Answer: C
Step-by-step explanation:
pythagorean theorem : a^2 + b^2 = c^2
8^2 + 8^2 = x^2
64 + 64 = x^2
128 = x^2
x = sqrt(128) square root both sides
x = 8sqrt(2) simplified
Answer: c, [tex]8\sqrt{2}[/tex]
Step-by-step explanation:
Since this is a right triangle, we will use the Pythagorean theorem to help us solve for x.
Theorem:
a² + b² = c²
Substitue values:
8² + 8² = c²
To the power of 2:
64 + 64 = c²
Addition:
128 = c²
Square root both sides of the equation:
[tex]\sqrt{128}[/tex] = c
Reflexive property and breaking up 128 into two factors:
c = [tex]\sqrt{64*2}[/tex]
Square root of 64:
c = 8[tex]\sqrt{2}[/tex]
So, x = 8[tex]\sqrt{2}[/tex]
Find the equation of the line.
Use exact numbers.
y= x+
Answer:
y = -2x + 5
Step-by-step explanation:
To find the slope use rise over run
To find the y-intercept see where the line intersects in the y-axis line
Kyle plans to invest $7000, part at 6% simple interest and the rest at 7% simple interest. What is the most that he can
invest at 6% and still be guaranteed at least $440 in interest per year?
Answer:
$5000
Step-by-step explanation:
Let x represent the amount invested at 6% interest. Then 7000-x is the amount invested at 7% interest
6% interest = 6/100 = 0.06 in decimal
7% interest = 7/100 = 0.07
Interest earned from depositing x dollars at 6% = 0.06x
Interest earned from depositing 7000-x at 7% = 0.07(7000-x)
Total interest earned would be
0.06x + 0.07(7000-x)
Since this must be at least $440 we get the equation interest as
0.06x + 0.07(7000-x) = 440
Simplifying
0.06x + 0.07 x 7000 - 0.07x = 440
0.06x + 490 -0.07x = 440
-0.01x = 440 - 490
-0.01x = -50
Multiply both sides by -1
==> 0.01x = 50
==> x = 50/0.01 = 5000
So max amount that can be invested at 6% interest = $5000
Solve the equation for x
(x-5)/10=5
x=____
Answer:
x = 55
Step-by-step explanation:
[tex]\frac{x-5}{10}[/tex] = 5 ( multiply both sides by 10 to clear the fraction )
x - 5 = 10 × 5 = 50 ( add 5 to both sides )
x = 55
You bought 8 apples at the store. The total cost was $6.00.
Let c be the cost of one apple.
Write and solve an equation to find the cost of one apple.
Answer:
Step-by-step explanation:
to put into an equation:
8c=6.00
c=6.00/8
c=$0.75
The cost of one apple is $0.75
The angle of rotation, (teta), is a(n) ____ angle used to rotate the xy-coordinate plane to a new x'y'-plane for graphing a rotated conic section. A. negative B. double C. acute D. obtuse
The correct option B. double; angle used to rotate the xy-coordinate plane to a new x'y'-plane for graphing a rotated conic section.
Explain the term rotated conic section?Any curve created by intersection of such a plane as well as a right circular cone is known in geometry as a conic section, sometimes known as a conic.
The intersection can be a circle, a ellipse, a hyperbola, or a parabola, depending on the angle the plane makes with the cone.A plane curve, lines, pair of intersection points, or point that connects to or encompasses the point where a plane as well as a cone with two nappes converge.The preceding classes' conics were all of the formula Ax² + Cy² + Dx + Ey + F = 0. These conics are all either vertical or horizontal. For conics that are neither horizontal nor vertical, the B word is needed. Conics take on the generic pattern Ax2 + Bxy + Cy2 + Dx + Ey + F = 0.Thus, teta is a double angle that is used to rotate the x-y coordinate plane into a new x'y' plane in order to graph a rotated conic section.
