Find the coordinates of the points of intersection of the graph of
y=2x+6 with the axes. Find the area of the right triangle
formed by this line and the coordinate axes.

Answers

Answer 1

The coordinate of intersection with the x-axis is: (-3, 0).

The coordinate of intersection with the y-axis is: (0, 6).

The area of the triangle is 9 unit²

What is the Linear equation?

A linear equation is defined as an equation in which the highest power of the variable is always one.

The linear equation is given as:

y = 2x+6

Intersection with the y-axis

Substitute, x = 0

⇒ y = 2x + 6

⇒ y = 2(0) + 6

⇒ y = 6

As a result,: y = 2x+6 intersects with the y-axis at (0, 6)

Intersection with the x-axis

Substitute, y = 0

⇒ y = 2x + 6

⇒ 0 = 2x + 6

⇒ 2x =  - 6

⇒ x = - 3

As a result,: y = 2x + 6 intersects with the x-axis at: (-3, 0)

The area of the right-angled triangle

The area is calculated as:

Area of triangle = 1/2×Base×Height

Area of triangle = 1/2×3×6

Area of triangle = 9 unit²

The coordinate of intersection with the x-axis is: (-3, 0).

The coordinate of intersection with the y-axis is: (0, 6).

The area of the triangle is 9 unit²

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Related Questions

please help with math homework

Answers

Using the Pythagorean Theorem, it is found that:

a) The hypotenuse is of 9.49 cm.

b) The new area of the triangle is of 30 cm².

What is the Pythagorean Theorem?

The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, according to the following equation:

[tex]h^2 = l_1^2 + l_2^2[/tex]

For this problem, the sides are given as follows:

3 cm and 9 cm.

Hence the hypotenuse is given by:

h² = 3² + 9²

h = sqrt(3² + 9²)

h = 9.49 cm.

The hypotenuse is of 9.49 cm.

What is the area of a right triangle?

The area of a right triangle of sides a and b is given by half the multiplication of the sides, as follows:

A = 0.5ab.

For this problem, we have that:

The side of 3 cm is increased by 2 cm, hence a = 5 cm.The side of 9 cm is increased by 3 cm, hence b = 12 cm.

Then:

A = 0.5 x 5 x 12 = 30 cm².

The new area of the triangle is of 30 cm².

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A group of friends were working on a student film that had a budget of $1400. They
used 67% of their budget on props. How much money did they spend on props?

Answers

They spent $938 on the props.

Answer:

That is wrong it is not $938 its $322

Step-by-step explanation:

The telephone company offers two billing plans for local calls. Plan 1 charges $23 per month for unlimited calls and Plan 2 charges $19 per month plus $0.04 per call.
a. Use an inequality to find the number of monthly calls for which Plan 1 is more economical than Plan 2.
b. Explain the meaning of the answer to part a.
a. Let x represent the number of monthly calls. The answer is
(Type an inequality.)

Answers

a. an inequality to find the number of monthly calls for which Plan 1 is more economical than Plan 2 is : 19 +0.04x >23

b. the meaning of the answer to part a is : Cost of Plan 2 > Cost of Plan 1

c.  the number of monthly calls x  is x > 100

What is inequality ?

In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.

Plan 1: $23 per month for unlimited calls

Plan 2: $19 per month + $0.04 per call

Let the number of calls be x

a. 19 +0.04x >23

0.04x >4

x > 100

b. If Plan 1 should be more economical, then the above inequality represents that cost of plan 2 should be more than plan 1. therefore, the plan 2 is greater than plan 1.

On solving the above inequality, we get over 100 calls should be made  so that Plan 1 is more economical than Plan 2.

c. x > 100

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STRUCTURE The students in Mrs. Mangione’s class attempt to guess the number of marbles in a jar to earn 2 extra credit points on their next exam. Suppose there are 1206 marbles in a jar and a student makes a guess of m marbles. Which expression represents the difference between the student's guess and the actual number of marbles. Select all that apply.

Answers

The expression that represents the difference between the student's guess and the actual number of marbles will be 1206 - 2m.

How to illustrate the information?

When there are 1206 marbles in a jar and a student makes a guess of m marbles. The expression for the guesses will be:

= 2 × m

= 2m

The expression that represents the difference between the student's guess and the actual number of marbles will be:

= 1206 - 2m

= 2(603 - m)

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It is given that M is the midpoint of segment . Therefore by the definition of a midpoint. It is also given that Angles and are right angles. Thus, because all right angles are congruent. Since vertical angles are congruent by the vertical angles theorem, . Then, it follows that by the criteria. In congruent triangles, corresponding sides are congruent, thus . In conclusion by definition of congruent angles.

Answers

The congruency can also be tested by three postulates shown in the lesson: ASA (angle-side-angle), SAS (side-angle-side), and SSS (side-side-side). The first one claims that triangles are congruent if two angles and one side (between the angles) of one triangle are equal to two angles and one side of another triangle.

If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the triangles are congruent.

A ∠ ≅ ∠ .

Vertical Angles Theorem: ...

If two angles are supplements of the same angle (or congruent angles), then the two angles are congruent. ...If two angles are complements of the same angle (or congruent angles), then the two angles are congruent. ...If two angles are congruent and supplementary, then each is a right angle.

Indicator marks for sides and angles in a triangle diagram. Indicator marks are used to show whether two or more sides are congruent (equal in measure).

Thus, because all right angles are congruent. Since vertical angles are congruent by the vertical angles theorem.

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Need as soon as possible please

Answers

Answer:

Just graph, first one Y int: 2 and X is rise over run 1 and 2

Step-by-step explanation:

Complete the congruence statements for each pair of congruent figures below

Answers

Triangles are congruent if their matching interior angles and sides are all congruent.

What is congruence in math?

If it is possible to superimpose one geometric figure on the other so that their entire surface coincides, that geometric figure is said to be congruent, or to be in the relation of congruence.

Congruent figures: what are they?

Congruent figures have sides that are the same length and angles that are the same measurement. In other terms, two figures are said to be congruent when they are superimposed upon one another. Even when they are flipped or rotated, they perfectly fit on top of one another.

What is congruent shapes?

Shapes that are identical to one another are said to be congruent. Both the matching sides and the corresponding angles match. We must examine all of the shapes' angles and sides in order to accomplish this. Two shapes that are similar to one another can be stacked perfectly.

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Consider the set t = {1, 2, 3, 4, 5, 6}. let r = {(a, b) | a divides b} be a relation on the set t. the tabular representation for the ordered pairs of the given relation r on the set t is:_________

Answers

The ordered pairs of the given relation r on the set t is ungrouped data.

What is ungrouped data?

The data you initially collect from an experiment or study is known as ungrouped data. The data is unsorted, unclassified, or otherwise grouped; it is therefore considered to be raw. A list of numbers is an ungrouped piece of data.

Ungrouped data is a distribution type where each piece of information is presented in its rawest form. For instance, a batsman's five most recent scores are 45, 34, 2, 77, and 80.

Raw data is another name for ungrouped data.

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Write the standard form of the equation of the circle that passes through the given point and whose center is at the origin.
(-6,0)

Answers

The equation of the circle that passes through the point (-6 , 0) and has a center located at the origin is x^2 + y^2 = 36.

Using the distance formula, get the radius of the circle by solving for the distance between the center and the point (-6 , 0).

radius = distance = √(x2 - x1)^2 + (y2 - y1)^2

radius = √(-6 - 0)^2 + (0 - 0)^2

radius= √36

radius = 6

The standard form of the equation of the circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.

Given the radius and center of the circle, substitute these values to the standard form of the equation of the circle.

(x - h)^2 + (y - k)^2 = r^2

where (h , k) = (0 , 0)

r = 6

(x - 0)^2 + (y - 0)^2 = 6^2

x^2 + y^2 = 36

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Is -71 - 43 positive or negative?​

Answers

Answer:

Negative

Step-by-step explanation:

write each subtraction equation as an addition equation

a - 9 = 6

p - 20 = -30

z - (-12) = 15

x - (-7) = -10

Answers

Answer:

try it's your self i am sure you can do it.

Step-by-step explanation:

Let's go together

PLEASE ANSWER THIS!! ASAP! GIVE EXPLANATION OF HOW YOU GOT THE ANSWER (show your work!!) ASAP MATHE QUESTION

Answers

For this, we need to make ratios(unit per unit, in this case, red paint per white paint).

Sydney's Mix - [tex]\frac{7 red}{4 white}[/tex]

Maria's Mix - [tex]\frac{5 red}{3 white}[/tex]

Both of these fractions are improper, so you can make mixed fractions and then find their common denominators:

Sydney's Mix - 1[tex]\frac{3}{4}[/tex] = 1[tex]\frac{9}{12}[/tex]

Maria's Mix - 1[tex]\frac{2}{3}[/tex] = 1[tex]\frac{8}{12}[/tex]

Therefore, they do not have the same shade of pink because 1[tex]\frac{9}{12}[/tex] [tex]\neq[/tex] 1[tex]\frac{8}{12}[/tex] :)

What is line parallel to -x?

Answers

Answer:

I think its -y

Step-by-step explanation:

Answer:

x is my answer

Step-by-step explanation:

i don't know sorry

Two shops are selling the same DVD. In Tesco the DVD cost £11.49. In Asda the DVD
costs £13.99. Asda have an offer- "20% off all DVDs". Which shop should you buy the DVD
from?

Answers

100 -20= 80% = 0.8

0.8 x 13.99= £11.19 (Asda)

£11.49 (Tesco)

Therefore Asda is cheaper.
Buy from Asda
Ans: Asda


find the average of -1/12 + 4/17 - 3/28

Answers

Answer:

16/1071

Step-by-step explanation:

The average is the given by summing all the numbers and deciding by how many numbers you have

So, the answer is given by:

(-1/12 + 4/17 - 3/28) / 3 which yields to 16/1071

A triangle has three interior angle measures; x is the largest angle, y is the next largest angle, and z is the smallest angle.

The measure of the largest angle is 40 degrees less than the sum of the measure of the other two angles.
The largest angle is twice the smaller angle minus 30 degrees.
The sum of the triangle's interior angles is x + y + z = 180.

Which two equations represent the remaining angle relationships?

Select each correct answer.
1) x=y−z+40
2) x=2z−30
3) x=y+z−40
4) x=30−2z
5) x = y + z + 40

Answers

The correct answer would be option 2 and 3:

2) x=2z−303) x=y+z−40

How to solve for the angles

We have to sove the problem by carefully trying to understand the statements

x = largest angle

y =  next largest angle

z = smallest.

1. For the first statement: The measure of the largest angle is 40 degrees less than the sum of the measure of the other two angles.

largest angle < y + z

This would be represented as

x = y + z - 40

2. The largest angle is twice the smaller angle minus 30 degrees.

This is represented as

2 times of smallest = 2 * z = 2z

minus 30 degrees = 2z - 30

Hence the solutions to the question from the option that we have would be the options

2) x=2z−303) x=y+z−40

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Answer:

2) x=2z−30

3) x=y+z−40

Step-by-step explanation:


Simplify each sum or difference. State any restrictions on the variables.
5y + 2 / x y² + 2 x-4 / 4xy

Answers

Simplification of each sum or difference of the given equation [tex]\frac{(5y+2)}{(xy^{2} )}+ \frac{(2x-4)}{4xy}[/tex] is equal to [tex]\frac{(xy+8y+4)}{2xy^{2} }[/tex] .Restriction on the variables is given by x≠0 , y≠0 .

As given in the question,

Given equation is [tex]\frac{(5y+2)}{(xy^{2} )}+ \frac{(2x-4)}{4xy}[/tex]

Simplify the given equation by taking the least common multiple,

[tex]\frac{(5y+2)}{(xy^{2} )}+ \frac{(2x-4)}{4xy}\\\\\\= \frac{20y +8+2xy-4y}{4xy^{2}}\\ \\\\= \frac{2xy+16y+8}{4xy^{2}}\\ \\\\= \frac{xy+8y+4}{2xy^{2}}[/tex]

Restriction on the variables are x≠0 , y≠0.

