An inverse variation is represented as:
[tex]y=\frac{k}{x}[/tex]To find the missing value we need to find k first. Using the first pair we have:
[tex]\begin{gathered} 16=\frac{k}{3} \\ k=3\cdot16 \\ k=48 \end{gathered}[/tex]Now, we plug the value of k and use the second pair to find y:
[tex]\begin{gathered} y=\frac{48}{10} \\ y=\frac{24}{5} \end{gathered}[/tex]Therefore, y=24/5.
Given the definitions of f(x) and g(x) below, find the value of (gof)(9). f(x) = -x + 11 g(x) = 3x2 - x + 14
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
f(x) = -x + 11
g(x) = 3x² - x + 14
(gof)(9) = ?
Step 02:
(gof)(x) = 3(-x+11)² - (-x+11) + 14
= 3(x² + 2(-x)(11) + 121) + x - 11 + 14
= 3(x² - 22x + 121) + x - 11 + 14
= 3x² - 66x + 363 + x - 11 + 14
= 3x² - 65x + 366
(gof)(9) = 3(9)² - 65(9) + 366
= 3(81) - 585 + 366
= 243 - 585 + 366
= 24
The answer is:
(gof)(9) = 24
A train travels from City A to City B. The table below shows the distance and
the amount of time it takes on the train.
Distance (km)
6
9
14
Time (in minutes)
2 3 7
O The train does not always go the same distance each minute.
O The train appears to go the same distance each minute.
Predicted distance traveled in 9 minutes: km
Yes, The train does not always go the same distance each minute.
Given,
A train travels from City A to City B.
The distance and the amount of time it takes on the train is
Distance (km) Time (in minutes)
6 2
9 3
14 7
Now According to the question:
Does the train go the same distance each minute?
In order to determine if the train travels the same distance each minute, the average speed of the train has to be determined. Average speed is the total distance travelled per time.
Average speed = total distance / total time
Average speed when distance is = 6/ 2 = 3 km/hrAverage speed when distance is = 9/3 = 3 km/hrAverage speed when distance is = 14/7 = 2 km/hrHence Yes, The train does not always go the same distance each minute.
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The graph of f(x) = x^3 is stretched vertically by a factor of 6. The graph
is then translated 9 units to the right and 3 units down. Write the equation of the transformed function.
Answer:
Transformed equation: 6(x-9)³ - 3
Step-by-step explanation:
Answer:
6(x - 9)^3 - 3
Step-by-step explanation:
1. Vertical Stretching : f(x) -> g(x): [tex]g(x) = 6x^{3}[/tex]
2. Horizontal Move: g(x) -> h(x): [tex]h(x) = 6{(x - 9)}^{3}[/tex]
3. Vertical Move: h(x) -> F(x): [tex]F(x) = 6{(x - 9)} ^{3} - 3[/tex]
Calculate the perimeter and area of the triangle formed by the coordinates K (-4,-1), L (-2,2), and M (3,-1). Round your answer to two decimal places.
