Answer:
The approximate remaining grass area is 144 square feet.
Explanation:
To find the area of the rectangular yard, we use the formula:
Area of rectangle [tex]= \text{length} \times \text{width} \)[/tex]
Given that the length is 20 feet and the width is 8 feet, we have:
Area of Rectangle [tex]= 20 \times 8 = 160 \text{ square feet} \)[/tex]
Next, we find the area of the equilateral triangle. Since we know the length of each side (5 feet) and an equilateral triangle can be divided into two congruent 30-60-90 triangles, we can use the formula for the area of an equilateral triangle:
Area of equilateral triangle [tex]= \frac{\sqrt{3}}{4} \times (\text{side length})^2 \)[/tex]
Plugging in the value of the side length (5 feet), we get:
Area of equilateral triangle [tex]= \frac{\sqrt{3}}{4} \times (5)^2 \)[/tex]
Area of equilateral triangle [tex]= \frac{\sqrt{3}}{4} \times 25 \)[/tex]
Area of equilateral triangle [tex]= \frac{25\sqrt{3}}{4} \text{ square feet} \)[/tex]
Now, to find the remaining grass area after Pythagoras digs up the rose-bed section, we subtract the area of the equilateral triangle from the total area of the rectangle:
Remaining grass area [tex]= \text{Area of rectangle} - \text{Area of equilateral triangle} \)[/tex]
Remaining grass area [tex]= \ 160 - \frac{25\sqrt{3}}{4} \)[/tex]
Using a calculator, we find:
Remaining grass area [tex]\approx 144.3 \text{ square feet} \)[/tex]
Rounded to the nearest foot, the approximate remaining grass area is 144 square feet.
(05.01)
Which statement best explains if the graph correctly represents the proportional relationship y = −2x?
No, the points shown would not be part of y = −2x
No, proportions cannot be represented on a graph
Yes, all proportions can be shown on a graph of this line
Yes, the points shown on the line would be part of y = −2x
The best statement which is true for the graph y=-2x is that Yes, the points shown on the line would be a part of y=-2x.
What is line?A line is collection of various points on a surface which together joins two points on a surface. Equation of a line looks like y=a +b x where b is the slope of line.
How to make graph?We have been given an equation y=-2x and we have to find the graph of equation and for that we need to find points and for this we have to put the values of x which gives the values of y.
At x=0 ,y=0
At x=1 ,y=-2*1=-2
At x=2 ,y=-2*2=-4
At x=-1 ,y=-2*-1=2
Coordinates will be (0,0),(1,-2),(2,-4),(-1,2)
If we find these points on this line then will surely be able to find these points.
Hence the statement which is true is that Yes, the points shown on the line would be part of y = −2x.
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A cube has side lengths of 8 inches. What is the volume of the cube
the ratio of boys to girls are 8 to 7. if there was a total of 195 students, how many boys and girls are there?
The population of snakes at a wildlife park over the course of six months is modeled by the equation y = x5 − 5x4 + 2x3 − 10x2 + 100x + 5, where x is the number of months. If the park officials count 505 snakes, how many months have passed since the initial count was taken?
What are the two equations that need to be solved to find the solutions for the absolute value equation |2x-3|=x+6?
2x – 3 = x + 6 and 2x – 3 = –x – 6
2x – 3 = x + 6 and 2x + 3 = –x + 6
2x – 3 = x + 6 and 2x – 3 = x – 6
2x – 3 = x + 6 and 2x + 3 = x + 6
The equations to solve for [tex]\( |2x-3|=x+6 \)[/tex] are [tex]\( 2x - 3 = x + 6 \)[/tex] and [tex]\( 2x - 3 = -(x + 6) \).[/tex]
Let's solve the absolute value equation |2x-3|=x+6 step by step.
We'll start by writing down the equation:
|2x - 3| = x + 6
Since the absolute value expression |2x - 3| can be either positive or negative, we'll split the equation into two cases:
Case 1: 2x - 3 = x + 6
Case 2: 2x - 3 = -(x + 6)
Let's solve Case 1:
2x - 3 = x + 6
Subtract x from both sides:
2x - x - 3 = 6
Simplify:
x - 3 = 6
Add 3 to both sides:
x = 9
Now, let's solve Case 2:
2x - 3 = -(x + 6)
Distribute the negative sign:
2x - 3 = -x - 6
Add x to both sides:
2x + x - 3 = -6
Simplify:
3x - 3 = -6
Add 3 to both sides:
3x = -3
Divide both sides by 3:
x = -1
So, the solutions to the equation |2x-3|=x+6 are x = 9 and x = -1.
Which best explains if quadrilateral WXYZ can be a parallelogram?
WXYZ can be a parallelogram with one pair of sides measuring 15 mm and the other pair measuring 9 mm.
WXYZ can be a parallelogram with one pair of sides measuring 15 mm and the other pair measuring 7 mm.
WXYZ cannot be a parallelogram because there are three different values for x when each expression is set equal to 15.
WXYZ cannot be a parallelogram because the value of x that makes one pair of sides congruent does not make the other pair of sides congruent.
If quadrilateral WXYZ is a parallelogram, the opposite sides will be equal, in length from which the value of x will satisfy the two equations.
Response:
WXYZ can be a parallelogram with one pair of sides measuring 15 mm and the other pair measuring 9 mm.How can the option that best indicates if WXYZ can be a parallelogram be obtained?Properties of a parallelogram
The length of the opposite sides of a parallelogram are equal, which gives;
2·x - 5 = x + 2
2·x - x = 2 + 5
x = 7Similarly, we have;
x + 8 = 15
x = 15 - 8 = 7
The lengths of the opposite sides are therefore;
2·x - 5 = 2 × 7 - 5 = 9 and x + 8 = 15
The option that indicates if WXYZ is a parallelogram is therefore;
WXYZ can be a parallelogram with one pair of sides measuring 15 mm and the other pair measuring 9 mm.Learn more about parallelograms here;
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A piece of rope 94.2 inches long will enclose a circular child’s wading pool. What is the diameter of the pool?
Identify the factors of x2 − 4x − 12. (1 point)
(x + 4)(x − 3)
(x − 4)(x + 3)
(x − 2)(x + 6)
(x + 2)(x − 6)
Answer:
D. [tex](x-6)(x+2)[/tex]
Step-by-step explanation:
We have been given a polynomial [tex]x^2-4x-12[/tex]. We are asked to find the factors of our given polynomial.
We will use splitting the middle term format of factoring quadratic polynomial.
We need two numbers, whose product is [tex]-12[/tex] and whose sum is [tex]-4[/tex]. Such two numbers are [tex]-6\text{ and }2[/tex].
[tex]x^2-6x+2x-12[/tex]
[tex](x^2-6x)+(2x-12)[/tex]
Factor out GCF of each group:
[tex]x(x-6)+2(x-6)[/tex]
[tex](x-6)(x+2)[/tex]
Therefore, factors of our given expression are [tex](x-6)(x+2)[/tex] and option D is the correct choice.
What is the quotient and remainder when x2 + x − 12 is divided by x − 2?
The population of a local species of beetle can be found using an infinite geometric series a1=960 and the common ratio is .25 write the sum in sigma notation and calculate the sum of possible that will be the upper limit of this population
Sigma 960 (1/4)^i-1 ; the sum is 1280
Signa 960 (1/4)^-1 the sun is divergent
Sigma 960 (1/4)^i sum is 1280
Sigma (1/4)^i sum is divergent
I=1 for them all
The answer is:
Sigma 960 (1/4)^i-1 ; the sum is 1280
Step-by-step explanation:We are given the first term of the geometric sequence as:
[tex]a_1=960[/tex]
Also, the common ratio of the terms in geometric sequence is: [tex]\dfrac{1}{4}[/tex]
We know that if the series is a geometric series than the sum of the terms is given by:
[tex]a+ar+ar^2+.....\\\\=a(1+r+r^2+....)\\\\=\sum ar^{n-1}[/tex]
where a is the first term of the series and r is the common difference.
Here a=960
and r=1/4
Hence,
The sum of the series is:
[tex]=\sum 960(\dfrac{1}{4})^{i-1}[/tex]
Now we know that the sum of the infinite geometric series is given by:
[tex]S=\dfrac{a}{1-r}[/tex]
where S is the sum of the series.
Hence, here the sum of the series is calculated by:
[tex]S=\dfrac{960}{1-\dfrac{1}{4}}\\\\\\S=\dfrac{960}{\dfrac{3}{4}}\\\\\\S=\dfrac{960\times 4}{3}\\\\\\S=1280[/tex]
Hence, the sum is: 1280
what is .00463 in fraction form
Can anyone help!? Points are high!
total was 49.10
mileage would be 49.10 = 2.10x +5.00
total miles =
49.10 = 2.10 +5.00
44.10 = 2.10x
x = 44.10/2.10 = 21 miles
The sine function is an odd function
Answer:
The given statement is true.
Step-by-step explanation:
We have been given a statement and we are supposed to determine whether our given statement is even or odd.
Statement: The sine function is an odd function.
We know that sine is symmetric about origin and [tex]\text{sin}(-x)=-\text{sin}(x)[/tex]. Therefore, sine is an odd function and our given statement is true.
Assume that you randomly select 6 cards from a deck of 52. what is the probability that all of the cards selected are hearts?
Which of the relationship below are function
A functions B and D are valid functions because they meet the criteria of each x value having only one corresponding y value.
Function B: You mentioned that B is a function because each x value has only one corresponding y value. In mathematical terms, a function is defined as a relation between a set of inputs (x values) and a set of outputs (y values), where each input (x) maps to exactly one output (y). So, if B satisfies this definition, it is indeed a function.
Function D: Similar to B, if D also adheres to the definition of a function, where each x value corresponds to only one y value, then it is a function as well.
Function A: You mentioned that for A, the x value of 1 has 2 y values. In mathematical terms, a function cannot have one input (x) mapping to multiple outputs (y). If this is the case for A, it does not meet the definition of a function.
Function C: You mentioned that for C, the x value of 7 has 2 y values, 10 and 3. Again, if one input (x) is associated with multiple outputs (y) in C, it does not qualify as a function.
In summary, functions B and D are valid functions because they meet the criteria of each x value having only one corresponding y value. Functions A and C do not meet this criterion and are not functions in the mathematical sense.
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The value of m in the following system of equations is:
m-2n=8
n=m-2
A) m= -4
B) m= -6
C) m= 2
D) None of the choices are correct
The correct option is A. [tex]m=-4[/tex]. By substituting the second equation into the first one in the system of equations, the value of m is -4.
The value of m in the system of equations can be found by substitution or elimination. Starting with the given equations:
[tex]m - 2n = 8 (1)[/tex]
[tex]n = m - 2 (2)[/tex]
Using the second equation (2) to substitute for n in the first equation (1):
[tex]m - 2(m - 2) = 8[/tex]
[tex]m - 2m + 4 = 8[/tex]
[tex]-m + 4 = 8[/tex]
[tex]-m = 8 - 4[/tex]
[tex]-m = 4[/tex]
[tex]m = -4[/tex]
This means that the value of m is -4, which corresponds to option A.
A 7.5 kg block is placed on a table. If it's bottom surface area is 0.6m2, how much pressure does the block exert on the tabletop?
Final answer:
The pressure exerted by a 7.5 kg block on a tabletop is calculated as the force due to its weight divided by the surface area. This results in a pressure of 122.5 Pascals (Pa).
Explanation:
The pressure exerted by an object on a surface is calculated by dividing the force it applies, which is its weight (a result of gravity), by the area over which the force is distributed. In this case, to find the pressure exerted by a 7.5 kg block on a tabletop with a bottom surface area of 0.6m2, we use the formula for pressure (P), which is P = Force (F) / Area (A).
To calculate the force, we need to know that the weight of the block is the product of its mass (m) and the acceleration due to gravity (g), where g is approximately 9.8 m/s2. So, the weight (F) is:
F = m × g = 7.5 kg × 9.8 m/s2 = 73.5 N
To calculate pressure (P), we then divide the force by the area:
P = F / A = 73.5 N / 0.6 m2 = 122.5 Pa
Therefore, the pressure exerted by the block on the tabletop is 122.5 Pascals (Pa).
Which number is irrational, an integer, and a real number?
A)there are no such numbers
B) 0
C) sq root of 4
D) -4/2
Answer:
Option A is the correct answer.
Step-by-step explanation:
An Irrational Number is a real number that cannot be written as a simple fraction. All the integers can be written as a simple fraction. So an integer is not an Irrational Number. So there is no number is irrational, an integer, and a real number.
Option A is the correct answer.
the question is.......... ASAP
Find the volume of the cylinder shown. Use 3.14 for pi. Round your answer to the nearest hundredth.
Answer: Volume of cylinder is 1846.32 cubic yd.
Step-by-step explanation:
Since we have given that
Height of a cylinder = 12 yard
Radius of a cylinder = 7 yard
As we know the formula of "Volume of cylinder":
[tex]Volume=\pi r^2h\\\\Volume=3.14\times 7\times 7\times 12\\\\Volume=1846.32\ yd^3[/tex]
Hence, Volume of cylinder is 1846.32 cubic yd.
Answer:
1846.32 cubic yards
Step-by-step explanation:
In triangle ABC, m∠A=55 triangle ABC, m∠A=55°, c=11c=11, and m∠B=19m∠B=19°. Find the perimeter of the triangle
Ten children are to be divided into an a team and a b team of 5 each. the a team will play in one league and the b team in another. how many different divisions are possible?
ILL GIVE BRAINLIEST !!!1 A student writes an incorrect step while checking if the sum of the measures of the two remote interior angles of triangle ABC below is equal to the measure of the exterior angle.
Step 1: m∠x + m∠y + m∠z = 180 degrees (sum of angles of a triangle)
Step 2: m∠w − m∠z = 90 degrees (corresponding angles)
Step 3: Therefore, m∠x + m∠y + m∠z = m∠w + m∠z
Step 4: So, m∠x + m∠y = m∠w
In which step did the student first make a mistake and how can it be corrected?
Step 1; it should be m∠x + m∠y + m∠z = 180 degrees (sum of corresponding angles)
Step 2; it should be m∠w + m∠z = 180 degrees (supplementary angles)
Step 1; it should be m∠x + m∠y + m∠z = 90 degrees (corresponding angles)
Step 2; it should be m∠w + m∠z = 90 degrees (alternate exterior angle)
A person purchased a leather jacket that was marked down by 40%. if the sale price of the jacket was $101.79, what was its original price?
What is 180 as product of prime factors and 180 as a Square root?
Find the congruence transformation that maps ∆ABC to ∆A’B’C’. Explain your reasoning
P(A∩B)=1150,P(A|B)=1120,P(B)=?
For the given probabilities P(A∩B) = 1150 and P(A|B) = 1120, using Bayes' theorem for conditional probability, the probability of event B, P(B), is found to be approximately 1.027.
Explanation:The topic of this question is probability, specifically concurrent events in probability theory. Here, we use Bayes' theorem for conditional probability which states that P(A|B) = P(A ∩ B) / P(B).
Given that P(A∩B) = 1150 and P(A|B) = 1120, we can plug these values into the formula to find P(B). Hence, P(B) = P(A ∩ B) / P(A|B), substituting the given numbers, we get P(B) = 1150 / 1120 = 1.027 approximately.
So P(B), the probability of event B occurring, we would expect to be approximately 1.027 (or 102.7% assuming the probabilities were in decimal form to start with).
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Alright, let's solve the problem with these given values.
The formula for calculating the probability of B in the context of A and B both happening is:
`P(A and B) / P(A|B)`.
In this case, the probability of A and B occurring is 1150, while the likelihood of A given that B has occurred is 1120. We can substitute these values into the formula:
So, P(B) = P(A and B) / P(A|B)
Substitute the given into the formula:
P(B) = 1150 / 1120 = 1.0267857142857142
Therefore, the Probability of event B (P(B)) is approximately 1.027 when rounded to three decimal places.
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What is the slope of the line whose equation is 3x-5y=10?
You make both rocking chairs and bar stools. You charge $100 for every rocking chair and $40 for every bar stool. Which expression represents your income if you sell r rocking chairs and b bar stools?
Answer:
The answer is [tex]Income=100*r+40*b[/tex]
Step-by-step explanation:
In this case we have to construct an expression that describe the income of selling the rocking chairs ($100 each - r) and the bar stool ($40 each - b), so the total income will depend on the addition of this two variables multiplied by its individual price, this is:
[tex]Income=100*r+40*b[/tex]
The answer is [tex]Income=100*r+40*b[/tex]
Please help!!! Geometry.