100 were students interviewed, 28 took PE, 31 took bio, 42 took English, 9 took PE and biology, 10 took PE and english, 4 took all three subjects.
(1) how many students took none of the three subjects.
(2) how many students took PE, but not biology or English.
(3) how many students took biology and PE but no English. ​

Answer:

y=ln(x) minus five

Step-by-step explanation:

y=ln(x) five units down

Five units down could mean minus five(-5)

The expression can be written as

y=ln(x)-5

That is,

y=ln(x) minus five

The equation that translates y = ln(x) 5 units down is y' = ln(x) - 5

The function is given as:

y = ln(x)

When translated down by 5 units, the rule of translation is:

(x, y) => (x, y - 5)

So, we have:

y' = ln(x) - 5

Hence, the equation that translates y = ln(x) 5 units down is y' = ln(x) - 5

Read more about transformation at:

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Answer:

([tex]\frac{2}{3} , \frac{1}{5}[/tex])

Step-by-step explanation:

The fastest way to do this is to convert both equations into slope-intercept form and graph it to find the solution point. If you wanted to do this algebraically, you might want to start out by getting rid of the fractions and using either substitution or elimination to find x and y.

Answer:

The perimeter of the playground is 65 metres

Step-by-step explanation:

Questions like this requires attachment; See attachment for diagram.

From the diagram, we have the following parameters

[tex]Length = 2cm[/tex]

[tex]Width = 4.5cm[/tex]

Required

Calculate the parameter of the actual diagram

First, the actual length and width has to be calculated;

Given that the scale drawing is 1:500

[tex]Actual\ Length = 500 * 2cm = 1000cm[/tex]

[tex]Actual\ Width = 500 * 4.5cm = 2250cm[/tex]

Now, the perimeter can be calculated;

[tex]Perimeter\ of\ a\ Rectangle = 2(Length + Width)[/tex]

[tex]Perimeter = 2(1000cm + 2250cm)[/tex]

[tex]Perimeter = 2(3250cm)[/tex]

[tex]Perimeter = 6500cm[/tex]

However, the question requires answer to be in meters

If 100 cm = 1 m, then

[tex]6500cm = \frac{6500m}{100}[/tex]

[tex]6500cm = 65m[/tex]

Hence, the perimeter of the playground is 65 metres

Answer:

36

Step-by-step explanation:

9+9+9+9=36

Answer: 36 cm

Step-by-step explanation:

The perimeter is the sum of all side lengths of the figure. Since this is a square, all sides have the same length.

9 * 4 = 36

Answer:

k = 4, t = 2

Step-by-step explanation:

Express 2025 as a product of its prime factors

2025 = [tex]3^{4}[/tex] × 5², that is

[tex]3^{4}[/tex] × 5² = [tex]3^{k}[/tex] × [tex]5^{t}[/tex]

Comparing exponents of same bases on both sides, gives

k = 4 and t = 2

Answer:

12x^2 - 8xy + y^2 + 12x - 2y

Step-by-step explanation:

Answer:

The length is 40 units.

Step-by-step explanation:

You need to use a triangle for the base then use the hypotenuse of the base as the base of the diagonal shown in the prism.

[tex]0.5*8*2=\\4*2=\\16[/tex]

The hypotenuse of the triangle of the base is 16.

[tex]0.5*16*5=\\8*5=\\40[/tex]

The diagonal shown in the prism is 40 units.

Answer:

Yes, it is true that [tex]x^2+3x-1[/tex]  is a factor of [tex]x^4+3x^3-2x^2-3x+1[/tex].

Step-by-step explanation:

Let us try to factorize [tex]x^4+3x^3-2x^2-3x+1[/tex]

[tex]x^4+3x^3-2x^2-3x+1\\\Rightarrow x^4-2x^2+1-3x+3x^3[/tex]

Let us try to make a whole square of the given terms:

[tex]\Rightarrow (x^2)^2-2\times x^2 \times 1+1^2+3x^3-3x\\\Rightarrow (x^2-1)^2+3x^3-3x\\[/tex]

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

Formula used above:

[tex]a^{2} -2 \times a \times b +b^{2} = (a-b)^2[/tex]

In the above equation, we had [tex]a = x, b = 1[/tex].

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

Further solving the above equation, taking [tex]3x[/tex] common out of [tex]3x^3-3x[/tex]

[tex]\Rightarrow (x^2-1)^2+3x(x^2-1)\\[/tex]

Taking [tex](x^{2} -1)[/tex] common out of the above term:

[tex]\Rightarrow (x^2-1)((x^2-1)+3x)\\\Rightarrow (x^2-1)(x^2+3x-1)[/tex]

So, the two factors are [tex](x^2-1)\ and\ (x^2+3x-1)[/tex].

[tex]\therefore[/tex] The statement that [tex]x^2+3x-1[/tex]  is a factor of [tex]x^4+3x^3-2x^2-3x+1[/tex] is True.

Answer:

the one with a vertical line at the x value of -22

Step-by-step explanation:

subtract negative 21 to 1 to get -22

Then x=-22

Graph.

Answer:

Loss %age = 25%

Step-by-step explanation:

Cost Price of Item = 250,000/-

Loss = 1/4 = 0.25 of 250,000

=> 62,500 /-

%age Loss = [tex]Loss*100/Cost Price[/tex]

=> 62,500 * 100 / 250,000

=> 6,250,000/250,000

=> 25 %

Answer:

x=5

Step-by-step explanation:

(the goal is to get x by itself)

subtract x on both sides

5x-11=14

add 11 on both sides

5x=25

divide 5 on both sides

x=5

and check your work by plugging x back in to see if the two sides equal each other.

Step-by-step explanation:

6x-11=x+14

[tex]6x - x - 11 - 14 = 0 \\ 5x - 25 = 0 \\5x = 25 \\ x = 5[/tex]

Answer:

$2,800 and $6,400

Step-by-step explanation:

Aquí, sabemos que hay un 20% de descuento en compras.

Entonces, para una persona que compró cosas por valor de $ 3,500, el monto que debe pagar será; 20/100 * 3500 = $ 700

Entonces, la cantidad a pagar = 3500-700 = $ 2,800

Para la persona que compró $ 8000, monto a pagar = 20/100 * 8,000 = $ 1,600

Cantidad a pagar = 8000-1600 = 6400

Answer:

12 cups

Step-by-step explanation:

there are 4 cups in 1 quart.  You multiply both of them by 3 so there are 12 cups in 3 quarts

Answer:

12 cups

Step-by-step explanation:

1 quart = 4 cups

4*3 = 12

12 cups

brainliest??

Answer:

5. 2 terms; 3xy, 2

6. 3

7. 0, can't be factored

Step-by-step explanation:

Answer:

1st Graph

Step-by-step explanation:

Easiest and quickest way is to graph the function in a graphing calc and then choosing the best answer.

Answer:

127

Step-by-step explanation

x3+3x2−4

________

9x4−12x2

Algebra isn't fun. Hope that helps though!

Answer:

A) prove that QR = QR by reflexive property of congruence

Answer:

Salutations!

The slope is (2)

And the y-intercept is (-5)

Hope you're having a good day, and may god bless :)

Slope of the given inequality is 2 and the y-intercept of the given inequality is (0, - 5).

"An inequality is the relationship between two values that are not equal is defined by inequalities. Inequality means not equal."

The given inequality is:

y > 2x - 5

By plotting this inequality, we get:

Slope of the given inequality is 2.

The y-intercept of the given inequality is (0, - 5)

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Answer:

Christian made $191.25 and Kenneth made $127.50 each.

Step-by-step explanation:

With each dog, you multiply how many dogs with the amount of cash they get each dog.

Christian: 15x12.75= $191.25

Kenneth: 10x12.75= $127.50

So you just multiply the amount of dogs with money :)

Answer:

21 quarters, 6 dimes, and 11 nickels

Step-by-step explanation:

# of Quarters = x.

# of Dimes = y.

# of Nickels = z.

(i)x = 3y+3.

