If anyone could please help me with this I would greatly appreciate it!!

If Anyone Could Please Help Me With This I Would Greatly Appreciate It!!

Answers

Answer 1

Answer:

The area of the house is approximately 309.54 feet²

Step-by-step explanation:

* Lets describe the figure

- It has a quarter circle with radius = the width of the rectangle

- It has a rectangle with length = 26 - the length of the radius, and

 width 10 feet

- It has a triangle with base equal the length of the rectangle and

 height 8 feet

- It has a trapezoid, the length of its two parallel bases are 2 , 5 and

 height 2 feet

* Lets revise the area of all the shape above

- Area the quarter circle = 1/4 π r²

- Area of the rectangle = length × width

- Area of the triangle = 1/2 × base × height

- Area of the trapezoid = 1/2( the sum of the parallel bases) × height

* Now lets solve the problem

# Area of the quarter circle

∵ The radius of the circle = the width of the rectangle

∵ The width of the rectangle = 10 feet

∴ The radius of the circle = 10 feet

∵ The area of the quarter circle = 1/4 π r²

∴ Its area = 1/4 π (10)² = 25π feet²

# Area of the rectangle

∵ The length of the rectangle = 26 - the length of the radius

∵ the length of the radius = 10 feet

∴ The length of the rectangle = 26 - 10 = 16 feet

∵ The width of the rectangle = 10 feet

∵ The area of the rectangle = length × width

∴ Its area = 16 × 10 = 160 feet²

# Area of the triangle

∵ The base = the length of the rectangle

∵ The length of the rectangle = 16 feet

∴ The base = 16 feet

∵ The height = 8 feet

∵ The area of the triangle = 1/2 × base × height

∴ Its area = 1/2 × 16 × 8 = 64 feet²

# Area of the trapezoid

∵ The length of its two parallel bases are 2 feet , 5 feet

∵ The height = 2 feet

∵ The area = 1/2( the sum of the parallel bases) × height

∴ Its area = 1/2 (2 + 5) × 2 = 7 feet²

- Lets add all of these areas to find the area of the house

∴ The area of the house = 25π + 160 + 64 + 7 = 309.5398 feet²

* The area of the house is approximately 309.54 feet²


Related Questions

What is the area of the triangle formed from (-2,2), (1,2), and (0,-6)?

A.12 square units
B.48 square units
C.8 square units
D.24 square units

Answers

Answer:

Option A.12 square units

Step-by-step explanation:

Let

[tex]A(-2,2), B(1,2), C(0,-6)[/tex]

Plot the vertices

see the attached figure

we know that

The area of triangle is equal to

[tex]A=\frac{1}{2}(b)(h)[/tex]

where

[tex]b=AB=(1-(-2))=3\ units[/tex]

[tex]h=(2-(-6))=8\ units[/tex]

substitute

[tex]A=\frac{1}{2}(3)(8)[/tex]

[tex]A=12\ units^{2}[/tex]

Answer:

Step-by-step explanation:

A. 12

What is the total surface area of this square pyramid?

Answers

Answer:

S.A. = 297 mm²

Step-by-step explanation:

We have a square in the base and four triangles on the lateral surface.

The formula of an area of a square:

[tex]A_{\square}=s^2[/tex]

s - side

We have s = 9mm. Susbtitute:

[tex]A_{\square}=9^2=81\ mm^2[/tex]

The formula of an area of a triangle:

[tex]A_{\triangle}=\dfrac{bh}{2}[/tex]

b - base

h - height

We have b = 9 mm and h = 12 mm. Substitute:

[tex]A_{\triangle}=\dfrac{(9)(12)}{2}=54\ mm^2[/tex]

The Surface Area:

[tex]S.A.=A_{\square}+4A_{\triangle}[/tex]

Substitute:

[tex]S.A.=81+4(54)=297\ mm^2[/tex]

Answer:

278

Step-by-step explanation:

EMERGENCY!!

What are the solutions to the equation (x-6)(X + 8) = 0?
x= -6 or x = 8

x=-6 or x = -8

x = 6 or x = -8

x= 6 or x = 8

Answers

The answer is x=6 x=-8


Because

X -6=0 we add 6 to both sides and get

X=6


X+8=0 we minus 8 from both sides to find x

X=-8


Hope this helps

The nth term of a sequence is n^2 + 20.
a) work out the first three terms of the sequence
b) how many terms in the sequence are less than 50?

Answers

Answer:

[tex]\large\boxed{a)\ 21,\ 24,\ 29}\\\boxed{b)\ \text{five terms}}[/tex]

Step-by-step explanation:

[tex]a_n=n^2+20\\\\a)\\\\\text{Substitute}\ n=1,\ n=2\ \text{and}\ n=3\ \text{to the }\ a_n:\\\\a_1=1^2+20=1+20=21\\\\a_2=2^2+20=4+20=24\\\\a_3=3^2+20=9+20=29[/tex]

[tex]b)\\\\\text{You have to solve the inequality:}\\\\n^2+20<50\qquad\text{subtract 20 from both sides}\\\\n^2<30\to n<\sqrt{30}\to n\leq5\\\\a_1,\ a_2,\ a_3,\ a_4\ \text{and}\ a_5\ \text{are less than 50.}[/tex]

a) The first three terms of the sequence are 21, 24 and 29.

b) The no. of terms less than 50 are 6.

What are arithmetic and geometric sequence?

An arithmetic sequence is a set of numbers in which every no. next to the previous number has the same common difference

d = aₙ - aₙ₋₁ = aₙ₋₁ - aₙ ₋₂.

In a geometric sequence numbers are written in the same constant ratio(r).

It means every next number is a multiple of a common constant and the previous number.

r = aₙ/aₙ₋₁ = aₙ-₁/aₙ₋₂.

Given, The nth term of a sequence is n² + 20.

The first three terms we'll get by replacing 1, 2, and 3 in place of n.

The first term is (1)² + 20 = 21.

The second term is (2)² + 20 = 24.

The third term is (3)² + 20 = 29.

No. of terms that are less than 50 are

n² + 20 < 50.

n² < 30.

n < ± √30.

n < 6 approx.

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what is the circumference of the pie​

Answers

Answer:

34.54

Step-by-step explanation:

C= 2pir

11/2= 5.5

5.5* pi=17.27

17.27*2=34.54

Answer:

The circumference of the circle is [tex]\pi * 11[/tex] inches, which is about [tex]34.54[/tex] inches.

Step-by-step explanation:

The circumference of a circle when you only have the diameter ([tex]11[/tex] inches in this case) can be calculated with the formula [tex]C=\pi d[/tex] where [tex]C[/tex] represents the circumference and [tex]d[/tex] represents the diameter.

Plug in the value for the diameter, which is [tex]11[/tex] inches, to get [tex]C=\pi * 11[/tex].

[tex]\pi * 11[/tex] inches is the final exact answer, but you can estimate the answer by replacing [tex]\pi[/tex] with [tex]3.14[/tex] to get [tex]C=3.14 * 11[/tex].

This can be simplified to get [tex]C=34.54[/tex], but this is only an estimate.

2/2 - 7x-4
Simplify
- 58+4
2x + 1
2-1
2x + 1
*+1
2-72

Answers

Answer:

A or (2x+1)/(x-1)

Step-by-step explanation:

Let's simplify the top of the fraction first.

1. Simplify the numerator.

2x^2 -7x-4=(2x+1)(x-4)

2. Simplify the denominator.

x^2-5x+4=(x-4)(x-1)

Now we have:

((2x+1)(x-4))/((x-4)(x-1))

We see that there is an (x-4) both on the numerator and denominator.

We can remove (x-4) by division.

Doing that, we have:

(2x+1)/(x-1) or A

What is the equation of the line passing through the points (-25,50) and (25,50 in slope intercept form?

