Answer:
A) 3/4
Step-by-step explanation:
Given: Both circle A and circle B have a central angle measuring 50°.
The area of circle A's sector is 36π cm2.
The area of circle B's sector is 64π cm2.
We know, area of the circle= [tex]\pi r^{2}[/tex]
lets assume the radius of circle A be "[tex]r_1[/tex]" and radius of circle B be "[tex]r_2[/tex]"
As given, Area of circle A and B´s sector is 36π and 64π repectively.
Now, writing ratio of area of circle A and B, to find the ratio of radius.
⇒[tex]\frac{\pi r_1^{2} }{\pi r_2^{2} } = \frac{36\pi }{64\pi }[/tex]
Cancelling out the common factor
⇒ [tex]\frac{r_1^{2} }{r_2^{2} } = \frac{36 }{64}[/tex]
⇒ [tex](\frac{r_1 }{r_2} )^{2} = \frac{36 }{64}[/tex]
Taking square on both side.
Remember; √a²= a
⇒ [tex](\frac{r_1 }{r_2} ) =\sqrt{ \frac{36 }{64}}[/tex]
⇒ [tex](\frac{r_1 }{r_2} ) = \frac{6}{8}[/tex]
⇒[tex]\frac{r_1 }{r_2} = \frac{3}{4}[/tex]
Hence, ratio of the radius of circle A to the radius of circle B is 3:4 or 3/4.
If 2 meters of fabric costs $3.45, what should 7 meters cost?
Answer:
10.07$
Step-by-step explanation:
6 meters of fabric = 10.35
divide 3.45 by 2
1.72
add 1.72+10.35
10.07$
Answer:
Set up a proportion 2m/$3.45 = 7m/x
then cross multiply
7(3.45)=2x
then divide both sides by 2
x=12.075 which is roughly $12.08
Step-by-step explanation:
Which of the following expressions is equivalent to (12x^4-4x^3+7x+6)+(3x^2-4x+14)
An expression that is equivalent to [tex](12x^4-4x^3+7x+6)+(3x^2-4x+14)[/tex] include the following: D. [tex]12x^4-4x^3+3x^2+3x+20[/tex]
In Mathematics and Euclidean Geometry, the degree of a polynomial function is the highest power among each of its term.
The leading coefficient represents the coefficient of the leading term while the leading term is the term with the highest degree. Also, a constant polynomial is a polynomial that has only a constant term and no variable.
In this exercise and scenario, your are required to add the polynomial functions together.
First of all, we would rearrange the polynomial functions by collecting like terms and then add them together as follows;
[tex]12x^4-4x^3+3x^2-4x+7x+6+14\\\\12x^4-4x^3+3x^2+3x+20[/tex]
Complete Question:
Which of the following expressions is equivalent to [tex](12x^4-4x^3+7x+6)+(3x^2-4x+14)[/tex]?
A [tex]12x^4-x^3+3x+20[/tex]
B [tex]15x^6-8x^4+21x+6[/tex]
C [tex]15x^6-4x^3+3x+20[/tex]
D [tex]12x^4-4x^3+3x^2+3x+20[/tex]
Final answer:
To find the equivalent expression, add like terms from both expressions, resulting in 12x⁴ - 4x³ + 3x² + 3x + 20.
Explanation:
To find the expression equivalent to (12x⁴-4x³+7x+6)+(3x²-4x+14), we simply add the like terms from both expressions.
Firstly, observe that there are no other terms with the same degree as 12x⁴ and -4x³, so they will remain as they are.
Next, add the coefficients of the x terms and the constants: 7x + (-4x) = 3x and 6 + 14 = 20.
However, there's a 3x² term in the second expression which doesn't have a matching term in the first expression, so it also remains unchanged.
Combining all these, the equivalent expression is 12x⁴ - 4x³ + 3x² + 3x + 20.
Does anyone know this?
Answer:
About 51.43 degrees.
Step-by-step explanation:
In order to find the angle measures, you divide 360 by the number of sides your shape has. In this case you divide 360 by 7.
A business owner pays $1,200 per month in rent and a total of $120 per hour in employee salary for each hour the store is open. On average, the store brings in $200 in net sales per hour.
Which equations can be solved to determine the break-even point if C(x) represents the cost function, R(x) represents the revenue function, and x the number of hours per month the store is open?
C(x) = 1,200+120x R(x) = 200x
C(x) = 1,200+120 R(x) = 200x
C(x) = 200x R(x) = 1,200+120x
C(x) = 200x R(x) = 1,200+120
Option A: [tex]C(x)=1,200+120 x R(x)=200 x[/tex] is the equation.
