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
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
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?
Answer:
S.A. = 297 mm²Step-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
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?
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
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
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?
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.
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
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
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
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
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
Answer:
[tex]\displaystyle y' = -4e^{-4x}[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative 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
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
Answer:
x = 20, y = -12Step-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)
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
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)
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?
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.
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
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
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
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
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.
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
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.
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 ..
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
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!
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
Identify this conic section.
x2 - y2 = 16
o line
circle
ellipse
parabola
hyperbola
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.