 newspapers
Step-by-step explanation:
Given : Mr. Wilkins delivers 27 papers every day, Monday through Saturday, and 32 papers on Sunday.
i.e. Total newspaper deliver in a week = 27 +32 =59
Then, Total newspapers deliver in 4 weeks = 4 x (Total newspaper deliver in a week)
= 4 x 59
= 236
Hence, 236 newspapers deliver to the homes on Maple Street in 4 weeks.
Correct option is B.
Sheila lives in a $95,000 brick home in the country with contents valued at
$15,000. Use the table below to calculate her monthly property insurance
premium.
Annual Premium per $100 of coverage
Brick
Steel
Mixed
Wood
Area
Building Contents Building Contents Building Contents Building Contents
rating
City 0.39 0.43 0.5 0.54 0.55 0 65 0.66 0.76
Suburb 0.45 0.52 0.56 0.63 0.72 0.74 0.83
0.85
Rural 0.6 0.69 0.71 0.8 0.89 0.91 1
1.02
A. $95.00
B. $56.13
C. $173.50
D. $78.65
Answers
Her annual property insurance premium is $673.50.
Option A is the correct answer.
What is insurance?Insurance is a means of protection from financial loss in which, in exchange for a fee, a party agrees to compensate another party in the event of a certain loss, damage, or injury. It is a form of risk management, primarily used to hedge against the risk of a contingent or uncertain loss.
here,
We have,
To calculate Sheila annual property insurance premium, we need to determine the appropriate rating based on the type of house and the area where it is located. Aida's house is a brick house in the country,
So we need to use the "Brick" and "Rural" ratings from the table.
The rating for the building is 0.6 per $100 of coverage, so for a value of $95,000, the premium for the building is:
0.6 x $950 = $570
The rating for the contents is 0.69 per $100 of coverage, so for a value of $15,000, the premium for the contents is:
0.69 x $150 = $103.50
The total annual premium is:
$570 + $103.50 = $673.50
Thus,
Her annual property insurance premium is $673.50.
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The triangle on the right is a scaled copy of the triangle on the left. Identify the scale
factor. Express your answer in simplest form.
Answers
9514 1404 393
Answer:
7/6
Step-by-step explanation:
The ratio of corresponding sides is ...
right/left = 14/12 = 7/6
The scale factor is 7/6.
Tom and Jerry were asked to solve the equation - 2y + 10 = -16. Tom wrote
y = 13 but Jerry wrote 13 = y. Tom is correct, but Jerry is wrong.
A.True
B.False
Answers
Answer:
false
Step-by-step explanation:
Both are correct
-2(13)+10=-16
both their answers satisfy the equation
Find the diameter of the object. 2 in
Answers
Answer:
Step-by-step explanation:
Can you write your questions clearly, so we can answer it well
Answer:
is it 2 inches?
Step-by-step explanation:
Part A: Calculate how much Portfolio 2 earns. Show all work.
Part B: Using your values from Part A, identify the portfolio that earns the most. What information from the table could be used to justify why that portfolio has higher earnings?
Answers
The total amount that Portfolio 2 earns is approximately $567.75.
How much does Portfolio 2 earn?To calculate the earnings for Portfolio 2, we need to calculate the return on each investment and then sum them up.
Return on Savings Account:
= $1,450 * 2.80%
= $40.60
Return on Government Bond:
= $2,200 * (-1.55%)
= -$34.10
Return on Preferred Stock:
= $3,700 * 11.70%
= $432.90
Return on Common Stock:
= $1,500 * 8.49%
= $127.35
Total earnings for Portfolio 2 is:
= $40.60 + (-$34.10) + $432.90 + $127.35
= $567.75.
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2 3/4 of 500grams in step by step calculator
Answers
Answer:
To calculate 2 3/4 of 500 grams, follow these steps:
1. Convert the mixed number to an improper fraction:
2 3/4 = (2 x 4 + 3)/4 = 11/4
2. Multiply the improper fraction by 500:
11/4 x 500 = (11 x 500)/4 = 2,750/4
3. Simplify the fraction by dividing the numerator and denominator by their greatest common factor, which is 2:
2,750/4 = (2 x 1,375)/(2 x 2) = 1,375/2
Therefore, 2 3/4 of 500 grams is equal to 1,375/2 grams or 687.5 grams.
Step-by-step explanation:
Tom would like to take out a secured loan to help pay for a vacation this summer. He has offered his car as collateral. His car is worth $3,500. His bank can offer loans for 80% of collateral value. The vacation he has planned will cost $4,750. Approximately how much additional collateral will Tom need to offer in order to borrow enough to go on his vacation as planned?
Answers
Answer:
c took me a wiel but then realized it was just butterfly method to solve.
Step-by-step explanation:
Kelsey had 8 entries in her science journal. Last week, she wrote x more entries. How many entries are in her science journal now?
Answers
Answer:
8 + x
Step-by-step explanation:
She started with 8 entries.
She added x entries.
The total now is the sum of 8 and x.
Answer: 8 + x
answer pls sussy baka
Answers
Answer:
All besides the first one
Step-by-step explanation:
If you can split the shape in half and both the sides are equal, its semetrical.
Answer:
Of course susposter, 2,3,4,5
Step-by-step explanation:
I assuming you aren't doing specifically horizontal or vertical symmetricality.
