Write an equation that represents the line.
Use exact numbers.

Hello,

The parabola has vertex=(0,1) and is passing through (1,3)

y=k(x-0)²+1

3=k*1+1 ==> k= 2

y=2*x²+1

Answer:

Step-by-step explanation:

Answer:

1/√2

Step-by-step explanation:

The value of sin 45 is 1/√2

Answer:

The height of the tree=8.42 m

Step-by-step explanation:

We are given that

Height of Joshua, h=1.45 m

Length of tree's shadow, L=31.65 m

Distance between tree and Joshua=26.2 m

We have to find the height of the tree.

BC=26.2 m

BD=31.65m

CD=BD-BC

CD=31.65-26.2=5.45 m

EC=1.45 m

All right triangles are similar .When two triangles are similar then the ratio of their corresponding sides are equal.

[tex]\triangle ABD\sim \triangle ECD[/tex]

[tex]\frac{AB}{EC}=\frac{BD}{CD}[/tex]

Substitute the values

[tex]\frac{AB}{1.45}=\frac{31.65}{5.45}[/tex]

[tex]AB=\frac{31.65\times 1.45}{5.45}[/tex]

[tex]AB=8.42m[/tex]

Hence, the height of the tree=8.42 m

I got 20.

I may have done it wrong so maybe wait until others have answered.

Answer:

the answer is 8 because DEF is 8 times larger than ABC.

Step-by-step explanation:

hope that helps>3

Answer:

3

Step-by-step explanation:

To find scale factor, you need to divide two of the given sides. Meaning you can do any corresponding sides. So, for now, I will do 12 from DEF and 4 from ABC.

12 ÷ 4 = 3

To check if it is accurately 3, you will do it again (optional). You can use 15 from DEF and 5 from ABC

15 ÷ 5 = 3

Since both are 3, that will be the scale factor.

The answer is 3.

Answer:

60

Step-by-step explanation:

the two angles are equal angle x and the one opposite

=180-40

=120 ÷2

=60

Answer is

z = 70

x = 70

Step-by-step explanation:

z is also equal to x because two sidess are equal

40 + x + x =180

40 + 2x = 180

2x = 140

x =70

so x and z are 70 each

Answer:

h=31.4 cm

Step-by-step explanation:

A=lateral surface area

c=circumference

h=height

A= c*h

solving for h we get:

h=A/c=120pi/12=10pi

Answer:

4(– 6)

6(– 4)

12(– 2)

Step-by-step explanation:

average =65%

average = (60+70)/(100+100)*100

= 130/200*100

= 65%

Answer:

<-56, -16>

Step-by-step explanation:

multiply the values by 8 because that's what the question tells you to do

Answer:

2

Step-by-step explanation:

Answer:

The answer is D.

Step-by-step explanation:

Step-by-step explanation:

13x - 12 = 7x - 6( remaining side of the similar triangle is equal).

Answer:

HCF = 6

Step-by-step explanation:

Listing the factors of each number

18 is 1, 2, 3, 6, 9, 18

30 is 1, 2, 3, 5, 6, 10, 15, 30

36 is 1, 2, 3, 4, 6, 9, 12, 18, 36

common factors are 1, 2, 3, 6

the HCF is 6

Answer:

45

Step-by-step explanation:

4[tex]x^{3}[/tex] - 7[tex]x^{2}[/tex] for x = 3

Substitute 3 in for x

4([tex]3^{3}[/tex]) - 7([tex]3^{2}[/tex])

4(3·3·3) - 7(3·3)

4(27) - 7(9)

108 - 63

45

Answer:

45

Step-by-step explanation:

Hi there!

We are given 4x³-7x² and we need to evaluate the expression if x=3.

To do this, substitute 3 as x into the expression, and then use the order of operations to solve

so substitute 3 as x into the expression (remember: x² is x*x, or (x)²)  

4(3)³-7(3)²

now using the order of operations, start by evaluating the exponents

(3)³=3*3*3=9*3=27

(3)²=3*3=9

the expression then becomes:

4*27-7*9

multiply

108-63

subtract

45

Hope this helps! :)

Answer:

no solutions

Step-by-step explanation:

Hi there!

We're given this system of equations:

x+y=3

4y=-4x-4

and we need to solve it (find the point where the lines intersect, as these are linear equations)

let's solve this system by substitution, where we will set one variable equal to an expression containing the other variable, substitute that expression to solve for the variable the expression contains, and then use the value of the solved variable to find the value of the first variable

we'll use the second equation (4y=-4x-4), as there is already only one variable on one side of the equation. Every number is multiplied by 4, so we'll divide both sides by 4

y=-x-1

now we have y set as an expression containing x

substitute -x-1 as y in x+y=3 to solve for x

x+-x-1=3

combine like terms

-1=3

This statement is untrue, meaning that the lines x+y=3 and 4y=-4x-4 won't intersect.

Therefore the answer is no solutions

Hope this helps! :)

The graph below shows the two equations graphed; they are parallel, which means they will never intersect. If they don't intersect, there's no common solution

Answer:

The answer is A.

How I got it:

Formula of finding a triangle: 1/2 bh.

In this case, the base is R and the Height is X.

1/2rx.

Answer:

The distance between the two points is about 7.1 units.

Step-by-step explanation:

We want to find the distance between the two points (-3, 6) and (2, 1).

To find the distance between any two points, we can use the distance formula:

[tex]\displaystyle d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Let (-3, 6) be (x₁, y₁) and (2, 1) be (x₂, y₂). Substitute:

[tex]\displaystyle d=\sqrt{((2)-(-3))^2+((1)-(6))^2}[/tex]

Simplify:

[tex]\displaystyle d=\sqrt{(5)^2+(-5)^2}[/tex]

Evaluate:

[tex]d=\sqrt{25+25}=\sqrt{25(2)}=5\sqrt{2}\approx 7.1\text{ units}[/tex]

The distance between the two points is about 7.1 units.

Answer:

7/(6 + x) = 3/(6 - x)

Step-by-step explanation:

The current of the Red Cedar River (the speed with which the river is flowing), v = 6 mph

The time it takes the canoe to travel 7 miles downstream = The time it takes the canoe to paddle 3 miles upstream

Let x represent the rate of the canoe, we have;

7/(v + x) = 3/(v - x)

Substituting v = 6 mph, we get the following rational equation, from which the rate of the canoe, x, can be found;

7/(6 + x) = 3/(6 - x).

Answer:

B. point B

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

B(-1, -3)

y = 3x

When x = -1,

y = 3(-1) = -3

Answer: B.

Step-by-step explanation:

X-1/X=3

X-1=3×X

X-1=3X

-3X+X=1

-2X=1

X=1/2 Answer

Answer:

5km

Step-by-step explanation:

Please check the attached image for a diagram explaining this question

The distance from A to C can be determined using Pythagoras theorem

The Pythagoras theorem : a² + b² = c²

where a = length

b = base

c =  hypotenuse

3² + 4²

= 16 + 9

= 25

determine the square root of 25

√25 = 5km

Answer:

Step-by-step explanation:

Cross multiplication can be used but not in the beginning. First x should be isolated.

[tex]3 +\frac{5}{x}=\frac{7}{x}\\\\[/tex]

Now subtract [tex]\frac{5}{x}[/tex] from both sides

[tex]3 = \frac{7}{x}-\frac{5}{x}\\\\3=\frac{7-5}{x}\\\\3=\frac{2}{x}[/tex]

In this stage, cross multiplication can be used.

[tex]\frac{3}{1}=\frac{2}{x}\\\\3*x=2*1\\\\x = \frac{2}{3}[/tex]

Answer:

x =0 and x =2/3

Step-by-step explanation:

as is no

but if you put an x under the 3 to make 3x/x

then you'd have 3x+5/x = 7/x

to make

3x^2 + 5x = 7x

this makes

3x^2 -2x =0

using the quadratic formula

answers

x =0 and x =2/3

Answer:

The formula to find the area of a rectangle is A=BH

so the area equals the base times the height

Hope This Helps!!!

Answer:

Answer 1 :-

[tex]\implies m_1 = -3 [/tex]

[tex]\implies y - intercept = 7 [/tex]

Answer 2 :-

[tex]\implies m_1 = -\dfrac{1}{2} [/tex]

[tex]\implies y - intercept = -4 [/tex]

Step-by-step explanation:

The Slope Intercept Form of the line is given to us . The equations given are ,

[tex]\implies y + 3x = 7 [/tex]

[tex]\implies y + \dfrac{1}{2}x = -4 [/tex]

Now we know the standard equation of slope intercept form , is

[tex]\implies y = mx + x [/tex]

Where ,

So , we can write about the equations as ,

[tex]\implies y = -3x + 7 [/tex]

[tex]\implies y = - \dfrac{1}{2}x -4 [/tex]

On comparing to the Standard form ,

Answer 1 :-

[tex]\implies m_1 = -3 [/tex]

[tex]\implies y - intercept = 7 [/tex]

Answer 2 :-

[tex]\implies m_1 = -\dfrac{1}{2} [/tex]

[tex]\implies y - intercept = -4 [/tex]