Answer:
Step-by-step explanation:
-2y=2-3x-5y=10-5x
-2y=10-5x
2-3x-5y-5x
(SIMPLIFY)
5x-2y=10
2x-5y=8
(MULTIPLY BOTH SIDES)
-25x-10y=-50
4x-10y=16
(ELIMINATE ONE VARIABLE BY ADDING THE EQUATIONS)
-21x=-34
(DIVIDE BOTH SIDES)
X=34/21
(SUBSTITUTE THE VALUE OF X)
2x34/21-5y=8
(SOLVE EQUATION)
Y=-20/21
(A POSSIBLE SOLUTION IS)
(X,Y)=(34/21 , -20/21)
(CHECK THE SOLUTION)
-2x(-20/21)=2-3x 34/21 - 5x (-20/21)=10-5 X 34/21
(SIMPLIFY)
40/21=40/21=40/21
(X,Y)= (34/21 , -20/21)
(SOLUTION)
A cylindrical rod measures 8 inches long and the circumference of one of its bases is 8π inches. The rod is cut into two equally-sized pieces and then all surfaces are painted.
What is the area that is painted?
Use π≈3.14.
Enter your answer, rounded to the nearest tenth, in the box.
Answer:
128π in.² ≈ 402.1 in.²
Step-by-step explanation:
The rod can be cut into two equal sized pieces in different ways, so there are different answers to this question. I assume the question is asking when the rod's length is cut in half, so now there are two rods, each one being a cylinder with 4 inch height.
We need the area of the original rod and then add two more base areas.
C = 8π in.
r = 4 in.
total surface area = lateral area + 4 × area of base
SA = 8 in. × 8π in. + 4 × π × (4 in.)²
SA = 64π in.² + 64π in.²
SA = 128π in.² ≈ 402.1 in.²
Answer:
401.9
Step-by-step explanation:
I got this question wrong on my quiz
A local company manufactures custom truck parts for big rigs. The company's average profit can be modeled by a(p) = 60p-3p, where alp) is the average profit in dollars per p parts produced. What is a reasonable domain for this function?
A. 0 to 10 parts
B. 0 to 14 parts
C. 0 to 18 parts
D. 0 to 20 parts
The reasonable domain for the Funtion is 0 to 14 parts. So,the correct option is B.
This function's domain is the set of all potential input values for the variable p. Because the variable p reflects the number of components generated, it must be non-negative.
Because the function is defined for p is larger than or equal to 0, the domain includes all non-negative p values. Because the function is linear, it is defined for all non-negative real numbers; however, in this case, the company manufactures custom truck parts for big rigs.
Which means the company may have a limit on the number of parts it can produce; this limit is 14 parts, so the reasonable domain for this function is 0 to 14 parts.
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identify the type of data that would be used to describe a response (quantitative discrete, quantitative continuous, or qualitative). time in line to buy groceries
Time in Line to Buy Groceries is Quantitative-Discrete type of data. So the option C is correct.
We can observe data in a straightforward integer format or monitor quantitative discrete data in a real line at regular intervals.
We need to utilize an integer time point, which cannot be a decimal, to keep track of time while standing in line for groceries. It cannot be delivered in 2.45 days because a grocery store is unable to provide a delivery schedule in fractions.
The correct solution is therefore quantitative discrete.
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The complete question is:
Identify the type of data that would be used to describe a response.
Time in Line to Buy Groceries
A. Qualitative (Categorical)
B. Quantitative - Continuous
C. Quantitative - Discrete
is the tendency for extreme scores on one variable to be followed by, or accompany, less extreme scores on another. a. the extreme return effect b. regression to the mean c. the robust average effect d. extreme minimization
The majority of human physical, mental, and personality factors have a mean in the middle of the distribution, where there are also the most cases. For example, in baseball, the rookie of the year often has a poor second season.
Correct answer is b) regression to the mean.
Regression to the mean is the propensity of outcomes that are extreme by chance on the first measurement to move closer to the average when tested a second time. Results that are susceptible to regression to the mean are those that are vulnerable to some degree of chance. When exceptional scores are the result of chance or a fluke, it's improbable that those extreme scores will be obtained again.
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A rectangle pool is 11 feet wide and 12 feet long. The owner of the pool will create a rectangular walkway, 3 feet wide, around the pool. What is the area, in square feet, of the walkway?
The area of the walkway around swimming pool is 78 square feet.
The outer sides of the walkway will have a length of 12 feet and the breadth will be 11 feet.
The area of the pool along without the walkway will be 12 X 11 = 132 square feet.
The outer sides of the walkway will have a length of 15 feet and the breadth will be 14 feet after the owner create the walkway.
The area of the pool along with the walkway will be 15 X 14 = 210 square feet.
Therefore ,
area of the walkway will be:-
= 210 - 132
= 78 square feet.
so, the area of the walkway around swimming pool is 78 square feet.
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33. let a d 2 4 1 0 4 0 3 2 2 6 3 3 5 and b d 2 4 4 1 4 3 5 . denote the columns of a by a 1, a 2, a 3, and let w d span fa 1; a 2; a 3g. a. is b in fa 1; a 2; a 3g? how many vectors are in fa 1; a 2; a 3g? b. is b in w ? how many vectors are in w ? c. show that a 1 is in w . [hint: row operations are unneces-sary.]
a1 is a linear combination of w1, w2, and w3, and is thus a vector in w.
a. No, b is not in fa 1; a 2; a 3g. There are 3 vectors in fa 1; a 2; a 3g.
b. Yes, b is in w. There are 4 vectors in w.
c. To show that a1 is in w, we need to show that a1 is a combination of the vectors in w. We can do this by constructing a linear combination of the vectors in w that results in a1. In this case, we can take w1 = (2, 4, 1, 0), w2 = (4, 0, 3, 2), and w3 = (2, 6, 3, 3). Now we can set up a linear combination of these vectors, with coefficients c1, c2, and c3, to equal a1. Thus, we have: c1(2, 4, 1, 0) + c2(4, 0, 3, 2) + c3(2, 6, 3, 3) = (2, 0, 0, 0). Solving for c1, c2, and c3, we get c1 = 2, c2 = -2, and c3 = 0. Therefore, a1 is a linear combination of w1, w2, and w3, and is thus a vector in w.
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Express tan Y as a fraction in simplest terms.
what is the surface area
Answer:
518.4 cm²
Step-by-step explanation:
We have two triangles so
2 × (9×10/2) = 90
We have a base so
14 × 10 = 140
We have two other rectangles so
2 × 14 × 10.3 = 288.2
Now we add it all together
288.4 + 140 + 90 = 518.4
how many repetitions should be done for each exercise in the preparation drill? group of answer choices seven nine five three
Five repetitions should be done for each exercise in the preparation drill.
Preparation drills are an important part of any fitness routine, as they allow the muscles and joints to be prepared for the workout ahead. Doing the correct number of repetitions for each exercise in the preparation drill is key to getting the most out of the workout. Generally, five repetitions is recommended for each exercise. This should give the body just enough time to get used to the exercise while still providing enough of a challenge. Doing too many repetitions may lead to fatigue or overstretching, leading to injury. Doing too few repetitions may not be enough to prepare the body and prevent injury. Five repetitions is the ideal number for most preparation drills.
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Find the equation of the perpendicular bisector of AB where A and B are the points (3,6) and (-3,4) respectively. Also find its point of intersection with (i) x-axis and (ii) y-axis.
The point of intersection with x - axis is (5/3,0) and the point of intersection with y - axis is (0,5).
Any point on AB's perpendicular bisector, P(x,y), shall be considered. Then, PA = PB.
√(x-3)²+(y-6)² = √(x+3)²+(y-4)²
(x-3)²+(y-6)² = (x+3)²+(y-4)²
x² -6x+ 9 + y²- 12y + 36 = x² +6x+ 9 + y²- 8y + 16
12x + 4y -20 = 0
3x+ y-5 =0 ---(1)
Consequently, 3x+y-5=0 is the equation for the perpendicular bisector of AB.
We know that the coordinates of any point on x-axis are of the form (x,0). In other words, any point on the x-axis has a y-coordinate of zero. Thus, if we enter y = 0 in (1), we get
3x -5 = 0
x = 5/3
Thus, the x-axis is cut by the perpendicular bisector of AB at (5/3, 0).
(ii) Any point's y-axis coordinates have the following format: (0,y). When we enter x = 0 in (1), we obtain
y − 5 = 0
⇒ y = 5
Thus, the y-axis is where the perpendicular bisector of AB intersects (0,5).
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Mr Musk bought a £75000 car at the beginning of the year 2016.
Each year the value of the car decreased by 8%.
a) Calculate the value of the car at the beginning of the year 2020.
Give your answer correct to the nearest £100
Answer:
53700
Step-by-step explanation:
Depreciation of every year is 8%, 2016-2017-18-19-20 - 4 years
in the beginning of 2017 it'll be 0.92*75000
so it'll be (1-8%)^4 = 0.71639
multiply by 75000 = 53729. to the nearest 100 = 53700
Factor completely.
-3x² + 6x + 9 =
Answer:
-3(x - 3) (x + 1)
Step-by-step explanation:
Let's check
-3(x - 3) (x + 1)
(-3x + 9) (x + 1)
-3[tex]x^{2}[/tex] -3x + 9x + 9
-3[tex]x^{2}[/tex] + 6x + 9
Answer:
-3(x-3)(x+1)
Step-by-step explanation:
A common factor that all three numbers share is that they are divisible by 3, so we can factor 3 out. Typically, I take out the negative first:
-3([tex]x^2-2x-3[/tex]) (always remember to change signs!)
Now, we are left with [tex]x^2-2x-3[/tex], and to factor that out, we need to find two numbers that add up to -2 and multiply to -3. These two numbers will be 1 and -3, so we can write our factor like this:
(x-3)(x+1)
Let's add back in the -3 from earlier to complete our factoring:
-3(x-3)(x+1)
For the vectors u = (-4,-1) and v= (1,3), express u as the sum u=p+n, where p is parallel to v and n is orthogonal to v. + 7 21 33 11 u=p+n= 10 10 10 10 (Type integers or simplified fractions. List the terms in the same order as they appear in the original list.)
The vector u can be expressed as a sum of n and p when n= (-33/10, 11/10) and p= (-7/10, -21/10).
To find the vector p that is parallel to v, we need to project u onto v. We can use the formula for projection:
p = (u . v) / (||v||^2) * v
where . represents dot product and ||v|| represents the magnitude of v.
First, we need to find the dot product of u and v:
(-4,-1) . (1,3) = -4*1 + -1*3 = -4 + -3 = -7
Next, we need to find the magnitude of v:
||v|| = sqrt(1^2 + 3^2) = sqrt(1 + 9) = sqrt(10)
Then, we can plug these values into the projection formula:
p = (-7) / (sqrt(10))^2 * (1,3) = (-7/10) * (1,3) = (-7/10, -21/10)
So the vector p that is parallel to v is (-7/10, -21/10)
To find the vector n that is orthogonal to v, we can subtract p from u:
n = u - p = (-4,-1) - (-7/10, -21/10) = (-4 + 7/10, -1 + 21/10) = (-33/10, 11/10)
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a car dealership has 24 sedans and 18 sports coupes on its lot. what is the ratio of sedans to sports coupes on the lot? responses 2:3 2 colon 3 3:2 3 colon 2 3:4 3 colon 4 4:3
The ratio of sedans to sports coupes on the lot is 2:3, which can also be expressed as 3:2, 3:4, or 4:3. This means that there are two sedans for every three sports coupes, or three sedans for every two sports coupes, etc.
The ratio of sedans to sports coupes on the lot can be expressed as a fraction, which is the number of sedans divided by the number of sports coupes. In this case, there are 24 sedans and 18 sports coupes, which can be written as 24/18. This fraction can be simplified to 2/3, which is equivalent to the ratio 2:3. This ratio can also be expressed as 3:2, 3:4, or 4:3, which means that there are two sedans for every three sports coupes, three sedans for every two sports coupes, three sedans for every four sports coupes, or four sedans for every three sports coupes. In summary, the ratio of sedans to sports coupes on the lot is 2:3, which can also be expressed in several other ways.
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(Simple)......Classify the transformation pls
Find the distance between the two points.
Check the picture below.
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-3}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{3})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~2 - (-3)~~)^2 + (~~3 - (-2)~~)^2} \implies d=\sqrt{(2 +3)^2 + (3 +2)^2} \\\\\\ d=\sqrt{( 5 )^2 + ( 5 )^2} \implies d=\sqrt{ 25 + 25 } \implies d=\sqrt{ 50 }[/tex]
i need to explain how i got the answer also
The triangle proportionality theorem, used to evaluate the figures indicates that we get;
8. [tex]\overline{ST}[/tex] ║ [tex]\overline{PR}[/tex]
9. [tex]\overline{ST}[/tex] ║ [tex]\overline{PR}[/tex]
10. [tex]\overline{ST}[/tex] ∦ [tex]\overline{PR}[/tex]
11. x = 57.6
12. x = 27.3
13. x = 11
14. x = 10
15. x = 5
16. x = 17
What is the triangle proportionality theorem?The triangle proportionality theorem states that, in a triangle, a line drawn parallel to one of the sides of a triangle and intersects the other two sides at two different points, then the ratio in which the other two sides are divided by the line are the same.
8. The triangle proportionality theorem indicates, if [tex]\overline{ST}[/tex] and [tex]\overline{PR}[/tex] are parallel, [tex]\overline{ST}[/tex] ║ [tex]\overline{PR}[/tex], we get; QS/SP = QT/TR
QS/SP = 7/11.2 = 0.625
QT/TR = 10/16 = 0.625
Therefore, QS/SP = QT/TR = 0.625, [tex]\overline{ST}[/tex] and [tex]\overline{PR}[/tex] are parallel9. Where [tex]\overline{ST}[/tex] and [tex]\overline{PR}[/tex] are parallel, [tex]\overline{ST}[/tex] ║ [tex]\overline{PR}[/tex], we get;
PS/SQ = RT/TQ
PS = 102 - 45 = 57
PS/SQ = 57/45 = 1.2[tex]\overline{6}[/tex]
RT/TQ = 41.8/33 = 1.2[tex]\overline{6}[/tex]
PS/SQ = RT/TQ, therefore, [tex]\overline{ST}[/tex] is parallel to [tex]\overline{PR}[/tex]10. Where [tex]\overline{ST}[/tex] is parallel to [tex]\overline{PR}[/tex], we get;
QS/SP = QT/TR
QS/SP = 19/38 = 0.5
QT/TR = 24/52 = 6/13 ≠ 0.5
QS/SP ≠ QT/TR, therefore, [tex]\overline{ST}[/tex] ∦ [tex]\overline{PR}[/tex]11. The triangle proportionality theorem, indicates that we get;
48/25 = x/30
x/30 = 48/25
x = (48/25) × 30 = 57.6
12. Making use of the triangle triangle proportionality theorem, we get;
(49 - 28)/28 = x/36.4
x/36.4 = (49 - 28)/28
x = ((49 - 28)/28) × 36.4 = 27.3
x = 27.313. 32/60 = (2·x + 6)/52.5
(2·x + 6)/52.5 = 32/60
(2·x + 6) = (32/60) × 52.5 = 28
(2·x + 6) = 28
2·x = 28 - 6 = 22
x = 22/2 = 11
x = 1114. (x - 3)/21 = (x - 1)/27
27 × (x - 3)= 21 × (x - 1)
27·x - 27 × 3 = 21·x - 21
27·x - 21·x = -21 + 27 × 3 = 60
6·x = 60
x = 60/6 = 10
x = 1015. (7·x - 11)/(4·x - 2) = 20/(35 - 20)
(7·x - 11)/(4·x - 2) = 20/(35 - 20) = 20/15
(7·x - 11)/(4·x - 2) = 20/15
15 × (7·x - 11) = (4·x - 2) × 20
105·x - 165 = 80·x - 40
105·x - 80·x = 25·x = 165 - 40 = 125
25·x = 125
x = 125/25 = 5
x = 516. 35/(x - 3) = (x - 7)/4
35 × 4 = (x - 3) × (x - 7)
140 = x² - 10·x + 21
x² - 10·x + 21 - 140 = 0
x² - 10·x - 119 = 0
x² - 10·x - 7 × 17 = 0
x² + 7·x - 17·x - 17 × 7 = 0
x·(x + 7) - 17·(x + 7) = 0
(x + 7)·(x - 17) = 0
x = -7, or x = 17
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David took out a 20-year $70,000 loan from his bank in 2010. The quadratic equation that approximates the year/loan balance relationship is y = -98^2 - 1,531x + 69,718, where x is the number of years and y is the balance. In what year will his loan balance be $37,234?
A. 2022
B. 2023
C. 2024
D. 2025
his loan will be $37,234 in the year 2022.
What is a Quadratic equation?ax2+bx+c=0, with a not equal to 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.
Given, David took out a 20-year $70,000 loan from his bank in 2010.
The quadratic equation that approximates the year/loan balance relationship is y = -98*x^2 - 1,531x + 69,718,
where x is the number of years and
y is the balance
Since the Loan balance is given $37,234.
Thus to calculate the year
$37,234 = -98*x^2 - 1,531x + 69,718,
98 x² + 1534x - 32484 = 0
Comparing with the general form of the quadratic equation.
ax² + bx + c = 0
The discriminant b² - 4ac > 0 thus it has Two real roots.
using the Quadratic Formula
x = [tex]\frac{-b +- \sqrt{b^{2} - 4ac } }{2a}[/tex]
x = -27.62
and
x = 12
Thus year = 2010 + 12 = 2022
Therefore, In the year 2022, his loan will be $37,234.
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1. Provide an appropriate response.
Calculate the coefficient of determination, given that the linear correlation coefficient, r, is .845. What does this tell you about the explained variation and the unexplained variation of the data about the regression line?
2. Provide an appropriate response.
Calculate the coefficient of determination, given that the linear correlation coefficient, r, is 1. What does this tell you about the explained variation and the unexplained variation of the data about the regression line?
3. Provide an appropriate response.
Find the standard error of estimate, se, for the data below, given that = -2.5x.
x -1 -2 -3 -4
y 2 6 7 10
4. Provide an appropriate response.
The data below are the gestation periods, in months, of randomly selected animals and their corresponding life spans, in years. Find the standard error of estimate, se, given that y = 1.523x + 6.343
Gestation x -- 8, 2.1, 1.3, 1, 11.5, 5.3, 3.8, 24.3
Life Span y -- 30, 12, 6, 3, 25, 12, 20, 40
Answer: The coefficient of determination, r^2, is a measure of how well a linear regression model fits the data. It is calculated by squaring the linear correlation coefficient, r. In this case, r^2 = 0.845^2 = 0.7146. This tells us that 71.46% of the variation in the data is explained by the regression line, while 28.54% is unexplained.
The coefficient of determination, r^2, is a measure of how well a linear regression model fits the data. It is calculated by squaring the linear correlation coefficient, r. In this case, r^2 = 1^2 = 1. This tells us that 100% of the variation in the data is explained by the regression line, and 0% is unexplained.
The standard error of estimate (SEE) for a linear regression model is a measure of the average difference between the predicted values and the actual values. In this case, we can use the formula SEE = sqrt(SSE/n) where SSE is the sum of the squared differences between the predicted and actual values, and n is the number of observations. The given equation is y = -2.5x, so we can use this equation to find the predicted values and then calculate the SSE and SEE.
The standard error of estimate (SEE) for a linear regression model is a measure of the average difference between the predicted values and the actual values. In this case, we can use the formula SEE = sqrt(SSE/n) where SSE is the sum of the squared differences between the predicted and actual values, and n is the number of observations. The given equation is y = 1.523x + 6.343, so we can use this equation to find the predicted values and then calculate the SSE and SEE by using the given data.
would there be an ordered pair that is a sulution to both 4x + 3y < 12 and -x + 3y < = -3? explain
The ordered pair that is a solution of given two expressions is (3,0) .
What is Algebraic expression ?
Algebraic expression can be defined as the combination of variables and constants.
Given expressions,
4x + 3y < 12
-x + 3y < -3
First find where the 2 lines intersect
4x + 3y = 12
-x + 3y = -3
Subtract :
5x = 15
x = 3
and y = -3 + 3 / 3 = 0
So they intersect at the point (3,0).
Therefore , The ordered pair that is a solution of given two expressions is (3,0) .
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PLSS HELP
What is the radical form of each of the given expressions?
Drag the answer into the box to correctly match each expression.
Answer:
SEE ATTACHED
Step-by-step explanation:
Harper and Joe want to buy season passes for Disneyland but neither of them has the $1,300 needed to purchase a pass. Harper decides to get a job that pays $25 a week. She has nothing saved right now. Joe already has $80 and plans to save $15 of her weekly allowance.
a) When will they have the same amount of money saved up? How much money will they both have?
b) How long will it take each of them to save up for the season pass?
They needed a total of 8 weeks to save the same amount of money, and after 8 weeks, everyone would have $200.
What are mathematical operations?The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.
Given, Harper and Joe want to buy season passes for Disneyland but neither of them has the $1,300 needed to purchase a pass.
Since Harper decides to get a job that pays $25 a week. She has nothing saved right now. Joe already has $80 and plans to save $15 of her weekly allowance.
To save up for the season pass:
Harper needs = 1300$
Since, She earns 25$ a week
Harper needs total weeks = 1300/25
Harper needs total weeks = 52 weeks
joe also needs 1300 $
Since, joe already has $80 and plans to save $15 of her weekly allowance.
Joe needs total weeks = (1300 -80)/15
Joe needs total weeks = 81.33
To have the same amount of money saved up:
Let "x" be the weeks they required to save the equal money:
25 *x = 80 + 15*x
10*x = 80
x = 8
Everyone will have = 25 * 8
Everyone will have = 200$
Therefore, they required total of 8 weeks to have the same amount of money saved up and everyone will have 200$ after 8 weeks.
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find the surface area of a sphere with a diameter of 12 m.
A) 452.2 m
B) 150.7 m
C) 113.0 m
D) 904.3 m
Find the volume of a sphere with a redius of 4 ft.
A) 33.5 ft
B) 67.0 ft
C) 267.9 ft
D) 803.8 ft
Answer:
First question: 452.2
Second question: 267.9
Step-by-step explanation:
Not a hundred percent sure on second ques
Mr. Bernard needs to order boxes for his 18-inch diameter "Super Pizza. "
What is the approximate circumference of the Super Pizza? Use 3. 14 for π. Show your work.
What is the approximate area of the Super Pizza? Use 3. 14 for π. Show your work.
Please help and hurry!! Ty!!
The circumference of the Super Pizza is 56.52 inches and approximate area of the Super Pizza 253.34 inches2.
To calculate the circumference of the Super Pizza
Circumference = π x diameter
Circumference = 3.14 x 18
Circumference = 56.52 inches
To calculate the area of the Super Pizza
Area = π x radius2
Area = 3.14 x (18/2)2
Area = 3.14 x 81
Area = 253.34 inches2
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2 cups ofcoffee and 5 bottles of water cost $12
7 cups of coffe and 4 bottles of water cost $15
use c to represent the cost of a cup of coffe and w to represent the cost of a bottle of water
Answer:They use the process of photosynthesis to transform water, sunlight, and carbon dioxide into oxygen, and simple sugars that the plant uses as fuel. These primary producers form the base of an ecosystem and fuel the next trophic levels
Step-by-step explanation:
Please help I need the answers ASAP!
Answer:
Refer to the step-by-step
Step-by-step explanation:
Since ∠1 and ∠2 are alternate exterior angles, m∠2=108°
Find the value for the following determinant.
[ 2 3]
[ 1 4]
-5
5
11
Answer:
5
Step-by-step explanation:
(2x4)-(3x1)
=(8)-(3)
= 5
So its 5
if you have a logical statement in five variables how many rows do you need in the truth table that you would use to evaluate it?
32 rows are needed in the truth table that we would use to evaluate a logical statement in five variables
As per the given data:
If we have a logical statement in five variables then we have to determine how many rows we need in the truth table that you would use to evaluate it.
It is calculated by both from truth table and by using the formula.
A table with rows and columns is created for a compound statement, and the number of rows depends on the number of statements.
As we know that the formula for number of rows need in the truth table.
Number of rows = [tex]2^{n}[/tex]
Where n = Number of variables
Here given number of variables are 5.
n = 5
[tex]2^{n}[/tex] = [tex]2^{5}[/tex]
= 32
Therefore 32 rows are needed in the truth table.
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What kind of triangle is this please help me find the relationship and value please.
Answer: x=14°
Step-by-step explanation:
All angles of a triangle added together is 180°. So we can add the angles together.
7x-11+5x-2+2x-3=180 [combine like terms]
14x-16=180 [add both sides by 16]
14x=196 [divide both sides by 14]
x=14
Therefore, x=14°.
The ratio of the angle measures in a triangle is 1:2:3. What is the measure of the largest angle?
Answer:
Step-by-step explanation:
Let the 3 angles be x , 2x , and 3x
notice x:2x:3x = 1:2:3
we know x+2x+3x = 180
6x = 180
x = 30
so the largest angle is 3(30) or 90 degrees