Write an equation of the line that passes through the point (4,5) and has a slope of -2.

Answer:

(2, 7, 1)

Step-by-step explanation:

We have three equations, and using Gauss-Jordan Elimination, we can solve for x, y, and z

3x + y - 2z = 11

4x - 2y + z = -5

x + 5y - 4z = 33

We can start by taking out the z from all rows except one. To do this, we can work with the second row. I chose the second row because -5 is small and easy to add up with other numbers, and z has no coefficient in this row.

We can add 2 times the second row to the first row and 4 times the second row to the third row to get

11x - 3y = 1

4x - 2y + z = -5

17x -3y = 13

We then have the first and third rows having two variables. Since the y coefficients are the same, we can eliminate the y by adding the negative of the first row to the third row. Our result is then

11x - 3y = 1

4x - 2y + z = -5

6x = 12

From the third row, we can gather that x= 2. We can then plug that into the first row to get

22 -3y = 1

subtract 22 from both sides

-3y = -21

divide both sides by -3

y = 7

We can then plug our x and y values into the second row to get

4(2) - 2(7) + z = -5

8 - 14 + z = -5

-6 + z = -5

add 6 to both sides

z = 1

Our answer is thus (2, 7, 1)

Answer:

i need more information to answer this question

Step-by-step explanation:

Answer:

1. 5 min : 3 min

2. 10 cm : 7 cm

3. 9 sec : 10 sec

Step-by-step explanation:

1. Since 60 minutes = 1 hour

Thus;

100 minutes : 60 minutes

10 minutes : 6 minutes

5 minutes : 3 minutes

The simplest form = (5:3) minutes

2. 100 cm = 1 m,

⇒ 15 m =  15 x 100 cm = 1500 cm

Thus;

1500 cm : 1050 cm

150 cm : 105 cm

30 cm : 21 cm

10 cm : 7 cm

The simplest form = (10:7) cm

3. 60 seconds = 1 minute

⇒ 9 minutes = 9 x 60

                 = 540 seconds

Thus;

540 seconds : 600 seconds

54 seconds : 60 seconds

9 seconds : 10 seconds

The simplest form = (9:10) seconds

4. A common fraction is one that has the same value on each side of an expression or equation.

Answer:

x = 29

Step-by-step explanation:

The three angles add to 90 degrees

x+3  + x-1   + x+1 = 90

Combine like terms

3x +3 = 90

Subtract 3 from each side

3x+3-3 = 90-3

3x = 87

Divide by 3

3x/3 = 87-3

x = 29

Answer:

x = 29

Step-by-step explanation:

The 3 angles sum to 90° , that is

x + 3 + x - 1 + x + 1 = 90

3x + 3 = 90 (subtract 3 from both sides )

3x = 87 ( divide both sides by 3 )

x = 29

Answer:

pq=su

Step-by-step explanation:

its the only one that makes sense

Answer:

184

Step-by-step explanation:

A = 2(wl+hl+hw) = 2 · (6 · 2 + 10 · 2 + 10 · 6) = 184

Answer:

SA = 184 m²

Step-by-step explanation:

The opposite faces of the cuboid are congruent , then surface area (SA) is

SA = 2(2 × 6) + 2(6 × 10) + 2(2 × 10)

     = 2(12) + 2(60) + 2(20)

     = 24 + 120 + 40

     = 184 m²

Answer:

Value of opposite ∠2 = 120°

Step-by-step explanation:

Given question:

Quadrilateral inscribed in a circle

Value of ∠1 = 60°

Find:

Value of opposite ∠2

Computation:

In Quadrilateral inscribed in a circle, sum of opposite angle is 180

So,

Value of ∠1 + Value of ∠2 = 180°

60 + Value of ∠2 = 180

Value of ∠2 = 180 - 60

Value of ∠2 = 120

Value of opposite ∠2 = 120°

Step-by-step explanation:

Given that,

The length of a ladder, H = 20 feet

The height of the wall, h = 15 ft

We know that,

[tex]\sin\theta=\dfrac{h}{H}[/tex]

h is perpendicular and H is hypotenuse

So,

[tex]\sin\theta=\dfrac{15}{20}\\\\\theta=\sin^{-1}(\dfrac{15}{20})\\\\\theta=48.59^{\circ}[/tex]

Now using Pythagoras theoerm,

[tex]b=\sqrt{H^2-h^2}\\\\b=\sqrt{20^2-15^2}\\\\b=13.2\ ft[/tex]

Hence, the angle made by the ladder and the ground is 48.59° and the ladder is 13.2 feet from the wall on the ground.

Step-by-step explanation:

mmm Next no se...........

A -> A

B -> E

C -> D

Theyre similar triangles, ABC = AED

The corresponding vertex of the similar triangles are

A ≈ A

B ≈ E

C ≈ D

The triangles ABC and AED are similar triangles

What are similar triangles?

If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.

Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides

Given data ,

Let the first triangle be represented as ABC

Let the second triangle be represented as AED

The measure of AB = 3

The measure of AD = 8

The measure of AC = 4

The measure of AE = 6

Now , for the similar triangles , corresponding sides of similar triangles are in the same ratio

So ,

AB / AE = AC / AD

Substituting the values in the equation , we get

3/6 = 4/8

1/2 = 1/2

Therefore , the triangles are similar

Hence , the triangles ABC and AED are similar triangles

To learn more about similar triangles click :

https://brainly.com/question/29378183

#SPJ2

Answer:

3 x 5 is the gcf of 45 and 75. gcf(45,75) = 15.

Step-by-step explanation:

hope this helped! yw :}

Answer:

third side = 4

Step-by-step explanation:

third side is hypoenuse as it is opposite to 90 degree.

using pythagoras theorem

(perpendicular)^2 + (base)^2 = (hypotenuse)^2

2^2 + (2[tex]\sqrt{3[/tex] )^2 = hypotenuse^2

4 + 4*3 = hypotenuse^2

16 = hypotenuse^2

[tex]\sqrt{16}[/tex] = hypotenuse

4 = hypotensue

Answer:

- 2x² + 2x + 11

Step-by-step explanation:

Given

x² + 6 - (3x² - 2x - 5) ← distribute parenthesis by - 1

= x² + 6 - 3x² + 2x + 5 ← collect like terms

= - 2x² + 2x + 11

Answer:

Step-by-step explanation:

Answer:

30cm x 72 cm

Step-by-step explanation:

The perimeter is the measurements of all sides added together. Let's start by dividing the perimeter by 2, so we have the sum of the length and width. This gives us 102cm. Let's call the width x, and the length y. We know y is x times 2 plus 12. (2x + 12) So, we know [x + y = x + (2x + 12)]. So let's solve.

x + y = x + (2x + 12)

102 = x + (2x + 12)

102 = 3x + 12

102 - 12 = 3x + 12 - 12

90 = 3x

90/3 = 3x/3

30 = x

The width is 30cm.

Answer:

11

Step-by-step explanation:

Answer:

[tex]{ \tt{ = \frac{7 {p}^{2} \times 3p}{14 {p}^{4} } }} \\ = { \tt{ \frac{21 {p}^{3} }{14 {p}^{4} } }} \\ = { \tt{1.5 {p}^{ - 1} }}[/tex]

Answer:

Let length be x and width be y

[tex]perimeter = 2(l + w) \\ 600 = 2(x + y) \\ x + y = 300 - - - (a) \\ \\ area = l \times w \\ 21600 = xy - - - (b) \\ from \: (a) : \\ y = 300 - x \\ \therefore21600 = x(300 - x) \\ 21600 = 300x - {x}^{2} \\ {x}^{2} - 300x + 21600 = 0 \\ (x - 180)(x - 120) = 0 \\ x = 180 \: \: or \: \: 120 \: m \\ \\ y = 120 \: \: or \: \: 180 \: m \\ \\ { \boxed{ length = 180 \: m}} \\ { \boxed{width = 120 \: m}}[/tex]

Answer:

x = 39°

Step-by-step explanation:

51° + 90° = 141°

180° - 141° = x

x = 39°

They often don't label the 90° angle, so watch out for that in the future

Answer:  [tex]3\dfrac{2}{6}\ h[/tex]

Step-by-step explanation:

Given

Rami practices his saxophone for [tex]\frac{5}{6}[/tex] hour on 4 day each week

So, for a week she practices around

[tex]\Rightarrow \dfrac{5}{6}\times 4\\\\\Rightarrow \dfrac{20}{6}[/tex]

Converting it into mixed fraction

[tex]\Rightarrow \dfrac{20}{6}=\dfrac{18+2}{6}\\\\\Rightarrow 3\dfrac{2}{6}\ h[/tex]

Answer:

33/100

Step-by-step explanation:

Answer:

f(x) = 30 • 0.989x

Step-by-step explanation:

Given the data :

10 26.8

20 23.9

30 21.3

40 19

50 16.9

60 15.1

Using technology, the exponential model equation obtained by plotting the data is :

y = 30.068(0.989)^x

Based on the general exponential formula :

y = ab^x

y = predicted value

Initial value, a = 30.068

Rate = b = 0.989

The most appropriate model equation from the options given is :

f(x) = 30 • 0.989^x

Answer:

11.5 degrees

Step-by-step explanation:

For future reference trianglecalculator.net is very helpful

The angle of elevation to the nearest tenth of a degree is 11.54°.

An angle of elevation is defined as the angle between the slant horizontal line of an eye and the object in relation to the baseline called the adjacent.

In trigonometry, the angle of elevation can be determined by using the sine rule.

[tex]\mathbf{sin \ \theta = \dfrac{opp}{hyp} }[/tex]

[tex]\mathbf{sin \ \theta = \dfrac{5}{25} }[/tex]

[tex]\mathbf{ \theta =sin^{-1} (0.2)}[/tex]

[tex]\mathbf{ \theta =11.54^0}[/tex]

Learn more about the angle of elevation here:

https://brainly.com/question/88158

Answer:

your answer to this question is C.

∠ABC = 76°

BC = 20.1

CA = 28.0

Solving the triangle means finding all unknown angles and sides of the triangle.

(i) Two of the angles (∠BCA = 60° and ∠CAB  = 44°) are given. To find the third angle (∠ABC), use one of the theorems stating that the sum of angles of a triangle is equal to 180°.

Therefore, the sum of angles of the triangle ABC is 180°. i.e

∠ABC + ∠BCA + ∠CAB = 180°

=> ∠ABC + 60° + 44° = 180°

=> ∠ABC + 104° = 180°

=> ∠ABC = 180° - 104°

=> ∠ABC = 76°

(ii) One side (BA) of the triangle is given. To get the other sides, we use the sine rule as follows;

=> [tex]\frac{sin60}{25} = \frac{sin44}{BC} = \frac{sin76}{CA}[/tex]

=> [tex]\frac{sinBCA}{BA} = \frac{sinCAB}{BC} = \frac{sinABC}{CA}[/tex]

Substitute the necessary values

[tex]\frac{sin60}{25} = \frac{sin44}{BC} = \frac{sin76}{CA}[/tex]      ---------------------(ii)

(a) To get side BC, use the first two terms of equation (ii)

[tex]\frac{sin60}{25} = \frac{sin44}{BC}[/tex]

Cross multiply

BC x sin 60 = 25 x sin 44

BC x 0.8660 = 25 x 0.6947

0.8660 x BC = 17.3675

BC = [tex]\frac{17.3675}{0.8660}[/tex]

BC = 20.05

=> BC = 20.1 to the nearest tenth

(b) To get CA, use any two terms of equation (ii). Using the first and third terms, we have;

[tex]\frac{sin60}{25} = \frac{sin76}{CA}[/tex]

Cross multiply

CA x sin 60 = 25 x sin 76

CA x 0.8660 = 25 x 0.9703

0.8660 x CA = 24.2575

CA = [tex]\frac{24.2575}{0.8660}[/tex]

CA = 28.01

=> CA = 28.0 to the nearest tenth

Answer:

1/4

Step-by-step explanation:

Answer:

[tex]x=10[/tex]

Step-by-step explanation:

For all right triangles, the Pythagorean Theorem states:

[tex]a^2+b^2=c^2[/tex], where [tex]c[/tex] is the hypotenuse, or the longest side, of the right triangle.

Therefore, we have (starting from the blanks):

[tex]x^2+576=676,\\x^2+576-676=676-676,\\x^2=100,\\x=\boxed{10}[/tex]

Answer:

The expanded form of 6,398 is 6000 + 300 + 90 + 8

Answer:

translated 5 units to the right

Step-by-step explanation:

Answer:

Solution given:

letA=(10,-4)

B=(-2,-4)

centre[C](h,k)=[tex]\frac{10-2}{2},\frac{-4-4}{2}=(+4,-4)[/tex]

radius=[tex]\sqrt{(4-10)²+(-4+4)²}=6[/tex]units

we have

Equation of a circle is;

(x-h)²+(y-k)²=r²

(x-4)²+(y+4)²=36

or.

x²-8x+16+y²+8y+16=36

x²-8x+8y+y²=36-32

x²-8x+8y+y²=4

The equation is (x-4)²+(y+4)²=36 or x²-8x+8y+y²=4.

Answer:

[tex] \rm\displaystyle (x - 4) ^{2} + {(y + 4)}^{2} = 36[/tex]

Step-by-step explanation:

the given points are the diameter points of circle because notice that in the both points y coordinate is the same therefore it's a horizontal diameter

since (10,-4),(-2,-4) are the diameter points of the circle the midpoint of the diameter will be the centre of the circle

remember midpoint formula,

[tex] \displaystyle M = \left( \frac{x _{1} + x_{2} }{2} , \frac{ y_{2} + y_{2}}{2} \right)[/tex]

let,

thus substitute:

[tex] \rm\displaystyle M = \left( \frac{10 + ( - 2)}{2} , \frac{ - 4 + ( - 4)}{2} \right)[/tex]

simplify addition:

[tex] \rm\displaystyle M = \left( \frac{8}{2} , \frac{ - 8}{2} \right)[/tex]

simplify division:

[tex] \rm\displaystyle M = \left( 4, - 4 \right)[/tex]

so the centre of the circle is (4,-4)

since it's a horizontal diameter the the redious will be the difference between the x coordinate of the Midpoint and the any x coordinate of the given two points but I'll use (-2,-4) therefore the redious is

[tex] \displaystyle r = 4 - ( - 2)[/tex]

simplify which yields:

[tex] \displaystyle\boxed{ r =6}[/tex]

recall the equation of circle

[tex] \displaystyle (x - h) ^{2} + {(y - k)}^{2} = {r}^{2} [/tex]

we acquire that,

therefore substitute:

[tex] \rm\displaystyle (x - 4) ^{2} + {(y - ( - 4))}^{2} = {6}^{2} [/tex]

simplify:

[tex] \rm\displaystyle (x - 4) ^{2} + {(y + 4)}^{2} = 36[/tex]

and we are done!

also refer the attachment

(the graph is web resource of desmos)