Graph the line with y- intercept 1 and slope -1/2

Answer:

6.2 ft

Step-by-step explanation:

a² + b² = c²

a² + 5² = 8²

a² = 64 - 25

a² = 39

a = √39

a = 6.2

Answer: 6.2 ft

If y varies directly as x and z, and y=4 when x=6 and z=1, then value of y will be 56/3 when x=7 and z=4.

One kind of proportionality relationship is the direct proportion. When two values are in direct proportion, one value rises when the other rises and vice versa when one value falls. A proportionate relationship is represented by the symbol. When one of the variables is a multiple of the other, there is a direct proportion between the two. For instance, 1 cm equals 10 mm. The multiplier for converting cm to mm is always 10. Petrol prices and foreign exchange rates are determined using a direct proportion.

Given,

We know that y fluctuates in direct proportion to x and z.

We are aware that the form of the equation y = kx for two quantities that are directly proportional is, where k is the proportionality constant.

Because y directly varies as x and z, our equation would be y = kxz

Additionally, it is stated that and y = 4, x = 6 and z = 1. Let's define the proportionality constant as follows:

4 = k × 6 × 1

4 = k ×6

k = 2/3

y = 2/3 × x ×z

Substituting value of x by k = 2/3 , x = 7 and z = 4

y = 2/3 × 7 × 4

y = 56/3

If y varies directly as x and z, and y=4 when x=6 and z=1, then value of y will be 56/3 when x=7 and z=4.

To learn more about direct proportionality, visit:

https://brainly.com/question/11449153

#SPJ1

Answer: True.

Step-by-step explanation:

        First, a right angle will always be equal to 90 degrees.

        Next, bisecting an angle means cutting it into two parts.

        Since the resulting two angles will always be less than 90 degrees, they will always be acute angles. The answer to this question is true.

Answer:

Step-by-step explanation:

180 = x + 50 +50

180 = x + 100

x + 100 = 180

x = 80

80 is the value of x.

Answer:

12 units

Step-by-step explanation:

V = (area of base) × height

height = V/(area of base)

height = 960 units³ / 80 units²

height = 12 units

Inequality:

y > 1/3x - 3

Answer:69.69

Step-by-step explanation:

FIrst add the sides then subtract the top and then mutilpy it by 2

Answer:

D

Step-by-step explanation:

as a negative exponent always means 1/..., D is the correct answer.

9^-4 = 1/(9^4)

that is the precise definition of a negative exponent.

Answer: x

Step-by-step explanation:

-3x-7+4x+7

than because the 7's cancel each other out it would become

-3x+4x which would be equal to x

The equation of the line in slope-intercept form is y = 3x - 11.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

We know slope(m) = (y₂ - y₁)/(x₂ - x₁).

∴ Slope(m) = (- 5 + 8)/(1 - 0) = 3.

So, y = mx + b can be written as - 5 = 3(2) + b ⇒ b = - 11.

So, The required line is y = 3x - 11.

learn more about lines and slopes here :

https://brainly.com/question/3605446

#SPJ1

The equation of the conic represents a circle with an area of 36π square units.

In this problem we find the equation of the conic in general form, on which we need to determine what kind of conic it represents. This can be done by finding the standard form of the equation by means of algebra properties, using a strategy known as completing the square. The quadratic equation in general form is described by the quadratic equations of the form:

A · x² + B · y² + C · x + D · y + E · x · y + F = 0

Now we proceed to find the standard form of the equation. First, write the equation in standard form:

x² + y² - 3 · x + 6 · y = 7 · x + 2

x² + y² - 10 · x + 6 · y - 2 = 0

Second, complete the square:

(x² - 10 · x + 25) + (y² + 6 · y + 9) = 2 + 25 + 9

(x - 5)² + (y + 3)² = 36

The standard form of the quadratic equation indicates the equation of a circle with a diameter of 12 units and a center at (h, k) = (5, - 3). The area of the circle is calculated below:

A = 0.25π · D²

Where D is the diameter of the circle, in units.

A = 0.25π · 12²

A = 36π

To learn more on conics: https://brainly.com/question/29757055

#SPJ1

Answer:

$5160

Step-by-step explanation:

Each year, he earns 5% of 8600 = 0.05 * 8600 = $430

After 12 years, she will earn 12 * 430 = $5160 in interest

We can say that the given Quadrilateral is Parallelogram

What is Parallelogram?

A parallelogram is a quadrilateral with two parallel sides (and therefore opposite angles equal). A rhombus is a quadrilateral with equal sides, while a rectangle is a parallelogram with all right angles.

Solution:

Since, the given Quadrilateral has all the opposite angles equal

and we do not know weather the opposite sides are equal or not it is closest to assume that the given Quadrilateral is Parallelogram

To learn more ab out Parallelogram from the given link

https://brainly.com/question/970600

#SPJ1

Using rule of volume integral , The answer of y=x, y-=0 and x=6 is [tex]216 \pi[/tex].

The process of combining smaller parts into a single, cohesive whole is known as integration.

A volume integral is a specific instance of multiple integrals and is used to denote an integral across a 3-dimensional domain in mathematics, notably multivariable calculus. In physics, volume integrals are crucial for many applications, such as calculating flux densities.

area covered by y=x y=0 and x=6 is [tex]\frac {1}{2} * 6 * 6[/tex]

=18 [tex]unit^{2}[/tex]

Perimeter covered by revolving the area about x-axis, y-axis , x=6 and x=9 is [tex]2*\pi *6[/tex]

=[tex]12 \pi[/tex]

Volume = [tex]18 * 12 \pi[/tex]

=[tex]216 \pi unit ^{3}[/tex]

To learn more about integration visit:

https://brainly.com/question/18125359

Equation of the line passes through (10,2) and is perpendicular to the line y = 2x is given by  y = -x / 2 + 7.

As given in the question,

Given equation of the line :

y = 2x

Line passes through the point (x₁ , y₁ ) = (10, 2)

Standard form of slope intercept form

y = mx + c

'm' is the slope

slope of the given line 'm₁' = 2

let 'm₂' be the slope of the required line

Multiplication of the Slope of two perpendicular lines is given by :

m₁ × m₂ = -1

⇒2 × m₂ = -1

⇒m₂ = -1/2

Equation of the line perpendicular to the given line and passes through

(x₁ , y₁ ) = (10, 2)

y - y₁ = m₂ ( x - x₁ )

⇒ y - 2 = (-1/2) ( x - 10 )

⇒ y = -x / 2 + 7

Therefore, the required equation of the line in slope intercept form is given by  y = -x / 2 + 7 .

Learn more about equation here

brainly.com/question/29657983

#SPJ4

Answer:

-3x + y = -39

Step-by-step explanation:

If it is perpendicular to y=-1/3x+2, then the slope is positive 3. If it passes through (9, -12), then we can set up our equation:

y+12 / x-9 = 3. Simplifying, we have:

y=3x-39, which in standard form is:

-3x+y= -39

Hope this helps!

The number that must be added to complete the square in the expression is 0.9².

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

x² + 1.8x

The complete square is given as,

(a + b)² = a² + 2ab + b²

Now,

x² + 2 x 0.9(x) + 0.9²

(x + 0.9)²

Thus,

0.9² completes the square in the expression.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ1

The answer to this Question based on circles is 9

What is circle?

A circle is a two-dimensional geometric shape defined by a set of points equidistant from its center. It is the set of all points in a plane that are the same distance from a given point, called the center. A circle is a special type of ellipse, and all circles are similar. It is one of the most fundamental shapes in geometry, and is used in art, architecture, engineering, and many other disciplines. The circumference of a circle is the length of its perimeter, which is determined by its radius. A circle's area is the space enclosed by its circumference, and is equal to the value of pi multiplied by the square of the radius.

In the given Circle
Lets us denotes the 2 chords by AB and CD and let their intersecting point be E
Then from property of intersecting chords in circle we can write
(AE)(BE) = (CE)(DE)
4x = 36
x = 9

Hence proved

To learn more about Circles:

https://brainly.com/question/11833983

#SPJ1

Answer:

Step-by-step explanation:

The sum of exterior angles in a quadrilateral is always 360 degrees.

So, 2x+x+4x+3x=10x=360

Soling for x, we get x=36 degrees.

We can say that the view in which one or more faces of the object are not perpendicular to the rest of the faces, but are inclined projections, are the auxiliary views.

Initially, we must know that the views of an object or body are orthogonal projections associated with it.

In this sense, auxiliary views are a type of view that are characterized by arising from a change in projection plane, they are usually used when highly complex parts or objects must be represented.

¡Hope this helped!

The percentage error when the weight was found to be 62.5 ounces is 3.2%.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

The percentage therefore refers to a component per hundred. Per 100 is what the word percent means. It is represented by %.

Since the the weight of the sample as 60.5 ounces and the true weight was found to be 62.5 ounces.

The percentage error will be:

Error / Initial value × 100

= (62.5 - 60.5) / 62.5 × 100

= 2 / 62.5 × 100

= 3.2%

The percentage error is 3.2%.

Learn more about percentages on;

brainly.com/question/24877689

#SPJ1

Answer:

5x + 15

Step-by-step explanation:

5(x + 3) ← multiply each term in the parenthesis by 5

= 5x + 15

"5x+15" is an expression equivalent to "5(x+3)".

If we expand this factorization, the resulting expression is equivalent to the original expression. This is how you expand it:

[tex]5(x+3)[/tex]

Check the attached image.

[tex](5)(x)+(5)(3)=\\ \\5x+15[/tex]

3. Conclude.

5x+15 is an expression equivalent to 5(x+3).

The amount invested in the account that pays 1.5% interest is $584,285.71.

The amount invested in the account that pays 8.5% interest is $155,714.29.

The system of equations that represent the information in the question is:

x + y = 740,000 equation 1

0.015x + 0.085y = 22,000 equation 2

Where:

In order to determine the values, the elimination method would be used.

Multiply equation 1 by 0.015

0.015x + 0.015y = 11,100 equation 3

Subtract equation 3 from equation 2

0.070y = 10,900

Divide both sides of the equation by 0.070

y = 10,900 / 0.07

y = 155,714.29

Subtract 155,714.29  from $740,000

x = 740,000 - 155,714.29

x = 584,285.71

To learn more about system of equations, please check: https://brainly.com/question/25875552

#SPJ1

The option 1 "Similar due to SSS and a scale factor of 3.5. Triangle QRS is similar to triangle VUT." is correct.

In the given question, the triangles below are similar.

So, we have to state the reason and write the similarity statement.

ΔQRS≈

(a) Similar due to SSS and a scale factor of 3.5. Triangle QRS is similar to triangle VUT.

(b) Similar to due SAS and a scale factor of 0.29. Triangle QRS is similar to triangle TUV.

(c) Similar due to AA. Triangle QRS is similar to triangle VUT.

(d) Similar due to SSS and a scale factor of $0.29$. Triangle QRS is similar to triangle VUT.

As we know that, the ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor.

Since the both triangle area similar so using the SSS theorem;

Triangle QRS congruence to triangle VUT.

QR/VU = RS/UT = SQ/TV

So QR/VU = 56/16; RS/UT = 70/20; SQ/TV = 98/28

QR/VU = RS/UT = SQ/TV = 3.5

Hence, ΔQRS≈ΔVUT using the SSS theorem with the scale factor of 3.5. So the option 1 "Similar due to SSS and a scale factor of 3.5. Triangle QRS is similar to triangle VUT." is correct.

To learn more about SSS theorem link is here

brainly.com/question/29789250

#SPJ4

Answer:

[tex]4mn^{2}[/tex] is their common factor.

Step-by-step explanation:

It is the common factor of both as it is a number they are both easily divisible by.

Answer:

  4mn^2

Step-by-step explanation:

You want the common factor of the terms in 16m^2n^2 -12mn^5.

The terms can be factored as ...

  16m^2n^2 = (4)(4)(m)(m)(n^2)

  -12 mn^5 = (-3)(4)(m)(n^2)(n^3)

The factors that are in both lists are ...

  (4)(m)(n^2)

The common monomial factor of the expression is 4mn^2.

__

Additional comment

Factoring out that common factor gives ...

  = 4mn^2(4m -3n^3)

15 pieces will there be.

 .5 is the same as  1/2, while 7.5 is the same as 7 1/2. To determine how many strips may be cut, use the following expression:

.5x = 7.5

This is due to the fact that the ribbon length that has to be cut is .5 feet, and we are attempting to determine how many pieces of that length might be cut from a roll of ribbon that is 7.5 feet long.

Divide both sides by 2.5 to separate the variable, and that's all there is to it.

7.5/.5 is 15.

x = 15.

Eli is able to slice a ribbon into three pieces that are each .5 feet long.

The complete question is: The red strips that are  1/2 feet long. The roll of ribbon is 7 1/2 feet long. Which expression could be one of the steps in determining how many strips can be cut?

To learn more about length refer to:

https://brainly.com/question/7221283

#SPJ1

Answer:

I'm not sure exactly me myself

Answer:

the correct answer is 144

Step-by-step explanation:

Hence, the measure of each interior angle is 144∘.

hope this helps

Answer:

Step-by-step explanation:

each exterior angle=360/n=360/10=36°

each interior angle=180-36=144°

For 10.75 years I'll receive an amount of $1,193 for an annuity of $12,083.

Simple interest is often a predetermined percentage of the principle amount borrowed or lent paid or received over a specific time period.

We know simple interest (SI) is given by SI = (p×r×t)/100, where

p = principle, r = rate in percentage, and t = time in years.

A principle of $12,083 with 6.1% interest rate becomes $(12,083×1.061)

= $12,820.063.

∴ The no. of years the annuity provides you with payments of $1,193 is

= (12,820.063/1193).

= 10.75 years Or 10 years 9 months.

learn more about simple interests here :

https://brainly.com/question/11564235

#SPJ1