The shorter base of the isosceles trapezoid is approximately 6 cm.
Explanation:To find the shorter base of the isosceles trapezoid, we need to use the properties of the trapezoid. Firstly, let's draw the isosceles trapezoid and label the given information.
The longer base is 12 cm, the side is 5 cm, and the acute angle is 37º. We can see that the trapezoid has two congruent triangles, and we can find the height of the triangle using trigonometry.
Step 1: Find the height of the triangle using the sine of the acute angle.
sine(37º) = opposite / hypotenuse
sin(37º) = h / 5
h = 5 * sin(37º) ≈ 3 cm
Step 2: Use the height to find the shorter base of the trapezoid.
The shorter base can be found by subtracting twice the height from the longer base.
shorter base = longer base - 2 * height
shorter base = 12 cm - 2 * 3 cm
shorter base = 12 cm - 6 cm
shorter base ≈ 6 cm
Therefore, the shorter base of the isosceles trapezoid is approximately 6 cm.
Explain how the common difference in an arithmetic sequence is like the slope of a linear function. read more >>
Given: x - 5 > -2.
Choose the solution set.
{x | x R, x > -7}
{x | x R, x > -3}
{x | x R, x > 3}
{x | x R, x > 7
x-5>-2
x> -5+2
X>3
Answer is: {x | x R, x > 3}
Rewrite and simplify ln(4500) in terms of ln5 and ln6
Simplified form of the given logarithmic expression ln(4500) will be ln(4500) = 3ln(5) + 2ln(6)
Given logarithmic expression in the question is,
ln(4500)We have to convert this expression in terms of ln(5) and ln(6).
Since, Factored form of 4500 = 5×5×5×6×6
= 5³×6²
Therefore, ln(4500) = ln(5³×6²)
= ln(5³) + ln(6²) [Since, ln(a × b) = ln(a) + ln(b)]
= 3ln(5) + 2ln(6) [Since, ln(a³) = 3ln(a)]
Hence, ln(4500) = 3ln(5) + 2ln(6) will be the answer.
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A circle with radius 5 and a center at (2, 3) was transformed to a circle with radius 10 and a center of (‒1, 4).
Show that the two circles are similar by describing the transformations that would have to be performed.
Answer:
First of all, remember that all circles are similar to each other regardless of how to twist the cartesian plane.
Let the origin in first case(radius 5) be at (0,0) , so if we shift the origin to (2-(-1),3-(4)) = (3,-1) {shifting origin to shift the first circle to second's place}. So, we arrive at a circle of radius 5 and center (-1,4).
Since similarly has no constraints on size comparison increase the radius to 10 units. Thus we arrive at the circle of radius 10 and center (-1,4).
Step-by-step explanation:
First of all, remember that all circles are similar to each other regardless of how to twist the cartesian plane.
Jaime had $37 in his bank account on Sunday. The table shows his account activity for the next four days. What was the balance in Jaime’s account after his deposit on Thursday?
To support a tree damaged in a storm, a 12-foot wire is secured from the ground to the tree at a point 10 feet off the ground. The tree meets the ground at a right angle.
At approximately what angle does the wire meet the ground?
Tiana's checking account charges a $7.75 monthly service fee and a $0.16 per-check fee. If Tiana writes 17 checks per month, should she switch to a checking account that charges a $10.50 monthly service fee and no per-check fee? A. No, because her monthly fees are currently greater than $10.50. B. No, because her monthly fees are currently less than $10.50. C. Yes, because her monthly fees are currently less than $10.50. D. Yes, because her monthly fees are currently greater than $10.50.
the answer to this question is B
Answer:
Option B. is correct.
Step-by-step explanation:
Tiana's checking account charges a $7.75 monthly service fee and $0.16 per check fee.
If Tiana writes 17 checks per month, her total charges =
0.16 × 17 = 2.72 + 7.75 = $10.47
Her total account charges $10.47 for 17 checks.
In the question it is asking that she should switch to a checking account that charges a $10.50 monthly service fee and no per check fee.
Answer : No, because her monthly fees are currently less than $10.50.
Decide which of the two points lies on the graph of the line
X+y=6
A. 2,2
B. 5,1
Hi can I find the missing coordinates of this parallelogram ?
Think about what you have learned about parallel and perpendicular lines. In what profession might a person rely upon this information? Describe how that person would apply these concepts.
A red candle is 8 inches tall and burns at a rate of 710 inch per hour. a blue candle is 6 inches tall and burns at a rate of 15 inch per hour. after how many hours will both candles be the same height? enter your answer in the box.
Answer:
5 hour
Step-by-step explanation:
There are 180 pages in the book Diana is reading. Diana has read 90 pages. What percent of the book has she read?
2 people are going to equally share 5 kg, of chocolate. how many kilograms of chocolate should each person get?
5 kilograms divided by 2 is 2.5 kilograms
21: stan bought a monster truck for $2,000 down and payments of $450 a month for five years. what's the total cost of the monster truck?
Answer:
The total cost of the monster truck = 29000 $
Step-by-step explanation:
Stan bought a monster truck for $2,000 down and payments of $450 a month for five years.
Initial payment = 2000 $
Monthly payment = 450 $
Number of years paid = 5
Number of months in 5 years = 12 x 5 = 60
Total amount paid = 2000 + 60 x 450 = 29000 $
The total cost of the monster truck = 29000 $
the table shows the sales of admission tickets to a science museum. A table labeled Science Museum Admission Revenue. It contains a row for Tickets Sold with the amounts 128, 264, 308, 514, 520, 650, 722, and a row for Sales with the amounts 1088, 2244, 2618, 4369, 5525, and 6137. The equation y = 9.75x represents the number of dollars, y, earned by an art museum for selling x tickets. Which statements about the costs of the admission tickets at the museums are true? Select each correct answer. It costs $9.75 per ticket for admission to the art museum. It costs $8.75 per ticket for admission to the science museum. Art museum tickets are more expensive than science museum tickets. Given the same number of ticket sales, the science museum earns more revenue. 1 2 3 4 5
Answer: It costs $9.75 per ticket for admission to the art museum.
Art museum tickets are more expensive than science museum tickets.
Step-by-step explanation:
From the given table of Science Museum Admission Revenue, we can see that the sales amount by selling 128 tickets = $1088
Therefore, the cost of each ticket for science museum =[tex]\frac{1088}{128}=\$8.5[/tex]
∴ It costs $8.5 (not 8.75) per ticket for admission to the science museum.
Also,The equation [tex]y = 9.75x[/tex] represents the number of dollars, y, earned by an art museum for selling x tickets.
At x=1, y=9.75
∴ It costs $9.75 per ticket for admission to the art museum.
Clearly, 9.75>8.5
∴ Art museum tickets are more expensive than science museum tickets.
If the number of ticket sales will be same then art museum will earn more revenue.
Since the price of one ticket to an art museum ($9.75) is higher than the price per ticket for science museum ($8.5), therefore the following statements about the cost at both museums would be true:
Price per ticket for admission to the art museum cost $9.75 (Option A)
Art Museum tickets cost more than that of science (Option C).
Price per ticket to a science museum:
Given the table showing the sales of admission tickets to a science museum:
Thus,
The unit rate/price per ticket sold at the science museum using a pair of values from the table, say, (128, 1088) is: y/x
Thus:
unit rate/price per ticket = [tex]\frac{1088}{128} = 8.5[/tex]That is, a ticket to a science museum costs $8.5.
Price per ticket to an art museum:
The equation, y = 9.75x is given as the equation modelling the situation.
Where x = number of tickets soldy = amount in dollarsThus, this means that the price per ticket to the art museum is: $9.75.
Therefore, since the price of one ticket to an art museum ($9.75) is higher than the price per ticket for science museum ($8.5), therefore the following statements about the cost at both museums would be true:
Price per ticket for admission to the art museum cost $9.75 (Option A)
Art Museum tickets cost more than that of science (Option C).
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Which of the following has the ability to turn light energy into chemical energy? A. a generator B. an automobile C. a tree D. water
Which transformations are needed to change the parent cosine function to y=3cos(10(x-pi))
The parent cosine function is transformed [tex]y=3cos(10(x-\pi ))[/tex] by vertically stretching it by a factor of 3 (amplitude), horizontally compressing it by a factor of 10 (frequency), and shifting it to the right by [tex]\pi[/tex] units (horizontal shift or phase shift).
The question asks which transformations are required to alter the parent cosine function to [tex]y=3cos(10(x-\pi ))[/tex]. The transformations involved in this equation are:
Amplitude modification: The coefficient '3' indicates that the amplitude of the cosine function is scaled by a factor of 3.Frequency adjustment: The factor '10' inside the cosine function affects the function's frequency, indicating the function has 10 complete cycles within the interval of [tex]2\pi[/tex] radians. This is a horizontal scaling transformation.Horizontal shift (or phase shift): The subtraction of [tex]\pi[/tex] within the argument of the cosine function translates the function [tex]\pi[/tex] units to the right along the x-axis.No vertical shift is present because there is no addition or subtraction outside the cosine function.
To transform the parent cosine function [tex]\(y = \cos(x)\) to \(y = 3 \cos(10(x-\pi))\)[/tex], apply a vertical stretch by 3, horizontal compression by 1/10, and a right shift by [tex]\(\pi\)[/tex] units.
To transform the parent cosine function[tex]\(y = \cos(x)\)[/tex] to the function [tex]\(y = 3 \cos(10(x-\pi))\)[/tex], we need to apply the following transformations:
1. Amplitude change: Multiply the function by [tex]\(3\)[/tex], which increases the amplitude.
2. Horizontal compression: Multiply the input of the cosine function by [tex]\(10\),[/tex]which compresses the graph horizontally.
3. Phase shift: Shift the graph to the right by [tex]\(\pi\)[/tex]units, indicated by the term [tex]\(x - \pi\).[/tex]
So, the transformations needed are:
- Amplitude change: Vertical stretch by a factor of [tex]\(3\).[/tex]
- Horizontal compression: Compression by a factor of [tex]\(1/10\).[/tex]
- Phase shift: Right shift by [tex]\(\pi\)[/tex] units.
the top of a certain mountain in California has an altitude of 14,721 ft above sea level. The bottom Death Valley is 282 ft below sea level. using 0 as sea level, find the difference between these two elevations. what is the difference between these two elevations?
Which postulate or theorem can be used to prove that △ABD≅△CBD?
ASA Congruence Postulate
SAS Congruence Postulate
SSS Congruence Postulate
HL Congruence Theorem
Answer:
SAS
Step-by-step explanation:
Max rented a motorbike at $465 for 5 days. If he rents the same motorbike for a week, he has to pay a total rent of $625.
Write an equation in the standard form (Ax + By = C) to represent the total rent (y) that Max has to pay for renting the motorbike for x days.
A painter uses 1.2 liters of the paint to cover 1m2 of the wall. How many square meters he can cover with (1)12 liters; (2)6.6 liters; (3)4.8 liters of paint?
Answer:
He can cover 10 sq. meters using 12 liters, 5.5 sq. meters using 6.6 liters, and 4 sq. meters using 4.8 liters of paint.
Step-by-step explanation:
1. 12 LITERS/ 1.2 LITERS = 10 SQ. METERS
2. 6.6 LITERS/ 1.2 LITERS = 5.5 SQ. METERS
3. 4.8 ITERS/ 1.2 LITERS = 4 SQ. METERS
Solve. 5m+72=−2m+52 Drag and drop the answer into the box.
rewrite the expression as a multiple of a sum of two numbers with no common factor 15+24 _____
To rewrite the expression as a multiple of a sum of two numbers with no common factor, find the prime factorizations of the given numbers and then multiply them together which brings the result as 39.
Explanation:To rewrite the expression as a multiple of a sum of two numbers with no common factor, we need to find two numbers that have no common factors and multiply them together. Let's find the prime factorizations of 15 and 24:
15: 3 × 524: 2 × 2 × 2 × 3Now we can rewrite the expression as:
15 + 24 = (3 × 5) + (2 × 2 × 2 × 3) = 3 × (5 + 8) = 3 × 13 = 39
So, 15 + 24 can be written as a multiple of 3 × 13, which is 39.
You forget the last two digits of your password for a website. What is the probability that you randomly choose the correct digits?
What is the significance of the mean of a probability distribution? choose the correct answer below.
a. it gives information about how the outcomes vary.
b. it represents the most likely possible outcome.
c. it is the expected value of a discrete random variable.
d. it can never be negative?
Answer:
Step-by-step explanation:
ANSWER C : It is the expected value of a discrete random variable
Which is the next number in this pattern. What is the rule ? 0,1,1.5,1.75
A.2
B.1.875
C.1.85
D.1.8
Determine the ordered pair that lies on the unit circle corresponding to startfraction 5 pi over 4 endfraction .
A small airplane used 5 2/3 gallons of fuel to fly 2 hour trip. How many gallons were used each hour
How many complex roots does the polynomial equation have?
−3x^4−7x+17=0
2
3
4
5
For a normal distribution, the z value for an x value that is to the right of the mean is always:
In a normal distribution, the Z value for an X value that is to the right of the mean is always positive. It indicates how many standard deviations X is larger than the mean. Conversely, Z values are negative for X values to the left of the mean because they are smaller than the mean.
Explanation:In a normal distribution, the Z value corresponds to the number of standard deviations a value X is from the mean. Specifically, for an X value that is to the right of the mean, the Z score will always be positive. This is because values to the right of the mean are larger than the mean.
For example, if X = 10 and the mean is 5, and this corresponds to a Z score of 2.5, it means that X is 2.5 standard deviations to the right of the mean. In other words, X is larger than the mean by 2.5 times the standard deviation. The actual Z score, such as 2.5 in this example, indicates how far the score is from the mean, with greater Z scores indicating values further to the right of the mean.
In contrast, X values to the left of the mean have negative Z scores, indicating they are smaller than the mean. Finally, if X equals the mean, then X has a Z score of zero. This basic understanding of Z scores and their relation to the mean in a normal distribution is crucial in many statistical analyses.
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