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Given equation:
[tex]v\text{ - 42 = 11}[/tex]The first step is to solve the equation i.e. find the value of v
[tex]\begin{gathered} Collect\text{ like terms} \\ v\text{ = 11 + 42} \\ v\text{ = 53} \end{gathered}[/tex]The given options
Related Questions
if x varies directly as y, and x = 10 when y = 5, find x when y = 9. x = ______
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Solution:
Since x varies directly as y, consider the following diagram:
by cross-multiplication, we get:
[tex]5x\text{ = (9)(10)}[/tex]this is equivalent to:
[tex]5x\text{ = 90}[/tex]solving for x, we get:
[tex]x\text{ = }\frac{90}{5}=18[/tex]so that, we can conclude that the correct answer is:
x = 18.
UVW is a regular triangle and the length of UV is 3 meters. What is the length of UW?A) 2 mB) 3 mC) 6 mD) 9 m
Answers
When a polygon is regular, all its sides are congruent (that is, they have the same length).
So, if the triangle is regular and one of the sides has a length of 3 meters, therefore all sides have a length of 3 meters.
Correct option: B.
A rectangular box, closed at the top, with a square base, is to have a volume of 4000 cm^ 3 . W What must be its dimensions (length, width, height ) if the box is to require the least possible material?
Answers
Solution
Area of square base of sides x is
[tex]Area=x^2[/tex]Volume = 4000cm^3
[tex]\begin{gathered} Volume=Bh \\ B=Base\text{ }Area \\ h=height \end{gathered}[/tex]Thus,
[tex]\begin{gathered} Volume=Bh \\ 4000=x^2h \\ \\ h=\frac{4000}{x^2} \end{gathered}[/tex]For the box to require the least possible material, is to simply minimize the surface area of the rectangular box
The surface Area is given as
[tex]\begin{gathered} Area=2(lw+wh+lh) \\ Since,\text{ it is a square base} \\ l=x \\ w=x \\ \\ Area=2(x^2+xh+xh) \\ Area=2(x^2+2xh) \\ Area=2(x^2+2x(\frac{4000}{x^2})) \\ \\ Area=\frac{16000}{x}+2x^2 \end{gathered}[/tex]Now, we differentiate
[tex]\begin{gathered} Area=\frac{16,000}{x}+2x^{2} \\ A=16000x^{-1}+2x^2 \\ By\text{ differentiating} \\ \frac{dA}{dx}=-16000x^{-2}+4x \\ \\ At\text{ minimum area, }\frac{dA}{dx}=0 \\ 4x=16000x^{-2} \\ x^3=4000 \\ x=10\sqrt[3]{4} \end{gathered}[/tex]Now, to find h
[tex]\begin{gathered} h=\frac{4000}{x^2} \\ h=\frac{4000}{100(4)^{\frac{2}{3}}} \\ h=4^{\frac{1}{3}}\times10 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} Length=10\sqrt[3]{4}cm=15.874cm\text{ \lparen to three decimal places\rparen} \\ Width=10\sqrt[3]{4}cm=15.874cm\text{ \lparen to three decimal places\rparen} \\ height=15.874cm\text{ \lparen to three decimal places\rparen} \end{gathered}[/tex]Which function is undefined for x = 0?O y=³√x-2Oy=√x-2O y=³√x+2Oy=√x+2
Answers
The above function is defined for (x=0)
From the question, we have
Function 1 - y = ∛x-2
Function 2 - y = √x-2
Function 3 - y = ∛x+2
Function 4 - y = √x+2
substituting (x = 0) to determine which function is undefined for (x = 0).
Function 1 - y = ∛x-2
substituting (x = 0), we get
y=∛-2
The above function is defined for (x=0).
Function 2 - y = √x-2
substituting (x = 0), we get
y = √-2
The above function is defined for (x=0).
Function 3 - y = ∛x+2
substituting (x = 0), we get
y = ∛2
The above function is defined for (x=0).
Function 4 - y = √x+2
substituting (x = 0), we get
y = √2
The above function is defined for (x=0).
Hence, it can be concluded that the above function is defined for (x=0)
Subtraction:
Subtraction represents the operation of removing objects from a collection. The minus sign signifies subtraction −. For example, there are nine oranges arranged as a stack (as shown in the above figure), out of which four oranges are transferred to a basket, then there will be 9 – 4 oranges left in the stack, i.e. five oranges. Therefore, the difference between 9 and 4 is 5, i.e., 9 − 4 = 5. Subtraction is not only applied to natural numbers but also can be incorporated for different types of numbers.
The letter "-" stands for subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation. A minuend is the first number in a subtraction process and is the number from which we subtract another integer in a subtraction phrase.
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wХ14. Given: WX || YZ, WX = YZProve: AWXZ AYZXZ
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A bus travel's at an average speed of 65.1 miles in 3 hours in the city. how far could the bus travel in 8.2 hours?
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177.94miles
Explanations:From the question, distance is directly proportional to the time taken. Mathematically;
[tex]\begin{gathered} d\alpha t \\ d=kt \\ k=\frac{d}{t} \end{gathered}[/tex]where:
d is the distance traveled
t is the time
If the bus travel's at an average speed of 65.1 miles in 3 hours in the city, the variation constant "k" is calculated as;
[tex]\begin{gathered} k=\frac{65.1\text{miles}}{3\text{hours}} \\ k=\frac{21.7mi}{hr} \end{gathered}[/tex]In order to determine how far could the bus travel in 8.2 hours
[tex]\begin{gathered} d=kt \\ d=\frac{21.7miles}{\cancel{hr}}\times8.2\cancel{\text{hrs}} \\ d=177.94\text{miles} \end{gathered}[/tex]Therefore the bus can travel for 177.94miles in 8.2hours
Match an appropriate graph to each equation. t (x) = 1/x+3t (x)= -1/x+3
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t (x) = 1/x + 3
t (x) ⇒ y
y = 1/x + 3
when x = 1
y = 1/1 + 3 = 1 + 3 = 4
y = 4(Graph 4)
t (x)= -1/x + 3
t (x) ⇒ y
y = -1/x + 3
when x = 1
y =-1/1 + 3 = - 1 + 3 = 2
y = 2(Graph 2 )
Hence, the correct graph to these equations is Graph 4 & Graph 2
One gram is approximately 2.2 x 10-pounds. Which of the following represents this number in standard notation? OA. 0.0022 OB. 0.022 OC. 2200 OD. 0.00022
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One gram is approximately 2.2 x 10^-3
10^-3 = 1/1000
= 0.001
= 2.2 x 0.001
= 0.0022
The answer is option A
VFind the area of the figure. (Sides meet at right angles.)3 in5 in5 in10 in8 in
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Given the shown composite figure
We will find the area of the figure using the following figure
as shown, the figure is divided into 2 shapes
shape (1) is a rectangle with dimensions 3 in and 5 in
The area of shape (1) = 3 x 5 = 15 in²
shape (2) is a rectangle with dimensions 8 in and 5 in
The area of shape (2) = 8 x 5 = 40 in²
The total area of the figure = 15 + 40 = 55 in²
So, the answer will be Area = 55 in²
In the figure below, AB AD andAC bisects A. Solve for x. Then, using that value, find the length of AC
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Since AB = AD
15x + 4 = 2x + 160
15x - 2x =160 - 4
13x = 156
x =156/13
x = 12
AC = 11X + 35
Since x = 12
AC = 11 x 12 + 35
AC = 132 + 35
AC =167
Find the slope of each line
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The equation of the slope of a line is given by the formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]The coordinates (x1, y1) and (x2, y2) are the coordinates that we need to identify in the graph:
(x1, y1) = (-4, 4)
(x2, y2) = (0, -3)
Then, applying the formula to find m:
[tex]m=\frac{y2-y1}{x2-x1}=\frac{-3-4}{0-(-4)}=\frac{-7}{4}\rightarrow m=-\frac{7}{4}[/tex]Therefore, the slope for the line is m = -7/4.
I need help with this. You could select more than one answer
Answers
given expression is,
[tex]30x^2-5x-10[/tex]to find the expression equal to the given expression.
the expression is,
[tex]\begin{gathered} -5(-6x^2+x+2) \\ =-5(-6x^2)-5x-5\cdot \\ =30x^2-5x-10 \end{gathered}[/tex]if Df and Gi are parallel lines and m≤ihj=60° what is m≤FEH
Answers
Answer:
m∠FEH = 60
Explanation:
Angle IHJ and angle FEH are corresponding angles, they are in the same relative position to the parallel lines and the diagonal.
Corresponding angles have the same measure, so the measure of angle FEH is:
m∠FEH = m∠IHJ
m∠FEH = 60
Which Story can be represented as 36 divided by 4 A. Jim has 36 pennies. May has four more pennies Than Jin.B. Jin has 4 fewer pennies than May. May has 36 pennies. C.Jin has 4 pennies. May has 36 times as many pennies as Jin.D.Jin has 36 pennies. She shares the pennies equally among 4 friends.
Answers
D is the answer.
In all the other cases the operations that we will have to make are not divisions.
In case A we have an addition.
In case B we have a substraction.
In case C we have a multiplication.
The correct story which an be represented as 36 divided by 4 is,
D. Jin has 36 pennies. She shares the pennies equally among 4 friends.
We have to given that,
All expressions are,
A. Jim has 36 pennies. May has four more pennies Than Jin.
B. Jin has 4 fewer pennies than May. May has 36 pennies.
C. Jin has 4 pennies. May has 36 times as many pennies as Jin.
D. Jin has 36 pennies. She shares the pennies equally among 4 friends.
Hence, In all the other cases the operations that we will have to make are not divisions.
In case A we have an addition.
In case B we have a subtraction.
In case C we have a multiplication.
In case of D;
D. Jin has 36 pennies. She shares the pennies equally among 4 friends.
This shows the operation division.
As, Each friends get, 36 / 4 = 9 pennies
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(1 4/7)_____-(15/21)
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(1 4/7)
_____
-(15/21)
To solve;
we will cange the division to multiplication. By doing that 15/21 becomes 21/15
That is;
[tex]\frac{14}{7}\times-\frac{21}{15}[/tex]7 can divide 21 to give 3
Hence;
[tex]\frac{14}{1}\times-\frac{3}{15}[/tex]3 can also divide 15 to give 5
[tex]\frac{14}{1}\times-\frac{1}{5}[/tex]we will now multiply
[tex]=\frac{-14}{5}[/tex][tex]=-2\frac{4}{5}[/tex]11. Which set of points could you use to create a line with slope of -3/2? (A) (5,7) (7,4) (B) (-1,4) (1,7) (C) (3,2) (1,-3)(D) (-3,0) (0,-2)
Answers
Answer:
(A) (5,7) (7,4)
Explanation:
To determine the set of points that could be used to create a line with a slope of -3/2, we use the slope formula below.
[tex]\text{Slope}=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}}[/tex]Option A
[tex]\begin{gathered} \text{Slope}=\frac{7-4}{5-7} \\ =-\frac{3}{2} \end{gathered}[/tex]Therefore, the set of points is (5,7) and (7,4).
A flower garden is shaped like a circle. Its radius is 18 yd. A ring-shaped path goes around the garden. The width of the path is 5 yd.
The gardener is going to cover the path with sand. If one bag of sand can cover 6 yd^2, how many bags of sand does the gardener need? Note that sand comes only by the bag, so the number of bags must be a whole number. (Use the value 3.14 for pi.)
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The number of gallons of the coating must be a whole number will be 114 gallons.
What is the area of the circle?Let d be the diameter of the circle. Then the area of the circle will be
A = (π/4) d² square units
At the recreation area, there is a pool molded like a circle with a measurement of 24 yds. A ring-molded way circumvents the pool. Its width is 6 yds.
The area of the path will be given as,
A = (π/4) (24 + 6 + 6)² - (π/4) (24)²
A = (π/4) [36² - 24²]
A = (π/4) [720]
A = 565.5 square yards
We will give another layer of covering to the way. On the off chance that one gallon of covering can cover 5 yd². Then the number of gallons of coating is given as,
⇒ (565.5) / 5
⇒ 113.097
⇒ 114 gallons
The number of gallons must be a whole number will be 114 gallons.
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Complete the table for the missing values of r .PT101812161416
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To complete the table, it is observed that as p-values increase by 2 downward, the r-value decreases by 2
Thus
p r
10 18
12 16
14 14
16 12
The equation for the number of points Sydney's needed is
r = 28 - p
find volume of the right triangular prism round to hundred
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V = 594mm^3
In order to calculate the volume of a prisma you must multiply the area of the base times the height. The base is a triangle.
However, we don't have the value of the height in it, but we find it by solving the Pythagorean theorem on the triangle.
Find an nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using a graphing utility, use it to graph the function and verify the real zeros and the given function value.n=34 and 4i are zeros;f(-1)=85F(x) = ________
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Given that at n=3: 4 and 4i are zeros:
Then:
[tex]\begin{gathered} (x-4)(x-4i)(x+4i)\Rightarrow(x-4)(x^2-(4i)^2) \\ (x-4)(x-4i)(x+4i)\Rightarrow(x-4)(x^2+16) \\ (x-4)(x-4i)(x+4i)\Rightarrow x^3+16x-4x^2-64 \\ (x-4)(x-4i)(x+4i)\Rightarrow x^3-4x^2+16x-64 \end{gathered}[/tex]Hence the function is:
[tex]F=x^3-4x^2+16x-64[/tex]can you please solve this practice problem for me I really need assistance and also ONLY SOLVE THE SECOND PROBLEM.
