Given data:
The given ratio is a=5:8.
Multiply 2 on numerator and denominator both.
[tex]\begin{gathered} a=\frac{2(5)}{2(8)} \\ =\frac{10}{16} \end{gathered}[/tex]Multiply 3 on numerator and denominator both.
[tex]\begin{gathered} a=\frac{3(5)}{3(8)} \\ =\frac{15}{24} \end{gathered}[/tex][tex]\begin{gathered} a=\frac{4(5)}{4(8)} \\ =\frac{20}{32} \\ \end{gathered}[/tex]A team digs 12 holes every 20 hours, what is the unit rate?
The unit rate = 0.6 holes per hour
Explanation:Number of holes dug by the team = 12
Total time taken = 20 hours
The unit rate = (Number of holes) / (Time)
The unit rate = 12/20
The unit rate = 0.6 holes per hour
The standard form of the equation of a parabola isy=x²-4x+21. What is the vertex form of the equation?O A. y = ¹/(x-4)² +13OB. y=(x-4)² +21C. y = 1/(x+4)² +1+13O D. y = 1/(x+4)² +21
Answer:
[tex]y=\frac{1}{2}(x-4)^2+13\text{ }\operatorname{\Rightarrow}(A)[/tex]Explanation: We have to find the vertex form of the parabola equation from the given standard form of it:
[tex]y=\frac{1}{2}x^2-4x+21\rightarrow(1)[/tex]The general form of the vertex parabola equation is as follows:
[tex]\begin{gathered} y=A(x-h)^2+k\rightarrow(2) \\ \\ \text{ Where:} \\ \\ (h,k)\rightarrow(x,y)\Rightarrow\text{ The Vertex} \end{gathered}[/tex]Comparing the equation (2) with the original equation (1) by looking at the graph of (1) gives the following:
[tex](h,k)=(x,y)=(-4,13)[/tex]
Therefore the vertex form of the equation is as follows:
[tex]y=\frac{1}{2}(x-4)^2+13\Rightarrow(A)[/tex]Therefore the answer is Option(A).
what is the smallest angle of rotational symmetry of a pentagon
Answer:
72°
Step-by-step explanation:
Origin is completely 360° and its divided into 5 sides. So,360÷5=72°
what is an equation of the line that passes through the point (-2,-3) and is parallel to the line x+3y=24
Solve first for the slope intercept form for the equation x + 3y = 24.
[tex]\begin{gathered} \text{The slope intercept form is }y=mx+b \\ \text{Convert }x+3y=24\text{ to slope intercept form} \\ x+3y=24 \\ 3y=-x+24 \\ \frac{3y}{3}=\frac{-x}{3}+\frac{24}{3} \\ y=-\frac{1}{3}x+8 \\ \\ \text{In the slope intercept form }y=mx+b,\text{ m is the slope. Therefore, the slope of} \\ y=-\frac{1}{3}x+8,\text{ is }-\frac{1}{3}\text{ or } \\ m=-\frac{1}{3} \end{gathered}[/tex]Since they are parallel, then they should have the same slope m. We now solve for b using the point (-2,-3)
[tex]\begin{gathered} (-2,-3)\rightarrow(x,y) \\ \text{Therefore} \\ x=-2 \\ y=-3 \\ \text{and as solved earlier, }m=-\frac{1}{3} \\ \\ \text{Substitute the values to the slope intercept form} \\ y=mx+b \\ -3=(-\frac{1}{3})(-2)+b \\ -3=\frac{2}{3}+b \\ -3-\frac{2}{3}=b \\ \frac{-9-2}{3}=b \\ b=-\frac{11}{3} \end{gathered}[/tex]After solving for b, complete the equation.
[tex]y=-\frac{1}{3}x-\frac{11}{3}\text{ (final answer)}[/tex]Patios Plus sold an outdoor lighting set for $119.95. The Markup on the set was $25.99. Find the selling price as a percent of cost. Round to the nearest percent
The selling price as a percent of the cost is given by the ratio between the selling price and the the cost. The selling price is given, which is $119.95 the cost is given by the difference between the selling price and the Markup($25.99). Combining all those informations in an equation, we have
[tex]\frac{119.95}{119.95-25.99}=1.27660706684\ldots[/tex]To write this as a percentage, we just multiply the ratio by 100.
[tex]1.27660706684\ldots\times100=127.660706684\ldots\approx128[/tex]The selling price is 128% of the cost.
Find cosθ, cotθ, and secθ, where θ is the angle shown in the figure. Give exact values, not decimal approximations.cosθ=cotθ=secθ=
First let's find the missing value of the hypotenuse:
[tex]\begin{gathered} c^2=a^2+b^2 \\ a=4 \\ b=5 \\ \Rightarrow c^2=(4)^2+(5)^2=16+25=41 \\ \Rightarrow c=\sqrt[]{41} \\ \end{gathered}[/tex]we have that the hypotenuse equals sqrt(41). Now we can find the values of the trigonometric functions:
[tex]\begin{gathered} \cos (\theta)=\frac{adjacent\text{ side}}{hypotenuse} \\ \Rightarrow\cos (\theta)=\frac{4}{\sqrt[]{41}} \\ \sec (\theta)=\frac{1}{\cos (\theta)} \\ \Rightarrow\sec (\theta)=\frac{1}{\frac{4}{\sqrt[]{41}}}=\frac{\sqrt[]{41}}{4} \\ \tan (\theta)=\frac{opposite\text{ side}}{adjacent\text{ side}} \\ \Rightarrow\tan (\theta)=\frac{5}{4} \\ \cot (\theta)=\frac{1}{\tan (\theta)} \\ \Rightarrow\cot (\theta)=\frac{1}{\frac{5}{4}}=\frac{4}{5} \end{gathered}[/tex]Please give me an explanation and the answers on question 3
We will illustrate on how to find the inverse function.
First, recall that the inverse function is a function that given the output of a function, it will give you back the input out of which that output came from.
when athe function has a formula, we can follow some steps to find the inverse function. Suppose we are given the function
[tex]f(x)=3x+5[/tex]Now, we first change f(x) with the letter y. So we get
[tex]y=3x+5[/tex]now, we interchange variables x and y. So we get
[tex]x=3y+5[/tex]Finally we solve this equation for y. We will first subtract 5 on both sides and then divide both sides by 3. So we get
[tex]y=\frac{x\text{ -5}}{3}[/tex]and now we replace the y with the symbol of the inverse function. So we have that
[tex]f^{\text{ -1}}(x)=\frac{x\text{ -5}}{3}[/tex]4/8=28/x show your work
Given:
[tex]\frac{4}{8}=\frac{28}{x}[/tex]Simplify the equation,
[tex]\begin{gathered} \frac{4}{8}=\frac{28}{x} \\ 4x=28(8) \\ 4x=224 \\ x=\frac{224}{4} \\ x=56 \end{gathered}[/tex]Answer: x = 56.
Given the recursive formula shown, what are the first 4 terms of the sequence? A) 5, 25, 100, 400B) 5, 14, 60, 236C) 5, 25, 125, 625D) 5, 20, 80, 320
SOLUTION:
Step 1:
In this question, we have the following:
Step 2:
Given:
[tex]\begin{gathered} f(n)=5,\text{ if n =1,} \\ f(n)\text{ = 4 f(n-1) if n > 1} \end{gathered}[/tex][tex]\begin{gathered} f(1)\text{ = 5} \\ f(2)\text{ = 4 f(2-1) = 4 x f(1) = 4 x 5 = 20} \\ f(3)\text{ = 4f(3-1) =4 x f(2) = 4x20 = 80} \\ f(4)\text{ = 4 f(4-1)=4xf(3) = 4 x 80 = 320} \\ \text{Hence, the first 4 terms of the sequence are:} \\ 5,\text{ 20, 80 , 320 --- OPTION D} \end{gathered}[/tex]If f(x) = 2x + 3 and g(x) = 4x - 1, find f(4).A. 11B. 15C. 5D.17
You have the following expression for the function f(x):
f(x) = 2x + 3
In order to calculate the value of f(4), just replace x=4 into the function f(x) and simplify it:
f(4) = 2(4) + 3
f(4) = 8 + 3
f(4) = 11
Hence, the answer is:
A) 11
Question 4 When changing 67,430,000 to scientific notation, how many places is the decimal point mc 5 07
Observe that the given number is 67,430,000.
If we express it as a scientific notation, then we would have to move the decimal point 7 spots to the left.
[tex]6.743x\times10^{-7}[/tex]Therefore, the answer is 7.Solve each system by elimination 10x-2y= -44x+5y= -19
10x - 2y = -4 ==== (1)
4x + 5y = -19 ==== (2)
To solve the system we should make the coefficients of y have the same values to eliminate it, then
Multiply equation (1) by 5 and equation (2) by 2
5(10x) - 5(2y) = 5(-4)
50x - 10y = -20 ===== (3)
2(4x) + 2(5y) = 2(-19)
8x + 10y = -38 ===== (4)
Now add equations (3) and (4) to eliminate y
(50x+8x) + (-10y + 10y) = (-20 + -38)
58x + 0 = -58
58x = -58
Divide both sides by 58 to find x
x = -1
Substitute the value of x in equation (1) or (2) to find the value of y
4(-1) + 5y = -19
-4 + 5y = -19
Add 4 to both sides
-4 + 4 + 5y = -19 + 4
0 + 5y = -15
5y = -15
Divide both sides by 5 to find y
y = -3
The solution of the system is (-1, -3)
The circle below has center S. Suppose that m QR = 84°. Find the following.
Given:
[tex]\text{m}\hat{\text{QR}}=84^{\circ}[/tex]b) To find:
[tex]\angle QSR[/tex]We know that,
[tex]\hat{QR}=\angle QSR=84^{\circ}[/tex]Thus, the answer is,
[tex]\angle QSR=84^{\circ}[/tex]a) To find:
[tex]\angle QPR[/tex]We know that,
[tex]\begin{gathered} \angle QPR=\frac{1}{2}\angle QSR \\ \angle QPR=\frac{1}{2}(84^{\circ}) \\ \angle QPR=42^{\circ} \end{gathered}[/tex]Thus, the answer is,
[tex]\angle QPR=42^{\circ}[/tex]-16 = m - 3 solve m
m = -13
Explanations:-16 = m - 3
Add 3 to both sides of the equation
-16 + 3 = m - 3 + 3
-13 = m
m = -13
14. What is the volume of a box with these dimensions? 4 cm 5 cm 10 cm.
The volume of a rectangular prism is given by the product of its three dimensions.
Since the box dimensions are 4 cm, 5 cm and 10 cm, its volume is:
[tex]\begin{gathered} V=4\cdot5\cdot10 \\ V=200\text{ cm}^3 \end{gathered}[/tex]So the volume of the box is equal to 200 cm³.
For a football game, 5,600 tickets were sold. The price for each adult ticket is $27.25, and the price for each childrens ticket is $12.00. The total revenue for the game was $117,311.50. How many children's tickets were sold for the football game?
We have a problem that can be solved with a system of equations.
First we need to identify the equations of the system.
We have two unknown variables, the number of adult's tickets sold and the number of children's tickets sold. Let's call them:
- number of adult's tickets sold: x
- number of children's tickets sold: y.
The total number of tickets sold, 5600, is the sum of these:
[tex]x+y=5600_{}[/tex]And since the prices are 27.25 (adult) and 12.00 (children), the total revenue (117311.50) will be the sum of these prices multiplyied by the number of tickets of each of them:
[tex]27.25x+12.00y=117311.50[/tex]So, the system of equations is:
[tex]\begin{gathered} _{}x+y=5600_{} \\ 27.25x+12.00y=117311.50 \end{gathered}[/tex]Since we want y the number of children's tickets sold, we can solve for the other varible, x, in one equation, and substitute into the other.
Solving in the first equation, we have:
[tex]\begin{gathered} x+y=5600 \\ x=5600-y \end{gathered}[/tex]And substituting into the other:
[tex]\begin{gathered} 27.25x+12.00y=117311.50 \\ 27.25(5600-y)+12.00y=117311.50 \\ 27.25\cdot5600-27.25y+12.00y=117311.50 \\ 152600-15.25y=117311.50 \\ -15.25y=117311.50-152600 \\ -15.25y=-35288.50 \\ y=\frac{-35288.50}{-15.25} \\ y=2314 \end{gathered}[/tex]Since y is the number of children's tickets sold, then the number of children's tickets sold is 2314.
Find the solution of the system of equations. 2x + 3y=-4 , x + 9y = 13
(-5, 2)
1) Solving this Linear System with the method of Addition/Elimination:
2x + 3y=-4
x + 9y = 13 x-2 Multiply the whole equation by -2
2x +3y = -4
-2x -18y= -26
--------------------
-15y= -30
15y= 30 Divide both sides by 15
y = 2
2) Plug into the simpler equation y=2
x +9y = 13
x + 9(2) = 13
x +18 = 13
x =13-18
x= -5
3) So the answer is (-5, 2)
Multiply.
7.
-2 7
-5 -6
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Write your answer in simplest form solve this
The simplest form of 7 × (-2/-5) × (7/-6) is - 49/15.
Multiplication of fractions:A whole number or another fraction is produced when one fraction is multiplied by another fraction. We all know that a fraction has two components: a numerator and a denominator. In order to multiply any two fractions, we must multiply the numerators and denominators, respectively.
Here we have
=> [tex]7. \frac{-2}{-5} .\frac{7}{-6}[/tex]
Can be multiplied as given below
=> [tex]7 \times\frac{-2}{-5} \times\frac{7}{-6}[/tex]
=> [tex]7 \times\frac{1}{5} \times\frac{7}{-3}[/tex]
=> [tex]-\frac{49}{15}[/tex]
Therefore,
The simplest form of 7 × (-2/-5) × (7/-6) = -49/15
Learn more about Fractions at
https://brainly.com/question/1050042
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Identify any congruent figures in the coordinate plane. Explain. This is a fill in the blank question based off of the options that are listed down below!
Solution
For this case we can conclude the following:
triangle HJK ≅ triangle QRS because one is rotation of 90º about the origin of the other
Rectangle DEFG ≅ rectangle MNLP because one is a translation of the other
triangle ABC ≅ no given figure because one is not related by rigid motions of the other
convert the rectangular equation to polar form.Assume a > 0x=18
To convert a rectangular equation to polar forma, we use
[tex]x=r\cos (\theta),y=r\sin (\theta)[/tex]In the equation x=18, we only have x, so
[tex]\begin{gathered} 18=r\cos (\theta) \\ r=\frac{18}{\cos(\theta)}=18\sec (\theta) \end{gathered}[/tex]solve the system of equations by graphing. y = -5x + 4 andy = 3x + 4
1) To solve this System of Solutions graphically, we'll need to plot those lines described by those respective equations.
2) Let's set two tables
y=-5x +4
x | y
1 -1 ( 1,-1)
2 -6 ( 2,-6)
3 -11
y=3x + 4
x | y
1 | 7 ( 1,7)
2 |10 ( 2,10)
3 | 13
2.2 Let's plot those equations and interpret the results:
3) As these lines have point (0,4) as their common point. Therefore we can state that the solution for this consistent system is S=(0,4)
PerioAlgebra 2NameUsing Linear Equations to Solve Problems Date1) The chess club is selling popcorn balls for $1.00 and jumbo candy bars for$1.50 each. This week they have made a total of $229 and have sold 79popcorn balls. How many candy bars have they also sold?
The popcorn balls cost $1.00 each
Jumbo candy bars cost $1.50 each
This week they have made a total of $229 and have sold 79
popcorn balls.
First, let's make a function with includes this information.
Let's say that popcorn balls are x and Jumbo candy bars are y.
So the function would be
1.00x+ 1.50y = 229
We already have the x value which represents the total of popcorn balls sold this week, so replace this value in the function:
1.00x+ 1.50y = 229
1.00(79)+ 1.50y = 229
79.00 + 1.50y = 229
Solve the equation for y to find the total of candy bars sold.
79 + 1.50y = 229
1.50y = 229 - 79
1.50y = 150
y = 150/1.50
y = 100
So the have sold 100 candy bars this week
The sum of three numbers is 106. The second number is 2 times the third. The first number is 6 more than the third. What are the numbers?First numberSecond number Third number
Let's call the numbers a, b and c.
The first statement tells us that the sum of the three numbers is 106, so:
[tex]a+b+c=106.[/tex]The second statement tells us that the second number is two times the third so:
[tex]b=2c\text{.}[/tex]The final statement tells us that the first number is 6 more than the third, so:
[tex]a=c+6.[/tex]This gives us a system of three equations with three variables. Let's take the value of a given by the third equation, use it in the first one and isolate another variable:
[tex](c+6)+b+c=106,[/tex][tex]2c+b+6=106,[/tex][tex]2c+b=100,[/tex][tex]b=100-2c\text{.}[/tex]Let's take this value of b and use it in the second equation:
[tex]100-2c=2c,[/tex][tex]100=4c,[/tex][tex]c=25.[/tex]Now we know the exact value of c, so let's go back to the third equation:
[tex]a=25+6=31,[/tex]and now we also know the exact value of a, so let's go back to the second equation:
[tex]b=2(25)=50.[/tex]So, the first number (a) is 31, the second (b) is 50 and the third (c) is 25.
31+50+25=106.
(40s + 100t) + 6 distributive property to write the products in standard form
The given expression is
[tex](40s+100t)\div10[/tex]We will use the distributive property to solve it
Divide each term in the bracket by 10
[tex]\frac{40s}{10}+\frac{100t}{10}[/tex]Simplify each term
[tex]\begin{gathered} \frac{40s}{10}=4s \\ \\ \frac{100t}{10}=10t \\ \\ 4s+10t \end{gathered}[/tex]The answer in standard form is 4s + 10t
Find at least three solutions to the equation y = 3x - 1, and graph the solutions as points on the coordinate plane.Connect the points to make a line. Find the slope of the line.
To find a solution to the equation y = 3x - 1, we have to replace a variable by a number and compute the other variable.
Assuming x = 0, then
y = 3(0) - 1
y = 0 - 1
y = -1
Then, the point (0, -1) is a solution
Assuming x = 1, then
y = 3(1) - 1
y = 3 - 1
y = 2
Then, the point (1, 2) is a solution
Assuming x = 2, then
y = 3(2) - 1
y = 6 - 1
y = 5
Then, the point (2, 5) is a solution
In the next graph, the solutions and the line are shown
The slope of the line that passes through the points (x1, y1) and (x2, y2) is computed as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Replacing with points (0, -1) and (1,2) we can compute the slope, as follows:
[tex]m=\frac{2-(-1)}{1-0}=3[/tex]The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is nine times the measure of the first angle. The third angle is 26 more than the second let x,y, and z represent the measures of the first second and third angles, find the measures of the three angles
Answer:
x = 18, y = 68, z = 94.---------------------------------
Set equations as per given details.The sum of the measures of the angles of a triangle is 180:
x + y + z = 180 (1)The sum of the measures of the second and third angles is nine times the measure of the first angle:
y + z = 9x (2)The third angle is 26 more than the second:
z = y + 26 (3)SolutionSubstitute the second equation into first:
x + y + z = 180,y + z = 9x.Solve for x:
x + 9x = 180,10x = 180,x = 18.Substitute the value of x into second and solve for y:
y + z = 9x,y + z = 9*18,y + z = 162,y = 162 - z.Solve the third equation for y:
z = y + 26,y = z - 26.Compare the last two equations and find the value of z:
162 - z = z - 26,z + z = 162 + 26,2z = 188,z = 94.Find the value of y:
y = 94 - 26,y = 68.Answer:
x = 18°
y = 68°
z = 94°
Step-by-step explanation:
Define the variables:
Let x represent the first angle.Let y represent the second angle.Let z represent the third angle.Given information:
The sum of the measures of the angles of a triangle is 180°. The sum of the measures of the second and third angles is nine times the measure of the first angle. The third angle is 26 more than the second.Create three equations from the given information:
[tex]\begin{cases}x+y+z=180\\\;\;\;\;\;\:\: y+z=9x\\\;\;\;\;\;\;\;\;\;\;\;\;\: z=26+y\end{cases}[/tex]
Substitute the third equation into the second equation and solve for x:
[tex]\implies y+(26+y)=9x[/tex]
[tex]\implies 2y+26=9x[/tex]
[tex]\implies x=\dfrac{2y+26}{9}[/tex]
Substitute the expression for x and the third equation into the first equation and solve for y:
[tex]\implies \dfrac{2y+26}{9}+y+26+y=180[/tex]
[tex]\implies \dfrac{2y+26}{9}+2y=154[/tex]
[tex]\implies \dfrac{2y+26}{9}+\dfrac{18y}{9}=154[/tex]
[tex]\implies \dfrac{2y+26+18y}{9}=154[/tex]
[tex]\implies \dfrac{20y+26}{9}=154[/tex]
[tex]\implies 20y+26=1386[/tex]
[tex]\implies 20y=1360[/tex]
[tex]\implies y=68[/tex]
Substitute the found value of y into the third equation and solve for z:
[tex]\implies z=26+68[/tex]
[tex]\implies z=94[/tex]
Substitute the found values of y and z into the first equation and solve for x:
[tex]\implies x+68+94=180[/tex]
[tex]\implies x=18[/tex]
verizon charges $200 to start up a cell phone plan. then there is a $50 charge each month. what is the total cost (start up fee and monthly charge) to use the cel phone plan for 1 month?
write the total costs a linear function in the form
[tex]y=mx+b[/tex]in which:
y= total cost
x= number of months
m= charge per month
b= fixed start up fee
replace all data in the equation
[tex]\begin{gathered} y=50\cdot x+200 \\ y=50x+200 \end{gathered}[/tex]Since the question is the cost for 1 month, x=1
[tex]\begin{gathered} y=50(1)+200 \\ y=250 \end{gathered}[/tex]The cost for the use of the cellphone is $250
How to: determine if the side lengths could form a triangle. use an inequality to prove your answer
We need to simply use the triangle inequality Theorem, This theorem state that the sum of the two side lengths of a triangle must always be greater than the third side.
Now let's check from the given lengths
16 + 21 = 37 and 37 is less than 39 which is the third side
Hence, it cannot form a triangle
7. In physics, the equation PV = nRT is called the ideal gas law. It is used toapproximate the behavior of many gases under different conditions. Whichequation is solved for T?
ANSWER:
[tex]\frac{PV}{nR}=T[/tex]STEP-BY-STEP EXPLANATION:
We have the following equation:
[tex]PV=nRT[/tex]We solve for T:
[tex]\begin{gathered} \frac{PV}{nR}=T \\ T=\frac{PV}{nR} \end{gathered}[/tex]Therefore, the correct answer is option 2.
If f(x) = 6x + 8(x + 2), find f-1(x).f-1(x) = (x - 16)/14f-1(x) = x +16/14f-1(x) = -x - 16/14f-1(x) = -x + 16/14
SOLUTION:
We want to find the inverse of f(x);
[tex]f(x)=6x+8(x+2)[/tex]We solve for x;
[tex]\begin{gathered} y=6x+8(x+2) \\ y=6x+8x+16 \\ y=14x+16 \\ y-16=14x \\ x=\frac{y-16}{14} \\ interchange\text{ }y\text{ }and\text{ }x \\ f^{-1}(x)=\frac{x-16}{14} \end{gathered}[/tex]Thus the answer is OPTION A