Answer:
(7n-2p)(7n−2p) + (2n+4q)(2n+4q) + (q-5p)(q−5p) OR
53n² +29p² +17q² -14np +8nq -10pq
Step-by-step explanation:
The perimeter is found by adding all the side lengths.
P = (7n-2p)(7n−2p) + (2n+4q)(2n+4q) + (q-5p)(q−5p)
We know that (a+b)(a+b) = (a+b)², and (a-b)(a-b) = (a-b)²
P = (7n-2p)² + (2n+4q)² + (q-5p)²
We know that (a+b)² = a²+b²+2ab, and (a-b)² = a²+b²-2ab
P = 49n² + 4p² - 14np +4n² +16q² + 8nq +q²+25p² -10pq
Combine like terms
P = 53n² +29p² +17q² -14np +8nq -10pqMO bisects LMN, mLMN = 6x-28, mLMO = x+34. Find mNMO.
Answer:
D. 58°Step-by-step explanation:
MO is angle bisector of ∠LMN, so:
m∠LMN = 2*m∠LMOSubstitute with expressions:
6x - 28 = 2(x + 34)Solve for x:
6x - 28 = 2x + 686x - 2x = 68 + 284x = 96x = 24Find m∠NMO:
m∠NMO = m∠LMO = x + 34 = 24 + 34 = 58°Correct choice is D
Use the Echelon Method
1. Solve
x + 3y = 7
3x + 4y = 11
Answer:
x = 1 y = 2
Step-by-step explanation:
x + 3y = 7
- Subtract x from both sides.
3y = -x + 7
- Divide both sides by 3 to isolate the variable.
y = -1/3x + 7/3
- Plug the value of y into the other equation.
3x + 4(-1/3x + 7/3) = 11
3x - 4/3x + 28/3 = 11
- Add like terms.
5/3x + 28/3 = 11
5/3x = 5/3
x = 1
- Plug the value of x into the equation.
x + 3y = 7
(1) + 3y = 7
3y = 6
y = 2
A test has 20 questions. The test awards 3 points if the answer is correct and takes
away 1 point if the answer is incorrect. A student answered 5 questions incorrectly.
How many points did the student lose?
Show your work.
Answer:
55
Step-by-step explanation:
20 * 3 = 60
60 marks - 5 Incorrect answer (5 marks deducted)
55 Marks
If $1000 is invested for 2 years with a 3% yearly interest rate. What is the amount of simple interest
Answer:
Total: 1060 Gain: 60
Step-by-step explanation:
1000 (Current Amount) x 0.03 (3% as a decimal) x 2 (year amount) = 60 + 1000 (Original Amount Invested) = 1060
An airplane is flying in a direction of 165° with an airspeed of 650 mph. The wind is blowing at 50 mph in a direction of N 30° E. What is the ground speed and direction of the plane?
A) ground speed: 658 mph; direction 108°
B) ground speed: 639 mph; direction 161°
C) ground speed: 686 mph; direction 108°
D) ground speed: 698 mph; direction 161°
Answer:
B) Ground speed: 639 mph; direction 161°
Step-by-step explanation:
165° = 75° South of East = S15°E, therefore;
The component of the speed of the airplane are;
650 × cos(75°) East or x-direction in vector form:[tex]$650 \times \cos \left(75^{\circ}\right) \mathrm{i}$[/tex]
650 × sin(75°) South or negative y-direction in vector form: [tex]$-650 \times \sin \left(75^{\circ}\right) \mathrm{j}$[/tex]
The speed of the airplane is [tex]$650 \times \cos \left(75^{\circ}\right) \mathrm{i}-650 \times \sin \left(75^{\circ}\right) \mathrm{j}$[/tex]
The speed of the wind in vector form is 25i + 25·√3 j
The combined speed of the airplane and the wind is found as follows;
Combined: [tex]$\left(650 \times \cos \left(75^{\circ}\right)+25\right)\left[\dot{i}+\left(25 \cdot \sqrt{3}-650 \times \sin \left(75^{\circ}\right)\right) \mathrm{j}\right.$[/tex], which gives;
The resultant speed of the airplane, [tex]$\left.R=\sqrt{(} 193.23^{2}+(-584.55)^{2}\right)=615.66$[/tex]
The resultant speed of the airplane, [tex]$\mathrm{R}=615.66 \mathrm{mph}$[/tex]
The direction =[tex]$\arctan ((-584.55) /(193.23))=-71.7^{\circ}$[/tex]
The bearing [tex]$=90^{\circ}+71.7^{\circ}=162^{\circ}$[/tex]
Therefore, the closest option is option B, ground speed: 639 mph; direction 161°
Learn more about speed refer:
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Find the domain of the function using interval notation.
f(x) =
1
x2 − x − 6
Answer:
(x+3)(x-2)
Step-by-step explanation:
A golfer observed that 2 out of every 3 balls she hit landed near the hole. If she hits 72 shots, approximately how many times will her ball land near the hole?
9514 1404 393
Answer:
48
Step-by-step explanation:
About 2/3 of her 72 shots will land near the hole.
2/3 × 72 = 48
Her ball will land near the hole approximately 48 times.
The volume of a cube is 27 cubic inches. What is the length of each edge of this cube?
a. 13.5 inches
b. 9 inches
c. 3 inches
Answer:
Option c. 3 inches
Step-by-step explanation:
Volume=27 inches³
By applying the volume formula of cube, we get
L³=27 inches³
L³=(3 inches)³
Hence the cube cancels the opposite side's cube
L=3 inches
how do you write 9 7/9 as a decimal?
Answer:
9.777777778
Step-by-step explanation:
7/9 written as a decimal is 0.777777778 when we add this on to the whole number 9, we get 9.777777778.
hope this helps!
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please help help
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1.) x = 67 y = 32
Here's the Solution:
for x:(x-15)° and 52° are vertical Angles so they are congurent.
(x-15)° = 52°x - 15 = 52x = 52 + 15x = 67for y:4y° and 128° are vertical Angles so they are congurent.
4y° = 128°4y = 1284y/4 = 128/4y = 32HOPE THIS HELPS. GOODLUCK:)
If using the method of completing the square to solve the quadratic equation x^2-19x+9=0x
2
−19x+9=0, which number would have to be added to "complete the square"?
N and (2 + 6)
What is the answer
Answer:
8n
Step-by-step explanation:
distribute n between 2 and 6 then add
Which type of parent function does the equation f(x) = va represent?
A. Cube root
B. Reciprocal
C. Square root
D. Absolute value
Answer:
reciprocal
Step-by-step explanation:
The function f(x) = √x is represented by the square root type of parent function.
What is Square Root?Square root of a number is the value such that the value when multiplied to itself two times gives the original number.
It is denoted by the symbol √.
Given function is,
f(x) = √x
Here for any value of x, the function is mapped to √x.
That is, the function is mapped to the square root of the x.
Thus it is a square root function.
Hence the function is the square root function.
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The range of the function shown is.
Answer:
(4;infinity) because the arrows on the diagram drawn in pink .show that the probability of the graph increasing is unlimited that's why we use infinity in mathematics do describe it
7. If y + z = 4, and yz = 3.then find y + z = ?
Answer:
7
Step-by-step explanation:
I added the answer of y + z and yz it gave me 7
3.32x10^-5 divided by 1.1x10^7=
Answer:
is it 301.818181818
Step-by-step explanation:
if not i don't know i never learned that and that's wat the calculator gave me
Help will give allot of Brainly points
Answer:
Both triangles have marked congruent angles
Step-by-step explanation:
I don’t know how to do this. Can someone help?
Answer:
x1=8
x2=1/5
Step-by-step explanation:
[(-5+1) = 2] - |-7 l
Answer:
-9
Step-by-step explanation:
Find f(g(-1)) for the pair of functions.
f(x)=x^2+6
g(x)=3x^2-9
Answer:
42Step-by-step explanation:
Given:
f(x) = x² + 6g(x) = 3x² - 9Find g(-1):
g(-1) = 3(-1)² - 9 = 3 - 9 = -6Find f(-6):
f(-6) = (-6)² + 6 = 36 + 6 = 42First we have to find g(x) at -1
[tex]\\ \sf\longmapsto g(-1)[/tex]
[tex]\\ \sf\longmapsto 3(-1)^2-9[/tex]
[tex]\\ \sf\longmapsto 3(1)-9[/tex]
[tex]\\ \sf\longmapsto 3-9[/tex]
[tex]\\ \sf\longmapsto -6[/tex]
Now
[tex]\\ \sf\longmapsto f(-6)[/tex]
[tex]\\ \sf\longmapsto (-6)^2+6[/tex]
[tex]\\ \sf\longmapsto 36+6[/tex]
[tex]\\ \sf\longmapsto 42[/tex]
Please answer this in less then 5 mins
Which is the best estimate for the capacity of a glass vase?
A. 200 ml
B. 500 ml
C. 5,000 ml
D. 5,000 kl
Answer:
D, x = 3
Step-by-step explanation:
to know if a line is parallel, we need to know what kind of line x = 6 is
we can use the mnemonic VUX/HOY to determine the slope, the type of line, and which axis it corresponds to. VUX/HOY stands for:
Vertical line
Undefined slope
X axis
Horizontal line
0 is the slope
Y axis
according to this, the equation x = 6 is a vertical line
now we can start eliminating answer choices
A. a line containing the point (6,2)
the point lies on the line x = 6, as the x-coordinate in the ordered pair is 6. this is not parallel to the line
B. y = 6
this intersects x = 6 and is not parallel
C. y = 4
this intersects x = 6 as well and is not parallel
D. x = 3
this leaves us with x = 3, which is a vertical line as seen by the equation and therefore x = 3 is our answer
Step-by-step explanation:
How did growers in the South attempt to rebuild their cotton market?
Produced more cotton
Raised the price of cotton
Hired more laborers
Sold their land
The ratio of cats to dogs at a pet store is 4:5 which means
Step-by-step explanation:
The ratio of cats to dogs at a pet store is 4:5. It means that if there are 4 cats in the store then there are 5 dogs, if there are 8 cats(4×2) there then there will be 10 dogs(5×2).
The number of cats is 16 if the ratio of cats to dogs is 4:5 if there are 20 dogs.
What is the ratio?It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.
The complete question is:
The ratio of cats to dogs is 4;5 if there are 20 dogs. How many cats are there?
It is given that:
The ratio of cats to dogs at a pet store is 4:5
Let 4x be the cats and 5x be the dogs
5x = 20
The above equation is a linear equation in one variable.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
x = 20/5
x = 4
Number of cats = 4x
Plug x = 4 in the above expression:
= 4(4)
= 16
Thus, the number of cats is 16 if the ratio of cats to dogs is 4:5 if there are 20 dogs.
Learn more about the ratio here:
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Write an equation for a line perpendicular to y=5x−5 and passing through the point (-15,8)
Answer:
Step-by-step explanation:
Dont know how to explain but just switch the slope for the recipcal
Find x.
7/8 of x is 14.
Answer:
16
Step-by-step explanation:
7x/8 = 14
7x = 112
x = 16
Have a good day
Answer:
16
Step-by-step explanation:
7/8 × x=14
7/8x=14
14÷7/8
x=16
{ (-2, 4), (0, 2), (-1,3), (4, -2)}
The set of ordered pairs above:
A: Function
B: not a function
Answer:
its a function
Step-by-step explanation:
hope that helps>3
1,000,000,000,000 x 4
How do you write this with an exponet of 10
Answer:
12
Step-by-step explanation:
their is 12 zeros so it's 12
The histogram below shows the number of points scored by a high school basketball team over two seasons.
One player on the team wants to emphasize that his team generally scored a lot of points. Which measure of center should he report: the mean or the median?
a. He should report the mean.
b. He should report the median.
c. He could report either because they are equal.
d. The exact number of points per game are needed to decide.
To median should be reported in the to show th general measure of center since we have a skewed distribution.
The plot of the histogram Given is skewed to the right, hence it is positively skewed.
In a positively skewed distribution, the mean value of the distribution is always greater than the median. However, it does not give an accurate measure of center as much as the median does.
Therefore, if a player want to emphasize that his team generally scored a lot of points, then reporting the median would be best as it gives a better measure of center.
If the data was normally distributed, then the mean would be a better measure of center.
Learn more : https://brainly.com/question/1363341?referrer=searchResults
Answer:
b
Step-by-step explanation:
becuse it looks like she talking about the letter b
What is the graph of the solution set of the compound inequality?
-5 < a – 6 < 2
Answer: the third option I believe
Step-by-step explanation:
