The area of triangle A is 98 sq cm. Option B is correct.
Since triangle A is a scaled version of triangle B, the ratio of their areas is equal to the square of the ratio of their corresponding side lengths.
If the dimensions of triangle A are twice the dimensions of triangle B, then the ratio of their side lengths is 2:1.
The ratio of their areas, therefore, is (2:1)² = 4:1.
Given that the area of triangle B is 24.5 sq cm, we can find the area of triangle A by multiplying 24.5 by the ratio of their areas:
Area of triangle A = 24.5 × 4 = 98 sq cm
Therefore, the area of triangle A is 98 sq cm.
Learn more about the Scale images here:
brainly.com/question/13194929
#SPJ1
$11,335
is invested, part at 9%
and the rest at 6%
. If the interest earned from the amount invested at 9%
exceeds the interest earned from the amount invested at 6%
by $865.35
, how much is invested at each rate? (Round to two decimal places if necessary.)
Answer:
9% : $10,3036% : $1032Step-by-step explanation:
You want the amounts invested at 9% and 6% if they total $11,335 and the interest from the 9% investment exceeds the interest from the 6% investment by $865.35.
SetupIf we let x represent the amount invested at 9%, the amount invested at 6% is (11335-x). The relation between the values of interest earned is ...
(x)·9% -(11335-x)·6% = 865.35
Solution0.15x -680.10 = 865.35 . . . . . simplify
0.15x = 1545.45 . . . . . . . . add 680.10
x = 10303 . . . . . . . . . . . divide by 0.15
11335 -x = 1032
$10,303 was invested at 9%; $1,032 at 6%.
__
Additional comment
It is convenient to use a single variable, and to let it represent the amount invested at the higher rate. If you use a system of 2 equations, you can effectively do this by substituting for the variable representing the amount invested at the lower rate. Using this approach keeps all of the numbers positive, tending to reduce errors.
Answer:
Amount invested at 9% = $6832.15; Amount invested at 6% = $4502.85
Step-by-step explanation:
We'll need a system of equations to find the amounts invested at both 9% and 6% and we'll need to convert the percentages to decimals (i.e., 0.09 and 0.06):
Let x represent interest earned from the 9% investmentLet y represent interest earned from the 6% investmentLet 0.09x represent the amount invested at 9%Let 0.06y represent the amount invested at 6%First equation in system:
We know that the interest earned from the 9% investment is $865.35 greater than the interest earned from the 6% investment.
Thus, one equation we can use is x = y + 865.35
Second equation in system:
We also know that the amount invested at 9% plus the amount invested at 6% equals $11335.00
Thus, our second equation is 0.09x + 0.06y = 11335
Step 1: We can use substitution to solve. We must plug in x from the first equation for x in the second equation to solve for y:
0.09(y + 865.35) + 0.06y = 11335
0.09y + 77.8815 + 0.06y = 11335
0.15y + 77.88 = 11335
0.15y = 11257.12
y = 75047.46667
y = 75047.47
Step 2: Now we can plug in 75047.47 for y into any of the two equations in our system to solve for y. Because the first equation is simpler, let's use this one:
x = 75047.47 + 865.35
x = 75912.82
Step 3: We can now find the amount invested by multiplying x by 0.09 and y by 0.06:
0.09x = 0.09(75912.82) = 6832.1538 = $6832.15
0.06y = 0.06(75047.47) = 4502.8482 = $4502.85
Optional Step 4: We can check that our numbers are correct by substituting 75912.82 for x and 75047.47 for y in the two equations in our system:
Checking solutions for first equation:
75912.82 = 75047.47 + 865.35
75912.82 = 75912.82
Checking solutions for second equation:
0.09(75912.82) + 0.06(75047.47) = 11335
6832.1538 + 4502.8482 = 11335
6832.15 + 4502.85 = 11335
11335 = 11335
The curved road at the right is part OC which has a radius of 88 feet. What is AB? Round to the tenth
The length of the AB in the curved road path comes out to be 98.2 feet
Given:
Radius = 88 feet
DE = 15 feet
CD is the radius of the circle
CD = CE + DE
88 = CE + 15
CE = 73 feet
Since the CD is the perpendicular bisector the AE and BE are equal in length
In triangle CBE,
It is right-angled at E,
By Pythagoras' theorem:
hyp² = height² + base²
88² = 73² + BE²
7744 = 5329 + BE²
BE² = 2415
BE = 49.1 feet
AB = BE + AE
AB = BE + BE
AB = 2BE
AB = 2 * 49.1
= 98.2 feet
Learn more about Pythagoras' theorem here:
https://brainly.com/question/23715284
#SPJ1
The complete question is:
The curved road at the right is part of circle C which has a radius of 88 feet. What is AB as shown in the figure? Round to the tenth
Write an expression to match
the statement "the product of
6 and 8 subtracted from 64"
Answer:
64 - (6 x 8)
Step-by-step explanation:
"The product of 6 and 8" means 6 and 8 multiplied together, therefore this part can be expressed as 6x8. "Subtracted from 64" means that the product of 6x8 is being taken away from 64, therefore it is 64-(6x8).
Thorium 234 is a radioactive isotope that decays according to the eqaution At=A0e^-10.498t, where A0 is the initial amount present and At is the amount present after t years. is the amount present after t years. If you begin with 1000 grams of strontium 90,
(a) How much thorium 234 will be left after 0.5 years? Round your answer to the nearest tenth of a gram.
------------------- grams
(b) When will 115 grams of thorium 234 be left? Round your answer to the nearest tenth of a year.
-------------------- years
Answer: yes 2,0193-029712123,
Step-by-step explanation:
NEED HELP W QUESTIONS 4-6
The volume of the figures are;
4. 27. 18 in³
5. 3. 024 m³
6. 23 6/18 yd³
How to determine the volumeThe formula for calculating the volume of a triangular prism is expressed with the equation;
V = Bl
Given that the parameters are;
V is the volume of the triangular prisml is the length of the triangular prismB is the base area of the triangular prism4. We have that;
Base area = 1/2 × 2.6 × 4.1
Multiply the values
Base area = 5. 33in²
Then,
Volume = 5.33 × 5.1
Volume = 27. 18 in³
5. Base area = 1/2 × 2. 4 × 1.4
Multiply the values
Base area = 1. 68 m²
Volume = 1.8 ×1.68
Multiply the values
Volume= 3. 024 m³
6. Base area = 1/2 × 10/3 × 14/3
Multiply the values
Base area = 7 14/18yd²
Volume = 140/18 × 3
Multiply the values
Volume = 23 6/18 yd³
Learn about volume at: https://brainly.com/question/1972490
#SPJ1
How far up the building does the top of the ladder reach?
help me ASAP pleaseee
1. The location of point A and B in complex (a + bi) form is 4 + 3i, B is -6 + 4i.
2. The modulus of point A is 5.
3. The length of AB is 10.
4. B in polar form is 2√13 × (cos(146°) + i sin(146°))
5. The product of two complex numbers in rectangular form is -36 - 2i
6. z1/z2 in polar form is z1/z2 = 4 cis (7π/6 - π/4)
How do we solve for the complex (a + bi) form?1. The location of each point A and B are as follows Arrow A is at (4, 3) and arrow B (-6, 4). therefore the location in complex (a + bi) form is 4 + 3i, B is -6 + 4i.
2. The modulus of a complex number (a + bi) is represented as √(a² + b²) ⇒ √(4² + 3²) = √(16 + 9) = √25 = 5.
3. We can calculate the length of vector AB with √(x₂-x₁)² + (y₂-y₁)²)
AB = √((-6 - 4)² + (4 - 3)²)
AB = √((-10)² + 1)
AB = √(100 + 1)
AB = √101 ⇒ 10
4. The modulus of B, r = √((-6)² + 4²) = √(36 + 16) = √52 = 2√13
θ = 180° - arctan(|4/-6|) = 180° - arctan(2/3)
θ = 180° - 33.69° = 146.31°
5. The product of the complex number can be see as follows
(4 + 3i) × (-6 + 4i) = (4×-6 - 34) + (4×4 + 3×-6)i
= (-24 - 12) + (16 - 18)i
= -36 - 2i.
6. (7π/6 - π/4) = (14π/12 - 3π/12) = 11π/12.
11π/12 × (180/π) = 165°.
In Polar form z1/z2 = 4 cis (7π/6 - π/4)
= 4 cis 165°.
Find more exercises on complex (a + bi) form;
https://brainly.com/question/13659794
#SPJ1
The population of a city began with 1500 people. After 5 years, the population grew to 3000 people.
Answer:
300 per year??
Step-by-step explanation:
I'm not sure what you're trying to find...I'm guessing it's how many people it grew by per year
3000-1500 is 1500
1500/5 is 300
hope this helped
desperately need help!!!
The classification , symmetry , maximum r-values and the zeroes of the function are solved
Given data ,
a)
Let the function be represented as A
Now , the value of A is
r² = 25 sin( 2θ )
The equation represents a cardioid
It is symmetric about the polar axis.
The maximum values of r occur at θ = (π/4) + kπ/2, and the maximum value of r is 5.
The equation has zeroes at θ = kπ/2, and the corresponding values of r are given by r = 0
b)
The equation represents a limaçon.
It is symmetric about the polar axis.
The maximum value of r is 7.
The equation has zeroes at θ = arccos(1/3) + 2kπ or θ = -arccos(1/3) + 2kπ, and the corresponding values of r can be found by substituting into the equation r = 4 - 3cos(θ).
c)
The equation represents an Archimedean spiral.
It does not possess any symmetry.
There is no maximum r value.
The equation has a zero at θ = 1/2.
Hence , the zeroes of the function are solved
To learn more about symmetry of functions click :
https://brainly.com/question/29292066
#SPJ1
30.6
735
——
3.14
find the square root, then multiply it by 2
Step-by-step explanation:
First, let's find the square root of 30.6:
√30.6 ≈ 5.53 (rounded to two decimal places)
Now, let's multiply the square root by 2:
5.53 × 2 = 11.06
you roll a aix sided die one time. what is the probability of not rolling a 1? write your answer as a percent rounded to the nearest whole number
The probability of not rolling a 1 when rolling a six-sided die is approximately 83%. This means that if you roll the die many times, you would expect to get a 1 about 1/6 of the time and not get a 1 about 5/6 of the time.
When you roll a six-sided die, there are six possible outcomes, each with equal probability. These outcomes are rolling a 1, 2, 3, 4, 5, or 6. If you want to find the probability of not rolling a 1, you can count the number of outcomes that are not 1 and divide by the total number of outcomes.
Since there are five outcomes that are not 1 (2, 3, 4, 5, and 6) and six total outcomes, the probability of not rolling a 1 is 5/6.
To write this as a percentage rounded to the nearest whole number, we can multiply by 100 and round to the nearest whole number:
5/6 × 100 ≈ 83%.
For such more questions on Probability:
https://brainly.com/question/3084656
#SPJ11
Select the graph for the solution of the open sentence. Click until the correct graph appears. 2|x| + 1 < 5
Answer:
Step-by-step explanation:
Please help thank you
A point that best represent the location for them to put the science project is: A. (6.5, 6).
How to determine the midpoint of a line segment?In order to determine the midpoint of a line segment with two (2) end points, we would add each point together and then divide by two (2):
Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]
By substituting the given end points into the formula for the midpoint of a line segment, we have the following;
Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]
Midpoint = [(5 + 8)/2, (8 + 4)/2]
Midpoint = [(13)/2, 12/2]
Midpoint = (6.5, 6).
Read more on midpoint here: brainly.com/question/29298470
#SPJ1
Option A above
Option B above
Option C above
Help please foe math assignment
The area of the figure will be 17 square centimeters.
The area of a two-dimensional figure is the area that its perimeter encloses. The quantity of unit squares that occupy a closed figure's surface is its region.
The area of the figure is the summation of the area of the two rectangles. Then the area of the figure is calculated as,
A = 3 x 5 + 1 x 2
A = 15 + 2
A = 17 square cm
More about the area link is given below.
https://brainly.com/question/27683633
#SPJ1
Rewrite using rational exponents 2⁴√x⁷
Answer:
16x^(7/2)
Step-by-step explanation:
When rewriting radicals as fractions, the numerator is the power the term is to and the denominator is how many times the term is “rooted”:
2^4 sqrt(x^7) —> 16x^(7/2)
Find the solution of the exponential equation
5^-x/16=5
in terms of logarithms, or correct to four decimal places.
x= ------------
here is the picture if you need to see it more clear.
The solution of the exponential equation [tex]5^{({\frac{-x}{16})}}= 5[/tex] in terms of logarithms, or correct to four decimal places, is x ≈ -4.4431.
An exponential function is a mathematical function in the form of [tex]f(x) = a^x[/tex], where "a" is a constant and "x" is a variable. The value of the function at a particular value of "x" is found by raising "a" to the power of "x". Exponential functions are characterized by their rapid growth or decay.
We can solve for x by taking the logarithm of both sides with base 5:
[tex]5^{(\frac{-x}{16})} = 5[/tex]
[tex]log_5(5^{(\frac{-x}{16}))} = log_5(5)[/tex]
(-x/16)log₅(5) = 1
-x/16 = 1/log₅(5)
x = -16/log₅(5)
Using a calculator, we get:
x ≈ -4.4431
Therefore, the solution of the exponential equation [tex]5^{({\frac{-x}{16})}}= 5[/tex] in terms of logarithms, or correct to four decimal places, is x ≈ -4.4431.
To know more about exponential function follow
https://brainly.com/question/14355665
#SPJ1
Custom Office makes a line of executive desks. It is estimated that the total cost for making x units of their Senior Executive model is represented by the following function, where C(x) is measured in dollars/year. Find the following functions (in dollars) and interpret your results.
Find the average cost and marginal cost.
The marginal cost (MC) function tells us the additional cost of producing one more unit of the Senior Executive model.
To find the average cost, we need to know the fixed costs, which are not given in the problem. Therefore, we cannot calculate the average cost.
To find the marginal cost, we need to take the derivative of the total cost function with respect to x:
MC(x) = dC(x) / dx
MC(x) = [tex]0.3x^2[/tex] - 16x + 500
Interpreting the results, the marginal cost (MC) function tells us the additional cost of producing one more unit of the Senior Executive model. It is an increasing function, which means that the cost of producing an additional unit increases as the production level increases. When MC is greater than the price of the product, it is not profitable to produce additional units, and the optimal production level is reached when MC equals the price.
for such more question on marginal cost
https://brainly.com/question/8993267
#SPJ11
Question
Custom Office makes a line of executive desks. It is estimated that the total cost for making x units of their Senior Executive model is represented by the following function:
C(x) = 0.1x^3 - 8x^2 + 500x + 4000
where C(x) is measured in dollars/year.
Please help! will mark Brainliest! Thanks!
Answer: 48 cm square
Step-by-step explanation:
We can first divide this shape into two rectangles, cutting it off at the 6cm line. The rectangle below has an area of 20cm square, noted by the 10 cm base and 2 cm base thickness. For the other rectangle, we can see that the height is 9cm, but since we already have done the bottom rectangle, we can subtract 2cm away from the 9cm ad get 7 cm. So the height for the top rectangle is 7cm. Then doing the same thing for the width with 10cm and 6cm gives us 4 cm. This then gives us a total of 28cm for the top and 20cm for the bottom. This combines to get us 48 cm. THE FIGURE IS NOT TO SCALE.
Factor the trinomial: 5x^2 + 26x +24
Answer: (5x+6)(x+4)
Step-by-step explanation:
5x^2 + 26x + 24
5x^2 + 20x + 6x + 24
(5x^2 + 20x) + (6x + 24)
5x(x + 4) + 6(x + 4)
5x(x + 4) + 6(x + 4)
(5x + 6)(x + 4)
gcd of 120 70 and 30 using prime factorisation
The greatest common divisor of 120, 70, and 30 using prime factorization is 10.
How to find the greatest common divisorTo find the greatest common divisor (GCD) of 120, 70, and 30 using prime factorization we need to first express each number as a product of its prime factors.
Prime factorization of 120
2³ × 3 × 5
Prime factorization of 70
= 2 × 5 × 7
Prime factorization of 30
= 2 × 3 × 5
common prime factors among the three numbers
common prime factors
= 2 × 5
= 10
Learn more about prime factorization at
https://brainly.com/question/18187355
#SPJ1
Carl has a ribbon that is 4/5 of a meter long. He wraps 2/5 of a meter of a meter of the ribbon around a package. He uses another 1/4 of a meter of the ribbon to tie a bow on a gift box. What is the length of the ribbon carl has left
A. 13/20 of a meter
B. 2/5 of a meter
C. 3/20 of a meter
D. 4/5 of a meter
Answer:
C. 3/20 of a meter
Step-by-step explanation:
Step 1: To find out how much ribbon Carl has left, we need to subtract the length of ribbon used from the total length of the ribbon.
Step 2: To add the lengths of the ribbon used, we need to find a common denominator for the fractions used. The least common multiple of 5 and 4 is 20, so we can convert both fractions to twentieths.
Step 3: 2/5 of a meter is equivalent to 8/20 of a meter, and 1/4 of a meter is equivalent to 5/20 of a meter.
Step 4: To add the lengths of ribbon used, we add the two fractions: 8/20 + 5/20 = 13/20.
Step 5: To find the length of ribbon Carl has left, we subtract the fraction of the ribbon used from the total length of the ribbon: 4/5 - 13/20 = 16/20 - 13/20 = 3/20.
Step 6: Therefore, Carl has 3/20 of a meter of ribbon left.
3. Given that f(x)=x+2 and g(x)=3x² -1.
What is (fg)(x)?
Answer:
fg(x) = 3x² + 1
Step-by-step explanation:
f(g(x))
f(3x² - 1)
(3x² - 1) + 2
an artist made a fine of stainless steel, then sliced it into three pieces. what is the volume of the largest piece? PLEASE HELP I WILL MARK YOU BRAINLIEST
The volume of the largest piece is given as follows:
V = 10603 cm³.
How to obtain the volume?The volume of a cone of radius r and height h is given by the equation presented as follows:
V = πr²h/3.
The dimensions for the largest piece in this problem are given as follows:
r = 15 cm -> as the diameter is of 30 cm and the radius is half the diameter.h = 3 x 15 = 45 cm.Hence the volume of the largest piece is given as follows:
V = π x 15² x 45/3
V = 10603 cm³.
More can be learned about the volume of a cone at brainly.com/question/12004994
#SPJ1
I’m not good at these
That's quadratic.
y=x^2
It's a very simple version of y=ax^2+bx+c. Just in this case, a = 1, b = 0 and c = 0.
Can someone help me with 6-11. Directions: Find the volume of each figure. Round to the nearest hundredth when necessary.
The calculated volumes of the figures are 11264 cubic units, 14482.28 cubic units, 3744 cubic units, 475.2 cubic units, 18824.14 cubic units and 91.99 cubic units
How to find the volume of the figuresThe cylinder
The volume is calculated as
V = πr²h
Where
r = Radius
h = Height
So, we have
V = 22/7 * (32/2)² * 14
Evaluate
Volume = 11264
The cylinder
The volume is calculated as
V = πr²h
Where
r = Radius
h = Height
So, we have
(2r)² = 40² - 32²
(2r)² = 576
So, we have
r = 12
So, we have
V = 22/7 * (12)² * 32
Evaluate
Volume = 14482.28
The rectangular prism
The volume is calculated as
V = lwh
Where
l = Length
w = Width
h = Height
So, we have
V = 8 * 12 * 39
Evaluate
Volume = 3744
The triangular prism
The volume is calculated as
V = 1/2lwh
Where
l = Length
w = Width
h = Height
So, we have
V = 1/2 * 11 * 5.4 * 16
Evaluate
Volume = 475.2
The sphere
The volume is calculated as
V = 4/3πr³
Where
r = Radius
So, we have
V = 4/3 * 22/7 * (33/2)³
Evaluate
Volume = 18824.14
The sphere
The volume is calculated as
V = 4/3πr³
Where
r = Radius
So, we have
V = 4/3 * 22/7 * 2.8³
Evaluate
Volume = 91.99
Read more about volumes at
https://brainly.com/question/463363
#SPJ1
The total number of atoms represented by Cd(CH₂CICO₂)2 is:
O a) 13
Ob) 16
O c) 17
Od) 15
Oe) 14
The total number of atoms represented by Cd(CH₂CICO₂)₂ is 15.
What is addition?In addition, items are combined and counted as a single large group. The process of adding two or more numbers together is known as addition in mathematics. The terms "addends" and "sum" refer to the numbers that are added and the result of the operation, respectively.
To find the total number of atoms represented by Cd(CH₂CICO₂)₂, we need to count the number of atoms of each element in the molecule and add them up.
Cd(CH₂CICO₂)₂ contains:
1 cadmium (Cd) atom
2 carbon (C) atoms
6 hydrogen (H) atoms
4 oxygen (O) atoms
2 chlorine (Cl) atoms
Adding these up, we get:
1 + 2 + 6 + 4 + 2 = 15
Therefore, the total number of atoms represented by Cd(CH₂CICO₂)₂ is 15.
The answer is (D) 15.
To learn more about the addition;
brainly.com/question/29464370
#SPJ2
Given a polynomial, complete the following statements.
3x^4-9x^3-30x^2
In order to solve this polynomial, the equation MUST be set equal to ___
There are ___ (enter a number) roots for this polynomial.
The equation written in factored form is ____
The solution(s) for this polynomial is/are x= { _______}
The solutions are x = 0, 0, -2 and 5.
Given is a polynomial we need to solve it,
3x⁴-9x³-30x².
We know that a polynomial will have the number of solutions equal to its highest degree,
Here the highest degree of the polynomial is 4 so there will be 4 solutions.
3x⁴-9x³-30x²
[tex]= 3x^2\left(x^2-3x-10\right)[/tex]
[tex]= x^2-3x-10 =\quad \left(x+2\right)\left(x-5\right)[/tex]
[tex]= 3x^2\left(x+2\right)\left(x-5\right)[/tex]
Therefore, the solutions are x = 0, 0, -2 and 5.
Learn more about polynomial click;
https://brainly.com/question/11536910
#SPJ1
car cost #450,000 and is sold for #540,000. find the profit as a percentage of the cost price
The profit percentage is 20% when car cost 450000 and sold for 540000.
The formula i.e., Profit = Selling Price - Cost Price can be used to determine the profit when the price at which something is sold and the cost price of a product are known. The formula for calculating profit percentage is then applied, which is profit % = (profit/cost price) x 100 (A profit algorithm is used to determine how much profit was generated from the sale of a specific product.)
Cost Price= 4500000
Selling price= 540000
Profit = Selling price - cost price
Profit= 540000-450000
Profit = 90000
Profit as a percentage of cost price= [tex]\frac{90000}{45000}*100= 20%[/tex]
Therefore, the profit as a percentage of cost price is 20%.
To Know more about Profit Percentage Visit:
brainly.com/question/30938251
Steve says to find the difference in temperature between 7 AM and
12 PM Wednesday, he can use a number line. He says because one
temperature is negative and the other is positive, he can add together their
distances from 0.
Kelly says that she can find the change by subtracting -5.1 from the temperature
at 12 PM on Wednesday.
Who is correct? Use the drop-down menus to explain your reasoning and find the
change in temperature.
and the distance from 0 to the Wednesday 12 PM temperature is 2.5
Steve is correct. Steve can find the difference in temperature between 7 AM and 12 PM on Wednesday by adding the distances from 0.
By using a number line, Steve can find the difference in temperature between 7 AM and 12 PM on Wednesday by adding the distances from 0. One temperature is negative and the other is positive, but by adding their distances, he can find the difference. Kelly's method of subtracting -5.1 from the temperature at 12 PM on Wednesday is not necessarily incorrect, but it does not give the exact difference in temperature between the two times. Therefore, using Steve's method, the change in temperature would be the sum of the distance from 0 to the temperature at 7 AM (which is 2.5) and the distance from 0 to the temperature at 12 PM (which is also 2.5), resulting in a difference of 5 degrees.
For more questions on difference in temperature
https://brainly.com/question/18295743
#SPJ11