Find the value of x.

Answer:

a) [tex]a+b+c=\begin{pmatrix}-2\\-3\end{pmatrix}[/tex]

b) (i) [tex]a+2c=\begin{pmatrix}-4\\2\end{pmatrix}[/tex]

   (ii) [tex]k=2[/tex]

Step-by-step explanation:

It is given that,

[tex]a=\begin{pmatrix}4\\-10\end{pmatrix},b=\begin{pmatrix}-2\\1\end{pmatrix},c=\begin{pmatrix}-4\\6\end{pmatrix}[/tex]

a)

We need to find the value of a+b+c.

[tex]a+b+c=\begin{pmatrix}4\\-10\end{pmatrix}+\begin{pmatrix}-2\\1\end{pmatrix}+\begin{pmatrix}-4\\6\end{pmatrix}[/tex]

[tex]a+b+c=\begin{pmatrix}4+(-2)+(-4)\\-10+1+6\end{pmatrix}[/tex]

[tex]a+b+c=\begin{pmatrix}-2\\-3\end{pmatrix}[/tex]

b)

(i) We need to find the value of a+2c.

[tex]a+2c=\begin{pmatrix}4\\-10\end{pmatrix}+2\begin{pmatrix}-4\\6\end{pmatrix}[/tex]

[tex]a+2c=\begin{pmatrix}4\\-10\end{pmatrix}+\begin{pmatrix}-8\\12\end{pmatrix}[/tex]

[tex]a+2c=\begin{pmatrix}4+(-8)\\-10+12\end{pmatrix}[/tex]

[tex]a+2c=\begin{pmatrix}-4\\2\end{pmatrix}[/tex]

(ii) It is given that a+2c=kb, where k is an integer. We need to find the value of k.

[tex]a+2c=k\begin{pmatrix}-2\\1\end{pmatrix}[/tex]

[tex]\begin{pmatrix}-4\\2\end{pmatrix}=\begin{pmatrix}-2k\\k\end{pmatrix}[/tex]

On comparing both sides, we get

[tex]k=2[/tex]

Answer:

B

Step-by-step explanation:

The side you have drawn in is 4√3 (calculate via pythagoras as √(8²-4²) = √48 = √16·3 = √4²·3 = 4√3)

So the area of the small triangle is 4*2√3 and the area of the small rectangle is 2*4√3. Together makes 4*2√3 + 2*4√3 =  16√3

Answer:

Step-by-step explanation:

Angle 1 and angle 4 are Alternative angles:

Alternative angles are pair of angles on the inner side of each of those two lines but on opposite sides.

∠2-∠2=180  ,∠2=180-62=118

∠4+118=180  ⇒∠4=180-118 ⇒∠4=62 degrees

  ∠1=∠4                  alternative angles        

Answer:

x - y - 2 ≥ 0

Step-by-step explanation:

Answer:

The triangle is not equilateral.

Step-by-step explanation:

Distance formula:

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

Distance from (a, a) to (-a, -a):

[tex] d_1 = \sqrt{(-a - a)^2 + (-a - a)^2} [/tex]

[tex] d_1 = \sqrt{(-2a)^2 + (-2a)^2} [/tex]

[tex] d_1 = \sqrt{8a^2} [/tex]

Distance from (-a, -a) to (-3a, 3a):

[tex] d_2 = \sqrt{(-3a - (-a))^2 + (3a - (-a))^2} [/tex]

[tex] d_2 = \sqrt{(-2a)^2 + (4a)^2} [/tex]

[tex] d_2 = \sqrt{20a^2} [/tex]

Distance from (-3a, 3a) to (a, a):

[tex]d_3 = \sqrt{(-3a - a)^2 + (3a - a)^2}[/tex]

[tex]d_3 = \sqrt{(-4a)^2 + (2a)^2}[/tex]

[tex]d_3 = \sqrt{20a^2}[/tex]

The three sides do not have the same length, so the triangle is not equilateral.

Answer:

28

Step-by-step explanation:

[tex]4 {x}^{2} + - - x + 49 \\ this \: is \: the \: expanded \: form \: of \\ {(2x + 7)}^{2} = 4 {x}^{2} + 28x + 49[/tex]

Answer:

[tex]\huge \boxed{28}[/tex]

Step-by-step explanation:

The trinomial is a perfect square.

Take the square root of the first term and the last term.

[tex](\sqrt{4x^2}+\sqrt{49})^2[/tex]

[tex]\sqrt{4x^2}=2x\\ \sqrt{49} =7[/tex]

[tex](2x+7)^2[/tex]

Expand to find the second term of the trinomial.

[tex](2x+7)(2x+7)\\2x(2x+7)+7(2x+7)\\4x^2 +14x+14x+49\\4x^2 +28x+49[/tex]

The second term of the trinomial is 28x.

Answer:

cos(A) = 4/5

Step-by-step explanation:

3sinA+4cosA=5

Divide by 5 on both sides

(3/5)sinA+(4/5)cosA = 1 .................(1)

from which sin(A) = 3/5, cos(A) = 4/5  by inspection, since

(3/5)^2+(4/5)^2 = 1

For more details,

Let

cos(B) = (3/5), then

sin(B) = (4/5)

Substitute in (1)

cos(B)sin(A) + sin(B)cos(A) = 1          substitute trigonometric sum

sin(A+B) = 1  => A & B are complementary

cos(A) = sin(B) = 4/5

Answer:

(a) The standard deviation of the amount spent is $3229.18.

(b) The probability that a household spends between $4000 and $6000 is 0.2283.

(c) The range of spending for 3% of households with the highest daily transportation cost is $12382.86 or more.

Step-by-step explanation:

We are given that the average annual amount American households spend on daily transportation is $6312 (Money, August 2001). Assume that the amount spent is normally distributed.

(a) It is stated that 5% of American households spend less than $1000 for daily transportation.

Let X = the amount spent on daily transportation

The z-score probability distribution for the normal distribution is given by;

                          Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = average annual amount American households spend on daily transportation = $6,312

           [tex]\sigma[/tex] = standard deviation

Now, 5% of American households spend less than $1000 on daily transportation means that;

                      P(X < $1,000) = 0.05

                      P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{\$1000-\$6312}{\sigma}[/tex] ) = 0.05

                      P(Z < [tex]\frac{\$1000-\$6312}{\sigma}[/tex] ) = 0.05

In the z-table, the critical value of z which represents the area of below 5% is given as -1.645, this means;

                           [tex]\frac{\$1000-\$6312}{\sigma}=-1.645[/tex]                

                            [tex]\sigma=\frac{-\$5312}{-1.645}[/tex]  = 3229.18

So, the standard deviation of the amount spent is $3229.18.

(b) The probability that a household spends between $4000 and $6000 is given by = P($4000 < X < $6000)

      P($4000 < X < $6000) = P(X < $6000) - P(X [tex]\leq[/tex] $4000)

 P(X < $6000) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{\$6000-\$6312}{\$3229.18}[/tex] ) = P(Z < -0.09) = 1 - P(Z [tex]\leq[/tex] 0.09)

                                                            = 1 - 0.5359 = 0.4641

 P(X [tex]\leq[/tex] $4000) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{\$4000-\$6312}{\$3229.18}[/tex] ) = P(Z [tex]\leq[/tex] -0.72) = 1 - P(Z < 0.72)

                                                            = 1 - 0.7642 = 0.2358  

Therefore, P($4000 < X < $6000) = 0.4641 - 0.2358 = 0.2283.

(c) The range of spending for 3% of households with the highest daily transportation cost is given by;

                    P(X > x) = 0.03   {where x is the required range}

                    P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{x-\$6312}{3229.18}[/tex] ) = 0.03

                    P(Z > [tex]\frac{x-\$6312}{3229.18}[/tex] ) = 0.03

In the z-table, the critical value of z which represents the area of top 3% is given as 1.88, this means;

                           [tex]\frac{x-\$6312}{3229.18}=1.88[/tex]                

                         [tex]{x-\$6312}=1.88\times 3229.18[/tex]  

                          x = $6312 + 6070.86 = $12382.86

So, the range of spending for 3% of households with the highest daily transportation cost is $12382.86 or more.

Answer:

1) [tex]DIAGRAM \mapsto B[/tex]  

2) DEFINITION [tex]\mapsto A[/tex]

3) THEOREM [tex]\mapsto C[/tex]

4) POSTULATE [tex]\mapsto D[/tex]

Step-by-step explanation:

1) DIAGRAM  B) A visual tool representing mathematical ideas to be interpreted

A diagram is the depiction or representation of information using symbols

2) DEFINITION A) A formal statement declaring the meaning of a word

A definition is a statement that outlines the meaning of a word or a group of words or a diagram, or a symbol or sign

3) THEOREM C) A mathematical statement proven using postulates and definitions

A general statement of a proposition that is by itself not evident, but given proof by a combination of postulates

4) POSTULATE D) A mathematical statement taken as a fact

An assumed truth taken as the foundation for further reasoning

Answer:

12) 1/8 inch =  0.125 inch

    = 0.003175 m

    = 3.175 x 10-3 m

    = 0.3175 cm

13) 2 is rational and  π  is  irrattional.  π   is approximately   3.14 and is the bigger of two

14) C= 40,005,306.33 m

  = 4.0005 x 107 m

15)  12,615,800,000

= 1.26158 x 1010

=126158 x 105

16) Let's take speed of ant as 1Km/h=1000m/h. Then time 1666.875 days

Step-by-step explanation:

Answer:

the positive integers or whole numbers include 1, 2, 3, and etc. sometimes zero.

Whole numbers are 0, 1, 2, 3, 4, 5, 6. Whole numbers include positive integers along with 0.

17, 99, 267, 8107 and 999999999 are examples of whole numbers.

A rational number is a number that can be express as the ratio of two integers. A number that cannot be expressed that way is irrational. For example, one third in decimal form is 0.33333333333333

A real number that can NOT be made by dividing two integers (an integer has no fractional part). "Irrational" means "no ratio", so it isn't a rational number.

Example: π is an irrational number.

The real numbers include all the rational numbers, such as the integer −5 and the fraction 4/3, and all the irrational numbers, such as √2.

Included within the irrationals are the transcendental numbers, such as π

Answer:

w/2 = 7.5/5

3kg

Step-by-step explanation:

Remaining question below:

Which proportion could Maddy use to model this situation?

a. w/2 = 7.5/5

b. w/7.5 = 5/2

Solve the proportion to determine the weight of a 2 liter jug.

_____kg

5 liters jug of sport drink weighs 7.5kg

2 liters jug of sport drink will weigh x kg

Find w

Ratio of weight to volume

7.5kg : 5liters=7.5/5

wkg : 2 liters=w/2

Equates the ratio

7.5 / 5 = w / 2

Cross product

7.5*2=5*w

15=5w

Divide both sides by 5

3=w

w=3kg

Therefore, weight of the 2liters jug of sport drink is 3kg

Answer:

The answer is 3kg!

Step-by-step explanation:

Answer: D

Step-by-step explanation:

The common difference is  -2/3  so using the last term which is -8/27 multiply it by -2/3 to find the next terms.

[tex]-\frac{8}{27} * -\frac{2}{3}[/tex] = [tex]\frac{16}{81}[/tex]    

[tex]\frac{16}{81} * -\frac{2}{3} = -\frac{31}{243}[/tex]  

[tex]-\frac{32}{243} * -\frac{2}{3} = \frac{64}{729}[/tex]  

Answer:

1). Algebraic expression - a letter or symbol used to represent an unknown.

2). Coefficient - a numerical value.

3). Constant - the constant preceding the variables in a product.

4). Expression - a mathematical expression containing one or more variables.

5). Variable - a mathematical phrase that cannot be determined true or false.

Answer:

705 meters

Step-by-step explanation:

[tex]cos~60=\frac{650^2+750^2-d^2}{2 \times 650 \times 750} \\2 \times 650 \times 750 \times \frac{1}{2}=50^2(13^2+15^2)-d^2 \\487500=2500(169+225)-d^2\\487500=2500(394)-d^2\\487500=985000-d^2\\487500-985000=-d^2\\d^2=497500\\d=\sqrt{497500}\\or~d\approx705.337 \approx 705~meters[/tex]

Answer:

7 0 5  M E T E R S !!!!!

Step-by-step explanation:

Answer:

Z - score = 2.83

Step-by-step explanation:

Given the following :

Number of samples (N) = 60

Sample mean (x) = 41.9mg

Population mean (μ) = 40mg

Population standard deviation (sd) = 5.2

Using the relation :

Z = (x - μ) / (sd / √N)

Z = (41.9 - 40) / (5.2 / √60)

Z = 1.9 / (5.2 / 7.7459666)

Z = 1.9 / 0.6713171

Z = 2.8302570

Therefore, the z-score = 2.83

Answer:

51

Step-by-step explanation:

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

The reference angle has AC = 12.3 as the opposite side and BC = 8.4 as the adjacent side. The tangent ratio ties the opposite and adjacent sides together.

--------

tan(angle) = opposite/adjacent

tan(theta) = AC/BC

tan(theta) = 12.3/8.4

theta = arctan(12.3/8.4)

theta = 55.6697828044967

theta = 55.7 degrees approximately

--------

arctan is the same as inverse tangent which is written as [tex]\tan^{-1}[/tex]

make sure your calculator is in degree mode

Answer:

B. 255 m

Step-by-step explanation:

use similar triangle

L / 60 = 85 / 20

L = (85 * 60) / 20

L = 255 m

The distance across the lake will be 255 meters. Then the correct option is B.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

If the two triangles are similar, the ratio of the corresponding sides will be constant.

In an isosceles triangle, two angles and their opposite sides are equal.

The dimensions of the first triangle are L, 85, and y. And the dimensions of the second triangle are 60, 20, and x.

It is given that the triangles are similar.

Then the ratio of their corresponding sides will be

L / 60 = 85 / 20 = x / y

From first two terms, then the equation will be

L / 60 = 85 / 20

L / 60 = 4.25

       L = 4.25 x 60

       L = 255 m

The distance across the lake will be 255 meters.

Then the correct option is B.

More about the triangle link is given below.

https://brainly.com/question/25813512

#SPJ5

Answer:

A

Step-by-step explanation:

First, we are already given the sides adjacent and opposite to ∠x. Therefore, we can use the tangent function. Recall that:

[tex]\tan(x)=opp/adj[/tex]

The opposite side is 20 while the adjacent side is 14.

Plug in the numbers. Use a calculator:

[tex]\tan(x)=20/14=10/7\\x=\tan^{-1}(10/7)\\x\approx55.0080\textdegree\approx55\textdegree[/tex]

Edits: Improved Answer. Removed Wrong Answer.

Answer:

55

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp/ adj

tan x = 20/14

Taking the inverse tan of each side

tan ^-1 tan x = tan ^ -1 (20/14)

x =55.0079798

To the nearest degree

x = 55

Answer:

x=-12

Step-by-step explanation:

8x=-104

8x÷8=-104÷8

x=-104÷8

x=-13

Step-by-step explanation:

8x:-104

8÷8x:-104÷8

x:13

Answer:

[tex]\Large \boxed{-10x-50}[/tex]

Step-by-step explanation:

[tex]-10(x+5)[/tex]

Distribute -10 to the terms in the brackets.

[tex]-10(x)-10(5)[/tex]

[tex]-10x-50[/tex]

Answer: -10x - 50

Step-by-step explanation:

Distribute -10 to both terms.

-10 * x = -10x

-10 * 5 = -50

The equation now looks like this:

-10x - 50

You have nothing to simplify, so you're finished.

Hope this helps!

Answer:

$0.20

Step-by-step explanation:

4 x 1.45 = $5.80

6.00 - 5.80 = 0.20

Answer: $0.20

Step-by-step explanation:

Do 4 *$1.45 = $5.80

This is how much her total was.

She gave $6 in cash.

Subtract.

6-5.80=$.20

Answer:

[tex]\Large \boxed{{(10x+10)=110}}[/tex]

Step-by-step explanation:

Vertical opposite angles are equal.

[tex](10x+10)=110[/tex]

Answer:

The answer is C.

Step-by-step explanation:

Reason:

For the angles shown, angle (10z+10)° is the same with 110°

So the equation is (10z+10)° = 110°

That's the answer. (C).

Answer:

Jonathan's Unit rate = 4 hr (reading/homework)/(1 hour for video games)

Lucas' Unit rate = 3 hr (reading/homework)/(1 hour for video games)

Step-by-step explanation:

The unit rate is the rate per unit of a quantity, that is the rate at which the denominator has been made a unit or one

The given parameters are;

The number of hours of homework or reading Jonathan needs to do for his parents to allow him to play video games for 30 minutes = 2 hours

The number of hours of homework or reading Lucas needs to do for his parents to allow him to play video games for 30 minutes = 1.5 hours

We note that 30 minutes = 0.5 hours

For Jonathan we have

Unit rate = (Number of hours of reading or homework)/(Number of hours playing video games)

Unit rate = (2 hours)/(0.5 hours) = 4 hours of reading or homework per hour of paying video games

Jonathan's Unit rate = 4 hr (reading/homework)/(1 hour for video games)

For Lucas we have

Unit rate = (Number of hours of reading or homework)/(Number of hours playing video games)

Unit rate = (1.5 hours)/(0.5 hours) = 3 hours of reading or homework per hour of paying video games

Lucas' Unit rate = 3 hr (reading/homework)/(1 hour for video games).

Answer:

Area= 108ft²

Step-by-step explanation:

To find the area of a rectangle, you must do the following formula:

Area= Length × Width

A represents Area

L represents Length

W represents Width

Because the length (length is always longer than width) is 12 ft and the width (width is always shorter than length) is 9 ft. Your equation should be:

A= L × W

= 12ft × 9ft

= 108 ft²

Remember: The answer to a question asking for the area of a shape that is 2D, is always squared (let x represents the answer: x²). And the question asking the area of a shape that is 3D always cubed (let x represents the answer: x³). Always write the unit of measurement (let x represent the answer and cm as the example of unit of measurement: x cm²)

I hope this helps! I'm sorry if it's too complicated.

Answer:

D { -1,0,3,5}

R { -3,-1,1,7}

Step-by-step explanation:

The domain is the input values

3,-1,5,0

We normally put them from smallest to largest

D { -1,0,3,5}

The range is the output values

1,-3,7, -1

We normally put them from smallest to largest

R { -3,-1,1,7}

Answer:

D

Step-by-step explanation:

Answer:

2 in

Step-by-step explanation:

18/3=6 , 6 is the scale factor

12/6=2

Answer:

width= 2

Step-by-step explanation:

18 inches is the original height and we are now reducing that to 3 inches.

In order to do that, we have to divide 18 by 3 which equals 6.

Next, take the width of the rectangle, which is twelve and divide it by the scale factor of 6 which  equals 2.

Your final answers should be: width= 2

Answer:

about 2.72 cm.

Step-by-step explanation:

Since, all the bowls are identical, I just added the heights of bothe stacks together and I divided that sum by the number of bowls in each stack all added together.

16.82+21.2=38.02 cm in total height of both stacks.

8+6=14 bowls in all from both stacks

38.02 cm/14 bowls=2.71571428, or rounded, about 2.72 cm

Answer:

no solutions

Step-by-step explanation:

2y = 4x+6

y = 2x+6

Divide the first equation by 2

y = 2x+3

These are parallel lines ( same slope) but different y intercepts

They will never intersect, so they have no solutions

Answer:

B   No solutions

Step-by-step explanation:

2y = 4x + 6       first equatión

 y  = 2x + 6       second equation

from the first equation

y = (4x+6)/2

y = 4x/2 + 6/2

y = 2x + 3       third equation

matching second equatión and third equation

2x + 6 = 2x + 3

2x - 2x = 3 - 6

0 ≠ -3

then:

Β  No solutions