Answer:
x = -11
Step-by-step explanation:
Hello!
This is a one-step equation. To solve for x, you simply have to isolate it.
Since -16 is being added to x, we can add 16 to both sides to cancel out the negative 16.
Solve for x-16 + x = -27-16 + x + 16 = -27 + 16x = -11The value of x is -11.
Solve the following LP formulation and determine the number of Surplus units in constraint B.
SOLUTION
From the what is given
[tex]\begin{gathered} x+y\le5 \\ x\ge3 \\ 2y\le8 \\ x\ge0 \\ y\ge0 \end{gathered}[/tex]We have the graph as shown below
We are told that the MAX is
[tex]5x+2y[/tex]Substituting these required points into the equation, our maximum becomes
[tex]\begin{gathered} 5x+2y \\ \text{For (3, 2)} \\ 5(3)+2(2)=15+4=19 \\ \text{For }(3,\text{ 0)} \\ 5(3)+2(0)=15+0=15 \\ \text{For (5, 0)} \\ 5(5)+2(0)=25+0=25 \end{gathered}[/tex]We can see that the maximum is 25 at for units of 5, that is x = 5
But we are told in (B) that
[tex]x\ge3[/tex]Hence the surplus unit is
[tex]5-3=2[/tex]Hence the answer is 2
For 7 y = 2 x − 5 , which of the following expressions gives x in terms of y ?
The expressions that gives x in terms of y from the given expression 7 y = 2 x − 5 is x = (7y +5)/2.
How can the expression be simplified?The concept that will be used in this question is solving of linear equation, because the equation is linear, then we perform the simplification.
The given expression is is 7 y = 2 x − 5
Then from the expression we can make 2x the subject of the formula by rearranging it as 2x = 7y +5
Then this can be further expressed by dividing the both sides by the factor of 2, which can be expressed as ;
x = (7y +5)/2
Therefore, option A is correct because it is the expression that gives the x in terms of y.
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Check the missing options:
A. x = (7y +5)/2
B. y = (7x +5)/2
C. x=(7y +5)/3
sarah has 85 and 89 on her first two math 23 tests. what must she get on the third test to have at least 90% test average?Assume three tests and represent the problem with an inequality
The value that Sarah must she get on the third test to have at least 90% test average is represented by the inequality x ≥ 96.
What is an inequality?Inequalities are created through the connection of two expressions. It should be noted that two expressions in an inequality aren't always equal. They are denoted by the symbols ≥ < > ≤.
In this case, Sarah has 85 and 89 on her first two math 23 tests.
Let the third test be represented as x. This will be illustrated as:
(85 + 89 + x) / 3 ≥ 90
Cross multiply
85 + 89 + x ≥ 90 × 3
174 + x ≥ 270
Collect like terms
x ≥ 270 - 174
x ≥ 96
The value is x ≥ 96.
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a company that manufactures mufflers for cars offers a lifetime warranty on its products, provided that ownership of the car does not change. suppose that only 20% of its mufflers are replaced under this warranty. a button hyperlink to the salt program that reads: use salt. (a) in a random sample of 400 purchases, what is the approximate probability that between 70 and 90 (inclusive) mufflers are replaced under warranty? (round your answer to four decimal places.)
The approximate probability that between 70 and 90 is 0.728.
Using normal distribution,
Mean = xbar = np = 400 × 0.2 = 80
Standard deviation = √[np(1-p)] = √(80 × 0.8) = 8
To ensure that the distribution is normal,
np ≥ 10
80 ≥ 10
And,
np(1-p) ≥ 10
80(0.8) = 320 ≥ 10
Hence, we use the z-tables for this
a) Convert 75 and 100 into standardized scores.
A value's standardized score is equal to the value minus the mean divided by the standard deviation.
z = (x - xbar) ÷ σ
For 75
z = (75 - 80) ÷ 8 = - 0.625
For 100
z = (100 - 80) ÷ 8 = 2.5
To calculate the approximate likelihood that between 75 and 100 (inclusive) mufflers will be replaced under warranty.
P(75 ≤ x ≤ 100) = P(-0.625 ≤ z ≤ 2.5)
For these probabilities, use data from the normal probability table.
P(75 ≤ x ≤ 100)
= P(-0.625 ≤ z ≤ 2.5)
= P(z ≤ 2.5) - P(z ≤ -0.625)
= 0.994 - 0.266
= 0.728
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Someone please answer this I'm offering all my points.
DJ Joe wants to organize 127 CD's into storage boxes. Each storage box can hold a
maximum of 10 CD's. What is the least number of storage boxes needed?
Answer:
13 storage boxes is the least
Step-by-step explanation:
What we know:
- We have 127 cd's
- We have boxes only able to hold 10
What we need to figure out:
- how many boxes at the least are we going to need
Step 1: Divide
Since we need to figure out how many times 10 goes into 127 we divide 127 by 10 so...
127/10 = 12 with a remainder of 7.
Step 2: Figure out the remainder
Since there are seven left over and you cannot put them in boxes already being used then we put them in a new box, not yet used. That would make it a total of 13 boxes needed at the least.
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Find the volume of a cone with a base diameter of 6 m and a height of 10 m.
Use the value 3.14 for , and do not do any rounding.
Be sure to include the correct unit in your answer.
ANSWER:
94.2m^3
STEP BY STEP:
V = 1/3 x PI x R^2 x h = 1/3 x 3.14 x 3^2 x 10 =94.2^3
Answer:
V = 94.25m³
I don't have enough time to show work because I have to go, but I hope this helped.
jon's bathtub is rectangular and its base is 18 ft2. how fast is the water level rising if jon is filling the tub at a rate of 0.6 ft3/min? (use decimal notation. give your answer to three decimal places.)
Jon's bathtub exists rectangular and its base exists 18 ft². The water level rising if Jon is filling the tub at a rate of 0.2 ft³/min is 0.011 ft/min.
What is meant by differential equation?A differential equation in mathematics exists an equation that links the derivatives of one or more unknown functions. Applications often involve functions that reflect physical quantities, derivatives that depict the rates at which those values change, and a differential equation that establishes a connection between the three.
If we take a look at a rectangular bathtub, the volume of the bathtub can be expressed as:
Volume (V) = length × breadth × height
where; base = length × breadth = 18ft²
The volume of the rectangular bathtub = 18h ......... (1)
Using differentiation to differentiate 18h with respect to t implicitly, then:
[tex]$\frac{\mathrm{dV}}{\mathrm{dt}}=18 \frac{\mathrm{dh}}{\mathrm{dt}}$$[/tex]
When the rate of rising of the volume is 0.2 ft² / min
[tex]$0.2=18 \frac{\mathrm{dh}}{\mathrm{dt}}$$[/tex]
substitute the values in the above equation, we get
[tex]$\frac{\mathrm{dh}}{\mathrm{dt}}=\frac{1}{18} \times(0.2)$$[/tex]
[tex]$\frac{\mathrm{dh}}{\mathrm{dt}}=0.011 \mathrm{ft} / \mathrm{min}$$[/tex]
Therefore, we can conclude that the rate at which the water level rises if Jon is filling the tub at 0.2 ft³/min exists 0.011 ft/ min.
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if it takes 3/4 of an hour to fill 3/5 of a pool how many hours will it take to fill the pool completely
The time taken to completely fill the pool is 5/4 hour
How to determine the time to fill the pool?From the question, the given parameters are:
Time =3/4 hour
Size of the pool = 3/5
The time to fill the pool is then calculated as
Time = Given time/Proportion of the pool
Substitute the known values in the above equation
So, we have the following equation
Time = 3/4 hour ÷ 3/5
Express the quotient as product
So, we have the following equation
Time = 3/4 hour x 5/3
Evaluate the products
Time = 5/4 hour
Hence, the time taken is 5/4 hour
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23 times 20 algorithom
Answer: using traditional algorithom
23
x 20
__________
0 0
+ 4 6
____________
4 6 0
which property is used in the problem below, the commutative property or the associative property??
(4 x 2) x 3 = (2 x 4) x 3
The cost (in dollars) of a basic music streaming service for m months
is represented by B(m) = 5m. The cost of the premium service is represented by
P(m) 10m. Describe the transformation from the graph of B to the graph of P.
The transformation from the graph of B to the graph of P is a vertical stretch by a scale factor of 2
How to determine the transformation?From the question, the function definitions are given as
B(m) = 5m
P(m) = 10m
Rewrite the function P(m) as follows
P(m) = 2 x 5m
Substitute B(m) = 5m in the equation P(m) = 2 x 5m
P(m) = 2 x B(m)
When a function is represented as
f(x) = kg(x), then the transformation is a vertical stretch by k
Hence. the transformation a vertical stretch by 2
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complete the slope-intercept form of an equation that represents the relationship in the table
Answer:
y = 3x -4
Step-by-step explanation:
You want the slope intercept equation representing the relationship between x and y, given (x, y) = (1, -1) and (4, 8).
SlopeThe slope can be found using the formula ...
m = (y2 -y1)/(x2 -x1)
m = (8 -(-1))/(4 -1) = 9/3 = 3
InterceptThe y-intercept can be found using the equation ...
b = y1 -m(x1)
b = -1 -3(1) = -4
Slope-intercept equationThe slope-intercept equation of a line has the form ...
y = mx + b
Using the above values of m and b, this becomes ...
y = 3x -4
__
Additional comment
Attached is a graph showing the points and the line the equation represents.
<95141404393>
Simplify nine square root of two minus three square root of seven plus square root of eight minus square root of twenty eight. eleven square root of two minus five square root of seven eleven square root of four minus five square root of fourteen six square root of five six square root of nine
Squares are the numbers that are produced when a value is multiplied by itself.
If expression be [tex]$9 \sqrt{2}-3 \sqrt{7}+\sqrt{8}-\sqrt{28}$[/tex] then the value exists [tex]$11 \sqrt{2}-5 \sqrt{7}$[/tex].
What is meant by square root?The radical symbol for the number's root is "√" in this instance. The square of the positive number is represented by multiplying it by itself.
Squares are the numbers that are produced when a value is multiplied by itself. In contrast, a number's square root exists a value that, when multiplied by itself, returns the original value.
The original number can be attained by multiplying the square root of an integer by itself.
Only a perfect square number can have a perfect square root. Even perfect squares have an even square root. An odd perfect square will contain an odd square root. A perfect square cannot be negative and hence the square root of a negative number exists not defined.
Let the expression be [tex]$9 \sqrt{2}-3 \sqrt{7}+\sqrt{8}-\sqrt{28}$[/tex]
Now, [tex]$\sqrt{8}=\sqrt{2 \times 2 \times 2}=2 \sqrt{2}$[/tex]
[tex]$\sqrt{28}=\sqrt{2 \times 2 \times 7}=2 \sqrt{7}$[/tex]
therefore [tex]9 \sqrt{2}-3 \sqrt{7}+\sqrt{8}-\sqrt{28}$[/tex]
simplifying the given expression, we get
[tex]$=9 \sqrt{2}-3 \sqrt{7}+2 \sqrt{2}-2 \sqrt{7}$[/tex]
[tex]$=9 \sqrt{2}+2 \sqrt{2}-3 \sqrt{7}-2 \sqrt{7}$[/tex]
[tex]$=11 \sqrt{2}-5 \sqrt{7}$[/tex]
Therefore, the correct answer is option a) [tex]$11 \sqrt{2}-5 \sqrt{7}$[/tex]
The complete question is:
Simplify [tex]$9 \sqrt{2}-3 \sqrt{7}+\sqrt{8}-\sqrt{28}$[/tex]
a) [tex]$11 \sqrt{2}-5 \sqrt{7}$[/tex]
b) [tex]$11 \sqrt{4}-5 \sqrt{14}$[/tex]
c) [tex]$6 \sqrt{5}$[/tex]
d) [tex]$6 \sqrt{9}$[/tex]
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working together, it takes two different sized hoses minutes to fill a small swimming pool. if it takes minutes for the larger hose to fill the swimming pool by itself, how long will it take the smaller hose to fill the pool on its own?
Time taken by the smaller hose to fill the pool on its own = 75 minutes
Time taken to fill the swimming pool by the larger hose and smaller hose working together = 30 minutes
Time taken by the larger hose to fill up the swimming pool = 50 minutes
Let 'x' be the time taken by the smaller hose to fill the swimming pool on its own.
In 30 minutes, the larger and smaller hoses together can fill the swimming pool. So in 1 minute, it can fill up 1/30 of the swimming pool.
In 50 minutes, the larger hose can fill up the swimming pool on its own. So the larger hose can fill up 1/50 of the pool in 1 minute.
It takes 'x' minutes for the smaller hose to fill up the pool on its own. So in 1 minute, the smaller hose alone can fill up 1/x of the pool.
Hence 1/30 = 1/x +1/50
⇒ 1/30 = (50+x)/50x
⇒ 30 = 50x/(50+x)
⇒ 30 (50 + x) = 50x
⇒ 1500 + 30x = 50x
⇒ 20x = 1500
⇒ x = 1500/20
⇒ x = 75 minutes.
Thus the smaller hose alone takes 75 minutes to fill up the pool.
The question is incomplete. Find the complete question below:
Working together, it takes two different sized hoses 30 minutes to fill a small swimming pool. If it takes 50 minutes for the larger hose to fill the swimming pool by itself, how long will it take the smaller hose to fill the pool on its own?
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help meeeeeeee pleasee
Answer:
2(5*7) + 2(4*7) + 2(4*5)
Step-by-step explanation:
I can't really see all the values on the cuboid. I'm going to assume the dimensions are 5cm by 4cm by 7cm.
Surface area of this cuboid would be:
2(5*7) + 2(4*7) + 2(4*5)
Estimate 81.244.+65.33 by first rounding each number to the nearest whole number
If we round 81.244 to the nearest whole number then it would be 81.
For 65.33 is 65. Then, we sum.
[tex]81+65=146[/tex]Hence, the answer is 146.8. Find the value of x and y.
(7x-2)°
18y°
(11x - 34)°
The degrees of the following expression are
(7x-2)° => x = 2/7°
18y° => y = 0°
(11x - 34)° => x = 34/11°
Degrees:
Degree is the unit of measure is used to measure the magnitude of an angle.
1 degree = 1/360 of a complete revolution in magnitude.
Given,
Here we have the following expressions
(7x-2)°
18y°
(11x - 34)°
Now, we have to find the value of x and y from it.
In order to find the value x and y , we have to equate every equation with 0. then we get the value of variables x and y.
When we take the first expression, and then we have to equate it with zero, then we get,
(7x - 2)° = 0°
7x = 2°
x = 2/7°
Therefore, the value of x is 2/7°.
Now, we have to take the second one and equate it with zero, then we get,
18y° = 0
y = 0°
Therefore, the value of y is 0°.
Finally, the value of the expression in degrees,
11x - 34° = 0
11x = 34°
x = 34/11°
Therefore, the value of x is 34/11 degrees.
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A Ford F-150 truck is considered a half-ton truck because that is how much it can haul. How many pounds can the truck haul?
The truck can haul 1102 pounds.
According to the question,
We have the following information:
A Ford F-150 truck is considered a half-ton truck because that is how much it can haul.
(We will not directly convert ton into pounds. We will follow the following steps.)
Now, we know that 1 ton is equal to 1000 kilograms.
So, half ton makes 500 kg.
Now, to convert this into pounds, we will multiply 500 kg by 2.205 because we know that 1 kg is equal to 2.205 pounds.
1 kg = 2.205 pounds
500 kg = (500*2.205) pounds
500 kg = 1102.5 pounds
Hence, the truck can haul 1102.5 pounds.
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Triangle ABC has the following angle measures:
m∠A = (x + 6)°, m∠B = (3x − 15)°, m∠C = (5x + 36)°
What is m∠C?
The measure of ∠C is 121 degrees.
Given that:-
There is a triangle ABC.
m∠A = (x + 6)°
m∠B = (3x - 15)°
m∠C = (5x + 36)°
We have to find the measure of ∠C.
We know that,
The sum of all the angles of a triangle is 180 degrees.
Hence, we can write,
m∠A + m∠B + m∠C = 180 degrees
(x + 6)° + (3x - 15)° + (5x + 36)° = 180 degrees
(x + 3x + 5x) + (6 - 15 + 36) = 180 degrees
9x + 27 = 180 degrees
9x = 180 - 27
9x = 153 degrees
x = 153/9 degrees
x = 17 degrees
Hence,
The measure of ∠C = 5x + 36 = 5*17 + 36 = 85 + 36 = 121 degrees.
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hi how are you today can you please help me with this question
If:
[tex]\frac{a}{b}=\frac{c}{d}=\frac{e}{f}=\frac{a+c+e}{b+d+f}[/tex]so:
[tex]\begin{gathered} 15\colon9\colon4 \\ \frac{15}{1}=\frac{9}{1}=\frac{4}{1}=\frac{15+9+4}{3}=\frac{28}{3} \end{gathered}[/tex][tex]\begin{gathered} \frac{3}{x}=\frac{28}{3} \\ x=\frac{9}{28} \end{gathered}[/tex]Or:
0.32 liters
(b)
We need to find the volume of the rectangular prism, therefore:
[tex]\begin{gathered} V=l\cdot w\cdot h \\ V=40\cdot20\cdot35 \\ V=28000cm^3 \end{gathered}[/tex]However, we need to express the volume in liters, so:
[tex]28000cm^3\times\frac{1L}{1000cm^3}=28L[/tex]Since we need to know the amount of mango juice:
[tex]28\cdot\frac{2}{5}=11.2L[/tex]bradley consumes an energy drink that contains caffeine. after consuming the energy drink, the amount of caffeine in bradley's body decreases exponentially. the 10-hour decay factor for the number of mg of caffeine in bradley's body is 0.2722. what is the 5-hour growth/decay factor for the number of mg of caffeine in bradley's body?
The 5-hour growth/decay factor for the number of mg of caffeine in Bradley's body is 0.521
In mathematics, the term "exponential decay" refers to the process of a constant percentage rate decline in a value over time. Exponential decay differs from linear decay in that the decay factor depends on a percentage of the initial sum, meaning that the amount by which the original sum may be lowered will fluctuate over time as opposed to a linear function, which reduces the original sum by the same amount each time.
Given,
10 hour decay factor = 0.2722
Let us calculate the one-hour decay factor first,
One-hour decay factor = (10 hour decay factor)^1/10 = (0.2722)^1/10 = 0.8779
Now, Calculating the 5-hour decay factor,
5 hour decay factor = ( 1 hour decay factor )^5 = (0.8779)^5 = 0.521
Hence, the 5-hour growth/decay factor for the number of mg of caffeine in Bradley's body is 0.521
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Tell which of the following is a linear equation in one variable:
a) x² - 4x + 3 = 0
b) 6x - 2y = 7
c) 3x - 1 = -2x
d) pq - 3 = p
e) 3x + 2 = 4 ( x +7 ) + 9
For 100 Points
Answer:
c and e
Step-by-step explanation:
(a)
x² - 4x + 3 = 0 ← is a quadratic and not linear
(b)
6x - 2y = 7 ← is a linear equation in 2 variables, x and y
(c)
3x - 1 = - 2x ( add 2x to both sides )
5x - 1 = 0 ← is a linear equation in 1 variable
(d)
pq - 3 = p ← is a linear equation in 2 variables , p and q
(e)
3x + 2 = 4(x + 7) + 9 ← is a linear equation in 1 variable
PLEASE HELP!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
2nd one
Consider the line y = = 8 x-4. Find the equation of the line that is parallel to this line and passes through the point (7, -2). Find the equation of the line that is perpendicular to this line and passes through the point (7, -2).
