Write the equation of the line passing through point (4, -1) and perpendicular to the line whose equation is 2x - y - 7 = 0.

Answers

Answer 1

Answer:

x + 2y + 4 =0

Explanation:

1) You know a point (4 - 1) and that the line is perpendicular to a given line.

2) From the equation of the perpendicular line whose equation was given, you determine the slope, for which you can use the slope-intercept form of the equation:

2x - y - 7 = 0 => y = 2x + 7.

The slope is the coeffiicient of x, which is 2.

Therefore, slope = 2.

3) The slope of the other line is the negative inverse of the slope of the perpedicular line:

slope = - 1/2

4) Now that you have the slope of your line and the point (4, - 1) you determine the equation with this procedure:

y - b
------- = slope
x - a

where a y b are the coordinates of the point (4, - 1) and the slope is -1/2

=>

y - (-1)
---------- = - 1/2
x - 4

5) Simplify

2(y + 1) = - (x - 4)

2y + 1 = - x + 4

2y + x +1 + 4 = 0

x + 2y + 4 =0 <---------- this is the equation searched.

Related Questions

Miss Watson runs a distance of 200 meters in 25 seconds. Workout the average speed of Mrs Watson in meters per second.

Answers

Hey there!

Divide 200 by 25.

200/25= 8

She is running an average of 8 m/s. (that's how we represent meters per second)

I hope this helps!
~kaikers

The correct answer to your question is... 8mps. (meters per second)

Explanation:
To workout the average speed of Mrs Watson in meters per second, you would solve the problem 200 ÷ 25.

200 ÷ 25 = 8

So... we now figured out that the average speed Mrs Watson runs, is 8 meters per second.

I hope this helps!
Please Rate & Thank!
Please mark as Brainliest!

Have a wonderful day! : )

The cost, c(x), for a taxi ride is given by c(x) = 3x + 2.00, where x is the number of minutes. On a piece of paper, graph c(x) = 3x + 2.00. Then determine which answer matches the graph you drew, including the correct axis labels.

Answers

Since this is time and cost, we have no need for negatives, so we begin our graph at the origin (0, 0). At 0 minutes, the cost would be $2.00, so 2 is our y-intercept. For each successive minute, the cost goes up $3, so we go from (0, 2) to (1, 5), then to (2, 8), etc.

The y-intercept of 2.00 indicates that even if the ride was 0 minutes, there is still a flat fee of $2.00.

What is a slope?

If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,

then the equation of a line is

y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)

To find the slope;

m = (y₂- y₁) / (x₂ - x₁)

The characteristics of the graph of the equation c(x) = 3x + 2.00.

The graph of c(x) = 3x + 2.00 is a straight line with a slope of 3 and a y-intercept of 2.00.

The x-axis represents the number of minutes, and the y-axis represents the cost in dollars.

The slope of 3 indicates that for every additional minute of the taxi ride, the cost increases by $3.

The y-intercept of 2.00 indicates that even if the ride was 0 minutes, there is still a flat fee of $2.00.

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Write an inequality for the sentence. Then solve the inequality. Fifteen less than a number is at most 6.
pls help

Answers

i believe the correct answer is 15i hope this helps out.

The requried inequality for the sentence is x - 15 ≤ 6 and the solution to the inequality is x ≤ 21.

What is inequality?

Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

Here,

The inequality for the sentence "Fifteen less than a number is at most 6" can be written as:

x - 15 ≤ 6

where x represents the unknown number.

To solve for x, we will add 15 to both sides of the inequality:

x - 15 + 15 ≤ 6 + 15

Simplifying,

x ≤ 21

Therefore, the solution to the inequality is x ≤ 21.

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Steve ordered plastic cases for storing his baseball cards. Each case has a length of 12 centimeters, a width of 6.5 centimeters ,and a height of 1.25 centimeters, what is the volume, in cubic centimeters, of one baseball card case?

Answers

For this case you should see the box as a rectangular prism.
The volume of a rectangular prism is given by:
V = (L) * (W) * (H)
Where,
L: length
W: width
H: height.
Substituting the values we have:
V = (12) * (6.5) * (1.25)
V = 97.5 cm ^ 3
Answer:
the volume, in cubic centimeters, of one baseball card case is:
V = 97.5 cm ^ 3

Answer:

97.5

Step-by-step explanation:

Factor completely.

15x^2y^2-3x^3y+75x^4

Answers

15x2y2+3x3y+75x4 Final result : 3x2 • (25x2 + xy + 5y2)

Step by step solution :Step 1 :Equation at the end of step 1 : (((15•(x2))•(y2))+((3•(x3))•y))+(3•52x4) Step 2 :Equation at the end of step 2 : (((15•(x2))•(y2))+(3x3•y))+(3•52x4) Step 3 :Equation at the end of step 3 : (((3•5x2) • y2) + 3x3y) + (3•52x4) Step 4 :Step 5 :Pulling out like terms :

5.1 Pull out like factors :

75x4 + 3x3y + 15x2y2 = 3x2 • (25x2 + xy + 5y2)

Trying to factor a multi variable polynomial :

5.2 Factoring 25x2 + xy + 5y2

Try to factor this multi-variable trinomial using trial and error

Factorization fails

Final result : 3x2 • (25x2 + xy + 5y2)

The factorized form of the algebraic expression 15x²y² - 3x³y + 75x⁴ is 3x²(5y² - xy + 15x²).

What is the factorization of algebraic expressions?

Factorization of algebraic expressions is a process to break the expression and show it as a product of two or more smaller expressions by grouping and taking the greatest common factor out of the groups.

How to solve the question?

In the question, we have been asked to factor the expression 15x²y² - 3x³y + 75x⁴ completely.

We know that factorization is the process of breaking the expression into smaller expressions.

We first try to find the greatest common factor among the three terms provided in the expression.

First, we will go with the numerical part.

We have 15, -3, and 75.

The greatest common factor for these three is 3.

No, we will go with the variable part.

We have x²y², x³y, and x⁴.

The greatest common factor for these three is x².

Thus, the greatest common factor for the expression is 3x²

Taking 3x² common throughout, we get:

3x²(5y² - xy + 15x²), which is the required factored form.

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Peter has 6 sweaters, 4 pairs of jeans, and 3 pairs of shoes. how many different outfits can peter make using one sweater, one pair of jeans, and one pair of shoes?

Answers

the answer is 72 because 6x4x3=72

James needs to clock a minimum of 9 hours per day at work. The data set records his daily work hours, which vary between 9 hours and 12 hours, for a certain number of days.

{9, 9.5, 10, 10.5, 10.5, 11, 11, 11.5, 11.5, 11.5, 12, 12}.

The median number of hours James worked is 10 11 12 13 . The skew of the distribution is negative positive zero zero with symmetry .

Answers

The median is the 11 as median is the middle value

and it will be a negative skew

helpppppppppppppppppppppppp

Answers

The first thing to is factor the denominator of the rational function:
[tex] x^{2} -2x-3[/tex] to do this we'll need to find two number whose product is -3 and its sum is -2; those numbers are 1 and -3, so:
[tex] x^{2} -2x-3=(x+1)(x-3)[/tex]
Now we can rewrite our rational function as follows:
[tex]f(x)= \frac{x-3}{(x+1)(x-3)} [/tex]
Notice that we have a common factor (x-3) in both numerator and denominator; therefore we can cancel them:
[tex]f(x)= \frac{1}{x+1} [/tex]

Taking all the above into consideration we realize that x=3 is a removable discontinuity; the correct answer is the first one: there is a hole in x=3 and asymptote at x=-1.

Quick!!!Geoffrey buys 48 shares of Ignyta, Inc. (RXDX) at $6.15 each, and his broker charges him a commission of $81. How much did Geoffrey pay for his stock?A.$376.20
B.$295.20
C.$450.30
D.$219.60

Answers

B, Add 48 with 6.15 and add the sum with 81

a game is played where 26 tiles are in a bag. each tile has a different letter of the alphabet on it. if you draw 5 letters what is the probability of the letters being m-u-s-i-c in order if there is no replacement?

Answers

Final answer:

The probability of drawing the letters M-U-S-I-C in order from a bag of 26 tiles without replacement is approximately 0.000207.

Explanation:

The probability of drawing the letters M-U-S-I-C in order from a bag of 26 tiles without replacement can be calculated as follows:

First, we need to determine the total number of ways to draw 5 tiles from 26, which is represented by the combination formula: C(26,5) = 26! / (5! * (26-5)!).Next, we need to determine the number of ways to draw the letters M-U-S-I-C in order. Since there is only 1 M, 1 U, 1 S, 1 I, and 1 C in the bag, the number of ways to draw these 5 letters in order is 1.Finally, we divide the number of ways to draw the letters M-U-S-I-C in order by the total number of ways to draw 5 tiles from 26 to get the probability: P = 1 / C(26,5).

Using a calculator or computer program, the probability can be calculated to approximately 0.000207.

Final answer:

The probability of drawing the letters 'M-U-S-I-C' in order from a bag of 26 alphabetic tiles without replacement is calculated by multiplying the individual probabilities of drawing each letter consecutively, starting with 1/26 and decreasing with each draw.

Explanation:

The question involves calculating the probability of drawing a specific sequence of letters from a bag containing all the letters of the alphabet without replacement. Here's how to calculate it step by step:

The probability of drawing the letter 'M' first is 1/26 since there are 26 letters and only one 'M'.

After drawing 'M', the probability of drawing 'U' is 1/25 because there are now 25 letters remaining.

Following this pattern, the probability of then drawing 'S' is 1/24, 'I' is 1/23, and 'C' is 1/22.

To find the combined probability of drawing 'M-U-S-I-C' in that order, multiply these probabilities together: (1/26) * (1/25) * (1/24) * (1/23) * (1/22).

The final calculation gives us the probability of the sequence occurring without any tiles being replaced.

If c is a constant such that 9x^2+10x+c is equal to the square of a binomial, then what is c?

I NEED HELP SO BAD PLEASE PLEASE PLEASE

Answers

(9x^2+10x+c) = (3x+b)^2
= 9x^2 + 6b x+ b^2

1) 6b= 10
b+ 5/3

2) c=b^2
c= (5/3) ^2
c= 25/9

(9x^2+10x+25/9)=(3x+5/3)^2

I hope this helps:)

Eudora ran from her home to her secret laboratory at an average speed of 12\text{ km/h}12 km/h12, space, k, m, slash, h. she then took one of her jetpacks and flew to her school at an average speed of 76\text{ km/h}76 km/h76, space, k, m, slash, h. eudora traveled a total distance of 120120120 kilometers, and the entire trip took 222 hours. how long did eudora spend running, and how long did she spend flying using her jetpack? eudora ran for hours and flew for hours using her jetpack.

Answers

Let x be the amount of time she runs. 12x would then represent the distance she runs (d=rt; distance = speed (rate) * time). 2-x, or the total time minus the time she spends running, would be the amount of time she uses her jetpack. 76(2-x) would then represent the distance she flies on her jetpack. We know the total distance is 120 km; so
12x + 76(2-x) = 120
Use the Distributive Property:
12x + 76*2 - 76*x = 120
12x + 152 - 76x = 120
Combine like terms:
-64x + 152 = 120
Cancel the 152 by subtracting:
-64x + 152 - 152 = 120 - 152
-64x = -32
Cancel the -64 by dividing:
-64x/-64 = -32/-64
x = 0.5
She runs for 0.5 hours. She would use her jetpack for 2-0.5=1.5 hours.

Eudora ran 0.5 hours and flew 1.5 hours using her jetpack.

Given that, Eudora ran from her home to her secret laboratory at an average speed of 12 km/h.

What is a linear system of equations?

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Let x = the time she ran (in hours) and y = the time she flew (in hours).

Remember that distance traveled is simply the rate times the time. So she traveled 12x kilometers by running and 76y kilometers by flying.

The total time is simply the running time plus the flying time: x + y = 2.

The total distance is simply the running distance plus the flying distance: 12x + 76y = 120

If you solve the time equation for x, you get: y = 2 - x.

This allows you to substitute 2 - x into the distance equation for y.

12x + 76(2 - x) = 120

12x + 152 - 76x = 120

152 - 64x = 120

-64x = -32

x = 0.5

Using the result, we can find y.

y = 2 - 0.5 = 1.5

Therefore, Eudora ran 0.5 hours and flew 1.5 hours using her jetpack.

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1.4 + 2/5x = 3/15x - 0.8 How do you solve this?

Answers

it appears you are looking for x.
1.4+2/5x=3/15x-.08

you have to isolate the x
first add .08 to both sides
1.48+2/5=3/15x
i would now find the equivalence fraction of 2/5 with the denominator of 15. To do this you have to multiply 5 by 3 to get 15 so, you multiply the original numerator to get the equivalent one. 2(3)=6
1.48+6/15x=3/15x
now i am going to subtract 6/15x from both sides
1.48= -3/15x
to get rid of the fraction i am going to convert it to a decimal.
-3/15= -.2

1.48= -.2x

now i have to divide both sides by -.2
7.4=x

Lauren is shopping and finds 6 bracelets, 2 pairs of earrings, and 3 necklaces that she likes. How many ways can Lauren select 4 pieces of jewelry to buy?

Answers

Because it does not specify that she has to choose one or two from each category all pieces of jewelry can be treated as choices in a combination set.

the formula for a combination is

[tex]C(n,r)= \frac{n!}{r!(n-r)!} [/tex]

where n is a total number of choices ( 11 )
and r is number chosen out of those choices (4)
so

C(11,4)= \frac{11!}{4!(11-4)!}

She has 330 possible choices to come home with 4 pieces of jewelry

There are 330 ways can Lauren select 4 pieces of jewelry to buy.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Lauren is shopping and finds 6 bracelets, 2 pairs of earrings, and 3 necklaces that she likes.

Now, We have;

Total number of jewelry = 6 + 2 + 3 = 11

Hence, Number of ways can Lauren select 4 pieces of jewelry to buy is,

⇒ ¹¹C₄

⇒ 330

Thus, There are 330 ways can Lauren select 4 pieces of jewelry to buy.

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WILL GIVE BRAINIEST IF CORRECT (20 PTS)

A survey asked 10 boys and 10 girls how many text messages they sent the previous day. The number of texts are given in the line plots.
Select from the drop-down menus to complete each statement.

The data set with the greater range is __________The median ___________

Blank 1: a. the boys, b. the girls, c. neither as the range is the same

Blank 2: a. its the same for both sets of dats, b. its greater for the boys, c. its greater for the girls.

Answers

the answer for blank 1 is the girls and blank 2 is b

he is right lol ... b for 1 .. and b for 2

Will mark brainliest.. There are 3 questions related to the problem in the first picture. please help thanks.

Answers

see attached picture for the answers:

Based on the graphic, which three-dimensional figure has the greatest volume?

Answers

Using the assumptions that the prisms have a square base and that the side of the square is the same length as the diameter:
The first prism would have a volume of s²h.
The second prism, under Cavalieri's principle, would have the same area as the first (if they have the same cross-sectional area and same height, they have the same volume).
The cylinder at the end would have a volume of π(r²)h = π(1/2s)²h = π(1/4s²)h = 1/4πs²h. 1/4 of π is less than 1, so that means the cylinder would have the smallest volume.

Answer:

all three have the same volume

Step-by-step explanation:

Cavalieri's principle states that if the areas of the cross sections of two solids are equal, and the height of the two solids are equal, then the volumes of the two solids are equal.

Which graph represents y – 1 = 2(x – 2)?

Answers

Answer:

The graph is attached below

Step-by-step explanation:

y – 1 = 2(x – 2)

y-1 = 2x - 4

add 1 on both sides

y = 2x - 3

To graph the given equation we make a table

Plug in some number for x and find out the value of y

x y = 2x-3

-1 2(-1)-3= -5

0 2(0) -3= -3

1 2(1) -2= -1

The point to get the graph of the given equation is

(-1,-5) (0,-3) (1,-1)

The graph is attached below

Answer:

The answer is the first graph or graph A.

BTW this is just the short answer...

Its quicker. :-)

Matt and ming are selling fruit for a school fundraiser.customers can buy small boxes of oranges and large boxes of oranges. matt sold 3 small boxes of oranges and 14 large boxes of oranges for a total of 203. ming for a total of 203. ming sold 11 small boxes of oranges and 11 large boxes of oranges for a total of 220. find the cost of one small box of oranges and one large box of oranges

Answers

$7 for the small boxes and $13 for the large

.
The acronym CPCTC stands for “__________ parts of congruent triangles are congruent.”

calculated

congruent

corresponding

coordinated

Answers

corresponding is the answer.

Answer:

The acronym CPCTC stands for " Corresponding parts of congruent triangles are congruent. "

Step-by-step explanation:

CPCTC--

It is a rule which states that if any of the two triangles are congruent by any of the congruency such as ASA, RHS , SAS or SS then the remaining sides and the remaining angles which were not covered in the congruency are also congruent.

Also, the acronym is:

Corresponding parts of congruent triangles are congruent.

Let f(x)= -5x+6. Find and simplify f(3n−5).

f(3n-5)= ?

Answers

We know that our function is [tex]f(x)=-5x+6[/tex]; the only thing we need to find [tex]f(3n-5)[/tex] is replace [tex]x[/tex] with [tex](3n-5)[/tex] in our original function:
[tex]f(x)=-5x+6[/tex]
[tex]f(3n-5)=-5(3n-5)+6[/tex]

Now, lets simplify our function:
[tex]f(3n-5)=-15n+25+6[/tex]
[tex]f(3n-5)=-15n+31[/tex]

After simplify our function, we can conclude that [tex]f(3n-5)=-15n+31[/tex]

Does the equation x2 - 4x + y2 = -3 intersect the x-axis?

Answers

To find out whether or not the equation x^2 - 4x + y^2 = -3 intersects the x-axis, we must set y = 0 in the equation (because at every point on the x-axis, y = 0).

x^2 - 4x + 0 = -3

We then want to solve for x. We can do this by factoring.

x^2 - 4x + 3 = 0

By factoring...

(x - 3)(x - 1)

We can set each of these equations = 0 to solve where the function crosses the x-axis.

x - 3 = 0
x = 3

x - 1 = 0
x = 1

So we know at x = 1 and x = 3, the function x^2 - 4x + y^2 = -3 intersects the x-axis.

Answer:

Yes, because the center is on the x-axis.

Step-by-step explanation:

First, write the equation in standard form by completing the square.

x2 - 4x + y2 = -3

x2 - 4x + 4 + y2 = -3 + 4

(x - 2)2 + y2 = 1

The circle is centered at (2, 0) with a radius of 1. Since the circle is centered on the x-axis, it intersects the x-axis two times, at (3, 0) and (1, 0).

Im really confused can someone help me

Answers

I believe you would create and equation to find x and y.

When csc(theta) sin(theta) is simplified, what is the result?

Answers

Cosec theta = 1/sin theta

Therefore, csc theta * sin theta = 1.

cosec theta = 1/sin theta, sec theta = 1 / cos theta.

Therefore, Equation 2 reduces to,
(1/sin theta) / (1/cos theta) = cos theta/sin theta = 1/tan theta = cot theta.

tan theta + cot theta = tan theta + 1/tan theta. Taking LCM,
= (1 + tan^2 theta)/tan theta
From the identities, 1 + tan^2 theta = sec^2 theta.
Hence, equation 3 reduces to,
sec^2 theta/tan theta = (1/cos^2 theta) / (sin theta/cos theta)
= cos theta / (sin theta * cos^2 theta)
= 1 / (sin theta*cos theta). This cannot be reduced, hence is equal to sec theta*cosec theta.

1-sin^2 theta / 1+sin theta = (1 + sin theta)*(1-sin theta) / (1 + sin theta)
= 1 - sin theta.

Hope this helped :)

The result of cosecθsinθ is 1.

What is Trigonometric functions?

Trigonometric functions defined as the functions which show the relationship between angle and sides of a right-angled triangle.

⇒ cosecθsinθ

∵sinθ = 1/cosecθ

⇒ cosecθ(1/cosecθ)

⇒ 1

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Find the perimeter of the shaded figure

Answers

The perimeter of the shaded figure is 38 units.

Perimeter of the given figure is 38 units.

Perimeter is the measure of the boundary of any figure. It measures the total length around the outside of a shape. Generally it is calculated as the sum of all sides of the figure.

Name the figure as ACDEFGHB, image attached below:

Perimeter of the given figure,P = Sum of all its sides.

P= AC+CD+DE+EF+FG+GH+HB+AB...........................1

AC=7 units

CD=2 units

DE=2 units

EF=6 units

FG=2 units

GH=2 units

HB=7 units

AB=10 units

On substituting values in 1

P=7+2+2+6+2+2+7+10

P=38 units.

Thus, perimeter is 38 units.

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Write an equation of the line pictured in the graph.

Answers

The equation is y= -2x + 1

The answer is y = -2x + 1

what is 1,000,000,000 x 1,000,000,000

Answers

The answer is 1e18
That is the answer

1000000000000000000
thats the awnser

Which expression is equivalent to the given expression? 17x−32x A. x(32−17) B. 17(x−32) C. 17x(1−32) D. x(17−32)

Answers

D is correct
good luck

Hey there!

When "[tex]x[/tex]" is by itself , it substitute as a invisible [tex]1 [/tex]

[tex]x(32 - 17) = 32x - 17x (Incorrect) \\ \\ 17(x - 32) = 17x - 544 (Incorrect) \\ \\ 17x (1 - 32 ) = 17x - 32 (Incorrect) \\ \\ x(17 - 32) = 17x - 32 (Correct) \\ \\ Answer: D. \\ \\ \\ Good \\ luck \\ on \\ your \\ assignment \\ and \\ enjoy \\ your \\ day! \\ \\ \\ LoveYourselfFirst:)[/tex]

At a family cookout, each guest gets an equal amount of hot dogs.there are 10 guests and 32 hot dogs. how many hot dogs will be leftover

Answers

32/10= 3...2
there are 2 hot dogs will be left

A metal Fabricating Company produces 150,000 souvenir tokens each year. In a random sample of 400 tokens, 3 have stamping errors. Predict the total number of coins that will have stamping errors in a year.

Answers

1125
150000 divided by 400 equals 375, times 3 equals 1125.

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