PERIMETER:
You can calculate the perimeter of a triangle knowing the coordinates, by calculating the distance between every point, as follows:
[tex]\bar{KL}=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Where x1=-4, y1=-1, x2=-2 and y2=2, replace these values:
[tex]\begin{gathered} \bar{KL}=\sqrt[]{((-2)-(-4))^2+(2-(-1))^2} \\ \bar{KL}=\sqrt[]{(2)^2+(3)^2} \\ \bar{KL}=\sqrt[]{4+9}=\sqrt[]{13}=3.61 \end{gathered}[/tex]Now, you have to do the same for the other segments, let's continue with LM:
[tex]\begin{gathered} \bar{LM}=\sqrt[]{(x_3-x_2)^2+(y_3-y_2)^2} \\ x_3=3\text{ and }y_3=-1\text{ by replacing:} \\ \bar{LM}=\sqrt[]{(3_{}-(-2))^2+((-1)-2)^2} \\ \bar{LM}=\sqrt[]{(5)^2+(-3)^2} \\ \bar{LM}=\sqrt[]{25+9}=\sqrt[]{34}=5.83 \end{gathered}[/tex]Same for segment KM:
[tex]\begin{gathered} \bar{KM}=\sqrt[]{(x_3-x_1)^2+(y_3-y_1)^2} \\ \bar{KM}=\sqrt[]{(3-(-4))^2+((-1)-(-1))^2} \\ \bar{KM}=\sqrt[]{(7)^2+(0)^2} \\ \bar{KM}=\sqrt[]{49+0^{}}=\sqrt[]{49}=7 \end{gathered}[/tex]The perimeter can be calculated as KL+LM+KM:
[tex]\begin{gathered} P=\bar{KL}+\bar{LM}+\bar{KM}=3.61+5.83+7 \\ P=16.44 \end{gathered}[/tex]AREA:
The area can be calculated by using the next formula:
[tex]A=\frac{1}{2}\mleft\lbrace\lbrack(x_1\cdot y_2)+(x_2\cdot y_3)+(x_3\cdot y_1)\mright]-\lbrack(x_1\cdot y_3)+(x_3\cdot y_2)+(x_2\cdot y_1)\rbrack\}[/tex]Then, you have to replace the values to find the area:
[tex]\begin{gathered} A=\frac{1}{2}\lbrace\lbrack((-4)_{}\cdot2)+((-2)\cdot(-1))+(3\cdot(-1))\rbrack-\lbrack((-4)\cdot(-1))+(3\cdot2)+((-2)\cdot(-1))\rbrack\} \\ A=\frac{1}{2}\lbrace\lbrack(-8)+(2)+(-3)\rbrack-\lbrack(4)+(6)+(2)\rbrack\} \\ A=\frac{1}{2}\lbrace\lbrack-9\rbrack-\lbrack12\rbrack\} \\ A=\frac{1}{2}\mleft\lbrace\lvert-21\rvert\mright\rbrace \\ A=\frac{21}{2}=10.50 \end{gathered}[/tex]Which is the better buy: 18 oz. of rice for $6.30, 12 oz. of rice for $4.56, or 7 oz. of rice for $2.59?
Answer:
18oz for 6.30 is the cheapest
Step-by-step explanation:
0.35$ per oz
0.38$ per oz
0.37$ per oz
:]
Artrigerator contains 5 cans of diet soda and 8 cans of regular soda. If three cans of soda are randomly selected without replacement, determine the probability that all can selected are diet soda. Use combinations to determine theprobabilityThe probability that all can selected are diet soda is(Type an integer or a simplified fraction)
The total number of cans in the refrigerator is 5 + 8 = 13
The number of diet soda cans is 5 while the number of regular soda cans is 8
If three cans are selected, the probability that the can is a diet soda can is
5/13
Since it was not replaced, the number of diet soda cans left would be 4 and the total number of cans left would be 12. The probability that the next selected can is a diet can is
4/12 = 1/3
Since it was not replaced, the number of diet soda cans left would be 3 and the total number of cans left would be 11. The probability that the next selected can is a diet can is
3/11
Thus, the probability that the three selected cans are diet soda cans is
5/13 * 1/3 * 3/11 = 5/143
= 0.035
the probability that the three selected cans are diet soda cans is 0.035
da can
r
convert 430 cm² to m²
Answer:
4.3
Step-by-step explanation:
Find the area of the following figure. Show your work.area of odd shapes.
To find the area of the complex figure, divide it into simpler figures and the areas of these. Then find the sum of these areas.
Now, find the area of each of the simpler figures, in these case, the rectangles:
[tex]\begin{gathered} A=b\cdot h \\ A_A=7\cdot3=21 \\ A_B=6\cdot2=12 \\ A_C=7\cdot2=14 \\ A_D=5\cdot3=15 \\ A_E=3\cdot1=3 \end{gathered}[/tex]Finally, find the sum of all these areas to find the area of the figure:
[tex]A_F=21+12+14+15+3=65[/tex]The area of the figure is 65.
