In an expression, two or more terms are like terms if they have the same variable and exponents.
For example the terms:
2a and -8a → these terms have the same variable "a" and the same exponent "1"
9y³ and 8x⁴ → these terms have different variables "y" and "x" and different exponents "3" and "4", so they are not like terms.
Constants, for example, -10 or 6, are also considered to be like terms.
Look again at the table of refrigerator sizes and prices. Is the relation a function?A. The relation is not a function. All input values are paired with only oneoutput value.B. The relation is not a function. Some of the input values are paired withmore than one output value.C. The relation is a function. The input values are paired with more than oneoutput value.D. The relation is a function. All input values are paired with only one outputvalue.HINTSUBMIT
B. The relation is not a function. Some of the input values are paired with
more than one output value.
Explanation
A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Step 1
Identify the input values and compare with the outputs
as we can see one input is related to TWO outputs, for example
[tex]\begin{gathered} 1.7\rightarrow80 \\ 1.7\rightarrow79 \end{gathered}[/tex]hence, the relation is not a function
B. The relation is not a function. Some of the input values are paired with
more than one output value.
I hope this helps you
one-half of a number y is more than 22
1) Writing that statement as an inequality we have:
[tex]\begin{gathered} \frac{y}{2}>22\text{ } \\ Multiplied\text{ by 2 on both sides} \\ y>44 \end{gathered}[/tex]2) Hence, we can say that if one-half of a number y is more than 22
then y > 44
Solve |x| < 12 a{ x| x < -12 or x > 12}b { x|-12 < x < 12} c{-12, 12}Pllzzzzz alot of points
We need to solve the inequality:
[tex]|x|<12[/tex]See question below as I tried to ask another tutor
Given the word problem, we can deduce the following information:
1. The formula V=2.5r can be used to estimate the maximum safe velocity,v, in miles per hour, at which a car can travel if it is driven along a curved radius of curvature r in feet.
2. The radius of curvature is 280 feet.
To determine the maximum safe speed, we use the given formula as shown below:
[tex]V=2.5r[/tex]where:
V= Maximum safe velocity in miles per hour
r=radius of curvature = 280 feet
We plug in what we know:
[tex]\begin{gathered} V=2.5r \\ =2.5(280) \\ Calculate \\ V=700\text{ }\frac{miles}{hour} \end{gathered}[/tex]Therefore, the maximum safe speed is 700 miles per hour.
how many kiloliters are in 32,500 centiliters325 kl3,250,000,000 kl32.5 kl0.325 kl
0.325 kl
Explanation:We need to convert from centiliters to Kiloliters:
[tex]\begin{gathered} 1liter=100^{}\text{centiliter} \\ 1\text{ kilo = 1000} \\ 1\text{ kiloliter = 1000liter} \\ 1\text{ kiloliter = 100000 centiliter} \end{gathered}[/tex][tex]\begin{gathered} 100000\text{ centiliter = }1\text{ kiloliter} \\ 32500\text{ centiliter = }\frac{\text{32500(1)}}{100000} \\ \text{= }\frac{32500}{100000} \\ 32500\text{ centiliter }=\text{ 0.325 kl} \end{gathered}[/tex]For almost all mortgage lenders, a home buyer must put down a certain percentage ofthe selling price towards the sale and financing of a home. Different banks and differentkinds of loans have set standards. Based on the given information, solve the problems.A buyer decides to put a contract on a house he/she would like to purchase. For eachscenario given, find the amount of down payment, the loan amount, the realestate commission, and tax assessment.#1 Selling price is $250,000.00 10% down payment would be $______ the real estate commissionthe seller would pay (at 6% commission) would be $______ and the amount for the mortgage(selling price - down payment) would be $______ House assesses for $245,000.00 and the taxrate is $1.15 per $100.00 of assessed value so taxes on the house would be $_____ for theyear#2 Selling price is $195,000.00 10% down payment would be $______ the real estate commissionwould be (at 6%) $______ and the mortgage amount would be for $_______ House assesses for$189,000.00 and the tax rate is $1.09 per $100.00 so the real estate taxes for the yearwould be $______
Answer:
(1)
• 10% down payment would be $25,000.
• The real estate commission would be $15,000.
• The amount for the mortgage would be $225,000.
• Taxes on the house would be $2817.50 for the year.
(2)
• 10% down payment would be $19,500.
• The real estate commission would be $11,700
• The amount for the mortgage would be $175,000.
• Taxes on the house would be $2060.10 for the year.
Explanation:
Part 1
The selling price is $250,000.00.
[tex]\begin{gathered} \text{ Down Payment}=10\%\text{ of }250,000 \\ =0.1\times250,000 \\ =25,000 \end{gathered}[/tex]• 10% down payment would be $25,000.
[tex]\begin{gathered} \text{ Real Estates Commission}=6\%\text{ of }250,000 \\ =0.06\times250,000 \\ =15,000 \end{gathered}[/tex]• The real estate commission the seller would pay (at 6% commission) would be $15,000.
[tex]\begin{gathered} \text{ Mortgage Amount}=\text{ Selling Price}-\text{ Down Payment} \\ =250,000-25,000 \\ =225,000 \end{gathered}[/tex]• The amount for the mortgage would be $225,000.
[tex]Tax=\frac{1.15}{100}\times245,000=2817.50[/tex]• Taxes on the house would be $2817.50 for the year.
Part 2
The selling price is $195,000.00.
[tex]\begin{gathered} \text{ Down Payment}=10\%\text{ of }195,000 \\ =0.1\times195,000 \\ =19,500 \end{gathered}[/tex]• 10% down payment would be $19,500.
[tex]\begin{gathered} \text{ Real Estates Commission}=6\%\text{ of }195,000 \\ =0.06\times195,000 \\ =11,700 \end{gathered}[/tex]• The real estate commission the seller would pay (at 6% commission) would be $11,700.
[tex]\begin{gathered} \text{ Mortgage Amount}=\text{ Selling Price}-\text{ Down Payment} \\ =195,000-19,500 \\ =175,500 \end{gathered}[/tex]• The amount for the mortgage would be $175,000.
[tex]Tax=\frac{1.09}{100}\times189,000=2060.10[/tex]• Taxes on the house would be $2060.10 for the year.
Find the probability of X successes, using Table B in Appendix A of the textbook or some other method.n = 10, p = 0.3, X = 7
SOLUTION
The probability is a binomial probability
The probability is given as
[tex]\text{nCxp}^xq^{n-x}[/tex]Where p= proability of succes=0.3
q=probability of failure=1-p=1-0.3=0.7
n=10, x=7
Then, substitute the parameters into the formula
[tex]10C_7(0.3)^7(0.7)^3[/tex][tex]\begin{gathered} 10C_7=120 \\ 120\times2.187\times10^{-4}\times0.343 \end{gathered}[/tex]Then we have
[tex]\begin{gathered} 9.0017\times10^{-3} \\ 0.0090017 \end{gathered}[/tex]The probability of x-success is 0.009
write an equation of a line passing through the point (-6,-3) and perpendicular to JK with J (-2, -7) and K (6,5)
EXPLANATION
Given the point: (-6,-3) and the vector JK with J=(-2,-7) K=(6,5)
First we need to the slope of the vector applying the slope formula:
[tex]\text{Slope}=\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]Replacing the ordered pairs J=(-2,-7) and K=(6,5) give us the slope:
[tex]\text{Slope}=\frac{(5-(-7))}{(6-(-2))}=\frac{12}{8}=\frac{3}{2}[/tex]Now, we have the slope and we can use this to find the line that contains the point (-6, -3) applying the generic form:
y= -2x/3 + b where -2/3 is the negative and reciprocal slope perpendicular to the vector JK.
