All right angles are congruent which is determined by the definitions of a right angle and congruent angles.
What are congruent angles?Congruent angles are two or more angles that are identical to each other. As a result, the measurements of these angles are equivalent.
Given that ∠1 and ∠2 are right angles.
By the definition of right angles i.e. right angle is one that is exactly 90 degrees. It is precisely one-quarter of a circle. When a pie is divided into four equal pieces, the tip of each slice forms a straight angle.
⇒ m ∠1 =90° ; m ∠2 = 90°
By the substitution to get
⇒ m ∠1 = m ∠2
Therefore, ∠1 ≅ ∠2
Hence, all right angles are congruent which is determined by the definitions of a right angle and congruent angles.
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help me please help :)
Step-by-step explanation:
12/4 = x/8
1st: cross multiply
96 = 4x
2nd: divide both sides by 4
96/4 = 4x/4
therefore x = 24
Triangle ABC is congruent to triangle XYZ. In AABC, AB = 12 cm and AC = 14 cm. In AXYZ, YZ = 10 cm and XZ = 14
!
cm.
The perimeter of triangle ABC that is congruent to triangle XYZ is: 36 cm.
What are Congruent Triangles?Triangles that are congruent to each other have corresponding side lengths that have the same lengths that are equal to each other.
What is the Perimeter of a Triangle?The sum of all the three sides of a triangle is equal to the perimeter of the triangle.
Since triangle ABC is congruent to triangle XYZ, their corresponding side lengths will also be congruent to each other. That is, they will have the same lengths.
Therefore:
Side AB = side XY = 12 cm [corresponding congruent sides]
Side AC = side XZ = 14 cm [corresponding congruent sides]
Side BC = side YZ = 10 cm [corresponding congruent sides]
Find the perimeter of triangle ABC by adding all three triangles together.
Perimeter of triangle ABC = side AB + side AC + side BC
Perimeter of triangle ABC = 12 + 14 + 10
Perimeter of triangle ABC = 36 cm
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Write the equation of the line passing through the point (6,-9) that is perpendicular to the line y=1/2x+11.
The line that is perpendicular to the equation of a line given is y = -2x + 3
What is the equation of a perpendicular line?The equation of a perpendicular line can be found using the slope of the line first and then applying the points through which the line passes through.
For the given question, the equation of the line is y = 1/2x + 11 and the point is (6, -9).
To find an equation of a line;
Identify the slope.Identify the point.Substitute the values into the point-slope form, y − y₁ = m ( x − x₁) . y − y₁ = m (x − x₁) .Write the equation in slope-intercept formThe equation of the line can be modified into y - y₁ = m(x - x₁)
substituting the values into the equation above gives y = -2x + 3
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Need help with #6 don’t know how to find truth values.
The statement p is: Saturn is a planet.
The statement q is: Hong Kong is a city.
Now the first part of our composite proposition is:
[tex]p\lor\sim q[/tex]This means that we have to negate the statement q, this would be: Hong Kong is not a city.
Now we make the disjunction between the statement p and the negation of q, then we have:
[tex]p\lor\sim q\text{ means: Saturn is a planet or Hong Kong is not a city}[/tex]The second part of our composite porposition is:
[tex]\sim p\wedge q[/tex]This means that we have to negate the statement p, then we have: Saturn is not a planet. Then we make the conjunction between the negation of p and q, then we have:
[tex]\sim p\wedge q\text{ means: Saturn is not a planet and Hong Kong is a city}[/tex]Finally we make the disjunction between the statements discussed so far, hence the statament
[tex](p\lor\sim q)\lor(\sim p\wedge q)[/tex]means:
Saturs is a planet or Hon kong is not a city OR Saturn is not a planet and Hong Kong is not a city.
Now, to determine the truth value of the composite proposition we have to remember that a disjunction is TRUE if one of the statements that make it is true and that the conjunction is TRUE only if both stataments that make it are true.
The first statement is: Saturn is a planet or Hong kong is not a city. Since this is a disjunction and the statement Saturn is a planet is TRUE, then the proposition is true.
The second statement is: Saturn is not a planet and Hong Kong is not a city. Since this is a conjunction and the statement Saturs is not a planet is FALSE, the the second statement is FALSE.
Now since the composite statemtent is made of a TRUE and a FALSE statement and it is a disjunction we conclude that the truth value of the statement given is TRUE.
Solven - 8 + n = 1 -4n
We will solve as follows:
[tex]n-8+n=1-4n\Rightarrow2n+4n=1+8[/tex][tex]\Rightarrow6n=9\Rightarrow n=\frac{3}{2}[/tex]FInd the probability that a student walks to school
The probability that a student walks to school is 7/15
How to determine the probability of walking to school?The tree diagram represents the given parameter
From the tree diagram, we have the following parameters
P(Rain) = 2/5
P(Rain and walk) = 1/6
P(No rain) = 3/5
P(No rain and walk) = 2/3
The probability of walking to school is then calculated as
P = P(Rain) x P(Rain and walk) + P(No rain) x P(No rain and walk)
Substitute the known values in the above equation
So, we have
P = 2/5 x1/6 + 3/5 x 2/3
Evaluate the products
P = 1/15 + 6/15
Evaluate the sum
P = 7/15
Hence, the probability is 7/15
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The perimeter of a rectangle is 82 cm the length is 1 cm more than three times the width find the length and the width of the rectangle
The length will then be L = 18(41/19) = 738/19 cm.
As a check, the area should be A = LW = (738/19)(41/19) = 30258 cm2
sorry if this isn't much help but i had a similar problem once and i used the same steps for your question
The sum of an integer and 6 times the next consecutive odd integer is 61. Find the
value of the lesser integer.
If the sum of an integer and 6 times the next consecutive integer is 61, the the value of lesser integer is 7
Consider the first odd integer as x
Then the next consecutive odd integer = x+2
The 6 times the second integer= 6(x+2)
= 6x+12
Sum of an integer and 6 times the next consecutive odd integer is 61
Then the equation will be
x + 6x+12 = 61
Add the like terms in the equation
(1+6)x + 12 = 61
7x +12 = 61
Move 12 to the right hand side of the equation
7x = 61-12
7x = 49
x = 49/7
x = 7
The second number is
x+2 = 7+2
= 9
Hence, if the sum of an integer and 6 times the next consecutive integer is 61, the the value of lesser integer is 7
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it is known that a certain kind of algae in the dead sea can double in population every 4 days. suppose that the population of algae grows exponentially, beginning now with a population of 3,000,000. (a) how long it will take for the population to quadruple in size? days (b) how long it will take for the population to triple in size? days
Since the algae grow exponentially with doubling time of 4 days, then the population will be quadruple in size in 8 days and will be triple in size in 6.34 days.
The easiest way is to consider the situation as a geometric sequence. If the population doubles its size in 4 days, then it will be quadruple in:
2 x 4 days = 8 days.
In general, we can use the growth formula:
P(t) = Po . 2^(t/Td)
Where:
P(t) = population at time t
Po = initial population
Td = doubling time
Parameters given:
Td = 4 days
P(t) = 3Po
Plug those parameters into the formula:
3 Po = Po . 2^(t/4)
3 = 2^(t/4)
log 3 = (t/4) log 2
t = 4 . log 3 / log 2 = 6.34 days.
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With his new trainer, jacob now bikes at an average speed of 21 mph. that is 5% faster than he averaged with his old trainer. how fast did he bike, on average, before training with the his new trainer?
The average before training with new trainer is 20 mph.
Let the average speed with old trainer be x. Forming the equation as per given information- Average speed with new trainer = 5% × Average speed with old trainer + Average speed with old trainer
Keep the values in formula to find the average speed with old trainer.
21 = 5/100x + x
Multiplying the equation with 100
2100 = 5x + 100x
Performing addition
105x = 2100
Shifting 105 to Right Hand Side of the equation
x = 2100 ÷ 105
Performing division on Right Hand Side of the equation
x = 20
Thus, average speed with old trainer was 20 mph.
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The graphs of the fuctions f and g are shown below, find all values of x for which f(x) < g(x). 30 points!!!
Answer: [tex]-10 < x < 0, x > 12[/tex]
Step-by-step explanation:
[tex]f(x) < g(x)[/tex] when the graph of [tex]f(x)[/tex] is below the graph of [tex]g(x)[/tex].
insert parentheses to make the expression true
4×2+3×2=32
Answer:
4 * ( 2 + 3 * 2) = 32
Step-by-step explanation:
The strategy I used in this question is generally trial and error. The most important thing here to remember is to follow the order of operations. If you think a little out of the box, then you will see the answer. To solve, first multiply 3*2, then add two, which should result in 8. 4*8 is 32, which makes the equation true.
Find the measures of the complementary angles that satisfy each case. The measure of the first angle is 40% less than the measure of the second.
The measure of the angles are 56.25° and 33.75°.
How to calculate the angles?The value in a complementary angle is equal to 90°.
Let the first angle = x
The second angle will be: 1 - (40% × x) = 1 - 0.4x = 0.6x
Therefore, they'll be added together as follows:
x + 0.6x = 90°
1.6x = 90°
Divide
x = 90/1.6
x = 56.25
The second angle will be:
= 0.6x
Since x = 56.25, this will be used in the illustration below.
= 0.6x
= 0.6 × 56.25
x = 33.75
Therefore, the second angle is 33.75.
This illustrates the concept of complimentary angles.
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Question 1
A triangle has sides of length 2 cm, 8 cm and 9 cm.
Calculate the value of the largest angle in this triangle.
Answer: You have to use a calculator
Step-by-step explanation:
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Hello, is there any way I can get some assistance in my practice work? I need to find the width of the backyard and how much the fence in the backyard will cost
Given that the backyard is rectangular and the length is 56 feet while the area is 1400 square feet. Recall that the area A of a rectangle is the product of the length L and the width B.
A = L * B
Hence the width B may be found from
1400 = 56 * B
B = 1400/56
B = 25 feet
b. If the fencing cost $10 per foot then because a rectangle has two lengths and two widths,
the total cost to fence the backyard will be
= $10 * 2(56 + 25)
= $1,620
juan went out to eat dnner,and the meal cost $60.00.If juan recived a 18% discount,what was the total value of the discount
Multiply by the decimal form of the percentage,
60 * 0.18 = 1.08
So the discount is for $1.08 off,
60 - 1.08 = 58.92
Giving a total of $58.92 after the discount is applied
24. The temperature in ° F on 20 days during the month of June
was as follows:
70° F, 76° F,
74° F, 74° F,
76° F,
78° F,
74° F,
76° F,
70° F, 70° F, 72° F,
78° F, 76° F,
74° F,
74° F, 78° F, 80° F,
80° F, 76° F
78° F
What is the mode of temperature for the month of June?
Simplify by combining like terms. 9x + 6 - 4x - 2x + 1 - 15
9x + 6 - 4x - 2x + 1 - 15
9x - 4 x- 2x = (9-4-4)x = 3x
6 +1 -15 = -8
____________
Answer
3x -8
______________
Please tell me if you can see the updates
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________________
Solve for x to the nearest tenth.
Answer:
x = 11.2 cms.
Step-by-step explanation:
I infer that the units are in centimeters.
8-3 = 5
One side = 5 cm
Other side = 10 cm
By the Pythagorean Theorem:
x² = 5² + 10²
x² = 25 + 100
x² = 125
√x² = √125
x = 11.18 cms
To the nearest tenth:
x = 11.2 cms
2) m angle2=x+88 50° 2 A) -8 C) 8 B) -7 D) 7
A
1) Since the sum of the interior angles of any triangle is 180º, and this is an isosceles triangle
2) Then the other angle, has the same measure 50º since this is an isosceles triangle, at least two congruent sides, and two congruent angles.
We can finally write
x+88 +50 +50 = 180
x +188 =180 subtract 188 from both sides
x= 180-188
x= -8
3) So x=-8 is the answer.
Select the correct answer.
What is the range of the function shown on the graph above?
A. -9 [tex]\leq[/tex] y [tex]\leq[/tex] 8
B. -7[tex]\leq[/tex] y [tex]\leq[/tex] -2
C.-8[tex]\leq[/tex] y [tex]\leq[/tex] 8
D.-2 [tex]\leq[/tex] y [tex]\leq[/tex] -7
Answer:
A
Step-by-step explanation:
The range is the y values. The y value is as low as -10 and as high as 8.
I need help with this practice I attempted this and got 13.96? Make sure your answer is rounded to the nearest hundredth
Law of Cosines
Given two side lengths a and b of a triangle and the angle included by them θ, the length of the third side can be calculated as:
[tex]c^2=a^2+b^2-2ab\cos \theta[/tex]We have a = 14, b = 9, θ = 71°. Substituting:
[tex]\begin{gathered} c^2=14^2+9^2-2\cdot14\cdot9\cos 71^o \\ c^2=196+81-252\cdot0.325568 \\ c^2=194.956825 \\ c=\sqrt[]{194.956825} \\ c=13.96 \end{gathered}[/tex]The length of CD is 13.96
At 6:00 A.M. the temperature was 5°F below zero. At noon the temperature was 2°F above zero. At 6:00 P.M. the temperature was 7°F above zero. Which equation shows the change in temperature from 6:00 A.M. to 6:00 P.M.?
A. |5 – 7| = |–2| = 2°F
B. |2 – 7| = |–5| = 5°F
C. |–5 – 2| = |–7| = 7°F
D. |–5 – 7| = |–12| = 12°F
Based on the temperature at 6:00 am and the temperature at 6:00pm, the change in temperature can be shown by the formula D. |–5 – 7| = |–12| = 12°F.
How to find the change in temperature?To find the change in temperature, you need to subtract the temperature at 6: 00 pm from the temperature at 6: 00 am.
The change in temperature is therefore:
= | temperature at 6 am - temperature at 6pm |
= | -5 - 7 |
= | - 12 °F|
The absolute value of - 12 °F is 12 °F which was therefore the change in temperature.
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Use the following two points to answer parts a -c . (2, 3) , (- 1, - 6) a. Find the slope of the line passing through the two pointsb . Write an equation of a line passing through the two points in point slope form . c . Rewrite the equation of the line in slope -intercept form .
sSlope means the inclination of the line
Intercept is the point where the line touches the Y axis.
oan, omb, apb and mpn are straight lines and an = 3oa. m is the midpoint of ob. oa = a ов = b ap = kab where k is a scalar quantity. express ab and mn in terms of a and b. express mp in terms of a, b and k. finally, find the value of k.
The values of the vectors obtained from the vector diagram are;
[tex]\overrightarrow{AB} = - a + b[/tex]
[tex]\overrightarrow{MN} = ( -2\cdot a + 0.5 \cdot b)[/tex]
[tex]\overrightarrow{MP} = ( -0.5\cdot b + a+ K \cdot ( - a + b)[/tex]
K = 2.5
What is a vector in geometry?A vector can be expressed as a line segment that has a direction.
The given parameters are;
The straight lines are; OAN, OMB, APB, and MPN
AN = 3•OA
The midpoint of OB = M
The vectors
[tex] \overrightarrow{OA} = a[/tex]
[tex] \overrightarrow{OB} = b[/tex]
[tex]\overrightarrow{AP} = K \cdot \overrightarrow{AB} [/tex]
From the question diagram, we have;
[tex]\overrightarrow{AB} = - a + b[/tex]
[tex]\overrightarrow{AP} = K \cdot ( - a + b)[/tex]
[tex]\overrightarrow{MN} = ( -2\cdot a + 0.5 \cdot b)[/tex]
[tex]\overrightarrow{AN} [/tex] = 2•a
[tex]\overrightarrow{NP} = \overrightarrow{AP} - \overrightarrow{AN} [/tex]
[tex]\overrightarrow{NP} = -2\cdot a + K \cdot ( - a + b)[/tex]
[tex] \overrightarrow{MB} = 0.5 \cdot b[/tex]
[tex]\overrightarrow{PB} = -a + b - K \cdot ( - a + b)[/tex]
[tex]\overrightarrow{MP} =0.5 \cdot b - -a + b - K \cdot ( - a + b) = ( -0.5\cdot b + a+ K \cdot ( - a + b)[/tex]
[tex]\overrightarrow{MP} = ( -0.5\cdot b + a+ K \cdot ( - a + b)[/tex]
Given that we can write;
[tex]x \cdot \overrightarrow{NP} = \overrightarrow{NM}[/tex]
x × (-2•a + k•(-a + b)) = -3•a + 0.5•b
-2•x•a - k•x•a + x•k•b = -3•a + 0.5•b
Which gives;
-2•x - k•x = -3...(1), and x•k = 0.5...(2)
From (2), x = 0.5÷k
From (1), -2×(0.5÷k) - k×(0.5÷k) = 3
-k - 0.5 = -3
-k = -3 + 0.5 = -2.5
k = 2.5
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5. How many ways are there to distribute 10 indistinguishable candies among 4 different
children? Children may end up with no candies.
PLSSSSS HELP IT IS EXTREMELY URGENT PLSSSS
By application of the combination formula, there are 210 ways for distributing 10 indistinguishable candies among 4 children.
What is combination?Combination is the arrangement of objects in which order is not taken into account.
The applicable formula is:
n combination r = n!/[(n - r)!r!]
where n is the number of indistinguishable items (10 candies), and r is the possible number of recipients (4 kids).
Hence;
10 combination 4 = 10!/[(10 - 4)!4!] ways
10 combination 4 = 10!/(6! × 4!) ways
10 combination 4 = (10 × 9 × 8 × 7 × 6!)/(6! × 4 × 3 × 2 × 1) ways
10 combination 4 = 10 × 3 × 7 ways
10 combination 4 = 210 ways
Therefore, there are 210 ways for the 10 indistinguishable candies to be distributed among the 4 children by with the application of combination formula.
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Write an equation in standard form of the line that passes through the given points.
7. (-3, 2); m = 1
Answer:
y=x+1
Step-by-step explanation:
y-y1=m(x-x1)
y-2=1(x+3)
y-2=x+3
y=x+1
If f(x) = 5x, what is f¹(x)?
O f¹(x) = -5x
○ f¹(x) = -1/2 x
0 r²(x) = ²/1 x
O f¹(x) = 5x
The value of f¹(x) = x/5
What is function?
A function in maths is a special relationship among the inputs (i.e. the domain) and their outputs (known as the codomain) where each input has exactly one output, and the output can be traced back to its input.
We are given f(x) = 5x
and we are to find inverse of f(x).
Replace f(x) by y.
So,
y = 5x
Isolate x
x = y/5
Replace x by f'(y)
So,
f'(y) = y/5
Replace all occurrences of y by x.
So,
f'(x) = x/5
Therefore, the inverse of function f(x) = 5x is f'(x) = x/5
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Please help thank you
The value of the unknown angle in the triangle is as follows;
m∠S = 40 degreesHow to find the angle of a triangle?The exterior angle theorem states that the measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles.
In other words, an exterior angle of a triangle is equal to the sum of the two opposite interior angles.
The external angle is ∠JRS.
Therefore, m∠S can be found as follows:
∠JRS = m∠S + m∠T
Hence,
m∠S = 3x + 4
m∠T = 8x + 4
∠JRS = 140°
Hence,
140 = 3x + 4 + 8x + 4
140 = 3x + 8x + 4 + 4
140 = 11x + 8
140 - 8 = 11x
132 = 11x
x = 132 / 11
x = 12
Therefore,
m∠S = 3(12) + 4 = 40 degrees.
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Hey , I have a quick question about a Homework in math I got confused on how to solve the listed to formula [tex] \frac{x - 3}{2} - 4 \ \textless \ \frac{x}{3} [/tex]
Solution
- The question would like us to solve the following
[tex]\frac{x-3}{2}-4<\frac{x}{3}[/tex]- The solution is outlined below:
[tex]\begin{gathered} \frac{x-3}{2}-4<\frac{x}{3} \\ \\ Collect\text{ like terms:} \\ Add\text{ 4 to both sides and Subtract }\frac{x}{3}\text{ from both sides} \\ \\ \frac{x-3}{2}-\frac{x}{3}<4 \\ \\ We\text{ need the LCM of 2 and 3. } \\ The\text{ LCM is }2\times3=6 \\ \\ Thus,\text{ multiply both sides by 6 in order to remove the denominator} \\ 2\frac{}{} \end{gathered}[/tex][tex]\begin{gathered} 6\left(\frac{x-3}{2}\right?-6\left(\frac{x}{3}\right?<4\times6 \\ \\ 3\left(x-3\right)-2x<24 \\ Expand\text{ the bracket} \\ 3x-9-2x<24 \\ x-9<24 \\ Add\text{ 9 to both sides} \\ x<33 \end{gathered}[/tex]Final Answer
The answer is x < 33