Recall than a direct variation implies the following type of relationship between y and x:
y = k * x
where k is a constant value
Then you have (by dividing by x, the following:
y / x = k (the constant)
then, we are told that when y = 90 , x = 15, so we have:
90 / 15 = k
6 = k
so,now that we know what the constant k is (6), we can answer the question: What is y when x = 4?
so we write:
y = k * x
y = 6 * 4
y = 24
This is the value of y when x is 4 since the constant k is 6 as we found above.
Another example:
We need to find the variation relationship for a case that when y = 6, x = 12
We think the same way we did before, starting with the fact that a direct variation is of the form:
y = k * x
given the info that when x = 12, y = 6, we can find the constant k:
6 = k * 12
divide by 12 both sides:
6/12 = k
1/2 = k
So k is 1/2 (one half)
Then we can write the variation as:
y = (1/2) x
(the product of 1/2 times x)
Find the average value of the following numbers 87, 79, 84, 70, 90
82
Explanation
the average is calculated by dividing the sum of the values in the set by their number.
Step 1
Let
[tex]\begin{gathered} \text{set}=\lbrace87,79,84,70,90\rbrace \\ the\text{ sum of the values is=87+79+84+70+90}=410 \\ n\text{umber of values= 5} \end{gathered}[/tex]Step 2
apply the equation
[tex]\text{Average}=\text{ }\frac{the\text{ sum of the values}}{\nu mber\text{ of values}}=\frac{410}{5}=82[/tex]so, the answer is 82
The graph shows melting points in degrees Celsius of selected elements. Use the graph to answer the question.The melting point of a certain element is -5 times the melting point of the element C. Find the melting point of the certainelement.***The melting point of the certain element is °C.(Simplify your answer.)
The melting point of element C is 41 degrees C
The question states "The melting point of a certain element is -5 times the melting point of the element C."
Multiply the melting point of Element C by -5 to get the melting point of the certain element
-5 * 41
Solution
-205
Mark the corresponding with a check to in the boxplease!
The whole numbers are defined as the positive integers including zero. The whole number does not contain any decimal or fractional part.
An integer is a number with no decimal or fractional part, from the set of negative and positive numbers, including zero.
A rational number is a number that is of the form p/q where p and q are integers and q is not equal to 0.
An irrational number is a type of real number which cannot be represented as a simple fraction.
Real numbers include rational numbers like positive and negative integers, fractions, and irrational numbers. In other words, any number that we can think of, except complex numbers, is a real number.
Therefore,
Wouldnt 8-4 be 8? because if u think about it your taking away the 4 so its not there anymore so then 8 is left ?
The subtraction of 4 from 8 is equal to 4 and not 8
What is subtraction of numbers?
In math, subtracting means to take away from a group or a number of things. When we subtract, the number of things in the group reduces or becomes less. The minuend, subtrahend, and difference are parts of a subtraction problem.
Now in this question, let's assume you have 8 apples in your bag. During lunchtime, you gave 4 out to your friends to share with you. If you check your bag again, you would notice that you no longer have 8 apples again in your bag because you have given 4 out and you would be left with 4 apples.
So, whenever we subtract 4 from 8 i.e. 8 - 4, the answer is and must always be equal to 4 and not 8.
Mathematically, this is written as 8 - 4 = 4.
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In 2019, the USDA reported that acreage for wheat was approximately 45.6 million acres;this is down 5% from 2018. Which of the following can you conclude?a) The 2018 wheat acreage was 47.88 million acres.b) The 2018 wheat acreage was 48.0 million acres.c) The 2019 wheat acreage was 43.43 million acres.d) The 2019 wheat acreage was 43.32 million acres.
Given that the USDA reported the acreage for wheat in 2019 was approximately 45.6 million acres; and was down 5% from 2018. We were asked to pick an option that would represent the right conclusion to the given statement.
To do this, we would assume that the acreage for wheat in 20 18 is x. Since 2018 differs from 2019 by 5%
This implies that the representation of 2019 acreage would be;
[tex]100\text{\%-5\%=95\%}[/tex]Therefore, we can have
[tex]\begin{gathered} \frac{95}{100}\times x=45.6 \\ \text{Cross multiply} \\ 95x=45.6\times100 \\ \text{Divide both sides by 95} \\ \frac{95x}{95}=\frac{45.6\times100}{95} \\ x=48 \end{gathered}[/tex]Therefore the 2018 acreage was;
Answer: Option B
Which equivalent equation results when completing the square to solve x^2-8x+7=0?
