Answer:
CD = 32 units
Step-by-step explanation:
The midpoint divides the segment into congruent parts:
CM = MD
8(x -2) = 4(5x -16)
2(x -2) = 5x -16 . . . . . . divide by 4
2x -4 = 5x -16 . . . . . . . eliminate parentheses
12 = 3x . . . . . . . . . . . . . add 16-2x to both sides
4 = x . . . . . . . . . . . . . . . divide by 3
Then the segment measures are ...
CM = 8(x -2) = 8(4 -2) = 16
CD is twice that length. CD = 32 units.
_____
Additional comment
There are many ways to solve equations like this. The one usually recommended is to simplify it first. That generally means eliminating parentheses and collecting terms. Doing that would give ...
8x -16 = 20x -64
Since there is a common factor of 4 on both sides, we can divide by that, making the numbers smaller and eliminating one set of parentheses.
Of course, the properties of equality require that whatever operation you perform on one side of the equal sign must also be done on the other side. So "divide by 4" means "divide by 4 on each side of the equal sign."
A line passes through the point (-6,9) and has a slope of 3/2. Write an equation in slope-intercept form for this line.
Answer:
y=3/2x+18
Step-by-step explanation:
Hi there!
We are given a point (-6,9) and a slope of 3/2
We want to write the equation of this line in slope-intercept form
Slope-intercept form is written as y=mx+b, where m is the slope and b is the y intercept
Since we already know the slope of the line as 3/2, we can substitute it as m into the equation:
y=3/2x+b
Now let's find b
Since the equation of the line passes through (-6,9), we can use it to help solve for b
Substitute -6 as x and 9 as y:
9=3/2(-6)+b
Multiply
9=-9+b
Add 9 to both sides
18=b
Substitute 18 as b into the equation.
y=3/2x+18
Hope this helps!
6(x + 7.50) = 4(2x + 9.50), what is the value of x?
Answer:
x=3.50
Step-by-step explanation:
6(x+7.50)=4(2x+9.50)
6x+45=8x+38
6x-8x=38-45
-2x = -7
x = -7/-2
x = 3.50
10, 18, 26, 34, 42, ...
Write the simplified formula (expression) for the given Arithmetic Sequence
Answer:
[tex]10 + (n - 1) 8[/tex]
Step-by-step explanation:
All arithmetic sequence can be written as:
[tex]a_{n} = a_{1} + (n - 1)d[/tex]
Where [tex]a[/tex] is the [tex]n^{th}[/tex] term of the sequence, [tex]a_{1}[/tex] the first term of the sequence and [tex]d[/tex] the common difference between terms.
So in our sequence we have [tex]a_{1} = 10[/tex] and for find the difference substract two sequence terms.
[tex]d = a_{n+1} - a_{n} = 18 - 10 = 8[/tex]
Now replace the knowns terms in the general form:
[tex]a_{n} = 10 + (n - 1)8[/tex]
The simplified formula for the given arithmetic sequence is:
a(n) = a + 8 (n - 1)
What is an arithmetic sequence?It is a sequence where the difference between each consecutive term is the same.
We have,
The common difference between any two consecutive terms in an arithmetic sequence is constant.
In this case, the common difference is 8, as each term is obtained by adding 8 to the previous term.
Let the first term of the sequence be 'a', then the second term is 'a + 8', the third term is 'a + 16', and so on.
Therefore, the nth term of the sequence can be expressed as:
a + (n-1)d
where d is a common difference, which is 8 in this case.
So, the simplified formula for the given arithmetic sequence is:
a(n) = a + 8 (n - 1)
where a is the first term of the sequence and n is the position of the term in the sequence.
Thus,
The simplified formula for the given arithmetic sequence is:
a(n) = a + 8 (n - 1)
Learn more about arithmetic sequence here:
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What is the solution?
Answer:
(4, 4)
Step-by-step explanation:
y = 7/4 x - 3 graph (0, -3) (2, .5), (4, 4) (8, 11). Draw the line
y = x graph (0,0) (2, 2), (4, 4) , ( -2, -2). Draw the line
The two lines intersect at point (4, 4)
Given: F(x) = 2x - 1; G(x) = 3x + 2; H(x) = x 2 Find H(x+a) - H(x)/a
Answer:
Step-by-step explanation:
The stumbling block for most people is what exactly do you do the what's in the brackets of something like g(x+ 4) = 2x
The answer is, whatever you see on the left side where g(x) gets modified, you put on the right side wherever you see an x.
