Answer:
Step-by-step explanation:
Distance : [tex]\sqrt{(x2-x1)^2 + (y2 - y1)^2} = \sqrt{(9-2)^2 + (-9+14)^2}= \sqrt{49 + 25} = \sqrt{74}[/tex]
Midpoint :
x (m) = (2+9)/2 = 11/2
y (m) = (-14-9)/2 = -23/2
M (11/2, -23/2)
The police station has a parking lot that is 72 feet long by 41 feet wide. Each parking spot measures 8 feet wide and 18 feet deep. Each spot has 23 feet behind it Por the cars to back out. How many parking spots can the police station have?
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Answer:
9
Step-by-step explanation:
The total depth of a parking space must be (18 ft +23 ft) = 41 ft. The lot is 72 ft by 41 ft, so can have (72 ft)/(8 ft) = 9 parking spaces.
Find the volume of the parallelepiped with one vertex at the origin and adjacent vertices at (1, 4, 0), (-2, -5, 2), and (-2, 2, 1).
17 cubic units.
Step-by-step explanation:
The volume (V) of a parallelepiped with one vertex at the origin is given by the absolute value of the scalar vector product of the vectors at the adjacent vertices.
V = |(a x b) · c|
In this case,
a = (1,4,0) = i + 4k + 0j
b = (-2,-5,2) = -2i -5j + 2k
c = (-2,2,1) = -2i + 2j + k
First, let's calculate the cross product of vectors a and b. i.e a x b as follows:
(i) Arrange the vectors in a matrix form
a x b = | i j k |
| 1 4 0 |
| -2 -5 2 |
(ii) Calculate the determinant of the matrix
a x b = i(8 - 0) -j(2-0) + k(-5+8)
a x b = i(8) -j(2) + k(3)
a x b = 8i - 2j + 3k
Secondly, calculate the scalar product of the cross product found above and the vector c as follows;
(a x b) . c = (8i - 2j + 3k) · (-2i + 2j + k)
Multiply like terms
(a x b) . c = (8 * -2)(i.i) + (-2 * 2)(j.j) + (3 * 1)(k.k) [i.i = j.j = k.k = 1]
(a x b) . c = (-16) + (-4) + (3)
(a x b) . c = -16 - 4 + 3
(a x b) . c = -17
Thirdly, find the absolute value of the result found above. i.e
|(a x b) . c| = |-17|
|(a x b) . c| = 17
Therefore, the volume of the parallelepiped is 17 cubic units.
[tex]f(x)=\sqrt(x) \\ g(x)=\sqrt((4)/(5)x)[/tex]
Identify a horizontal or vertical stretch or compression of the function f(x)=\sqrt(x) by observing the equation of the function g(x)=\sqrt((4)/(5)x)
A. A vertical compression by a factor of 5/4
B. A horizontal compression by a factor of 5/4
C. A horizontal stretch by a factor of 5/4
D. A vertical stretch by a factor of 5/4
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Answer:
C. A horizontal stretch by a factor of 5/4
Step-by-step explanation:
Replacing x in f(x) by kx introduces a horizontal compression by a factor of k, or a stretch by a factor of 1/k. Here, we have k=4/5, so the curve is stretched horizontally by a factor of 5/4.
Evaluate A= 2
B= 3
C= 5
) A2+B 2+ C2
C2-4A + 2B
ESTION 1
T1
- Say whether you think each statement is True or False. Motivate your answer.
1 It always makes sense to talk about a certain percentage of a number, for example 1%
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Answer:
False
Step-by-step explanation:
"Always" and "never" statements are generally false--especially when they relate to something like a topic of conversation. Even in the context of math and physics, we find exceptions to most "rules."
Circle P contains a diameter AB with coordinates A(1, 2) and B(-7, 2).
5a) State the coordinates of the center.
5b) Determine the length of the radius.
5c)Johnny used the above information for the center and radius and come up with the equation below. Do you agree or disagree with his answer? Explain.
PLEASE ANSWER I DONT HAVE MUCH TIME
Answer:
[tex]centre = ( \frac{1 - 7}{2} , \: \frac{2 + 2}{2} ) \\ = ( - 3, \: 2)[/tex]
[tex]length = \sqrt{ {( - 7 - 1)}^{2} + {(2 - 2)}^{2} } \\ = \sqrt{ { - 8}^{2} } \\ = 8 \: units[/tex]
radius = 8÷2
= 4 units
Johnny was right
Complete the explanation on why it is a good idea to use multiple samples when making comparative inferences about two populations.
It is a good idea to use multiple random samples to see how statistical measure vary among the ————-(different/same) samples.
Given that tangent squared theta = three-eighths, what is the value of secant theta?
Answer:
[tex]\sec \theta = \frac{\sqrt{22}}{4}[/tex]
Step-by-step explanation:
Given
[tex]\tan^2 \theta = \frac{3}{8}[/tex]
Required
[tex]\sec\ \theta[/tex]
We have:
[tex]\sec^2\theta = 1 + \tan^2 \theta[/tex]
This gives:
[tex]\sec^2\theta = 1 + \frac{3}{8}[/tex]
Take lcm and solve
[tex]\sec^2\theta = \frac{9+3}{8}[/tex]
[tex]\sec^2\theta = \frac{11}{8}[/tex]
Take square roots
[tex]\sec \theta = \frac{\sqrt{11}}{\sqrt 8}[/tex]
[tex]\sec \theta = \frac{\sqrt{11}}{2\sqrt 2}[/tex]
Rationalize
[tex]\sec \theta = \frac{\sqrt{11}}{2\sqrt 2} * \frac{\sqrt 2}{\sqrt 2}[/tex]
[tex]\sec \theta = \frac{\sqrt{22}}{4}[/tex]
Answer:
answer is B
Step-by-step explanation:
i got it right on edg
Patrick wanted to gather data about the cost of joining a community pool in his area. He plotted the data and determined that the average community pool membership cost consists of a one-time registration fee and a monthly fee modeled by the equation y = 15x + 40.
Identify and interpret the y-intercept in this model.
Answer:
40
Step-by-step explanation:
You can find y intercept by looking at the end of the equation, that’s what’s added. So +40 is the y intercept
The y intercept in this equation represents the one-time registration fee
What value of x will make the triangle congruent
Answer:
x = 3/5 = 0.6
Step-by-step explanation:
By the ASA Triangle Congruence Theorem, the two given triangles are congruent (vertical angles are congruent). Because we know that corresponding parts of congruent triangles are congruent, we can write the following equation: 7x - 3 = 2x. Now we can solve:
7x - 3 = 2x
-3 = -5x
3/5 = x
Pls help LOL I WILL MARK U BRAINLIEST‼️‼️‼️‼️
Answer:
B=17
A=16
Step-by-step explanation:
It is my friend OK if you want say again and I can ans
Triangle ABC is similar to triangle EFD what scale factor is required to dilate triangle abc so that it's image, ABC is congruent to triangle EFD
Step-by-step explanation:
the scale factor k = 5/12
The scale factor k = 5/12 is required to dilate triangle ABC thus, its image, ABC is congruent to triangle EFD.
What is the scale factor?The ratio between comparable measurements of an item and a representation of that thing is known as a scale factor in arithmetic.
From the figure attached, we are given that Triangle ABC is similar to triangle EFD.
Therefore,
BC/ FD = AC/ ED
These corresponding sides are proportional.
Scale factor;
EF / AB = 5/12
Then Angle between this sides is also equal.
The SAS rule of similarity of triangles states that two triangles will be similar if their corresponding two sides are proportional and the angle between these two sides is equal.
The scale factor k = 5/12 is required to dilate triangle ABC thus, its image, ABC is congruent to triangle EFD.
Learn more about scale factors here:
https://brainly.com/question/11178083
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Evaluate the expression 53 ÷ (13 − 8) × 2.
Numerical Answers Expected!
Answer:
21.2
Step-by-step explanation:
BODMAS : First bracket, then Division then multiplication.
[tex]53 \div (13-8) \times 2\\53 \div 5 \times 2\\10.6 \times 2\\21.2[/tex]
help help please help help
Answer:
The range is 5.
Step-by-step explanation:
You can deduce this by concluding all other statements are true, or by calculating the range. 10 - 1 = 9
Simplify the polynomial (4n2 + 3n - 5) - (2n2 + 3n+ 6)
We keep brackets
(4n^2 + 3n - 5 ) - (2n^2 + 3n + 6)
We change signs and we group
4n^2 - 2n^2 + 3n - 3n - 5-6
We simplify
2m^2 - 11
Answer: = 2.n^2 - 11
The value of (4n^2 + 3n - 5) - (2n^2 + 3n+ 6) is 2n^2 - 11
How to simplify the expression?The polynomial expression is given as;
(4n^2 + 3n - 5) - (2n^2 + 3n+ 6)
Open the bracket
4n^2 + 3n - 5 - 2n^2 - 3n- 6
Evaluate the like terms
2n^2 - 11
Hence, the value of (4n^2 + 3n - 5) - (2n^2 + 3n+ 6) is 2n^2 - 11
Read more about polynomials at:
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plz plz guys solve this i will give you brainliest with procedure
Answer:
5:9
Step-by-step explanation:
1/5kg:360g
kg to g
1kg=1000g
1/5kg=1/5x1000
=200g
200g:360g
200g/360g
200/360
5/9
5:9
PLS HELP ASAP !!! PLSSS !! will mark whoever answers correctly as brainliest !
Answer:
60° is the answer sure
I hope the above pic explanation helps
I HOPE IT HELPS
HAVE A GREAT DAY
#Liliflim
Answer:
60°
Step-by-step explanation:
....................................
Question 3
Simplify
4x² × 2x³
Step-by-step explanation:
[tex]4 {x}^{2} \times 2 {x}^{3} = 8 {x}^{5} [/tex]
Answer:
Step-by-step explanation:
4x^2 * 2x^3
(2)^2 *x^2 *2*x^3
(2)^2+1 *x^2+3
(2)^3 *x^5
8*x^5
8x^5
another method
4*x^2*2*x^3
multiply 4 and 2
8*x^2+3
8x^5
in multiplication if the bases are same we add their power(exponent).In division if the bases are same we subtract their power(exponent).
please help! (listing BRAINLIST and giving points)
What are the domain and range of this function?
Answer:
first one. domain: all real numbers, range: {y | y ≥ 0}
Answer:
The domain is all real numbers
The range is y ≥ 0
Step-by-step explanation:
The domain is the values that x can take
The domain is all real numbers
The range is the values that y can take
The range is y ≥ 0
I’m stuck between 51 or 42 HELP!!!
Answer:
51
Step-by-step explanation:
Have a nice day :)
Need explanation and answer
1=22e 3663 30-4949-29238342
Answer:
[tex]x = \sqrt{12} = 3.464[/tex]
Step-by-step explanation:
[tex]AC=AD+DC=13\\\text{Because ABC is a right triangle then}\\AB^2=AD.AC\\\Rightarrow AB^2=1 \times 13=13\\\Rightarrow AB = \sqrt{13}\\\text{In the right triangle ABD, since Pythagoras we also have}\\AB^2=AD^2+BD^2\\\Rightarrow BD^2=AB^2-AD^2\\\Rightarrow x^2= 13 - 1=12\\\Rightarrow x = \sqrt{12} = 3.464.[/tex]
In 2002 the Supreme Court ruled that schools could require random drug tests of students participating in competitive after-school activities such as athletics. Does drug testing reduce use of illegal drugs? A study compared two similar high schools in Oregon. Wahtonka High School tested athletes at random and Warrenton High School did not. In a confidential survey, 6 of 108 athletes at Wahtonka and 28 of 129 athletes at Warrenton said they were using drugs. Regard these athletes as SRSs from the populations of athletes at similar schools with and without drug testing.
Required:
a. You should not use the large-sample confidence interval. Why not?
b. The plus four method adds two observations, a success and a failure, to each sample. What are the sample sizes and the numbers of drug users after you do this?
Answer:
b
Step-by-step explanation:
A jeweler purchases a necklace for $80. She will increase the cost by 50% to sell in her
store. What will the jeweler charge for the necklace to her customers?
Answer:
120
Step-by-step explanation:
First find the markup
80 * 50%
80*.5
40
Add this to the original cost
80+40
120
The price will now be 120
[tex]inverse function of \frac{3^x+2}{3^x-5}[/tex]
Answer:
[tex](3 {}^{x} + 2)(3 {}^{x} + 2)[/tex]
hope it is helpful to you
1,4,1,8,1,16,1 what’s next in the sequence?
Answer:
32
hope this helps
have a good day :)
Step-by-step explanation:
In rhombus LMNO, diagonals top enclose L N end enclose and top enclose M O end enclose intersect at P. If the measure of angle L P M is represented by 2x + 70. Solve for x.
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Answer:
x = 10
Step-by-step explanation:
The diagonals of a rhombus cross at right angles.
2x +70 = 90
2x = 20 . . . . . . . subtract 70
x = 10 . . . . . . . . . divide by 2
if a student is selected at random, find the probability that the student is 14 year old
Answer:
If the student is selected at random the answer is if you put 14 years apart of the student selected at random means the answer are not apart.
Step-by-step explanation:
14 years selected the problem is that 14-9 is more then 9 and u add that up to get the right equation for the 14 years apart
fill in the missing digits pls asap
Answer:
3 8
× 2 7
______
2 6 6
+ 7 6
_______
1 0 2 6
Answer:
38
x 27
266
+ 76_
1026
4 1) Which of the following is the correct way to solve
(i( 11 x 44? 4 X 11 44 (0) (ii) 4 X 44 11 X 44 4 X 44 11 (iii) (iv) 11 X 44
Answer:
c)4*44 / 11
Step-by-step explanation:
which of the following is the correct way to solve 4/11 * 44
a) 4*11 / 44
= 44/44
= 1
b) 4*44 / 11*44
= 176/484
= 44/121
c)4*44 / 11
= 176/11
= 16
d)11*44 / 4
= 484/4
= 121
Correct way
4/11 * 44
= (4 * 44) / 11
= 16