The line y = 2x + 6 cuts the x-axis at A and the y-axis at B. Find
(a) the length of AB,
(b) the shortest distance of O to AB, where O is the origin (0,0)​

Answers

Answer 1

Answer:

(a)

[tex]3 \sqrt{5} [/tex]

(b)

[tex] \frac{6}{ \sqrt{5} } [/tex]

Step-by-step explanation:

A(-3,0)

B(0,6)

[tex]d = \sqrt{{( - 3 - 0)}^{2} + {(0 - 6)}^{2} } = \sqrt{9 + 36} = 3 \sqrt{5} [/tex]

[tex]d = \frac{ax0 + by0 + c}{ \sqrt{ {a}^{2} + {b}^{2} } } [/tex]

2x-y+6=0

a=2, b=-1, c=6

x0=0, y0=0

[tex]d = \frac{6}{ \sqrt{4 + 1} } = \frac{6}{ \sqrt{5} } [/tex]


Related Questions

Which of the following terms is best described as the point halfway between
the endpoints of a line segment?
O A. Midpoint
O B. Ordered pair
O C. Coordinate
O D. Vertex

Answers

The answer should be A midpoint

The number 6 is a solution to which of the following inequalities?
X - 13 > 7
6x < -12
6x > 32
21 + x < 28

Answers

Answer

6x<-12

Step-by-step explanation:

Answer:

There would be 2 answers in this case:

C. 6x > 32

and

D. 21 + x < 28

Step-by-step explanation:

A. Incorrect

6-13 = -7, and -7 is NOT greater than 7

B. Incorrect

6(6) = 36, and 36 is NOT less than -12.

C. Correct

6*6 = 36, which is greater than 32.

D. Correct

21+6 = 27, which is less than 28.

measured the volume of an object and recorded it as 46 cubic cm
which was 15% high from the actual volume. Find the actual volume.

Answers

Answer:

[tex]40\ cm^3[/tex]

Step-by-step explanation:

Let the actual volume is V.

The measured volume of an object is 46 cubic cm  which was 15% high from the actual volume.

According to the given condition,

[tex]V+\dfrac{15V}{100}=46\\\\\dfrac{115V}{100}=46\\\\V=\dfrac{4600}{115}\\\\V=40\ cm^3[/tex]

So, the actual volume was [tex]40\ cm^3[/tex].

What is the product?

Answers

21x^7y^11 ur welcome cuh

find 22×28×25×30 in acres?

Answers

Answer:

22x 28 x 25 x 30 = 462000

whats are the units.....cm or m

[tex]\huge\text{Hey there!}[/tex]

[tex]\large\textsf{22(28)(25)(30)}\\\large\textsf{22(28) = \bf 616}\\\large\textsf{616(25)(30)}\\\large\textsf{616(25) = \bf 15,400}\\\large\textsf{15,400(30)}\\\large\textsf{ = \bf 462,000}\\\\\\\\\\\\\boxed{\boxed{\large\textsf{Answer: \huge \bf 462,000}}}\huge\checkmark[/tex]

[tex]\large\textsf{Good luck on your assignment and enjoy day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Please help me solve this problem

Answers

multiply both sides by lh, V=wlh

Answer:

V = wlh

Step-by-step explanation:

Given

w = [tex]\frac{V}{lh}[/tex] ( multiply both sides by lh to clear the fraction )

wlh = V

Can some help with this problem

Answers

30
As it an equilateral so it would be 60
Its split into two 60/2 = 30

Can someone please help me with this?

Answers

Answer is x=1.5 100% jus took it lol

the principal argument of z = —4+i4√3 is​

Answers

Answer:

Let z=−4+0i. Then, ∣z∣=

(−4)

2

+0

=4

Clearly, the point (−4,0) representing z=−4+0i lies on the negative side of real axis. Therefore, principal argument of z is π.

Someone pls help me ill give out brainliest pls don’t answer if you don’t know

Answers

Answer:

(1/3) r2 =(1/3) r +14

1/6 divided by 83 r + 14

97r

i think...

I hope this helps you!

XoXo Mashayla

Step-by-step explanation:

30g of cornflakes contain 2.5 grams of fat how many grams of fat are there in 320g of cornflakes

Answers

Hello :)

Use proportionality

We know that :

30g of cornflakes ⇒ 2.5g of fat

320g of cornflakes ⇒ xg of fat

x = 320 * 2.5 ÷ 30 ≈ 26.7 g of flat

Have a nice day!

(-9g5+ 9) + (4g5- 5)

Answers


−9​g5+9+4g5−5

−9g5+4g5+9−5

−5g5+9−5

Answer: −5g5+4



Simplify 5^3 x 5^4

5^12
5^7
25^12
25^7

Please help ASAP. Please. The answer is one of those above.

