Answer:
See explanation
Step-by-step explanation:
3x/(-8)=-21/4
-3x/8=-21*8/4
-3x*8/8=-21*8/4 ==> multiply 8 on both sides to get rid of denominator
-3x=-21*2
-3x=-42
3x=42 ==> Multiply by -1 on both sides to get positive values on both sides
x=14
The value of a piece of factory equipment was $20,000 when it was purchased. During each 1 -year period after the equipment was purchased, the value of the equipment at the end of the period was 10% less than its value at the beginning of the period. Which of the following statements identifies the most appropriate type of function to model this scenario and provides a reason to support its appropriateness?
A- A linear function is appropriate to model this scenario because, at the end of each year after purchase, the value of the equipment was $10 less than its value 1 year before.
B- A linear function is appropriate to model this scenario because, at the end of each year after purchase, the value of the equipment was $2,000 less than its value 1 year before.
C- An exponential function is appropriate to model this scenario because, at the end of each year after purchase, the value of the equipment was 0.1 times its value 1 year before.
D- An exponential function is appropriate to model this scenario because, at the end of each year after purchase, the value of the equipment was 0.9 times its value 1 year before.
The correct option for the function in this problem is:
D- An exponential function is appropriate to model this scenario because, at the end of each year after purchase, the value of the equipment was 0.9 times its value 1 year before.
What is an exponential function?A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal.For this problem, during each 1 -year period after the equipment was purchased, the value of the equipment at the end of the period was 10% less than its value at the beginning of the period, hence r = 0.1 and the equation is:
[tex]A(t) = A(0)(1 - 0.1)^t[/tex]
[tex]A(t) = A(0)(0.9)^t[/tex]
Which means that option D is correct.
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The grid above shows the graph of the parent function f(x) = |x| and a translated functions graph.
Write the equation for the translated graph.
The equation of the translated graph is g(x) = |x + 2| + 1
How to write the equation of the translated graph?The parent function is given as
f(x)= |x|
From the graph, we can see that the parent function f(x) is translated as follows:
2 units left1 unit upThis is represented as
(x, y) = (x + 2, y + 1)
So, we have
g(x) = |x + 2| + 1
Hence, the equation of the translated graph is g(x) = |x + 2| + 1
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There are $13.30 worth of nickels and dimes in a piggy bank. There are 5 more nickels than dimes. How
many of each are in the piggy bank? You must solve this problem algebraically (no guess and check). Show
each step for full credit. Circle your final answer. (4 points)
Answer:
92 nickels87 dimesStep-by-step explanation:
You want the number of nickels and dimes that make up $13.30 when there are 5 more nickels than dimes.
SetupLet d represent the number of dimes. Then (d+5) is the number of nickels. The total value in cents is ...
10d +5(d+5) = 1330
SolutionSimplifying the equation, we get ...
15d +25 = 1330
15d = 1305 . . . . . . . . subtract 25
d = 87 . . . . . . . . . . . divide by 15
(d+5) = 92 . . . . . . the number of nickels
[tex]\boxed{\text{There are 92 nickels and 87 dimes in the piggy bank.}}[/tex]
the length of a rectangle is 6 m longer than its width. of the perimeter of the rectangle is 36 m, find its area
The length of a rectangle is 6 m longer than its width. of the perimeter of the rectangle is 36 m, its area is 72 m².
Any polygon's area is the amount of space it takes up or encloses. The amount of square units that make up the polygon. Because the area is a two-dimensional object, it has both length and width. Typically, the area is expressed in square meters, square feet, or square inches. Acres, hectares, and square kilometers are used to measure the size of larger shapes like cities and farms.
Let l be the length of the rectangle
And w be the width of the rectangle.
Given, l=6+w
Perimeter,p =36m
We know that, p= 2(l+w)
p =36=2(6+w+w)
36/2= 6 +2w
18-6=2w
w=6m
Therefore, l=6+w
l=12m
Area of rectangle= lw
A = 12×6
A=72 m².
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I need help with add and sub poly
Answe[tex]10c^{2} +5c+4[/tex]
Step-by-step explanation:
Step 1 -(((6•(c2))-2c)-1)+((22c2+7c)+5)
Step 2-(((2•3c2) - 2c) - 1) + (4c2 + 7c + 5)
in conclusion, you get [tex]10c^{2} +5c+4[/tex]
I hoped i have helped u have a wonderful day or night !
write an equation in slope intercept form for this line
Answer:
Step-by-step explanation:
Use the figure below to list the slopes m₁, m₂, m3, and m4 in order of decreasing size.
In decreasing size, the slopes of the linear functions are given as follows:
m4, m3, m2, m1.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.Regarding the slope, we have that:
Increasing lines have positive slopes.Decreasing lines have negative slopes.Hence, for the lines in this graph:
m4 and m3 are positive.m2 and m1 are negative.Then, we consider the intensity of growth/decay.
The pink line increases faster than the green line, meaning that it has a greater slope, that is, m4 > m3.The red line falls faster than the blue line, meaning that it's slope has a greater absolute value, but is less than m2, as they are negative, hence m2 > m1.Thus the list is given by:
m4, m3, m2, m1.
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what is 4 less than 1
Answer:
±3
Step-by-step explanation:
4 - 1 = 3
1 - 4 = -3
Either way you subtract them, the answer is still 3, whether negative or positive.
What is the area of the trapezoid shown? Show your work
The Area of the trapezoid in the image attached below is: 204 units².
How to Find the Area of a Trapezoid?To find the area of a trapezoid, the following formula is used:
Area of trapezoid = 1/2 × (a + b) × h, where h is the height of the trapezoid, and a and b are the length of the two parallel bases of the trapezoid.
Given the trapezoid in the image attached below, we have the following parameters:
a = 10
b = 24
h = 12
Area of trapezoid = 1/2 × (10 + 24) × 12
Area of trapezoid = 1/2 × (34) × 12
Area of trapezoid = 34 × 6
Area of trapezoid = 204 units²
Therefore, the Area of the trapezoid in the image attached below is: 204 units².
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hector paid $56 for 7 books what is the unit rate
Jordan jogs 6.9 miles each day. How many miles does he jog in 8 days
Answer:
55.2 miles
Step-by-step explanation:
6.9 x 8 = 55.2
Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day :)
Exercise
Squats
Crunches
Lunges
Curls
Time (h)
0.08
0.03
0.04
0.05
Javier likes to work out for 1 hour. If he
doesn't use the full hour on his exercises, he
runs on a treadmill for the remaining time. If
he completed 3 repetitions of each exercise,
how long did he run on the treadmill on
Monday? (Example 1)
By addition of all the exercise and substracting it from 1 hourJavier runs on treadmill on Monday is 0.40 hour.
Now According to the question javier completed 3 repetitions of each exercise so by multiplication time taken by javier to complete each exercise is as follow;
Squats = 0.8*3= 0.24 hour
Crunches = 0.03*3 = 0.09 hour
Lunges = 0.04*3 = 0.12 hour
curls = 0.05*3 = 0.15 hour
we can calculate total time taken to complete all exercise by Addition is,
0.24 + 0.09 + 0.12 + 0.15
0.60 hour
time taken on treadmill by javier;
1 hour - 0.60 hour
0.40 hour
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The elevation of a sunken ship is $-120$ feet. You are in a submarine at
an elevation that is $\frac{5}{8}$
of the ship’s elevation. What is your elevation?
The supplied statement indicates that the angle of elevation will be = -75 feet.
What is angle of elevation?The term angle of elevation refers to the angle between the horizontal and an object. The line of sight of an observer would be over the horizontal. The term angle of depression refers to the angle between the horizontal and an item. The line of sight of an observer would fall below the horizontal.
In arithmetic, how do you find elevation?"rise over run" is an easy-to-remember equation for calculating a change in elevation as a decimal, which means the rise (the change in vertical distance) divided by that of the run (the change in horizontal distance). As an example, suppose the increase is two and the run is six. So you'd multiply 2 by 6 (or 2/6) to get.
According to the given information:Given The elevation of a sunken ship = 120 feet
the elevation of a submarine = 5/8
So,
Your elevation will be given by employing the MULTIPLICATION OPERATION.
(5/8) x -120 feet
= -75 feet
The supplied statement indicates that the angle of elevation will be = -75 feet.
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a) Find The rate of change of f.
b) Express f in the form f(x) = ax + b
Answer:
this is hard , I suggest you see a tutor
Reverse the roles of the variables by solving for the indicated variable. Solve for t: w = uv + t
The subject of the function is t = w - v
How to solve the function?It should be noted that the function that's given is illustrated as:
w = uv + t
Subtract uv from both sides.
w - uv = uv + t - uv.
w - uv = t
Therefore, it can be seen that the subject of the function is t = w - v
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Two trains leave towns 900 miles apart at the same time and travel toward each other. One train travels 20mi/h slower than the other. If they meet in 6 hours, what is the rate of each train?
Answer:
Hello,
Step-by-step explanation:
The time they travel is t=6 hours
v is rate of the fastest train
v-2 the slower one.
v*t+(v-20)*t=900
2vt-20t=900
12v-120=900
12v=900+120
v=1020/12
v=85 (mi/h)
v-20=65 (mi/h)
Help I need the answer to this question
The Density of the given plank with dimensions is; 33.82 kg/m³
How to calculate the density of an Object?We are given;
Length of plank = 2.3 meters
Width of plank = 30 cm = 0.3 m
Height of Plank = 3 cm = 0.03 m
Mass of plank = 0.7 kg
Now, formula for density = mass/volume
Volume of the plank is gotten from the formula;
Volume = Length * width * height
V = 2.3 * 0.3 * 0.03
V = 0.0207 m³
Thus;
Density = 0.7/ 0.0207
Density = 33.82 kg/m³
Thus, we can conclude that the Density of the given plank with dimensions is 33.82 kg/m³
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(01.05 LC)
Which of the following is an equivalent form of the compound inequality -22 > -5x - 7≥-33?
O-5x-7<-22 and -5x - 72 -33
O-5x-7-22 and -5x - 72-33
O-5x > -22 and -7 ≥-33
O-5x-7<-22 and -5x - 7 ≤-33
The equivalent form of the compound inequality -22 > -5x - 7≥-33 is -22 > -5x - 7 and -5x - 7≥-33
Inequality:
A mathematical phrase in which the sides are not equal is referred to as being inequal. In essence, a comparison of any two values reveals the existence of an inequality when one of the values is less than, larger than, or equal to the value on the opposite side of the equation.
Given inequality is -22 > -5x - 7≥-33
The equivalent inequality is -22 > -5x - 7 and -5x - 7≥-33
Therefore,The equivalent form of the compound inequality -22 > -5x - 7≥-33 is -22 > -5x - 7 and -5x - 7≥-33.
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The function f(x) = + 9-3 is one-to-one and therefore invertible. Determine f1. Graph both f
and f-1, along with the identity function f(x) = x.
Answer: I hope this helps.
Step-by-step explanation:
Use the figure below to complete the following problem.
Given:
ZH=2x+60
LT=x+ 30
HALT is a
H
ZA =
O 30
045
O 60
The value of angle A is 60.
In Euclidean geometry, a parallelogram is a simple quadrilateral having two sets of parallel sides. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size.
We have the angles as:
∠H = 2x + 60
∠T = x + 30
Now, HALT is a parallelogram.
Therefore, angles H and T are supplementary.
So,
∠H + ∠T = 180
2x + 60 + x + 30 = 180
3x + 90 = 180
3x = 180 - 90
3x = 90
x = 90 / 3
x = 30
Substituting the value of x in the angles, we get:
∠H = 2x + 60
∠H = 2(30) + 60
∠H = 60 + 60 =120
∠T = x +30
∠T = 30 + 30
∠T = 60
Now, angles T and A are congruent angles.
Therefore, ∠T = ∠A
∠A = 60
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13. A large group of 30 people attended a hockey game. Each person ordered a hotdog or a slice of pizza from the concession stand. Hot dogs cost $2.50 each and a slice of pizza costs $3.25 each. If the total bill for these items was $81.75, how many of each type was purchased?
Answer:
21 hot dogs
9 pizza slices
Step-by-step explanation:
Given information:
Group = 30 peopleCost of a hot dog = $2.50Cost of a slice of pizza = $3.25Total bill = $81.75Define the variables:
Let x = the number of hot dogs purchased.Let y = the number of pizza slices purchased.Create two equations from the given information:
[tex]\textsf{Equation 1}: \quad x + y = 30[/tex]
[tex]\textsf{Equation 2}: \quad 2.5x+3.25y=81.75[/tex]
Rewrite Equation 1 to make x the subject:
[tex]\implies x=30-y[/tex]
Substitute this into Equation 2 and solve for x:
[tex]\implies 2.5(30-y)+3.25y=81.75[/tex]
[tex]\implies 75-2.5y+3.25y=81.75[/tex]
[tex]\implies 75+0.75y=81.75[/tex]
[tex]\implies 0.75y=6.75[/tex]
[tex]\implies y=9[/tex]
Substitute the found value of y into the rewritten form of Equation 1 and solve for x:
[tex]\implies x=30-9[/tex]
[tex]\implies x=21[/tex]
Solution
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Answer:
Number of hot dogs purchased = 21
Number of pizza slices purchased = 9
Step-by-step explanation:
Let the number of people buying hot dogs be represented by the variable H and the number of people buying pizzas be represented by the variable P
Since H hot dogs were purchased and each hot dog costs $2.50, total amount spent on hot dog purchase = $2.50H
Since P slices of pizza were purchased and each slice of pizza costs $3,25, total amount spent on hot dog purchase = $3,25P
Total amount spent (in $) = 2.50H + 3.25P and we are given that this total amount is $81.75
So we have an equation in two variables
2.50H + 3.25P = 81.75 (1)
We know the number of people is 30 and that should equal the number of hot dogs and pizza slices purchased
So
H + P = 30 (2)
Multiply Equation (2) on both sides by 2.50
==> 2.50(H + P) = 2.50 x 30
2.50H + 2.50P = 75 (3)
Subtract equation (3) from equation (1) to eliminate the H terms
(1) - (3):
2.50H + 3.25P - (2.50H + 2.50P) = 81.75 -75
2.50H + 3.25P - 2.50H - 2.50P = 6.75
Collect like terms and simplify
==> (2.50H -2.50H) + (3.25P - 2.50P) = 6.75
==> 0.75P = 6.75
Divide both sides by 0.75
==> 0.75P/0.75 = 6.75/0.75
==> P = 9
So number of people who bought pizza slices = 9
This is the same as the number of pizza slices that were bought
Substitute for P in Eq (2) H + P = 30
==> H + 9 = 30
Subtract 9 from both sides
==> H + 9 - 9 = 30 - 9
==> H = 21
So number of people who bought hot dogs = 21
This is the same as the number of hot dogs purchased
FREE BRAINLIEST!!! What is the slope of the line?
2
-2
-1/2
1/2
Answer:
i think its 2
Step-by-step explanation:
Answer: 2.
Step-by-step explanation: Because if you see where the dot of line is you will see that the dot is right next to number 2
8,282 in verbal form
Eight thousand two hundred and eighty two
Can someone tell me if this is right if not can u help me
Answer:
It is incorrect. It is supposed to be set at -8 to 9 but instead it is at -8 to 7.
The decimal should go up 2 places higher!
Step-by-step explanation:
3 to the 4th power minus -6 to the 2nd power
Answer:
45
Step-by-step explanation:
3 to the 4th power is the same as 3 x 3 x 3 x 3
3 x 3 x 3 x 3 = 81
-6 x -6 = 36 (a negative times a negative is always positive)
81 - 36 = 45
14. Find a counterexample for each of the following: a. If n is a natural number, then(n+5)/5 -n-1. b. If n is a natural number, then (n + 4)² = n² + 4².
n = 1 is a counterexample for both the given equations.
Here, we are given two equations, let us look at them one by one-
a. (n + 5) / 5 = n + 1
let us take n = 1
the, (1 + 5) / 5 = 1 + 1
6/ 5 = 2
This equation does not hold as 6/5 ≠ 2. Thus, n = 1 doesn't satisfy the given equation and hence is a counterexample.
b. (n + 4)² = n² + 4²
Let us take n = 1
(1 + 4)² = 1² + 4²
5² = 1 + 16
25 = 17
Again, this equation does not hold as 25 ≠ 17. Thus, n = 1 doesn't satisfy the given equation and hence is a counterexample.
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Marie ran 5.9 miles on Tuesday. This was 1.9 miles less than she ran on Monday. How many miles did she run on Monday?
Answer:
7.8 miles
Step-by-step explanation:
5.9 + 1.9 = 7.8miles
Sherry will mail a square
photo to her grandma.
The area of the photo is
about 71.4 square inches.
All of Sherry's envelopes
are perfect squares.
What's the length of one
side of the smallest
envelope she can use?
Answer:
Take the root
Step-by-step explanation:
Area of the square equal
[tex] {x}^{2} [/tex]
Then the side length of the pictures equal
[tex] \sqrt{71.4 } [/tex]
The result will be 8.44
P=2(x+y) Solve for y
[tex] \bf \implies \: y \: = \frac{1}{2} p - x[/tex]
Step-by-step explanation:Let's solve for yp = 2(x + y)p = 2x + 2yp - 2x = 2y2y = p - 2x[tex] \bf \frac{ \cancel{2}y}{ \cancel{2}} = \frac{p \: - \: 2x}{2} [/tex][tex]y = \frac{p}{2} - \frac{ \cancel{2}x}{ \cancel{2} }[/tex][tex] \boxed{y = \frac{1}{2}p - x} \: \bf \mathfrak {ans}[/tex]3/2(6x+2)=-3(x-1) need help with this
Answer:
x=0
Step-by-step explanation:
:)
Answer:
[tex]{ \tt{ \frac{3}{2}(6x + 2) = - 3(x - 1) }} \\ \\ { \tt{3(3x + 1) = - 3(x - 1)}} \\ { \tt{3x + 1 = - (x - 1)}} \\ { \tt{3x + 1 = - x + 1}} \\ { \tt{3x + x = 0}} \\ { \tt{x = 0}}[/tex]