Answer: [tex]72z^{2} +55z-7[/tex]
Step-by-step explanation:
We multiply each component with each other:
8z * 9z = 72z^2
8z * -1 = -8z
9z * 7 = 63z
7 * -1 = -7
We then add it all together, 63z + -8z = 55z and get
[tex]72z^{2} +55z-7[/tex]
A gymnast joined a yoga studio to improve his flexibility and balance. He pays a monthly fee and a fee per class he attends. The equation y = 20 + 10x represents the amount the gymnast pays for his membership to the yoga studio per month for a certain number of classes.
Which graph represents this situation?
graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 20 through the point 1 comma 30
graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 20 through the point 1 comma 10
graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 10 through the point 1 comma 30
graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 10 through the point one half comma zero
The graph of the linear equation y = 20 + 10x for the given scenario is attached below.
The Cartesian coordinates of a specific point on the Euclidean plane can be thought of as each solution inside the scenario involving two variables.
A linear equation's solutions define a line inside the Euclidean plane, and each line may be viewed as the aggregate of all solutions to a linear model with two variables. This is how this category of equations came to be known as "linear." The solutions to a system of equations with integer variables collectively constitute a hyperplane in the Euclidean space with size n. (a subdomain of dimension n₁).Because linear equations may frequently accurately represent non-linear systems, they are used extensively in all branches of mathematics as well as in physics and engineering.Here the equation is given as y = 20 + 10x
Therefore at x = 0 , y = 20 and at y = 0, x = -2
This represents that the fixed monthly fee is 20 and the daily fee is 10.
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Answer:
i think its c because every time the it goe it goes were its suposefd to
Step-by-step explanation:
hope this helps dont minf my typing
If BC=5 in and AB=12in. Find the exact circumference of the circle.
EXPLANATION
We can get the circunference of the circle by applying the Pythagorean Theorem as shown as follows:
[tex]\text{AC}^2=AB^2+BC^2[/tex]Repalcing terms:
[tex]AC^2=12^2+5^2=144+25=169[/tex]Aplying the square root to both sides:
[tex]AC^{}=\sqrt[]{169}=13\text{ inches}[/tex]The circunference is 13 inches.
b) Draw the graph of y = 3x - 1
on the grid.
c) Use the graph to estimate the
value of y when x = 2.5
The graph is attached below.
We are given a linear function.The function "y" equals 3x-1.We have to graph the function.In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.y = 3x - 1Now, we can get several pairs of coordinates that satisfy the above linear function.We plot the points on the graph and join them.We can see that the given function is an equation of a straight line that has a positive slope of magnitude 3 and a y-intercept of -1.If x = 2.5, then:y = 3(2.5) - 1y = 7.5 - 1y = 6.5To learn more about functions, visit :
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Given: ΔABC with vertices A(-3,0), B(0,6), and C(4,6),
find equation of the three altitudes in ΔABC
9792381 ÷ 13ven: ΔABC with vertices A(-3,0), B(0,6), and C(4,6),
find equation of the three altitudes in
I need help with the following
Let x be the number of miles and y the total cost; therefore, the equations that model the two plans are
[tex]\begin{gathered} PlanA: \\ y_A=30+0.20x \\ PlanB \\ y_B=50 \end{gathered}[/tex]Then, set y_A=y_B as shown below
[tex]\begin{gathered} y_A=y_B \\ \Rightarrow30+0.20x=50 \\ \Rightarrow0.20x=20 \\ \Rightarrow x=\frac{20}{0.20}=100 \end{gathered}[/tex]Therefore, once the mileage is greater than 100 miles, the total cost of plan B will be less than that of plan A.
The answer is 100 miles.18) Before Santiago donated 84 of his books to the Goodwill store, he had twice as many books
as Alex. After the donation, Alex has twice as many books as Santiago. How many books
does Alex have?
Alex has 56 books.
Let the number of books Santiago has be x. So, after the donation, the number of books with Santiago is (x - 84). Let the number of books with Alex be y.
Before the donation -
x = 2y : equation 1
After the donation -
y = 2(x - 84) : equation 2
Keep the value of x from equation 1 in equation 2
y = 2(2y - 84)
Performing multiplication on Right Hand Side of the equation
y = 4y - 168
Rearranging the equation
4y - y = 168
Performing subtraction on Left Hand Side of the equation
3y = 168
y = 168 ÷ 3
Performing division on Right Hand Side of the equation
y = 56
Therefore, Alex has 56 books.
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Please help me help help me please help help me
ANSWER
t = 10.27
EXPLANATION
Step 1: Given
[tex]500e^{0.0675t}\text{ = 1000}[/tex]Step 2: Divide both sides by 500
[tex]\begin{gathered} \frac{500e^{0.0675t}}{500}\text{ = }\frac{1000}{500} \\ e^{0.0675t}\text{ = }2 \end{gathered}[/tex]Step 3: Take the natural logarithm of both sides
[tex]\begin{gathered} 0.0675t\text{ = ln 2} \\ 0.0675t\text{ = }0.69314718056 \end{gathered}[/tex]Step 4: Divide both sides by 0.0675
[tex]\begin{gathered} \frac{0.0675t}{0.0675}\text{ = }\frac{0.69314718056}{0.0675} \\ t\text{ = 10.268847} \end{gathered}[/tex]Hence, t = 10.27 (rounded to the nearest hundredth).
June, Gavyn and Alex share some sweets in the ratio 3:5:4. June gets 39 sweets. How many sweets are there altogether?
Answer:
156
Step-by-step explanation:
This is a question in proportion and ratio
Since the ratio in which the sweets are shared is 3: 4 : 5 we can say that the proportion of total sweets that June gets is 3/(3 + 4 + 5) = 3/12 = 1/4
Let the total number of sweets be S
Then 1/4th of this will be June's share and we are given that the actual number June gets is 30
So we have 1/4 x S = 39
Multiplying both sides by 4:
4 x 1/4 x S = 39 x 4
S = 156
So there were 156 sweets altogether
$15 per hour is the basic rate at a factory. After a 48-hour basic work week, overtime is paid time and a half.
(a) If no one worked overtime and the factory paid $15 840 in wages one week, how many workers are in the factory?
(b) During another week, a worker in the factory earns $810 in wages for himself. How many hours did he work for?
Answer:
(a) There are 22 workers are available in the factory.
Step-by-step explanation:
(a) Let the number of workers in the factory be x.
Basic rate = $15
Working hours in a week = 48 hours
Total wages in a week = $ 15840
If no overtime is to be paid then according to question,
Amount paid to 1 worker = 48 X 15 = $ 720
Amount paid to x worker = 720x
15840 = 720
x = 15840/720
x = 22
Solve for x to the nearest tenth.
Answer:
Step-by-step explanation:
first from the lower triangle, the unknown length is [tex]\sqrt{10^2-4^2} =\sqrt{100-16}=\sqrt{84}[/tex] so then x is equal to [tex]\sqrt{84-4^2}=\sqrt{68}[/tex] or about 8.2
answer the following question below.
30
Explanation:Angle = 67°
To solve the question, we will use an illustration:
To get the horizontal distance from the base of the skycrapper to the ship, we will apply tangent ratio:
[tex]\tan \text{ 67}\degree\text{ = }\frac{opposite}{\text{adjacent}}[/tex]opposite = 903 ft
adjacent = horizontal distance from the base of the skycrapper to the ship = x
[tex]\begin{gathered} \tan \text{ }67\degree\text{ = }\frac{903}{x} \\ \text{cross multiply:} \\ x(\tan \text{ }67\degree)\text{ = 903} \\ x\text{ = }\frac{903}{\tan 67\degree} \end{gathered}[/tex][tex]\begin{gathered} x\text{ = }\frac{903}{2.3559} \\ x\text{ = 383.29} \end{gathered}[/tex]To the nerest hundredth, the horizontal distance from the base of the skycrapper to the ship is 383.30ft
What is the solution to the system of equations?A. The solution is (2, 7) because the solution to the system must satisfy both equations simultaneously.B. The solution is (1, 6) because the solution to the system must satisfy one equation or the other equation.C. The solution is (3, 5) because the solution to the system must represent the y-intercepts of both equations.D. The solution is (-1.5, -5) because the solution to the system must represent the x-intercepts of both equations.
GIven a graph.
to find the solution of the system of equaion.
The intersection point is the soution of the system of equation in the graph.
thus, (2,7) is the solution of the given system of equation.
The answer is, option A The solution is (2, 7) because the solution to the system must satisfy both equations simultaneously.
Section 5.2-9. Solve the following system of equations by substitution or elimination. Enter your answer as (x,y).2x+y = 2-3x-2y = -8
Answer: In terms of (x,y), using substitution, the answer is (-4,10)
Step-by-step explanation:
y=2-2x
-3x-2y=-8
~
-3x-2(2-2x)=-8
-3x-4+4x=-8
x-4=-8
x=-4
~
y=2-2(-4)
y=2+8
y=10
Answer please please
Answer: 31,000
Step-by-step explanation: You need to find two numbers that if you add the two variables will equal 76,000 and i checked 40,000-14,000=A=40,000 which equaled 66,000 and then 50,000-14,000=A+50,000 which equaled 86,000 so i knew the number in between was the one which was 45,000 and 45,000-14,000=31,000
50 points
You want to buy the newest gaming system, which costs $500. In addition, you want to be able to buy the accessories that go with it (e.g., controllers, games, headsets, etc.). You already have $150 saved up from your birthday but decide to ask your neighbors if you could wash their dogs to earn more money. You charge $10 per dog.
Write an equation or inequality to represent the situation. Then solve for your variable [show all steps].
The equation or the inequality of the situation is $10x + $150 > $500.
Inequality:
Inequality is defined as relation which makes a non-equal comparison between two numbers or other mathematical expressions.
Given
You want to buy the newest gaming system, which costs $500. In addition, you want to be able to buy the accessories that go with it (e.g., controllers, games, headsets, etc.). You already have $150 saved up from your birthday but decide to ask your neighbors if you could wash their dogs to earn more money. You charge $10 per dog.
Here we need to find the equation or inequality to represent the situation.
Based on the given details we have identified the following details,
He need the total cost for buying gaming system = $500.
Amount in hand = $150
Charge for one dog = $10.
So, it can be written as the inequality as,
$10x + $150 > $500
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one hundred and twenty one million, two hundred and twelve thousand and eighty-eight in number
Find the x-intercept and y-intercept of the line.
2x+5y = -10
The x-intercept is when y=0.
[tex]2x+5(0)=-10 \\ \\ 2x=-10 \\ \\ x=-5 \\ \\ \therefore (-5, 0)[/tex]
The y-intercept is when x=0.
[tex]2(0)+5y=-10 \\ \\ 5y=-10 \\ \\ y=-2 \\ \\ \therefore (0, -2)[/tex]
A rectangle has perimeter 40cm and was a width. What is an expression of the length in terms of w? What is an expression of the area in terms of w? What is the greatest area that the rectangle could have?
The expression of the length in terms of w is l = 20 - w cm
The expression of the area in terms of w is 20w - w² cm²
The greatest area that the rectangle could have is 400cm²
How to determine the values of the perimeter, length and areaIt is crucial to note that the calculating the perimeter of a rectangles is expressed as;
Perimeter = 2( l +w )
Where;
l is the length of the rectanglew is the width of the rectangleFrom the information given, the perimeter of the rectangle is 40cm
Now, substitute the value for perimeter
40 = 2( l +w )
Divide both sides by the coefficient, we have;
40/2 = 2(l + w)/2
Find the quotient
l + w = 20
Make 'l' the subject of formula
l = 20 - w cm
The formula for determining the area of a rectangle is expressed as;
Area = lw
Now, substitute the value of l as 20 -w in the formula, we have;
Area = 20- w(w)
expand the bracket
Area = 20w - w² cm²
For the greatest area;
Length = perimeter/4 = 40/ 4 = 20 cm
Width =perimeter/4 = 40/ 4 = 20cm
Area = 20(20)
Area = 400cm²
Thus, the expression of the length is l = 20 - w cm
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On your own paper, graph the system of equations and identify the solution.=2−4=−12+1
The Slope-Intercept Form of the equation of a line is:
[tex]y=mx+b[/tex]Where "m" is the slope of the line and "b" is the y-intercept.
You have the first line:
[tex]=2x-4[/tex]You can identify that the y-intercept is:
[tex]b_1=-4[/tex]You can find the x-intercept substituting the following value of "y" into the equation of the line:
[tex]y=0[/tex]And, after the substitution, you can solve for "x":
[tex]\begin{gathered} 0=2-4 \\ 4=2x \\ \\ \frac{4}{2}=x \\ \\ x=2 \end{gathered}[/tex]Now you know that the first line passes through these points:
[tex]\begin{gathered} (0,-4) \\ (2,0) \end{gathered}[/tex]Then, you can graph it.
Given the second line:
[tex]y=-\frac{1}{2}x+1[/tex]You can identify that:
[tex]b_2=1[/tex]And you can find the x-intercept by following the same procedure applied for the first line:
[tex]\begin{gathered} 0=-\frac{1}{2}x+1 \\ \\ -1=-\frac{1}{2}x \\ \\ (-1)(2)=-x \\ \\ -2=-x \\ x=2 \end{gathered}[/tex]Then, this line passes through these points:
[tex]\begin{gathered} (0,1) \\ (2,0) \end{gathered}[/tex]Now you can graph it.
See the graph below:
By definition, when the lines intersect, the solution of the System of equations is the point where the two lines intersect.
The answer is: First option.
If a rotation takes triangle CAT to C’A’T where is AT
Answer:
The measure of C'T' after rotation of transformation is option (B) square root of 17 is the correct answer.
Step-by-step explanation:
What is a rotation transformation?
A rotation is a transformation that turns the figure in either a clockwise or counterclockwise direction on the coordinate plane. In both transformations the size and shape of the figure stays exactly the same.
For the given situation,
The graph shows the triangle CAT.
If a rotation takes triangle CAT to C'A'T',
then from the definition of rotation transformation the size and shape of the figure stays exactly the same.
Thus the measure of C'T' is same as CT.
Hence we can conclude that the measure of C'T' after rotation of transformation is option (B) square root of 17 is the correct answer.
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guys I understand this question is still unsolved, however still maybe, just maybe one among you can simply figure it out, so this is the question...what is 1 divided by 0...?
Plot 2.379 on a number line on which the long tick marks are tenths.
A number line which represents the given number (2.379) is plotted and shown in the image attached below.
What is a place value?A place value can be defined as a numerical value which denotes a digit based on its position in a given number and it includes the following:
TenthsHundredthsThousandthsUnitTensHundredsThousands.Tens of thousands.Hundred of thousands.Millions.Tens of millions.Hundreds of millions.Billions.What is a number line?A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numbers (numerical values) that are placed at equal intervals along its length.
In conclusion, the number (2.379) should be placed close to 4 as plotted on the number line shown in the image attached below.
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48 candies 12 are red and 14 are yellow what is the raito to red to yellow
Answer:
12:14
Step-by-step explanation:
RED=12
YELLOW=14
what is the ratio red to yellow u put the amount of red first then the amount of yellow
All the fruit a farmers' market booth is on sale for 1.75 per pound. William bought 2 2/5 pounds of peaches and 2 1/3 pounds of apricots. To the nearest cent, what was the total cost of the fruit?
Algebra - The total cost of the fruit 8.26
What is Algebra ?
One of the many branches of mathematics is algebra. Algebra, which is a common thread throughout practically all of mathematics, is broadly defined as the study of mathematical symbols and the rules for manipulating these symbols in formulas.
Given that,
The cost of all fruit is = 1.75/pound
William bought Peaches = 2(2/5)pounds = 12/5pounds
William bought Apricot = 2(1/3)pounds = 7/3pounds
The cost of Peaches = 12/5 x 1.75
= 12 x 0.35
= 4.2
The cost of Apricot = 7/3 x 1.75
= 7 x 0.58
= 4.06
Total cost of the fruit = 4.2 +4.06
= 8.26
Hence, the total cost of the fruit is 8.26
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Answer this question pls
Answer:
No
Step-by-step explanation:
Two different inputs can not have the same output. Although they can have two different outputs and the same input the reverse is not a thing. Each input has only one output, and the fact that it is the same output does not matter. It is supposed to be a function and by definition, functions are a special kind of relations allowing precisely one output for each input.
Factor PLS PLS PLS:
b(a+1)^2 -5(a+1)
The value of the expression given as b(a+1)² -5(a+1) will be a²b + 2ab + 2b - 5a - 5.
How to illustrate the information?It should be noted that based on the information that given, we want to factor out the variables that are given.
This will be illustrated thus:
b(a+1)² -5(a+1)
= b(a + 1)(a + 1) - 5(a + 1)
= b(a² + 2a + 2) - 5a - 5
= a²b + 2ab + 2b - 5a - 5
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The perimeter of the rectangle below is 176 units. Find the length of side BC.
Write your answer without variables
Answer:
(5y-3)+(4y+1)+(5y-3)+(4y+1) = 176
18y - 4 = 176
18y = 180
y = 10
BC = 4y + 1 = 4(10) + 1 = 41 units
Find two numbers that the quotient 3,382/6 is between
The most appropriate choice for division will be given by
Quotient of [tex]\frac{3382}{6}[/tex] is between 563 and 564
What is division?
The process of dividing a certain number into equal parts is called division
The answer obtained after division is called quotient and the other part is the remainder. The number which is divided is called the dividend and the number by which the dividend is divided is called divisor.
General rule of division
Divisor x Quotient + Remainder = Dividend
Here,
Quotient of [tex]\frac{3382}{6}[/tex] = 563
563 is between 562 and 564
So, quotient of [tex]\frac{3382}{6}[/tex] is between 563 and 564
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A bakery makes fruit pies and cream pies.
Twelve out of every 20 pies baked are fruit
pies. What is the ratio of cream pies to fruit
pies?
Answer:
12:20 because for ever 12 fruite pies 20 cream pies are made so it would look like the following!
12:20
Step-by-step explanation:
Hope it helps! =D
The slope of the line below is
-1 over 7
Write a point-slope equation of the line
using the coordinates of the labeled point
The point slope form of the given equation is [tex](y-3)=\frac{-1}{7} (x-3)[/tex] .
What is a equation of line?The equation y = mx + c is the general equation of any straight line where m is the gradient of the line (how steep the line is) and c is the y -intercept (the point in which the line crosses the y -axis).
If a line passes through the point with slope m, then the point slope form of the line is
[tex](y-y_{1} )=m(x-x_{1} )[/tex]
Given that,
The slope of the line m = [tex]\frac{-1}{7}[/tex].
From the graph it is clear that the line passes through the point (3,3).
Substitute x₁= 3, y₁= 3 and in the above equation.
[tex](y-3) = \frac{-1}{7}(x-3)[/tex]
Hence, The point slope form of the given equation is [tex](y-3)=\frac{-1}{7} (x-3)[/tex] .
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The above question is not complete.