Given g(x)=5x+4g(x)=5x+4, solve for xx when g(x)=9g(x)=9.
Answer:
[tex]\huge\boxed{\sf x = 1}[/tex]
Step-by-step explanation:
Given function:g(x) = 5x + 4
Given that, g(x) = 9
So,
9 = 5x + 4
Subtract 4 to both sides
9 - 4 = 5x
5 = 5x
Divide 5 to both sides
1 = x
OR
x = 1
[tex]\rule[225]{225}{2}[/tex]
Answer:
x = 1
Step-by-step explanation:
The given information is,
→ g(x) = 5x + 4
→ g(x) = 9
Now the value of x will be,
→ 5x + 4 = g(x)
→ 5x + 4 = 9
→ 5x = 9 - 4
→ x = 5/5
→ [ x = 1 ]
Hence, the value of x is 1.
ILL GIVE BRAINLY AND 10 PONITS Which inequality matches the graph?
Answer: not 100% but i think its A
Step-by-step explanation:
Each student in Ms. Lee's class is either a junior or a senior. Ms. Lee took some students from her class on a field trip. Of the 18 juniors in her class, 5/6 went on the trip, and 17 seniors from her class also went on the trip.
Use this information to answer the questions below.
If not, enough information is given to answer a question, click on "Not enough information."
(a) How many juniors from the class did not go on the field trip?
(b) How many juniors from the class went on the field trip?
(c) How many students from the class did not go on the field trip?
What is Equation Modelling?
Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given is each student in Ms. Lee's class is either a junior or a senior. Ms. Lee took some students from her class on a field trip. Of the 18 juniors in her class, 5/6 went on the trip, and 17 seniors from her class also went on the trip.
[A] - Juniors that did not went are -
18 - (5/6 x 18)
18 - 15
3
[B] - Juniors that went are -
(5/6 x 18)
15
[C] - Not enough information
Therefore -
3 Juniors that did not went to trip.15 Juniors went to trip.Not enough informationTo solve more questions on equation modelling, visit the link below-
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City A and City B had two different temperatures on a particular day. On that day, five times the temperature of City A was 8° C more than three times the temperature of City B. The temperature of City A minus twice the temperature of City B was −4° C. The following system of equations models this scenario: 5x = 8 + 3y x − 2y = −4 What was the temperature of City A and City B on that day? City A was 1° C, and City B was −1° C. City A was 4° C, and City B was 4° C. City A was 7° C, and City B was 9° C. City A was 10° C, and City B was 14° C.
The temperature of City A and City B on that day was 4° C respectively.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
WE have been given system of equations as;
5x = 8 + 3y
x − 2y = −4
Now we can multiply equation B by -5 to eliminate the x variable in both equations.
Add them together;
5x = 8 + 3y
-5x + 10y = 20
Then add both of them A + B:
-5x + 10y + 5x - 3y = 20 + 8
7y = 28
y = 4
To solve for x;
5x = 8 + 3y
5(x) = 8 + 3(4)
x = 4
Hence, the temperature of City A and City B on that day was 4° C respectively.
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Answer:
B. City A was 4° C, and City B was 4° C.
Step-by-step explanation:
It is right i did it on the test
Simplify
√ 96x³
please help
Answer:
4x[tex]\sqrt{6x}[/tex]
Step-by-step explanation:
This can be written:
[tex]\sqrt{(3)(2)(2)(2)(2)xxx}[/tex] Pull out all the pairs. There are 2 pairs of 2 and 1 pair of x's
(2)(2)x[tex]\sqrt{(3)(2)x}[/tex] Clean up
4x[tex]\sqrt{6x}[/tex]
Evaluate. (5/6+2/3)−(3/4+1/12) Enter your answer as a fraction in simplest form by filling in the boxes. $$
The evaluation of the fraction (5/6 + 2/3) - (3/4 + 1/12) in its simplest form is 2/3
How to evaluate fractions?A fraction is a number which consists of a numerator and a denominator.
A numerator is the upper or top value of a fraction while a denominator is the lower or bottom value of a fraction.
(5/6 + 2/3) - (3/4 + 1/12)
= (5+4)/ 6 - (9+1) / 12
= 9/6 - 10/12
= 3/2 - 5/6
= (9-5) / 6
= 4/6
= 2/3
Consequently, the answer to the given fraction in its simplest form is 2/3
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The Garcias bought a $328,000 house. They made a down payment of $49,000 and took out a mortgage for the rest. Over the course of 15 years they made monthly payments of $2354.37 on their mortgage until it was paid off. What was the total amount they ended up paying for the house (including the down payment and monthly payments)? $0 (b) How much interest did they pay on the mortgage? $0 (a) t 5
Answer:
328,000-49,000= 279000
the amount of mortgage they paid
15 x 2354.37= 35315.55
Step-by-step explanation:
What is the test statistic for a hypothesis test where H0: μ=12.5, x¯¯¯=14.1, s=2.7, and n=12? Responses
The test statistic for the hypothesis test using the parameters is 2.05
A test statistic is used to access how consistent sample data are with the null hypothesis in a hypothesis test.
How to calculate test hypothesis of given parameters?
Using the parameters
Hₙ: ц=12.5, x=14.1, s=2.7, and n=12
The test statistic (t) is given by the formula
t=[tex]\frac{x-U}{s/\sqrt{n} }[/tex]
Substituting the given parameters;
t=[tex]\frac{14.1-12.5}{2.7/\sqrt{12} }[/tex]
t=[tex]\frac{1.6}{2.7/3.46}[/tex]
t=[tex]\frac{1.6}{0.78}[/tex]
t=2.05
This figure is round up to 2 decimal places
The test statistic using the parameters is 2.05
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Evaluate : -15 + 6 =
Answer: -11
(absolute value) (15 - 6) x -1 = 11 x -1 = -11
Answer:
6 on edge
Step-by-step explanation:
K
A car rental agency rents 440 cars per day at a rate of $40 per day. For each $1 increase in rate, 10
fewer cars are rented. At what rate should the cars be rented to produce the maximum income? What
is the maximum income?
...
The rental agency will earn a maximum income of $
when it charges $
per day.
Time Remaining: 01:44:21
Next
The maximum income is Maximum cost C is $19740
What is the maximum income?Let Q represent the number of cars rented per day and P the rate.
To form the demand equation;
Q = a - bP
A car rental agency rents 440 cars per day at a rate of $40 per day
440 = a - 40b ......1
For each $1 increase in rate, 10 fewer cars are rented
(440-10) = a - (40+1)b
430 = a - 41b ......2
Subtracting equation 2 from 1
10 = b
From equation 1;
440 = a - 10(40)
a = 440 + 400 = 840
So;
Q = 840 - 10P
Cost C = Q×P = P (840-10P) = 840P - 10P^2
Maximum cost is at dC/dP = 0
dC/dP = 840 - 20P = 0
P = 840/20 = $42
Maximum cost C is
C = P(840-10P) = 42(840-370) = 42 × 470 = $19740
The maximum income is Maximum cost C is $19740
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Jenny collected donations at a pet store for the local animal shelter. As she left, Jenny
estimated she had collected $85. After counting the donations, she learned she had actually
collected $110. What is the percent error for her estimate?
If necessary, round your answer to the nearest tenth of a percent.
Answer:
Step-by-step explanation
Initial amount = $85
Final amount = $110
percentage error = ((Final amount - Initial amount)*100)/Final amount
= (25*100)/110
=22.7272
=22.7 (to the nearest tenth of a percent, which is 1 decimal place)
The solution is 22.7 %
The percentage error in the estimation of donations at the pet store by Jenny is 22.7 %
What is Percentage Error?
The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.
Percentage error is the difference between the measured value and the true value , as a percentage of the true value
Percentage Error = [ ( | Measured Value - True Value | ) / True Value ]x 100
Given data ,
Let the percentage error be represented as A
Now , the value of A is
The estimated donation amount by Jenny = $ 85
The actual donation amount collected by Jenny = $ 110
Now , the percentage error in the estimation of Jenny A is calculated by the equation ,
Percentage error in the estimation of Jenny A = ( ( | estimated donation amount - actual donation amount collected by Jenny ) | / actual donation amount collected by Jenny ) ) x 100
Substituting the values in the equation , we get
Percentage error in the estimation of Jenny A = ( | 85 - 110 | / 110 ) x 100
On simplifying the equation , we get
Percentage error in the estimation of Jenny A = ( 25/110 ) x 100
Percentage error in the estimation of Jenny A = 2500 / 110
Percentage error in the estimation of Jenny A = 22.72 %
Therefore , the value of A is 22.7 %
Hence , the percentage error in the estimation is 22.7 %
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Set up the triple Integral SI V over the tetrahedron formed by the coordinate planes and the plane X + y + 24 using six different orders of Integration de dy dx dx dy dy do dy dx de ar ddy dr dy (b) Find the volume of the tetrahedron.
Step-by-step explanation:
For Part A:
Refer to the photo for an explanation on how to graph z=x+y+24 and how to set up the first integral. I will not explain how to do the other five but I have placed them beneath....
[tex]\int\limits^{24}_0 {} \,\int\limits^{z-24}_0 {} \,\int\limits^{z-y-24}_0 {} \, 1dxdydz \\\\[/tex]
Where limits are, [tex]0\leq x\leq z-y-24\\0\leq y\leq z-24\\0\leq z\leq 24[/tex]
[tex]\int\limits^{-24}_0 {} \,\int\limits^{y+24}_0 {} \,\int\limits^{z-y-24}_0 {} \, 1dxdzdy\\\\[/tex]
Where limits are, [tex]0\leq x\leq z-y-24\\0\leq z\leq y+24\\0\leq y\leq -24[/tex]
[tex]\int\limits^{24}_0 {} \,\int\limits^{z-24}_0 {} \,\int\limits^{z-x-24}_0 {} \, 1dydxdz\\\\[/tex]
Where limits are,[tex]0\leq y\leq z-x-24\\0\leq x\leq z-24\\0\leq z\leq 24[/tex]
[tex]\int\limits^{-24}_0 {} \,\int\limits^{x+24}_0 {} \,\int\limits^{z-x-24}_0 {} \, 1dydzdx\\\\[/tex]
Where limits are, [tex]0\leq y\leq z-x-24\\0\leq z\leq x+24\\0\leq x\leq -24[/tex]
[tex]\int\limits^{-24}_0 {} \,\int\limits^{-y-24}_0 {} \,\int\limits^{x+y+24}_0 {} \, 1dzdxdy\\\\[/tex]
Where limits are, [tex]0\leq z\leq x+y+24\\0\leq x\leq -y-24\\0\leq y\leq -24[/tex]
[tex]\int\limits^{-24}_0 {} \,\int\limits^{-x-24}_0 {} \,\int\limits^{x+y+24}_0 {} \, 1dzdydx[/tex]
Where Limits are, [tex]0\leq z\leq x+y+24\\0\leq y\leq -x-24\\0\leq x\leq -24[/tex]
For Part B:
All the above limits equal the same volume. So I will just solve for one of the limits.
