[tex]\text{Given that,}\\\\y = -\dfrac 4{15} x + 24\\\\\text{When x = 120,}\\\\y = -\dfrac 4{15} (120) + 24\\\\\implies y = - \dfrac{480}{15} +24\\\\\implies y=-32+24 \\\\\implies y = -8[/tex]
Help please
Simplify the difference quotient (f(x + h) − f(x) )/h if h ≠ 0.
f(x) = x2 + 38
Answer:
2x + h
Step-by-step explanation:
[tex]\frac{f(x+h)-f(x)}{h}[/tex]
= [tex]\frac{(x+h)^2+38-(x^2+38)}{h}[/tex]
= [tex]\frac{x^2+2hx+h^2+38-x^2-38}{h}[/tex]
= [tex]\frac{2hx+h^2}{h}[/tex]
= [tex]\frac{h(2x+h)}{h}[/tex] ← cancel h on numerator/ denominator
= 2x + h
A car travels 220 miles in 3 hours 20 minutes. What is its average speed?
Answer:
66 miles per hour
Step-by-step explanation:
average speed = distance / time
distance : 220 miles
time : 3 hours 20 minutes or 3.33 hours
220 miles / 3.33 hours = 66 miles per hour
Given each function and domain, find the range values. y=3/5x+2; domain: {-10,0,5}
Given the function
[tex]y=\dfrac{3}{5}x+2[/tex]
and its domain [tex]\{-10,0,5\}[/tex], its range is [tex]\{-4,2,5\}[/tex]
The domain of a function is the set of all possible values that we can input to the function.
The range of a function is the set of all possible values that a function can output.
For the function
[tex]y=\dfrac{3}{5}x+2[/tex]
if the domain is the set [tex]\{-10,0,5\}[/tex], we can get the range by substituting each value in the domain into the function. The resulting set of values gives the range of the function.
The range will then be
[tex]\left\{\dfrac{3}{5}(-10)+2, \dfrac{3}{5}(0)+2,\dfrac{3}{5}(5)+2\right\}\\\\=\left\{3(-2)+2, 3(0)+2, 3(1)+2\right\}\\\\=\left\{-4, 2, 5\right\}\\\\[/tex]
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Which graph best represents the solution to this system of inequalities?
A.
B.
C.
D.
Answer:
letter A po
Step-by-step explanation:
thanks for brain less
Every eight minutes the river raft can load 88 passengers what is the loading rate for passengers per minute
Answer:
11 passengers per minute.
Step-by-step explanation:
To find how many passengers board the boat in a minute, you'd have to divide 88 with 8.
88/8 = 11
To check:
11 passengers per min x 8 mins = 88 passengers.
what is the solution to the equation 4(x - 3) - 8 = 16?
Step-by-step explanation:
4(x-3)-8=16
4x-12-8=16
4x-20=16
4x-20+20=16+20
add
4x=36
divide both
4x/4 36/4
Simplify
x = 9
Find sum of arithmetic series where a1 = 7, n=31, nth a =127
Answer:
Sum of arithmetic series is [tex]2077[/tex]
Step-by-step explanation:
We have [tex]n[/tex]th term of arithmetic sequence
[tex]a+(n-1)d[/tex]
Here
[tex]a+(n-1)d=127\\\\7+(31-1)d=127\\\\d=\frac{120}{30} \\\\=4[/tex]
Sum of arithmetic sequence [tex]=\frac{n}{2} (2a+(n-1)d)[/tex]
[tex]=\frac{31}{2} (2\times7+(31-1)4)\\\\=\frac{31}{2} (14+120)\\\\=31\times67\\\\=2077[/tex]
Answer:
The sum of arithmetic series is 2077.
Step-by-step explanation:
Solution :
Here we have provided that :
»» [tex]\rm{a_1}[/tex] = 1»» [tex]\rm{n}[/tex] = 31»» [tex]\rm{a_n}[/tex] = 127We need to find :
»» The sum of arithmetic series.Here's the required formula to find the sum of arithmetic series :
[tex]\longrightarrow{\pmb{\sf S = \dfrac{n}{2} \Big(a_1 + a_n \Big)}}[/tex]
Substituting all the given values in the formula to find the sum of arithmetic series :
[tex]{\longrightarrow{\sf S = \dfrac{n}{2} \Big(a_1 + a_n \Big)}}[/tex]
[tex]{\longrightarrow{\sf S = \dfrac{31}{2} \Big(7 + 127 \Big)}}[/tex]
[tex]{\longrightarrow{\sf S = \dfrac{31}{2} \Big(134 \Big)}}[/tex]
[tex]{\longrightarrow{\sf S = \dfrac{31}{2} \times 134 }}[/tex]
[tex]{\longrightarrow{\sf S = \dfrac{31}{\cancel{2}} \times \cancel{134 }}}[/tex]
[tex]{\longrightarrow{\sf S = 31 \times 67}}[/tex]
[tex]{\longrightarrow{\sf S = 2077}}[/tex]
[tex]\star \: {\underline{\boxed{\sf{\red{S = 2077}}}}}[/tex]
Hence, the sum of arithmetic series is 2077.
[tex]\rule{300}{1.5}[/tex]
A store owner bought 15001500 pencils at \$0.10$0.10 each. If he sells them for \$0.25$0.25 each, how many of them must he sell to make a profit of exactly \$100.00$100.00
Based on the information given, the number of pencils that should be sold will be 1000 pencils.
Let the number that should be sold be x.
A store owner bought 1500 pencils at $0.10 each. Therefore, the cost price will be:
= 1500 × $0.10 = $150
Profit = Selling price - Cost price
100 = 0.25x - 150
0.25x = 100 + 150
0.25x = 250
x = 250/0.25
x = 1000
Therefore, 1000 pencils should be sold.
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y³ written in expanded form is
A recursive rule for a geometric sequence is
a1 = 9; an = 2/3 (an−1)
What is the iterative rule for this sequence?
A.) an = 9 • (2/3)^n
B.) an = 2/3 • 9^n
C.) an = 9 • (2/3)^n-1
Answer:
C. [tex]a_n=(9)(\frac{2}{3})^{n-1}[/tex]
Step-by-step explanation:
Iterative geometric sequence:
[tex]a_n=a_1x^{n-1}[/tex]
Recursive geometric sequence:
[tex]a_n=xa_{n-1}[/tex]
The equations are very similar and you only really need to rearrange it. The factor (2/3) and the first term (9) are given, so you can write the iterative equation:
[tex]a_n=(9)(\frac{2}{3})^{n-1}[/tex]
And so the answer is C.
Sketch the graph of each linear inequality
Answer:
hope you can see these, the red graph is problem 3 and the blue graph is problem 5 :)
The sum of a number and six is 22. What is the number?
Answer:
16
Step-by-step explanation:
22-6=16 16+6=22
hope this helps! :)
5 What rate of interest is paid on a deposit of $2000 which earns $400
interest in 5 years?
Answer:
4%
Step-by-step explanation:
Given
I = 400P = 2000R = ?T = 5 yearsFormula
I = PRTSolving.
I = PRT400 = 2,000 × R × 5400 = 10,000 × R400 / 10,000 = R0.04 = RChange 0.04 to percent
0.04 × 100 = 4%Answer:
4%Please answer!!!!!!!!!!!!!! 25 PTS!
Answer:
b
Step-by-step explanation:
b
hi pls help me solve this
Answer:
-23.33
Step-by-step explanation:
C = 5/9 (F - 32)
C = 5/9 (-10 - 32)
C = 5/9 (-42)
C = -23.33
A triangle has vertices at (1, 1), (1, 4), and (−3, 4).
What are the coordinates of the circumcenter?
Answer:
(-1, 2.5) is correct
Step-by-step explanation:
Given
Let A(1, 1)
Let B(1, 4)
Let C(-3, 4)
Let coordinates of the circumcenter is (x, y)
Using distance formula put the y value in this equation
So the coordinates of the circumcenter is (1, 2.5)
Step-by-step explanation:
Sorry it's so long.
Rita’s earnings are based on how many hours she works. Rita worked 22 hours and earned $379.50. What would Rita earn for working 52 hours?
Rita will earn $897 for working 52 hours.
Word problems in mathematics are mathematical operations that are applied to solve real life cases.
From the information given:
Rita's earnings are dependent on the hours she worksIf Rita worked for 22 hours, she earns $379.50
Now, if Rita worked for 52 hours, the amount Rita will earn can be expressed by using the relation:
[tex]\mathbf{= \dfrac{52 \ hours \times \$379.50}{22 \ hours} }[/tex]
= $897
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2(1+a) * 5(1+a)
help u u want to help or else continue helping
Step-by-step explanation:
We simply multiply what there is to multiply:
10(1+a)^2 = 10a^2 + 20a + 10
Use the factorial operation to evaluate 4!
4×3×2×1
4+3+2+1
4.321
4-3-2-1
Answer:
4x3x2x1=25
Step-by-step explanation:
hope this helps :)
Blake gives piano lessons in the evenings. He earns $20 for each piano lesson and has between 0 and 6 lessons each evening. The amount he earns in an evening depends on the number of lessons he gives. What is the range of this relation?.
The range of the relation will be expressed as 0 ≤ g(x) ≤ 120
Let the number of lessons he gives be xIf he earns $20 for each piano lesson, the amount he will earn on x lessons will be $20xWriting this as a function will give:
g(x) = 20xwhere g(x) is the range of the relation.
If he has between 0 and 6 lessons each evening, the corresponding range at x = 0 and x = 6 is given as;
g(0) = 20(0) = 0g(6) = 20(6) = 120Therefore the range of the relation will be expressed as 0 ≤ g(x) ≤ 120
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Answer: {0, 20, 40, 60, 80, 100, 120}
Step-by-step explanation: Remember we only use inequality signs for continuous relations with an infinite amount of values or data points or values or points. When we're given a set finite amount of data points we use brackets for this data because it is a discrete relation.
And for this problem we're looking for the range of the relation and recall the range is the dependent values or variables that depend on the domain or independent variables. The amount of money he earns depends on the amount of hours he works. Hence, the range is {0, 20, 40, 60, 80, 100, 120} the amount of possible money he can earn.
In this diagram shown,
PQRS is a rectangle
Answer:
In the figure, PQRS is a rectangle. If the shaded area is 72 sq. cm,...In the figure, PQRS is a rectangle. If the shaded area is 72 sq. cm, find h
EXPLANATION
From the diagram, PQRS is a rectangle
Area of shaded part = 72sq.cm
But 72 = 3h - 4 + 6h - 4 + 4h
= 72 - 16h - 8
= 16h - 72 + 8
=16h = 80
h = 80/16
= 5cm
x-2/7=8
Give your answer in improper fraction
y=1.5x+8 which represents the equation when solved for x?
[tex]y=1.5x+8\\\\\implies 1.5x = y-8\\\\\implies x = \dfrac{y-8}{1.5}\\\\\implies x = \dfrac{y-8}{\tfrac 32}}\\\\\implies x = \dfrac{2(y-8)}{3}\\\\\implies x = \dfrac 23 y- \dfrac{16}3[/tex]
How to rationalize the denominator that is a radical.
Answer:
Option B is the correct answer, 3√2
What is the area of a rectangle with the following measurements:
Answer:
24x^5
Step-by-step explanation:
3 x 8 = 24
x multiplied by x^4 = x^5
(the exponents add to each other when multiplied)
Please help me please please please
Answer:
Perpendicular bisector
Step-by-step explanation:
Help please, 9th grade math.
Answer:
table k
Step-by-step explanation:
4:3 ratio
6x+3y=-3 how to graph it need answers quick
Answer:
Equation in slope intercept form: y = -2x -1
Step-by-step explanation:
First you must convert this equation from standard form to slope intercept form (y=mx+b).
Subtract 6x on both sides to get 3y = -6x - 3. Then divide by 3 on both sides to get y = -2x - 1.
Now to graph:
First we will plot the y-intercept, which will be (0,-1). The point will be on the y-axis, since that's the point in which the line will cross.
Next we will go down 2 units and over to the right 1 unit, until we get to the next point.
(Picture is attached above for your convenience⤴⤴⤴)
Hope this helps you :)
rectangle A and B are identical. each has a perimeter of 40cm. they are put together to make a new rectangle. the perimeter of the new rectangle is 68cm. work out the length and width of rectangle A.
Answer:
6 cm by 14 cm
Step-by-step explanation:
The perimeter of the joined figure will be the sum of the perimeters of rectangles A and B, less the lengths of the sides that are joined. The two joined sides have a total length of ...
(40 cm) +(40 cm) -(68 cm) = 12 cm
Then the length of the joined sides is 6 cm. The length of the other side of the rectangle is the difference between half the perimeter and this, or ...
(40 cm)/2 -6 cm = 14 cm
The length and width of rectangles A and B are 14 cm and 6 cm. When put together, they are joined on the 6 cm side.
Sally saved 65% of her pay check. If she made $500, how much did she save?
Answer: 325 dollars
Step-by-step explanation:
In order to find out a percentage of somethin, you can simply multiply and divide
[tex]500*65=32500[/tex]
32500÷100= 325