5) 13% of score
On a blueprint of a house, the living room has dimensions of 3 inches by 5 inches. If the scale for the
blueprint is 1 inch for every 7 feet, then what is the area of the actual living room?
A. 15 ft²
C. 735 ft²
B.
D.
105 ft2
56 ft²
Based on the dimensions of the blueprint of the house, the area of the actual living room can be found to be 735 ft²
How to find the area?The first thing to do is to convert the dimensions on the blueprint to their actual figures.
If 1 inch on the blueprint is 7 feet, then the actual dimensions are:
= 3 inches x 7
= 21 feet
Dimension B:
= 5 inches x 7
= 35 feet
The area can then be found by:
= Dimension A x Dimension B
= 21 x 35
= 735 ft²
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Hello! Please take a look at the picture to see the questions, thank you!
In the question, we are asked to find the degree and the leading coefficient of the polynomial below
[tex]f(x)=3x^4+2x^3+5x^2+7[/tex]Explanation
The degree of the polynomial is the highest of all the degrees that make up the polynomial. Since each term in the polynomial has a degree we will pick the largest one.
Also, the leading coefficient is the coefficient of the term with the largest degree. Using these concepts, we can derive our answer as.
Answer:
[tex]4,3[/tex]Option A
Omg guys can y’all please help i’m begging
The equation of the function g(x) is -√(x-7).
We are given a function f(x).The function f(x) equals √x.Our objective is to do some transformations on the graph of the function f(x) and reach the equation of the function g(x).We first need to reflect the function on the x-axis.We just take negative of the function f(x) to reflect it about the x-axis.f(x) = -√xWe now need to translate the function to the right by 7 units.We subtract 7 from the argument of the function to translate it to the right by 7 units.f(x-7) = -√(x-7)This is our required function.Thus, the equation of the function g(x) is -√(x-7).To learn more about functions, visit :
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The factors of 6 are also the factors of which number? A 5 C 20 B 10 D 30
Solution:
Factors of a number are defined as numbers that divide another number evenly or exactly without giving any remainder.
Hence,
The factors of 6 are the numbers that can divide 6 without any remainder.
[tex]\text{Factors of 6 =1,2,3,6}[/tex][tex]\begin{gathered} \text{Factors of 5=1,5} \\ \text{Factors of 20=1,2,4,5,10,20} \\ \text{Factors of 10=1,2,5,10} \\ \text{Factors of 30=1,2,3,5,6,10,15,30} \end{gathered}[/tex]From the above, we can deduce that the factors of 6 are also the factors of 30.
The corr
Jose made $143 for 11 hours of work.
At the same rate, how many hours would he have to work to make $117?
Answer:
9 hours
Step-by-step explanation:
Mrs. Casen plans to have 3 3/4 rolls of carpet installed in her new house. The cost of the carpet including installation is $450 per 1/2 carpet roll. How much will Mrs. Cassen be charged for the carpet and installation?
1. 1368
2. 2736
3. 3420
4. 3420
Answer:
$3375
Step-by-step explanation:
3 3/4 ÷ 1/2
=15/4 × 2/1
=7 1/2
7 1/2 multiply by carpet cost
7 1/2 × 450
= $3375
(your 3rd and 4th option in the multiple choice are the same btw)
Find the length of CD.express the awnser as a fraction times pie.
Given the figure of the circle B
the radius of the circle = r = BC = 9
the measure of the angle CBD = 40°
We will find the length of the arc CD
The length of the arc is given by the formula:
[tex]l=\theta\cdot r[/tex]where: θ is the central angle opposite to the arc measured in radians
so, we will convert the given angle from degree to radian
[tex]\theta=40\cdot\frac{\pi}{180}=\frac{2}{9}\pi[/tex]Substitute with the given values
so, the length of the arc =
[tex]l=\frac{2}{9}\pi\cdot9=2\pi[/tex]So, the answer will be:
The length of the arc CD = 2π
9 divided by 927. ……………………
depending on the question but it's most likely 103
Step-by-step explanation:
Sam reads 30 pages of a book in 40 minutes. Which statement identifies a person with the same reading rate as Sam.
Answer:
The correct option is B
Leroy reads 22.5 pages in 30 minutes
At the rate of 3 pages in 4 minutes
Explanation:
Given that Sam reads 30 pages of books in 40 minutes, he reads at the rate of 3 pages in 4 minutes (3/4 = 0.75).
To know which of the options has the same rate as Sam's, we need to find which rate is equal to his'
A. Francine reads 40 pages in 55 minutes
Rate = 40/55 = 8/11
B. Leroy reads 22.5 pages in 30 minutes
Rate = 22.5/30 = 0.75
C. Paul reads 150 pages in 3.25 hours. Since 3.25 hours = 195 minutes
Rate = 150/195 = 0.77
D. Bill reads 60 pages in 2 hours
Rate = 60/120 = 0.5
Given the equation 5X-10=50 which properties will be used to solve for XA. Adition and subtractionB. Subtraction and divisionC. Adition and division D. Subtraction and Multiplication
Let's solve for x and see what properties are used
First, add 10 to both sides of the equation
[tex]\begin{gathered} 5x-10=50 \\ 5x-10+10=50+10 \\ 5x=60 \end{gathered}[/tex]Now, divide by 5 on both sides of the equation
[tex]\begin{gathered} \frac{5x}{5}=\frac{60}{5} \\ x=12 \end{gathered}[/tex]Therefore, the correct answer is C. Adition and division
I need help can someone help me?
The sum [tex]S_4[/tex] = 80
How is the summation calculated?
[tex]S_4= \sum_{k=1}^{4} 2(3^{n-1}) \\\\= 2 \sum_{k=1}^{4} (3^{n-1})\\\\=2[3^{1-1}+3^{2-1}+3^{3-1}+3^{4-1}]\\\\=2[3^{0}+3^{1}+3^{2}+3^{3}]\\\\=2[1+3+9+27]\\\\=2 [40]\\\\=80[/tex]
What is summation?
When a group of numbers, known as addends or summands, are added together in mathematics, the outcome is their sum or total. Series are summations of infinite sequences. A succession of adds is the summation of an explicit sequence. A regular pattern defines a sequence's elements according to their positions within the sequence.If the summation has no summands, then the evaluated sum is zeroBecause zero is the identity for addition and this is known as the empty sum.To learn more about summation, refer:
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When a number is divided by 5, the result is 50 less than if the number had been divided by $6$. What is the number?
IT SAYS 50 LESS NOT GREATER
The number will be 1500
Given in the question:
A number is divided by 5, the result is 50 less than
and, if the number had been divided by $6$.
To find the number.
Now, According to the question:
Let the number be x
x is divided by 5 = x/5
also, The number is divided by 6 = x/6
Here, The expression will be:
x/5 - 50 = x/6
30(x/5 - 50) = 30(x/6)
6x - 1500 = 5x
1500 = x
Hence, The number will be 1500 .
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0.103125 to the nearest integer
⇒When we round to the nearest integer we are to round to the nearest whole
⇒We look at the first term after the comma which is in the tenths place.
⇒In this case it is 1 does it allow me to round up or down?
It allows me to round down meaning the integer will be 0
13 (6x – 5) – x = 13 – 2(x + 1) find x
Answer:
x = 76/79 or 0.962
Step-by-step explanation:
Use the Pareto chart to tell the percent of students that enrolled in a private 4 year college.
20%
1) Analyzing that Pareto Chart, we can tell that the percentage of students enrolled in a private-4 year college is indicated by the height of the bar and the corresponding value for its vertical axis
2) Therefore, the answer is 20%
Cuál es la probabilidad de obtener exactamente 5 caras en 10 lanzamientos de una moneda?
The probability of getting exactly 5 heads in 10 tosses of a coin 24.6%
What is Probability ?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Ten times are spent flipping coins.
Total number of results = 2¹⁰ = 1024
C(10, 5) = 252 is the total number of favorable outcomes.
Probability is
252/1024,
which equals :
=0.24, or
=24.6%.
Therefore, the chance of getting exactly 5 "heads" out of a possible 10 is 0.246, or 24.6%.
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If the events have the same theoretical probability of happening, then they are called
Answer:7937
Step-by-step explanation:7596
Write the equation in vertex form for the parabola with vertex (0, 6) and focus (0, 3).
Answer:
Step-by-step explanation:
the axis of the parabola is x=0So the parabola is of the form (x−0)2=4a(y−6)Now the length of latus rectum =4a=4× the distance between focus and vertex =4×3=12Hence the parabola is x2=−12(y−
(-5, 3) slope -4 into slope intercept form
The equation using slope intercept form would be...
[tex]y=-4x-17[/tex]
Hope this helps!
can you help me find the derivatives of these questions please
(Number 5)
[tex]\frac{dy}{dx}=\text{ }x(2^x)\ln 2\text{ }+2^x[/tex]Explanations:The given equation is:
[tex]y=x(2^x)[/tex]This function represents the product of x and 2^x, therefore, to find the derivative, we will use the product rule.
When y = UV, dy/dx is given as:
[tex]\frac{dy}{dx}\text{ = U}\frac{dV}{dx}+V\frac{dU}{dx}[/tex]In the equation y = x (2^x):
[tex]\begin{gathered} U\text{ = x} \\ \frac{dU}{dx}=\text{ 1} \\ V=2^x \\ \frac{dV}{dx}=2^x\ln 2 \end{gathered}[/tex]Substituting the U, V, dU/dx, and dV/dx into the given formula for dy/dx:
[tex]\begin{gathered} \frac{dy}{dx}=x(2^x)\ln 2+2^x(1) \\ \frac{dy}{dx}=\text{ }x(2^x)\ln 2\text{ }+2^x \end{gathered}[/tex]Bags A and B each contain counters.
Bag A
60 counters
Each counter is green, blue or yellow
P(green counter from A) = P(red counter from B)
Work out the number of green counters in A.
Bag B
12 counters
9 blue and 3 red
In probability, A is 8 out of 16 and C is 3 out of 15.
What is probability explain?
The likelihood or chance that a specific event will occur is represented by a probability. Both proportions between 0 and 1 and percentages between 0% and 100% can be used to describe probabilities.Out of the 17 counters in the bag 3 are yellow , 6 are red and the rest i.e., 17–3–6 or 8 nos.are green.
When selected randomly once one counter the probability of selecting one is
A. green is 8 out of 17 or 8/17 ,
B. getting a red one is 6 out of 17 or 6/17.
C. getting a yellow is 3 out of 17.
This is when the counter is put back in the bag for selecting.
If the selected one is not put back remaing counters are less by one each time it's drawn and then the probability figure is one out of 16 in the second case and one out of 15 for the third draw ime., then A is 8 out of 16 and C is 3 out of 15.
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A rectangular prism has dimensions of 2 cm by 2 cm by 5 cm. What is its surface area? Explain or show your reasoning
If a rectangular prism has dimensions of 2cm by 2 cm by 5 cm, then the surface area of the rectangular prism is 48 centimeter square
The length of the rectangular prism = 2 cm
The width of the rectangular prism = 2 cm
The height of the rectangular prism = 5 cm
The surface area of the rectangular prism = 2(lw+lh+hw)
Where l is the length
w is the width
h is the height
Substitute the values in the equation
The surface area of the rectangular prism = 2(2×2+2×5+2×5)
= 2(4+10+10)
= 2×24
= 48 centimeter square
Hence, if a rectangular prism has dimensions of 2cm by 2 cm by 5 cm, then the surface area of the rectangular prism is 48 centimeter square
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