Answers

Answer:

y=50

Step-by-step explanation:

Since the y value doesn't change and it is a line

y=50

Answer:

[tex]y= 0x + 50[/tex]

Step-by-step explanation:

Since, the slope intercept form of a line is,

y = mx + c,

Where, m is the slope of the line.

Also, the equation of a line passes through [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is,

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

Thus, the equation of the line passes through (-25, 50) and (25, 50) is,

[tex]y-50= \frac{50-50}{25+25}(x+25)[/tex]

[tex]y-50=0[/tex]

[tex]\implies y = 0x + 50[/tex]

Which is the required equation.

Please help! Evaluate 1 + ( - 2/3 ) - (-m) where m - 9/2.

Answers

Answer:

[tex]m + \frac{1}{3} [/tex]

Step-by-step explanation:

[tex]1. \: 1 - \frac{2}{3}+m \\ 2. \: m + (1 - \frac{2}{3}) \\ m + \frac{1}{3} [/tex]

Answer:

29/6

Step-by-step explanation:

1+ -2/3 - (-m)

1 - 2/3 + m

1/3 + m

Let m = 9/2

1/3 +9/2

Get a common denominator of 6

1/3 *2/2 = 2/6

9/2 *3/3 = 27/6

2/6 + 27/6

29/6

Grandpa Ernie is shrinking! Over the past 4 years his height decreased by a total of 2.4 cm.It decreased by the same amount each year. What was the change in Grandpa Ernie's height each year

Answers

Answer:

He shrunk .6 cm each year

Step-by-step explanation:

To find the decrease per year, we take the total decrease and divide by the number of years

2.4 cm/ 4 years

.6 cm/ year

He shrunk .6 cm each year

F(x)=3.7-2x
g(x)=0.25x-5
what is f(x) +g(x)
Pls help

Answers

Answer:

f(x) +g(x)  = -1.3 - 1.75x

Step-by-step explanation:

f(x) +g(x) is simply obtained by adding the two given functions, f(x) and g(x). We are given that;

F(x)= 3.7-2x and g(x)= 0.25x-5

f(x) +g(x)  = 3.7-2x + (0.25x-5)

f(x) +g(x)  = 3.7 -5 + 0.25x - 2x

f(x) +g(x)  = -1.3 - 1.75x

For this case we have the following functions:

[tex]f (x) = 3.7-2x\\g (x) = 0.25x-5[/tex]

We must find[tex]f (x) + g (x):[/tex]

We have to:

[tex]f (x) + g (x) = 3.7-2x + (0.25x-5)\\f (x) + g (x) = 3.7-2x + 0.25x-5[/tex]

We add similar terms:

[tex]f (x) + g (x) = - 1.75x-1.3[/tex]

Thus, the result is:[tex]-1.75x-1.3[/tex]

Answer:

[tex]-1.75x-1.3[/tex]

HELP Geometry does anyone know this

Answers

Answer: second option.

Step-by-step explanation:

You need to remember the following identity:

[tex]sin\alpha=\frac{opposite}{hypotenuse}[/tex]

In this case, we can observe that:

[tex]\alpha=45\°\\opposite=6\\hypotenuse=x[/tex]

Now you must substitute these values into  [tex]sin\alpha=\frac{opposite}{hypotenuse}[/tex] and solve for the hypotenuse. Then:

[tex]sin(45\°)=\frac{6}{x}\\\\(x)(sin(45\°))=6\\\\x=\frac{6}{sin(45\°)}\\\\x=6\sqrt{2}[/tex]

Answer:

The correct answer is second option

6√2

Step-by-step explanation:

From the figure we can see a right angled triangle, with angles 45°, 45° and 90°

The height of triangle is 6 units

Points to remember

If the angles of a right angled triangle are  45°, 45° and 90° then the sides are in the ratio, 1 : 1 : √2

To find the value of x

From the figure we can see that, the angles are  45°, 45° and 90°

Therefore the two sides are equal and one side is x

The equal side is 6 units

Therefore 6 : 6 : x = 6 : 6 : 6√2

The value of x = 6√2

The second option is the correct answer.

