Answer:
Answer is 33
Step-by-step explanation:
5²= 25
2³= 8
add them equal 33!
For each expression, combine like terms and write an equivalent expression with fever terms.
1. 4x + 3x
2. 3x + 5x - 1
3. 5 + 2x + 7 + 4x
4. 4 - 2x + 5x
5. 10x - 5 + 3x - 2
Answer:
1. 7x
2. 8x - 1
3. 6x + 12
4. 3x + 4
5. 13x - 7
Step-by-Step Explanation:
Hope this helps!
Answer:
1. 7x
2. 8x -1
3. 6x+12
4. 3x + 4
5. 13x -7
Step-by-step explanation:
It is given that:
1. 4x + 3x
7x
2. 3x + 5x - 1
8x -1
3. 5 + 2x + 7 + 4x
2x+4x+5+7
6x+12
4. 4 - 2x + 5x
4 + 3x
3x + 4
5. 10x - 5 + 3x - 2
10x + 3x -5 -2
13x - 7
Therefore,
1. 7x
2. 8x -1
3. 6x+12
4. 3x + 4
5. 13x -7
If point A is reflected across both axes, what are the coordinates of the reflected point? ( -6 -3 )
(-6, 3)
(6, -3)
(6, 3)
(-6, -3)
Answer with step-by-step explanation:
When you are reflecting a point, you are reversing its' axes. In this case, the reflection of (-6,-3) is (6,3).
Hope this was helpful!
The length of a rectangle is 4 inches more than 3 times the width. If the area of the rectangle is 224 square inches, find the length and the width.
Answer:
width = 8 inches; length = 28 inches
Step-by-step explanation:
Length = 4 + 3w
width = w
Area = lw
224 = (4 + 3w) w
224 = 4w + 3w²
0 = 3w² + 4w - 224
( 3w + 28 )( w - 8) = 0
3w + 28 =0 ; w - 8 = 0
3w = -28 ; w = 8
w = -28/3
reject negative answer So width = 8 and the length = 4 + 3w
length = 4 + 3(8) = 4 + 24
Length = 28
Three objective functions for linear programming problems are 7A+10B,6A+4B, and −4A+7B. Show the graph of each for objective function values equal to 420 .
Graph of each objective function using linear programming.
Here,
Putting the equation equal to 420 and plotting the graph by finding the value of A and By putting A=0 and finding B then putting B=0 and finging A.
For example putting A=0 in 7A+10B=420 will yield (0,42) and Putting B=0 will yield (60, 0). plotting theses points on graph and joining them to generated the line.
Repeating thin step for each objective function and plotting the graph.
7A + 10B = 420 is labelled as a.
6A+4B = 420 is labelled as b.
-4A + 7B = 420 is labelled as c .
The graph of each function is attached below.
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An investment doubles its value in 3 years. A) what is the average rate of change in the value of this investment over the 3 year period? B) what continuously compounded interest rate would yield this return?
Citrus County's assets have an average duration of 8 and a market value of $1 million. The market interest rate is 5%. Use the duration formula to estimate the market value if the interest rate changes to 4%. 1,055,284 1,097.331
The estimated market value of Citrus County's assets, with an average duration of 8 and a market value of $1 million, would be approximately $1,055,284 if the interest rate changes to 4%.
In this case, the assets have an average duration of 8. When the interest rate changes from 5% to 4%, the change in interest rates is 1%. By applying the duration formula, the estimated percentage change in the market value of the assets would be approximately -8% (negative duration multiplied by the change in interest rates).
To calculate the estimated market value, we need to multiply the estimated percentage change (-8%) by the current market value ($1 million) and add it to the current market value. Thus, the estimated market value would be approximately $1,055,284 (1,000,000 + (1,000,000 * -8%)).
Duration is a measure of the sensitivity of an asset's price to changes in interest rates. It provides an estimate of the percentage change in the market value of an asset for a given change in interest rates. The duration formula states that the percentage change in the market value of an asset is approximately equal to the negative duration multiplied by the change in interest rates.
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what is 5/2x + 1/2x = 9 + 7/2
Answer: x = 25/6
Step-by-step explanation: yes
Answer: x=25/6
Step-by-step explanation:
combine multiplied terms into 1 fraction
5/2*+1/2x=9+7/2
5x/2+1/2x=9+7/2
combine
5x/2+1/2x=9+7/2
5x/2+1x/2=9+7/2
multiply by 1
5x/2+1x/2=9+7/2
5x/2+x/2=9+7/2
there are two scales one of them is five one of them measures to -4.
on the first scale, there's three pink squares and two green triangles.
on the 2nd, two pink squares and five green triangles.
what is the weight of one green triangle?
The weight of one green triangle is equal to: D. -2.
How to determine the weight of one green triangle?In this scenario and exercise, you are required to write a system of equations that represents the balance by using the balance shown in the image attached below and then determine the weight of one green triangle.
Since it is a balance, we can reasonably infer and logically deduce that all of the pink squares (s) and green triangles (t) on the left-hand side must be equal to the all of the parameters (numerical values) on the right-hand side of the balance as follows;
3s + 2t = 5 ......equation 1
2s + 5t = -4 ......equation 2
By solving the system of equations simultaneously using the elimination method and multiplying equation 2 by 3/2, we have:
3s + 2t = 5
3s + 7.5t = -6
(3s - 3s) + (2t - 7.5t) = (5 + 6)
-5.5t = 11
t = -11/5.5
t = -2.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Please help with this congruence question
Answer: it B i did it in class
Step-by-step explanation:
You need to buy a piece of canvas that is large enough to stretch and secure around a wooden frame. You plan that the length of your finished piece will be 5 inches less than twice the width, and you will need 2 inches extra on each side to secure the canvas to the frame. Which expression represents the area of the canvas?
A.) 2w^2+7w-4
B.) 2w^2+2w-5
C) 5w^2+7w-2
D.) 5w^2+3w-2
The area of the canvas can be calculated by taking the product of its length and width, which is 2w-5 and w+2, respectively, and then simplifying this expression to 5w²+3w-2, which is option D.
What is an expression?An expression is a mathematical statement that contains numbers, variables, and operations but lacks the equal sign.
To calculate the area of the canvas, we need to know the length and width of the canvas.
Since the length of the canvas will be 5 inches less than twice the width, the length can be expressed as:
2w-5.
The width of the canvas must include the extra 2 inches of fabric on each side to stretch and secure it around the frame, so the width is expressed as:
w+2.
The area of the canvas is then the product of the length and width,
= (2w-5)(w+2).
When this equation is simplified, it reduces to 5w²+3w-2, which is option D.
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Greek mathematicians said that quantities a, b, c. , y. are "in continuous proportion" if the ratio between each quantity and the next one is always the same, i.e., if a/b = b/c = .... = y/z Translate this into modern algebraic notation. (Hint: Work out what the nth quantity equals, in terms of the first quantity and the common ratio.)
modern algebraic notation, the statement "quantities a, b, c, ..., y are in continuous proportion" can be represented as a/b = b/c = c/d = ... = y/z, where the ratio between each quantity and the next one is always the same.
we can say that if we let r be the common ratio between consecutive terms, then we can write:
b = ar
c = br = a r^2
d = cr = a r^3
and so on, where each term is obtained by multiplying the previous term by r.
Therefore, we can write the nth term as a r^(n-1), and we can express any term in terms of the first term a and the common ratio r as:
a_n = a r^(n-1)
By using this algebraic notation, we can easily determine any term in the sequence by knowing the first term and the common ratio between consecutive terms.
Overall, by understanding the concept of continuous proportion and using modern algebraic notation, we can express the relationship between a sequence of quantities and find any term in the sequence.
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When searching within the list
Lewis, Maurice, Nathan, Oliver, Pat, Quincy, Roger, Stan, Tom
which of the following entries will be found most quickly using the binary search algorithm?
A. Lewis B. Pat C. Tom
The binary search algorithm is most effective when the list is sorted. In this case, since the list of names is not sorted, the binary search algorithm may not be the most efficient method for finding entries. However, if we assume the list is sorted, the entry "Lewis" would be found most quickly using the binary search algorithm.
The binary search algorithm is a divide-and-conquer approach that efficiently searches for a specific value in a sorted list. It works by repeatedly dividing the search interval in half until the desired value is found.
However, in the given list of names, the names are not sorted alphabetically. Therefore, the binary search algorithm may not be the optimal choice for finding entries quickly. To utilize the binary search algorithm effectively, the list of names would need to be sorted in alphabetical order.
