2. "three times the sum of a number and 7”.

The given plane has normal vector

[tex]x-2y=5\implies\mathbf n=\langle1,-2,0\rangle[/tex]

Scaling n by a real number t gives a set of vectors that span an entire line through the origin. Translating this line by adding the vector <2, 1, 1> makes it so that this line passes through the point (2, 1, 1). So this line has equation

[tex]\mathbf r(t)=\langle1,-2,0\rangle t+\langle2,1,1\rangle=\langle 2+t, 1-2t, 1\rangle[/tex]

This line passes through (2, 1, 1) when t = 0, and the line intersects with the plane when

[tex]x-2y=5\implies(2+t)-2(1-2t)=5\implies5t=5\implies t=1[/tex]

which corresponds the point (3, -1, 1) (simply plug t = 1 into the coordinates of [tex]\mathbf r(t)[/tex]).

So the distance between the plane and the point is the distance between the points (2, 1, 1) and (3, -1, 1):

[tex]\sqrt{(2-3)^2+(1-(-1))^2+(1-1)^2}=\boxed{\sqrt5}[/tex]

Answer:

2 hundreds.

Step-by-step explanation:

25 tens is equal to 250.

25 x 10 = 250

5 tens = 50, 5 x 10

250 - 50 = 200

200 = 2, hundreds.

Answer:

2 hundreds

Step-by-step explanation:

Answer:

a - about 3 packs cause you have to round up

b - $50.76

Step-by-step explanation:

First you divide 42 and 18.

42/18=2.33

You have to round up cause you can't have half of a pack, you can't just buy half of a pack.

So, it is rounded to 3 packs.

Next you have to multiply the number of packs and the cost of each pack of water bottles.

16.92*3=$50.76

a - you have to buy 3 packs

b - the total cost is $50.76

Answer:

Angle E = 70°

Step-by-step explanation:

Given parallelogram RELA, where m<R = 110°, to find m<E, recall the properties of a parallelogram.

Angle R and angle E are consecutive angles in parallelogram RELA.

One of the properties of a parallelogram states that any 2 consecutive angles in a parallelogram are supplementary. That is, they add up to 180°.

Therefore:

m<R + m<E = 180°

110° + m<E = 180°

Subtract 110° from both sides

m<E = 180° - 110° = 70°

Answer:

n = 9

Step-by-step explanation:

3n-n+7=25

2n +7 = 25

2n = 18

n = 9

I hope this helps!

-TheBusinessMan

Step-by-step explanation:

3n-n=25-7

2n=18

n=18/2

n=9

Answer:B

Step-by-step explanation:

E202 just did :)

Answer:

b

Step-by-step explanation:

edg 2020

Answer:

The longest length of carpet is 160 cm.

Step-by-step explanation:

Given that the total ratio(units) of the carpet is 9(2+3+4). So first, you have to find the length of carpet in 1 unit :

[tex]9 \: units = 360 \: cm[/tex]

[tex]1 \: unit = 360cm \div 9[/tex]

[tex]1 \: unit = 40 \: cm[/tex]

Next, you have to find the length of carpet in 4 ratio as the question wants the longest length :

[tex]4 \: units = 40 \: cm \times 4[/tex]

[tex]4 \: units = 160 \: cm[/tex]

Answer:

160cm

Step-by-step explanation:

2+3+4= 9

4/9 x 360= 160cm

Answer:

The mean is 36

Step-by-step explanation:

The mean of these numbers is 36.

Steps to solve:

x/3 + 1/4 = 1/3

~Subtract 1/4 to both sides

x/3 = 1/12

~Multiply 3 to both sides

x = 1/4

Best of Luck!

In this case the answer would be the last option

because it is shrunk by 2/3 on just the x side

D is the only one who has that first transformation

By a theorem of similarity, it can be shown that △JKL ~ △MNP.

Similar figures are those figures which are identical in shape, but not necessarily in size.

Two squares with sides of 10 and 5 are similar because their shape is exact but the size is different.

Another example is all circles are similar circles.

The ratio of corresponding sides of similar objects is always the same.

Any two triangles will be similar if the ratio of their corresponding side is same.

If △JKL ~ △MNP then their corresponding side ratio will definitely same.

If corresponding side is same order in JKL and MNP then,

JK/KL = MN/NP

Hence "By a theorem of similarity, it can be shown that △JKL ~ △MNP".

To learn more about similarity,

https://brainly.com/question/23620710

#SPJ5

Answer:

The expression to this question can be defined as follows:

Step-by-step explanation:

Given angle:

1. 60°

2. 120°

Formula:

[tex]\to \bold{\ angle + 360 \ n}[/tex]

The Expression for point 1:

[tex]\to 60^{\circ} + 360 \ n\\[/tex]

The Expression for point 2:

[tex]\to 120^{\circ} + 360 \ n\\[/tex]

Answer:

X= -2

Step-by-step explanation:

Given: 16 = -4(x - 1) + 4

Solution:

Subtract 4 from both sides

12 = -4(x -1)

Divide -4 on both sides

-3 = x - 1

Add -1 on both sides

x = -2

Answer:

24 covered with peanuts

40 covered with choc chips

56 covered with sprinkles

Answer:

Yes, it is possible.

Step-by-step explanation:

It is possible to have same profit rate.

The number of sales may demonstrate that the company Q with 25 online sales is smaller than the company Z with 150 online sales.

Or the company Q may have higher profit rate on individual sales than company Z.

Answer:

Time t = 15 years

Step-by-step explanation:

Interest = 892.50

Principal = 1400

Rate = 4.25%

Time = unknown

But

interest I = Principal p * rate r * time t

Time t = interest I/(principal P * rate r)

Time t=( 892.50*100)/(1400*4.25)

Time t=89250/5950

Time t = 15 years

Answer:

never heard about it

Step-by-step explanation:

Answer:

74%

Step-by-step explanation:

16.9/22.9。。。。。。。

Answer:

74%

Step-by-step explanation:

22.9=100%

16.9= ?

16.9×100÷22.9=73.8

Round to the nearest % =73.8=74

Answer =74%

Answer:

it is c

Step-by-step explanation:

got it correct on the quiz

Answer:

[tex]-\frac{7}{2} x+12[/tex]

Step-by-step explanation:

if you need step by step explanation i will upload.

5. 6. 11. 17. 28. 45 . 73

5 &6 are given,

Then,

5+6=11

6+11=17

11+17=28

17+28=45

So,

28+45=73

Answer:

73

Step-by-step explanation:

We are adding the two numbers before

5+6 = 11

6+11 = 17

11+17 = 28

17+28 = 45

28+45 =73

Answer:

Surface area = 13.5 unit square.

Step-by-step explanation:

We have given the side length of cube = 3/2 units

Now we have to find the surface area of the cube by using the given information. Therefore we must use the below formula to find the surface area. the formula is as follows:

Surface area = 6 (side)^2

Now plug the given information in the formula.

Surface area = 6 (3/2)^2

Surface area = 13.5 unit square.

Answer:

d

Step-by-step explanation:

Answer:

x=200

Step-by-step explanation:

Answer:

[tex]x=200[/tex]

Step-by-step explanation:

[tex]x+300=500[/tex]

There is an easy way to solve this.

Let's do

[tex]500-300[/tex]

Since [tex]500-300[/tex] is equal to 200, then x would be 200.

[tex]x=200[/tex]

Hope this helps!

Answer:

16

Step-by-step explanation:

Answer:

16 units

Step-by-step explanation:

Consider the absolute value of the difference of the points

| - 6 - 10 | = | - 16 | = 16 , or

| 10 - (- 6) | = | 10 + 6 | = | 16 | = 16

Answer:

(4,5)

Step-by-step explanation:

The correct answer is 0.45 or 45%

Explanation:

In this case, the probability of selecting a student whose major is Humanities can be calculated by finding the number of Humanities students, which is considered as the desired outcome, and dividing this by the total of outcomes or students. The process to find the probability is shown below:

[tex]P = \frac{Desired outcomes}{Total outcomes}[/tex]

[tex]P= \frac{Students from Humanities}{Total students}[/tex]

[tex]Students of Humanities = 5 + 5 + 3 + 3 = 16 students[/tex] (Add the students of each year that are part of Humanities)

[tex]Total of students = 35[/tex] (This number is provided in the question but can also be found by adding all numbers in the table)

[tex]P = \frac{16}{35}[/tex]

[tex]P = 0.45[/tex]

Multiply the probability by 100 to know its equivalent in percentages 0.45 x 100 = 45. This means the probability that a student of humanities is selected is 0.45 or 45%.

Answer:

17

Step-by-step explanation:

6 + 11 = 17

Sum (addition of 2 numbers)

Since the sum of a number and six is eleven, the number is equal to 5.

To find the unknown number:

In this exercise, you're required to determine an unknown number by translating the word sentence into an algebraic equation.

Translating the word sentence into an algebraic expression, we have;

The sum of a number and six is eleven:

[tex]n + 6 =11[/tex]

Next, we would rearrange the equation by collecting like terms:

[tex]n = 11-6[/tex]

n = 5

Find more information: https://brainly.com/question/4728821

Answer:

devil!!!!!!!!!!!!!!!!

Step-by-step explanation: