Year 11 Maths:
500ml of water is used to make 80g of pasta. How many grams of pasta could be made with 2.5 litres of water?

The equation for this would be 6x=42

Here's an explanation.

You have 6 sheets of paper, and you draw some number of stars on each paper. The number of stars are the same. Let's put the stars one each paper as x. Now it's also given that the total number of stars are 42. Since there are x stars on each paper, then 6 times x would be the total number of stars, which is 42. So 6x=42, and x=7

Answer:

4. 24.39°

5. 27.29°

6. 38.21°

Step-by-step explanation:

Given:

Δ ABC is right angle at A

Δ PQR is right angle at Q

Δ XYZ is right angle at X

To find:

∠ C = ?

∠ P = ?

∠ Z = ?

Solution:

For 4.)

We Know the Identities,

[tex]\sin C = \frac{\textrm{side opposite to angle C}}{Hypotenuse}  \\[/tex]

∴ [tex]\sin C=\frac{AB}{BC} \\\sin C =\frac{19}{46} \\\sin C =0.413\\\therefore C= sin^{-1}(0.413)\\ \angle C=24.39\°[/tex]

For 5.)

[tex]\tan P = \frac{\textrm{side opposite to angle P}}{\textrm{side adjacent to angle P}}\\\tan P = \frac{QR}{QP}\\\tan P = \frac{16}{31}\\\tan P = 0.5161\\\angle P=\cos^{-1}(0.5161)\\\angle P=27.29\°[/tex]

For 6.)

[tex]\cos Z = \frac{\textrm{side adjacent to angle Z}}{Hypotenuse}\\\cos Z = \frac{XZ}{YZ}\\\cos Z = \frac{11}{14}\\\cos Z = 0.7857\\\angle Z= \cos^{-1}(0.7857)\\\angle Z= 38.21\°[/tex]

Answer: 13y-5

Step-by-step explanation: Remove parentheses.

4y-5+9y4y−5+9y

2 Collect like terms.

(4y+9y)-5(4y+9y)−5

Step-by-step explanation:

(3 × 70) + (3 × 2)

210 + 6 = 216

Answer:

7.5% < 7.49 <  [tex]7\frac{49}{50}[/tex]

Step-by-step explanation:

To make this easier to look at, first you change them into the same form. Let us make them all into fractions and compare:

7.49 as a fraction is [tex]7\dfrac{49}{100}[/tex]

[tex]7\dfrac{49}{50}[/tex] is already a fraction so let's leave it first.

7.5% in fraction form is [tex]\dfrac{75}{1000}[/tex]

Now knowing this, we can already say that 7.5% is already the least comparing it to the others.

Now we compare the two:

[tex]7\dfrac{49}{100} < 7\dfrac{49}{50}[/tex]

If we make them into similar fractions:

[tex]7\dfrac{49}{50} = 7\dfrac{98}{100}\\\\Then\\\\7\dfrac{49}{100}<7\dfrac{98}{100}[/tex]

Answer:

should be D.

Step-by-step explanation:

hopefully that helps u out!

Answer:

This might be late but D I think

See in the explanation:

Here we have the following system of linear equations in two variables:

[tex](1) \ 2x+7y=-8 \\ \\ (2) \ 2x-5y=-1[/tex]

So if you graph these two equations you will get two lines with different slopes. The question is:

What is the result of subtracting the second equation from the first?

So this can be written mathematically as:

[tex]2x+7y-(2x-5y)=-8-(-1) \\ \\ Breaking \ parentheses: \\ \\ 2x+7y-2x+5y=-8+1 \\ \\ \\ Combining 'like 'terms: \\ \\ 2x-2x+7y+5y=-7 \\ \\ 12y=-7 \\ \\ y=-\frac{7}{12}[/tex]

So the result of subtracting the second equation from the first is:

[tex]12y=-7[/tex]

and from this we can calculate y.

Methods for solving System of Linear Equations:

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One adult ticket costs £11 and one child ticket costs £8.5

Step-by-step explanation:

Let,

Adult ticket = a

Child ticket = c

According to given statement;

3a+4c=67   Eqn 1

5a+6c=106   Eqn 2

Multiplying Eqn 1 by 5;

[tex]5(3a+4c=67)\\15a+20c=335\ \ \ Eqn\ 3[/tex]

Multiplying Eqn 2 by 3;

[tex]3(5a+6c=106)\\15a+18c=318\ \ \ Eqn\ 4[/tex]

Subtracting Eqn 4 from Eqn 3

[tex](15a+20c)-(15a+18c)=335-318\\15a+20c-15a-18c=17\\2c=17\\[/tex]

Dividing both sides by 2

[tex]\frac{2c}{2}=\frac{17}{2}\\c=8.5[/tex]

Putting c=8.5 in Eqn 1

[tex]3a+4(8.5)=67\\3a+34=67\\3a=67-34\\3a=33[/tex]

Dividing both sides by 3;

[tex]\frac{3a}{3}=\frac{33}{3}\\a=11[/tex]

One adult ticket costs £11 and one child ticket costs £8.5

Keywords: Linear equation, subtraction

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Answer:

4x+9

Step-by-step explanation:

x^2+8x+9-(x^2+4x)

x^2-x^2+8x+9-4x

8x-4x+9

4x+9

Live Fund receive [tex]\bold{\$2500 A}[/tex] it they sold half thier holding in Marks Brothers.

Solution:

Given: Sale price of Live Fund holding = 5000 dollar

To find: Amount that Live Fund will get if they sell half of their holding in Marks Brothers.

Assume the total number of shares held by Live Fund in Marks Brothers as A

Therfore, half the holdings (or half the number of shares) of Live Fund will be [tex]\frac{A}{2}[/tex].

Thus, if each share is valued at [tex]\$5000[/tex], then the total value of the number of shares sold will be as follows,

[tex]\Rightarrow5000\times\frac{A}{2}\text{ dollars }\rightarrow\frac{5000\times A}{2}\text{ dollars }[/tex]

[tex]\Rightarrow2500 A\text{ dollars }[/tex]

Hence, Live Fund will receive [tex]\$2500 A[/tex]

Answer:

The number is -16.

Step-by-step explanation:

3/4x=-12

x=-12/(3/4)

x=(-12/1)(4/3)

x=-48/3

x=-16

Answer:

5 part symmetry

Step-by-step explanation:

I did the test

Answer:

5 part symmetry.

Step-by-step explanation:

I took the test and got it right.

Answer:

5 cm

Step-by-step explanation:

What you have there is an equilateral triangle. An equilateral triangle is a triangle that has sides with equal lengths and interior angles are equal as well. So if all angles are equal in a triangle, then that means that this is an equilateral triangle. So we can say that if one side of this triangle is 5cm

then the n would also be equal to 5cm.

Answer:

[tex]x^{4}[/tex] - 256

Step-by-step explanation:

Each term in the second factor is multiplied by each term in the first factor, that is

x²(x² - 16) + 16(x² - 16) ← distribute both parenthesis

= [tex]x^{4}[/tex] - 16x² + 16x² - 256 ← collect like terms

= [tex]x^{4}[/tex] - 256

Answer:

Step-by-step explanation:

(x²+16)(x²-16) = (x²)² - 16² = x^4 - 256 use identity a²-b² = (a-b)(a+b)

Answer:

The price of the glove is $8.5 and the price of the hat is $6.5.

Step-by-step explanation:

2x+4y=43

2x+2y=30

---------------

2x+4y=43

x+y=15

--------------

x=15-y

2(15-y)+4y=43

30-2y+4y=43

30+2y=43

2y=43-30

2y=13

y=13/2

x+13/2=15

x=15-13/2

x=30/2-13/2=17/2

x=17/2, y=13/2.

The price of the glove is $8.5 and the price of the hat is $6.5.

Answer:

A u B = {3,5,6,7,8,11,12}

Step-by-step explanation:

A = {3,6,7,11}

B = {3,5,7,8,12}

A u B = {3,5,6,7,8,11,12}

Answer:

C)  It will take  14 weeks for Edurado to make a profit.

Step-by-step explanation:

The money spent on obtaining the merchandise = $ 7500

The general expense per week = $300

Let us assume Eduardo has to work for N weeks to break Even.

So, the general expense in N weeks  = N x( Expense per week)

=  N x ( $300)  = 300 N

So, the total expense in N weeks  =  Money spent on merchandise + general expense

or, the TOTAL EXPENSE =  $ 7500 +  300 N     .... (1)

Now, the earning per week = $850

So, the total earning in N weeks = N x ( Earning in 1 week) =  N x ( $850)

or, the TOTAL EARNING  =  850 N    .... (2)

Now, for N weeks ,

TOTAL EXPENSE  = TOTAL EARNING

⇒ $7500 +  300 N = 850 N

or, 7500 = 850 N -  300 N = 550 N

⇒ N  = 7500/550 = 13.63

So, number of weeks should at least be 13.63

Among the given options, N = 14 weeks is the most feasible answer.

Hence, it will take  14 weeks for Edurado to make a profit.

Answer:

Mean = 3.25°C

Step-by-step explanation:

The mean (or average) is given by the formula:

Mean = Sum/Number of Numbers

For first 7 days, the mean was 3, so we can say:

Mean = Sum/Number of Numbers

3 = Sum/7

Sum = 3 * 7 = 21

Then on 8th day, the temperature was 5, so the new sum would be (for 8 numbers):

New Sum = 21 + 5 = 26

Now we calculate the mean for 8 numbers:

Mean = 26/8

Mean = 3.25°C

To minimize the cost, the packaging that should be used is the rectangular prism boxes.

From the complete information, the pencils needed is 2400. The prism can hold 60 pencils. Therefore, the number of prisms needed will be:

= 2400/60 = 40 prisms

The total cost for the prism will be:

= $0.50 × 40

= $20

The cylinder can hold 80 pencils. Therefore, the numbers needed will be:

= 2400/80

= 30

The cost of the cylinders will be:

= 30 × $0.75

= $22.50

Therefore, it implies that to minimize the cost, the packaging that should be used is the rectangular prism boxes.

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The company should use rectangular prism boxes, as they require fewer units and incur lower total cost.

To minimize cost, we need to find out which packaging option, between the rectangular prism box and the cylindrical container, requires fewer units and hence incurs lower total cost.

First, let's calculate how many units of each packaging option are needed to package 2,400 pencils:

1. **Rectangular Prism Box:**

  Each box holds 60 pencils.

  Number of boxes needed [tex]\(= \frac{2400}{60} = 40\)[/tex]

2. **Cylindrical Container:**

  Each container holds 80 pencils.

  Number of containers needed [tex]\(= \frac{2400}{80} = 30\)[/tex]

Now, let's calculate the total cost for each option:

1. **Cost for Rectangular Prism Boxes:**

  Number of boxes: 40

  Cost per box: $0.50

  Total cost: [tex]\(40 \times \$0.50 = \$20\)[/tex]

2. **Cost for Cylindrical Containers:**

  Number of containers: 30

  Cost per container: $0.75

  Total cost: [tex]\(30 \times \$0.75 = \$22.50\)[/tex]

Comparing the total costs, we can see that using the rectangular prism boxes incurs a lower cost $20 compared to using the cylindrical containers $22.50.

The reason for the lower cost with rectangular prism boxes is that each box holds fewer pencils (60) compared to cylindrical containers (80). Therefore, even though the cost per unit for the cylindrical containers is lower ($0.75) compared to the rectangular prism boxes ($0.50), the higher number of units required for cylindrical containers results in a higher total cost.

Therefore, to minimize cost, the company should use the rectangular prism boxes for packaging the pencils.

Length of the rectangle is 51 inches

Solution:

Given that

Length of the rectangle in 34 miles less than 5 times its width

Area of rectangle = 867 square inches

Need to determine length of the rectangle.

Let assume width of the rectangle be represented by variable x.

So 5 times width of the rectangle =5x

34 inches less than 5 times width of the rectangle = 5x – 34

As Length of the rectangle in 34 miles less than 5 times its width

=> Length of the rectangle = 5x – 34

The formula for rectangle is given as:

[tex]\text { area of rectangle }=length \times width[/tex]

As given that Area of rectangle = 867 square inches

[tex]\begin{array}{l}{=>867=(5 x-34) \times(x)} \\\\ {=>5 x^{2}-34 x-867=0}\end{array}[/tex]

On solving quadratic equation by using quadratic formula

[tex]x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]

In our case a = 5, b = -34 and c = -867

On substituting value of a, b and c in quadratic formula we get

[tex]\begin{array}{l}{x=\frac{-(-34) \pm \sqrt{(-34)^{2}-4 \times 5 \times(-867)}}{2 \times 5}} \\\\ {=>x=\frac{34 \pm \sqrt{18496}}{10}=\frac{34+136}{10}} \\\\ {=>x=\frac{34+136}{10}=17 \text { or } x=\frac{34-136}{10}=-10.2}\end{array}[/tex]

Since x represents width, it cannot be negative, so x = 17

Length of the rectangle = 5x – 34 = 5(17) – 34 = 51

Hence length of the rectangle is 51 inches

Answer: Junior is 3 3/10 feet tall .

Step-by-step explanation:

As given

Junior's brother is 5 1/2 feet tall

i.e

Junior's brother is 11/2 feet tall

Junior is 3/5 of his brother's height

Thus

Junior's heights = 3/5 times his brother's height

Putting all the values in the formula

Junior's Height = 3/5 X 11/2

Junior's height = 33/10

Junior's height = 3 3/10 feet

Therefore Junior is 3 3/10 feet tall .

Junior's height is calculated by taking 3/5 of his brother's height, which is 5.5 feet. Multiplying these, we find out that Junior is 3.3 feet tall.

The student is asking to solve a problem involving fractions and proportions to find out how tall Junior is compared to his brother. Junior's brother is 5 1/2 feet tall, which is equivalent to 5.5 feet. Junior is 3/5 of his brother's height. To find out Junior's height, we multiply the brother's height by 3/5:

To find Junior's height, we need to multiply his brother's height by \( \frac{3}{5} \). If Junior's brother is 5 1/2 feet tall, we can first express this height as an improper fraction:

\[ \text{Brother's height} = 5 \frac{1}{2} = \frac{11}{2} \text{ feet} \]

Now, we can find Junior's height by multiplying his brother's height by \( \frac{3}{5} \):

\[ \text{Junior's height} = \frac{3}{5} \times \frac{11}{2} \]

Multiplying the numerators and denominators:

[tex]\[ \text{Junior's height} = \frac{33}{10} \text{ feet} \][/tex]

To express this as a mixed number:

[tex]\[ \text{Junior's height} = 3 \frac{3}{10} \text{ feet} \][/tex]

Therefore, Junior is 3 feet 3 inches tall, or 3.3 feet, which is [tex]\( \frac{3}{10} \)[/tex]than 3 feet.

Height of Junior = 5.5 feet x 3/5

Height of Junior = 3.3 feet

Therefore, Junior is 3.3 feet tall.

The asymptotes of the function f(x) = 7/(x^2 - 2x - 24) are located at x = 6 and x = -4.

The function f(x) is a rational function, which means it's a fraction of two polynomials. The function has vertical asymptotes where the denominator (x^2 - 2x - 24) equals zero.

To find the asymptotes, set the denominator equal to zero and solve for x:

x^2 - 2x - 24 = 0

Factor the equation: (x - 6)(x + 4) = 0

Therefore, x = 6 and x = -4 are the roots of the denominator.

Since the denominator becomes zero at x = 6 and x = -4, these points represent vertical asymptotes where the function approaches positive or negative infinity.

Therefore, the function f(x) has asymptotes at x = 6 and x = -4.

Answer:

step 1: addition property of equality

step 2: additive inverses

step 3: additive identity

step 4: multiplication property of equality

Step-by-step explanation:

edg 2020

Answer:

step 1: addition property of equality

step 2: additive inverses

step 3: additive identity

step 4: multiplication property of equality

Step-by-step explanation:

Answer:

80%

Step-by-step explanation:

=20/25  x 100

= 4/5 x 100

=4 x 20

= 80%

Law of Sines

[tex]\displaystyle \frac{sin∠C}{c} = \frac{sin∠B}{b} = \frac{sin∠A}{a} \\ \\ \frac{sin\:40°}{5} = \frac{sin∠C}{7} → \frac{7sin\:40°}{5} = sin∠C → 0,8999026535... = sin∠C → 64,14527443...° = sin^{-1}\:0,8999026535... \\ \\ 64° ≈ m∠C[/tex]

As you can see, the inverse function had to be used towards the end, or the answer would have been thrown off.

I am joyous to assist you at any time.

Answer:

11.3%

Step-by-step explanation:

[tex]\%\ increase=\frac{final-initial}{initial} \times 100\%\\\%\ increase=\frac{69-62}{62} \times 100\%\\\%\ increase=\frac{7}{62} \times 100\%\\\%\ increase=11.3\%[/tex]

Answer:

16.1%

Step-by-step explanation:

Answer:

u

Step-by-step explanation:

the endpoint will be the last one to the right

Answer:

[tex]\$84[/tex]

Step-by-step explanation:

we know that

The simple interest formula is equal to

[tex]A=P(1+rt)[/tex]

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

in this problem we have

[tex]t=1\ years\\ P=\$80\\ A=\$?\\r=5\%=5/100=0.05[/tex]

substitute in the formula

[tex]A=80(1+0.05*1)[/tex]

[tex]A=80(1.05)[/tex]

[tex]A=\$84[/tex]