Given:
The dimensions of the room are,
[tex]\begin{gathered} l=80ft \\ b=50ft \end{gathered}[/tex]The dimensions of the carpet are,
[tex]\begin{gathered} l_1=10ft \\ b_1=50ft \end{gathered}[/tex]To find:
The number of rolls of carpet.
Explanation:
The number of rolls of carpet is calculated by,
[tex]\begin{gathered} \frac{Area\text{ of the room}}{Area\text{ of a carpet rool}}=\frac{l\times b}{l_1\times b_1} \\ =\frac{80\times50}{10\times50} \\ =8rolls\text{ of carpet} \end{gathered}[/tex]Therefore, the number of rolls of carpet is 8.
Final answer:
The number of rolls of carpet is 8.
Mai drove 754 miles in 13 hours.
At the same rate, how many miles would she drive in 11 hours?
Answer:
At the same rate, she will travel 638 miles if she drives 11 hours.
Step-by-step explanation:
[tex]\frac{754 miles}{13 hours\\} = \frac{x}{11 hours}[/tex]
x=11*754/13
x=638
Write the augmented matrix for the system of linear equations. (Do not perform any row operations.)X- y + 4z = 46x - 8y +Z = -14x +y0:
For you to input the information in a Matix you only have to consider the coefficients corresponding to each variable in each equation, in this case the matrix is:
1 -1 4 : 4
6 -8 1 : -1
4 1 0 : 0
This is the matrix for the given equations
What is the slope of the line that passes through (2, 2) and (10, 6) ?
Enter your answer in the box.
Please help asap! I havn't got help all day
The slope of the line that passes through (2, 2) and (10, 6) is; 1/2.
What is the slope of a line which passes through points ( p,q) and (x,y)?The slope of parallel lines is the same. Slopes of perpendicular lines are negative reciprocals of each other. The slope of a line or straight object is the ratio of how much amount of rising occurs in correspondence to the increment in the run.
Its slope would be:
[tex]m = \dfrac{y-q}{x-p}[/tex]
We have been given that the line that passes through (2, 2) and (10, 6).
Let ( p,q) and (x,y) are (2, 2) and (10, 6) respectively.
Slope = [tex]m = \dfrac{y-q}{x-p}[/tex]
m = (2-6)/(2-10)
m = 4/8
m = 1/2
Then the slope is 1/2.
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Answer this graph based Question I will provide you 50 points + make you brainliest.
Part a: The value of y is 11 for x = 2.
Part b: The graph for the function y = x² + 4x -1 is drawn.
Part c: Range; (-∞,-3.75]∪[-0.25,∞)
Part d: The function is y = -5 - (x + 2)².
Part e: The approximate value of √3 is 1.732.
What is defined as the term function?A function is an expression, rule, or law in mathematics that defines a relationship between one dependent variable (a independent variable) and also one more variable (the dependent variable). Functions are common in mathematics and are required for the formulation of actual relationships with in sciences.For the given function;
y = x² + 4x -1, the values of y for the corresponding x is given in tables shown.
Part a: value of y when x = 2.
Put x = 2 in the function;
y = x² + 4x -1
y = 2² + 4×2 -1
y = 11
The value of y is 11 for x = 2.
Part b: The graph for the function y = x² + 4x -1 is drawn using the scale of 10 small divisions as 1 unit along x and y axis.
Part c: Range of value of x for which y ≥ -2.
Locate the point of x from the graph for which the value of y y ≥ -2.
Range; (-∞,-3.75]∪[-0.25,∞)
Part d: The function in the form of y = k - (x - h)², where k and h are the vertex.
The vertex from the graph is found as (-2, -5) (h, k)
Putt in the equation;
y = k - (x - h)²
y = -5 - (x - (-2))²
y = -5 - (x + 2)²
Part e: 2 - √3 is the root of the equation 0 = x² + 4x -1.
It 2 - √3 is the root of the equation, then by putting this value at x the equation becomes zero.
The approximate value of √3 is 1.732 which is found by long division method.
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P (8, 4) is a point on a circle, centre O.