Finally, replacing the point (-6,-3) give us the y-intercept, b,
-3 = -2(-6)/3 + b
Multiplying terms:
-3 = 12/3 + b ---> -3 = 4 + b
Subtracting 4 to both sides:
-3 - 4 = b
Switching sides:
b= -7
The linear equation is y = (-2/3)x - 7 OPTION B
Jackson types 120 words in 2 minutes. Enter the number of words Jackson types in 4 minutes at this ratewords
if in 2 minutes Jackson Typed 120 words, in 4 minutes will type twice the amount. SO
[tex]w=120\cdot2=240[/tex]he will type 240 words in 4 minutes
Chris tries to copy
The Chris's error is that he does not consider he can not draw the upper oblique line crosses trough the end the of the arc.
To coorect that, Chris must to draw the upper line crosses trough the center of the arc. In this way he is going to obtain a exact copy of angle ∠T.
By taking into account the previous specifications you obtain the following draw of the angle:
As you can notice, it is necessary that the upper line crosses trough the center of the arc.
this graphic organizer is being used to classify triangles based on their angle measures or sideways which list shows all of the ways that strangle could be classified
D
1) Examining the sides of that triangle, we can state that this is an equilateral triangle (at least 2 sides have the same measure). But Since isosceles is a triangle that has 2 sides with the same measure.
Then we can state that about their sides this is an equilateral and isosceles triangle.
2) Examining their angles. An equilateral triangle has 3 angles with 60º measure. A 60º angle is lesser than 90º, then we can classify this triangle as an acute triangle
3) Hence, the answer is D
The Hudson family is saving for a
family vacation to Disney World.
They determine that the trip will
cost $3,200. Mr. and Mrs.
Hudson have already set aside
$1,500 for the trip. If they leave
in 16 weeks, then how much
will they need to save
each week?
The amount of money that Hudson will need to save each week is $106.25.
How to calculate the value?From the information, they determine that the trip will cost $3,200. Mr. and Mrs. Hudson have already set aside $1,500 for the trip.
Let the amount saved each week be represented as w.
Based on the information given, this will be illustrated as:
1500 + 16w = 3200
Collect like terms
16w = 3200 - 1500
16w = 1700
Divide
w = 1700 / 16
w = 106.25
The amount is $106.25.
Learn more about money on:
brainly.com/question/24373500
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Multiply the following [tex] \sqrt{ - 15} \times \sqrt{ - 15} [/tex]
Answer: -15
Given:
[tex]\sqrt[]{-15}\times\sqrt[]{-15}[/tex]Since the radical rule states that:
[tex]\begin{gathered} \sqrt[]{a}\sqrt[]{a}=a \\ \Rightarrow\sqrt[]{-15}\times\sqrt[]{-15}=-15 \end{gathered}[/tex]Therefore, the answer is -15.
A sales person is given a choice of two salary plans. Plan 1 is a weekly salary of 700 plus 4% commission of sales. Plan 2 is a straight commission of 12%Of sales. How much in sales must he make in a week for both plans to result in the same salary?
Let 's' represent the amount of sales.
Plan 1:
[tex]\text{ \$700 + (4\% of s)}[/tex][tex]\begin{gathered} \text{ \$700+(}\frac{\text{4}}{100}\times s) \\ \text{ \$700+(0.04}\times s)=\text{ \$700}+0.04s \end{gathered}[/tex]Plan 2:
[tex]12\text{ \% of s}[/tex][tex]\begin{gathered} \frac{12}{100}\times s \\ 0.12\times s=0.12s \end{gathered}[/tex]Equating the two plans together and solving for the amount of sales,
[tex]\begin{gathered} \text{Plan 2=Plan 1} \\ 0.12s=\text{ \$700+0.04s} \\ \end{gathered}[/tex]Collecting like terms,
[tex]\begin{gathered} 0.12s-0.04s=\text{ \$700} \\ 0.08s=\text{\$700} \end{gathered}[/tex]Divide both sides by 0.08,
[tex]\begin{gathered} \frac{0.08s}{0.08}=\frac{\text{ \$700}}{0.08} \\ s=\text{ \$8750} \end{gathered}[/tex]Hence, the amount of sales is $8,750.
Find the area of each rectangle using the given information.(A=W x H)Question 9:6 and a height of 36 inches.
The rule of the area of a rectangle is
[tex]A=W\times H[/tex]W is the width
H is the height
Since the ratio between width and height is 9: 6 and the height is 36 inches, then we will use the ratio method
[tex]\begin{gathered} W\rightarrow H \\ 9\rightarrow6 \\ W\rightarrow36 \end{gathered}[/tex]By using the cross multiplication
[tex]\begin{gathered} W\times6=9\times36 \\ 6W=324 \end{gathered}[/tex]Divide both sides by 6
[tex]\begin{gathered} \frac{6W}{6}=\frac{324}{6} \\ W=54 \end{gathered}[/tex]Then the width of the rectangle is 54 inches
Substitute W by 54 and H by 36 in the rule of the area to find it
[tex]\begin{gathered} A=54\times36 \\ A=1944inches^2 \end{gathered}[/tex]The area of the rectangle is 1944 square inches
Question 7 using radians, find the amplitudeand period of each function and graph it
Given:
y = 4 sin 4θ
The amplitude is 4.
Period:
[tex]\begin{gathered} P=\frac{2π}{B};\text{ }hence: \\ \\ P=\frac{2π}{4}=\frac{π}{2} \end{gathered}[/tex]The period is π/2.
Graph:
hey ms or mr can you please help me out?
B'C' = 3BC
Explanations:Note:
When a figure is dilated by a scale factor, a similar figure of the same shape but of different size is formed.
When a triangle ABC is dilated by a scale factor of 3, the vertices of the image of ΔA'B'C' formed will have a distance from the center of dilation that is three times that of the vertices of ΔABC
Therfore:
A'B' = 3AB
B'C' = 3BC
A'C' = 3AC
The correct choice is option B
That is, B'C' = 3BC
b.InOut133171066co38Rule:
Suppose that the rule is of the form
[tex]y=mx+b[/tex]Where m is the slope and b is the intercept
The slope can be found using the formula
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]You can take any two consecutive x and y values from the given table.
[tex]\frac{17-3}{3-1}=\frac{14}{2}=7[/tex]Similarly,
[tex]\frac{66-17}{10-3}=\frac{49}{7}=7[/tex]As you can see, you will end up with the same slope.
Now let us find the intercept b.
Take any x, y coordinates from the table
[tex](x,y)=(1,3)[/tex]Now substitute them in the slope-intercept equation.
[tex]\begin{gathered} y=7x+b \\ 3=7(1)+b \\ 3=7+b \\ b=-7+3 \\ b=-4 \end{gathered}[/tex]So the rule is
[tex]y=7x-4[/tex]Verification:
Let us verify whether we got the correct rule or not
Substitute the input x coordinates into the rule and check the outputs y coordinates.
[tex]\begin{gathered} y=7(1)-4=7-4=3 \\ y=7(3)-4=21-4=17 \\ y=7(10)-4=70-4=66 \\ y=7(6)-4=42-4=38 \end{gathered}[/tex]As you can see, we have got the same results therefore, the rule is correct.
i need help with this
graphing the points
answer: (- 8, 6)
i’m taking an algebra pretest & i’m very confused. i haven’t learned this material. please help!!
ANSWER
7 (Option D)
EXPLANATION
Given:
Number of times the traffic light Green = 6
Number of times the traffic light Yellow = 2
Number of times the traffic light Red = ?
Desired Outcome:
Number of times the traffic light Red
Total number of times for the traffic lights
[tex]\begin{gathered} \text{ Total times = Times for traffic light Red + Times for traffic light Green + Times for traffic light Yellow} \\ 15=Red+6+2 \\ 15=Red+8 \\ substract\text{ 8 from both sides} \\ 15-8=Red+8-8 \\ \text{ Times for traffic light Red = 7} \end{gathered}[/tex]Hence, the number of times the traffic light Red was 7.
What transformations were applied to the toolkit function to create the new function?
The parent functions is f(x) = 1/x
We have 1/(x+2) -1
The 1/(x+2) is f(x+2) which is a horizontal translation left 2 units
Then we have -1 which is f(x+2) -1 which is a vertical translation down 1 unit
The total transformation is a horizontal translation left 2 units and a vertical translation down 1 unit
Answer: left 2 units down 1 unit
Marcia sells lemonade for $2 per cup and candy for $1.50 per candy bar. She earns $425 selling lemonade and candy bars. If marcia sold 90 bars of candy, which equation could be used to figure out how many cups of lemonade she sold?
Answer: 145 cups of lemonade
Step-by-step explanation:
hope it helped :)
Calculate the volume of the rectangular prism.A. 179 cm³B. 187 cm³C. 189 cm³D. 198 cm³
ANSWER
[tex]C.\text{ }189\text{ }cm^3[/tex]EXPLANATION
We want to calculate the volume of the rectangular prism.
The volume of a rectangular prism is given by:
[tex]V=L*W*H[/tex]where L = length
W = width
H = height
Therefore, the volume of the rectangular prism is:
[tex]\begin{gathered} V=9*7*3 \\ \\ V=189\text{ }cm^3 \end{gathered}[/tex]The answer is option C.
2. Find each of the following products of monomials. (a) (3x?) (10x) (b) (-2x)(-9x) (c) (4x+y)(8x*y) (d) (5x) (e) (-41)(-151") 2 (f) (7x)(5xy^) ** | (12x) (h) (2xP)(5x)(-6x4)
In order to solve the products between the followings monomials you take into account that the multiplication is in between coefficients, and also you take into account that it is necessary to multiply the involved signs.
a)
[tex](3x^3)(10x^4)=(3)(10)x^{^{3+4}}=30x^7[/tex]when the product is between the same variable but different exponents, you sum the exponents
b)
[tex](-2x^5)(-9x)=(-2)(-9)x^{5+1}=18x^6[/tex]where you have used that minus multiplied by minus is equal to positive
c)
[tex](4x^2y)(8x^5y^3)=(4)(8)x^{2+5}y^{1+3}=32x^7y^4[/tex]where you sum the exponents of x and y
d)
[tex](5x^4)^2=(5)^2(x^4)^2=25x^{4\cdot2}=25x^8[/tex]In the case in which you have a variable with an exponent, power to another exponent, these exponents must be multiplied. The coeeficient also has to be exponentiated
e)
[tex](-4t^2)(-15t^5)=(-4)(-15)t^{2+5}=60t^7[/tex]f)
[tex](7x)(5xy^4)=35x^2y^4[/tex]g)
[tex](\frac{2}{3}x^4)(12x)=\frac{2\cdot12}{3}x^5=8x^5[/tex]f)
[tex](2x^2)(5x)(-6x^4)=(2)(5)(-6)x^{2+1+4}=-60x^7[/tex]where you multiply all coefficientes and signs, and sum the exponents of x
Part 2: Write limits given outputs.Use the graph of the function to write limit equations given limit values.Use the graph to write a limit equation for f(x) that satisfies each given condition. (2 points for each)a. b. c. d. e. Are there other values than what you chose for x where the limit of the function approaches 4? Is the graph continuous at these points? Explain your reasoning. (4 points)
a) From the graph, we see that the function takes the value y = 4 when x = 4, so we have:
[tex]\lim _{x\rightarrow4}f(x)=4.[/tex]b) We see that the curve tends to -∞ when x approaches zero from the left, so we have:
[tex]\lim _{x\rightarrow0^-}f(x)=-\infty.[/tex]c) We see that curve increases without limit when x tends to infinity, so we have:
[tex]\lim _{x\rightarrow\infty}f(x)=\infty.[/tex]d) From the graph, we see that the function tends to y = 0 when x approaches zero from the right, so we have:
[tex]\lim _{x\rightarrow0^+}f(x)=0.[/tex]e) Yes, there are two possible values of x for the limit of the function approaching 4:
• x = 2,
,• x = 4.
By definition, a function is continuous when its graph is a single unbroken curve.
We see that at the points x = 2 and x = 4 the curve is a single unbroken curve, so we conclude that the function is continuous at those points.
Answers
a, b, c, d
[tex]\begin{gathered} \lim _{x\rightarrow4}f(x)=4 \\ \lim _{x\rightarrow0^-}f(x)=-\infty \\ \lim _{x\rightarrow\infty}f(x)=\infty \\ \lim _{x\rightarrow0^+}f(x)=0 \end{gathered}[/tex]e. Yes, there are two possible values of x for the limit of the function approaching 4:
• x = 2,
,• x = 4.
By definition, a function is continuous when its graph is a single unbroken curve.
We see that at the points x = 2 and x = 4 the curve is a single unbroken curve, so we conclude that the function is continuous at those points.
how would I solve the system of equations using elimination?8x - 5y = 114x - 3y =5
Using elimination. In elimination process the two system of equations are multiplied by a apropiate factor , in order to eliminate one of the variables
then
multiplicate first equation by 4
and multiplicate second equation by 8
once obtained both results, then substract them
So then
4• (8x-5y) = 4•11= 44
8• (4x-3y) = 8•5= 40
32x -20y= 44
32x - 24y= 40
4y= 4 then y=1
now replace y=1 in any of both equations
8x -5= 11. Then x= (11+5)/8= 2
x=2
write a recursive rule for the sequence -10,-3,4,11
Let the given sequence is -10,-3,4,11
The objective is to write recursive rule for the sequence.
In the given sequence each number has an equal difference between them
[tex]\begin{gathered} -3-(-10)=7 \\ 4-(-3)=7 \\ 11-4=7 \end{gathered}[/tex]So, consider the terms as,
[tex]\begin{gathered} a_1=-10 \\ a_2=-3 \\ a_2=a_1+7 \\ a_3=a_2+7 \\ a_4=a_3+7 \end{gathered}[/tex]Hence the recursive series is
[tex]a_n=a_{n-1}+d[/tex]- 3/4 m - 1/2 = 2 + 1/4 m2345
Please just put the answer for this question On D
Answer
The liters of air takes in during 150 seconds is 25 liters
Step-by-step explanation:
A man takes in 5 liters of air in 30 seconds
Firstly, we need to find the rate
Given:
Volume = 5 liters
time = 30 seconds
Rate =?
Volume = rate x time
5 = rate * 30
rate = 5/30 liters / second
Find the volume of air takes in during 150 seconds at the same rate
Volume = rate * time
Volume = 5/30 * 150
Volume = 5 * 150 / 30
Volume = 25 liters
Hence, the liters of air takes in during 150 seconds is 25 liters
Select the following that are true.Select one or more:a.If a quadrilateral is a square, then it is a rectangle.b.If a quadrilateral is a square, then it is a parallelogram.c.If a quadrilateral is a rhombus, then it is a parallelogram.d.If a quadrilateral is a rectangle, then it is a rhombus.e.If a quadrilateral is a square, then it is a rhombus.f.If a quadrilateral is a parallelogram, then it is a rectangle.
a. One of the properties of squares is all sides are congruent (they have the same length) and this is not a property of rectangles. But the square is a special rectangle since it fits in the properties of rectangles, but rectangles are not squares. In this case, this is TRUE.
b. A parallelogram is a quadrilateral with two pairs of opposite parallel sides and the opposite sides are congruent. The square fits into this description, so this is TRUE.
c. A rhombus has four equal opposite parallel sides, so we can say it fits into the parallelogram definition. This is TRUE.
d. As we said in part a, a rectangle doesn't have all of its sides congruent, but the rhombus does. Then, this is FALSE.
e. Squares have four equal opposite parallel sides, and rhombus too. Then, a square is a rhombus. This is TRUE.
f. Not all parallelograms have the properties of rectangles, then this is FALSE.