Answer:
f(x) = (x+3)^2 + 5
Step-by-step explanation:
Hope this is right :)
Find the matrix A such that
A
1 0
−1 3
=
−1 −3
1 6
A = [-4/3 -1/3; 10 10/3] is the matrix that fulfills the equation A × [1 0; -1 3] = [-1 -3; 1 6].
What in mathematics is a matrix?Rows and sections of integers are arranged in a matrix. Learn about matrices' lengths and components as you begin your study of them. A rectangle matrix is a grouping of integers into rows as well as columns. The matrix A, for instance, has two rows along with three columns.
To find the matrix A, we need to solve the matrix equation:
A × [1 0; -1 3] = [-1 -3; 1 6]
We can do this by multiplying both sides by the inverse of [1 0; -1 3] on the left:
A × [1 0; -1 3] × [3 0; 1 1/3] = [-1 -3; 1 6] × [3 0; 1 1/3]
Simplifying the left-hand side using the associative and commutative properties of matrix multiplication, we get:
A × [3 0; -1 1] = [-3 -1; 10 3]
Now, we can solve for A by multiplying both sides by the inverse of [3 0; -1 1]:
A × [3 0; -1 1] × [1/3 0; 1/3 1] = [-3 -1; 10 3] × [1/3 0; 1/3 1]
Simplifying the left-hand side using the associative and commutative properties of matrix multiplication, we get:
A × [1 1/3; 0 1] = [-2/3 -1/3; 10/3 3]
Multiplying both sides by the inverse of [1 1/3; 0 1]:
A = [-2/3 -1/3; 10/3 3] × [1 1/3; 0 1]⁻¹
We can easily find the inverse of [1 1/3; 0 1]:
[1 1/3; 0 1]⁻¹ = [1 -1/3; 0 1]
So, substituting this into the equation for A, we get:
A = [-2/3 -1/3; 10/3 3] × [1 -1/3; 0 1]
Multiplying the matrices on the right-hand side, we get:
A = [-2/3 -1/3; 10/3 3] × [1 -1/3; 0 1] = [-4/3 -1/3; 10 10/3]
Therefore, the matrix A that satisfies the equation A × [1 0; -1 3] = [-1 -3; 1 6] is:
A = [-4/3 -1/3; 10 10/3]
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during last nights basketball game the number of points scored by the hornets was triple the number of points scored by the raiders the raiders scored 6 points how many points did the hornets score?
2
9
12
18?
Answer:
18
Step-by-step explanation:
siz times three is eighteen
Suppose 50 rabbits are on Groff Farm… DOUBLING every year…
How many rabbits after 5 years?
How many rabbits after 10 years?
Answer:
Step-by-step explanation:
After the first year, the number of rabbits will double from 50 to 100.
After the second year, the number of rabbits will double again from 100 to 200.
This doubling process will continue for a total of 5 years, so after 5 years, the number of rabbits will be:
Number of rabbits after 5 years = 50 x 2^5 = 50 x 32 = 1600
Therefore, there will be 1600 rabbits on Groff Farm after 5 years.
Similarly, after 10 years, the number of rabbits will double 10 times:
Number of rabbits after 10 years = 50 x 2^10 = 50 x 1024 = 51200
Therefore, there will be 51,200 rabbits on Groff Farm after 10 years.
What is the measure of the intercepted arc of the inscribed angle shown in the image below?
Therefore, the measure of the intercepted arc by the inscribed angle of 61 degrees is 122 degrees.
What is circle?A circle is a closed shape in geometry that is defined as the set of all points in a plane that are at a fixed distance from a given point, called the center of the circle. The distance between any point on the circle and the center is called the radius of the circle.
Given by the question.
In a circle, an inscribed angle is an angle formed by two chords of the circle that have a common endpoint on the circle. The measure of an inscribed angle is half the measure of its intercepted arc.
Let's call the intercepted arc by the inscribed angle "x". Then, the measure of the inscribed angle is 61 degrees, and we can use the formula mentioned above to find the measure of the intercepted arc:
61 = x/2
To solve for x, we can multiply both sides of the equation by 2:
122 = x
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Find the Volume of the rectangular prism
Answer:
421.875 ft³
Step-by-step explanation:
Since the length, width, and heigh are equal, this is a cube.
V = s³
V = (7.5 ft)³
V = 421.875 ft³
Answer:421.875 ft^3
Step-by-step explanation:
please help immediately
please go to my profile and answer the other I need them asap.
10³•10⁵•10³
Step-by-step explanation:
10³means 10×3,10⁵means 10×5and 10³means 10×3 30+50+30=110
Bob drove 845 miles in 13 hours.
At the same rate, how many miles would he drive in 9 hours ?
Answer:
585 miles
Step-by-step explanation:
845 miles ÷ 13 hours = 65 mph
645 mph * 9 hours = 585 miles
A certain triathlon consists of a 2.6 mile swim, a 110 mile bicycle ride, and a 26.2mile run. At one point, a participant had completed as many miles as the number of miles left to complete. How many miles had he completed at that mark?
Answer:
Let x be the number of miles completed by the participant before the mark. Then, the total distance of the triathlon is:
2.6 + 110 + 26.2 = 138.8 miles
At the mark, the participant has completed x miles and has the remaining distance to complete, which is:
138.8 - x
According to the problem, x is equal to the remaining distance:
x = 138.8 - x
Solving for x, we get:
2x = 138.8
x = 69.4
Therefore, the participant had completed 69.4 miles at the mark.
What is the measure of ∠m
Answer:
26° 180 -81 - 73 = 26
Step-by-step explanation:
Answer:
26
Step-by-step explanation:
triangle= 180
81 + 73 = 154
180 - 154= 26
3) The Algebros go paintballing. Mr. Kelly and Mr. Sullivan climb up and lie on the top of a shed that is 5 feet off
the ground. The others send Mr. Brust up a tree to hide and he was doing a great job picking off the competition
when he stands up and shouts "Guys....Gee.... I'm a Tree!" The guys on the shed decide to just take him out so he
doesn't give away their position. They look up at about a 65° angle of elevation and know that the tree is 40 feet in
front of them. How far will Mr. Brust fall out of the tree when they shoot him?
Mr. Brust is standing at a height of approximately 90.6 feet in the tree. When they shoot him, he will fall from this height.
How to solveLet's break down the problem and solve it step by step.
First, we'll find the height from which Mr. Brust falls, and then we'll find the total distance he falls considering the tree's height and the height of the shed.
Find the height of the tree where Mr. Brust is standing:
We can use the tangent function to find the height of the tree above the shed where Mr. Brust is hiding.
tan(θ) = opposite/adjacent
We know the angle of elevation (θ) is 65°, and the tree is 40 feet in front of the shed. So, we have:
tan(65°) = height_above_shed / 40 ft
height_above_shed = 40 ft * tan(65°)
Using a calculator, we find:
height_above_shed ≈ 40 ft * 2.14 ≈ 85.6 ft
Find the total height of the tree where Mr. Brust is standing:
Since Mr. Kelly and Mr. Sullivan are 5 feet off the ground, we need to add this height to the height_above_shed we just calculated:
total_height = height_above_shed + height_of_shed
total_height = 85.6 ft + 5 ft = 90.6 ft
So, Mr. Brust is standing at a height of approximately 90.6 feet in the tree. When they shoot him, he will fall from this height.
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What is the function’s average rate of change from x=-1 to x=1
Answer:
The average rate of change of the function from x=-1 to x=1 is 6.
Step-by-step explanation:
The average rate of change of a function from x=-1 to x=1 is the change in the output of the function (y-value) divided by the change in the input of the function (x-value). In other words, it is the slope of the line connecting the two points (x=-1 and x=1).
Sally opens a savings account with $9,000 that earns 7% interest per year, not compounded How much interest, to the nearest penny, will Sally earn in 7 years?
Answer: Sally will earn $4,830.00 in interest over 7 years.
Step-by-step explanation:
If the interest is not compounded, then Sally will earn simple interest, which can be calculated using the formula:
I = P * r * t
where:
I = the interest earned
P = the principal amount (initial investment)
r = the annual interest rate (as a decimal)
t = the time period, in years
In this case, we have:
P = $9,000 (the initial deposit)
r = 7% = 0.07 (the annual interest rate)
t = 7 (the number of years)
So, plugging in the values:
I = $9,000 * 0.07 * 7
I = $4,830.00
Therefore, Sally will earn $4,830.00 in interest over 7 years.
Compute the probability that a randomly selected person does not have a birthday on the 1st day of the month.
Answer:
0.9973 or 364/365
Step-by-step explanation:
Assuming that every day of the year is equally likely to be someone's birthday, the probability that a randomly selected person has a birthday on the 1st day of the month is 1/365, since there are 365 possible birthdays in a year.
Therefore, the probability that a randomly selected person does not have a birthday on the 1st day of the month is:
P(not on 1st day) = 1 - P(on 1st day)
P(not on 1st day) = 1 - 1/365
P(not on 1st day) = 364/365
So, the probability that a randomly selected person does not have a birthday on the 1st day of the month is 364/365 or approximately 0.9973.
HELPPP ASAP IM AWARDING 80 POINTS!!!!
A cylindrical candle has a radius of 4 cm and a height of 10.4 cm.
What is the exact surface area of this candle?
32.0π cm²
83.2π cm²
91.2π cm²
115.2π cm²
Answer:
D) 115.2π cm².
Step-by-step explanation:
The surface area of a cylinder can be calculated using the formula:
Surface Area = 2πr² + 2πrh
where r is the radius and h is the height of the cylinder.
In this case, r = 4 cm and h = 10.4 cm. Substituting these values in the formula, we get:
Surface Area = 2π(4)² + 2π(4)(10.4)
Surface Area = 2π(16) + 2π(41.6)
Surface Area = 32π + 83.2π
Surface Area = 115.2π
Therefore, the exact surface area of the candle is 115.2π cm².
The answer is (D) 115.2π cm².
Answer: The answer is D, 115.2π cm²
Step-by-step explanation: When we use the formula of 2πrh+2πr2=2·π·4·10.4+2·π·42 to get the surface area, which equals 361.91
We can divide this by pi to get 115.2π cm²
Hope this helped!
Elmer invested $100 into a savings account that earns annual simple interest. At the end of 3 years, he earned $15 in interest. What is the interest rate on the savings account? Round to the nearest tenth of a percent.
Answer:
To find the interest rate, we can use the formula for simple interest:
I = Prt
Where:
I = Interest earned
P = Principal (initial investment)
r = Interest rate
t = Time
We are given that P = $100, t = 3 years, and I = $15. Substituting these values, we get:
15 = 100 * r * 3
Solving for r, we get:
r = 15 / (100 * 3) = 0.05
Therefore, the interest rate on the savings account is 5%.
Angles M, N, and P are supplementary.
What is the measure of angle P?
60°
34°
45°
36°
Step-by-step explanation:
The measure of angle p is 60°
solve using the standard algorithm. check your quotient and remainder and by using multiplication and addition 93÷7
In the standard algorithm
Reminder = 2
quotient = 13
What does quotient in mathematics mean?
The number being divided is known as the dividend, in this case, 15. The number being divided is known as the divisor (in this case, 3). The remainder following division is the quotient.
When we divide two integers, the result is a quantity known as the quotient. As an example, since the division resulted in the number 2, the quotient in the equation 8 4 = 2 is 2.
= 93÷7
Reminder = 2
quotient = 13
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In 1964, a car manufacturer introduced a new sports car that retailed for $2000. On average, the value of the car has appreciated at
1964.
11.3% per year. Using the standard form of an exponential, given below, write an equation to model the value of the car, z years after
y = ab^x
A=??
B=??
We may conclude after answering the presented question that where equation V(z) is the value of the car z years after 1964.
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the number "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilized in many different areas of mathematics, such as algebra, calculus, and geometry.
To model the value of the car, we can use the exponential growth formula:
[tex]V(t) = V0 * (1 + r)^t\\V(t) = ab^t\\a = V0 = $2000\\b = 1 + r = 1 + 0.113 = 1.113\\V(z) = 2000 * 1.113^z\\[/tex]
where V(z) is the value of the car z years after 1964.
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100 POINTS + BRAINLIEST!!
Answer:
The figure has an area of 70 cm² and is a trapeziumStep-by-step explanation:
The figure is a rectangular trapezoid, and this answers one question, the second question is the area, which we find by making the major base plus the minor base multiplied by the height and we divide everything by two, the two bases are the parallel ones (12 and 8) and the height is 7.
Then it is resolved with this expression
Area = [(12 + 8) × 7] : 2
Area = (20 × 7) : 2
Area = 140 : 2
Area = 70 cm²
Help ASAP DUE IN 30 MINUTES
Answer:
53 in2 is the answer for this question
Answer:
53
Step-by-step explanation:
If you divide the figure into two parts by extending the 4 in side, you get a right triangle and a rectangle.
Area of rectangle:
6*8 = 48 in²
Area of triangle:
1/2*(13 - 8)*(6 - 4) = 1/2 times 5 times 2 = 5 in²
Total area is:
48 + 5 = 53 in²
hope this helps x
Que volumen debería tener un recipiente para introducir en el 205 kg de mercurio
the container needs to have a volume of 0.01514 cubic meters to hold 205 kg of mercury.
Define volumeVolume is the measure of the amount of three-dimensional space enclosed by an object or space. It is typically expressed in cubic units, such as cubic meters (m³) or cubic centimeters (cm³).
The density of mercury is approximately 13,534 kg/m³.
We can use the formula:
Volume = mass/density
To find the volume of mercury that has a mass of 205 kg:
Volume = 205 kg / 13,534 kg/m³
Volume ≈ 0.01514 m³
Therefore, the container needs to have a volume of approximately 0.01514 cubic meters to hold 205 kg of mercury.
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The complete question is:
What volume should a container have to hold 205 kg of mercury?
21 20 18 15 11 ? WHAT COMES NEXT
Answer: 6
Step-by-step explanation:
21 - 1 = 20
20 - 2 = 18
18 - 3 = 15
15 - 4 = 11
11 - 5 = 6
Consider the table shown at left . What is the value of g( f ( -1) )
Answer:
4
Step-by-step explanation:
f(-1) = 2
g(2)= 4
The function S=m^(2)+6m+8 models the growth of book sales in m months, where S is an amount in thousands of dollars. In how many months do book sales reach $80,000 ?
Answer:
We are given the function S = m^2 + 6m + 8 which models the growth of book sales in m months, where S is an amount in thousands of dollars. We want to find in how many months book sales reach $80,000.
We can set up an equation as follows:
S = m^2 + 6m + 8 = 80
Subtracting 80 from both sides, we get:
m^2 + 6m - 72 = 0
We can factor this quadratic equation as:
(m + 12)(m - 6) = 0
This gives us two possible solutions:
m + 12 = 0 or m - 6 = 0
Solving for m in each case, we get:
m = -12 or m = 6
Since we are looking for a number of months, we can discard the negative solution.
Therefore, book sales reach $80,000 in 6 months.
So, the answer is: 6 months.
A seed company planted a floral mosaic of a national flag. The perimeter of the flag is 2,120 ft Determine the flag's width and length if the length is 400 ft greater than the width.
The flag's width is and the length is what?
PLEASE HURRY
Answer:
Step-by-step explanation:
Let's assume that the width of the flag is "w" ft.
According to the problem, the length of the flag is 400 ft greater than the width, which means it can be expressed as:
length = w + 400
Now, we know that the perimeter of the flag is 2,120ft. The perimeter of a rectangle is given by:
perimeter = 2(length + width)
Substituting the values, we get:
2120 = 2[(w+400) + w]
2120 = 2[2w + 400]
2120 = 4w + 800
4w = 1320
w = 330
Hence, the width of the flag is 330ft.
From our equation for the length, we have:
length = w + 400
length = 330 + 400
length = 730
Therefore, the length of the flag is 730ft.
If you place a 26-foot ladder against the top of a building and the bottom of the ladder is 20 feet from the bottom of the building, how tall is the building? Round to the nearest tenth of a foot. help please now.
Answer: The building is approximately 16.6 feet tall.
Step-by-step explanation:
Use Pythagorean theorem (a²+b²=c²) to solve this.
We know that the ladder is 26 feet long so that would be our hypotenuse (c²). and the distance between the ladder and the building is 20 feet. So, this is the base. The remaining side is x.
Your equation would be: 20²+x²=26²
subtract 20² from 26² --> 276=x²
then take the square root --> 16.6=x
Show how the model in problem 7 would change if
pl>lql. Draw the model, labeling p, q, and p + q.
Then write an addition equation using integers that
could represent p, q, and p + q.
Problem 7) The model labelling p, q and p + q is given in the attached. The addition equation using integers that could represent p, q, and p + q are:
(-1) + 2 = 1
Problem 8) The model would change if p > q
What is the explanation for the above response?7) Addition equation is given as:
(-1) + 2) = 1
Where ;
p = -1
q = 2
Hence,
-1 + 2 = 1
8) The model in the equation above would change if p > q
That is
|p| > |q|
⇒ p > q
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Full Question:
Although part of your question is missing, you might be referring to this full question: See attached image.
41 and 51 are two side lengths of a right triangle. The three sides form a Pythagorean triple. Find the value of the third side, x. State whether it is the hyp or a leg.
What is an undefined slope
Answer: The slope of a line can be positive, negative, zero, or undefined. A horizontal line has slope zero since it does not rise vertically (i.e. y1 − y2 = 0), while a vertical line has undefined slope since it does not run horizontally (i.e. x1 − x2 = 0).
Step-by-step explanation:
I hope it helped! :)
4. The fence around a circular pool is 75 ft long.
Diameter:0ft
Radius:0ft
Is it radius diameter or circumference
The resultant values are as follows:
Radius = 11.94 ft; Diameter: 23.87 ft; Circumference = 75 ft
What is the circumference?The circumference of a circle or ellipse in geometry is its perimeter.
That is, if the circle were opened up and straightened out to a line segment, the circumference would be the length of the arc.
The curve length around any closed figure is more often referred to as the perimeter.
The length of a circle's outline is referred to as its circumference, and the length of a form with straight sides is referred to as its perimeter.
So, since the fence around the circular pool is given, then it will also be the value of the circumference of the pool.
Circumference = 75 ft
Radius:
2πr = 75
r = 75/2π = 75/(2×3.14) ≈ 11.937
radius = 11.94 ft
Diameter:
2r = 2×11 ≈ 23.87 ft
Therefore, the resultant values are as follows:
Radius = 11.94 ft; Diameter: 23.87 ft; Circumference = 75 ft
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Complete question:
The fence around a circular pool is 75 ft long. Find: Radius, Diameter, and Circumference.