The tangent at P intersects the axes at points A and B.
a) Find the gradient, m, of the tangent.
Your final line should say, m =...
(2)
b) Find the equation of the tange the
form y = mx + c where m and c are integers. (1)
y =
X +
c) Find the coordinates of point A.
d) Work out the length of AB,
giving your answer in the form a√5 where a is an integer.
(1)
B
P (8,4)
A
5 (2)
Total marks: 6
The equation of tangent is y = -2x + 20. The slope of the tangent line is negative 2. And coordinate of point A is (10, 0). And the length of AB is 22.36 units.
What is the equation tangent line to circle?The equation of the circle with center at origin and radius r is given as,
x² + y² = r²
The slope of the tangent line to the circle at points (8, 4) is given as,
2x + 2y (dy/dx) = 0
dy / dx = - 8 / 4
m = - 2
Then the equation of the line is given as,
y = -2x + c
The equation is passing through (8, 4), then we have
4 = -2(8) + c
c = 4 + 16
c = 20
The equation is y = -2x + 20. Then the x-intercept is given as,
y = 0
-2x + 20 = 0
2x = 20
x = 10
Then the length of the line is given as,
AB² = (10 - 0)² + (0 - 20)²
AB² = 100 + 400
AB = √(500)
AB = 22.36 units
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See question below. I am not sure how to set this up.
Answer and Explanation:
Let x represent the number of hours Sandy needs to work.
We can go ahead and set up the required inequality as shown below;
[tex]150<10x+20<200[/tex]Let's go-ahead and determine x by splitting the compound inequality above as shown below;
[tex]\begin{gathered} 150<10x+20 \\ 150-20<10x \\ 130<10x \\ x>\frac{130}{10} \\ x>13 \end{gathered}[/tex][tex]\begin{gathered} 10x+20<200 \\ 10x<180 \\ x<\frac{180}{10} \\ x<18 \end{gathered}[/tex][tex]13We can see from the above that Sandy needs to work between 13 and 18 hours to be able to meet her goal.What is the factored form of the polynomial?x^2 + 2x - 24
Let's try to factorize this polynomial
[tex]x^2+2x-24=(x+)(x-)[/tex]in the blank spaces we have to put numbers that multiplied are 24, and substracted are +2. So we have 6 and 4
[tex]x^2+2x-24=(x+6)(x-4)[/tex]So the factored form of the polynomial is (x+6)(x-4)
The answer is 78 ft provided by my teacher, I need help with the work
ok
To solve this problem, I'll use trigonometric functions,
The trigonometric function that relates the opposite side and the hypotenuse is sine
Formula
sin 48 = Opposite side / hypotenuse
hypotenuse = 105 ft
opposite side = H
Substitution
sin 48 = H/105
Solve for H
H = 105*sin 48
Simplification
H = 105*0.743
Result
H = 78 ft
You invest $275 to start a sandwich stand and decide to charge 515 per sandwich set of a linear model that determines your profit or loss based on the number of sandwiches
The linear model that determines your profit or loss based on the number of sandwiches is 15y-275, where y is the number of sandwiches sold.
What is a linear model?A continuous response variable is described as a function of one or more predictor variables in a linear model. They can assist you in comprehending and forecasting the behaviour of complex systems, as well as analyzing experimental, financial, and biological data. Linear regression is a statistical technique for developing a linear model.
It is given that the investment amount is $275.
The charge per sandwich is $15
So, generated revenue= 15 y
where y is the number of sold sandwiches.
Profit/ Loss= Revenue- total investment= 15y-275
So, the linear model determining the profit or loss is 15y-275, where y is the number of sandwiches.
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Far from home: A survey asked first-year college students, “How many miles is this college from your permanent home?” Students had to choose from the following options: 5 or fewer, 6 to 10, 11 to 50, 51 to 100, 101 to 500, or more than 500. The side-by-side bar chart shows the percentage of students at public and private 4-year colleges who chose each option.
The average distance between students in public is smaller than that in private.
While the data for the public appears to closely follow a bimodal distribution, the data for the private appears to be negatively skewed, meaning that the tail is lopsided to the left. However, it might be nearly symmetrical. While the modal class for the public is 11–50, it is 101–500 for private.
