The expression that represents the area of the rectangle is [tex]6x^{2}[/tex]+29x + 35 square units , the degree of the obtained expression is 2.
According to the question,
We have the following information:
A rectangle has sides measuring (2x + 5) units and (3x + 7) units.
A) We know that following formula is used to find the area of rectangle:
Area = length*breadth
Area = (3x+7)(2x+5)
Area = [tex]6x^{2}[/tex] + 15x +14x + 35
Area = [tex]6x^{2}[/tex] +29x + 35 square units
B) The degree of an expression is the highest power of the expression. In this case, the highest power is 2. Hence, the degree of the expression obtained is 2.The expression can be classifies as a quadratic polynomial.
C) Part A demonstrates the closure property for the multiplication of polynomials because the expression within the brackets are polynomials and the result obtained is also a polynomial.
Hence, the area of the rectangle is [tex]6x^{2}[/tex] +29x + 35 square units and the degree of the obtained expression is 2.
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how do i solve the equation?
Answer: 7x=63 and 12x+9= 117
Step-by-step explanation:
add those two equations and set it to 180 degree
7x+12x+9=180
19x=171
x= 9
7x = 7 (9) = 63
12x+9 = 12 (9)+9 = 117
9 + 4 + (-1) +(-1) +...+ (-546) = 0X X80Σ (-3 + 10) = 0E=1
Answer
The sum of the sequence = -30072
Explanation
We are given a sequence of numbers and asked to find the sum of the terms up until the last term given. The sequence given is
9, 4, -1,.............., -546
On careful observation of this sequence, we can see that it is an arithmetic progression with a common difference of -5 between consecutive terms.
Common difference = (n + 1)th term - nth term
= 4 - 9 Or -1 - 4
= -5
For an arithmetic progression, the formula for the last term is given as
Last term = a + (n - 1)d
where
L = last term = -546
a = first term = 9
n = number of terms in the sequence = ?
d = common difference = -5
So, we can solve for the number of terms
-546 = 9 + (n - 1)(-5)
-546 = 9 - 5n + 5
-546 = 14 - 5n
14 - 5n = -546
-5n = -546 - 14
-5n = -560
Divide both sides by -5
(-5n/-5) = (-560/-5)
n = 112
We can now use the formula for the sum of an arithmetic progression to find the sum of this sequence.
[tex]\text{Sum of an A.P. = }\frac{n}{2}\lbrack2a+(n-1)d\rbrack[/tex]We know all of these parameters now
Sum of this AP = (112/2) [(2 × 9) + (112 - 1)(-5)]
= 56 [18 + (111 × -5)]
= 56 [18 - 555]
= 56 [ -537]
= -30072
Hope this Helps!!!
Kala the trainer had two solo workout plans that she offers her clients. PlanA and plan B. Each client does either one or the other (not both) on Friday there were 3 clients who did plan A and 5 who did plan B. On Saturday there were 9 clients who did plan A and 7 who did plan B. Kala trained her Friday clients for a total of 6 hours and her Saturday clients for a total of 12 hours. How long does each of the workout plans last?
Answer:
Each of the workouts plans lasts 45 minutes.
Explanation:
Let the duration for Plan A workout = x
Let the duration for Plan B workout = y
Friday
• Plan A --> 3 clients
,• Plan B --> 5 clients
,• Kala trained her Friday clients for a total of 6 hours
[tex]3x+5y=6[/tex]Saturday
• Plan A --> 9 clients
,• Plan B --> 7 clients
,• Kala trained her Saturday clients for a total of 12 hours
[tex]9x+7y=12[/tex]The system of equations is solved simultaneously.
[tex]\begin{gathered} 3x+5y=6\cdots(1) \\ 9x+7y=12\cdots(2) \end{gathered}[/tex]Multiply equation (1) by 3 in order to eliminate x.
[tex]\begin{gathered} 9x+15y=18\cdots(1a) \\ 9x+7y=12\cdots(2) \end{gathered}[/tex]Subtract.
[tex]\begin{gathered} 8y=6 \\ y=\frac{6}{8}=0.75\text{ hours} \\ 0.75\times60=45\text{ minutes} \end{gathered}[/tex]Substitute y=0.75 into equation (2) to solve for x.
[tex]\begin{gathered} 9x+7y=12 \\ 9x+7(0.75)=12 \\ 9x+5.25=12 \\ 9x=12-5.25=6.75 \\ x=\frac{6.75}{9} \\ x=0.75 \end{gathered}[/tex]x=y=0.75 hours = 45 minutes,
Each of the workouts plans lasts 45 minutes.
need help assap look at file attached
Answer:
length is 27, width is 9
Step-by-step explanation:
72/4= 18
2x27+ 2x9 = 54 + 18 = 72
Solve for w. 3w + 2w - 3w = 8
Answer
w = 4
Explanation
We are asked to solve for w
3w + 2w - 3w = 8
5w - 3w = 8
2w = 8
Divide both sides by 2
(2w/2) = (8/2)
w = 4
Hope this Helps!!!
Need help with all of them please help me serious
we have 4,5,6
In a right triangle
c^2=a^2+b^2
where
c is the hypotenuse (greater side)
a and b are the legs
In an acte triangle
c^2 < a^2+b^2
we have
c=6
a=4
b=5
substitute
c^2=6^2=36
a^2=4^2=16
b^2=5^2=25
36 < 16+25
36 < 41
therefore
is an acute triangle
Part 2
10,24,26 and also classify the triangle
we have
c=26
a=10
b=24
so
c^2=676
a^2=100
b^2=576
in this problem
c^2=a^2+b^2
therefore
Is a right triangle
Which of the following polar coordinates would not be located at the point?
Explanation
We are asked to select the option that would not be located at the given point
To do so, let us find the original coordinates of the given polar point
The point is located 6 units away from the origin in a direction of 270 degrees
The equivalent coordinates are
[tex]\begin{gathered} (6,\frac{3\pi}{2}) \\ (6,\frac{-\pi}{2}) \\ (-6,90^0) \end{gathered}[/tex]Thus, we are to eliminate any option that is not equivalent to the above, we are left with
[tex](6,\frac{-3\pi}{2})[/tex]Thus, the answer is option A
Use the table to write an equation that relates the cost of lunch Y and the number of students X
In order to determine what is the equation which describes the values of the table, consider that the general form of the equation is:
y = mx
where m is the constant of proportionality between both variables x and y.
To calculate m you calculate the quotient between any pair of data from the table.
If you for example use the following values:
Students = 8.00
Lunch cost = 2
the constant of proportionality is:
m = 8.00/2 = 4.00
Next, you replace the value of m in the equation y=mx:
y = $4.00x
[tex] \sqrt{18} (523 \div 8)[/tex]help I need help
Solution
Given question
11.85 = 2.1n + 4.5
Requirement
To isolate n
Step 1
Using the subtraction property of equality to isolate the variable
11.85 - 4.5 = 2.1n + 4.5 -4.5
7.35 = 2.1n
Step 2
use the division property of equality to isolate the variable
7.35/2.1= 2.1n/2.1
n = 3.5
Answers are 1 first, then 2 next, those are the 2 steps
A rectangular board is 1200 millimeters long and 900 millimeters wide what is the area of the board in square meters? do not round your answer
Answer: Area of the rectangular board is 1.08 square meters
The length of the rectangular board = 1200 milimeters
The width of the rectangular board = 900 milimeters
Area of a rectangle = Length x width
Firstly, we need to convert the milimeter to meters
1000mm = 1m
1200mm = xm
Cross multiply
x * 1000 = 1200 x 1
1000x = 1200
Divide both sides by 1000
x = 1200/100
x = 1.2 meters
For the width
1000mm = 1m
900mm = xm
cross multiply
1000 * x = 900 * 1
1000x = 900
Divide both sides by 1000
x = 900/1000
x = 0.9m
Length = 1.2 meters
Width = 0.9 meter
Area = length x width
Area = 1.2 x 0.9
Area = 1.08 square meters
question 18:Evaluate: summation from n equals 2 to 8 of 12 times 4 tenths to the n plus 1 power period Round to the nearest hundredth. (1 point)
Given:
[tex]\sum_{n\mathop{=}2}^812(0.4)^{n+1}[/tex]Required:
Sum of the numbers
Explanation:
Let
[tex]A_n=\sum_{n\mathop{=}2}^812(0.4)^{n+1}[/tex]when n = 2, Aₙ becomes
[tex]A_2=12(0.4)^{2+1}=12\times(0.4)^3=0.768[/tex]when n = 3, Aₙ becomes
[tex]A_3=12(0.4)^{3+1}=12\times(0.4)^4=0.3072[/tex]when n = 4, Aₙ becomes
[tex]A_4=12(0.4)^{4+1}=12\times0.4^5=0.12288[/tex]
when n = 5, Aₙ becomes
[tex]A_5=12(0.4)^{5+1}=12\times0.4^6=0.049152[/tex]when n = 6, Aₙ becomes
[tex]A_6=12(0.4)^{6+1}=12\times0.4^7=0.0196608[/tex]when n = 7, Aₙ becomes
[tex]A_7=12(0.4)^{7+1}=12\times0.4^8=0.007866432[/tex]when n = 8, Aₙ becomes
[tex]A_8=12(0.4)^{8+1}=12\times0.4^9=0.003145728[/tex]So now,
[tex]\begin{gathered} A=A_1+A_2+A_3+A_4+A_5+A_6+A_7+A_8 \\ \\ A=0.768+0.3072+0.12288+0.049152+0.0196608+0.00786432+0.003145728 \\ \\ A=1.277902848\approx1.28 \end{gathered}[/tex]Final answer:
The
Find the length of the third side. If necessary, write in simplest radical form.
4
4√5
clarissa's division test was a 60% the first six weeks and a 72% the second six weeks. find the percent change.
The required change in the percentage is 20%.
Given that,
clarissa's division test was 60% in the first six weeks and 72% in the second six weeks. To determine the percent change.
The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
Here,
According to the question,
The change in the percentage = (72 - 60) / 60 × 100
The change in the percentage = 20%
Thus, the required change in the percentage is 20%.
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help meeeeeeeeee pleaseee !!!!!
The value of the composite function is as follows:
(gof)(5) = 6How to find composite function?The composite function can be solved as follows:
Composite functions are when the output of one function is used as the input of another.
In other words, a composite function is a function that depends on another function.
f(x) = x² - 6x + 2
g(x) = -2x
Therefore,
(gof)(5) = g(f(5))
So we need to find g(f(x)) first.
Therefore,
g(f(x)) = -2(x² - 6x + 2)
g(f(x)) = - 2x² + 12x - 4
Therefore,
g(f(x)) = - 2x² + 12x - 4
(gof)(5) = g(f(5)) = - 2(5)² + 12(5) - 4
(gof)(5) = g(f(5)) = -50 + 60 - 4
(gof)(5) = g(f(5)) = 6
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New York City is a popular field trip destination. This year the senior class at High School A and
the senior class at High School B both planned trips there. The senior class at High School A
rented and filled 2 vans and 6 buses with 244 students. High School B rented and filled 4 vans
and 7 buses with 298 students. Every van had the same number of students in it as did the buses.
Find the number of students in each van and in each bus.
There are eight students in each van and 38 students are in each bus.
What is the equation?The term "equation" refers to mathematical statements that have at least two terms with variables or integers that are equal.
