{(-4,-9), (-4,4),(-2,2), (9,5)}
Because the x values of -4 occurs more than once, the set of ordered pairs is not a function.
The histogram to the right represents the weights (in pounds) of members of a certain high-school programming team.What is the class width? What are the approximate lower and upper class limits of the first class?
Looking at the given histogram
we have that
120-110=10
130-120=10
140-130=10
150-140=10
160-150=10
170-160=10
180-170=10
therefore
The class width is 10 lbs
First-class is 110-120 lbs
lower-class limit=110
upper class limit=120
Mike can make 7 holiday cards with the cardstock he already has on hand. He is also buying more paper, and he can make 12 additional cards with each package of cardstock he buys. Write an equation that shows how the total number of cards Mike can make, y, depends on the number of packages of cardstock he buys, x.
Answer:y = 12x + 7
Step-by-step explanation:
Part 2 of 2 Using x as the unknown number, write the statement below as an equation. Four times a number, minus 9, is equal to three times the number, plus 8 solve the equation for x
Answer:
4x-9=3x+8
17
Step-by-step explanation:
Consider the following equation.
7x +9y = 5y-6
Step 2 of 2: Find the equation of the line which passes through the point (-8,-6) and is perpendicular to the given line. Express your answer in slope-intercept
form. Simplify your answer.
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]7x+9y=5y-6\implies 7x+4y=-6\implies 4y=-7x-6 \\\\\\ y=\cfrac{-7x-6}{4}\implies y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{7}{4}}x-\cfrac{3}{2}\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{-7}{4}} ~\hfill \stackrel{reciprocal}{\cfrac{4}{-7}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{4}{-7}\implies \cfrac{4}{7}}}[/tex]
so we're really looking for the equation oif a line whose slope is 4/7 and it passes through the point (-8 , -6)
[tex](\stackrel{x_1}{-8}~,~\stackrel{y_1}{-6})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{4}{7} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-6)}=\stackrel{m}{ \cfrac{4}{7}}(x-\stackrel{x_1}{(-8)}) \implies y +6= \cfrac{4}{7} (x +8) \\\\\\ y+6=\cfrac{4}{7}x+\cfrac{32}{7}\implies y=\cfrac{4}{7}x+\cfrac{32}{7}-6\implies {\Large \begin{array}{llll} y=\cfrac{4}{7}x-\cfrac{10}{7} \end{array}}[/tex]
m=1/4(w+d) solve for d , how do I solve for this equation?
The value of d in the equation is d= 4m-w
How to calculate the value of d ?The first step is to write out the equation given
m=1/4(w+d)
The value of d can be calculated as follows
m= w + d/4
Cross multiply both sides
4m= w + d
collect the like terms
4m -w= d
d= 4m-w
Hence the value of d in the equation is 4m-w
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8. James is at a gift sale where everything costs $4 (tax included).James has $50.James must have at least $28 rer ining when he is finished buyinggifts.What is the greatest number of gifts James can buy?
Let the number of gift be x
The total amount James has is $50
Since he must have $28 remaining
Thus, the amount he would spend must not exceed
[tex]\text{ \$50-\$28=\$22}[/tex]Therefore,
If for every gift, $4 tax is included
[tex]x\text{ }\times\text{ \$4 =\$4x}[/tex]The number of gift James can buy
[tex]\begin{gathered} 4x\leq22 \\ x\leq\frac{22}{4} \\ x\leq5.5 \end{gathered}[/tex]Hence, the maximum number of gift James can buy is 5
basketball player made 76 out of 100 attempted free throws. What percent of free throws was made?
Percentages measure the frequency of occurrence of a certain event with respect to the occurrence of another event.
This is measured as a division or ratio:
[tex]P=\frac{\text{frequency of event 1}}{frequency\text{ of event 2}}[/tex]The basketball player made 76 out of 100 attempts. Here, our event 1 is the basketball player making a free throw. Event 2 is the player throwing the ball, regardless of its result.
Since he/she made 76 out of 100, the percent is:
[tex]P=\frac{76}{100}=0.76[/tex]The percent is 0.76*100 = 76%
Use the graph to fill in the blank with the correct number.
f(0) =
6
5
4
3
2
1
-5-4-3-2-1
-1
-2-
23
-3-
-4
-5
1
2345
Numerical Answers Expected!
Answer for Blank 1:
Answer:
3029
Step-by-step explanation:
Help me pls this is hard :,)
Answer: My friend could rewrite the fraction as a percent and compare that to the given percent. This is a good strategy if the denominator is `5`, `10`, `20`, or `50`. She could also turn the percent into a fraction by writing the percent over `100`. This is a good strategy if the new fraction can be simplified to have a common denominator with the original fraction.