While the mean for public data is close to 50, it is close to 100 for private data.
Therefore, it is clear from the graphs that students' average distances from Public are closer than those from Private.
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If $8^7)^2 = 2^y, what number is y?
The value of y based on the information given about the expression (8^7)² = 2^y is 21.
How to illustrate the information?It should be noted that based on the information, the power rule will be essential. This will be illustrated thus:
(8^7)² = 2^y
It should be noted that 8 = 2 × 2 × 2 = 2³
Therefore, 8^7 = 2^(3 × 7) = 2^21
Therefore, the value of y is 21.
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64,32,16,8 what is the next three terms of it? (no negatives)
Notice that each new term is half the previous one. For example, 32 is half 64, 16 is half 32, and so on.
Having said that, the constant ratio is 1/2. Using this ratio we can find the next three terms.
[tex]\begin{gathered} 8\cdot\frac{1}{2}=4 \\ 4\cdot\frac{1}{2}=2 \\ 2\cdot\frac{1}{2}=1 \end{gathered}[/tex]Therefore, the next three terms are 4, 2, and 1.. What is the number of terms in this expression? m + 4.6 5 Enter your answer in the box.
Question: What is the number of terms in this expression? m/5 + 4.6
Answer:
Two terms
Explanation:
Addition and subtraction separate terms but division and multiplication do not, so they are two terms in the below expression;
[tex]\frac{m}{5}+4.6[/tex]The terms are m/5 and 4.6
(d) Find the domain of function R. Choose the correct domain below.
Answer:
d
Step-by-step explanation:
The number of years must be non-negative.
This eliminates all of the options except for d.
Write the curve equation associated to those parametric equations.x(θ) = 3 cos θy(θ) = 6 sin θ
We want to rewrite the following parametric equations
[tex]\begin{gathered} \begin{cases}x={3\cos\theta} \\ y={6\sin\theta}\end{cases} \\ \frac{\pi}{2}<\theta<\frac{3\pi}{2} \end{gathered}[/tex]as one equation. Using the following property
[tex]\sin^2\theta+\cos^2\theta=1[/tex]We can eliminate the parameter theta adding the square of the coordinates
[tex]\begin{gathered} \sin^2\theta+\cos^2\theta=1 \\ 6^2(\sin^2\theta+\cos^2\theta)=6^2 \\ 6^2\sin^2\theta+6^2\cos^2\theta=6^2 \\ (6\sin\theta)^2+(6\cos\theta)^2=6^2 \\ (6\sin\theta)^2+(2\cdot3\cos\theta)^2=6^2 \\ (y)^2+(2x)^2=6^2 \\ y^2+4x^2=36 \\ \frac{x^2}{9}+\frac{y^2}{36}=1 \end{gathered}[/tex]And this is the standard equation of an ellipse
[tex]\frac{x^{2}}{9}+\frac{y^{2}}{36}=1[/tex]The constrain
[tex]\frac{\pi}{2}<\theta<\frac{3\pi}{2}\implies x<0[/tex]tells us that x can only assume negative values, therefore, the graph is only the left side of the ellipse.
2 The half-life of a substance is defined as the period of time it takes for the amount of the
substance to decay by half. The sequence shows the amount of a substance that will remain
after a certain number of half-lives have elapsed.
1, 1/2, 1/4, 1/8
Describe this sequence.
The given sequence is
1, 1/2, 1/4, 1/8......
we can see that the ratio of the consecutive terms is the same. We have
1/2/1 = (1/4)/(1/2) = (1/8)/(1/4) = 1/2
This means that it is a geometric sequence
To find the amount of the substance left after 21 half lifes, we would find the 21st term of the sequence. The formula for finding the nth term of a geometric sequence is
an = a1r^(n - 1)
a1 = 1
n = 21
r = 0.5
Thus,
a21 = 1 * 0.5^(21 - 1) = 0.5^20
a21 = 0.00000095367
a21 = 1/1048576
The answer makes sense in the problem context because it follows the common ratio that was established at the begining.
If g(x) = -4x + 5, what is the value of (g o g) (3)?
A -7
B 48
C -23
D 33
Answer:
A. -7
Step-by-step explanation:
g(x) = -4x+5
We know that g(x)= (3) so just substitute 3 for x.
g(3)= -4(3)+5
g(3)= -12+5
g(3)=-7 answer.
What is the slope of a line perpendicular to the line whose equation is x+4y=16. .
Answer:
The slope is [tex]-\frac{1}{4}[/tex].
Step-by-step explanation:
This is the slope formula equation.
[tex]y=mx+b[/tex]
[tex]x+4y=16[/tex]
First, you divide the entire equation by 4 to get rid of the 4 in 4y.
[tex]\frac{x}{4} +y=4[/tex]
Then, you subtract [tex]\frac{x}{4}[/tex] on both sides.
[tex]y=-\frac{x}{4} +4[/tex]
In front of the x should be and invisible 1. So this should be your slope.
[tex]m=-\frac{1}{4}[/tex]
Write the correct inequality for the following statement and then solve for the given number of
guests.
You are in charge of planning your mother's surprise party. You have
found a hall that rents for $225 and a caterer that will charge you $15 per
guest. Write an inequality to calculate your total cost (T) based on the
number of guests (g).
If you have a total budget of $1000 how many guests can you
invite?
The inequality that can be used to calculate total cost (T) based on the number of guests (g) is 225 + 15g ≤ 1000.
If you have a total budget of $1000, 51.67 guests can be invited.
How to write inequality equation?Cost of hall rent = $225Caterer's charge per guest = $15Total cost = TNumber of guests = gTotal cost = Cost of hall rent + Caterer's charge per guest(Number of guests)
225 + 15g ≤ T
If you have a total budget of $1000
225 + 15g ≤ T
225 + 15g ≤ 1000
substract 225 from both sides15g ≤ 1000 - 225
15g ≤ 775
divide both sides by 15g ≤ 775 / 15
g ≤ 51.66666666666666
Approximately,
g ≤ 51.67
So therefore, the inequality to represent the situation is 15g ≤ 1000 - 225 and about 51.67 guests can be invited if you have a budget of $1000
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(NEED ANSWER ASAP) Tom and Jessica are going to Disneyworld. Snacks are EXPENSIVE there. They each got a Mickey ice cream, and Jessica also got cotton candy. Tom only had $9, so Jessica paid for the rest, which was $4. The ice cream cost $5 each, what was the cost of the cotton candy? Write an equation to represent the word problem and solve it. (Show all of your steps)
The cost of the cotton candy that Jessica purchased is $3.
What is the cost of candy?The first step is to determine total amount spent on snacks. The total amount spent is the sum of the amount paid by Tom and Jessica.
Total amount spent = $9 + $4 = $13
Two ice creams and one cotton candy is bought. This can be represented with:
$13 = total cost of ice cream + cost of the cotton candy
$13 = (2 x$5) + c
$13 = $10 + c
c = $13 - $10
c = $3
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S = 1/3 x pi x r^2 + pi x r^2 x h
The solved equation for h is h= S/ pi x r^2-1/3.
The problem we are dealing with here is related to the literal equation, where a literal equation is an equation that comprises basically letters. Formulas are an illustration of strict equations. Each variable within the condition "truly" speaks to an important part of the full relationship expressed by the equation. To illuminate a literal equation implies modifying the equation so a different variable stands alone on one side of the equals sign. We got to be told which variable we need to solve.
For the given equation,S= 1/3 x pi x r^2 + pi x r^2 x h
for th the equation will be
=>S= pi x r^2(1/3 +h)
=>S/ pi x r^2= 1/3+h
=>h= S/ pi x r^2-1/3
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S = 1/3 x pi x r^2 + pi x r^2 x h , solve for h
Identify the parent function for the function g (x) = x+9 from its function rule. Then graph g and identify what transformation of the parent function it represents.
The parent function of g(x) = x + 9 is the function f(x) = x.
The function f(x) = x is a linear function, that is, it has degree 1 (the higher exponent of the variable x is 1).
