Answer:
see explanation
Step-by-step explanation:
(1)
Using the relationship
distance (d) = speed (s) × time (t)
The freight train leaves the station 1 hour earlier than the passenger train, so
d = 40(t + 1) ← Freight train
d = 50t ← Passenger train
We require to find when they are at the same distance from the station, then equating the 2 equations
50t = 40(t + 1) ← distribute
50t = 40t + 40 ( subtract 40t from both sides )
10t = 40 ( divide both sides by 10 )
t = 4
The passenger train will overtake the freight train after 4 hours
-------------------------------------------------------------------------------------
(2)
let l represent length, then width = l - 32
perimeter (P) = 2l + 2w = 290, that is
2l + 2(l - 32) = 290 ← distribute and simplify left side
2l + 2l - 64 = 290
4l - 64 = 290 ( add 64 to both sides )
4l = 354 ( divide both sides by 4 )
l = 88.5 and w = 88.5 - 32 = 56.5
Then dimensions are 88.5 yards by 56.5 yards
----------------------------------------------------------------------------------
(3)
Plan A : 100 + 15n
Plan B : 25n
When is Plan A better than Plan B , that is
100 + 15n > 25n ( subtract 25n from both sides )
100 - 10n > 0 ( subtract 100 from both sides )
- 10n > - 100
Divide both sides by - 10, reversing the symbol as a result of dividing by a negative quantity.
n < 10
Plan A is better when number of hours (n) is less than 10
Answer:
3. Jeanette can be paid in one of two ways for painting a house. : Plan A; $100 plus $15 per hour; Plan B: $25 per hour. Suppose that a job takes n hours to complete. For what values of n is Plan is Plan A better for Jeanette?
simplify (-4/5)^9/(-4/5)^10
Answer:
- 5/4
Step-by-step explanation:
exact form:-5/4
decimal form:-1.25
mixed number form: -1 1/4
Evaluate m2 + 12q if m= 5 and q =-3 plz
Answer:
-11
Step-by-step explanation:
m²+12q
= (5)² + 12(-3)
= 25 -36
= -11
Solve the equation x² = 5. (must show equality properties in work so I can earn full credit)
A. x = 5
B. x = 25
C. x = √5
D. x = ±√5
The given matrix is the augmented matrix for a linear system. Use technology to perform the row operations needed to transform the augmented matrix to reduced echelon form, and then find all solutions to the corresponding system. (If there are an infinite number of solutions use s1 as your parameter. If there is no solution, enter NO SOLUTION.)
[9 -2 0 -4 8]
[0 7 -1 -1 9]
[8 12 -6 5 -2]
(x1, x2, x3, x4)=_______
Answer:
[tex]x_{1} = \frac{176}{127} + \frac{71}{127}x_{4}\\\\ x_{2} = \frac{284}{127} + \frac{131}{254}x_{4}\\\\x_{3} = \frac{845}{127} + \frac{663}{254}x_{4}\\[/tex]
Step-by-step explanation:
As the given Augmented matrix is
[tex]\left[\begin{array}{ccccc}9&-2&0&-4&:8\\0&7&-1&-1&:9\\8&12&-6&5&:-2\end{array}\right][/tex]
Step 1 :
[tex]r_{1}[/tex]↔[tex]r_{1} - r_{2}[/tex]
[tex]\left[\begin{array}{ccccc}1&-14&6&-9&:10\\0&7&-1&-1&:9\\8&12&-6&5&:-2\end{array}\right][/tex]
Step 2 :
[tex]r_{3}[/tex]↔[tex]r_{3} - 8r_{1}[/tex]
[tex]\left[\begin{array}{ccccc}1&-14&6&-9&:10\\0&7&-1&-1&:9\\0&124&-54&77&:-82\end{array}\right][/tex]
Step 3 :
[tex]r_{2}[/tex]↔[tex]\frac{r_{2}}{7}[/tex]