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The first four numbers in a pattern are 4,3.6,3.2 and 2.8. What is the next three next numbers in the pattern
Answer:
2.4 and 2
Step-by-step explanation:
x-0.4
Answer:
2.4, 2, 1.6
Explanation:
The sequence is counting down by 0.4.
help meeeeeeeeeee pleaseee
(a) The population of the state was 18.5 million in 2000. (b) The population of the state reaches 26.6 million by 2002
What do you mean by Population?A population is a distinct collection of people, whether that group consists of a nation or a population that shares a particular trait. A population is the people from which a statistical sample is taken in statistics. As a result, a population can be defined as any group of people with something in common.
(a) The right response is 18.5
Given that
t = 0,
A = 18.5
(b) 2002.
Using the formula
18.5e 0.173 x t
Given,
A= 26.6
Then,
A = 18.5 x
[tex]e^{(0.1708t)} 26.6 = 18.5 x[/tex]
[tex]\frac{26.6}{18.5}= e^{(0.1708t)}[/tex]
[tex]1.437838 = e^{(0.1708t)}[/tex]
[tex]Ln \frac{1.437838}{0.1708}[/tex]
About
t = 2.126116
t =2
As a result, 2 represents the closest year when rounding down.
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Write a polynomial f(x) that satisfies the given conditions
The least polynomial with degree 3 is equal to f(x) = x³ - (8 / 7) · x² + 4 · x - 32 / 7.
What is the least polynomial that contains a given set of roots?
In this problem we need to determine the least polynomial such that its degree is 3 and - i 2 and 8 / 7 are roots of the resulting expression. By quadratic formula, the roots - i 2 is along with its conjugate i 2 to obtain a quadratic equation with real coefficients. The factor form of the cubic polynomial is:
f(x) = a · (x - r₁) · (x - r₂) · (x - r₃)
Where:
a - Lead coefficient.r₁, r₂, r₃ - Roots of the polynomial.And we must determine the standard form of the polynomial by means of algebra properties. This form is shown below:
f(x) = a · x³ + b · x² + c · x + d
Where a, b, c, d are real coefficients.
First, write the polynomial in factor form: (a = 1)
f(x) = (x - 8 / 7) · (x + i 2) · (x - i 2)
f(x) = (x - 8 / 7) · (x² + 4)
f(x) = x³ - (8 / 7) · x² + 4 · x - 32 / 7
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A trail mix recipe calls for 3 cups of raisins and 4 cups of peanuts. Mitt made trail mix for a party and used 5 cups of raisins and 6 cups of peanuts. Did he use the correct ratio of raisins to peanuts?
Answer: no
Step-by-step explanation:
Recipe calls for a 3:4 ratio of raisins to peanuts
If his intention was to make a 1.5x recipe, he should have used 6 cups peanuts and 4-1/2 cups raisins (not 5!) to make the recipe in the correct ratio.
For the function f(x) = 5(x - 5)7, find f-¹(x).
Answer:
Step-by-step explanation:
(NEED HELP ASPAD- WORTH 70 POINTS!)
Mr. [name] wants to order sandwiches for his class. Each sandwich, x, costs 6 dollars and there is a delivery fee of 12 dollars.
1.) Write an equation representing the cost, y, of this order of 7 sandwiches.
2.) Show your work to represent the cost of an order of 7 sandwiches.
3.)Show your work to solve how any sandwhitches you could buy with 78 dollars.
x=6
d=12
7x+12 or 7x+d
7(6) + 12 or (7x6) + 12 = 54
78-12 = 66
66/6 = 11
11x + 12 =78.
A store owner decides to mark up all items by 30%. What is the selling price of an item that originally cost $30?
After the markup, the selling price of the item will be $39.
What is the selling price of an item that originally cost $30?
We know that a store owner decides to mark up all items by 30%, so basically we need to increase all the costs by 30%.
If the original cost is C, then the cost after the mark up will be:
P = C*(1 + 30%/100%)
P = C*(1 + 0.3)
P = C*(1.3)
In this case, we want to find the selling price P for an object whose original cost C is $30, then we can replace C in the equation above so we get:
P = $30*1.3 = $39
The selling price P is $39.
