The square had a side length of 3x+13.
Because the perimeter is 12x+52, you have to divide that by each of the four sides.
Yoda purchases a light saber for $1,678 with an installment loan that has an APR of 12%. The store financing requires a 15% down payment for 12 monthly payments. What is the finance charge?
Answer:$2,000
Step-by-step explanation:
Suppose you have 52 feet of fencing to enclose a rectangular dog pen. The function A = 26x – x2, where x = width, gives you the area of the dog pen in square feet. What width gives you the maximum area? What is the maximum area? Round to the nearest tenth as necessary. width = 26 ft; area = 364 ft2 width = 26 ft; area = 169 ft2 width = 13 ft; area = 507 ft2 width = 13 ft; area = 169 ft2
Answer:
width = 13 ft; area = 169 ft^2
Step-by-step explanation:
The equation for the area can be factored as ...
A = x(26 -x)
This has zeros at x=0 and x=26. The vertex of this downward-opening parabola will be halfway between those, at x=13. Then the area for a width of 13 feet is ...
A = 13(26 -13) = 13^2 = 169 . . . . ft^2
The maximum area is 169 ft^2, when the width is 13 ft.
_____
You will note that these dimensions make the pen be a square. It can be useful to remember that a square is the rectangle with the largest area for a given perimeter length.
The width that gives the maximum area for the given fencing is 13 feet, and the maximum area is 169 square feet (option B).
Explanation:
The formula given is a quadratic function where x is the width and A is the area. In a quadratic function, the maximum or minimum value occurs at the vertex. The x-coordinate of the vertex can be found using the formula -b/2a where a and b are the coefficients of the quadratic function. Here, a is -1 and b is 26, therefore the x-coordinate of the vertex is -26/-2*-1 = 13. This means that a width of 13 ft will give the maximum area. To find the maximum area, we substitute x = 13 into the function: A = 26*13 - 13^2 = 169 ft2. So, the width that will give the maximum area is 13 feet and the maximum area is 169 square feet.
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Anna wants to rent movies from either Service A or Service B. Service A charges $37.92 as a subscription fee with a charge of $2.18 per movie.Service B charges $33.25 as a subscription fee plus $3.55 per movie. Service B is running a special offer where the first movie is free. Given that Anna always rents at least 1 movie in a given subscription period, how many movies would she have to rent for the average cost per movie to be equal at Service A or Service B?
Answer:
6 movies
Step-by-step explanation:
:Service A
1. $37.92 +&2.18=$40.1
2. $41.1+$2.18=$42.28
3....
4....
5....
6. $48.82+$2.18=$51
Service B
1. $33.25+free movie=$33.25
2. $33.25+$3.55=$36.8
3....
4....
5....
6. $47.45+$3.55=$51
NEED HELP WITH A MATH QUESTION WITH FINDING A SURFACE AREA OF A SQAURE PYRAMID
ANSWER
[tex]S.A = 125 {in}^{2} [/tex]
EXPLANATION
The total surface area of a square pyramid is the area of the 4 triangular faces plus the area of the square base.
This is given by the formula!
[tex]S.A = 4 \times \frac{1}{2} bh + {l}^{2} [/tex]
From the diagram, the base is 5 inches and the height is 10 inches.
We substitute the values to get:
[tex]S.A = 4 \times \frac{1}{2} \times 5 \times 10 + {5}^{2} [/tex]
This simplifies to;
[tex]S.A = 100 + 25[/tex]
[tex]S.A = 125 {in}^{2} [/tex]
Find the solution of this system of equations -4x-y=-18 , -7x+y=-4
Answer:
(x, y) = (2, 10)
Step-by-step explanation:
Adding the two equations will eliminate the y-variable:
(-4x -y) +(-7x +y) = (-18) +(-4)
-11x = -22 . . . . . simplify
x = 2 . . . . . . . . . divide by -11
__
Put this into the first equation to find y:
-4·2 -y = -18
-8 +18 = y = 10 . . . . . add 18+y
The solution is (x, y) = (2, 10).
Answer:
x = 2 and y = 10
Step-by-step explanation:
It is given that,
-4x - y = -18 ---(1)
-7x + y= -4 ---(2)
To find the solution of equations
Step 1: Add eq(1) + eq(2)
-4x - y = -18 ---(1)
-7x + y= -4 ---(2)
-11x + 0 = -22
11x = 22
x = 22/11 = 2
Step 2: Substitute the value of x in eq (2)
-7x + y= -4 ---(2)
-7*2 + y = -4
-14 + y = -4
y = -4 + 14 = 10
Therefore x = 2 and y = 10
Read the passage and examine the text in bold. Then, answer the question.
I always loved my grandfather's explanations of our seasons, "This is the country of three seasons. From June on to November it lies hot, still, and unbearable, sick with violent and unrelenting storms; then on until April, it is chill, quiet, and drinks its scant rain and scanter snows. From April to the hot season again, it is blossoming, radiant, and a seductress." His months were only approximate, later or earlier the rain-laden wind may drift up the water gate of the Colorado River from the Gulf and bring to us our heat, chill, or radiance. In the desert, we see the land sets its seasons by the rain.
Does the bolded portion contain an error? Choose the correction if one is needed.
a) seasons; "This is the
b) seasons: "This is the
c) seasons; however, "This is the
d) No correction needed
Answer:
The correct option is:
a) seasons; "This is the
A semicolon is most commonly used to link (in a single sentence) two independent clauses that are closely related in thought.When a semicolon is used to join two or more ideas (parts) in a sentence, those ideas are then given equal position or rank.
Step-by-step explanation:
Answer:
A. seasons: "This is the
Step-by-step explanation:
Write an equation of a line in point-slope form that has a slope of -2 and passes through (5, -1).
A. y + 1 = -2(x – 5)
B. y – 1 = -2(x – 5)
C. y – 5 = -2(x + 1)
D. y -5 = -2(x – 1)
Answer:
A. y + 1 = -2(x – 5)
Step-by-step explanation:
For a line with slope m through point (h, k), the equation is ...
y -k = m(x -h)
Fill in your values of m=-2, h=5, k=-1 and you have ...
y -(-1) = -2(x -5)
y +1 = -2(x -5) . . . . . . simplify. Matches selection A.
What is the equation of the line best fit for the following data? Round the slope and y-intercept of the line to three decimal places. X=4,7,10,12,13 y= 5,7,12,14,18
Answer:
y = 1.383x - 1.526
Step-by-step explanation:
Intercept- -1.526
Slope- 1.383
Line of best fit- y = 1.383x - 1.526
Answer:
[tex]y=1.383x-1.526[/tex]
Step-by-step explanation:
The given data table is
x : 4 7 10 12 13
y : 5 7 12 14 18
We need to find the equation of the best fit line.
The general form of a best fit line is
[tex]y=mx+b[/tex] .... (1)
where, m is slope and b is y-intercept.
[tex]m=\frac{\sum_{i=1}^nx_iy_i-n\overline{x}\overline{y}}{\sum_{i=1}^nx_i^2-n\overline{x}^2}[/tex]
[tex]b=\overline{y}-b\overline{x}[/tex]
Using the graphing calculator we get
[tex]m=1.38321\approx 1.383[/tex]
[tex]b=-1.52555\approx -1.526[/tex]
Substitute m=1.383 and b=-1.526 in equation (1).
[tex]y=1.383x-1.526[/tex]
Therefore, the equation of best fit line is [tex]y=1.383x-1.526[/tex].
If the system of the linear equations above has infinitely many solutions, and c is a constant, what is the value of c?
A) - 6
B) - 3
C) - 2
D) - 1
1. For the system of linear equations to have an infinite number of solutions, the two lines must cross over an infinite number of times, ie. they would be the same line.
Now, if they are the same line and we were to write out both equations in the form y = mx + c, this would mean that the m value (the gradient) and the c value (the y-intercept) would be the same. Thus, the first step is to write out both equations in the form y = mx + c.
a) Equation 1:
3x - 9y = -6
3x = -6 + 9y (Add 9y to both sides)
3x + 6 = 9y (Add 6 to both sides)
(1/3)x + 2/3 = y (Divide both sides by 9)
Thus, the first equation may be written as y = (1/3)x + 2/3
b) Equation 2:
(1/2)x - (3/2)y = c
(1/2)x = c + (3/2)y (Add (3/2)y to both sides)
(1/2)x - c = (3/2)y (Subtract c from both sides)
(1/3)x - (2/3)c = y (Multiply both sides by 2/3)
Thus, the second equation may be written as y = (1/3)x - (2/3)c.
2. Now that we have both equations in the form y = mx + c, we can look at their gradients and y-intercepts:
Equation 1: gradient = 1/3, y-intercept = 2/3
Equation 2: gradient = 1/3, y-intercept = -(2/3)c
As we can see above, the gradients of the two lines are the same, however for them to be the same line their y-intercepts must also be equal. Thus, we must equate the two y-intercepts to find c:
2/3 = -(2/3)c
1 = -c (Multiply both sides by 3/2)
-1 = c (Multiply both sides by -1)
Thus, if the system of linear equations has infinitely many solutions, and c is a constant, the value of c is -1 (answer D).
The value of 'c' for the given system of the linear equations with infinitely many solutions is - 1.
What is a linear equation?"A linear equation is an equation in which the highest power of the variable is always 1."
Given system of linear equations are
1. [tex]3x - 9y=-6[/tex]
⇒ [tex]x - 3y = - 2[/tex]
Therefore, [tex]a_{1} = 1, b_{1} = -3, c_{1} = -2[/tex]
2. [tex]\frac{x}{2}-\frac{3y}{2} =c[/tex]
⇒ [tex]x - 3y = 2c[/tex]
Therefore, [tex]a_{2} = 1, b_{2} = -3, c_{2} = 2c[/tex]
For the system of the linear equations with infinitely many solutions,
[tex]2c = -2[/tex]
⇒ [tex]c = -1[/tex]
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Cube shaped box for packing tape Cube shaped container the edge of the length of the storage container is 2 and 1/2 ft of each block is 1/5 of the storage container what is the volume in cubic feet of one of the shape
Answer:
1/8 ft³
Step-by-step explanation:
Apparently cubic blocks that are 1/5 of 2 1/2 ft on a side are used to fill the cube that is 2 1/2 ft on a side. Then each edge of the block is ...
(1/5) × (5/2 ft) = 1/2 ft
The volume of the block is the cube of that:
(1/2 ft)³ = 1/8 ft³
write a verbal expression to represent
w^2 =32w
BRAINLIEST!
Verbal expression of w^2 = 32w is:
W to the second power equals 32 with a variable of w.
To the second power means exponent of 2.
Variable is an unknown number represented by a letter. In this case, the variable is "w".
Hope this helps!
- Melanie
Answer:
Step-by-step explanation:
The square of variable w is equal to 32 times that variable.
Solve x − 7y = 8 for x.
A.x = −7y + 8
B.x= −7y − 8
C.x = 7y − 8
D.x = 7y + 8
Answer:
D
Step-by-step explanation:
you need to get the x alone so to do that, you need to add 7y so you do it on both sides and it gives you x=7y+8
The value of the expression x − 7y = 8 will be x = 7y + 8. The correct option is D.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given expression is x − 7y = 8. The value of x will be calculated as below:-
x − 7y = 8
x = 7y + 8
Therefore, the value of the expression x − 7y = 8 will be x = 7y + 8. The correct option is D.
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Skylar and Wyatt both play soccer. Wyatt scored 2 times as many goals as Skylar. Together they scored 15 goals. Could Skyler have scored 3 goals? Why or why not?
Answer:
No, he did not score 3,
Because, 2 times of 5 is 10 and the sum of 10 and 5 is 15.
Step-by-step explanation:
Let x be the score of Skylar,
Since, Wyatt scored 2 times as many goals as Skylar.
So, Wyatt's score = 2x
Thus, total scores = x + 2x = 3x
According to the question,
3x = 15
x = 5
Hence, Skyler have scored 5 goals.
Because, 2 times of 5 is 10 and the sum of 10 and 5 is 15.
Final answer:
Skylar could have scored 3 goals because, based on the information provided, they scored 5 goals after solving the equation that evaluates the total goals scored by both Skylar and Wyatt.
Explanation:
To determine if Skylar could have scored 3 goals, given that Wyatt scored 2 times as many goals as Skylar and together they scored 15 goals, we can set up a simple algebraic equation. Let's denote the number of goals Skylar scored as S, which means that Wyatt scored 2S goals.
The total number of goals is the sum of the goals scored by both Skylar and Wyatt, which is S + 2S = 15. This simplifies to 3S = 15. By dividing both sides of the equation by 3, we get S = 5.
Therefore, Skylar could have scored 3 goals because the calculations show that Skylar scored 5 goals.
A group of friends go to the movies. The function h(x) represents the amount of money spent where x is the number of friends at the movies. Does a possible solution of (6.5,$95.25) make sense for this function?
Answer:
not really
Step-by-step explanation:
The number of friends (x) is expected to be an integer. 6.5 friends does not really make sense.
_____
There are all kinds of ways this might make sense, but none of them are supported by the information given in the problem statement.
No, the solution (6.5,$ 95.25) do not make a sense.
Since, the number of people going for a movie can't be in decimals.
Step-by-step explanation:The function h(x) represents the amount of money spent where x is the number of friends at the movies.
The domain of such a function has to be whole numbers.
Because the number of people that go for a movie must exist as a whole they can't exist in decimals.
( i.e. either no one will go.
1 will go.
2 friends will go and so on)
i.e. the domain is the set of all non-negative integers.
Anthony deposited $14,000 with a bank in a 5-year certificate of deposit yielding 6% compounded daily. Find the compound amount
A) $18,897.56
B) $32,897.56
C) $17,976.05
D) $16,542.10
Answer:
Total = 14,000 * 1 + (.06 / 365) ^365*5
Total = 14,000 * 1.0.000164383561643836^1,825
Total = 14,000 * 1.3498255274
Total = 18,897.56
Step-by-step explanation:
what is the measure of xyz
Answer:
The correct answer is option B. 65
Step-by-step explanation:
To find the measure of <VYX
Central angle of arc VW = 44°
Therefore m<VXY = 44/2 = 22°
And central angle of arc XZ = 86° therefore <XVY = 86/2 = 43
To find the mesure of <XYZ
m<XYZ = m<VXY + m<XVY
= 22 + 43
= 65°
Therefore the correct answer is option B. 65°
Lori purchases a new set of watercolor paints and some canvases to create art for her next exhibit. The watercolor paint set costs $15 and the canvases are $24.50 each. If Lori buys 6 canvases, what is the total amount of money she spends for her next exhibit?
Answer:172
Step-by-step explanation:
24.5 times 6 is 157
Plus 15 for the paint is 172 for the TOTAL for ALL she spent
Answer:
The answer is $162.00Step-by-step explanation
What is the name of the thick, lower end of the digestive tract where solid waste is gathered and leaves the body?
The lower end of the digestive tract that gathers and expels solid waste from the body is called the rectum. The process involves the colon, where digestion occurs, water is reabsorbed, and waste is turned into feces, which is then eliminated through the anus.
The thick, lower end of the digestive tract where solid waste is gathered and leaves the body is called the rectum. After digested food passes through the small intestine, it enters the large intestine, or colon, where it undergoes further digestion and water reabsorption. The colon is home to a diverse microbiota that aids in digestion. The waste material, now known as feces, is then moved to the rectum. The rectum stores the feces until it triggers neural signals that lead to the urge to eliminate this waste through the anus.
What are the zeros of f(x) = (x − 7)(x − 3)(x − 2)?
For this case we must find the zeros of the following function:
[tex]f (x) = (x-7) (x-3) (x-2)[/tex]
If we equate each term to 0 and we clear the variable "x", we will find the values that make the function equal to zero. So:
[tex]x-7 = 0\\x = 7[/tex][tex]x-3 = 0\\x = 3[/tex][tex]x-2 = 0\\x = 2[/tex]Thus, the zeros of the function are:
7,3,2
Answer:
Option C
The zeros of the function f(x) = (x - 7)(x - 3)(x - 2) are 7, 3, 2. The correct option is the third option 7, 3, 2
From the question,
We are to determine the zeros of the given function
The given function is
f(x) = (x - 7)(x - 3)(x - 2)
To determine the zeros of this function, we will set f(x) = 0
That is ,
f(x) = (x - 7)(x - 3)(x - 2) becomes
0 = (x - 7)(x - 3)(x - 2)
∴ (x - 7)(x - 3)(x - 2) = 0
Then,
We can write that
x -7 = 0 OR x - 3 = 0 OR x - 2 = 0
∴ x = 7 OR x = 3 OR x = 2
Hence, the zeros of the function f(x) = (x - 7)(x - 3)(x - 2) are 7, 3, 2. The correct option is the third option 7, 3, 2
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TW is a perpendicular bisector of chord QE. Identify the diameter. The answer with the red arrow is Incorrect!
Answer:
50m.
Step-by-step explanation:
When 2 chords of a circle intersect the following products are equal:
15 * 15 = 5 * (TW - 5)
5TW = 225 + 25 = 250
TW = 250/5 = 50 m
Option c 50m
What is the theorem of the chord from the center?When a line passes through the center of the circle to the chord then the line is perpendicular bisector of the same chord which means it divide the chord in equal parts and makes an angle of 90 degrees with the chord.
What is the Pythagoras theorem?Pythagoras theorem is the theorem used to calculate the hypotenuse in a right-angled triangle from the two legs of the triangle.
hypotenuse² = base²+height².
Solving the problemLet the center (the point in bold be C) and the point of intersection between QE and TW be R, So CQ is the radius, CR = radius-5.
Let the radius be 'r' so In Triangle CQR using the Pythagoras theorem
r² = (r-5)²+15²
r²-(r-5)²=225
(r-(r-5))(r+r-5) = 225
5.(2r-5)=225
(2r-5)=45
2r - 5 =45
2r=50
r = 25 and diameter is equal to 2*r and hence the diamter is 50.
The diameter in the figure is 50m
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At a snack bar, 3 hamburgers and a small drink cost $8.75. The cost of 2 hamburgers and 2 small drinks is $7.50. What is the cost of 4 hamburgers and 3 small drinks?
Answer:
13.75
Step-by-step explanation:
3b + d = 8.75
2b + 2d = 7.50
(3b + d = 8.75) times 2
(2b + 2d = 7.50) times -3
6b + 2d = 17.5
-6b + (-6d) = -22.5
the b's cancel out, 2d - 6d = -4d and 17.5 - 22.5 = -5
-4d = -5 Divide it and d = 1.25
then plug in 1.25 for d.
2b + 2(1.25) = 7.50
2b + 2.5 = 7.50
2b = 5
b= 2.5
3(2.5) + 1.25 = 8.75 ? Yes.
2(2.5) + 2(1.25) = 7.50 ? Yes.
4(2.5) + 3(1.25) = 13.75.
I NEED HELP
Analyze the diagram below and complete the instructions that follow.
Find the value of x and the value of y.
answer is B)
x= 85, y = 100
Answer:
D, x=100 and y=85
Step-by-step explanation:
Hello
In every convex polygon, the sum of the measure of the interior angles is given by the expression SUM = 180 ° (n - 2) where n is the number of sides
the polygon has our sides MN, NO,OP and PM, the sum of the interior angles is
[tex]sum=180(4-2)\\sum=360 degrees[/tex]
[tex]360= x +y +80+95\\360-80-95= x+y\\x+y=185[/tex]
looking at the graph it is observed that angle x° is obtuse (more than 90° but less than 180°.) and the angle y is acute (The acute angle is the small angle which is less than 90°)
so
[tex]x>y[/tex]
[tex]x+y=185[/tex]
the response option that meets these two conditions is D, x=100 and y=85
Why is MAE ≅ TON
HL
HA
LL
Answer:
HL
Step-by-step explanation:
HL (Hypotension-Leg) postulate of congruence : In two right triangles if the hypotenuses are equal and any two corresponding legs are equal in both triangles then the triangles are congruent.
In the given right triangles MAE and TON,
AM = OT,
EM = NT,
Thus, by the HL postulate,
Δ MAE ≅ Δ TON
First option is correct.
Which products result in a difference of squares? Check all that apply.
(x – y)(y – x)
(6 – y)(6 – y)
(3 + xz)(–3 + xz)
(y2 – xy)(y2 + xy)
(25x – 7y)(–7y + 25x)
(64y2 + x2)(–x2 + 64y2)
Answer:
(x-y)(y-x)
Step-by-step explanation:
because x-y=y-x
Which is one of the transformations applied to the graph of [tex]f(x)=x^2[/tex] to produce the graph of [tex]p(x)=-50+14x-x^2[/tex]?
A. a shift down 1 unit
B. a shift left 7 units
C. a shift right 1 unit
D. a shift up 7 units
Could you explain your answer?
If it's wrong it should be report called "improper answer."
No need to spamming answers! If you spamming and that's going to mark your answer report.
Thank you!
-Charlie
Answer:
A
Step-by-step explanation:
Write each parabola in standard form.
f(x) = x²
f(x) = (x − 0)² + 0
For p(x), complete the square.
p(x) = -50 + 14x − x²
p(x) = -(x² − 14x + 50)
p(x) = -(x² − 14x + 49 + 1)
p(x) = -(x² − 14x + 49) − 1
p(x) = -(x − 7)² − 1
The transformation from f(x) to p(x) includes a reflection about the x-axis, a shift right 7 units, and a shift down 1 unit.
The answer is A.
3x = 729
Solve for x
plz help. it's urgent. Will mark brainly
Answer: x=243
Step-by-step explanation:
need help with this question.
Answer:
distributive propertycommutative propertyassociative propertyStep-by-step explanation:
The distributive property lets you multiply each term inside parentheses by a factor outside parentheses. Here, we've gone from 4(x -1) to 4x -4.
The commutative property lets you change the order of elements of a sum or product. Here, we've gone from 3 + ( ) to ( ) + 3.
The associative property lets you move the parentheses from one group of elements of a sum or product to a different group of elements of the same sum or product. Here, we moved the parentheses from the first two terms to the last two terms of the sum.
_____
Comment on these properties in relation to the Order of Operations
The order of operations for evaluating an expression virtually ignores all of these properties, with the possible exception of the distributive property.
For evaluation of numerical expressions, any sum inside parentheses is evaluated to a single number before the multiplication implied by the parentheses is done. Hence the distributive property is not needed. (The distributive property must be used to remove parentheses when literal or mixed expressions are being evaluated.)
Likewise, the associative and commutative properties are ignored, because operations of addition or multiplication are always carried out left-to-right according to the order of operations. In actual practice, the associative and commutative properties can be used to simplify the evaluation of expressions, provided they are used properly and the meaning of the expression is not altered.
UGH SOMEONE PLS HELP IF YOUR GOOD AT GEOMETRY
Answer: First option.
Step-by-step explanation:
Knowing that the transformation T maps triangle XYZ onto triangle X'Y'Z', you can identifyfrom the figure that the triangle XYZ is the preimage, because it is the original shape and the triangle X'Y'Z' is the image, because is the shape obtained after the transformation.
You can observe in the figure that the image of the vertex X is the vertex X', the image of the vertex Y is the vertex Y' and the image of the vertex Z is the vertex Z'.
Therefore, the conclusion is: The image of Y is Y'.
Avery has a total of $12.50 in her piggy bank at home. Each week she takes out $1.25 to ride the city bus. Write an equation representing the balance, c, in the piggy bank, where w, represents weeks.
Answer:
1.25(w)-12.50=C
The number of fish in a lake can be modeled by the exponential regression equation y = 14.08 • 2.08x, where x represents the year. Which is the best prediction for the number of fish in year 5? Round your answer to the nearest whole number. A. 39 B. 548 C. 1464 D. 146
Answer: B. 548
Step-by-step explanation:
You know that the exponential regression equation [tex]y = 14.08* 2.08^x[/tex] models the number of fish in a lake.
You know that the variable "x" represents the year. Therefore, ir order to predict the number of fish in year 5, you need to substitute [tex]x=5[/tex] into the given exponential regression equation.
Then, you get:
[tex]y = 14.08* 2.08^x\\\\y = 14.08* 2.08^5\\\\y=548.17[/tex]
Rounded to the nearest whole number:
[tex]y=548[/tex]
Answer:
The correct answer option is C. 548.
Step-by-step explanation:
We are given that the number of fish in a lake can be modeled by the following exponential regression equation:
[tex] y = 1 4 . 0 8 \times 2 . 0 8 ^ x [/tex]
where [tex]x[/tex] represents the number of year.
We are to determine whether which of the given answer options best predict the number of fish in year 5.
[tex] y = 1 4 . 0 8 \times 2.08^5[/tex]
[tex]y = 548.17[/tex] ≈ 548