Explanation:
Let x represents the number of hours per month the store is open.
It is given that the the monthly rent(expense) = $1200
Also, the employee salary for each hour(expense) = $120x
Thus, the total expense C(x) is [tex]1200+120x[/tex]
It is also given that the income per hour(revenue) is $200x
Thus, the revenue function R(x) is [tex]200x[/tex]
The break - even point is given by
Total expense = Revenue
Thus, [tex]C(x)=1,200+120 x R(x)=200 x[/tex] is the equation.
Hence, Option A is the correct answer.
Answer:
A
Step-by-step explanation:
Please help me due today i beg of u plzz I’m desprate no one would help me
a) The expression for perimeter of rectangle is 4x+34.
b) The expression for area of rectangle is 24x+60.
Step-by-step explanation:
Given figure is a rectangle;
Length of rectangle = 12
Width of rectangle = (x+5)+x = 2x+5
a) Perimeter of model
Perimeter of rectangle = 2(Length + Width)
Perimeter of rectangle = [tex]2(12+2x+5)[/tex]
Perimeter of rectangle = [tex]2(2x+17)[/tex]
Perimeter of rectangle = 4x+34
The expression for perimeter of rectangle is 4x+34.
b) Total area of rectangle
Area of rectangle = Length * Width
Area of rectangle = [tex]12*(2x+5)[/tex]
Area of rectangle = 24x+60
The expression for area of rectangle is 24x+60.
Keywords: area, rectangle
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A milk tank is in the form of cylinder whose radius is 1.5 m and length is
7m. Find the quantity of milk in litres that can be stored in the tank.
Answer
49500litres
Step-by-step explanation:
Check attachment
Natalia Knox tosses a fair die six times. What is the probability that she will toss exactly two 5's?
Answer:
[tex]\large\boxed{\large\boxed{1/36}}[/tex]
Explanation:
1. By definition
Probability = # favorable outcomes / # possible outcomes2. Possible outcomes
The possible outcomes is the sample space. The first toss has 6 possible outcomes and the second toss has other 6 possible outcomes; thus, the sample space has 6 × 6 = 36 different outcomes.
3. Favorable outcomes
Tossing exactly two 5's is just one of the 36 possible outcomes. Thus. the number of favorable otucomes is 1.
4. Computation
Probability = 1/36What is two plus two divided by four?
Answer:1
Step-by-step explanation:2+2=4
4/4=1
1. Kelly has a rock garden with a length of 6 feet. She constructs a scale model of the rock garden using the scale 1 inch:2 feet.
(a) What is the length of the garden in her model? Show your work, including your proportion.
(b) If the width is 5 inches for the scale model and the scale is still 1 inch to 2 feet, will her scale model drawing fit on a piece of paper that is 8.5 inches by 7 inches? Why or why not?
Answer:
(a) 3 inches
(b) Her scale model drawing WILL fit on the piece of paper 8.5 by 7 inches
Step-by-step explanation:
Scaling
We use scales to represent realities in reduced spaces. In the case of lengths or surfaces, the scale allows us to draw the shapes in normal sheets of paper.
(a)
Kelly's rock garden has a length of 6 feet. She uses a 1 inch:2 feet scale. this means that the model length is
6 feet*1 inch/2 feet = 3 inches
(b)
The width of the model is 5 inches, keeping the same scale it means the real length is
5 inches * 2 feet / 1 inch = 10 feet
The model will have 3 inches by 5 inches, it perfectly fits on any regular piece of paper
Which expression is equivalent to 8x + 12y?
Answer:
4(2x+3y)
Step-by-step explanation:
20+20+20+20+20+10+5+5
the answer to this equation is 120
Answer:
120
Step-by-step explanation:
the length of a rectangle is 7 meters more than the width. if the perimeter is 166, what are the length and width?
Answer:
Length = 45
Width = 38
Step-by-step explanation:
2a + 2(a + 7) = 166
4a + 14 = 166
4a = 152
a = 38
a = Width
38 = Width
a + 7 = Length
(38 + 7) = Length
45 = Length
Gerald earns $150.00 per week selling magazine subscriptions. For each subscription he sells, he earns 25% on his total sales (S). If he wants to earn at least $450.00 next week, how much does he need to sell?
Answer:
At least 12
Step-by-step explanation:
25 percent of 150 is 37.50. 0.25 X 150
450/37.5 = 8
Answer:12
Step-by-step explanation:
Find 25% of 150 and then divide 450 with the answer of 25%.
Quiz
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Which of the following is most likely missing from your financial plan if you are not prepared for an emergency?
a financing
b. a budget
c. investments
d. savings
Please select the best answer from the choices provided
Answer:
the answer is savings (d).
Step-by-step explanation:
I had a test and this helped a LOT so now I can help you,
hope it helped.
If you are not prepared for an emergency, the most likely missing element from your financial plan is savings.
What do you mean by financial planning?Setting and accomplishing financial objectives through the process of developing a plan to control income, spending, and investments is known as financial planning. Financial planning is to assist people and families in achieving independence, stability, and security in their financial lives.
In conclusion, financial planning is a thorough process that includes establishing financial objectives, assessing your present financial condition, creating a budget and savings plan, controlling debt and risk, and routinely reviewing and modifying your plan. Individuals and families may attain financial security and stability by following these steps as they work towards their long-term financial objectives.
Given data ,
Savings are most likely the component of your financial plan that is lacking if you are not ready for an emergency.
Each financial plan must include savings since they provide as a safety net in the event of crises like unanticipated medical costs, auto repairs, or job loss. Lack of funds may compel you to rely on high-interest loans or credit cards, which might result in long-term financial issues.
While having funds to cover unexpected costs should be a key concern, a financial plan should also include a budget, investments, and financing.
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What is 17 equals 5y - 3
Answer:
4
Step-by-step explanation:
5y-3=17
5y=17+3
5y=20
y=20/5
y=4
jack wants to build a square picture frame for his mother if the area of the franks is 49 square inches what is the perimeter
Answer:7
Step-by-step explanation:
7+7+7+7 is 49
Answer:
perimeter is 36
Step-by-step explanation:
49 square root is 9
since it is a square 4 side lengths x 9 = 36
y intercept of a number that has the points (-30,-9)and a slope of -5/6
Answer:
Y= -5/6 - 9
Step-by-step explanation:
How would you solve ((-x^2)-(12x^3)-8)^2
Answer:
[tex]\left(\left(-x^2\right)-\left(12x^3\right)-8\right)^2:\quad 144x^6+24x^5+x^4+192x^3+16x^2+64[/tex]
Step-by-step explanation:
Considering the expression
[tex]\left(\left(-x^2\right)-\left(12x^3\right)-8\right)^2[/tex]
Solving the expression
[tex]\left(\left(-x^2\right)-\left(12x^3\right)-8\right)^2[/tex]
[tex]\mathrm{Remove\:parentheses}:\quad \left(a\right)=a[/tex]
[tex]\left(-x^2-12x^3-8\right)^2[/tex]
As
[tex]\left(-x^2-12x^3-8\right)^2=\left(-x^2-12x^3-8\right)\left(-x^2-12x^3-8\right)[/tex]
So
[tex]\left(-12x^3-x^2-8\right)\left(-12x^3-x^2-8\right)[/tex]
[tex]\mathrm{Expand}\:\left(-x^2-12x^3-8\right)\left(-x^2-12x^3-8\right):\quad 24x^5+144x^6+192x^3+x^4+16x^2+64[/tex]
i.e.
[tex]\left(-x^2\right)\left(-x^2\right)+\left(-x^2\right)\left(-12x^3\right)+\left(-x^2\right)\left(-8\right)+\left(-12x^3\right)\left(-x^2\right)+\left(-12x^3\right)\left(-12x^3\right)+\left(-12x^3\right)\left(-8\right)+\left(-8\right)\left(-x^2\right)+\left(-8\right)\left(-12x^3\right)+\left(-8\right)\left(-8\right)[/tex]
[tex]\mathrm{Apply\:minus-plus\:rules}[/tex]
[tex]\left(-a\right)\left(-b\right)=ab[/tex]
[tex]x^2x^2+12x^3x^2+8x^2+12x^3x^2+12\cdot \:12x^3x^3+12\cdot \:8x^3+8x^2+8\cdot \:12x^3+8\cdot \:8[/tex]
[tex]\mathrm{Group\:like\:terms}[/tex]
[tex]12x^3x^2+12x^3x^2+12\cdot \:12x^3x^3+12\cdot \:8x^3+8\cdot \:12x^3+x^2x^2+8x^2+8x^2+8\cdot \:8[/tex]
[tex]\mathrm{Add\:similar\:elements:}\:8x^2+8x^2=16x^2[/tex]
[tex]12x^3x^2+12x^3x^2+12\cdot \:12x^3x^3+12\cdot \:8x^3+8\cdot \:12x^3+x^2x^2+16x^2+8\cdot \:8[/tex]
[tex]\mathrm{Add\:similar\:elements:}\:12x^3x^2+12x^3x^2=24x^3x^2[/tex]
[tex]24x^3x^2+12\cdot \:12x^3x^3+12\cdot \:8x^3+8\cdot \:12x^3+x^2x^2+16x^2+8\cdot \:8[/tex]
[tex]\mathrm{Add\:similar\:elements:}\:12\cdot \:8x^3+8\cdot \:12x^3=2\cdot \:8\cdot \:12x^3[/tex]
[tex]24x^3x^2+12\cdot \:12x^3x^3+2\cdot \:8\cdot \:12x^3+x^2x^2+16x^2+8\cdot \:8[/tex]
As
[tex]24x^3x^2=24x^5[/tex]
[tex]12\cdot \:12x^3x^3=144x^6[/tex]
[tex]2\cdot \:8\cdot \:12x^3=192x^3[/tex]
[tex]x^2x^2=x^4[/tex]
[tex]8\cdot \:8=64[/tex]
So
[tex]24x^5+144x^6+192x^3+x^4+16x^2+64[/tex]
[tex]\mathrm{Rewrite\:in\:standard\:form}[/tex]
[tex]144x^6+24x^5+x^4+192x^3+16x^2+64[/tex]
Therefore,
[tex]\left(\left(-x^2\right)-\left(12x^3\right)-8\right)^2:\quad 144x^6+24x^5+x^4+192x^3+16x^2+64[/tex]
Keywords: expression
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Indicate whether each statement is true or false by checking the appropriate box in the table below.
Statement
2x is a factor of the expression (2x+y)
(2x+y) is a factor of the expression 3(2x+y).
(2x+y) is a sum of two terms.
3(2x+y) is a product of two terms
Answer:
False, False, True, False
Step-by-step explanation:
The correct statements are:
(2x+y) is a factor of the expression 3(2x+y).
(2x+y) is a sum of two terms.
a) 2x is a factor of the expression (2x+y): False.
2x is not a factor of (2x+y) because it doesn't divide evenly into it.
b) (2x+y) is a factor of the expression 3(2x+y): True.
(2x+y) is a factor of 3(2x+y) because it divides evenly into it.
c) (2x+y) is a sum of two terms: True.
(2x+y) is a sum of the two terms 2x and y.
d) 3(2x+y) is a product of two terms: False.
3(2x+y) is a product of three terms: 3, 2x, and y.
Hence the b and c are the correct statements.
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Solve for a side in right triangles
Answer:
2.30
Step-by-step explanation:
The side of interest is opposite the given angle, and the hypotenuse is given. The sine relation tells you ...
sin(A) = a/c
a = c·sin(A) = 3·sin(50°)
a = BC ≈ 2.2981 ≈ 2.30
Three runners run along a 1.5 mile trail one Saturday morning. The graph shows the runner’s locations starting at 9:00 a.m.
Who is at the trail start at 9:00 a.m.?
Answer:
Andy
Step-by-step explanation:
Since hes 0 away from it meaning he’s there
Answer: 1) Andy 2) Caedin 3) 9:08am 4) Berta
Step-by-step explanation: first is Andy because it says “the locations starting at 9am “and the starting point is 0 and Andy is the only one there. Second is Caedin because he decreases at first but increases later on. Third because they started at 9am and the x-axis (minutes) says 8 so it could only mean they cross paths at 9:08am, the last one is Berta because she closest
Is 100 a solution of 10-0.035d > 4? Write a question that solving this problem could answer
Answer:
Therefore d = 100 is a solution of the given equation.
A question that solving this problem could answer is "what is the range of d"
d < 171.43
Step-by-step explanation:
i) the given equation is 10 - 0.035d > 4
ii) if d = 100 then 10 - (0.035[tex]\times[/tex] 100) = 10 - 3.5 = 6.5 > 4
Therefore d = 100 is a solution of the given equation.
A question that solving this problem could answer is "what is the range of d"
10 - 0.035d > 4
therefore -0.035d > 4 - 10
therefore -0.035d > -6
therefore 0.0035d < 6
therefore d < 6 / 0.035 [tex]\Rightarrow[/tex] d < 171.43
Final answer:
100 is a solution to the inequality 10 - 0.035d > 4 because, after substituting d with 100, the inequality 6.5 > 4 holds true.
Explanation:
To determine whether 100 is a solution of the inequality 10 - 0.035d > 4, we substitute d with 100 and check if the inequality holds true:
10 - 0.035(100) > 4
10 - 3.5 > 4
6.5 > 4
Since 6.5 is indeed greater than 4, we can confirm that 100 is a solution to the inequality.
A corresponding question this problem could answer might be: "If a part-time employee loses $0.035 from their savings for each day they work, after how many days will their savings be reduced to less than $4 if they initially had $10?" Solving the inequality would help find the maximum number of days the employee can work before their savings fall below $4.
factor 3x^5-7x^4+6x2-14x
Answer:
x ( 3x − 7 ) ( x ^3 + 2 )
Step-by-step explanation:
How many triangles can be made with the angle 70°, 70°, and 70°
The number of boys in the classroom is three more than the number of girls if there are 19 students how many are boys and how many are girls
Answer:
11 boys 8 girls
Step-by-step explanation:
There are 19 total students.
There are 3 more boys than girls
girls + 3 = boys ( because there are three more boys)
boys + girls = 19
You can substitute g +3 for b so:
2 girls +3 = 19
19 - 3 = 16
16/2 = girls
8 = girls
Once you find g just subtract the amount of girls from 19 to get the amount of boys.
19 kids - 8 girls = 11 boys
PLS HELP!!
A graphic designer created a logo on 8 1/2 by 11 inch paper. In order to be placed on a business card, the logo needs to be 1 7/10 by 2 1/5. What is the scale factor of the dilation?
Answer:
0.2 (compression)
Step-by-step explanation:
Given
Length of paper = 11 inches,
Width of paper = 8 1/2 = 17/2 inches
Length of logo = 2 1/5 = 11/5 inches
Width of logo = 1 7/10 = 17/10 inches
Scale factor based on Length
=Length of Logo ÷ Length of paper
= 11/5 ÷ 11
= 0.2 (since it is less than 1, this is a compression)
(Sanity Check: Check width scale factor = length scale factor)
Scale factor based on width
=Width of Logo ÷ Width of paper
= 16/10 ÷ 17/2
= 0.2 (this is the same as the length scale factor so this checks out ok!)
please help!!
I thought it was c but its not
Answer:
Choice D.
82.8
Step-by-step explanation:
We can use law of cosines since we are given three sides.
[tex]z^2=y^2+x^2-2yx \cos(Z)[/tex]
Since [tex]z[/tex] is opposite side of angle [tex]Z[/tex], then [tex]z=12[/tex]:
[tex]12^2=10^2+8^2-2(10)(8) \cos(Z)[/tex]
[tex]144=100+64-160 \cos(Z)[/tex]
[tex]144=164-160 \cos(Z)[/tex]
[tex]-20=-160 \cos(Z)[/tex]
[tex]\frac{-20}{-160}=\cos(Z)[/tex]
[tex]\frac{20}{160}=\cos(Z)[/tex]
[tex]\frac{1}{8}=\cos(Z)[/tex]
[tex]\cos^{-1}(\frac{1}{8})=Z[/tex]
[tex]82.819^\circ=Z[/tex]
Option D is correct.
Pleaaassseee help me help my son!!! How do I get the sequence for the next 3 numbers 2,4,8,14,...?
The next three numbers in sequence are 22, 32 and 44
Solution:
Given sequence is:
2, 4, 8, 14, ...
We have to find the next 3 numbers in sequence
Let us understand the logic used in this sequence
[tex]First\ term = 1^2 -1+2 = 1 + 1 = 2\\\\Second\ term = 2^2 -2 + 2 = 4\\\\Third\ term = 3^2 - 3 + 2 = 9 - 1 = 8\\\\Fourth\ term = 4^2 -4 + 2 = 16-2 = 14[/tex]
Thus the formula used is:
[tex]a_n = n^2 - n +2[/tex]
Where, "n" is the location of term in sequence
To find the next three terms:
[tex]Fifth\ term = 5^2 - 5 + 2 = 25 - 3 = 22\\\\Sixth\ term = 6^2 - 6 + 2 = 36 - 4 = 32\\\\Seventh\ term = 7^2 -7 + 2 = 49 - 5 = 44[/tex]
Thus the next three numbers in sequence are 22, 32 and 44
Graph g(x)=4cos(2x)−2 . Use 3.14 for π .
Answer:
The graph is shown attached.
Step-by-step explanation:
i) The graph is shown attached
ii) The values shown are for the points with black dots.
write 3 different subtraction equations that equal 14.
Answer:
17-3=14
37-23=14
20-6=14
Answer:
15-1=14
48-34=14
137-123=14
Step-by-step explanation:
To check work
14+1=15
14+34=48
14+123=137