(ii) 0.25x + 0.1y + 0.05z = 6.4

(iii) x + y + z = 38.

Multiplying (iii) by -0.05, and adding it to (ii),

we then get:

0.2x + 0.05y = 4.5.

Now plug in (i) into this.

0.65y + 0.6 = 4.5.

0.65y = 3.9

y = 6.

Since y = 6, we can subsitute this into our equation.

0.2x + 0.3 = 4.5

0.2x = 4.2

x = 21.

Since x = 21, y =6, then z = 11.

Answer:

the correct one is y < 2x

Step-by-step explanation:

Answer:

y  2x + 1 or B

Step-by-step explanation:

thats whats right on edge

Answer:

(-4.58, -2)

Step-by-step explanation:

[tex]\theta $ is in between \pi$ and $\frac{3\pi}{2}$ radians \\Therefore, \theta$ is in Quadrant III\\If \csc \theta = -\dfrac{5}{2}$ and cosec \theta = \dfrac{Hypotenuse}{Opposite} \\ $Therefore:\\Hypotenuse = 5\\Opposite $=-2[/tex]

Using Pythagoras Theorem

[tex]5^2=(-2)^2+ x^2\\25=4+x^2\\x^2=21\\x=\sqrt{21} \approx 4.58[/tex]

Since the angle is in the third Quadrant, Adjacent = -4.58.

Therefore, the coordinates of P(x,y) is (-4.58, -2)

Answer: a

Step-by-step explanation: edge 2021

Answer:

8 pi square units

Step-by-step explanation:

AB=V[3-(-1)]^2+[2-(-2)]^2=V16+16=V4^2*2=4V2

radius =4V2/2=2V2

Area=pi*(2V2)^2=8pi square units

Answer:

3234

4312

5390

Step-by-step explanation:

3x +4x + 5x = 12936

12x = 12936

Answer:

SA = 967.6 cm²

Step-by-step explanation:

Surface Area of cylinder = [tex]2\pi r h + 2\pi r^2[/tex]

Where r = 7 cm, h = 15 cm

=> SA = 2(3.14)(7)(15)+2(3.14)(7)²

=> SA = 659.7 + 2(3.14)(49)

=> SA = 659.7 + 307.9

=> SA = 967.6 cm²

Answer:

967.12 cm^2

Step-by-step explanation:

To find surface area of cylinder:

Find area of cross section x 2 = pi x r ^2 = 153.86 x 2 = 307.72cm^2

Area of curved surface = 3.14 x 14 x 15 = 659.4 cm^2

Total Surface Area = 659.4 + 307.72  = 967.12cm^2

Hope this helps

Answer:

25 units

Step-by-step explanation:

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

Our points: (0, 0) and (7, -24)

[tex]d = \sqrt{7^2+(-24)^2}[/tex]

d = √(49+576)

d = √625

d = 25

Answer:

25

Step-by-step explanation:

You can also use the pythagorean theorem.

From  (0, 0) to (7, -24), one of the side lengths of the triangle is 24, and the other is 7.

Now we can use the pythagorean theorem with these numbers

[tex]7^2 +24^2=x^2[/tex], and now we can solve these squares to get

[tex]49+576=x^2\\625=x^2\\\sqrt{625} = x\\[/tex], So x = 25

Answer:

The wheel completed a total of 212 turns.

Step-by-step explanation:

A wheel has a circular form, therefore its length is given by the following formula:

[tex]length = 2*\pi*radius[/tex]

Where radius is half the diameter. Applying the data from the problem to calculate the length of the wheel gives us:

[tex]length = 2*\pi*(\frac{1.5}{2})\\length = 1.5*\pi = 4.7124[/tex]

Since the engine traveled a distance of 1000 metres and each turn of the wheel has 4.7124 metres, in order to calculate the number of turns the wheel made in that course we need to divide both numbers as shown below:

[tex]turns = \frac{1000}{4.7124} = 212.21[/tex]

The wheel completed a total of 212 turns.

Answer:

(-7,10)

please see the attached picture for full solution..

hope it helps..

Good luck on your assignment