Answer: [tex]x=4[/tex]
Simplify both sides of the equation.
[tex]-7x+8=-4(x+1)\\-7x+8=(-4)(x)+(-4)(1)(Distribute)\\-7x+8=-4x+-4[/tex]
Add 4x to both sides
[tex]-7x+8+4x=-4x-4+4x\\-3x+8=-4[/tex]
Subtract 8 from both sides
[tex]-3x+8-8=-4-8\\-3x=-12[/tex]
Divide both sides by -3
[tex]-3x/-3=-12/-3\\x=4[/tex]
Answer:
x=4
Step-by-step explanation:
Let's first simplify the equation.
-7x+8= -4x-4
You get -4x-4 by distributing the -4 into the numbers in the parenthesis because -4 is right outside the parenthesis.
-4 times x= -4x
-4 times 1= -4
-7x+8= -4x-4
Next, move the -4x to where the -7x is because we want to combine like terms. When a number moves to the opposite side, it changes from positive to negative or negative to positive. Like here: -4x moves to a different side, so it becomes +4x.
-7x+4x+8= -4
Do the same for 8. Since -4 is on the other side, move 8 to that side. It turns from +8 to -8.
-7x+4x= -4-8
Combine like terms and solve.
-7x+4x= -3x
-4-8= -12
So we have this now: -3x= -12
Since 12 divided by 3 is 4, and negative with negative is positive, it becomes positive 4. :)
Sally's house is located at (5, −1) and her school is located at (−9, 7). Her best friend Molly lives at the midpoint of Sally's house and school. What coordinate represents Molly's house? A. (2, −3) B. (−2, 3) C. (3, −2) D. (−3, 2)
Answer:
B. (-2, 3)Step-by-step explanation:
Given two coordinates (x₁, y₁) and (x₂, y₂), the coordinate of their midpoint is equivalent to X = (x₁+x₂)/2 and Y = (y₁+y₂)/2.
Given the coordinate of Sally's house and her school to be (5, −1) and (−9, 7) respectively, the midpoint of Sall's house and school is expressed as shown;
from the coordinates, x₁ = 5, y₁ = -1, x₂ = -9 and y₂ = 7
X = (5+(-9))/2
X = 5-9/2
X = -4/2
X = -2
Y = -1+7/2
Y = 6/2
Y = 3
The coordinate of the midpoint of Sally's house and school will be expressed as (X, Y) which is equivalent to (-2, 3).
SOMEONE PLZ HELP ASAP !!!!!!
Answer:
a = 53.13
b = 42.76
c= 0
Step-by-step explanation:
as the question said i was supposed to use a calculator which i did
Evaluate the following expression if v = 5 and w = -3: 6v - w. Type the number answer only. For example: if the answer was value is 17, then you would type 17 in the blank.
Answer:
33
Step-by-step explanation:
6v - w =
6(5) - (-3) =
30 + 3 =
33
A. Y=2/9x
B. Y=1/4x
C. Y=1/5x
D Y=2/11x
Answer:
the slope of the line represented by the table is y = 2/11x
Step-by-step explanation:
y = mx + b
slope: (y² - y¹) / (x² - x¹)
(4 - 2) / (22 - 11) = 2/11
plug in an x and y value to find b
y = 2/11x + b
2 = (2/11)(11) + b
2 = 2 + b
b = 0
the y-intercept is 0
your equation is y = 2/11x
Hi how do I solve this simultaneous equation
Answer:
M (-3, -5/2)
N (3, -1)
Step-by-step explanation:
Solve the first equation for x.
4y = x − 7
x = 4y + 7
Substitute into the second equation.
x² + xy = 4 + 2y²
(4y + 7)² + (4y + 7)y = 4 + 2y²
Simplify.
16y² + 56y + 49 + 4y² + 7y = 4 + 2y²
18y² + 63y + 45 = 0
2y² + 7y + 5 = 0
Factor.
(y + 1) (2y + 5) = 0
y = -1 or -5/2
Plug back into the first equation to find x.
x = 4(-1) + 7 = 3
x = 4(-5/2) + 7 = -3
M (-3, -5/2)
N (3, -1)
Two pipes A and B can fill an empty tank in 3hrs and 5hrs respectively. Pipe C can empty the full tank in 6 hours. If the three pipes A, B, and Care opened at the same time, find how long it will take for the tank to be full. *
Answer:
30/11 (hours)
Step-by-step explanation:
Pipe A can fill the tank until it is full in 3 hours.
=> In 1 hour, pipe A can fill 1/3 of tank
Pipe B can fill the tank until it is full in 5 hours.
=> In 1 hour, pipe A can fill 1/5 of tank
Pipe C can empty the full tank in 6 hours.
=> In 1 hour, pipe A can empty 1/6 of tank
Assume that we open 3 pipes A, B, and C at the same time.
Then, in 1 hour, the amount of water in tank is:
A = 1/3 + 1/5 - 1/6 = 10/30 + 6/30 - 5/30 = 11/30 (tank)
=> The time to fill up the tank is:
T = 1/A = 1/(11/30) = 30/11 (hours)
Answer:
30/11
Step-by-step explanation:
Imagine the tank can hold x litre of water
So,A can fill x/3 litre water per hour
And B can fill x/5 litre water per hour
And C can reduce x/6 litre of water per hour which is filled by A and B.
So the gross calculation per hour is:
(x/3+x/5)-x/6
=11x/30
Now suppose it tooks 'a' hour to fill the tank.
So, a(11x/30)=x
⇨ a= (30/11x)x
⇨a=30/11
SELF-CHECK 1: Evaluate the expression given. Write the numerical answer
as a fraction below. *
1 point
2 3
+
5.7
Your answer
Step-by-step explanation:
so 2.3 + 5.7 is 8.0 is the answer
What is the image point of (-5,9) after a translation left 1 unit and down 1 unit?
Answer: (-6,8)
Step-by-step explanation:
Translation is a rigid motion inn which every point of the figure moved in the same direction and for the same distanceTranslation rules are
Left c units : [tex](x,y)\to(x-c,y)[/tex]
Down c units : [tex](x,y)\to(x,y-c)[/tex]
The image point of (-5,9) after a translation left 1 unit and down 1 unit will be:
[tex](-5,9)\to(-5-1,9-1)=(-6,8)[/tex]
Hence, the image point is (-6,8).
What is the answer?
About how much farther is it to drive than to walk directly from building A to building B? Round to the nearest whole number.
183 meters
250 meters
366 meters
683 meters
Answer:
A. 183 meters
Step-by-step explanation:
Building A and building B are 500 meters apart. There is no road between them, so to drive from building A to building B, it is necessary to first drive to building C and then to building B. About how much farther is it to drive than to walk directly from building A to building B? Round to the nearest whole number. A) 183 meters B) 250 meters C) 366 meters D) 683 meters
Find distance BC
Cos (60°)=BC / AB (Adjacent divided by the hypotenuse)
Cos (60°)=1/2
BC=a
AB=500
Cos (60°)=BC / AB
1/2=a/500
1/2 * 500=a
250=a
a=250m
Find distance AC
Sin(60°)=AC/AB (opposite side divided by hypotenuse)
Sin(60°)=√3/2
AC=b
AB=500
Sin(60°)=AC/AB
√3/2=b/500
√3/2 * 500=b
250√3=b
b=433m
Distance AC and BC=AC+BC
433m+250m=683m
Subtract the distance AB from AC+BC
= 683m - 500m
=183m
Answer is A. 183 meters
Answer:
A. 183 meters
Step-by-step explanation:
sin(60) = x/500
= 433
tan(60) = 433/x
= 250
This is the driving distance. 433+250= 683. Directly walking (using hypotenuse distance) is 500.
683-500=183!
Write a real-life problem that you can solve using a 45 degree, -45 degree, -90 degree triangle with an 18-ft hypotenuse. Describe your solution
Answer:
A triangle with angles:
"45°, 45°, 90°"
Is a triangle rectangle, with two catheti of equal length.
Now, there is a lot of problems that you can solve with this:
"Suppose that you want to find the height at which you need to attach a wire in a tree, such that the distance between the tree and the ground is 18ft, and the distance between the base of the tree and the two points where the wire is fixed is exactly the same"
Well, here we have a triangle rectangle with a hypotenuse of 18 ft, with cathetus of equal length (the catheti are the tree and the distance between the base of the tree and the point where the wire is attached at the ground)
And because the catheti are equal, then the angles are 45°, 45° and 90°.
15 lwholes 5 over 8 % of a number is 555 find the number
Answer:
The number is 3,552
15⅝% of 3,552 is 555
Step-by-step explanation:
15⅝% of a number is 555.
To determine what number it is, let the number be x.
Thus,
15⅝%*x = 555
[tex] \frac{125}{8}*\frac{1}{100}*x = 555 [/tex]
[tex] \frac{125}{800}*x = 555 [/tex]
[tex] \frac{125*x}{800} = 555 [/tex]
Multiply both sides by 800
[tex] \frac{125*x}{800}*800 = 555*800 [/tex]
[tex] 125*x = 444,000 [/tex]
Divide both sides by 125
[tex] \frac{125*x}{125} = \frac{444,000}{125} [/tex]
[tex] x = 3,552 [/tex]
The number = 3,552
15⅝% of 3,552 is 555
If cot^(4)x − cot^(2)x = 1, then the value of cos^(4)x + cos^(2)x is
Answer:
1
Step-by-step explanation:
[tex]cot^4x-cot^2x=1\\cot^4x=1+cot^2x\\cot^4x=cosec^2x\\ cos^4xsin^2x=sin^4x\\cos^4x=\frac{sin^4x}{sin^2x}\\cos^4x=sin^2x[/tex]------- (1)
Putting the value of [tex]cos^4x[/tex] in the equation:
[tex]cos^4x+cos^2x\\sin ^2x +cos^2x\\1[/tex] (Using the identity [tex]cos^2x +sin^2x=1)[/tex]
if a white birch tree and a pin oak tree each now have a diameter of 111 foot, which of the following will be closest to the difference, in inches, of their diameters 101010 years from now? (1(1(, 1 foot = 12=12equals, 12 inches))
Answer:
Can you solve #18 from practice test 5 calculator section? ... years old and a pin oak tree with a diameter of 12 inches is ... because on the test you would have figured these mechanics out on ... Now, note that the concept of a “growth factor” as provided in the table ... That's a difference of about 1.3 inches.
Step-by-step explanation:
Find the quotient and remainder when p (x) divides with g (x) question (i) P (x) = x raise to 4 - 3 x square +4x + 5, g (x) = x square +5
Answer: [tex]x^2-8+\dfrac{4x+5}{x^4-3x^2+4x+5}[/tex]
Step-by-step explanation:
P(x) = x⁴ - 3x² + 4x + 5
g(x) = x² + 5
_x²_- 8
x² + 5) x⁴ + 0x³ - 3x² + 4x + 5
-(x⁴ + 0x³ + 5x²) ↓ ↓
-8x² + 4x + 5
-(-8x² + 0x - 40)
4x + 45
[tex]\dfrac{x^4-3x^2+4x+5}{x^2+5}=\large\boxed{x^2-8+\dfrac{4x+5}{x^4-3x^2+4x+5}}[/tex]
Find the mean of the given frequency distribution table
Answer:
Mean = 32.8
Step-by-step Explanation:
Mean is given as Mean = (Σfx)/Σf
First, find the mid-point, x, of each class, and multiply by the frequency (f) of the class to get fx:
Class ==> f ==> x ==> fx
0-10 => 3 => 5 => 15
10-20 => 8 => 15 => 120
20-30 => 10 => 25 => 250
30-40 => 15 => 35 => 525
40-50 => 7 => 45 => 315
50-60 => 4 => 55 => 220
60-70 => 3 => 65 => 195
Sum the fx of all classes together to get Σfx:
Σfx = 15 + 120 + 250 + 525 + 315 + 220 + 195 = 1,640
Σf = 3 + 8 + 10 + 15 + 7 + 4 + 3 = 50
(Σfx)/Σf = [tex] \frac{1,640}{50} [/tex]
(Σfx)/Σf = [tex] 32.8 [/tex]
Mean = 32.8
Three friends are at a carnival. Beth goes on 2 rides for $5.00. Zane goes on 5 rides for $12How much does it cost Tina to go on 9 rides?.50.
Answer:
$22
Step-by-step explanation:
Beth=$5.00 for 2 rounds
Zane=$12 for 5 rounds
Tina=$x for 9 rounds
Find x
9 rounds=5 rounds + 2 rounds + 2 rounds
5 rounds costs =$12
2 rounds costs=$5
2 rounds costs=$5
Then,
5 rounds + 2 rounds + 2 rounds= $12 + $5 + $5
9 rounds=$22
It will cost Tina $22 to go on 9 rounds
Simplify: (-2)(-3)+(4)(-8)
Simplify: (3)(-6)-18
Answer:
4
Step-by-step explanation:
Answer:
-26, and -36
Step-by-step explanation:
(-2) (-3) + (4) (-8)
6 + -32 = -26
(3) (-6) - 18
-18 + -18 = -36
Gavin combines Thirty-two and two-fifths ounces of water and 7.15 ounces of lemon juice in a pitcher to make lemonade. Which is the most reasonable estimate for the amount of liquid in the pitcher? 39 ounces 42 ounces 45 ounces 47 ounces
Answer:
OPTION A is correct
39 ounces
Step-by-step explanation:
Given:
The amount of water in the pitcher= 32 ounces
The amount of lemon juice in the pitcher = 7.15 ounces
We were to calculate the most reasonable estimate for the amount of liquid in the pitcher
To do this we need to sum up the Amount of water and Amount of lemon juice in the pitcher because the water is a liquid as well as the lemon juice which is
32 ounces + 7.15 ounces
=39.15 ounces
Therefore, the Estimated amount of liquid in the pitcher is approximately 39 ounces
one-third of a number is subtracted from 11.The result is one and half times the original number. what is the number.
If 11 is subtracted from 3 times the number, the result is the square of 5 less than the number. What are the set of numbers that satisfy
How many gallons of 30% alcohol solution and how many of 60% alcohol solution must be mixed to produce 18 gallons of 50% solution?
Answer:
x = 6 gallons (of 30% alcohol)
y = 12 gallons (of 60% alcohol)
Step-by-step explanation:
Let
x = liters of 30% alcohol
y = liters of 60% alcohol
There are two unknowns, we need two equations
x + y = 18. (1)
0.30x + 0.60y = 0.50(x+y) (2)
From (1)
x + y = 18
y = 18-x
Substitute the value of y into (2) and solve for x:
0.30x + 0.60y = 0.50(x+y)
0.30x + 0.60(18-x) = 0.50(x+18-x)
0.30x + 10.8 - 0.60x = 0.50(18)
10.8 - 0.30x = 9
-0.30x = -1.8
Divide both sides by -0.30
x = 6 gallons (of 30% alcohol)
Substitute x=6 into (1) and solve for y:
x + y = 18
6 + y = 18
y = 12 gallons (of 60% alcohol)
Ten people were chosen at random and surveyed. The survey asked participants for the number of hours they sleep per night and the amount of their annual income. Letting X represent the number of hours the participant sleeps per night and Y represent the participant's annual income, the surveyor calculated the correlation coefficient between X and Y to be 0.29. Interpret the correlation coefficient calculated by choosing the statement below which correctly describes the correlation between X and Y. A. weak negative correlation B. strong negative correlation C. strong positive correlation D. weak positive correlation
Answer:
A. R=0.86; strong correlation
Step-by-step explanation:
The correlation coefficient of 0.29 indicates that the correlation is a weak positive correlation. Thus option (D) is the correct answer.
What is correlation?"Correlation is a statistical tool that studies the relationship between two variables. Data sets have a positive correlation when they increase together, and a negative correlation when one set increases as the other decreases".
For the given situation,
Correlation coefficient = 0.29
Positive correlation: the two variables change in the same direction.
Negative correlation: the two variables change in opposite directions.
No correlation: there is no association or relevant relationship between the two variables.
The correlation coefficient lies between 0 to 0.3 indicating that the correlation is a weak positive correlation.
Hence we can conclude that option (D) weak positive correlation is the correct answer.
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What roles did militias play in the American Revolution? Your answer:
Hey there! I'm happy to help!
A militia is a local army. During the Battle of Lexington and Concord, the local militia (called minutemen), the militia outnumbered the British at Concord and chased them all the way back to Boston. The militia aided in many American victories during the Revolutionary War.
I hope that this helps! Have a wonderful day! :D
evaluate x³ for x=2.
Answer:
8
Step-by-step explanation:
If we have anything to the third power, we are multiplying the number by itself 3 times.
If x = 2, then the expression is [tex]2^3[/tex].
[tex]2\cdot2\cdot2=8[/tex]
Hope this helped!
Answer:
8
Step-by-step explanation:
Exponents is repeated multiplication, so what we are doing in this problem is that we are multiplying 2 by itself 3 times.
2 * 2 = 4
4 * 2 = 8
(08.02)How many solutions are there for the system of equations shown on the graph? No solution One solution Two solutions Infinitely many solutions
Answer: Infinitely many solutions
Step-by-step explanation:
There are many solutions because the lines lies on top of each other.
i dont know the exact answer but its not
One solution
Two solutions
so its most likely
Infinitely many solutions
a garden is 18 feet 3 inches long and 10 feet 8 inches wide. the amount of fencing needed to enclose the garden is Need help and will mark brainlist
Answer:
[tex]\boxed{57ft 10in}[/tex]
Step-by-step explanation:
Hey there!
Well if the length is 18 and 3 inches we need to find the sum of both lengths,
18ft 3in + 18ft 3in = 36ft 6in
Width- 10ft 8in + 10ft 8in = 20ft 16 in -> 21ft 4in
l + w = 57ft 10in
Hope this helps :)
plz help thanks, will give brainliest!
Answer:
D.
Step-by-step explanation:
[tex]\frac{x^{2/3}}{y^{-3/4}}[/tex]
= [tex]x^{2/3}y^{3/4}[/tex]
= [tex]\sqrt[3]{x^2} * \sqrt[4]{y^3}[/tex]
So, D is your answer.
Hope this helps!
At dinner, 100 students pass through the cafeteria line and were served meals. 40 fish entrees and 60 pasta entrees were served to the students. A total of 20 students chose neither entree. Assuming all students were served zero, one, or two entrees, how many students were served two entrees
Answer: 20
Step-by-step explanation:
Given: Total students at the dinner = 100
Number of fish entrees = 40
Number of pasta entrees = 60
Number of students chose neither entree = 20
Now , Number of students chose either fish or pasta = (Total students) - (Number of students chose neither entree)
= 100-20
= 80
Now , Number of students chose either fish or pasta = (Number of fish entrees) + (Number of pasta entrees)- (Number of students chose both)
⇒ Number of students chose both = (Number of fish entrees) +(Number of pasta entrees)-(Number of students chose either fish or pasta)
= 40+60-80
= 20
Hence, the number of students were served two entrees = 20
20 students were served two entrees.
Given,
total student pass through cafeteria line and were served meal is 100.
No. of students choose fish entries is 40.
No. of students choose pasta entrees is 60.
No. of student choose neither entree is 20.
We have to calculate the no. of students served two entrees.
Now Number of students chose either fish or pasta will be,
[tex]N=100-20[/tex]
[tex]N=80[/tex]
Now no. of students choose both will be,
[tex]N=(fish\ entree+\ pasta \ entree )-Entree\ either \ pasta \ or \ fish[/tex]
[tex]N=60+40-80[/tex]
[tex]N=20[/tex]
Hence 20 students were served two entrees.
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I NEED HELP ASAP PLEASE!!!
Q2 If 2w + 7 = ─9, what is the value of 15 – 4w? (4 is negative)
Q3 Solve the following equations: a) 3/4(16m − 24) = –48 (24 is negative) b) –20 = 1/6(36 + 12g)
Answer:
Q2: -17
Q3: a) -5/2 b) g = -13
Step-by-step explanation:
2w+7 = -9
2w = -9 - 7
w = -16/2
w = -8
---
15 - 4w
= 15 - 4(-8)
= 15 - 32
= -17
----------------------
Q3:
a) 3/4(16m-24) = -48
16m -24 = -48 ÷ 3/4
16m = -64 + 24
16m = -40
m = -5/2
b) -20 = 1/6(36+12g)
-20 = 1/6 × 6(6+2g)
(cross out the 6 from 1/6 and 6)
-20 = 6 + 2g
-20-2g= 6
-2g = 6+20
-2g = 26
g = 26/-2
g = -13
If a population grows 3.5% per year, how much does it grow per decade? A. 35% B. 41.1% C. 38% D. 27.6%
Answer: 35%
Step-by-step explanation: It grows 3.5% every year. A decade is 10 years. 10 x 3.5% = 35% because you move the decimal one point to the right.
The population grows 41.1% per decade. Therefore, option B is the correct answer.
What is population growth and population decrease formula?If a constant rate of growth be R% per annum, then population after n years = P(1+R/100)ⁿ.
Given that, a population grows 3.5% per year.
Now, D(n)=P(1+R/100)ⁿ
Let P=1
So, D(1)=1(1+0.035)¹
D(1)=1.035
Similarly per 10 years with the same rate
D(10)=1(1+0.035)¹⁰
= (1.035)¹⁰
= 1.41059
= 1.411-1 (Initial population is 1)
= 0.411
= 0.411×100
= 41.1%
The population grows 41.1% per decade. Therefore, option B is the correct answer.
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