5) Find the slope of each line.

Answer:

a) The equation of line perpendicular to above line and passes through point (-7,-4) is [tex]\mathbf{y=\frac{7}{2}x+\frac{41}{2}}[/tex]

b) The equation of line parallel to above line and passes through point (-7,-4) is [tex]\mathbf{y=-\frac{2}{7}x-6}[/tex]

Step-by-step explanation:

We are given the line: [tex]y=-\frac{2}{7}x-7[/tex]

The slope of the above equation is: [tex]m=-\frac{2}{7}[/tex] (By comparing with general form [tex]y=mx+b[/tex] where m is slope)

a) Find equation of line perpendicular to above line and passes through point (-7,-4)

If two lines are perpendicular there slopes are opposite reciprocal i.e [tex]m_1=-\frac{1}{m_2}[/tex]

The slope of new line will be: [tex]m = \frac{7}{2}[/tex]

Now finding y-intercept using slope and point (-7,-4)

[tex]y=mx+b\\-4=\frac{7}{2}(-7)+b \\-4=\frac{-49}{2}+b \\b=-4+\frac{49}{2}\\b=\frac{-8+49}{2}\\b=\frac{41}{2}[/tex]

So, the equation of line perpendicular to above line and passes through point (-7,-4) will be:

[tex]y=mx+b\\y=\frac{7}{2}x+\frac{41}{2}[/tex]

So, the equation of line perpendicular to above line and passes through point (-7,-4) is [tex]\mathbf{y=\frac{7}{2}x+\frac{41}{2}}[/tex]

b) Find equation of line parallel to above line and passes through point (-7,-4)

If two lines are parallel there slopes are same i.e [tex]m_1=m_2[/tex]

The slope of new line will be: [tex]m = -\frac{2}{7}[/tex]

Now finding y-intercept using slope and point (-7,-4)

[tex]y=mx+b\\-4=-\frac{2}{7}(-7)+b \\-4=-2(-1)+b\\-4=+2+b \\b=-4-2\\b=-6[/tex]

So, the equation of line parallel to above line and passes through point (-7,-4) will be:

[tex]y=mx+b\\y=-\frac{2}{7}x-6[/tex]

So, the equation of line parallel to above line and passes through point (-7,-4) is [tex]\mathbf{y=-\frac{2}{7}x-6}[/tex]

Total time taken by Andrew and bob is 2hr.

given, time taken by Andrew to paint the room = 3hrtime taken by bob to paint the room =6hr rate of Andrew as x =1/3.

rate of bob as y=1/6x+y=1/3+1/6=1/2

total time taken by Andrew and bob =1/x + y      

                                                             =1/1/3+1/6

                                                             = 2hr.

therefore total time taken by Andrew and bob is 2 hr.

The formula for time is given as [Time = Distance ÷ Speed]. To calculate the distance, the time formula can be molded as [Distance = Speed × Time].

To get the total decimal hours we use the formula: h = hours + (minutes / 60) + (seconds / 3600). To get the total decimal minutes we use the formula: m = (hours * 60) + minutes + (seconds / 60).

The types of functions can be broadly classified into four types. Based on Element: One to one Function, many to one function, onto function, one to one and onto function, into function.

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Step-by-step explanation:

Parallel lines have the same slope so they can therefore never touch. Just change the y-int. (Any number as long as it's not the same as the previous)

I.E.:

y = -3x - 12

Answer:

c

Step-by-step explanation:

you substract both numbers to get 29. Difference in math problems means to subtract!

Answer:

The first table

Step-by-step explanation:

Answer:

[tex]3.75\ \text{m}[/tex]

Step-by-step explanation:

A escala da réplica é  [tex]1:80[/tex]. Isso significa que 1 metro da réplica da escala representa 80 metros do edifício real.

Portanto, 1 metro do edifício real representa [tex]\dfrac{1}{80}[/tex] metros da réplica.

Precisamos encontrar a altura da réplica

[tex]420\ \text{m}=420\times\dfrac{1}{80}=5.25\ \text{m}[/tex]

Assim, a réplica da escala terá uma altura 5.25 m.

Está colocado numa sala com 9 m de altura.

A distância entre o topo da réplica e o teto do corredor é [tex]9-5.25=3.75\ \text{m}[/tex].

are u sure it's - 24 in the middle one of the sequence. ?

Answer:

its D/ 56.25

Step-by-step explanation:

because the other numbers are too small

Answer:

x = 5

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define equation

4x - 1 = 7x - 16

Step 2: Solve for x

Step 3: Check

Plug in x into the original equation to verify it's a solution.

Here we see that 19 does indeed equal 19.

∴ x = 5 is a solution to the equation.

Answer:

4x−1=7x−16

Step 1: Subtract 7x from both sides.

4x−1−7x=7x−16−7x

−3x−1=−16

Step 2: Add 1 to both sides.

−3x−1+1=−16+1

−3x=−15

Step 3: Divide both sides by -3.

−3x

−3

=

−15

−3

x=5

Step-by-step explanation:

Answer:

We get value of the value of b = 5

Step-by-step explanation:

Line AB passes through points A(−6, 6) and B(12, 3). If the equation of the line is written in slope-intercept form, y=mx+b, then m=m equals negative StartFraction 1 Over 6 EndFraction.. What is the value of b?

We have slope m: [tex]m=-\frac{1}{6}[/tex]

We need to find value of b (y-intercept)

Using the point A(-6,6) and slope [tex]m=-\frac{1}{6}[/tex] we can find b.

Using slope-intercept form, putting values of m and x and y we get the value of b:

[tex]y=mx+b\\6=-\frac{1}{6}(-6)+b\\6=1+b\\b=6-1\\b=5[/tex]

So, we get value of the value of b = 5

Answer:

C: 5

Step-by-step explanation:

Edg 2022

Answer: 97

Step-by-step explanation:

Answer:

97 natural numbers

Step-by-step explanation:

[tex]49^2-48^2\\2401-2304=97[/tex]

The function f(x) = x^4 + 4/x^2 + 1 is an even function

The equation of the function is given as

f(x) = x^4 + 4/x^2 + 1

Calculate f(-x)

So, we have

f(-x) = (-x)^4 + 4/(-x)^2 + 1

Evaluate the exponents

f(-x) = x^4 + 4/x^2 + 1

Calculate -f(x)

So, we have

-f(x) = -[x^4 + 4/x^2 + 1]

Evaluate the product

-f(x) = - x^4 + 4/x^2 + 1

From the above computations, we have

f(x) = f(-x)

This represents an even function

Hence, the function f(x) = x^4 + 4/x^2 + 1 is an even function

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Answer:

B. 96%

Step-by-step explanation:

Sara only missed 7 days of 184 days this year meaning 184 - 7 = 177 and

177 is how many days she attended school, so to figure out percentage take the number of days she attended school and divide by the total amount of days in this year which is 184: 177/184 = 0.96195652173

then multiply by 100 to get percentage so approximately 96%.

Answer:

y=1/2x-5.................

Step-by-step explanation:

hope this is what your looking for

In the given figure , two sides of the triangle are equal , so it is isosceles triangle . So , as we know that in an isosceles triangle equal side's opposite answers are also equal . Now ,

=> x = 75°

Hence , x = 75°

Using the same property which we used in the above problem ,

• x = x

Now using angle sum property of triangle ,

=> x + x + 40° = 180°

=> 2x + 40° = 180°

=> 2x = 180° - 40°

=> 2x = 140°

=> x = 140° / 2

=> x = 70°

Hence , x = 70° .

Answer:

The ans to the first question would be 75, Coz....

It's an Isosclese triangle, as both sides are equal [The two lines on the triangle indicate that its equal]

So,the angle given is 75 degrees, the other angle would be 75 degrees too.

For the second question-

The same rule applies here, the triangle shown is an isosclese triangle,so the angle x & the angle opposite to x should be equal [The angle opposite or next to angle x is blank, so lets just call it y]

The equation of a triangle goes-

The angles of a triangle add upto 180

So 40+x+y=180

180-40 will give the sum of both angle x & y

180-40=140 [Now we know that x+y=140, we also know that both angles have the same value, so basically they're equal]

this means that we can divide 140 equally into two parts to disturbute the value to both x & y

140/2=70 degrees

So, the ans of x=70 [y is also 70, but the question doesnt  ask for it]

Answer:

B. 0.75

Step-by-step explanation:

this is what I think cuz the graph at 1 is 0.75

Answer:

The most common interval is 10 to 14.99 $ with 11 items

Step-by-step explanation:

See attached for details.

$10.00-$14.99 is the most common interval of dinner prices.

To find the most common interval of dinner prices,

Organize the data into the specified intervals and then count the occurrences in each interval.

Here are the intervals:

1. $5.00-$9.99

2. $10.00-$14.99

3. $15.00-$19.99

4. $20.00-$24.99

5. $25 and up

Now, let's categorize the dinner prices from the given list into these intervals:

1. $7.50, $7.98, $6.50, $8.25, $8.75, $9.00, $9.99 (7 prices)

2. $10.00, $12.00, $12.98, $12.99, $11.50, $13.50, $11.25, $13.00, $12.50 (9 prices)

3. $14.00, $14.75, $15.00, $17.49, $16.00, $17.99 (6 prices)

4. $21.00, $20.00, $22.00 (3 prices)

5. $26.00, $28.50, $25 and up (3 prices)

Now, let's see which interval has the highest number of prices.

It appears that the second interval, $10.00-$14.99, has the most prices (9 prices), making it the most common interval of dinner prices.

Hence, $10.00-$14.99 is the most common interval of dinner prices.

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Answer:

a. 2w + 2(w+4) = 60

Answer:

the answers a

Step-by-step explanation: the width is 10 and the length is 20

Answer:

-4.08333

Step-by-step explanation:

2 1/3 + 1 3/4 = 4912 = 4 112 ≅ 4.0833333. Spelled result in words is forty-nine twelfths (or four and one twelfth)

Answer:

This answer is D

Step-by-step explanation:

Answer:

C, Perimeter is 40

Step-by-step explanation:

To find perimeter add up all the sides, to find area, multiply the sides.

Answer:

[tex]\frac{2}{3}[/tex]

Step-by-step explanation:

let n be the number , then

[tex]\frac{1}{6}[/tex] n + [tex]\frac{1}{3}[/tex] = [tex]\frac{2}{3}[/tex] n

multiply through by 6 ( the LCM of 6 and 3 ) to clear the fractions

n + 2 = 4n ( subtract n from both sides )

2 = 3n ( divide both sides by 3 )

[tex]\frac{2}{3}[/tex] = n

Answer:

[tex]{\mathsf {n=\frac{2}{3}}}[/tex]

Step-by-step explanation:

In word problems like this, you have to break down the problem description into math form

This is an equation description so we need a variable to work with. Let's call this variable n

1/6th of this number can be translated to:
[tex]\displaystyle \mathsf {\frac{1}{6}n}[/tex]  

1/6th of this number plus one-third translates to:
[tex]\displaystyle \mathsf {\frac{1}{6}n} + \frac{1}{3}[/tex]

1/6th of this number, plus one-third returns two-thirds of that number
returns is just a fancy way of saying equal to.

So returns two-thirds of that number translates to
= two-thirds of that number

Two-thirds of the number is
[tex]\displaystyle \mathsf {\frac{2}{3}n}[/tex]

So putting all this together we get the equation
[tex]\displaystyle \mathsf {\frac{1}{6}n} + \frac{1}{3} = \frac{2}{3}\mathsf n[/tex]

We have to now solve for the equation.

Bring all the n terms to the left side and the constant(1/3) to the right to solve for n

[tex]\displaystyle \mathsf{ Subtract\:}\frac{1}{3}\mathsf {\:from\:both\:sides}[/tex]
[tex]\mathsf {\frac{1}{6}n+\frac{1}{3}-\frac{1}{3}=\frac{2}{3}n-\frac{1}{3}}[/tex]

Simplify to get
[tex]\mathsf {\frac{1}{6}n=\frac{2}{3}n-\frac{1}{3}}[/tex]

Subtract [tex]\mathsf {\frac{2}{3}}[/tex] from both sides
[tex]\mathsf {\frac{1}{6}n-\frac{2}{3}n=\frac{2}{3}n-\frac{1}{3}-\frac{2}{3}n}[/tex]

Simplify  to get
[tex]\mathsf{\frac{1}{6}n-\frac{2}{3}n= -\frac{1}{3}}[/tex]

The left side term is [tex]\mathsf {\frac{1}{6}n-\frac{2}{3}n}[/tex]
Factor out the common term [tex]n[/tex]:
[tex]\mathsf {n\left(\frac{1}{6}-\frac{2}{3}\right)}[/tex]
[tex]\mathsf {\frac{1}{6}-\frac{2}{3}=-\frac{1}{2} }[/tex]

So we get our equation as
[tex]\mathsf {-\frac{1}{2}n=-\frac{1}{3}}[/tex]

Multiply both sides by -2 to get

[tex]\boxed {\mathsf {n=\frac{2}{3}}}[/tex]

the distance between the points A and B that is AB is equal to 5.39 units.

We are given the points as:

A = ( 2, 3 )

B = ( 0, - 2 )

We need to find the distance AB between the points.

The distance between the points is given by the formula:

Distance = √ ( y₂ - y₁ )² + ( x₂ - x₁ )²

Substituting the values in the formula, we get that:

Distance AB = √ ( - 2 - 3 )² + ( 0 - 2 )²

Distance AB = √ ( - 5 )² + ( - 2 )²

Distance AB = √ 25 + 4

Distance AB = √ 29 units

Distance AB = 5.39 units.

Therefore, we get that, the distance between the points A and B that is AB is equal to 5.39 units.

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[ -8, 2 ] [ -6 , 0 ] [ -4 , - 2 ] are probability of the cards into three pairs with the same total .

What is probability?

( -8 ) + 0 + ( - 6) + 2 + ( -4 ) + ( -2 )   =   -20 + 2 = -18

                                                              { addition of negative numbers }

So, each pair  =  -18 / 3  = -6  { division }

so the pairs are = [ -8, 2 ] [ -6 , 0 ] [ -4 , - 2 ]

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If f(x) = 2x + 1, then f(3) =9.

A function is a relation between a set of inputs having one output each. In simple words.

We have

[tex]f(x)=2^{x} +1\\f(3)=2^3+1\\f(3)=8+1\\f(3)=9.[/tex]

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d=first diver depth

s=second diver depth

d= 30

S= 30-12=18

the equation given and the gauge must be wrong because the equation for the second duvet souls be s=d-12 since the first diver is DEEPER than the second.

I think the answer would be A because 5% ×100=0.05 , and in the question they have been telling us that it decreased by 5 from the last week so the equation would be g of the last week - 0.05

Answer:

she can go on 30 rides I think

Answer:

30 rides

Step-by-step explanation:

Ok first you have to subtract 5 because you payed 5$ to get in and then you divide 15$ by 0.50 and that will give you 30. So she can ride 30 rides total!