Using complete the square method:
[tex]\begin{gathered} x^2\text{ - 8x + 7 = 0} \\ x^2\text{ - 8x = -7} \\ \text{Add half the square of the coefficient of x to both sides:} \\ \text{half the coefficient = -8/2 = -4} \\ \text{square half the coefficient = (-4)}^2 \end{gathered}[/tex][tex]\begin{gathered} x^2-8x+(-4)^2=-7+(-4)^2 \\ \text{making it a p}\operatorname{erf}ect\text{ square:} \\ (x-4)^2\text{ = -7 }+(-4)^2 \end{gathered}[/tex][tex]\begin{gathered} (x-4)^2\text{ = -7 + 16} \\ (x-4)^2\text{ = 9 (option D)} \end{gathered}[/tex]33. Let f(x) = 5x2 - 4 and g(x) = 3x + 1. Find f(x) + g(x):
The addition of f(x) and g(x) is derived as follows;
5x^2 - 4 + (3x + 1)
5x^2 - 4 + 3x + 1
5x^2 + 3x - 4 + 1
5x^2 +3x -3
The correct answer is option D
Geometric mean of36 and 21
The Geometric Mean is:
[tex]6\sqrt[]{21}[/tex]Explanation:Given 36 and 21, the Geometric Mean is given as:
[tex]\begin{gathered} m=\sqrt[]{36\times21} \\ =\sqrt[]{6^2\times21} \\ =6\sqrt[]{21} \end{gathered}[/tex]what is the effect on the graph of the function f(x) = x² when f(x) is changed to f(x + 8) ?A) shifted up B) shifted left C) shifted right D) shifted down
Solution
- In order to solve the question, we need to understand the rules guiding the translation of graphs. This rule is given below:
[tex]\begin{gathered} f(x)\to f(x+h) \\ \text{ If h is positive, then, the graph is shifted to the left} \\ \text{ If h is negative, then, the graph is shifted to the right} \end{gathered}[/tex]- The question given to us has h = 8. This means that h is positive, therefore, the graph of f(x) must be shifted to the left by 8 units
Final Answer
The answer is "Shifted Left" (OPTION B)
Hi I am the mom can you help me on this question so I can show my daughter too because I am confused
Using the area method in finding the quotient.
The values of A and B are as follows,
A = C/6
B = D/6
A is the quotient of C and 6,
B is the quotient of D and 6.
From the problem, we only have choices of number to input in the boxes.
48, 9, 90, 8, 540, 36 and 0
We will select one to number to be the value of C and the value A must be in the given numbers to be used.
Let's say C = 48
A = 48/6 = 8
Since 8 is included in the list of numbers. This is applicable.
Now for D and B,
Note that the sum of C and D must be equal to the given dividend, the dividend from the problem is 588
Since we already have the value of C = 48, the value of D must be :
588 - C = D
588 - 48 = 540
And 540 is also included in the list of numbers, so D = 540
The value of B will be :
B = D/6
B = 540/6
B = 90
90 is also included in the list of numbers.
The final diagram will be :
For part B, the quotient is the sum of A and B
A = 8, B = 90
Quotient = A + B
= 8 + 90
Quotient = 98
If RT = 36, RS = 2x + 3 and ST = 7x + 6, find RSand ST.
We know that RT=36 and that RS=2x+3 and ST=7x+6. We notice that
[tex]RT=RS+ST[/tex]Then, plugging the corresponding values and expressions we have
[tex]36=(2x+3)+(7x+6)[/tex]Solving this equation for x,
[tex]\begin{gathered} 36=(2x+3)+(7x+6) \\ 36=2x+3+7x+6 \\ 36=9x+9 \\ 36-9=9x \\ 27=9x \\ x=\frac{27}{9} \\ x=3 \end{gathered}[/tex]Then te value of x is 3.
Once we have the value of x we are able to find the value of RS and ST, we just have to substitute said value in the expressions. Then
[tex]\begin{gathered} RS=2(3)+3=6+3=9 \\ ST=7(3)+6=21+6=27 \end{gathered}[/tex]Therefore RS=9 and ST=27.
A herd of 23 white-tailed deer is introduced to a coastal island where there had been no deer before. Their population is predicted to increase according to A=276/1+11e^(- .35t)where A is the number of deer expected in the herd after t years.(a) How many deer will be present after 3 years? Round your answer to the nearest whole number.(b) How many years will it take for the herd to grow to 50 deer? Round your answer to the nearest whole number.
Given:
[tex]A=\frac{276}{1+11e^{-0.35t}}[/tex]Where A is the number of deer expected in the herd after t years.
We will find the following:
(a) How many deer will be present after 3 years?
So, substitute t = 3 into the given equation:
[tex]A=\frac{276}{1+11e^{-.35*3}}\approx56.9152[/tex]Rounding to the nearest whole number
So, the answer will be A = 57
=========================================================
(b) How many years will it take for the herd to grow to 50 deer?
substitute A = 50 then solve for t
[tex]\begin{gathered} 50=\frac{276}{1+11e^{-.35t}} \\ 1+11e^{-.35t}=\frac{276}{50} \\ \\ 11e^{-.35t}=\frac{276}{50}-1=4.52 \\ e^{-.35t}=\frac{4.52}{11} \\ -0.35t=ln(\frac{4.52}{11}) \\ \\ t=\frac{ln(\frac{4.52}{11}_)}{-0.35}=2.54 \end{gathered}[/tex]Round your answer to the nearest whole number.
So, the answer will be t = 3
Find the distance between the two points.(-3,2)10,0)✓ [?]Enter the number thatgoes beneath theradical symbolEnter
The distance between two points on a coordinate grid can be calculated as follows;
[tex]\begin{gathered} d^2=(x_2-x_1)^2+(y_2-y_1)^2 \\ \text{The given points are} \\ (-3,2) \\ (0,0) \\ d^2=(0-\lbrack-3\rbrack)^2+(0-2)^2 \\ d^2=(0+3)^2+(-2)^2 \\ d^2=3^2+(-2)^2 \\ d^2=9+4 \\ d^2=13 \\ d=\sqrt[]{13} \end{gathered}[/tex]The number that goes beneath the radical symbol is 13, that means the answer is square root 13.
The product of two integers is -24. The difference between the two integers is 14. The sum of two integers is 10. What are the two integers?
Answer:
12 & -2
Step-by-step explanation:
i need help with my homework PLEASE CHECK WORK WHEN DONE
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given data
[tex]\begin{gathered} \mu=27 \\ \sigma=2 \\ x=25 \end{gathered}[/tex]STEP 2: Write the formula for calculating the z-score
[tex]z=\frac{x-\mu}{\sigma}[/tex]STEP 3: Calculate the z-score
[tex]z=\frac{25-27}{2}=-\frac{2}{2}=-1[/tex]STEP 4: Find the probability
Using the z-score calculator,
A manufacturer knows that their items have a normally distributed length, with a mean of 8.4 inches, and standard deviation of 1.4 inches.If one item is chosen at random, what is the probability that it is less than 11.8 inches long?
We will make use of the z-score to calculate the probability. The z-score is calculated using the formula:
[tex]z=\frac{x-\mu}{\sigma}[/tex]where x is the score, μ is the mean, and σ is the standard deviation.
From the question, we have the following parameters:
[tex]\begin{gathered} x=11.8 \\ \mu=8.4 \\ \sigma=1.4 \end{gathered}[/tex]Therefore, we have the z-score to be:
[tex]\begin{gathered} z=\frac{11.8-8.4}{1.4} \\ z=2.43 \end{gathered}[/tex]Using a calculator, we can get the probability value to be:
[tex]P=0.9925[/tex]The probability is 0.9925 or 99.25%.
What is the slope of a line that is perpendicular to the line whose equation is 2x−y=7?A. −1/2B. 3/2C. −3/2D. 1/2
We have the following line:
[tex]\begin{gathered} 2x-y=7 \\ y=2x-7 \end{gathered}[/tex]and we must determine the slope of its perpendicular line.
Slopes of two perpendicular lines, m1 and m2, have the following property:
[tex]m_1\cdot m_2=-1[/tex]Given the slope of the first line (the coefficient that multiplies the x):
[tex]m_1=2[/tex]and using the formula above for the slope of its perpendicular line, we get:
[tex]\begin{gathered} m_1\cdot m_2=-1 \\ m_2=-\frac{1}{m_1} \\ m_2=-\frac{1}{2} \end{gathered}[/tex]Answer
A. −1/2
Hello! I need some assistance with this homework question for precalculus, please?HW Q5
Explanation:
We were given the function:
[tex]g(x)=-1+4^{x-1}[/tex]We are to determine its domain, range and horizontal asymptote. This is shown below:
Domain:
[tex]\begin{gathered} g(x)=-1+4^{x-1} \\ 4^{x-1} \\ when:x=-10 \\ 4^{-10-1}=4^{-11} \\ when:x=1 \\ 4^^{1-1}=4^0=1 \\ when:x=20 \\ 4^{20-1}=4^{19} \\ \text{This shows us that the function is valid for every real number. This is written as:} \\ \left\{x|x∈R\right\} \end{gathered}[/tex]Range:
[tex]\begin{gathered} g(x)=-1+4^{x-1} \\ \begin{equation*} -1+4^{x-1} \end{equation*} \\ when:x=-10 \\ =-1+4^{-10-1}\Rightarrow-1+4^{-11} \\ =-0.9999\approx-1 \\ when:x=1 \\ =-1+4^{1-1}\Rightarrow-1+4^0\Rightarrow-1+1 \\ =0 \\ when:x=5 \\ =-1+4^{5-1}\Rightarrow-1+4^4\Rightarrow-1+256 \\ =255 \\ \text{This shows us that the lowest value of ''y'' is -1. This is written as:} \\ \left\{y|y>−1\right\} \end{gathered}[/tex]Horizontal asmyptote:
For exponential functions, the equation of the horizontal asymptote is given as:
[tex]y=-1[/tex]Hi I am really confused on this problem and would like help on solving it step by step
Given:
An exponential function represents the graph of some of the functions given in the option.
Required:
The correct equation represents the given function.
Explanation:
The graph of the function
[tex]y\text{ = 2\lparen}\sqrt{0.3})^x[/tex]is given as
Also, the graph representing the function
[tex]y=2e^{-x}[/tex]is given as
Answer:
Thus the correct answer is option B and option D.
graph the inequality 3x+y<4
Subsituting (0,0) in the inequality,
[tex]\begin{gathered} 3\times0+0<4 \\ 0<4 \end{gathered}[/tex]Hence the line 3x+y=4, demarcating the plane contains the origin.
Thus, the above graph gives the required region of inequality.
The tax on a property with an assessed value of $63,000 is $550. Using a proportion, findthe tax on a property with an assessed value of $94,000. Round to two decimal places
Answer:
$820.63
Explanation:
For two different properties, we have the following:
• Assessed Value = $63,000
,• Tax = $550
• Assessed Value = $94,000
,• Tax = $x
Using a proportion, we have:
[tex]\begin{gathered} \frac{63,000}{94,000}=\frac{550}{x} \\ \text{Cross multiply} \\ 63,000x=94,000\times500 \\ x=\frac{94,000\times500}{63,000} \\ x=\$820.63 \end{gathered}[/tex]The tax on a property with an assessed value of $94,000 is $820.63 (correct to 2 decimal places).
Paola says that when you apply the Distributive Property to multiply (3j+6) and (-5j), the result will have two terms. Is she correct?
Explain.
Choose the correct answer below.
A. No, because there will be one j-term
B. Yes, because there will be a j-term and a j²-term
C. Yes, because there will be a j-term and a numeric term
D. No, because there will be one j2-term
The Distributive Property to multiply (3j+6) and (-5j), the result will have two terms because there is a j-term and a j²-term.
What is distributive property of multiplication over addition ?
If we multiply a number by the sum of more than two, we use the distributive property of multiplication over addition.
Here the expression given is :
(3j+6) and (-5j)
and it is to multiply using Distributive Property of multiplication :
now, applying that ;
(3j+6) x (-5j)
= 3j x (-5j) + 6 x (-5j)
= -15j² - 30j
It is seen from the above expression that the Distributive Property to multiply (3j+6) and (-5j), the result will have two terms because there is a j-term and a j²-term.
Therefore, option B is the correct answer.
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Melissa standing 40 feet from a tree the angle of elevation from where she is standing on the ground to the top of the tree is 50° how tall is the tree round the final answer to the nearest 10th.
Given:
• Melissa standing 40 feet from a tree.
,• The angle of elevation from where she is standing on the ground to the top of the tree is 50°.
Required: To determine the height of the tree.
This is achieved thus:
First, we represent the given information diagrammatically as follows:
Using the diagram above, in relation to the given angle, we can determine the height of the tree by using the tangent ratio as follows:
[tex]\begin{gathered} \tan\theta=\frac{opposite}{adjacent} \\ \therefore\tan50\degree=\frac{h}{40} \\ h=40\tan50\degree \\ h\approx47.7ft \end{gathered}[/tex]Hence, the answer is:
[tex]47.7ft[/tex]May someone please help me solve this and explain? thanks:)
Given:
Mean,
[tex]\mu=46[/tex]Standard deviation,
[tex]\sigma=7[/tex]To find: The indicated values
Explanation:
The values are calculated as follows,
[tex]\begin{gathered} \mu-3\sigma=46-3(7) \\ =46-21 \\ =25 \\ \mu-2\sigma=46-2(7) \\ =46-14 \\ =32 \\ \mu-\sigma=46-7 \\ =39 \\ \mu=46 \\ \mu+\sigma=46+7 \\ =53 \\ \mu+2\sigma=46+2(7) \\ =46+14 \\ =60 \\ \mu+3\sigma=46+3(7) \\ =46+21 \\ =67 \end{gathered}[/tex]Final answer: The values are,
[tex]\begin{gathered} \mu-3\sigma=25 \\ \mu-2\sigma=32 \\ \mu-\sigma=39 \\ \mu=46 \\ \mu+\sigma=53 \\ \mu+2\sigma=60 \\ \mu+3\sigma=67 \end{gathered}[/tex]Directions:For questions 12-16 simplify using the given replacement valued. There should be no decimals, convert all decimals to fractions. (Do not change whole numbers)I need help with 14
14. Given:
[tex]\frac{3}{2}r-rs+4,r=\frac{6}{7},s=\frac{2}{3}[/tex]Substitute the value of r and s in the given problem.
We get,
[tex]\begin{gathered} \frac{3}{2}(\frac{6}{7})-(\frac{6}{7})(\frac{2}{3})+4=3(\frac{3}{7})-(\frac{2}{7})(2)+4 \\ =\frac{9}{7}-\frac{4}{7}+4 \\ =\frac{5}{7}+4 \\ =\frac{33}{7} \end{gathered}[/tex]Hence, the answer is
[tex]\frac{33}{7}[/tex]Write an equivalent expression to the following expression: (5^2)7
Here, we want to write an equivalent expression
To do this, we use one of the laws of indices
The law is as follows;
HELP ASAPwrite an expression to represent:"the sum of a number b and 24"
The sum of a number 'b' and 24 can be written like this:
[tex]b+24[/tex]A motor scooter travels 22 mi in the same time that a bicycle covers 8 mi. If the rate of the scooter is 6 mph more than twice the rate of the bicycle, find both rates.The scooter’s rate is ____ mph. (Type an integer or a decimal)
Let's use the variable x to represent the speed of the scooter and y to represent the speed of the bicycle.
For a same time t, the scooter travels 22 mi and the bicycle travels 8 mi, so we can write the following equation:
[tex]\begin{gathered} distance=speed\cdot time\\ \\ 22=x\cdot t\\ \\ t=\frac{22}{x}\\ \\ 8=y\cdot t\\ \\ t=\frac{8}{y}\\ \\ \frac{22}{x}=\frac{8}{y} \end{gathered}[/tex]Then, if the rate of the scooter is 6 mph more than twice the rate of the bicycle, we have the following equation:
[tex]x=2y+6\\[/tex]Using this value of x in the first equation, let's solve it for y:
[tex]\begin{gathered} \frac{22}{2y+6}=\frac{8}{y}\\ \\ 22y=8(2y+6)\\ \\ 22y=16y+48\\ \\ 6y=48\\ \\ y=8\text{ mph} \end{gathered}[/tex]Now, calculating the value of x, we have:
[tex]\begin{gathered} x=2y+6\\ \\ x=16+6\\ \\ x=22\text{ mph} \end{gathered}[/tex]Therefore the scooter's rate is 22 mph and the bicycle's rate is 8 mph.
Write the expression as a sum and/or difference of logarithms. Express powers as factors.log7(343x)
Recall the product rule of logarithms
[tex]\log _b(xy)=\log _b(x)+\log _b(y)[/tex]Apply the product rule to the given and we get
[tex]\log _7(343x)=\log _7(343)+\log _7(x)[/tex]write a quadratic fuction f whose zeros are -3 and -13
The zeros of a quadratic function are the points where the graph cuts the x axis.
If one zero is - 3, it means that
x = - 3
x + 3 = 0
Thus, one of the factors is (x + 3)
If another zero is - 13, it means that
x = - 13
x + 13 = 0
Thus, one of the factors is (x + 13)
Thus, the quadratic function would be
(x + 3)(x + 13)
We would open the brackets by multiplyingeach term inside one bracket by each term inside the other. Thus, we have
x * x + x * 13 + 3 * x + 3 * 13
x^2 + 13x + 3x + 39
x^2 + 16x + 39
Thus, the quadratic function is
f(x) = x^2 + 16x + 39