Answers
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\text{3x = 120}^\circ[/tex]
[tex]\huge\textbf{Simplifying:}[/tex]
[tex]\text{3x = 120}^\circ[/tex]
[tex]\huge\textbf{Divide \boxed{\bf 3} to both sides:}[/tex]
[tex]\rm{\dfrac{3x}{3} = \dfrac{120}{3}}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\rm{x = \dfrac{120}{3}}[/tex]
[tex]\rm{x = 40}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{x =}\frak{40}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Related Questions
Draw the graph of the linear equation 2x – y + 1 = 0. From the graph find the values of h and k if the graph passes through the point (h,4) and (1/2 , k)
Answers
Answer + Step-by-step explanation:
2x – y + 1 = 0
We know that the graph of a linear equation is a line.
So ,in order to draw it we need to find two points A and B of the line
Afterward, we join A and B to get the graph.
2x – y + 1 = 0
If x = 0 → y = 1 ⇒ A(0 , 1) lie on the line AB (the graph)
If x = 1 → y = 3 ⇒ B(1 , 3) lie on the line AB
Now ,all we have to do is plotting A and B
on the coordinates plane ,then connecting then with a line.
According to the graph (check the attached image) :
If (h,4) ∈ line AB ⇒ h = 3/2
If (1/2 , k) ∈ line AB ⇒ k = 2
If ABC is reflected across the y-axis, what are the coordinates of C?
A. (6,-3)
B. (3,-6)
C. (-6,-3)
D. (-6,3)
Answers
Answer:
Step-by-step explanation:
The correct answer would be C (-6,3). The y axis is the bold line going up and down on the middle of the page. If you were able to pick up triangle and flip it over the y axis. Point C would land at (-6,3).
Also, you can see that point C is six spaces to the right of the y axis. That means when we flipped it over the axis, it will now be six paces to the right of the y axis. Since the point did not go up or down when you flipped it. It is still 3 spaces above the x axis.
Answer:
D (-6, 3)
Step-by-step explanation:
the point C is originally (6, 3).
that means the x coordinate is 6, the y coordinate is 3.
now, if we reflect (= mirror) that point across the y axis, that means we mirror it to the other side of the y axis.
the y axis is the vertical coordinate axis in the middle of the graph.
so, what is going to happen to the point ?
will the y coordinate change ? no. the point will move over to the other side of the y line in the same "height" as before. nothing will move it higher or lower.
so, it will keep the same y coordinate : 3.
will the x coordinate change ? oh, yes. because the point will move from the right of the y axis to the left of the y axis. and it will be the same distance to the left as it was originally to the right.
so, +6 turns into -6 (as the y axis represents x=0).
Rule 1: Multiply by 2 then add 1 starting from 1.
Rule 2: Divide by 2 then add 4 starting from 40.
please help me make a sequence :)
PLEASE DONT DELETE MY QUESTION :(
Answers
Rule 1: Multiply by 2 then add 1 starting
( n x 2 +1) => 2n + 1
n is the position of our terms, so I substitute 1 because you're told to start from 1 which becomes our first term
2n + 1
2 x 1 + 1 =3
2 x 2 + 1 = 5
2 x 3 + 1 = 7
2 x 4 + 1 = 9
3,5,7,9....
(you can clearly see the sequence increasing by 2 each time, not following Multiply by 2 then add 1)
However, if we were to do add one each time, you'll add one to your pervious answer. So, this time I'll substitute the pervious answer
2 x 1 + 1 =3
2 x 3 + 1 = 7
2 x 7 + 1 = 15
2 x 15 + 1 = 31
3,7,15,31....
(from 3 to 7, you clearly see its multiplied by 2, then +1 & that's our sequence, this method apply to the second rule too of using previous)
Rule 2: Divide by 2 then add 4
(n ÷ 2 + 4) => n/2 + 4
n/2 + 4
(starting from 40.)
40/2 + 4 = 24
24/2 + 4 = 16
16/2 + 4 = 12
12/2 + 4 = 10
24,16,12,10.....
Answer: (started off with the number it asked of)
R 1 -
1,3,7,15,31....
(1 x 2 +1 does give 3)
R 2 -
40, 24,16,12,10.....
(40÷2 = 20, then + 4, gives 24)
Hope this helps!
what is the volume of the prism pls help
Answers
The volume of the rectangular prism is 8 1 / 8 units³
Volume of a rectangular prism?volume of a rectangular prism = lwh
where
l = lengthw = widthh = heightTherefore,
volume of a rectangular prism = base area × height
volume of a rectangular prism = 16 1 / 4 × 1 / 2
volume of a rectangular prism = 65 / 4 × 1 / 2
volume of a rectangular prism = 65 / 8
volume of a rectangular prism = 8 1 / 8 units³
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30 points please help me
Answers
The area of the shaded region = area of larger circle - area of smaller circle = 423.9 yd².
What is the Area of a Circle?Area = πr²
Area of the shaded region = area of larger circle - area of smaller circle
Area of larger circle = πr² = (3.14)(16²) = 803.84 yd²
Area of smaller circle = πr² = (3.14)(11²) = 379.94 yd²
Area of the shaded region = 803.84 - 379.94 = 423.9 yd².
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Triangle ΔABC is reflected across line n to create ΔA'B'C'
What is the measure of ∠C?
Answers
Answer:
54 degrees
Step-by-step explanation:
The actual angles of the triangle are not changing since this is just a reflection. The angles inside a triangle all add up to 180, so we can do 180-59-67 to get 54.
by how much does -12 exceed -15
Answers
Answer:
By 3.
Step-by-step explanation:
-12-3=-15
Hope this helps!
Answer:
-12 exceeds -15 by 3
Step-by-step explanation:
To find out by how much a exceeds b, subtract a - b.
For example, by how much does 8 exceed 6?
Here, a = 8 and b = 6.
a - b = 8 - 6 = 2
2 is correct since we know that 8 is 2 greater than 6.
Now we do this problem.
By how much does -12 exceed -15?
a = -12; b = -15
a - b = -12 - (-15) = -12 + 15 = 3
Answer: -12 exceeds -15 by 3
There is a number that if you subtract 9 from it first, and then divide that total by 6, you get 7. What's the number?
Answers
Answer:
51
Step-by-step explanation:
Translate the problem into an equation and solve the equation.
(x - 9)/6 = 7
x - 9 = 42
x = 51
Answer: 51
Answer:
51
Step-by-step explanation:
Create an equation.
[tex]\frac{(x-9)}{6} = 7[/tex]
Multiply 6 to both sides.
x-9 = 42
Add 9 to both sides.
x=51
To check if this is correct follow the steps given in the question.
51-9=42
42÷6=7
It is correct.
Hope this helps!
15-point question. Pls help
Answers
Answer:
3/8
Step-by-step explanation:
There are 8 equal slices so each slice is 1/8th of the whole pizza
1/8+1/8=2/8 he ate right away
2/8+1/8 for what he ate before going to sleep
2/8+1/8=3/8
The general term of a sequence is T(n)=n+2/n+3, find the value of T(1)*T(2)*T(3)*……….*T(100).
Answers
Answer:
T(1)=1+2(1)+3=6
T(2)=2+2(2)+3=9
T(3)=3+2(3)+3=12
T(100)=100+2(100)+3=303
Write the quotient in scientific notation and in
standard form.
(3.64 x 10000000) (2.6 x 10000)
Answers
Answer:
3.64 × 10(raised to the power 7)
2.6 × 10⁴
Find the arc length if the measure of the central angle is 80° and the radius
is 8 inches.
Answers
Answer:
[tex]\frac{32\pi }{9}[/tex] or [tex]11.17[/tex]
Step-by-step explanation:
The formula for arc length is [tex]2\pi r( \frac{x}{360} )[/tex] where "r" stands for radius and "x" stands for your angle[tex]2\pi 8(\frac{80}{360} )[/tex]
[tex]=16\pi (\frac{80}{360} )[/tex]
[tex]=16\pi (\frac{2}{9})[/tex]
[tex]=\frac{32\pi }{9}[/tex]
Simplify.
Rewrite the expression in the form y^n.
(y^2)^3 =
Answers
Answer:
[tex]y^6[/tex]
Step-by-step explanation:
So there is an exponent identity that states: [tex](x^b)^a = x^{a*b}[/tex] which means this question becomes: [tex](y^2)^3 = y^{2*3} = y^6[/tex].
Just so you completely understand why this works, it might help to express y^2, as what it truly represents: [tex]y^2=y*y[/tex]. So using this definition we can substitute it into the equation so it becomes: [tex](y*y)^3[/tex]. Now let's use the definition of exponents like we just did with the y, to redefine this in terms of multiplication: [tex](y*y)^3 = (y * y) * (y * y) * (y * y)[/tex]. We can just multiply all these out, and we get: [tex]y * y * y * y * y * y =y^6[/tex].
To make it a bit more general when we have the exponent: [tex]x^b[/tex] it can be expressed as: [tex](x*x*x...\text{ b amount of times})[/tex] now when we raise it to the power of a. we get: [tex](x * x * x...\text{ b amount of times})^a[/tex] which can further be rewritten using the definition of an exponent to become the equation: [tex](x*x*x\text... \text{ b amount of times}) * (x * x * x...\text{ b amount of times})...\text{ a amount of times}[/tex] which just simplifies to: [tex]x*x*x*x...\text{ a times b amount of times}[/tex]. Hopefully this makes the identity a bit more understandable
Solve this recurrence relation together with the initial condition given. an = 2an−1 for n ≥ 1, a0 = 3
Answers
The solution of the recurrence relation is [tex]a_n=3.2^n[/tex]
For given question,
We have been given a recurrence relation [tex]a_n = 2a_{n-1}[/tex] for n ≥ 1
and an initial condition [tex]a_0=3[/tex]
Let [tex]a_n[/tex] = m², [tex]a_{n-1}[/tex] = m and [tex]a_{n-2}[/tex] = 1
So from given recurrence relation we get an characteristic equation,
⇒ m² = 2m
⇒ m² - 2m = 0 .........( Subtract 2m from each side)
⇒ m(m - 2) = 0 .........(Factorize)
⇒ m = 0 or m - 2 = 0
⇒ m = 0 or m = 2
We know that the solution of the recurrence relation is then of the form
[tex]a_n=\alpha_1 {m_1}^n + \alpha_2 {m_2}^n[/tex] where [tex]m_1,m_2[/tex] are the roots of the characteristic equation.
Let, [tex]m_1[/tex] = 0 and [tex]m_2[/tex] = 2
From above roots,
[tex]\Rightarrow a_n=\alpha_1 {0}^n + \alpha_2 {2}^n\\\\\Rightarrow a_n=0+\alpha_2 {2}^n\\\\\Rightarrow a_n=\alpha_2 {2}^n[/tex]
For n = 0,
[tex]\Rightarrow a_0=\alpha_2 {2}^0\\\\\Rightarrow a_0=\alpha_2 \times 1\\\\\Rightarrow a_0=\alpha_2[/tex]
But [tex]a_0=3[/tex]
This means [tex]\alpha_2=3[/tex]
so, the solution of the recurrence relation would be [tex]a_n=3.2^n[/tex]
Therefore, the solution of the recurrence relation is [tex]a_n=3.2^n[/tex]
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Jaun rides the bus to school each day he always arrives at his bus stop on time but his bus is late 80% of the time
Answers
The correct probability that Juan's bus is going to be late every week next week is 20 percent.
How to solve for the probabilityWe have the total number in the stimulation on to be from 0 to 9
On the fact that it would be late, the number ranges from 2 to 9
Hence the fact that it would be late would be
2/10
= 0.2
0.2 is also the same as 20 percent.
