DE = AB, EF = BC and AC = DF, hence triangle ABC is congruent to triangle DEF.
Congruent shapeTwo shapes are said to be congruent if they have the same shape, all their corresponding angles and sides are congruent to one another.
Given that DE = AB and BC = EF.
In right triangle DEF, using Pythagoras:
DF² = DE² + EF²
Also, In right triangle ABC, using Pythagoras:
AC² = AB² + BC²
But DE = AB and EF = BC, hence:
AC² = DE² + EF²
AC² = DF²
Taking square root of both sides, hence:
AC = DF
Since DE = AB, EF = BC and AC = DF, hence triangle ABC is congruent to triangle DEF.
Find out more on Congruent shape at: https://brainly.com/question/11329400
pythagorean theorem, division, substatution, SAS
Step-by-step explanation:
edmentum
Find the product of (x − 5)2. X2 10x 25 x2 − 10x 25 x2 − 25 x2 25.
Answer:
x^2 -10x+25
Step-by-step explanation:
(x − 5)^2
(x-5)(x-5)
FOIL
first x*x = x^2
Outer -5 *x = -5x
inner -5*x = -5x
last -5*-5 =25
Add them together x^2 -5x-5x+25
Combine like terms x^2 -10x+25
Hey there!
(x - 5)^2
= (x - 5)(x - 5)
= x(x) + x(-5) - 5(x) - 5(-5)
= x(x) - 5(x) - 5(x) - 5(-5)
= x^2 - 5x - 5x + 25
COMBINE the LIKE TERMS
= x^2 - 10x + 25
Therefore, your answer is:
x^2 - 10x + 25
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Graph this line using the slope and y-intercept:
y=8x+2
Answer:
Two points, (0,2) & (1,10)
Step-by-step explanation:
We already know the first point (0,2) just by looking at the +2 in the problem
Now we use the system rise/run to solve the problem
Go up vertically 8 to get to 10 (this is the rise part)
Next, go over 1 to get your x-axis point (this is the run part)
So our next point is (1,10)
Hope this helps and please award brainliest if possible :)
Answer:
Step-by-step explanation:
Using the equation given:
8 is the gradient and 2 is the y-intercept
We can draw a point at (0,2) y-intercept
And we can substitute x with 1 to give us (1,10)
Use the diagram below for further details
Simplify the radical.
√
15
4
A.
It is simplified
B.
3
√
5
4
C.
√
15
2
D.
-
3
√
5
4
Answer:
[tex]\sqrt{154}[/tex] is A) already simplified
Step-by-step explanation:
13. If a toy rocket is launched vertically upward from ground level with an initial
velocity of 100 feet per second, then its height h after t seconds is given by the
equation h(t) = - 16+ + 100t (if air resistance is neglected).
Check the picture below.
how long will it take for it to hit the ground, or namely, what is "t" when h(t) is 0.
[tex]~~~~~~\textit{initial velocity in feet} \\\\ h(t) = -16t^2+v_ot+h_o \quad \begin{cases} v_o=\textit{initial velocity}&100\\ \qquad \textit{of the object}\\ h_o=\textit{initial height}&0\\ \qquad \textit{of the object}\\ h=\textit{object's height}&h\\ \qquad \textit{at "t" seconds} \end{cases}[/tex]
[tex]h(t)=-16t^2+100t+0\implies h(t)=-16t^2+100t\implies \stackrel{h(t)}{0}=-16t^2+100t \\\\\\ 16t^2-100t=0\implies 4t(4t-25)=0\implies \begin{cases} 4t=0\\ t=0\\[-0.5em] \hrulefill\\ 4t-25=0\\ 4t=25\\ t=\cfrac{25}{4}\\[1em] t=6\frac{1}{4} \end{cases}[/tex]
so h(t) is 0, as you saw on the picture, at two instances, once it was on the ground, 0 seconds, or t=0, and then t = 6.25, or 6 seconds and some change later.
Please help need both answers
Answer:
5) 13% 7) 3/28
Step-by-step explanation:
5)
total number of marbles: 2 + 3 + 5 + 1 + 2 + 2 = 15 marbles.
probability its blue: [tex]\frac{2}{15}[/tex] __in fraction
in percentage: [tex]\frac{2}{15}[/tex] * 100 = 13%
7)
total number of marbles: 4 + 5 + 2 + 9 + 1 = 21
probability of selecting a red marble: 5/21
then 1 marbles is reduced as not replaced.
total marbles: 21 - 1 = 20
probability of getting orange marble: 9/20
total probability: 9/20 * 5/21 = 3/28
The following graph shows the amounts customers say they are willing to pay for jeans. What is the likelihood that a customer is willing to pay at least $95?
Considering that 30 out of 120 clients are willing to pay at least $95, we use the it's concept and find that there is a 0.25 = 25% probability that a customer is willing to pay at least $95.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, we suppose that 30 out of 120 clients are willing to pay at least $95, hence:
[tex]p = \frac{30}{120} = 0.25[/tex]
There is a 0.25 = 25% probability that a customer is willing to pay at least $95.
More can be learned about the probability concept at https://brainly.com/question/15536019
Can someone help me please? Thank you.
Answer:
(2,2)
Step-by-step explanation:
x + 6y = 14
-3x + 5y = 4
x + 6y = 14
subtract 6y from both sides
x = 14 - 6y
-3(14 - 6y) + 5y = 4
-42 + 18y + 5y = 4
add 42 to both sides and simplify
23y = 46
y = 2
x = 14 - 6y
x = 14 - 6(2)
x = 14 - 12
x = 2
I need help please! I've been stuck on this for a week and its really stressful lol
Answer:
[tex]y=0.2*4^{x}[/tex]
Step-by-step explanation:
Notice when x increases 1, y is 4 times the previous one, so
the function is like [tex]y=C*4^{x}[/tex]
To determine the constant C, put any pair of (x, y)
Use x = 0, y = 0.2, so
0.2 = [tex]C*4^{0}[/tex] = C * 1 = C
then [tex]y=0.2*4^{x}[/tex]
Answer:
[tex]y=(0.2)4^x[/tex]
Step-by-step explanation:
General form of the exponential function: [tex]y=ab^x[/tex]
Substituting the first point (0, 0.2) into the function:
[tex]\implies 0.2=ab^0[/tex]
As any number to the zero power always gives one, [tex]b^0=1[/tex]
[tex]\implies0.2=a \times 1[/tex]
[tex]\implies a=0.2[/tex]
Therefore, [tex]y=(0.2)b^x[/tex]
Substituting the second point (1, 1.8) into the function:
[tex]\implies0.8=(0.2)b^1[/tex]
[tex]\implies0.8=(0.2)b[/tex]
[tex]\implies b=\frac{0.8}{0.2}[/tex]
[tex]\implies b=4[/tex]
So the final exponential equation is:
[tex]y=(0.2)4^x[/tex]
Checking the equation with the remaining two points:
[tex]x=2 \implies (0.2)4^2=3.2 \ \ \ \checkmark[/tex]
[tex]x=3 \implies (0.2)4^3=12.8 \ \ \ \checkmark[/tex]
A, B, C, or D please?
I just don’t understand this
Answer:
[tex]f(x)=\dfrac25x+\dfrac35[/tex]
Step-by-step explanation:
The data in the table means that if you input the value of x into the function, the output will be f(x).
The first two answer options are linear functions. If a function is linear, the ratio of the difference in y-values to the difference in x-values is always constant.
We can see that the x-values in the table increase by 3 each time, so the difference in x-values is 3.
By calculation, we can also see that the y-values increase by 6/5 each time, so the difference in y-values is 6/5.
Therefore, the ratio of differences is 6/5 ÷ 3 = 2/5 and is constant.
So the function is linear and has a slope (gradient) of 2/5
Therefore, the function is: [tex]f(x)=\dfrac25x+\dfrac35[/tex]
During Ms. Pepper's health class, you can calculate the recommended maximum heart rate using the formula M = 176 - have a you 0.8A. If M stands for the maximum heart rate, and A stands for a person's age, at what recommended maximum heart rate of 135 beats per minute? Round your answer to the nearest whole number. age would
The age at which the maximum heart rate would be 135 beats per minute is 51 years.
What is the age at which the maximum heart rate would be 135 beats per minute?In order to determine the age, take the following steps given this equation - M = 176 - 0.8A:
Substitute for M
135 = 176 - 0.8A
Combine similar terms
176 - 135 = 0.8A
Subtract 135 from 176
41 = 0.8A
Divide both sides by 0.8
A = 51 years
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Does anyone know the answer?
Supplementary angles are two angles whose measures add up to 180° . The two angles of a linear pair , like ∠1 and ∠2 in the figure below, are always supplementary. But, two angles need not be adjacent to be supplementary. In the next figure, ∠3 and ∠4 are supplementary, because their measures add to 180° so
angle ∠ABC 90° therefore subtract the 90 to 180 to get the final answer
180-90=90
Final Answer is ∠QRS 90
The model represents an inequality. What is the solution set for the inequality?
10. What is the circumference of a circular swimming pool with a diameter of 6 1 feet?
ft. (use 22 forpi)
Answer:
[tex]C=1342[/tex]
Step-by-step explanation:
Calculate circumference of the circle:
[tex]C=1342[/tex]
Which step could be used to solve x 3. 6 = negative 1. 7 for x in one step? Select two options. Add 3. 6 to both sides. Add Negative 3. 6 to both sides. Add 1. 7 to both sides. Add Negative 1. 7 to both sides. Subtract 3. 6 from both sides.
The steps which could be used to solve x are add negative 3. 6 to both sides and subtract 3. 6 from both sides.
What is the property of equality?Property of equality says that by performing any mathematical operation, of both sides of a expression does not change the original value of the equation.
The expression given in the problem is,
[tex]x +3.6 = -1.7[/tex]
To isolate the terms x, add Negative 3. 6 to both sides as,
[tex]x +3.6+(-3.6) = -1.7+(-3.6)\\x=-1.7-3.6\\x=5.3[/tex]
Thus, by adding negative 3. 6 to both sides, the problem can be solved.
Instead of adding negative 3.6, subtract 3.6 from both sides in the given equation can also be work and give same result as,
[tex]x +3.6-3.6 = -1.7-3.6\\x=5.3[/tex]
Thus, a step which could be used to solve x add negative 3. 6 to both sides and subtract 3. 6 from both sides.
Learn more about the property of equality ehre;
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.what is the factored form of 8x^24 - 27y^6
Answer:
I couldn't figure out how to type it so I typed it somewhere else lol. Hope it helps:)
Step-by-step explanation:
Two angles form a linear pair. The measure of one of the angles is 62°
What is the measure of the other angle in the linear pair?
The measure of the other angle in the linear pair is: 118°.
What is a Linear Pair?A linear pair is formed by two angles, whose sum equals 180 degrees.
Given that one of the angles of a linear pair is 62 degrees, the measure of the other angle will be its supplement.
Thus:
The other angle = 180 - 62 = 118°
Therefore, the measure of the other angle in the linear pair is: 118°.
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múltiplying polynomial (x+4)^2
Step-by-step explanation:
that's the answer bbbbbbbb
PLEASE HELP WILL GIVE 20 POINTS AND POSSIBLY THE BRAINLIEST THING.
Which pair of expressions are equivalent using the Associative Property of Multiplication?
6(4a ⋅ 2) = 24a ⋅ 12
6(4a ⋅ 2) = (4a ⋅ 2) ⋅ 6
6(4a ⋅ 2) = 6 ⋅ 4a ⋅ 2
6(4a ⋅ 2) = (6 ⋅ 4a) ⋅ 2
Answer:
A and D
Step-by-step explanation:
I really hope this helps, because this took me forever to figure out.
Members of a junior high basketball team want to brag about how tall they are. First, they measured each player’s height in inches. Now they have to decide whether the mean or the median is better. Which measure of center should the team use? Basketball team’s height (in inches) 64, 67, 83, 65, 66, 62, 69 The team’s mean height is. The team’s median height is. If the team members wants to brag about how tall they are, they should use their height.
If the team members want to brag about how tall they are, they should use the mean height of approximately 65.14 inches.
The basketball team should use the mean height as the measure of center to brag about how tall they are.
The team’s mean height is calculated by summing up all the heights and dividing by the total number of players. In this case, the sum of the heights is 64 + 67 + 83 + 65 + 66 + 62 + 69 = 456. Dividing 456 by the total number of players (7) gives us a mean height of approximately 65.14 inches.
The team’s median height is the middle value when the heights are arranged in ascending order. In this case, the heights arranged in ascending order are 62, 64, 65, 66, 67, 69, 83. The middle value is 66 inches.
