[tex]\begin{cases} a = shortest\\ b = medium\\ c = longest \end{cases} \begin{array}{llll} \stackrel{\textit{perimeter is 57}~\hfill }{a + b + c = 57}~\\\\\stackrel{\textit{twice longest minus shortest}}{2c-a=22~\hfill }\\\\ \stackrel{\textit{longest plus twice others}}{c + 2(a+b) = 94~\hfill } \end{array} \\\\[-0.35em] ~\dotfill\\\\ 2c-a=22\implies 2c=a+22\implies \boxed{2c-22=a} \\\\\\ \stackrel{\textit{we know that}}{c+2(a+b)=94}\implies c+2a+2b=94\implies c+2(2c-22)+b=94[/tex]
[tex]c+4c-44+2b=94\implies 5c-44+2b=94\implies 5c+2b=138 \\\\\\ 2b=138-5c\implies \boxed{b = \cfrac{138-5c}{2}} \\\\\\ \stackrel{\textit{we know the perimeter is}}{57=a + b + c}\implies 57 = \stackrel{a}{(2c-22)}+\stackrel{b}{\cfrac{138-5c}{2}}+c \\\\\\ 57=2c-22+\cfrac{138}{2}-\cfrac{5c}{2}+c\implies 57=3c-22+69-\cfrac{5c}{2} \\\\\\ 57=3c-47+\cfrac{5c}{2}\implies 10=3c-\cfrac{5c}{2}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{2}}{20=6c-5c}[/tex]
[tex]\blacktriangleright 20=c \blacktriangleleft \\\\\\ \boxed{2c-22=a}\implies 40-22=a\implies \blacktriangleright 18=a \blacktriangleleft \\\\\\ \boxed{b = \cfrac{138-5c}{2}}\implies b=\cfrac{138-5(20)}{2}\implies b=\cfrac{38}{2}\implies \blacktriangleright 19 \blacktriangleleft[/tex]
2 show by calculation of nature of triangle AMK
3 CULCULATE BP MK AK
Answer:
if he is the to form a 666
Step-by-step explanation:
what
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I
I
want to
be
a
story
about
I
2
2
'निसंस्मरण' कसको कृति हो
Answer:
ok
Step-by-step explanation:
The heights of students in a class are normally distributed with mean 63 inches and standard deviation 4 inches. Use the Empirical Rule to determine the interval that contains the middle 68% of the heights.
Answer:
The interval that contains the middle 68% of the heights is between 59 and 67 inches.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean of 63, standard deviation of 4.
The interval that contains the middle 68% of the heights.
By the Empirical rule, within 1 standard deviation of the mean. So
63 - 4 = 59
63 + 4 = 67
The interval that contains the middle 68% of the heights is between 59 and 67 inches.
Write the word sentence as an equation.
The quotient of a number n and 5 is 18.
Answer:
n/5 = 18
Step-by-step explanation:
Quotient means division.
n/5 = 18
The Independent party received one-eleventh of the 6,185,894 votes cast. How many votes did the party receive?
Answer:
562,354 votes
Step-by-step explanation:
1/11 of 6,185,894
=>1/11 x 6,185,894
=>562,354
What is the range of this function?
Answer:
D. {-8, -5, 3, 7}
Step-by-step explanation:
__________
What is the answer to this question
Answer:
its b because when subtract 30-24=6
which rule applies to this equation? (6)(3p) = 18p
Answer:
multiplication rule
Step-by-step explanation:
because 6 * 3p
is equal to 18p
hope this helps you please like and mark as brainliest
What is the value of c?
A. 68
B. 71
C. 38
D. 34
Answer: C
Step-by-step explanation:
See diagram above
Can anyone help me? Find the value of x
Answer:
x = 7
Step-by-step explanation: 6 25 13 55
since these are similiar triangles the sides of one triangle are equal to the other triangle by the same ratio
The ratio of 90/27 is the same as the (9x-13)/15 ratio
(9x-13)/15 = 90/27
9x - 13 = 15 × 90/27
9x - 13 = 15 × 3 1/3
9x - 13 = 50
9x = 63
x = 7
petrol cost 99p per litre. How much would 47 cost?