Assuming the list is sorted, the binary search algorithm starts by comparing the target value with the middle element of the sorted list. If the target value is equal to the middle element, the search is successful. If the target value is less than the middle element, the search continues in the lower half of the list, and if it is greater, the search continues in the upper half. This process is repeated until the target value is found.
In the given list, "Lewis" would be found most quickly using the binary search algorithm if the list were sorted in alphabetical order. However, without sorting the list, the binary search algorithm may not be the most efficient method for finding entries.
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Consider triangle DEF. The legs have a length of 36 units each. What is the length of the hypotenuse of the triangle 18 units units 36 units units
Answer:
(っ◔◡◔)っ ♥ 36 square root 2 ♥
Step-by-step explanation:
The length of the hypotenuse of the triangle is approximately 48.99 units.
What is the Pythagorean theorem?Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
We can apply this theorem only in a right triangle.
Example:
The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.
Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm
We have,
We can use the Pythagorean theorem to find the length of the hypotenuse of the triangle:
c² = a² + b²
where c is the length of the hypotenuse, and a and b are the lengths of the legs.
Substituting the values given in the problem.
c² = 18² + 36²
c² = 324 + 1296
c² = 1620
Taking the square root of both sides.
c = √(1620)
Simplifying.
c = 6 √(90) or approximately 48.99
Therefore,
The length of the hypotenuse of the triangle is approximately 48.99 units.
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Each of the following figures shows three identical capacitors connected to a battery. Which arrangement has the greatest equivalent capacitance? (A) EL HHH HA (D) HA + €
The arrangement with the greatest equivalent capacitance is (A) EL HHH HA. arrangement A is uniquely identifiable as having the highest equivalent capacitance when compared to the others.
Determine the equivalent capacitance?In this question, the letters represent the capacitors, and the symbols represent their connections. The equivalent capacitance of capacitors in series can be calculated using the formula:
1/C_eq = 1/C₁ + 1/C₂ + 1/C₃
In arrangement (A), the capacitors are connected in parallel (HHH), resulting in an increased equivalent capacitance. Then, this parallel combination is connected in series with another capacitor (EL) which does not affect the overall capacitance. Therefore, arrangement (A) has the greatest equivalent capacitance.
In arrangement (D), the capacitors are connected in series (HA) and then connected to an unknown symbol (€), which is not specified in the question. Without knowing the specific connection represented by (€), it is not possible to determine the equivalent capacitance.
Thus, arrangement (A) is the only one that can be determined to have the greatest equivalent capacitance among the given options.
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Several friends (Calvin, Dean, Kelli, and Lee) went to Cal's Late Night Diner for a bite to eat. Match each person to their drink (Iced tea, Lemonade, Root Beer, and Water) and determine how much each paid ($4.99, $5.99, $6.99, and $7.99) for their meal.
Clues:
1. The Diner who paid $4.99 was either Calvin or the one who got the Root Beer.
2. Kelli paid $6.99
3. The one who got the water paid 1 dollar less than Dean.
4. Calvin paid more than Lee.
5. The one who got the Root beer paid 1 dollar less than the one who got the Iced Tea.
Based on the given clues, we can determine the person, drink, and price paid for each individual:
Calvin: Root Beer, $4.99
Dean: Lemonade, $7.99
Kelli: Water, $6.99
Lee: Iced Tea, $5.99
How to determine how much each friends paidFrom clue 1, we know that either Calvin or the person who got the Root Beer paid $4.99. Since Calvin paid more than Lee according to clue 4, Calvin cannot be the one who got the Root Beer. Therefore, Calvin paid $4.99.
From clue 2, Kelli paid $6.99.
From clue 3, the person who got the water paid $1 less than Dean. Since Dean paid the highest price, the person who got the water paid $1 less, which means Lee paid $5.99.
From clue 5, the person who got the Root Beer paid $1 less than the person who got the Iced Tea. Since Calvin got the Root Beer, Lee must have gotten the Iced Tea.
Therefore, the final assignments are:
Calvin: Root Beer, $4.99
Dean: Lemonade, $7.99
Kelli: Water, $6.99
Lee: Iced Tea, $5.99
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what is (2x+45)° x° = what?
Answer:
x = 45.
Step-by-step explanation:
Given a straight line with the equation.
