Answer: The value of x = 16 units, y = 4.5 units and z = 7.5 units.
Step-by-step explanation:
Since we have given that
ABCD and EFGH are two similar polygons.
Dimensions of ABCD are as follows :
AB = 6 units
BC = 8 units
AD = x units
CD = 10 units
Dimensions of EFGH are as follows :
EF = y
FG = 6 units
EH = 12 units
GH = z
Since they are similar:
[tex]\dfrac{AB}{EF}=\dfrac{BC}{FG}=\dfrac{CD}{GH}=\dfrac{AD}{EH}\\\\\dfrac{6}{y}=\dfrac{8}{6}=\dfrac{10}z}=\dfrac{x}{12}[/tex]
First we take,
[tex]\dfrac{6}{y}=\dfrac{8}{6}\\\\y=\dfrac{36}{8}\\\\y=4.5\ units[/tex]
similarly,
[tex]\dfrac{8}{6}=\dfrac{10}{z}\\\\z=\dfrac{60}{8}\\\\z=7.5\ units[/tex]
similarly,
[tex]\dfrac{8}{6}=\dfrac{x}{12}\\\\x=\dfrac{96}{6}\\\\x=16\ units[/tex]
Hence, the value of x = 16 units, y = 4.5 units and z = 7.5 units.
Answer:
its not 7.5!!! i just took the test and its wrong!!
A train went 224 miles in 4 hours. A jet is ten times as fast as the train. Find the jet’s speed. plz answer ASAP
Answer:
560 miles per hour
Step-by-step explanation:
First, what you do is divide 224 by 4.
224 ÷ 4 = 56
You do this because you need to find the rate it goes in one hour.
Next, you do 56 times 10.
56 × 10 = 560
Hope that helps!
560miles per hour is the jets speed .
What is Speed?Speed is the time rate at which an object is moving along a path,
Given,
A train went 224 miles in 4 hours
A jet is ten times as fast as the train.
We need to find the jets speed.
Speed = Distance / time
Train speed=224/4
=56miles/hour
So train travels 56 miles in one hour.
As given, A jet is ten times as fast as the train
So we have to multiply 10 with the 56
10×56
560miles per hour
Hence, 560miles per hour is the jets speed .
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Write as a numeral: 200,000+20,000+3,000+200+20+8
[tex]200,000+20,000+3,000+200+20+8=223,228\\\\200,000\\.\ 20,000\\.\ \ 3,000\\.\ \ \ \ \ 200\\.\ \ \ \ \ \ \ 20\\\underline{+\qquad\ 8}\\223,228[/tex]
Point M is between points L and N on segment LN. LM=5x, MN=2x+4, and LN=10x-16
Use the information to solve for x, and then find LN, LM, and MN.
Answer:
x= 6.6
LM= 33
MN= 17.2
LN=50
Step-by-step explanation:
10x-16= 5x+2x+4 (LN=LM+MN)
10x-16=7x+4
3x-16=4
3x=20
x=6.6
then plug 6.6 back into equation and round to the nearest whole number.
Complete this sentence: The Longest side of a triangle is always opposite the _________.
The longest side of a triangle is opposite the largest interior angle, same goes to the opposite. The shortest side of a triangle is opposite the smallest interior angle.
Hope this helps! <3
Answer:
Largest angle
Step-by-step explanation:
In any triangle, the longest side is opposite the largest angle. The smallest side is opposite the smallest angle.
There are 40 girls and 32 boys who want to participate in the relay race. If each team must have the same number of girls and boys, A) what is the greatest number of teams that can race? B) How many boys and girls will be on each team?
Answer:
8 teams
5 girls and 4 boys
Step-by-step explanation:
To determine how many teams we can have , we need to determine the greatest common factor.
girls:40 = 5*8
boys:32 = 4*8
The greatest common factor is 8
So we will have 8 teams
There will be 5 girls and 4 boys on each team
The area of the sheet of paper is square inches
multiplying integers
3(-7)
Answer:
-21
Step-by-step explanation:
3(-7)
3*7 =21
A positive times a negative is a negative
-21
Answer:
3x-7=21 ( i think )
Step-by-step explanation:
when you have a parenthesis beside a number you always multiply. A negative times a positive is a negative,
how to solve 18 + 3(9f-13)
Answer:
Distribute so it would be 18+27f-39
Step-by-step explanation:
Step 1: Distrbute 3 into (9f - 13)
3 • 9f = 27f
3 • 13 = 39
18 + 27f - 39
Step 2: Solve like-terms
(18 and 39 are the only like terms. 27f and 39 aren't like terms since 39 doesn't have a variable therefore, you can't solve 27f - 39)
39 - 18 = 21
ANSWER:
27f - 21
Hope this is correct!
- justy⊕∪rultimαtefαngirlWhat number is 0.95 of 3500
Answer:
Alright well Convert fraction to an decimal, then multiply by 100
0.02714285% Hope this helps have a nice day :)
Step-by-step explanation:
he revenue, in dollars, of a company that produces jeans can be modeled by 2x2 + 17x – 175. The cost, in dollars, of producing the jeans can be modeled by 2x2 – 3x – 125. The number of pairs of jeans that have been sold is represented by x. The profit is the difference between the revenue and the cost, 20x – 50. If 75 pairs of jeans are sold, what is the company’s profit?
Answer:
So, the company profit if 75 pairs of jeans are sold is $1450
Step-by-step explanation:
The number of pairs of jeans that have been sold is represented by x
We are given
The profit is the difference between the revenue and the cost , 20x-50
Let's assume profit function as P(x)
[tex]P(x)=20x-50[/tex]
There are 75 pairs of jeans
so, x=75
we can plug x=75 and find profit
[tex]P(75)=20\times 75-50[/tex]
[tex]P(75)=1500-50[/tex]
[tex]P(75)=1450[/tex]
So, the company profit if 75 pairs of jeans are sold is $1450
Jorge wrote the expression x + x + x + x + 3 to represent the sequence shown in the diagram at right. Does his expression make sense? Explain.
Answer:
Step-by-step explanation:
no because x can equal anything. It should at least write down a second number for it to be solved correctly.
What is the probability that both spinners will land on 2? AMSWERS- A)1/12 B)1/6 C)1/4 D)1/3
ONE GRAPH IS 1,2,3 AND THE OTHER GRAPH SHOWS 1,2,3,4 OUTCOMES
Answer:
The probability that both spinners will land on 2 is A) 1/12.
Step-by-step explanation:
To get this answer you must:
-First, take the total number of outcomes and set that as you denominator, which would be 3.
-Since, your looking for the probability of two, and there is only one two you would put one as your numerator. By now you should have a fraction of: 1/3.
-Next, do the same exact thing for the next graph. Take the total number of outcomes for the graph which is 4, and set that as your denominator.
-Then, set one as your numerator since there is only one two in the other graph. You should now have a second fraction of: 1/4.
-Lastly, multiply both of the fractions. Multiply both of the numerator together and you should get one. Then, multiply both of the numbers which would result in you getting a number of 12.
1/3(1/4) = 1/12.
what is the algebr expression for the following word phrase: the produc of 4 more then x and 6?
a)4(x+6)
b) 6(x+4)
c)6+(x+4)
d)6-(x+4)
Answer:
b) 6(x + 4)
Step-by-step explanation:
The given word phrase "The product of 4 more than x and 6"
4 more than x = 4 + x
The product "4 + x" and 6
6(x + 4)
Answer: b) 6(x + 4)
Are the equations 2x + 14 = 8 and x = -3 equivalent? Explain.
Answer:
They are equivalent
Step-by-step explanation:
2x+14 = 8
Lets solve for x
Subtract 14 from each side
2x+14-14 = 8-14
2x = -6
Divide by 2
2x/2 = -6/2
x = -3
They are the same
Answer:
Yes
Step-by-step explanation:
Solving for 2x+14=8
Subtract 14 on both sides: 2x= 8-14
2x = -6
Divide by 2: x = -3
-3 = -3
Hope this helps!!
An office building casts a shadow that is 55 m long. At the exact same time, a 5 m tree casts a shadow that is 1.1 m long. Use similar triangle ratios, to calculate the height of the office building.
The ratio of the triangle is 55/1.1, which is 50/1.
This means that the building is 50/1 = x/5
x = 250
The office building is 250 m tall.
The height of the office building is calculated using similar triangle ratios, by setting up a proportion between the tree's dimensions and the building's shadow, and solving for the building's height to get 250 meters.
To calculate the height of the office building using similar triangle ratios, compare the tree's height and shadow length to those of the building. Since the tree is 5 m tall and casts a 1.1 m long shadow, we can set up a proportion with the building's shadow, which is 55 m long.
Step-by-step calculation:
Write the proportion using the tree's height and shadow: 5 m (tree height) / 1.1 m (tree shadow) = building height / 55 m (building shadow).
Cross multiply to find the building's height: 5 m × 55 m = 1.1 m × building height.
Perform the calculations: 275 m² = 1.1 m × building height.
Divide both sides by 1.1 m to solve for building height: building height = 275 m² / 1.1 m.
Complete the division: building height = 250 m.
What type of correlation is suggested by the scatter plot?
Answer: no correlation is suggested bc it's al over the graph or the scatter plot or whatever u wanna call it. but there is no correlation.
Step-by-step explanation: hope this helps ;D
What is the pattern in this sequence?
1,9,17,25,33,...
Select from the drop down box to correctly complete the rule.
First Box
Add
Multiply by
Subtract
Divide by
Second box
9
8
-5
-9
Choose one from each box!
2. The ordered pairs model an exponential growth function
{(-1, 21.875), (0,35), (1,56), (2, 89.6)}
what is the function equation?
Enter your answer in the box
F(x)=
Answer in #1 it ads up by 8
Number 1 is Add by 8
& I'm not sure about number 2
Given cos a= 3/5, sin B = 5/13 and a and B are first quadrant angles find cos(a + B)
A. 1/3
B. 16/65
C. -33/65
Please explain
Answer:
Option B is correct.
Value of cos(a+B) is, [tex]\frac{16}{65}[/tex]
Step-by-step explanation:
Using the formula:
[tex]\cos(a+B) = \cos a \cos B -\sin a \sin B[/tex]
Given the values:
[tex]\cos a = \frac{3}{5}[/tex] and [tex]\sin B = \frac{5}{13}[/tex]
Using trigonometric identity:
[tex]\sin^2 \theta + \cos^2 \theta =1[/tex]
or
[tex]\sin \theta = \sqrt{1-\cos^2 \theta}[/tex]
or
[tex]\cos \theta = \sqrt{1-\sin^2 \theta}[/tex]
Find the value of sin a and cos B;
Using trigonometric identity:
[tex]\sin a = \sqrt{1-\cos^2 a}[/tex]
[tex]\sin a = \sqrt{1-(\frac{3}{5})^2}[/tex] = [tex]\sqrt{1-\frac{9}{25}} = \sqrt{\frac{25-9}{25}}=\sqrt{\frac{16}{25} } =\frac{4}{5}[/tex]
Similarly;
[tex]\cos B = \sqrt{1-\sin^2 B}[/tex]
[tex]\cos B = \sqrt{1-(\frac{5}{13})^2}[/tex] = [tex]\sqrt{1-\frac{25}{169}} = \sqrt{\frac{169-25}{169}}=\sqrt{\frac{144}{169} } =\frac{12}{13}[/tex]
Substitute these given values equation [1] we have;
[tex]\cos(a+B) =\frac{3}{5} \cdot \frac{12}{13}-\frac{4}{5} \cdot \frac{5}{13}[/tex]
[tex]\cos(a+B) =\frac{36}{65}-\frac{20}{65}[/tex]
then;
[tex]\cos(a+B) =\frac{36-20}{65}=\frac{16}{65}[/tex]
Since, the angles a and B are in first quadrant angles therefore the value of cos(a+B) is, [tex]\frac{16}{65}[/tex]
To find cos(a + B), use the formula cos(a + B) = cos(a)cos(B) - sin(a)sin(B). Substitute the given values of cos(a) = 3/5 and sin(B) = 5/13, and solve for cos(B) using the Pythagorean identity. Then substitute all the values into the formula and simplify to find cos(a + B) = 16/65.
Explanation:To find cos(a + B), we can use the formula:
cos(a + B) = cos(a)cos(B) - sin(a)sin(B)
Given that cos(a) = 3/5 and sin(B) = 5/13, we can substitute these values into the formula:
cos(a + B) = (3/5)(cos(B)) - (sin(a))(5/13)
To find cos(B), we can use the Pythagorean identity:
cos²(B) + sin²(B) = 1
Substituting the given value of sin(B), we can solve for cos(B):
cos(B) = √(1 - (5/13)²)
Now we can substitute the values of cos(a), sin(B), and cos(B) into the formula for cos(a + B):
cos(a + B) = (3/5)(√(1 - (5/13)²))) - (5/13)(5/13)
Simplifying this expression gives us the final answer: cos(a + B) = 16/65.
plz help me with these two questions :)
If the original price is $23.99 and the mark down is 44% what is the sale price
Answer:
The sale price is $13.43
Step-by-step explanation:
In order to find the sale price of an item, we multiply it by the remaining percentage of cast left. Since we are subtracting 44% of the cost, that means that we are paying 56% of it. Therefore, we can multiply the cost by 56%
23.99 * .56 = $13.43
Answer: $13.43
Step-by-step explanation:
make your 22% a decimal by dividing it by 100 equaling 0.22 then since its markDOWN you subtract 1.00 - 0.22 equaling 0.88 then multiply 0.88 by $23.99 which is supposed to equal $13.43
What is the sum of the first seven terms of the geometric series? 3 + 12 + 48 + 192 + ... 4,372 12,288 16,383 65,535
Answer:
16,383 or C
Step-by-step explanation:
Answer:
Option 3rd is correct.
Step-by-step explanation:
Given: 3 + 12 + 48 + 192 + .......
We have to find : Sum of first seven term of the given Geometric series.
First term , a = 3
Common ratio , r = [tex]\frac{12}{3}=4[/tex]
Sum of the n term of series, [tex]S_n=\frac{a(1-r^n)}{1-r}[/tex]
So,
[tex]S_7=\frac{3(1-4^7)}{1-4}[/tex]
[tex]S_7=\frac{3(1-4^7)}{-3}[/tex]
[tex]S_7=-(1-16384)[/tex]
[tex]S_7=-(-16383)[/tex]
[tex]S_7=16383[/tex]
Therefore, Option 3rd is correct.
Brandon buys a radio for $46.49 in a state where the sales tax is 7%.
Answer:
Brandon pays $49.74 in total
Step-by-step explanation:
$46.49 x 1.07 = $49.74
Is (0,0) a solution to this system? y ≥ x^2 - 4 y < 2x - 1
A. Yes. (0,0) satisfies both inequalities.
B. No. (0,0) satisfies y < 2x - 1 but does not satisfy y ≥ x^2 - 4.
C. No. (0,0) does not satisfy either inequality.
D. No. (0,0) satisfies y ≥ x^2 - 4 but does not satisfy y < 2x - 1.
The inequality y ≥ x^2-4 satisfies (0,0) but the inequality y < 2x-1
does not satisfy (0,0).
Finding solution of both the inequalities:Consider the inequality y ≥ x^2-4 -------(i)Substitute (x,y)= (0,0) in the above inequality
0 ≥ (0^2)-4
0 ≥ -4
The above inequality is true.
Hence, (0,0) is the solution of inequality (i)
Consider the inequality y < 2x-1 ---------(ii)Substitute (x,y)= (0,0) in the above inequality
0 < 2(0) - 1
0 < -1
The above inequality is not true.
Hence (0,0) does not satisfy the above inequality (ii).
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Is the system of equations consistent, consistent and coincident, or inconsistent? y=3x+4y=3x+3 Select the correct answer from the drop-down menu.
Answer: Inconsistent
Step-by-step explanation:
y = 3x + 4 → m = 3, b = 4
y = 3x + 3 → m = 3, b = 3
These equations have the same slope but different y-intercepts so they are parallel lines which means they will never intersect.
NOTES
one solution: consistent & independent lines crossinfinite solutions: consistent & dependent same lineno solution: inconsistent parallel linesAnswer:
Inconsistent
Step-by-step explanation:
A moving walkway at an airport moves at a pace of 1.75 feet per second. If you stand on the walkway as it moves, how long will it take to transport you 280 feet? CLEAR CHECK 160 seconds 278.25 seconds 490 seconds 625 seconds
Answer:
2 minutes 40 sec
Step-by-step explanation:
Recall that distance = rate times time.
Thus, time = distance / rate.
Here,
time = 280 ft / (1.75 ft/sec) = 160 sec, or 2 minutes 40 sec
To calculate the time it takes to travel 280 feet on a moving walkway at an airport moving at a pace of 1.75 feet per second, we use the formula time = distance/pace. This equates to approximately 160 seconds.
Explanation:The question is asking about the time it takes to transport someone along a distance of 280 feet by a moving walkway in an airport, given that the pace of the walkway is 1.75 feet per second. To answer this, you use the formula of time = distance/pace. So we have time = 280 feet / 1.75 feet per second. This calculation will give you the answer in seconds. When you do this calculation, you will find that it takes approximately 160 seconds to cover that distance on the moving walkway.
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HELP PLEASE! 49 POINTS!
show work!!!!!!
Answer:
1. y = 2/3 x +2
2. y = -x -8
Step-by-step explanation:
The slope intercept form of a line is y = mx+b where m is the slope and b is the y intercept
1. y = 2/3 x +2
2. y = -x -8
ANSWER:
1. y = 2/3x + 2
2. y = -1x + -8
ABOUT SLOPE INTERCEPT FORM:
y = mx + bm represents the slopeb represents the starting point AKA the y - interceptHope this helps you!!! :)
Is 121 an irrational number?
Answer:
121 is a rational number because it can be expressed as the quotient of two integers: 121/ 1
Step-by-step explanation:
The number 121 is not a irrational number
How to determine the type of the numberFrom the question, we have the following parameters that can be used in our computation:
The number 121
When evaluated, we have
The number 121 = 121
The above number is represented by the quotient of 2 integers
using the above as a guide, we have the following:
We can conclude that the number is a rational number
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Given that lines a and b are parallel, what angles formed on line b when cut by the transversal are congruent with ∠3?
A) ∠5 and ∠6
B) ∠5 and ∠7
C) ∠6 and ∠7
D) ∠6 and ∠8
Answer:
C) ∠6 and ∠7
Step-by-step explanation:
We have been given that lines a and b are parallel. We are asked to find the angle on line b that will be congruent to angle 3.
We can see that angle 3 is under the line a and on the left side of transversal.
We know that the corresponding angles and alternate interior angles formed by two parallel lines are equal.
We can see that angle 7 corresponds to angle 3 and angle 6 is alternate interior angle of angle 3.
Therefore, angle 7 and angle 6 will be congruent with angle 3 and option C is the correct choice.
Megan purchased a new gadget for her technology hobby. She plans to sell it sometime in the future, however, its value depreciates monthly. The expression below shows the depreciated sales value of the gadget: 2020 – 22m What does the variable of the expression represent? The monthly depreciation value of the gadget. The amount of money Megan will get when she sells the gadget. The number of months Megan will wait to sell the gadget. The original value of the gadget.
Answer:
3. The number of months Megan will wait to sell the gadget.
Step-by-step explanation:
We have been given that Megan purchased a new gadget for her technology hobby. She plans to sell it sometime in the future, however, its value depreciates monthly.
The expression below shows the depreciated sales value of the gadget: [tex]2020-22m[/tex]
From above expression we can see that gadget's original value is $2020 and its value falls by $22 every month and m represents the number of months after which Megan will sell her gadget.
Therefore, the variable m represents the number of months Megan will wait to sell the gadget and 3rd option is the correct choice.
The variable m represents the number of months Megan will wait to sell the gadget and 3rd option is the correct choice. The variable m in the expression 2020 – 22m represents the number of months Megan will wait to sell the gadget.
The original value of the gadget is 2020, and the monthly depreciation value is 22.
So, the expression 2020 – 22m represents the amount of money Megan will get when she sells the gadget after m months.
If Megan waits for 0 months to sell the gadget, then m = 0 and she will get
2020 – 22 * 0 = $2020.
If Megan waits for 1 month to sell the gadget, then m = 1 and she will get
2020 – 22 * 1 = $1998.
Therefore, the variable m in the expression 2020 – 22m represents the number of months Megan will wait to sell the gadget.
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What is the pattern and slope ? Please answer !!
Answer:
The slope is 3
Step-by-step explanation:
To find the slope we can use the formula
m = (y2-y1)/ (x2-x1)
Using the points (5,14) and (-5,-16)
m= (-16-14)/ (-5-5)
= -30/-10
= 3