Answer: -5, 3
Step-by-step explanation:
Equation:
x² + 2x -15 = 0 The equation is already set =0 so you will factor.
To factor, find 2 numbers that multiply to the last term (-15) but add up to the middle term (+2). Be careful with signs, signs matter
+5 and -3 multiply to -15 but add up to the +2 so these are your factored numbers
put it in factored form
(x+5)(x-3)=0 set each parenthesis =0 to solve for x
x+5 = 0 x-3=0
x= -5 and x=3
The ratio of the reclusive to gregarious was 3 to 14. And 15,300 lived in the valley, how many were gregarious?
The ratio of gregarious that lived in the valley is 126,00
What is Ratio?Ratio is the comparison of two quantities of the same kind or for comparing two or more quantities that are measured in the same units. It is also is a relationship between two things when it is expressed in numbers or amounts.
How to determine this
The total who lived in valley = 15,300
The ratio of Reclusive = 3
The ratio of Gregarious = 14
And the ratio of reclusive gregarious = 3 : 14
The total ratio = 3 + 14 = 17
To calculate the total amount of gregarious
= 14/17 * 15,300
= 12,600
Therefore, the total amount of gregarious is 12,600
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Drag each length to the correct location on the triangle. Each length can be used more than once, but not all lengths will be used.
What are the missing side lengths for triangle ABC?
4
4√2 8
8√2
12 4√3 8√3
60°
4√3
30°
The missing side lengths for triangle ABC are 4, 4√3, and 8.
Based on the given information, it seems that the triangle is a right-angled triangle with angles of 30°, 60°, and 90°. Let's find the missing side lengths for triangle ABC using the given lengths and angles.
Identify the triangle type.
Since we have angles of 30°, 60°, and 90°, we are working with a 30-60-90 right-angled triangle.
Determine the ratio of side lengths.
In a 30-60-90 triangle, the ratio of the sides is 1:√3:2.
Find the corresponding side lengths.
Using the given lengths and the 1:√3:2 ratio, we can determine the side lengths for triangle ABC:
- If the shortest side (opposite the 30° angle) is 4, then the other sides would be 4√3 (opposite the 60° angle) and 8 (hypotenuse, opposite the 90° angle).
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CAN SOMEONE HELP WITH THIS QUESTION?
If company's marginal cost function is c(x)= 14 / √x, the total cost of producing the first 25 units is $10.67.
The marginal cost function is given as c(x) = 14 / √x, where x is the number of units produced.
To find the total cost of producing the first 25 units, we need to integrate the marginal cost function from x=0 to x=25, as follows:
Total cost = ∫₀²⁵ 14 / √x dx
We can use integration by substitution to solve this integral. Let u = √x, then du/dx = 1/(2√x), and dx = 2u du. Substituting these into the integral, we get:
Total cost = ∫₀⁵ √14/u du
This can be integrated using the power rule of integration. We have:
Total cost = 2√14 [[tex]u^{(3/2)[/tex]/3]₀⁵
Substituting back u = √x, we get:
Total cost = 2√14 [[tex](\sqrt{x})^{(3/2)[/tex]/3]₀²⁵
= 2√14 [[tex](\sqrt{25})^{(3/2)[/tex]/3 - [tex](\sqrt{0})^{(3/2)[/tex]/3]
= 2√14 (5/3)
= 10.67
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7 root 98 + 3 root 242 divided by 6 root 50
The expression (7√98 + 3√242) divided by 6√50 simplifies to the fraction of 4/3.
To simplify the expression (7√98 + 3√242) ÷ 6√50, we need to rationalize the denominator. This means we need to simplify the expression in such a way that there are no radical signs in the denominator. To do this, we can use the fact that the product of a radical and its conjugate is a rational number.
First, let's simplify the terms under the radicals by factoring out the perfect squares:
√98 = √(49*2) = 7√2
√242 = √(121*2) = 11√2
Now the expression becomes:
(7√2 + 311√2) ÷ (6√(252))
= (7√2 + 33√2) ÷ (6*5√2)
= 40√2 ÷ 30√2
= 4/3
In conclusion, to simplify expressions involving radicals, we need to factor out perfect squares and use the property of the conjugate to rationalize the denominator.
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A trapezoid has bases of 6 1/3 yd and 8 1/5 yd, and a height of 3 3/4 yd. Compose the trapezoid into a parallelogram. What is the area of this trapezoid?
The area of this trapezoid is 14.42 square yards.
To compose the trapezoid into a parallelogram, we need to add a triangle to the top of the trapezoid, so that the top and bottom sides are parallel. The area of the triangle is equal to half the product of the base and height.
