1) Type in the formula for slope

2) Find the slope of the line that contains (0, -5) and (-3, 1).

Applying the distance formula, the value of a is 2 or -2.

The distance formula is:

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

Given the following:

d = XY = 10 units

X(a - 5, -2a) = (x1, y1)

Y(a + 1, 2a) = (x2, y2)

Plug in the values into the distance formula

10 = √[((a + 1) - (a - 5))² + (2a - (-2a))²]

10 = √[(a + 1 - a + 5)² + (2a + 2a)²]

10 = √(6² + (4a)²)

10 = √(36 + 16a²)

10² = 36 + 16a²

100 = 36 + 16a²

0 = -100 + 36 + 16a²

0 = 16a² - 64

16a² - 64 = 0

Factorize

16(a² - 4) = 0

16(a - 2)(a + 2) = 0

a = 2 or a = -2

Therefore, applying the distance formula, the value of a is 2 or -2.

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Answer:

x=8

Step-by-step explanation:

starts with 0.5x+2=6, so move the constant to the right, 0.5x=6-2, then calculate the right side, 0.5x=4, then divide both sides, and x=8

Answer:

x = 8

Step-by-step explanation:

Get variable on left and constants on right

0.5x = 6 - 2

0.5x = 4

Divide both sides by 0.5

x = 8

Answer:

$3.48

Step-by-step explanation:

Divide the number of hamburgers by the total cost:

13.95 / 4 =

3.4875

$3.48

Answer:

[11000, 11600]

Step-by-step explanation:

Give me Brainliest if that helped! :)

The equation of line is y = -4

Given the points:

(x₁, y₁) = (-1, -4)

(x₂, y₂) = ( 3, -4)

The slope-intercept form:

y = mx + b

Where, m is the slope and b is the y-intercept, that is (0, b)

The formula for slope:

m = (y₂ – y₁) / (x₂ – x₁)

We have given

x₁ = -1

x₂ = 3

y₁ = -4

y₂ = -4

So,

m = (-4 – (-4)) / (3 – (-1)) = (-4 + 4) / (3 + 1) = 0/4 = 0

Therefore we have the equation of the line as:

y = mx + b

-4 = 0(x) + b

-4 = 0 + b

b = -4

Therefore, the equation of line y = -4

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Two vertex angles of an isosceles triangle are equal but not necessarily all three so the given statement is not always true.

A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices.

In a triangle, the sum of all three angles is 180°

Triangle is a very common figure to deal with our daily life for example in our daily life to measure the height of any tower then there is a huge application of the right angle triangle.

An isosceles triangle is a triangle whose two sides will be the same, but the third side may or may not be equal.

So, the angle associated with the same side will same but the remaining angle will or will not be the same.

Hence "Two vertex angles of an isosceles triangle are equal but not necessarily all three so the given statement is not always true".

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A 94.6 L gasoline with a density of 0.680 g/cm^3 has a mass of 64328 g.

Density is defined as the ratio between the mass of a substance and the volume it occupies. Denoted by ρ, density is mass per unit volume and the formula is given below:

ρ =  mass / volume

Converting first the volume from L to cm^3.

1 L = 1000 cm^3

94.6 L = 94.6(1000 cm^3)

94.6 L = 94,600 cm^3

Given the density of the gasoline and its volume, solve for the mass of the gasoline using the formula for the density.

ρ =  mass / volume

0.680 g/cm^3 = mass / 94,600 cm^3

mass = 0.680 g/cm^3 (94,600 cm^3)

mass = 64328 g

mass = 64.328 kg

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Answer:

2 times as much

Step-by-step explanation:

1 hour 2/3 = 60 + (2/3) 40 mins = 100 minutes

3 hours 1/3 = (60 ×3 ) + 20 mins = 200 mins

200 is twice as much as 100

The answer is :

a) 27 m= 2700 cm.

b) 38 dam = 380 m.

c) 34 m = 0.34 hm.

Lets know about the given prefix first,

    m = Meter means one hundred centimeter so,

1 m = 100 cm

   cm =  Centimeter means one-hundredth of a meter so,

1 cm = 0.01 m

  mm = Millimeter means one-thousandth of a meter so,

1 mm = 0.001m

  hm = Hectometer means one hundred meters so,

1 hm = 100 m

  dam = Decameter means ten meters so,

1 dam = 10 m

So,  

a) 27 m = 2700 cm

b) 38 dam = 380 m

c) 34 m = 0.34 hm.

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The required sequences are The first pair is rotated and translated, the second pair is reflected and translated, and the third pair is reflected and translated.

Translation means the displacement of a figure or a shape from one place to another. In translation a figure can move upward, downward, vertical and horizontal.

Some of the Translation are,

A reflection is a mirror image of the shape. An image will reflect through a line, known as the line of reflection. A figure is said to reflect the other figure, and then every point in a figure is equidistant from each corresponding point in another figure.

