The number of hours the diesel train traveled before the cattle train caught up is 15 hours
Solution:
Let t = travel time of the diesel train
Then (t - 2) is the travel time of the cattle train (Left 2 hrs later)
Average speed of diesel train = 52 mph
Average speed of cattle train = 60 mph
To find: number of hours the diesel train traveled before the cattle train caught up
Distance = speed x time
Distance traveled by diesel train:
Distance = 52 x t = 52t
Distance traveled by cattle train:
Distance = 60 x (t - 2) = 60t - 120
When the cattle train catches the diesel, they will have traveled the
same distance
Distance traveled by diesel train = Distance traveled by cattle train
52t = 60t - 120
60t - 52t = 120
8t = 120
t = 15
Thus the number of hours the diesel train traveled before the cattle train caught up is 15 hours
Which congruence theorems can be used to prove ΔABR ≅ ΔACR? Select three options
Answer:
SAS , ASA, SSS
Step-by-step explanation:
SAS , side A= side A . Angle B= Angle C, side R= side R
ASA, Angle A= Angle A . Side B= side C, Angle R= Angle R
SSS
side A= side A . Side B= side c, side R= side R
how to solve 4x + 7 = -2x + 19
subtract 7 from both sides
4x = -2x + 12
add 2x to both sides
6x = 12
divide both sides by 6
x = 2
if oak plywood costs $56.00/sheet sq ft. how much is 17 sq ft.
Answer:
$952
Step-by-step explanation:
I don't know why sheet is after 56, but I think they just want you to multiply 57 and 17.
find the domain of the function below if the domain is {-1,0,2} f(x)=x^2 -2x+3
Answer:
The Range is {3, 6}.
Step-by-step explanation:
The correct question is
Find the range of the function below if the domain is {-1,0,2} f(x)=x^2 -2x+3
we know that
The domain represents all possible values of x.
The range represents all possible values of f(x)
Substitute all of the possible x-values (domain) into the formula to find all possible f(x) values (the range).
For x=-1
[tex]f(-1)= (-1)^{2} - 2(-1) + 3[/tex]
[tex]f(-1)=1+2+ 3[/tex]
[tex]f(-1)=6[/tex]
For x=0
[tex]f(0)= (0)^{2} - 2(0) + 3[/tex]
[tex]f(0)=0-0+ 3[/tex]
[tex]f(0)=3[/tex]
For x=2
[tex]f(2)= (2)^{2} - 2(2) + 3[/tex]
[tex]f(2)=4-4+ 3[/tex]
[tex]f(2)=3[/tex]
therefore
The Range is {3, 6}.
Solve for y.
K=4yz
????
Answer:
y=K/4z
Step-by-step explanation:
K=4yz
y=K/4z
Answer:
Step-by-step explanation:
The function f(x) varies inversely with x and f(x)= -10 when x = 20
What is the inverse variation equation?
A. f(x) = -2/x
B. f(x) = - 50/x
C. f(x) = - 0.5/x
D. f(x) = -5/x
Answer:
The inverse variation function can be written as:
[tex]f(x)=\frac{-200}{x}[/tex]
Step-by-step explanation:
Given :
[tex]f(x)[/tex] varies inversely with [tex]x[/tex]
when [tex]x=20[/tex], [tex]f(x)=-10[/tex]
To find the inverse variation equation.
Solution:
[tex]f(x)[/tex] varies inversely with [tex]x[/tex] can be represented as:
[tex]f(x)[/tex] ∝ [tex]\frac{1}{x}[/tex]
Thus, [tex]f(x)=\frac{k}{x}[/tex]
where [tex]k[/tex] represents the constant of proportionality.
We can determine the value of [tex]k[/tex] by plugging in the values given.
when [tex]x=20[/tex], [tex]f(x)=-10[/tex]
So, we have
[tex]-10=\frac{k}{20}[/tex]
Multiplying both sides by 20.
[tex]20\times (-10)=20\times \frac{k}{20}[/tex]
[tex]-200=k[/tex]
Thus the inverse variation function can be written as:
[tex]f(x)=\frac{-200}{x}[/tex]
Various dilations of square A are shown. Which square was obtained by dilating square A by the scale factor of
1
2
This question is incomplete. I found similar question with picture. Please refer to the attachment to relate with my answer
Full Question:
Various dilations of square A are shown. Which square was obtained by dilating square a by the scale factor of 3.
Answer:
E
Step-by-step explanation:
The square a is a 2 unit x 2 unit square. With scale factor of 3. Any unit length of the object must be multiplied by 3
In this case, since the object side is 2, the image side must be 2x3 = 6 units.
Therefore, the dilation of square A with factor of 3 is square E
A worker at a snack stand opened a new box of cups. The first day he used 30 cups , the second day the worker used 15 percent of the remaining cups. A total of 90 cups were used the second day.what was the original amount of cups in the box before any were used?
plz help asap will give u brainliest :)
Answer:
Step-by-step explanation:
the first day he used 30 cups
the second day he used 15% of the remaining cups...a total of 90 cups were used on second day.
so 15%of the remaining cups = 90.....so if u let x be the total cups, then the remaining cups would be x - 30
15% of (x - 30) = 90.....turn ur percent to a decimal..." of " means multiply
0.15(x - 30) = 90
0.15x - 4.5 = 90
0.15x = 90 + 4.5
0.15x = 94.5
x = 94.5 / 0.15
x = 630 total cups <==
lets check..
start with 630 cups....used 30 the first day....leaving u with 600 cups....15% of the remaining cups = 90.....so 15% of 600 = 90....lets check it
15%of 600 = 0.15(600) = 90...yep, thats correct....there were 630 cups in the new un-opened box
Answer:
630
Explanation:
15% * number of remaining cups = 90
15% * (x-30) = 90
0.15(x-30) = 90
0.15x - 4.5 = 90
0.15x = 94.5
x = 630
-6y+13+9y=8y-3−6y+13+9y=8y−3
Answer:
y=3/8
Step-by-step explanation:
-6y+13+9y=3y+13
3y+13=8y-3-6y+13+9y
3y+13=2y+9y-3+13
3y+13=11y+10
13=11y-3y+10
13=8y+10
8y=13-10
8y=3
y=3/8
Math word problem we need help?
The total profit is :$37.46. Number of boxes for pop B to purchase more is 56 boxes.
Step-by-step explanation:
1.
Pop B number =36
Remaining Pop B after meeting = 36-17 =19
Amount obtained after selling remaining Pop B = 19* 0.75 = $14.25
Pop A number =75
Remaining Pop A after meeting = 75-8 =67
Amount obtained after selling pop A = 67*0.5 =$33.5
Profit in Pop B = $14.25-$3.79 =$10.46
Profit in Pop A =$33.5 -$6.50 = $27
Total profit after sell of Pop A and B = $10.46+$27 = $37.46
2.
The target profit is $250
Subtracting profit meet = $250 - $ 37.46 =$212.54
Profit to be attained by the sell of pop B only should be =$212.54
Selling price of pop B per box is $3.79
Number of boxes for pop B to purchase more will be;
$212.54/ $3.79 = 56.08 ⇒ 56 more boxes
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Keywords ; pop, profit, goal, more boxes, sale price , brand
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If the interest earned on an account after 7 years at 6% is $1785 ,what is the initial value
Answer:
$4250
Step-by-step explanation:
i = prt
or
p = i / rt
where,
i = $1,785
r = 6% = 0.06
t = 7 years
So, we can calculate initial vale by putting the values in above equation;
p = $1,785 / (0.06 x 7)
p = $1,785 / 0.42
p = $4,250
Hence the initial value will be $4250
The ratio of two complementary angles is 7:2. What is the measure, in degrees, of the larger angle?
Answer:
70 degrees
Step-by-step explanation:
Complementary angles sum up to 90.
To find the larger angle, you find the total of the values in the ratio, divide the larger value of the ratio by the total and multiply it by 90.
(7/7+2)×90=7/9×90
=7×10
=70
OR
Write an equation:
7x+2x=90
9x=90
x=10
Then multiply x by the larger value.
7x=7 (10)=70
20 POINTS BRAINLIEST
First solving for log5(92):
log5(92) = log(92) / log(5) = 2.8095 = 2.810
Now to change to base 3:
log3(x) = log5(92)
Solve for x:
x = 3^(log5(92)
x = 3^2.810
x = 21.903
The answer would be the first one.
Answer:
I got A
Hope this helps
Step-by-step explanation:
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar.
Determine the equation for the parabola graphed below.
y =
x2 +
x +
Answer:
[tex]\large\boxed{y=\dfrac{1}{2}x^2-2x+1}[/tex]
Step-by-step explanation:
The vertex form of an equation of a parabola:
[tex]y=a(x-h)^2+k[/tex]
(h, k) - vertex
a - leading coefficient in equation y = ax² + bx + c
From the grap we can read coordinates of the vertex (2, -1) and y-intercept (0, 1).
Therefore h = 2, k = -1
Put the values of h, k and coordinates of the y-intercept to the equation of parabola:
[tex]1=a(0-2)^2-1[/tex] add 1 to both sides
[tex]1+1=a(2)^2-1+1[/tex]
[tex]2=4a[/tex] divide both sides by 4
[tex]\dfrac{2}{4}=\dfrac{4a}{4}\\\\\dfrac{1}{2}=a\to a=\dfrac{1}{2}[/tex]
Therefore we have the equation:
[tex]y=\dfrac{1}{2}(x-2)^2-1[/tex]
Convert to the standard form:
[tex]y=\dfrac{1}{2}(x-2)^2-1[/tex] use (a - b)² = a² - 2ab + b²
[tex]y=\dfrac{1}{2}(x^2-2(x)(2)+2^2)-1[/tex]
[tex]y=\dfrac{1}{2}(x^2-4x+4)-1[/tex] use the distributive property
[tex]y=\dfrac{1}{2}x^2-\dfrac{1}{2}\cdot4x+\dfrac{1}{2}\cdot4-1[/tex]
[tex]y=\dfrac{1}{2}x^2-2x+2-1[/tex] combine like terms
[tex]y=\dfrac{1}{2}x^2-2x+1[/tex]
an inline 3-cylinder engine has a 11 cm bore, the stroke is 6cm. Calculate the total stroke volume of the engine in cm3
Answer:
544.5π cm³ ≈ 1711 cm³
Step-by-step explanation:
Each cylinder has a bore (diameter) of 11 cm, and stroke (height) of 6 cm.
V = πr²h
V = π (11 cm / 2)² (6 cm)
V = 181.5π cm³
There are 3 cylinders, so the total volume is:
3V = 544.5π cm³
3V ≈ 1711 cm³
To calculate the total stroke volume of an inline 3-cylinder engine with an 11 cm bore and a 6 cm stroke, calculate the area of the bore, find the volume of one cylinder by multiplying by the stroke, and then multiply by the number of cylinders. The total stroke volume of the engine is 1710.6 cm³.
The student asked to calculate the total stroke volume of an inline 3-cylinder engine with an 11 cm bore and a 6 cm stroke. The formula to calculate the volume of a single cylinder is V = rac{ ext{ extpi}}{4} imes D^2 imes S, where V is the volume, D is the diameter of the bore, and S is the stroke. In this case, D would be 11 cm, and we would need to square this value, then multiply by extpi/4 and by the stroke length of 6 cm, then multiply the result by the number of cylinders, which is 3, to get the total engine displacement.
Step by step, we first calculate the area of the bore (cylinder base):
Area = extpi imes (radius)² = extpi imes (5.5 cm)²
= extpi imes 30.25 cm²
= 95.0332 cm². Next, we calculate the volume of one cylinder: Volume = Area imes Stroke = 95.0332 cm² imes 6 cm = 570.1992 cm³. Finally, we find the total volume for all three cylinders: Total Volume = 570.1992 cm³ imes 3
= 1710.5976 cm³. Thus, the total stroke volume of the engine is 1710.5976 cm³ or rounded to 1710.6 cm³.
16 equals m-14 what is the value of m
Answer:
16=m-14
To find the value of m you want to add 14 to each side
30=m
Step-by-step explanation:
5. Which polynomial is equal to (x^5+ 1) divided by (x + 1)?
AXA - X3 .x² - x + 1.
B X - X² + x² - x + 1
C x4 + x3 -- x2 + x + 1
D x + x3 + x² + x 1
Answer:
B [tex]x^4-x^3+x^2-x+1[/tex]
Step-by-step explanation:
Given,
Dividend = [tex](x^5+1)[/tex]
Divisor = [tex](x+1)[/tex]
Now According to the rule of Division.
Step 1: At first dividend is [tex](x^5+1)[/tex] and Divisor is [tex](x+1)[/tex] when it is divided for the first time the quotient will be [tex]x^4[/tex] and remainder will be [tex]-x^4+1[/tex]
Step: 2 Now the remainder of step 1 will be new dividend which is [tex]-x^4+1[/tex] and Divisor is [tex](x+1)[/tex] so when it is divided the quotient will be [tex]x^4-x^3[/tex] and remainder will be [tex]x^3+1[/tex]
Step: 3 Now the remainder of step 2 will be new dividend which is [tex]x^3+1[/tex] and Divisor is [tex](x+1)[/tex] when it is divided the quotient will be [tex]x^4-x^3+x^2[/tex] and remainder will be [tex]-x^2+1[/tex]
Step: 4 Now the remainder of step 3 will be new dividend which is [tex]-x^2+1[/tex] and Divisor is [tex](x+1)[/tex] when it is divided the quotient will be [tex]x^4-x^3+x^2-x[/tex] and remainder will be [tex]x+1[/tex]
Step: 5 Now the remainder of step 4 will be new dividend which is [tex]x+1[/tex] and Divisor is [tex](x+1)[/tex] when it is divided the quotient will be [tex]x^4-x^3+x^2-x+1[/tex] and remainder will be 0.
Hence When the polynomial [tex](x^5+1)[/tex] is divided by [tex](x+1)[/tex] the answer or quotient will be equal to [tex]x^4-x^3+x^2-x+1[/tex] and remainder will be 0.
Question on photo, there are two parts, read carefully! Will mark brainliest
A landscaper installed a circular sprinkler system using 50.25 feet of copper tubing to create the circle. To the nearest whole foot, what is the diameter of the circular sprinkler
Answer:
4 foot
Step-by-step explanation:
√50.25 / 3.1416 = 4
The diameter of the circular sprinkler is 16 feet.
Explanation:To find the diameter of the circular sprinkler, we can use the formula for the circumference of a circle: C = πd, where C is the circumference and d is the diameter. In this case, we are given the length of the copper tubing used, which is equal to the circumference. So we can rearrange the formula to solve for the diameter: d = C/π. Plugging in the given values, we have d = 50.25/π. Using the value of π as approximately 3.14, we can calculate the diameter to the nearest whole foot.
d ≈ 50.25/3.14 ≈ 16.01 feet
Therefore, the diameter of the circular sprinkler to the nearest whole foot is 16 feet.
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If f(x) = 4x - 3, what is f(x)^-1
Answer:
[tex]f^{-1}[/tex](x) = [tex]\frac{x+3}{4}[/tex]
Step-by-step explanation:
let y = f(x) and rearrange making x the subject, that is
y = 4x - 3 ( add 3 to both sides )
y + 3 = 4x ( divide both sides by 4 )
[tex]\frac{y+3}{4}[/tex] = x
Change y back into terms of x
[tex]f^{-1}[/tex](x) = [tex]\frac{x+3}{4}[/tex]
Should perimeter or area be used to find the amount of fencing for a paddock?
Find the sum.
7x + 15x=
Answer:
7x + 15x= 21x
Step-by-step explanation:
7x + 15x
= (7 + 15)x
= 22x
Answer: 22x
Step-by-step explanation: +7x and +15x are called terms and the numbers in front of the variables, +7 and +15 are called coefficients.
Because the variables, x and x, are identical, the two terms in this problem are called like terms. Like terms can be added together by simply adding their coefficients. So in this problem, since 7 + 15 is 22, 7x + 15x is simply 22x.
how to solve this equation
-6=b/18
Answer:
b=-108
Step-by-step explanation:
To solve this equation for b, you simply multiply each side by 18. The reason you do this is to isolate the b.
[tex]-6=\frac{b}{18}[/tex]
[tex]18(-6)=(\frac{b}{18} )(18)[/tex]
[tex]-108=b[/tex]
Quadrilateral ABCD is dilated by a scale factor of 1 over 3 centered around (1, 2). Which statement is true about the dilation?
segment B prime D prime will run through (1, 2) and will be shorter than segment BD.
segment B prime D prime will run through (1, 2) and will be longer than segment BD.
segment B prime D prime will be parallel to segment BD and will be shorter than segment BD.
segment B prime D prime will be parallel to segment BD and will be longer than segment BD.
Note: Since you missed to add the figure. So, after a little research I am kind of able to find the figure and hence, assuming it as a reference. Hence, I am attaching the figure and solution of that figure is also visible in the same figure. Please check the attached figure (a)
Answer:
Segment B'D' will be parallel to segment BD and will be shorter than segment BD. Please see the attached figure (a) for better understanding.
Step-by-step explanation:
As we know that there are certain rules when a quadrilateral is dilated by a certain scale centered around a certain point.
So,
Let suppose P(a, b) is the point.
The dilation rule by a scale factor of 1 over 3 or (1/3) centered around (1, 2) is
P(a, b) → [tex]P(\frac{x+2}{3}, \frac{y+4}{3})[/tex]
Hence,
A(1, 2) → A'(1, 2)
B(2, 3) → B'(4/3, 7/3)
C(4, 2) → C'(2, 2)
D(2, 1) → D'(4/3, 5/3)
The attached figure show that if we draw the all these points in the coordinate plan i.e. A(1, 2), B(2, 3), C(4, 2), D(2, 1) and A'(1, 2), B'(4/3, 7/3), C'(2, 2), D'(4/3, 5/3), we can determine that Segment B'D' will be parallel to segment BD and will be shorter than segment BD.
Keywords: dilation, quadrilateral, segment
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Answer: C) segment B prime D prime will be parallel to segment BD and will be shorter than segment BD.
Emma buys and sells truck parts. she bought 2 tires for $35 and later sold them for $65. she bought three rims for $75 and later sold them for $136. she bought 4 headlight covers for $4 and later sold them for $15. what is Emma's total profit?
Answer:
The two tires she bought is $35+$35 which then equals to $70. She spent $70 on tires. She then sold them for $65. She bought three rims, each $75... $75+$75+$75 which then equals her $225. And then sold them for $136. She then bought four headlight covers for $4 each... $4+$4+$4+$4, which equals her $16. Then sold them for $15. Her total profit is -$95. How i got that answer you say, well, if you calculate how much she spent on everything in total, she spent -$311 on everything. You then calculate how much she gained by selling everything she had bought, which was a total of $216. Add both of the total prices, -$311+216= you get -$95.
Step-by-step explanation:
Answer:
298
Step-by-step explanation:
35*2=70 65*2=130 130-70=60
75*3=225 136*3=408 408-225=183
5*4=20 15*5=75 75-20=55
55+60+183=298
Bryson’s dad is 38 years old. If this is four years less than three times Bryson’s age, how old is Bryson?
Answer:
Bryson’s age is 14 years
Step-by-step explanation:
Let
x ----> Bryson’s age
we know that
Bryson’s age multiplied by 3 minus 4 must be equal to 38
so
The linear equation that represent this situation is
[tex]3x-4=38[/tex]
solve for x
Adds 4 both sides
[tex]3x=38+4[/tex]
[tex]3x=42[/tex]
Divide by 3 both sides
[tex]x=14[/tex]
therefore
Bryson’s age is 14 years
The car is purchase for $18,000 after each year the resell value decreases by 25% what will the resale value be after three years
Answer:
18000×75÷100 =13500 ×3 =40500 .
Kedwin has $150.00 and wants to buy a new pair of headphones that cost $175.00 plus 10% shipping. He decides to wait until the headphones go on sale. What is the smallest sale rate that he needs to be able to afford them?
Answer:
I believe its 20% thats counting the 10% shipping cost
Step-by-step explanation:
Final answer:
Kedwin needs a minimum sale rate of approximately 24.29% in order to afford the headphones.
Explanation:
To calculate the minimum sale rate that Kedwin needs to be able to afford the headphones, we first need to calculate the total cost of the headphones including shipping. The headphones cost $175.00 and the shipping is 10% of the cost, which is $17.50. So the total cost is $175.00 + $17.50 = $192.50.
Next, we subtract Kedwin's current funds, $150.00, from the total cost, $192.50, to find the amount he still needs, which is $192.50 - $150.00 = $42.50.
Finally, we divide the amount he still needs by the original cost of the headphones and multiply by 100 to find the minimum sale rate. In this case, the calculation is ($42.50 / $175.00) * 100 = 24.29%. Therefore, Kedwin needs a minimum sale rate of approximately 24.29% in order to afford the headphones.
What kind of molecule is represented in the diagram?
Fatty Acid
Glycerol
Fatty Acid
Fatty Acid
A. A nucleic acid
B. A lipid
C. A nucleotide
D. A carbohydrate
Answer:
A lipid
Step-by-step explanation:
When 1 "Glycerol "and 3"Fatty Acids" form a bond the new molecule is called "Triglyceride" which is a type of "Lipid"
Need help with this Asap.
Answer:
B
Step-by-step explanation: