All in one, or one expression for each property?
a) Zero property
[tex]\text{ (x + y)}^0\text{ = 1}[/tex]b) Multiplication property
[tex]\text{ x}^2\cdot x^5=x^{2+5}=x^7[/tex]c) Power property
[tex]\text{ (x}^2)^3=x^{2\cdot3}=x^6[/tex]d) All in one (this is the expression)
[tex]\mleft\lbrace\text{(x}^0)(x^3)\mright\rbrace\text{ }(x^2)^5[/tex][tex]\text{ }\mleft\lbrace1(x^3\mright)\}(x^{10})[/tex]
Tell whether the graph would be continuous or discrete2. A pet store is selling puppies for $200 each. It has 8 puppies for sale.AcontinuousB) discrete
Given:
Cost of each puppy = $200
Number of puppies = 8
Here, the equation for total cost of puppies will be:
C = 200x
Where x represents the number of puppies sold
Cost of 1 puppy = $200
Cost of 2 puppies = $200(2) = $400
Cost of 3 puppies = $200(3) = $600
If you continue with the pattern you'll see the graph has a rate of change of 200
To determine if the graph will be continuous or discrete, we have:
For a graph to be continuous, the points on the graph must be connected with a continuos line, while for a graph to be discrete the points are series of unconnected points just like in a scatter plot.
The graph of this will be a discrete graph. A discrete graph have set of values(points)
ANSWER:
B. discrete
Select the table of values that contains ordered pairs that, when plotted, provide the best representation of the curve of the function
As given by the question
There are given that the equation:
[tex]y=-2(x+3)^2+4[/tex]Now,
Put the value of x into the given equation and find the value of y from all the tables one-by-one and match their value of x and y are equal or not.
Then,
Form the option third,
Put x = -2 to find the value of y, then match the value of y with the given value of y in the table.
So,
[tex]\begin{gathered} y=-2(x+3)^2+4 \\ y=-2(-2+3)^2+4 \\ y=-2(1)^2+4 \\ y=-2+4 \\ y=2 \end{gathered}[/tex]Now,
Put x = -1, then:
[tex]\begin{gathered} y=-2(x+3)^2+4 \\ y=-2(-1+3)^2+4 \\ y=-2(2)^2+4 \\ y=-2(4)+4 \\ y=-8+4 \\ y=-4 \end{gathered}[/tex]Then,
Put x = 0, then:
[tex]\begin{gathered} y=-2(x+3)^2+4 \\ y=-2(0+3)^2+4 \\ y=-2(3)^2+4 \\ y=-2(9)+4 \\ y=-18+4 \\ y=-14 \end{gathered}[/tex]Then,
Put 1 into the given equation instead of x:
So,
[tex]\begin{gathered} y=-2(x+3)^2+4 \\ y=-2(1+3)^2+4 \\ y=-2(4)^2+4 \\ y=-2(16)+4 \\ y=-32+4 \\ y=-28 \end{gathered}[/tex]And,
Put x = 2, so:
[tex]\begin{gathered} y=-2(2+3)^2+4 \\ y=-2(5)^2+4 \\ y=-2(25)+4 \\ y=-50+4 \\ y=-46 \end{gathered}[/tex]Now,
From option d, all values of x and y are matched also but curve representation is matched in option D.
Hence, the correct option is D.
I need help please!!
Find the equation of the linear function represented by the table below in slope-intercept form. Answer: y=
Answer:
y = 2x + 6
Explanation:
The slope-intercept form of a linear equation can be found as:
[tex]y=m(x-x_1)+y_1[/tex]Where m is the slope and it is calculated as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]And (x1, y1) and (x2, y2) are values from the table. So, we can replace (x1, y1) by (0,6) and (x2, y2) by (1, 8):
Then, the slope is:
[tex]m=\frac{8-6}{1-0}=\frac{2}{1}=2[/tex]Therefore, the equation of the line is:
[tex]\begin{gathered} y=2(x-0)+6 \\ y=2x+6 \end{gathered}[/tex]So, the answer is y = 2x + 6
If a red and a blue fair six sided die are rolled what is the probability the result is 8 or divisible by 3?
SOLUTION:
Step 1:
In this question, we are given that;
If a red and a blue fair six-sided die are rolled.
What is the probability the result is 8 or divisible by 3?
Step 2:
The table for the two dice rolled together is as shown below:
Green 1 2 3 4 5 6
Red
1 2 3 4 5 6 7
2 3 4 5 6 7 8
3 4 5 6 7 8 9
4 5 6 7 8 9 10
5 6 7 8 9 10 11
6 7 8 9 10 11 12
Step 3:
The probability that the result is 8 =
[tex]\begin{gathered} =\text{ }\frac{\nu mber\text{ of 8}}{\text{Total number }} \\ =\text{ }\frac{5}{36} \end{gathered}[/tex]Next,
The probability that the result is divisible by 3
=
[tex]\frac{12}{36}[/tex]Finally, the probability that the result is 8 or divisible by 3, we have that:
[tex]\frac{5}{36}+\frac{12}{36}\text{ =}\frac{17}{36}[/tex]
I got the first part I’m not sure of the 2nd is it 38.5
We will have the following:
The surface area of the onion can be best modeled by a sphere. Base on the model, the approximate area of the onion is 38.5 square inches:
[tex]A_s=4\pi(\frac{3.5}{2})^2\Rightarrow A_s\approx38.5[/tex]This year, Buffalo, New York had 45 inches of snow in January. Last year, Buffalo had 19 inches of snow in January. How much more snow did Buffalo receive this January? Show your work in the space below. Don't forget to label the units on your answer.
In January this year, 45 inches of snow. In January last year, it was 19 inches. The difference betwen the measures gives us how much more was received this year.
This difference
= 45 inches - 19 inches
= 26 inches
Consider the following equation of a parabola.y? + 4y = 8r + 4Step 1 of 3: Find the focus of the parabola.
Given the equation:
[tex]y^2+4y=8x+4[/tex]Let's find the focus of the parabola.
To find the focus of the parabola, let's first rewrite the equation in vertex form:
[tex]y=a(x-h)^2+k[/tex]We have:
[tex]undefined[/tex]Find the sin t as a fraction in simplest terms
We are asked to determine the sinT. To do that let's remember that the function sine is defined as:
[tex]\sin x=\frac{opposite}{hypotenuse}[/tex]In this case, we have:
[tex]\sin T=\frac{VU}{VT}[/tex]To determine the value of VU we can use the Pythagorean theorem which in this case would be:
[tex]VT^2=VU^2+TU^2[/tex]Now we solve for VU first by subtracting TU squared from both sides:
[tex]VT^2-TU^2=VU^2[/tex]Now we take the square root to both sides:
[tex]\sqrt[]{VT^2-TU^2^{}}=VU[/tex]Now we plug in the values:
[tex]\sqrt[]{(6)^2+(\sqrt[]{36^{}})^2}=VU[/tex]Solving the squares:
[tex]\sqrt[]{36+36}=VU[/tex]Adding the values:
[tex]\sqrt[]{2(36)}=VU[/tex]Now we separate the square root:
[tex]\sqrt[]{2}\sqrt[]{36}=VU[/tex]Solving the square root:
[tex]6\sqrt[]{2}=VU[/tex]Now we plug in the values in the expression for sinT:
[tex]\sin T=\frac{6\sqrt[]{2}}{6}[/tex]Now we simplify by canceling out the 6:
[tex]\sin T=\sqrt[]{2}[/tex]And thus we obtained the expression for sinT.
Determine the angle relationship. Drag the correct answer to the blank. what is the angle relationship of < 3 & <7
we have that
between m<3 and m<7 -----> no relationship (because q and p are not parallel)
Part 2
the relationship between m<12 and m<10
is
vertical angles
m<12=m<10 ------> by vertical angles
Question 13 of 18Graph the solution to the following inequality on the number line.x² - 4x ≥ 12
Step 1
Given; Graph the solution to the following inequality on the number line.
x² - 4x ≥ 12
Step 2
[tex]\begin{gathered} x^2-4x\ge \:12 \\ Rewrite\text{ in standard form} \\ x^2-4x-12\ge \:0 \\ Factor\text{ the inequality} \\ \left(x+2\right)\left(x-6\right)\ge \:0 \end{gathered}[/tex][tex]\begin{gathered} Identify\text{ the intervals} \\ x\le \:-2\quad \mathrm{or}\quad \:x\ge \:6 \end{gathered}[/tex]Thus, the number line will look like
Answer; The solution to the inequality graphed on a number line is seen below
[tex]x\le \:-2\quad \mathrm{or}\quad \:x\ge \:6[/tex]2+2 is what i need help???
