Solve the equation. (Enter your answers as a comma-separated list.)2b2 − 18 = −9b
Answers
Given
The equation,
[tex]2b^2-18=-9b[/tex]To solve for b.
Explanation:
It is given that,
[tex]2b^2-18=-9b[/tex]That implies,
[tex]\begin{gathered} 2b^2-18=-9b \\ 2b^2+9b-18=0 \\ 2b^2-3b+12b-18=0 \\ b(2b-3)+6(2b-3)=0 \\ (2b-3)(b+6)=0 \\ 2b-3=0,b+6=0 \\ 2b=3,b=-6 \\ b=\frac{3}{2},b=-6 \end{gathered}[/tex]Hence, the answer is 3/2, -6.
Related Questions
The temperature, in degrees Fahrenheit, of a cup of water placed in a freezer can be modeled by the function f(m)=210(0.94)^m , where m represents the number of minutes after the water was placed in the freezer.
What is the average rate of change from Minute 4 to Minute 11 and how can that rate of change be interpreted?
Answers
1. The average rate of change from Minute 4 to Minute 11 is of -8.23 º/min.
2. This means that the temperature decreased from Minute 4 to Minute 11 by an average of 8.23 º/min.
How to obtain the average rate of change of a function?The average rate of change of a function is obtained by the change in the output of the function divided by the change in the input of the function. Hence, over an interval [a,b], the rate is given as follows:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
The function in this problem is defined as follows:
f(m) = 210(0.94)^m.
The numeric value of the temperature at Minute 11 is of:
f(11) = 210(0.94)^11 = 106.32º.
The numeric value of the temperature at minute 4 is of:
f(4) = 210(0.94)^4 = 163.96º.
The change in the input is of:
11 - 4 = 7.
Hence the average rate of change is of:
(106.32 - 163.96)/67 = -8.23º min -> decrease of 8.23º each min.
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The sum of the two numbers is 106. The bigger number is 22 more than the smaller number. Then what is half of the smaller number?(1 Point)a) 84b) 21c) 42d) 32
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
The sum of the two numbers is 106. The bigger number is 22 more than the smaller number. Then what is half of the smaller number?
(1 Point)
a) 84
b) 21
c) 42
d) 32
Step 2:
The details of the solution are as follows:
[tex]\begin{gathered} Le\text{t the two numbers be x and y , such that:} \\ \text{x + y = 106 --- equation 1} \\ x\text{ + \lparen x+ 22 \rparen = 106} \\ 2x\text{ + 22 = 106} \\ \text{2x = 106 - 22} \\ 2x=84 \\ Divide\text{ both sides by 2, we have that:} \\ \text{ x =}\frac{84}{2} \\ \text{x = 42} \\ This\text{ means that the smaller number is 42 and} \\ The\text{ larger number is \lparen 42 + 22 \rparen = 64} \\ Then,\text{ Half of the smaller number = }\frac{42}{2}\text{ = 21 \lparen OPTION B \rparen} \end{gathered}[/tex]CONCLUSION:
The final answer = 21 ( OPTION B )
Hi I’ve been struggling with these two problems for sometime now
Answers
Answer
The answer is Distributive property
SOLUTION
Problem Statement
We are given the mathematical statement below:
[tex]5(x-3)=5x-15[/tex]We are asked to find the property that justifies the above statement.
Solution
To solve this problem, we need to understand what the distributive property is.
The distributive property states:
[tex]A(B+C)=AB+AC[/tex]If A = 5, B = x and C = -3
Thus, applying the Distributive property on the left-hand side of the mathematical equation given:
[tex]\begin{gathered} A(B+C)=AB+BC \\ 5(x-3)=5(x)+5(-3)_{} \\ =5x-15 \end{gathered}[/tex]This conforms to the Distributive property
Final Answer
The answer is Distributive property
Is a triangle with sides that measure 3 inches, 4 inches, and 5 inches a right triangle?
Answers
Solution:
To figure out if a triangle with sides that measure 3 inches, 4 inches, and 5 inches, is a right triangle, we use the Pythagorean theorem.
According to the Pythagorean theorem, the square of the longest side of the triangle (hypotenuse) is equal to the sum of the squares of the other two sides (adjacent and opposite) of a right-triangle.
This implies that
[tex](hypotenuse)^2=(adjacent)^2+(opposite)^2[/tex]In this case, the longest side is 5 inches.
[tex]hypotenuse=5[/tex]Thus,
[tex]\begin{gathered} (hypotenuse)^2=3^2+4^2 \\ =9+16 \\ =25 \\ \end{gathered}[/tex]Since the sum of the squares of the two sides (adjacent and opposite) is exactly equal to the hypotenuse, we can conclude that the triangle is a right triangle.
A student is measuring the length of an icicle, y, every hour, x. The icicle is currently 14 inches long and is melting at a rate of 0.9 inches per hour. Find and interpret the slope for this relationship. −0.9; for every additional hour, the length of the icicle decreases by 0.9 inches 0.9; for every additional hour, the length of the icicle increases by 0.9 inches −14; the length of the icicle when the student first measures it 14; the length of the icicle when the student first measures it
Answers
The answer is: −0.9; for every additional hour, the length of the icicle decreases by 0.9 inches
i need help i don’t understand the questions are down below
Answers
A picture and a frame are given with dimensions. It is required to find the area of the frame.
To find the area of the frame, subtract the area of the picture from the total area (frame + picture).
Recall the area of a rectangle with a length l and a width w:
[tex]A=l\cdot w[/tex]Substitute l=22 and w=20 into the formula to find the area of the picture:
[tex]A=22\cdot20=440[/tex]Notice that the total length of the picture and frame is l=22+x+x=22+2x, while the total width is w=20+x+x=20+2x.
Substitute these dimensions into the area formula:
[tex]\begin{gathered} A=(22+2x)\cdot(20+2x) \\ A=4x^2+40x+44x+440 \\ \Rightarrow A=4x^2+84x+440 \end{gathered}[/tex]Subtract the areas to find the area of the entire frame:
[tex]\text{ Area of frame}=4x^2+84x+440-440=4x^2+84x+0[/tex]The area of the entire frame is 4x²+84x+0.
First-term is 4x², the second term is 84x, and the third term is 0.
To find the area when x=2, substitute x=2 into the expression for the area:
[tex]4(2)^2+84(2)+0=4(4)+168+0=16+168=184[/tex]The area of the frame when x=2 inches is 184 inches squared.
The perimeter is the sum of the side lengths of the frame given as:
[tex]P=2(l+w)[/tex]Substitute l=22+2x and w=20+2x into the formula:
[tex]P=2(22+2x+20+2x)=2(4x+42)=8x+84[/tex]Substitute x=10 to find the perimeter when x=10:
[tex]P=8(10)+84=80+84=164[/tex]The perimeter is 164 inches.
Answers:
The area of the entire frame is 4x²+84x+0.
First-term is 4x², the second term is 84x, and the third term is 0.
The area of the frame when x=2 inches is 184 inches squared.
The perimeter when x=10 is 164 inches.
in a board game players draw cards to move tokens along a path •A card with the number 2 means to move 2 spaces forward •A card with the number -3 means to move 3 spaces backwards , what is most likely the meaning of a card with the number 0
Answers
When the player draws a card with a positive number it let him move forward as many spaces as the number of the card, with negatives number the player must move backward, when the player draws a zero card, it means that he can't move his tokens, neither forward or backward, his tokens must stay where they are.
Find the area under the standard normal distribution curve to the left of z=1.93.
Answers
We are given the image of the curve and asked to find the area under the curve to the left of z=1.93.
Since we have been given the z score already all we need to do is look up the z score on a left tailed z-table.
The picture above shows a left-tailed z- table. To find the area under the curve to the left of z=1.93, we look up 1.9 under .03.
From the table, we can therefore see that answer would be
ANSWER=0.97320
1. Patty is arranging the chairs for an awards ceremony. She wants to put the 36 chairs into a rectangular array. Choose the ways that Patty can arrange the chalrs. 1. Select all the expressions that have a product of 640. 16 x 40 (4 x 4) * (4 x 10) 40 = 16 (4 x 4) * (8 x 6) (2 x 5) * (8 x 2) x (2 x 2)
Answers
The pieces of construction paper ordered can be determined as,
[tex]\begin{gathered} N=22\times64 \\ =1408 \end{gathered}[/tex]Thus, the required pieces of construction paper is 1408.
6200 in standard form
Answers
Answer: Six Thousand Two Hundred
Step-by-step explanation:
If u = 2i - j; v= -5i + 4j and w = j find 4u (v -w).
Answers
Answer:
-40
Explanation:
Given
u = 2i - j; v= -5i + 4j and w = j
Required
4u(v-w)
4u = 4(2i) = 8i
v - w = -5i + 4j - j
v - w = -5i + 3j
Substitute
4u(v-w)
= 8i(-5i+3j)
= -40(i*i) [since i*i = 1]
= -40
Hence the required solution is -40
At a carnival, there is a game where you can draw one of 10 balls from a bucket if you pa $16. The balls are numbered from 1 to 10. If the number on the ball is even, you win $22 If the number on the ball is odd, you win nothing. If you play the game, what is the expected profit?
Answers
ANSWER
[tex]\text{\$-5}[/tex]EXPLANATION
To find the expected profit, we have to first find the expected payout.
There is a possibility of drawing up to 10 balls, numbered 1 to 10.
There are 5 even balls and 5 odd balls.
We have to find the probabilty of drawing even or odd balls:
=> The probability of drawing an even ball is:
[tex]P(\text{even)}=\frac{5}{10}=\frac{1}{2}[/tex]=> The probability of drawing an odd ball is:
[tex]P(\text{odd)}=\frac{5}{10}=\frac{1}{2}[/tex]The expected payout is the sum of the product of the probability of drawing each ball and the prize of each ball.
That is:
[tex]\begin{gathered} E(X)=\Sigma\mleft\lbrace X\cdot P(X)\mright\rbrace \\ E(X)=(22\cdot\frac{1}{2})+(0\cdot\frac{1}{2}) \\ E(X)=11+0 \\ E(X)=\text{ \$11} \end{gathered}[/tex]The expected profit can be found by subtracting the cost of playing the game from the expected payout:
[tex]\begin{gathered} Exp.Profit=11-16 \\ Exp.Profit=\text{ \$-5} \end{gathered}[/tex]That is the answer.
Tommy throws a ball from the balcony of his apartment down to the street. The height of the ball, in meters, is modeled by the function shown in the graph. What's the average rate of change of the height of the ball, in meters per second, while it's in the air?Question options:A) 2∕3B) –2∕3C) –3∕2D) 3∕2
Answers
Solution
The average rate of change of the height of the ball is given by
[tex]\frac{f(b)-f(a)}{b-a}[/tex]Here,
[tex]\begin{gathered} a=0 \\ b=10 \\ f(a)=f(0)=15 \\ f(b)=f(10)=0 \end{gathered}[/tex][tex]\begin{gathered} AverageRate=\frac{f(b)-f(a)}{b-a} \\ AverageRate=\frac{0-15}{10-0} \\ AverageRate=\frac{-15}{10} \\ AverageRate=-\frac{3}{2} \end{gathered}[/tex]The average rate is -3/2
Option C
Consider the data regarding car costs. The mean is $22,000 and the standard deviation is $2,000.a) Not everyone pays the same price for the same model of car. Use the 68-95-99.7% Rule to find what percentage ofbuyers paid between $18,000 and $26,000.b) The middle 99.7% of car costs are between what values?c) What is the probability a car will cost less than $24,000?d) What is the probability a car will cost more than $26,000?
Answers
Answer:
a) 95%
b) $16,000 to $28,000
c) 84%
d) 2.5%
Step-by-step explanation:
Given the mean of car costs is $22,000 with a standard deviation of $2,000, you want to use the empirical rule to find ...
percentage of buyers paying $18–26 thousandrange of values for middle 99.7% of costsprobability of cost less than $24,000probability of cost more than $26,000Empirical ruleThe empirical rule tells you that the center 68% of costs will be between -1 and +1 standard deviations from the mean: $20,000 to $24,000.
95% of costs will lie within 2 standard deviations: $18,000 to $26,000.
The "tails" of the distribution are split equally between the upper values of these ranges and the lower values.
a) 18-26These values are ±2 standard deviations from the mean.
95% of buyers will pay between $18 and 26 thousand.
b) 99.7%The middle 99.7% of the distribution lies between ±3 standard deviations from the mean:
22,000 ± 3(2000) = 22,000 ± 6,000 = {16000, 28000}
The middle 99.7% of costs are between $16,000 and $28,000.
c) < 24We know that 68% of costs are between $20,000 and $24,000, and 50% of costs are below $22,000. The distribution is symmetrical, so 68%/2 = 34% of costs are between $22,000 and $24,000..
The fraction below $24,000 is ...
P(<24) = P(<22) +P(22 to 24) = 0.5 + 0.34 = 0.84
The probability a car will cost less than $24,000 is about 84%.
d) > 26The empirical rule tells us 95% of the distribution is between 18 and 26 thousand. Half the remaining amount is above 26 thousand.
P(> 26) = (1 -0.95)/2 = 2.5%
The probability a car will cost more than $26,000 is about 2.5%.
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Find the circumference of a circular swimming pool with a diameter of feet. Use as an approximation for . Round your answer to the nearest foot. Enter only the number.
Answers
To determine the circumference of any circle we need to use the following formula:
[tex]C=2\cdot\pi\cdot r[/tex]Where r is the radius, which is half of the diameter. For this problem we have a pool with diameter equal to 18 feet, therefore the circumference is:
[tex]\begin{gathered} C=2\cdot3.14\cdot\frac{18}{2}=2\cdot3.14\cdot9 \\ C=56.52\text{ ft} \end{gathered}[/tex]The circumference of the pool is approximately 57 feet.
on Core Math 6 A What is the greatest common factor of 16 and 24? O4 X 6 O 8 O 10
Answers
The Greatest Common Factor
The greatest common factor (or divisor) (GCF or GCD or HCF) of a set of whole numbers is the largest positive integer that divides evenly into all numbers of that set.
For example, we have the numbers 16 and 24. One common divisor is 2 because 16/2=8 and 24/2=12. Both divisions are exact.
But 2 is not the greatest common divisor. To find the GCF, the procedure is:
* Write the prime factor of each number:
16 = 2*2*2*2
24 = 2*2*2*3
Select the maximum number of common prime factors from the numbers, even if they repeat.
We can select the product of 2*2*2 = 8 as the GCF, thus:
Answer = 8
Use logarithmic differentiation to find the derivative of y with respect to xy = (10x + 2)^x
Answers
Given: An equation-
[tex]y=(10x+2)^x[/tex]Required: To determine the differentiation of y with respect to x.
Explanation: The differentiation of a logarithmic function is-
[tex]\begin{gathered} y=a^x \\ \frac{dy}{dx}=a^x\ln(a) \end{gathered}[/tex]Taking log both sides on the given equation as-
[tex]\begin{gathered} \ln y=\ln(10x+2)^x \\ =x\ln(10x+2) \end{gathered}[/tex]Now, differentiating with respect to x using product rule as-
[tex]\frac{1}{y}\frac{dy}{dx}=\ln(10x+2)\frac{d}{dx}(x)+x\frac{d}{dx}\ln(10x+2)[/tex]Further simplifying as-
[tex]\frac{dy}{dx}=y[\ln(10x+2)+\frac{10x}{10x+2}][/tex]Substituting the value of y as-
[tex]\frac{dy}{dx}=(10x+2)^x[\ln(10x+2)+\frac{10x}{10x+2}][/tex]Final Answer: Option D is correct.
On a hike, each hiker carries the items shown. Write an expression in simplest form that represents the weight (in pounds) carried by x hikers. sleeping bag: 3.4lb bag: 4.6lb water bottle: 2.2lb
Answers
ok
Weight(x) = 3.4x + 4.6x + 2.2x or
W(x) = 3.4x + 4.6x + 2.2x
or
W(x) = 10.2x this is the expression
( 3y + 1 )( 3y - 1 )Determine each product
Answers
It is important to know that a Product is the result of a multiplication.
You have the following expression given in the exercise:
[tex]\mleft(3y+1\mright)\mleft(3y-1\mright)[/tex]Notice that it is the multiplication of two Binomials and it has this form:
[tex](a+b)(a-b)[/tex]By definition:
[tex](a+b)(a-b)=a^2-b^2[/tex]This is called "Difference of two squares".
You can identify that, in this case:
[tex]\begin{gathered} a=3y \\ b=1 \end{gathered}[/tex]Therefore, you get:
[tex]\mleft(3y+1\mright)\mleft(3y-1\mright)=(3y)^2-(1)^2=9y^2-1[/tex]The answer is:
[tex]9y^2-1[/tex]Match the figure at the right with the number that represents the sum of the interior angles for that figure.
Answers
To calculate the sum of the internal angles of a polygon you have to use the following formula:
[tex](n-2)\cdot180º[/tex]Where "n" is the number of sides of the polygon.
So you have to subtract 2 to the number of sides of the polygon and then multiply the result by 180º to determine the sum of the interior angles.
1) The first polygon has n=4 sides. To calculate the sum of its interior angles you have to do as follows:
[tex]\begin{gathered} (n-2)\cdot180º \\ (4-2)\cdot180º \\ 2\cdot180º=360º \end{gathered}[/tex]2) The second polygon has n=5 sides. The sum of its interior angles can be calculated as:
[tex]\begin{gathered} (n-2)\cdot180º \\ (5-2)\cdot180º \\ 3\cdot180º=540º \end{gathered}[/tex]3) The third polygon has n=6 sides. You can calculate the sum of its interior angles as:
[tex]\begin{gathered} (n-2)\cdot180º \\ (6-2)\cdot180º \\ 4\cdot180º=720º \end{gathered}[/tex]4) The fourth polygon has n=7 sides, so you can calculate the sum of its interior angles as:
[tex]\begin{gathered} (n-2)\cdot180º \\ (7-2)\cdot180º \\ 5\cdot180º=900º \end{gathered}[/tex]Mayra bought x grams of rice.Anika boughtmore than Mayra bought.Select ALL of the equations that represent therelationship between the amount of rice that Mayrabought, x, and the amount of rice that Anika bought, y.#1. y=4/3x #2.Y=2/3x 3#.Y=1/3x #4.y=x+1/3x #5.Y=X-1/3x
Answers
Given that the amount of rice Anika bought is
more than Mayra bought and Mayra bought x grams while Anika bought y grams then considering the options
#1. y=4/3x - this is true
#2.Y=2/3x - this is not true as this means that the value of y is less than that of x
3#.Y=1/3x - this is not true as this means that the value of y is less than that of x #4.y=x+1/3x - this is same as #1
#5.Y=X-1/3x - this is same as #2
Hence th
can you help I dont know how to do it
Answers
four segments
[tex]MS,MT,MN,MY[/tex]A ray
[tex]\bar{MY}[/tex]Collinear points
[tex]Y,M,N[/tex]how much it is -6 1/2 + 12?
Answers
In the given fraction, the value of -6 1/2 + 12 is 11/2
Fraction:
The fraction represents the part of a whole. And the fraction is the number is expressed as a quotient, in which the numerator is divided by the denominator.
Given,
Here we have the fraction -6 1/2 + 12.
Now, we need to find the value of this fraction.
To solve this one, first we have to convert the mixed fraction into normal one, then we get,
To convert the mixed fraction fist we have to multiply the denominator by the whole number, then we get
6 x 2 = 12
Then add these value into the numerator, then we get
12 + 1 = 13
So, the fraction is -13/2.
Now, we have to add these two,
=> -13/2 + 12
The fractions have unlike denominators.
First, we have to find the Least Common Denominator and rewrite the fractions with the common denominator.
LCD(-13/2, 12/1) = 2
Then we have to multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD. Then we get,
=> -13/2 + 24/2
=> 11/2
Therefore, the resulting fraction is 11/2.
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A house is on a 60,000-squarefoot lot. Rounded to the nearest tenth, approximately how many acres are inthe lot?Note: There are 43,560 square feet in an acre.A 1.3 acresB 1.0 acres1.7 acres1.4 acres
Answers
Given:-
[tex]60,000\text{sqfeet}[/tex]To find the given area in acre.
So now we use the formula,
[tex]1\text{acre}=43560[/tex]So now we get,
[tex]\frac{60000}{43560}=1.3774[/tex]So rounding to the nearest tenth we get,
[tex]1.4[/tex]So the required solution is 1.4acres.
Using the following image, solve for CD. 2x - 9 Сс X-9 • E 12 CD |
Answers
Answer
CD = 11 units
Explanation
From the image, we can see that
CD = 2x - 9
DE = x - 9
CE = CD + DE
CE = 12
CE = CD + DE
CE = (2x - 9) + (x - 9)
12 = 2x - 9 + x - 9
12 = 3x - 18
We can rewrite this as
3x - 18 = 12
3x = 12 + 18
3x = 30
Divide both sides by 3
(3x/3) = (30/3)
x = 10
CD = 2x - 9 = 2(10) - 9 = 20 - 9 = 11 units
Hope this Helps!!!
Solve the system.x + y + 2z = -1x+ y + 8z = -7(x-9y - 2z = -37
Answers
Given the three variable simultaneous equations;
[tex]\begin{gathered} x+y+2z=-1\ldots\ldots.i \\ x+y+8z=-7\ldots\ldots.ii \\ x-9y-2z=-37\ldots\ldots.iii \end{gathered}[/tex]To solve;
let's solve for z by subtracting equation i from ii;
[tex]\begin{gathered} x+y+8z-(x+y+2z)=-7-(-1) \\ x-x+y-y+8z-2z=-7+1 \\ 6z=-6 \\ \frac{6z}{6}=\frac{-6}{6} \\ z=-1 \end{gathered}[/tex]next let's solve for y by subtracting equation i from iii;
[tex]\begin{gathered} x-9y-2z-(x+y+2z)=-37-(-1) \\ x-x-9y-y-2z-2z=-37+1 \\ -10y-4z=-36 \\ \text{ since z=-1} \\ -10y-4(-1)=-36 \\ -10y+4=-36 \\ -10y+4-4=-36-4 \\ -10y=-40 \\ \frac{-10y}{-10}=\frac{-40}{-10} \\ y=4 \end{gathered}[/tex]We have z and y, to get x let us substitute te values of y and z into equation i;
[tex]\begin{gathered} x+y+2z=-1 \\ x+(4)+2(-1)=-1 \\ x+4-2=-1 \\ x+2=-1 \\ x+2-2=-1-2 \\ x=-3 \end{gathered}[/tex]Therefore the values of x, y and z are;
[tex]\begin{gathered} x=-3 \\ y=4 \\ z=-1 \end{gathered}[/tex]Answer is A.
I will show you the pic .
Answers
we have the equation
(2/3)x+5=1
step 1
multiply by 3 both sides
2x+15=3
step 2
subtract 15 both sides
2x=3-15
2x=-12
step 3
divide by 2 both sides
x=-12/2
x=-6Which pair of functions are inverse functions?()=3+5f(x)=3x+5and()=−3−5g(x)=−3x−5 ()=−+57f(x)=−x+57and()=−7+5g(x)=−7x+5 ()=−3−57f(x)=−3x−57and()=3+57g(x)=3x+57 ()=3−5f(x)=3x−5and()=−53
Answers
1) Let's examine the f(x) functions and find the inverse function of f(x), in the first pair of functions:
a) At first, let's swap x for y in the original function
[tex]\begin{gathered} f(x)=3x+5 \\ y=3x+5 \\ x=3y+5 \\ -3y=-x+5 \\ 3y=\text{ x-5} \\ \frac{3y}{3}=\frac{x-5}{3} \\ y=\frac{x-5}{3}\text{ } \\ f^{-1}(x)=\frac{x-5}{3} \end{gathered}[/tex]Note that after swapping x for y, we can isolate y on the left side. So as regards g(x) this is not the inverse function of f(x)
2) Similarly, let's check for f(x)
[tex]\begin{gathered} f(x)=\frac{-x+5}{7} \\ y=\frac{-x+5}{7} \\ x=\frac{-y+5}{7} \\ 7x=-y+5 \\ y=-7x+5 \\ f^{-1}(x)=-7x+5 \end{gathered}[/tex]Note that in this case, we can state that these are inverse functions
[tex]f^{-1}(x)=g(x)[/tex]3) Finally, let's find out the last pair of functions.
[tex]\begin{gathered} f(x)=\frac{-3x-5}{7} \\ y=\frac{-3x-5}{7} \\ x=\frac{-3y-5}{7} \\ 7x=-3y-5 \\ 3y=-7x-5 \\ f^{-1}(x)=\frac{-7x-5}{3} \end{gathered}[/tex]So in this pair, g(x) is not the inverse function of f(x).
4) Hence, the answer is following pair:
[tex]\begin{gathered} f(x)=\frac{-x+5}{7}\text{ } \\ g(x)=f^{-1}(x)=-7x+5 \end{gathered}[/tex]Higher Order Thinking The bakery had
84 muffins. Ms. Craig bought 5 packs of
6 muffins. Did she purchase an even or an
odd number of muffins? Is the number of
muffins left even or odd? Explain.
shi
Answers
Answer:
Even and 54
Step-by-step explanation:
Based on the given conditions, formulate: 84-6x5
Calculate the product or quotient: 84-30
Calculate the sum or difference: 54
Ayako took a trip to the store 4 1/2mi away. If she rode the bus for 3 5/8mi and walked the rest of the way, how far did she have to walk? Express you answer as a simplified fraction or mixed number
Answers
Ayako took a trip to the store 4 1/2mi away. If she rode the bus for 3 5/8mi and walked the rest of the way, how far did she have to walk? Express you answer as a simplified fraction or mixed number
we have that
total distance=4 1/2 miles
Let
x ----> number of miles walked
so
4 1/2=3 5/8+x
solve for x
But first, convert mixed number to an improper fraction
4 1/2=4+1/2=9/2
3 5/8=3+5/8=29/8
substitute
9/2=(29/8)+x
x=(9/2)-29/8
the fractions have different denominators
so
Find out an equivalent fraction
9/2=(9/2)*(4/4)=36/8
so
x=(36/8)-29/8
x=7/8
the answer is 7/8 miles