Answer:
B & D
Step-by-step explanation:
The quadratic formula can be used to solve for x for any quadratic. Recall a quadratic is any function whose highest exponent known as degree is 2. Looking at the answer selections, A has one term with exponent 3. This isn't possible in the formula. Looking at answer C, the term with exponent 2 has the same coefficient on each side of the equal sign. When it is rearranged these will cancel out no exponent of 2 will be in the equation anymore. Only B & D work after being rearranged and simplified
The two equations after simplifying will give quadratic equations are:-
x ²-6x-7=2x² and 5x²-3x+10=2x².
What is a quadratic equation?
The polynomial having a degree of two or the maximum power of the variable in a polynomial will be 2 is defined as the quadratic equation and it will cut two intercepts on the graph at the x-axis.
Solving for the quadratic equation:-
Option B:-
x ² - 6x - 7 = 2x²
- 2x² + x ² - 6x - 7 = 0
x ² + 6x + 7 = 0
Option D:-
5x² - 3x + 10 = 2x².
5x² - 2x². - 3x + 10 = 0
3x² - 3x + 10 = 0
Therefore two equations after simplifying will give quadratic equations are- x ²-6x-7=2x² and 5x²-3x+10=2x².
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A merchant travels with 269 pounds of silver goods, 167 pounds of fruit, and 51 pounds of herbs, but only has 11 camels to carry everything. How many pounds of goods does each camel have to carry and how many goods are left over?
pounds each and
pounds of goods left over
Answer: The number of pounds each camel have to carry=44 pounds
The pounds of goods left=3 pounds
Step-by-step explanation:
The total pounds of goods the merchant have=[tex]269+167+51[/tex]
=487 pounds
The total number of camels the merchant have = 11
If each camel carry same weight of goods, then we divide total weight by 11, we get
487÷11=44.27
The number of pounds each camel have to carry=44 pounds
The pounds of goods left=487-44×11=487-484=3 pounds
•Marble City has a population of 52,348 and covers an area of 125 square miles.
•Pebble City has the same population density as Marble City.
•The shape of Pebble City resembles a rectangle with a width of 11.8 miles and a length of x miles.
•The population of Pebble City is 85,312.
–Which measure is closest to the value of x?
Answer Choices:
A) 11
B) 17
C) 36
D) 77
Answer:
B) 17Step-by-step explanation:
The population density is the ration between the population and the area covered. So, the population density of Marble City
[tex]M=\frac{52348}{125}\approx418.78[/tex]
If both cities have the same population density, this can be used to find the dimension of Pebble City:
[tex]P=\frac{85312}{A}\\ 418.78=\frac{85312}{A}\\A=\frac{85312}{418.78}\approx 203.72[/tex]
Now, knowing the area of Pebble City, we can find its length
[tex]A=(length)(width)\\203.72=l(11.8)\\l=\frac{203.72}{11.8}\approx 17[/tex]
Therefore, the length of Pebble City has a length of 17 miles, approximately.
I just need to know if they have equivalent volumes and an explanation.
Answer: Yes, they have equivalent volumes.
Step-by-step explanation:
For the volumes to be equal, a would have to be equal to b. We'll assume x=x
1. Set the volumes equal to each other
x +a +2b =x +2a +b
2. Simplify
[x +a +2b =x +2a +b] -x
[a +2b =2a +b] -a
[2b =a +b] -b
b =a
Therefore, 2a=2b, a=b, and x=x
Since the two prisms have the same measurements, they have the same volumes.
You deposit $500 in an account that earns 5% compounded annually. What is the balance in your account after 5 years? Round your answer to the nearest cent.
F $2,625.00
G $625.00
H $886.89
J $638.14
Answer:
J. $638.14
Step-by-step explanation:
We will use compound interest formula to solve our given problem.
[tex]A=P(1+\frac{r}{n})^{nT}[/tex], where,
A=Final amount after T years.
P= Principal amount.
r= Interest rate in decimal form.
n= Period of compounding.
T= Time in years.
Let us convert our given interest rate in decimal form.