First collect like terms:
2x + x = 180 - 45
Then calculate:
3x = 135
Finally after dividing both sides by 3:
x = 45
an inverted cone has a height of 11 inches and an initial radius of 18 inches. the volume of the inverted cone is decreasing at a rate of 541 cubic inches per second, with the height being held constant. what is the rate of change of the radius, in inches per second, when the radius is 5 inches?
Answer:
-4.697 in/s
Step-by-step explanation:
You want to know the rate of change of radius of a cone 11 inches high with a radius of 5 inches and a volume that is decreasing at the rate of 541 cubic inches per second.
VolumeThe volume of a cone is given by ...
V = π/3r²h
The rate of change is found by implicit differentiation:
V' = (π/3)((2rr')h +r²h')
Here, the height is constant, so h' = 0. Solving for r', we find ...
r' = 3V'/(2πrh)
ApplicationUsing the given values of V', r, and h, we find the rate of change of radius to be ...
r' = 3(-541 in³/s)/(2π(5 in)(11 in)) = -1623/(110π) in/s ≈ -4.69652 in/s
The radius is decreasing at about -4.697 inches per second.
__
Additional comment
The initial radius of the cone is irrelevant to the problem, since we want to know the rate of change at a specific different radius. Whether the cone is inverted or not is also irrelevant to its volume.
When writing an expression or equation to represent a real-world situation, why is it important to be able to describe what each part of the expression or
equations represents?
Answer:
If you know what each part of the expression or equations represents, it means that you understand the equation. You can solve the problem and know what you are doing.
I hope this helps! I'm sorry if it doesn't.
A restaurant wants to study how well its salads sell. The circle graph shows the sales over the past few days. If 5 of the
salads sold were Caesar salads, how many total salads did the restaurant sell?
Salads Sold
Caesar 25%
Garden 60%
Taco 15
The total number of salads sold by the restaurant is 20
How to get the total number of salads soldThe sentence given shows that 25% is representative of the 5 Caesar salads sold.
Let's say that the total number of salads sold was x. So, we are told that 25% of the total number of salads sold is for the Caesar type.
Then, if 0.25x = 5 salads.
Thus x = 5/0.25
= 20
So, the total number of salads sold by the restaurant is 20.
Of these, Garden salads = 0.6 × 20
= 12
Also, Tacos = 0.15 × 20 = 3
3 + 12 + 5 = 20
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how many ways are there to select a committee of five members of the department if at least one woman must be on the committee?
Answer: 16
Step-by-step explanation:
Nina has $40 in the bank. She writes a check for $63, deposits $80 and writes another check for $140. What is her balance?
Answer:
-$83
Step-by-step explanation:
Create an equation to model Nina's balance.
\(40-63+80-140=-83\)
What step isolates the variable in the equaiton x/2 = 16?
(Will mark yo brainliest)
Answer:
Multiply 2 i think!
Step-by-step explanation:
Hope this helped!
find f. f ''(x) = 6 6x 36x2, f(0) = 2, f (1) = 13
The final solution for f(x) is: f(x) = x^3 + 3x^4 + 2. We can use integration to find f(x) given the second derivative f ''(x) = 6x + 36x^2 and the initial conditions f(0) = 2 and f(1) = 13.
First, we integrate f ''(x) once to obtain the first derivative f'(x):
f'(x) = ∫(6x + 36x^2)dx = 3x^2 + 12x^3 + C₁
Since f(0) = 2, we know that f'(0) = C₁ = 0. Therefore, we have:
f'(x) = 3x^2 + 12x^3
Next, we integrate f'(x) to obtain f(x):
f(x) = ∫(3x^2 + 12x^3)dx = x^3 + 3x^4 + C₂
Using the initial condition f(0) = 2, we can solve for C₂:
f(0) = C₂ = 2
Thus, the final solution for f(x) is:
f(x) = x^3 + 3x^4 + 2
We can verify that this is the correct solution by checking that f ''(x) = 6x + 36x^2 and that f(1) = 13, as given by the initial conditions.
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Given A(-3, K) and B(9, -1), if the length of AB is 13 units, find the possible values of K
A (-3, -1) B (9, -1)
Step-by-step explanation:
start at B (9,- 1) move 13 units end at A (-3, -1)
K = -1
Polygon ABCD is defined by the points A(-4, 2), B(-2, 4), C(1, 3), and D(2, 2). Match the coordinates of the points of the transformed polygons to their correct values. the coordinates of D′ if polygon ABCD rotates 90° counterclockwise to create A′B′C′D′ (-2, 2) the coordinates of C″ if polygon ABCD rotates 90° clockwise to create A″B″C″D″ (4, -2) the coordinates of A′′′ if polygon ABCD rotates 180° clockwise to create A′′′B′′′C′′′D′′′ (3, -1) the coordinates of B″ if polygon ABCD rotates 270° counterclockwise to create A″B″C″D″ (4, 2) arrowBoth arrowBoth arrowBoth arrowBoth
Answer:
The answer is below
Step-by-step explanation:
Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.
If a point A(x, y) is rotated 90° counterclockwise, the new point is at A'(-y, x).
If a point A(x, y) is rotated 90° clockwise, the new point is at A'(y, -x).
If a point A(x, y) is rotated 180° counterclockwise, the new point is at A'(-x, -y).
If a point A(x, y) is rotated 270° counterclockwise, the new point is at A'(y, -x).
Polygon ABCD is defined by the points A(-4, 2), B(-2, 4), C(1, 3), and D(2, 2).
The coordinates of D′ if polygon ABCD rotates 90° counterclockwise to create A′B′C′D′ is D'(-2, 2)
The coordinates of C″ if polygon ABCD rotates 90° clockwise to create A″B″C″D″ is C"(3, -1).
the coordinates of A′′′ if polygon ABCD rotates 180° clockwise to create A′′′B′′′C′′′D′′′ is A''"(4, -2)
the coordinates of B″ if polygon ABCD rotates 270° counterclockwise to create A″B″C″D″ is B"(4, 2)
Answer:
Answer:
The answer is below
Step-by-step explanation:
Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.
If a point A(x, y) is rotated 90° counterclockwise, the new point is at A'(-y, x).
If a point A(x, y) is rotated 90° clockwise, the new point is at A'(y, -x).
If a point A(x, y) is rotated 180° counterclockwise, the new point is at A'(-x, -y).
If a point A(x, y) is rotated 270° counterclockwise, the new point is at A'(y, -x).
Polygon ABCD is defined by the points A(-4, 2), B(-2, 4), C(1, 3), and D(2, 2).
The coordinates of D′ if polygon ABCD rotates 90° counterclockwise to create A′B′C′D′ is D'(-2, 2)
The coordinates of C″ if polygon ABCD rotates 90° clockwise to create A″B″C″D″ is C"(3, -1).
the coordinates of A′′′ if polygon ABCD rotates 180° clockwise to create A′′′B′′′C′′′D′′′ is A''"(4, -2)
the coordinates of B″ if polygon ABCD rotates 270° counterclockwise to create A″B″C″D″ is B"(4, 2)
Step-by-step explanation:
Please answer my question quickly.
Answer:
b=sqrt7
Step-by-step explanation:
16=9+b^2
What are the steps to verify trigonometric identities?
Answer:Here you go
Step-by-step explanation:
Change everything into terms of sine and cosine.
Use the identities when you can.
Start with simplifying the left-hand side of the equation, then, once you get stuck, simplify the right-hand side. As long as the two sides end up with the same final expression, the identity is true.
Which words or variables mean OUTPUT? Select all possible answers. help me out
a. domain
b .range
c .x
d .y
e. f(x)
A home security company provides security systems for $6 per week, plus an installation fee. The total fee for 10 weeks of service is $345. Write and solve a linear equation to find the cost of the installation fee.
Answer: $285
Step-by-step explanation:
Let the installation fee be represented by x.
Therefore, the equation to solve the question will be:
= x + 6w
where,
x = installation cost
w = number of weeks
x + 6w = 345
x + 6(10) = 345
x + 60 = 345
x = 345 - 60.
x = 285
Therefore, the installation fee is $285
How many solutions does this nonlinear system of equations have?
Answer:
zero
Step-by-step explanation:
This nonlinear system of equations has 0 solutions.
What is a nonlinear system of equations?
A system of nonlinear equations is a system of two or more equations in two or more variables containing at least one equation that is not linear. Recall that a linear equation can take the form Ax+By+C=0. Any equation that cannot be written in this form is nonlinear.
What is an example of a nonlinear equation?
An equation in which the maximum degree of a term is 2 or more than two is called a nonlinear equation. + 2x + 1 = 0, 3x + 4y = 5, this is the example of nonlinear equations, because equation 1 has the highest degree of 2 and the second equation has variables x and y.
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