We have the following problem given:
[tex]2+2=4[/tex]Then the final answer for this case would be 4
Jim began a 156 mile bike trip to build up stamina . Unfortunately his bike chain broke so he finished walking. Th whole trip took 6 hours. If Jim walks at a rate of 5 miles per hour and rides at 33 miles per hour find the amount he spent on the bike.
This diagram represents the problem
We know that distance = speed*time; D=S*t
Total distance: 156 miles
time: 6 h
Speed1: 33 miles/h
Speed2: 5 miles/h
for interval 1:
[tex]\begin{gathered} D_1=S_1\cdot t_1 \\ D_1=33\cdot t_1 \end{gathered}[/tex]for interval 2:
[tex]\begin{gathered} D_2=S_2\cdot t_2 \\ D_2_{}=5\cdot t_2 \end{gathered}[/tex]for the whole trip: -Eq 1. Distance
[tex]\begin{gathered} D=D_1+D_2 \\ D=33\cdot t_1+5\cdot t_2 \\ 156=33\cdot t_1+5\cdot t_2 \end{gathered}[/tex]and also: -Eq 2. Time
[tex]\begin{gathered} t=t_1+t_2 \\ 6=t_1+t_2 \end{gathered}[/tex]Now we have a system of 2 equations with 2 unknowns.
Let's solve it!
[tex]\begin{gathered} 156=33t_1+5t_2 \\ t_1=\frac{156-53t_2}{33} \\ \frac{156-5t_2}{33}+t_2=6 \\ t_2=\frac{3}{2} \\ t_1=\frac{156-5\cdot\frac{3}{2}}{33} \\ t_1=\frac{9}{2} \end{gathered}[/tex]We can see that he spent 4.5 hours riding the bike and 1.5 h walking
The court ruled that Lox Auto was liable in the death of an employee.The settlement called for the company to pay the employee's widow $60,000 at theend of each year for 20 years. Find the amount the company must set aside today,assuming 5% compounded annually.
We have to calculate the present value PV of a annuity.
The payment is yearly and it is P=60,000.
The interest rate is 5% (r=0.05), compounded annually (m=1).
The number of periods is n=20 years.
Then, we can use the formula for the present value of a annuity:
[tex]\begin{gathered} PV=P\cdot\frac{1-\frac{1}{(1+r)^n}}{r} \\ PV=60000\cdot\frac{1-\frac{1}{1.05^{20}}}{0.05} \\ PV\approx60000\cdot\frac{1-\frac{1}{2.653}}{0.05} \\ PV\approx60000\cdot\frac{1-0.377}{0.05} \\ PV\approx60000\cdot\frac{0.623}{0.05} \\ PV\approx60000\cdot12.462 \\ PV\approx747720 \end{gathered}[/tex]Answer: the company must set aside $747,720.
In a robotics competition, all robots must be at least 37 inches tall to enter the competition.Read the problem. Which description best represents the heights a robot must be?Any value less than or equal to 37Any value greater than or equal to 37Any value greater than 37Any value less than 37
Solution
Since the robots must be at least 37 inches tall to enter the competition.