[tex]5\%=\frac{5}{100}=0.05[/tex]
Let us substitute our given values in above formula.
[tex]A=500*(1+\frac{0.05}{1})^{1*5}[/tex]
[tex]A=500*(1+0.05)^{5}[/tex]
[tex]A=500*(1.05)^{5}[/tex]
[tex]A=500*1.2762815625[/tex]
[tex]A=638.14078125\approx 638.14[/tex]
Therefore, we will have an amount of $638.14 after 5 years and option J is the correct choice.
The balance in your account after depositing $500 with an annual compound interest rate of 5% for 5 years would be $638.14, according to the formula for compound interest.
Explanation:To calculate the balance in an account after a certain period of time, we would use the formula for compound interest. This formula is
[tex]A = P(1 + r/n)^{nt}[/tex], where 'A' is the amount of money accumulated after n years, taking into account interest. 'P' is the principal amount (the initial amount of money), 'r' is the annual interest rate (in decimal), 'n' is the number of times that interest is compounded per year, and 't' is the time the money is invested for in years.
Here, P = $500, r = 5/100 = 0.05 (because the rate was given in percentage), n = 1 (because the interest is compounded annually), and t = 5 years. Inserting these values into the formula gives us
[tex]A = 500(1 + 0.05)^{1\times 5}[/tex]which simplifies to A = $638.14. So, the balance in your account after 5 years would be $638.14, rounded to the nearest cent.
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best rentals charges a daily fee plus a mileage fee for renting its cars. barney was charged $159 for 3 days and 300 miles, while mary was charged $289 for 5 days and 600 miles. what does best rental charge per day and per mile?
Answer:
Let charge per day be $x and charge per mile be $y
then:
as per the given condition we have;
3x + 300y =159 .....[1]
5x + 600y = 289 .....[2]
Multiply equation [1] both sides by 5 we get;
[tex]5(3x+300y) = 5 \cdot 159[/tex]
Using distributive property: [tex]a \cdot(b+c) = a\cdot b+ a\cdot c[/tex]
15x+1500y = 795 .....[3]
Multiply equation [2] by 3 both sides we get;
[tex]3(5x+600y) = 3 \cdot 289[/tex]
Using distributive property: [tex]a \cdot(b+c) = a\cdot b+ a\cdot c[/tex]
15x+1800y = 867 .....[4]
Subtract equation [3] from [4] to eliminate x and solve for y;
15x+1800y-15x-1500y = 867 -795
Combined like terms;
300y = 72
Divide both sides by 300 we get;
[tex]y = \frac{72}{300}=0.24[/tex]
⇒ y =$0.24 per mile.
Now substitute this value y in equation [1] to solve for x;
3x + 300(0.24) =159
3x + 72 =159
Subtract 72 both sides we get;
3x + 72 -72 = 159 -72
Simplify:
3x = 87
Divide both sides by 3 we get;
[tex]x = \frac{87}{3} = 29[/tex]
Therefore, the best rental charges per day is, $ 29 and the charges per mile is, $0.24
The problem can be solved by setting up a system of linear equations from the given information. Then, solving these equations will yield the daily fee and mileage fee that Best Rental charges.
Explanation:To solve this problem, we can create a system of linear equations. Let's denote the daily fee as 'd' and the mileage fee as 'm'
From Barney's rental, we know that 3d + 300m = 159.
From Mary's rental, we know that 5d + 600m = 289.
We solve these two equations to find the values of 'd' and 'm'. This is an application of algebra in solving real-world problems
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what is -3.5 divided by 0.05
Answer:-70
Step-by-step explanation:
Answer:-70
Step-by-step explanation:
−3.5
0.05
=−70
Please Help, Thanks~
Explain how you can use the terms from the binomial expansion to approximate 4.02^5
1st term: 1024
2nd term: 25.6
3rd term: 0.256
4th term: 0.001
Answer:
See below. The result using the binomial theorem is 1049.8560 compared with 1049.8573 using a calculator.
Step-by-step explanation:
Binomial theorem:-
( a + x)^n = a^n + nC1 a^(n-1) x + nC2 a^(n - 2)x^2 + .......
(4 + 0.02)^5 = 4^5 + 5C1* 4^4 *0.02 + 5C2* 4^3* 0.02^2 + 5C3*4^2*0.02^3
+ 5C4 * 4 * 0.02^4 + 0.02^5
= 1024 + 5*4^4*0.02 + 10*4^3*0.02^2 + 10*4^2*0.02^3 + 5*4*0.02^4 + 0.02^5
= 1024 + 25.6 + 0.256 + 0.0000032
Answer:
Keisha's Response: The 4th term is almost 0, so the 5th and 6th terms are also close to 0. Add the terms shown to approximate 4.025: 1024 + 25.6 + 0.256 + 0.001 = 1049.857.
Step-by-step explanation:
EDGINUITY
30 Points!!! Remember show your work!
Answer:
see explanation
Step-by-step explanation:
(a)
1.2² = 1.2 × 1.2 = 1.44
(b)
2³ + 17 - 3 × 4 ← evaluate exponent and multiplication before adding/subtracting
= 8 + 17 - 12 = 25 - 12 = 13
(c)
9² ÷ 3³ ← evaluate exponents before dividing
= 81 ÷ 27 = 3
Answer:
a = 1.44
b = 21.6
c = 3
Step-by-step explanation:
a is 1.44 because 1.2 × 1.2 = 1.44
b is 21.6 because 2 × 2 × 2 = 8 so it is 8 + 17 - 3.4 which is 21.6
c is 3 because 9 × 9 = 81 and 3 × 3 × 3 = 27 so 81 ÷ 27 = 3
Which of the following is the binomial factor in the factorization of m ^15 - 1,000?
m5 - 10
m5 + 10
m5 + 100
m3 + 10
[tex]Use\ (a^n)^m=a^{nm}\ and\ a^3-b^3=(a-b)(a^2+ab+b^2).\\\\m^{15}=m^{5\cdot3}=(m^5)^3\\\\m^{15}-1,000=(m^5)^3-10^3=(m^5-10)[(m^5)^2+(m^5)(10)+10^2]\\\\=(m^5-10)(m^{10}+10m^5+100)\\\\Answer:\ \boxed{m^5-10}[/tex]
Final answer:
The binomial factor in the factorization of [tex]m^{15}[/tex] - 1,000 is [tex]m^{5}[/tex] - 10
Explanation:
To find the binomial factor in the factorization of [tex]m^{15}[/tex] - 1,000, we should recognize this expression as a difference of two powers. Both [tex]m^{15}[/tex] and 1,000 (which is the cube of 10, or 103), can be written as a power of their respective bases. We can factor this expression using the difference of cubes formula, which states that [tex]a^{3}[/tex] - [tex]b^{3}[/tex] = (a - b)([tex]a^{2}[/tex] + ab + [tex]b^{2}[/tex]). Applying this formula, we look for a cube of m that matches one of the options provided. The closest match here is [tex](m^{5})^3[/tex] [tex]-10^{3}[/tex], which gives us the factor of ([tex]m^{5}[/tex] - 10). Therefore, the binomial factor is [tex]m^{5}[/tex] - 10.
Please help!
Explain your answer.
Answer:
D
Step-by-step explanation:
5+7(8r-2)
5+56r-14
-9+56r=56r-9
d
Answer:
D) 56r - 9
Step by Step Explanation:
What function is graphed below?
Answer: y = 2x^4
The graph represents a parabolic-looking shape so it's either a quadratic or some even degree polynomial. This rules out y = -2x^3 and y = 2x^3 as they are cubics with odd degrees
The degree of a polynomial is the largest exponent. It determines the end behavior. In this case, both ends are rising upward together. Because they are rising up in the positive y direction, this means that we cannot have y = -2x^4 as the answer. For example, if x = 2 then y = -2*x^4 = -2*2^4 = -32, but the point (x,y) = (2,-32) isn't on the blue curve. So we can rule y = -2x^4 out.
The fact that y = 2x^4 has a positive leading coefficient tells us that the endpoints point upward.
Write an expression for the eighth partial sum of the series using summation notation
Answer:
option B
Step-by-step explanation:
9/10 + 6/5 + 3/2...........
We find the difference between the terms
[tex]\frac{6}{5} - \frac{9}{10}[/tex]
[tex]\frac{12}{10} - \frac{9}{10} = \frac{3}{10}[/tex]
We will get the same difference when we subtract consecutive terms.
so , d= 3/10, a= 9/10
we find the formula for nth term
a_n = a+(n-1) d
[tex]a_n = \frac{9}{10} + (n-1)\frac{3}{10}[/tex]
[tex]a_n = \frac{9}{10} +\frac{3}{10}n-\frac{3}{10}[/tex]
[tex]a_n = \frac{6}{10} +\frac{3}{10}n[/tex]
[tex]a_n = \frac{3}{5} +\frac{3}{10}n[/tex]
we need to find eighth partial sum so we take n=1 to 8
sum of 8 terms ([tex]\frac{3}{5} +\frac{3}{10}n[/tex])
So option B is correct
The eighth partial sum of a series, denoted as S8, sums up the first 8 terms in the series. In summation notation, it can be expressed as S8 = Σ_[k=1]^8 a_k.
Explanation:In mathematics, specifically in series and sequences, the notation for the eighth partial sum of a series is denoted by S8. Here the numeral 8 indicates the number of terms in that partial sum which is 8 in this case. The general formula for the sum of an arithmetic series is S_n = n/2 * (a + l) where n is the number of terms, a is the first term, and l is the last term.
If the terms of the series are denoted by a_k where k=1,2,3,... is the index of the term, the eighth partial sum of a series can be written in summation notation as:
S8 = Σ_[k=1]^8 a_k
This means that the eighth partial sum is the sum of the first 8 terms of the series.
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537 people attended a $100 dollar a plate fund raising dinner for the Nscc foundation. how much money did this dinner raise?
Answer:
$53,700
Step-by-step explanation:
If we have 537 people coming and paying $100 each, we multiply 537 and $100
537 * $100
$53,700
Can someone help me answer this question.
Hello from MrBillDoesMath!
Answer:
Choice B (176)
Discussion:
Volume of a box = (area of base) * height.
In our case this becomes
"2 of the boxes have a height of 3" + "and one box has a height of 5"
16 * 3 + 16 * 3 + 16 * 5 =
48 + 48 + 80 =
96 + 80 =
176
which is choice B
Thank you,
MrB
at maximum speed, an airplane travels 1720 miles against th wind in 5 hours. Flying with the wind, the plane can travel the same distance in 4 hours. Let x be the maximum speed of the plane and y be the speed of the wind. What is the speed if the plane with no wind?
Answer:
x = 387
Step-by-step explanation:
The wind acts in the opposite direction to the plane when the time is longer.
The wind acts in the same direction as the plane when the time is shorter.
Equation
d = r*t
Givens
d = 1720x = plane's speedy = wind speedt1 = 5 hourst2 = 4 hours.Substitution
d = (x + y) * t1720 = (x + y) * 41720 = (x - y) * 5Since the two distances are the same, you can equate the right hand sides.
(x + y) * 4 = (x - y)*5 Remove the brackets.4x + 4y = 5x - 5y Add 5y to both sides4x + 4y + 5y = 5x - 5y + 5y Combine all the terms.4x + 9y = 5x Subtract 4x from both sides9y + 4x - 4x = 5x - 4x Combine9y = xNow use one of the given equations with the distance
1720 = (x + y)*4 Substitute 9y for x1720 = (9y + y) * 4 Combine1720 = 10y * 4 Multiply the right1720 = 40y Divide by 401720/40 = 40y/40 Do the division43 = y y = wind speek9y = x x = 9*y 9*43 = x x = 387 miles per hour.Rearrange the formula P = 2(l + b) to solve for b.
Answer:
p= 2l+2b
Step-by-step explanation:
distribution
Answer:
P = 2 * 1 + 2 * B
Step-by-step explanation:
This equation needs to be written using the distributive property:
A (B + C) = A * B + A * C
Put in the numbers:
P = 2 (1 + B)
=
P = 2 * 1 + 2 * B
Best Of Luck,
- I.A. -
What are the coordinates of point c after the blue figure is rotated 180 degrees counterclockwise around the origin and translated 2 units to the right?
Answer:
(0, - 4 )
Step-by-step explanation:
under a counterclockwise rotation about the origin of 180°
a point (x, y ) → (- x, - y ), hence
C(2, 4) → (- 2, - 4)
A translation of 2 units to the right means add 2 to the original x- coordinate while the y-coordinate remains unchanged.
(- 2, - 4 ) → (- 2 + 2, - 4 ) → (0, - 4 )
Answer:
(0, - 4 )
Step-by-step explanation:
Write the equation of the given circle.
center (1, -5)
radius of 10
Answer:
[tex](x-1)^2+(y+5)^2=100[/tex]
Step-by-step explanation:
The equation of a circle has the following form:
[tex](x-h)^2+(y-k)^2=r^2[/tex] where (h,k) is the center of a circle with radius r.
Our equation center is (1.-5) and radius is 10.
[tex](x-1)^2+(y--5)^2=10^2[/tex]
[tex](x-1)^2+(y+5)^2=100[/tex]
Annalisa uses 2/3 cup of all purpose flour and 1/2 cup of whole wheat flour to make pancakes how many cop of flour does she use altogether
Answer:
Annalisa uses 7/6 cups altogether.
Step-by-step explanation:
First you find common denominators for both fractions, which is 6, then convert the fractions to the denominator 6.
You get 3/6+4/6.
The answer is 7/6!
What is the best estimate for 5.07 x 0.81 ?
A. 0.4
B. 4
C. 4.5
D. 5
Please help and if so correct and answered then I’ll mark you as Brainiest Answered.
Thank you.
Answer:
I'mma be honest someone else asked the same question and this is the answer they gotten They gotten 4 and 5 and 4.1 but in my opinion I say the answer should be 4
Step-by-step explanation:
Best estimate would be B, because the answer is 4.1067 and you would round down
Jean junction is selling jeans at 15% off the regular price the regular price is 25.00 per pair what is the discount amount
Answer:
$3.75
Step-by-step explanation:
To find the price after discount subtract this from $25.00
25.00 - 21.25 = 3.75
21.25 + 3.75 = 25
Hope this helped!
If the Greatest Common Factor of L and M is 6, write the expression for the Least Common Multiple of these numbers.
Answer:
[tex]\frac{(L x M)}{6}[/tex]
Step-by-step explanation:
The greatest common factor is the greatest number that will divide two values. We have two values L and M. Each has numbers which multiply together to give the number. The highest value or most in common they share is 6. This is the GCF.
The least common multiple is the smallest positive number which is a multiple of the two. This means both L and M divide into it evenly.
We know L x M is a multiple because L and M will be factors of it. But we don't know its the least.
As an example if L= 42 and M = 60, they have GCF 6. We can multiply them to find a multiple 42 x 60 = 2520 but we don't know this is the smallest or least multiple we can find. If we divide by the GCF, 2520/6=420. Interestingly, 42 x 10 =420 and 60 x 7 =420. This means 420 is the least common multiple.
We can multiply (L x M) and then divide by the GCF of L & M to find the least common multiple.
[tex]\frac{(L x M)}{6}[/tex]
A market buys mixed nuts at $15 per pound. They want to make a $20 profit.what would you pay for 1 pound of nuts?
Answer:
We need to sell the nuts at 35 dollars to make $20 profit
Step-by-step explanation:
Profit = Selling price - cost
We know we want a 20 dollar profit
The cost of the nuts is 15 dollar
Substitute this in
20 = Selling price -15
Add 15 to each side
20+15 = Selling price -15+15
35 = Selling price
We need to sell the nuts at 35 dollars to make $20 profit
Simplifying the expression and enter your answer below (15^1/5)^5
Answer:
15
Step-by-step explanation:
Via the law of exponents power of a power property we have:
[tex](a^b)^c=a^{bc}[/tex]
Therefore:
[tex](15^{1/5})^5=15^{\frac{1}{5} \times 5}=15^{\frac{5}{5}}=15^1=15[/tex]
~~~Brainliest Appreciated~~~
Which expression is equivalent to 1 -2/3 -3
Answer:
-8\3
Hope That Helps!
List 3 values that would make this inequality true 3n < 18
For [tex]\( n = 0, 1, \) and \( 2 \)[/tex], the inequality [tex]\( 3n < 18 \)[/tex] holds true. These are the values that satisfy the inequality.
To solve the inequality 3n < 18, we need to find values for ( n ) that make the inequality true. Here are three such values:
n = 0 , n = 1 , n = 2
Let's go through the detailed calculation step-by-step:
Starting with n = 0:
Plug n = 0 into the inequality:
[tex]\( 3(0) < 18 \)[/tex]
Simplify:
[tex]\( 0 < 18 \)[/tex]
Since ( 0 ) is less than ( 18 ), this statement is true.
Next, n = 1 :
Plug n = 1 into the inequality:
[tex]\( 3(1) < 18 \)[/tex]
Simplify:
[tex]\( 3 < 18 \)[/tex]
Again, this statement is true.
Finally, [tex]\( n = 2 \)[/tex]:
Plug [tex]\( n = 2 \)[/tex] into the inequality:
[tex]\( 3(2) < 18 \)[/tex]
Simplify:
[tex]\( 6 < 18 \)[/tex]
This statement is also true.
Therefore, for [tex]\( n = 0, 1, \) and \( 2 \)[/tex], the inequality [tex]\( 3n < 18 \)[/tex] holds true. These are the values that satisfy the inequality.
What is the pattern and the slope ? Please answer
Answer:
slope = -1/2
Step-by-step explanation:
To find the slope, we can use the formula
m = (y2-y1)/(x2-x1)
= (4-3)/(-2-0)
= 1 /-2
= -1/2
The slope is -1/2
Help me bois, ;w; IDK how to do this.
4 rectangles are 3 in x 2 in = 6 square inches each.
4 * 6 = 24 square inches.
2 squares are 3 in x 3 in = 9 square inches each
2 * 9 = 18 square inches.
Total area = 24 + 18 = 42 square inches.
Sophie pays m dollars to rent a car for the weekend. On the drive home, she buys $25 worth of gasoline. Her friend Melody pays for one-half the cost of the car rental only. Write an expression you could use to determine how much Sophie spent.
Answer:
25/2
Step-by-step explanation:
Answer:
a= 1/2m+25
Step-by-step explanation:
As the statement says that Sophie pays for one half of the cost of the car rental (m) and that she spent $25 on gasoline, the expression that could be used to determine the amount that she spent would be equal to the sum of one half of the cost of the car rental plus 25:
a= 1/2m+25
a= amount Sophie spent
m= cost of the car rental
the x-values in the table for f(x) were multiplied by -1 to create the table for g(x) what isbthe relationship between the graphs of the two functions
Answer: g(x) is the image of f(x)
Step-by-step explanation:
multiplying the x value by -1 means you reflect that point across y-axis, therefore, g(x) is the reflection of f(x) across y-axis.
Multiplying the x value by -1 means you reflect that point across y-axis,
therefore, g(x) is the reflection of f(x) across y-axis.
You are basically assigning the same y-value to the opposite x-values to make g(x). So, for the point (x, 31), on f(x), x is -2, but on g(x), x is 2. Thinking about this visually, you can imagine that this represents a reflection of f across the y-axis.
Here is the general rule for reflection across the y-axis: Given an equation y=f(x) y = f ( x ) , the new reflection equation of the reflected graph will be y=f(−x) y = f ( − x ).
The relationship between the graphs is Option 3 . they are reflection of each other across the y axis.
What is reflection equation?The reflection vector is generated by applying the equation R = U − 2NT(U · N), where N is the vertex normal transformed into eye space. The reflection equation used is the standard for computing the reflection vector given a surface normal and incident vector.
What is the formula for a reflection?The line of reflection is usually given in the form y = m x + b y = mx + b y=mx+by, equals, m, x, plus, b.
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