[tex]\left[\begin{array}{ccccc}1&-14&6&-9&:10\\0&1&-\frac{1}{7} &-\frac{1}{7} &:\frac{9}{7} \\0&124&-54&77&:-82\end{array}\right][/tex]
Step 4 :
[tex]r_{1}[/tex]↔[tex]r_{1} + 14r_{2}[/tex] , [tex]r_{3}[/tex]↔[tex]r_{3} - 124r_{2}[/tex]
[tex]\left[\begin{array}{ccccc}1&0&4&-11&:-8\\0&1&-\frac{1}{7} &-\frac{1}{7} &:\frac{9}{7} \\0&0&- \frac{254}{7} &\frac{663}{7} &:-\frac{1690}{7} \end{array}\right][/tex]
Step 5 :
[tex]r_{3}[/tex]↔[tex]\frac{r_{3}. 7}{254}[/tex]
[tex]\left[\begin{array}{ccccc}1&0&4&-11&:-8\\0&1&-\frac{1}{7} &-\frac{1}{7} &:\frac{9}{7} \\0&0&1&-\frac{663}{254} &:-\frac{1690}{254} \end{array}\right][/tex]
Step 6 :
[tex]r_{1}[/tex]↔[tex]r_{1} - 4r_{3}[/tex] , [tex]r_{2}[/tex]↔[tex]r_{2} + \frac{1}{7} r_{3}[/tex]
[tex]\left[\begin{array}{ccccc}1&0&0&-\frac{71}{127} &:\frac{176}{127} \\0&1&0&-\frac{131}{254} &:\frac{284}{127} \\0&0&1&-\frac{663}{254} &:\frac{845}{127} \end{array}\right][/tex]
∴ we get
[tex]x_{1} = \frac{176}{127} + \frac{71}{127}x_{4}\\\\ x_{2} = \frac{284}{127} + \frac{131}{254}x_{4}\\\\x_{3} = \frac{845}{127} + \frac{663}{254}x_{4}\\[/tex]
Which number is an integer?
-3/4
1/5
2
4/2/3
Answer:
2
Step-by-step explanation:
7515.904 rounded to nearest tenth
Answer:
7515.9
Step-by-step explanation:
Tenth is basically like 1 decimal point.
0-4 round dowm 5-9 round up
The Maine Public Health Department reported that there have been 90 flu cases requiring hospitalization in Portland, ME (population of 70,000) since the beginning of 2018 - today is July 4th, 2018. On February 1st, 2018, 43 of those cases were hospitalized. What was the prevalence rate of flu cases requiring hospitalization thus far in 2018?
Answer:
The prevalence rate of flu cases requiring hospitalization thus far in 2018 is:
= 0.13%
Step-by-step explanation:
a) Data and Calculations:
Population of Portland, ME = 70,000
Number of flu cases requiring hospitalization on February 1st, 2018 = 43
Number of flu cases requiring hospitalization on July 4th, 2018 = 90
The prevalence rate of flu cases requiring hospitalization thus far in 2018 = 90/70,000 * 100 = 0.13%
b) The prevalence rate represents the proportion of the population of Portland, ME, who have the flu at the time that the Maine Public Health Department reported the number of flu cases requiring hospitalization on July 4th, 2018.
The distance from the ground to where the ladder is touching the wall is 7
feet. The distance from the wall to the base of the ladder is 4 feet. What is
the length of the ladder?
wall
ladder
Answer:
L=8.062 feet
Step-by-step explanation:
wall=7
distance=4
Pythagorean theorem
7^2+4^2=L^2
49+16=L^2
65=L^2
L=8.062 feet
The required length of the ladder is given as 8.06 feet.
What are Pythagorean triplets?In a right-angled triangle, its sides, such as hypotenuse, perpendicular, and base are Pythagorean triplets.
here,
As mentioned in the question,
perpendicular length = 7, base length = 4 feet,
Let the length of the ladder be x,
Following the Pythagoras theorem,
x² = 7 ² + 4²
x ² = 49 + 16
x² = 65
x = √65
x = 8.06
Thus, the required length of the ladder is given as 8.06 feet.
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Geoff earns 10% commission on his total sales at work. To pay for a concert ticket, Geoff needs to earn $135 in commission. What must Geoff's sales total for the week be?
A. $13.50
B. $135.00
C. $148.50
D. $1,350.00
Answer:6
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
9) Linda and Maria share £200. Linda has 4 times as much money as Maria.
How much money does Maria have?
Answer:
40
Step-by-step explanation:
maria is x
linda is 4x
x+ 4x = 200
5x = 200
x= 40
Q. Abby lives in a home worth $115,000. She has a mortgage of $98,000. she owes $5,200 on her car that is worth $11,000. she has a credit card balance of $2,300. she also has a checking account with a balance of $900 and $300 in gift cards. What is Abby's net worth?
A. 127,200
B. 105,500
C. 232,700
D. 21,700
Write the percent as a fraction and as a decimal.
5% tax
Answer:
The answer would be 0.05
Step-by-step explanation:
This is because it is PER Cent so 5% is 0.05 of 1
Answer:
1/20 and 0.05
Step-by-step explanation:
QUESTION: Use the two way table below to answer the question: How
many chemical engineers chose science as their favorite subject? *
The table shows the results of a survey about what the engineers said their favorite subject was in middle school
Answer:
B.91
Step-by-step explanation:
Because it says so on the table.
Solve the following equation for x.
10 = 2 – 4(ar – 3)
OA. -
a
OB.
Oc.
OD.
5
a
Answer:
Options C. -5/a
x =1/a is the solution for the given equation. Option D is correct.
What is algebraic Expression?Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.
Let's simplify the equation first:
10 = 2 - 4(ax - 3)
10 = 2 - 4ax + 12 (distribute the negative 4)
10 = -4ax + 14 (combine like terms)
Now we can isolate the variable x by subtracting 14 from both sides and then dividing by -4:
10 - 14 = -4ax
-4 = -4ax
x = 1/a
Therefore, the solution to the equation is x = 1/a.
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5 (a) Write the ratio 15:35 in its simplest form.
Answer:
Step-by-step explanation:
5 is a factor of 15 and 35
15:35 = 3:7
If m∠4 = 101.9°, find each of the following in degrees.
(a) m∠5
(b) m∠8
Answer:
m<5=101.9 m<8=101.9
Step-by-step explanation:
alternate interior and vertical angles
Answer:
(a) m∠5=<4[alternate angle]=101.9°,
(b) m∠8=<5[vertically opposite angle]=101.9°,
Lisa ran 3 1/2 miles in 21 minutes at that rate how long will it take her to run 5 miles
Answer:30
Step-by-step explanation: please
Lisa take approximately 30 minutes(time) to run 5 miles at the same rate she ran 3 1/2 miles in 21 minutes.
To find out how long it will take Lisa to run 5 miles at the same rate, we can set up a proportion using the distance and time data.
Let's denote the time it will take her to run 5 miles as "t" (in minutes).
The proportion can be set up as follows:
(3.5 miles) / (21 minutes) = (5 miles) / (t minutes)
Now, cross-multiply and solve for "t":
3.5 × t = 21 × 5
3.5t = 105
Divide both sides by 3.5 to isolate "t":
t = 105 / 3.5
t = 30
So, it will take Lisa approximately 30 minutes to run 5 miles at the same rate she ran 3 1/2 miles in 21 minutes.
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Consider a student loan of $22,500 at a fixed APR of 9% for 30 years.
a. Calculate the monthly payment.
b. Determine the total amount paid over the term of the loan
c. Of the total amount paid, what percentage is paid toward the principal and what percentage is paid for interest.
a. The monthly payment is 5
(Do not round until the final answer. Then round to the nearest cent as needed.)
b. The total payment over the term of the loan is s
(Round to the nearest cent as needed.)
c. Of the total payment over the term of the loan, % is paid toward the placipal and % is paid toward interest.
(Round to the nearest tenth as needed)
Answer:
Lo averiguaste, lo siento, amigos míos, por haberlos ayudado. pero la respuesta es 456 $.
