Sun shades are sold in the shape of right isosceles triangles. if the equation represents one shade that shields 64 square feet of area, which system can be used to find the lengths of the legs of the sun shade?

Generally, the equation of a circle is organized like this: [tex](x-h)^2+(y-k)^2=r^2[/tex], where (h,k) is the centre and r is the radius.

We're given the endpoints of the diameter: [tex](-6,-3)[/tex] and [tex](-6,-8)[/tex].

First, we can find the centre of the circle by finding the midpoint of these two endpoints.

[tex]midpoint=(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})[/tex]

Plug in the points:

[tex]midpoint=(\dfrac{-6+-6}{2},\dfrac{-3+-8}{2})\\\\midpoint=(-6,\dfrac{-11}{2})[/tex]

Therefore, the centre of the circle is [tex](-6,\dfrac{-11}{2})[/tex]. Plug this into the general equation:

[tex](x-h)^2+(y-k)^2=r^2\\\\(x-(-6))^2+(y-(-\dfrac{11}{2}))^2=r^2\\\\(x+6)^2+(y+\dfrac{11}{2})^2=r^2[/tex]

To find the radius of the circle, we can calculate the distance between the centre and one of the given endpoints:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]

Plug in the centre and one of the endpoints:

[tex]d=\sqrt{(-6-x_1)^2+(\dfrac{-11}{2}-y_1)^2}\\d=\sqrt{(-6-(-6))^2+(\dfrac{-11}{2}-(-3))^2}\\d=\sqrt{(-6+6)^2+(\dfrac{-11}{2}+3)^2}\\\\d=\sqrt{(0)^2+(-5.5+3)^2}\\\\d=\sqrt{(0)^2+(-2.5)^2}\\\\d=\sqrt{(0)^2+(-\dfrac{5}{2})^2}\\\\d=\sqrt{0+\dfrac{25}{4}}\\d=\sqrt{\dfrac{25}{4}}\\\\d=\dfrac{5}{2}[/tex]

Therefore, the radius of the circle is [tex]\dfrac{5}{2}[/tex]. Plug this into the general equation:

[tex](x+6)^2+(y+\dfrac{11}{2})^2=r^2\\\\(x+6)^2+(y+\dfrac{11}{2})^2=(\dfrac{5}{2})^2\\\\(x+6)^2+(y+\dfrac{11}{2})^2=\dfrac{25}{4}[/tex]

[tex](x+6)^2+(y+\dfrac{11}{2})^2=\dfrac{25}{4}[/tex]

It is important to be able to express a clear and coherent argument visually or in writing because without establishing coherence, your reader will not be able to know or understand the key points that you are trying to express or show.

Coherence is known to be a key quality for kind of good academic write up.

Note that in the area of academic writing, the ways that ideas flows is very important and as such, it need to be smooth and logical.

Therefore  without coherent argument , the reader cannot understand the key points that a person is trying to show and thus hinders the readability of your work.

Learn more about coherent argument from

https://brainly.com/question/1415305

#SPJ1

Answer:

7/13

Step-by-step explanation:

in all there are 13 balls and the number of balls that aren't white are 7

Answer:

7/13

Step-by-step explanation:

To find the probability that it is not white

P( not white) = number of balls that are not white / total balls

The balls that are not white are red and green = 4+3

                      = (4+3)/ ( 4+6+3)

                       = 7/13

The correct option is C. find the real range, find the interval width, and construct the frequency distribution.

To make the information easier to understand, frequency distributions are textured look which organise and present frequency counts. Absolute frequencies as well as frequency distributions, such as percentages or ratios, can be displayed in frequency distributions.

The real range is find by the following method-

The interval width is find by the following method-

To know more about the frequency distribution table, here

https://brainly.com/question/27820465

#SPJ4

The correct question is-

The three steps for constructing a simple frequency distribution are -

Group of answer choices

A. find the observed range, find the interval width, and construct the frequency distribution

B. find the real range, count the scores, and construct the frequency distribution

C. find the real range, find the interval width, and construct the frequency distribution

D. all of the above

The transformations that are applied to pentagon ABCDE to create A"B"C"D"E" are:

1) Translation (x, y) → (x + 8, y + 2)

2) Reflection across the x-axis (x, y) → (x, -y)

So, the overall transformation given in the graph is (x, y) → {(x + 8), -(y + 2)}.

The transformation rules are:

The pentagons in the graph have vertices as

For the pentagon ABCDE: A(-4, 5), B(-6, 4), C(-5, 1), D(-2, 2), and (-2, 4)

For the pentagon A"B"C"D"E": A"(4, -7), B"(2, -6), C"(3, -3), D"(6, -4), and E"(6, -6)

Consider the vertices A(-4, 5) from the pentagon ABCDE and A"(4, -7) from the pentagon A"B"C"D"E".

Applying the Translation rule for the pentagon ABCDE:

The rule is (x, y) → (x + a, y + b)

So, the variation is

-4 + a = 4

⇒ a = 4 + 4 = 8

5 + b = 7

⇒ b = 7 - 5 = 2

So, the pentagon ABCDE is translated by (x + 8, y + 2).

Applying the Reflection rule for the translated pentagon:

The translated pentagon has vertices (x + 8, y + 2).

When applying the reflection across the x-axis,

(x + 8, y + 2) → {(x + 8), -(y + 2)}

Therefore, the complete transformation of the pentagon ABCDE to the pentagon A"B"C"D"E" is (x, y) → {(x + 8), -(y + 2)}

Verification:

A(-4, 5) → ((-4 + 8), -(5 + 2)) = (4, -7)A"

B(-6, 4) → ((-6 + 8), -(4 + 2)) = (2, -6)B"

C(-5, 1) → ((-5 + 8), -(1 + 2)) = (3, -3)C"

D(-2, 2) → ((-2 + 8), -(2 + 2)) = (6, -4)D"

E(-2, 4) → ((-2 + 8), -(4 + 2)) = (6, -6)E"

Learn more about transformation rules here:

https://brainly.com/question/4289712

#SPJ1

The 95% confidence interval based on the same data is 5.15 < μ < 6.05

Because it has a longer interval, the 95 percent confidence interval offers more details.

The likelihood that a parameter will fall between two values near the mean is shown by a confidence interval.

Confidence intervals quantify how certain or uncertain a sampling technique is.

Confidence intervals are used by statisticians to gauge the degree of uncertainty in a sample variable.

The 90% confidence interval is given by:

Mean - 1.645(S.D./[tex]\sqrt{n}[/tex]) < μ < Mean + 1.645(S.D./[tex]\sqrt{n}[/tex])

2μ = 5.22 + 5.98 = 11.2

μ = 11.2 / 2 = 5.6

Thus,

5.6 - 5.22 = 1.645(S.D./[tex]\sqrt{n}[/tex]) = 0.38

S.D./[tex]\sqrt{n}[/tex] = 0.38 / 1.645 = 0.231

The 95% confidence interval is given by:

Mean - 1.96(S.D./[tex]\sqrt{n}[/tex]) < μ < Mean + 1.96(S.D./[tex]\sqrt{n}[/tex])

=5.6 - 1.96(0.231) < μ < 5.6 + 1.96(0.231)

= 5.6 - 0.4528 < μ < 5.6 + 0.4528

= 5.15 < μ < 6.05

The 95% confidence interval provides more information because it has a larger interval.

Learn more about confidence intervals here:

https://brainly.com/question/14294413

#SPJ4

Answer:A Venn diagram is an illustration that uses circles to show the relationships among things or finite groups of things. Circles that overlap have a commonality while circles that do not overlap do not share those traits. Venn diagrams help to visually represent the similarities and differences between two concepts

Step-by-step explanation:

Answer:

uses overlapping circles or other shapes to illustrate the logical relationships between two or more sets of items

Step-by-step explanation:

looks like circles that meet and overlap and

the middle part explains the relationship of both circles

example

if the left circle says water & right circle says freezing the middle part would say ice

mathworldwolfram

The sequence for the cost of bracelet in dollars = $0, $3, $6, $9 and $12.

Also the sequence for the cost of necklace is = $0, $6, $12, $18, $24.

The column given concerning the products contains the following amounts of products such as 0, 1, 2, 3, and 4 pieces.

Therefore to calculate the amount to be used to buy each product of bracelet and necklace in each column multiplication is carried out.

That is, 0×3, 1 ×3, 2×3, 3×3, and 4×3

which is = $0, $3, $6, $9 and $12 respectively for the bracelet.

0×6, 1 ×6, 2×6, 3×6, and 4×6

Which is = $0, $6, $12, $18, $24. respectively for the necklace.

Learn more about sequences here;

https://brainly.com/question/7882626

#SPJ1

The company earned 68 billion dollars from 2008 to 2018.

According to the statement

we have given that the company's particular sales in expression are represented by (t² + 10t + 68)

And we have to find the constant terms in this expression which represent the sale of the company.

So, The given expression is (t² + 10t + 68)

From above expression it is clear that the it is in the form of Quadratic Equations.

So, The Quadratic equation, is an equation containing a single variable of degree 2. Its general form is ax^2 + bx + c = 0, where x is the variable and a, b,c are the known numbers and C is the Constant.

The general representation of Quadratic equation is

ax^2 + bx + c = 0  -(1)

and the given expression are

(t² + 10t + 68)  -(2)

After comparing both equations

Here C =68 = Constant.

So, 68 is the Constant term of the expression represent in terms of the context.

Learn more about Quadratic Equation here https://brainly.com/question/1214333

Disclaimer: The question was incomplete. Please find the full content below.

Question:

A particular company's net sales, in billions, from 2008 to 2018 can be modeled by the expression t2 + 10t + 68, where t is the number of years since the end of 2008. What does the constant term of the expression represent in terms of the context?

The company earned 68 billion dollars from 2008 to 2018.

The company earned 68 billion dollars in 2008.

The company earned 10 billion dollars from 2008 to 2018.

The company earned 10 billion dollars in 2008.

#SPJ4

Answer:

Step-by-step explanation:

Substitution is a method that rewrites one of the equations in terms of one variable, and substitutes that in the other equations.

We can easily rewrite x + y = 6 by subtracting y from both sides, giving us

[tex]x = -y+6[/tex]

By putting this equation in place of x in the first equation, we can solve for y:

[tex]4(-y+6)-2y=6[/tex]

[tex]-4y+24-2y=6[/tex] [Distributing 4 into the parentheses]

[tex]-6y+24=6[/tex] [Combining like terms]

[tex]-6y = -18[/tex] [Subtracting 24 from both sides]

[tex]y=3[/tex] [Dividing both sides by -6]

Since we solved for y, we can again substitute by putting it into the second equation.

[tex]x+3=6[/tex]

[tex]x=3[/tex] [Subtracting 3 from both sides]

The solution for this system of equations is (3,3).

Elimination is another method of solving systems of equations. In this method, we multiply one equation such that when both equations are combined, only one variable is left.

We can first multiply both sides of the second equation by 2.

[tex]2x+2y=12[/tex]

Now, let's add both equations to cancel out y.

[tex]4x-2y=6[/tex]

[tex]2x+2y=12[/tex]

[tex]6x=18[/tex]

Now, we can divide 6 from both sides to get the value of x.

[tex]\frac{6x}{6} = \frac{18}{6}[/tex]

[tex]x=3[/tex]

We can now substitute this value into one of the equations to get the value of y. Here, I used the second equation.

[tex]3+y=6[/tex]

[tex]y=3[/tex]

The solution to our system of equations is (3,3).

Answer:

150g for 6 servings

x grams for 15 servings

150/6 = 25

15 x 25 = 375

375g of sugar will be required to make 15 servings.

Answer:

2 hours

Step-by-step explanation:

4 square yards to feet: 4*3 = 12ft

3 cows grazing grass at 2 ft per hour: 2*2 = 6 square ft per hour

Time taken: 12ft/6ft per hour = 2 hours

ANSWER - The first seems more accurate according to my view it's A

Answer:

1083 seats

Step-by-step explanation:

i just answered that.

arithmetic sequence

a1 = 10

an = an-1 + 1 = a1 + (n-1)×1 = 10 + (n-1) = 9 + n

a38 = 9 + 38 = 47 seats

the sum of such an arithmetic sequence

n×(a1 + an)/2

in our case

38×(10 + 47)/2 = 19×57 = 1083 seats

The volume of a solid oblique pyramid with a square base with edges measuring x cm and height (x + 2) cm is (x³ + 2x²)/3 cm³

An equation is an expression that shows the relationship between two or more numbers and variables.

The base of the pyramid is x cm while the height is x + 2, hence:

Volume of pyramid = (1/3) * area of square base * height = (1/3) * x * x * (x + 2) = (x³ + 2x²)/3 cm³

The volume of a solid oblique pyramid with a square base with edges measuring x cm and height (x + 2) cm is (x³ + 2x²)/3 cm³

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

The y-intercept which is the point at which x = 0 is; A: -10

The general form of an equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

We are given the slope;

m = -4

Now, the line passes through the point 0, -10. Thus;

(y - y1)/(x - x1) = -4

(y + 10)/(x - 0) = -4

y + 10 = -4x

y = -4x - 10

Thus, the y-intercept which is the point at which x = 0 is; y = -10

Read more about y-intercept at; https://brainly.com/question/1884491

#SPJ1

Applying the area of a rectangle, the cost to make the part of the compass is: $129.85.

Area of a triangle = 1/2(base)(height).

Find the height of the triangle using the Pythagorean theorem:

Height = √(5² - 1²) ≈ 4.9 cm.

Base = 2 cm

Area of the two triangles = 2[1/2(base)(height)]

Area of the two triangles = 2[1/2(2)(4.9)] = 9.8 cm².

Cost to to make this part of the compass = 9.8 × $13.25 = $129.85.

Learn more about the area of triangle on:

https://brainly.com/question/17335144

#SPJ1

Answer: 129.82

Step-by-step explanation: its on edge I got it right :)

The length of the brace required is 4.3m

What is sine rule?

In a ΔABC a, b and c are the sides and A, B and C are angles then,

[tex]\frac{a}{SinA}=\frac{b}{sinB}=\frac{c}{sinC}[/tex]

We can find the length, l as shown below:

Let AB=3m, BC=2m and AC=l

Let ∠A=25°

So, in ΔABC

[tex]\frac{BC}{sinA}=\frac{AB}{sinC}=\frac{AC}{SinB}[/tex]

[tex]\frac{BC}{sinA}=\frac{AB}{sinC}[/tex]

[tex]\frac{2}{sin25}=\frac{3}{sinC}[/tex]

[tex]\angle{C}=sin^{-1}(\frac{3\times sin25}{2} )[/tex]

∠C=39.34°

∠A+∠B+∠C=180°

∠B=180°-25°-39.34°

∠B=115.66°

[tex]\frac{BC}{sinA}=\frac{AC}{SinB}[/tex]

[tex]\frac{2}{sin25}=\frac{l}{sin(115.66)}[/tex]

[tex]l=\frac{2\times sin(115.66)}{sin25}[/tex]

l=4.2659

Rounding to nearest tenth of meter.

l=4.3m

Hence, the length of the brace required is 4.3m

Learn more about Sine Rule here:

https://brainly.com/question/25852087

#SPJ1

Answer:

( 3 , 4 )

Step-by-step explanation:

Midpoint Formula: ( (x1+x2)/2 , (y1+y2)/2 )

Distance Formula: d = √[(x1-x2)^2 + (y1-y2)^2]

Gradient (Slope) Formula: (y2-y1) / (x2-x1)

Midpoint Formula:

( (x1+x2)/2 , (y1+y2)/2 )

(2,3) and (4,5)

( (2+4)/2 , (3+5)/2 )

( (6)/2 , (8)/2 )

( 3 , 4 )

wyzant sean w

2000 feet can be represented as 20 blue whales in a row of each 100 feet.

What is a blue whale?

I feet = 30.48 centimeters

To explain what the length of 2000 feet looks like:

Take the example of a blue whale of 100 feet.

Now, imagine placing up 20 blue whales one behind the other.

20 × 100 feet = 2000 feet

Therefore, 2000 feet can be represented as 20 blue whales in a row of each 100 feet.

Know more about feet here:

https://brainly.com/question/1739912

#SPJ4

The distance travelled is 10 m

The velocity gained at the end of the time is 2 m/s

From the question, we are to determine distance travelled and the velocity gained

From one of the equations of motion for linear motion, we have that

S = ut + 1/2at²

Where S is the distance

u is the initial velocity

t is the time taken

and a is the acceleration

First, we will calculate the acceleration

Using the formula,

F = ma

Where F is the force

m is the mass

and a is the acceleration

∴ a = F/m

Where F is the force

and a is the acceleration

From the given information,

F = 50 N

m = 250 kg

Putting the parameters into the equation,

a =  50/250

a = 0.2 m/s²

Thus,

From the information,

u = 0 m/s (Since the object was initially at rest)

t = 10 s

S = 0(t) + 1/2(0.2)(10)²

S = 10 m

Hence, the distance travelled is 10 m

For the velocity

Using the formula,

v = u + at

Where v is the velocity

v = 0 + 0.2×10

v = 2 m/s

Hence, the velocity gained at the end of the time is 2 m/s

Learn more on Motion here: https://brainly.com/question/10962624

#SPJ1

Answer:

He has 2 maple boards and 13 oak boards.

