Find the equation of the line shown.
y
X
0 1 2 3 4 5 6 7 8 9 10
10
987654321

We know the slope formula

Parallel lines have equal slope so it has m=-2

to get the equation of any straight line, we simply need two points off of it, so let's use the ones provided in the table above.

[tex]\begin{array}{|cc|ll} \cline{1-2} \stackrel{millions}{population}&year\\ \cline{1-2} 161&1950\\ 291&2000\\ \cline{1-2} \end{array}\hspace{5em} (\stackrel{x_1}{161}~,~\stackrel{y_1}{1950})\qquad (\stackrel{x_2}{291}~,~\stackrel{y_2}{2000}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2000}-\stackrel{y1}{1950}}}{\underset{run} {\underset{x_2}{291}-\underset{x_1}{161}}} \implies \cfrac{ 50 }{ 130 }\implies \cfrac{5}{13}[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1950}=\stackrel{m}{\cfrac{5}{13}}(x-\stackrel{x_1}{161}) \\\\\\ y-1950=\cfrac{5}{13}x-\cfrac{805}{13}\implies y=\cfrac{5}{13}x-\cfrac{805}{13}+1950\implies y=\cfrac{5}{13}x+\cfrac{24545}{13}[/tex]

Answer:

17

Step-by-step explanation:

at f(7) means x is 7

7+10 is 17

Using the Empirical Rule, it is found that the interval that would represent a similar percentage of Great Danes would fall between 130 and 170 pounds.

It states that, for a normally distributed random variable:

68% fall within 1 standard deviation of the mean, hence for the Great Danes, the values are given as follows:

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Answer:

∠ QPR = 125°

Step-by-step explanation:

the angles subtended by 2 congruent arcs are congruent , that is

5x = 4x + 25 ( subtract 4x from both sides )

x = 25

Then

∠ QPR = 4x + 25 = 4(25) + 25 = 100 + 25 = 125°

Answer:

648 in^2

Step-by-step explanation:

your must find the surface area of the rectangular prism

this can be modelled by

2(9 * 9) + 2(13.5 * 9) + 2(13.5 * 9)

or

2(9 * 9) + 4(13.5 * 9)

then you do whats inside the parenthesis

2(81) + 4(121.5)

and lastly you multiply and add

162 + 486 = 648

the answer is 648 in^2

Answer:

341 cm²

Step-by-step explanation:

Formula :

Surface area = Area of 4 triangle faces + Area of square base

===============================================================

Solving :

⇒ Surface area = 4 × 1/2 × 11 × 10 + 11²

⇒ Surface area = 2 × 110 + 121

⇒ Surface area = 220 + 121

⇒ Surface area = 341 cm²

The surface area of the square pyramid is 341 square centimeter.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

The surface area of a square pyramid is calculated by the equation S = B + 1/2 × P × S

where B is the area of the base,

P is the perimeter of the base, and

S is the slant height of the pyramid.

the area of the base =11×11

B=121 square centimeter

The perimeter of the base = 2(11+11)

P= 44 cm

Slant height (S) is 10 cm.

Surface Area = 121 + 1/2 (44×10)

=121+220

=341 square centimeter

Hence,  the surface area of the square pyramid is 341 square centimeter.

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Answer:

Dimensions:  150 m x 150 m

Area:  22,500m²

Step-by-step explanation:

Given information:

Let [tex]x[/tex] = width of the field

Let [tex]y[/tex] = length of the field

Create two equations from the given information:

  Area of field:   [tex]A= xy[/tex]

  Perimeter of fence:   [tex]2(x + y) = 600[/tex]

Rearrange the equation for the perimeter of the fence to make y the subject:

[tex]\begin{aligned} \implies 2(x + y) & = 600\\ x+y & = 300\\y & = 300-x\end{aligned}[/tex]

Substitute this into the equation for Area:

[tex]\begin{aligned}\implies A & = xy\\& = x(300-x)\\& = 300x-x^2 \end{aligned}[/tex]

To find the value of x that will make the area a maximum, differentiate A with respect to x:

[tex]\begin{aligned}A & =300x-x^2\\\implies \dfrac{dA}{dx}& =300-2x\end{aligned}[/tex]

Set it to zero and solve for x:

[tex]\begin{aligned}\dfrac{dA}{dx} & =0\\ \implies 300-2x & =0 \\ x & = 150 \end{aligned}[/tex]

Substitute the found value of x into the original equation for the perimeter and solve for y:

[tex]\begin{aligned}2(x + y) & = 600\\\implies 2(150)+2y & = 600\\2y & = 300\\y & = 150\end{aligned}[/tex]

Therefore, the dimensions that will give Tanya the maximum area are:

150 m x 150 m

The maximum area is:

[tex]\begin{aligned}\implies \sf Area_{max} & = xy\\& = 150 \cdot 150\\& = 22500\: \sf m^2 \end{aligned}[/tex]

Answer:

A. 3/10

B.1/7

Step-by-step explanation:

Answer:

Objects mostly have one or more geometrical shapes like the following. These types of shapes are called three dimensional (3-D) shaped solids. All these geometrical shapes have faces. We have learned about faces like triangular faces, rectangular face, square face and circular face.

Answer:

The bird's speed is 50mph.

The bird's feeder is 25 miles away.

Step-by-step explanation:

10/6=x/30

6*x=30 is 6/30=x

x=5

6*5=30 so 10*5=50

x=50

mph/time=distance per hour

50/(1/2)=25 miles

Order matters is permutation

Order doesn't matters is combination

So

The correct combinations are

Answer:

59 degrees

Step-by-step explanation:

Angles on a straight line add up to 180 degrees

Angles in a triangle add up to 280 degrees

180 minus 149 is 31

31 add 90 is 121

180 minus 121 is 59

Answer:

A got it right

Step-by-step explanation:

got it right

Answer: The area of a triangle is the region enclosed between the sides of the triangle. Area of ΔABC = 1/2 × Base × Height

Step-by-step explanation:

Area of ΔABC= 1/2 × Base × Height = 1/2 × h × BC

If ABC is an equilateral triangle, Area of ΔABC = (√3/4)a2 where a is the length of a side of the equilateral triangle.

Thus, we have seen the formula and definition of the area of triangle ABC.

Answer:

f(x) = 3x + 9:  y - intercept is option  c. (0,-9)

f(x) = 3x - 9:  y - intercept is option   b. (0, 9)

Step-by-step explanation:

option a and d cant be correct since y = 0 in those answer when the y - intercept is when x = 0

If the function f(x) = 3x + 9

than x = 0

f(x) = 3(0) + 9

f(x) = 0 + 9

f(x) = 9

x = 0 and y = 9 (0, 9)

If the function f(x) = 3x - 9

than x = 0

f(x) = 3(0) - 9

f(x) = 0 - 9

f(x) = -9

x = 0 and y = -9 (0, -9)

Answer:

[tex]x = 2, y = -3[/tex]

Step-by-step explanation:

Add the 2 equations together, then solve for x.

[tex](2x + 2y) + (3x - 2y) = (-2) + (12)\\ 2x + 3x + 2y - 2y = -2 + 12\\5x = 10\\x = 2[/tex]

Now that we know the value of x, we can easily find y by substitution.

[tex]3x - 2y = 12\\3(2) - 2y = 12\\6 - 2y = 12\\-2y = 6\\y = -3[/tex]

These are the answers

- Kan Academy Advance

Answer:

Step-by-step explanation:

The triangles are congruent when corresponding sides are congruent.

__

ΔFGH ≅ ΔABC means corresponding sides are ...

  (GH, BC) = (V, 16)

  (HF, CA) = (48, W)

Corresponding sides being congruent means ...

  V = 16

  W = 48

Answer:

Points on the inverse are [tex](1,-1), (4,2), \text{and } (0,0)[/tex]

Step-by-step explanation:

When writing the inverse function of a set of points, you simply switch the coordinates:

[tex]\text{Function}: (x,y)\\\text{Inverse}: (y,x)[/tex]

We are given the points

[tex](-3,9), (-1,1), (0,0), \text{and } (2,4)[/tex]

Using our rule for function, our new points will be

[tex](9,-3), (1,-1), (0,0), \text{and } (4,2)[/tex]

From the list, the points we have for the graph of the inverse are

[tex](1,-1), (4,2), \text{and } (0,0).[/tex]

Answer:

0.705

Step-by-step explanation:

| -1/2 - 1/8| + ( -3/4 + 5/6)

| -1/2 - 1/8| + ( -0.75 + 0.83)

| -1/2 - 1/8| + 0.08

| -0.5 - 0.125| + 0.08

|-0.625| +0.08

0.625+0.08

0.705

hope it helps

Answer:

Step-by-step explanation:

Answer:

  410 g

Step-by-step explanation:

Radioactive decay can be modeled by an exponential equation. The amount remaining (y) after a time period (t) can be expressed in terms of the initial amount (a) and the half-life (h).

  y = a(1/2)^(t/h)

__

We can use this equation with the given values to find the amount remaining.

  y = (680 g)(1/2)^((19 yrs)/(26 yrs)) ≈ (680 g)(0.602583)

  y ≈ 410 g

About 410 grams of element X will remain after 19 years.

Answer:

12

Step-by-step explanation:

127491733816383827i 9273

Answer:

I can find at least 10 4-letter words out of hexagon.

Step-by-step explanation:

1.) Hexa (means 6)

2.) gone

3.) nage (a type of bullion)

4.) gane (to yawn)

5.) hage (a frightening old woman; a witch)

6.) hane (ghostly)

7.) axon (a part of a nerve cell)

8.) hang

9.) oxen

10.) hoax

Answer: its c

Step-by-step explanation: im a smarty boy i hope u its right or not

Answer:

The first one with the number 38

Step-by-step explanation:

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]5x-y=-7\implies 5x-y+7=0 \\\\\\ \stackrel{\stackrel{m}{\downarrow }}{5} x+7=y\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

so a line perpendicular to that one above will have a slope of

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{5\implies \cfrac{5}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{5}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{5}}}[/tex]