Slope of line y = -2x+ 4

Check the picture below.

let's notice those two corresponding angles of 90° - 2x, and also recall that the sum of all interior angles in a triangle is 180°.

[tex]\bf 60+3x+(90-2x)=180\implies x+150=180\implies x=30[/tex]

Answer:

The cotangent of 61.6° is .5407.

Step-by-step explanation:

Refer to the sketch attached.

61.6° + 28.4° = 90°. In other words, 61.6° is the complementary angle of 28.4°.

Consider a right triangle OAB with a 61.6° angle [tex]\rm O\hat{A}B[/tex]. The other acute angle [tex]\rm O\hat{B}A[/tex] will be 28.4°.

[tex]\displaystyle \tan{61.6\textdegree{}}=\tan{\rm O\hat{A}B} = \frac{\text{Opposite of }\rm O\hat{A}B}{\text{Adjacent of }\rm O\hat{A}B} = \frac{a}{b}[/tex].

The cotangent of an angle is the reciprocal of its tangent.

[tex]\displaystyle \cot{61.6^{\circ}}=\frac{1}{\tan{\rm O\hat{B}A}} = \frac{\text{Adjacent of }\rm O\hat{B}A}{\text{Opposite of }\rm O\hat{B}A} = \frac{a}{b} = \tan{\rm O\hat{A}B} = \tan{28.4^{\circ}}[/tex].

In other words,

[tex]\cot{61.6^{\circ}} = \tan{28.4^{\circ}} \approx 0.5407[/tex].

Answer:

Option a: Line slants down.

Step-by-step explanation:

 It is important to remember that the equation of the line in Slope-Intercept form is the following:

[tex]y=mx+b[/tex]

Where "m" is the slope of the line and "b" is the y-intercept.

The slope of a line can be positive (The line slopes upwards to the right), negative (The line slopes downwards to the right), zero (Horizontal line), or undefined (Vertical line).

Therefore, the statement that best describes a line in a slope-intercept form when the coeficient of the x-term (The slope) is negative is: "Line slants down".

Answer:

C

Step-by-step explanation:

The vertical line test is basically just drawing a vertical line and seeing if the line intersects the graph more than once. If it does, then it is not a function, if it doesn't than it is a function.

Answer:

C

Step-by-step explanation:

Mapping A shows x--->y. A is the answer. Exactly one x value is matched to exactly one y value.

Answer:

(2.5, - 2)

Step-by-step explanation:

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

(2.5, - 2 ) ← point of intersection

Answer:

Option D is the correct answer.

Step-by-step explanation:

Refer the given figure showing the graph.

We can see the point of intersection is (2.5, -2).

Option D is the correct answer.

Alternatively:

2x + y = 3  ---------------------eqn 1

2x - 5y = 15  ---------------------eqn 2

eqn1 - eqn 2 gives

  2x + y - ( 2x - 5y) = 3 - 15

           6y = -12

             y = -2

Substituting in eqn 1

         2x - 2 = 3

            x = 2.5

Point of intersection is (2.5, -2).

Option D is the correct answer.

Answer:

Step-by-step explanation:

6,-5 ON APEXXXXX

Answer: (6, -5)

Step-by-step explanation:

The general equation of a circle is given by :-

[tex](x-h)^2+(y-k)^2=r^2[/tex], where (h,k) is center and r is radius of the circle.

Given : The equation of a circle : [tex](x-6)^2+(y+5)^2=15^2[/tex]

[tex]\Rightarrow\ (x-6)^2+(y-(-5))^2=15^2[/tex]

Comparing to the general equation of circle , we get

[tex](h,k)=(6, -5)[/tex]

Hence, the coordinates of the center of the circle = (6, -5)

Answer:  Nick

Step-by-step explanation:

Nick is the one who will go to bed first because he needs the most sleep. Nick needs 10 hours of sleep, then it would be Brad who needs 9 , then Will who needs 8

Nick will be the first to bed on Friday evening out of Will, Brad, and Nick.

On Friday evening, Nick would be the first to bed among Will, Brad, and Nick. Nick needs 10 hours of sleep every night, so to wake up at 6 a.m. on Saturday, he would have to go to bed earlier than Will and Brad who need 8 and 9 hours of sleep, respectively.

Answer:

Step-by-step explanation:

Remember, a sphere is defined as a three-dimensional object where all points on its surface are equidistant form its center.

According to its definition, all point on the boundaries can be called a point on the sphere.

So, among the options, only point B is on the sphere, because J and S are inside.

Therefore, the right answer is Point B.

Answer:

No, because they look like they are different sizes. Or you could say the first answer

Hello There!

The answer is "C"

In this problem, you need dilation to map onto each-other.

Dilation is transformation hat changes the size of something

[tex]\bf (-5u)(-5u)(-5u)(-5u)\implies (-5u)^1(-5u)^1(-5u)^1(-5u)^1 \\\\\\ (-5u)^{1+1+1+1}\implies (-5u)^4\implies (-5)^4u^4\implies 625u^4[/tex]

Answer:

20/6 or 3.33 or 3 1/3 or 3 hours and 20 mins

Step-by-step explanation:

5/6 * 4 = (5*4)/6 = 20/6

Answer:

she will have praticed 3 hours and 20 min

Step-by-step explanation:

Answer:

x = 2

Step-by-step explanation:

Given 2 secants intersecting a circle from an external point, then

The product of the external part and the entire part of one secant is equal to the product of the external part and the entire part of the other secant, that is

(x + 1)(x + 1 + 11) = (x + 4)(x + 4 + 1)

(x + 1)(x + 12) = (x + 4)(x + 5) ← expand both sides

x² + 13x + 12 = x² + 9x + 20

Subtract x² + 9x from both sides

4x + 12 = 20 ( subtract 12 from both sides )

4x = 8 ( divide both sides by 4 )

x = 2

Answer:

22.5 pages

Step-by-step explanation:

First divide the page number by the minutes it takes to read them to find pages per minute-

4.5 / 12 = .375

Then take that number and multiply it by the minutes in an hour-

(.375) (60) = 22.5

22.5 pages in one hour.

Answer:

22 1/2 pages

Step-by-step explanation:

60/12 = 5

5(4.5) = 22 1/2

Answer:

the square root of thirteen is 3.6

Step-by-step explanation:

if you put the 13 with the square root box and press the = button you will get the square root of 13 is 3.6

Answer:

Option B , D and E are correct.

Step-by-step explanation:

We set the denominator equal to zero to find the number to put in division box

So, if 3 is in the division box then the denominator will be

x-3 = 0 => x=3 is the root.

So, Option E is correct

2x^2-2x-12 ÷ x-3 = 2x+4 is correct.

because after division the result given is 2x+4 which is correct.

So, Option B is correct

x-3 is a factor of 2x^2-2x-12 because because when the term is divided we get the remainder 0.

So, Option D is correct

So, Option B,D and E are correct.

Answer:

Step-by-step explanation:

the nth term of the geometric sequence  is :  An =A1 × r^(n-1)

A1 = -10

r= -40/20=20/-10=-2

n =11

A11 = -10× (-2)^(11-1)

A11 = -10× (-2)^(10)

A11 = - 10240

Answer:

-10,240.

Step-by-step explanation:

This is a geometric sequence with common ratio 20/-10 = -40/20 = -2.

The nth term = a1r^(n-1)   where a1 = the first term and r = the common ratio, so the 11th term = -10 * (-2)^ (11-1)

= -10 * 1024

= -10,240.

To find the volume of the new sphere, calculate the volume of the original sphere and then multiply it by the scale factor cubed. Convert the volume from cubic centimeters to cubic inches using the conversion factor: 1 cm³ = 0.0610237 in³. The approximate volume of the new sphere in cubic inches is 255.3 in³.

To find the volume of the new sphere, we need to first find the volume of the original sphere and then multiply it by the scale factor cubed. The formula for the volume of a sphere is V = (4/3)πr³, where r is the radius.

Given that the radius of the original sphere is 5 cm, we can calculate its volume using the formula:

V1 = (4/3)π(5 cm)³ ≈ 523.6 cm³.

Next, we can calculate the volume of the new sphere by multiplying the volume of the original sphere by the scale factor cubed:

V2 = V1 × (2)³ = 523.6 cm³ × 8 ≈ 4188.8 cm³.

Finally, to convert the volume from cubic centimeters to cubic inches, we need to use the conversion factor: 1 cm³ = 0.0610237 in³. Therefore, the approximate volume of the new sphere in cubic inches is:

V2 ≈ 4188.8 cm³ × 0.0610237 in³/cm³ ≈ 255.3 in³.

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Answer:

14! Hope you ace your test!!

Step-by-step explanation:

The value of the side 'a' will be 14 units.

The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.

The value of a is calculated as:-

Sin 30  =  P / H

Sin  30  =  7  /  a

1  /  2  =  7  /  a

a  =  7  x  2

a  =  14 units

Therefore the value of the side 'a' will be 14 units.

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Answer:

The original price of the car can be written in percentage which is 100%. Because the price increased by 6%, therefore, the new price should be represented as:

100% + 6% = 106% = 1.06 (remember: not 0.06, that is how much the price increased, not 0.94 either, because the price increased, not decreased).

So the answer for the first question should be:

(a) new price = 1.06 × original price

from that, we can appy the answer above for the second question:

(b) new price: $33390

Answer:

B and E

Step-by-step explanation:

By looking at the discriminant, which is [tex]b^2-4ac[/tex], you get that [tex]5^2-4*1*7=25-28=-3[/tex]. Therefore, the only two answers with a -3 inside the square root are B and E.

Answer:

B & E

Step-by-step explanation:

see attached

Answer:

25

Step-by-step explanation:

look B=C

so,

A+B+C=180 Sum of all <s of Tri

x+5+3x+3x=180

7x=175

x=175÷7

x=25

Answer: A or 25

Step-by-step explanation:

did the exam on edge 2020

Answer:

C

Step-by-step explanation:

(f - g)(x) = f(x) - g(x)

f(x) - g(x) = [tex]4^{x}[/tex] - 8 - (5x + 6)

              = [tex]4^{x}[/tex] - 8 - 5x - 6 ← collect like terms

              = [tex]4^{x}[/tex] - 5x - 14 → C

Answer:

(3 x - 2) (4 x + 3)

Step-by-step explanation:

Factor the following:

12 x^2 + x - 6

Factor the quadratic 12 x^2 + x - 6.

The coefficient of x^2 is 12 and the constant term is -6.

The product of 12 and -6 is -72. The factors of -72 which sum to 1 are -8 and 9.

So 12 x^2 + x - 6 = 12 x^2 + 9 x - 8 x - 6 = 3 (3 x - 2) + 4 x (3 x - 2):

3 (3 x - 2) + 4 x (3 x - 2)

Factor 3 x - 2 from 3 (3 x - 2) + 4 x (3 x - 2):

Answer:  (3 x - 2) (4 x + 3)

The answer is (3 x - 2) (4 x + 3).

Polynomial exists an algebraic expression with terms divided utilizing the operators "+" and "-" in which the exponents of variables exist always nonnegative integers.

Factor the following:

[tex]$$12x^{2}+x-6$$[/tex]

Factor the quadratic

[tex]$12x^{2} +x-6$[/tex]

The coefficient  [tex]x^{2}[/tex] is 12 and the constant term is -6.

The product of 12 and -6 is -72.

The factors of -72 which sum to 1 exist at -8 and 9.

So

[tex]$12 x^{2} +x-6=12 x^{2} +9 x-8 x-6[/tex]

[tex]=3(3 x-2)+4 x(3 x-2)$[/tex]

[tex]$3(3 x-2)+4 x(3 x-2)$[/tex]

Factor 3 x - 2 from 3 (3 x - 2) + 4 x (3 x - 2)

Hence, The answer is (3 x - 2) (4 x + 3).

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Answer:

12x=2pi*r

Step-by-step explanation:

2*22/7*r=12x

r=12x*7/44

r=21x/11

The radius of a circle is calculated by dividing the given circumference by 2π. When given circumferences of 6 inches, 6π inches, 12 inches, and 24π inches, the corresponding radii are approximately 0.955 inches, 3 inches, 1.91 inches, and 12 inches, respectively.

To find the radius of a circle given its circumference, we use the formula for the circumference of a circle, which is C = 2πr, where C is the circumference and r is the radius. Since we are given the circumference, we can rearrange this formula to solve for the radius as follows: r = C / (2π).

Given the possible circumferences provided, we can calculate the radius for each.

For 6 inches: r = 6 / (2π) = 6 / (2 * 3.14) = 6 / 6.28 = approximately 0.955 inches

For 6π inches: r = 6π / (2π) = 6 / 2 = 3 inches

For 12 inches: r = 12 / (2π) = 12 / (2 * 3.14) = 12 / 6.28 = approximately 1.91 inches

For 24π inches: r = 24π / (2π) = 24 / 2 = 12 inches

Answer:

Δ TUW ≅ ΔVWU ⇒ by AAS case

Step-by-step explanation:

* Lets revise the cases of congruent for triangles

- SSS  ⇒ 3 sides in the 1st Δ ≅ 3 sides in the 2nd Δ

- SAS ⇒ 2 sides and including angle in the 1st Δ ≅ 2 sides and  

 including angle in the 2nd Δ  

- ASA ⇒ 2 angles and the side whose joining them in the 1st Δ  

 ≅ 2 angles and the side whose joining them in the 2nd Δ  

- AAS ⇒ 2 angles and one side in the first triangle ≅ 2 angles

 and one side in the 2ndΔ

- HL ⇒ hypotenuse leg of the first right angle triangle ≅ hypotenuse

 leg of the 2nd right angle Δ

* Lets solve the problem

- There are two triangles TUW and VWU

- ∠T and ∠V are right angles

- LINE TW is parallel to line VU

∵ TW // VU and UW is a transversal

∴ m∠VUW = m∠TWU ⇒ alternate angles (Z shape)

- Now we have in the two triangles two pairs of angle equal each

 other and one common side, so we can use the case AAS

- In Δ TUW and ΔVWU

∵ m∠T = m∠V ⇒ given (right angles)

∵ m∠TWU = m∠VUW ⇒ proved

∵ UW = WU ⇒ (common side in the 2 Δ)

∴ Δ TUW ≅ ΔVWU ⇒ by AAS case

Answer:

Step-by-step explanation:

Given ∠T and ∠V are right angles.

TW ║ UV

To prove ⇒ ΔTUW ≅ ΔVWU

Proof ⇒ In ΔTUW and ΔVUW,

∠T ≅ ∠ V ≅ 90° (given)

Side UW ≅ UW ( Common in both the triangles )

TW ║ UV

and UW is a transverse.

So ∠TWU ≅ ∠WUV [alternate interior angles]

Since Angle = Angle = side are equal

Therefore, ΔTUW ≅ ΔVWU

Answer:

(x-8) (x+5)

Step-by-step explanation:

x^2-3x-40

What 2 numbers multiply to -40 and add to -3

-8 *5 = -40

-8+5 = -3

(x-8) (x+5)

Answer:

24x - 20

Step-by-step explanation:

4(6x-5)

= 4(6x) - 4(5).............. (Distributive property)

= 24x - 20 (Ans)

Hello There!

The answer would be (24x-20)

We use order of operations so first we would multiply 4 by 6 and get 24x

then, we would multiply 4 by -5 and get -20

Your answer would be 24x - 20