All categories

2 years ago

Can you help me with this, please?

Mathematics

1 answer:

Aloiza [94]2 years ago

3 0

Answer:

y =x-12

Step-by-step explanation:

$(x_1, y_1) = (16, 4) \ \ \ and \ \ \ (x_2, y_2) = (17, 5)$

Equation of straight line is

$y-y_1 =\frac{y_2-y_1}{x_2-x_1} (x-x_1)$

$y-4 =\frac{5-4}{17-16} (x-16)$

$y =(x-16)+4$

$y =x-12$

You might be interested in

Kayla paints a bookcase she uses 1 5/6 cups of paint on the outside of the bookcase and 3/8 cup of paint on the inside. How many

olchik [2.2K]

Answer: Kayla used 2 5/24 cups of paint all together.

Step-by-step explanation:

Kayla paints a bookcase by using

1 5/6 cups of paint on the outside of the bookcase. Converting 1 5/6 cups to improper fraction, it becomes 11/6 cups of paint.

She also used 3/8 cup of paint on the inside.

Therefore, the total number of cups of paint that Kayla used all together would be

11/6 + 3/8 = (44 + 9)/24 = 53/24 cups of paint. Converting to mixed fraction, it becomes

2 5/24 cups of paint

3 0

2 years ago

An eagle perched 40 ft up in a tree looks down at a 35 degree angle(angle of depression) and spots a vole. How far is the vole f

maria [59]

Answer:

$X=49ft$

Step-by-step explanation:

From the question we are told that:

Height of Eagle $h=40ft$

Angle of depression $\theta=35\textdegree$

Generally the trigonometry equation for diagonal X is mathematically given by

$Cos\theta \textdegree=\frac{Adjacent}{Hypotenuse} }$

$Cos\theta \textdegree=\frac{h}{X} }$

$X=\frac{40}{Cos 35 } }$

$X=48.83ft$

$X=49ft$

3 0

2 years ago

I don’t understand how to solve this

Bezzdna [24]

Answer:

42.1

Step-by-step explanation:

The height of the main triangle is,

h = 47√3/2 (since it's an 30-60-90 triangle)

so to find x,

tan(44) = h/x

x = h/tan(44)

x = 42.1 (rounded to the nearest tenth)

Answered by GAUTHMATH

8 0

2 years ago

on a scale drawing, 5 metres is represented by 4 centimetres. write the scale as a ratio in it's simplest form.

ryzh [129]

Answer:

<em>The scale factor is 1:125</em>

Step-by-step explanation:

<u>Scaling</u>

Objects can be represented in a reduced or augmented size by using scaling which consists of multiplying or dividing by a constant factor. We use scaling when representing geographic locations on a map.

On a scale drawing, a distance of 5 meters = 500 cm is represented by 4 centimeters. The scale factor is usually represented as a ratio of the smallest to the biggest magnitude:

$\frac{4}{500}=\frac{1}{125}$

The scale factor is 1:125

8 0

3 years ago

Suppose that f: R --> R is a continuous function such that f(x +y) = f(x)+ f(y) for all x, yER Prove that there exists KeR su

Pachacha [2.7K]

<h2>Answer with explanation:</h2>

It is given that:

f: R → R is a continuous function such that:

$f(x+y)=f(x)+f(y)------(1)$ ∀ x,y ∈ R

Now, let us assume f(1)=k

Also,

f(0)=0

( Since,

f(0)=f(0+0)

i.e.

f(0)=f(0)+f(0)

By using property (1)

Also,

f(0)=2f(0)

i.e.

2f(0)-f(0)=0

i.e.

f(0)=0 )

Also,

f(2)=f(1+1)

i.e.

f(2)=f(1)+f(1) ( By using property (1) )

i.e.

f(2)=2f(1)

i.e.

f(2)=2k

Similarly for any m ∈ N

f(m)=f(1+1+1+...+1)

i.e.

f(m)=f(1)+f(1)+f(1)+.......+f(1) (m times)

i.e.

f(m)=mf(1)

i.e.

f(m)=mk

Now,

$f(1)=f(\dfrac{1}{n}+\dfrac{1}{n}+.......+\dfrac{1}{n})=f(\dfrac{1}{n})+f(\dfrac{1}{n})+....+f(\dfrac{1}{n})\\\\\\i.e.\\\\\\f(\dfrac{1}{n}+\dfrac{1}{n}+.......+\dfrac{1}{n})=nf(\dfrac{1}{n})=f(1)=k\\\\\\i.e.\\\\\\f(\dfrac{1}{n})=k\cdot \dfrac{1}{n}$

Also,

when x∈ Q

i.e. $x=\dfrac{p}{q}$

Then,

$f(\dfrac{p}{q})=f(\dfrac{1}{q})+f(\dfrac{1}{q})+.....+f(\dfrac{1}{q})=pf(\dfrac{1}{q})\\\\i.e.\\\\f(\dfrac{p}{q})=p\dfrac{k}{q}\\\\i.e.\\\\f(\dfrac{p}{q})=k\dfrac{p}{q}\\\\i.e.\\\\f(x)=kx\ for\ all\ x\ belongs\ to\ Q$