Answer:
134 hamburgers
Step-by-step explanation:
Let H = # of hamburgers
# of cheeseburgers = 2H
H + 2H = 402
3H = 402
H = 402/3
H = 134
verify x+(y+z) =(x+y) +z, when x=-4/15, y=-4/5and z =17/8
Answer:
The equality is true
Step-by-step explanation:
x+(y+z)=(x+y)+z
x+(y+z)=(x+y)+zwhen we plug in -4/15 for x,-4/5 for y
x+(y+z)=(x+y)+zwhen we plug in -4/15 for x,-4/5 for yand 17/8 for z,we get
x+(y+z)=(x+y)+zwhen we plug in -4/15 for x,-4/5 for yand 17/8 for z,we get-4/15+(-4/5+17/8)=(-4/15+-4/5)+17/8
x+(y+z)=(x+y)+zwhen we plug in -4/15 for x,-4/5 for yand 17/8 for z,we get-4/15+(-4/5+17/8)=(-4/15+-4/5)+17/817/24=17/24
x+(y+z)=(x+y)+zwhen we plug in -4/15 for x,-4/5 for yand 17/8 for z,we get-4/15+(-4/5+17/8)=(-4/15+-4/5)+17/817/24=17/24so this equality is true
Suppose that $575.75 is invested in a savings account with an APR of 12% compounded monthly. What is the future value of the account in 5 years?
Answer:
FV= $1,045.96
Step-by-step explanation:
Giving the following information:
Initial investment (PV)= $575.75
Number of periods (n)= 15*5= 60 months
Interest rate (i)= 0.12 / 12= 0.01
To calculate the future value (FV), we need to use the following formula:
FV= PV*(1+i)^n
FV= 575.75*(1.01^60)
FV= $1,045.96
Can somebody help me!!??
Answer:
D) 8
Step-by-step explanation:
We're looking for [tex]x[/tex], which means the 7x and 5x will have the SAME x.
7(8) = 56
For the C corner, it is cornered as a 90 degree angle, so that means the (7x) + 34 degrees NEEDS to equal 90.
7(8) = 56 + 34 = 90!!
Now we have to see if 5(8) is correct
5(8) = 40 + 50 [The degree mark] = WHICH EQUALS 90 TOO..
Therefore, the answer is D) 8
A student saves $15 per week toward the purchase of a guitar. Her grandmother gives her $50 to help her reach her goal. Which function can be used to find the amount in dollars the student has saved after x weeks?
y=15x+50 it should look something like that
Which of the following sets of numbers could not represent the three sides of a right
triangle?
Answer:
{48, 64, 81}
Step-by-step explanation:
Seats in a theater are curved from the front row to the back. The front row has 10 chairs, the second has 16 and the third has 22, and so on.
A. Write a recursive rule for this series
B. Write an explicit rule for this series
C. Using the explicit formula, find the number of chairs in row 5
D. The auditorium can hold 17 rows of chairs. Write a sigma notation for this series, and then use either series formula to calculate how many chairs can fit in the auditorium
Answer:
The first term is 10.
The second term is 16
The third term is 22.
We can see that the first term plus 6, is:
10 + 6 = 16
Then the first term plus 6 is equal to the second term.
And the second term plus 6 is:
16 + 6 = 22
Then the second term plus 6 is equal to the third term.
A) As we already found, the recursive rule is:
Aₙ = Aₙ₋₁ + 6
B) The explicit rule is:
Aₙ = A₁ + (n - 1)*6
Such that A1 is the first term, in this case A₁ = 10
Then:
Aₙ = 10 + (n - 1)*6
C)
Now we want to find A₅, then:
A₅ = 10 + (5 - 1)*6 = 34
There are 34 chairs in row 5.
D)
Here we have 17 rows, then we can have 17 terms, this means that the total number of chairs will be:
C = A₀ + A₁ + ... + A₁₆
This summation can be written as:
∑ 10 + (n - 1)*6 such that n goes from 0 to 16.
The formula for the sum of the first N terms of a sum like this is:
S(N) = (N)*(A₁ + Aₙ)/2
Then the sum of the 17 rows gives:
S(17) = 17*(10 + (10 + (17 - 1)*6)/2 = 986 chairs.
There are total 986 chairs in the considered auditorium and there are 34 chairs in the fifth row.
The recursive rule for this series is: [tex]T_n = T_{n-1} + 6[/tex]The explicit rule for this series is: [tex]T_n = 6n + 4[/tex]What is recursive rule?A rule defined such that its definition includes itself.
Example: [tex]F(x) = F(x-1) + c[/tex] is one such recursive rule.
For this case, we're provided that:
Seats in rows are 10 in front, 16 in second, 22 in third, and so on.
10 , 16 , 22 , .....
16 - 10 = 6
22 - 16 = 6
...
So consecutive difference is 6
If we take [tex]T_i[/tex] as ith term of the series then:
[tex]T_2 - T_1 = 6\\T_3 - T_2 = 6\\T_4 - T_3 = 6 \\T_5 - T_4 = 6\\\cdots\\T_{n} - T_{n-1} = 6[/tex]
Thus, the recursive rule for the given series is [tex]T_{n} - T_{n-1} = 6[/tex] or [tex]T_n = T_{n-1} + 6[/tex]
From this recursive rule, we can deduce the explicit formula as:
[tex]T_n = T_{n-1} + 6\\T_n = T_{n-2} + 6 + 6\\\cdots\\T_n = T_{n-k} + k \times 6\\T_n = T_1 + 6(n-1)\\T_n = 10 + 6(n-1) \: \rm (as \: T_1 = 10)\\[/tex]
Thus, the explicit rule for this series is [tex]T_n = 10 + 6(n-1)[/tex]
For 5th row, putting n = 5 gives us:
[tex]T_n = 10 + 6(n-1) = 6n + 4\\T_5 = 6(5) + 4 = 34[/tex]
If the auditorium has 17 rows, then total chairs are:
[tex]T = T_1 + T_2 + \cdots + T_{17} = \sum_{n=1}^{17} T_n\\\\T = \sum_{n=1}^{17} (10 + 6(n-1))\\\\T = \sum_{n=1}^{17} (6n + 4)\\\\T = 6\sum_{n=1}^{17} n + \sum_{n=1}^{17}4 = 6\sum_{n=1}^{17} n + 4 \times 17\\\\T = 6\left( \dfrac{17(18)}{2}\right) + 68 = 918 + 68\\\\T = 986[/tex]
(it is because [tex]\sum_{k=1}^n k = 1 + 2 + \cdots + n = \dfrac{n(n+1)}{2}[/tex] )
Thus, there are total 986 chairs in the considered auditorium. There are 34 chairs in the fifth row. The recursive rule for this series is: [tex]T_n = T_{n-1} + 6[/tex] The explicit rule for this series is: [tex]T_n = 6n + 4[/tex].
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The distance y (in miles) that a truck travels on x gallons of gasoline is represented by the equation y=18x The graph shows the distance that a car travels. Which vehicle gets the better gas mileage?
Answer:
Car M:
50.4/2 = 25.2
car M uses up 1 gallon every 25.2 miles
Car P:
Just from the graph, you can see that it uses up 1 gallon every 30 miles
The two graphs vary the /miles slightly but it is around their zones of 25.2 and 30. It varies slightly because the cars may be traveling at a fast speed or slower speed thus using up more or less fuel by the time they've reached the recorded distances on the graphs.
Answer:
Step-by-step explanation:
1. El ayuntamiento de un pueblo quiere asfaltar
una plaza circular que tiene en el centro una
fuente, también circular, para celebrar allí con-
ciertos de música a lo largo del año. Si la fuente
tiene un diámetro de 4 m y la plaza, uno de 16
m, ¿cual será el área de la región por asfaltar?
What is the value of y when
IN
The value of y varies directly with x. When y = 75, x =
x is 2
A 84
B 337
С
- 162
D 168
4
В.
Answer:
I think that the answer is B , 337/5 i mean .
Good luck ^^
Given f(x)=3x^2+kx+9, and the remainder when f(x) is divided by x-3 is 6, then what is the value of k?
Answer:
k = - 10
Step-by-step explanation:
6=9+3(k+9)
3(k+9)=-3
k+9= -1
k= -10
The value of k is -10.
What is Division?Division is one of the operation in mathematics where number is divided into equal parts as that of a definite number.
Given a function 3x² + kx + 9.
Divide the function with x - 3.
Do the long division process.
After doing the long division,
(3x² + kx + 9) / (x - 3), we get the quotient as 3x + (k + 9) and the remainder as 9 + 3(k + 9).
9 + 3(k + 9) = 6
3(k + 9) = -3
k + 9 = -1
k = -1 - 9
k = -10
Hence the number k has the value -10.
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Reflex angle of 95 degrees
Step-by-step explanation:
a a reflex angle is more than 180° but less than 360° so in this case the reference angle of 95 degrees we are going to take 360° - 95 degrees to get255°
How do you find the greatest common denominator, when comparing two numbers? Explain your thought process, in the example I provided. What is the greatest common Denominator for the numbers 20 and 40. Explain each step you do. Your answer will start with these words. "How to find the the greatest common denominator between 20 and 40?
Answer:
20 is the greatest common denominator. You can find this by listing the factors of each number. The highest number that can fit into both individual numbers is the common denominator. Since 40 is just 20 doubled, and 20 is just 20 once, it fits into both numbers and is also the highest number that can fit.
A trapezoid was broken into a rectangle and a triangle. What is the length, b, of the base of the triangle?
O 2 cm
O 4 cm
O 6 cm
O 8 cm
Answer:
2
Step-by-step explanation:
because if 10 is the whole line of the base at the bottom of the trapezoid
and 8 is the whole top 10-8=2
Ben opened a savings
account with $75,
Every week he added
$20 more. Write on
equation to model this
situation.
Answer:
The equation would be y = 75 + 20x
Help pleaseeeeeeeeeee
Answer:
d
Step-by-step explanation:
A cylindrical soup can has a radius of 1.9 in. and is 5.9 in. tall. Find the volume of the can.
Answer:
66.93 in^3
Step-by-step explanation:
Volume = πr^2h
=> V = 22/7*(1.9)^2*5.9 = 66.93 in^3
2. Including the outlier, what is the Q1, Q3, and IQR of the data set?
id
A.Q1 = 29; Q3 = 29; IQR = 2
B.Q1 = 27; Q3 = 29; IQR = 28
C.Q1 = 28; Q3 = 27; IQR = 1
D.Q1 = 27; Q3 = 29; IQR = 2
2 hot
The dimensions of two square pyramids formed of sand are shown. How much more sand is in the pyramid with the greater volume?
Answer:
The pyramid with the greater volume has 5in^3 more sand
Step-by-step explanation:
Given
Pyramid A
[tex]B = 25in^2[/tex] -- Base Area
[tex]h = 9in[/tex] --- height
Pyramid B
[tex]B = 30in^2[/tex]
[tex]h = 7in[/tex]
See attachment for pyramids
The volume of a square pyramid is:
[tex]V = \frac{1}{3}Bh[/tex]
First, calculate the volume of pyramid A
[tex]V_A = \frac{1}{3} * 25in^2 * 9in[/tex]
[tex]V_A = 25in^2 * 3in[/tex]
[tex]V_A = 75in^3[/tex]
Next, the volume of pyramid B
[tex]V_B = \frac{1}{3} * 30in^2 * 7in[/tex]
[tex]V_B = 10in^2 * 7in[/tex]
[tex]V_B = 70in^3[/tex]
To calculate how much more sand the greater pyramid has, we simply calculate the absolute difference (d) between their volumes
[tex]d = |V_B - V_A|[/tex]
[tex]d = |70in^3 - 75in^3|[/tex]
[tex]d = |- 5in^3|[/tex]
[tex]d = 5in^3[/tex]
A line passes through the points (-1, 10) and (3, 2). Which shows the graph of this line?
8
8
4
2
- 108
2
46
8 10
X
12
-8
-10
10
6
Answer:
C
Step-by-step explanation:
EDGE 2021
In the diagram, point K is a point of tangency, MK = 720, and MN = 648. What is the radius of J
A. 76
B. 70
C. 72
D. 64
The radius of J is 76. so option A is correct.
What is the Pythagoras theorem?The Pythagoras theorem states that the square of the longest side must be equal to the sum of the square of the other two sides in a right-angle triangle.
|AC|^2 = |AB|^2 + |BC|^2
By applying Pythagoras theorem In right triangle,
(Hypotenuse)² = (Leg 1)² + (Leg 2)²
(720 + J)² = (648)² + J²
518400+ J² + 1440J = 419904 + J²
1440J = 518400- 419904
J = 76
Therefore, J = 76 units is the answer.
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please help.I don’t understand
Answer:
y=13 degrees
Step-by-step explanation:
This is an isosceles triangle, we know this because NO and NM are equal.
In an isosceles triangle, the base angles are congruent. In this case, they are angle NOM and angle NMO.
We also know that the sum of the interior angles of a triangle are equal to 180.
With this information, we can make an equation by gathering all the interior angles:
8y+2(3y-1)=180
Solve for y.
8y+6y-2=180
14y-2=180
14y=182
y=13
Mrs. Dawson is researching what it would cost to order flower arrangements for a fancy party. She wants one large centerpiece for the head table, and smaller arrangements for the smaller tables. Hampton Florist charges $12 for each smaller arrangement, plus $27 for the large centerpiece. Farid's Flowers, in contrast, charges $32 for the large centerpiece and $7 per arrangement for the rest. If Mrs. Dawson orders a certain number of small arrangements, the cost will be the same at either flower shop. How many small arrangements would that be? What would the total cost be? If Mrs. Dawson orders small arrangements, it will cost $ at either shop.
The number of flower arrangement and the costs are illustrations of linear equation
If Mrs. Dawson orders 1 small arrangement, it will cost $39 at either shop.
How to determine the number of small arrangements?Represent the number of small arrangements with x, and the total cost with y.
Using the data from the question, we have:
Hampton Florist: y = 12x + 27.
Farid's Flowers: y = 32 + 7x
When both flower arrangements cost the same, we have the following equation
12x + 27 = 32 + 7x
Collect like terms
12x - 7x = 32 - 27
Evaluate the like terms
5x = 5
Divide both sides by 5
x = 1
This means that 1 small arrangement would cost the same in both flower shops
How to determine the total cost?In (a), we have:
y = 12x + 27.
Substitute 1 for x
y = 12(1) + 27
y = 39
Hence, if Mrs. Dawson orders 1 small arrangement, it will cost $39 at either shop.
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AHH HELP ME PLS
Choose the values of x that are solutions to the inequality 5 <,
Select all that apply
Ax=2
= 6
E *=-7
F1 = 10
Answer:
x = 5
x = 6
x = 10
Step-by-step explanation:
NOTE: IT HAS TO BE MORE THAN 5 OR EQUAL TO 5
Please mark as brainliest
Have a great day, be safe and healthy
Thank u
XD
Need help with this question
Answer:
Function A rate = 5/1
Function B rate = -4.5
Function A because its rate is positive while Function B's rate is negative
help with this please lol
Answer:
x = 107
Step-by-step explanation:
44+29+107=180
a triangle equals 180 with all the degrees added together :)
What is the ratio of yellow butterflies to total butterflies? Choose the correct option
Answer:2/3
Step-by-step explanation: there is 2 yellow out of 3 butterfiles
3 Jazmin is mailing two packages. One package weighs 3 pounds, and the other package weighs 20 ounces. What is the total weight of both packages? (1 pound = 16 ounces)
Answer:
68oz
Step-by-step explanation:
1) 3lbs x 16oz = 48
Now we know 3lbs is 48oz. since one pound is 16 ounces, 3 pounds is 48 ounces.
2) 48 + 20 = 68oz
3) The total weight of both packages is 68 ounces.
Jesus loves ya, have a great day!
---------------------
John 8:12 - When Jesus spoke again to the people, he said, "I am the light of the world. Whoever follows me will never walk in darkness, but will have the light of life."
Solve 5/4=x/12.
x=
Please help!
Answer: x=15
Step-by-step explanation:Step 1: Cross-multiply.
5
4
=
x
12
(5)*(12)=x*(4)
60=4x
Step 2: Flip the equation.
4x=60
Step 3: Divide both sides by 4.
4x
4
=
60
4
x=15
Answer:
x=15
You are saving money to buy a car. You put $2500 in a savings account that pays 4% annual interest compounded monthly (hint n = 12). A. Write a function that models the amount of the money in the account over time. B. Find the cost of the car after 10 years.
Answer:
FV= $3,726.93
Step-by-step explanation:
Giving the following information:
Initial investment (PV)= $2,500
Interest rate (i)= 0.04/12= 0.003333 monthly
Number of periods (n)= x months
To calculate the future value giving any number of months, we need to use the following formula:
FV= PV*(1 + i)^n
For 10 years:
n=10*12= 120 months
FV= 2,500*(1.003333^120)
FV= $3,726.93
At 2 pm, the temperature was -9 degrees. If the temperature drops 8 degrees, what is the new temperature?
Answer:
At 2 pm, the temperature was -9 degrees. If the temperature drops 8 degrees, what is the new temperature?
Step-by-step explanation:
sorry I can't delete it
Answer:
-15
Step-by-step explanation:
-7 Dropping 8 would be -15 because 8+7 is 15 but its negative so its -15 (im terrible at explaining)