Step-by-step explanation: BOOM I'M A PRO
I got you
find the equation of the line in slope–intercept form that passes through the following point with the given slope. Simplify your answerPoints (-10, -6); Slope = -4
Given:
[tex](x_1,y_1)=(-10,-6)\text{ ; slope(m)=-4}[/tex][tex]y-y_1=m(x-x_1)[/tex][tex]y+6=-4(x+10)[/tex][tex]y+6=-4x-40[/tex][tex]y=-4x-46[/tex]Above equation is the slope intercept form.
Master input values on the left x with the output values on the right why
Given the function;
y = x/2 + 1
x is the input value
y is the output value
If x = 2
y = 2/2 + 1
y = 1 + 1
y = 2
when x = 4
y = 4/2 + 1
y = 2 + 1
y = 3
when x = 7
y = 7/2 + 1
y = 3.5 + 1
y = 4.5
when x = 9
y = 9/2 + 1
y = 4.5 + 1
y = 5.5
A store owner buysy scooter for $40.99 and sells it for $94. What is the percent of increase for the price of the scooter? Round to the nearest tenth if necessary.
Percentage increase in the price of scooter = 129.3%
What is percentage?The word "percentage" refers to a figure that is stated as a percentage of 100, a relative value that denotes hundredths of any amount. Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.
For example 2% means [tex]\frac{2}{100}[/tex]. Here 2 is expressed as a fraction of 100.
Cost price of scooter = $40.99
Selling price of scooter = $94
Increase in price of the scooter = $(94 - 40.99)
= $53.01
Percentage increase in the price of scooter = [tex]\frac{53.01}{40.99}\times 100[/tex]
= 129.3%
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A falcon swoops down to snatch an animal from the ground before flying back into the air. Her height above the ground in feet is shown after x seconds. What does the x intercept(s) represent?
We are given a graph of the height of a falcon with respect to time. The x-intercept of the graph represents the height of the falcon when x = 0, that is, the initial height. since the graph shows that the x-intercept is 8, this means that the falcon starts 8 feet in the air.
I NEED HELP! this is the problem. The area of the trapezoid is 3/4x - 1/4 square centimeters. write two different pairs of expressions that represent possible lengths of the bases
Answer:
Step-by-step explanation:
The area of a trapezoid is A=(a+b/2)*h
So if you plug in what you know
3/4x-1/4 = (a+b/2)h
You would need the height but if you do have the height you can plug that in then just add a and b together as one variable so you can make a pair that equals that.
5 pointsWhich is the image of vertex Lafter the triangle is rotated 180 degrees about the origin?
The image of vertex L after the triangle is rotated 180 degrees about the origin= (-2, -1).
Option B.
First let's stae the the original location of the figure on the graph.
From the graph:
L (2, 1)
W(1, -3)
O (-1, -2)
A rotation of 180 degrees about the origin will change the x and y axis of each location to the opposite of those numbers;
Positive numbers becomes negative and negative numbers becomes positive.
The new location for L = L'
L' = (-2, -1)
The new location for W = W'
W' = (-1, 3)
The new location for O = O'
O' = (1, 2)
Hence, the image of vertex L after the triangle is rotated 180 degrees about the origin= (-2, -1).
Option B.
Calculate percentage: 75 people to 25 people
Given:
75 people to 25 people
To find:
The percentage value.
Explanation:
The percentage is,
[tex]\begin{gathered} \frac{75}{25}\times100\text{ \% =3}\times100\text{ \%} \\ =300\text{ \%} \end{gathered}[/tex]Hence, the percentage is 300%.
Final answer:
The percent value is 300%
Owners of a recreation area are filling a small pond with water. They are adding water at a rate of 26 liters per minute. There are 600 liters in the pond to start.
Let W represent the total amount of water in the pond (in liters), and let I represent the total number of minutes that water has been added. Write an equation
relating I to T. Then use this equation to find the total amount of water after 19 minutes
The equation for the conditions given in the question can be written as: W = 600 + (26)I and the total amount of water after 19 minute is 1094.
What is an equation?
There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. Mathematical algebraic equations typically have one or more variables.
As given in the question,
The amount of the water at the beginning is 600 liters.
And the rate of water being added is 26 liters per minute.
Let I be the number of minutes. So, the amount of water added in I minute is 26I.
Adding the initial amount and the amount of water after I minute. We get the equation as:
W = 600 + (26)I
Here, W represents the total amount of water in the pond.
