What is the area of the kitchen floor in this floor plan?
A-24 sq meters
B-28 sq meters
C-35 sq meters
D-42 sq meters
Answer: The correct option is (C) 35 sq. meters.
Step-by-step explanation: We are given to find the area of the kitchen floor in the floor plan shown in the figure.
From the figure, we see that
the kitchen is in the form of a rectangle with length 7 meters and breadth 5 meters.
We know that
the area of a rectangle with length l units and breadth b units is given by
[tex]A=l\times b.[/tex]
For the rectangular kitchen, we have
length, l = 7 meters
and
breadth, b = 5 meters.
Therefore, the area of the kitchen floor in the floor plan is given by
[tex]A=l\times b=7\times 5=35~\textup{sq. meters}.[/tex]
Thus, option (C) is CORRECT.
What is the solution of the system of equations?
-3x-4y-3z=-7
2x-6y+2z=3
5x-2y+5z=9
Answer:
Given equations have no solution
Step-by-step explanation:
Given -
Three set of equations -
[tex]-3x-4y-3z=-7\\2x-6y+2z=3\\5x-2y+5z=9[/tex]
We will now equate "x" in the first equation in terms of "y" and "Z" and put it in second equation -
[tex]-3x-4y-3z=-7\\x = \frac{1}{3} (-4y -3z+7)\\\frac{2}{3}(-4y -3z+7) -6y+2z=3\\-8.667 y = -1.667\\y = 0.192\\[/tex]
We will substitute the value of y in the under given equation-
[tex]x = \frac{1}{3} (-4y -3z+7)\\x = \frac{1}{3} (-4*0.192 -3z+7)\\x= 2.077-z[/tex]
substituting the derived values in last equation, we get -
[tex]5x-2y+5z=9\\5(2.077-z)-2(0.192)+5z=9\\10.385-5z-0.384+5z=9\\0=-1[/tex]
Hence, the given equations have no solution
What is the equation of the line that is parallel to the line 5x+2y=12 and passes through the point (-2, 4)?
The equation of the line parallel to [tex]\(5x + 2y = 12\)[/tex] and passing through the point (-2, 4) is given as [tex]\(y = -\frac{5}{2}x - 1\).[/tex]
To find the equation of a line parallel to [tex]\(5x + 2y = 12\)[/tex] and passing through the point (-2, 4), we need to follow these steps:
1. Convert the given equation[tex]\(5x + 2y = 12\)[/tex] into slope-intercept form [tex]\(y = mx + b\).[/tex]
2. Determine the slope of the given line.
3. Use the slope and the given point to find the equation of the parallel line using the point-slope form.
4. Convert the equation into slope-intercept form if needed.
Let's start with step 1:
1. Convert [tex]\(5x + 2y = 12\)[/tex] into slope-intercept form [tex]\(y = mx + b\):[/tex]
Subtract [tex]\(5x\)[/tex] from both sides:
[tex]\[2y = -5x + 12\][/tex]
Divide both sides by 2:
[tex]\[y = -\frac{5}{2}x + 6\][/tex]
Now, we know that the slope of the given line is [tex]\(-\frac{5}{2}\)[/tex] . Since the line we're looking for is parallel to this line, it will have the same slope.
2. The slope [tex](\(m\))[/tex] of the parallel line is [tex]\(-\frac{5}{2}\).[/tex]
Next, we use the point-slope form[tex]\(y - y_1 = m(x - x_1)\),[/tex]where [tex]\((x_1, y_1)\)[/tex] is the given point (-2, 4) and [tex]\(m\)[/tex] is the slope.
3. Substitute the values into the point-slope form:
[tex]\[y - 4 = -\frac{5}{2}(x - (-2))\][/tex]
[tex]\[y - 4 = -\frac{5}{2}(x + 2)\][/tex]
Now, distribute[tex]\(-\frac{5}{2}\):[/tex]
[tex]\[y - 4 = -\frac{5}{2}x - 5\][/tex]
4. Convert to slope-intercept form:
Add 4 to both sides:
[tex]\[y = -\frac{5}{2}x - 5 + 4\][/tex]
[tex]\[y = -\frac{5}{2}x - 1\][/tex]
So, the equation of the line parallel to [tex]\(5x + 2y = 12\)[/tex] and passing through the point (-2, 4) is [tex]\(y = -\frac{5}{2}x - 1\).[/tex]
Complete question:
What is the equation of the line that is parallel to the line 5x+2y=12 and passes through the point (-2, 4)?
Brainly use a matrix to find the solution to the system of equations -8x-8y=-16 6x-9y=-108
sam is paid $50 per room that he paints and he can paint a room in exactly 2 hours. on sunday sam hopes to make at least $150 painting rooms and can work for exactly 12 hours. which of the following sets represents the range of rooms(r) that sam can paint without violating either his monetary or time restriction?
A. r={3,6}
B. r={6,10}
C. r={3,5}
D. r={3,10}
the answer would be A because 3 rooms would equal 150 and that would only take 6 hours to complete.
original cost: 1.25; Markup %:80
You have 120 pieces of fabric to make a blanket. Each piece of fabric is a square with a side length of 6 inches. you can use as many pieces of fabric as possible to create a square blanket. What is the area of the blanket? How many pieces of fabric or left over. How many more pieces of fabric what you need to increase the size of the blanket
Multiply or divide as indicated 10x^5/2x^2
The expression [tex]10x^5/2x^2[/tex] simplifies to [tex]5x^3[/tex] by dividing the coefficients (10/2) to get 5 and subtracting the exponents (5 - 2) in [tex]x^5[/tex] and[tex]x^2[/tex]to get 3.
Explanation:To solve the given expression, [tex]10x^5/2x^2[/tex], you would first divide the coefficients and then deal with the bases (x) separately.
The coefficients (numbers without variables), 10 and 2, divide to give you: 10/2 = 5.
For the part that includes x, [tex]x^5/x^2[/tex], you subtract the lower exponent from the higher exponent because when you divide powers with the same base you subtract the exponents. So 5 - 2 = 3.
Thus, the final answer is: [tex]5x^3[/tex].
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5. 7x + 2 + 4y Identify the terms
I'm sorry... I'm a dumb person and these confuse me the most
What is 997,000 rounded to the nearest 10 thousand?
The following data show the number of questions different students of a class could answer in a quiz competition:
2, 4, 2, 5, 1, 4, 5, 7, 3, 5, 6, 2, 2, 5, 5, 5, 4, 6
The dot plot below was made to represent the data.
For which number is the data plotted incorrectly?
2 3 4 5
Answer:
Number 4 plot incorrectly represent on dot plot.
C is correct
Step-by-step explanation:
The following data show the number of questions different students of a class could answer in a quiz competition:
2, 4, 2, 5, 1, 4, 5, 7, 3, 5, 6, 2, 2, 5, 5, 5, 4, 6
We are given the dot plot of the data set.
Data : 1 2 3 4 5 6 7
Frequency : 1 4 1 3 6 2 1
We need to choose which data number plot incorrectly.
For 2: Number of dot should be 4, In graph also 4, 4=4 (True)
For 3: Number of dot should be 1, In graph also 1, 1=1 (True)
For 4: Number of dot should be 3, In graph also 2, 3≠2 (False)
For 5: Number of dot should be 6, In graph also 6, 6=6 (True)
Hence, number 4 plot incorrectly
1. Mrs.vega brought a new aquarium for her turtles. How much space will the turtles have in the aquarium if the length is 3.2 ft, the width is 1.5 ft and the height is 27 ft?
2. What is the volume of a cylinder that has a radius of 6 inches and height of 8 inches?
Convert into mixed number 81/3 and -29/2
81/3 is 27
-29/2 is -14.5
Which are the solutions of the quadratic equation? x2 = –5x – 3 –5, 0 5, 0
The solutions of the quadratic equation x² = -5x - 3 are [tex]\( x = \frac{-5 - \sqrt{13}}{2} \)[/tex] and [tex]\( x = \frac{-5 + \sqrt{13}}{2} \)[/tex].
To find the solutions of the quadratic equation x² = -5x - 3, first we rearrange it to the standard form:
x² + 5x + 3 = 0
We solve this using the quadratic formula, which is given by:
x = [tex]\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
For our equation, a = 1, b = 5, and c = 3. Substituting these values in, we get:
x = [tex]\frac{-5 \pm \sqrt{5^2 - 4*1*3}}{2*1}[/tex]
x =[tex]\frac{-5 \pm \sqrt{25 - 12}}{2}\\[/tex]
x =[tex]\frac{-5 \pm \sqrt{13}}{2}[/tex]
Hence, the solutions are:
x = [tex]\frac{-5 - \sqrt{13}}{2}[/tex] and x = [tex]\frac{-5 + \sqrt{13}}{2}[/tex]
Complete question: Which are the solutions of the quadratic equation? x² = -5x - 3
-5, 0[tex]\frac{-5 - \sqrt{13}}{2}[/tex], [tex]\frac{-5 + \sqrt{13}}{2}[/tex][tex]\frac{5 - \sqrt{13}}{2}[/tex], [tex]\frac{5 + \sqrt{13}}{2}[/tex]5,02 questions
4. Each small square is 1 in². Which estimate best describes the area of this figure? (first image)
a. 10 in²
b. 15 in²
c. 20 in²
d. 35 in²
5. Which estimate best describes the area under the curve in square units? (second image)
a. 20 units²
b. 25 units²
c. 35 units²
d. 40 units²
Answer: here are the correct answers for the k12 test. Have a great day!!!
Step-by-step explanation:
1/4 (4r - 8) = r - 2
TWO EASY QUESTIONS 8TH GRADE MATH
9. Complete the missing steps in the paragraph proof of Theorem 3-8.
11. Solve for the value of x in the triangle shown below. Show your work! (1 point for equation, 1 point for answer)
The transitive property of equality states that:
if a = b, then b = a
if a = b, then ac = bc
if a = b and b = c, then a = c
if a = b and c = c, then a + b = b + c
Answer: The correct option is
(C) if a = b and b = c, then a = c.
Step-by-step explanation: We are given to select the correct statement for the transitive property of equality.
We know that
if x, y and z are three real numbers, then the transitive property of equality states that
if x = y and y = z, then x = z.
So, for reals a, b and c, the property states that
if a = b and b = c, then a = c.
Option (C) is CORRECT.
Is (2,5) a solution of y=3x-10?
No, (2,5) is not a solution of y = 3x-10
What is equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that, an equation y = 3x-10, we need to check whether (2,5) is solution of the give equation or not,
For that put x = 2 in 3x-10 and check whether it equals to 5 or not, if not then (2,5) is not a solution of the equation,
= 3×2-10
= 6-10
= -4
∵ -4 ≠ 5
Hence, No, (2,5) is not a solution of y = 3x-10
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What is the area of a circle with a diameter of 12.6 in.?
Use 3.14 for pi and round your final answer to the nearest hundredth
suppose you planted 3 trees around the north and west sides of one of the houses worth $100,000 on the map. You have increased he property value of the house by $10,000. In addition, the owner will save an average of$50 per year in heating costs. Assuming that the homeowner lives in the house for another 20 years, what is the total dollar value of the trees to the homeowner and the community?
The total dollar value of the trees to the homeowner and the community will be $11,000.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
PEMDAS rule means the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
Suppose you planted 3 trees around the north and west sides of one of the houses worth $100,000 on the map. You have increased the property value of the house by $10,000. In addition, the owner will save an average of$50 per year in heating costs.
Assuming that the homeowner lives in the house for another 20 years.
Then the total dollar value of the trees to the homeowner and the community will be
⇒ 10,000 + 50 x 20
⇒ 10,000 + 1,000
⇒ $11,000
The total dollar value of the trees to the homeowner and the community will be $11,000.
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Use the Remainder Theorem to determine if [tex]x-2[/tex] is a factor of the polynomial [tex]f(x)=3x^5-7x^3-11x^2+2[/tex].
Solve for x.
x+8-3=19
x is 14.
Do the problem backwards.
19 - 8 + 3 = x
11 + 4 = x
14 = x
Which mathematical symbol would best fill in the blank to compare the two real numbers?
square root of 7 blank 14 over 5
<
>
=
≈
Answer: The correct option is (A) < .
Step-by-step explanation: We are given to select the correct mathematical symbol that would best fill in the blank to compare the following two real numbers :
[tex]\sqrt7~~~?~~~\dfrac{14}{5}.[/tex]
First , we need to find the values of both the real numbers in decimal form.
We have
[tex]\sqrt7=2.64575...,\\\\\dfrac{14}{5}=2.8.[/tex]
Since, [tex]2.64575<2.8,[/tex] so we get
[tex]\sqrt7<\dfrac{14}{5}.[/tex]
Thus, the correct mathematical symbol is <.
Option (A) is CORRECT.
A scale model of a merry-go-round and the actual merry-go-round are similar.
a. How many times greater is the base area of the actual merry-go-round than the base area of the scale model? Explain. The ratio of the corresponding lengths is : 1. So, the ratio of the areas is : 1 and the base area of the actual merry-go-round is times greater than the base area of the scale model.
b. What is the base area of the actual merry-go-round in square feet? The base area of the actual merry-go-round is square feet.
The base area of the actual merry-go-round is the same as the model due to the 1:1 scale. Without further information, the actual base area of the merry-go round cannot be calculated.
Explanation:To understand this, we need to know a key principle of scale models. In a scale model, when the ratio of the lengths is 1:n, the ratio of the areas is square of that, or 1:n2. Hence, if the scale of models is 1:1 as given, the base area of the actual merry-go-round is equal to the base area of the scale model, meaning the ratio is also 1:1.
For part b, without the specific measurements of the base area of the scale model or the scale used, it is impossible to calculate the base area of the actual merry-go-round in square feet. We need one or the other to make this calculation.
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The base area of the actual merry-go-round is 16 times greater than the base area of the scale model. The base area of the actual merry-go-round in square feet can be calculated using the base area of the scale model.
Explanation:The base area of the actual merry-go-round is 16 times greater than the base area of the scale model. This is because the ratio of the corresponding lengths is 1:4, so the ratio of the areas is 1:16.
To find the base area of the actual merry-go-round in square feet, you will need to know the base area of the scale model in square feet. If you provide the base area of the scale model, I can help you calculate the base area of the actual merry-go-round.
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My number has nine digits it is evenly divisible by 100 the value of one of the digits is 700,000 the digit in the millions place is both even and prime the digit in the hundreds place is the temperature at which water freezes the digit in the ten millions place is triple the number in the millions place the digit in the thousands place is the number of fluid ounces in a cup the digit in the hundred millions place is a special number because it is a factor of every number.
*PLEASE HELP* BRAINLIEST* A 10% discount is offered on a certain item that sells for $10.95. How much is the discount and what is the discounted sales price?
Amount of discount =
Discounted sales price =
The amount of discount is $1.095 and the discounted sales price is $9.855.
We need to calculate the amount of discount and then subtract it from the original sales price to find the discounted sales price.
First, we calculate the amount of discount. A 10% discount on an item selling for $10.95 means we need to find 10% of $10.95. To find 10% of a number, we can multiply the number by 0.10 (which is the decimal equivalent of 10%).
Amount of discount = 10% of $10.95
= 0.10 [tex]\times[/tex] $10.95
= $1.095
Now that we have the amount of discount, we can calculate the discounted sales price by subtracting the discount from the original sales price.
Discounted sales price = Original sales price - Amount of discount
= $10.95 - $1.095
= $9.855
What are the missing parts that correctly complete the proof?
The missing parts of the question is required.
The blanks are
2 Definition of bisector
3 Definition of perpendicular
4 [tex]\angle AXP=\angle AXQ[/tex]
6 SAS congruence postulate
7 Corresponding parts of congruent triangles
In the given figure.
Line AX is a perpendicular bisector of PQ.
This means [tex]PX\cong QX[/tex]
[tex]\angle AXP=\angle AXQ=90^{\circ}[/tex]
[tex]AX\cong AX[/tex] because it is the same side.
[tex]\triangle AXP\cong \triangle AXQ[/tex] because of the above three points SAS congruence.
[tex]AP\cong AQ[/tex] because they are corresponding parts of congruent triangles
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Find an equation of a line whose graph intersects the graph of the parabola y=x^2 at (a) two points, (b) one point, and (c) no point.
Martin drew a pair of perpendicular lines and a pair of parallel lines.which of these statements best compares the pairs of perpendicular and parallel lines?