SOLUTION
The polygons are enclosed together to form a triangle.
To know if the triangle are similar, we use the ratio of the sides,
Using the Sides-Sides-Sides(SSS) rule which states that two triangles are similar if all the corresponding three sides of the given triangles are in the same proportion.
From triangle EFG, we have
\(\begin{gathered} |EF|=8\text{ units } \\ |FG|=4\text{unit} \\ |EG|=8\text{units } \end{gathered}\)Considering the triangle JLR, we have
\(\begin{gathered} |JL|=4\text{unit} \\ |LR|=2\text{unit } \\ |JR|=4\text{unit} \end{gathered}\)Comparing the ratio of the sides,
we have
\(\begin{gathered} \frac{|EF|}{|JL|}=\frac{8}{4}=2 \\ \text{Also} \\ \frac{|FG|}{|LR|}=\frac{4}{2}=2 \\ \text{And} \\ \frac{|EG|}{|JR|}=\frac{8}{4}=2 \end{gathered}\)Since the sides are in the same proportion,
Hence
The polygons are similar
the bakery sold 60 cheesecakes yesterday. 4/5 of the cheesecakes were vanilla. How many vanilla cheesecakes were sold?
Answer:
60 x 4/5 = 240/5 = 48
48 vanilla cheesecakes
what are composite numbers out of 49, 35, 32, 41, and 47
Step-by-step explanation:
Composite numbers are 32,35,and 49 .
I hope it's helpful!
Simon drove 55 miles per hour for 4 hours then 65 miles per hour for 3 hours how far did Simon drive in all
Answer:
415 miles
Step-by-step explanation:
Start with the speed equation:
speed = distance/time
Now solve the speed equation for distance:
distance = speed × time
Apply the speed equation solved for distance to the two parts of the trip.
4 hours at 55 mph:
distance = 55 mph × 4 hours = 220 miles
3 hours at 65 mph:
distance = 65 mph × 3 hours = 195 miles
Add the two distances to find the total distance:
total distance = 220 miles + 195 miles = 415 miles
Answer: 415 miles
Answer:
415 miles
Step-by-step explanation:
Simon drove 55 miles per hour for 4 hours then 65 miles per hour for 3 hours.
How far did he drive?
d=rt
For the first part of the trip:
d = 55 * 4 = 220 miles
For the second part of the trip:
d = 65*3 =195 miles
Add the miles together
220+195 = 415 miles
URGENT!!!! Find the y-intercept of the line that passes through the points (-3, 7) and (3, −9).
Answer:
\(m = \frac{ - 9 - 7}{3 - ( - 3)} = \frac{ - 16}{6} = - \frac{8}{3} \)
\(7 = - \frac{8}{3} ( - 3) + b\)
\(7 = 8 + b\)
\(b = - 1\)
\(y = - \frac{8}{3} x - 1\)
The y-intercept is -1.
Scott runs 3 km in 30 minutes and then rests for 15 minutes. He then runs 2 km in 15
minutes. What was Scott's average speed?
Answer:
5km/hr
Step-by-step explanation:
Given
Distance = 3km and 2km
Time = 30 mins, 15 mins, 15 mins
Required
Determine the average speed
To answer this, we need to determine the total distance.
Distance =3km + 2km = 5km
Then, we calculate the total time
Time = 30 mins + 15 mins + 15 mins = 1 hr
Next, we can now determine the average speed using:
Average Speed = Total Distance/Total Time
Average Speed = 5km/1 hr
Average Speed = 5km/hr
Select all lengths that are equal to 3 yards 16 inches.
The lengths equal to 3 yards 16 inches are 3 yards, 108 inches, 3.44 yards (approximately), and 108.44 inches (approximately).
To determine the lengths that are equal to 3 yards 16 inches, we need to convert the measurements into a consistent unit. Since both yards and inches are units of length, we can convert the inches into yards or the yards into inches to find the equivalent lengths.