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The answer is the third choice
x - 5 because the temperature diminishes 5 degrees
2 because the temperature doubled
40 because the final number is 40
A gardener wishes to create raised beds. She wants the bedsto follow the golden ratio. If the shorter side is 4 feet, whatwill be the longer side of the beds? Round answer to the nearesttenth.
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The golden ratio is equal to 1.618. This means that the ratio between the two sides of the bed must be equal to that value. We were given the shorter side of the bed, therefore to find the length of the longer side we need to multiply the short one by the golden ratio.
[tex]\text{longer = 1.618}\cdot4=6.472\text{ ft}[/tex]The longer side will be approximately 6.5 ft
This is the last question we have been stuck on it is there anyway you can help us out
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Clearly,
[tex]1.3\cdot10^{12}[/tex]Is the largest number.
That's because it has more zeros due to its exponent is the most bigger of the four options.
hello can you help me i think the answer is 2
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From the graph given,
The Swans are on the x-axis and the Geese are on the y-axis
Where there are 5 swans, the number of geese are 2
Hence, there are 2 geese when there are 5 swans.
Answer:
2 geese
Step-by-step explanation:
Reading a graph
The input is swans and the output is gees
When there is 5 on the x axis, there is 2 on the y axis
For 5 swans, there are 2 geese
Writing the equation for each line. slope 6 and y-intercept (0,-2).
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We are given slope and the y-intercept. The formula y = mx + c can be used to determine the equation of the line.
m = slope
c= y-intercept.
For this question,
m = 6
c = -2
The equation of the line is
y = 6x + (-2)
y = 6x -2
The answer is y = 6x -2
the probability of the complement of an event is _______ less than the probability of the event itd self possible answers sometimesalwaysnevernot enough information provided to answer the question
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The complement rule states that the sum of the probabilities of an event and its complement must equal to 1. That is, for an event A and its complement A', we have
[tex]P(A)+P(A^{\prime})=1[/tex]so, as long as the sum is 1, the probability of the complement of an event is sometimes less than the probability of the event itself .
The measures of the angles of a triangle are shown in the figure below. Solve for x. 47 74
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ThisThe sum of angles in a triangle
[tex]=180^0[/tex]The angles given in the triangle are
[tex]x^0,74,47^0^{}^{}^{}_{}^{}[/tex]Which means that,
[tex]x^0+47^0+74^0=180^0[/tex][tex]\begin{gathered} x^0+121^0=180^0 \\ \text{collecting like terms,we will have} \\ x^0=180^0-121^0 \\ x^0=59^0 \end{gathered}[/tex]Hence,
The final answer is x=59°
The school population for a certain school is predicted to increase by 50 students per year for the next 14 years. If the current enrollment is 600 students, what will the enrollment be after 14 years?
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Suppose that the school population is 600 students, and that it is predicted to increase by 50 students per year for the next 14 years. Thus we will have:
[tex]\begin{gathered} \text{Year 0: }600 \\ \text{Year 1: }600+50=600+1\cdot50 \\ \text{Year 2: }600+50+50=600+2\cdot50 \\ \ldots \\ \text{Year 14: }600+\underbrace{50+\cdots+50}=600+50\cdot14=600+700=1300 \end{gathered}[/tex]This means that the enrollment after 14 years will be of 1300 students in total.
Simplify using expressions 15m^3n^5 / 3m^2n^2
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Simplify using expressions
15m^3n^5 / 3m^2n^2
1. The number
15/3 = 5
____________________
2. m
m^3 / m^2 = m*m*m/m*m = m
____________________
3. n
n^5 /n^2 = n^3
_______________
The simplified expression is 5mn^3
________________________
n^a /n^b = n^(a-b)
n^a x n^b = n^(a+b)
Seth's father is thinking of buying his son a summer movie pass for $30 dollars. With the pass, matinees cost $2 each. Without thepass each movie is normally $6. If Seth plans to go to 30 movies this summer how much money would he save?
Answers
Theres a number of passes to purchase
Normal price (without pass) is $6
If Seth goes to all 30 movies without pass he will spend
30x6 = $180 dollars
WITH the pass Seth have $30 dollars , then dividing by 2 , this means he can go to 30/2 = 15 movies in summer with pass
Then remains another 15 movies that he can vo WITHOUT PASS
in this 15 movies Seth spends 15x6= $90 dollars
add this to the $30 spent in the other 15 movie
it gives 30+90 = $120 dollars
Finally substract
$180- $120= $60 dollars he can save