What are the slopes of these lines and how are they perpendicular

From the equations we get 'x' as '-2' and 'y' as '-7'

What is an equation?

An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equals symbol =. The word equation and its cognates in various languages may have somewhat different definitions; for example, in French, an équation is defined as including one or more variables, but in English, an equation is any well-formed formula consisting of two expressions linked by an equals sign. An equation consists of two expressions joined by an equals sign ("="). The expressions on each side of the equals sign are referred to as the equation's "left-hand side" and "right-hand side." The right-hand side of an equation is frequently considered to be zero.

4x - 2y = 6....................equation (1)

-2x + 4y = -24...............equation (2)

Multiply equation (1) by 2 and add with equation (2)

8x - 4y =   12

-2x + 4y = -24

----------------------

6x         = -12

or, x = -12/6 = -2

from equation (1),

     4x - 2y = 6

or, 4(-2) - 2y = 6

or, -2y = 6 + 8

or, y = 14/-2 = -7

Hence, from the equations we get 'x' as '-2' and 'y' as '-7'

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Answer:

see below

Step-by-step explanation:

km   *   miles/km  

     see how the 'km' then 'cancels out' and you are left with 'miles'         the underlined shows the units of the conversion factor

When we want to find the slope of a line,

We find two points and connect them to form a right triangle.

We then divide the increase in the [tex]y[/tex]-axis by the increase in the [tex]x[/tex]-axis to find the slope.

Since the line is tilted to the right, the slope is positive.

Answer:

factored form: [tex]2x(x-5)[/tex], standard form: [tex]2x^2-10x[/tex]

Step-by-step explanation:

so we're given the expression: [tex]7x^2 - 5x(x+2)[/tex]

In this case we want to use the distributive property, which essentially states that: [tex]a(b+c)=ab+ac[/tex]

So we can use this to rewrite:

[tex]-5x(x+2)=(-5x)(x)+(-5x)(2)[/tex]

which simplifies to

[tex]-5x^2-10x[/tex]

this just simplifies the last part of our expression, so using this instead of what we originally had gives us

[tex]7x^2-5x^2-10x[/tex]

Since the 7x^2 and the -5x^2 have the same variable, we can subtract their coefficients.

Another way to think of it is

[tex]7x^2-5x^2\implies x^2(7-5)[/tex]

so in a way we're "factoring" out the x^2, which means we can simply subtract the coefficients for this reason.

This of course gives us 2, by we're multiplying by x^2 so we get

[tex]2x^2-10x[/tex]

Now if you want you can factor out a 2x, to get

[tex]2x(x-5)[/tex]

Add 5 x 3 + 7

5 x 3 + 7
15 + 7
22

Answer:

Alternatively, you may use addition to solve

Step-by-step explanation:

5+5 = 10 and 5+7 = 12, and we know that 10+10 = 20

Just add the number 2 from the number 12 to 20, and you have the same answer

The inequality that Matt could solve to find out how many more miles he can run if he keeps his current pace is less than 6 miles.

It should be noted an inequality is used to show the expressions that are not equal.

In this case, Matthew wants his run today to take no more than 90 minutes and he already has run 30 minutes at a pace of 10 minutes per mile.

Therefore, the appropriate inequality will be;

Let miles = m

m <= 90/10 - 30/10

m <= 9 - 3

m <= 6

He has about 6 miles more.

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The matching of the mathematical terms to the equations, and expressions is as follows;

Area of a circle → π•r²

Percent equation → P = %dec × w

Percent proportion → [tex] \displaystyle{ \frac{p}{w} = \frac{\%}{100} }[/tex]

Circumference → π × d

Pi → π

Base equation → y = k•x

Constant of proportionality → [tex] \frac{y}{x} [/tex]

% increase → [tex] \frac{Amount \: increase}{Original \: amount} [/tex]

%decrease →[tex] \frac{Amount \: decrease}{Original \: amount} [/tex]

Interest Earned → P×r×t

An expression in mathematics consists of mathematical symbols and variables joined together operators in the proper manner

The area of a circle is π × r²

Where;

r = The radius of the circle

A percent equation equation is one of the sides of the equation consists of a percentage

A percent proportion express a proportion as a percentage

The circumference of a circle is the distance round the circle, which is given by the product of Pi and the radius of the circle

The symbol Pi is π

The base equation is one written in simple form

The constant of is the constant ratio between variables that are proportional

This is the ratio of the increase to the original amount expressed as a percentage

The ratio of the decrease to the original amount expressed as a percentage

This is the amount added to an investment sum or amount and it is given by the product of the principal, P, rate, r and time, t

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Answer: You would pay $2,302 back.

Step-by-step explanation:

Compound interest occurs when the interest is reinvested rather than paying it out. When it happens interest in the next period is then earned on the principal sum plus previously accumulated interest.

According to the flight on certain routes, the experiment is a binomial experiment and this will be determined by observing that Flights on a certain route are on-time 80% of the time and 10 flights are randomly selected and the number of​ on-time flights is recorded.

(a) This is a binomial experiment since there are only two possible outcomes for each data that is a flight is either on time (p = 80% = 0.8) or late (q = 1 - p = 1 - 0.8 = 0.2).

​(b) Using the formula:

P(a out of n) = (nCa)(pᵃ)(qⁿ⁻ᵃ), where n = 10 flights, a = the number of flights that arrive on time:

P(7/10) = (10C7)(0.8)⁷ (0.2)³= 0.2013

Therefore, 0.2013 chance is there that exactly 7 of 10 flights will arrive on time.

​(c) Fewer than 7 flights are on time means that we must add up the probabilities for P(0/10) up to P(6/10).

P(0/10) + P(1/10) + ... + P(6/10) = 0.1209

This means that 0.1209 chance that less than 7 flights will be on time.

​(d) The probability that at least 7 flights are on time is the exact opposite of part (c), where less than 7 flights are on time. So instead of calculating each formula from scratch, we can simply subtract the answer in part (c) from 1.

1 - 0.1209 = 0.8791.

So there is a 0.8791 chance that at least 7 flights arrive on time.

(e) For this, we must add up P(5/10) + P(6/10) + P(7/10), which gives us

0.0264 + 0.0881 + 0.2013 = 0.3158, so the probability that between 5 to 7 flights arrive on time is 0.3158.

According to the flight on certain routes, the experiment is a binomial experiment

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DISCLAIMER: The question provided is incomplete as some data are missing. The above answer is solved as per a relevant question

According to an​ airline, flights on a certain route are on time 80 ​% of the time. suppose 10 flights are randomly selected and the number of​ on-time flights is recorded. ​(a) explain why this is a binomial experiment. ​(b) find and interpret the probability that exactly 7 flights are on time. ​(c) find and interpret the probability that fewer than 7 flights are on time. ​(d) find and interpret the probability that at least 7 flights are on time. ​(e) find and interpret the probability that between 5 and 7 ​flights, inclusive, are on time.

Answer:

What happened to each packet of washing powder

please finish the question so i can answer xD

if i infer right then each packet of washing powder was washed up in the washing machine! :)

Answer:

d

Step-by-step explanation:

3 multiplied by ricks salary minus 150

Answer:

Vertex: (-3,-1)

Domain : (negative inf. , inf.)

Range: (negative inf. , 1]

The length of the panel is 0.5 meter.

To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.

Given that,

Area of the panel = 0.8 [tex]m^{2}[/tex]

width of the panel = 1.6 meter

Here, solar panel is in the form of rectangle.

Area of rectangle = length× width

                     0.8 =   1.6 × length

                   length = [tex]\frac{0.8}{1.6}[/tex]

                   length = 0.5 meter

Hence, The length of the panel is 0.5 meter.

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Answer:

(2x+1)(x-5)

Step-by-step explanation:

factorsed by grouping them

roots are -1/2 and 5

The slope-intercept form of a function f(x) = mx + c therefore,f(x) = -3x + 4 is the correct notation of the function 9x + 3y = 12 so option (B) is correct.

The function is a relationship between variables, and the nature of the relationship defines the function for example y = sinx and y = x +6 like that.

The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.

As per the given function,

9x + 3y = 12

Subtract 9x both sides,

9x - 9x + 3y = 12 - 9x

3y = 12 - 9x

Divide by 3 into both sides,

y = 12/3 - 9x/3

y = -3x + 4

Since,y = f(x)

f(x) = -3x + 4 .Here -3 is the slope while 4 is the y-intercept.

Hence "The slope-intercept form of a function f(x) = mx + c therefore,f(x) = -3x + 4 is the correct notation of the function 9x + 3y = 12".

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Using the pythagorean theorem we get that:

Note: the shortest distance between two points in a plane is a stright line, that is why we calculated d.

The Recurrence interval for tornadoes in tuscaloosa county is 0.909

What is recurrence interval ?

The time period in which a new occurrence of something that happened or appeared before : a repeated occurrence or The time frame in which a previously occurring event or appearance first occurs: a recurring occurrence

Given that,

Total number of tornadoes is 77

Total time for Recurrence is 70 years

Using these data,

Recurrence = Total time for recurrence / Total number of tornadoes

Substituting we get,

Recurrence interval = 70/77

= (70/77)

= (0.909)

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Answer: 20x

Step-by-step explanation:

Answer:

20x

Step-by-step explanation:

just trust me because you have to mulitply

Answer:

x = -1/2 , 1

Step-by-step explanation:

The most appropriate choice for distance will be given by-

Michael drove [tex]350[/tex] miles

What is Distance?

The length of the path an object takes without taking into account the direction of motion of the object is known as distance.

If [tex]s[/tex] is the speed of the object and [tex]t[/tex] is the time, then

Distance = [tex]s \times t[/tex]

Here,

Amount of money charged by a rental company for one day  = $[tex]80[/tex]

Amount of money charged by a rental company for four days = $[tex](80 \times 4)[/tex]

                                                                                                       = $320

Total bill charged by the rental company = $[tex]460[/tex]

Remaining bill = $[tex](460 - 320)[/tex]

                        = $[tex]140[/tex]

Amount of money charged by a rental company for one mile = [tex]40[/tex] cents

                                                                                                      = $[tex]0.40[/tex]

Number of miles driven by Michael = [tex]\frac{140}{0.40}[/tex]

                                                           = [tex]350[/tex] miles

Michael drove [tex]350[/tex] miles

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Answer:

Month:

1             = 32$

2            =  64$

3            = 96$

4            = 128$

Step-by-step explanation:

Answer: 8.75

Step-by-step explanation:

(0, 20) and (40, 370) any two coordinate points can be chosen

(370 - 20) / (40 - 0)

= 35/4 or 8.75

Answer: The slope is 0.

Step-by-step explanation:

      We will use the slope formula to find the slope of the line going through these two points.

[tex]\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

[tex]\displaystyle \frac{3-3}{2--4}=\frac{0}{2+4} =0[/tex]

      The slope of this line is 0.

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By completing squares we will rewrite the equation as:

(x + 2)^2 - 2

Here we have the quadratic equation:

x^2 + 4x + 2

And we want to complete squares, remember that the square trinomial is:

(a + b)^2 = a^2 + 2ab + b^2

We can rewrite the quadratic as:

x^2 + 2*2*x + 2

Now, adding and subtracting 2 we get:

x^2 + 2*2*x + 2 + 2 - 2

x^2 + 2*2*x + 4 - 2

(x^2 + 2*2*x + 2^2) - 2

(x + 2)^2 - 2

So the first option is the correct one.

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Total Smaller balls measuring 5mm diameter will be 12.

A sphere is a geometrical object that resembles a two-dimensional circle in three dimensions. In three-dimensional space, a sphere is a collection of points that are all located at the same r-distance from a single point. The radius of the sphere is denoted by the letter r, and the specified point represents its center.

1 cm = 10mm

6 cm = 60mm

Ball diameter is 5 mm.

diameter of the lead sphere divided by the number of balls

= 60mm/ 5mm

= 12 balls

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Answer:

the answer to the question is 1/8

The percent error of the shipment pipes is 1.01%

Percent error:

Percent error is defined as a difference between estimated value and the actual value in comparison to the actual value and is expressed as a percentage.

It can be calculated using the formula,

PE = (|Estimated value-Actual value|/ Actual value) × 100

Given,

A shipment of 22-inch pipes contains a pipe that is exactly 21.78 inches.

Here we need to find the percent error of the shipment.

According to the percent error formula,

Here we have the values of the shipment are

Estimated value = 22

Actual value = 21.78

So, now we have to apply the values on the formula, then we get,

PE = (|22 - 21.78/21.78|) x 100

When we simplify it, then we get,

PE = 0.0101 x 100

PE = 1.01%

Therefore, the percent error in the shipment is 1.01%.

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