Create a system of equations

Janet is 5 years older than her brother David. The sum of their ages is 27. How old are Janet and David

Answer with steps please

See

In plane ABC or ABCD and plane BFGC or BFG. the common side is

So both the planes intersect at line BC

Answer:

Step-by-step explanation:

difference of x-coordinates = 4-(-3) = 7

difference of y-coordinates = 0-(-2)  = 2

length of MN = √(7²+2²) = √53 ≅ 7.28 units

tanθ = 2/7

θ = arctan(2/7) ≅ 15.9°

heading = 74.1° from north

The magnitude and direction of points M(-3, -2) and N(4, 0) is 7.28 units and 74.1 degrees

We have:

M(-3, -2) and N(4, 0)

Calculate the magnitude using

[tex]MN =\sqrt{(x_2 -x_1)^2 +(y_2 -y_1)^2[/tex]

This gives

[tex]MN =\sqrt{(4 + 3)^2 +(0 + 2)^2[/tex]

Evaluate

MN = 7.28

The direction is calculated as:

[tex]\theta = 90 - \tan^{-1}(\frac{y_2 - y_1}{x_2 -x_1})[/tex]

This gives

[tex]\theta = 90 -\tan^{-1}(\frac{0+2}{4+3})[/tex]

[tex]\theta =90 - \tan^{-1}(\frac27)[/tex]

Take the arc tan

[tex]\theta = 90 - 15.9\°[/tex]

Evaluate

[tex]\theta = 74.1\°[/tex]

Hence, the magnitude and direction of points M(-3, -2) and N(4, 0) is 7.28 units and 74.1 degrees

Read more about magnitude and direction at:

https://brainly.com/question/3184914

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Answer:

5 cubes. 5 cubes. 4 cubes 5 cubes

Step-by-step explanation:

is easy and no hard

Answer:

the answer to your question is m22=120

Answer:

If we assume 'x' an odd number let's say 1, then the other two consecutive odd integers are 1+2 and 1+4,

So assume the three consecutive odd integers be x, x+2 and x+4.

It's obvious that x is the smallest and x+4 is the largest.

Therefore 3x=9+2(x+4)

Solving for x: we get x = 17.

Hence, the three consecutive odd no. are 17, 19, 21

I hope it's helpful!

Answer:

Step-by-step explanation:

Im not all the way sure, but I think it would be 1.8.

11+2 = 13

24/ 13 = 1.84...

rounded, 1.8

Answer:

The answer is 2.

Step-by-step explanation:

11 × 2 = 22

22 + 2 = 24

Therefore, 2 is the answer.

Answer:

[tex]\frac{3}{8}[/tex] Or 0.375

Step-by-step explanation:

From the picture attached,

A circle is divided into 8 sections.

Out of which 3 sections have been shaded.

So the ratio of the shaded sections to the total number of sections will be,

3 : 8

Therefore, fraction representing the ratio will be = [tex]\frac{3}{8}[/tex]

And the decimal form of the fraction will be = 0.375

Answer:

2, 4, & 6 = 84 degrees

1, 3, 5 , & 7 = 96 degrees

Step-by-step explanation:

Answer:

15.75

Step-by-step explanation:

Answer:

Step-by-step explanation:

As per the diagram, the triangles on the left and right are similar.

The ratio of corresponding sides is equal:

The height of the wall is 18 feet

Answer:

[tex]\Huge\mathtt{\underline\pink {Answer}}[/tex]

[tex] \tt \frac{27}{9} = \frac{x}{6} [/tex]

[tex] \tt \: x = 6 \times 3 = 18[/tex]

So, height is 18 feet

Answer:

14°

Step-by-step explanation:

deltamath

Answer:

x = 2

Step-by-step explanation:

m<WUV = 2(m<1) (angle bisector)

28x = 2(13x + 2)

28x = 26x + 4

Collect like terms

28x - 26x = 4

2x = 4

2x/2 = 4/2

x = 2

This question is incomplete, the complete question is;

Suppose u and v are functions of x that are differentiable at x=0

and that { u(0) = 7, u'(0) = -5 }  { v(0)= -1, v'(0) = -4 }

Find the values of the following derivatives at x = 0.

a) [tex]\frac{d}{dx}[/tex]( uv )

b)  [tex]\frac{d}{dx}[/tex]( [tex]\frac{u}{v}[/tex] )

c)  [tex]\frac{d}{dx}[/tex]( [tex]\frac{v}{u}[/tex] )

Answer:

a) [tex]\frac{d}{dx}[/tex]( uv ) = -23  

b) [tex]\frac{d}{dx}[/tex]( [tex]\frac{u}{v}[/tex] )  = 33

c) [tex]\frac{d}{dx}[/tex]( [tex]\frac{v}{u}[/tex] ) = -32/49 or - 0.6531

Step-by-step explanation:

Given that;

{ u(0) = 7, u'(0) = -5 }  { v(0)= -1, v'(0) = -4 }

a)

[tex]\frac{d}{dx}[/tex]( uv )

we differentiate

[tex]\frac{d}{dx}[/tex]( uv )  = uv' + vu'

at x = (0), we substitute our values

[tex]\frac{d}{dx}[/tex]( uv ) = ( 7 × -4 ) + ( -1 × -5)

[tex]\frac{d}{dx}[/tex]( uv )  = -28 + 5

[tex]\frac{d}{dx}[/tex]( uv ) = -23  

b)

[tex]\frac{d}{dx}[/tex]( [tex]\frac{u}{v}[/tex] )

we differentiate

[tex]\frac{d}{dx}[/tex]( [tex]\frac{u}{v}[/tex] ) = ( vu' - uv' ) / v²

at x=0, we substitute our values

[tex]\frac{d}{dx}[/tex]( [tex]\frac{u}{v}[/tex] ) = ( (-1 × -5) - (7 × -4 ) ) / (-1)²

[tex]\frac{d}{dx}[/tex]( [tex]\frac{u}{v}[/tex] ) = (( 5 - ( -28 )) / 1

[tex]\frac{d}{dx}[/tex]( [tex]\frac{u}{v}[/tex] )  = 33 / 1

[tex]\frac{d}{dx}[/tex]( [tex]\frac{u}{v}[/tex] )  = 33

c) [tex]\frac{d}{dx}[/tex]( [tex]\frac{v}{u}[/tex] )

we differentiate

[tex]\frac{d}{dx}[/tex]( [tex]\frac{v}{u}[/tex] )  = ( uv' - vu' ) / u²

at x=0, we substitute our values

[tex]\frac{d}{dx}[/tex]( [tex]\frac{v}{u}[/tex] )  = ( (7 × -4) - (-1 × -4) ) / (7)²

[tex]\frac{d}{dx}[/tex]( [tex]\frac{v}{u}[/tex] ) = ( -28 - ( 4 ) ) / 49

[tex]\frac{d}{dx}[/tex]( [tex]\frac{v}{u}[/tex] )  = ( -28 - 4 ) /49

[tex]\frac{d}{dx}[/tex]( [tex]\frac{v}{u}[/tex] )  = -32 / 49

[tex]\frac{d}{dx}[/tex]( [tex]\frac{v}{u}[/tex] ) = -32/49 or - 0.6531

Answer:

x= -2

y= 0

Step-by-step explanation:

check answer

5(-2)-4(0)= -10

-10-0= -10 (TRUE)

-4(-2)+5(0)= 8

8+0= 8 (TRUE)

Answer: 5x−4y=−10;−4x+5y=8

Step-by-step explanation:

Answer:

k = 7

Step-by-step explanation:

3(k - 2) + 7 = 29 - k

3k + k = 29 + 6 - 7

4k = 28

k = 7

Answer:

135.4166

Step-by-step explanation:

Answer: kari makes 33 and 51 all together

Step-by-step explanation:

Answer:

y = 2x/3 + 2/3

Step-by-step explanation:

1. Find the slope of the given line.

y = mx + b

6x + 7y = 3y -3

4y = -6x - 3

y = (-6x-3)/4 = -3x/2 - 3/4

The slope of y = -3/2

The slope of a line perpendicular to the line of 6x + 7y = 3y -3 would be the negative reciprocal of the slope so the slope of the line perpendicular would be -1/(-3/2) = 2/3

The equation would be:

y = 2x/3 + b

Since b is unknown, but a point is known, we plug in x and y values.

-8 = 2*(-13)/3 + b

Then solve for b:

b = 2/3

A. 3 2/5

B. 1 3/5

C. 2 1/2

hope this helps!!

BRAINLIEST PLS??

Answer:

i cant read that but if you looking for the answer to 550 divided by 6 it is 96.6

Step-by-step explanation:

Answer:

! not sure if correct !

Step-by-step explanation:

54% of anna's workout was lifting weight

Answer:

45%

Step-by-step explanation:

21+45=66=1 hour 6 mins

2 hours=120 min

120-66=54

(54/120)x100=45 45%

Answer:

1,600

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

3 + 2 = 5

Answer:

5

Step-by-step explanation:

Answer:

C. -3

Step-by-step explanation:

Subtract 6 from 27 and then divide 21 (27-6) by -7 to get -3

Answer:

0.6864 = 68.64% probability out of the 8 new cars it just received that, when each is tested, no more than 2 of the cars have defective radios

Step-by-step explanation:

The cars are chosen without replacement, so the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

48 new cars being shipped to local dealerships, corporate reports indicate that 12 have defective radios installed.

This means that [tex]N = 48, k = 12[/tex]

8 cars received.

This means that [tex]n = 8[/tex]

What is the probability out of the 8 new cars it just received that, when each is tested, no more than 2 of the cars have defective radios

This is

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]

In which

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 0) = h(0,48,8,12) = \frac{C_{12,0}*C_{36,8}}{C_{48,8}} = 0.0802[/tex]

[tex]P(X = 1) = h(1,48,8,12) = \frac{C_{12,1}*C_{36,7}}{C_{48,8}} = 0.2655[/tex]

[tex]P(X = 2) = h(2,48,8,12) = \frac{C_{12,2}*C_{36,6}}{C_{48,8}} = 0.3407[/tex]

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0802 + 0.2655 + 0.3407 = 0.6864[/tex]

0.6864 = 68.64% probability out of the 8 new cars it just received that, when each is tested, no more than 2 of the cars have defective radios

Answer:

6.28 hours

Step-by-step explanation:

103880/18.55 = 35168/x

103880x = 652366.4

x = 6.28

6.28 hours or 6 hours 28 minutes

Answer:

if I am not mistaken.. the median would be 9 and the the mean is also 9.

Step-by-step explanation:

first you order the numbers from least to greatest and the find with is the middle number to find the median.

6,7,8,8,8,9,10,12,13 (answer: 9)

To find the mean you will add all of the numbers up and then divide that number by the amount of numbers there are.

1) 6+7+8+8+8+9+10+12+13= 81

2) 81 ÷ 9 =9

Answer:

Mean: 9, Median: 8 Mode: 8

Step-by-step explanation:

MEAN:   The AVERAGE total of all the values divided by the numbers of values.

6 + 7+ 8 + 8 + 8 + 9 + 10 + 12 + 13 = 81        81/9 (set of #'s)= 9

MEDIAN:  The number in the MIDDLE of the list of values.

6, 7, 8, 8, 8, 9, 10, 12, 13         So, the middle value is 8

MODE:   The number that appears the most.

6, 7, 8, 8, 8, 9, 10, 12, 13         So, 8 appears 3 times.

Hope this helps!