The volume of the trough is V(w) = w³ + 20w² - 429w and the rate of change of the volume over a width of 38 inches to 53 inches is 4695 in³/in
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let w represent the width, hence:
length = w + 33, height = w - 13
Volume (V) = w(w + 33)(w - 13) = w³ + 20w² - 429w
V(w) = w³ + 20w² - 429w
Rate of change = dV/dw = 3w² + 40w - 429
When w = 38, dV/dw = 3(38)² + 40(38) - 429 = 5423
When w = 53, dV/dw = 3(53)² + 40(53) - 429 = 10118
Rate = 10118 - 5423 = 4695 in³/in
The volume of the trough is V(w) = w³ + 20w² - 429w and the rate of change of the volume over a width of 38 inches to 53 inches is 4695 in³/in
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Cassandra already has $224 in a bank account.
She decides to save more by depositing $18 each week.
The amount of his savings M depends on the number of weeks elapsed n .
This relationship is represented using the equation M = 18n + 224.
Graphically, how would the line of this relationship change if Cassandra deposited $14 a week?
Please choose an answer.
The line will undergo a downward vertical translation.
The line will undergo a vertical translation upwards.
The inclination of the line will decrease.
The inclination of the line will increase.
Answer:
the inclination of the line will decrease
Step-by-step explanation:
If Cassandra changes the amount she deposits from 18 to 14, the slope changes to 14. So the new equation is M=14n + 224. The 224 is still the same, because that is the initial amount, and the new situation hasn't said anything about changing that, so it will not have any vertical translations. With that being said, as a result the slope will be less, so you can see it as "less vertical", so the inclination of the line will decrease
What are the solutions to the equation x2−12x+100=0?
Answer:
[tex]x=6+8i[/tex]
[tex]x=6-8i[/tex]
Step-by-step explanation:
[tex]x^2-12x+100=0[/tex]
solve by quadratic formula.
[tex]\frac{-b+-\sqrt{b^2-4(a*c)} }{2*a}[/tex]
[tex]\frac{12+\sqrt{(-12)^2-4*(1*100)} }{2*1}[/tex]
[tex]\frac{12-\sqrt{(-12)^2-4*(1*100)} }{2*1}[/tex]
which is
[tex]x=\frac{12+16i}{2}[/tex]
[tex]x=\frac{12-16i}{2}[/tex]
Simplify.
[tex]x=6+8i[/tex]
[tex]x=6-8i[/tex]
Solved.
Hope this helps.
Write the ratio of sin X and cos X
Show your work
(20 points)
Answer:
see explanation
Step-by-step explanation:
sinX = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{YZ}{XY}[/tex] = [tex]\frac{\sqrt{119} }{12}[/tex]
cosX = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{XZ}{XY}[/tex] = [tex]\frac{5}{12}[/tex]
A princess has two pet dragons. The dragons can eat 300kg of chocolate in 12 days. How many DAYS will the same 300kg last if got 4 more dragons for her birthday?
The chocolate will last for 1 day, if she gets 4 more dragons
How to determine the number of days?The expression can be represented using the following ratio:
Ratio = Dragons : Days : Chocolate
For the 2 dragons she has, we have:
Ratio = 2 : 12 : 300
When she gets 4 more dragons, we have:
Ratio = 6 : days : 300
Equate both ratios
6 : days = 12 : 2
Express as fraction
days/6 = 2/12
Multiply both sides by 6
days = 6 * 2/12
Evaluate
days = 1
Hence, the chocolate will last for 1 day
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Express the following linear equations in the form ax + by + c = 0 and indicate the values of a , b , c in each case :
i ) -2x + 3y = 6
ii) 2x = -5y
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let's solve ~
Question - 1 :
[tex]\qquad \sf \dashrightarrow \: - 2x + 3y = 6[/tex]
[tex]\qquad \sf \dashrightarrow \: - 2x + 3y - 6[/tex]
[tex]\qquad \sf \dashrightarrow \: (- 2)x + (3)y + (- 6)[/tex]
comparing it to general equation, we get :
[tex] \sf\dashrightarrow \: a = - 2[/tex][tex] \sf\dashrightarrow \: b = 3[/tex][tex] \sf\dashrightarrow \: c= - 6[/tex]Similarly,
Question - 2 :
[tex]\qquad \sf \dashrightarrow \: 2x = - 5y[/tex]
[tex]\qquad \sf \dashrightarrow \: 2x + 5y = 0[/tex]
[tex]\qquad \sf \dashrightarrow \: (2)x + (5)y + 0 = 0[/tex]
comparing it with general equation, we get :
[tex] \sf\dashrightarrow \: a = 2[/tex][tex] \sf\dashrightarrow \: b = 5[/tex][tex] \sf\dashrightarrow \: c = 0[/tex]A store sells 3 categories of kitchen items: cups, bowls, and spoons. There are 5 typess of cups. 4 types of bowls, and 2 types of spoons. How many different combinations can you buy in this store of: A set of objects fom two different categories?
You can by 24 combinations of items from the store
How to determine the number of combination?The given parameters are:
Cups = 3
Bowl = 4
Spoon = 2
The number of combination is:
Combination = Cups * Bowl * Spoon
So, we have:
Combination = 3 * 4 * 2
Evaluate
Combination = 24
Hence, you can by 24 combinations of items from the store
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Which expression is equivalent to the following complex fraction? StartFraction 2 Over x EndFraction minus StartFraction 4 Over y EndFraction divided by StartFraction negative 5 Over y EndFraction + StartFraction 3 Over x EndFraction StartFraction 3 y + 5 x Over 2 (y minus 2 x) EndFraction StartFraction 2 (y minus 2 x) Over 3 y minus 5 x EndFraction StartFraction 2 (y minus 2 x) (3 y minus 5 x) Over x squared y squared EndFraction StartFraction x squared y squared Over 2 (y minus 2 x) (3 y minus 5 x) EndFraction
The equivalent expression of [tex]\frac{\frac 2x - \frac 4y}{-\frac 5y + \frac 3x}[/tex] is [tex]\frac {2(y - 2x)}{ 3y-5x}[/tex]
How to determine the equivalent expression?The complete question is in the attached image
We have:
[tex]\frac{\frac 2x - \frac 4y}{-\frac 5y + \frac 3x}[/tex]
Take the LCM
[tex]\frac{\frac {2y - 4x}{xy}}{\frac{-5x + 3y}{xy}}[/tex]
Divide through by xy
[tex]\frac {2y - 4x}{-5x + 3y}[/tex]
Rewrite as:
[tex]\frac {2y - 4x}{ 3y-5x}[/tex]
Factor out 2
[tex]\frac {2(y - 2x)}{ 3y-5x}[/tex]
Hence, the equivalent expression of [tex]\frac{\frac 2x - \frac 4y}{-\frac 5y + \frac 3x}[/tex] is [tex]\frac {2(y - 2x)}{ 3y-5x}[/tex]
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The triangles are similar. Write a similarity statement for the triangles.
Hope this helps you
.......
y varies directly with x. If y = -4 when x = -1, what is the constant of variation?
the constant variation, K= 4
Step-by-step explanation:
i have replace the constant variation by the letter K
First step is to write down the information
y directly proprotional to x
So, y= Kx
Replace the value given for x and y to find k
y= -4 and x = -1
Kx= y
K( -1) = -4
K = -4 ÷ -1
K= 4
Further answer
if you are asked the connecting equation between y and x just replace the value of K in the equation
y= Kx
y= 4x
22. A house is sliding down a mountain. It moves one inch the first day, two more inches the
second day, four more inches the third day, etc. What is the total distance it will have moved in 15
days? Convert your unit of measure to a more reasonable one
Please help me I’ll mark you brainlest
The house would have slid 910 yards in 15 days.
What is a Geometric progression?A geometric progression is a sequence in which successive terms differ by a common ratio.
It is a sequence in which the ratio of two consecutive terms is a constant.
Analysis:
first term, a= 1
second term, ar = 2
third term, ar^2= 4
common ratio = ar/a = 2/1 = 2
Sum of the G.P where n = 15
sum of G.p = a([tex]\frac{r^{n} - 1}{r-1}[/tex])
= 1([tex]2^{15}[/tex] - 1)/2 - 1 = 32768 - 1 = 32768 inches
converting the inches to yard, where 1 yard = 36 inches
so 32768/36 = 910 yards
In conclusion, the house would slide 910 yards in 15 days.
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Find the value of z.
In a board game, negative number cards represent moving backward and positive number cards represent moving forward. For example, Nuha drew a card with 444 and moved forward 444 spaces.
Raha draws a card with 000.
What does 000 represent in the board game?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
The number of spaces she moved on her last turn.
(Choice B)
B
Not moving any spaces.
(Choice C)
C
Losing all points.
Answer:
not moving any spaces
74. REAL-WORLD APPLICATIONS
A car rental company offers two plans for renting a car. Plan A: $30 per day and $0.18 per mile Plan B: $50 per day with free unlimited mileage How many miles would you need to drive for plan B to save you money?
Answer:
For plan B to save money car rental need to drive 111.1 miles as [tex]\frac{x}{y}[/tex] expresses the average amounts of miles per day car rental drive and its obtained value is 111.1.
Step-by-step explanation:
In the question it is given that a car rental company offers two plans for renting a car.
Plan A: $30 per day and [tex]$\$ 0 \cdot 18$[/tex] per mile.
Plan B: $50 per day with free unlimited mileage
It is required to find that how many miles would be needed to drive for plan B to save money. be needed to drive for plan B to save money.
Step 1 of 5
In Plan A $30 per day and [tex]$\$ 0 \cdot 18$[/tex] per mile are costed so the cost of Plan A is given by following equation,
[tex]$$A=30 y+0 \cdot 18 x$$[/tex]
In Plan B $50 per day with free unlimited mileage are costed so the cost of Plan B is given by following equation,
[tex]$$B=50 y$$[/tex]
Step 2 of 5
Now comparing the obtained equations [tex]$A=30 y+0 \cdot 18 x$[/tex]
and B=50y.
[tex]$$30 y+0 \cdot 18 x=50 y$$[/tex]
Step 3 of 5
Subtract 30y from both the sides of the obtained equation 30 y+0.18x=50y and simplify using subtraction properties.
[tex]$$30 y+0 \cdot 18 x-30 y=50 y-30 y$$\\ $0 \cdot 18 x=20 y$[/tex]
Step 4 of 5
Divide both the sides of the obtained equation [tex]$0 \cdot 18 x=20 y$[/tex] by [tex]$0 \cdot 18$[/tex] and simplify using division properties.
[tex]$$\begin{aligned}&\frac{0 \cdot 18 x}{0 \cdot 18}=\frac{20 y}{0.18} \\&x=\frac{1000 y}{9}\end{aligned}$$[/tex]
Step 5 of 5 save money car rental need to drive 111.1 miles.
[tex]$$\begin{aligned}&\frac{x}{y}=\frac{1000 y}{9 y} \\&\frac{x}{y}=111.1\end{aligned}$$[/tex]
Please help ill give whoever answers the best the brainliest answer :0
Answer: Exponential
Step-by-step explanation:
Because every time x increases by 1, y increases by a factor of 3.
6/2 = 3
18/6 = 3
54/18 = 3
162/54 = 3
P.S.: I ANSWERED ONE OF YOUR PROBLEMS WITH EXACTLY THE DATA IN THIS TABLE BY COINCIDENCE HAHA
HELP HELP HELP HELP
HELP HELP HELP HELP
HELP HELP HELP HELP
HELP HELP HELP HELP
Answer:
19 inches
Step-by-step explanation:
So the perimeter of a triangle is the sum of the three sides. So the perimeter is [tex]\sqrt{65} + \sqrt{35} + \sqrt{26}[/tex] which is approximately 19.077 inches but in this case the answer is 19 inches
You are the coordinator for a program that is going to take place at night in a rectangular amphitheater in the mountains. You will have no access to any electricity, but you must be able to illuminate the entire grounds. You know the intensity of the light from a lantern varies inversely as the square of the distance from the lantern. Suppose the intensity is 90 when the distance is 5 m.
a. Write an equation to model the situation.
b. Solve for the constant of variation.
c. Write the equation to model the situation using the constant () of variation.
d. You have been given lanterns with 40 light intensity. Use your equation to solve for the distance from the lantern.
e. You need to illuminate 225 km. How many meters do you need to light?
f. How many lanterns will you need?
The equation to model the situation is [tex]\mathbf{y = \dfrac{k}{x^2}}[/tex]. The constant for the variation is 2250.
What is the intensity of light?The intensity of light from a lantern varies inversely to the square of the distance from the lantern.
From the given information:
Let y be the intensity of light, andx be the distance from the lanternThen:
[tex]\mathbf{y \alpha \dfrac{1}{x^2} }[/tex]
[tex]\mathbf{y = \dfrac{k}{x^2} }[/tex] here, k = constant.
2.
If y = 90 W/m² when the distance x = 5m
Then:
[tex]\mathbf{90 = \dfrac{k}{(5)^2}}[/tex]
k = 90 × 25
k = 2250
c.
The equation to model the situation by using the constant variation is:
[tex]\mathbf{y = \dfrac{2250}{x^2}}[/tex]
d.
If the light intensity y = 40, then x is determined as:
[tex]\mathbf{40 = \dfrac{2250}{x^2}}[/tex]
[tex]\mathbf{x = \sqrt{\dfrac{2250}{40}}}[/tex]
x = 7.5 m
e.
The light is needed in (225 × 1000)m = 225000 km of illumination.
f.
The lantern required for the new light estimation is:
y = 2250/225000
y = 0.01 intensity
Therefore, we can conclude that to get an intensity of 1 W/m², we need to put 100 lanterns.
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helpppp quick pointssss
Answer:
x = - 6
Step-by-step explanation:
The length of one side of a triangle is 2 feet less than three times the length of its second side. The length of the third side is 3/4
of the sum of the lengths of the first two sides. Find the lengths of all three sides if the perimeter of the triangle is 17.5 feet.
P=17.5 feet
Using a system of equations, it is found that the lengths of the sides of the triangle are given as follows:
0.91 feet, 0.73 feet, 1.23 feet.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are the lengths, given by x, y and z.
The length of one side of a triangle is 2 feet less than three times the length of its second side, hence:
y = 3x - 2.
The length of the third side is 3/4 of the sum of the lengths of the first two sides, hence:
[tex]z = \frac{3(x + y)}{4} = \frac{3(4x - 2)}{4}[/tex]
The perimeter of the triangle is 17.5 feet, hence:
[tex]x + y + z = 17.5[/tex]
[tex]x + 3x - 2 + \frac{3(4x - 2)}{4} = 17.5[/tex]
[tex]4x + \frac{3(4x - 2)}{4} = 19.5[/tex]
[tex]16x + 12x = 25.5[/tex]
x = 25.5/28
x = 0.91.
Then the other sides are:
y = 3x - 2 = 3(0.91) - 2 = 0.73 feet.[tex]z = \frac{3(4 x 0.91 - 2)}{4} = 1.23 feet[/tex]More can be learned about a system of equations at https://brainly.com/question/24342899
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What are the x-intercepts for the graph below?
A. (6,0), (-3,0)
B. (-6,0), (-3,0)
C. (-6,0), (3, 0)
OD. (6,0), (3, 0)
Answer:
-6,0 & -3,0
Step-by-step explanation:
Can someone help me with these geometry questions? I can’t seem to understand them. If u find the answers, can u explain it too? It’s urgent
Question 5
Vertical angles are congruent. Therefore, [tex]3y=\boxed{150}[/tex]. The sum of two supplementary angles equals [tex]\boxed{180^{\circ}}[/tex].
Therefore, [tex]6x+150=\boxed{180}[/tex]
Question 6
[tex]\angle b-14=90-\angle b\\\\2\angle b=104\\\\\angle b=\boxed{52^{\circ}}[/tex]
Question 7
[tex]\angle d+32=180-\angle d\\\\2\angle d=146\\\\\angle d=\boxed{73^{\circ}}[/tex]
Question 8
[tex]7x-80=3x\\\\-80=-4x\\\\x=20\\\\\implies \boxed{m\angle 1=m\angle 3=60^{\circ}}[/tex]
Using a significance level of 5%, the appropriate conclusion for a test with a p-value of 0.0421 would be:
A significance level of 5% (more commonly referred to as 95%) corresponds to a statement that (only) a probability of 5% or less is that a particular randomly generated observation is accepted as significant.
In this example, the p-level (the true probability that the observations are randomly generated) is less than 5% (0.0421 <0.05), so we can draw the conclusion that the observations are significant.
p = 0.0421 means that the probability is only 0421/1000. The choice of significance level to reject the null hypothesis is optional. Traditionally, 5%, 1%, and 0.1% levels have been used. In rare situations, a 10% significance level is also used.
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i need help asapp...
The value of b is -16 and the value of ac is 60 after comparing with the standard equation.
What is a quadratic equation?Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
As we know, the formula for the roots of the quadratic equation is given by:
[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]
We have a quadratic function:
= 3x² - 16x + 20
On comparing with standard function:
b = -16
a = 3
c = 20
ac = 3(20) = 60
Thus, the value of b is -16 and the value of ac is 60 after comparing with the standard equation.
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An angle measures 76.8° less than the measure of its supplementary angle. What is the measure of each angle?
Answer:
128.4°, 51.6°
Step-by-step explanation:
x + x - 76.8 = 180
2x = 256.8
x = 128.4
x - 76.8 = 51.6
Math HELP!!! 100PTS!!!
Sketch the region given by the set {(x,y)|xy<0} on a piece of paper. Which quadrants of the plane are included in the set? Input Yes or No at the corresponding space below:
quadrant 1:
quadrant 2:
quadrant 3:
quadrant 4:
Answer:
Quadrants 1 and 4 EDIT: Quadrants 2 & 4
Step-by-step explanation:
Quadrant 1 : Edit: no
Quadrant 2 : Edit: yes
Quadrant 3 : No
Quadrant 4 : Yes
For the upcoming parade, Lauren needed to make her school's triangular flag into a larger, similar triangular flag. Using the information given, determine which (if any) similarity postulate she used in making her school's new flag.
In order to make the new flag, Lauren decided to triple the sides of the old flag in order to get a new one.
What is the difference between these trianglesThe old triangle is the smaller one. We can see that this triangle has increased by a factor of 3 on all sides.
We have 4 x 3= 12
2 x 3 = 6
7 x 3 = 21
The calculated values above is what produced the new larger flag.
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Find the first five terms of the sequence described:
a sub 1 = 3
a sub n+1 = a sub n + 5
From the given recursive definition,
[tex]a_1 = 3[/tex]
[tex]a_2 = a_1 + 5 = 3 + 5 = 8[/tex]
[tex]a_3 = a_2 + 5 = 8 + 5 = 13[/tex]
[tex]a_4 = a_3 + 5 = 13 + 5 = 18[/tex]
[tex]a_5 = a_4 + 5 = 18 + 5 = 23[/tex]
CCAT Numerical Sample Question
A home appliance store has recently seen an increase in TV sales. Having noticed this, the
store manager decides to raise the TV price by 25% in order to increase the store's profits.
If the original price of a TV was 140$, how many could be bought post-raise for 4,200$?
Answer:
24
Step-by-step explanation:
140 times .25 = 35
140 + 35 = 175
4,200 divided by 175 =
24
jobtestprep
The number of TV bought post-raise for $4,200 is 24 if the store manager decides to raise the TV price by 25% in order to increase the store's profits.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
We have:
A home appliance store has recently seen an increase in TV sales.
The store manager decides to raise the TV price by 25% in order to increase the store's profits.
Original price of TV = $140
Price after increasing:
= 140 + 25% of 140
= $175
The number of TV bought post-raise for $4,200 = 4200/175
= 24
Thus, the number of TV bought post-raise for $4,200 is 24 if the store manager decides to raise the TV price by 25% in order to increase the store's profits.
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A beauty supply store surveyed 1,000 customers to determine which of 3 brands of concealer they like the best. 335 customers chose Brand A, 402 customers chose Brand B, while 263 customers chose Brand C. What percent of customers chose Brand B? Round off your answer to the nearest tenths place.
40.2 percent of the customers at the beauty supply store choose brand B.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The percent of customers that choose brand B = (number of brand B customers / total number of customers) * 100%
The percent of customers that choose brand B = (402/1000) * 100% = 40.2%
40.2 percent of the customers at the beauty supply store choose brand B.
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At noon, Bradley began steadily increasing the
speed of his car by 2 miles per hour every minute. At 12:15 p.m., he realized he was going
15 miles per hour over the speed limit. If his speed at noon was 40 miles per hour, what was the speed limit at 12:15 p.m.?
Please show work step by step
Answer:
25.5 mph
Step-by-step explanation:
So Bradley's speed can be modeled by the equation y=2x+40 where y=speed, x=time in hours after noon, and b=initial speed
So 12:15 is 15 minutes after noon, which is also 0.25 or 1/4 of an hour after noon. This is the x-value. Plug this into the equation to get his speed at 12:15
y=2(0.25)+40
y=0.5+40
y=40.5
So his speed was 40.5 at the time and since he was going 15 miles over the speed limit, the speed limit is 15 less than his speed
40.5 - 15 = 25.5
Answer:
25.5 mph
Step-by-step explanation:
Given information:
Bradley increases the speed of his car by 2 miles per hour. 12.00 pm: Bradley's speed = 40 mph12.15 pm: Bradley is driving at 15 miles over the speed limit.Calculate Bradley's speed at 12.15 pm:
60 minutes = 1 hour
⇒ 15 minutes = 1/4 hour
⇒ speed at 12.15 pm = speed at 12.00pm + 1/4 of 2 mph
= 40 mph + 0.5 mph
= 40.5 mph
If he was 15 miles over the speed limit at 12.15 pm then:
⇒ speed limit = speed at 12.15pm - miles over the limit
= 40.5 mph - 15
= 25.5 mph
Therefore, the speed limit was 25.5 mph.
I don’t understand this that much
By using the definitions of distance and number line, the distance between a and b on the number line is 10.97 units, not 0.47 units. (Right choice: A)
What choice is wrong about two integers?
Herein we must determine what choice is false with respect to two integers, one negative and other positive. The first choice represents a false proposition as:
|a - b| = |- 5.72 - 5.25| = |- 10.97|
|a - b| = 10.97
By using the definitions of distance and number line, the distance between a and b on the number line is 10.97 units, not 0.47 units. (Right choice: A)
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