Therefore, simplification of each sum or difference of the given equation [tex]\frac{(5y+2)}{(xy^{2} )}+ \frac{(2x-4)}{4xy}[/tex] is equal to [tex]\frac{(xy+8y+4)}{2xy^{2} }[/tex] .Restriction on the variables is given by x≠0 , y≠0 .

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Find the geometric mean between pair of numbers.
3√5/4 and 5√5/4

Answers

The geometric mean of 3√5/4 and 5√5/4 is 5√3/4.

Geometric mean, like arithmetic mean, is a kind of average and a measure of central tendency.

To solve for the geometric mean, we multiply the numbers together and then take a square root (for two numbers), cube root (for three numbers) etc. In other words, geometric mean is the nth root of the product of n values.

The formula for the geometric mean is given by:

GM = n√x1 x2 . . . xn

Solving for the geometric mean between 3√5/4 and 5√5/4 using the formula:

GM = n√x1 x2 . . . xn

where n = 2, x1 = 3√5/4, and x2 = 5√5/4

GM = √(3√5/4)(5√5/4)

GM = √(75/16)

GM = 5√3/4

Hence, the geometric mean of 3√5/4 and 5√5/4 is 5√3/4.

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PLEASE PLEASE PLEASE HELP!! ASAP!! BRAINLIEST FOR WORK THAT SHOWS ALL STEPS AND CORRECT ANSWERS!! :)

1. Factor the expression: x^6–729. Show your work for full credit.

2. Solve the equation 2x^2+16x–11= -7 by completing the square. Show your work for full credit.

3. Factor over the complex numbers. Show your work for full credit. x^4–5x^2–36

Answers

1) Factorizing the expression x⁶ - 729 is; (x + 3)(x - 3)(x⁴ + 9x² + 81)

2) Solving the equation 2x² + 16x – 11 = -7 by completing the square is; x = -4 + √18 or -4 - √18

3) Factorizing x⁴ – 5x² – 36 over the complex numbers is; (x + 3i)(x - 3i)(x + 2)(x - 2)

How to factorize expressions?

1) We are given the expression; x⁶ - 729

It can also be written as;

(x²)³ - 9³

Now, from factorization of algebra, we  know that;

a³ - b³ = (a - b)(a² + ab + b²)

Thus;

(x²)³ - 9³ = (x² - 9)((x²)² + 9x² + 9²)

= (x² - 9)(x⁴ + 9x² + 81)

= (x + 3)(x - 3)(x⁴ + 9x² + 81)

2) We want to solve the equation 2x² + 16x – 11 = -7 by completing the square.

Add 7 to both sides to get;

2x² + 16x – 11 + 7 = -7 + 7

2x² + 16x – 4 = 0

Divide through by 2 to get;

x² + 8x – 2 = 0

Add 2 to both sides to get;

x² + 8x = 2

Take half of the x term and square it and then add the result to both sides to get;

x² + 8x + 16 = 2 + 16

Rewrite the perfect square on the left to get;

(x + 4)² = 18

Take square root of both sides to get;

x + 4 = ±√18

Subtract 4 from both sides to get;

x = -4 ± √18

x = -4 + √18 or -4 - √18

3) We want to factorize x⁴ – 5x² – 36

Using the difference of squares identity, we know that;

a² - b² = (a + b)(a - b)

Thus;

x⁴ – 5x² – 36 = (x² + 9)(x² - 4)

Now, (x² + 9) factored over the complex numbers gives;

(x² + 9) = (x + 3i)(x - 3i)

Thus;

x⁴ – 5x² – 36 = (x + 3i)(x - 3i)(x + 2)(x - 2)

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Evaluate this exponential expression.
5•(3+6)²-62

Answers

I evaluated this and got 343

Explaintion:

5 x 9 ( the 9 has a 2 on top) -62

5 x 81 -62

405 - 62

=

343

Answer:

343

Step-by-step explanation:

5×(3+6)²-62=

5×9²-62=

5×81-62=

405-62=

343

The temperature yesterday was 14 degrees Celsius. Today the
temperature dropped 14 degrees Celsius.
What is the current temperature?

Answers

Answer:

0

Step-by-step explanation:14 subtracted by 14 is 0


Determine whether each set of numbers can be the measure of the sides of a triangle. If so, classify the triangle as acute, right, or obtuse. Justify your answer.

a. 11,60,61

Answers

The following set of numbers, 11, 60, and 61, can be the measures of the sides of a right triangle.

A triangle is a polygon with three sides and three vertices.

To know if a set of number is a valid measure of the sides of a triangle, it must follow the Triangle Inequality Theorem which states that the sum of any two sides must be greater than the third side, such that a + b > c, a + c > b, and b + c > a.

let a = 11, b = 60, and c = 61

a + b > c     11 + 60 > 61     71 > 61     True

a + c > b     11 + 61 > 60     72 > 60     True

b + c > a     60 + 61 > 11     121 > 11     True

To know what type of triangle based on the length of its side:

1. Take the sum of the squares of the two smaller sides.

11^2 + 60^2 = 3721

2. Compare it to the square of the largest side.

61^2 = 3721

3721 = 3721

If the sum of the squares of the 2 is larger than the square of the 3rd, it is an acute triangle.

if they are equal, it is a right triangle.

if they are smaller, then it is an obtuse triangle.

Hence, 11, 60, and 61 can be the measure of the sides of a right triangle.

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1. Which method would be the simplest way to solve the system?
7x + 5y = 19
-7x-2y = -16
Ographing
substitution
O elimination
distributive
(1 point)

Answers

Are they together or separate

Suppose a total of 15 ounces of medicine is added to the original mixture (so that the total volume is now 25 ounces with 18 ounces of medicine and 7 ounces of water). How much water must now be added so that the mixture has the same proportion of medicine and water as the original mixture?

Answers

We have to add 35 ounces of water to the mixture to make the proportion of medicine and water same as the original mixture.

Given,

The quantity of medicine added to the original mixture = 15 ounces

New quantity of medicine in the mixture = 18 ounces

Quantity of water in the mixture = 7 ounces

Total new quantity of mixture = 18 + 7 = 25 ounces

Original quantity of medicine in the mixture = 18 - 15 = 3 ounces

Original quantity of water in the mixture = 7 ounces

Total original quantity of mixture = 3 + 7 = 10 ounces

We have to find the amount of water to add into the new mixture to make the proportion of medicine and water same as the original mixture.

Here,

Proportion of medicine and water in original mixture = 3:7

Quantity of medicine and water in new mixture = 18:7

Now,

18 ÷ 3 = 6

Then, 7 × 6 = 42

So, 42 - 7 = 35

Therefore, we have to add 35 ounces of water to the mixture to make the proportion of medicine and water same as the original mixture.

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what is a non-repeating decimal, give examples of nom repeating decimals.

Answers

A non-repeating decimal is simply a decimal that goes on and on with no group of digits that repeat itself.

For example, pi = 3.14159265359...

Answer:

Recurring Decimal

Recurring Decimal, also called as repeating decimal, is a decimal number only that consists of digits repeating after a fixed interval after the decimal. For example, 46.374374374..., 5173.838383... etc. Decimals can be classified into different categories depending upon what type of digits occur after the decimal point, whether the digits are repeating, non-repeating, end, or unending (infinite digits after the decimal point).

Examples are

0.6666666666,

1.456456456

Step-by-step explanation:

Set as brainliest

An electronic store has television sets marked down 30 percent. What is the total price of five television sets that regularly sell for $115.75, $218.95, $320.75, $125.65, and $221.75?

Answers

Answer:

why did the teacher give an exam

Samuel Sandoval sells furniture. He earns 4% commission on the first $2000 of sales. He earns 6%commission on all sales over $2000. Last week his furniture sales totaled $8230. How much did he earn make sure to show your work.

Answers

Answer:

Step-by-step explanation:

hi


Find the sum of each finite arithmetic series. 5+6+7+ . . . . . . +11

Answers

The sum of the given arithmetic series  5+6+7+ . . . . . . +11 is 56.

Suppose we are given an arithmetic series:

   a(1) + a(2) + a(3) + a(4) + .... + a(n)

Then, each term of the series follow the general formula:

a(n) = a(1) + (n-1) . d

Where:

a(n) = nth term

a(1) = first term

d = common difference = a(n) - a(n-1)

We are given:

        5+6+7+ . . . . . . +11

Parameters we get from this series:

a(1) = 5

d = 6 - 5 = 1

a(n) = 11

We need to find n that results in a(n) = 11

Substitute a(n) = 11, a(1) = 5, and d = 1:

a(n) = a(1) + (n-1) . d

11 = 5 + (n-1) . 1

11 = n + 4

n = 7

The sum of the first n terms of an arithmetic series is:

S(n) = n/2 [ a(1) + a(n) ]

S(7) = 7/2 (5 + 11)

       = 7 . 8 = 56

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Find the sum of pair of vectors. <6,-31> + (-22,3)

Answers

According to the given statement The sum of pair of vectors are  =  (-16 , -28).

What precisely is vector addition?

The operation of combining two or even more vectors into a vector sum is known as vector addition. The rule for addition and multiplication of two or more vectors is given by the so-called parallelogram law. When two vectors are placed head to tail, the vector total is determined by drawing this same vector from of the free tail towards the free head.

According to the given data:

Given two vectors are:

a =(6,-31)

b = (-22,3)

The vector sum is,

M = (a1 + b1, a2 + b2)

   = (Mx, My).

Substitution of the value we  get:

M = (6 + (-22), (-31) + (3))

   = (-16 , -28)

The sum of pair of vectors are  =  (-16 , -28).

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Anyone know how to solve ?

Answers

Should be y equals zero
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Consuming energy drink in excess can cause an overabundance in b vitamins. one consequence of excess b vitamins is a strain on the __________. Do you think the journey of sound to your brain takes a short time or a long time? Why do you think so? Do I have to wear an orange shirt on Orange Shirt Day? Suppose a total of 15 ounces of medicine is added to the original mixture (so that the total volume is now 25 ounces with 18 ounces of medicine and 7 ounces of water). How much water must now be added so that the mixture has the same proportion of medicine and water as the original mixture? Complete the congruence statements for each pair of congruent figures below Im confused can someone help? Does being overweight lower the chances of someone getting asked out? Does it matter in a relationship? Is -71 - 43 positive or negative? Help wanted! Im Im desperate need of assistance! can anybody help me with this question The Dual Monarchy gave Hungary its owna. ruler.b. parliament.Please select the best answer from the choices providedOAOBCCDODc. monetary system.army. Is it possible that the music you now hear is quieter than it was with only the first speaker playing? Ryan lives in an apartment where he pays $7,000 a year in rent. Sarah lives in a house that she bought for $200,000, and that she could rent out for $21,000 a year. How much do these housing services contribute to gdp?. Does a reaction occur when aqueous solutions of manganese(ii) sulfate and chromium(ii) nitrate are combined? _____ is communicating with business associates, classmates, friends, loved ones, and other people you don't already know. The vasquez family visits their grandmother every 3 weeks and hosts a neighborhood party every 8 weeks. every 16th week, the vasquez family takes a day to go hiking. a. after how many weeks will the vasquez family both visit their grandmother and host the neighbor hood party? b. after how many weeks will all three events occur? Eddie used 9.6 cups of flour to bake 3 cakes. How much flour, on average, did he put in each cake? Which statements prove that m || n? Which political figure understood that democratic government must be responsive to the will of the people and once claimed, our government rests on public opinion?. machine that inadvetently lead to slavery