If Horizontal- 2,3,4
If Vertical- 4,5
WILL GIVE BRAINLIEST FOR ANSWER I’m gonna fail help please
Answers
Answer: A
Step-by-step explanation:
might as well tell ur teachers ur awesome no matter wat.
The scale on a map is 1:320000
What is the actual distance represented by 1cm?
Give your answer in kilometres.
Answers
By answering the presented question, we may conclude that Therefore, 1 expressions cm on the map corresponds to a real distance of 3.2 km.
what is expression ?In mathematics, an expression is a collection of integers, variables, and complex mathematical (such as arithmetic, subtraction, multiplication, division, multiplications, and so on) that describes a quantity or value. Phrases can be simple, such as "3 + 4," or complicated, such as They may also contain functions like "sin(x)" or "log(y)". Expressions can be evaluated by swapping the variables with their values and performing the arithmetic operations in the order specified. If x = 2, for example, the formula "3x + 5" equals 3(2) + 5 = 11. Expressions are commonly used in mathematics to describe real-world situations, construct equations, and simplify complicated mathematical topics.
Scale 1:
320000 means that 1 unit on the map represents his 320000 units in the real world.
To find the actual distance represented by 1 cm on the map, you need to convert the units to the same scale.
1 kilometer = 100000 cm
So,
1 unit on the map = 320000 units in the real world
1 cm on the map = (1/100000) km in the real world
Multiplying both sides by 1 cm gives:
1 cm on the map = (1/100000) km * 320000
A simplification of this expression:
1 cm on the map = 3.2 km
Therefore, 1 cm on the map corresponds to a real distance of 3.2 km.
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Lucas recorded his lunch expenditure each day for one week in the table below.SEE IMAGEFind the mean, standard deviation, and variance of Lucas’s lunch expenditures. Round to the nearest thousandth.
Answers
Mean)
In general, the formula is
\(\operatorname{mean}=\frac{\text{ sum of elements in the dataset}}{\text{ number of elements in the dataset}}\)Thus, in our case,
\(\begin{gathered} \Rightarrow X=\operatorname{mean}=\frac{4.85+5.10+5.50+4.75+4.5+5+6}{7} \\ \Rightarrow X=\operatorname{mean}=5.1 \end{gathered}\)Thus, the mean is 5.1
Variance)
In general, the formula is
\(\text{Variance}=S^2=\sum ^{}_{}\frac{(x_i-X)^2}{N-1}\)Where x_i is each of the elements in the data set, X is the mean, and N is the number of elements in the data set.
Therefore, in our case,
\(\begin{gathered} N=7,X=5.1 \\ \Rightarrow S^2=\frac{1}{7-1}((4.85-5.1)^2+(5.1-5.1)^2+(5.5-5.1)^2+(4.75-5.1)^2+(4.5-5.1)^2+(5-5.1)^2+(6-5.1)^2) \\ \Rightarrow S^2=0.2541666\ldots \\ \Rightarrow S^2\approx0.254 \end{gathered}\)The variance is 0.254
Standard deviation)
If S^2 is the variance; then,
\(\text{ standard deviation}=\sigma=\sqrt[]{S^2}\)Hence, in our case,
\(\begin{gathered} \Rightarrow\sigma=\sqrt[]{0.2541666\ldots}\approx0.504149\ldots \\ \Rightarrow\sigma\approx0.504 \end{gathered}\)The standard deviation is 0.504
find the solution set 7x^2-9x-10=0
Answers
Answer:
x = -5/7, 2
Step-by-step explanation:
Step 1: Factor
(5x + 7)(x - 2) = 0
Step 2: Find x roots
5x + 7 = 0
x = -5/7
x - 2 = 0
x = 2
Answer:
x = -5/7 or x = 2
Step-by-step explanation:
7x² - 9x - 10 = 0
Factor the left side of the equation.
(7x + 5) (x - 2) = 0
Set the factors equal to 0.
7x + 5 =0
7x = -5
x = -5/7
x - 2 = 0
x = 2
How many
1/4-foot cubes would fill the inside of the prism?
Write the answer in the box.
Answers
There are 4 cubes of size 1/4 foot would fill the inside of the prism.
We have to given that;
Height of cuboid = 3 feet
Length of cuboid = 3/4 feet
Width of cuboid = 1/2 feet
We know that;
Volume of cuboid = Length x width x height
Hence,
V = 3/4 x 3 x 1/2
V = 9/8
Thus, Number of 1/4-foot cubes which would fill the inside of the prism is,
= (9/8) ÷ (1/4)
= (9/8) x 4
= 9/2
= 4.5
Thus, There are 4 cubes of size 1/4 foot would fill the inside of the prism.
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what are the LDC between 4/9 & 2/3
Answers
Answer:
the least common denominator between 4 and 9 is 36
Step-by-step explanation:
eli cut a pizza into 6 equal slices. he ate 1/2 of the pizza which fraction best shows the part of the pizza eli ate
Answers
Answer:
3/6
Step-by-step explanation:
Eating 1/2 of a pizza that has 6 slices means you ate 3/6 slices of the entire pizza. Also 3/6 is the only answer which is equivalent to 1/2.
PLEASE HELP
Solve the following system algebraically. y = x^2 + 11 and y = –12x
Answers
Answer:
x^2+12x=-11
Step-by-step explanation:
Answer:
(-1, 12) and (-11, 132)
Step-by-step explanation: