The equations which have the same value of x as "three-fifth(30x minus 15 ) 72 are "18 x minus 9 = 72", "3 (6 x minus 3) = 72", and "x = 4.5".
What is an equation?Two or more expressions with an equal sign are defined as an equation.
The given equation is Three-fifths(30x - 15) = 72.
Simplify the equation as follows:
Three-fifths(30x - 15) = 72
3/5(30x - 15) = 72
18x - 9 = 72
Which is equivalent to "18x minus 9 = 72".
Solve for the value of x:
18x -9 = 72
18x = 72 + 9
18x = 81
x = 81/18
x = 27/6
x = 4.5
Now, solve the equation in the first option:
18x - 15 = 72
18x = 87
x = 4.83
Solve the equation in the second option:
50x - 25 = 72
50x = 97
x = 1.94
The third equation is already shown to be equivalent to the given equation.
The solution to the fourth equation is:
3(6x - 3) = 72
18x -9 =72
Which is the same as the given equation.
The last equation is x = 4.5
Hence, the equations which have the same value of x as "three-fifth(30x minus 15 ) 72 are "18 x minus 9 = 72", "3 (6 x minus 3) = 72", and "x = 4.5".
Learn more about equations here:
https://brainly.com/question/10413253
#SPJ1
A toy rocket is shot vertically into the air from a launching pad 7 feet above the ground with an initial velocity of 40 feet per second. The height h, in feet, of the rocket above the ground at t seconds after launch is given by the function h(t) = -16t²+40t+7. How long will it take the rocket to reach its maximum height? What is the maximum height?
The rocket reaches its maximum height at ___ second(s) after launch.
(Simplify your answer.)
The maximum height of 32 feet is reached after 1.25 second of flight by the rocket
How to determine the time to reach the maximum heightThe function is given as
h(t) = -16t² + 40t + 7
Differentiate the function and set it to 0
-32t + 40 = 0
Add 32t to both sides
32t = 40
Divide both sides by 32
t = 1.25
Hence, the time is 1.25 seconds
How to determine the maximum heightIn part (a) of this solution, we have
t = 1.25
Recall that
h(t) = -16t² + 40t + 7
So, we have
h(1.25) = -16(1.25)² + 40(1.25) + 7
This gives
h(1.25) = 32
Hence, the maximum height is 32 feet
Read more about height functions at
https://brainly.com/question/10837575
#SPJ1
Question 12(Multiple Choice Worth 2 points)
(Writing Two-Step Equations MC)
A new gaming chair costs $455.95. You have already saved $136.45 and earn $35.50 each week babysitting. Write and solve an equation to determine how many weeks, w, you must babysit to earn enough money to buy the new gaming chair.
35.5 + 136.45w = 455.95; w = 9
35.5w + 136.45 = 455.95; w = 9
35.5w − 136.45 = 455.95; w = 17
35.5w − 455.95 = 136.45; w = 17
Answer:
(b) 35.5w + 136.45 = 455.95; w = 9
Step-by-step explanation:
You want an equation to determine how many weeks, w, you must babysit to earn $455.95 at the rate of $35.50 each week, having already saved $136.45.
RelationsIf you earn $35.50 each week for w weeks, your total earnings will be ...
35.50w
When that amount is added to the amount you already have, $136.45, the sum is ...
35.5w +136.45
You want that total to be $455.95, which gives you the equation ...
35.5w +136.45 = 455.95
SolutionTo solve this 2-step equation, subtract the left-side constant:
35.5w = 319.50
The second step is to divide by the coefficient of the variable:
w = 319.50/35.5
w = 9
Baker barrowed $7,400 at 10.5% for 1/4 years. How much interest will he pay
back?
Answer: $194.25
Step-by-step explanation:
Given data
Principal= $7400
Rate= 10.5%
time= 1/4 years
The simple interest formula is given as
SI= PRT/100
substitute
SI= 7400*10.5* 0.25/100
SI= 19425/100
SI= $194.25
Hence Mark will pay $194.25
What is 70% of 45???????
Answer: 31.5
Step-by-step explanation:
Answer:
31.5
Step-by-step explanation:
[tex]45 \times .7 = 31.5[/tex]
Evaluate the following permutations and combination
a) N = ( 3P4 ) ( 5P2 ) b) N = (3C2) / (4C2)
By using the definitions of combinations and permutations:
a) The first permutation is not defined.
b) N = (³C₂) / (⁴C₂) = 1/2.
How to evaluate the permutations and combinations?A permutation:
ⁿPk is written as:
ⁿPk= n!/(n - k)!
(the denominator only appears if nk)
And a combination is written as:
ⁿCk = n!/(n - k)ka)
We have the product of two permutations, but there is a problem:3P4 The first number is the size of the set, and the second is the number of elements we take from that set.
In that permutation we have a set of 3 elements and we need to select 4, so that permutation is not defined.
b) (³C₂) = 3!/(3 - 2)!*2! = (3*2*1)/(2*1) = 3
(⁴C₂) = 4!/(4 - 2)!*2! = (4*3*2*1)/[(2*1)*(2*1)]
= 3*2 = 6
Then the quotient can be written as:
(³C₂) (⁴C₂) = 3/6 = 1/2.
Note that A quotient is seen as the outcome of dividing two numbers by each other.
Learn more about permutations and combinations:
https://brainly.com/question/11732255
#SPJ1
Help me please!!!!!!
Answer:5 35/36
Step-by-step explanation:
63 13/18 − 57 3/4 =?
Solving the whole number parts
63−57=6
Solving the fraction parts
13/18−3/4 is equal to 26/36 − 27/36
Combining the whole and fraction parts
6−1/36 = 5 35/36
What is the value of x?
C 5
C42
(+6)
(3-16)
22
38
What is the rate of change (slope) of this graph? Explain how you found the answer.
to get the slope of any straight line, we simply need two points off of it, wait a minute!!!! holy smokes!! the graph already has two points for us, yeahhh, let's use those then
[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-7}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-7}-\stackrel{y1}{0}}}{\underset{run} {\underset{x_2}{0}-\underset{x_1}{5}}} \implies \cfrac{ -7 }{ -5 } \implies {\Large \begin{array}{llll} \cfrac{7 }{ 5 } \end{array}}[/tex]
If you have 6 eggs and 2 bananas for 4 people how many eggs and bananas would you need for 10 people?
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!!!
Answer:
X = 67, Y = 113
Step-by-step explanation:
To find y: 180-62-51=67
To find x: 180-67 = 113
Total angle in a triangle sums to 180 degrees
Total angle in a straight line is also 180 degrees
The difference between two whole numbers is 6. Twice the smaller number is 10 more than the larger number. What is the smaller number?
The smaller number from the given situation is 16.
Given that, the difference between two whole numbers is 6.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the larger number be x and the smaller number be y.
The difference between two whole numbers is 6.
So, x-y=6
x=6+y --------(I)
Twice the smaller number is 10 more than the larger number.
x+10=2y
x=2y-10 --------(II)
Substitute equation (I) in equation (II), we get
6+y=2y-10
⇒ y=16
Hence, the smaller number from the given situation is 16.
To learn more about an equation visit:
https://brainly.com/question/14686792.
#SPJ1
If a bus is charged $122, how many people do you think it contains?
Answer:
38 people
Step-by-step explanation:
In this case, we can see that, being two people, the cost is 14 and when it is double, that is, 4 people, the value is not 28 but 20.
Which means that there is an additional value that is being charged for the vehicle, that is:
let "c" be the value of the vehicle and "x" be the value per person
c + 2 * x = 14
c + 4 * x = 20 => c = 20 - 4 * x
replacing:
20 - 4 * x + 2 * x = 14
-2 * x = 14-20
-2 * x = -6
x = 6/2
x = 3
for C:
c = 20 - 4 * 3
c = 8
Which means that the formula for the value of the input would then be:
e = 8 + 3 * n
where "n" is the number of people.
Now, we are told that for e = 122
122 = 8 * + 3 * n
3 * n = 122 -8
n = 114/3
n = 38
which means that for that bus there are a total of 38 people
Which expressions are equal to 3 1/4 - (-5/8)
Answer:B 3 1/4 + (5/8)
D 3 1/4 + (+5/8)
Step-by-step explanation:
Calculation
an expression is the combination of numbers and operators like +, - * or /
If we have any equal sign then it is an equation .
Given expression is :
to find out equivalent expression we remove the parentheisis by multiplying negative inside the parenthesis
Negative times negative becomes positive
first fraction is positive . So it remains the same
Multiply negative inside the parenthesis . Negative times negative is positive
so, the equivalent expressions are
please help me with these questions there not answered by the way
The equivalent expression of 6⁵ is 6² × 6³.
The equivalent expression of 5⁻² × 5⁵ × 5 is 5⁴.
How to find equivalent expression?Two algebraic expressions are said to be equivalent if their values obtained by substituting the values of the variables are same.
Equivalent expressions are expressions that work the same even though they look different.
Therefore, let's find the expression, equivalent to 6⁵,
Using law of indices,
[tex]A^{x} X A^{y} = A^{x +y }[/tex]
Hence,
6² × 6³ = 6²⁺³ = 6⁵
5⁻² × 5⁵ × 5 = 5⁻²⁺⁵⁺¹ = 5⁴
learn more on equivalent expression here:https://brainly.com/question/27911936
#SPJ1
Condense each expression to a single logarithm
The single logarithms found by logarithm properties are listed below:
Case 31
㏒₃ 277809109776
Case 32
㏒₅ 134456
Case 33
5 · ㏒₇ (a / b²)
Case 34
㏑ (a⁶ / b)⁶
Case 35
㏒₇ (c⁴ · [tex]\sqrt[3]{a}[/tex])
Case 36
㏒₈ [w · (√u · v)]
How to simplify logarithmic expressions
In this problem we find six cases of logarithmic expressions that must be simplified into a single logarithm by logarithm properties. The complete procedure for each case is shown below:
Case 31
8 · ㏒₃ 11 + 4 · ㏒₃ 6
㏒₃ 11⁸ + ㏒₃ 6⁴
㏒₃ (11⁸ · 6⁴)
㏒₃ 277809109776
Case 32
5 · ㏒₅ 7 + 3 · ㏒₅ 2
㏒₅ 7⁵ + ㏒₅ 2³
㏒₅ (7⁵ · 2³)
㏒₅ 134456
Case 33
5 · ㏒₇ a - 10 · ㏒₇ b
㏒₇ a⁵ - ㏒₇ b¹⁰
㏒₇ (a⁵ / b¹⁰)
㏒₇ (a / b²)⁵
5 · ㏒₇ (a / b²)
Case 34
36 · ㏑ a - 6 · ㏑ b
㏑ a³⁶ - ㏑ b⁶
㏑ (a³⁶ / b⁶)
㏑ (a⁶ / b)⁶
Case 35
4 · ㏒₇ c + (1 / 3) · ㏒₇ a
㏒₇ c⁴ + ㏒₇ [tex]\sqrt[3]{a}[/tex]
㏒₇ (c⁴ · [tex]\sqrt[3]{a}[/tex])
Case 36
㏒₈ w + (1 / 2) · ㏒₈ u + (1 / 2) · ㏒₈ v
㏒₈ w + ㏒₈ √u + ㏒₈ √v
㏒₈ [w · (√u · v)]
To learn more on logarithms: https://brainly.com/question/20785664
#SPJ1
Write an equation in standard form on the line shown in the graph. (-4,3) (-5,2)
The equation to line is x-y+7=0.
What is a line?
A line is an indefinitely long, straight object that, despite being drawn with a minimum width, is considered to have no particular width in mathematics.
Main Body:
We know that equation of line in two point form =
y-y₁ =( y₂-y₁)/(x₂-x₁)(x-x₁)
points given are (-5,2) and (-4,3).
