Let
x -------> the time in hours
y -------> the distance in miles
we know that
To find the average rate of change, we divide the change in the output (y) value by the change in the input value (x)
so
For x=2 h ------> y=140 mi
For x=7 h ------> y=480 mi
rate of change=(480-140)/(7-2)
rate of change=340/5=68 mi/h
The average rate of change is equal to the speed in this problem
The sum of 3 and r is less than 7.What number sentence represents the statement?
The sum of 3 and r can be represented by "3 + r"
If this sum is less than 7, we can use the symbol "lesser than" (<) to compare the sum with the number 7, so our number sentence is:
[tex]3+r<7[/tex]Select the correct answer. Which equation, when solved, gives 8 for the value of x? OA. +3 = =+14 OB. 5-9=31-12 OC. 21-2=r-4 OD. 5.-7=*=+14
Let's solve for each and see which gives 8
For A
5/2 x + 7/2 = 3/4 x + 14
collect like term aand solve for x
5/2 x - 3/4 x = 14 - 7/2
[tex]\frac{10x-3x}{4}=\frac{28-7}{2}[/tex][tex]\frac{7x}{4}=\frac{21}{2}[/tex][tex]x=\frac{21}{2}\times\frac{4}{7}=6[/tex]For B
5/4 x - 9 = 3/2 x -12
collect like term and solve for x
[tex]\frac{5}{4}x-\frac{3}{2}x=-12+9[/tex][tex]=\frac{5x-6x}{4}=-3[/tex][tex]-\frac{x}{4}=-3[/tex][tex]x=12[/tex]For C
5/4 x - 2 = 3/2 x - 4
collect like term and then solve for x
[tex]\frac{5}{4}x-\frac{3}{2}x=-4+2[/tex][tex]\frac{5x-6x}{4}=-2[/tex][tex]-\frac{x}{4}=-2[/tex][tex]x=8[/tex]For D
5/4 x - 7 = 3/4 x + 14
collect like term and solve for x
[tex]\frac{5}{4}x-\frac{3}{4}x=14+7[/tex][tex]\frac{2x}{4}=21[/tex][tex]x=42[/tex]Therefore, the correct option is C
y = 3× - 1y = -3× + 1
Given two equations,
[tex]\begin{gathered} y=3x-1 \\ y=-3x+1 \end{gathered}[/tex]Comapring both equations,
[tex]\begin{gathered} 3x-1=-3x+1 \\ 3x+3x=1+1 \\ 6x=2 \\ x=\frac{2}{6}=\frac{1}{3} \end{gathered}[/tex]Therefore, x = 1/3.
Given the venn diagram below, what is the correct notation?A. ⊘B. (M∩F)′C. (M∪F)′D. none of these
Given
SolutionThe complement of a set using Venn diagram is a subset of U. Let U be the universal set and let A be a set such that A ⊂ U. Then, the complement of A with respect to U is denoted by A' or AC or U – A or ~ A and is defined the set of all those elements of U which are not in AThe shaded region is
[tex](M\cup\text{ F \rparen'}[/tex]The final answerOption C
simplifying with like terms; 2(m+10)
In order to simplify the expression, we would multiply the terms inside the bracket by the term outside. It becomes
2 * m + 2 * 10
= 2m + 20
A __ is a polynomial with one term.
ANSWER
Monomial
EXPLANATION
A polynomial is a expression that contains variables, coefficients and sometimes constants.
These terms relate with one another by the use of mathematical signs like addition, subtraction, multiplication, etc
A polynomial with just one term is called monomial.
An example of a polynomial is:
[tex]x^2\text{ + x + 1}[/tex]An example of a monomial is:
[tex]\begin{gathered} x^2 \\ or\text{ } \\ \frac{x}{2} \end{gathered}[/tex]Answer:
monomial
Step-by-step explanation:
what are the two moves you can use to get the first figure to the second figure (dilation,rotation, reflection,and translation)
ANSWER:
Dilation and translation
EXPLANATION:
Looking at the figures, the two moves used to get the first figure to the second figure is dilation and translation.
The figure was translated 6 units right and 7 units down.
The translation rule that occured here is==> (x+6, y-7)
Also, a dilation with a scale factor of 2 occured here.
Therefore, a dilation and translation occured in order to get the first figure to the second figure.
Find the equation of the linear function represented by the table below in slope-intercept form.xy1-82-123-164-20
Given :
The table for y and x is given as
Explanation :
The slope-intercept form is determined as
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]First find the slope of the equation using the coordinates from the table.
[tex]m=\frac{-12-(-8)}{2-1}=\frac{-12+8}{1}=-4[/tex]Now substitute the values in the slope-intercept form.
[tex]\begin{gathered} y-(-8)=-4(x-1) \\ y+8=-4(x-1) \\ y=-4x+4-8 \\ y=-4x-4 \end{gathered}[/tex]Answer:
Hence the equation of line is determined as
[tex]y=-4x-4[/tex]Match each expression on the left to its equivalent value on the right. Some answer options on the right will not be used.
Let us write out our expressions:
[tex]\begin{gathered} -29+(-7) \\ -34+(-94) \\ -8+(-14) \\ -12+(-48) \end{gathered}[/tex]The trick here is to get rid of the minus, then solve the sum as usual, and add a minus to the result. Let us do that for each of them:
-29+(-7)] Step one gives us:
[tex]29+7[/tex]Step two gives us:
[tex]36[/tex]Step three gives us:
[tex]-36[/tex]Then, -29+(-7) should be linked to -36.
-34+(-94)] Step one gives us:
[tex]34+94[/tex]Step two gives us:
[tex]128[/tex]Step three gives us:
[tex]-128[/tex]Thus, -34+(-94) should be linked to -128.
-8+(-14)] Step one gives us:
[tex]8+14[/tex]Step two gives us:
[tex]22[/tex]And step three gives us:
[tex]-22[/tex]This implies that -2+(-14) should be linked to -22.
-12+(-48)] Step one gives us:
[tex]12+48[/tex]Step two gives us:
[tex]60[/tex]And step three gives us:
[tex]-60[/tex]Then, -12+(-48) should be linked to -60.
i am stuck on this question. any help would be greatly appreciated
step 1
determine the slope of the given line
y=(3/5)x-17
The slope is m=3/5
Remember that
If two lines are parallel, then their slopes are equal
that means
The slope of the parallel line to the given line is m=3/5 too
step 2
Find out the equation of the line parallel to the given line
y=mx+b
we have
m=3/5
point (-5,15)
substitute and solve for b
15=(3/5)(-5)+b
15=-3+b
b=18
therefore
The equation of the line is
y=(3/5)x+18What is an example of a situation from your professional or personal life that requires you to compare, understand, and make decisions based on quantitative comparison? Be sure to describe the types of quantitative comparisons you had to make, what decisions you made, and why.
An example of situation involving quantitative comparison is:
The game-plan of an offensive coach for a NFL game.
What are quantitative variables?
Quantitative variables are variable that assume numbers as results, instead of labels such as yes/no or good/bad.
When an NFL offensive coordinator is game-planning, he has to consider numeric stats of the opponent defense, such as these ones:
Average passing yards allowed per play.Average rushing yards allowed per play.These stats are also compared to the NFL average to verify if the weak point of the opponent defense is the run or the pass, hence the game-plan is adjusted accordingly as follows:
Bad run defense: the coordinator should call more running plays.Bad pass defense: the coordinator should call more passing plays.A similar problem, also about quantitative variables, is given at https://brainly.com/question/15212082
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Michael and Ashley each buy x pounds of turkey and y pounds of ham. Turkey costs $3 per pound at Store A and $4.50 per pound at Store B. Ham costs $4 per pound at Store A and $6 per pound at Store B. Michael spends $18 at Store A, and Ashley spends $27 at Store B. Could Michael and Ashley have bought the same amount of turkey and ham?
Step 1
Michael spends $18 at store A
He buys x pounds of turkey and y pounds of ham.
But turkey costs $3 in-store A and ham costs $4 in-store A
Therefore, we will have the following equation for Michael
[tex]3x+4y=18---(1)[/tex]Step 2
Ashley spends $27 in-store B
She buys x pounds of turkey and y pounds of ham.
But turkey costs $4.50 in-store B and ham costs $6 in-store B.
Therefore, we will have the following equation for Ashley
[tex]4.5x+6y=27----(2)[/tex]Step 3
Solve the equations graphically
If the graphs of the equations are the same, then there are an infinite number of solutions that are true for both equations. Since the graphs are the same, then there are infinitely many solutions true for both equations.
For instance, the points if we test for the points on the graph, we will conclude if both Michael and Ashley bought the same amount of turkey and ham.
[tex]\begin{gathered} 3x+4y=18_{} \\ 4.5x+6y=27 \\ At\text{ x =2 and y=3} \\ we\text{ have,} \\ 3(2)+4(3)=18_{} \\ 6+12=18 \\ 18=18 \\ 4.5(2)+6(3)=27 \\ 9+18=27 \\ 27=27 \\ \text{At x=6, y=0} \\ we\text{ have} \end{gathered}[/tex][tex]\begin{gathered} 3(6)+4(0)=18 \\ 18=18 \\ 4.5(6)+6(0)=\text{ 27} \\ 27=27 \end{gathered}[/tex]Therefore yes, Michael and Ashley could have bought the same amount of turkey and ham.
What do the following two equations represent?y-3=2(x - 3)y+5 = 2(x + 1) a. the same lineb. distinct parallel linesc. perpendicular linesd. intersecting, b it not perpendicular
Option A: The same line
Explanations:The slope-intercept form of the equation of a line can be written as:
y = mx + c
Where m is the slope
and c is the intercept
Let us express the two equations given in the slope-intercept form
For the first equation:
y - 3 = 2(x - 3)
y - 3 = 2x - 6
y = 2x - 6 + 3
y = 2x - 3
The slope, m = 2
The intercept, c = -3
For the second equation:
y + 5 = 2(x + 1)
y + 5 = 2x + 2
y = 2x + 2 - 5
y = 2x - 3
We can see that both equations simplify to y = 2x - 3, this means the both equations represent the same line
60% discount on $500 sweater
The discount price of the sweater will be, the original price minus the percentage of discount of the original price.
First, express the percentage of discount as a decimal:
60% = 60/100 = 0.6
so:
[tex]\begin{gathered} 500-0.6\cdot500 \\ 500-300=200 \end{gathered}[/tex]The discount price of the sweater is $200
Tan (a) cos (a)= sin (a)Trig: use trigonometric identities to transform the left side of the equation into the right side
hello
the question here relates to trionometric identies and we can easily solve this once we know some of the identities
for example
[tex]undefined[/tex]Kayla bought 2 1/2 yards of blue cloth for 6.97 and 1 1/2 yards of yellow cloth for half as much. She used 1/4 of the blue cloth to make her mother a apron. How much cloth did it take to make the apron
She used 1/4 of the blue cloth to make her mother a apron:
[tex]\frac{5}{2}\times\frac{1}{4}=\frac{5}{8}=0.625[/tex]She used 5/8 yd or 0.625yd of blue coth to make the apron
Find the missing number to make the fractions equivalent. 3/4 = 9/?
We have the following:
[tex]\frac{3}{4}=\frac{9}{x}[/tex]solving:
[tex]\begin{gathered} x=\frac{9\cdot4}{3} \\ x=12 \end{gathered}[/tex]Therefore, the answer is [B] 12
how the position of the decimal point changes in a q u o t i e n t as you divide by Precinct power of 10.
When we divide a number by a power of 10, the decimal point changes its position. Specifically, the decimal points will move to the left according to the exponent of the power. For example, let's say we have the following division.
[tex]\frac{542}{10^3}[/tex]As we said before, we just have to move the decimal point to the left. In this case, we have to move it to 3 spots.
[tex]\frac{542}{10^3}=0.542[/tex]Hence, the division is equivalent to 0.542.
That's how the division works when you divide by a power of 10.
There is a total of $4,840 in an account after 2 years of earning compound interest at a rate of 10%. What was the original amount invested?
In order to find the original amount invested, we can use the following formula:
[tex]P=P_0(1+i)^t[/tex]Where P is the final amount, P0 is the original amount, i is the interest rate and t is the amount of time invested.
So, using P = 4840, i = 10% = 0.1 and t = 2, we have:
[tex]\begin{gathered} 4840=P_0(1+0.1)^2_{} \\ 4840=P_0\cdot1.1^2 \\ 4840=P_0\cdot1.21 \\ P_0=\frac{4840}{1.21} \\ P_0=4000 \end{gathered}[/tex]So the original amount invested is $4,000.
sorry its blurry[tex] \frac{3x - 2}{4} = 2x - 8[/tex]
the given expression is,
[tex]\frac{3x-2}{4}=2x-8[/tex][tex]\begin{gathered} 3x-2=4(2x-8) \\ 3x-2=8x-32 \\ 8x-3x=32-2 \end{gathered}[/tex][tex]\begin{gathered} 5x=30 \\ x=\frac{30}{5} \\ x=6 \end{gathered}[/tex]thus, the answer is x = 6
Find x rounded to the nearest whole degree. Be sure to round correctly!
answer: 36°
What is the value of the expression 2c( a + b) when a = 2, b = 5, and c = 4
The given expression is
2c(a + b)
From the information given,
a = 2
b = 5
c = 4
By substituting these values into the expression, it becomes
2 * 4(2 + 5)
= 8(7)
= 56
The value of the expression is 56
How does the graph of f(x) = (x + 7)^3 − 8 compare to the parent function g(x) = x^3
The ways in which the graph of f(x) = (x + 7)^3 − 8 compare to the parent function g(x) = x^3 are as follows:
Shifted 7 units to the left.Shifted 8 units down. What is a translation?In Mathematics, the translation a geometric figure to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image while translating a geometric figure down simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image.
In Geometry, g(x + 7) simply means shifting a graph 7 units to the left while subtracting 8 from the function simply means moving the graph down.
In this context, we can reasonably infer and logically deduce that the parent function g(x) was shifted 7 units to the left and 8 units down.
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Evaluate the expression 10 to the 2 power + (3 +5 to the power 2) -5
The answer is 159
The value of the expression 10 to the 2 power + (3 +5 to the power 2) -5 is 159.
What is an expression?An expression is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
The expression will be illustrated thus:
10² + (3 + 5)² - 5
= 100 + 8² - 5
= 100 + 64 - 5
= 164 - 5
= 159
The value is 159.
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the probability he chooses orange fruit
Consider that the total number of fruits are 10. The probability to get some fruit is given by the quotient in between the number of suc a fruit and the total number of fruits.
Then, at the first time, the probability of getting a kiwi is:
p1 = 1/10 = 0.1 (becasue there is one kiwi)
After the kiwi is taken out, the number of fruits are 9. In this case, the probability of getting one orange is:
p2 = 3/9 = 0.33 (because there are three oranges)
THe probability of the two previous events, that is, to obtain one kwi and then one orange is the product of the probabilities p1 and p2:
P = p1*p2 = (0.1)(0.33) = 0.03
Hence, the probabilty is approximately 0.03
List the elements in the set
{x 1 x is a negative multiple of 5}
S={-5,-10,-15,-20,-25......}; these are few negative multiples of 5 as stated in the set builder form of set theory {x :x is a negative multiple of 5}.
What is set?A set contains elements or members that can be mathematical objects of any kind, including numbers, symbols, points in space, lines, other geometric shapes, variables, or even other sets. A set is the mathematical model for a collection of various things.
What is set builder form?Set builder notation is a type of mathematical notation used to describe sets by listing their components or highlighting the requirements that each member of the set must meet. We write sets in the form of in the set-builder notation.
{y | (properties of y)} OR {y : (properties of y)}
Here,
{x :x is a negative multiple of 5}
S={-5,-10,-15,-20,-25.....}
According to the set builder form of set theory, {x:x is a negative multiple of 5} S={-5,-10,-15,-20,-25...}; these are a few negative multiples of 5.
To know more about set,
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What is a plane that is perpendicular to the base of a Cube and slices through the cube
The figure formed will be hexagonal
Use the graph to find the horizontal asymptote of the rational function
Horizontal Asymptote
Observing the graph with the red dashed line, the horizontal asymptote of the function is at y = 6
Vertical asymptote
If we draw a line the graph we have the following
This indicates that the vertical asymptote is at x = 2.
Compare f(0) and g(0)f(0) is <, =, or > to g(0)
From the graph of f(x), it can be obseved that function f(x) value at x = 0 is -3, which means that f(0) = -3.
From the graph of g(x), it can be observed that g(0) = 0.
As value 0 is greater than -3. So f(0) is lesser than g(0).
Answer: f(0) < g(0)
Graph the line with the given slope m and y-intercept b.
m = 1, b =0
Answer:
See graph
Step-by-step explanation: