Instructions: Solve the following linear
equation
4(n + 5) – 2(5 + 7n) = -70
n =
Answers
Answer:
Step-by-step explanation:
4*(n +5) - 2*(5 + 7n) = -70
4*n + 4*5 + 5*(-2) + 7n*(-2) = -70
4n + 20 - 10 - 14n = -70
4n - 14n + 20 - 10 = -70
- 10n + 10 = -70
Subtract 10 from both sides
-10n = -70 - 10
-10n = -80
Divide both sides by (-10)
n = -80/-10
n = 8
Step-by-step explanation:
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Related Questions
In an experiment, the initial temperature of a solution is -5 °C. The solution is heated up at 3 °C per minute for 19 minutes and then it is cooled at 4 °C per minute for 6 minutes. Calculate the final temperature, in °C, of the solution.
Answers
Answer:
28°C
Step-by-step explanation:
First you do 3*19=57°C
-5+57= 52°C
then you do 4*6=24 °C
as its being cooled you takeaway
52-24=28°C
A bicyclist is at point A on a paved road and must ride to point C on another paved road. The two roads meet at
an angle of 38° at point B. The distance from A to B is 18 mi, and the distance from B to C is 12 mi (see
the figure). If the bicyclist can ride 22 mph on the paved roads and 6.8 mph off-road, would it be faster for the bicyclist to ride from A to C on the paved roads or to ride a direct line from A to C off-road? Explain.
Answers
Answer:
Step-by-step explanation:
The diagrammatic expression to understand this question very well is attached in the image below.
By applying the law of cosine rule; we have:
a² = b² + c² - 2bc Cos A --- (1)b² = a² + c² - 2ac Cos B --- (2)c² = a² + b² - 2ab Cos C --- (3)From the diagram attached below, we need to determine the side "b" by using equation (2) from above:
b² = a² + c² - 2ac Cos B
From the information given:
a = 12 miles; c = 18 miles; ∠B = 38°
∴
replacing the values into the above equation:
b² = 12² + 18² - 2(12)(18) Cos (38°)
b² = 144 + 324 - 432 × (0.7880)
b² = 468 - 340.416
b² = 127.584
[tex]b = \sqrt{127.584}[/tex]
b = 11.30 miles
However, we are also being told that the speed from A → C = 6.8 mph
Thus, the time required to go from A → C can be determined by using the relation:
[tex]\mathbf{speed = \dfrac{distance}{time}}[/tex]
making time the subject of the formula, we have:
[tex]\mathbf{time= \dfrac{distance}{speed }}[/tex]
[tex]\mathbf{time= \dfrac{11.30}{6.8}}[/tex]
time = 1.66 hours
By using the paved roads, the speed is given as = 22 mph
thus, the total distance covered = |AB| + |BC|
= (18+12) miles
= 30 miles
∴
[tex]\mathbf{time= \dfrac{distance}{speed }}[/tex]
[tex]\mathbf{time= \dfrac{30}{22}}[/tex]
time = 1.36 hours
Therefore, the time used off-road = 1.661 hours while the time used on the paved road is 1.36 hours.
Since we are considering the shortest time possible;
We can conclude that it would be faster for the bicyclist to ride from A to C on the paved roads since it takes a shorter time to reach its destination compared to the time used off-road.
Learn more about Law of cosine here:
https://brainly.com/question/24077856?referrer=searchResults
It would be faster for the bicyclist to ride from A to C on the paved roads since the time to go from A to C on the paved roads is 1.4 h and the time to go from A to C off-road is 1.7 h.
To calculate which way would be faster we need to find the distance from point A to C with the law of cosines:
[tex] \overline{AC}^{2} = \overline{AB}^{2} + \overline{BC}^{2} - 2\overline{AB}\overline{BC}cos(38) [/tex]
Where:
[tex]\overline{AB}[/tex]: is the distance between the point A and B = 18 mi
[tex]\overline{BC}[/tex]: is the distance between the point B and C = 12 mi
[tex] \overline{AC} = \sqrt{(18 mi)^{2} + (12 mi)^{2} - 2*18 mi*12 mi*cos(38)} = 11.3 mi [/tex]
Now, let's find the time for the two following cases.