Answer:
4653
Step-by-step explanation:
I am not sure if that 47 in also in litres but if yes then
step 1
1litre=99p
47litre=?
step2
cross multiply such that
47litre × 99p
step3
devide by by 1litre
47litre ×99p
------------------
1litre
so litre counsels litre then your answer will be in pounds so 47×97p÷1=4653
Plot the image of point B under a reflection across line m
Answer:
Step-by-step explanation:
If a point (x, y) is reflected across a line, image of the point will be at the same distance from the line as the original point is.
In fact line of reflection works like a mirror.
In the figure attached,
Distance of point B from the line 'm' = 6 units
Therefore, distance of the image point B' from line 'm' = 6 units (on opposite side of the line of reflection)
The radius of a plant pot is 4.5 cm, and its height is 6 cm. What is the volume of the pot?
Use the value 3.14 for , and round your answer to the nearest whole number.
Be sure to include the correct unit in your answer.
Answer:
381 cm³
Step-by-step explanation:
Volume of the pot = volume of a cylinder
Volume of the pot = πr²h
Where,
π = 3.14
radius (r) = 4.5 cm
h = 6 cm
Substitute
Volume of the pot = 3.14*4.5²*6
Volume of the pot = 381.51 ≈ 381 cm³ (nearest whole number)
Lines s and t are perpendicular. If the slope of line s is 5, what is the slope of line t
Is there a local minimum at x= -4?
9514 1404 393
Answer:
yes
Step-by-step explanation:
Yes, the turning point at (-4, -16) is a local minimum. It is a minimum because the curve goes upward either side of it. It is local (not global) because the curve has values that are lower than -16 at other values of x.
__
Similarly, the point (4, 16) is a local maximum.
consider the polygon shown. Determine the value of y. PLEASE HELP
Answer:
y = 64°
Step-by-step explanation:
From the picture attached,
m(∠E) = 90°
m(∠E) = m(∠D)
m(∠B) + 67° = 180° [pair of linear angles]
m(∠B) = 113°
m(∠C) + 75° = 180°
m(∠C) = 180° - 75°
= 105°
Since, sum of interior angles of a polygon = (n - 2) × 180°
Here, n = number of sides
For n = 5,
Sum of interior angles = (5 - 2) × 180°
= 540°
m(∠A) + m(∠B) + m(∠C) + m(∠D) + m(∠E) = 540°
m(∠A) + 113° + 105° + m(∠D) + 90° = 540°
(m∠D) + m(∠D) = 540 - 308 [Since, m(∠A) = m(∠D)]
2(m∠D) = 232
m(∠D) = 116°
m(∠D) + y° = 180° [Linear pair of angles]
116 + y = 180
y = 64°
I can not seee the answers
Answer:
What do you mean
Step-by-step explanation:
3 16. If 270º < AS 360° and cos(A)= 3/4 then determine the exact values of sin (A) and tan ( A)
Answer:
[tex]{ \boxed{ \tt{trig \: identity : { \bf{ { \cos}^{2} A + { \sin }^{2} A = 1}}}}} \\ \therefore \: { \green{ \tt{ \sin A = \sqrt{1 - { \cos }^{2}A } }}} \\ \sin A = \sqrt{1 - {( \frac{3}{4}) }^{2} } \\ \sin A = \frac{ \sqrt{7} }{4} = 0.661 \\ \\ { \green{ \tt{ \tan A = \frac{ \sin A }{ \cos A} }}} \\ \tan(A ) = \frac{ \frac{ \sqrt{7} }{4} }{ \frac{3}{4} } = \frac{ \sqrt{7} }{3} = 0.882 \\ \\ { \underline{ \blue{ \tt{ becker \: jnr}}}}[/tex]
The exact values of sin (A) and tan ( A) are 0.661 and 0.882 respectively.
What are trigonometric identities?Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.
We have been given that 270º < AS 360° and cos(A)= 3/4.
We are required the exact values of sin (A) and tan ( A)
Since, cos(A)= 3/4.
cos ²A + sin² A = 1
sin A = √ 1- cos ²A
sin A = √ 1- (3/4) ²
Sin A = 0.661
Tan A = sin A / Cos A
Tan A = 0.661/ 3/4 = 0.882
Hence, the exact values of sin (A) and tan ( A) are 0.661 and 0.882 respectively.
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The circle shown has a radius of 4 cm.
What is the area of the circle to 1 decimal place?