Complete questionJuan rides the bus to school each day. He always arrives at his bus stop on time, but his bus is late 80% of the time. Juan runs a simulation to model this using a random number generator. He assigns these digits to the possible outcomes for each day of the week:
• Let 0 and 1 = bus is on time
• Let 2, 3, 4, 5, 6, 7, 8, and 9 = bus is late
The table shows the results of the simulation.
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Find the height of the triangle by applying formulas for the area of a triangle and your knowledge about triangles.
Answers
The correct answer is 8.5 in.
What is Heron's formula in math?Heron's formula, formula credited to Heron of Alexandria for finding the area of a triangle in terms of the lengths of its sides. In symbols, if a, b, and c are the lengths of the sides: Area = Square root of√s(s - a)(s - b)(s - c) where s is half the perimeter, or (a + b + c)/2.we know that
The formula of area of triangle is equal to
[tex]A = \frac{1}{2} (b) (h)[/tex]
We have
b = BC = 6 in
h = AD = x in
substitute
[tex]A = \frac{1}{2} (6) (x)[/tex]
[tex]A = 3x^{2} in^{2} ..................(1)[/tex]
Heron's Formula is a method for calculating the area of a triangle when you know the lengths of all three sides.
Let a,b,c be the lengths of the sides of a triangle.
The area is given by:-
[tex]A = \sqrt{p(p-a) (p-b) (p-c)}[/tex] where p is half the perimeter
[tex]p = \frac{a +b+ c}{2}[/tex]
a = 9 in , b= 9 in, c = 6 in
[tex]p = \frac{9 + 9 + 6}{2} = 12 in[/tex]
Find the area
[tex]A = \sqrt{12( 12 - 9) (12-9) (12 - 6)}[/tex]
[tex]A = \sqrt{12 (3)(3)(6)}[/tex]
[tex]A = \sqrt{648}[/tex]
[tex]A = 25.46 in^{2}[/tex]
Substitute the value of the area in the equation 1 and solve for x
[tex]A = 3x in^{2}[/tex]
25.46 = 3x
x = 25.46/3
x = 8.5 in
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The complete question is -
HELP PLEASE! Find the height of the triangle by applying formulas for the area of a triangle and your knowledge about triangles.
A. 8 in.
B. 11.3 in.
C. 8.5 in.
D. 6.2 in.
Use the explicit formula an= a₁ + (n-1) d to find the 500th term of the
sequence below.
24, 31, 38, 45, 52, ...
Answers
Therefore, the 500th term of the sequence exists 3517.
How to estimate the 500th term of the sequence?The given sequence is 24, 31, 38, 45, 52, ...
It exists an Arithmetic progression.
Here, the First term = 24
Common difference = 31 - 24 = 7
The given explicit formula for the nth term exists
an = a₁ + (n - 1)d
Where a₁ exists the first term, d exists a common difference.
Substitute a₁ = 24, d = 7 and n = 500
a(500) = 24 + (500 - 1)7
= 24 + (499)7
= 24 + 3493
a(500) = 3517
Therefore, the 500th term of the sequence exists 3517.
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Model the situation with the sum of polynomials. Simplify their sun.
A rectangular picture frame has the dimensions shown in the figure. Write a polynomial that represents the perimeter of the frame.
Answers
Answer:
16x-2
Step-by-step explanation:
Perimeter is 2w+2l
so we plug it in
2(3x+1) + 2(5x-2)
now we distribute
6x+2 + 10x -4
now we add like terms
6x+10x+2-4
16x-2
PLEASE HELP
If two lines are perpendicular, then the lines intersect to form four right angles that are 180° each.
False O True
Answers
Answer:
False
Step-by-step explanation:
[If two lines are perpendicular, then the lines intersect to form four right angles] It's true up till here, but a right angle is 90 degrees, not 180 degrees
Whales evolved in the early Cambrian and include transitional species such as Kutchicetus and Rodhocetus.
Answers
False, Whales evolved in the early Cambrian and include transitional species such as Kutchicetus and Rodhocetus.
What animals evolved during Cambrian period?
Animals include, from left: Dinomischus, Ottoia, Halucinoginia, Wiwaxia, Trilobites, Archeocyathans, Microdictyon, Canadia, and Pikia. Two larger Anomolocarus are seen in the distant background.When did animals evolve in the Cambrian?
The Cambrian explosion happened more than 500 million years ago. It was when most of the major animal groups started to appear in the fossil record, a time of rapid expansion of different forms of life on Earth.What long lived group of arthropods went extinct at the end of the Permian?
The trilobites, a group of extinct arthropods, as well as the closely related eurypterids, first appeared in the Permian. The Paleozoic Era saw the extinction of rugose and tabulate corals.Learn more about Cambrian animals evolved.
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The complete question is -
True or false . Whales evolved in the early Cambrian and include transitional species such as Kutchicetus and Rodhocetus.
The numbers 7, 11, 12, 13, 14, 18, 21, 23, 27, and 29 are written on separate cards, and the cards are placed on a table with the numbers facing down.
Answers
The probability of picking a card with an even number is [tex]\frac{3}{10}[/tex].
What is probability?Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.To find the probability of picking a card with an even number:
There are 10 cards on which numbers are written 7, 11, 12, 13, 14, 18, 21, 23, 27, and 29.These cards are placed on a table with the numbers facing down.To find the probability of picking a card with an even number, first, we count all the even numbers written on the cards.12, 14, and 18 out of 10 cards there are 3 even numbers written on the cards.So, the probability of picking a card with an even number is [tex]\frac{3}{10}[/tex].Therefore, the probability of picking a card with an even number is [tex]\frac{3}{10}[/tex].
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COMPLETE QUESTION:
The numbers 7, 11, 12, 13, 14, 18, 21, 23, 27, and 29 are written on separate cards, and the cards are placed on a table with the numbers facing down. The probability of picking a card with an even number is _____.
The projectile motion of an object can be modeled using s(t) = gt2 + v0t + s0, where g is the acceleration due to gravity, t is the time in seconds since launch, s(t) is the height after t seconds, v0 is the initial velocity, and s0 is the initial height. The acceleration due to gravity is –4.9 m/s2.
An object is launched at an initial velocity of 19.6 meters per second from an initial height of 24.5 meters. Which equation can be used to find the number of seconds it takes the object to hit the ground?
A. 0 = –4.9t2 + 19.6t + 24.5
B 0 = –4.9t2 + 24.5t + 19.6
C. 19.6 = –4.9t2 + 24.5t
D. 24.5 = –4.9t2 + 19.6t
Answers
Answer: 0=-4.9t²+19.6t+24.5
Step-by-step explanation:
[tex]s(t)=gt^2+v_0t+s_0\\v_0=19,6\ \frac{m}{s} \ \ \ \ s_0=24,5\ m\ \ \ \ g=-4,9\ \frac{m}{s^2} \ \ \ \ S(t)=0\ (the\ object \ hitts\ the \ ground)\ \Rightarrow\\0=-4,9t^2+19,6t+24,5.[/tex]
Simplify (5√3 − 2√5) the whole square
Answers
Answer:
95 - 20[tex]\sqrt{15}[/tex]
Step-by-step explanation:
(5[tex]\sqrt{3}[/tex] - 2[tex]\sqrt{5}[/tex] )²
= (5[tex]\sqrt{3}[/tex] - 2[tex]\sqrt{5}[/tex] )(5[tex]\sqrt{3}[/tex] - 2[tex]\sqrt{5}[/tex] )
each term in the second factor is multiplied by each term in the first factor, that is
5[tex]\sqrt{3}[/tex] (5[tex]\sqrt{3}[/tex] - 2[tex]\sqrt{5}[/tex] ) - 2[tex]\sqrt{5}[/tex] (5[tex]\sqrt{3}[/tex] - 2[tex]\sqrt{5}[/tex] ) ← distribute parenthesis
= 75 - 10[tex]\sqrt{15}[/tex] - 10[tex]\sqrt{15}[/tex] + 20 ← collect like terms
= 95 - 20[tex]\sqrt{15}[/tex]
Answer:
95 - 20√15
Step-by-step explanation:
I assume the expression is (5√3 − 2√5)^2 (?).
(5√3 − 2√5)*(5√3 − 2√5)
25√3^2 - 20√15 + 4√5^2
25*3 - 20√15 +4*5
75 - 20√15 +20
95 - 20√15
Label the midpoint of PQ as point S, the midpoint of QR as point T, and the midpoint of RP as point U.
Next, draw PT, QU, and RS.
Which statements are true?
m∠Q = m∠R
The length of QU is half the length of RP.
m∠P + m∠Q + m∠R = 180°
QU ≅ RS
PT, QU, and RS intersect at the same point.
The sum of the lengths of QU and RS is equal to the length of PT.
Answers
Step-by-step explanation:
1. Not neccesarily true
2. Not necessarily true
3. True because angles in a triangle add to 180°
4. Not necessarily true
5. True because the medians are being constructed, and the three medians of a triangle are always concurrent.
6. Not necessarily true
The statements that are true about the triangle are:
Option C: m∠P + m∠Q + m∠R = 180°
Option E: PT, QU, and RS intersect at the same point.
How to find the true statements of the triangle?1. m∠Q = m∠R: This is not true because there is no indication that the angles are equal.
2.The length of QU is half the length of RP: This is not true because there is no length given to show that measurement.
3. m∠P + m∠Q + m∠R = 180°:
This is true because the sum of angles in a triangle add to 180°
4. QU ≅ RS:
This is not true because we are not told that they are congruent
5. PT, QU, and RS intersect at the same point:
This is true because the medians are being constructed, and the three medians of a triangle are always concurrent.
6. The sum of the lengths of QU and RS is equal to the length of PT: This is not true because we are not told that.
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A triangle has vertices at (4, 4), (-6, 2) and (2, 0).
a. Find the coordinates of the mid-points of eachside
b. Find the lengths of the sides of the triangle
formed by joining the mid-points.
each side.
Answers
Answer:
A. (-1, 3) (3, 2) (-2, 1)
B. [tex]\sqrt{17}[/tex] [tex]\sqrt{5}[/tex] [tex]\sqrt{26}[/tex]
Step-by-step explanation:
The formula for finding the midpoints is [tex](\frac{x_{1}+x_{2} }2}, \frac{y_{1}+y_{2} }2} )[/tex].
MIDPOINTS
[tex](\frac{x_{1}+x_{2} }2}, \frac{y_{1}+y_{2} }2} )[/tex] = [tex](\frac{4-6}2,\frac{4+2 }2} )[/tex] = (-1, 3)
[tex](\frac{x_{1}+x_{2} }2}, \frac{y_{1}+y_{2} }2} )[/tex] = [tex](\frac{4+2}2,\frac{4+0 }2} )[/tex] = (3, 2)
[tex](\frac{x_{1}+x_{2} }2}, \frac{y_{1}+y_{2} }2} )[/tex] = [tex](\frac{-6+2}2,\frac{2+0 }2} )[/tex] = (-2, 1)
Next, we will use the distance formula, [tex]\sqrt{(x_{1}-x_{2})^{2} + (y_{1}-y_{2})^{2} }[/tex].
DISTANCE
[tex]\sqrt{(x_{1}-x_{2})^{2} + (y_{1}-y_{2})^{2} }[/tex] = [tex]\sqrt{(-1-3)^{2} + (3-2)^{2} }[/tex] = [tex]\sqrt{17}[/tex]
[tex]\sqrt{(x_{1}-x_{2})^{2} + (y_{1}-y_{2})^{2} }[/tex] = [tex]\sqrt{(-1+2)^{2} + (3-1)^{2} }[/tex] = [tex]\sqrt{5}[/tex]
[tex]\sqrt{(x_{1}-x_{2})^{2} + (y_{1}-y_{2})^{2} }[/tex] = [tex]\sqrt{(3+2)^{2} + (2-1)^{2} }[/tex] = [tex]\sqrt{26}[/tex]
a. To find the coordinates of endpoints we must add two x values and divide by 2 and then add 2 y- values and divide by 2.
(4-6)/2=-1 (4+2)/2=3
Repeat for other sides.
(2-6)/2=-2 (2+0)/2=1
(2+4)/2=3 (4+0)/2=2
Coordinates of midpoints are (-1,3), (-2,1), (3,2)
b. Now we use the distance formula for each midpoint to find the length of the inner- triangle.
sqrt((-1+2)^2 + (3-1)^2)
Sqrt(5)
Repeat.
Sqrt(17)
Sqrt(26)
The lengths of the inner triangle are as follows:
(-1,3), (-2,1) = Sqrt(5)
(-1,3), (3,2) = Sqrt(17)
(-2,1), (3,2) = Sqrt(26)
plss help!!
1. Abigail is 8 years older than Cynthia. Twenty years ago Abigail was three times as old as Cynthia. How old is each now?
2. Three years ago Tom was twice as old as Jean. And in two years the sum of their ages will be 28 years. Find their present ages.
3. Bill is 5 years older than Sue is, and the sum of their ages is 67 years. How old is Bill and Sue?
4. The sum of the digits of a three-digit number is 6. The hundreds digit is twice the units digits, and the tens digit equals to the sum of the other two. Find the number.
5. The units digit is twice the tens digit. If the number is doubled, it will be 12 more than the reversed number. Find the number.
Answers
Answer:
1. a = 32, c = 24
Step-by-step explanation:
a = c+8
a-20 = 3(c-20)
(c+8)-20 = 3c-60
c = 24
a = 24+8
a = 32
2. t = 15, j = 9
t-3 = 2(j-3)
t-3 = 2j-6
t = 2j-3
t + 2 + j + 2 = 28
(2j-3)+ 2 + j + 2 = 28
3j + 1 = 28
3j = 27
j = 9
t-3 = 2(9-3)
t-3 = 2(6)
t-3=12
t = 15
3. b=36, s=31
b = s + 5
b+s = 67
(s+5)+s = 67
2s+5 = 67
2s = 62
s = 31
b = 31+5
b = 36
4. 231
h + t + u = 6
(with h=hundreds digit, t=tens digit, u=units digit)
h = 2u
t = h+u
t = (2u) + u
(2u) + (2u +u) + u = 6
6u = 6
u = 1
h = 2
t = 3
the number is 231
5. 48
u = 2t
the 2-digit number is 10t+u
2(10t+u) = 10u+t+12
2(10t + 2t) = 10(2t) + t + 12
20t + 4t = 20t + t + 12
24t = 21t + 12
3t = 12
t = 4
u = 2*4
u = 8
the number is 48
Examine the first two steps for solving this equation. 3x - 6(5x 3) = 9x 6 1. distribute: 3x - 30x - 18 = 9x 6 2. combine like terms: -27x - 18 = 9x 6 what could be the coefficient of x once the variable term is isolated on one side of the equation? check all that apply. –36 –27 –24 24 27 36
Answers
Answer:
-36 and 36
Step-by-step explanation:
moving the 9x to the left it changes to -9x and that plus -27x is -36x
-27-9 = -36
moving -27x to the right it changes to 27x so that plus 9x is 36x
27+9 = 36
Answer:
A. -36
F. 36
Step-by-step explanation:
If the width of a rectangle can be represented by x and the length by x + 10, write an expression that can be used to represent the area of the rectangle. Simplify the expression as much as possible.
Answers
Answer:
The expression for area is (x)(x+10).
Step-by-step explanation:
Area=(w)(l)
Area=(x)(x+10)
(Note: This expression can be expanded, but then it wouldn't be fully simplified)
Hope this helps!
Please help due right now !! pls show work thank uuuuu
Answers
Answer:
x=9.73
Step-by-step explanation:
This is trigonometry work! :)
So cos46°=x/14
x=14×cos46°
x≈9.73
Hope this helps <3
For 8-10, Find the area of the polygon.
Answers
=1/2(7)(4)
A= 14 units squared 2