Therefore
y-2 =( 3-2)/(-4+5) *( x+5)
y-2 = x+5
x-y+7=0
Hence the equation is x-y+7=0.
To learn more about line click on the link below.
https://brainly.com/question/13763238
#SPJ13
Find the exact solution(s) to the equation 2 sin²x-cosx + 1 = 0
Answer: x=2πn (n=0, 1, 2, 3,...)
Step-by-step explanation:
2sin²x-cosx+1=0
2(1-cos²x)-cosx+1=0
2(1)-2(cos²x)-cosx+1=0
2-2cos²x-cosx+1=0
-2cos²x-cosx+3=0
Multiply both parts of the equation by -1:
2cos²x+cosx-3=0
Let cosx=t
Domain:
-1≤cosx≤1
Hence, -1≤t≤1
2t²+t-3=0
D=b²-4ac
a=2 b=1 c=-3
D=1²-4(2)(-3)
D=1+24
D=25
√D=√25
√D=5
[tex]\displaystyle\\t=\frac{-bб\sqrt{D} }{2a} \\\\t=\frac{-1б5}{2(2)}\\\\t=\frac{-1б5}{4}\\\\t=-1.5\notin domain\\\\t=1\in domain\\\\cosx=1\\\\x=2\pi n\ where\ n=0, \ 1,\ 2,\ 3,\ ...[/tex]
What is the total perimeter of this figure?
The compound figure formed by a square and four circular sections has an approximate perimeter of 308.496 centimeters.
How to calculate the perimeter of a compound figure
In this question we find a compound figure formed by a square with a side length of 30 centimeters and four circular sections with central angle of 270° and a radius of 10 centimeters. The perimeter of the compound figure (p), in centimeters, is the sum of the perimeter of the square and the perimeter of the four circular sections:
p = p' + 4 · p''
Where:
p' - Perimeter of the square, in centimeters.p'' - Perimeter of the circular section, in centimeters.p = 4 · (30 cm) + 4 · (3π / 2) · (10 cm)
p = 120 cm + 60π cm
p ≈ 308.496 cm
The perimeter is approximately equal to 308.496 centimeters.
To learn more perimeters: https://brainly.com/question/6465134
#SPJ1
The function d(x)=-1/3|x-15|-5 represents the elevation (in meters) of a scuba diver x seconds after descending from the surface.
The x-intercepts 0 and 30 indicate it takes 30 seconds to return to the surface of the water
The vertex (15, -5) indicates the scuba diver descends for 15 seconds to a depth of 5 meters under the surface before ascending
How to interpret the x-interceptThe equation of the function is given as
d(x) = 1/3|x - 15| - 5
Set d(x) to 0, to determine the x-intercept
So, we have
1/3|x - 15| - 5 = 0
This gives
1/3|x - 15| = 5
So, we have
|x - 15| = 15
Remove the absolute brackets
x - 15 = 15 and x - 15 = -15
Evaluate the equations
x = 30 and x = 0
This means that the diver is at the surface at 0 and 30 seconds
How to interpret the vertexAn absolute value function represented as f(x) = a|x - h| + k has a vertex of (h, k)
This means that
(h, k) = (15, -5)
It means that the diver dived for 15 seconds to get to 5 meters below the water surface
Read more about absolute value functions at
https://brainly.com/question/10538556
#SPJ1
Which values are in the solution set of the compound inequality? Select two options. 4(x + 3) ≤ 0 or x+1>3 –6 –3 0 3 8
The values -3 , -6 , 3 , 8 are in the solution set of the compound inequality 4(x + 3) ≤ 0 and x + 1 > 3
Given, a compound inequality
4(x + 3) ≤ 0 and x + 1 > 3
Now, on solving the first inequality, we get
4(x + 3) ≤ 0
4x + 12 ≤ 0
On subtracting both the sides by 12, we get
4x + 12 - 12 ≤ 0 - 12
4x ≤ -12
On dividing both the sides by 4, we get
4x/4 ≤ -12/4
x ≤ -3
So, the solution set of the 4(x + 3) ≤ 0 inequality be, x ≤ -3 i.e. all the real numbers less than -3.
Now, on solving the second inequality, we get
x + 1 > 3
On subtracting both the sides by 1, we get
x + 1 - 1 > 3 - 1
x > 2
So, the solution set of the x + 1 > 3 inequality be, x > 2 i.e. all the real number greater than 2.
Now, the values in the solution set of the compound inequality
4(x + 3) ≤ 0 and x + 1 > 3 be,
x ≤ -3 and x > 2.
As, we can see -3 , -6 , 3 , 8 are satisfying the condition.
Hence, -3 , -6 , 3 , 8 are the values in the solution set of the compound inequality 4(x + 3) ≤ 0 and x + 1 > 3.
Learn more about Linear Inequality here https://brainly.com/question/28418226
#SPJ1
A chef is going to use a mixture of two brands of Italian dressing. The first brand contains 6% vinegar, and the second brand contains 11% vinegar. The chef wants to make 320 milliliters of a dressing that is 8% vinegar. How much of each brand should she use?
The total mixture to contain 8% vinegar so: .06F plus .11S equal to .08(320).Now, we can solve the system of equations using substitution.F + S is 310
How much of each brand should she use?.06F + .11S = .08(310)
F = 310 - S [solve 1st equation for F]
.06(310 - S) + .11S = .08(320) [substitute into 2nd equation]
18.6 -.06S +.11S = 24.8
.05S = 6.2
S = 124
F + 124 = 310
F = 186
make a 320mL mixture that contains 8% vinegar, use 186mL of the first brand and 124mL of the second brand.
To learn more about brand refer
https://brainly.com/question/29096513
#SPJ13
A line passes through the points (6,0) and (9,1). What is its equation in slope-intercept form?
Equation of line will be y = x/3 - 2
A line's equation can be written in many forms in which one is slope-intercept form.
Equation in slope-intercept form is written as y = mx + c where
m = slope
c = y intercept
Slope shows the steepness of the line. It can be given by change in y axis by change in x axis.
y intercept is the point where the line cuts the y axis that is x = 0 at this point.
Points given to us are (6 , 0) and (9 , 1)
slope = [tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]
m = (1 - 0) / (9-6)
m = 1/3
For c put values of either point in the equation as they both are on the line so they both will satisfy the equation.
y = mx + c
0 = (1/3)*6 + c
0 = 2 + c
c = -2
now put values of m and c in the equation and get a general equation.
Therefore of equation of line will be y = x/3 - 2
To know more about equation of line here
https://brainly.com/question/12985143
#SPJ1
"A toy rocket is shot vertically into the air from a launching pad 7 feet above the ground with an initial velocity of 72 feet per second. The height in feet, of the rocket above the ground at t seconds after launch is given by the function h(t)=-16 t²+72 t+7. How long will it take the rocket to reach its maximum height? What is the maximum height?
The rocket reaches its maximum height at second(s) after launch.
(Simplify your answer.)
The maximum height reached by the object is feet.
(Simplify your answer.)"
The time taken for the rocket to reach its maximum height is; 2.25 seconds.
The maximum height reached by the toy rocket by evaluation is; 88 feet.
What is the maximum height reached by the rocket?It follows from the task content that the maximum height reached by the rocket is to be determined.
The given function is; h (t) = -16 t² + 72t + 7.
Since it follows from evaluation that; at maximum height, the rate of change of height to time is equal to 0.
Therefore; at maximum height;
h'(t) = 0
h'(t) = -32t + 72 = 0
-32t = -72
t = -72/-32
t = 2.25 seconds.
Ultimately, the time taken for the rocket to reach its maximum height is; 2.25 seconds.
Also, the maximum height reached by the rocket is at; h (2.25);
h(2.25) = -16(2.25)² + 72 (2.25) + 7
= -81 + 162 + 7
= 88.
The maximum height reached is; 88 feet.
Read more on maximum height;
https://brainly.com/question/82347
#SPJ1
PLEASE HELP THIS IS OVER DO
Answer:
its the third one
oh this is easy
What is the domain of the relation? {(3,4),(2,3),(2,0),(4,2),(3,6)} Responses {0,2,3,4,6} {0,2,3,4,6} {0,3,6} {0,3,6} {0,2,3,4} {0,2,3,4} {2,3,4}
The domain of the given relation is: {2, 3, 4].
What is the Domain of a Relation?A relation has ordered pairs of values that are given as x and y coordinates, (x, y) In a relation, the values of the x coordinates are the domain of the relation while the values of the y coordinates are the range of the relation.
Given the relation, {(3,4),(2,3),(2,0),(4,2),(3,6)}, the set of x-values is: {2,3,4}. the set of y-values is: {0, 2, 3, 4, 6}.
{2,3,4} represents the domain while {0, 2, 3, 4, 6}. represents the range.
Therefore, the domain of {(3,4),(2,3),(2,0),(4,2),(3,6)} is given as: {2, 3, 4].
Learn more about the domain of a relation on:
https://brainly.com/question/2272412
#SPJ1
simplify (4^7/5^2) ^3
1. 4^10/5^5
2. 4^4/5
3. 4^21/5^6
4. 12^7/15^2
Answer: 3: 4^21/5^6
Step-by-step explanation:
Remember when you are raising you need to multiple the powers.
How does the US tax policy encourage long-term investments?
A.
by making long-term investments tax exempt
B.
by making Treasury bonds tax exempt
C.
by making it illegal to earn short-term gains
D.
by providing a lower tax rate for long-term gains
Answer: its D
Step-by-step explanation
Long Term Capital Gains Taxes tend to be lower than short term
Answer: D by providing a lower tax rate for long-term gains
solve 3x + 5 = 2x + 7
Answer:
x = 2
Step-by-step explanation:
3x + 5= 2x + 7
Subtract 2x from both sides
3x + 5 −2x = 7
Combine 3x and −2x to get x
x + 5 = 7
Subtract 5 from both sides
x = 7 − 5
Subtract 5 from 7 to get 2
x = 2
Carmen purchased 11/12 lbs. of grapes and Hunter purchased 2/12 lbs. of grapes. How many more grapes did Carmen purchase than Hunter?
The amount of grapes Carmen purchase than Hunter is 3/4 lbs
How to determine the count of more grapes Carmen purchase than Hunter?From the question, we have the following parameters that can be used in our computation:
Carmen = 11/12 lbs
Hunter = 2/12 lbs
The difference between these parameters is the amount of grapes Carmen purchase than Hunter
This is represented as
Difference = Carmen - Hunter
Substitute the known values in the above equation, so, we have the following representation
Difference = 11/12 - 2/12
Evaluate
Difference = 9/12 = 3/4
Hence, the amount of grapes is 3/4 lbs
Read more about difference at
https://brainly.com/question/1328439
#SPJ1
help me please (asap)
(C) represents a function with the same rate of change at the function [tex]y = \frac{7}{4}x+3[/tex].
Given equation,
[tex]y = \frac{7}{4}x+3[/tex]
Slope = m = 7/4
Slope = (x2-x1)/(y2-y1)
Now we will check every option and find slope which we be 7/4.
(A) A(1,0) and B(5,-4)
Slope = (-4-0)/(5-1)
= -4/4
= -1
≠ m
(B) A(-1,1) and B(0,4)
Slope = (4-1)/(0+1)
= 3/1
= 3
≠ m
(C) A(-4,-6) and (0,1)
Slope = (1+6)/(0+4)
= 7/4
= m
(D) A(0,-2) and B(-4,5)
Slope = (5+2)/(-4-0)
= 7/-4
= -7/4
≠ m
Hence, only (C) satisfies the situation.
To learn more about function here:
https://brainly.com/question/5975436
#SPJ1