The area of the isosceles trapezoid is 72 square units.
What is isosceles trapezoid ?A quadrilateral having at least one set of parallel sides and equal length non-parallel sides is called an isosceles trapezium. To put it another way, it is a trapezium whose two non-parallel sides are congruent. The trapezoid's parallel sides are referred to as the bases, and the segments that link the bases are referred to as the legs. The angle between the bases of an isosceles trapezoid determines its height.
Given:
[tex]\[d = 12 \quad \text{(length of one diagonal)}\][/tex]
Let;
[tex]\[h = \text{height of the trapezoid}\][/tex]
[tex]\[a = \text{smaller base of the trapezoid}\][/tex]
[tex]\[b = \text{larger base of the trapezoid}\][/tex]
Using the given information that the height and median are equal, we have:
[tex]Median(m)=\frac{1}{2} {(a+b)}\\\\Height(h)=\frac{1}{2} {(a+b)}\\\\2h=a+b ........(1)[/tex]
[tex]\[\text{Area} = \frac{1}{2} \cdot (a + b) \cdot h\][/tex]
[tex]\[\text{Area} = m \cdot h\] = h^2 ............(2)[/tex] (∵ [tex]Median(m)=\frac{1}{2} {(a+b)}[/tex] and m=h)
Now,
[tex]\[ d = \sqrt{h^2 + \frac{(a+b)^2}{4}} \][/tex] for isosceles trapezoid,
[tex]\[ 12^2 = h^2 + \frac{(a+b)^2}{4}}[/tex]
[tex]\[ 12^2 = h^2 + \frac{(2h)^2}{4}}[/tex] (∵from eq (1))
[tex]\[ 12^2 = h^2 + {(h)^2}}\\ \\144= 2h^2\\\\h^2=72 ..........(2)[/tex]
Lastly, we may change the values of "a," "b," and "h" in the following formula to find the area as;
[tex]\[\text{Area} = \frac{1}{2} \cdot (a + b) \cdot h\][/tex]
[tex]\[\text{Area} = \frac{1}{2} \cdot (2h) \cdot h\][/tex]
[tex]\[\text{Area} = h \cdot h\] = h^2 = 72 sq units[/tex]
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You are decorating a parade float for a Cinco de Mayo parade. The area of the entire parade float is 192 square feet.
What is the area covered by paper flowers?
9 ft (x+12) ft x ft 5 ft
The area covered by paper flowers is square feet.
The area covered by paper flowers is; 45 square feet.
How to find the area of the rectangle?The formula for area of a rectangle is;
Area = Length * width
Parameters of the parade float are;
Length = 9 + x + 12 = (x + 21) ft
Width = (x + 5) ft
Since entire area is 192 sq.ft, then;
(x + 5)(x + 21) = 192
x² + 5x + 21x + 105 = 192
x² + 26x - 87 = 0
Using online quadratic equation calculator gives;
x = 3
Thus;
Length of paper flower = x + 12 = 3 + 12 = 15 ft
Width of paper flower = 3 ft
Area of paper flowers = 15 * 3 = 45 square feet.
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The following points represent a relation where x represents the independent variable and y represents the dependent variable.
Does the relation represent a function? Explain.
Yes, because for each output there is exactly one input
Yes, because for each input there is exactly one output
No, because for each output there is not exactly one input
No, because for each input there is not exactly one output
Answer:
No, because for each input there is not exactly one output
Step-by-step explanation:
Each input, x-coordinate, must have one and only one output (y-coordinate) to be a function.
Since 3/4 is used as an x-coordinate twice, the input 3/4 has two different outputs, -2 and -1/2. That means this relation is not a function.
Answer: No, because for each input there is not exactly one output
Answer: is A
Step-by-step explanation:
2. Find the length of the hypotenuse.
45°
3√2
The triangle is an isosceles right-angle triangle. Then the hypotenuse of the triangle will be 3 units.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
The measure of one angle of right-angle is 45°. Then the right triangle is an isosceles right-angle triangle.
Then the hypotenuse is given by the sine of angle 45°. Then the equation is given as,
sin 45° = 3√2 / H
1/√2 = 3√2 / H
H = 3√2 x (1 / √2)
H = 3 units
The triangle is an isosceles right-angle triangle. Then the hypotenuse of the triangle will be 3 units.
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a tent that usually sells for $220 is on sale for 15% off what is the sale price
Answer:
Step-by-step explanation:
$220.00x .15 = $187.00
HELLO CAN U HELP ME PLEASE??
Answer:
B
Step-by-step explanation:
The rate at which she travels is called the rate of speed.
rate of speed = distance / time
r = d/t
She wants to know the time, so we solve the above equation for time.
r = d/t
rt = d
t = d/r
t = 300/r
300/r = t
Answer: B
Answer:
B. t = 300/r
Step-by-step explanation:
translate the question into math
usually
speed is shown as
kilometers per hour
RATE MEANS SPEED
translate kilometers per hour
kilometers = 300 km
per= /
hour = t
speed = 300 km/t
SPEED MEANS RATE
rate = r
r = 300 km/t or 300/t
r = 300/t
t = 300/r
note: rate or speed can be gotten by
SLOPE of line in a graph
HYPOTENUSE of a triangle from a slope of a line in a graph
DERIVATIVE which is a slope of curve in a graph
the bill fir dinner at a retuaruarnt was $81.75 A sales tax for 7.5% was first added to the bill and then an 18% gratuity will br added
The total amount of the bill is $102.59625.
What is Percentage?Percentage is defined as the parts of a number per fraction of 100 or a part per 100.
Percentage is usually denoted by the symbol '%'.
We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.
Given that,
Amount of bill for a restaurant = $81.75
Percentage of sales tax = 7.5%
Amount of sales tax = 7.5% of $81.75
= 7.5% × 81.75
= 0.075 × 81.75
= $6.13125
Percentage of gratuity = 18%
Amount of gratuity = 18% of $81.75
= 18% × 81.75
= 0.18 × 81.75
= $14.715
Total amount in the bill = $81.75 + $6.13125 + $14.715
= $102.59625
Hence the total bill from the restaurant is $102.59625.
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In a right triangle, the length of one leg is 4 units. The length of the other leg is 10 units. What is the length of the hypotenuse? A. B. C. D.
values showing on the dice.
(a) How many sample points are possible? (Hint: use the counting rule for multiple-step experiments.)
(b) List the sample points.
a) For a single roll of a standard six-sided dice, there are 6 possible outcomes.
b) Sample points for rolling a dice twice are:
(1,1), (1,2), (1,3), (1,4), (1,5), (1,6),
(2,1), (2,2), (2,3), (2,4), (2,5), (2,6),
(3,1), (3,2), (3,3), (3,4), (3,5), (3,6),
(4,1), (4,2), (4,3), (4,4), (4,5), (4,6),
(5,1), (5,2), (5,3), (5,4), (5,5), (5,6),
(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)
a) If we want to find the number of sample points for multiple rolls of a dice, we use the counting rule for multiple-step experiments, which states that if an experiment consists of k steps and there are n1 possible outcomes for the first step, n2 possible outcomes for the second step, and so on, then the total number of possible outcomes for the experiment is:
n1 x n2 x ... x nk
For example, if we roll a dice twice, then there are 6 possible outcomes for the first roll and 6 possible outcomes for the second roll. Therefore, the total number of possible outcomes for rolling a dice twice is:
6 x 6 = 36
b) Here are the sample points for a single roll of a standard six-sided dice:
1, 2, 3, 4, 5, 6
Here are the sample points for rolling a dice twice:
(1,1), (1,2), (1,3), (1,4), (1,5), (1,6),
(2,1), (2,2), (2,3), (2,4), (2,5), (2,6),
(3,1), (3,2), (3,3), (3,4), (3,5), (3,6),
(4,1), (4,2), (4,3), (4,4), (4,5), (4,6),
(5,1), (5,2), (5,3), (5,4), (5,5), (5,6),
(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)
Each sample point consists of two values, representing the outcomes of the first and second rolls, respectively. The sample points are written in parentheses and separated by commas.
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The top of a square coffee table has an area of
64x48x + 9. What is the perimeter of the
tabletop?
I need Help Quick!!!
Answer:
150-200
Step-by-step explanation:
From the diagram below, if AC = 27, CD = 9, and DB = 3, then what would be the length of AB?
As a result of answering the question, we may state that triangle Because of this, AB is longer than 33. But since we don't know the precise angle at B, we can't be positive of its length.
What precisely is a triangle?Since a triangle has four or so more sections, it is a polygon. It has an easy rectangular form. Triangle ABC refers to a rectangle with edges A, B, and C. A single plane and cube are produced by Euclidean geometry when the sides are really not collinear. A triangle is a polygon if it has 3 components and three angles. Where a triangle's three edges come together are known as the corners. A triangle's sides add up to 180 degrees.
A+B plus D > A (1)
Applying this to triangle ADC, we get the following:
A + C > A (2)
AC equals 27, CD equals 9, and BD equals 3. Equation (2) may be used to determine AD:
[tex]A + C > A\\27 + 9 > AD\\36 > AD[/tex]
So, we are aware that AD is lower than 36. We may now find AB using equation (1):
[tex]A+B plus D > A\\AB + 3 > AD\\AB + 3 > 36\\AB > 33[/tex]
Because of this, AB is longer than 33. But since we don't know the precise angle at B, we can't be positive of its length.
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Which of the following statements are true. Will make best answer brainliest. 30 points
Answer:
ac and bd
Step-by-step explanation:
iii I will get it on Monday or tomorrow if possible so we will have it done and done so that you will get the information you needed and you are going for it on a day 5o and you have to be my mom when I come back home and you are going out to the
What is the difference between percent error and percent different?
The difference between percent error and percent difference is that percent error is used to measure the accuracy of a predicted value compared to the actual value, while percent difference is used to compare two values to determine how much they differ from each other.
Percent error is calculated using the formula:
Percent error = (|actual value - predicted value| / actual value) x 100
Percent difference is calculated using the formula:
Percent difference = (|value 1 - value 2| / ((value 1 + value 2)/2)) x 100
In summary, percent error is used to measure the accuracy of a prediction or measurement, while percent difference is used to compare two values and determine how much they differ from each other.
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The diagram shows a garden in the shape of a rectangle.
4 + 3x
The perimeter of the garden is 32 metres.
Work out the value of x
x+6
The dimensions of the rectangular garden are 8.5 meters and 7.5 meters.
What is Perimeter?Perimeter of a straight sided figures or objects is the total length of it's boundary.
The diagram is given below.
Given,
Perimeter of a rectangle = 2 (l + w), where l is the length and width.
Length of the rectangle = 4 + 3x
Width of rectangle = x + 6
Perimeter = 32 meters
Substituting,
2 (l + w) = 32
2(4 + 3x + x + 6) = 32
2(4x + 10) = 32
4x + 10 = 16
4x = 6
x = 6 / 4 = 3/2 = 1.5
Length = 4 + 3x = 8.5 meters
Width = x + 6 = 7.5 meters
Hence the length and width of the rectangle are 8.5 meters and 7.5 meters respectively.
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A juice drink contains 100 oz of concentrated juice and water, and is 28%
concentrated juice. If the drink is to be weakened to 20%, how much water must be added?
Actually answer. I will, and have, reported for people faking the asnwer or not answering at all. Please.
Answer: We need to add 40 ounces of water to the 100 oz of concentrated juice and water to obtain a new mixture that is 20% concentrated juice.
Step-by-step explanation:
We can begin by setting up an equation based on the given information.
Let's say we need to add x ounces of water to the 100 oz of concentrated juice and water to obtain the new 20% mixture.
The amount of pure juice in the original 100 oz mixture is 28% of 100 oz, which is 0.28(100) = 28 oz.
After x ounces of water are added, the total volume of the mixture becomes 100 + x oz. The amount of pure juice remains the same at 28 oz. We want to find the amount of water that needs to be added to reach a concentration of 20%.
Setting up the equation:
0.20(100 + x) = 28
Expanding and simplifying:
20 + 0.20x = 28
0.20x = 8
x = 40
Answer:
143
Step-by-step explanation:
100 oz is 28 % of the drink
So total volume of the drink = 357 oz.
A drink that of 100 oz juice and is 20% juice has a volume of 500 oz.
So, we need to add 500 - 357
= 143 oz water.
Solve for x In the triangle. Round your answer to the nearest tenth.
47°
X =
Answer:
x=5.4Step-by-step explanation:from TOAtan47°=x/5to find x;
cross multiply
x=5tan47°
x=5×(1.07236871002)
x=(5.36184355012)
to the nearest tenth
x=5.4
Which one of the following statements about probability is not true?If Events A and B are mutually exclusive, then Event A or Event B must occur.If Events A and B are mutually exclusive, then both events cannot occur simultaneously.
The statement "If Events A and B are mutually exclusive, then both events cannot occur simultaneously." is true.
Therefore the answer is B.
This statement is true, but it is not a general property of probability. In probability, events are considered mutually exclusive if they cannot occur at the same time, but there is no requirement that one of the events must occur. For example, if Events A and B are the rolling of a dice resulting in an even number and rolling a dice resulting in a number greater than 4, respectively, they are mutually exclusive events but both events may not occur (if a 3 is rolled, for example).
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Show how you get each answer (show work) on number 1 and 2 (Lesson 2.05)
What is the measurement of ∠1 if g∥h? (2pts) (this one does not need work shown
What is the measurement of ∠3 if g∥h? (2pts) need work shown
please help
The measure of the angle ∠1 and ∠3 is 90°
What are lines and angles?The lines are the collection of collinear points arranged in a straight path. Types of lines can be a ray, segment, etc. The angle is the space between the two intersecting lines calculated in degrees.
Since g and h are parallel lines cut by the transversal i, we know that alternate interior angles are congruent. Therefore, the measurement of ∠1 is equal to the measurement of ∠3. We do not need to show any work to answer this question.
Since g and h are parallel lines cut by the transversal j, we can see that ∠3 and ∠5 are corresponding angles, and ∠5 and ∠6 are vertical angles. Therefore, ∠3 and ∠6 are congruent. Since ∠3 and ∠6 forms a linear pair, their sum is 180 degrees. Thus, we can set up an equation:
∠3 + ∠6 = 180
Substituting ∠6 for ∠3, we get:
∠3 + ∠3 = 180
Simplifying, we get:
2∠3 = 180
Dividing both sides by 2, we get:
∠3 = 90°
Therefore, the measurement of ∠3 is 90 degrees.
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1000000000000000000000000000
Step-by-step explanation:
are u also MS hitsman?
what is 148lb to kg ?
Using the conversion formula of converting pounds to kilograms, we get that 148 lb is 67.131478 kilograms
To convert 148 pounds (lb) to kilograms (kg), we need to use the conversion factor 1 lb = 0.45359237 kg.
So, we can multiply 148 lb by 0.45359237 kg/lb to get the equivalent weight in kilograms:
148 lb x 0.45359237 kg/lb = 67.131478 kg
Therefore, 148 lb is equal to 67.131478 kg.
To understand the conversion factor, we need to know that pounds and kilograms are both units of mass, but they are used in different parts of the world. In the United States and some other countries, pounds are the common unit of mass, while in most other countries, kilograms are used. The conversion factor relates the number of pounds to the number of kilograms, so that we can easily convert from one unit to the other. It is important to use the correct conversion factor to ensure accurate conversions.
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How many pages is 3,000 words?
In Single spaced pages 3000 words will be in 6 pages and in Double Spaced pages 3000 words will be in 12 pages.
3,000 words equates to approximately 6 single-spaced A4 pages and 12 double-spaced A4 pages. This assumes normal 1 - inch margins and standard fonts such as Times New Roman or Arial at 12 pt.
Adjusting certain settings in a text editor or using other layout software can greatly affect the appearance of your final text. Many journal articles are around 3,000 words in length, as are student essays and lengthy blog posts. You may also be interested in the fact that adults can read about 3,000 words in 10 minutes.
3000 words in Single spaced Pages:
3000 words is 6 pages. A standard single-spaced page contains 500 words.
3000 words in Double Spaced page:
3000 double spaced words make up 12 pages. Teachers may ask you to double-space your essay to make it easier to read and add comments/reviews. A standard double-spaced page contains 250 words.
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26. Which function is increasing and decreasing over the same intervals as the function in the graph?
The function is increasing and decreasing over the same intervals as the function in the graph is y = | x+ 2|. The correct option is B.
What is an absolute function?The absolute value or modulus of a real number x, denoted |x| in mathematics, is the non-negative value of x regardless of its sign. Specifically,|x|=x.
In the given image the function is represented by the equation y = | x - 2 |. Now the similar function which is increasing and decreasing over the same intervals as the function in the graph is y = | x+ 2|.
Therefore, the correct option for the function is B.
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The scale on a map is 5 centimeters = 75 kilometers. Two lakes on the map are located 8.1 cm apart. What is the actual distance between the two lakes?
Answer:
If 5 centimeters on the map represent 75 kilometers in the real world, then we can use proportion to find the actual distance between the two lakes.
Let x be the actual distance between the two lakes in kilometers. Then we can set up the following proportion:
5 cm / 75 km = 8.1 cm / x km
To solve for x, we can cross-multiply:
5 cm * x km = 75 km * 8.1 cm
Simplifying:
5x = 607.5
x = 121.5 km
Therefore, the actual distance between the two lakes is 121.5 kilometers.
17/22 as a decimal rounded to the nearest hundreth
The decimal equivalent of 17/22 rounded to the nearest hundredth is 0.77. The result of dividing the quantifier by the denominator is 0.7727272727272727.
The decimal equivalent of the fraction 17/22 can be found by dividing the numerator by the denominator. To round the decimal to the nearest hundredth, we look at the third decimal place and round up or down accordingly. Step-by-step explanation:
Divide the numerator by the denominator ⇒ 17/22 = 0.7727272727272727Look at the third decimal place ⇒ 2Since the third decimal place is less than 5, we round down to the nearest hundredth ⇒ 0.77Learn more about decimal: https://brainly.com/question/28393353
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What is the lateral surface area of the triangular prism shown below?
Responses
40 cm2
150 cm 2
170 cm2
170 cm 2,
190 cm
The lateral surface area of the triangular prism shown below is C.170 cm².
How can the lateral surface area of the triangular prismbe calculated?The concept that will be used here is triangular prism breakdown and calculation.
We can break down the triangular prism so as to make it simpler as :
We have (2 triangles) as well as ( 2 side rectangles) and (1 back rectangle)
We can calculate the area of triangle as ( ¹/₂ * base * height)
= (¹/₂ * 5 * 4)
=10cm
We can calculate the area of rectangle as ( length * width)
=(10 * 5)
=50
Then the Area of trapezoid = 2(10) + 3(50)
=20 + 150
= 170 cm²
Therefore, option C is correct.
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what is the answer to this
Answer:
y=13 x=16 i think
Step-by-step explanation:
the Cost of stamps depends on the number of slaves purchase because the cost why for example is represented by the equation Y equals 0.49X graph the function unit function table
Answer:
Step-by-step explanation:
I'm sorry, but I'm having trouble understanding your question. Could you please clarify what you mean by "the cost of stamps depends on the number of slaves purchase because the cost why"? It's important to provide clear and accurate information in order for me to provide a helpful response. Thank you!
Function A and Function B are linear functions.
Function A
x y
–4 –21
–2 -11
4 19
Function B
y=x+1
which statement is true?