Evaluate, [tex]\int\limits^{24}_0 {} \,\int\limits^{z-24}_0 {} \,\int\limits^{z-y-24}_0 {} \, 1dxdydz \\\\[/tex]
[tex]\int\limits^{24}_0 {} \,\int\limits^{z-24}_0 {} \, (x]^{z-y-24} _0){} dydz \\\\[/tex]
[tex]\int\limits^{24}_0 {} \,\int\limits^{z-24}_0 {} \, [(z-y-24)-0]{} dydz \\\\[/tex]
[tex]\int\limits^{24}_0 {} \,\int\limits^{z-24}_0 {} \,z-y-24{} dydz \\\\[/tex]
[tex]\int\limits^{24}_0 {} \,[0-\frac{y^{2} }{2} -0]{} dz \\\\[/tex]
[tex]\int\limits^{24}_0 {} \,\frac{y^{2} }{2} ]^{z-24} _{0} {} dz \\\\[/tex]
[tex]\int\limits^{24}_0 {} \,[(\frac{(z-24)^{2}}{2})-0] {} dz \\\\[/tex]
[tex]\int\limits^{24}_0 {} \,[\frac{z^2}{2}-288] {} dz \\\\[/tex]
[tex][\frac{z^3}{6}-288z]^{24} _{0} {} \\\\[/tex]
[tex][(\frac{24^3}{6}-288(24))-0] {}[/tex]
[tex](4608-6912)=-2304\\[/tex]
Answer: -2304
If V is an independent variable and W is a variable that depends on V which of the following could be a function notation representations of W select all that apply …
The function notations that could represent the variable, w, are:
f(v) = 2v - 1
f(v) = 1 - 8v
What are the Variables of a Function?For example, if we are given the function notation as f(b) = b, where a and b are the variables, it means that:
b is the independent variablea is the dependent variable, which is equivalent to f(b)The value of f(b) is dependent on the value of b.In the same vein, if v is an independent variable and w is a dependent variable, it means that:
w which is the dependent variable is equivalent to f(v)
The value of f(v) is dependent on the value of v.
The function notation can therefore be:
f(v) = 2v - 1
f(v) = 1 - 8v
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Jim is a preschool teacher. While he was getting ready for his class's snacktime, he put 6 carrots on each plate. If he used 48 total carrots, which equation could be used to determine the number of plates, p, that he used?
The equation that can be used to determine the number of plates used is p = 48 / 6.
What is the equation?In order to determine the number of plates that Jim used, divide the total number of carrots by the number of carrots used for each plate.
Division is the mathematical process used to put a number into equal groups using another number. The sign that represents division is ÷.
Total number of plates used = total number of carrots / carrot used per plate
Total number of plates used = 48 / 6
Total number of plates used = 8
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Wyatt was out at a restaurant for dinner when the bill came. He wanted to leave a tip of 19%. What number should he multiply the cost of the meal by to find the total plus tip in one step?
Answer:
The cost of the meal should be multiplied by 1.19.---------------------------------------
Let the cost of the meal be x.
Adding a tip of 19%:
x + 19% = x + 0.19x = x (1 + 0.19) = 1.19xAnswer:
Wyatt should multiply with 1.19.
Step-by-step explanation:
Forming the expression,
→ 1 + (19% of 1)
Now the required number is,
→ 1 + (19% of 1)
→ 1 + ((19/100) × 1)
→ 1 + (19/100)
→ 1 + 0.19 = 1.19
Hence, required number is 1.19.
The mean points obtained in an aptitude examination is 159 points with a standard deviation of 13 points.
What is the probability that the mean of the sample would differ from the population mean by more than 1 point if 60 exams are sampled? Round your answer to four decimal places.
don't for get to round
Answer:
[tex]0.4514 = 45.14%[/tex]
Step-by-step explanation:
Use the equation:
[tex]Z=\frac{X-u}{a}[/tex]
Given:
[tex]u=159, o=13,n=60,s=1.68[/tex]
This is the pvalue of Z when [tex]X = 159+1 = 160[/tex] subtracted by the pvalue of Z when [tex]X = 159-1 = 158[/tex]
[tex]x = 160[/tex]
[tex]Z=\frac{X-u}{o}[/tex]
Central Limit Theorem applied:
[tex]Z=\frac{X-u}{o}[/tex]
[tex]Z=\frac{160-159}{1.68}[/tex]
[tex]Z=0.6[/tex]
[tex]Z=0.6(\text{P-value}:0.7257)[/tex]
[tex]X=150[/tex]
[tex]Z=\frac{X-u}{o}[/tex]
[tex]Z=\frac{158-159}{1.68}[/tex]
[tex]Z=-0.6[/tex]
[tex]Z=-6(\text{P-value}:0.2743[/tex]
[tex]0.7257-0.2743=0.4514[/tex]
This means that there is a 45.14% probability.
Can someone help me I don’t understand this question it’s geometry
The entire missing lengths as well as the missing angles of the given right angle triangle are as calculated below using Pythagoras theorem and trigonometric rules.
How to use trigonometric rules?We are given a right angle triangle and as such we can use both Pythagoras theorem and even trigonometric rules such as sine rule and cosine rules.
a) W are given that A = 30°, Thus;
B = 180 - (90 + 30)
B = 60°
Using sine rule;
a/sin A = b/sin B
a/sin 30 = 6/sin 60
a = 3.464
c/sin 90 = 6/sin 60
c = 6.928
b) a = 13 and b = 13
Using Pythagoras theorem;
c = √(13² + 13²)
c = 18.385
Since a = b, it means it is an isosceles triangle and so;
A = B = 45°
c) B = 30°, c = 10
A = 180 - (30 + 90)
A = 60°
10/sin 90 = b/sin 30
b = 5
10/sin 90 = a/sin 60
a = 8.66
d) A = 45°, c = 12
B = 45°
c/sin 90 = b/sin 45 = a/sin 45
b = a = 12 * sin 45 = 8.485
e) c = 1, b = 1/√2
c/sin 90 = b/sin B
1/sin 90 = (1/√2)/ sin B
B = 45° = A
a = √(1² - (1/√2)²)
a = 0.7071
f) c = 4 and b = 4;
a = √(4² - (4)²)
a = 0
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II. Reacting Metals with Solutions of Metallle Salts
appearance of 0.5 M Al2(SO4)3 :
metal description of reaction mixture 5 min did reaction occur?
after mixing with 0.5 M Al2(SO4)3
Fe
Cu
From the position of the metals on the electrochemical series, there would be no reaction of the solution with iron and copper.
What is the reactivity?We know that a reaction is said to have occurred between a metal and a solution if the metal is able to displace the cation that is in the solution. This displacement would in turn have a lot to do with the position of the metals in the electrochemical series.
Given that iron and copper are all less than aluminum which is the cation in the solution in the electrochemical series then it would not be possible for these metals to displace it in solution thus there would be no reaction.
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Zoe can rent space for her gelato stand for $275.50 per month for the year, or for
$575.25/month for only the four summer months. She is debating whether she should
run the business all year, or only during the summer months. She knows that after all
other expenses, not considering rent, she makes a profit $700.00/month for each of the
summer months, but only $150.00 for each of the rest of the months. She is paying
herself a wage in her expenses.
A campfire has a flame 24 inches tall after burning for 4 hours. After 6 hours, it is 20 inches tall. Write a linear equation to model the relationship between height h of the fire and time t. Predict how tall the fire will be after burning 8 hours.
(I dont have many points as this is a new account but i will mark brainiest if work is shown and correct answer)
The linear equation that model the above is h = 32 -2t and the height of fire after 8 hours is 16 inches
What is a linear equation?A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant.
Using the equation for a straight line and writing similar
h = mt + c
h = height, t = hours m and c are constants
at h = 24, t = 4
Equation becomes
24 = 4m + c--------------1
at h = 20, t = 6
20 = 6m + c---------------2
Subtract equation 2 from 1 so that the eqution reduces to
4 = -2m
m = 4/-2
m = -2
substitute m in equation 1
24 = 4( -2) + c
24 = -8 + c
c = 32
substituting m and c in he linear equation above we have
h = 32 - 2t
After 8 hours, the height h = 32 -2(8) which is 16 inches
In conclusion the linear equation is h = 32 - 2t and the height of fire after 8 hours is 16 inches
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Which of the following is true
Answer:
The answer is answer choice E.
Step-by-step explanation:
Complementary angles add up to 90 degrees, while supplementary angles add up to 180 degrees
24 children were asked which is their favourite colour from a choice of red, blue
green or yellow. Their answers are shown below:
Blue
Red
Red
Green
Yellow
Red
Red
Red
Complete the frequency table.
Colour
Red
Blue
Red
Yellow
Red
Blue
Green
| Yellow 1111
Green
Blue
Green
Blue
Tally
Un Un
un
Analysing and Displaying Data
Yellow
Yellow
Blue
Red
Frequency
Red
Red
Blue
Yellow
The frequencies will be Red : 6, Blue: 4, Green: 8, Yellow : 1 (half of 2), Pink: 1 (half of 2).
What is a conditional relative frequency?It is defined as the frequency that can be evaluated by the two-way frequency table. Usually, we can obtain this frequency by dividing the frequency that is not in the total frequency cell to total frequency.
It is given that:
24 children were asked which is their favourite colour from a choice of red, blue
green or yellow
From the data given in the question.
Red : 6
Blue: 4
Green: 8
Yellow : 1 (half of 2)
Pink: 1 (half of 2)
Thus, the frequencies will be Red : 6, Blue: 4, Green: 8, Yellow : 1 (half of 2), Pink: 1 (half of 2).
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WILL ASSIGN BRAINLIEST
determine the quadratic function of the form f(x)=a(x-h)^2+k
Whose graph is given below
Graph shows -3,8 and 0,-19
The quadratic function of the graph is f(x) = [tex]-3(x+3)^2+8[/tex]
The coordinates of the vertex of the graph = (-3, 8)
The coordinates of the point on the parabola = (0, -19)
The quadratic function of the form
f(x) = [tex]a(x-h)^2+k[/tex]
Where (h, k) is the coordinates of the vertex of parabola
y = [tex]a(x-(-3))^2+8[/tex]
y = [tex]a(x+3)^2+8[/tex]
The coordinates of the point = (0, -19)
-19 = [tex]a(0+3)^2+8[/tex]
Take the square of the number
-19 = a × 9 +8
Multiply the terms
-19 = 9a + 8
9a = -19 - 8
Subtract the terms
9a = -27
a = -27 / 9
Divide the terms
a = -3
Hence, the quadratic function of the graph is f(x) = [tex]-3(x+3)^2+8[/tex]
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Question content area top left
Part 1
On July 8, the billing date, Marvin Zug had a balance due of $ 294.95 on his credit card. His card charges an interest rate of 1.25% per month. The transactions he made are to the right.
a) Find the finance charge on August 8, using the previous balance method.
b) Find the new balance on August 8 .
a. The finance charge on August 8 is given by: $3.69.
b. The new balance on August 8 is given by: $298.64.
What is a proportion?A proportion represents a fraction relative to a total amount, which is combined with the basic arithmetic operations, especially multiplication and division, to find the desired amounts in whichever context is needed in the problem.
A proportion is applied in this problem to find the finance charge, which is of 1.25% of 294.95, hence:
Finance charge = 0.0125 x 294.95 = $3.69.
Then the new balance on August 8 is obtained by the previous balance on July 8 added to the finance charge which we obtained above, hence it is of:
New balance = 294.95 + 3.69 = $298.64.
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In the following equation of straight line Y = 5X+12, then the slope and y-intercept
are? (WITH EXPLAINATION)
The slope and y-intercept of the equation of straight line y=5x+12 is 5 and 12.
What is equation of straight line?
A line that does not curl or bend is said to be straight. A line has length but no width, making it a one-dimensional figure. A line consists of points that extend infinitely in opposite directions. Two points in a 2D plane determine it. A, B, and C are real-based constants in the formula Ax + By + C = 0, A, B 0. The geometric representation of the equation is always a straight line.
Here we know that equation of straight line is y=mx +c.
Where m=slope and c=y-intercept.
Here the given equation is ,
=> y=5x+12
Compared with general form then,
=> m = 5 and c=12.
Therefore slope and y-intercept of the equation of straight line y=5x+12 is 5 and 12.
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Convert 33kilo to pounds using unit fraction
The conversion of 33 kilo to pounds using unit fractions is given by 72.765 pounds
How to convert from kilo to pounds?There are several units used by scientist to measure different things such as weight, temperature, mass, length etc. Units can be converted from one form to another.
Kilograms written as kg is a unit of mass
Milligrams written as mg is also a unit of mass.
Convert kilo to pounds:
1 kilo = 2.205 pounds
33 kilo = 2.205 × 33
= 72.765 pounds
That is,
A kilo is equivalent to 2.205 pounds
In conclusion, the conversion of 33 kill to pounds is 72.765 pounds.
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Given the function h(x) = -x² - 9x + 23, determine the average rate of change of the function over the interval -8 ≤ x ≤ -2
The average rate of change of the function h(x) = -x² - 9x + 23, over the interval -8 ≤ x ≤ -2 is 1
What is average rate of change?
The average rate of change of function f over the interval, a ≤ x ≤ b is given by this expression: f(b) - f(a) / b - aIt is a measure of how much the function changed per unit, on average, over that interval.It is derived from the slope of the straight line connecting the interval's endpoints on the function's graph.Let's find the average rate of change of h(x) = -x² - 9x + 23 in the interval of -8 ≤ x ≤ -2
h(-8) = -(-8)² - 9(-8) + 23
= -64 + 72 + 23
= 31
h(-2) = -(-2)² - 9(-2) + 23
= -4 + 18 + 23
= 37
Average rate of change = f(b) - f(a) / b - a
= h(-2) - h(-8)
= 37 - 31 / -2 - (-8)
= 6 / -2 +8
= 6/6
= 1
Here, the average rate of change of the function h(x) = -x² - 9x + 23, over the interval -8 ≤ x ≤ -2 is 1.
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Multiple Choice You are taking guitar •lessons. The cost of the first lesson is twice the cost of each additional lesson. You spend $360 for 8 lessons. How much did the first lesson cost'7 A $40 (C $50 (E $80 B) $45 (D $60
Answer:
E $80
Step-by-step explanation:
This would be like paying for 9 lessons
9 x 40 is 360
The first lesson costs twice as much, so it costs 80.
In each figure, a is parallel to b. Determine whether the third figure is a translation image of the first figure. Write yes or no. Explain your answer.
a. Yes; it is one reflection after another with respect to the two parallel lines.
b. No; it is a reflection followed by a translation.
c. No; it is a reflection followed by a rotation.
d. No; it is one reflection after another with respect to the two parallel lines.
Considering the figure the third figure relates to first figure by reflection and not translation hence No; it is one reflection after another with respect to the two parallel lines
What is reflection in math?A reflection is a transformation that works similarly to a mirror by switching all pairs of points that are directly across from one another along the line of reflection.
The equation or the two points it passes through can be used to define the line of reflection.
In the problem, the parallel lines are the line of reflection. The parallel lines displays the mirror image of the line segment
The first image relates with the first image as a result of reflections
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Solve the system of equations by the substitution method.
The system of equations given have infinite number of solutions
System of EquationA system of equations, also known as a set of simultaneous or an equation system, is a finite set of equations for which we sought the common solutions. A system of equations can be classified in a similar manner as single equations.
In the equations given;
4x + y = 10 ...eq(i)
16x + 4y = 40 ...eq(ii)
Solving both equations;
The value of x and y is
y = 10 - 4x
This shows that the system has infinite number of solutions.
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