Answer: slope = -3/7
Step-by-step explanation:
m(slope) = (y2-y1)/(x2-x1)
m = (-2+-1)/(5--2)
m = (-2-1)/5+2)
m = -3/7
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]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
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]The width of a rectangle is [tex] \frac{3}{4} [/tex] its length. The perimeter of the rectangle is 420 ft. What is the length, in feet, of the rectangle?
The width of a rectangle is 3/4 its length.
[tex]w=\frac{3}{4}l[/tex]The perimeter of the rectangle is 420 ft.
Recall that the perimeter of a rectangle is given by
[tex]P=2(w+l)[/tex]Let us substitute the value of the given perimeter and the width
[tex]\begin{gathered} P=2(w+l) \\ 420=2(\frac{3}{4}l+l) \end{gathered}[/tex]Now simplify and solve for length
[tex]\begin{gathered} 420=2(\frac{3}{4}l+l) \\ 420=\frac{3}{2}l+2l \\ 420=3.5l \\ l=\frac{420}{3.5} \\ l=120\: ft \end{gathered}[/tex]Therefore, the length of the rectangle is 120 feet.
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;
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
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).
Select the correct answer. Angela is driving across the state to her friend's house. She just filled her fuel tank to its maximum capacity of 26 gallons. If the amount of gas in her car decreases by 2 gallons every 48 miles, which of the following graphs best represents the number of gallons of fuel remaining?
Let L be the amount of gas Angela has at distance d. At d=0 she has 26, and we know that every 48 miles the gas decreases 2 gallons, so the rate of decrease of gas per mile is
[tex]\frac{2\text{ }}{48}=\frac{1}{24}[/tex]Then, the linear equation that models this problem is
[tex]L=-\frac{1}{24}d+26[/tex](I used the minus sign since the amount decreases).
The gas will run out of gas whe she has driven
[tex]\begin{gathered} 0=-\frac{1}{24}d+26 \\ \frac{1}{24}d=26 \\ d=624\text{ miles} \end{gathered}[/tex]Then the graph that best fits the model is number Z. And the answer is D.
Application machinist is drawing a triangular piece of an industrial machine. Write an equation and solve to find the value of x. Show your work?
Answer:
125
Step-by-step explanation:180=180-(2x+45)+x+80
2x-x=80+45
x=125
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]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
Prove that if 3/5 x = 9 then x = -15
Given: 3/5 x = 9
Prove: x = -15
There is no proof because X ≠ -15 when 3/5 x = 9
What is multiplication?Multiplication is defined as one of the basic arithmetic operations that is used for the repeated addition of similar figures together.
From the given expression,
3/5x = 9
But X= -15
Substitute X = -15 into the given expression;
That is,
3/5 * -15 = 9
-45/5= 9
-9 = 9
Therefore, there is no proof that in the expression 3/5 x = 9, X ≠ -15 because the final answer is -9 and not ,9.
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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.
G(x) = 1/x^10 g’(x)=
Differentiation - The value of g'(x) = [tex]\frac{1}{10}x^{-9}[/tex].
Apart from integration, differentiation is among the two key ideas in calculus. A technique for determining a function's derivative is differentiation. Mathematicians use a process called differentiation to determine a function's instantaneous rate of change predicated on one of its variables. The most typical illustration is velocity, which is the rate at which a distance changes in relation to time. Finding an antiderivative is the opposite of differentiation. The rate of change of signal with respect to y has been given by dy/dx if x and y are two variables. The general representation of a function's derivative is given by the equation f'(x) = dy/dx, where y = f(x) is any function.
Given that,
G(x) = [tex]\frac{1}{x^{10} }[/tex]
g’(x)=?
g’(x) is the derivative of g(x).
The derivative of [tex]x^{n} = nx^(n-1)[/tex]
[tex]x^{10} = 10x^(10-1)[/tex]
[tex]x^{10}= 10x^9[/tex]
Then,
[tex]\frac{1}{x^{10} }[/tex] = [tex]\frac{1}{10}x^{-9}[/tex]
Hence, The derivative of g(x) is [tex]\frac{1}{x^{10} }[/tex] = [tex]\frac{1}{10}x^{-9}[/tex].
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Which of the following data collection methods best describes the situation below?A polling company wants to predict which candidate will win an election. Company employees randomly call 1482 likely voters and ask them how they plan to vote.a. sample surveyb. experimentc. observational studyd. correlation
Answer
Option A is correct.
Explanation
Sample survey refers to the statistic
What is the probability that a random selected yard will have fewer than 6 trees
Based on the given histogram on yards and the number of trees they have, the probability that a random selected yard will have fewer than 6 trees is 60%
How to find the probability?The probability that in a random yard, the number of trees would be less than 6 trees can be found by the formula:
= Proportion of yards with 0 - 2 trees + Proportion of yards with 2 - 4 trees + Proportion of yards with 4 - 6 trees
The probability that a random yard would have fewer than six trees is therefore:
= 0.35 + 0.20 + 0.05
= 0.60
= 60%
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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
Can you help me with question number 4 and double check all my other work. (I don’t really understand functions.)
SOLUTION
The relation is a function because each x-value has a unique y-value. That is each domain has only one image. Therefore, the relation is a function
Consider the following equation: - 6x – 8y =—2A) Write the above equation in the form y = mx + b. Enter the values of m and b in theappropriate boxes below as integers or reduced fractions in the form A/B.)Answer: y =+Preview m: ; Preview b:B) Use your answer in part (A) to find the ordered pair that lies on this line when x = – 40.Answer: (-40,Enter your answer as an integer or a reduced fraction in the form A/B.
we have the equation
-6x-8y=-2
step 1
Isolate the variable y
Adds 6x both sides
-6x-8y+6x=-2+6x
simplify
-8y=6x-2
Divide both sides by -8
-8y/8=(6x-2)/-8
y=-(6/8)x+(2/8)
simplify
y=-(3/4)x+(1/4)therefore
m=-3/4b=1/4Part b
For x=-40
substitute in the equation above
y=-(3/4)(-40)+(1/4)
y=30+1/4
y=121/4
therefore
the answer part b is
(-40,121/4)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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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.
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,
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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Mr. Rodriguez is preparing photos for an international client. The client has requested a photo that is 20 cm by 15 cm. Mr. Rodriguez knows that the formula c = 2.54n can be used to convert n inches to c centimeters. Which formula can he use to convert centimeters to inches?
Given:
The formula to convert from inches to centimeters is c = 2.54n
To find:
The formula that can be used to convert from centimeters to inches
To determine the formula, we need to make n the subject of formula:
[tex]\begin{gathered} \text{c = 2.54n} \\ where\text{ c = value in cm} \\ n\text{ = value in inches} \end{gathered}[/tex][tex]\begin{gathered} To\text{ make n, the subject of formula, we will divide both sides by 2.54:} \\ \frac{c}{2.54}=\text{ }\frac{2.54n}{2.54} \\ n\text{ = }\frac{c}{2.54} \\ This\text{ means when we have a value in cm and substitute, the answer will be in inches} \end{gathered}[/tex][tex]n\text{ = }\frac{c}{2.54\text{ }}\text{ \lparen option B\rparen}[/tex]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
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
(a + 3)-(a + 2) Please help bc im stuck :>
Answer: 1
Step-by-step explanation:
We are given (a + 3) - (a + 2)
To think of this another way, we can distribute the negative sign out into the (a + 2)
(a + 3) -(a) - (2)
Now our expresssion looks like this:
(a + 3) - a - 2
Simplifying, we get
a - a + 3 - 2
The a terms cancel leaving us with
3-2
and that equals
1
Answer:
1
Step-by-step explanation:
1. Rewrite
: (a+3)-(a+2) = a + 3 - a - 2
2. Subtract
: 3-2 = 1 ... so now the equation is a + 1 - a
3. Combine like terms
: a -a = 0 (the a's cancel out) ... now you're left with 1
Since there is nothing left, your answer is 1.
8.5 cm 6.5 cm 2.25 cm Which measurement is closest to the surface area of the triangular prism in square centimeters?
This problem provides the faces of a triangular prism, and we need to calculate the surface area.
The surface area of the prism is equal to the sum of the area of all individual faces. Three faces are rectangles, while two are triangles.
The area of a rectangle can be found by using the following expression:
[tex]A_{rectangle}=length*width[/tex]While the area of a triangle can be found by using the following expression:
[tex]A_{triangle}=\frac{base*height}{2}[/tex]Two rectangles are equal, with measurements 2.25 cm by 8.5 cm, one rectangle has a measurement of 6.5 cm by 2.5 cm, and the two triangles are equal with a base equal to 6.5 cm and a height of 8.5 cm, therefore we have:
[tex]\begin{gathered} A_{rectangle}1=2.25\cdot8.5=19.125\text{ cm}\\ \\ A_{rectangle}2=6.5\cdot2.25=14.625\text{ cm}\\ \\ A_{triangle}=\frac{6.5\cdot8.5}{2}=27.625\text{ cm}\\ \\ \end{gathered}[/tex]And the total area is:
[tex]\begin{gathered} A_{total}=2\cdot A_{rectangle}1+A_{rectangle}2+2\cdot A_{triangle} \\ A_{total}=2\cdot19.125+14.625+2\cdot27.625 \\ A_{total}=108.125\text{ square centimeters} \end{gathered}[/tex]The surface area of the prism is approximately 108 square centimeters.
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]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]