1. From point A to C on the paved roads (t₁)
[tex] t_{1} = t_{AB} + t_{BC} [/tex]
The time can be calculated with the following equation:
[tex] t = \frac{d}{v} [/tex] (1)
Where:
d: is the distance
v: is the velocity
Then, the total time that it takes the bicyclist to go from point A to C on the paved roads is:
[tex] t_{1} = t_{AB} + t_{BC} = \frac{18 mi}{22 mph} + \frac{12 mi}{22 mph} = 1.4 h = 84 min [/tex]
2. From point A to C off-road (t₂)
With equation (1) we can calculate the time to go from point A to C off-road:
[tex] t_{2} = \frac{\overline{AC}}{v_{2}} = \frac{11.3 mi}{6.8 mph} = 1.7 h = 102 min [/tex]
Therefore, it would be faster for the bicyclist to ride from A to C on the paved roads.
To find more about the law of cosines, go here: https://brainly.com/question/15740431?referrer=searchResults
I hope it helps you!
Can some please help please thank you
Answers
Answer:
b the answer
Step-by-step explanation:
You have $90 in your bank account. Each work you plan to deposit $3 from your allowance and $25 from your paycheck. The equation b: 90+ (25+5)w gives the amount b in your account after w woeks. How rary works from
now will you have $220 in your bank account?
There will be 5220 in the account after works
(Type a whole number
Answers
33w=220-90
33w=130 /33
W = 3.94
PLEASE ANSWER
Triangle ABC is similar to triangle DEF. find the length of median CP
A. 12
B. 16
C. 24
D.48
Answers
12/16 = (3x-12)/(2x+8)
16(3x-12)=12(2x+8)
48x-192=24x+96
48x-24x=192+96
24x=288
X=288/24
X=12
3x-12
=(12x3)-12
=36-12
=24
C is the answer
Hope this helps!
Answer:
48
Step-by-step explanation:
2x+8=3x-12(ABCP ~FDQE)
2x-3x= -8-12
-x= -20
x=20
now,
CP=3x-12
3*20-12
48
1. Write a survey question for which you would expect to collect numerical
data.
2. Write a survey question for which you would expect to collect categorical
data.
Answers
Answer:
How many siblings do you have?
I hope this helps you out :)
For the partially complete factorization, find the other binomial which will complete the factorization n^2-8n-20=(n+2)(_____)
Answers
Answer:
(n-10)
Step-by-step explanation:
Jdjdjdhbejdudjkdff
How do you complete the square of x2+8x+26?
Answers
Answer:
see below
Step-by-step explanation:
x^2+8x+26
Take the coefficient of the x term
8
Divide by 2
8/2 = 4
square it
4^2 =16
we need to add 16 to 26 = 16+10
x^2 + 8x+16 +10
(x+4)^2 +10
The answer you are looking for is (x+4)²+10.
Solution/Explanation:
Selecting the "x" term's coefficient,
It would be 8.
Now, dividing it by 2,
8/2=4.
Squaring 4,
4²=16.
So, now, since (x+4)²=x²+8x+16, you must solve for 26-16, which equals 10, which you would supplement into the equation.
So, therefore, (x+4)²+10.
I hope this has helped you. Enjoy your day.
if a circumference of a circle is 22cm.find it diameter take pie 22/7.
Answers
Answer:
➕
Step-by-step explanation:
i know the answer ok it is easy
 evaluate P(6,2) or 6p2
Answers
Answer:
30
Step-by-step explanation:
Permutation equation: [tex]\frac{n!}{(n-r)!}[/tex]
n = Total number of objects, r = Number of objects selected
[tex]_6P_2=\frac{6!}{(6-2)!}=30[/tex]
HELPPPP PLZ
Witch statement is true about the value of |6|?
Answers
Answer:
The third choice is the correct one.
Step-by-step explanation:
The absolute value of six means that it's the distance from 0 to six, and that distance will be positive regardless of the number being negative or not.
Answer: The third answer is correct
Step-by-step explanation:
Since |6| is the absolute value of positive six, the value of an absolute value of any number is always positive.
