use vectors to decide whether the triangle with vertices p(3, −4, −2), q(4, −1, −4), and r(8, −3, −5) is right-angled. yes, it is right-angled. no, it is not right-angled.

Answer:

-2

Step-by-step explanation:

I did the math, trust me. Just input -2 into the x's and solve.

Answer:

D. x = -6

( 3x-6² - 30x-6 - 72 = 0 )

Step-by-step explanation:

So first you work out:

3x² = ( 3 x -6²) = -108

Then work out 30x = ( 30 x -6 ) = -180

-108 - -180 => 72

Then just do 72 - 72 =

Which would be 0! ☆*:.｡.o(≧▽≦)o.｡.:*☆

hope this helped! xx

The revolution per minutes of the wheels rotation is 912 rev/ min

Given the parameters;

Convert the velocity

[tex]v = 65mph = 65 mil/h - (1609m/mil0/(3600s/h)[/tex]

v = 29. 1 m/s

Let's find the circumference

Circumference = 2 π r

radius = diameter/ 2 = 0. 6096 meters/ 2 = 0. 30 meters

Circumference= 2 × 3. 142 × 0. 30 = 1. 915

Number of revolutions = 29. 1/ 1. 915 = 15.2 rev/ sec

Let's convert to rev/ min

= 15. 2 × 60

= 912 rev/ min

Thus, the revolution per minutes of the wheels rotation is 912 rev/ min

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The value of the function f(-8) if f(x) = -x^2 +8x + 4 is f(-8) = -124

The equation of the function is given as

f(x) = -x^2 +8x + 4

The expression f(-8) means that x = -8

So, we have:

f(-8) = -(-8)^2 + 8(-8) + 4

Evaluate the exponent and the product

f(-8) = -64 - 64 + 4

Evaluate the sum and the difference

f(-8) = -124

Hence, the value of the function f(-8) if f(x) = -x^2 +8x + 4 is f(-8) = -124

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Using complementary and supplementary angles, we have that:

c. The angles are complementary, hence the equation is 4x - 3 + 2x + 1 = 90 and the solution is x = 15.33.

d. The angles are supplementary, hence the equation is 43x + 16 + 110 = 180 and the solution is x = 18.

When the measures of two angles add to 90º, the angles are complementary.

This is the case in item c, hence:

4x - 3 + 2x + 1 = 90

6x = 92

x = 92/6

x = 15.33.

When the measures of two angles add to 180º, the angles are supplementary.

This is the case in item d, hence:

3x + 16 + 110 = 180.

3x = 54

x = 54/3

x = 18.

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Quadrilateral b, is not a scaled copy of Quadrilateral a.

The side length of Quadrilateral a=2,3,5, and 6.

The side length of Quadrilateral b=4,5,8 and 10

Now comparing the Ratio of the Corresponding Sides of two quadrilaterals a and b

2/4 ≠ 5/8

3/5 ≠  6/10

Since the ratio of corresponding opposite sides is not equal. The two Quadrilateral are Not Similar.

So, We can say that Quadrilateral b, is not a scaled copy of Quadrilateral a.

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Expression of the rate per minute at which air freshener dispenses sprays is equal to fraction 4 over 30.

As given,

The graph represents

x-axis: Time in minutes

y-axis: Number of sprays

Ordered pairs ( 30,4) ,(60, 8) ,( 90,12), and ( 120, 16)

Consider any two points ( 90,12) ,(120 , 16)

Expression of the rate per minute=( y₂ -y₁)/(x₂ -x₁)

                                                     =( 16 - 12)/(120 -90)

                                                     = 4/30

Therefore, expression of the rate per minute at which air freshener dispenses sprays is equal to fraction 4 over 30.

The complete question is :

The graph shows the number of sprays an automatic air freshener dispenses, y, in x minutes: A graph is shown. On the x-axis, the values are from 0 till 150 in increments of 30 for each grid line, and on the y-axis, the values are from 0 to 20 in increments of 4 for each grid line. The title of the graph on the x-axis is Time in minutes, and the title on the y-axis is Number of Sprays. A line is shown connecting ordered pairs 30, 4 and 60, 8 and 90, 12 and 120,16. The title for the graph is Dispense Rate. Which expression can be used to calculate the rate per minute at which the air freshener dispenses sprays?

fraction 4 over 30

fraction 30 over 4

fraction 30 over 16

fraction 16 over 30

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Answer: x>10

Step-by-step explanation:

X-5 > 25-20

x-5+5>5+5

x>5+5

x>10

Answer:

8/3 or 2 2/3 gallons

Step-by-step explanation:

1/3 of gallon covers 1/8 of a wall, therefore, the amount of pain is needed to cover the entire wall is 1/3 x 8 = 8/3 or 2 2/3 gallons

Answer: -1.9696969696969696969696

Step-by-step explanation:

Answer:

Exact form: -65/33

Decimal form: -1.96

Mixed number: - 1 32/33

Step-by-step explanation:

Answer in decimal form = -0.2

Answer as a fraction = -1/5

=========================================================

Explanation:

The term "rate of change" is the same as "slope" for linear equations.

Use the slope formula to get the steps shown below.

[tex](x_1, y_1) = (-3, 3.6) \text{ and } (x_2, y_2) = (5, 2)\\\\m = \frac{y_2 - y_1}{x_2 - x_1}\\\\m = \frac{2-3.6}{5-(-3)}\\\\m = \frac{2-3.6}{5+3}\\\\m = \frac{-1.6}{8}\\\\m = \frac{-16}{80}\\\\m = -\frac{1}{5}\\\\m = -0.2\\\\[/tex]

The decimal value is exact without any rounding done to it.

A slope of -1/5 means we go down 1 unit and to the right 5 units.

slope = rise/run = -1/5

rise = -1 = go down 1

run = 5 = go to the right 5

The next day they will drive for about 5.5 hours

In given question, Vijay's house is 544 miles from the resort.

after 3 hours of driving, they stop and spend the night at a hotel and  then complete the rest of the trip on the second day.

Let in 3 hours of driving, they completed the 'x' miles of distance from their home.

So, they complete the rest of the trip of 544 - x miles on the second day.

Let t be the time in hours they drive on the second day.

Their average speed is 64 miles per hour.

⇒ 64 = [x + (544 - x) ] / [3 + t]

⇒ 64 = 544 / 3 + t

⇒ 64(3 + t) = 544

⇒ 192 + 64t = 544

⇒ 64t = 352

⇒ t = 5.5 hours

Therefore, The next day they will drive for about 5.5 hours

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The expression contains FOUR terms, each with TWO factors.

Expression information: In algebra, the word term defined the single numbers(10), variables(y), and the product of the two (10y).

There are four terms:

A factor is a component of a product.

Therefore, the expression contains FOUR terms, each with TWO factors.

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The correct question is given below:
Complete the statement to describe the expression ab+cd+ef+ghab+cd+ef+gha, b, plus, c, d, plus, e, f, plus, g, h. The expression consists of ----- terms, and each term contains ----- factors. Please fill in the blanks!

The answer is H, B and C; And Z, K and R

Step-by-step explanation:

H, B and C; And Z, K and R form a straight line

The required solution is,

1. Gardner can put a maximum of 4 flowers in each row

2. At 150 minutes both the student will meet each other

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,

1. For the planting of trees in even rows,

The greatest number of plants he can have in each row to keep the rose bushes and tulips in their own rows,

Taking HCF of number of plants 24 and 28

HCF of 24 and 28 is 4

Thus, Gardner can put a maximum of 4 flowers in each row.

2.

Time taken by the first student to complete one lap is 25 minutes,

So,

1 lap = 25 minute

1 minute = 1 / 25 lap

For the second student,

1 lap = 30 minute

1 minute = 1/30 lap

At time x minute both will meet each other,

x/25 -x/30 = 1

5x/750 = 1

x = 750/5

x = 150 minute

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Answer:

4

Step-by-step explanation:

As the angle is greater than 0° and less than 90°, then the angle ABC is acute. (Answer: A)

Herein we find the locations of the three vertices of the figure, of which we must determine the lengths of the two sides of the angle and determine the value of the angle by trigonometry:

BA = 5, BC = 2

θ = tan⁻¹ (BA / BC)

θ = tan⁻¹ (5 / 2)

θ ≈ 68.199°

As the angle is greater than 0° and less than 90°, then the angle ABC is acute. (Answer: A)

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Answer: x=9

Step-by-step explanation:

x+1= 10

x-1+1=10-1

x=10-1

x=9

The expression, evaluated to the simplest form is -4

From the question, we are to simplify the given expression

The given expression is

(9² + 19)/(10² - 5³)

Simplifying the expression

(9² + 19)/(10² - 5³)

9² = 81

10² = 100

5³ = 125

Thus,

The expression becomes

(81 + 19)/(100 - 125)

= 100/-25

= -4

Hence, the expression, evaluated to the simplest form is -4

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30 is the correct value of the expression in linear equation .

What in mathematics is a linear equation?

The error starts from here- 36-10 + 4

If we are doing addition or subtraction start from left

=36−10+4

=26+4

= 30

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The possible coordinates of point G on this number line are either -10 or 14.

A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numerical values that are placed at equal intervals along its length.

Given the following data:

E = 2.

EG = 12.

On this number line, the coordinate of EG is given by this mathematical expression:

EG = |E - G|

Substituting the given parameters into the expression, we have;

12 = |2 - G|

2 - G = ±12

G = 2 ± 12

Simplifying and evaluating the above expression, we have:

G = 2 + 12

G = 14.

OR

G = 2 - 12

G = -10

Therefore, the possible coordinates of point G on this number line are either -10 or 14.

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Complete Question:

On a number line, suppose point E has a coordinate of 2, and EG= 12. what are the possible coordinates of point G?

To solve the equation, add 18 to both sides, then divide by 6. The solution is t = 8.

A linear equation is an equation of which the highest degree of its variables is 1.

Steps to solve linear equations:

Recall that if  we subtract or add the same number to both sides of an equation, it does not change the equality.

The given problem:

Solve 6t-18 = 30

The variable is t. Isolate the variable by adding 18 to both sides:

6t -18 +18 = 30 +18

6t = 48

Divide both sides by 6

6t : 6 = 48 : 6

t = 8 (solved)

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The lateral area of the regular octogonal prism is 528 square inches.  

Regular octogonal prisms has two regular octogonal base sides and eight rectangular lateral sides. In this problem we must look for the sum of the areas of the eight rectangular lateral sides, where each area is equal to the product of base side (l) and height (h), both in inches. Then,

A = l · h

A = (6 in) · (11 in)

A = 66 in²

A' = 8 · A

A' = 8 · (66 in²)

A' = 528 in²

The lateral area of the regular octogonal prism is 528 square inches.

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Answer:

[tex]4.4161 \times 10 ^{2} [/tex]

[tex]4.3 \times 1027 \times 10 { \\ \\ }^{2} [/tex]

[tex]4416.1 \times 10^{2} [/tex]

[tex]4.4161 \times 10 ^{2} [/tex]

Answer:

The answer is C

Step-by-step explanation:

First there are 2x first then there are other x's then two 1 equals 2

Answer: 36 years old

Step-by-step explanation:

T=Tanya. M=Marcus

T=M+28

T+6=3(M+6)

T+6-6=3(M+6)-6

T=3(M+6)-6

M+28=3(M+6)-6

M+34=3M+18

34=2M+18

2M=16

M=8

T=M+28

T=8+28

T=36 years old

The current age of Tanya is equivalent to 45 years old.

Given is that Tanya is 28 years older than Marcus. In 6 years, Tanya will be three times as old as Marcus

Assume the initial age of Tanya is {x} years and that of Marcus is {y} years old. So, we can write -

x = y + 28         ....... Eq[1]

x + 6 = 3y         ........ Eq[2]

Using Eq[1] in Eq[2], we get -

y + 28 + 6 = 3y

y + 34 = 3y

2y = 34

y = 17

Than, we can write [x] as -

x = 17 + 28

x = 45

Therefore, the current age of Tanya is equivalent to 45 years old.

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The mean and variance of the lengths are 590. 50  and 0. 075 respectively

Given that the lengths are;

590.1,  590. 2, 590. 3, 590. 4, 590. 5, 590. 6, 590. 7 , 590. 8, 590. 9

Mean = sum of terms/ number of terms

Mean = 590.1 +  590. 2 + 590. 3 + 590. 4 + 590. 5 + 590. 6 + 590. 7 + 590. 8 + 590. 9/ 9

Find the sum of the numerator

Mean = 5314. 5/ 9

Mean = 590. 500

Variance = sum of the distances from the mean/ total number - 1

Variance = (590. 1 - 590. 5)² + (590. 2 - 590. 5)² +  (590. 3 - 590. 5)² +  (590. 4 - 590. 5)² +  (590. 5 - 590. 5)² +  (590. 6 - 590. 5)² +  (590. 7 - 590. 5)² +  (590. 8 - 590. 5)² +  (590. 9 - 590. 5)² ÷ 9 - 1

Variance = 0. 16 + 0. 09 + 0. 04 + 0. 01 + 0 + 0. 01 + 0. 04 + 0. 09 + 0. 016 ÷8

Variance = 0. 6/ 8

Variance = 0. 075

Thus, the mean and variance of the lengths are 590. 50  and 0. 075 respectively

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Answer:

440

Step-by-step explanation:

To do this problem, you have to follow the PEMDAS order.

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

We have to do 5x62 first, which is 310. Next, we multiply 6 and 33, which gets us 198. Then, we add 310 to 198, which is 508. Finally, we subtract 68 from 508 to get 440.

Hope this helps!

Have a wonderful day! :D

The length and width of the rectangle are 21cm and 19cm.

Let the dimensions be represented by x and x+2.

The perimeter of a rectangle is:

= 2(length + width)

= 2(x + x+2) = 80

2x + 2x + 4 = 80

4x + 4 = 80

4x = 80 - 4

4x = 76

Divide

x = 76/4

x = 19

Therefore, the second number will be:

= 19 + 2 = 21

The numbers are 19 and 21.

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The values compared to the greatest :

-2 1/4,-1 1/4,-1 3/4, 1/4

Comparing and ordering fractions is an essential part of developing a sense of numbers. This is also an essential skill to have when facing practical questions, such as:

"Would you like to have {\displaystyle {\frac{3}{4}}}{\frac{3}{4 }} d 'a pizza does not, or {\displaystyle {\frac{6}{7}}}{\frac{6}{7}} of a pizza?" There are several ways to compare and order fractions. If you have a calculator, the fastest way is to convert fractions to decimals. If you don't have a calculator, you can make comparisons easily by finding a common denominator or simply using your reasoning skills and what you already know about fractions.

In this way, the given fractions are compared from largest to smallest

-2 1/4,-1 1/4,-1 3/4, 1/4

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answer:

3/8

explanation:

(m/n)

count units from point a and b vertically, that is m.

count units from point a and b horizontally, that is n.