I NEED HELP ASAP


The graphs of f(x) = –2x and
g(x) = (1/2)^x are shown.
What are the solutions to the equation
-2x = (1/2)^x ?
Select each correct answer.
-2, -1, 2, 4

Answers

Answer:

I have not the slightest clue but there's an app called cam calc and I swear its the best

Answer:

-2!

Step-by-step explanation:

im just finished this exact test and i swear thats the right answer!!

Find the derivative of y=e^-4x

Answers

Answer:

[tex]\displaystyle y' = -4e^{-4x}[/tex]

General Formulas and Concepts:

Calculus

Differentiation

DerivativesDerivative Notation

Derivative Property [Multiplied Constant]:                                                          [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]

Basic Power Rule:

f(x) = cxⁿf’(x) = c·nxⁿ⁻¹

Derivative Rule [Chain Rule]:                                                                                 [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle y = e^{-4x}[/tex]

Step 2: Differentiate

Exponential Differentiation [Derivative Rule - Chain Rule]:                       [tex]\displaystyle y' = e^{-4x}(-4x)'[/tex]Basic Power Rule [Derivative Property - Multiplied Constant]:                 [tex]\displaystyle y' = -4e^{-4x}[/tex]

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

Final answer:

The derivative of y = e^-4x is -4e^-4x.

Explanation:

To find the derivative of y = e-4x, we can use the power rule for derivatives. The power rule states that if we have a function of the form y = axb, then the derivative is given by dy/dx = abxb-1. Applying this rule to the given function, we have dy/dx = -4e-4x. Therefore, the derivative of y = e-4x is -4e-4x.

y= -3/4x+3 and y=-12

Answers

Answer:

x = 20, y = -12

Step-by-step explanation:

[tex]y=-\dfrac{3}{4}x+3\ and\ y=-12\\\\\text{Substitute the value of y to the first equation:}\\\\-12=-\dfrac{3}{4}x+3\qquad\text{multiply both sides by 4}\\\\-48=-3x+12\qquad\text{subtract 12 from both sides}\\\\-60=-3x\qquad\text{divide both sides  by (-3)}\\\\20=x\to x=20[/tex]

Answer:

x = 20, y = -12

Step-by-step explanation:

y= -3/4x+3 and y=-12

x = 20, y = -12

Find the area of a parallelogram PGRM with vertices at (0,0) (6,0) (2,4) and (8,4)

Answers

Answer:

[tex]A=24\ un^2.[/tex]

Step-by-step explanation:

Plot points A(0,0), B(6,0), C(2,4) and D(8,4) on the coordinate plane (see attached diagram). The segment CE is the height of the parallelogram ABDC.

The area of the parallelogram is

[tex]A=\text{Base}\cdot \text{Height}[/tex]

Base= AB

Height =CE

So,

[tex]AB=\sqrt{(6-0)^2+(0-0)^2}=\sqrt{36+0}=\sqrt{36}=6\\ \\CE=\sqrt{(2-2)^2+(4-0)^2}=\sqrt{0+16}=\sqrt{16}=4[/tex]

Hence, the area of the parallelogram is

I'll tell you how to do it for any polygon in the cartesian plane with the vertices listed in order.

First we have to list the vertices in order so each pair is a side:

(0,0) (6,0) (8,4) (2,4)

Now for each side (a,b)(c,d) we calculate the cross product ad-bc

(0,0)(6,0)   0(0)-0(6)=0

(6,0)(8,4)   6(4)-0(8)=24

(8,4)(2,4)   8(4)-4(2) = 24

(2,4)(0,0)   2(0)-4(0)=0

We add up the cross products, and take half the absolute value of the sum for the area:

Area = (1/2) | 0 + 24 + 24 + 0 | = 24

Answer: 24

5 1/8 - 2/ 78 my little sister's homework ​

Answers

Answer:

5 1/8 - 2 7/8 =

3 -6/8 =

2 2/8 =

2 1/4 =

2.25

Step-by-step explanation:

What is the length of AB?
A(2,-6). BIZ, 1)

Answers

Answer:

The length of AB is [tex]\sqrt{74}\ units[/tex]

Step-by-step explanation:

we know that

The formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

[tex]A(2,-6)\\B(7,1)[/tex]  

substitute

[tex]d=\sqrt{(1+6)^{2}+(7-2)^{2}}[/tex]

[tex]d=\sqrt{(7)^{2}+(5)^{2}}[/tex]

[tex]d=\sqrt{49+25}[/tex]

[tex]AB=\sqrt{74}\ units[/tex]

What is the factored form of 8x2 + 12x?

Answers

Answer:

[tex]4x(2x + 3)[/tex]

Step-by-step explanation:

We have the expression

[tex]8x^2 + 12x[/tex]

and we must factor it

Note that the expression has no independent term

Then we can factor the expression by taking the variable 4x as a common factor

[tex]8x^2 + 12x[/tex]

[tex]4x(2x + 3)[/tex]

Finally the factored form of [tex]8x^2 + 12x[/tex] is [tex]4x(2x + 3)[/tex]

Answer: 4x(2x+3).

Step-by-step explanation: To factor a number means to break it up into numbers that can be multiplied together to get the original number. In the given problem, we can factorize the expression by taking out a common factor, in this case 4x:

[tex]8x^{2} +12x=[/tex]

[tex]4x(2x+3)[/tex]

as we can see, if we multiply 4x*(2x+3) we obtain the original expression.

Question 14 (1 point)
Larry deposits $15 a week into a savings account. His balance in his savings account grows by
a constant percent rate.

Answers

Answer:

Step-by-step explanation:

I don't think it really does grow by a constant rate. As he puts money in, the amount he puts in becomes less significant to the total.

Suppose he starts at 100 dollars.

After week one, he puts in 100 + 15 = 115 dollars.

The 15 dollars represents an increase of  15/100

After the second week, he puts in another 15 dollars. He has 115 in there already.

(15/115) * 100% = 13.04%

After the third week, he puts in another 15 dollars. (15/130 ) * 100% = 11.53

And so one

Can someone help me plz

Answers

Answer:

Half gallon

Step-by-step explanation:

at the least expensive price per ounce (60 cents), half gallon is the answer.

Help pls !!! A waitress kept track of whether her customers ordered and appetizer and dessert

Answers

D
Multiply 3•100 to get the percent, and since the number is in the column with no appetizer and row with dessert, 30% ordered dessert but no appetizer
please make me brainliest if I helped ;-)

The 0.3 in the highlighted cell mean 30% ordered dessert but no appetizer.

The correct option is (D).

What is mean?

The mean (aka the arithmetic mean, different from the geometric mean) of a dataset is the sum of all values divided by the total number of values.

As, the number is in the column with no appetizer and row with dessert

So, 0.3 = 0.3*100/100

= 30/100

= 30% ordered dessert but no appetizer.

Hence, 30% ordered dessert but no appetizer.

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Review: To simplify an expression, combine like terms by adding or
subtracting coefficients only. Like terms have the same variable (letter or
symbol that represents a quantity).
Example: 17a + 4 - 5a - 3 = (17a - 5a) + (4-3) = 12a + 1
Simplify this expression. 10b + 7 - 3 - 2​

Answers

Answer:

10b + 2

Step-by-step explanation:

To simplify this expression. 10b + 7 - 3 - 2​ use the sample you demonstrated above to simplify it

10b + 7 -3 -2

combine the like terms

10b + 7 - 5

10b + 2

Final answer:

The expression 10b + 7 - 3 - 2, when simplified by grouping and adding or subtracting like terms, becomes 10b + 2.

Explanation:

To simplify an expression, like the one you've given which is 10b + 7 - 3 - 2,  it is necessary to group like terms and combine them.

First, let's combine like terms. In this case, you only have a single term with a variable:

10b (which we will leave as is since there are no other terms with 'b' in them)

Then, you have constants (numbers without variables) 7, -3, and -2. We can combine these by adding or subtracting them: 7 - 3 - 2 = 2

So your simplified expression becomes: 10b + 2

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If y varies inversely as x, find the constant of variation if y = 2 as x = -9.

Answers

Answer:

Constant of variation (k) = -18

Step-by-step explanation:

We are given that y varies inversely as x and we are to find the constant of variation (lets assume its [tex] k [/tex] if [tex] y = 2 [/tex] and [tex] x = - 9 [/tex].

[tex] y [/tex] ∝ [tex] \frac { 1 } { x } [/tex]

Changing this inverse proportionality to equality to get:

[tex] y = \frac { k } { x } [/tex]

Substituting the given values:

[tex] 2 = \frac { k } { -9 } [/tex]

[tex]k=-9 \times 2[/tex]

k = -18

what are the soultion(s) to the quadratic equation 40- x^2=0

Answers

Answer:

40 - x² = 0

x² = 40

x = ±√40 = ±√4√10 = ±2√10

Find the x-intercepts of the parabola with
vertex (-1,-108) and y-intercept (0,-105).
Write your answer in this form: (x1,71), (x2,y2).
If necessary, round to the nearest hundredth.

Answers

Answer:

The x-intercept are (-7 , 0) and (5 , 0)

Step-by-step explanation:

* Lets revise the general form of the equation of the parabola

- The general form of the equation of the parabola is:

  y = ax² + bx + c , a , b , c are constant

- The y-intercept is c, because the parabola intersect the y-axis at

  point (0 , c)

- The x-coordinate of the vertex point is -b/2a

* Now lets solve the problem

∵ The general form of the equation of the parabola is y = ax² + bx + c

∵ The y-intercept is -105

∴ c = -105

∴ y = ax² + bx - 105

∵ The vertex point is (-1 , -108)

∴ The x-coordinate of the vertex of the parabola = -1

∵ The x-coordinate of the vertex of the parabola = -b/a

∴ -b/2a = -1 ⇒ using cross multiplication

∴ -b = -2a ⇒ multiply two sides by -1

∴ b = 2a

- Substitute the value of b in the equation

∴ y = ax² + 2ax - 105

- Substitute the value of x , y in the equation by the coordinates of

 the vertex point

∵ The vertex point lies on the parabola

∴ put x = -1 and y = -108

∴ -108 = a(-1)² + 2a(-1) - 105

∴ -108 = a - 2a - 105 ⇒ add the like term

∴ -108 = -a - 105 ⇒ add 105 to both sides

∴ -3 = -a ⇒ multiply both sides by -1

∴ a = 3

- Substitute the value of a in the equation

∵ y = ax² + 2ax - 105

∴ y = 3x² + 2(3)x - 105

∴ y = 3x² + 6x - 105

- To find the x-intercept put y = 0

∴ 3x² + 6x - 105 = 0

- All the terms have 3 as a common factor

∴ divide all the terms by 3

∴ x² + 2x - 35 = 0

- Now factorize it into two factors

∵ x² = x × x ⇒ the 1st term in the bracket and the 1st term in the

  2nd bracket

∵ -35 = -5 × 7 ⇒ the 2nd term in the 1st bracket and the 2nd term in the    

  2nd bracket

∵ x × - 5 = -5x ⇒ means

∵ x × 7 = 7x ⇒ extremes

∵ 7x - 5x = 2x ⇒ the middle term

∴ (x - 5)(x + 7) = 0

- Equate each bracket by 0

∴ x - 5 = 0 ⇒ add 5 to both sides

∴ x = 5

OR

∴ x + 7 = 0 ⇒ subtract 7 from both sides

∴ x = -7

∴ The x-intercept are -7 , 5

* The x-intercept are (-7 , 0) and (5 , 0)

Answer:

Step-by-step explanation:

Can someone please help me ..

Answers

(0+1+2+3+4) /5 = 2
Hope this helps!

Answer:

The mean of pictures is 2

Step-by-step explanation:

To find the mean we add up all the pictures then divide it by the amount of newspapers, there are 10 and 5 newspapers. 10/5=2.

The ratio of the height of two similar cylinders is 4 to 3 What is the ratio of their volumes

Answers

Answer:

  64 : 27

Step-by-step explanation:

When using scale factors

Length = scale factor

Area = scale factor squared

Volume = scale factor cubed

The ratio is 4:3

The ratio of the volume is 4^3 : 3^3

                                            64 : 27

Answer ASAP!!It takes 1 1/2 cups of flour, cups of sugar, and 1 1/4 cup of butter to bake fifteen shortbread cookies. If Ramon has 5 cups of flour, 4 cups of sugar, and 13/4 cups of butter, how many shortbread cookies can he bake? Plz don't copy and paste the answer from another site. I need it to be answered in fraction form and well explained. Brainliest for first correct!

Answers

Answer:

Up to 39 shortbread cookies.

Step-by-step explanation:

Start by considering: how many cookies can Ramon make if

Flouring runs out first,Sugar runs out first, and Butter runs out first?

Assume that flour runs out before the other two ingredients. How many cookies can Ramon make?

It takes 1 1/2 = 3/2 cups of flour to bake fifteen cookies. 5 cups of flour is available. How many batches of fifteen cookies will that 5 cups of flour make?

[tex]\displaystyle \frac{5}{3/2}\right = \frac{10}{3}[/tex].

That's

[tex]\displaystyle 5\times \frac{10}{3} = 50\;\text{cookies}[/tex].

Similarly, assume that sugar runs out before the other two ingredients. How many cookies can Ramon make?

It takes one cup of sugar to bake fifteen cookies. 4 cups of sugar is available. That 4 cups of sugar will make up to four batches of fifteen cookies. That's 60 cookies.

Assume that butter runs out before the other two ingredient. How many cookies can Ramon make?

It takes 1 1/4 = 5/4 cups of butter to bake fifteen cookies. 13/4 cups of butter is available. That 13/4 cups of butter will make up to 13/5 batches of fifteen cookies. That's

[tex]\displaystyle 15 \times \frac{13}{5} = 39\;\text{cookies}[/tex].

These three numbers differ. How many cookies will these materials actually make? The ingredient that will make the smallest number of cookies will run out before other ingredients. In this case, butter runs out first. These materials will make up to 39 shortbread cookies.

What is the solution to the compound

Answers

B is the correct answer
3x-8 >= -5

3x>= 3
X>=1
There’s only one answer that has x>=1 so the answer is B

Identify this conic section.
x2 - y2 = 16
o line
circle
ellipse
parabola
hyperbola

Answers

Answer:

hyperbola

Step-by-step explanation:

hyperbola

Ax^2+By^2+Cx+Dy+E=0

A=B you probably have a circle

A and B have same sign but A isn't B you probably have an ellipse

A and B are opposite in sign you probably have an hyperbola

If either A or B=0 (but not both) then you have a parabola

ANSWER

Hyperbola

EXPLANATION

The given conic has equation:

[tex] {x}^{2} - {y}^{2} = 16[/tex]

We divide through by 16.

[tex] \frac{ {x}^{2} }{16} - \frac{ {y}^{2} }{16} = \frac{16}{16} [/tex]

We simplify the right hand side to get

[tex] \frac{ {x}^{2} }{16} - \frac{ {y}^{2} }{16} = 1[/tex]

Or

[tex] \frac{ {x}^{2} }{ {4}^{2} } - \frac{ {y}^{2} }{ {4}^{2} } = 1[/tex]

This is a hyperbola, that has its vertex at the origin because the quadratic terms have different signs. One is positive and the other is negative.

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