Answer:
A = 50.2 cm^2
Step-by-step explanation:
The area of a circle is given by
A = pi r^2 where r is the radius
A = (3.14) * 4^2
A =50.24
To 1 decimal place
A = 50.2 cm^2
Answer:
50.3 cm^2 to 1 dec. place.
Step-by-step explanation:
Area = pi r^2
= pi * 4^2
= 16 * pi
= 50.265
Heyy!! Can someone help me please!!
3 (5x + 2) - 2 (4x -4)
I don’t know what to doooo!!
Answer:
7x + 14
Step-by-step explanation:
the first thing to do is expand the parentheses/brackets.
3(5x + 2) -2(4x - 4) will be
3(5x) + 3(2) -2(4x) -2(-4)
= 15x + 6 - 8x + 8
collect like terms
15x - 8x + 6 + 8 = 7x + 14
the answer is 7x + 14
Answer:
3(5x+2)-2(4x-4)
15x+6-8x+8
15x-8x+6+8
7x+14
Express the null hypothesis and the alternative hypothesis in symbolic form.
Use the correct symbol (μ,p,σ) for the indicated parameter.
A cereal company claims that the mean weight of the cereal in its packets is at least 14 oz.
a. H0: μ<14
H1: μ≥14
b. H0: μ=14
H1: μ<14
c. H0: μ>14
H1: μ≤14
d. H0: μ=14
H1: μ>14
Answer:
a. H0: μ<14
H1: μ≥14
Step-by-step explanation:
Mean symbol:
The mean symbol is given by [tex]\mu[/tex]
A cereal company claims that the mean weight of the cereal in its packets is at least 14 oz.
At the null hypothesis, we test if the proportion is of less than 14 oz, that is:
[tex]H_0: \mu < 14[/tex]
At the alternative hypothesis, we test if this proportion is of at least 14 oz, that is:
[tex]H_1: \mu \geq 14[/tex]
So the correct answer is given by option a.
Plz help with this question I don’t get it is an image
Answer:
D
Step-by-step explanation:
For this question, we know that x represents the thousands of square feet in the stadium. We also know that the stadium is 18 thousand square feet. Therefore, the amount of thousands of square feet, or x, is 18. We can then plug 18 in for x in the equation, getting
[tex]C(x) = \frac{7250000}{18+60} \\= \frac{7250000}{78}\\= 92948[/tex]
as our cost
For each of the following properties write down a matrix that has this property or explain why there is no such matrix (Hint: Check first whether the dimensions add up)
(a) The column space contains (1,0,0)T, (0,0,1)T while the row space contains (1,1)T and (1, 2)T.
(b) The column space is generated by (1,1,1)7T, the null space (or kernel) is generated by (1,2,3)T
(c) The column space is R4 and the row space is R3.
Answer:
a) A = [tex]\left[\begin{array}{ccc}1&0\\0&0\\0&1\end{array}\right][/tex] 3*2
b) attached below ( Matrix dose not exist )
c) attached below ( Matrix does not exist )
Step-by-step explanation:
a) Matrix
A = [tex]\left[\begin{array}{ccc}1&0\\0&0\\0&1\end{array}\right][/tex] 3*2
From the matrix ; Column 1 and Column 2 Belong to COL(A)
while : (1,1)^T = ( 1,0 )^T + ( 0,1 )^T i.e. (1,1)^T ∈ Row( A )
and (1, 2)^T. = ( 1,0 )^T + 2 ( 0,1 )^T i.e. (1, 2)^T ∈ Row( A )
Hence ; all requirements are fulfilled in Matrix A
b) The column space is generated by (1,1,1)7T, the null space (or kernel) is generated by (1,2,3)T
Matrix is Non-existent because condition is not met
attached below
c) Rank | A |
dimension of column space= 4 , dimension of Row space = 3
Given that ; column space ≠ Row space
Hence Matrix does not exist
Pls ASAP Select the correct answer.
What is the sum of this geometric series?
9514 1404 393
Answer:
D. 21/2
Step-by-step explanation:
It is probably easiest to add up the three terms.
For n=1, the first term is ...
8(1/4)^(0) = 8
The second term is ...
8(1/4)^1 = 2
The third term is ...
8(1/4)^2 = 8/16 = 1/2
The sum of the series is ...
8 + 2 + 1/2 = (16 +4 +1)/2 = 21/2
Express the following repeating decimal as a fraction in simplest form.
Answer:
[tex]0.\overline{369} = \frac{41}{111}[/tex]
Step-by-step explanation:
x = 0.369369369...
10x = 3.69369369...
100x = 36.9369369...
1000x = 369.369369...
1000x - x = 369
999x = 369
[tex]x = \frac{369}{999} \\\\x = \frac{123}{333}\\\\x = \frac{41}{111}[/tex]
3x – 4(x - 4) + 4 = 13
Solve for x step by step
Please answer quickly
Answer:
7
Step-by-step explanation:
3x – 4(x - 4) + 4 = 13
=> 3x - 4x + 16 + 4 = 13
=> - x + 20 = 13
=> - x = 13 - 20
=> - x = - 7
=> x = 7
Answer:
x = 7
Step-by-step explanation:
3x – 4(x - 4) + 4 = 13
3x - 4x + 16 + 4 = 13
-x + 20 = 13
-x + 20 - 20 = 13 - 20
-x = -7
(-x = -7)/-1
x = 7
Hope this helps.
Niu earned $312 on an investment of $800. How much would $1100 have earned in the same
investment?
Answer:
429
Step-by-step explanation:
312/800 = .39
1100 x .39 = 429
Answer:
$429
Step-by-step explanation:
--------------------
[tex]\frac{312}{800} =\frac{x}{100}[/tex]
Cross multiply
[tex]800x=31200[/tex]
Divide both sides by 800
[tex]x=39[/tex]
So, Niu earned 39% on the investment of $800
So, let's find out how much $1,100 would have earned him in the same investment.
--------------->>>>
[tex]\frac{x}{1100}=\frac{39}{100}[/tex]
Cross multiply
[tex]100x=42900[/tex]
Divide both sides by 100
[tex]x=429[/tex]
--------------------
This means that Niu $1,100 would have earned Niu $429 in the same investment.
Hope this is helpful
PLEASE HELP!!!
WILL MARK BRAINLIEST
WORTH A LOT OF POINTS!!!!!!!
In circle P, m WPX = 28 degrees, m ZPY = 38 degrees. ZW and VX are diameters. Find each angle measure.
Answer:
2.28°
3.28°
4.28°
5.114°
6.180°
7.114°
8.332°
9.322°
10.152°
Step-by-step explanation:
The required measure of the angles are given as,
2] 28° 3] 28° 4] 28° 5] 114° 6] 180° 7] 114° 8] 332° 9] 322° and 10] 152°.
Given that,
In circle P, m WPX = 28 degrees, m ZPY = 38 degrees. ZW and VX are diameters. Find each angle measure.
orientation of one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.
Here,
The diameter of the circle has a measure of angle 180°,
So, mVXZ = 180°,
Since,
mVZ = mWX
mVZ = 28°
Similarly, all the angles can be evaluated,
Thus, the required measure of the angles are given as,
2] 28° 3] 28° 4] 28° 5] 114° 6] 180° 7] 114° 8] 332° 9] 322° and 10] 152°.
Learn more about Angles here:
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NEED ASAP
What is the product?
а-3
11
5
15а а-3
о
о
Cul —
за
о за
O3
Answer:
1/3a
Step-by-step explanation:
[tex] \frac{(a - 3)}{15a} \times \frac{5}{(a - 3)} = \frac{5}{15a} = \frac{1}{3a} [/tex]
The amount of time needed to complete a job, t, varies inversely with the number of workers, w. If 10 workers can complete a job in 20 minutes, how many minutes would it take 5 workers?
The amount of time needed to complete a job by 5 workers is
40 minutes.
What is a unit rate?It is the quantity of an amount of something at a rate of one of another quantity.
In 2 hours, a man can walk for 6 miles
In 1 hour, a man will walk for 3 miles.
We have,
The amount of time needed to complete a job, t, varies inversely with the number of workers.
Number of workers = W
Time to complete 1 work = T
This means,
T = 1 / W
W = 1 / T
10 workers can complete a job in 20 minutes.
This can be written as:
10 W = 1 / 20
Divide 10 on both sides.
1 W = 1 / 200
This means,
1 worker can complete a job in 200 minutes.
Now,
1 W = 1/ 200
Multiply 5 on both sides.
5 W = 5/200
5 W = 1 / 40
This means 5 workers will take 40 minutes to complete the work.
Thus,
The amount of time needed to complete a job by 5 workers is
40 minutes.
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