Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. What is the distance between points F and G? F G -5 -4 -3 -2 -1 0 1 2 3 4 5 The distance between F and G is​

We can divide the given shape into a triangle and a rectangle.

We'll have to use Pythagoras Theorem.

[tex]\large\boxed{Formula:{a}^{2}={b}^{2}+{c}^{2}}[/tex]

In this question we have to find the hypotenuse so we'll have to add.

Let's substitute the values according to the formula.

[tex]BC= {6}^{2}+{7}^{2}[/tex]

[tex]BC= 85[/tex]

[tex]BC = \sqrt{ 85} [/tex]

[tex]\boxed{BC=9.22 \: cm}[/tex]

Now, we can find the value of "x"

We can use any one from SOHCAHTOA.

Here I'm using tan.

[tex]\large\boxed{Formula: tan(a)= \frac{opp}{adj}}[/tex]

Let's substitute the values according to the formula.

[tex]tan \: x= \frac{6}{7}[/tex]

We'll have to use tan inverse.

[tex]x= {tan}^{-1}(\frac{6}{7})[/tex]

[tex]\boxed{x=40.6°}[/tex]

1)

=9.22 cm

2)

=40.6°

hope this helps

The statements that apply are:

Jorge could count how far each pre-image point is from the line of reflection along the perpendicular from the point to the line of reflection

Jorge will not move any point that lies on the line of reflection.

Reflection is a transformation phase of a plane shape by moving vertices of the shape equal distance across the line of reflection.

Analysis:

If the line of reflection is along the x-axis only the y coordinates would be changed.

If reflection is along then x-axis only X-coordinates would be changed.

If a point is on the reflection line, it cannot be reflected.

Learn more about reflection: brainly.com/question/1908648

#SPJ1

Answer:

B. D. E.

explanation: edge 2023

Answer:

1584/7 in² ≈ 226.3 in²

Step-by-step explanation:

Given,

We know that,

Volume(Cylinder) = πr²h

Substitute values,

Taking π as 22/7

An equation is formed of two equal expressions. It will take for the radioactive element to decay from 960 grams to 295 grams in 25.54 minutes.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The radioactive decay of an element is given by the formula,

[tex]N = N_0 \cdot e^{-\lambda t}[/tex]

Given the half-life of the element is 15 minutes, therefore, we can write,

[tex]\dfrac12 = e^{-\lambda\times 15}\\\\\ln (0.5) = -\lambda\times 15\\\\\lambda = 0.0462[/tex]

Now, the time it will take for 960 grams to decay to 295 grams is,

[tex]295 = 960 \cdot e^{-0.0462 \times t}\\\\\ln (\dfrac{295}{960}) = -0.0462 \times t\\\\t = 25.54\rm\ minutes[/tex]

Hence, it will take for the radioactive element to decay from 960 grams to 295 grams in 25.54 minutes.

Learn more about Equation:

https://brainly.com/question/2263981

#SPJ1

Answer:

B ( -3/2; 13/2 )

Step-by-step explanation:

Midpoint AD : X1 + X2 /2 ; Y1 + Y2 /2

-4 + 6 /2 ; 5 + 11 /2

1 ; 8

C (1 ; 8)

Midpoint B : X1 + X2 /2 ; Y1 + Y2 /2

-4 + 1 /2 ; 5 + 8 /2

-3/2 ; 13/2

B (-3/2 ; 13/2)

Answer: Hope this helps you!

Multiply by -2

-96, 192, -384

Answer:

C

Step-by-step explanation:

You would have to find the probability of what you already know then use that to find the whole thing

The area of the triangle is 52,000 cm².

A triangle is a three-sided polygon with three edges and three vertices. the sum of angles in a triangle is 180 degrees

Area of a triangle = 1/2 x base x height

Area = 1/2 x 320 x 325 = 52,000 cm²

To learn more about triangles, please check: https://brainly.com/question/22949981

#SPJ1

Answer:

4x^2-13x+4

Step-by-step explanation:

(x^2-5x+6)+(3x^2-8x-2)

Combine like terms

x^2+3x^2-5x-8x+6-2

4x^2-13x+4

Answer:

Secant: a straight line that intersects a circle at two points.

Intersecting Secants Theorem

If two secant segments are drawn to the circle from one exterior point, the product of the measures of one secant segment and its external part is equal to the product of the measures of the other secant segment and its external part.

