Billy invites 11 friends to his house for a meal.
He decides to make apple pie.
Billy has this list of ingredients.
Apple pie
serves 4 people
750 g apples
25 g caster sugar
150 g plain flour
50 g butter
75 g brown sugar
Billy has 2500 g of apples.
(a) Does he have enough apples to make apple pie for 12
people?
Show a check of your working.
(4)
Answer:
the answer is in the photo
Step-by-step explanation:
given h(x) =3x-4 find x if h(x) =17
Answer:
x=7
Step-by-step explanation:
h(x) = 17 so you would input 17 for h(x). The equation should look like this. 17= 3x-4. Add 4 to both sides changing the equation to 21 = 3x. Finally divide both side by 3 and you should get x = 7.
Domain
Range
Discrete or continuous?
It is continuous and it domain
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Question
Write a linear function f with f(5)=7 and f(2)=0
f(5) = 7 is another to say a point at (5 , 7)
f(2) = 0 is another to say a point of (2 , 0)
to get the equation of any straight line, we simply need two points off of it, let's use those two above
\((\stackrel{x_1}{5}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{0}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{0}-\stackrel{y1}{7}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{5}}} \implies \cfrac{ -7 }{ -3 } \implies \cfrac{ 7 }{ 3 }\)
\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{7}=\stackrel{m}{ \cfrac{ 7 }{ 3 }}(x-\stackrel{x_1}{5}) \\\\\\ y-7=\cfrac{ 7 }{ 3 }x-\cfrac{ 35 }{ 3 }\implies y=\cfrac{ 7 }{ 3 }x-\cfrac{ 35 }{ 3 }+7\implies {\Large \begin{array}{llll} y=\cfrac{ 7 }{ 3 }x-\cfrac{14}{3} \end{array}}\)
2 Tom argues that his PAYE for the following year will increase by R593.09. The following year Tom's salary increases by 8.5%. How much tax will Tom pay per year, if he still contributes only 7.5% of his gross salary to a pension fund but increases his contribution to the charity organization by further R50.00 a month? Calculate as if the tax table for the following year remains the same.
Tom's total annual tax for the following year, assuming the tax table remains the same, is R325,287.17.
How much tax will Tom pay per year?To calculate Tom's tax for the following year, we need to first calculate his current monthly PAYE (Pay As You Earn) deduction. We can use the current tax table to do this.
Tom's gross salary is R25,780.25 per month, and he is 45 years old, so according to the 2021/2022 tax table for individuals under 65 years old, his monthly PAYE deduction is:
= R1,458.75 + 25% of the amount over R14,958
= R4,569.96
Tom argues that his PAYE will increase by R593.09 for the following year. This means that his expected monthly PAYE deduction for the following year is:
= R4,569.96 + R593.09
= R5,163.05
Tom's salary for the following year will increase by 8.5%, so his new gross salary will be:
= R25,780.25 + (8.5% x R25,780.25)
= R27,959.83
Tom's pension fund contribution remains the same at 7.5% of his gross salary:
= R27,959.83 x 7.5%
= R2,097.49
His charity organization contribution increases by R50.00 per month:
= R50.00 x 12
= R600.00
Assuming the tax table remains the same as the previous year, Tom's new monthly PAYE deduction is:
= R1,577.98 + 26% of the amount over R17,708
= R5,502.86
To calculate Tom's total annual tax, we need to subtract his annual PAYE deduction from his gross salary and then add back his pension and charity contributions:
Total annual tax = (R27,959.83 x 12) - (R5,502.86 x 12) + R2,097.49 + R600.00
Total annual tax = R325,287.17.
Full question "Tom is 45 years old. He earns a gross salary of R25,780.25 per month.. Tom argues that his PAYE for the following year will increase by R593.09. The following year Tom's salary increases by 8.5%. How much tax will Tom pay per year, if he still contributes only 7.5% of his gross salary to a pension fund but increases his contribution to the charity organization by further R50.00 a month? Calculate as if the tax table for the following year remains the same."
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In the diagram below, FC = 10.9,
DE = 17.5, and DF = 13.1. Find the
length of EB. Round your answer to the
nearest tenth if necessary.
D
F
E
C
B
The length of EB is approximately 14.6 units when rounded to the nearest tenth.
To find the length of EB, we can use the property of similar triangles in this diagram. By looking at triangle DFE and triangle CFB, we can see that they are similar triangles.
Using the similarity ratio, we can set up the proportion:
DF / CF = DE / EB
Plugging in the given values, we have:
13.1 / 10.9 = 17.5 / EB
To find EB, we can cross-multiply and solve for EB:
13.1 * EB = 10.9 * 17.5
EB = (10.9 * 17.5) / 13.1
EB ≈ 14.6
Therefore, the length of EB is approximately 14.6 units when rounded to the nearest tenth.
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Does anyone know the correct answer
Answer:
B: 26
Step-by-step explanation:
A boat travels with velocity vector (25, 25√3). What is the directional bearing of the boat?
ON 30° E
OE 30° S
OE 30° N
ON 30° W
In a case whereby a boat travels with velocity vector (25, 25√3) the directional bearing of the boat is ON 30° E.
How can the directional bearing of the boat be determined?The given velocity vector are; 25 and 25√3)
horizontal components =25
vertical components =25√3
Then the angle
Tan(θ) = {vertical component / horizontal component }
= 25√3 / 25
= √3 / 1
= √3
Tangent √3= 60 degrees, Then the directional bearing of angle 60 degrees is 30° E
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Please answer this correctly
Answer:
Step-by-step explanation:
area =area of rectangle 1 +area of rectangle 2 + area of rectangle 3 + area of triangle
= 17*6 + 9*9 + 8*6 + (1/2) * 3*7
= 102 + 81 + 48 + 10.5
= 241.5 sq . ft
Answer: 241.5 ft²
Step-by-step explanation:
I divided the image into 3 rectangles and 1 triangle:
top rectangle: length = 17, height = 6 --> A = 17 x 6 = 102
middle rectangle: length = 9, height = 9 --> A = 9 x 9 = 81
bottom rectangle: length = 6, height = 8 --> A = 6 x 8 = 48
triangle: base = 3, height = 7 --> A = (3 x 7)/2 = 10.5
Total = 241.5
pls help help help help help
Answer:
Both equal sides have a length of 29 cm.
The third inequal side is 9 cm.
Step-by-step explanation:
System of Equations
With the data provided in the problem, we can form a system of two equations with two unknowns.
Let's call x to each equal side of the isosceles triangle and y to the other side. One condition states that each equal side is 2 cm more than three times the other side. It can be written as:
\(x=3y+2\)
We also know the perimeter of the triangle is 67 cm. Since we have to equal sides to x:
\(x+x+y=67\)
\(2x+y=67\)
Let's put together both equations:
\(x=3y+2\)
\(2x+y=67\)
To solve the system, we can use the x from the first equation and replace it into the second equation:
\(2(3y+2)+y=67\)
Operating:
\(6y+4+y=67\)
Joining like terms:
\(7y=67-4=63\)
Solving for y:
\(y=63/7=9\)
The third inequal side is 9 cm. Now find the value of x.
\(x=3y+2=3(9)+2=27+2=29\)
Both equal sides have a length of 29 cm.
The base of a rectangle measures 20 cm. By joining the two vertices of the base with the midpoint of the opposite side, an isosceles triangle is obtained whose perimeter is 72 cm. Calculate the perimeter of the rectangle.
The perimeter of the rectangle is 68 cm .
In the Euclidean plane, a square is a trapezoid with four peculiar angles. Other definitions include an equiangular quadrilateral or a quadrilateral with a right angle parallelogram, where equiangular indicates that a portion of the angles are equal (360°/4 = 90°).
Rectangle comes from the Latin words longitudinal (an adjective that means "right," "appropriate," and "proper") and angle.
Due to the perpendicular alignment of every pair of its adjacent sides, a rectangle is a unique type of parallelogram.
In a parallelogram, the lengths of the two opposing team pairs are parallel. This shape is also known as a trapezoid.
We will use the properties of the Pythagoras theorem to form a equation for the side of the triangle.
let the equal side of the rectangle be x.
therefore perimeter = x +x + 20 = 72
or, 2x = 52
or, x = 26 cm
Now the side of the triangle forms an right angled triangle with the side of the rectangle
let the side be a.
therefore a²+10² = 26²
a² = 676-100
a² = 576 cm
or , a =24 cm
now the perimeter of the rectangle is
2(24 + 10)
= 68 cm
Hence the perimeter of the rectangle is 68 cm .
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For numbers 3, 4, and 5, find the value of the indicated length(s) in ⨀C. A and B are points of tangency. Simplify all radicals.
I just need help with these three problems!
As a result, AB = 52 and AC = BC = 5 as AC and BC are both the circle's radii since A and B are points of tangency .
what is circle ?A circle is a closed object made up of all points in a plane that are separated from the center by a predetermined distance, known as the radius. The diameter is the distance across the circle that passes through its center, while the circumference is the distance around the circle. The ratio of a circle's circumference to its diameter is always pi (), or roughly 3.14. Pi is also known as the proportionality constant. Circles are significant geometric forms that are used frequently in mathematics, science, and daily life.
given
AC and BC are both the circle's radii since A and B are points of tangency. Hence, AC = BC = 5.
We can apply the Pythagorean theorem to segment AB as follows:
\(AB^2 = 52 + 52 \\AB^2 = AC^2 + BC^2\)
AB² = 50
AB = √50 = 5√2
As a result, AB = 52 and AC = BC = 5 as AC and BC are both the circle's radii since A and B are points of tangency .
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1. A taxi cab costs $4.50 for the first mile and $0.75 for each additional mile. Write & solve an equation that could be solved to find how many miles you can travel in a taxi for $30, given that m is the number of additional miles?
Equation: 0.75 divided by 30
Solution:_______________________
PLEASE ANSWER THE WHOLE QUESTION!
Answer:
55x-5=78
Step-by-step explanation:
Find the value of x. If necessary, round to the nearest tenth.
5
6
x
The value of x in the circle using the intersecting secants and tangents equation is 4
How to find the value of x in the circleFrom the question, we have the following parameters that can be used in our computation:
The circle
The value of x in the circle can be calculated using the intersecting secants and tangents equation
So, we have
6² = x * (x + 5)
When expanded, we have
x² + 5x - 36 = 0
When factored, we have
(x + 9)(x - 4) = 0
Using the zero product property , we have
x = -9 or x = 4
The valiue of x cannot be negative
So, we have
x = 4
Hence, the value of x in the circle is 4
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Brooklyn is trying to pick out an outfit for the first day of school. She can
choose from 6 pairs of pants, 8 t-shirts, 3 sweaters or hoodies, and 5 pairs of
shoes. How many different outfits does Brooklyn have to choose from?
Therefore , the solution to the given problem of combination comes out to be thus, we might deduce that Brooklyn has 720 options from which to choose.
What is the Combination?Combinations are mathematical procedures that count the number of possible configurations from a set of things, where the ordering of the selection of the elements is not important. You can select any set of items in any arrangement. Combinations and permutations are frequently wrong.
Here,
For the predicament,
six pants pairs
8 t-shirts
5 pairs equal 1 pair.
hoodies= 3
The formula to determine how many ways there are in a combination is = C. (n,r)
The number of possible outfit combinations is equal to C(n,r)* C(n,r)* C(n,r)* C (n,r)
=> C(6,1)*C(8,1)* C(5,1)* C(3,1) (3,1)
=> 6*8*5*3
=> 720
Therefore , the solution to the given problem of combination comes out to be thus, we might deduce that Brooklyn has 720 options from which to choose.
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Answer:
720
Step-by-step explanation below:
Brainly pls
Write a recursive formula for an, the nth term of the sequence 50, -10, 2, ....
a1
an
11
Answer:do homework
Step-by-step explanation:
If f(x)
=
OA.
A.
2+1, what is the value of f-¹ (3)?
22
B. 19
OB.
C.
O D.
13
OE. 11
The value of the inverse function f-¹ (3) is (e) 11
Calculating the value of the inverse functionFrom the question, we have the following parameters that can be used in our computation:
f(x) = x - 8
To calculate the inverse value at f-¹ (3)
We set the value to 3
using the above as a guide, we have the following:
x - 8 = 3
Evaluate the like terms
x = 11
Hence, the value of the inverse function is (e) 11
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Complete question
if f(x) = x - 8, what is the value of f-¹ (3)?
87°
A
74°
C
B
What is mZB?
mZB =
O
using Inscribed Quadrilateral Theorem
Answer:
m<B = 93°
Step-by-step explanation:
Based on the inscribed quadrilateral theorem, the opposite angles of a cyclic quadrilateral are supplementary.
Thus:
m<B + m<D = 180°
Substitute
m<B + 87° = 180°
m<B = 180° - 87°
m<B = 93°
f(x)=x^2-12x+20
a. f(0) = ?
b. f(2) = ?
c. f(x) = 0,x = ?
d. f(x)= 9,x = ?
Answer:
c . f(x)=0,x=????????????