Step-by-step explanation:

Assuming all boards are oak : 6*15=90

Maple minus oak = 3

96-90=6 6/3=2 maple boards

Verification : 2*9+6*13 = 96

Answer:

13 oak, 2 maple

Step-by-step explanation:

o = oak

m = maple

o + m = 15

6o + 9m = 96

o + m = 15

o = 15 - m

6o + 9m = 96

6(15 - m) + 9m = 96

90 - 6m + 9m = 96

90 + 3m = 96

3m = 6

m = 2

o + 2 = 15

o = 13

6(13) + 9(2) = 96 (Yes, correct!)

Brainliest, please :)

Answer:

y = 2x + 4

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

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

with (x₁, y₁ ) = (- 2, 0) and (x₂, y₂ ) = ( 0, 4) ← 2 points on the line

m = [tex]\frac{4-0}{0-(-2)}[/tex] = [tex]\frac{4}{0+2}[/tex] = [tex]\frac{4}{2}[/tex] = 2

the line crosses the y- axis at (0, 4 ) ⇒ c = 4

y = 2x + 4 ← equation of line

Here,

y=mx+c

the slope of the line 6x+4y= -16 is -20.

if the two lines are perpendicular, the slope of 1st line * slope of second line=-1

the slope of the 2nd line is -1/2

y-y1=m(x-x1)

y-13=-1/2(x- -18)

when you solve, you get the equation of the line as 2y+x=50

In basic geometry, if two geometry objects intersect at right angles (90 degrees or π / 2 radians), they are vertical.

If two lines intersect at right angles, the line is perpendicular to another line. Explicitly (1) if two lines intersect, the first line is perpendicular to the second line. (2) At the intersection, the straight line angle on one side of the first line is cut by the second line into two congruent angles. Verticality can be shown as symmetric. That is, if the first line is perpendicular to the second line, then the second line is also perpendicular to the first line. Therefore, two straight lines can be said to be perpendicular (to each other) without specifying the order.

Learn more about Perpendicular here: https://brainly.com/question/7098341

#SPJ4

The area of the shape is 84.78 square units

The formula for calculating the area of a circle is expressed as:

A = πr²

where

r is the radius of a circle

Given the following

r = 6 units

pi = 3.14

Substitute

A = 3.14 * 6²

A = 113.04 square units

If the figure is 3/4 of a circle, the area of the shape will be:

A = 3/4 * 113.04

A = 84.78 square units

Hence the area of the shape is 84.78 square units

Learn more on area of a circle here: https://brainly.com/question/10645610

#SPJ1

Answer:

One dollar

Step-by-step explanation:

So you divide 8.70 by 87 to get 0.10. So then you multiply 0.10 by 10 to get a dollar

Sending 87 text messages cost $8.70. Sending 10 text messages would cost $1.00.

Use the concept of fraction defined as:

A fraction is a part of the whole number and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called a fraction. It can be written in the form of p: q, which is equivalent to p / q.

Given that,

Cost to send 87 text messages: $8.70

Number of text messages: 87

To find out how much it would cost to send 10 text messages,

Use a proportion.

If it cost Jose $8.70 to send 87 text messages,

Set up the proportion:

$8.70 / 87 messages = x / 10 messages

To solve for x,

Cross-multiply and divide:

($8.70 x 10) / 87 = $1.00

Therefore, it would cost $1.00 to send 10 text messages.

To learn more about fractions visit:

https://brainly.com/question/5454147

#SPJ3

Answer:

10 m

Step-by-step explanation:

If we draw the diagonal of the rectangle, we form a right triangle where the diagonal is the hypotenuse and the legs are 6 and 8.

This is a well-known Pythagorean triple, which gives the diagonal to be 10 m.

Option 2) the first set of data has values that are closer to the mean because the standard deviation is lower is correct

If two samples have the same mean, then it means that the two values in the two samples are centered around the same value. However, this does not mean that the data values in the samples vary equally around this center and thus the standard deviations may also differ.

It depends what the standard deviations are. The standard deviation is a measure of how close the results are to the mean, a low standard deviation means that the measurements are accurate, so close to the mean. A high standard deviation means that the measurements are more spread out.

We need to find that if two sets of data both have a mean of 76. however, the first set has a standard deviation of 1.4 and the second set has a standard deviation of 5.7. what must be true about the two sets

The first set of data has values that are closer to the mean because the standard deviation is lower because in first set standard deviation is 1.4 and in second set standard deviation is 5.7

The one with smaller standard deviation are least spead from the mean

Hence the first set of data has values that are closer to the mean because the standard deviation is lower.

Learn more about mean and standard deviation here:

https://brainly.com/question/28052755

#SPJ4

Answer: this is the solutions