Answer: y=8x-58
Step-by-step explanation:
1. find the slope
Since the new line is parallel to the first one that means the slope of 8x will remain the same.
2. plug it into the point slope formula y-y1=m(x-x1)
which would look like
y-(-2)=8(x-7)
3. solve for y
y-(-2)=8(x-7)
y+2=8x-56
y=8x-58
find the 41st term 11, 16, 21…
Answer:
You can add up to 5 each time, so we just need to multiply 5 by 40 although we already have the first three terms.
A: 40*5 = 200
Step-by-step explanation:
21 + 200 = 221
PLEASE HELP ASAPPP!!!!!!!!!!!!!!!!!!!!!
PLEASE HELP ASAP!!!!
The quadratic function f(x) has roots of −4 and 2 and point (1, −5) lies on f(x). What is the equation of f(x)?
f(x) = (x − 2)(x + 4)
f(x) = (x − 2)(x − 4)
f(x) = 4(x − 2)(x + 4)
f(x) = 4(x − 2)(x − 4)
The function has an equation of f(x) = (x + 4)(x - 2)
How to determine the equation of f(x)?The given parameters in the question are
Roots = -4 and 2
Point = (1, -5)
The above parameters can be rewritten as
Roots: x = -4 and x = 2
Point: (x, y) = (1, -5)
A quadratic equation can be represented as
f(x) = a * (x - Roots)
Where Roots: x = -4 and x = 2
The above parameters imply that we have the following equation
y = a(x + 4)(x - 2)
From the question, we have
(x, y) = (1, -5)
This gives
-5 = a(1 + 4)(1 - 2)
Divide
a = 1
Substitute a = 1 in y = a(x + 4)(x - 2)
y = (x + 4)(x - 2)
Hence, the equation of the quadratic function f(x) is f(x) = (x + 4)(x - 2)
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Answer: The answer would be A: f(x) = (x − 2)(x + 4)
Step-by-step explanation: I got it right on my test
Please solve will mark as
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For the following equation, complete the given ordered pairs, and use the results to graph the solution set for the equation.
Given:
[tex]y=-\frac{3}{4}x+1[/tex]Aim:
We need to graph the given function.
Explanation:
Replace x =-4 in the given equation.
[tex]y=-\frac{3}{4}(-4)+1[/tex][tex]y=-3(-1)+1[/tex][tex]y=3+1[/tex][tex]y=4[/tex]We get the point (-4, 4).
Replace x = 0 in the given equation.
[tex]y=-\frac{3}{4}(0)+1[/tex][tex]y=1[/tex]We get the point (0,1).
Replace x =4 in the equation.
[tex]y=-\frac{3}{4}(4)+1[/tex][tex]y=-3+1[/tex][tex]y=-2[/tex]We get the point ( 4, -2).
Mark the points (-4, 4), (0,1), and ( 4, -2) on the graph and join them by ray.
Final answer:
[tex](-4,4),\text{ }(0,1),\text{ }(4,\text{ -2}).[/tex]The graph of the given eqaution:
I just need help with question 1 for exercise 3!
SOLUTION:
Case: Transformation:
To find the transformation, compare the equation to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.
Method:
1,
[tex]y=(5x)^3-3[/tex]Transformation features:
Horizontal: None
Shift: None
Stretch/Compression: None
Vertical:
Shift: Down by 3 units
Stretch/Compression: Stretch by a factor of 5
2.
[tex]y=-7(x+9)^2[/tex]Transformation features:
Horizontal:
Shift: left by 9 units
Stretch/Compression: None
Vertical:
Shift: None
Stretch/Compression: Stretches by a factor of 7.
Final answer:
1.
Vertical:
Shift: Down by 3 units
Stretch/Compression: Stretch by a factor of 5.
2.
Horizontal:
Shift: left by 9 units
Vertical:
Stretch/Compression: Stretches by a factor of 7.