Which statement is sufficient to prove that quadrilateral ABCD is a parallelogram?
A) m∠A ≅ m∠C, m∠B ≅ m∠D
B) AB ≅ CD
C) AC ≅ BD
D) BC // AD
Answers
Answer:
A) m∠A ≅ m∠C, m∠B ≅ m∠D
Step-by-step explanation:
If both pairs of opposite angles are congruent, then the figure is a parallelogram.
½ sejam berapa minit?
Answers
Answer:
1/2 jam 30 menit mungkin?
1/2 jam adalah 30 minit
1/2 × 60 = 30 mins
English translation
1/2 an hour is 30 minutes
1/2 × 60 = 30 mins
Answered by Gauthmath must click thanks and mark brainliest
look at the image below
Answers
Answer:
201.1 km²
Step-by-step explanation:
Surface area of the figure,
4πr²
= 4×π×4²
= 64π
= 201.1 km² (rounded to the nearest tenth)
Primo car rental agency charges $21 per day plus $0.20 por milo. Ultimo car rental agency charges $24 per day plus $1.00 per milo. Find the daily mileage for which the Ultimo charge is four times the Primo charge.
The mileage is
Answers
Answer:
300 miles
Step-by-step explanation:
Let us consider the miles they travelled is 'm'
Mileage for Primo= 21 + (m × 0.20) = 21+0.2m
Mileage for Ultimo= 24+ ( m× 1.00) = 24 + m
Question says The mileage is equal when Ultimo's charge is 4× Primo
Thus,
4 × (21+0.2m) = 24+ m
84 + 0.8m = 24 + m
60 = 0.2m
m = 300
9sin(Θ)-7=0. Solve the trigonometric equation
Answers
Step-by-step explanation:
here's the answer to your question
AABC is reflected across the x-axis and then translated 4 units up to create AA'BC. What are the coordinates of the vertices of AABC?
Answers
However the Triangle is then translated 4 units up, so the New and Final coordinates for Triangle ABC is A(-3,3) B(-1,0) and C(-2,4)
Hope this helps
vector v has a horizontal vector component with magnitude 19 and a vertical vector component with magnitude 35. what is the acute angle theta formed by v and positive x-axis?
Answers
9514 1404 393
Answer:
61.5°
Step-by-step explanation:
The tangent relation is useful here. The angle is opposite the vertical side and adjacent to the horizontal side of the right triangle.
Tan = Opposite/Adjacent
tan(α) = 35/19
α = arctan(35/19) ≈ 61.5°
The angle made by v and the positive x-axis is 61.5°.
Which of the following has the least value?
30% of 50
O 50% of 30
30% of 30
50% of 50
Answers
Answer:
30% of 30 has the least value out of all answer choices.
Step-by-step explanation:
Solve for the values of the given percentages of each number:
30% of 50:
Divide 50 by 100 to get 1%
50/100 = 0.5
Multiply 1% (0.5) by 50:
0.5 x 50 = 15
So 30% of 50 = 15
50 % of 30:
50% of a number means half of it since 50% is half of 100% so:
30/2 = 15
So 50% of 30 = 15
30% of 30:
Divide 30 by 100 to get 1%:
30/100 = 0.3
Multiply 1% (0.3) by 30:
0.3 x 30 = 9
So 30% of 30 = 9
50% of 50
50% of a number means half of it since 50% is half of 100% so:
50/2 = 25
So 50% of 50 = 25
Let’s arrange all of the values from greatest to least (left to right) to determine the most least value:
25, 15, 15, 9
9 is the most least, it is the value equal to the answer choice “30% of 30”
HOPE THIS HELPED!
To prepare for the town's race, Andrew runs around a rectangular field. The dimensions of the field are 450 feet
by 225 feet. How many times must Andrew run around the field in order to run 12 miles? One mile is 5,280
fect.
Round the answer to one decimal place if necessary?
Answers
Answer:
46.9 times
Step-by-step explanation:
First, we can calculate how many feet it takes to run around the field. To find the perimeter of a rectangle, we can use the formula
2* length + 2 * width. With the length being 450 and the width being 225 here, we can say that
2*450 + 2 * 225 = 1350 feet
Therefore, Andrew runs 1350 feet each time he runs around the field. Next, we need to figure out how much 1350 feet goes into 12 miles as we want to find how many times Andrew runs around the field to get to 12 miles. This can be represented by
12 miles/1350 feet
One thing that we can do here is multiply the fraction by 1 to keep it the same. Because 1 mile = 5280 feet, we can say that
1 mile/5280 feet = 1 = 5280 feet/1 mile. Therefore, it would be safe to multiply
12 miles/1350 feet by 1 = 5280 feet/1 mile. Note that feet is on the bottom in the first fraction (12 miles/1350 feet) and on the top in the second (5280 feet/1 mile) so they will cancel out. Similarly, miles are on top in the first and bottom in the second. We then have
12 miles/1350 feet * 5280 feet/1 mile =63360/1350 ≈ 46.9
Salaries of entry-level computer engineers have Normal distribution with unknown mean and variance. Three randomly selected computer engineers have following salaries (in $1000s): 70, 80, 90. The average and the standard deviation of the data in the sample are 80 and 10. Using hypothesis testing, determine if this sample provides a sufficient evidence, at a 10% level of significance, that the average salary of all entry-level computer engineers is different from $60,000.
a. Null hypothesis.
b. alternative hypothesis.
c. test statistic.
d. acceptance region.
Answers
Answer:
H0 : μ = 60000
H1 : μ ≠ 60000
Test statistic = 3.464
Step-by-step explanation:
Given :
Sample mean salary, xbar = 80000
Sample standard deviation, s = 10000
Population mean salary , μ = 60000
Sample size, n = 3
Hypothesis :
H0 : μ = 60000
H1 : μ ≠ 60000
The test statistic :
T = (xbar - μ) ÷ (s/√(n))
T = (80000 - 60000) ÷ (10000/√(3))
T = 20000 / 5773.5026
T = 3.464
The Decison region :
If Tstatistic >Tcritical
Tcritical at 10%, df = 2 ; two - tailed = 2.9199
Tstatistic > Tcritical ; He
Let f(x)=−5x+18 and g(x)=x2+15.
Find f(−2)−g(−2).
Answers
Answer:
21
Step-by-step explanation:
-5(-2)-(-2)²+15
10-(4)+15
10-4+15
21
Answer:
9
Step-by-step explanation:
f(x)=−5x+18
f(-2) = -5(-2)+18 = 10+18 = 28
g(x)=x^2+15
g(-2) = (-2)^2 +15 = 4+15 = 19
f(02) - g(-2) = 28 - 19 = 9
2. Solve the following system of equations. y = 5 + x 2x + 2y = 30
Answers
since we know y= 5 + x , plug this into y in the second equation.
2x + 2 (5 + x) = 30
distribute 2 into the 5 and x
2x + 10 + 2x = 30
combine like terms
4x + 10 = 30
subtract 10 from both sides
4x = 20
divide four by both sides to isolate the variable
x = 5
What are the slope and the y-intercept of the linear function that is represented by the graph?
Answers
In a 2-digit number, the tens digit is 5 less than the units digit. If you reverse the number, the result is 7 greater than double the original number. Find the original number.
Answers
The original number is 38
A 2-digit number can be written as:
N = a*10 + b*1
Where a is the tens digit, and b is the units digit, these two are single-digit numbers.
We know that:
"the tens digit is 5 less than the units digit."
This means that:
a = b - 5
(notice that a must be larger than zero and smaller than 10, from this, we can conclude that b is a number in the range {6, 7, 8, 9})
"If you reverse the number, the result is 7 greater than double the original number"
The reverse number is:
b*10 + a
and this is 7 greater than 2 times the original number, then:
b*10 + a = 7 + 2*(a*10 + b)
Then we found two equations:
a = b - 5
b*10 + a = 7 + 2*(a*10 + b)
Replacing the first equation in the second, we get:
b*10 + (b - 5) = 7 + 2*((b - 5)*10 + b)
Now let's solve that:
b*10 + b - 5 = 7 + 2*(11*b - 50)
11*b - 5 = 7 + 22*b - 100
-5 - 7 + 100 = 22*b - 11*b
88 = 11*b
88/11 = b = 8
Now that we know that b = 8, we can use the equation:
a= b - 5
a = 8 -5 = 3
Then the original number is:
a*10 + b = 3*10 + 8 = 38
The original number is 38
If you want to read more about this, you can see:
https://brainly.com/question/19902993
Dilate line f by a scale factor of 3 with the center of dilation at the origin to create line f'. Where are points A' and B' located after dilation, and how are lines f and f' related?
The locations of A' and B' are A' (0, 2) and B' (6, 0); lines f and f' intersect at point A.
The locations of A' and B' are A' (0, 6) and B' (2, 0); lines f and f' intersect at point B.
The locations of A' and B' are A' (0, 2) and B' (2, 0); lines f and f' are the same line.
The locations of A' and B' are A' (0, 6) and B' (6, 0); lines f and f' are parallel.
Answers
Answer:
Step-by-step explanation:
(D). The locations of A' and B' are A' (0, 6) and B' (6, 0); lines f and f' are parallel.
The location of the points A' and B' after dilation is Option(D) The locations of A' and B' are A' (0, 6) and B' (6, 0); lines f and f' are parallel.
What is dilation of a line segment ?The dilation of a line segment is longer or shorter in the ratio given by the scale factor. If the scale factor is greater than 1, the image of line segment will be larger than the original line, and if the scale factor is less than 1 , the image will be smaller than the original line.
How to find the coordinates of the points by dilation of given line segment ?The original line segment is given in the figure with points A and B as A(0,2) and B(2,0) .
When the line segment is dilated by a scale factor of 3, we can draw a parallel line which will be larger than the pre-image of the original line segment.
Also, the new coordinates of the points A and B will also increase by a factor of 3.
Therefore, we have A'(0,6) and B'(6,0) as the new coordinates of the line segment.
Thus, the location of the points A' and B' after dilation is Option(D) The locations of A' and B' are A' (0, 6) and B' (6, 0); lines f and f' are parallel.
To learn more about dilation of line segment, refer -
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Mariah owed her grandfather 52.25 but was recently able to pay him back $1.50. How much does Mariah currently
owe her grandfather?
Answers
The answer is 50.75.
Answer:
52.25 - 1.50 = 50.75
Step-by-step explanation:
I'd recommend using a calculator or pencil and paper
53.25
- 1.50
--------
50.75
the area of a rectangular park is 7/8 sqaure mile. the length of the park is 3/4 mile. what is the width of the park?
Answers
Answer:
7/6
Step-by-step explanation:
since the formula of area is length times width,you have to divide the area by the length to find the width
area=length×width
the width will be
width=area÷length
=7/8÷3/4
7/8×4/3
7/2×1/3
7/6
that's the width you can prove it by multiplying the length times the width to see if you will get 7/8..
I hope this helps
Which could be a binomial expansion of (4x + y)?
16x2 + xy + y2
16x2 + 4xy + y2
O 64x3 + 16x2y + 5xy2 + y3
64x3 + 48x2y + 12xy2 + y3
+
Answers
Answer: D
Step-by-step explanation:
[tex](4x+y)^3\\\\=(4x)^3+3*(4x)^2*y+3*(4x)*y^2+y^3\\\\=64x^3+48x^2y+12xy^2+y^3\\\\Answer\ D[/tex]
Answer:
D
Step-by-step explanation:
Given coordinates A(3,3),B(2,5),C(4,3) complete transformation. Complete double reflection over the lines y=2 followed by y=0.
Answers
9514 1404 393
Answer:
A"(3, -1)B"(2, 1)C"(4, -1)Step-by-step explanation:
Reflection over 'a' then over 'b' will result in a translation of 2(b -a). Here, we have a=2, b=0, so the translation is 2(0-2) = -4. The reflection is over horizontal lines, so the transformation is ...
(x, y) ⇒ (x, y -4)
A(3, 3) ⇒ A"(3, -1)
B(2, 5) ⇒ B"(2, 1)
C(4,3) ⇒ C"(4, -1)
