The answer is D) If one angle is a right angle, then the frame must be rectangular,
What is angle?An angle is a measure of the amount of rotation between two lines or planes. It is measured in degrees or radians. Angles are formed by the intersection of two lines, called the sides of the angle, and a point, called the vertex of the angle. There are different types of angles such as acute angle, right angle, obtuse angle, and straight angle.
What is rectangle?A rectangle is a four-sided polygon with four right angles. It has opposite sides that are parallel and congruent, and the opposite angles are also congruent. A rectangle can be defined by its length and width or by the coordinates of its vertices. Rectangles are a special case of parallelograms, which have opposite sides parallel but not necessarily congruent. The special properties of rectangles make them a popular shape in design and construction, such as in building and engineering.
A rectangle is defined as a four-sided polygon with four right angles. Opposite sides of a rectangle are congruent, but adjacent sides may or may not be congruent. Therefore, A and B are not sufficient to prove that the frame is a rectangle. Also, two adjacent angles being supplementary does not guarantee that the frame is a rectangle. The only way to be sure that the frame is a rectangle is if it has one right angle, this is the only way to ensure that all angles are right angles. Therefore, D) is the correct answer.
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A triangle ha two ide of length 7 and 17. What i the mallet poible whole-number length for the third ide?
According to triangle inequality theorem a triangle with two sides 7 units and 17 units, has a third side which measures 10 units.
What is Triangle Inequality Theorem?
According to triangle inequality theorem, the sum of the lengths of any two sides of a triangle is greater than the length of the third side.
The two sides of a triangle are -
a=7, b=x and c=17, where a, b and c are the sides of the triangle.
As, 17 is a bigger number so let it be the biggest side.
Now, according to triangle inequality theorem -
a + b = c
7 + x = 17
x = 17 -7
x = 10
Therefore, the third side of the triangle measures 10 units.
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How do you find the legs of a 45 45 90 triangle given the hypotenuse?
The value of the legs of the triangle would be hypotenuse/√2.
You can use basic trigonometry to solve this problem. We know that the sine of the angle made by the hypotenuse and the base is equal to the ratio of perpendicular height and the hypotenuse, given that the angle is 45° the perpendicular will be equal to ⇒ hypotenuse × sin(45°).
That is perpendicular=hypotenuse/√2
Similarly, the cosine of the angle made by the hypotenuse and the base is equal to the ratio of base length and the hypotenuse, given that the angle is 45° the base will be equal to ⇒ hypotenuse × cos(45°)
That is base=hypotenuse/√2
Therefore, the value of the legs of the 45°-45°-90° triangle would be hypotenuse/√2.
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Betsy and her sister have $15 to
spend on lunch. They buy several
mini-hamburgers, which cost $1. 80
cach. If they received change after
buying their food, which inequality
could be used to find h, the number
of mini-hamburgers Betsy and her
sister bought?
A 1. 89 s 15
B 1. 8 > 15
C 1. 82 > 15
D 1. 85 < 15
Therefore, the inequality 1.85 < 15 can be used to find h.
What is inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. Therefore, inequality emerges from a lack of balance. For instance, let's say you have 225 and want to purchase a new bicycle that costs $250.
Define expressions or values.When the expression's variables and constants are given values, the calculation it describes yields the expression's value. In an algebraic expression, numbers can be represented by letters.
The inequality 1.85 < 15 can be used to find h, the number of mini-hamburgers Betsy and her sister bought. This inequality represents the constraint that the total cost of the mini-hamburgers (1.85h) must be less than the amount of money they have to spend (15). To solve for h, you would divide both sides of the inequality by 1.85, giving you h < 8.1, so h can be any number less than 8.1.
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answer quick its due in ten minutes
The number of grams of sugar that would be in a 200 ml glass of juice, given the carton, is 13. 2 grams of sugar
How to find the number of grams of sugar ?In a 250 ml glass of juice, we would see 16. 5 g of sugar. Given this information, we can find the amount of sugar in a 200 ml of juice by using direct proportion.
The amount of sugar in 200 ml of juice is :
= ( Amount of sugar in 250 ml x Quantity of juice ) / Quantity of base quantity of juice
= ( 16. 5 x 200 ) / 250
= 3, 300 / 250
= 13. 2 grams of sugar
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What is the ratio for cos?
The ratio for cos (cosine) of angle θ is: cos(θ) = adjacent side of θ / hypotenuse
We know that in right triangle the cosine of an angle is nothing but the ratio of the side adjacent of given angle to the hypotenuse.
In right tirnagle for an angle θ, the ratio for cosine of angle θ would be:
cos(θ) = adjacent side of θ / hypotenuse
Consider following right triangle PQR with angle PQR = 90 degrees
Here, PR is the hypotenuse.
Assume that angle QPR measure α degrees and angle PRQ measures θ degrees.
By definition of cosine of angle θ,
cos(θ) = adjacent side of θ / hypotenuse
cos(θ) = QR / PR
And by definition of cosine of angle α,
cos(α) = adjacent side of α / hypotenuse
cos(α) = PQ / PR
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Find the measure of MN
Answer:
60 degrees
Step-by-step explanation:
The total measure of a circle is 360 degrees.
360-140-100 = 120
Angles MON and NOP are equivalent which makes MN and NP equivalent.
120/2 = 60 degrees = MN
Solve the inequality. Graph the solution.
-1/3h > or equal to 8
(step by step equation)
We can solve the inequality to get:
h ≤ -3
And its graph can be seen below.
How to solve the inequality?Here we have the following inequality:
-(1/3)*h ≥ 8
To solve the inequality, we need to isolate h.
So we can multiply both sides by -3 (notice that this will change the sign of the inequality symbol)
So we will get:
-3*(-1/3)*h ≤ -3*h
h ≤ -3
Now to graph this, we need to draw a closed circle at -3, and draw an arrow that gose to the left.
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What is the inverse of the inverse of P → Q?
The inverse of ∼P→∼Q is P->Q.
Given ∼P→∼Q
Its inverse, ∼(∼P)→∼(∼Q), means that P→Q.
If the hypothesis is correct but the conclusion is untrue, a conditional statement is false. If the statement in the example above read, "If you achieve good marks then you will not get into a good college," it would be untrue. A conditional statement that has been modified or rearranged is referred to as a related conditional. An if-then statement, also known as a conditional statement, is a set of hypotheses followed by a conclusion. It is noted that p→q. Read this: if p, then q.
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A conical paper cup is 10 cm tall with a radius of 7 cm. The cup is being filled with water so that the water level rises at a rate of 3 cm/sec. At what rate is water being poured into the cup when the water level is 9 cm
The rate exists water being poured into the cup when the water level is 9 cm exists [tex]$$1458 \pi \mathrm{cm}^3 s^{-1}$$[/tex].
What is meant by chain rule?To determine the derivative of a composite function in differential calculus, apply the chain rule formula. If y = f(g(x)), then according to the chain rule, the instantaneous rates of change of the functions f and g with respect to x produce the instantaneous rate of change of f with respect to x.
A composition of functions, such as the composition of the functions f and g, f(g(x)), can be used to determine the derivative using the chain rule.
Let us set up the following variables:
R, Radius of conical cup (cm) = 30 cm
H, Height of the conical cup (cm) = 10 cm
Our aim is to find dV/dt when h = 9 and we are given dh/dt = 2
By similar triangles we have
r : h = R : H
r/h = 30/10
⇒ r = 3h
The volume of a cone is 1/3π r²h, So:
V = 1/3π r²h
simplifying the equation, we get
= 1/3π (3h²)h
= 1/3π 9h²h
= 3π h³
Differentiating wrt h we get:
dV/dh = 9π h²
Applying the chain rule we have:
dV/dt = (dV/dh)(dh/dt)
= 9π h² × 2
= 18π h²
If h = 9 then
[tex]$\left[\frac{d V}{d t}\right]_{h=9}=18 \pi\left(9^2\right)=1458 \pi \mathrm{cm}^3 s^{-1}$$[/tex].
Therefore, the rate exists water being poured into the cup when the water level 9 cm exists [tex]$$1458 \pi \mathrm{cm}^3 s^{-1}$$[/tex].
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What is the value of x in the equation 2.5 6x 4 )= 10 4 1.5 0.5 x?
The value of x in this problem is 2.
Our given algebraic equation is 2.5 ( 6x - 4 ) = 10 + 4 ( 1.5 + 0.5x) and in this, we have to find the final value of x.
Use the transposing method to isolate the variable x and then solve for it.
distribute brackets on both sides of the equation.
= 2.5*6x - 2.5*4 = 10 + 4*1.5 + 4*0.5x
= 15x - 10 = 10 + 6 + 2x
collect terms in x to the left side and numeric values to the right side.
= 15x - 2x = 10 + 6 + 10
= 13x = 26
= x = 26/13 = 2
Therefore the final value of x in this equation will be 2.
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Can you pls help me with this
Answer:
y = x - 2
Step-by-step explanation:
Slope intercept form of an equation: y =mx +bHere m is the slope and b is the y-intercept.
Choose any two points on the line.
(2,0) ; (0,-2)
Now, find the slope.
[tex]\sf \boxed{Slope = \dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]= \dfrac{-2 - 0}{0 - 2}\\\\=\dfrac{-2}{-2}\\\\= +1[/tex]
m = 1.
Now, y = 1x + b
The (2 , 0) passes through the line. Substitute x = 2 and y = 0 in the above equation and find the value of 'b'.
0 = 1*2 + b
0 = 2 + b
-2 = b
Equation of line:
y = x - 2
Which bag of potatoes is the better deal?
Answer:
5 kg.
Step-by-step explanation:
2 kg for $0.96 is more expensive than 5 kg for $1.95
How do you check if a function has an inverse function?
We can check if a function has an inverse function using horizontal Line Test.
What is Function?
A relation between a collection of inputs and outputs is known as a function. In plain English, a function is an association between inputs in which each input is connect
horizontal Line Test
Make f a function. Any horizontal line that crosses the f graph more than once indicates that f lacks an inverse. F does have an inverse if there are no horizontal lines that cross the graph of f more than once.
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Bart and April are purchasing a house with a 15-year, 2/1 ARM for $315,000 at 5. 85% with a 2/8 cap structure. What will the difference in
payments be from year 2 to year 3?
$309. 69
$595. 18
$333. 68
$86. 56
The monthly payment for this difference would be $1,361.21. An Adjustable Rate Mortgage (ARM) is a type of mortgage in which the interest rate on the loan changes over time.
An Adjustable Rate Mortgage (ARM) payment is based on various factors such as the loan amount, interest rate, and the terms of the ARM. The interest rate is usually tied to a specific financial index, such as the U.S.
Here is the calculation format for the difference in payments between year 2 and year 3 for Bart and April's mortgage:
Total amount to be paid for the mortgage: $315,000
Rate of interest: 5.85% (Depreciating rate)
Time = 2 years:
a. Remaining amount to be paid after 2 years:
Principal × (1 - Rate/100)^time
= $315,000 × (1 - 5.85/100)²
= $315,000 × (1 - 0.0585)²
= $279,223.01
Time = 3 years:
a. Remaining amount to be paid after 3 years:
Principal × (1 - Rate/100)^time
= $315,000 × (1 - 5.85/100)³
= $315,000 × (1 - 0.0585)³
= $262,888.46
Difference in payments from year 2 to year 3:
= Remaining amount after 2 years - Remaining amount after 3 years
= $279,223.01 - $262,888.46
= $16,334.55
The monthly payment for this difference would be $1,361.21, which is calculated by dividing the difference in payments by 12:
$16334.546/12 = $1361.21
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I would like help with this, please. Someone give me an answer in the next day or two.
Answer:
one solution
Step-by-step explanation:
The two lines cross at exactly one point. That means there is one solution.
BUILD PERSEVERANCE Part A Simplify the expression. (8x + 6) + (5 − x) − 2 (3x+1)
The expression is x + 9.Generally speaking, an expression is at its simplest form when it is most usable.
What is its most basic form?Generally speaking, an expression is at its simplest form when it is most usable. as in this: 5x + x 3.To simplify an expression, create a similar expression devoid of any identical terms. Therefore, we shall rephrase the expression using the fewest number of terms possible.Determine the domain before you can simplify a rational expression.The collection of all possible inputs to a function, including all potential values for the variables, that enable the function to function.Explanation:
8x + 6+5 - x - 6x - 2
= x + 9.
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write an equation that expresses the following relationship p varies derectly with d and inversly with the square of u. In your equation use k as the proportionality
P= kd/u^2 is the equation which expresses the following relationship p varies derectly with d and inversly with the square of u.
What is Equation?Equation is a mathematical statement that expresses the equality of two expressions. An equation is written as an expression containing an equal sign, with each side of the equal sign representing a mathematical expression. The purpose of an equation is to show the relationship between two or more variables, such as a change in one variable resulting in a change in another. Equations are used to solve problems in mathematics, physics, economics, and many other fields.
The equation states that p is directly proportional to d, and inversely proportional to u squared. This means that as d increases, p increases, and as u increases, p decreases. The constant of proportionality, k, is a measure of the strength of the relationship between p, d, and u.
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BRAINLY GRANTED FOR CORRECT ANS PLEASE HELP
P (X)= [tex]x^3+4 x^2-3x+2[/tex] moreover, [tex]\frac{P(x)}{x - 1} = x^{2} + 5x +2[/tex] as a result, the actual claim is [tex]$p(x)=(x-1)\left(x^2+5 x+2\right)+\frac{4}{x-1}$[/tex]
How do you find the probability equation?The likelihood of an event occurring is determined by probability: P(A) = f / N. Probability and odds are related, but probability is necessary for odds to exist. Prior to calculating the likelihood that an event will occur, probability is required.
The steps listed below can be used to determine an event's likelihood: Step 1: Identify an event that has only one outcome. Step 2: Compile a list of all potential outcomes, including any positive ones. Step 3: Subtract the number of favourable outcomes from the total number of outcomes that are feasible. The probability of A or B is equal to p(A or B) = p(A) + p(B) if occurrences A and B are mutually exclusive (B). A probability is a number that expresses the possibility or likelihood that a specific event will take place.
Therefore the correct answer is option A ) [tex]$p(x)=(x-1)\left(x^2+5 x+2\right)+\frac{4}{x-1}$[/tex]
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A juice container advertises it now contains 20% more juice. Originally, it had 27.5 ounces, how
much juice does it now contain?
Answer:
33 ounces
Explanation:
20% of 27.5 ounces is 5.5 ounces.
To find how much more juice the container has, we add 5.5 to 27.5, which equals to 33 ounces
Elizabeth has a box that can hold exactly 24 unit cubes. It could also be said that her box has
A. An area of 12 cubic units, and its sides could measure 12 units and 2 units
B. An area of 24 cubic units, and its sides could measure 2 units, 3 units, and 4 units
O C. A volume of 12 cubic units, and its sides could measure 12 units and 2 units
D. A volume of 24 cubic units, and its sides could measure 2 units, 3 units, and 4 unit
Elizabeth has a box that can hold exactly 24 unit cubes. It could also be said that her box has 24 cubic units. So, option D. is correct.
What are cubic units?A cubic unit is a unit of measurement for volume. It represents the amount of space an object occupies in three dimensions: Length, Width and Height. It is often used to measure the volume of three-dimensional shapes such as cubes, square prisms, cylinders, and spheres. Cubic units are most commonly measured in cubic meters or cubic feet, but they can also be expressed in smaller units such as cubic centimeters or cubic inches.
The total volume of the box is 24 cubic units. A side of the box may measure 2 units x 3 units x 4 units = 24 cubic units.
Choice A is incorrect. This is because the area of a shape is a measure of the two-dimensional space it occupies, and the volume of a shape is a measure of the three-dimensional space it occupies.
Choice B is incorrect. This is because the area of a shape is a measurement of the two-dimensional space it occupies, not its volume.
Option C is incorrect because it states that the box has a volume of 12 cubic units, but it is not because the volume he has is 24 cubic units.
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If 16 inches of ribbon costs $2.08, how much will 36 inches of
ribbon cost? Show your thinking.
4.68
find unit rate by dividing 208 cents by 16 which is 13 than multiply by 36
Answer:
16 inches of ribbon cost- $2.08
36 inches of ribbon cost- ?
36*$2.08/ 16
$74.88/16
= $4.68
Thus, 36 inches of ribbon would cost $4.68
Tricia has $37.25 in her account. Which amount will she have left after she writes 3 checks for $8.33 each?
How does Earth's rotation cause day and night ?
Earth's rotation is what causes day and night. As Earth rotates on its axis, half of the planet is facing the Sun, while the other half is facing away from the Sun.
The half of the planet facing the Sun experiences daylight, while the half facing away from the Sun experiences darkness. This cycle repeats itself every 24 hours, resulting in the day and night cycle that we experience.
Earth's rotation causes day and night by rotating on its axis, with half of the planet facing the Sun and the other half facing away from the Sun. This cycle of daylight and darkness lasts for creating the day and night cycle that we observe.Earth's rotation is what causes day and night. As Earth rotates on its axis, half of the planet is facing the Sun, while the other half is facing away from the Sun.
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Hilda filled her aquarium with
water. On Monday, she put 8 cups
into the aquarium. On Tuesday she
put 2 pints. On Wednesday, she put
quarts. How many cups of water dic
she put into her aquarium in all?
The domain and scope of the identity function are the same. Equation for the identity function is f(x) = x, or y = x.
What is function?An statement, rule, or law in mathematics that specifies the connection between an independent variable and a dependent variable (the dependent variable. A relationship between a group of inputs and one output each is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. Y=X2 is an illustration of this. You only receive one output for y if you enter anything for x. The fact that x is the input value leads us to argue that y is a function of x.
identity function are the same.
Equation for the identity function is
f(x) = x, or y = x.
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Write an exponential function to describe the given sequence of numbers,
10, 60, 360, 2160, 12960,.
The exponential function to describe the given sequence of numbers, 10, 60, 360, 2160, 12960, ... is aₙ = 10 × [tex]6^{n-1}[/tex].
The given series 10, 60, 360, 2160, 12960, ... is a geometric progression.
a = 10
The common difference r = 60/10 = 6
As we know the general formula of the nth term of a geometric series is
aₙ = a × [tex]r^{n-1}[/tex]
Now, put the values of a = 10, r = 6 and n in the general formula,
aₙ = 10 × [tex]6^{n-1}[/tex]
Therefore, the required exponential function to describe the given sequence of numbers, 10, 60, 360, 2160, 12960, ... is aₙ = 10 × [tex]6^{n-1}[/tex].
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Ryan has a points card for a movie theater. He receives 85 rewards points just for signing up. He earns 7.5 points for each visit to the movie theater. He needs 160 points for a free movie ticket. Write and solve an equation which can be used to determine vv, the number of visits Ryan must make to earn a free movie ticket.
Answer:
85+7.5v=160
7.5v=160-85
7.5v=75
V=75/7.5
V=10
Ryan would need to take 10 visits to get a free ticket.
Find the output (y) of the function y= -7+5 if the input is (x) is 15
Y=
Answer: -100
Step-by-step explanation: -7(15)+5
It said x=15 so put 15 in and solve from there and that would be -100
HOPE THIS HELPS ANY I JUST completed FUNCTIONS AND MAN IT WAS FUN
A rectangle has a perimeter represented by the expression 4x−8. Which expression also represents this perimeter? 4(x-8), 2(2x-8), 2(2x-4), 4(2x-4)
The perimeter expression of a rectangle has a perimeter represented by the expression 4x−8 is 2(2x - 4)
How to determine the perimeter expressionFrom the question, we have the following parameters that can be used in our computation:
Perimeter = 4x - 8
Factor out 2 from the expression
So, we have the following representation
Perimeter = 2 * 2x - 2 * 4
So, we have
Perimeter = 2(2x - 4)
Hence, the perimeter is 2(2x - 4)
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the cube root parent function is reflected and stretched by four. it is translated six to the right and five down. write an equation that represents this new function
The equation for new function is,
⇒ f (x) = ∛( 1/4x - 6) - 5
What is Function?A relation between a set of inputs having one output each is called a function.
Given that;
The parent function is,
⇒ g (x) = ∛x
Now, After reflected and stretched by 4, we get;
⇒ g (x) = f (1/4x) = ∛ 1/4x
And, After translated 6 units to the right, we get;
⇒ g (x) = f (x - 6) = ∛ 1/4x - 6
And, After 5 unit down, we get;
⇒ g (x) = h (x) - 5 = ∛( 1/4x - 6) - 5
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Geometry: Applications of All Right Triangles
Look at the attachments below to answer this question.
Given:
A length of a side of an equilateral triangle = 32 cm
Formula Used:
If in an equilateral triangle with side length 'a' then,
Area of an equilateral triangle = [(√3)/4] × a2
Calculations:
Area of an equilateral triangle = [(√3)/4] × 322
⇒ (1024 × √3)/4
⇒ 256√3 cm2