Answers
Answer:
2(5) + 2√(3^2 + 7^2) = 10 + 2√58 = 25.2
B is the correct answer.
Related Questions
If a > O and y > 0, which expression is equivalent to v 768219 g372
• A.
162°y18 32g
• B.
-O c. 1604 ° V324,
O D.
8ay18 /12ry
Answers
The expression 16x⁹y¹⁸√3xy is equivalent to √769x¹⁹y³⁷
If a > O and y > 0, which expression is equivalent to √769x¹⁹y³⁷
Factor and rewrite the radicand in exponential form:
√16²×3x¹⁸×xy³⁶×y
Simplify the radical expression:
16x⁹y¹⁸ √2²×3xy
Factor and rewrite the radicand in exponential form:
8x⁹y¹⁸√2²×3xy
8x⁹y¹⁸.2√3xy
Multiply the monomials:
16x⁹y¹⁸√3xy
Hence, the expression 16x⁹y¹⁸√3xy is equivalent to √769x¹⁹y³⁷
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Rewrite the following in the form log(c). log(5) + log(2)
Answers
Answer:
log(10)
Step-by-step explanation:
We can use the product property for logarithms:
log(a)+log(b)=log(ab)
In our case, a=5 and b=2. We can multiply a and b now to get the new number we're taking the logarithm of.
log(2)+log(5)=log(2×5)=log(10)
The answer…………………..:
Answers
Answer:
what?
Step-by-step explanation:
Step by step
If r = 6 and the measure of the central angle 2pi/3, what is the length of the intercepted arc
Answers
The length of the intercepted arc is 4π unit.
We have,
Angle = 2π/3 = 2(180)/ 3 = 120 degree
r = 6 unit
So, length of Arc
= θ /360 x 2πr
= 120/360 2 π(6)
= 1/3 (12)π
= 4π unit
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Brenda's class took a field trip to the science museum. It took them 50 minutes to drive to the museum. They stayed at the museum for 3 hours and 45 minutes, and it took them 56 minutes to drive back to school. When the class arrived back at school, it was 3:47 P.M. What time did Brenda's class leave for the field trip?
Answers
Brenda's class left for the field trip at 10:16 A.M.
We have,
Let's break down the time of Brenda's class field trip:
50 minutes to drive to the museum
3 hours and 45 minutes (or 225 minutes) at the museum
56 minutes to drive back to school
Adding up all of these times, we get:
50 + 225 + 56 = 331 minutes
So the field trip took a total of 331 minutes.
If the class arrived back at school at 3:47 P.M., and we subtract 331 minutes from 3:47 P.M., we can determine the time they left for the field trip:
3:47 P.M. - 331 minutes
= 10:16 A.M.
Therefore,
Brenda's class left for the field trip at 10:16 A.M.
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Which pair of points are both located less than 3 units from the point (3,8) on a coordinate grid?
Answers
The required pair of points that are both located less than 3 units from points (3, 8) is (2, 7).
Following the condition given in the question,
Assuming there are 3 points on the graph beside (3, 8) are (2, 7), (5, 5), and (6, 10)
The distance formula between two points is given by:
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
So, for each point, we can plug in the coordinates and simplify the following:
Point (2, 7):
d = √[(2 - 3)² + (7 - 8)²]
d = √[1² + 1²]
d = √2 (<3)
Points (6, 10):
d = √[(6 - 3)² + (10 - 8)²]
d = √[3² + 2²]
d = √13 (>3)
Point (5, 5):
d = √[(5 - 3)² + (5 - 8)²]
d = √[2² + 3²]
d = √13 (>3)
Point (1, 1):
d = √[(1 - 3)² + (1 - 8)²]
d = √[(-2)² + (-7)²]
d = √53 (>3)
Thus, the pair of points that are both located less than 3 units from points (3, 8) is (2, 7).
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If the diameter of a circle is 8.4 in.. find the area and the circumference of the circle. Use 3.14 for pl. Round your answers to the nearest
hundredth.
Answers
Given that the diameter of a circle is 8.4 inches.
The radius (r) of the circle can be found by dividing the diameter by 2:
r = d/2 = 8.4/2 = 4.2 inches
The area (A) of a circle can be found using the formula:
A = πr^2
Substituting the value of r, we get:
A = 3.14 x 4.2^2 = 55.3896 ≈ 55.39 square inches
The circumference (C) of a circle can be found using the formula:
C = 2πr
Substituting the value of r, we get:
C = 2 x 3.14 x 4.2 = 26.3896 ≈ 26.39 inches
Therefore, the area of the circle is approximately 55.39 square inches and the circumference of the circle is approximately 26.39 inches.
We know that the area of a circle is given by the formula A = π×r²
Given the diameter of the circle = 8.4 in
Therefore radius of the circle = 8.4/2 = 4.2 in (diameter/2 = radius)
Now Area of the circle = π × 4.2²
= 3.14 × 17.64
= 55.3896
= 55.39 (round up to the nearest hundredth)
Circumference of the circle = 2 × π × r
= 2 × 3.14 × 4
= 26.376
= 26.38 (round up to the nearest hundredth)
Therefore the area of the circle is 55.39 in² and the circumference is 26.38 in.
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find sin 75 without using a calculator
Answers
The value of sin 75 without using a calculator is 1/4(√2 +√6)
Finding sin 75 without using a calculatorFrom the question, we have the following parameters that can be used in our computation:
sin(75)
This can be expanded as
sin(75) = sin(45 + 30)
Using the sine rule, we have
sin(75) = sin(45)sin(30) + cos(45)cos(30)
Evaluate the trigonometry ratios
So, we have
sin(75) = √2/2 * 1/2 + √2/2 * √3/2
So, we have
sin(75) = √2/4 + √6/4
Evaluate the sum
sin(75) = 1/4(√2 +√6)
Hence, the value is sin(75) = 1/4(√2 +√6)
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Construct a sinusoidal function that rises from a minimum point at (3,-2) to a maximum point at (7, 8)
Answers
The sinusoidal function that rises from a minimum point at (3,-2) to a maximum point at (7, 8) is y = 5 sin(π/2(x - 3)) + 3
We are given that;
Minimum point= (3,-2)
Maximum point= (7, 8)
Now,
To construct a sinusoidal function that rises from a minimum point at (3,-2) to a maximum point at (7, 8), we can use the following steps:
Find the amplitude A. The amplitude is the distance from the midline of the function to the maximum or minimum point. The midline is the average of the maximum and minimum values, which is (8 + (-2))/2 = 3. The distance from 3 to 8 or -2 is 5, so A = 5.
Find the period P. The period is the length of one cycle of the function, or the horizontal distance between two consecutive maximum or minimum points. In this case, the period is 7 - 3 = 4. The constant B is related to the period by the formula B = 2π/P, so B = 2π/4 = π/2.
Find the horizontal shift C. The horizontal shift is the amount that the function is shifted left or right from its standard position. In this case, we want the function to have a minimum point at x = 3, so we need to shift it right by 3 units. This means that C = 3.
Find the vertical shift D. The vertical shift is the amount that the function is shifted up or down from its standard position. In this case, we want the function to have a midline at y = 3, so we need to shift it up by 3 units. This means that D = 3.
Putting it all together, we get:
y = 5 sin(π/2(x - 3)) + 3
Therefore, by the function the answer will be y = 5 sin(π/2(x - 3)) + 3.
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Find the 13th term of the geometric sequence 4, −8, 16, ...
Answers
Answer:
Step-by-step explanation:
50 points. Out of 120 seventh and eighth grade CAVA students there were 30 students that chose Music as their elechive course and the rest chose World Language. There were a total of 60 eighth grade students and 40 of them chose
World Language as their elective.
Use this information to complete the two-way table.
Enter your answer by filling in the boxes to complete the table (6 pts)
Answer:
Answers
Based on the informtaion provided, the two-way table would be,
Music World Language Totals
8th Grade 20 40 60
7th Grade 10 50 60
Total 30 90 120
In this situation there were total 120 seventh and eighth grade CAVA students. And there were a total of 60 eighth grade students.
Total number of students = 120
This means that the number of students in 7th grade : 120- 60 = 60
Out of 120 seventh and eighth grade students, 30 students chose Music as their elechive course.
This means that remaining 120 - 30 = 90 students chose World Language as their elechive course.
Here, 40 eighth grade students chose World Language as their elective.
This means that out of total 90 students 90 - 40 = 50 students of 7th Grade chose World Language as their elective.
Now consider the 8th grade students,
Out of 60 students 40 chose World Language.
So, 60 - 40 = 20 must chose Music as their elective.
Now consider the 7th grade students,
Out of 60 students 50 chose World Language.
So, 60 - 50 = 10 students must chose Music as their elective.
Hence the required two-way table would be,
Music World Language Totals
8th Grade 20 40 60
7th Grade 10 50 60
Total 30 90 120
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Graph the line with slope
3/4
passing through the point (-4,-1)
.
Answers
Answer:
check attachment
Step-by-step explanation:
First write in point-slope form:
y-y1=m(x-x1)
Now substitute:
y-(-1)=3/4(x-(-4))
And then just solve. You should get a y-intercept of 2.
The constraints of a problem are listed below. What are the vertices of the feasible region?
[tex]x+y\leq 7\\x-2y\leq -2\\x\geq 0\\y\geq 0[/tex]
Answers
The vertices of the feasible region is (4, 3)
What are the vertices of the feasible region?From the question, we have the following parameters that can be used in our computation:
x + y ≤ 7
x - 2y ≤ -2
x ≥ 0
y ≥ 0
Express as equations
So, we have
x + y = 7
x - 2y = -2
Subtract the equations
3y = 9
So, we have
y = 3
Next, we have
x + 3 = 7
This gives
x = 4
Hence, the vertex of the feasible region is (4, 3)
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Two sets of data have the same measures of central tendency. Are the data sets the same? Explain.
Answers
Sample Response/ Explanation: The data sets could be the same, but not necessarily. It is possible for data sets to differ in their spread but still have the same measures of center. The measures of spread could be different.
The data sets could be the same, but not really. It is possible for the data sets to differ in their spread but still have the same measures of center. The measures of spread could be different though.
Willa sells cars. Last month, she had 124,000 dollars in sales. Her commission rate is 1.3 percent. How much did Willa earn for the month?
Answers
Her commission rate is 1.3%, which can be written as a decimal as 0.013.
Multiplying her sales by her commission rate, we get:
0.013 * 124,000 = 1,612
Therefore, Willa earned $1,612 for the month.
Find the amount in the account for the given principal, interest rate, time, and compounding period. P = $700, r=7%, t=8 years; compounded quarterly
Answers
I=PRT
I=$700*7%*8 years
I=$392
Now we have found the interest let us find the amount of the number
A=interest+principle
A=$392+$700
A=$1092
Answer:
$1092
Step-by-step explanation:
What is the value of c in the equation?
15.3 = StartFraction c Over 2.1 EndFraction
13.2
17.4
32.13
321.3
Answers
Answer:
32.13
Step-by-step explanation:
The value of c in the equation 15.3 = c/2.1 is 32.13. To solve for c, you can cross-multiply and simplify the equation to c = 15.3 x 2.1 = 32.13.
The solution to the equation "the quotient of a number and 8 is 16" is 128. To solve for the number, you can multiply both sides by 8 to get "the number is 16 x 8 = 128."
To translate the sentence "the quotient of a number and 8 is 16" into an equation, you can use "x" to represent the number and write x/8 = 16.
Answer:
c or a
Step-by-step explanation:
i thing a
Need help fast I will rate
Answers
The formula for p(x) is p(x) = -0.1(x - 5)²(x + 3).
What is a polynomial graph?In Mathematics and Geometry, the graph of a polynomial function touches the x-axis at zeros, roots, solutions, x-intercepts, and factors with even multiplicities.
Also, the graph has a zero of multiplicity 2 at x = 5 and zero of multiplicity 1 at x = -3;
x = 5 ⇒ x - 5 = 0.
(x - 5)²
x = -3 ⇒ x + 3 = 0.
(x + 3)
In this context, an equation that represent the polynomial function is given by:
p(x) = a(x - 5)²(x + 3)
By evaluating and solving for the leading coefficient "a" in this polynomial function based on the y-intercept (0, -7.5), we have;
-7.5 = a(0 - 5)²(0 + 3)
-7.5 = a75
a = -7.5/75
a = -0.1.
Therefore, the required polynomial function is given by:
p(x) = -0.1(x - 5)²(x + 3)
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The number of bacteria in a certain population increases according to a continuous exponential growth model, with a growth rate parameter of 8.5% per hour. How many hours does it take for the size of the sample to double?
Answers
N(t) = N₀e^(rt)
where:
N(t) is the size of the population at time t
N₀ is the initial size of the population
r is the growth rate
t is time
To find the time it takes for the population to double, we need to solve for t in the equation:
2N₀ = N₀e^(rt)
Dividing both sides by N₀, we get:
2 = e^(rt)
Taking the natural logarithm of both sides, we get:
ln(2) = rt
Solving for t, we get:
t = ln(2)/r
The growth rate is given as 8.5% per hour, which is equivalent to 0.085 per hour. Substituting this into the formula, we get:
t = ln(2)/0.085
t ≈ 8.14
Therefore, it takes approximately 8.14 hours for the size of the population to double.
Find the indicated vector
Answers
Answer:
(d) 5i -j
Step-by-step explanation:
You want the value of the expression 2u -v where u=3i and v=i+j.
SubstitutionUse the given definitions of u and v, and simplify in the usual way.
2u -v = 2(3i) -(i+j)
= 6i -i -j . . . . . . . . . eliminate parentheses
= 5i -j
__
Additional comment
The unit vectors i and j can be treated as though they were variables. The usual properties of equality and (scalar) arithmetic apply.
Find the volume of rectangular prism. (You should have at least 2 steps shows in your work!)(show all decimal places or a fraction)
Answers
The volume of this rectangular prism include the following: 84.375 cubic meters.
How to calculate the volume of a rectangular prism?In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:
Volume of a rectangular prism = L × W × H
Where:
L represents the length of a rectangular prism.W represents the width of a rectangular prism.H represents the height of a rectangular prism.By substituting the given dimensions (parameters) into the formula for the volume of a rectangular prism, we have the following;
Volume of rectangular prism = 5 × 4 1/2 × 3 3/4
Volume of rectangular prism = 5 × 4.5 × 3.75
Volume of rectangular prism = 84.375 cubic meters.
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The large solid below is made from small cubes. Each has a side length of 1/5. Answer the questions below. Write your answers in simplest form. (c) What is the volume of the large solid?
Answers
The volume of the large solid is equal to 8/25 cm³.
How to calculate the volume of a cube?In Mathematics, the volume of a cube can be calculated by using the following formula:
V = m³
Where:
V represents the volume of a cube.m is the side lengths of a cube.By substituting the given points into the formula for the volume of a cube, we have the following;
Volume of cube, V = m³
Volume of cube, V = (1/5)³
Volume of cube, V = 1/125 cm³.
For the volume of the large solid, we have:
Volume of large solid = 5 × 2 × 4 × 1/125
Volume of large solid = 8/25 cm³.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Malick is forming clay blocks in the shape of rectangular prisms.
Two faces of the blocks are squares.
First, find the missing length of the clay block. Then, find the volume.
Answers
The missing length is 4 in.
The volume of a rectangular prism is 32 in³.
We have,
Since the two faces of the blocks are squares.
The face that has the missing length can be considered as a square face.
i.e
The front and back faces are squares.
So,
The missing length is 4 in.
Now,
The volume of a rectangular prism.
= length x width x height
= 4 x 2 x 4
= 32 in³
Thus,
The missing length is 4 in.
The volume of a rectangular prism is 32 in³.
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i need help with calculus
Answers
Find area of polygon where n=14 and radius= 1
Answers
Answer:16.484
Step-by-step explanation:
find the area of a regular polygon with n sides and radius r, we can use the formula:
Area = (n * r^2 * sin(2*pi/n)) / 2
where pi is the mathematical constant pi (approximately equal to 3.14159).
Plugging in n = 14 and r = 1, we get:
Area = (14 * 1^2 * sin(2*pi/14)) / 2
= (14 * sin(pi/7)) / 2
≈ 16.484
Therefore, the area of the polygon with 14 sides and a radius of 1 unit is approximately 16.484 square units.
Find the remainder when f(x) is divided by x-k, ( SYNTHETIC DIVISION)
[tex]f(x)=2x^3 +5x^2 -12x ; k=-1[/tex]
Explain well, please.
Answers
Answer:
15
Step-by-step explanation:
You want the remainder from division of f(x) = 2x³ +5x² -12x by x -(-1).
Synthetic divisionThe table used for synthetic division is built by listing the zero of the divisor at upper left, and the coefficients of the polynomial across the top to the right of that. They are listed in order of decreasing degree, with any necessary zero coefficients put in the appropriate place(s).
The attachment shows the table and the instructions for filling it out. The value at the bottom in the rightmost column is the remainder from the division.
The remainder theorem tells you that is also the value of the function for x = k.
The remainder from f(x) ÷ (x +1) is 15.
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Helppppp
I really neeed this answer
Answers
s√3 is the distance from point A to point B. Therefore, the correct option is option D among all the given options.
While distance and displacement appear to have the same meaning, they actually have very different definitions and meanings. Displacement is the measurement of "how far an object is out of place," whereas distance refers to "the amount of ground the object has travelled over during its motion."
Distance² = s² + s² + s²
Distance² = 3 s²
Distance = s√3
Therefore, the correct option is option D among all the given options.
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Need help??? With this question
I don’t think I’m solving it correctly.
Answers
Answer:
116
Step-by-step explanation:
san
3
Mia is the new CEO of a sales company. In her first year, the company made $475,000 in sales. In each of
the following years, her sales are expected to increase at a rate of 1796. If this trend continues, what will be
her company's sales in year 14?
A $6,201,709
B $5,129,458
C $3,656,872
D
$2,935,294
Answers
The company sales in year 14, given the rate of increase and the amount made in sales would be C $3,656,872.
How to find the sales ?In the first year, the sales of the company were $ 475, 000 and this sales is scheduled or predicted to grow at 17 %.
This means that the company sales in year 14 would be :
= Initial sales x ( 1 + rate ) ^ number of years
Initial sales = $ 475, 000
Rate = 17 %
Number of years = 14 years
The company sales in year 14 is:
= 475, 000 x ( 1 + 17 %) ¹⁴
= $3, 656, 872
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Simplify. (5 x sqrt 2 - 1)^2