Putting the value of I as 19 in the above equation.
W = 600 + (26)(19)
W = 600 + 494
W = 1094
Hence, the total amount of water after 19 minute is 1094 liters.
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Please help me with this problem i am not sure if what I calculated is correct please help.Let f(x)=12x2+4. The function g(x) is a vertical stretch of f(x) by a factor of 4. What is the equation of g(x)? Enter your answer in the box.g(x) = ---------
SOLUTION
The given equation is
[tex]f(x)=\frac{1}{2}x^2+4[/tex]Recall the definition of vertical stretch
vertical stretch occurs when a base graph is multiplied by a certain factor that is greater than 1
For a vertical stretch of a scale factor of 4 on f(x) g(x) will be
[tex]g(x)=4(\frac{1}{2}x^2+4)_{}[/tex]Expand the bracket
[tex]g(x)=2x^2+16[/tex]Therefore, the answer is
[tex]g(x)=2x^2+16[/tex]A line passes through the point (8, -3) and has a slope of 5/4.
Write an equation in slope-intercept form for this line.
Answer: y = 5/4x - 13
Step-by-step explanation:
m = 5/4
y = mx + b
substitute the coordinate into the equation to find b
-3 = 5/4(8) + b
b= -13
Lin is reading a 47 page book. She read the first 20 pages in 35 minutes. If she continues to read at the same rate will she be able to complete in under an hour? If not, how much more time is needed?
Answer:
No, 40 pages would take 70 minutes.
Step-by-step explanation:
20 more pages would take 35 more minutes which would be 40 pages at 70 minutes, then you will divide your 7 pages left by the 35 minutes it took to read the the first two 20 page sections of the book.
35 min.+ 35 min = 70 min. 35 mins./7 pages = 5 minutes
So it took a total of 75 minutes for Line to read her 47 page book.
Suppose there is a 26.2% probability that a randomly selected person aged 20 years or older is a jogger. In addition, there is a 10.2% probability that arandomly selected person aged 20 years or older is male, given that he or she jogs. What is the probability that a randomly selected person aged 20years or older is male and jogs? Would it be unusual to randomly select a person aged 20 years or older who is male and jogs?The probability that a randomly selected person aged 20 years or older is male and jogs is(Round to three decimal places as needed.)
Answer:
P(J∩M) = 0.027
Explanation:
Let's call J the event that a selected person aged 20 years or older is a jogger and M the event that a selected person aged 20 years or older is male.
Then, the probability P(J∩M) that a randomly selected person aged 20
years or older is male and jogs can be calculated as:
P(J∩M) = P(J) * P(M|J)
Where P(J) is the probability that a selected person aged 20 years or older is a jogger and P(M|J) is the probability that hat a selected person aged 20 years or older is male given that he or she jogs.
So, replacing P(J) by 26.2% and P(M|J) by 10.2%, we get:
P(J∩M) = 0.262 * 0.102
P(J∩M) = 0.027
P(J∩M) = 2.7%
Therefore, the probability that a randomly selected person aged 20 years or older is male and jogs is 0.027
Hey anyone mind helping me please? Without the random numbers.. I actually need help.
Answer:
A
Step-by-step explanation:
Corresponding sides of similar figures have proportional side lengths.
Factor the polynomial completely.
x3 + 6x + x2 + 6
Group of answer choices
(x2 + 1)(x + 6)
(6x + 1)(x + 1)
(x2 + 6)(x + 1)
(x2 + 1)(6x + 1)
The factors of the given polynomial are (x² +6) (x +1) =0.
Define polynomial.A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. x² + 4x + 7 is an illustration of a polynomial with a single indeterminate x. An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable). A sizable subset of algebraic expressions are polynomials. Polynomials are any expressions where the powers of the variables are all whole numbers. They frequently have a wide range of applications since they encompass such a sizable portion of all algebraic expressions.
Given Data
Polynomial
x ³+ x²+6x +6
Factorizing,
x²(x +1) + 6(x+1) =0
(x² +6) (x +1) =0
Option C) is correct.
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The value of a stock decreases by an average of 10 dollars each week. Which of the following represents the total average decrease in the stock after 8 weeks? O-101-18) = 2 dollars O-8|10|= 80 dollars O1-10)-8=2 dollars 81-101 = 80 dollars
The decrease on the value of stock is found to be 80 dollars and the second option is correct option
What is decrease on value of stock?The decrease on value of stock refers to reduction from the original value of the stock.
From the question we have that:
value of a stock decreases by an average of 10 dollars each week
This means that each week 10 dollars is subtracted from the value of the stock
How to find the total average decrease in the stock after 8 weeksif the stock reduces 10 dollars every week this is written mathematically as
1 week = 10 dollars
8 weeks = ?
cross multiplying gives
1 week * ? = 8 weeks * 10 dollars
? = 80 dollars
The unknown variable represented as ? is calculated to be 80 dollars
Hence multiplying the number of weeks by the amount reduced per week gives the decrease in stock and option b has modulus of 10 and the correct option
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Determine the slope of the line passing through the points (5,6) and (-5,-1)m=____
GIVEN:
We are given two points on a line and these are;
[tex]A=(5,6),\text{ }B=(-5,-1)[/tex]Required;
We are required to determine the slope of the line passing through these points.
Step-by-step solution;
The slope of a line is given by the formula;
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]The variables are;
[tex]\begin{gathered} (x_1,y_1)=(5,6) \\ \\ (x_2,y_2)=(-5,-1) \end{gathered}[/tex]We can now substitute these into the formula and then simplify;
[tex]\begin{gathered} m=\frac{-1-6}{-5-5} \\ \\ m=\frac{-7}{-10} \\ \\ m=\frac{7}{10} \end{gathered}[/tex]ANSWER:
The slope of the line passing through the given points is;
[tex]m=\frac{7}{10}[/tex]You buy a bag of skittles that contains 500 pieces of candy in it. Each day you eathalf of the amount that is in the bag.1.Write an explicit and recursive formula for this sequence2.How many days will it take to where there is less than one skittle in the bag?
1. the sequence is:
500, 250, 125, ...
the common ratio (r) is:
250/500 = 1/2 = 0.5
125/250 = 1/2 = 0.5
So, the sequence is a geometric sequence.
Explicit formula:
[tex]\begin{gathered} a_n=a_1\cdot r^{n\text{ - 1}} \\ a_n=500\cdot0.5^{n\text{ - 1}} \end{gathered}[/tex]Recursive formula:
[tex]\left\{ \begin{aligned}a_1=500 \\ a_n=r\cdot a_{n\text{ - 1}}\end{aligned}\right.[/tex]2. In the formulas, n represents days. Using the explicit formula with an = 1, we get:
[tex]\begin{gathered} 1\text{ = 500}\cdot0.5^{n\text{ - 1}} \\ \frac{1}{500}=0.5^{n\text{ - 1}} \\ ln(\frac{1}{500})\text{ = (n - 1)}\cdot\ln (0.5) \\ \frac{ln(\frac{1}{500})}{ln(0.5)}+1\text{ = n} \\ 9.965=\text{ n} \end{gathered}[/tex]then, after 10 days there will be less than 1 skittle in the bag
Find the measures of angle x and angle y
the 2 angles are equal so both are 148
Assuming no denominator equals zero which expression is equivalent to the given expression
From the problem :
[tex]\frac{\frac{r-5}{9r}}{\frac{5-r}{3r^2}}[/tex]We can rewrite the expression as multiplication :
[tex]\begin{gathered} \frac{r-5}{9r}\times\frac{3r^2}{5-r} \\ \Rightarrow\frac{-(5-r)}{9r}\times\frac{3r^2}{5-r} \\ \Rightarrow-\frac{r}{3} \end{gathered}[/tex]The answer is C -r/3
Determine whether one figure is a dilation of the other. Complete the justification of your answer.Triangle XYZ has angles measuring 53° and 23º. Triangle X'Y'Z' has angles measuring 23°and 90°.Triangle X'Y'Z' is not a dilation of Triangle XYZ. The ratios of the lengths of the correspondingsides are equal because the triangles havethree pairs of congruent angles.havedo not have
If one triangle is the dilation of the other triangle, then they are similar
The addition of the angles in a triangle is equal to 180°
Triangle XYZ has angles measuring 53° and 23º, then the third angle measure:
53° + 23° + x = 180°
x = 180° - 53° - 23°
x = 104
AA similarity postulate states that If two angles in one triangle are congruent to two angles in another triangle, the two triangles are similar
In this case, the two triangles have only one angle in common, then the AA postulate is not satisfied, and the triangles are not similar nor dilated.
Triangle X'Y'Z' is not a dilation of Triangle XYZ. The ratios of the lengths of the corresponding sides are not equal because the triangles do not have three pairs of congruent angles.
Evaluate f(x) at the given values of x.
f(x) = 4x x = -5, 3
Step-by-step explanation:
x=-5 f(x)=4x
f(x)=4(-5)
f(x)=-20
x=3 f(x)=4(3)
f(x)=12