First, we need to convert the mixed numbers to improper fractions:
Base 1: 6 1/3 yd = 19/3 yd
Base 2: 8 1/5 yd = 41/5 yd
Height: 3 3/4 yd = 15/4 yd
The length of the top side of the triangle is equal to the difference between the two bases:
Top side = 41/5 - 19/3 = (123 - 95)/15 = 28/15
Now we can calculate the area of the triangle:
Triangle area = (1/2) x (28/15) x (15/4) = 7/4
The trapezoid can now be composed into a parallelogram, with base 1 as one side and base 2 as the other side. The height of the parallelogram is the same as the height of the trapezoid, which is 15/4 yd.
The area of a parallelogram is equal to the product of its base and height, so the area of the trapezoid is:
Parallelogram area = (19/3 + 41/5) x (15/4) = 865/60 = 14.42
Therefore, the area of the trapezoid is 14.42 square yards.
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Given ƒ(x) = −3x², find ƒ(−10)
Answer:
-300
Step-by-step explanation:
You want the value of f(-10) given that f(x) = -3x².
EvaluationPut the value where the variable is and do the arithmetic.
f(-10) = -3(-10)² = -3(100) = -300
The value of f(-10) is -300.
<95141404393>
Compute (a) x₁ and (b) 2 for the iterative process defined by n+1 = 4x (3-xn) with x = 5.
(a) x₁ =???
Using the defined iterative process, xₙ ₊ ₁ = 4xₙ(3 - xₙ) with x₀ = 5,
The value of x₁ is -40
The value of x₂ is -6880
Computing the value of x₁ and x₂ from an iterative processFrom the question, we are to compute the values of x₁ and x₂ from the given iterative process
The definition of the iterative process is:
xₙ ₊ ₁ = 4xₙ(3 - xₙ)
From the given information,
x₀ = 5
To determine the value of x₁, we will substitute n = 0
xₙ ₊ ₁ = 4xₙ(3 - xₙ)
x₀ ₊ ₁ = 4x₀(3 - x₀)
x₁ = 4x₀(3 - x₀)
Substitute x₀ = 5
x₁ = 4(5)(3 - 5)
x₁ = 20(-2)
x₁ = -40
To determine the value of x₂, we will substitute n = 1
xₙ ₊ ₁ = 4xₙ(3 - xₙ)
x₁ ₊ ₁ = 4x₁(3 - x₁)
x₂ = 4x₁(3 - x₁)
Substitute x₁ = -40
x₂ = 4(-40)(3 - (-40))
x₂ = -160(43)
x₂ = -6880
Hence,
The value of x₁ is -40
The value of x₂ is -6880
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12 cm
He
4 cm 3 cm 5 cm
3 cm 5 cm
4 cm
4 cm
3 cm
What is the surface area of the solid?
A. 81 square centimeters
B. 192 square centimeters
C. 156 square centimeters
OD. 168 square centimeters
12 cm
Answer:
2(1/2)(3)(4) + 12(3) + 12(4) + 12(5)
= 12 + 36 + 48 + 60 = 156 cm^2
C is the correct answer.
Jill Janzen's gross weekly pay is $298. Her earnings to date for the year total $14,900. What amount is deducted from her pay each week for Social Security, which is taxed at 6.2%?
Jill's annual earnings can be calculated by multiplying her weekly pay by the number of weeks in a year: $298/week x 52 weeks/year = $15,496/year. Her earnings to date are $14,900, so she has earned an additional $596 in the current week.
Social Security is taxed at 6.2%, so the amount deducted from her pay each week is 6.2% of her gross weekly pay. That's 0.062 x $298 = $18.48.
Julie designs gardens for a living. For a year she kept track of the amount of time she spent designing the garden and whether or not the customer returned. She recorded the time and probability that a customer returned. To have the greatest probability of a returning customer, what amount of time should Julie spend per customer? Responses A 2 - 3 hours2 - 3 hours B 4 - 5 hours4 - 5 hours C 1 - 2 hours1 - 2 hours D 3 - 4 hours3 - 4 hours
Based solely on the information provided in the table, spending approximately 3-4 hours per customer would give Julie the best chance of a returning customer. So, correct option is C.
To determine the amount of time Julie should spend per customer to have the greatest probability of a returning customer, we need to find the time interval with the highest probability of return. Looking at the table, we see that the probability of return is highest for the 3-4 hour time interval with a probability of 7/8.
Therefore, Julie should spend 3-4 hours designing each customer's garden to have the greatest probability of a returning customer.
So, correct option is C.