In this question
H( x) = x ^2
So if you see anything besides x on the left, then that's what goes on the right for x.
H(x + a) - H(x)/a = (x + a)^2 - (x^2)/a
You can expand this, but I don't see a reason for doing it.
H(x + a) - H(x)/a = (x + a)^2 - (x ^2)/a = x^2 + 2a + a^2 - x^2/a which gets you nowhere.
Mrs. Johnson weighs her suitcases ready for her holidays. It weighs 7.3kg. She takes out shoes that weigh 2.6kg. how heavy is her suitcase now
Answer:
4.7kg
Step-by-step explanation:
since when ready it is 7.3
subtract
7.3_2.6
Therefore the answer is4.7kg
3/4 + 1/2 + 1/3 sum to infinity
Answer:
18/12
Step-by-step explanation:
Answer:
5/3 or u could make it 5/4 since only 2 n 4 can have 2468 u cant put 4 back
Step-by-step explanation:
solve pls brainliest
Answer:
1. yes
2.yes
3. no
4. no
5. no
Plz Help!!! Fast!!
A statue is made of gold and silver in the ratio of 2:5. If the weight of the silver in the statue is 140 pounds, what is the weight of the gold?
Show all work!
Answer:
if the gold in this ratio is the 2 out of the 2:5 then the answer is 56 but if its the 5 then its 350
Step-by-step explanation:
The weight of gold is 56
Step-by-step explanation:
gold= 2
sliver = 5
weight of gold = x
weight of silver = 140
2/5 = x/140 solve for x
280=5x
x=280/5
x= 56
Someone pls help!
Gabby owns 35 chickens and each one produces three eggs per day. How many eggs can she collect each day?
Answer:
Well 35 chickens. Each produce 3 eggs a day. 35*3= 105
105 eggs per day
Answer:
105 eggs
Step-by-step explanation:
Number of eggs per day = number of chickens x eggs per chicken
35 x 3 = 105
105 eggs
-Chetan K
how many 2/3's are in 4/5
Step-by-step explanation:
4/5 + 2/3 = 2215 = 1 715 ≅ 1.4666667. Spelled result in words is twenty-two fifteenths (or one and seven fifteenths).
Answer:
5/10's
Step-by-step explanation:
Trust me bro
Pleaseee helpppp me!!!!!!!!!!!!!
Answer:
The graph is linear and increasing from x = -6 to x = -2.
The graph is nonlinear and decreasing from x = -2 to x = 0.
Step-by-step explanation:
Linear means it has a constant slope, or a constant rate of change. That makes a straight line on a graph. On the given graph, you can see the straight line increasing from x = -6 to x = -2.
Non-linear is just anything that isn't a constant slope, and makes a curve on a graph. On the given graph, the curve decreases from x = -2 until x = 0, where it reaches its lowest point and starts heading upwards again.
When two pipes fill a pool together, they can finish in 4 hours. If one of the pipes fills half the pool then the other takes over and finishes filling the pool, it will take them 9 hours. How long will it take each pipe to fill the pool if it were working alone?
One pipe takes __ hours alone.
The other pipe takes __ hours alone.
One pipe takes 6 hours working alone.
The other pipe takes 12 hours working alone.
This is a rate of work problem. The formula utilized is
[tex]w=r\times t[/tex]
where
[tex]w[/tex] is the work done[tex]r[/tex] is the rate of work done[tex]t[/tex] is the time taken to do the workWe are looking for how long it will take each pipe to completely fill the pool
For pipe 1 working alone to fill 1 pool, the work done is 1;
[tex]w=r\times t\\\\1 = r_1 \times t_1\\\\t_1=\frac{1}{r_1}[/tex]
For pipe 2 working alone to fill 1 pool, the work done is 1;
[tex]w=r\times t\\\\1 = r_2 \times t_2\\\\t_2=\frac{1}{r_2}[/tex]
From the question, it would take 9 hours if each pipe took turns to fill half the pool. That is;
[tex]\frac{t_1}{2}+\frac{t_2}{2}=9\\\\t_1+t_2=18[/tex]
However, if both pipes worked together, it would take 4 hours for each pipe. That is;
[tex]w_1+w_2=w\\\\r_1t_1+r_2t_2=w\\\\4r_1+4r_2=1\\\\r_1+r_2=\frac{1}{4}[/tex]
Remember that [tex]r_1=\frac{1}{t_1}[/tex] and [tex]r_2=\frac{1}{t_2}[/tex]. So,
[tex]\frac{1}{t_1}+\frac{1}{t_2}=\frac{1}{4}\\\\\frac{t_1+t_2}{t_1t_2}=\frac{1}{4}[/tex]
Also recall that [tex]t_1+t_2=18[/tex]. So,
[tex]\frac{18}{t_1t_2}=\frac{1}{4}\\\\t_1t_2=72[/tex]
The only factors of 72 that satisfy the conditions
[tex]t_1+t_2=18\\\\t_1t_2=72[/tex]
are 6 and 12.
Therefore, pipe 1 will take 6 hours, and pipe 2 will take 12 hours to fill the pool if working alone.
The link below has a similar problem on rate of work
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Find the perimeter. Simplify your answer.
Answer:
20v-6
Step-by-step explanation:
To find the perimeter we have to add up all of our sides
9v-6+9v-6+2v+6
Combine light terms
20v-6
what is the value of x in the figure shown
Answer:
x = 66
Step-by-step explanation:
Have a nice day
plz help! so hardddddddd
Answer: The average temperature on Earth has risen.
Step-by-step explanation:
If you look at the graph, you can see that the average for temperature on Earth has risen since 1800s through 2000s
HELP QUICKLY!!! How can you use a set of steps to divide whole numbers? Explain.
Answer:
https://youtu.be/4yp5v64XuRc
Step-by-step explanation:
This is a very good video on to do it, it's hard to explain just typing it on here. I'm sorry.
Answer: 131
Step-by-step explanation:
Hi Looking for A helping hand
The first term in an arithmetic sequences is -9. The fifth term in the sequences is 15. The tenth term in the sequences is 45. Write the explicit form that would be used to find the nth term in the sequence. Show the steps you took to write the simplified explicit form.
Answer:
an = a1 + 6(n-1)
Step-by-step explanation:
a1 = -9, a5= 15, a10 = 45
Since is an arithmetic sequence we only add or subtract something to get to the next term. Since we got from -9 to 15 we know that we must add something and that we add it 4 times the same amount to get from -9 to 15.
a1= -9
a2= -9+6 = -3
a3= -3+6 = 3
a4= 3+6 = 9
a5= 9+6 = 15
We add 6 each time.
The explicit formula is an = a1 + 6(n-1) because
for example a5 = a1 the first term + 6* (5-1) times
a5 = -9 + 6* 4 = -9 + 24 = 15✅
a10 = a1 + 6* (10-1)
a10 = -9 + 6*9 = 45✅
If their food and beverages cost $25.30 and there is an 8% meals tax, how much is the bill? Enter your answer to the nearest cent.
Answer:
32.24
Step-by-step explanation:
fingernails grow about 0.0123 centimetres per day. write this rate in scientific nation
Answer:
1.23 x 10^-2
Assume you invest $5,000 in an account paying 8% interest compounded annually. How much money will be in the account after 5 years?
Answer:
$7346.64
Step-by-step explanation:
Amount after 5years=P(1+r/100)^t
let A = amount after 5years
A=$5000(1+8/100)^5
A=$7346.64 to 2 decimal places
a+3 1/4=5 2/9 how to solve this for me is hard
[tex]a + 3 \dfrac 14 = 5 \dfrac 29\\\\\\\implies a + 3 + \dfrac 14 = 5 + \dfrac 29\\\\\\\implies a+ \dfrac {13}4 = \dfrac{47}9\\\\\\\implies a = \dfrac{47}9 - \dfrac{13} 4 = \dfrac{188-117}{36} = \dfrac{71}{36} = 1 \dfrac{35}{36}[/tex]
Alacrosse player throws a ball in the air from an initial height of 7 feet.
The ball has an initial vertical velocity of 90 feet per second. Another player catches the ball when it is 3 feet
above the ground. How long is the ball in the air? Round your answer to the nearest hundredth.
Answer:
Modeling the situation with a quadratic equation, it is found that:
The maximum height of the ball is of 60.2 feet.
The ball hits the ground after 3.39 seconds.
Considering the gravity, the height of the ball, after t seconds, is given by the following quadratic equation.
In which:
is the initial velocity.
is the initial height.
In this problem:
Height of 8 feet, thus .
Initial velocity of 32 feet per second,
The equation is:
Which is a quadratic equation with .
The maximum height is the output of the vertex, which is:
Then, with the coefficients of this question:
The maximum height of the ball is of 60.2 feet.
It hits the ground at t for which , thus:
We want the positive value, so:
The ball hits the ground after 3.39 seconds.
A similar problem is given at brainly.com/question/24626341
Step-by-step explanation:
If their food and beverages cost $25.30 and there is an 8% meals tax, how much is the bill? Enter your answer to the nearest cent.A coffee ta
For the total multiply the amount by 1 + the meal tax:
25.30 x 1.08 = $27.32
Answer: $27.32
29 divided by 3/8.
help
Answer:
1.20833333333
PLEASE HELP! DUE IN 2 HOURS!! GEOMETRY PLEASE
Answer:
side lengths are 96 for HI and PQ and 64 for IJ and RQ
hypothenuse is 115
Step-by-step explanation:
delta HIJ = delta PQR
HI = PQ --> 3x = x + 64
divide both sides by x --> 3 = x/x + 64/x *x/x = 1
3 = 1 + 64/x subtract both sides by 1
2 = 64/x --> 2x = 64 divide both sides by 2
x = 32
IJ = RQ --> x + 32 = 2x
divide both sides by x
1 + 32/x = 2 (again, x/x = 1)
subtract both sides by 1
32/x = 1
x = 32
plug in 32 for x to get the side lenghts
so 3(32) = 96
and 32 + 32 = 64
use equation a^2 + b^2 = c^2
96^2 + 64^2 = c^
9216 + 4096 = c^2
13312 = c^2 square root 13312
c = 115.378
Which of the following sets here the closure property w.r.t. Addition
(A) {0}
(B) {0, -1)
(C) (0, 1)
)
(D) {1,V3.
Answer:
the answer is number 1 make my answer brainlist answer
Which expressions simplify to 0? Check all that apply.
8g – 8g
(–2g) – 2g
5g + (–5g)
One-half g + one-half g
Negative two-thirds g + two-thirds g
The expressions that simplify to zero are:
8g – 8g
5g + (–5g)
Negative two-thirds g + two-thirds g
Let us consider each of the expressions to determine the ones that simplify to zero (0)
For 8g - 8g
This is a direct subtraction of terms of the same value. Therefore, 8g - 8g = 0
For (–2g) – 2g
This can be further simplified as -2g - 2g = -4g
Therefore, (–2g) – 2g does not simplify to zero
For One-half g + one-half g
This can be written mathematically as:
[tex]\frac{1}{2}g + \frac{1}{2}g = g[/tex]
Therefore, One-half g + one-half g does not simplify to zero
Negative two-thirds g + two-thirds g
[tex]-\frac{2}{3}g+ \frac{2}{3}g = 0[/tex]
Therefore, Negative two-thirds g + two-thirds g simplifies to zero
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Answer:
A , C , E :)
Step-by-step explanation:
In the number 78.018, how does the value of the 8 in the thousandths place compare to the value of the 8 in the ones place?
Drag and drop a fraction into the box to correctly complete the statement.
The value of the 8 in the thousandths place is Response area the value of the 8 in the ones place.
Answer:
1/1000
Step-by-step explanation:
a protractors is used on an angle one ray of the angle is 46 degrees and the other way is a 95 degrees what is the measure of the angle
141 degrees hope this helps u
The measure of the angle will be 141°. Then the correct option is B.
What is an angle?The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.
The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
A protractor is used on an angle one ray of the angle is 46 degrees and the other way is 95 degrees.
The diagram is shown below.
Then the measure of the angle will be given as,
⇒ 46° + 95°
⇒ 141°
The measure of the angle will be 141°.
Then the correct option is B.
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