Answer:
C) a = 6, b = 4
Step-by-step explanation:
6 + 4 = 10
6 - 4 = 2
To solve the system, we first add both equations to find 'a = 6'. Then, substitute 'a' in one of the original equations to get 'b = 4'. The solution is 'a = 6' and 'b = 4', corresponding to answer choice C).
Explanation:To solve the system of equations:
a + b = 10a - b = 2We can add the two equations to eliminate the variable b. By adding them, we get:
2a = 12
Divide both sides of the equation by 2:
a = 6
With the value of a known, substitute a = 6 into either of the original equations. For example, substituting it into the first equation:
a + b = 10
6 + b = 10
b = 10 - 6
b = 4
Therefore, the solution to the system of equations is a = 6 and b = 4, which corresponds to answer choice C).
URGENT Consider the function f(x)=x3+6x2−20x+450.
What is the remainder if f(x) is divided by (x−12)? Report your answer as a number only. Do not include (x−12) in your answer.
Answer:
[tex]remainder=2802[/tex]
Step-by-step explanation:
Remainder Theorem: When a polynomial [tex]f(x)[/tex] is divided by [tex](x-a)[/tex] the remainder will be [tex]f(a)[/tex]
[tex]Here \ \ f(x)=x^3+6x^2-20x+450[/tex]
[tex]It\ is\ divided\ by\ (x-12)[/tex]
[tex]Then\ remainder =f(12)\\\\remainder=(12)^3+6(12)^2-20\times12+450\\\\remainder=1728+6\times144-240+450\\\\remainder=1728+864-240+450\\\\remainder=3042-240\\\\remainder=2802[/tex]
Final answer:
To find the remainder of the polynomial f(x) = x³ + 6x² - 20x + 450 when divided by (x - 12), we evaluate f(12) using the Remainder Theorem, which yields a remainder of 2802.
Explanation:
To find the remainder when the function f(x) = x³ + 6x² - 20x + 450 is divided by (x - 12), we use the Remainder Theorem. This theorem states that the remainder of a polynomial f(x) divided by (x - a) is f(a). Therefore, to find the remainder of f(x) divided by (x - 12), we evaluate f(12).
Substitute x with 12 into the function:
f(12) = (12)³ + 6(12)² - 20(12) + 450
f(12) = 1728 + 864 - 240 + 450
f(12) = 2802
Thus, the remainder is 2802.
Seven divided by four hundred ninety three
Seven divided by four hundred ninety three
Answer:
0.0141987829615
Step-by-step explanation:
Can you show me the steps when reducing 58/48 to 29/24?
Answer:
58/48 to 29/24
Step-by-step explanation:
An easy way that I always remember is that if both the numbers are even, divide by 2. Keep dividing until you get a odd number and then you know that you have your lowest form.
9.5 , 9 3/4 , 9.125 , 9 3/4 from greatest to least
Answer:
9 3/4, 9 3/4, 9.5, 9.125
Step-by-step explanation:
*I converted to decimal form*
9 3/4= 9.75
9.75 is greater than both 9.5 and 9.125, so therefore it is first on the list.
Next, since 9.5 is greater than 9.125, it is arranged next on the list.
9.125 is the only number left, and is clearly the smallest out of all of the numbers shown.
We want to order the given set of numbers from greatest to lest.
The correct order is:
{9 3/4, 9 3/4, 9.5, 9.125}
Let's see how to get that.
The given set is:
{9.5, 9 3/4, 9.125, 9 3/4}
Here we can see that we have two times the mixed number (9 3/4).
This can also be written as:
9 + 3/4
And we know that 3/4 = 0.75
Then:
9 + 3/4 = 9.75
Then the mixed number is the largest number.
Then comes the 9.5, and finally the 9.125
Then the correct order is:
{9 3/4, 9 3/4, 9.5, 9.125}
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What is the area of this parallelogram?
A. 28 m²
B. 56 m²
C. 84 m²
D. 120 m²
Parallelogram A B C D with side D C parallel to side A B and side A D parallel to side B C. Point F is between D and C and connects to point B by a dotted segment. Point E is between A and B and connected to point D by a dotted segment. D F B E is a rectangle with all right angles. DF is 8 meters. F C is 4 meters. A E is 4 meters. E B is 8 meters. F B is 7 meters.
Answer:
84m2
Step-by-step explanation:
it is not b because that is only the area of the square inside of the parallelogram i know that for a FACT sorry i answered late.
of 900 centimeters. The table shows the height of each bounce.
Bounce Height (cm)
1 800
2 560
3 392
The heights form a geometric sequence.
How high does the ball bounce on the 5th bounce? Round your answer to the nearest tenth of a centimeter, if necessary.
Answer:
Rounding to nearest tenth of centimeter, the ball bounces 192.1 cm high on the 5th bounce.Explanation:
The ball is dropped from a height of 900 centimeters.
Since the heights form a geometric sequence, you can find a common ratio between consecutive terms. This is:
Height bounce 2 / height bounce 1 = 560 / 800 = 0.7Height bound 3 / height bounce 2 = 392 / 560 = 0.7Hence, the ratio of the geometric sequence is 0.7, and taking bounce 1 as the start of the sequence, the general term of the sequence is:
[tex]a_n=800(0.7)^{n-1}[/tex]
With that formula you can find any term:
[tex]n=1,a_1=800(0.7)^{(1-1)}=800(0.7)^0=800\\ \\ n=2,a_{2}=800(0.7)^{(2-1)}=800(0.7)=560\\ \\n=5,a_{5}=800(0.7)^{(5-1)}=800(0.4)^4=192.08[/tex]
Rounding to nearest tenth of centimeter, the ball bounces 192.1 cm high on the 5th bounce.
A bag contains 7 red marbles, 5 yellow marbles, 6 blue marbles, 4 green marbles, and 3 orange marbles. What is the probability of randomly selecting a yellow marble out of the bag?
The probability of randomly selecting a yellow marble out of the bag is [tex]\frac{1}{5}[/tex]
Step-by-step explanation:
A bag contains:
7 red marbles5 yellow marbles6 blue marbles4 green marbles 3 orange marblesWe need to find the probability of randomly selecting a yellow marble out of the bag
Probability is the ratio of number of favorable outcomes to the total number of possible outcomes P(A) = [tex]\frac{n(A)}{n(outcoms)}[/tex]
∵ A bag contains 7 red marbles, 5 yellow marbles, 6 blue
marbles, 4 green marbles, and 3 orange marbles
- Add all the color to find the number of total marbles
∴ n(all) = 7 + 5 + 6 + 4 + 3 = 25
∵ There are 5 yellow marbles
∵ P(yellow) = [tex]\frac{n(yellow)}{n(all)}[/tex]
∴ P(yellow) = [tex]\frac{5}{25}[/tex]
- Divide up and down by 5 to simplify the fraction
∴ P(yellow) = [tex]\frac{1}{5}[/tex]
The probability of randomly selecting a yellow marble out of the bag is [tex]\frac{1}{5}[/tex]
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Answer:
1/5
Step-by-step explanation:
Solve using elimination
-3x + 4Y = 16
3x - y +14
Answer:
x = 8
y = 10
Step-by-step explanation:
We are given the equations;
-3x + 4Y = 16
3x - y =14
We are required to solve the two equations simultaneously using elimination
In this case, we will eliminate one unknown;
We eliminate x by adding the two equations;
That is;
-3x + 4Y = 16
3x - y =14
.............................
3y = 30
y = 10
Solving for x
3x - (10) = 14
3x = 14 +10
3x = 24
x = 8
Therefore, the solution of the equation is x=8 and y=10
simplify 3(2m^3n^-2)^4
Answer:
(48 m^12)/n^8
Step-by-step explanation:
Simplify the following:
3 ((2 m^3)/(n^2))^4
Multiply each exponent in (2 m^3)/(n^2) by 4:
3×2^4 m^(4×3) n^(-2×4)
4 (-2) = -8:
3×2^4 m^(4×3) n^(-8)
4×3 = 12:
(3×2^4 m^12)/(n^8)
2^4 = (2^2)^2:
(3 (2^2)^2 m^12)/(n^8)
2^2 = 4:
(3×4^2 m^12)/(n^8)
4^2 = 16:
(3×16 m^12)/(n^8)
3×16 = 48:
Answer: (48 m^12)/n^8
Answer:
On the screen shot
Step-by-step explanation:
pretty basic. you can't evaluate it to a single digit if there are 2 variables. lmk which variable you are solving for.
Write 2.3 as a mixed number.
2[tex]\frac{3}{10\\}[/tex]
What is 2 to the power of 3 over 2 equal to? (5 points) squre root of 8 cube root of 8 cube root of 16 square root of 16
Answer:
Square root of 8.
Step-by-step explanation:
Given:
Number given : 2 to the power of 3 over 2 equal ...