Answers

Answer:

5⁷

Step-by-step explanation:

5³×5⁴

when bases are same powers are added

so..

5(³+⁴)

5⁷

Answer:

5^7

Step-by-step explanation:

Think of it like x^3 * x^4. Since when two variables with exponents are multiplied, the exponents are added, you get x^7. (But just use 5 instead of x.)

You can also check by seeing the result of 5^3*5^4 is 78,125 and 5^7 is also 78,125. Hope that helps!

Choose the answer that is equivalent to the quotient.
(-4x3 + 16x2 21x + 22) divided by (2x – 3)
0-222 +51 - 3+
13
21-3
o 22 – 3+3
O-212 + 52 - 3+
16
21-3
0-222 + 52 - 3

Answers

I believe it would be B sorry if I’m wrong

What is 8 x 3 + 10 - 13 x 2? Show your work.
Will give first answer brainliest

Answers

Hello!

8 × 3 + 10 - 13 × 2 =

= 24 + 10 - 13 × 2 =

= 24 + 10 - 26 =

= 34 - 26 =

= 8

Good luck! :)

Answer:

8

Step-by-step explanation:

According to bdmas rule

First multiply 8 and 3 or 13 and 2

Then, there will be 24 + 10 - 26

Then add 24 + 10, there will be 34

and again minus by 26

Then finally answer will be 8

During his lunch hour, Matt asked 24 students how many after-school activities they participated in. This list shows the survey results.

Answers

Answer:

[tex]Ratio = 1 : 6[/tex]

Step-by-step explanation:

Given

[tex]n = 24[/tex]

Results:

[tex]1, 2, 0, 0, 3, 2, 4, 2, 1, 4, 3, 2[/tex]

[tex]1, 1, 2, 1, 0, 3, 3, 2, 4, 1, 1, 0[/tex]

Required

Ratio of students not participating to all students

Students not participating are represented with 0;

So, we have:

[tex]n(0)= 4[/tex]

The ratio is then calculated as:

[tex]Ratio = n(0) : n[/tex]

[tex]Ratio = 4 : 24[/tex]

Divide by 4

[tex]Ratio = 1 : 6[/tex]

what is the slope of the line shown below (6, 6) (1, -4)

Answers

Answer:

2

Step-by-step explanation:

To find the slope of a line, you must get two points off the line

Two points will be: (6, 6) and (1, -4)

Then use the Slope-Formula to solve for the slope of the line

m = slope
m = y2-y1/x2-x1
m = -4-6/1-6
m = -10/-5
m = 10/5
m = 2

The Slope of the line is 2

Answer:

2

Step-by-step explanation:

if you're looking at the table and you heard of rise/run, your rise is -10 if you go down from (6,6) and -5 if you go left to reach (1,-4). That will give you -10/-5 which gives you a positive 2. it would be the same if you went up 10 from (1,-4) and then 5 right to reach (6,6).

You are selecting meals for a school event and you are planning on at least 240 students at this event. The chicken meal will cost $5 and the beef meal will cost $8 per serving. Your total budget is $1200.00. Select a system of linear inequalities that shows the various numbers of Chicken and Beef meals you can prepare. Let x = number of chicken meals and let y = number of beef meals.

Answers

Answer:

x + y ≥ 240

5x + 8y ≤ 1200

Step-by-step explanation:

Assume;

Number of chicken meals = x

Number of Beef meals = y

Total budget = $1200

Find:

Inequality

Computation:

Number of chicken meals + Number of Beef meals  ≥ Total students

x + y ≥ 240

Total cost = (Number of chicken meals)(Cost of chicken meal) + (Number of Beef meals)(Cost of beaf meal)

5x + 8y ≤ 1200

Find the measure of the indicated angle.

Answers

2x + 40 = 180

2x = 140

x= 70

answer is 70

find the area of the rhombus. pic included, thank you

Answers

Answer:

80in 2

Step-by-step explanation:

Answer:

a=(d1×d2)÷2

(20×12)÷2

240/2

120

A tower is 543m from your house. The angle of elevation to the top of the tower is 33.4°. How high is the tower?

Answers

Answer:

358

Step-by-step explanation:

the step by step is in the photo so look at it

358 is the correct answer

A sum of money earns the interest ar the rate of Rs. 5 per Rs.25 in a year. how many years would it trible itself?
a. 5
b. 10
c.15
d. 20​

Answers

the sun to this is d. 20

Sandra y José son dos amigos que se encuentran en diferentes partes de la ciudad de Lima (Observa el plano), la distancia que los separa en el plano es de 7 cm ellos quisieran saber ¿Cuál es la distancia real en metros que los separa? Sabiendo que el plano ha sido dibujado a escala 1: 20 000.

Answers

Respuesta:

1,4 kilometros

Explicación paso a paso:

Dado que :

Distancia que separa a Sandra y José en el mapa = 7cm

Dibujo a escala = 1: 20.000; Esto se puede interpretar en el sentido de que 1 cm en el mapa equivale a 20.000 cm en el suelo.

Por tanto, una distancia de 7 cm en el mapa será:

20.000 * 7 = 140.000 cm en el suelo = distancia real

Por lo tanto, la distancia real = 140.000 cm.

Recordar :

1 cm = 10 ^ -5 km

140000 cm = 1.4 kilometros

Por lo tanto, la distancia real entre Sandra y José es de 1,4 km.

using the formula of Sin 2A ,cos2a and tan 2a establish that; tab A is = +- root under 1 - cos 2A by 1 + cos 2a​

Answers

Answer:

Step-by-step explanation:

Given identity is,

[tex]\text{tanA}=\pm\sqrt{\frac{1-\text{cos2A}}{1+\text{cos2A}}}[/tex]

To prove this identity, we will take left side of the identity,

[tex]\pm\sqrt{\frac{1-\text{cos2A}}{1+\text{cos2A}}}=\pm\sqrt{\frac{1-(1-2\text{sin}^2A)}{1+(2\text{cos}^2A-1)} }[/tex]

                  [tex]=\pm\sqrt{\frac{1-1+2\text{sin}^2A}{1+2\text{cos}^2A-1} }[/tex]

                  [tex]=\pm\sqrt{\frac{2\text{sin}^2A}{2\text{cos}^2A} }[/tex]

                  [tex]=\pm(\sqrt{\text{tan}^2A})[/tex]

                  [tex]=\text{tanA}[/tex] [Right side of the identity]

Hence, proved.

Find the length of UC

A. 54
B. 4
C. 39

Answers

Answer:

54

Step-by-step explanation:

It is the answer to this question

Wait waaaait Hol' up.

Answer:

Its 18.

Which must be true of a quadratic function whose vertex is the same as its y-intercept?

Answers

Answer:

A

Step-by-step explanation:

because y-intercept is when x=0, so right on the y axis.

Sort each function into the correct category.

Linear Functions

Quadratic Functions

Exponential Functions

f(x) = 0.45X-1

f(x) = 5

f(x) = 4.5x +18

Rx) = 19x2

f(x) = x² – 3x+4

f(x) = 2x - 6

Answers

Answer:

Linear functions are

f(x) = 0.45 x - 1

f(x) = 5

f(x) = 4.5 x + 18

Quadratic function is

R(x) = 19x^2

Step-by-step explanation:

The linear function is a function in which the degree of function is 1.

So,

f(x) = 0.45 x - 1

f(x) = 5

f(x) = 4.5 x + 18 are the linear functions.

The quadratic function is a function in which the degree of function is 2.

So,

R(x) = 19 x^2 is a quadratic function.

The exponential function is a function which involves the exponents.

Answer:

pic

Step-by-step explanation:

The vertex of this parabola is at (-1,-3). Which of the following could be its
equation?
(-1, -3)
O A. X=-2(y+3)2-1
B. x=-2(y - 3)2 - 1
C. X=-2(y + 1)2-3
D. X = -2(y - 1)2-3

Answers

Answer:

Step-by-step explanation:

Y equals mx plus b

If f(x) = k where k is a constant, and the points (6,1) and (8,1) lie on the graph of y = f(x), what is the value of f(0)?
I think the answer is 1 but not 100% sure.

Answers

Answer:

The value of f(0)=1

Step-by-step explanation:

We are given that

[tex]f(x)=k[/tex]

[tex]y=f(x)[/tex]

(6,1) and (8,1) lies on the graph of y=f(x)

We have to find the value of f(0).

[tex]f(6)=1[/tex]

[tex]f(8)=1[/tex]

[tex]f(x)=k[/tex]

By comparing ,we get

k=1

Therefore, [tex]y=f(x)=1[/tex]

Now, substitute x=0

[tex]f(0)=1[/tex]

Hence, the value of f(0)=1

evaluate f(x)=1/4x for x=-5
option 1. -1/20
option 2. -1 1/4
option 3. 20
option 4. -4/5

Answers

Answer:

option 2. -1 1/4

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

FunctionsFunction Notation

Step-by-step explanation:

Step 1: Define

Identify

f(x) = 1/4x

Step 2: Evaluate

Substitute in x [Function f(x)]:                                                                           f(-5) = 1/4(-5)Multiply:                                                                                                             f(-5) = -5/4Simplify:                                                                                                             f(-5) = -1 1/4
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