From inspection of the given diagram:

Therefore:

⇒ ML · MK = MN · MS

Given:

Substituting the given values into the formula and solving for x:

⇒ ML · MK = MN · MS

⇒ 6(x + 21) = 7 · 18

⇒ 6x + 126 = 126

⇒ 6x = 0

⇒ x = 0

Substituting the found value of x into the expression for KL:

⇒ KL = x + 15

⇒ KL = 0 + 15

⇒ KL = 15

Let's see

So

Step-by-step explanation:

please mark me as brainlest

Answer: 22.275

Step-by-step explanation:

-3 1/8 + 4 (5.6 + 3/4)

-3.125 + 4 (5.6 + 0.75)

-3.125 + 4 (6.35)

-3.125 + 25.4 = 22.275

Answer:

i think 75% is the answers

Step-by-step explanation:

please mark me as brainlest

Answer:

k = 48

Step-by-step explanation:

If 3 or more parallel lines are intersected by 2 or more transversals then the parallel lines divide the transversals proportionally , that is

[tex]\frac{24}{k}[/tex] = [tex]\frac{32}{64}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

k = 2 × 24 = 48

Answer: 5%

Step-by-step explanation:

15 is what percent of 300 =

15 = 300x

15/300 = x

5 = x

5%

The linear equation is y = 4 + 0.5x

The points are given as: (-2,3) and (4,6)

The equation is then calculated using:

[tex]y = \frac{y_2 -y_1}{x_2 -x_1} *(x - x_1) + y_1[/tex]

Substitute the known values

[tex]y = \frac{6-3}{4+2} *(x+2) + 3[/tex]

Evaluate

y = 0.5 *(x+2) + 3

Expand

y = 0.5x + 1 + 3

Evaluate the sum

y = 0.5x + 4

Rewrite as:

y = 4 + 0.5x

Hence, the equation is y = 4 + 0.5x

Read more about linear equations at:

https://brainly.com/question/14323743

#SPJ1

Lyra's speed of travel is 6.71 feet per seconds and Lyra's direction of travel is 27 degrees north of east

The diagram that represents the scenario is added as an attachment.

Let x represents Lyra's speed of travel.

The value of x is calculated using the following Pythagoras theorem.

[tex]x = \sqrt{3^2 + 6^2}[/tex]

Evaluate the exponents

[tex]x = \sqrt{9 + 36}[/tex]

Evaluate the sum

[tex]x = \sqrt{45}[/tex]

Evaluate the exponent

x = 6.71

Hence, Lyra's speed of travel is 6.71 feet per seconds

The direction (∅) is calculated using the following tangent ratio.

[tex]\tan(\theta) = \frac 36[/tex]

Evaluate the quotient

[tex]\tan(\theta) = 0.5[/tex]

Take the arc tan of both sides

[tex]\theta = \tan^{_1}(0.5)[/tex]

Evaluate

[tex]\theta = 27[/tex]

Hence, Lyra's direction of travel is 27 degrees north of east

Read more about speed and distance at:

https://brainly.com/question/4931057

#SPJ1

[tex] \sf{\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Let's add ~

[tex]\qquad \sf  \dashrightarrow \: 3 \sqrt{5} - 5 \sqrt{3} + (2 \sqrt{5} + 5 \sqrt{3} )[/tex]

[tex]\qquad \sf  \dashrightarrow \: 3 \sqrt{5} + 2 \sqrt{5 }- \cancel{5 \sqrt{3}} + \cancel{5 \sqrt{3} }[/tex]

[tex]\qquad \sf  \dashrightarrow \: 5 \sqrt{5} [/tex]

Hii!

_________________________________________________________

[tex]\leadsto\parallel\odot\boldsymbol{Answer.}\odot\parallel\gets[/tex]

value of the expression: [tex]\sf 5\sqrt5[/tex]

_________________________________________________________

[tex]\leadsto\parallel\odot\boldsymbol{Explanation.}\odot\parallel\gets[/tex]

ADD the given expressions.

[tex]\bullet~~[/tex]  [tex]\sf (3\sqrt{5} -5\sqrt{3} )+(2\sqrt{5}+5\sqrt{3})[/tex]

[tex]\bullet[/tex] [tex]\sf 3\sqrt5+2\sqrt5-5\sqrt3+5\sqrt{3}[/tex]

NOW it's just a matter of combining like terms. Upon doing this we obtain

[tex]\bullet \sf 5\sqrt5[/tex]

___________________________________________________________

Hope that this helped! Best wishes.

[tex]\textsl{Reach far. Aim high. Dream big.}[/tex]

[tex]\boldsymbol{-Greetings!-}[/tex]

_____________________________________________________

By inspection, we know the equation of the line is [tex]x=\frac{1}{2}[/tex].

Writing this in standard form, we get [tex]\boxed{2x=1}[/tex]

There are 24 sticks in pattern 6. The diagram indicates that one pattern is made up of one box built from four sticks.

A geometric pattern is a pattern made out of geometric forms that are generally repeated, much like a wallpaper design.

The given figure shows that one pattern consists of one box formed from the 4 sticks.

Pattrern 1 = 1 box  

Pattern 2 = 2 box

Pattern 6 = 6 box

1 box = 4 stick

Pattern 6 = 6 box = 6 ×4 = 24 sticks

Hence,there are 24 sticks in pattern 6.

To learn more about the geometric pattern refer;

https://brainly.com/question/14065302

#SPJ1

Answer:

[tex]\theta = 41^{\circ}[/tex]

Step-by-step explanation:

[tex]~~~~~~~\sin 49^{\circ} = \cos \theta\\\\\implies \theta = \cos^{-1}\left(\sin 49^{\circ} \right)\\\\\implies \theta = \cos^{-1} \left[\cos \left(90^{\circ} - 49 ^{\circ} \right) \right]\\\\\implies \theta= \cos^{-1}\left( \cos 41^{\circ} \right)\\\\\implies \theta = 41^{\circ}[/tex]

Answer:

58.86 mg

Step-by-step explanation:

8 mg = 16 kg

1 kg = 2.2 lb

use substitution

8 mg = 16 (2.2 lb)

8 mg = 35.2 lb

8 mg / 35.2 lb = x mg / 259 lb

2072 = 35.2 x

x = 58.86 mg

Answer:

4sin(x)

Step-by-step explanation:

That is the new equation hope it helps!

Using the first derivative test, it is found that the graph is increasing on the interval is (-5, ∞).

A function is a process or a relation that associates each element 'a' of a non-empty set A , at least to a single element 'b' of another non-empty set B.

Here, the function is given by:

        f(x)  =   x²/2 + 5x + 6

On differentiating both sides, with respect to x we get

      f'(x) = x + 5

Then, we test the signal of the derivative, which is the first derivative test.

      x + 5 ≥ 0

       x ≥ -5

Thus, It is found that the Function is increasing on the interval is (-5, ∞).

Learn more about Function from:

https://brainly.com/question/12431044

#SPJ1

The Dot plots clearly display clusters/gaps of data and outliers.

Twelve teachers attended a seminar on mathematical problem-solving. their attitudes were measured before and after the seminar.

a positive number change attitude indicates that a teacher's attitude toward math became more positive.

The twelve change scores are as follows:

3 8 -1 2 0 5 -3 1 -1 6 5 -2

First, we arrange the data in increasing order

-3,-2,-1,-1,0,1,2,3,5,5,6,8

Dot plots clearly display clusters/gaps of data and outliers. In dot plots, the frequency axis is not necessary but you need to count to find the frequency.

n=12 is even.

To learn more about the dot plots visit:

https://brainly.com/question/15853311

#SPJ1

Answer:

Number 1 and Number 4

Step-by-step explanation:

By factoring, you can figure out the roots (x = -2 or x = 2)...

1. x^2 - 4 = 0

--> (x + 2)(x - 2) = 0

--> x = -2, x = 2

2. x^2 + 4 = 0

--> factors weirdly, so I won't write it. You'd have to use the quadratic formula.

3. 3x^2 + 12 = 0

--> 3 (x^2 + 4) = 0

--> factors weirdly (same as above)

4. 4x^2 - 16 = 0

--> 4 (x^2 - 4) = 0

--> 4 (x+2) (x-2) = 0

--> x = -2, x = 2

5. 2 (x-2) 2 = 0

--> x = 2

Step-by-step explanation:

3(x+4) ≤ 36

3x + 12 ≤ 36

3x ≤ 24

x ≤ 8

Answer:   x ≤12

Step-by-step explanation:

3(x+4) ≤36

 3x+4 ≤36 (you should simplify)

     3x ≤36 (36 divided by 3 is 12)

       x ≤12

Answer:

The answer is (6.5,3)

Step-by-step explanation:

The solution is in the image

The endpoints of GH are G(10,1) and H(3,5), then, the midpoint of GH is M(6.5, 3).

Here, we have to find the midpoint of line segment GH, we can use the midpoint formula.

The midpoint formula states that the coordinates of the midpoint (M) of a line segment with endpoints (x₁, y₁) and (x₂, y₂) are given by:

M(x, y) = [tex]((x_1 + x_2) / 2, (y_1 + y_2) / 2)[/tex]

Then the midpoint will be

x = (x₁ + x₂) / 2

y = (y₁ + y₂) / 2

In this case, the endpoints of GH are G(10, 1) and H(3, 5).

Let's use the midpoint formula to find the midpoint (M) of GH:

x-coordinate of M = (x-coordinate of G + x-coordinate of H) / 2

x-coordinate of M = (10 + 3) / 2

x-coordinate of M = 13 / 2

x-coordinate of M = 6.5

y-coordinate of M = (y-coordinate of G + y-coordinate of H) / 2

y-coordinate of M = (1 + 5) / 2

y-coordinate of M = 6 / 2

y-coordinate of M = 3

So, the midpoint of GH is M(6.5, 3).

More about the midpoint link is given below.

brainly.com/question/17410964

#SPJ7

Answer:

A=1/2 B x H

207=1/2 B x 18

B=207/18 x 2

B= 23 inches

Based on the SSS similarity theorem, the pair of triangles that can be proven to be similar is the pair shown in the image attached below.

The SSS similarity theorem states that two triangle area similar to each other if the ratio of the three corresponding sides of both triangles are equal.

Thus, in the image attached below, the ratio of the three corresponding sides of the pair of triangles are:

10/2.5 = 11/2.75 = 8/2 = 4

Therefore, the pair of triangles that we can prove to be similar using the SSS similarity theorem is the pair shown in the image attached below.

Learn more about the SSS similarity theorem on:

https://brainly.com/question/4163594

#SPJ1