Answer:
t=2.5 hours after the freight train leaves the station they will meet.
Step-by-step explanation:
30t = 50 (t - 1)
30t = 50t - 50
30t - 50t = -50
-20t = -50
t= -50/-20
Therefor, t=2.5 hours after the freight train leaves the station they will meet.
Answer:
2:30
Step-by-step explanation:
At Jane's school there are 22 more girls than boys, b.
a) Write and expression for the number of girls in terms of the number of boys, b.
b) Using part a), write an equation involving b and solve it to find the number of boys at the school.
c) How many girls are there at the school?
ASAP no need to explain just the answer
Answer:
A) girls=boys +22 .B)Boys=girls-22
Step-by-step explanation:
Apply the distributive property to factor out the greatest common factor. 27-18r =
Answer:
9 (3 - 2r)
Step-by-step explanation:
27 = 9 (3)
18r = 9 (2r)
Final answer = 9 (3 - 2r)
Hope this helped! :)
Answer:
9(3-2r)
Step-by-step explanation:
I factored 9 out of 27-18r/
The hypotenuse of a right triangles is 7 inches longer than the base and 14 inches longer than the height. The perimeter is 84 inches. Find its area
Answer:
294 in^2 = A
Step-by-step explanation:
Let h represent the length of the hypotenuse, b the base and h the height. Because this is a right triangle, the Pythagorean Theorem applies.
(hypotenuse)^2 = (base)^2 + (height)^2
h^2 = (h - 7)^2 + (h - 14)^2
Perimeter of the triangle is 84 inches, equal to (h) + (h - 7) + (h - 14), which in turn simplifies to 84 = h + h - 7 + h - 14, or 84 = 3h - 21, or 3h = 105. Solving this for h, we get h = 35.
Then the base is (35 - 7), or 28, and the height is (35 - 14), or 21.
The area of the triangle is found using the formula
A = (1/2)(base)(height) = (1/2)(28)(21) = 294 in^2 = A
Two terms of an arithmetic sequence are a5=23 and a20=98. find the first 60 terms of the sequence
Answer:
[tex]-37,-32,-27,-22,-17,-12,-7,-2,3,8,\\13,18,23,28,33,38,43,48,53,58\\63,68,73,78,83,88,93,98,103,108\\113,118,123,128,133,138,143,148,153,158\\163,168,173,178,183,188,193,198,203,208,\\213,218,223,228,233,238,243,248,253,258[/tex]
Step-by-step explanation:
The nth term of an arithmetic sequence is obtained using the formula:
[tex]a_n=a+(n-1)d[/tex]
Given that: [tex]a_5=23$ and a_{20}=98.[/tex]
a_n=a+(n-1)d
[tex]a_5=23=a+(5-1)d \implies a+4d=23\\a_{20}=98=a+(20-1)d \implies a+19d=98\\$We solve simultaneously$:\\a+19d=98\\a+4d=23\\15d=75\\d=5\\Recall:a+4d=23\\a+4(15)=23\\a=23-60\\a=-37[/tex]
Therefore, the first 60 terms of the sequence are:
[tex]-37,-32,-27,-22,-17,-12,-7,-2,3,8,\\13,18,23,28,33,38,43,48,53,58\\63,68,73,78,83,88,93,98,103,108\\113,118,123,128,133,138,143,148,153,158\\163,168,173,178,183,188,193,198,203,208,\\213,218,223,228,233,238,243,248,253,258[/tex]
First 60 terms of the arithmetic sequence will be 3, 8, 13, 18, 23, 28, 33, 38, 43, 48, 53, 58, 63, 68, 73, 78, 83, 88, 93, 98, 103, 108, 113, 118, 123, 128, 133, 138, 143, 148, 153, 158, 163, 168, 173, 178, 183, 188, 193, 198, 203, 208, 213, 218, 223, 228, 233, 238, 243, 248, 253, 258, 263, 268, 273, 278, 283, 288, 293, 298.
Arithmetic sequence: If two consecutive terms of a sequence has a common
difference 'd', sequence will be an arithmetic sequence and the
explicit formula for the nth term of the sequence will be,
[tex]A_n=a+(n-1)d[/tex]
Here, [tex]a=[/tex] First term
[tex]n=[/tex] nth term
[tex]d=[/tex] common difference
Given in the question,
Two terms [tex]a_5=23, a_{20}=98[/tex]
If 5th term of the sequence is 23,
[tex]23=a+(5-1)d[/tex]
[tex]23=a+4d[/tex] -------(1)
If 20th term of the sequence is 98,
[tex]98=a+(20-1)d[/tex]
[tex]98=a+19d[/tex] ----------(2)
Subtract equation (1) from equation (2),
98 - 23 = a + 19d - (a + 4d)
75 = 15d
d = 5
Substitute the value of 'd' in equation (1),
23 = a + 4(5)
a = 23 - 20
a = 3
Therefore, first 60 terms of the arithmetic sequence will be 3, 8, 13, 18, 23, 28, 33, 38, 43, 48, 53, 58, 63, 68, 73, 78, 83, 88, 93, 98, 103, 108, 113, 118, 123, 128, 133, 138, 143, 148, 153, 158, 163, 168, 173, 178, 183, 188, 193, 198, 203, 208, 213, 218, 223, 228, 233, 238, 243, 248, 253, 258, 263, 268, 273, 278, 283, 288, 293, 298.
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Find the area of the square with a side length of 8 ft.
Answer:
The area of square is 64ft².
Step-by-step explanation:
Given that all sides of a square are equal. So you have to apply the formula for area of square :
[tex]area = length \times width[/tex]
[tex]let \: length = 8 \\ let \: width = 8[/tex]
[tex]area = 8 \times 8[/tex]
[tex]area = 64 \: {ft}^{2} [/tex]
Answer:
here,
side length (l)= 8 ft.
now, area = l^2
a= 8^2
=64ft^2 is the answer..
hope i helped uh..
Will give brainiest :)
Answer:
x= 116°
y= 127°
Step-by-step explanation:
x... The angle subtended at the centre is twice the angle subtended at the cicumfernce by the same arch
y.... Angle in a cyclic quadrilateral add up to 180°
hence 180-53=127
Someone please help me!!!!!!!
What is the slope of the line through (-2,5) and (4, 9)?
A. slope = 2/3
B. slope =3/2
C. slope = 2
in your own words, how geometric seqences are related to exponetiol functions
Answer:
Geometric sequences are exponential functions
Step-by-step explanation:
Geometric sequences are exponential functions.
The general term of a geometric sequence is given by the exponential function ...
a[n] = a[1]·r^(n-1)
where a[1] is the first term and r is the common ratio.
You will notice that the independent variable (n) is in the exponent of this function. Hence it is an exponential function.
The number 99 is increased to 104. What is the percentage by which the number was increased, to the nearest tenth of a percent?
Answer:
5%
Step-by-step explanation:
104/99=1.05
Answer: 5%
Step-by-step explanation:
if you do the math of 99+5% you will get 103.95 and if you round that to the tenth you get 104.
Image point B'(4, -8) was transformed using the translation (x-2, y + 3). What were the coordinates of B?
(2, -5)
(6,-5)
(2,-11)
(6.-11)
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Answer:
B(6 , -11)
Step-by-step explanation:
(x-2 , y+3) = (4 , -8)
Compare the x & y co ordinates
x - 2 = 4 ; y + 3 = -8
x = 4 +2 ; y = -8 - 3
x = 6 ; y = -11
B(6 , -11)
Could someone help with this?
Answer:
30t
Step-by-step explanation:
2(15)t
30t
Answer: 30t
Step-by-step explanation:
The group earned 15t, or 15$ an hour for t hours. Then it was doubled(15t * 2=30t)
Sign numbers, ratios & Proportion
(+10) + (+6) = ?
Answer:
16
Step-by-step explanation:
Putting a + in front of a number indicates that the number is positive. so we are just going to add it up.
10+6=16
10:6=5:3
Hope it helps:)
A 3-column table with 4 rows. Column 1 has entries Catfish, bass, trout, all fish. Column 2 is labeled Sample 1 with entries 3, 9, 8, 20. Column 3 is labeled Sample 2 with entries 5, 9, 6, 20. The proportion used to find the average number of trout you would expect to live in the pond is 7 20 = x 400 . Solve the proportion to find the expected number of trout in the population. The expected number of trout in the population is .
Answer:
140
Step-by-step explanation:
The table is:
|Sample 1 | Sample 2
catfish | 3 | 5
bass | 9 | 9
trout | 8 | 6
all fish | 20 | 20
The average number of trouts is (8 + 6)/2 = 7
The average number of the total amount of fish is 20
So, there are 7 trouts within 20 fish. To find the expected number of trouts in a population of 400 fish, we have to solve the next proportion:
7 trouts / 20 fish = x trouts / 400 fish
x = 7*400/20
x = 140 trouts
Answer:
140
hope this helps
can you also answer these?!?
i cannot see the question for #33, but for
#34, im sure there are a bit more efficent ways to find surface area, but i just find the area of each square. area of top and bottom=240 square inches (120+120); area of shorter sides=60 square inches (30+30); area of longer sides= 72 square inches (36+36). add all of those together, so the total surface area is 372 square inches. So basically Charlene will need 372 square inches of wrapping paper
#35 the formula for volume is length*width*height. So do 60*45.5*14=38,220 cubic ft.