Rotation means the circular movement of an object around a centre. It is possible to rotate different shapes by an angle around the centre point.

Translation means the displacement of a figure or a shape from one place to another. In translation, a figure can move upward, downward, right, left or anywhere in the coordinate system.

Thus, the required sequences are The first pair is rotated and translated, the second pair is reflected and translated, and the third pair is reflected and translated.

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The complete question image is attached.

Answer:

Step-by-step explanation:

brackets first

5 - (3-2) + 2

5 - (1) + 2

5 - 1 + 2

4 + 2

6

Answer:

5-(3-2)+2

5-1+2

4+2

6

Step-by-step explanation:

Follow PEMDAS

P ()

E: Exponent

M: Multiplication

D: Division

A: Addition

S: Subtraction

And you answer each equation going from Left to Right

if d increases c will decrease AND  if c increases d will decrease.

If b is not equal to 0, an ordered pair of numbers a and b, denoted as a / b, is a ratio. A proportion is an equation that equalizes two ratios. For illustration, the ratio may be expressed as follows: 1: 3 (If there are 1 boy and 3 girls, then there are 3 girls for every 1 boy.)

since c and d are inversely proportional

a) if d increases c will decrease

because it is the property of the ratio and proportion

and same will be applied in b

b) if c increases d will decrease

that is obvious....

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The number of windows which can be framed with three 10-foot long pieces of lumber given the dimensions of the windows is; two and a half.

It follows from the task content that the number of windows that can be made given the dimensions of the windows be determined.

On this note, it follows that since the windows are 3 feet high and 3 feet width, the perimeter of each window(square shaped) covered by lumber is;

P = 4s

P = 4 × 3

P = 12 feet.

Hence, each window requires 12 feet of lumber.

However, since the builder has only three 10-foot long pieces of lumber which is equivalent to; 3 × 10 = 30 feet worth.

The number of windows that can be made is;

= 30/12

= 2.5.

Ultimately, only 2 and a half windows can be framed from the three 10-foot long pieces of lumber.

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The statement which describes the effect of replacing the graph of f(x) with the graph of f(x) - 5 is : (b) the graph shifts 5 units down.

What is Transformation?

Transformation :- The transformations of functions define how to graph a function is moving and how its shape is being changed. There are basically three types of function transformations: translation, dilation, and reflection.

f(x) = f(x) + k

This is a translation transformation that shifts the original function f(x) either k units up or k units down. If k is more than 0 then k shifts up. If k is less than 0 then k shifts down.

Here, k = -5<0

Hence, the shift is 5 units down.

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Answer:8(7w+

Step-by-step explanation:

Answer: sure ummm...

r

=

1

d

cs

Step-by-step explanation:

Answer: n+s=c

Step-by-step explanation:

n=c-s

+s   +s

n+s=c

add s to both sides to get c by itself, and you end up with n+s=c

Answer:

1) 256, -128, 64, -32

2) 27, 9, 3, 1, 1/3

3) 5x², 5x⁴, 5x⁶, 5x⁸, 5x¹⁰,

Step-by-step explanation:

1. In this geometric series each term is obtained by multiplying the previous term by (-1/2) or dividing by (-2).

256 ÷ (-2) = - 128

-128 ÷ (-2) = 64

64 ÷ (-2) = (-32)

The geometric series is:

     256, -128, 64, -32...

We can find the common ratio by dividing the second term by first term.

2) 27, 9, ___, _________, 1/3

       [tex]\sf \boxed{\bf common \ ratio= \dfrac{second \ term}{first \ term}}[/tex]

                                 [tex]\sf = \dfrac{9}{27}\\\\ = \dfrac{1}{3}[/tex]

  [tex]\sf 9*\dfrac{1}{3}=3\\\\3*\dfrac{1}{3}=1[/tex]

The geometric series is:

  27, 9, 3, 1, 1/3....

3) 5x², _____, 5x⁶, 5x⁸, _____, ....

Here, we can take 3rd term and 4th term to find the common ratio.

  [tex]\sf common \ ratio = \dfrac{5x^8}{5x^6}\\\\[/tex]

                       [tex]\s = x^{8-6}\\\\=x^2[/tex]

5x² * x² = 5x⁴

8x⁸ * x² = 8x¹⁰

The geometric serious is:

5x², 5x⁴, 5x⁶, 5x⁸, 5x¹⁰, ...

[tex]\sf 1.) \ 256, -128, 64, -32,..\\ \\ 2.) \ 27, 9, 3, 1, 1/3,... \\ \\3.) \ 5x^2, 5x^4, 5x^6, 5x^8,5x^{10} , ...[/tex]

[tex]\sf Geometric \ formula: ar^{n-1}[/tex]

Find the common ratio:

Equation: [tex]256(-\frac{1}{2} )^{n-1}[/tex]

2nd term: [tex]256(-\frac{1}{2} )^{2-1}=-128[/tex]

3rd term: [tex]256(-\frac{1}{2} )^{3-1}=64[/tex]

Find common ratio:

Equation: [tex]27(\frac{1}{3} )^{n-1}[/tex]

3rd term: [tex]27(\frac{1}{3} )^{3-1}=3[/tex]

4th term: [tex]27(\frac{1}{3} )^{4-1}=1[/tex]

Find the common ratio:

Equation: [tex]5x^2 (x^2)^{n-1}[/tex]

2nd term: [tex]5x^2 (x^2)^{2-1} = 5x^2 (x^2) = 5x^{4}[/tex]

5ht term: [tex]5x^2 (x^2)^{5-1} = 5x^2 (x^8) = 5x^{10}[/tex]

According to the given function, we can throw it to the height of 6.6 m.  So, yes we can throw it high enough to reach the ledge.

The given equation is quadratic. A quadratic equation is defined as an equation of a single variable with the highest power of 2. In general, the quadratic equation can be expressed as h(x)= [tex]ax^2- bx + c[/tex], where a, b and c are arbitrary constants. The solution for a quadratic equation is given by:

[tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]

The maximum of a quadratic equation is given by:

= [tex]c-\frac{b^2}{4a}[/tex]

The length to be covered by throwing=6 meters

It is given that the height of the grappling hook you throw is a function h(t) = -4.9t² + 10t + 1.5

Here a =4.9, b = 10 and c = 1.5

The maximum of a quadratic equation is given by:

[tex]c-\frac{b^2}{4a}[/tex]

[tex]1.5-\frac{10^2}{4*(-4.9)}[/tex]

6.6

A throw can be made to reach the wall since the height of wall is less than the maximum value that is 6.6 m.

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Answer:

7-5=2

2+4=6

2×6=12

you always work the Parenthesis 1st

The function rule for h(x) = -3x -3.

In mathematics, functions can be manipulated algebraically to obtain graphs of functions through certain transformations. Such transformations are reflections of the x-axis or the y-axis. To flip a function f(x) on the x-axis, multiply the whole function by a negative value to get -f(x), and to flip a function f(x) on the y axis, f(-x ), specify the x variable with a negative value. If it is reflected around the y-axis, it will stay the same, which gives h(x) = 3x + 3. Flipping around the x-axis (assuming y = 0) has the y-axis as the axis of symmetry, but it is concave down.

The function rule around the x-axis gives a complementary sign of the value of the function, so

h(x) =-3x-3 will be reflection of f(x) =3x+3

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Answer:

1 box of brownie mix= 2 eggs and 1/2 cups of oil

ans=

2 boxes of brownie mix= (2 eggs ×2)(1/2 cups of oil × 2)

=4 eggs and 1 cup of oil

Answer:

4 eggs and 1 cup of oil.

Step-by-step explanation:

2x2=4 1/2x2=1

Step-by-step explanation:

2 + 3 = 5

the sign of the sum is "-", because the temperature dropped (in both cases).

the total change in temperature is -5°.

the sum of 2 positive integers ... is always positive.

both numbers have a positive sign. the sum means "+", so we are adding 2 positive numbers.

nowhere in the operation are we going in the negative direction or bring a negative sign in.

so, where would a "-" sign come from ?

if I have something on the plus side, and I put something positive on top of it, the resulting pile will still be positive.

Answer:y/5=5/6

Step-by-step explanation:based on given conditons

Based on the distance below sea level of the Japan Trench and the Peru-Chile Trench, the difference and the deeper trench is 1 km, and the Japan Trench is deeper.

The deeper trench is the one that is further down sea level. In other words, it is the one that is a larger distance below sea level.

The Japan Trench is 9 km below sea level while the Peru-Chile trench is 8 km below sea level. This means that the Japan Trench is deeper.

The difference is:

= 9 - 8

= 1 km

In conclusion, the Japan trench is deeper by 1 km.

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From the situation described, we have that:

a. The absolute value equation is: |w - 35| = 8.

b. The solutions are w = 27 and w = 43, meaning that the minimum weight is of 27 pounds and the maximum weight is of 43 pounds.

A home improvement store sells bags of sand, which are labeled as weighing 35 pounds. The equipment used to package the sand produces bags with a weight that is within 8 pounds of the labeled weight.

The absolute function is defined by:

It measures the distance of a point x to the origin, hence, for example, |-2| = |2| = 0.

For this problem, the difference between the weight w and 35 pounds is of 8 pounds, hence the equation is:

|w - 35| = 8.

From the definition, the solutions are given as follows:

The solutions are w = 27 and w = 43, meaning that the minimum weight is of 27 pounds and the maximum weight is of 43 pounds.

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