The given function is
[tex]y=3^x[/tex]when x = -1, the function becomes,
[tex]y=3^{-1}=\frac{1}{3}[/tex]when x = 1,
[tex]y=3^1=3[/tex]Next when x = 3,
[tex]y=3^3=27[/tex]Hence the missing terms are 1/3, 3 and 27.
If two lines intersect, what angles are congruent?adjacent anglessupplementary anglesvertical anglesopposite angles
Given the intersection of two lines:
From this, the congruent angles are:
[tex]\begin{gathered} a\cong c \\ b\cong d \end{gathered}[/tex]These are vertical angles
please helpType the correct answer in each box Use numerals instead of words, if necessary, use for the fraction bar(s) Determine the equation for the quadratic relationship graphed below. Submit Reset
From the graph, choose two points to find the values
choose (0, -1) and the vertex (1, -4)
the vertex formula of the quadratic equation is:
y = a(x – h)^2 + k
where the vertex is (h, k)
so, h = 1 and k = -4
so,
y = a (x - 1)^2 + (-4)
using the point (0, -1) to find a
so,
-1 = a ( 0 - 1)^2 - 4
a = -1 + 4 = 3
so,
y = 3(x - 1)^2 - 4
y = 3( x^2 - 2x + 1) - 4
y = 3 x^2 - 6x + 3 - 4
y = 3 x^2 - 6x - 1
Find a and b.
Please help this is due tomorrow and I forgot how to do this!!
This theorem states that:
[tex]a^2+b^2=c^2[/tex]
a and b are two legs of a right triangle (the sides that create the right angle)c is the hypotenuse (the longest side)Solving the QuestionIn this diagram, notice how there are two smaller triangles that create the large triangle.
To find a and b, we can look at the two small triangles instead of seeing everything as a whole.
Let the top triangle be Triangle A and the bottom triangle be Triangle B.
Triangle ASolve for a using the Pythagorean theorem:
[tex]a^2+b^2=c^2\\12^2+6^2=a^2\\a=\sqrt{12^2+6^2}\\a=13.42[/tex]
Triangle BSolve for b using the Pythagorean theorem:
[tex]a^2+b^2=c^2\\6^2+3^2=b^2\\b=\sqrt{6^2+3^2}\\b=6.71[/tex]
Answera = 13.42
b = 6.71
Area and Circumference of Circles (A)Calculate the area and circumference of each circle.r=9.5 mmr=2.7 cmcircumferencearea =circumferencearea =
Part 1
r=9.5 mm
The area is given by the formula
[tex]\begin{gathered} A=pi*r^2 \\ A=pi*9.5^2 \\ A=90.25pi\text{ mm}^2 \end{gathered}[/tex]The circumference is given by the formula
[tex]\begin{gathered} C=2*pi*r \\ C=2*pi*9.5 \\ C=19pi\text{ mm} \end{gathered}[/tex]Part 2
r=2.7 cm
Find out the area
[tex]\begin{gathered} A=pi*2.7^2 \\ A=7.29pi\text{ cm}^2 \end{gathered}[/tex]Find out the circumference
[tex]\begin{gathered} C=2*pi*2.7 \\ C=5.4pi\text{ cm} \end{gathered}[/tex]Part 3
r=7.3 in
Area
[tex]\begin{gathered} A=pi*7.3^2 \\ A=53.29pi\text{ in}^2 \end{gathered}[/tex]Circumference
[tex]\begin{gathered} C=2*pi*7.3 \\ C=14.6pi\text{ in} \end{gathered}[/tex]13. MP Identify Structure Write two different expressions to find the total cost of an item that costs $a if the sales tax is 6%. Explain why the expressions give the same result.
The phrases are the same since the cost is the same.
What is meant by expression?Mathematical expressions consist of at least two numbers or variables, at least one math operation, and a sentence. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Given ,
p+6/100 p it is expression 1
p+0. 06p it is expression 2
Suppose the item costs $100 to demonstrate that they are equal.
Expression 1
[tex]\begin{aligned}&p+\frac{6}{100} p \\&100+\frac{6}{100} 100 \\&100+6 \\&106\end{aligned}[/tex]
Expression 2
[tex]\begin{aligned}&p+0.06 p \\&100+0.06(100) \\&100+6 \\&106\end{aligned}[/tex]
The phrases are the same since the cost is the same.
There are two distinct formulations that represent the issue:
[tex]\begin{aligned}&p+\frac{6}{100} p \\&p+0.06 p\end{aligned}[/tex]
The complete question is : Arthur wants to buy an item that costs p dollars before tax. using a 6% sales tax rate, write two different expressions that represent the price of the item after tax show that the two expressions are equal
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Solving a compound linear inequality
Answer:
(-5, -2)
Step-by-step explanation:
Given inequalities:
[tex]4w+3 > -17[/tex]
[tex]3w-6 < -12[/tex]
Solve each inequality.
[tex]\begin{aligned}\implies 4w+3 & > -17\\4w & > -20\\w& > -5\end{aligned}[/tex]
[tex]\begin{aligned}\implies 3w-6 & < -12\\3w& < -6\\w& < -2\end{aligned}[/tex]
Therefore, combining the solutions gives:
[tex]-5 < w < -2[/tex]
Therefore, the solution to the compound inequality in interval notation is (-5, -2).
The amount of time a certain brand of light bulb lasts is normally distribued with a mean of 1300 hours and a standard deviation of 20 hours. Out of 755 freshly installed light bulbs in a new large building, how many would be expected to last than 1330 hours, to the nearest whole number?
361 light bulbs out of the 755 will last over 1330 hours
Here, we want to calculate the expected number of bulbs
The first thing we have to do here is to calculate the z-score
We have this as follows;
[tex]\begin{gathered} z\text{ = }\frac{x-\mu}{\frac{\sigma}{\sqrt[]{n}}} \\ x\text{ = 1330 hours} \\ \mu\text{ = 1300 hours (mean)} \\ \\ \sigma\text{ = 20 hours ( standard deviation)} \\ n\text{ = 755} \\ \\ z\text{ = }\frac{1330-1300}{\frac{20}{\sqrt[]{755}}}\text{ = 0.0546} \end{gathered}[/tex]Now, we have to calculate the probability that is equal to this z-score
So, the probability we want to calculate is that which is greater than the calculated z-score
[tex]P\text{ (z > 0.0546)}[/tex]We are going to use the standard normal distribution table here
By using the table, we have the equivalent probability as 0.47823 (about 48%)
So, out of the 755 freshly installed light bulbs, 47.823% will last more than 1330 hours
The exact number that will last will be;
[tex]0.47823\times755\text{ = 361}[/tex]What is the percent of change between the Unit rate of Car A and the Unit rate of Car B?
Car A travels 60 miles in 5 gallons of gas
so its mileage is 60/5 = 12
Car B travels 60 miles in 4 gallons of gas
so its mileage is 60/4 = 15
so change in unit rate in both the car is 15 - 12 = 3
so the percentage change is
[tex]\frac{3}{15}\times100\text{ = 20}[/tex]the change is 20 %
Barry has to tile his rectangular hallway. The hallway is 24 feet long and 15 feet wide. If the square tiles have dimensions of 6 inches x 6 inches, how many tiles will
Barry need to cover the entire hallway floor?
The number of tiles it would take for Barry to be able to cover the entire hallway floor is 1, 440 tiles
How to find the number of tiles?The first thing to do is the find the area of the rectangular hallway to know the area that needs to be covered:
Area = Length x Width
Area = 24 x 15
= 360 feet²
The dimensions of the tiles in feet is:
= 6 / 12 inches per feet
= 1/2 feet
The area of the tiles in feet is:
= 1/2 x 1/2
= 1/4 feet ²
The number of tiles needed is:
= Area of hallway / Area of tiles
= 360 / (1 / 4)
= 1, 440 tiles
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Recommendations Sixth grade > S.4 Convert between percents, fractions, a How do you write 31% as a decimal? Submit
I need to solve for h. V=1/3 s square h
Since the given equation is
[tex]V=\frac{1}{3}sh^2[/tex]We need to solve for each, then
We have to isolate h on one side and the other terms on the other side
Then multiply both sides by 3
[tex]\begin{gathered} (3)\times V=\frac{1}{3}\times(3)sh^2 \\ 3V=sh^2 \end{gathered}[/tex]Now, divide both sides by s
[tex]\begin{gathered} \frac{3V}{s}=\frac{sh^2}{s} \\ \frac{3V}{s}=h^2 \\ h^2=\frac{3V}{s} \end{gathered}[/tex]Take a square root for both sides
[tex]\begin{gathered} \sqrt[]{h^2}=\pm\sqrt[]{\frac{3V}{s}} \\ h=\pm\sqrt[]{\frac{3V}{s}} \end{gathered}[/tex]Find the value of each of the following:7 to 12
Given:
Here we have some expressions.
Required:
We need to find the values of the given.
Explanation:
7)
[tex]5^4=5*5*5*5=625[/tex]8)
[tex](13)^2=13*13=169[/tex]9)
[tex](1.2)^2=1.2*1.2=1.44[/tex]10)
[tex]18^0=1[/tex]11)
[tex]1000^2=1000000[/tex]12)
[tex]7^2*7^0=7*7*1=49[/tex]Using the information from the front page, solve problem D. Name all of the points.
Given,
The equations are,
[tex]\begin{gathered} y=-0.4x+40 \\ y=-0.1x+12 \\ y=-1.1x+80 \end{gathered}[/tex]The graph of the equation is,
The red line of the graph shows the equation of Alfred.
The green line of the graph shows the equations of Batgirl.
The blue line of the graph shows the equations of Robin.
Hence, the graph of the equation is obtained.
The Cutting Edge Salon schedules appointments for 30 minutes haircuts and 1 hour for highlights. Each
haircut costs $20 & highlights cost $45. The salon wants to schedule no more than 4 highlights per day
and at least 3 haircuts. A stylist works an 8 hour workday. What are the 3 inequalities and what are the solutions.
The three inequalities are :
0.5x+y ≤ 8
x ≥ 3
y ≤ 4
The inequality is the relationship between the two values except equal relation. The inequalities are greater than, greater than or equal to, less than and less than or equal to etc..
Time taken for haircut = 30 minute = 0.5 hours
Time taken for highlights = 1 hours
A stylist works an 8 hour workday
Consider the number haircuts = x
The number of highlights = y
The inequality is
0.5x+y ≤ 8
The salon wants to schedule no more than 4 highlights per day and at least 3 haircuts.
Therefore,
x ≥ 3
y ≤ 4
Hence, the three inequalities are
0.5x+y ≤ 8
x ≥ 3
y ≤ 4
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using what you learned about expressions and patterns complete the graphic organizer by giving a real world example, graph the patterns, and compare the patterns. my question is about the real world example. this is fifth grade math and this chapter did not use unknown numbers. so I am not sure if I should use two different expressions, one expression with an unknown number, two different tables, or if I'm even understanding the question properly
we have
Real world example
A pounds of banana cost $1.50
what is the cost of 6.5 pounds
Let
x -----> number of pounds
y -----> the total cost
the linear equation is
y=1.50x
so
the pattern is the equation of a line
see the attached figure
For x=6.5 pounds
substitute
y=1.5*(6.5)
y=$9.75
Compare the result of the equation with the graph
the result is the same
I chose EF congruent to YX and angle F congruent to angle X but they were not or not complete
We are given that:
[tex]\Delta\text{EFG}\cong\Delta YXZ.[/tex]Now, recall that when given two congruent triangles the order matters, in this case, the corresponding sides are:
[tex]\begin{gathered} EF\text{ and YX,} \\ FG\text{ and XZ,} \\ GE\text{ and ZY,} \end{gathered}[/tex]and the corresponding angles are:
[tex]\begin{gathered} E\text{ and Y,} \\ F\text{ and X,} \\ G\text{ and Z.} \end{gathered}[/tex]Using the CPCTC we get that:
[tex]\begin{gathered} EF\cong YX, \\ FG\cong XZ, \\ GE\cong ZY, \\ \angle E\cong\angle Y, \\ \angle F\cong\angle X, \\ \angle G\cong\angle Z. \end{gathered}[/tex]Answer:
[tex]\begin{gathered} EF\cong YX, \\ GF\cong ZX, \\ \angle F\cong\angle X. \end{gathered}[/tex]The demand and supply functions for football jerseys are:See photo
Given:
[tex]\begin{gathered} p=d(x)=-x^2+10x+47 \\ p=s(x)=15x-37 \end{gathered}[/tex]The equilibrium point will be obtained when,
[tex]d(x)=s(x)[/tex]It gives,
[tex]\begin{gathered} -x^2+10x+47=15x-37 \\ -x^2+10x-15x+47+37=0 \\ -x^2-5x+84=0 \\ x^2+5x-84=0 \end{gathered}[/tex]Solving it further,
[tex]\begin{gathered} x^2+12x-7x-84=0 \\ x(x+12)-7(x+12)=0 \\ (x+12)(x-7)=0 \\ \Rightarrow x=-12,x=7 \\ \text{The price can not be negative.} \\ \Rightarrow x=7 \end{gathered}[/tex]The number of thousands of jerseys is 7000.
The equilibrium price is,
[tex]\begin{gathered} p=d(x)=-x^2+10x+47 \\ p=-7^2+10(7)+47 \\ p=-49+70+47 \\ p=68 \end{gathered}[/tex]Answer: equilibrium quantity, x = 7, which corresponds to 7000 jerseys.
The equilibrium price p = 68 dollars
Graph the image of the given triangle, rotated 180° about the origin.
after rotation, the points will become (0, 6), (8, 2) and (3, -8).
Rotation 180 degrees about the origin:
Point (x, y) will become (-x, -y)
So, here the points of the triangle are:
(0, -6)
(-8, -2)
(-3, 8)
These will become:
(0, 6)
(8, 2)
(3, -8)
Therefore, after rotation, the points will become (0, 6), (8, 2) and (3, -8).
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14. Write an equation in slope-intercept form for the line that passes through
(-2, 3) and is parallel to the line with equation 3x + 2y = 6.
Answer:
[tex]y=\frac{-3}{2} x[/tex]
Step-by-step explanation:
[tex]3x+2y=6[/tex]
[tex]P(-2,3)[/tex]
Rewrite the first equation in slope-intercept form:
[tex]2y=-3x+6[/tex]
[tex]y=\frac{-3}{2} x+3[/tex]
The slope-intercept form is the following:
[tex]y=mx+b[/tex]
m = slope
parallel lines have the same slope, therefore we know that our new line will have a slope (-3/2).
Now write the line in the point-slope form:
[tex](y-y_1)=m(x-x_1)[/tex]
[tex]y-3=\frac{-3}{2} (x+2)[/tex]
Now we need to re-write into slope-intercept form. Distribute -3/2:
[tex]y-3=\frac{-3}{2} x-3[/tex]
Add 3 to both sides:
[tex]y=\frac{-3}{2} x[/tex]
Select all of the following values that can be classified as Whole NumbersA. -1/3B.31C.0D.-15
B. 31
C. 0
Explanations:Note that:
Whole numbers are positive integers (counting numbers) and zero
They are numbers from zero and above that are neither decimal nor fractions
The whole numbers among the options are 31 and 0
witch of these ordered pairs is a solution to the inequality.y - 2x < -3?(2, 4)(-2, 3)(3, 4)(1, -1)
ANSWER:
STEP-BY-STEP EXPLANATION:
[tex]undefined[/tex]compute the interest on a loan of 800 at 5% interest rate for 6 months simple interest.
The interest is given by:
[tex]I=Prt\text{ }[/tex]where P is the principal, r is the interest rate in decimal form and t is the time.
In this case the principal is $800, the interest rate is 0.05 and the time is 0.5 years (six months is half a year), then the interest is:
[tex]\begin{gathered} I=(800)(0.05)(0.5) \\ I=20 \end{gathered}[/tex]Therefore the interest gained is $20
You need a 10% alcohol solution. On hand, you have a 120 mL of a 85% alcohol mixture. How much pure water will you need to add to obtain the desired solution?A) Write an equation using the information as it is given above that can be used to solve this problem. Use x as your variable to represent the amount of pure water you need to use.Equation: ________ You will need ____mL of pure waterto obtain ____mL of the desired 10% solution.
Here the mixture (or solution) contains alcohol and water.
Given that you have 85% alcohol mixture. It means that each 1 mL of the mixture will contain 0.85 mL of alcohol, and the remaining 0.15 mL of pure water.
So the amount of alcohol in 120 mL of mixture is calculated as,
[tex]\begin{gathered} =120\times0.85 \\ =102 \end{gathered}[/tex]When 'x' mL of pure water is added to the solution, the total amount of water in the mixture becomes,
[tex]\begin{gathered} =x+(120\times0.15) \\ =x+18 \end{gathered}[/tex]Since no alcohol is added, the amount of alcohol in the final mixture will remain same, that is, 102 mL.
Now, it is given that the concentration of the final mixture is 10%, So the amount of alcohol in the solution should be 10% of the total mixture,
[tex]\begin{gathered} 0.10\times(x+18+102)=102 \\ x+120=\frac{102}{0.10} \\ x+120=1020 \\ x=1020-120 \\ x=900 \end{gathered}[/tex]Thus, you need to add 900 mL of pure water in order to have 10% alcohol solution.
And the equation used to solve this problem is,
[tex]0.10\times(x+18)=102[/tex]609 4 What is the length of u and vin this 30-60-90 A triangle? U = 16 v = 8 U = 8v = 473 U = 473 V = 8 U = 42 y = 8
For a 30-60-90 triangle, we have a fixed ratio for the length of the sides of the triangle
These lengths are in the ratio;
[tex]1\text{ : }\sqrt[]{3}\text{ : 2}[/tex]Since u faces the right angle, it has the longest length, followed by v which faces the angle 60
The lengths are thus;
[tex]\begin{gathered} u\text{ = 4 }\times\text{ 2 = 8} \\ v\text{ = 4 }\times\text{ }\sqrt[]{3}\text{ = 4}\sqrt[]{3} \end{gathered}[/tex]
The table below shows a dog's age at various points throughout its life in both human years, which is the independent variable, and dog years, which is the dependent variable. a. What is the domain of the function?b. What is the range of the function?
a. The domain of a function is the set of all possible values that the independent variable can take.
In this case, the independent variable is human years which takes values between 1 and 7, then the domain of the function is [1, 7].
b. The range of a function is the set of all possible values that the dependent variable can take.
In this case, the dependent variable is dog years which takes values between 15 and 44, then the range of the function is [15, 44].
A student has the following test scores in English class. 98 87 86 100 79 92 88 95 89 86 96 What is the IQR (interquartile range) of the student's scores? Enter your answer in the box. IQR =
We have the set of values: 98 87 86 100 79 92 88 95 89 86 96.
We have to calculate the IQR:
[tex]\text{IQR}=Q_3-Q_1[/tex]where Q3 is the third quartile and Q1 is the first quartile.
The first step is to sort the values in ascendent order:
solve the following problems by writing a proportion. 8 is 40% of what number?
Let x be the number
40% of x = 8
[tex]\frac{40}{100}\times x=8[/tex][tex]\frac{40x}{100}=8[/tex]Multiply both-side of the equation by 100
[tex]40x\text{ = 800}[/tex]
Divide both-side of the equation by 40
[tex]x=20[/tex]
Therefore, 8 is 40% of 20
The vertical number line is called the
SOLUTION
The vertical number line is called the the Y-axis
please help I need to know how to do it (show work) only #10 and #11
The substitution method works by solving one of the equations for one of the variables (you choose the equation and the variable) and then plugging this back into the other equation, substituying for the chosen variable and solving for the other.
For instance, lets solve problem 10. We have the following system:
[tex]\begin{gathered} 6x-9=y \\ y=-3x \end{gathered}[/tex]We can see that the "easiest" way to solve them is by substituting the value of y given in the second equation into the first one. It gives
[tex]6x-9=-3x[/tex]because y=-3x. Now, we must move -3x to the left hand side as +3x. It yields,
[tex]6x+3x-9=0[/tex]since 6x+3x=9x, we have
[tex]9x-9=0[/tex]Now, if we move -9 to the left hand side as +9, we obtain
[tex]\begin{gathered} 9x=9 \\ x=\frac{9}{9} \end{gathered}[/tex]then, x=1. Until now, we solved for x. Now. we must subsitute this value into the second equation. It yields,
[tex]y=-3(1)[/tex]which gives y=-3. Finally, the answer is x=1 and y=-3.
We can check that this is the correct solution by substituting these values into both equations:
[tex]\begin{gathered} 6(1)-9=-3 \\ 6-9=-3 \\ -3=-3\text{ Thats correct!} \end{gathered}[/tex]Now, in the second one, we have
[tex]\begin{gathered} -3=-3(1) \\ -3=-3\text{ Thats correct!} \end{gathered}[/tex]Then our answer is corrrect!
28 POINTS PLEASE HELP
Answer:
Step-by-step explanation:
Ok so the first one is 100 percent since 10* 10 grid bars= 100
The second one has 1 bar of 10+ 6 more squares
SO:
100+10+6=116 percent