Let the number of students fit into a van would be v
And the number of students fit into a bus would be b
School A:
2v + 6b = 244 ...(i)
2v = 244 - 6b
v = 122 - 3b
School B:
4v + 7b = 298 ...(ii)
Substitute the value of v = 122 - 3b in the equation (ii),
4(122 - 3b) + 7b = 298
Solve for b to get b = 38.
Substitute the value of b = 38 in equation (i),
2v + 6(38) = 244
2v + 228 = 244
2v = 16
v = 8
Therefore, eight students are in each van and 38 students are in each bus.
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Written as a percent, what is the probability of getting an odd number on a spinner with 5 equal parts numbered 1 to 5?A.20%B.40%C.60%D.80%
Given:
There are given that the spinner with 5 equal parts numbered 1 to 5.
Explanation:
In the given spinner, there are given the number: 1, 2, 3, 4, 5.
Now,
From all the given numbers, there are 3 odd numbers: 1, 3, and 5.
So,
From the probability:
[tex]P=\frac{Total\text{ number of odd numbers in the given spinner}}{Total\text{ numbers on the spinner}}[/tex]Then,
[tex]\begin{gathered} P=\frac{3}{5} \\ P=0.6 \end{gathered}[/tex]Now,
For the percentage:
[tex]\begin{gathered} P=0.6\times100\% \\ P=60\% \end{gathered}[/tex]Final answer:
Hence, the correct option is C.
The graph of f(x) is shown in black.Write an equation in terms of f(x) to match the redgraph.For example, try something like this:f(x)+3, f (x - 2), or 4f(x).
Notice that the red function is similar to the black function, which means the transformation applied was a translation.
The transformation is 5 units to the right, exactly.
Therefore, the function that represents the red figure is
[tex]f(x-5)[/tex]5. Jeannette has $5 and $10 bills in her wallet. The number of fives iseight more than five times the number of tens. Let t represent theNumber of tens. Write an expression for the number of fives.
The number of fives is eight more than five times the number of tens.
Therefore,
[tex]F=5\cdot T+8[/tex]where F represents the number of fives and T the number of tens
a store sells gift cards in preset amount. You can purchase gift cards for $20 or $30 . You spent $380 on gift cards. let x be the number of gift cards for $20 And let y be your gift cards for $30 . Write an equation in standards for to represent this situation
ANSWER= 20x+30y=380
but what ab this one
What are three combinations of gift cards you could have purchased?
The equation that represent the situation is as follows:
20x + 30y = 380The three combination of the gift cards you can purchase is as follows:
13 and 410 and 67 and 8How to represent equation in standard form?The store sells gift cards. One can purchase gift cards for $20 or $30 .
You spent $380 on gift cards. let x be the number of gift cards for $20 And let y be your gift cards for $30 .
The equation in standard form to represent the situation is as follows:
The standard form of a linear equation is A x + By = C. A, B, and C are
constants, while x and y are variables.
Therefore,
x = number of gift cards for 20 dollars
y = number of gift card for 30 dollars
Hence,
20x + 30y = 380
The three combination one could have purchased is as follows:
20(13) + 30(4) = 38020(10) + 30(6) = 38020(7) + 30(8) = 380learn more on equation here: https://brainly.com/question/7222455
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Graph the line with slope -2 passing through the point (3,5)
To graph the line, you need to know at least two points of it.
Knowing its slope and one point you can determine the equation of the line by using the point-slope form:
[tex]y-y_1=m(x-x_1_{})[/tex]Where
m is the slope of the line
(x₁,y₁) are the coordinates of one point of the line
For m=-2 and (x₁,y₁)=(3,5) the equation of the line is:
[tex]y-5=-2(x-3)[/tex]Next, replace the equation for any value of x and solve for y, for example, use x=2
[tex]y-5=-2(2-3)[/tex]-Solve the difference within the parentheses then the multiplication
[tex]\begin{gathered} y-5=-2(-1) \\ y-5=2 \end{gathered}[/tex]-Add 5 to both sides of the equation
[tex]\begin{gathered} y-5+5=2+5 \\ y=7 \end{gathered}[/tex]The coordinates for the second point are (2,7)
Plot both points and link them with a line
A restaurant offer 7 appetizers and 10 main courses.In how main ways can a person order a two-course meal
Take into account that there are 7 chices for the first course, and there are 10 choices for the entree.
The total number of choices is given bye:
total_choices = Choices_for_first_course x choices_fro_entree
Then, by replacing the values of the previous parameters you get:
total_choices = 7 x 10 = 70
There are 70 ways a person can order a two-course meal
1. what is the area of the board shown on the scale drawing? explain how you found the area.2. how can Adam use the scale factor to find the area of the actual electronics board? remember, he uses a different method than Jason.3. what is the area of the actual electronics board?
Answer:
1. 1800 square cm.
2. See below
3. 45000 square cm.
Explanation:
Part 1
The dimensions of the drawing are 36cm by 50cm.
[tex]\begin{gathered} \text{The area of the board}=36\times50 \\ =1800\operatorname{cm}^2 \end{gathered}[/tex]Part 2
Given a scale factor, k
If the area of the scale drawing is A; then we can find the area of the actual board by multiplying the area of the scale drawing by the square of k.
Part 3
[tex]\begin{gathered} \text{Area of the scale drawing}=1800\operatorname{cm}^2 \\ \text{Scale Factor,k=5} \end{gathered}[/tex]Therefore, the area of the actual drawing will be:
[tex]\begin{gathered} 1800\times5^2 \\ =45,000\operatorname{cm}^2 \end{gathered}[/tex]hello! i need help on this question and the (select) questions have the options of 1997 to 2006
To find the average rate of change, we use the following formula
[tex]r=\frac{f(b)-f(a)}{b-a}[/tex]Where a = 1998, f(a) = 856, b = 2001, and f(b) = 1591.
[tex]r=\frac{1591-856}{2001-1998}=\frac{735}{3}=245[/tex](a) The average rate of change between 1998 and 2001 is 245.We use the same formula between 2002 and 2006, where a = 2002, f(a) = 1483, b = 2006, and f(b) = 745.
[tex]r=\frac{745-1483}{2006-2002}=\frac{-738}{4}=-184.5[/tex](b) The average rate of change between 2002 and 2006 is -184.5.(c) As you can observe, the population was increasing from 1997 to 2001.(d) The population was decreasing from 2001 to 2006.ABCD is a rectangle. Find the length of AC and the measures of a and f.
SOLUTION
Consider the diagram
We need to obtain the value of length AC
Using the pythagoras rule, we have
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which expression is equivalent to 5^-2 x 5^5
Given the expression:
[tex]5^{-2}\ast5^5[/tex]To find the equivalent expression, let's simplify the expression using power rule.
[tex]a^m\ast a^n=a^{m+n}[/tex]Since they have the same base, we are to add the exponents.
We have:
[tex]5^{-2}\text{ }\ast5^5=5^{-2+5}=5^3[/tex]Therefore, the eqivalent expression is 5³
ANSWER:
[tex]5^3[/tex]We a
I need help part two and three of this question:A line passes through the following points: (6,3) and (2,9)1. Write the equation of the lineWhich I got y=-3/2 x+122. Write an equation of a line that is perpendicular to the original form. 3. Write the equation of a line that is parallel to the original form.
Part 2:
To determine an equation that is perpendicular to the line equation y = -3/2x + 12, get the negative reciprocal of the slope of the line equation.
[tex]\begin{gathered} \text{Given slope: }m=-\frac{3}{2} \\ \\ \text{The negative reciprocal is} \\ -\Big(-\frac{3}{2}\Big)^{-1}=\frac{2}{3} \\ \\ \text{We can now assume that any line in the form} \\ y=\frac{2}{3}x+b \\ \text{where }b\text{ is the y-intercept} \\ \text{is perpendicular to the line }y=-\frac{3}{2}x+12 \end{gathered}[/tex]Part 3:
An equation that is parallel to the line y = -3/2x + 12, is a line equation that will have the same slope as the original line.
Given that the slope of the line is m = -3/2, then any line equation in the form
[tex]\begin{gathered} y=-\frac{3}{2}x+b \\ \text{where} \\ b\text{ is the y-intercept} \end{gathered}[/tex]Substitute the given values into the given formula and alone the unknown variable if necessary round to one decimal place
c = 15
Explanation:The perimter, P = 37
The side lengths of the triangle are:
a = 10, b = 12, c = ?
The perimeter of the triangle is given by the formula:
P = a + b + c
Substitute a = 10, b = 12, and P = 37 into the formula P = a + b + c and solve for c
37 = 10 + 12 + c
37 = 22 + c
c = 37 - 22
c = 15
What is the average rate of change from f(-1) to f(1)?Type the numerical value for your answer as a whole number, decimal or fractionMake sure answers are completely simplified
The average rate of change of the function is the average rate at which one quantity is changing with respect to another.
Average rate of change = (y2 - y1)/(x2 - x1)
y represents the output values and it is also called f(x)
x represents the input values
For the given interval,
for f(- 1), x = -1 and f(x) = 8
For f(1), x = 1, f(x) = 4
Average rate of change = (4 - 8)/1 - - 1) = - 4/(1 + 1) = - 4/2
Average rate of change = - 2
A chemical company mixes pure water with their premium antifreeze solution to create an inexpensive antifreeze mixture. The premium antifreeze solution contains 65%pure antifreeze. The company wants to obtain 260 gallons of a mixture that contains 45% pure antifreeze. How many gallons of water and how many gallons of the premium antifreeze solution must be
Answer:
80 gallons of water
180 gallons of premium antifreeze solution.
Explanation:
Let's call X the number of gallons of water and Y the number of gallons of the premium antifreeze solution.
The company wants to obtain 260 gallons of the mixture, so our first equation is:
X + Y = 260
Additionally, the mixture should contain 45% of pure antifreeze and the premium antifreeze solution contains 65% pure antifreeze. So, our second equation is:
0.45(X + Y) = 0.65Y
Now, we need to solve the equations for X and Y. So, we can solve the second equation for X as:
[tex]\begin{gathered} 0.45(X+Y)=0.65Y \\ 0.45X+0.45Y=0.65Y \\ 0.45X=0.65Y-0.45Y \\ 0.45X=0.2Y \\ X=\frac{0.2Y}{0.45} \\ X=\frac{4}{9}Y \end{gathered}[/tex]Then, we can replace X by 4/9Y on the first equation and solve for Y as:
[tex]\begin{gathered} \frac{4}{9}Y+Y=260 \\ \frac{13Y}{9}=260 \\ 13Y=260\cdot9 \\ 13Y=2340 \\ Y=\frac{2340}{13} \\ Y=180 \end{gathered}[/tex]Finally, replacing Y by 180, we get that X is equal to:
[tex]\begin{gathered} X=\frac{4}{9}Y \\ X=\frac{4}{9}\cdot180 \\ X=80 \end{gathered}[/tex]Therefore, the solution should have 80 gallons of water and 180 gallons of premium antifreeze solution.
graph the line passing through (-6,1) whose slope is m= -6
As given by the question
There are given that the point (-6, 1) and slope (m) is -6.
Now,
To graph, the line, first, finds the equation of the line by using the given point and slope.
Then,
From the formula of point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]Where,
[tex]x_1=-6,y_1=1,\text{ and m=-6}[/tex]Then, put all given values into the above formula:
So,
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-1_{}=-6(x-(-6)_{}) \\ y-1=-6(x+6) \end{gathered}[/tex]Then,
[tex]\begin{gathered} y-1=-6(x+6) \\ y-1=-6x-36 \\ y-1+1=-6x-36+1 \\ y=-6x-35 \end{gathered}[/tex]Then, the graph of the above equation is shown below:
