HELP !! The equations of three lines are given below.
Line 1: 10x - 6y=8
Line 2: 3y = 5x +7
Line 3: y=5/3x -8
For each pair of lines, determine whether they are parallel, perpendicular, or neither.

Answer: 5.24 units, 10.48 units , 15.72  units

Step-by-step explanation:

Volume of a rectangular solid is given by :-

V = lwh, where l = length , w= width and h = height

Given: A rectangular solid has edges whose lengths are in the ratio 1:2:3.

Let lengths of the rectangular solid x , 2 x, 3x.

volume of the solid is 864 cubic units

Then, Volume of rectangle = [tex]x (2x)(3x) =864\ \text{cubic units}[/tex]

[tex]\Rightarrow\ 6x^3 = 864\\\\\Rightarrow\ x^3 =144\\\\\Rightarrow\ x=(144)^{\frac{-1}{3}}\approx5.24[/tex]

Lengths of rectangular solid 5.24 units, 2 (5.24) units , 3(5.24) units

= 5.24 units, 10.48 units , 15.72  units

Answer:

1.35 meters

Step-by-step explanation:

Let the original length of the string be x.

So, we started out with x centimeters. Rachel used 2/3 of it (the original amount) to tie some books together. Therefore, we now have:

[tex]x-\frac{2}{3}x[/tex]

centimeters of string left. This represents the original minus the amount she used.

Next, she used 1/3 of the remaining string. In other words:

[tex]x-\frac{2}{3}x-\frac{1}{3}(x-\frac{2}{3} x)[/tex]

The newly added terms is 1/3 of the remaining string length.

And she ends up with 30 centimeters. Therefore, we need to solve the equation for x:

[tex]x-\frac{2}{3}x-\frac{1}{3}(x-\frac{2}{3} x) =30\\\frac{1}{3}x-\frac{1}{3}x+\frac{2}{9}x=30\\\frac{2}{9}x=30\\ x=30\cdot \frac{9}{2}=135 \text{ centimeters}[/tex]

Therefore, the original length of the string was 135 centimeters or 1.35 meters (move the decimal two places to the left).

Answer:

135 cm or 1.35 m

Step-by-step explanation:

2/3(135) = 90

1/3(90) = 30

Answer:

The probability that a randomly selected group of four trees can be used as timber is 4.5 × 10⁻⁵

Step-by-step explanation:

The given parameters are;

Mean = 34 cm

The standard deviation = 8 cm

The mean

The Z score is [tex]Z=\dfrac{x-\mu }{\sigma }[/tex], which gives;

For x  = 30 we have;

[tex]Z=\dfrac{30-34 }{8 } = -0.5[/tex]

P(x>30) = 1 - 0.30854 = 0.69146

For x = 40, we have

[tex]Z=\dfrac{40-34 }{8 } = 0.75[/tex]

P(x < 40) = 0.77337

Therefore, the probability that the mean of four trees is between 30 and 40 is given as follows;

P(30 < x < 40) = 0.77337 - 0.69146 = 0.08191

The probability that a randomly selected group of four trees can be used as timber is given as follows;

Binomial distribution

[tex]P(X = 4) = \dbinom{4}{4} \left (0.08191\right )^{4}\left (1-0.08191 \right )^{0} = 4.5 \times 10^{-5}[/tex]

Answer: In zhi's equation, the 18 is the initial amount of tickets, and the 3g means 3 times the amount of games.  

Diegos equation is the same, but write in factorised form. The 3 multiplies with the 6 to create 18, and the 3 multiple with the g to create 3g

Answer:

26.25 cm²

Step-by-step explanation:

The area of the shaded part is the area of the shaded triangle subtract the area of the white triangle.

Since the triangles are similar then the ratios of corresponding sides are equal.

let the height of the white triangle be h, then

[tex]\frac{12}{9}[/tex] = [tex]\frac{10}{h}[/tex] ( cross- multiply )

12h = 90 ( divide both sides by 12 )

h = 7.5

shaded area = [tex]\frac{1}{2}[/tex] × 12 × 10 - [tex]\frac{1}{2}[/tex] × 9 × 7.5 = 60 - 33.75 = 26.25 cm²

Answer:

84 squared units.

Step-by-step explanation:

In order to find the surface area of the pyramid, you use the following formula:

[tex]S=b^2+\frac{1}{2}ps[/tex]           (1)

b: base of the pyramid = 6

p: perimeter of the base = 6*4 = 24

s: slant height

Then, you first calculate the slant height, by using the Pythagoras' theorem:

[tex]s=\sqrt{(5)^2-(\frac{6}{2})^2}=4[/tex]

Thus, you replace the values of b, p and s in the equation (1):

[tex]S=(6)^2+\frac{1}{2}(24)(4)=84[/tex]

The surface area of the pyramid is 84 squared units.

Answer:

Step-by-step explanation:

wrong

Answer: C.) - 896

Step-by-step explanation:

Given the explicit formula :

An = 7 × (-2)^(n-1)

The 8th term of the geometric sequence using the formula will be :

n = 8

A8 = 7 × (-2)^(8-1)

A8 = 7 × (-2)^7

A8 = 7 × (-128)

A8 = - 896

Answer:

Step-by-step explanation:

         |x+3| = 12    

x+3 = 12   or   x+3 = -12

x = 9        or    x = -15

Answer:

The correct option is;

0.28

Step-by-step explanation:

The given data values are;

x,      f(x)

8,     12

12,    40

6,      15

20,    20

Where;

x = The number of flowers in the bouquet

f(x) = The total cost (in dollars)

The equation for linear regression is of the form, Y = a + bX

The formula for the intercept, a, and the slope, b, are;

[tex]b = \dfrac{N\sum XY - \left (\sum X \right )\left (\sum Y \right )}{N\sum X^{2} - \left (\sum X \right )^{2}}[/tex]

[tex]a = \dfrac{\sum Y - b\sum X}{N}[/tex]

Where:

N = 4

∑XY = 1066

∑X = 46

∑Y = 87

∑X² = 644

(∑X)² = 2116

b = (4*1066 - 46*87)/(4*644 - 2116) = 0.5696

a = (87 - 0.5696*46)/4 = 15.1996

The standard deviation of the x- values

[tex]S_X = \sqrt{\dfrac{\sum (x_i - \mu)^2}{N} }[/tex]

[tex]\sum (x_i - \mu)^2}[/tex] = 115

N = 4

Sx =√(115/4)

Sx = 5.36

[tex]S_Y = \sqrt{\dfrac{\sum (y_i - \mu_y)^2}{N} }[/tex]

[tex]\sum (y_i - \mu_y)^2}[/tex] = 476.75

N = 4

Sy =√(476.75/4)

Sy= 10.92

b = r × Sy/Sx

Where:

r = The correlation coefficient

r = b × Sx/Sy = 0.5696*5.36/10.92 = 0.2796 ≈ 0.28

The correct option is 0.28.

Answer:

C on edge

Step-by-step explanation:

Answer:

[tex]\boxed{\mathrm{view \: explanation}}[/tex]

Step-by-step explanation:

Two numbers that only have 1 as a common factor are called co-prime numbers.

Example:

Factors of 3 ⇒ 1, 3

Factors of 4 ⇒ 1, 2, 4

These numbers only have 1 as a common factor. So 3 and 4 are co-prime numbers.

Answer:

Hey there! I’m happy to help!

Let’s first subtract 4 from 20 to see how much was lost.

20-4=16

Now, we see that 16 is a certain percent of twenty that we want to find. When talking about percents, the word “is” represents an equal sign. So, we can write this equation. We will have p represent our prevent.

16=20p (16 is a certain percent of 20)

Now, we solve by dividing both sides of the equation by 20 to isolate the p.

p=0.8

0.8 is 80% or 4/5, so 4/5 of the dam water has been lost.

Have a wonderful day! :D

Answer:

a. 46.9 m b. 56.1 m

Step-by-step explanation:

a. Width of the river

The angle of depression of the bottom of the second vertical cliff from the first vertical cliff = angle of elevation of the top of the first vertical cliff from the bottom of the second vertical cliff = 58°.

Since the height of the vertical cliff = 75.0 m, its distance from the other cliff which is the width of the river, d is gotten from

tan58° = 75.0 m/d

d = 75.0/tan58° = 46.87 m ≅ 46.9 m

b. Height of the second cliff

Now, the difference in height of the two cliffs is gotten from

tan22° = h/d, since the angle of depression of the top of second cliff from the first cliff is the angle of elevation of the top of the first cliff from the second cliff = 22°

h = dtan22° = 18.94 m

So, the height of the second cliff is h' = 75.0 - h = 75.0 m - 18.94 m = 56.06 m ≅ 56.1 m

Answer:

-21

Step-by-step explanation:

We are told to find f(x) + g(x) for x= -3. Therefore, we must evaluate f(-3) and g(-3), then add them together.

First, evaluate f(-3).

f(x)=4x-7

To find f(-3), we need to substitute -3 in for x.

f(-3)= 4(-3)-7

Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction First, multiply 4 and -3.

f(-3)= -12-7

Next, subtract 7 from -12

f(-3)= -19

Next, find g(-3).

g(x)=2x+4

To find g(-3), substitute -3 in for x.

g(-3)= 2(-3)+4

Solve according to PEMDAS. First, multiply 2 and -3.

g(-3)= -6+4

Next, add -6 and 4

g(-3)= -2

Now, we can add f(-3) and g(-3) together.

f(-3) + g(-3)

f(-3)= -19

g(-3)= -2

-19 + -2

Add

-21

Answer:

-21

Step-by-step explanation:

Adding f and g together, we get  (f + g)(x) = 4x + 2x -7 + 4, or

                                                                      = 6x - 3

Now replace x with -3.  We get:

(f + g)(-3) = 6(-3) - 3 = -21

Answer:

Step-by-step explanation:

The Area of the rectangular field is expressed as A = LB and its perimeter

P = 2(L+B)

L is the length of the rectangular field

B is the Breadth of the rectangular field

If the length of a rectangular field is twice its breadth i.e L = 2B and the area is 98m² then;

98 = LB

98 = 2B*B

98 = 2B²

B² = 98/2

B² = 49

B = √49

B = 7m

if B = 7m

L = 98/B

L = 98/7 = 14m

The perimeter of the field P = 2(L+B)

P = 2(14+7)

P = 2*21

P = 42m

The perimeter of the field is 42m.

The length of the diagonal of the field can be expressed using Pythagoras theorem.

d = √L²+B²

d = √14²+7²

d = √196+49

d = √245

d = 15.7m ≈ 16m

Hence, the approximate length of the diagonal of the field is 16m

Answer:

[tex]a^2+3\,a\,b-5\,a\,b-15\,b^2=(a-5\,b)\,(a+3\,b)[/tex]

Step-by-step explanation:

Work via factoring by groups:

!) re arrange the terms as follows:

[tex]a^2-5ab+3ab-15b^2[/tex]

then extract the common factor for the first two terms (a), and separately the common factors for the last two terms (3 b):

[tex]a^2-5ab+3ab-15b^2\\a\,(a-5\,b)+3\,b\,(a-5\,b)[/tex]

Now notice that the binomial factor (a-5 b) is in both expressions, so extract it:

[tex]a\,(a-5\,b)+3\,b\,(a-5\,b)\\(a-5\,b)\,(a+3\,b)[/tex]

which is the final factorization.

Answer:

[tex] \boxed{\sf (a + 3b)(a - 5b)} [/tex]

Step-by-step explanation:

[tex] \sf Factor \: the \: following: \\ \sf \implies {a}^{2} + 3ab - 5ab - 15 {b}^{2} \\ \\ \sf Grouping \: like \: terms, \\ \sf {a}^{2} + 3ab - 5ab - 15 {b}^{2} = {a}^{2} + (3ab - 5ab) - 15 {b}^{2} : \\ \sf \implies {a}^{2} + (3ab - 5ab) - 15 {b}^{2} \\ \\ \sf 3ab - 5ab = - 2ab : \\ \sf \implies {a}^{2} - 2ab - 15 {b}^{2} \\ \\ \sf The \: factors \: of \: - 15 \: that \: sum \: to \: - 2 \: are \: 3 \: and \: - 5. \\ \\ \sf So, \\ \sf \implies {a}^{2} + (3 - 5)ab - 15 {b}^{2} \\ \\ \sf \implies {a}^{2} + 3ab - 5ab - 15 {b}^{2} \\ \\ \sf \implies a(a + 3b) - 5b(a + 3b) \\ \\ \sf \implies (a + 3b)(a - 5b)[/tex]

Answer:

Step-by-step explanation:

In other to solve for the profit we have to solve for the unit cost of one lemon first

If 4 lemons cost Rs. 10

then 1 lemon will cost= 10/4= Rs 2.5

knowing that  one cost Rs 2.5

cost price of three would be 3* Rs 2.5=  Rs 7.5

Since three was sold for   Rs. 10.

The profit made is

cost of three- selling price of three=  Rs. 10- Rs 7.5=  Rs 2.5

Answer:

n = 132

Step-by-step explanation:

The external angle of a triangle is equal to the sum of the 2 opposite interior angles.

n is an exterior angle of the triangle, thus

n = 90 + 42 = 132

Answer:

n = 132

Step-by-step explanation:

Answer:

The correct option is;

y minus x = negative 4

(y - x = -4)

Step-by-step explanation:

Given that the line y  = x - 4 of the graph passes through the points (0, -4) and (4, 0)

Comparing with the general equation of a straight line, y = m·x + c, where m is the slope and c is the y-intercept gives;

The slope of the equation y = x - 4 = 1

The y-intercept of the equation y = x - 4 = -4

Two equations will have an infinite number of solutions when they are on the same line, that is having the same slope and intercept, we check for the slope and the intercept of the given options as follows;

For y - x = -4, we have;

y = x - 4 which is the same as the given equation and both equations will have an infinite number of solutions

For y - x = -2 we have;

y = x - 2

The slope is the same as the given equation but the intercept is different giving no solution

For y - 4 = x, we have;

y = x + 4

The slope is the same as the given equation but the intercept is different giving no solution

For y + 4x = 1, we have;

y = 1 - 4x

The slope and  intercept are different giving one solution.

Answer:

y - x = -4

Step-by-step explanation:

Answer: 1:1

Step-by-step explanation:

Let r be the radius and h be the height of a cylinder.

Formula: Curved surface area of cylinder = [tex]2\pi rh[/tex]

Now, if  radius of a cylinder is doubled and its height is halved, then new radius will be R= 2r and new height  will be  [tex]H=\dfrac{1}{2}[/tex]

Now, new surface area = [tex]2\pi RH= 2\pi(2r)\dfrac{h}{2}= 2\pi rh[/tex]

Ratio of curved surface areas : [tex]\dfrac{\text{Surface area}}{\text{New surface area}}=\dfrac{2\pi rh}{2\pi rh}=\dfrac{1}{1}[/tex]

Hence, the ratios of their surface areas = 1:1 .

Answer:

18

Step-by-step explanation:

8r - r s

r=6 and s=5

8*6 - 6*5

48 - 30

18

Answer:

you first take the equation 8r-rs and you substitute r=6 s=5, which will look like this 8(6)-6(5).

after that you distribute 8*6 and 6*5

and then you'll get 48-30

finally you subtract the two numbers which will leave you with = 18

Step-by-step explanation:

Answer:

74°.

Step-by-step explanation:

From the question given above,

Cos A = 0.2785

To get the value of angle A, we simply find the inverse of Cos as shown below:

Cos A = 0.2785

Take the inverse of Cos.

A = Cos¯¹ 0.2785

A = 73.8° ≈ 74°

Therefore, the value of angle A is approximately 74°

Answer:  x + 2x + x-40 = 180

First angle= 55º

Second angle= 110º

Third angle= 15º

​Step-by-step explanation:  The sum of the angles of a triangle is 180º

Take the values given and  use x as the unknown first angle. then create terms for the other two angles based on that:

The second angle of a triangle is double the first angle  becomes 2x

The third angle is 40 less than the first angle becomes x-40

x + 2x + x-40 = 180  Solve by adding like terms . x + 2x + x = 4x

4x -40 = 180   Add 40 to both sides to "cancel" the -40 on the left

4x + 40 -40 = 180 + 40   becomes  

4x = 220  Divide both sides by 4 to "cancel" the 4 on the left side

4x/4 = 220/4

x = 55   This is the first angle. Substitute 55 for the  "x" in the original terms

2(55) = 110   The second angle

(55) -40 = 15   the third angle

Answer:

The answer is

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

To find the equation of the line we must first find the slope

That's

Slope of the line using points

(8,-8) and (-5,-8) is

[tex]m = \frac{ - 8 + 8}{ - 5 - 8} = \frac{0}{ - 13} = 0[/tex]

So the equation of the line using point (8,-8) is

y + 8 = 0(x - 8)

y + 8 = 0

We have the final answer as

Hope this helps you

Answer: while solving an equation involving fractions we eliminate the fraction by multiplying the LCD of all the denominators present in the equation . LCD means Least common Denominator so for this question when we try to eliminate the denominator we first try to find the LCM (2,4,6) because that will give us the LCD.

2=2

4=2·2

6=2·3

LCM = 2·2·3

LCM = 12

It means we need to multiply the 12 to each term of equation to eliminate the fractions before solving.

12

To eliminate the fractions, multiply the equation by the 12

A equation is an expression that shows the relationship between two or more variables and numbers.

Given the equation:

[tex]x-\frac{5}{4}+2x=\frac{5}{6}+x[/tex]

To eliminate the fractions, multiply by the L.C.M of the denominator of the fraction i.e. 12 to get:

12x - 15 + 24x = 10 + 12x

Find out more on Equation at: https://brainly.com/question/2972832

Answer:

Alternate interior angles theorem

Step-by-step explanation:

DG // EF   and GE is the transversal. So, alternate interior angles are congruent

Therefore, ∠HGD ≅ ∠HEF

DG // EF   and DF is the transversal. So, alternate interior angles are congruent

Therefore, ∠HDG ≅ ∠HFE

Answer:

is there a y part of this equation?

Step-by-step explanation:

Answer:

66.63

Step-by-step explanation:

To find the diagonal length, use Pythagorean’s theorem.

Diagonal = √45^2 + 45^2 = √2025+2025 = √4050 = 63.63.

Hope this helps

Answer:

(2, 3 )

Step-by-step explanation:

The solution to a system of equations given graphically is at the point of intersection of the 2 lines.

point of intersection = (2, 3 ) ← is the solution