Therefore, the height of any robot must be Any value greater than or equal to 37
do you think you'd be able to help me with this
x = wz/y
Explanation:[tex]\frac{w}{x}=\frac{y}{z}[/tex]To solve for x, first we need to cross multiply:
[tex]w\times z\text{ = x }\times y[/tex]Now we make x the subject of the formula:
[tex]\begin{gathered} To\text{ make x stand alone, we n}ed\text{ to remove any other variable around x} \\ \text{divide both sides by y}\colon \\ \frac{w\times z}{y}\text{ =}\frac{\text{ x }\times y}{y} \end{gathered}[/tex][tex]x\text{ = }\frac{wz}{y}[/tex]McGraw-H….A ALEKS - Mi...O POLYNOMIAL AND RATIONAL FUNCTIONSThe Factor Theorem
SOLUTIONS
Using factor theorem to solve the equation below:
[tex]-x^3+4x^2-8=0[/tex][tex]\begin{gathered} -x^3+4x^2-8 \\ -x(x^2-4x+8) \end{gathered}[/tex]Find the equaton of the line in point-slope form that passes through (-4,6) and (-2,5)
In ACDE, J is the centroid. If JG=21 find CG. D F G C E H
Let's begin by identifying key information given to us:
We have triangle CDE
J is the centroid
[tex]\begin{gathered} JG=21 \\ \text{The centroid of a triangle divides }\frac{2}{3\text{ }}\text{the distance from}verte\text{x to midpoint of the sides} \\ \Rightarrow JG=\frac{2}{3}CG \\ \Rightarrow21=\frac{2}{3}CG=\frac{63}{2} \\ \therefore CG=\frac{63}{2}=31.5 \end{gathered}[/tex]need help with this as soon as possible, answer quick
Answer:
Given points are,
A'(2,3) and A(3,-4), under the translation.
we get the graph as,
where B is A(3,-4) and A is A'(2,3).
A translation by 1 unit left and 7 units up.
Answer is:
A translation by 1 unit left and 7 units up.
1. Caitlyn is going away to college and will need to rent a truck to helpmove. The cost of the truck is $35 plus $0.79 per mile. If her collegeis 85 miles away and she budgeted $100 for the rental, will she haveenough money?
1. Caitlyn is going away to college and will need to rent a truck to help
move. The cost of the truck is $35 plus $0.79 per mile. If her college
is 85 miles away and she budgeted $100 for the rental, will she have
enough money?
we know that
The equation in slope intercept form of this situation is
y=mx+b
where
m=$0.79 per mile
b=$35
y -----> is the total cost
x -----> the number of miles
so
y=0.79x+35
so
For x=85 miles
substitute
y=0.79(85)=35
y=$102.15
we have that
102.15 > 100
therefore
she not have enough moneyA snail starts crawling toward a flower 7 feet away. The snail crawls 2 feet every hour for 3 hours. What graph represents the distance of the snail to the flower over that time period? Use the graphing tool to graph your answer
y represents the distance of the snail to the flower, in ft
x represents time, in hours
In the beginning, the distance of the snail to the flower is 7 feet. Then, the point (0, 7) is on the graph
After the first hour, the snail crawls 2 feet, then its distance to the flower is 7 - 2 = 5 ft. Then, the point (1, 5) is on the graph.
After the second hour, the snail crawls another 2 feet, then its distance to the flower is 5 - 2 = 3 ft. Then, the point (2, 3) is on the graph.
After the third hour, the snail crawls another 2 feet, then its distance to the flower is 3 - 2 = 1 ft. Then, the point (3, 1) is on the graph.
The graph is
Fill in the table using this function rule.
Answer:
-8, 2, 12, 22
Step-by-step explanation:
[tex]y = 5x+2\\y = 5(-2)+2\\y=-10+2\\y=-8[/tex]
[tex]y = 5x+2\\y = 5(0)+2\\y=0+2\\y=2[/tex]
[tex]y = 5x+2\\y = 5(2)+2\\y=10+2\\y=12[/tex]
[tex]y = 5x+2\\y = 5(4)+2\\y=20+2\\y=22[/tex]
Evaluation the expression -19-9-(11)
Then the final answer will be -17.
Find the value of 5y-7 given that -2y+1=3.Simplify your answer as much as possible.
-2y + 1 = 3
Solving for y:
Add 2y to both sides:
-2y + 1 +
f(x) = x2 + 4 and g(x) = -x + 2Step 2 of 4: Find g(d) - f(d). Simplify your answer.Answer8(d) - f(d) =
Answer:
[tex]\begin{equation*} g(d)-f(d)=-d^2-d-2 \end{equation*}[/tex]Explanation:
Given:
[tex]\begin{gathered} f(x)=x^2+4 \\ g(x)=-x+2 \end{gathered}[/tex]To find:
[tex]g(d)-f(d)[/tex]We can find g(d) by substituting x in g(x) with d, so we'll have;
[tex]g(d)=-d+2[/tex]We can find f(d) by substituting x in f(x) with d, so we'll have;
[tex]f(d)=d^2+4[/tex]We can now go ahead and subtract f(d) from g(d) and simplify as seen below;
[tex]\begin{gathered} g(d)-f(d)=(-d+2)-(d^2+4)=-d+2-d^2-4=-d^2-d+2-4 \\ =-d^2-d-2 \\ \therefore g(d)-f(d)=-d^2-d-2 \end{gathered}[/tex]Therefore, g(d) - f(d) = -d^2 - d -2
Question is stated in picture. The figure is a triangular piece of cloth
Answer:
Alternative D - 8 sin(35°)
Step-by-step explanation:
Sin(x) is defined as:
[tex]\begin{gathered} \sin (x)=\frac{\text{Opposite side}}{Hypotenuse\text{ }} \\ \end{gathered}[/tex]In this exercise,
BC is the opposite side to 35°
AC is the hypotenuse and measures 8 in
Then:
[tex]\begin{gathered} \sin (35\degree)=\frac{BC}{8} \\ \sin (35\degree)\cdot8=BC \\ BC=8\sin (35\degree) \end{gathered}[/tex]Two right rectangular prisms are shown below. 2 inches 5 Inches 9 inches inches 7 NI inches inches Prism I Prism II If each prism is packed with small cubes of side length 1 inch, how many more cubes are in Prism Il than in Prism I? O 42 cubes О 210 cubes O 510 cubes O 720 cubes
The number of small cubes in the prism I can be determined as,
[tex]\begin{gathered} N_1=\frac{Volume\text{ of prism I}}{Volume\text{ of one small cube}} \\ =\frac{\frac{7}{4}\text{ in}\times\frac{5}{4}\text{ in}\times\frac{3}{2}\text{ in}}{\frac{1}{4}\text{ in}\times\frac{1}{4}\text{ in}\times\frac{1}{4}\text{ in}} \\ =210 \end{gathered}[/tex]The number of cubes in the prism II can be determined as,
[tex]\begin{gathered} N_2=\frac{2\text{ in}\times\frac{5}{2}\text{ in}\times\frac{9}{4}in}{\frac{1}{4}in\times\frac{1}{4}in\times\frac{1}{4}in} \\ N_2=720 \end{gathered}[/tex]The difference in the number of cubes is,
[tex]\begin{gathered} N_2-N_1=720-210 \\ =510 \end{gathered}[/tex]Thus, Prism II has 510 more cubes than Prism I.
Thus, option (c) is the correct solution.
In the triangle below, if B = 69°, A = 32°, c = 5.7, use the Law of Sines to find a. Round your answer to the nearest hundredth.
We know that the interior angles have to add to 180°, then we have that:
[tex]\begin{gathered} C=180-69-32 \\ C=79 \end{gathered}[/tex]Hence angle C=79°.
Now that we know the angle C we can use the law of sines to find a; the law of sines states that:
[tex]\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}[/tex]From this we have the equation:
[tex]\frac{\sin A}{a}=\frac{\sin C}{c}[/tex]Plugging the values given and solving for a we have:
[tex]\begin{gathered} \frac{\sin32}{a}=\frac{\sin 79}{5.7} \\ a=(5.7)\frac{\sin 32}{\sin 79} \\ a=3.08 \end{gathered}[/tex]Therefore a=3.08
In 2011, the average daily temperature in Darrtown was 65°F. In 2012, the average daily temperature increased by 3% but then decreased by 4.5% in 2013.What was the daily average temperature in Darrtown in 2013?A.62°FB.64°FC.68°FD.74°F (thank you in advanced for who helps i was having trouble with this question)
Solution
In 2011 The temperature in Darrtown is
[tex]65^{\circ}F[/tex]The temperature increased by 3% in 2012
The temperature will be
[tex](1+\frac{3}{100})\times65=(1.03)(65)=66.95^{\circ}F[/tex]The temperature decreased by 4.5% in 2013
The temperature will be
[tex]\begin{gathered} (1-\frac{4.5}{100})\times66.95=0.955\times66.95=63.93725 \\ \\ (1-\frac{4.5}{100})\times66.95=64^{\circ}F\text{ (to the nearest whole number)} \end{gathered}[/tex]Therefore, the temperature in 2013 is 64 degrees Fareheint
Option B