If the team members want to brag about how tall they are, they should use the mean height of approximately 65.14 inches. The mean takes into account all the heights and provides an overall average, whereas the median only represents the middle value and may not accurately reflect the heights of all the players.
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The distance between two rivers on a city map is 8. 5 centimeters. The scale on the map states that 3 centimeters represents 6 kilometers. What is the actual distance between the two rivers in kilometers? 2. 1 kilometers 4. 25 kilometers 17 kilometers 18 kilometers.
at the start of 2015, barry’s house was worth £270 000
the value of his house has increased by 3% every year
work out the value of his house at the start of 2020
Answer:
313003.6
Step-by-step explanation:
The number increases by 3 percent every year so 313003.6 is it.
Right triangle with a leg of 25 in. and hypotenuse of 50 in. Find the missing leg.
A radio station had 100 tickets to a concert. They gave away 4 times as many tickets to listeners as to employees. How many
tickets did they give away to employees?
A. 4
B. 24
C. 20
D. 5
Which of the following represents the measures of all angles coterminal with a 418° angle? 360 58n, for any whole number n 58 360n, for any integer n 58 360n, for any whole number n 360 58n, for any integer n.
Using the concept of the angle the conditions are solved. For any whole number n, 360+58n is coterminal with 418°. option C is correct.
What is an angle?Angle is the space between the line or the surface that meets. And the angle is measured in degree. For complete 1 rotation, the angle is 360 degrees.
Given
The measures of all angles are coterminal with a 418° angle.
a. 360+58n, for any whole number n.
For any whole number n, 360+58n is not coterminal with 418° except one.
b. 58+360n, for any integer n.
For any integer number n, 360+58n is coterminal with 418° except zero.
c. 58+360n, for any whole number n.
For any whole number n, 360+58n is coterminal with 418°.
d. 360 58n, for any integer n.
For any integer number n, 360+58n is not coterminal with 418° except one.
Thus, for any whole number n, 360+58n is coterminal with 418°. option C is correct.
More about the angle link is given below.
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Point Q" is the image of point Q after a composition of transformations: A reflection over line m, followed by a reflection over line n.
If m and n intersect to form a 44 degree angle, what is the angle of rotation from Q to Q" about the point of intersection?
Answer choices:
A. 22
B. 136
C. 44
D. 88
Answer:
B. 136 °
Step-by-step explanation:
Given: m and n intersect to form a 44° degree angle
⇒ (180 - 44)°
⇒ 136 °
Answer: B. 136 degrees
Number of 5 digit multiples of 13
Marcus ran 45 days to prepare for a race. One-third of those days he ran on a track. How many days did he NOT run on a track?
Answer:
30
Step-by-step explanation:
45/3=15
15 days on track
30 days not on track
Please find x I really need help.
Answer:
x = 20°
explanation:
Both the pair sides are parallel to each other.The whole sums up to total 360°Steps:
2(7x + x + 20°) = 360°8x + 20° = 180°8x = 160°x = 20°[tex]\qquad\huge\underline{\sf Answer}[/tex]
x = 20 Explanation :- 7x + ( x + 20 ) = 180 8x + 20 = 180now , subtract 20 from both sides which will give you, 160
8x = 180 - 20 8x = 160divide both sides by 8
x = 20Hope it helps ~
A bank is offering 3% simple interest on a savings account. If you deposit $5000 , how much interest will you earn in one year?
Answer:
It might be $5000 x .025 x 1 = $125
Step-by-step explanation:
Sorry if its wrong
A pen costs twice as much as a pencil. 7 pens and 12 pencils cost a total of $6.50. What is the price of one pencil?
- Please show your work, I know the answer, but I just don’t know HOW to get the answer.
Answer:
$ 2.167
Step-by-step explanation:Let the cost of a pencil be x and that of a pen be y.
A pen costs twice as much as a pencil.
==> cost of a pen = 2 × cost of a pencil
==> y = 2x
Their total cost is $6.50
==> x + y = $6.50
since y = 2x, substituting y for 2x
==> x + 2x = 6.50
==> 3x = 6.50
dividing both sides by 3
==> x = 2.16
As per our assumption, x is the cost of one pencil.
Therefore, the cost of a pencil is $2.167