1 yard is equal to 36 inches (since 1 yard = 3 feet and 1 foot = 12 inches).
Therefore, 3 yards is equal to 3 * 36 = 108 inches.
Now, we can compare 108 inches to 3 yards 16 inches.
108 inches is equal to 3 yards, so it matches the given length.
To convert 16 inches into yards, we divide it by 36 since 1 yard = 36 inches. 16 inches / 36 = 0.44 yards.
Therefore, 3 yards 16 inches is equivalent to:
3 yards
108 inches
3 yards 0.44 yards (or approximately 3.44 yards)
108 inches 0.44 yards (or approximately 108.44 inches)
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Fill in the table using this function rule y= - 2x + 3
Step-by-step explanation:
you just have to put that value in place of x in the function.
don't be so lazy you a hole do it yourself
A clothing eCommerce company has an Average Order Value of USD 65. It costs the company USD 35 to produce the clothes in the average order and USD 15 to ship it to the customer. What is the Average Order's Gross Profit?
USD 65
USD 30
USD 15
USD 50
The Average Order's Gross Profit for the clothing eCommerce company in this scenario is USD 15.
For the Average Order's Gross Profit for the clothing eCommerce company in this scenario, we need to subtract the cost of production and shipping from the Average Order Value as;
⇒ Gross Profit = Average Order Value - Cost of production - Cost of shipping Gross Profit
⇒ Gross Profit = USD 65 - USD 35 - USD 15
⇒ Gross Profit = USD 15
Therefore, the Average Order's Gross Profit for the clothing eCommerce company in this scenario is USD 15.
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The figure to the right shows the distance-time graph for a muscle car accelerating from a standstill. Use the information in the figure to answer parts (a) and (b). The table below lists the coordinates of the points.
The acceleration of the car is 8 m/s^2.
The figure shown in the question is the distance-time graph of a muscle car accelerating from a standstill. The table lists the coordinates of points on the graph.The following observations can be made from the graph and the table: The car is at rest at time t=0 and at distance x=0. It then starts accelerating, and its speed increases uniformly with time. The slope of the distance-time graph is the velocity of the car.
Since the velocity is increasing uniformly, the slope of the graph is a straight line with a positive slope. The area under the graph between two points gives the displacement of the car during that time interval. The displacement can be calculated as the product of the average velocity and the time interval. Using the coordinates in the table, we can calculate the average velocities for each time interval and the displacement during that interval.
(a) The average velocity of the car between t=0 and t=2 is equal to the slope of the graph between the two points (0,0) and (2,32). This can be calculated as the difference in distance divided by the difference in time:Average velocity = (32 - 0) / (2 - 0) = 16 m/sThe displacement during this time interval is given by the area under the graph between the two points:Displacement = (1/2) x 32 x 2 = 32 m
(b) The acceleration of the car is given by the slope of the velocity-time graph. Since the velocity is increasing uniformly with time, the velocity-time graph is also a straight line with a positive slope. The slope of the velocity-time graph is equal to the acceleration. We can calculate the slope of the velocity-time graph between two points using the coordinates in the table. For example, the slope between t=0 and t=2 is given by the difference in velocity divided by the difference in time:Slope = (16 - 0) / (2 - 0) = 8 m/s^2
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I need help , any of u guys have the answer?
how do you solve for x
-3x-6y=0
Answer:
x = 2y
Step-by-step explanation:
Simplifying
3x + -6y = 0
Solving
3x + -6y = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '6y' to each side of the equation.
3x + -6y + 6y = 0 + 6y
Combine like terms: -6y + 6y = 0
3x + 0 = 0 + 6y
3x = 0 + 6y
Remove the zero:
3x = 6y
Divide each side by '3'.
x = 2y
Simplifying
x = 2y
All numbers have postive absolute value true or false need help plz 10 point
Answer:True
There is no way to have a negative because it's the number's distance from zero
Find the median: 16.12.7.9.10.16
Answer:
hey hi mate
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When it rains, every student in Margo's school brings a raincoat, an umbrella, or both. And 50% of the students bring both. The total number of umbrellas brought is equal to twice the number of raincoats.
What percent of the students bring an umbrella only? Explain your solution in complete sentences.
71.4% of the students bring an umbrella only.
What is the percentage?
Percentage is a way of expressing a number as a fraction of 100. It is represented by the symbol %. It is a useful way of comparing values and calculating changes over time.
Let's denote the total number of students in Margo's school by the letter N. We can use a Venn diagram to represent the number of students who bring a raincoat, an umbrella, or both, as shown below:
RAINCOAT UMBRELLA
________ ________
| | | |
| | | |
| | | |
| A | | C |
| | | |
| | | |
|________| |________|
BOTH (B) ONLY (D)
We know from the problem statement that 50% of the students bring both a raincoat and an umbrella. Therefore, the number of students who bring both is equal to 0.5N.
We also know that the total number of umbrellas brought is twice the number of raincoats. Let's denote the number of raincoats brought by the letter A. Then the number of umbrellas brought is equal to 2A.
We can use these values to fill in the Venn diagram. The total number of students is N, so the number of students who bring only a raincoat is (A - 0.5N) and the number of students who bring only an umbrella is (2A - 0.5N). The number of students who bring both is 0.5N.
To find the percentage of students who bring an umbrella only, we need to divide the number of students who bring only an umbrella by the total number of students and multiply by 100:
(2A - 0.5N) / N * 100
We can simplify this expression using the fact that the number of umbrellas brought is twice the number of raincoats:
(2A - 0.5N) / N * 100
= (2 * A - 0.5N) / N * 100
= (3A - 0.5N) / N * 100
We can't directly solve for the value of A, but we can use the fact that the sum of the numbers in the Venn diagram adds up to N:
A - 0.5N + 0.5N + 2A - 0.5N = N
3.5A - N = N
A = 2N / 7
Substituting this value of A into the expression for the percentage of students who bring an umbrella only, we get:
(3A - 0.5N) / N * 100
= (3 * 2N / 7 - 0.5N) / N * 100
= 71.4%
Therefore, 71.4% of the students bring an umbrella only.
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A paint can has a radius of 4 inches and a height of 15 inches. What is the volume of the paint can? Round to t tenth. Use 3.14 for cubic inches
Answer:
Step-by-step explanation:
r=4 in
h=15 in
The paint can is a cylinder. The volume of the cylinder is: V=S×h (S stands for the area of the base, h is for height).
The area of our cylinder's base is a circle, so:
S=πr²=4²×π=16π≈50.24 (in²)
Thus, the volume is:
V≈50.24×15≈753.6 (in³)
The machinery in a cereal plant fills 350 g boxes of cereal. The specifications for the machinery permit for a certain amount of fill tolerance. It is found that the weights of filled cereal boxes are normally distributed with a mean of 350 g and a standard deviation of 4 g. What is the probability that a box of cereal is under filled by 5 g or more?
There is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.
To find the probability that a box of cereal is underfilled by 5 g or more, we need to calculate the probability of obtaining a weight measurement below 345 g.
First, we can standardize the problem by using the z-score formula:
z = (x - μ) / σ
Where:
x = the weight value we want to find the probability for (345 g in this case)
μ = the mean weight (350 g)
σ = the standard deviation (4 g)
Substituting the values into the formula:
z = (345 - 350) / 4 = -1.25
Next, we can find the probability associated with this z-score using a standard normal distribution table or a statistical calculator.
The probability of obtaining a z-score less than -1.25 is approximately 0.1056.
However, we are interested in the probability of underfilling by 5 g or more, which means we need to find the complement of this probability.
The probability of underfilling by 5 g or more is 1 - 0.1056 = 0.8944, or approximately 89.44%.
Therefore, there is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.
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Point: (2,7)
Reflected across y-axis: (-2,7)
Reflected across x-axis: ????
My options for the answer is
(-7,-2)
(-2,7)
(2,-7) which answer is it I have already tried the first one and it said it was wrong.
Answer:
(2,-7)
Step-by-step explanation:
Reflection rule for across the x-axis: \((x,y)\rightarrow (x,-y)\)
Using the rule and point (2,7):
\((2,7)\rightarrow(2,-7)\)
(2,-7) should be the correct answer.
Brainilest Appreciated.
HURYY PLEASE LIKE RN
Answer:
\(\huge\boxed{\sf 252\ in.\²}\)
Step-by-step explanation:
TOP and BOTTOM:
Surface Area = 2 ( Length * Breadth)
SA = 2 ( 6 * 12 )
SA = 2 (72)
SA = 144 in. ²
FRONT and BACK:
SA = 2 ( Length * Breadth)
SA = 2 ( 3*12 )
SA = 2 (36)
SA = 72 in.²
SIDES:
SA = 2 ( Length * Breadth )
SA = 2 ( 3 * 6 )
SA = 2 (18)
SA = 36 in.²
Adding all to get the SA of rectangular prism:
= 144 + 72 + 36
= 252 in.²
\(\rule[225]{225}{2}\)
Hope this helped!
~AH1807You can use the notation P(A), read “the probability of event B, given event A” to write a
A. Probability distribution
B. Frequency table
C. Conditional probability
D. Cumulative probability
You can use the notation P(A), read “the probability of event B, given event A” to write a conditional probability. The correct answer is C.
Conditional probability refers to the probability of one event occurring given that another event has already occurred. In this case, we are interested in the probability of event B occurring given that event A has already occurred, and we can represent this using the notation P(B|A), where '|' means 'given'.
For example, let's say we are interested in the probability of getting a head on a coin toss (event B), given that the coin was flipped and landed on heads (event A). We could represent this using the notation P(B|A). The value of P(B|A) would be 1, because if the coin already landed on heads, then the probability of getting a head on the next flip is certain.
Conditional probability is an important concept in probability theory and is often used in real-world applications, such as predicting the likelihood of a disease given certain symptoms, or the probability of an event occurring given certain conditions.
The correct answer is C.
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Finding Circumference The radius is cm. v cm OZ The circumference in terms of ais Using 3.14 for A, the approximate circumference of the circle is cm. d=2cm
Answer:7picm Circumference = pi x d Diameter = 7 C = pi x 7 C = 7pi cm.
Step-by-step explanation:
The circumference of the circle with diameter 2 cm is 6.28 cm.
What is a circle?A circle is a round-shaped figure that has no corners or edges. In geometry, a circle can be defined as a closed, two-dimensional curved shape.
Given that a circle has a diameter of 2 cm we need to find its circumference,
The circumference of a circle is given by, π × diameter
Therefore, the circumference of the circle with diameter 2 cm =
= π × diameter
= π × 2
= 3.14 × 2
= 6.28 cm
Hence, the circumference of the circle with diameter 2 cm is 6.28 cm
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In a right triangular prism, the area of the triangular base is 50 square feet. The height of the prism is 12 feet. What is the volume of the prism?
A.10yd
B.15yd
C.13yd
D.6yd
We know for all 3D shapes
Volume=Area of base×HeightNow
Area of base=50ft^2Height=12ftVolume:-
\(\\ \rm\rightarrowtail 50(12)\)
\(\\ \rm\rightarrowtail 600ft^3\)
1 yd=3 ft1yd^3=27ft^3\(\\ \rm\rightarrowtail Volume=600/27=22.2yd^3\)
Somewhat wrong in the options
Answer:
600ft
Step-by-step explanation:
The function h(t) =-5t^{2}+3t+1 represents the height of an apple, in meters, `t` seconds after it is tossed straight up in the air.
How many seconds will it take for the apple to reach the ground?
Round to three decimal places if necessary.
To find when the apple will reach the ground, we need to find when the height of the apple is zero.
So, we set h(t) = 0 and solve for t:
-5t^2 + 3t + 1 = 0
Using the quadratic formula, we get:
t = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = -5, b = 3, and c = 1.
Plugging in the values, we get:
t = (-3 ± sqrt(3^2 - 4(-5)(1))) / 2(-5)
Simplifying:
t = (-3 ± sqrt(49)) / (-10)
t = (-3 ± 7) / (-10)
t = 0.4 or t = 1.3
We discard the negative value since time cannot be negative, so the apple will reach the ground after approximately 1.3 seconds.
Therefore, it will take 1.3 seconds for the apple to reach the ground.
Hope this helped (:
Assume that y varies inversely
with x. Ify = 7 when x = 2/3, find
y when x = 7/3.
Y=?
Answer:
y = 2
Step-by-step explanation:
y varies inversely with x setup is:
y = k/x
7 = \(\frac{k}{2/3}\) (find 'k')
k = 7/1 · 2/3
k = 14/3
use what you know about 'k' and 'x' to solve for 'y'
y = 14/3 ÷ 7/3 (remember to multiply by the reciprocal when dividing fractions)
y = 14/3 · 3/7
y = 2
Which expressions are equivalent to k/2?
CHOOSE 2!
(Choice A)
k-2
(Choice B)
2/k
(Choice C)
1/2k
(Choice D)
k divided by 2
(Choice E)
k+k
Answer:
(Choice C)
1/2k
and
(Choice D)
k divided by 2
Step-by-step explanation:
k/2 is basically 1/2k and choice d is explaining what the expression is.
May I please have brainliest? Thank you!
In a board game, you gain 1.5x the number of coins in your purse every time you pass start. However, you max out at 300 coins. If you have 5 coins in your purse, how many times must you pass until you reach maximum?
Answer:
6
Step-by-step explanation:
The requried number of passes to reach the maximum is given as 10 passes.
What is an exponential function?The function which is in format f(x) =aˣ where a is constant and x is variable, the domain of this exponential function lies (-∞, ∞).
Here,
We have 5 coins in your purse,
We Gain 1.5x the number of coins in your purse every time you pass the start. The maximum number of coins is 300.
According to the quesiton,
5 . 1.5ˣ = 300
Where x is the number of passes,
1.5ˣ = 60
x ≈ 10
Thus, the requried number of passes to reach the maximum is given as 10 passes.
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Use the function below to find F(3)
F(x)=(1/5)^x
The value of the function F(3) will be 1/125. It is obtained by putting the value 3 in the place of x.
What is a function?A connection between independent variables and the dependent variable is defined by the function. Functions help to represent graphs and equations.
A function is represented by the two variables one is dependent and another one is an independent function. The relation between them is shown as y if dependent and x is the independent variable.
F(x)=(1/5)ˣ
F(3)=(1/5)³
F(3)=1/125
Hence, the value of the function F(3) will be 1/125.
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Which equation best represents the graph of the absolute value function?
Of(0) = 2x] – 5
O f(x) = 2x - 5]
O f() = 2x + 5)
O f() = 2x + 5
Pleaseeeee helppp quick
Answer:
A. The triangles are similar because the ratios of the corresponding sides are the same
Step-by-step explanation:
Both ∆sloom similar in shape. Let's find out if they are actually similar.
∆TUV and ∆QRS are similar if the ratio of their corresponding sides are the same all through.
Thus:
TU = 70, QR = 25, UV = 84, RS = 30, TV = 42, QS = 15
If both ∆s are similar, then, TU/QR = UV/RS = TV/QS
TU/QR = 70/25 = 2.8
UV/RS = 84/30 = 2.8
TV/RS = 42/15 = 2.8.
Ratio of corresponding sides is the same, therefore, both triangles are similar.
Therefore, the following statement is true:
A. The triangles are similar because the ratios of the corresponding sides are the same
What is the total surface area
Answer:
Step-by-step explanation:
graph the inequality 7< y -3x < 11
Answer:
X=5 Y=-4
Step-by-step explanation: