Given:
a function is given as h(x) = -2x + 9
Find:
we have to evaluate the function at x = -2 , 0 and 5.
Explanation:
when x = -2
h(-2) = -2(-2) + 9 = 4 + 9 = 13
when x = 0
h(0) = -2(0) + 9 = 0 + 9 = 9
when x = 5
h(5) = -2(5) + 9 = - 10 + 9 = -1
Therefore, the values of given function h(x) are 13, 9 , -1 at x = -2, 0 , 5 respectively.
Jack has an old scooter. He wants to sell it for 60% off the current price. The
market price is $130. What should his asking price be? Explain your reasoning.
a scratching post for a cat is in the shape of a cylinder. if you have had to find the amount of carpeting needed to completely cover the post which formula would you useC=2πRSA=2πRH+2πR^2V= πr^2h
The scratching post is in the shape of a cylinder.
To cover the scratching post with a carpet, the surface of the post has to be covered.
This means that the amount of carpeting to be used will be equal to the total surface area of the pole.
The total surface area of the pole is calculated using the formula:
[tex]SA=2πrh+2πr^2[/tex]where r is the radius of the pole and h is the height of the pole.
The SECOND FORMULA is correct.
How do I find the restrictions on x if there are any? [tex] \frac{1}{x - 1} = \frac{5}{x - 10} [/tex]
We have the expression:
[tex]\frac{1}{x - 1}=\frac{5}{x - 10}[/tex]When we have rational functions, where the denominator is a function of x, we have a restriction for the domain for any value of x that makes the denominator equal to 0.
That is because if the denominator is 0, then we have a function f(x) that is a division by zero and is undefined.
If we have a value that makes f(x) to be undefined, then this value of x does not belong to the domain of f(x).
Expression:
[tex]\begin{gathered} \frac{1}{x-1}=\frac{5}{x-10} \\ \frac{x-1}{1}=\frac{x-10}{5} \\ x-1=\frac{x}{5}-\frac{10}{5} \\ x-1=\frac{1}{5}x-2 \\ x-\frac{1}{5}x=-2+1 \\ \frac{4}{5}x=-1 \\ x=-1\cdot\frac{5}{4} \\ x=-\frac{5}{4} \end{gathered}[/tex]Answer: There is no restriction for x in the expression.
Lola jumps rope for 15 minutes on Monday. She jumps rope 10 more minutes each day. How many minutes does she jump rope on Thursday?
She jumped 25 minutes on Tuesday as the problem says, "Lola jumps rope for 15 minutes on Monday. She jumps rope 10 more minutes each day."
What is addition?One of the four fundamental operations in mathematics is addition, along with subtraction, multiplication, and division. The total amount or sum of the two whole numbers is obtained by adding them. Combining things and counting them as one big group is done through addition. In math, addition is the process of adding two or more numbers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation. The mathematical operation of addition is the process of adding two or more numbers together to determine the total, or sum. 5 + 11 + 3 equals 19, as an illustration of addition.
Here,
She jumped 15 minutes on Monday
On Tuesday, she will jump 10 more minutes,
=15+10
=25 minutes
As stated in the problem, she jumped 25 minutes on Tuesday "On Monday, Lola jumps rope for 15 minutes. She adds 10 more minutes of daily rope jumping."
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Which of the following sets is a finite set of rational numbers
The correct option is the third one.
In set notation, '...' indicates that the set is infinite. With this we can discard option 1 and 4.
If we look option 2, they're all irrational numbers.
Thus, the correct option is the third one.
Debra brought a desk on sale for $438. This price was 73% of the original price. What was the original price
Let x = the original price of the desk.
It's known that 73% of the price is $438, thus:
[tex]\frac{73}{100}x=438[/tex]Multiplying by 100 and dividing by 73:
[tex]x=\frac{100\cdot438}{73}=600[/tex]The original price of the desk was $600
using trig to find a side
we have that
tan(16)=NO/OM -------> by opposite side divided by the hypotenuse
solve for NO
NO=OM*tan(16)
x=16*tan(16)
x=4.6 ftHi, simplify the following rational expression, if possible: x + 2/ x^2 = 4x + 4
Given:
[tex]\frac{x+2}{x^2-4x+4}[/tex]To simplify the given rational expression, we first factor x^2-4x+4 by applying Perfect Square Formula as shown below:
[tex]\begin{gathered} a^2-2ab+b^2=(a-b)^2 \\ \end{gathered}[/tex]Hence,
[tex]x^2-4x+4=x^2-2x(2)+2^2=(x-2)^2[/tex]Now, we simplify the given expression:
[tex]\frac{x+2}{x^{2}-4x+4}=\frac{x+2}{(x-2)^2}[/tex]Therefore, the answer is:
[tex]\frac{x+2}{(x-2)^{2}}[/tex]Use the spinner shown in the figure below to find the probability indicated.Landing on green or a consonant
Based on the spinner, there are a total of 8 possible outcomes.
2 of which are green and 4 are consonants, however, 1 outcome is both consonant and a green (F green).
Therefore, the probability of landing on a green or consonant is:
[tex]\begin{gathered} P(A\text{ or B)}=P(A)+P(B)-P(A\text{ and B)} \\ P(A\text{ or B)}=\frac{2}{8}+\frac{4}{8}-\frac{1}{8} \\ P(A\text{ or B)}=\frac{5}{8} \end{gathered}[/tex]The probability of landing on a green or consonant is 5/8 or 62.5%.
Devonte creates a scatter plot of the relationship between his hourly pay in dollars, y, and the number of customers he serves at a coffee shop, X. He calculates the equation of the trend line to be y = 2.52 +7. Part A What does the y-intercept represent? Enter the correct answers in the boxes. per hour when he serves customers. The y-intercept represents that Devonte earns $
Given equation of line is,
What is 7×312 using mental math
Step-by-step explanation:
2184 simple ..... .............
Answer:
Its 2184
Step-by-step Explained
Show all work to receive credit. Write verbal questions in at least one complete sentence.For each of the following questions, decide if the data is qualitative or quantitative. If it is quantitative, decide if it’s discrete or continuous. Explain the reason for your answer. a)Janelle is collecting data on the number of ounces of water drank by college students during a typical math class. What type of data is this?
To answer this question let's remember the definitions of qualitative and quantitative data:
• Qualitative data is data that describes the attributes or properties of what we are studying.
,• Quantitative data that describes certain quantity or amount. It is usually express by numbers with some unit associated it with it and it can be discrete or continuous. Discrete data is described by particular numbers in a range and continuos data is described by any number in any range.
With this in mind we conclude that Janelle is measuring qualitative data, since she is measuring the amount of water the student takes, furthermore this is continuous data since each student can drink any amount of water, that is, we can even divide the ounces in any decimal.
Find the value of x 6 : 9 = x : 72
To find x we write the proportion as a fraction:
[tex]\begin{gathered} \frac{6}{9}=\frac{x}{72} \\ x=\frac{72\cdot6}{9} \\ x=48 \end{gathered}[/tex]Therefore x=48
A person tosses a coin twice. Find the set representing the event E that the first toss is tails.
Solution:
Given that;
A person tosses a coin twice.
The tree diagram representing when a coin is tossed twice is shown below
From the tree diagram above;
The set representing the event E that the first toss is tails is
[tex]TH,TT[/tex]Hence, the answer is
[tex]\lbrace TT,TH\rbrace[/tex]In IJK, the measure of K=90 degrees, JI=53, IK=45, and KJ=28, What ratio represents the sine of I?
The given triangle is a right angle triangle. The diagram is shown below.
From the triangle, considering angle I as the reference angle,
hypotenuse = JI = 53
adjacent side = IK = 45
opposite side = KJ = 28
To find Sin I, we would apply the Sine trigonometric ratio which is expressed as
Sin # = opposite side/hypotenuse
Thus,
Sin I = 28/53
Lesson 6: Relate Division and Multiplication Cool-down: A Different Relay Race 1. Lin and Han ran a 5 mile relay race as a team. They each ran the same distance. Dras diagram to represent the situation.
Lin and Han ran a 5 miles relay race.
If they both ran same distance, that means each of them ran;
[tex]\frac{1}{2}(5\text{miles)}=2.5\text{miles}[/tex]So, Lin and Han ran 2.5miles each.
The diadramatic representation of this scenario is;
The image above shows a track race of 5 miles divided into two. LIN ran half of it (2.5 miles) and also Han ran the other half, also (2.5 miles)
Danny uses an app that shows him how many kilometers he has ran to prepare for a marathon. The app said he ran 8.045 kil. He wants to post online how many miles he ran. Danny ran _____ miles.
1 kilometer is equivalent to 0.62 miles. To find how many miles are 8.045 kilometers, we can use the next proportion:
[tex]\frac{1\text{ km}}{8.045\text{ km}}=\frac{0.62\text{ mi}}{x\text{ mi}}[/tex]Solving for x,
[tex]\begin{gathered} 1\cdot x=0.62\cdot8.045 \\ x=5\text{ miles} \end{gathered}[/tex]Another way to solve this, is the next one:
[tex]8.045\text{ km}\cdot\frac{0.62\text{ miles}}{1\text{ km}}=5\text{ miles}[/tex]Danny ran 5 miles.
Fill in the blanks (B1, B2, B3) in the equation based on the graph.(a-B1)2 + (y-B2)² = (B3)²8182=83=Blank 1:
Given: a circle is given with center (3,-3) and equation
[tex](x-B_1)^2+(y-B_2)^2=(B_3)^2[/tex]Find:
[tex]B_{1,\text{ }}B_{2,}B_3[/tex]Explanation: the general equation of the circle with center (a,b) and radius r is
[tex](x-a)^2+(y-b)^2=r^2[/tex]in the given figure the center of the circle is at (3,-3)
so the equatio of the circle becomes
[tex](x-3)^2+(y+3)^2=(3)^2[/tex]on comparing eith the given equation we get
[tex]B_1=3,\text{ B}_2=-3\text{ and B}_3=3[/tex]Evaluate x^1 - x^-1 + x^0 for x = 2.
The value of x^1 - x^-1 + x^0 for x = 2 is 5
we need to evaluate x¹ - x⁻¹ + x⁰
A positive exponent tells us how many times to multiply a base number, while a negative exponent tells us how many times to divide a certain base number. Negative exponents can be re written. x⁻ⁿ as 1 / x
x¹ - 1/x + x⁰
(any number or variable which is raised to the power zero is considered as 1)
x¹ - 1/x + 1
x² - 1 + x
x² + x - 1
The value of this expression for x = 2
2² + 2 - 1
4 + 2 - 1
5
Therefore,the value of x^1 - x^-1 + x^0 for x = 2 is 5
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Find the measure of the following numbered angles and the feason: Measure Reason 1 1 3 1 m
Answer
Explanation
Using the image,
Calculate the maximum number of cylindrical paint cans that carvers auto custom can stock if the paint comes in a 2-pack hazmat box that mesures 15 inches by 7 inches by 6 inches
The volume of Hazmat box is,
[tex]v=15\times7\times6[/tex][tex]v=630in^3[/tex]Convert inches to feet ,
[tex]undefined[/tex]The volume of the warehouse when half of the warehouse is painted with cams and rims is.
[tex]V=\frac{8000}{2}\times20ft^3[/tex][tex]V=80,000ft^3[/tex](6,3) and (2, -9)equation in slope intercept form
Let:
(x1,y1)=(6,3)
(x2,y2)=(2,-9)
[tex]\text{slope}=m=\frac{y2-y1}{x2-x1}=\frac{-9-3}{2-6}=\frac{-12}{-4}=3[/tex]Using the point-slope equation:
[tex]\begin{gathered} y-y1=m(x-x1) \\ y-3=3(x-6) \\ \text{Solve for y:} \\ y=3x-15 \end{gathered}[/tex]7. A large cooler contains the following drinks: 5 lemonades, 9 Sprites, 7 Cokes, and 10 root beers. You randomly pick two cans, one at a time (without replacement). Compute the following probabilities.(a) What is the probability that you get two cans of Sprite? (b) What is the probability that you do not get two cans of Coke? (c) What is the probability that you get either two root beers or two lemonades? (d) What is the probability that you get one can of Coke and one can of Sprite? (e) What is the probability that you get two drinks of the same type?
A large cooler contains the following drinks,
5 Lemonades, let L reprersent Lemonade
9 Sprites, let S reprersent Sprite
7 Cokes, let C represent Coke and
10 Root beers, let R represent Root beer
Total drinks in the cooler is
[tex]=5+9+7+10=31[/tex]Total outcome = 31 drinks
The formula of probability is
[tex]\text{Probability}=\frac{required\text{ outcome}}{total\text{ outcome}}[/tex]a) The probability that you get two cans of Sprite is
[tex]\begin{gathered} Prob\text{ of picking the first Sprite without replacement is} \\ P(S_1)=\frac{9}{31} \\ Prob\text{ of picking the second Sprite is} \\ P(S_2)=\frac{8}{30} \\ \text{Probability of getting two cans of Sprite}=(PS_1S_2)=\frac{9}{31}\times\frac{8}{30}=\frac{12}{155} \\ (PS_1S_2)=\frac{12}{155} \end{gathered}[/tex]Hence, the the probability that you get two cans of Sprite is 12/155
b)
The probability that you get two cans of Coke
[tex]\begin{gathered} Prob\text{ of picking the first Coke without replacement is} \\ P(C_1)=\frac{7}{31} \\ Prob\text{ of picking the second Coke is} \\ P(C_2)=\frac{6}{30} \\ \text{Probability of getting two cans of Coke is} \\ P(C_1C_2)=\frac{7}{31}\times\frac{6}{30}=\frac{7}{155} \\ P(C_1C_2)=\frac{7}{155} \end{gathered}[/tex]The probability that you do not get two cans of Coke will be
[tex]\begin{gathered} \text{Prob that you do not get two cans of Coke is} \\ 1-P(C_1C_2)=1-\frac{7}{155}=\frac{155-7}{155}=\frac{148}{155} \\ \text{Prob that you do not get two cans of Coke }=\frac{148}{155} \end{gathered}[/tex]Hence, the probability that you do not get two cans of Coke is 148/155
c)
The probability that you get two cans of Root beers is
[tex]\begin{gathered} Prob\text{ of picking the first Root b}eer\text{ without replacement is} \\ P(R_1)=\frac{10}{31} \\ Prob\text{ of picking the second Root b}eer\text{ is} \\ P(R_2)=\frac{9}{30} \\ \text{Probability of getting two cans of Root b}eer\text{ is} \\ P(R_1R_2)=\frac{10}{31}\times\frac{9}{30}=\frac{3}{31} \\ P(R_1R_2)=\frac{3}{31} \end{gathered}[/tex]The probability that you get two cans Lemonades is
[tex]\begin{gathered} Prob\text{ of picking the first Lemonade without replacement is} \\ P(L_1)=\frac{5}{31} \\ Prob\text{ of picking the second Root b}eer\text{ is} \\ P(L_2)=\frac{4}{30} \\ \text{Probability of getting two cans of Lemonade is} \\ P(L_1L_2)=\frac{5}{31}\times\frac{4}{30}=\frac{2}{93} \end{gathered}[/tex]The probability that you get either two root beers or two lemonades is
[tex]P(R_1R_2)+P(L_1L_2)=\frac{3}{31}+\frac{2}{93}=\frac{11}{93}[/tex]Hence, the probability that you get either two root beers or two lemonades is 11/93
d)
[tex]\begin{gathered} Prob\text{ of picking the first Coke without replacement is} \\ P(C)=\frac{7}{31} \\ \text{Prob of picking a can of Sprite is} \\ P(S)=\frac{9}{30} \end{gathered}[/tex]After getting both Sprite and Coke you will multiply the probabilities and then multiply them with 2 because you may choose Coke in first try and Sprite in second or the other way around
The probability that you get one can of Coke and one can of Sprite is
[tex]P(CandS)=2\times(\frac{7}{31}\times\frac{9}{30})=2(\frac{21}{310})=\frac{21}{155}[/tex]Hence, the probability that you get one can of Coke and one can of Sprite is 21/155
e)
Prob of two of each of the cans of drinks (without replacement) are as follow
[tex]\begin{gathered} P(L_1L_2)=\frac{2}{93} \\ (PS_1S_2)=\frac{12}{155} \\ P(C_1C_2)=\frac{7}{155} \\ P(R_1R_2)=\frac{3}{31} \end{gathered}[/tex]The probability that you get two drinks of the same type is
[tex]\begin{gathered} \text{Prob of two drinks of the same type is} \\ =P(L_1L_2)+(PS_1S_2)_{}+P(C_1C_2)+P(R_1R_2) \\ =\frac{2}{93}+\frac{12}{155}+\frac{7}{155}+\frac{3}{31}=\frac{112}{465} \\ \text{Prob of two drinks of the same type}=\frac{112}{465} \end{gathered}[/tex]Hence, the probability that you get two drinks of the same type is 112/465
Explain how you know that the function represented by the data in the given table is quadratic.XV0-17123-13-313
Given:
Here a table of equation is given
Required:
How to know that the function represented by the data in the given table is quadratic.
Explanation:
here the first differences of y values are as below
[tex]\begin{gathered} -13-(-17)=-13+17=4 \\ -3-(-13)=-3+13=10 \\ 13-(-3)=13+3=16 \\ 35-13=22 \\ 63-35=28 \end{gathered}[/tex]now again take difference of the first difference which is called as second difference.
[tex]\begin{gathered} 10-4=6 \\ 16-10=6 \\ 22-16=6 \\ 28-22=6 \end{gathered}[/tex]so here we can see that the second difference is same which is 6
now if second difference of any table is equal we can say that the given table is the table of quadratic equation.
Final answer:
The second differences are all 6
I dont know how to do number 18 on my homework
Beth walked 3 blocks in 15 minutes.
Then, we have that:
[tex]\frac{3}{15}\cdot\frac{3}{3}=\frac{9}{45}[/tex]We have that multiplying the rate (ratio) by the same number in the numerator and in the denominator, we will have equivalent fractions (and the same ratio).
Option a is true. We have the result above.
Then, for option b, we cannot obtain an equivalent fraction. It is false.
For option c, we have the same as for option b. It is false.
For option d:
[tex]\frac{3}{15}\cdot\frac{4}{4}=\frac{12}{60}[/tex]Then, option d is true.
14. What property is used to show that 3(4-6) = 12-18?
Answer:
Distribution property method
a blueprint for a house has a scale factor of 1 inch 3 ft. a wall in the blueprint is 5 in what is the length of the actual wall in feet
15 ft
Explanation
you can easily solve this by using a rule of three
Step 1
Let x represents the actual length of the wall in feet
is
[tex]1\text{ inc}\rightarrow3\text{ ft}[/tex]then
[tex]5\text{ in}\rightarrow x[/tex]as the proportion is the same
[tex]\begin{gathered} \frac{1}{3}=\frac{5}{x} \\ \text{cross multiply} \\ x\cdot1=5\cdot3 \\ x=15\text{ ft} \end{gathered}[/tex]so, the answer is 15 ft
I hope this helps you
"Name the property used in the equation below
a) 3 x+9 y-1=3(x+3 y)-1
b) 7 x+5 y-5 y=7 x
c) (x-4)(x+3)=0
d) 4 x+5 x=5 x+4 x"
The property used in each equation are
a) 3x + 9y - 1 = 3(x + 3y) - 1 distributive property
b) 7x + 5y - 5y = 7x additive inverse property
c) (x - 4)(x + 3) = 0 distributive property
d) 4x + 5x = 5x + 4x commutative property
What is distributive property?The distributive property states that multiplying the total of two or more addends by a number produces the same outcome as multiplying each addend separately by the number and adding the products together.
Additive inverse involves adding which involves two numbers that has opposite sign. the addition lead to zero
b) 7x + 5y - 5y = 7x
= 7x + 0
= 7x
What is commutative property?
This law basically asserts that while adding and multiplying numbers, you can rearrange the numbers in a problem without changing the solution.
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Consider the diagram and angle measures shown below.m∠1 = (3x +25)m∠2 = (7x+5)m∠3 =(-2x + 70)4322 || 7What is the value of m∠3 ?
First, we need to find the value of x
m<4 = m<1 = (3x + 25)° ( corresponding angle)
Let the angle between m<2 and m<3 be m<5
m< 5 = m<4 = (3x + 25)° ( vertical angle)
m<2 + m<5 + m<3 = 180° (angles on a straight line
(7x+5)° + (3x+25)° + (-2x + 70)° = 180°
7x + 5 + 3x + 25 -2x + 70 = 180
Rearrange
7x + 3x -2x + 5 + 25 + 70 = 180
8x + 100 = 180
subtract 100 from both-side of the equation
8x = 180 - 100
8x = 80
Divide both-side of the equation by 8
x = 10
m<3 = -2x + 70
substitute x = 10 in the above
m<3 = -2(10) + 70 = -20 + 70 = 50°
Suppose you are riding in a roller coaster which
follows the curve in the graph and when you reach the point
(1.1) your hat falls off. This curve is defined by the equation
23 + 43
=2y. Find an equation of the line that the hat will
follow if you ignore gravity and air resistance.
x + y = 2 is the equation of the line that the hat will follow if we ignore the gravity and air resistance.
Given, we are riding in a roller coaster which follows the curve in the graph and when we reach the point (1 , 1) our hat falls off.
Now, we have to find the equation of the line that the hat follow,
The slope of the tangent to the curve x³ + y³ = 2xy is given by,
3x² + 3y²y' = 2y + 2xy'
at the point (1 , 1)
3 + 3y' = 2 + 2y'
y' = -1
Now, the slope of the line perpendicular to the tangent of the curve is,
-1
Now, the equation of the line that hat follows is,
(y - 1)/(x - 1) = -1
y -1 = 1 - x
x + y = 2
Hence, x + y = 2 is the equation of the line that the hat will follow if we ignore the gravity and air resistance.
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