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The functions S(t) = 1.0841t + 17.392 models the amount of money, S, in billions of dollars, the United States government spent on science, space, and technology for the time period 1999-2009, where t is the number of years since 1999.
a. Write the constraints for the variable t using set-builder notation.
b. Determine the value of S(7)
c. Interpret the value of S(7) in context
d. Name the key feature that is found when solving S(t) = 0. Then, label the key feature on the graph of S(t) = 1.084t + 17.392.
e. determine if the value for S(t) = 0 is reasonable for the context. Explain why or why not.
Hello,
I hope you and your family are doing well!
a. The variable t represents the number of years since 1999, so the constraints for t can be written as t ∈ {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}.
b. To find the value of S(7), we substitute t = 7 into the function: S(7) = 1.084(7) + 17.392 = 22.688.
c. In context, the value of S(7) represents the amount of money, in billions of dollars, that the US government spent on science, space, and technology 7 years after 1999.
d. The key feature that is found when solving S(t) = 0 is the y-intercept of the graph of S(t). The y-intercept is the point where the graph crosses the y-axis.
e. The value for S(t) = 0 is not reasonable for the context because it represents the amount of money spent on science, space, and technology in 1999, which would be a negative number of years after 1999.
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Answer:
x = 3
Step-by-step explanation:
Since ∠CAT = ∠DOG, ∠CAT = ∠DGO
Therefore AC = DO
8x - 6 = 3x + 9
8x - 3x = 9 + 6
5x = 15
x = 15/5
x = 3
24) Evaluate the expression with its given values.
x/4 + 3y; x = 12, y = 2
Answer:
9
Step-by-step explanation:
[tex]\frac{12}{4}+3(2) \\ \\ =3+6 \\ \\ =9[/tex]
Answer:
Answer is 9.
Step-by-step explanation:
If x is 12, then do 12 divided by 4, and you get 3. If y is 2, then di 3 times 2, which is 6. 3 plus 6 is 9.
The ratio of Pablo's age to Richard's age is 6 : 7. The ratio of Pablo's age to Tristan's age is 5 : 4. Find the ratio of Pablo's age to Richard's age to Tristan's age.
Ages of Tristan, Richard, and Pablo are in the order 6:7:4.
Detailed explanation:
Pablo is six years younger than Richard, seven years older than Tristan, and five years younger than Richard.
We can multiply the ratios of Pablo's age to Richard's age and Pablo's age to Tristan's age to determine the ratio of Tristan's age to Richard's age before determining the ratio of Tristan's age to Pablo's age.
These ratios add up to 6/7 * 5/4 = 30/28.
Pablo's age to Richard's age is 6:7, thus we may multiply this ratio by the age of Richard by Tristan's age to determine the age of Pablo, Richard, and Tristan.
Thus, the ratio of Pablo's age to Richard's age to Tristan's age is 6:7:4.
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how do i solve this question
Answer: (x-2)(x-10)
Step-by-step explanation:
1. Factor out 3x by diving everything by it, this makes the monomial 3x(x^2-12x+20)
2. From here, you do your basic factoring and reach that the answer is (x-2)(x-10)
lmk if you need more details for explanation
What is the area of ΔOPQ if
a=18 b=17.5 and c=13.5
Answer:
Problem
Solution
Solve for the missing components of the triangle.
A
=
69.62591065
B
=
65.69947977
C
=
44.67460956
a
=
18
b
=
17.5
Select all the expressions which are equivalent to 910x − 2.
A mathematical expression made up of variables, coefficients, constants, and operations like addition, subtraction, multiplication, and division is known as an algebraic expression.
What is an Algebraic Expression?A mathematical expression known as an algebraic expression is one that includes variables, coefficients, constants, and operations like addition, subtraction, multiplication, and division.In most cases, something is said to be equivalent if two of them are the same. Similar to this, analogous expressions in mathematics are those that, despite their differences in appearance, have the same meaning. The two expressions, however, produce the identical outcome when the values are inserted into them.Example910x − 2
simplify | 910 x - 2
2 (455 x - 1).