Using the laws of exponent:
We know that:
⇒ [tex]\sqrt{a} = (a)^1^/^2[/tex] and
⇒ [tex]\sqrt[3]{a}=(a)^1^/^3[/tex]
So,
According to the question:
2 to the power of 3 over 2 = [tex](2) ^3^/^2[/tex]
Using fractional exponent concept where : [tex]\sqrt[y]{a^x} = (a)^x^/^y[/tex]
This can be re-written as:
⇒ [tex](2^3)^1^/^2[/tex] and [tex]\sqrt{2^3}[/tex] that is equivalent to [tex]\sqrt{8}[/tex] as ...[tex]2^3=2\times 2\times 2=8[/tex]
Square root of 8 is our final answer.
Joe, John and Jason are each a year apart in age. If the
sum of their ages i 39, how old is Jason?
equality
Substitute and Check (Answer in a Complete Sentence
HELP PLEASE!!!
Answer:
Jason is 14 year old.
Step-by-step explanation:
Given: Joe, John and Jason are each a year apart in age.
Sum of their age is 39.
Lets assume the age of Joe be x
∴ Age of Jahn will be [tex](x+1)[/tex]
And age of Jason will be [tex](x+2)[/tex]
Now, putting up an equation for the sum of their age.
∴ [tex]x+(x+1)+(x+2)= 39[/tex]
Opening the parenthesis.
⇒[tex]x+x+1+x+2= 39[/tex]
⇒[tex]3x+3= 39[/tex]
Subtracting both side by 3
⇒ [tex]3x= 36[/tex]
Dividing both side by 3
⇒[tex]x= \frac{36}{3}[/tex]
∴ [tex]x= 12\ years[/tex]
Hence, Joe is 12 year old.
Next subtituting the value of x to find age of Jason and John.
Jason= [tex](x+2)= 12+2[/tex]
∴Jason= 14 years.
John age= [tex](x+1)= 12+1[/tex]
∴ John Age= 13 years.
Hence, Jason is 14 year of age.
solve the system using eliminationx+7y=-37 2x-5y=21
Answer:
y = -5
x = -2
Step-by-step explanation:
x+7y=-37
2x-5y=21
Multiply first equation by -2
-2 × (x + 7y) = -37 ➡ -2x -14y = 74
now add the equation up
2x-5y -2x -14y = 21 + 74 (-2x will eliminate 2x)
-19y = 95 divide both sides by 19
y = -5 we can find the value for x by using this information
x + 7y = -37 replace y by -5
x + 7×(-5) = -37
x = -2
write the equation of the line with the two given points (-12,14) . (6,-1)
Answer: 6y + 5x = 24
Step-by-step explanation:
The formula for calculating equation of line with two points is given as :
[tex]\frac{y-y_{1}}{x-x_{1}}[/tex] = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]x_{1}[/tex] = -12
[tex]x_{2}[/tex] = 6
[tex]y_{1}[/tex] = 14
[tex]y_{2}[/tex] = -1
substituting the values into the formula , we have
[tex]\frac{y-14}{x-(-12)}[/tex] = [tex]\frac{-1-14}{6-(-12)}[/tex]
[tex]\frac{y-14}{x+12}[/tex] = [tex]\frac{-15}{18}[/tex]
[tex]\frac{y-14}{x+12}[/tex] = [tex]\frac{-5}{6}[/tex]
cross multiplying , we have :
6(y - 14 ) = -5 ( x + 12 )
6y - 84 = -5x - 60
6y +5x = -60 + 84
6y + 5x = 24
In a year the number of people dying from cancer was 5 times the number who died from accidents. If the number of deaths from these two causes totaled 360,000, how many people died from each cause?
Based on the number of people dying from both causes and their relationship with each other, we can calculate that the number of people dead from cancer was 300,000 and those from accidents was 60,000.
Assuming x number of people died from accidents, the number that died from cancer would be 5 times that:
= 5x
The number of people dead from accidents is:
360,000 = 5x + x
6x = 360,000
x = 60,000 people
The number dead from cancer is:
= 5x
= 5 × 60,000
= 300,000 people
In conclusion, 60,000 died from accidents and 300,000 people died from cancer.
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Final answer:
To solve the problem, we created two equations: c = 5a and c + a = 360,000. After substituting and solving these equations, we found that 300,000 people died from cancer and 60,000 from accidents.
Explanation:
The question refers to a situation where the number of people dying from cancer is five times the number who died from accidents, and the total deaths from these two causes amounted to 360,000. To solve this, we can set up a system of equations. Let ‘c’ be the number of cancer deaths and ‘a’ the number of accident deaths. We are given:
c = 5a (the number of cancer deaths is five times accident deaths)c + a = 360,000 (the total number of deaths is 360,000)Substituting the first equation into the second, we get:
5a + a = 360,0006a = 360,000a = 60,000Then we substitute the value of ‘a’ back into the first equation to find ‘c’:
c = 5 * 60,000c = 300,000Therefore, 60,000 people died from accidents and 300,000 from cancer.
12x+60y≥540 what is x 4 times more than y
Answer: if y is equal to 18 and x is equal to 72
Step-by-step explanation: 18*4=72
How many times does 19 go into 133
To find out how many times 19 goes into 133, you can perform a simple division. 19 goes into 133 seven times with no remainder.
Dividing 133 by 19 results in 7, which means 19 goes into 133 seven times exactly. This division is a fundamental arithmetic operation, illustrating how many times one number can be evenly divided into another. It's part of the foundation of mathematics and has practical applications in everyday life, from splitting objects into equal groups to determining quantities in various contexts.
In this case, it's evident that 19 is a factor of 133, and understanding this relationship can help in tasks like distributing items evenly or solving problems involving proportions and ratios. Division is a mathematical concept with broad utility and relevance, making it essential in various mathematical, scientific, and real-world scenarios.
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The ratio of boys to girls in a class is 2 to 3. There are 12 boys in the class. How many girls are in the class?
Answer:
18
you do 2/3=12/n. and find out n (im to lazy to explain sorry)
Find the midpoint of the line segment
with end coordinates of:
(2,0) and (8,8)
Show working out pls
Answer:
midpoint (5,4)
Step-by-step explanation:
The midpoint(M) of a segment with endpoints (x₁ , y₁) and ( x₂, y₂) is
where x₁ = 2 and x₂ = 8
y₁ = 0 and y₂ = 8
M = [tex]\frac{x_1 + x_2}{2} ,\frac{y_1 + y_2}{2}[/tex]
M = [tex]\frac{2 + 8}{2} ,\frac{0 + 8}{2}[/tex]
M = 5 , 4
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In circle A, ∠BAE ≅ ∠DAE. Circle A is shown. Line segments A B, A E, and A D are radii. Lines are drawn from point B to point E and from point E to point D to form secants B E and E D. Angles B A E and E A D are congruent. The length of B E is 3 x minus 24 and the length of E D is x + 10. What is the length of BE? 14 units 17 units 27 units 34 units
Answer:
The missing figure is attached down
The length of BE is 27 units ⇒ 3rd answer
Step-by-step explanation:
In circle A:
∠BAE ≅ ∠DAELine segments A B, A E, and A D are radiiLines are drawn from point B to point E and from point E to point D to form secants B E and E DThe length of B E is 3 x minus 24 and the length of E D is x + 10We need to find the length of BE
∵ AB and AD are radii in circle A
∴ AB ≅ AD
In Δs EAB and EAD
∵ ∠BAE ≅ ∠DAE ⇒ given
∵ AB = AD ⇒ proved
∵ EA = EA ⇒ common side in the two triangles
- Two triangles have two corresponding sides equal and the
including angles between them are equal, then the two
triangles are congruent by SAS postulate of congruence
∴ Δ EAB ≅ Δ EAD ⇒ SAS postulate of congruence
By using the result of congruence
∴ EB ≅ ED
∵ EB = 3 x - 24
∵ ED = x + 10
- Equate the two expressions to find x
∴ 3 x - 24 = x + 10
- Add 24 to both sides
∴ 3 x = x + 34
- Subtract x from both sides
∴ 2 x = 34
- Divide both sides by 2
∴ x = 17
Substitute the value of x in the expression of the length of BE to find its length
∵ BE = 3 x - 24
∵ x = 17
∴ BE = 3(17) - 24
∴ BE = 51 - 24
∴ BE = 27
The length of BE is 27 units
Answer:
27
Step-by-step explanation:
I TOOK THE QUIZ, AND GOT 100%
if m=a/b, m=18, and a=7, find b
Answer:
11
Step-by-step explanation:
You will move the 7 to 18 but bc there is a equal sign you will change the positive sign to negative and just solve -7 plus 18 you will get 11 and that’s b
Answer:
Step-by-step explanation:
18 = 7/b
18b=7
b=7/18
Write the numbers in order from least to greatest.
-3, 3 1⁄3, -3 3⁄4, 3 1⁄10
Answer:
Step-by-step explanation:
-3 3/4, -3, 3 1/10, and then 3 1/3 i think this is correct...sorry if it is wrong though.
Convert the complex number z = -7 - 8i from rectangular form to polar form.
The polar form of z = -7 - 8i is:
z = 3√13 (cos 230.2° + i sin 230.2°)
Converting -7 - 8i to polar form:
The rectangular form of a complex number is given by z = a + bi, where a is the real part and b is the imaginary part. In this case, a = -7 and b = -8.
The polar form of a complex number is given by z = r(cos θ + i sin θ), where:
r is the modulus (or absolute value), which represents the distance of the complex number from the origin in the complex plane.
θ is the argument (or angle), which represents the direction of the complex number relative to the positive real axis.
1. Finding modulus (r):
r = √(a² + b²) = √((-7)² + (-8)²) = √(113) = √(13 * 9) = √13 * 3 (using factorization and perfect squares)
Therefore, r = 3√13.
2. Finding argument (θ):
θ = arctan(b/a) = arctan((-8)/(-7)) ≈ 50.2° (using the arctangent function on a calculator). However, this only gives one possible angle for the complex number.
Note: The arctangent function typically outputs values between -90° and 90°, which corresponds to Quadrant 1 or 4 in the complex plane. Since -7 - 8i lies in Quadrant 3, we need to add 180° to get the correct angle:
θ = 50.2° + 180° = 230.2°
Therefore, the polar form of z = -7 - 8i is:
z = 3√13 (cos 230.2° + i sin 230.2°)
If Raul Poland to run 30 miles this week but wants to run the same number of miles each day of the week what is the correct form of fraction to write this?
Answer:
Step-by-step explanation:
The correct fraction is simply 30/7, where 30 is the distance in miles and 7 is the number of days to complete it.
30/7 = 4.286miles daily but since you've asked to have this as a fraction, 30/7miles is good.
Final answer:
To achieve his goal of running 30 miles in a week, Raul should run 30 miles divided by 7 days, which is approximately 4 2/7 (⅔) miles every day.
Explanation:
If Raul wants to run 30 miles this week and he wants to run the same number of miles each day, we need to divide the total miles by the number of days in a week. There are 7 days in a week, so we will divide 30 miles by 7 days.
Using division: 30 miles ÷ 7 days = ⅔ miles per day. The fraction ⅔ represents the number of miles Raul plans to run each day to meet his goal of running 30 miles in a week.
what is 62% of eighty
Answer:
49.6 or 49 3/5
Step-by-step explanation:
62/100*80
Simplify the 62/100 (meaning to make it to its simplest terms as possible).
62/100= 31/50
Now we can solve:
31/50*80= 49.6 or 49 3/5
Answer:
Step-by-step explanation divide 62 by 100 and multiply by 80
= 49.6
Need help completing the table!!
Answer:
time | distance
2 | 50
1.5 | 37.5
t | 25*t
2 | 50
12 | 300
d/25 | d
Step-by-step explanation:
Which of the following decimal numbers is the greatest
Is it
0.206
2.06
0.026
0.26
Answer:
converting to fraction:
0.206 = 0.206/1000 =206//1000
2.06 = 2.06/100 = 206/100
0.026 = 0.026/1000 = 26/1000
0.26 = 0.26/100 = 26/100
answer = 2.06
Step-by-step explanation:
The fraction having the greatest value will be 2.06.
What is a number system?A numeral system is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set in a consistent manner using digits or other symbols. In different numeral systems, the same sequence of symbols can represent different numbers.
The greatest value of the fraction will be calculated as below in the calculation:-
0.206 = 0.206/1000 =206//1000
2.06 = 2.06/100 = 206/100
0.026 = 0.026/1000 = 26/1000
0.26 = 0.26/100 = 26/100
Therefore, the fraction having the greatest value will be 2.06.
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Barbara works in a bakery. She puts 12 blueberries in each blueberry muffin she makes. How many blueberries does Barbara need to make 8 blueberry muffins?
Answer:
96 blueberries
Step-by-step explanation:
x = number of muffins
Since each blueberry is going to contain 12 blueberries, we can multiply 12 by the number of muffins to get the total number of blueberries.
12x
12(8)
96
A bag contains 90 marbles some red and some blue. If there are 60 blue marbles what is the ratio of blue to red marbles
Answer:
2:1
Step-by-step explanation:
Answer:60:30
Step-by-step explanation:
90-60=30 so 60 blue to 30 red is 60:30