In order to get g(x) from f(x), we can see that the function value was increased by 9 units:
[tex]g(x)=f(x)+9[/tex]Adding 9 units to the function means we have a translation of 9 units up.
Therefore the correct option is the third one.
Graphing g(x), we have:
which inequality matches this situation : a number is at least 6a= x ≥ 6b= x > 6c= x ≤ 6d= x < 6
Answer:
a. x ≥ 6
Explanation:
If a number is at least 6, then, the number is greater than or equal to 6.
Since the symbol ≥ means greater than or equal, the correct answer is:
a. x ≥ 6
i need help asap!!! im bad at graphing
Points are (1, -3)
What is equation?In algebra, an equation is a declaration of equivalence that includes one or more variables or unknowable quantities. In mathematics, an equation is a relationship between two expressions that is expressed as an equality on each side of the equal to sign. An equation would be 3y = 16, for instance.
Given Data
Slope = -[tex]\frac{1}{2}[/tex]
Points (-1, -5)
The line's general equation is y=ax+b.
Since we are aware that the slope is -[tex]\frac{1}{2}[/tex], an is equal to -[tex]\frac{1}{2}[/tex].
We also understand that if x = -1, then y = -5.
Let's connect it:
-5=1*(-1)+b
-5=-1+b
b= -4
So, y=x -4 is the line's equation.
Let x = 1
y = 1 - 4
y = -3
(1, -3)
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1. Round to the nearest thousand. Use the number line to model your thinking.
9,340=
After rounding off the number we get ; 9,300
What does rounding off to thousand mean?When a number is rounded to the closest thousand, it is changed to an approximated value that is simpler to recall and utilize. The closest value to the supplied integer is this value, which is a multiple of 1000. For instance, 342984 becomes 343000 if it is rounded to the closest thousand.
So as in this question the number given is 9340
Since we have to round it off to thousands
and the number next to 9 is 3
Thus we can say that after rounding off the number will be
9,300.
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Find the distance between each pair of points. Round youranswer to the nearest tenth, if necessary.(7, 6), (0, 2)
Chris, this is the solution to the exercise:
• Point 1 = (7, 6)
,• Point 2, (0, 2)
Now, let's use the formula to calculate the distance between the two points, as follows:
d = √(0 - 7)² + (2 - 6)²
d = √-7² + (-4)
d = √49 + 16
d = √65
d = 8.0622
d = 8.1 (rounding to the nearest tenth)
(d) Find the domain of function R. Choose the correct domain below.
Answer:
d
Step-by-step explanation:
The number of years must be non-negative.
This eliminates all of the options except for d.
Factoring binomials math
we have the expression
[tex]x^3-125[/tex]we have that
x=5 is a zero of the given equation
so
Divide x^3-125 by (x-5)
x^3-125 : (x-5)
x^2+5x+25
-x^3+5x^2
---------------
5x^2-125
-5x^2+25x
------------------
25x-125
-25x+125
----------------
0
therefore
x^3-125=(x-5)(x^2+5x+25)
the answer is the fourth optionWill mark as brainlist
Which of the following best represents R= A - B ?
Please help, it’s due soon!
Answer: I would say it is C
Step-by-step explanation: If you think about it, if you have a pencil and the pencil is in A form, and you have to put it to B form, it kinda makes sence. BUT, I honestly don't know, so don't trust me...
GL LUCK THO AND GOD BLESS
PLEASE AWNSER NOW Sandy uses three and one half pounds of clay to make 7 small vases. Use a proportion to find how many pounds of clay she will use to make 21 small vases.
7 and one fourth pounds
8 and one half pounds
10 and one half pounds
14 and one fourth pounds
Answer:
The answer is 10 and one half pounds
Explanation:
3.5/7 = 2
21/2 = 10.5
10 and one half pounds use to make 21 small vases.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Sandy uses clay= 3 1/2 pounds for 7 vase
So, for 1 vase amount of clay used
= 7/2 x 1/7
= 1/2 pounds
Now, for 21 small vases amount of clay used
=21 x 1/2
= 21/2
= 10 1/2 pounds.
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