After calculating the diagonal of the doorway to be approximately 8.944 feet using the Pythagorean theorem, it's clear that the 10-foot square piece of plywood will not fit diagonally through the door. Thus, the correct answer is option (A).
The question is whether a 10-foot square piece of plywood can fit through an 8-foot by 4-foot doorway when tilted diagonally. To determine if the plywood can fit, we need to calculate the diagonal of the doorway using the Pythagorean theorem which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be expressed as c² = a² + b² where c is the hypotenuse, and a and b are the other two sides.
Let's apply the theorem to our doorway:
Height (a) = 8 feet
Width (b) = 4 feet
Diagonal (c) = ?
We calculate the diagonal:
c² = a² + b²
c² = 8² + 4²
c² = 64 + 16
c² = 80
c = sqrt(80)
c = 8.944 feet (approx)
The diagonal of the doorway is approximately 8.944 feet, which is less than the 10 feet length of the plywood. Therefore, the correct answer is:
No, because the length of the diagonal is close to 9 feet.
The option (A) is correct.
At a store, 2 gallons of milk cost $6. Which is the value of the ratio of dollars to gallons of milk?
Answer:
3:1 or 3/1
Step-by-step explanation:
We have the next information:
Gallons of Milk Cost
2 ⇒ $6
dividing both quantities by two, we get the price for a single gallon of milk:
Gallons of Milk Cost
1 ⇒ $3
We are asked for the ratio of dollars to gallons of milk (the order is important since dollars go first than gallons) so we will have the following:
dollars:gallons or dollars/gallons
and since $3 dollars pay for 1 gallon of milk, the ratio is:
3:1 or 3/1
What is the area of the region completely bounded by the curve y=-x^2+x+6?
To find the area of the region completely bounded by the curve y=-x^2+x+6, you can integrate the equation with respect to x and evaluate it between the x-values where the curve intersects the x-axis. By solving the quadratic equation -x^2+x+6=0, you can determine the x-values. Then, evaluate the definite integral between these x-values to find the area.
Explanation:The area of the region completely bounded by the curve y=-x^2+x+6 can be found by integrating the equation with respect to x and evaluating it between the appropriate bounds. The integral of the given equation is ∫(-x^2+x+6) dx. To find the area, we need to find the definite integral between the x-values where the curve intersects the x-axis. First, set the equation equal to zero and solve for x:
-x^2+x+6=0
This quadratic equation can be factored as: (x-2)(x+3). Therefore, the curve intersects the x-axis at x=2 and x=-3.
By evaluating the definite integral between x=-3 and x=2, we can find the area of the region:
Area = ∫-32 (-x^2+x+6) dx
Integrating this equation will give you the area of the region bounded by the curve y=-x^2+x+6.
The expression 4 square root of 81^3 can be rewritten as_____.
A. 81^3/4
B.81^4/3
C. 81^12
D. 81^1/12
Answer:
81^1/12
HAVE A GREAT DAY
The expression ''4 square root of 81³'' can be rewritten as,
⇒ [tex]81^{\frac{3}{4} }[/tex]
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression to write is,
⇒ 4 square root of 81³
Now, It can be written as;
⇒ 4 square root of 81³
⇒ [tex]\sqrt[4]{81^{3} }[/tex]
By rule of exponent we get;
⇒ [tex]81^{\frac{3}{4} }[/tex]
Thus, The expression ''4 square root of 81³'' can be rewritten as,
⇒ [tex]81^{\frac{3}{4} }[/tex]
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One bundle contains 500 $20 bills. what would be the total value of 44 bundles
How to find where the tangent line is horizontal?
Final answer:
To determine where the tangent line to a function is horizontal, find the derivative of the function, set it equal to zero, and solve for 'x'. This value of 'x' is where the slope is zero, indicating a horizontal tangent line.
Explanation:
How to Find Where the Tangent Line is Horizontal
To find where the tangent line to a curve is horizontal, you need to determine where the slope of the tangent (which is the derivative of the function) is zero. This involves calculating the derivative of the given function and solving for the value of 'x' where this derivative equals zero.
For example, if we have a function y = 4x - x², we first find its derivative: dy/dx = 4 - 2x. Setting this derivative equal to zero gives us 4 - 2x = 0. Solving for x gives us x = 2. This is the value of x where the tangent line is horizontal.
If we are given a graph, like in a velocity-time graph, a horizontal tangent indicates a moment where the velocity is zero, signifying a change in direction of the particle. At such points, we can see that the slope of the tangent line is zero, meaning it is a horizontal tangent.
The variable is Z is inversely proportional to X. When X is 6, Z has the value 0.5. What is the value of Z when X = 10
using the formula C=2TTr, find the circumference of a circle with a diameter of 28 in. round your answer to the nearest inch
A. 56in
B. 28 in
C. 44in
D.88in
radius = diameter/2
so 28/2=14
using 3.14 for PI
2*3.14*14 = 87.92 = 88 inches
What is the equation of the line that is parallel to y=-2/3x+4 and that passes through (–2,–2)?
Answers
-
-
-
y=-2/3x-4/3
y=-2/3x-10/3
y=-2/3x-2/3
y=-2/3x-17/4
The equation of the line parallel to y=-2/3x+4 and passing through (-2, -2) is y = -2/3x - 10/3.
Explanation:To find the equation of a line parallel to y = -2/3x + 4 and passing through the point (-2, -2), we need to use the fact that parallel lines have the same slope. The given equation has a slope of -2/3, so the parallel line will also have a slope of -2/3. Using the point-slope form of a line, we can write the equation as:
y - y1 = m(x - x1)
where (x1, y1) is the given point and m is the slope. Plugging in the values, we have:
y - (-2) = -2/3(x - (-2))
Simplifying the equation, we get:
y - (-2) = -2/3(x + 2)
y + 2 = -2/3x - 4/3
y = -2/3x - 4/3 - 2
y = -2/3x - 4/3 - 6/3
y = -2/3x - 10/3
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Assume a plane is flying directly north at 200 mph, but there is a wind blowing west at 23 mph. Part I: Express both the velocity of the plane and the velocity of the wind as vectors, using proper notation to represent each direction of motion. Part II: What is the velocity vector of the plane? Part III: What is the ground speed of the plane?
The velocity of the plane is 200 mph due north and the velocity of the wind is 23 mph due west. The velocity vector of the plane is 200 mph due north minus 23 mph due west. The ground speed of the plane can be found using the Pythagorean theorem.
Explanation:Part I: The velocity of the plane can be represented as 200 mph due north, and the velocity of the wind can be represented as 23 mph due west.
Part II: To find the velocity vector of the plane, we subtract the velocity of the wind from the velocity of the plane. The resultant velocity vector of the plane is 200 mph due north minus 23 mph due west.
Part III: The ground speed of the plane is the magnitude of the resultant velocity vector of the plane. We can calculate it using the Pythagorean theorem: ground speed = square root of (200^2 + 23^2).
The circumference of a circle is 19πinches. find the radius.c=2πr
What is a rule for the total cost of the tickets ? Give the rule in words and as a algebraic expression
What is the arc length of a circle that has a 6-inch radius and a central angle that is 65 degrees? Use 3. 14 for pi and round your answer to the nearest hundredth
Find the equation of the quadratic function with zeros 10 and 14 and vertex at (12, -8).
A fence is to be installed around a rectangular field. the field's perimeter is 204204 feet. find the dimensions of the field if the length of the field is 8 feet more than the width.
The solution is, the dimensions of the field if the length of the field is 8 feet more than the width is:
width = 51,047
length = 51,055
What is perimeter?A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimeter has several practical applications.
Here, we have,
given that,
A fence is to be installed around a rectangular field.
the field's perimeter is 204204 feet.
now, we have,
204204 - 16 = 204188
we get,
204188 / 4 = 51,047
so, we get,
width = 51,047
length = 51,055
Hence, The solution is, the dimensions of the field if the length of the field is 8 feet more than the width is:
width = 51,047
length = 51,055
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What's 9080 each number in expanded notation
Expand (2x-3y)^4 using Pascal's Triangle. Show work
Answer:
16x^4 - 96x^3y + 216x^2y^2 - 216xy^3 + 81y^4
Step-by-step explanation:
(2x - 3y)^4
Fifth line on a Pascal Triangle
1, 4, 6 4, 1
(1) 2x^4
2^4 = 16
2x^4 = 16x^4
16x^4
(4) 2x^3 (-3y)^1
2^3 = 8
-3^1 = -3
8 times -3 times 4 = -96
-96x^3y
(6) 2x^2 (-3y)^2
2^2 = 4
-3^2 = 9
4 times 9 times 6 = 216
216x^2y^2
(4) 2x^1 (-3y)^3
2^1 = 2
-3^3 = -27
2 times - 27 times 4 = -216
-216xy^3
(1) (-3y)^4
-3^4 = 81
81y^4
16x^4 - 96x^3y + 216x^2y^2 - 216xy^3 + 81y^4
Law of sines:
Triangle ABC has measures a = 2, b = 2, and m∠A = 30°. What is the measure of angle B?
15°
30°
45°
60°
Answer: Second option is correct.
Step-by-step explanation:
Since we have given that
ΔABC has measures a=2, b=2, m∠A=30⁰
As we know the "Law of sines " i.e.
[tex]\frac{a}{\sin A}=\frac{b}{\sin B}\\[/tex]
so, we put the given values in above formula:
[tex]\frac{2}{\sin 30\textdegree}=\frac{2}{\sin B}\\\\\implies \sin 30\textdegree=\sin B\\\\\implies B=30\textdegreee[/tex]
Hence, Second option is correct.
Two dice are rolled. Are the events, “rolling doubles” and “rolling an even sum”, mutually exclusive? Justify your response.
There are 8 students lined up at the classroom door. What is the probability that Laura and Kimiko will end up next to each other if the students arrange themselves blindfolded?
A polynomial function, f(x), with rational coefficients has roots of –2 and square root of 3. The irrational conjugates theorem states that which of the following must also be a root of the function?
Answer:
Step-by-step explanation:
option b
Given a polynomial with rational coefficients, if √3 is a root, its irrational conjugate -√3 must also be a root due to the Irrational Conjugates Theorem, ensuring that the polynomial maintains rational coefficients.
Explanation:The subject of this question is a polynomial function with rational coefficients, which is encountered in mathematics, particularly in algebra. When a polynomial has rational coefficients and one of its roots is an irrational number, such as the square root of 3 (√3), the Irrational Conjugates Theorem states that its conjugate, in this case, the negative square root of 3 (-√3), must also be a root of the polynomial. Therefore, the polynomial function in question must include both √3 and -√3 as roots to have rational coefficients.
Given that the function already has -2 as a root, we know that (x + 2) is a factor of the polynomial. Additionally, because √3 is a root, the factors (x - √3) and (x + √3) will also be part of the polynomial. To find the roots of a quadratic equation or higher-order polynomials, one can set the function equal to zero and solve for x, either by factoring, applying the quadratic formula, or other algebraic methods.
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Alex has been serving 2/3 cup of lemonade to each student. If he has 1 1/3 cups of lemonade left, how many students can still get lemonade?
Question 2 options:
1
2
3
0
Is it possible for a line segment to have more than one bisector?
Yes, it is possible to have more than one bisector in a line segment.
Bisector is a line that divides a line or an angle in to two equivalent parts. There are two types of Bisectors based on what geometrical shape it bisects.
Bisector of a Line Angle BisectorIn general 'to bisect' something means to cut it into two equal parts. The bisector is the one that doing the cutting process.
With a line bisector, we cut a line segment into two equal parts with another line - the bisector. Just imagine the line PQ is being cut into two equal lengths (PF and FQ) by the bisector line AB.
Whenever AB intersects at a right angle, it is called the "perpendicular bisector" of PQ. If it crosses at any other angle it is simply called a bisector. Drag the points A or B and see both types.
For obvious reasons, the point F is called the midpoint of the line PQ,
Graph the ellipse with equation x squared divided by twenty five plus y squared divided by four = 1.
What equation is solved by the graphed systems of equations? Two linear equations that intersect at the point negative 1, negative 4.
To solve this problem, we have to manually solve for the value of x for each choices or equations. The correct equation will give a value of -1 since the linear equations intersects at point (-1, -4).
1st: 7x + 3 = x + 3
7x – x = 3 – 3
6x = 0
x = 0 (FALSE)
2nd: 7x − 3 = x – 3
7x – x = 3 – 3
6x = 0
x = 0 (FALSE)
3rd: 7x + 3 = x − 3
7x – x = - 3 – 3
6x = -6
x = -1 (TRUE)
4th: 7x − 3 = x + 3
7x – x = 3 + 3
6x = 6
x = 1 (FALSE)
Therefore the answer is:
7x + 3 = x − 3
In this exercise, we are going to solve using our knowledge of systems and in this way we will find that the equation that satisfies the points.
As we know that the equation that will satisfy will have to have the values of X=-1, we will solve each one of the alternatives as:
First equation is:[tex]7x + 3 = x + 3\\6x = 0\\x = 0[/tex]
We realize that the value of x is not what we want so it doesn't satisfy us.
second equation is:[tex]7x - 3 = x - 3\\7x- x = 3- 3\\6x = 0\\x = 0[/tex]
We realize that the value of x is not what we want so it doesn't satisfy us.
third equation is:
[tex]7x + 3 = x − 3\\6x = -6\\x = -1[/tex]
fourth equation is:[tex]7x − 3 = x + 3\\7x – x = 3 + 3\\6x = 6\\x = 1[/tex]
We realize that the value of x is not what we want so it doesn't satisfy us.
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John translated parallelogram ABCD using the rule (x,y)→(x+3, y−2). If angle A is 110° and angle B is 70°, what is the degree measurement of angle A'?
Answer:
The correct answer is B. 110.
Help? @texaschic101
Parabola and its vertex
Which phrases can be used to represent the inequality mr024-1.jpg? Check all that apply. The product of 6.5 and the sum of a number and 1.5 is no more than 21. The sum of 1.5 and the product of 6.5 and a number is no greater than 21. The product of 6.5 and a number, when increased by 1.5, is below 21. The product of 6.5 and the sum of a number and 1.5 is at minimum 21. The sum of 1.5 and the product of 6.5 and a number is at least 21. The product of 6.5 and a number, when increased by 1.5, is at most 21.
Answer:
b and c
Step-by-step explanation:
2020 edge assignment
On a floor plan drawn at a scale of 1:100, the area of a rectangular room is 30
c. what is the actual area of the room?
2x-5y=-6; 2x-7y=-14
Solve by factoring and list only the positive solution: 2x2 - 5x = 88
A jar of 57 coins contains only dimes and quarters. The value of all the coins in the jar is $10.05. How many dimes are in the jar?
The dimes are 28 dimes
what is Algebra?Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions.
Given:
total coins = 57
So,
D + Q = 57
D= 57 - Q....(1)
0.10D + 0.25 Q = 10.05
Using (1), we get
0.10(57 - Q) + 0.25Q= 10.05
5.7 - 0.10Q + 0.25Q = 10.05
0.15Q = 4.35
Q= 29
So, dimes = 57- 29= 28 dimes
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