The slope of function a is greater than the slope of function b
the slope of function a is less than the slope of function b
The statement that is true is: The slope of function A is greater than the slope of function B.
What is the Slope of a Function?The slope of a function is a measure of how steeply the function increases or decreases as the input value (x) changes. It is defined as the rate of change of the output value (y) with respect to the input value (x).
Using two points form the table of Function A, (-2, -11) and (4, 19):
Slope (m) = change in y / change in x = (-11 - 19) / (-2 - 4)
= -5
Given Function B as y = x + 1, the slope is m = 1.
Therefore, we can state that, function A has a greater slope than B.
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Please answer this asap
Answer: F = 4
Step-by-step explanation:
Juts plug in the numbers that you know so you should have (5*20)/(5^2)
That is equal to 100/25 which is the same as 4. Therefore, F = 4
2
Ling's savings account increases by 1% every month from interest. He
deposits x dollars into his account. Select all of the expressions that
represent the amount of money in his account after the interest is paid for
the third month. 7.EE2
x(125)(125)(125)
x(10025)(10025)(10025)
(1.25)³x
3(10025)x)
x(1+0.25)(1+0.25)(1+0.25)
(10025)
x(0.0025)(0.0025)(0.0025)
(1+0.0025)(x)(1+0.0025)(1+0.0025) 3(1.25)(x)
After the third year, the amount in his account would be -
A{3} = $(125x/64).
What is interest?Interest is calculated as a percent of the principal.
Given is that Ling's savings account increases by {1/4}% every month from interest. He deposits {x} dollars into his account.
After the first year, the amount in his account would be -
A{1} = x + x/4 = (5x/4)
A{1} = $(5x/4) ... Eq { 1 }
After the second year, the amount in his account would be -
A{2} = (5x/4) + (1/4)% of (5x/4)
A{2} = 5x/4 + 5x/16
A{2} = (1/4)(5x + 5x/4)
A{2} = (1/4)(25x/4)
A{2} = $(25x/16) ... Eq { 2 }
After the third year, the amount in his account would be -
A{3} = (25x/16) + (1/4) of (25x/16)
A{3} = (25x/16) + (25x/64)
A{3} = (1/16)(25x + 25x/4)
A{3} = (1/16)(125x/4)
A{3} = $(125x/64) ... Eq { 3 }
Therefore, after the third year, the amount in his account would be -
A{3} = $(125x/64).
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Half of the sum of two numbers is 12, while one-fourth of their products is 35. Find the numbers
Answer:
The sum of two numbers = 12
x+y=12
product of two numbers = 35
xy=35
The sum of reciprocals = x
1
+
y
1
=
xy
x+y
=
35
12
Step-by-step explanation:
Answer: 10 and 14.
Step-by-step explanation:
Let the numbers be x and y.
Make and solve a system of equations:
[tex]\displaystyle\\\left \{ {{\frac{x+y}{2}=12\ \ \ \ (1) } \atop {\frac{1}{4}xy=35\ \ \ \ (2) }} \right. \\\\\\[/tex]
Multiply equation (1) by 2 and equation (2) by 4:
[tex]\displaystyle\\\left \{ {{x+y=24} \atop {xy=140}} \right. \\\\\\\left \{ {{x=24-y} \atop {(24-y)*y=140\right.\\\\\\\left \{ {{x=24-y} \atop {24y-y^2=140}} \right. \\\\\\\left \{ {{x=24-y} \atop {-y^2+24y-140=0\ \ \ \ (3)}} \right.[/tex]
Multiply equation (1) by (-1):
[tex]y^2-24x+140=0\\\\y^2-10x-14x+140=0\\\\y(y-10)-14(y-10)=0\\\\(y-10)(y-14)=0\\\\y-10=0\\\\y=10.\ \ \ \ \Rightarrow\\\\x=24-10\\\\x=14\\\\y-14=0\\\\y=14.\ \ \ \ \Rightarrow\\\\x=24-14\\\\x=10.[/tex]