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Function 2
y=x+4
Rate of Change: 3/4 Rate of Change:
Which has the greatest rate of change?
Answer:
function 2
Step-by-step explanation:
function 1 has a slope of 8/7 which is equal to 0.75 and function 2 has a slope of 1 so function 2 is greater than function 1.
Answer: <
Step-by-step explanation:
One number is less than another number if their difference is less than zero.
Since x=2y-4 - 0.75 = -0.75 which is less than zero, x=2y-4 is less than 0.75
Therefore, x=2y-4 is 0.75 less/lower than 0.75
You are playing a game that involves tossing a single die. If you roll a one, you win $100. If you roll a 2, you win $50. If you roll anything else, you lose $25. What are your expected winnings?
The required probability of winning is given as 0.32.
Given that,
Playing a game that involves tossing a single die. If roll one, you win $100. If you roll a 2, you win $50. roll anything else, you lose $25.
Probability can be defined as the ratio of favorable outcomes to the total number of events.
here,
total number of sample spaces = 6
total of favorable outcome = 2
Probability fo the winning = 2 / 6 = 0.3333 or 0.32
Thus, the required probability of winning is given as 0.32.
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Pls help. On a number line 13 less than 8 is
Which of the following examples illustrates the law of supply?
Select the correct answer below:
When the price of housing increases, more homeowners want to sell their house.
Johnathan will not sell his car unless he can get at least $5,000 for it.
Sylvia wanted to sell all her CDs when she saw that buyers are willing to pay more for them.
all of the above
Answer:
i think it would be a; When the price of housing increases, more homeowners want to sell their house.
Determine the equation for the line. Write the equation in standard form through
the points
(3,-4) and (6,-2)
The standard form equation for the line through the points (3,-4) and (6,-2) is -2/3 x + y = 4.
What is the equation of the line passing through the two-point?
To find the equation for the line through two points we can use the formula:
y - y1 = m(x - x1)
where (x1, y1) is one of the points, and m is the slope of the line. The slope of the line is equal to the change in y over the change in x, which can be calculated as:
m = (y2 - y1) / (x2 - x1)
where (x2, y2) is the other point.
Substituting the given points and the formula for the slope into the formula for the equation of the line, we get:
y - (-4) = ((-2) - (-4)) / (6 - 3) (x - 3)
This simplifies to:
y + 4 = -2/3 (x - 3)
To write the equation in standard form, we can distribute the -2/3 and then rearrange the terms:
-2/3 x + y = 4
Hence, the standard form equation for the line through the points (3,-4) and (6,-2) is -2/3 x + y = 4
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Mrs. James is on a train traveling 42 m.p.h. As Mrs. James is looking out the window, a freight train traveling at 18 m.p.h. moving in the opposite direction meets and passes her. She noticed it took 8 seconds for the freight train to pass her. The freight train is ___ feet long.
The freight train is 88.88 feet long.
What is Speed- Distance Formula?Speed = Distance/Time
Distance = Speed X Time
Time = Distance / Speed
As the trains travel in opposite direction then
Relative speed = (42 + 18) = 60 Km/ hr
= 60 x 5/18 = 300/ 18
= 100/9 m/s
So, length of the freight train = 100/9 x 8
= 88.88 feet
Hence, The freight train is 88.88 feet long.
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Find the value of zα.
Z0.47
The critical probability of a critical value of α = 0.47 is [tex]Z_{0.47}[/tex] = 0.77.
What is the critical value?A crucial value is the test statistic's value that establishes a confidence interval's upper and lower boundaries, or the level of statistical significance for a given test.
Given:
The critical value, α = 0.47
Calculate the critical probability by the formula given below,
[tex]Z_\alpha = 1 - ( \alpha / 2)[/tex]
[tex]Z_{0.47}[/tex] = 1 - (0.47 / 2)
[tex]Z_{0.47}[/tex] = 1 - 0.235
[tex]Z_{0.47}[/tex] = 0.765 = 0.77
Therefore, the critical probability of a critical value of α = 0.47 is [tex]Z_{0.47}[/tex] = 0.77.
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Which table(s) can represent values of a function? Select all that apply. Responses Input (x) 5 8 −8 −3 2 Output (y) 12 17 10 5 2 Input x 5 8 negative 8 negative 3 2 Output y 12 17 10 5 2 , Input (x) 18 20 22 24 26 Output (y) −9 −9 −6 −3 0 Input x 18 20 22 24 26 Output y negative 9 negative 9 negative 6 negative 3 0 , Input (x) 24 32 45 12 32 Output (y) 11 12 35 14 35 Input x 24 32 45 12 32 Output y 11 12 35 14 35 , Input (x) −4 8 3 −12 0 Output (y) 13 13 13 13 13 Input x negative 4 8 3 negative 12 0 Output y 13 13 13 13 13 , Input (x) 25 30 30 25 20 Output (y) 6 −2 0 13 11
The tables that represent a function are:
Input x 5 8 −8 −3 2
Output y 12 17 10 5 2
Input x 18 20 22 24 26
Output y -9 -9 -6 -3 0
Input x −4 8 3 −12 0
Output y 13 13 13 13 13
Options A, B, and D are the correct answer.
What is a function?
A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
A function can have many-to-one but not one-to-many.
Now,
The tables are given as,
Input x 5 8 −8 −3 2
Output y 12 17 10 5 2
This is a function.
Input x 18 20 22 24 26
Output y -9 -9 -6 -3 0
This is a function.
Input x 24 32 45 12 32
Output y 11 12 35 14 35
This is not a function because it has one-to-many.
Input x −4 8 3 −12 0
Output y 13 13 13 13 13
This is a function.
Input x 25 30 30 25 20
Output y 6 −2 0 13 11
This is not a function because it has one-to-many.
Thus,
The tables that represent a function are:
Input x 5 8 −8 −3 2
Output y 12 17 10 5 2
Input x 18 20 22 24 26
Output y -9 -9 -6 -3 0
Input x −4 8 3 −12 0
Output y 13 13 13 13 13
Options A, B, and D are the correct answer.
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what percentage of 64 is 16
Answer:
25%
Step-by-step explanation:
Andrew Industries purchased $163,000 of raw materials on account during the month of March. The beginning Raw Materials Inventory balance was $21,600, and the materials used to complete jobs during the month were $139,200 of direct materials and $12,800 of indirect materials. What is the ending Raw Materials Inventory balance for March?
The ending Raw Materials Inventory balance for March is 31,800.
What is arithmetic?
Arithmetic is an elementary a part of arithmetic that consists of the study of the properties of the normal operations on numbers—addition, subtraction, multiplication, division, involution, and extraction of roots.
Main Body:
We use the Inventory identity to solve for ending inventory
Beginning Inventory + Purchase = ending Inventory + used
20,800 +159,000 = ending inventory + used materials
used materials:
135,600 direct
12,400 indirect
148,000 total materials used
20,800 + 159,000 = Ending Inventory + 148,000
20,800 + 159,000 - 148,000 = Ending Inventory
Ending Inventory = 31,800
Hence the ending Raw Materials Inventory balance for March is 31,800.
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Find the slope of the line
Answer:
1/4 and -20
Step-by-step explanation:
"Slope" just means the change in y divided by the change in x. In the first graph, the slope is the change in depth divided by the change in hours.
Using the equation, slope = (y - y1)/(x - x1), you can plug in 2 points and solve. I see that the line goes through the points (4,1) and (8,2), so I'll use these. Make sure that (x,y) are from the same point and (x1,y1) are from the same point.
slope = (2 - 1)/(8 - 4)
slope = 1/4
You can do the same process for the second graph but you'll use different points. I see the points (2,80) and (4,40), so I'll use those.
slope = (40 - 80)/(4 - 2)
slope = -40/2
slope = -20