Yes , it is possible to fit a table 9 feet wide through a rectangular doorway 4 feet by 8.
The Pythagorean theorem states, "In a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides." The sides of this triangle were called the perpendicular, the base, and the hypotenuse. Here, the hypotenuse is on the opposite side of the 90° angle, so it is the longest side. The sides of a right triangle (a, b, c, etc.) with positive integer squared values are put into the equation, also known as the Pythagorean triple. which is given by [tex]c^2=a^2+b^2[/tex] here “a” is the perpendicular, “b” is the base, “c” is the hypotenuse.A table with folded legs can pass through a rectangular door at an angle of 45°, forming a triangle to which the Pythagorean theorem can be applied.
Let the two sides of the door be the two sides of triangles a and b, then
[tex]c^2=4^2+8^2\\c^2=16+64\\c^2=80\\c=8.94[/tex]
Conclusion: Using the Pythagorean theorem, we know that an 8.94 foot table can pass through the door. And we know that 8.94 ≈ 9
Hence , a 9-feet table can pass through a rectangular door.
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i ready help please . .. . .. . . . . . . . .. . . . .. .. . .. . . . .
The solution to the given expression when evaluated would be expressed as: 3a + 4b³ - 5 = 3(6) + 4(2³) - 5 = 45.
How to Evaluate an Expression?To evaluate the expression, 3a + 4b³ - 5, when a = 6 and b = 2, substitute the values of a and b into the expression and solve.
Thus, we would have:
3a + 4b³ - 5 = 3(6) + 4(2³) - 5
Solve the exponent
3a + 4b³ - 5 = 3(6) + 4(8) - 5
3a + 4b³ - 5 = 18 + 32 - 5
Add
3a + 4b³ - 5 = 45
Therefore, the solution to the given expression when evaluated would be expressed as: 3a + 4b³ - 5 = 3(6) + 4(2³) - 5 = 45.
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han followed these instructions to make the image
can someone help me with this ?
Using function concepts, it is found that:
a) Point (3,-13) is not on the graph, because substituting x = 3 on the equation does not result in 13.
b) If x = 1, f(x) = -3, hence point (1,-3) is on the graph of f.
c) if f(x) = 2, x = 16, so point (16,2) is on the graph of f.
d) The domain is all real numbers except x = 4.
e) The x-intercept is of x = -8.
f) The y-intercept is of y = -2.
What are the points on the graph?The function is given by:
f(x) = (x + 8)/(x - 4).
Hence, when x = 3:
f(3) = (3 + 8)/(3 - 4) = 11/-1 = -11.
Hence:
Point (3,-13) is not on the graph, because substituting x = 3 on the equation does not result in 13.
When x = 1, we have that:
f(1) = (1 + 8)/(1 - 4) = 9/-3 = -3.
If x = 1, f(x) = -3, hence point (1,-3) is on the graph of f.
For f(x) = 2, we have that:
2 = (x + 8)/(x - 4)
2x - 8 = x + 8
x = 16.
Hence:
if f(x) = 2, x = 16, so point (16,2) is on the graph of f.
What is the domain of the function?The domain of a function is the set that contains all possible input values of the function.
This function is a fraction, meaning that the denominator cannot be zero, so:
x - 4 = 0 -> x = 4.
Hence:
The domain is all real numbers except x = 4.
What are the intercepts of the function?The x-intercept of a function is given by the value of x when f(x) = 0, that is, the value of x when the function crosses the x-axis.The y-intercept of a function is given by the value of f(x) when x = 0, that is, the value of y when the function crosses the y-axis.For this problem, we have that:
f(x) = 0.
(x + 8)/(x - 4) = 0.
x + 8 = 0
x = -8.
f(0) = 8/-4 = -2.
Hence:
e) The x-intercept is of x = -8.
f) The y-intercept is of y = -2.
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the second side of a triangular deck is 5 feet longer than the shortest side, and the third side is 5 feet shorter than twice the length of the shortest side. is the perimeter of the deck is 64 feet, what are the lengths of the three sides
The lengths of the three sides are 16 feet, 21 feet, and 27 feet
let the shortest side be x
then the second side would be x+ 5 feet
and the third side would be 2x- 5 feet
as we are provided with the parameter of the deck as 64 feet
Parameter = sum of all sides
64 = x + (x+5) + (2x-5)
64 = 4x
So, in order to find out the measurement of the sides of the triangular deck we need to solve this linear equation
64 = 4x
X = 64/4
X = 16 feet
Therefore, first side/ shortest side = x= 16 feet
Second side = x+5 = 16+5 = 21 feet
Third side = 2x-5= 2(16) -5 = 27feet
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ERROR ANALYSIS Describe and correct the error in interpreting the statement.
If a figure is a rectangle, then the figure has four sides. A trapezoid has four sides.
X
Using the Law of Detachment,
you can conclude that a trapezoid
is a rectangle.
Answer:
The fact points to the conclusion of the conditional.
Step-by-step explanation:
Law Of Detachment:
p -> q (if p is true, then q is true)
***You cannot go backwards. In other words, you cannot say that if q is true, then p is true, this is due to counterexamples.
Simplify the variable expression below as much as possible.
3x+ 2y+5-3
Answer here
PLEASE HELP
Answer:
3x+2y+2
Step-by-step explanation:
it's just combining like terms
what is m=x+n/p solve for m
x = p / (m + n) is factor of algebraic expression .
What does a math factor mean?
A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor in mathematics. As an illustration, 3 and 6 are factors of 12 because 12 3 = 4 and 12 6 = 2, respectively. 1, 2, 4, and 12 are the other components that make up 12.mx + nx = p
You can factor x out of the mx + nx.
x(m + n) = p
Now, simply divide by the m + n.
x = p / (m + n)
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Fadi set out at 5am on his bike averaging at 6mph. At 8am Chris goes out on his moped averaging 15mph. What time will Chris catch up with Fadi?
Since at 8am Chris goes out on his moped averaging 15mph, the time Chris catches up with Fadi is at 10 am.
How to find the time will Chris catch up with Fadi?Since Fadi set out at 5am on his bike averaging at 6mph, the distance Fadi travels is d = vt where
v = Fadi's speed = 6 mph and t = time.So, Fadi's distance d = vt
= 6t
Now, At 8am Chris goes out on his moped averaging 15mph, the distance Chris travels is D = v't' where
v = Chris' speed and t = Chris' time of travel.So, Chris' distance D = v't'
= 15t'
Also, since Fadl sets out at 5 am on his bike and Chris goes out on his moped at 8 am, Chris sets out 8 am - 5 am = 3 hrs later.
So, Chris' time of travel t' = t - 3
So, Chris' distance D = 15t' = 15(t - 3)
Now, Chris will catch up with Fadi when they both cover the same distance
So, d = D
6t = 15(t - 3)
6t = 15t - 45
6t - 15t = -45
-9t = -45
t = -45/-9
t = 5 hours
Since Chris's time is t' = t - 3, substituting t = 5 into the equation, we have
t' = 5 - 3
= 2 hours
So, Chris catches up with Fadi 2 hours later at 8 am + 2 hours = 10 am.
So, the time Chris catches up with Fadi is at 10 am.
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Gayle biked 2.82 miles on an exercise bike. Lola biked 3.5 times as far as Gayle.
How much farther did Lola bike than Gayle?
Enter your answer in the box.
miles
Answer:
9.87
Step-by-step explanation:
If Gayle only biked 2.82 miles and Lola biked 3.5 TIMES MORE MILES
then you multiply 2.82 by Lola's miles and you get 9.87
Ryan made a table to show how much blue and red paint he mixed to get the shade of purple he will use to paint the room. He wants to use the table to make larger and smaller batches of purple paint. What ratio was used to create this table? Support your answer
The ratio that was used to create this table is 4:1.
What does a math ratio mean?
An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls.In the top row, they are all even numbers, and in the bottom row, they are all odd numbers
They all simplify to 4:1
Based on the table given, the ratio will be:
= 12/3
= 4/1
= 4:1
The values in each row related to each other as in the top row, they are all even numbers, and in the bottom row, they are all odd numbers.
The values in each column related to each other as they've a ratio of 4:1.
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What is the answer to
Sec 30° cos 30
Answer:
sec 30° + cos 30°
Important trigonometric values
Calculation:
sec 30° + cos 30°
⇒ 2/√3 + √3/2
⇒ (4 + 3)/2 √3
⇒ 7√3/6
∴ 7√3/6
what is the process to answer this equation 6x ?= 6/7
Answer: x = 1/7, or around 0.14
Step-by-step explanation: In the equation 6x = 6/7, you have to divide both sides by 6 (as x is multiplied by 6). (6/7)/6 = (6/7) * (1/6), which equals 6/42, thus simplifying to 1/7.
Please help I’ll mark brainly
Hello,
[tex]\boxed{-4} - 3 = - 7[/tex]
Kara brought $23 with her when she went shopping. She spent $3.27 for lunch and $14.98 on a shirt. How much money does she have left? $
Answer:
$4.75
Step-by-step explanation:
The two items that Kara bought must be subtracted from the amount of money she had in the beginning; $23.00 − $3.27 − $14.98 = $4.75.
Answer:
after thinking about this thoroughly I've got the answer.
its $19.73
Step-by-step explanation:
23-3.27-14.98=4.75
So the answer is $4.75
how do you do this ill give 20 points!!!!!!!
The measure of the angle ∠ABC will be equal to the measure of the angle ∠DEF which is ∠ABC = ∠DEF.
What is an angle?The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.
The angles are given below.
∠ABC = ∠DEF ...1
∠GHI = ∠DEF ...2
From equations 1 and 2, then we have
∠ABC = ∠DEF
The measure of the angle ∠ABC will be equal to the measure of the angle ∠DEF which is ∠ABC = ∠DEF.
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A bakery sold 138 mocha cupcakes in a day, which was 46% of the total number of cupcakes sold that day. How many total cupcakes did the bakery sell that day?
Answer:
x=300
Step-by-step explanation:
138=46%x
x=300
hope this helps!
The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Required percentage value = a
total value = b
Percentage = a/b x 100
46% = 138
100% = 300
The total number of cupcakes sold on that day is 300.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Number of mocha cupcakes sold in a day = 138
The percentage of mocha cupcakes sold in a day = 46%
The percentage of total cupcakes sold in a day = 100%
Now,
46% = 138
Multiply 100/46.
100/46 x 46% = 100/46 x 138
100% = 300
Thus,
The total number of cupcakes sold on that day is 300.
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Determine whether each relation is a function. {(3, 2), (-1, 3), (5, 2)} and {(9, -1), (3, 6), (-2, 4), (3, 0)}
We can state that the given relations:
{(3, 2), (-1, 3), (5, 2)} is a function.
{(9, -1), (3, 6), (-2, 4), (3, 0)} is not a function.
What Makes a Relation a Function?A relation is a function if each of the x-values in the relation has exactly one corresponding y-value it is related to.
Given the relation with the ordered pairs, {(3, 2), (-1, 3), (5, 2)}, we can see that each x-value has exactly one y-value.
For the relation, {(9, -1), (3, 6), (-2, 4), (3, 0)}, we can observe that the x-value "3" has three corresponding y-values, "6, and 0", therefore, it is not function.
Therefore, we can state that the given relations:
{(3, 2), (-1, 3), (5, 2)} is a function.
{(9, -1), (3, 6), (-2, 4), (3, 0)} is not a function.
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(a[tex](a^6)^2a^7[/tex]
Answer: a(a^6)^2a^7 = [tex]a^{20}[/tex]
Step-by-step explanation:
Given data,
= a(a^6)^2a^7
We can write,
= [tex]a * (a^{6}^)^{2} * a^{7}[/tex]
Simplify using exponent power rule, [tex](a^{n} ) ^{m}[/tex] = [tex]a^{mn}[/tex]
So, we can write using formula,
= [tex]a * a^{6*2} * a^{7}[/tex]
= [tex]a * a^{12} * a^{7}[/tex]
Multiply the monomials,
We can use the formula, [tex]x^{a} * x^{b} * x^{c}[/tex] = [tex]x^{a+b+c}[/tex]
So, we can write,
= [tex]a^{1+12+7}[/tex]
= [tex]a^{20}[/tex]
Therefore,
a(a^6)^2a^7 = [tex]a^{20}[/tex]
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A Mathematical fest was conducted in a school by a group of students. School's principal gave them the budget of ₹32000. They spend 1/4 of the budget on food stalls; 3/10 of the remainder on games and activities and 5/21 of the remainder on gift distribution event. How much money is still left with them?
The amount of money left with them is $12,800.
How much money is left?The first step is to determine the amount left after 1/4 of the budget is spent on food stalls.
Budget left : (1 - 1/4) x amount of budget
(1 - 1/4) x 32,000
3/4 x 32,000 = 24,000
The second step is to determine how much of the budget is left after spending on games and activities :
(1 - 3/10) x 24,000
7/10 x 24,000 = 16,800
The third step is to determine how much is left after spending the remainder on gift distribution
(1 - 5/21) x 16,800
16/21 x 16,800 = $12,800
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Which of the following represents an EFFICIENT point of production?
A. Point B
b. Point A
c. Point D
d. None
The EFFICIENT points of production in the given graph is represented by Point C and Point B , the correct option is option (d).
The given graph is for skateboards vs Bikes .
We need to find the point representing the Efficient Point of Production.
The Production Possibility Curve points are said to be Efficient when the resources are utilized to the fullest , that means the points on the curve represents the point of Efficiency.
In the given Production Possibility Curve between Skateboards and Bikers the point C and Point B are the Efficient point of production .
Therefore , the Efficient points of production in the given curve are represented by Point C and Point B , the correct option is option (d)
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How do I solve for this?
dy/dx =yx(x + 3)
Answer:
[tex]{ \tt{ \frac{dy}{dx} = yx( x + 3)}} \\ \\ { \tt{ \frac{dy}{y} = \frac{x(x + 3) \: dx}{1} }} \\ \\ { \tt{ \int \frac{dy}{y} = \int( {x}^{2} + 3x) \: dx }} \\ \\ { \tt{ ln(y) = \frac{ {x}^{3} }{3} + \frac{ {3x}^{2} }{2} + c }} \\ \\ [/tex]
graph the solution to this inequality on the number line. w -0.8 > -2.4 first select the correct ray. then select the location of the endpoint to plot the inequality on the number line.
Answer:
Step-by-step explanation:
The solution to the inequality is
Inequality
Inequalities are used to represent expressions of unequal values
The inequality is given as:
Add 0.9 to both sides of the inequality
Simplify the inequality
The above inequality means that:
The arrow on the number line points to the right
The arrow begins at point -1.2 with an open circle or dotted lines
calculate the slope between the two points (2, -7) and (2, 7).
A. zero
B. undefined
C. -4
D. 10
How do you write 75.9 in scientific notation?
Answer:
7.59*10^1
Step-by-step explanation:
write the number as a decimal - 75.9
make it a new number thats somewhere between 1&10 by moving the decimal place - 7.59
define the power of 10 -10^1
put them all together! - 7.59*10^1
Can any of you help me with this?
The ski team needs new uniforms. The students plan to sell plush toy lions (the school mascot) for $5 each. The students find three companies on-line that sell stuffed mascots. Company A sells 16 lions for $45.60. Company B sells 18 lions for 50.76. Company C charges $34.44 for 12 lions. Which company has the best buy?
In linear equation , The company which has the best buy is company C, they sell 1 lion for $2.77 (highest selling price among the three companies.
What in mathematics is a linear equation?
A linear equation is an algebraic equation with the formula y=mx+b, according to Wolfram MathWorld. m is the slope, and b is the y-intercept, and all that is involved is a constant and a first-order (linear) term. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."Company A = 16 lions for $45.60
Price per lion = $45.60 / 16
= $2.85
Company B = 18 lions for $50.76
Price per lion = $50.76 / 18 eagles
= $2.82
Company C = $34.44 for 12 lion
Price per lion = $34.44 / 12 lion
= $2.87
The company which has the best buy is company C, they sell 1 lion for $2.87 (highest selling price among the three companies)
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Estimate each product 75÷7
Answer:
10.7142857143
Step-by-step explanation:
Answer:
10.71428
10.71
About 10.7
What is the answer 1/3 of x is 14
The required answer for 1/3 of x is 14 is x = 42.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equal sign = .
Now the given equation is,
1/3 of x is 14
Thus converting it into numerical expression.
So we have,
1/3 of x = 1/3 * x= x/3
Thus is equal to 14
Thus, the equation we get is,
x/3 = 14
To solve the above isolate x on one side and other terms to another.
Thus multiplying whole equation by 3 we get,
3*x/3 = 14*3
Simplifying we get,
x = 42
This is the required answer for the given expression.
Thus, the required answer for 1/3 of x is 14 is x = 42.
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11. Find the measure of ABC. Show your work.
b(n)=−4−2(n−1)
What's the 12th term in the sequence?
The 12th term in the sequence is -26.
Given,
B (n) = -4 – 2(n – 1)
We have to find the 12th term in the sequence:
To find the nth term in an arithmetic sequence:
An arithmetic sequence's nth term is determined by the formula a = a + (n - 1)d. The common difference, or d, is the difference between any two consecutive terms in an arithmetic series; it can be calculated by deducting any pair of terms starting with a and an+1.
Here,
First term, a = -4
Common difference, d = -2
nth term = 12
Now, let’s find 12th term
B(n) = -4 -2(n – 1)
B(12) = -4 – 2(12 – 1)
B(12) = -4 -2(11)
B(12) = -4 -22
B(12) = -26
That is, the 12th term in the sequence is -26.
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F(B-g3)=2 solve for b
Solving for B gives B = 2/ F + g³
What is subject of formula?
Subject of formula can be defined as the variable that is expressed in terms of other variables in an equation or expression.
Given the equation;
F(B-g³)=2
To make 'B' the subject of formula, we have to take the following steps
Divide both sides by F, we have;
F(B-g³) / F = 2/ F
we then have;
B - g³ = 2/F
Now, make 'B' the subject of formula by making all the other terms over the equality sign
We have;
B = 2/ F + g³
Thus, solving for B gives B = 2/ F + g³
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