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Complete question is:
Julie designs gardens for a living. For a year she kept track of the amount of time she spent designing the garden and whether or not the customer returned. She recorded the time and probability that a customer returned.
To have the greatest probability of a returning customer, what amount of time should Julie spend per customer?
TIME DESIGNING PROBABILITY OF RETURN
1-2 Hours 5/8
2-3 Hours 5/9
3-4 Hours 7/8
4-5 Hours 3/4
5-6 Hours 1/2
6-7 Hours 3/7
7-8 Hours 2/9
A. 1-2 Hours
B. 2-3 Hours
C. 3-4 Hours
D. 4-5 Hours
can someone please help me what is 11 1/8 + 2 3/4??? please
Answer: 13 7/8
Step-by-step explanation:
11 + 1/8 + 3/4 + 2 = 13 7/8
One man fits the parts together, so that the bolt holes come
right. The next man fits the bolt holes into place. The next
has a pan of nuts before him and all day he scoops them up
and with his fingers starts them on the thread of the bolts.
The next man has a wrench and he gives the final twist that
makes them tight.
-John A. Fitch, 1914
This excerpt describes a work process established by Henry Ford. Which results did
Ford help to achieve by implementing the process described in this excerpt?
Based on this excerpt, the results that Ford helped achieve by implementing the described process was the development of an assembly line, capable of increasing productivity and production efficiency.
What are Ford's contributions to the administration?He was the founder of the Ford Company and the theory of Fordism, which consists of mass production, reducing costs, increasing efficiency through specialization of work.
Therefore, as we see in the excerpt, mass production generated the greatest speed and precision in each step of the work, increasing productivity and reducing losses and costs associated with production.
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Michel-Eugène Chevreul found that the greatest intensity came from placing ________colors next to each other.
tertirary
analogous
complementary
arbitrary
Answer:
C. complementary
Michel-Eugène Chevreul discovered that placing complementary colors next to each other can create the greatest contrast and vibrancy in color perception. This is because complementary colors are located opposite each other on the color wheel and, when placed side by side, they enhance each other and create a strong visual impact. For example, placing yellow next to violet or blue next to orange can create a dynamic and eye-catching effect. In contrast, placing tertiary colors (colors made by mixing primary and secondary colors) or arbitrary colors next to each other may not create as much contrast or visual interest. Overall, understanding color theory and the relationships between different colors can be helpful for creating visually appealing designs, artworks, or other color-based projects.
A student shapes a piece of clay into a small cube. The students places the clay at the bottom of the ramp in Setup 2. The student rolls the 1-kilogram ball down the ramp and observes the collision between the ball and the clay cube.
Answer: Reduce the height of the ramp from 1 meter to 0.5 meters
Step-by-step explanation:
Find the area of the figure. Round to the nearest Hundredth if necessary.
18 ft
33 ft
25 ft
Answer:522
Step-by-step explanation:
cut the shape on top to make a triangle and rectangle so then it would be 25x18=450 then for the triangle it would be 18x8=72 450+72=522
((46 – 15) × 32) + 5 =
Answer:
=997
Step-by-step explanation:
46-15=31
31×32=992
992+5=997
Answer: 997
Step-by-step explanation:
question in the picture
1) Brianna's average monthly income is $1,850.
2) Brianna's average monthly expenses are $3,135.
3) Brianna's total monthly cash flow is -$1,295.
What is the cash flow?The cash flow refers to the cash inflows and cash outflows.
Cash inflows are incomes while cash outflows are expenses.
Brianna's Monthly Budget:Monthly Rent = $700
Gas = $120
Car Insurance = $75
Health Insurance = $140
Renter's Insurance = $25
Cell phone = $110
Utilities = $100
Groceries = $300
Entertainment/eating out = $250
Total monthly expenses = $1,820
= $21,840 ($1,820 x 12)
Annual Expenses:College = $12,000
Gifts = $1,000
Vacations = $1,500
Clothes = $800
Charity =$600
Total monthly expenses = $21,840
Total annual expenses = $37,740
Average monthly expenses = $3,135 ($37,740 ÷ 12)
Monthly Income = $1,600
Yearly Income = $ 19,200 ($1,600 x 12)
Annual Scholarship = $3,000
Total annual income = $22,200
Average monthly income = $1,850 ($22,200 ÷ 12)
Cash Flows:Average monthly income = $1,850
Average monthly expenses = $3,135
Cash flows = -$1,295 ($1,850 - $3,135)
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HELP FIND MULTIPLE REPRESENTATION OF POLAR COORDINATES
What is the surface area of a right circular cylindrical oil can, if the radius of its base is 4 inches and its height is 11 inches?
A) 85π in
B)100π in
C)120π in
D)225π in
The surface area of the right cylindrical oil can is 120π in² and the right option is C) 120π in².
What is surface area?
The surface area of a solid object is a measure of the total area that the surface of the object occupies.
To calculate the surface area of the right cylindrical oil can, we us the formula below
Formula:
S.A = 2πr(r+h)...................Equation 1Where:
r = Radius of the baseh = Height of the cylinderS.A = Surface area of the cylinderFrom the question,
Given:
r = 4 inchesh = 11 inchesSubstitute these values into equation 1
S.A = 2×4×π(11+4)S.A = 120π squared in.Hence, the right option is C) 120π in².
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The students at Kayla's school are forming teams of three students for a quiz bowl competition. Kayla is assuming that each member of a team is equally likely to be male or female. She uses a coin toss (heads = female, tails = male) to simulate this probability. Here is Kayla's data from 50 trials of 3 coin tosses:
thh tth tth tht thh htt hth hht hth tth tth hht hth tht tht tth tth thh thh htt tht thh tth hht hth thh tht tth hht thh hhh tth tth hth htt tht thh hhh htt thh htt ttt tht ttt thh hht hth htt hht hth
According to this data, what is the experimental probability that a team will consist of two girls and a boy?
0.33
0.375
0.23
0.46
The required, experimental probability that a team will consist of two girls and a boy is 0.33. Option A is correct.
To find the experimental probability that a team will consist of two girls and a boy, we need to count the number of times that Kayla got a team with two girls and one boy and divide that by the total number of trials.
So, out of 50 trials, there were 17 trials where the team had two girls and one boy. Therefore, the experimental probability is:
17/50 = 0.34
Therefore, it is 0.34, which is closest to option (A) 0.33.
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which fraction is equavilent to - 3/2
Answer: -1 1/2
Step-by-step explanation:
You simplify -3/2, which becomes -1 1/2!
Need the right answers please
The measure of the angle of the triangle ∠BCD = 13°
Given data ,
Let the triangle be represented as ΔBCD
Now , in triangle BCD, we are given the following angle measurements:
angle CDE = (9x - 12)°
angle BCD = (2x + 3)°
angle DBC = (3x + 5)°
From the exterior angle theorem , we get
∠CDE = ∠BCD + ∠DBC
On simplifying , we get
9x - 12 = 2x + 3 + 3x + 5
9x - 12 = 5x + 8
Subtracting 5x on both sides and adding 12 , we get
4x = 20
Divide by 4 on both sides , we get
x = 5
So , the measure of angle ∠BCD = 2(5) + 3
m∠BCD = 13°
Hence , the angle is m∠BCD = 13°
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The complete question is attached below :
In triangle BCD , BD is extended through point D to point E , ∠CDE = ( 9x - 12 )° , ∠BCD = ( 2x + 3 )°, and ∠DBC = ( 3x + 5 )°, find ∠BCD
please help me do this i need it so bad
Car Make and Model that i choose is Toyota RAV4
The Cost of this car as of today is about $27,000
What is the Exponential about?To know the value of car after one year will be:
20% of $27,000
= $5,400.
So the car value will be:
$27,000 - $5,400
= $21,600 after year 1
3. Value of car after second year of ownership:
15% of $27,000
= $4,050.
So, the car value will be:
$21,600 - $4,050
= $17,550 after year 2.
4 The Exponential Function if the car continues to decrease in value by 15% each year will be;
V(x) = 27,000 x (0.85)ˣ
V(5) = 27,000 x (0.85)⁵
= 27,000 x 0.44370
= $11979.9
Therefore, the value of the car after owning it for five years is $11979.9
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See text below
Car Value: Exponential
1. Pick a car that you would be interested in buying someday. Research the cost of buying this car.
Car Make and Model:
Cost of this car as of today:
2. Cars depreciate in value over time, which means they lose a certain percent of their value each year. A car typically decreases in value by 20% within the first year. If the car you picked above decreased in value by 20% in its first year, how much will it be worth one year after owning it?
Value of car after one year:
3. Each year after the first year, a car typically decreases around 15% in value. How much will your car be worth after owning it for 2 years?
Value of car after second year of ownership:
4. If your car continues to decrease in value by 15% each year, write the equation of the exponential function that models its value x years after you purchased it.
Exponential Function:
Use your exponential function to calculate the predicted value of your car after you own it for five years.
Value after five years of ownership:
which is greater 0.04 or 5
Answer:
Step-by-step explanation:
5 is greater than 0.004
Answer: 5 is greater
Step-by-step explanation:
Yui is buying beverages for her friends. She buys a total of 6 bottles of water and sports drinks. Bottles of water cost $1.50 each, and sports drinks cost $2.50 each, she spends a total of $10. Write a system of equations to represent the information, and use substitution to determine how many of each type of drink yui buys
Answer:
Let x be the number of bottles of water that Yui buys, and let y be the number of sports drinks she buys.
Since Yui buys a total of 6 bottles of water and sports drinks, we know that:
x + y = 6
We also know that each bottle of water costs $1.50 and each sports drink costs $2.50, and that Yui spends a total of $10. Therefore, we can write another equation based on the total cost:
1.5x + 2.5y = 10
We now have a system of two equations with two variables:
x + y = 6
1.5x + 2.5y = 10
To solve for x and y, we can use substitution. Rearranging the first equation, we get:
x = 6 - y
Substituting this expression for x into the second equation, we get:
1.5(6 - y) + 2.5y = 10
Expanding and simplifying, we get:
9 - 1.5y + 2.5y = 10
Combining like terms, we get:
y = 2
Substituting this value of y back into the equation x + y = 6, we get:
x + 2 = 6
Solving for x, we get:
x = 4
Therefore, Yui buys 4 bottles of water and 2 sports drinks.
Use a net to find the surface area of the prism.
A. 426m2
B. 213m2
C. 306m2
D. 336m2
The surface area of the rectangular prism in this problem is given as follows:
A. 426 m².
What is the surface area of a rectangular prism?The surface area of a rectangular prism of height h, width w and length l is given by:
S = 2(hw + lw + lh).
This means that the area of each rectangular face of the prism is calculated, and then the surface area is given by the sum of all these areas. -> net method.
The dimensions for this problem are given as follows:
5 m, 12 m and 9 m.
Hence the surface area of the prism is given as follows:
S = 2(5 x 12 + 5 x 9 + 12 x 9)
S = 426 m².
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PLEASE HELP! CORRECT ANSWERS ONLY!
Part A: You invest 12% of your paycheck into your 401k retirement plan. If your paycheck is 2,100, how much is being invested?
Part B: Your company will contribute half of what you invest. If you invest 10% of your 2,100 paycheck, how much is your company putting in?
A. The amount invested is given as follows: $252.
B. The amount being put in is given as follows: $105.
How to obtain the amounts?The amounts are obtained applying the proportions in the context of the problem.
For item a, the amount is of 12% of 2100, hence it is given as follows:
0.12 x 2100 = $252.
For item b, the amount is half of 10% of 2100, hence it is given as follows:
0.5 x 0.1 x 2100 = $105.
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A company sampled two groups of students and asked them "How many books did you read this month?" The table shows the data they collected. Select all of the true statements about the samples.
The true statements about the samples:
Both groups have the same median (4).
Group A has a lower mean than Group B (4 vs 4.25).
Both groups have multiple modes.
The range of values in Group B is greater than in Group A.
How to solveFor Group A, the average number is 4 with a range of numbers from 2 to 6. The middle value, also known as the median, is 4.
Using this information, we find that values 3, 4, and 5 occur twice each within the dataset.
For Group B, the mean, or average, number is found to be 4.25 among eight total entries ranging from a low of 1 to a high of 7.
Calculating for the middle value, which is defined as the median, it can be seen that the resulting output is again equivalent to 4. Of all data inputs, the two top-occurring amounts are 4 and 5, both appearing twice in the listing.
Here are the true statements about the samples:
Both groups have the same median (4).
Group A has a lower mean than Group B (4 vs 4.25).
Both groups have multiple modes.
The range of values in Group B is greater than in Group A.
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A company sampled two groups of students and asked them "How many books did you read this month?" The table shows the data they collected:
Group A: [3, 4, 5, 2, 5, 6, 3, 4]
Group B: [1, 6, 4, 5, 2, 5, 4, 7]
Julio's Bikes rents bikes for $10 plus $8 per hour. Willie paid $34 to rent a bike. For how many hours did he rent the bike?
Answer:
He rented the bike for 3 hours
Step-by-step explanation:
they charge $10 for just the bike and an adittional of $8 per hour and Willie payed $34 so u subtract 10 from 34 it leaves u with 24 and u then divide by 8 and u get 3 which means that he rented the bike for 3 hours :)
themba has 6.75 cups of yogurt and needs to make 5 bowls of fruit dip. each bowl uses 1.5 cups of yogurt
complete the statements about the fruit dip
Answer: Themba needs a total of 7.5 cups of yogurt to make 5 bowls of fruit dip, so 0.75 cup(s) will be needed
Step-by-step explanation:
your welcome.