54943092 rounded to the nearest number
Ken and Leah are trying to solve a science homework question they need to find out how much a rock that weighs 5 lb on Earth with ways on Saturn they know they can multiply the amount the rock ways on Earth by 0.93 to find its weight on Saturn
Answer:
Step-by-step explanation:
4.65
Explain the percentage as a decimal. 9%
Answer:
the answer is 0.09 I think
Answer:
0.09
Step-by-step explanation:
First, drop the % sign. Next, move the decimal point two places to the left. Because 9 is only one digit, you have to add a placeholder zero to show the two decimal places. The answer is 9% written as a decimal is 0.09.
Given f(x)=x^2+6x and g(x)=4 x^2, find fg. fg(x)=
The composite function f·g(x) is 4x⁴+24x³.
The given functions are f(x)=x²+6x and g(x)=4x².
We need to find f·g(x).
We know that, f·g(x)=f(x)×g(x)
Here, f·g(x)=(x²+6x)×4x²
= x²×4x²+6x×4x²
= 4x⁴+24x³
Therefore, the composite function f·g(x) is 4x⁴+24x³.
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DONT IGNORE PLEASE!! What is the measure of angle c
A. 94°
B. 86°
C. 18°
D. 274°
Answer:
B
Step-by-step explanation:
the sum of the 3 angles in a triangle is 180° , so
∠ c + 56° + 38° = 180°
∠ c + 94° = 180° ( subtract 94° from both sides )
∠ c = 86°
Martha went to a restaurant with some friends. The three of them split a large pizza. Martha then ordered a large soda for $5. Martha spent a total of $11. How much was the large pizza? (pls!!!!)
Answer:
$6
Step-by-step explanation:
there was 11 total and 5 went into the soda and 6 went into the pizza so it's 6.
HsiwksjrINEEEDHELPPONTHISSS
Answer: 2) 2/7, 11/72 3) 2 2/5 licorice pieces
Step-by-step explanation:
2)
A fraction of another fraction is essentially the two fractions multiplied.
Therefore, 2/3 of 3/7 = (2*3)/(3*7) = 6/21 = 2/7
1/6 of 11/12 = (1*11)/(6*12) = 11/72
3) If the licorice is divided equally, that means each person would get 12/5 of licorice pieces. 12/5 as a mixed number would become 2 2/5.
Answer:
We will get 12 divided by 5 which it equals to 1.5 licornie will each person get.
Step-by-step explanation:
12/5 =2.4 2 and 1/3 of it
Consider a line whose slope is 6 and which passes through the point (8.–2).
3. Write the equation of the
4. Write the equation of the
line in point-slope form.
line in slope-intercept form.
Answer:
\(y=6(x-8)-2\qquad\text{point-slope form}\)
\(y=6x-50\qquad\text{slope-intercept form}\)
Step-by-step explanation:
The equation of a line can be written in several forms. Two of the most-used forms are the point-slope and the slope-intercept forms.
The point-slope form requires to have one point (xo, yo) through which the line passes and the slope m. The equation expressed in this form is:
\(y=m(x-xo)+yo\)
The slope-intercept form requires to have the slope m and the y-intercept b, or the y-coordinate of the point where the line crosses the y-axis. The equation is:
\(y=mx+b\)
The line considered in the question has a slope m=6 and passes through the point (8,-2). These data is enough to find the point-slope form of the line:
\(\boxed{y=6(x-8)-2\qquad\text{point-slope form}}\)
To find the slope-intercept form, we operate the above equation:
\(y=6x-48-2\)
\(\boxed{y=6x-50\qquad\text{slope-intercept form}}\)
Four times a number n is 5 more than n
Answer:
\(4n+5\)
Find the common difference of the sequence 4, 12, 20, ....
8
In this pattern, we have 4 12 then 20.
We can see that the difference 4 and 12 is 8.
Since the difference between 12 and 20 is also 8, the common difference of the sequence is 8.
What is length of Ef?
A.10
B.15
C.20
D.v200
E.v300
F.v500
Answer:
Answer E is correct
Step-by-step explanation:
Let the Length of EF be x
Use PYTHAGORAS theorem to find the length of EF
EF² + DF² = DE²
\( {x}^{2} + {10}^{2} = {20}^{2} \\ {x}^{2} + 100 = 400 \\ {x}^{2} = 400 - 100 \\ {x}^{2} = 300 \\ x = \sqrt{300} \)
So,
\(EF = \sqrt{300} \)
Hope this helps you.
Let me know if you have any other questions :-)