#36 first find the area of that triangle. (6*14)/2=42. Then find area of square which is 20*14=280. Add those (280+42) and get 322. So the area of the polygon is 322 square mm
Is 2(–2) + 6(2) equivalent to (–3)(–3) + (–1)(1)? Let negative numbers be represented with a "–" symbol and positive numbers be represented by "+" symbol. Use a pictorial model to justify your answer.
Answer:
Yes they are equivalent
Step-by-step explanation:
2(-2) = -4, plus 6(2) = 8 and
(-3)(-3) = 9, plus (-1)(1) = 8
Answer:
Yes they are equivalent
Step-by-step explanation:
the other fella right, check his reasons out, hope you guys learn from this question Stay safe everyone who sees this
Given that 0≤β<2π, find all the solutions to the equation 2sin^2β=7sinβ+4.
Answer:
Step-by-step explanation:
2sin²β-7sinβ-4=0
2sin²β-8sin β+1 sin β-4=0
2 sin β(sin β-4)+1(sin β-4)=0
(sin β-4)(2sin β+1)=0
either sin β-4=0
sin β=4 (rejected,as |sin β|≤1)
or
2 sin β+1=0
sin β=-1/2=-sin (π/6)=sin (π+π/6),sin (2π-π/6)
β=7π/6,11π/6
I will GIVE U Braniest!
Answer:
Hey there!
The correct answer would be:
The number of sandwiches the band sold: 73
The cost to make one sandwich: S
The profit the band earns from one sandwich: 0.2S
The amount of profit the band earns from one sandwich: S+0.2S
Answer:
The number of sandwiches the band sold: 73
The cost to make one sandwich: S
The profit the band earns from one sandwich: 0.2S
The amount of profit the band earns from one sandwich: S+0.2S
Step-by-step explanation:
Two retailers sell vanilla extract by the following price chart. When will their price be the same and how much?
Answer:
8 oz, $41
Step-by-step explanation:
For 4 oz, Chef Mate sells their's for $22 and Grocery Gourmet sells their's $25. Chef Mate sells his vanilla extract for $4.75/oz and Grocery Gourmet sells their's for $4/oz. At the 8th ounce, Chef Mate and Grocery Gourmet will charge the same amount, $41.
Chef Mate: $22 (price of 4 oz) + ($4.75 × 4) = $41
Gourmet Garden: $25 (price of 4 oz) + ($4 × 4) = $41
Please Help! A heptagon is shown. What is the area of the heptagon? Round your answer to the nearest hundredth if necessary. Enter your answer as a number, for example if the area is [tex]15m^{2}[/tex] enter 15
Answer: 90.85
I used an area calculator but at least you have the answer
QUICK 35 POINTS PLUS BRANLIEST. PLEASE ANSWER ALL THE QUESTIONS PROPERLY AND EXPLAIN HOW YOU GOT THEM. TRY TO ANSWER THEM BY TODAY.
THANKYOU
Hope it helps <3
(If it does, please give brainliest, only need one more for rank up :) )
Answer:
2. [tex]18\sqrt{5}[/tex]
3. [tex]52.303...[/tex]
4. [tex]11.608...[/tex]
Step-by-step explanation:
2. Using the Pythagorean Theorem, we can see that [tex]a^2+b^2=c^2[/tex]. Therefore, [tex]90^2+90^2=8100+8100=c^2[/tex]. We know that [tex]8100+8100[/tex] is [tex]16200[/tex]. The square root of [tex]16200[/tex] is [tex]90\sqrt{2}[/tex].
3. Same as before, we use the Pythagorean Theorem. This time, we're calculating [tex]b[/tex] instead of [tex]c[/tex]. This means we have to do [tex]60^2-29.4^2=b^2[/tex], which gives us [tex]3600-864.36[/tex], which equals [tex]2735.64[/tex]. We can put this in decimal form, which would give us [tex]52.303[/tex][tex]...[/tex]
4. This one, we do [tex]15^2-9.5^2[/tex], which would give us [tex]134.75[/tex]. Simplifying this would give us [tex]11.608...[/tex].
Hope this helped! Just remember the Pythagorean Theorem.
Select the products that are equivalent to -100.
1. -5(2)(-10)
2. -1(25)(4)
3. -4 (5)(5)
4. -2(25)(-2)
5. -1(-100)
-3(2x +5) how to solve this problem
Answer:
Step-by-step explanation:
-3×2x)+(-3×5)
-6x+-15
BC is tangent to circle A. Determine the length of AC . ANSWERS: 1) 3 2) 4 3) 5 4) 6
A circle is a curve sketched out by a point moving in a plane. The length of AC in the given figure is 5 units. The correct option is
3.
What is a circle?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the center.
In a circle, the angle between the radius and tangent is always equal to 90°. Therefore, we can write that in the given figure ΔABC, the triangle is a right angle triangle with ∠B as the right angle.
Now, for the triangle using the Pythagoras theorem we can write,
AC² = AB² + BC²
AC² = 3² + 4²
AC² = 9 + 16
AC = √25
AC = 5
Hence, the length of AC in the given figure is 5 units.
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simplify the expression (-h^4)^5
when a number is to a power then to another power, the answer is the number to the power TIMES the other power
it should be:
-h^20.
5. Points A, B and C are all
the circle.O represents the centre.
Angle AOB = 2x+28 Angle ADB = 3x-70
Calculate the value for x
Answer:
Step-by-step explanation:
angle acb=1/2angle aob=1/2(2x+28)------(anble subtended by an arc at centre is double the angle subtended by it at any other parts of the circle)
angle c+angle d=180....opp angles of a cyclic quad. are supplementry
hence,
x+14+3x-70=180
=>x=64
The value of x from the given figure is 59°.
Given that, points A, B and C are all the circle. O represents the center.
What is circle theorem to relate angle at circumference and central angle?
What is the circle?A circle is a two-dimensional figure formed by a set of points that are at a constant or at a fixed distance (radius) from a fixed point (center) on the plane. The fixed point is called the origin or center of the circle and the fixed distance of the points from the origin is called the radius.
Here, Reflection of ∠AOB= 360-(2x+28)
∠ADB=1/2 (Reflection of ∠AOB)
⇒ 3x-70=1/2 (360-(2x+28))
⇒ 3x-70=1/2 (360-2x-28)
⇒ 3x-70=180-x-14
⇒ 3x-70=166-x
⇒ 3x+x=236
⇒ 4x=236
⇒ x=59
Therefore, the value of x from the given figure is 59°.
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PLSSS HELPPP Simplify: (2 - i) (4 +2i)
Step-by-step explanation:
( 2 - 1)(4+2)
= (1)(6)
= 6
30 POINTS! Please HELP! (5.06 MC) Determine the equation for the line of best fit to represent the data
y = 1/5x + 1 y = -5/1x + 1 y = -1/5x + 1 y = - 1/5x - 1
Answer:
y=-1/5+1
Step-by-step explanation:
Answer:
y = -1/5x + 1
Step-by-step explanation:
In these types of problems you want to guesstimate the slope and draw an imaginary solid line amongst the dots. The slope you'll end up with is -1/5 because the graph is decreasing.
and just to check, i typed this into my graphing calculator and can confirm this as the answer. :)
Can you please help solve this division problem. If you explain I will give Brainly
Hey there! :)
Answer:
5a².
Step-by-step explanation:
Solve this expression by finding how many times 9a² goes into [tex]45a^{4}[/tex]. Since we are only dividing from a monomial, long division does not need to be used.
Begin by solving for the coefficient:
45 ÷ 9 = 5.
Solve for the exponent of a:
[tex]a^{4}[/tex] ÷ a² (subtract exponents when dividing) = a². Therefore:
[tex]45a^{4}[/tex] ÷ 9a² = 5a².
Question 5 (1 point)
(06.02 LC)
Which statement best describes the expression 3y = 8? (1 point)
O 1) 8 divided by 3 times y
O2) 8 times y divided by 3
03) 3 divided by 8 times y
O4) 3 times y divided by 8
Answer:
Step-by-step explanation:
None of these choices is correct.
3y = 8 is an equation, not an expression. It states that "y is 8 divided by 3," which again is an equation.
Answer:
3 times y divided by 8
Step-by-step explanation:
several people at a local mall were surveyed about the kind of vehicle they drive and whether they own or rent their home. Use the results listed in the table to find the probability that a randomly selected person from the survey either rents their home or drives an SUV.
Answer as a fraction = 18/25
Answer in decimal form = 0.72
Answer in percent form = 72%
=========================================================
Explanation:
We have A = 6+6+1 = 13 people who rent their home (add the values along the bottom row). There are B = 5+6 = 11 people who drive an SUV (add up the values in the SUV column). There are A+B = 13+11 = 24 people who either rent their home or drive an SUV. Keep in mind that 6 people have been double counted if we just go with A+B without adjustment. These 6 people both rent their home and drive an SUV. To correct for the double-count, we subtract off 6 from A+B to get A+B-6 = 24-6 = 18.
So there are 18 people who rent their home, drive an SUV, or both.
This is out of 4+5+3+6+6+1 = 25 people surveyed total.
The probability of selecting someone who rents their home or drives an SUV is 18/25. In decimal form that is equivalent to 0.72 which converts to 72%