Step-by-step explanation:
Name:
1. Dane deposited $5,000 in a savings account. The amount in the account after 1, 2, and 3 years is shown
below.
$5,240, $5,480, $5,720, ...
Which function represents the total amount in her account at the end of t years?
A. M(t) = 5000 + 2400
B. M(t) = 5240 +2400
C. M(t) = 5000t + 240
D. M(t) = 5240t + 240
Answer:
I dont kn0w try g00gle searches
Answer:
B. M(t)= 5240+240t
Step-by-step explanation:
cause
I need help with this
look at picture
Complementary angles
============================================================
Explanation:
The square marker indicates a 90 degree, or right angle.
The two smaller angles (3x and 75) both combine to the larger 90 degree angle. That's what it means when they say we have complementary angles.
Add up the smaller angles, set the sum equal to 90, and solve for x.
3x+75 = 90
3x+75-75 = 90-75 ....... subtracting 75 from both sides
3x = 15
3x/3 = 15/3 ..... divide both sides by 3
x = 5
---------------
If x = 5, then 3x = 3*5 = 15
Then we can see that 15+75 = 90 to help check our answer.
Evaluate the expression: 3a2 + 2b2 when a = -3 and b = 6
K 4x J 6x – 8 L 152° What is the measure of angle KJL? O A. 640 O B. 78° 0 C. 840 O D. 88°
Answer:
D
Step-by-step explanation:
180-152= 28°
4x+6x-8+28=180
10x=160
x=16°
kjl= 6x-8= 88°
Use the Discriminant to determine if the quadratic equation has complex/no real solutions, one real solution, or two real solutions. Give the value of the a. 2x^2 – 3x - 10 = 0 b.x^2 - 6x + 9 = 0 c.g(x)=x^2-8x+20
Answer:
Step-by-step explanation:
discriminant = 3² – 4·2(-10) = 89
discriminant > 0 ∴ two real solutions
Help with all 3 ASAP
Answer:
The second one is right
The third one is wrong.
Runner A had a minor accident and is now 0.25 miles behind Runner B.
Runner B is currently has a speed of 7 miles per hour.
Runner A attempts to catch up runner B by running 8.5 miles per hour.
How long will it take Runner A to catch up to Runner B?
Answer:
It will take one sixth of a hour, that is, 10 minutes for Runner A to catch up to Runner B.
Step-by-step explanation:
Runner A is 0.25 miles behind Runner B.
Runner B has a speed of 7mph, while Runner A has a speed of 8.5 mph.
This means that each hour, Runner A catches up at a speed of 8.5 - 7 = 1.5 mph.
How long will it take Runner A to catch up to Runner B?
1 hour - 1.5 miles
x hours - 0.25 miles
[tex]1.5x = 0.25[/tex]
[tex]x = \frac{0.25}{1.5}[/tex]
[tex]x = \frac{1}{6}[/tex]
It will take one sixth of a hour, that is, 10 minutes for Runner A to catch up to Runner B.
Find the value of x in the given
right triangle.
х
37°
10
X = [?]
Enter your answer as a decimal rounded to the nearest 10th
Answer:
cos37=10/y
0.8=10/y
y=12.5
y²=10²+x²
x=12.5²-10²
56.25
Step-by-step explanation:
Change 8.94 into a fraction
Answer:
447 / 50
Step-by-step explanation:
447 / 50 Because if you divide it you will get 8.94 same answer
Answer:
inproper fraction would be 447/50 but the proper fraction would be 8 47/50
Find the missing angle measurments geometry
Answer:
?????????
Step-by-step explanation:
wheres the equation
Given: E is the midpoint of DF.
Prove: DE = 23
Answer:
DE=23
Step-by-step explanation:
Since E is the midpoint of DF, we know that DE and EF are equal. Thus, we can set them equal to eachother and solve.
8x-1=6x+5
2x=6
x=3
After that, plug 3 back into DE.
6(3)+5= DE
18+5= DE
23=DE
pls help pls pls pls help
pls help him Step-by-step explanation: