Clarise evaluated this expression.

(66.3 – 14.62) ÷ 0.6 – 0.22

(51.68) ÷ 0.6 – 0.22

(51.68) ÷ 0.42

51.68 ÷ 0.16

32.3

Which errors did Clarise make?

Answer:

B, C, D

Step-by-step explanation:

if tan theta = 15/8 then the hypotenuse is 17

therefore the correct answers are B, C, D

Answer:

p < 2

Step-by-step explanation:

9p + 23 < 41

p < 2

Answer:

p < 2

Step-by-step explanation:

9p + 23 < 41

9p < 18

p < 2

Answer:

3.

A. Y = 2x + 30  (red line)

B. Y=5x  (blue line)

C. Y=70  (green line)

From 0 to 10 days, choose option B (shown on graph)

From 10 to 20 days, choose option A (first option)

From 20 days and more, choose option C.

4.

surface area of label = 471.2 cm^2

Step-by-step explanation:

Q1718436 Math Camp

2. At Math Camp, students can either pack their own lunch every day or buy lunch at camp. If they want to buy lunch there are 3 options:  

Option A: they pay an initial fee of $30 and lunches cost $2 each  

Option B: shown on the graph  

Option C: they pay a flat fee of $70 which includes all lunches  

Write an equation for each option. (3 marks) Option A: Option B: Option C:  

A. Y = 2x + 30  (red line)

B. Y=5x  (blue line)

C. Y=70  (green line)

b) Describe under what conditions, a student should choose each option. (Hint: you may want to graph all 3 lines on the same axes) (4 marks)  

Choose Option A if: Choose Option B if: Choose Option C if:  

Least cost is what is below the lowest possible line for the number of days stayed.

From 0 to 10 days, choose option B (shown on graph)

From 10 to 20 days, choose option A (first option)

From 20 days and more, choose option C.

Note that for days 10 and 20, there are two choices each.

3.  

4. A Campbell’s Soup can is 15cm tall and has a radius of 5 cm. How much paper is needed to make the label (think about what the label covers)? (3 marks) How much soup can this hold? (1 cm3 = 1 mL) (3 marks)

The label only covers the curved surface.

Curved surface area  

= 2 pi * r * h

= 2 pi (5) * 15

= 150 pi

= 471.2 cm^2

Answer:

Option B

Step-by-step explanation:

Hope it is right

The value of equation describes the line graphed is,

⇒ y = -1/5x - 4

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (0, -4) and (5, -5).

Now,

Since, The equation of line passes through the points (0, -4) and (5, -5).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (- 5 - (-4)) / (5 - 0)

m = - 1 / 5

Thus, The equation of line with slope - 1/5 is,

⇒ y - (-4) = -1/5 (x - 0)

⇒ y + 4 = -1/5x

⇒ y = -1/5x - 4

Therefore, The equation of line passes through the points (0, -4) and

(5, -5). will be;

⇒ y = -1/5x - 4

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Answer:

y = - 4x - 10

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - 4 , thus

y = - 4x + c ← is the partial equation

To find c substitute (- 4, 6) into the partial equation

6 = 16 + c ⇒ c = 6 - 16 = - 10

y = - 4x - 10 ← equation of line

Answer:

y = -4x+10

Step-by-step explanation:

Using the slope intercept form of a line

y = mx+b where m is the slope and b is the y intercept

y = -4x +b

Substituting the point in

6 = -4(-4) + b

6 = 16+b

Subtract 16 from each side

-10 =b

The equation is

y = -4x+10

Answer:

3 cups

Step-by-step explanation:

We can use a proportion to find how many cups of chocolate chips she needs for 30 servings. Assuming c = cups of chocolate chips and b = batches

[tex]\frac{c}{b}[/tex]

[tex]\frac{1}{10} = \frac{c}{30}[/tex]

We can now multiply the diagonal values that don't include the missing variable (30 and 1) and then divide it by the value that is diagonal to the variable (10)

[tex]30 \cdot 1 = 30\\30 \div 10 = 3[/tex]

Therefore, she needs 3 cups of chocolate chips to make 30 servings.

Answer:

3 cups

Step-by-step explanation:

We can use ratios to solve

1 cup               x cups

---------------- = ----------------

10 servings     30 servings

Using cross products

1*30 = 10x

Divide by 10

30/10 = x

3 =x

3 cups

Answer:

G(x) = (1 - x)/4

is the inverse function required.

Step-by-step explanation:

Given F(x) = -4x + 1

Let y = F(x)

Then y = -4x + 1

=> y - 1 = -4x

4x = 1 - y

x = (1 - y)/4

That is, the inverse is (1 - x)/4

Therefore, G(x) has to be (1 - x)/4

Hi,

[tex]y=5x^{2} +12x-2\\y=x(5x+12)-\frac{46}{5} \\y=5(x+\frac{6}{5} )^{2}-\frac{46}{5} \\[/tex]

Have a good day.

Answer:

5x-18 this angle is equal to 92

3x+22 this angle is equal to 88

angle a=88

angle b=92

Step-by-step explanation:

set 5x-18 and 3x+22 equal to 180 and solve to get x=22. Now look for ways to fill in a and b. A is an alternate interior angle that will be equal to 3x+22

angle b will be equal to the angle 5x-18

Answer:

The value of x is22°, a is 88° and b is 92°.

Hope it helps..

Answer:

2 - bedroom apartment = 4

3 - bedroom apartment = 2

Step-by-step explanation:

Given the following :

2 - bedroom apartment = $700 / month

3 - bedroom apartment = $900 / month

Last month:

Number of vacant apartment = 6

Amount of Lost rent = $4600

Let a = 2 - bedroom apartment and b = 3 - bedroom apartment

Vacant apartment :

a + b = 6 - - - (1)

Lost rent :

700a + 900b = 4600 - - - (2)

From (1),, a = 6 - b

Substitute a = 6 - b into (2)

700(6 - b) + 900b = 4600

4200 - 700b + 900b = 4600

4200 + 200b = 4600

200b = 4600 - 4200

200b = 400

b = 400/200

b = 2

From (1) ;

a + b = 6

a + 2 = 6

a = 6 - 2

a = 4

a = 2 - bedroom apartment = 4

b = 3 - bedroom apartment = 2

Answer:

x=1.75

Step-by-step explanation:

3*2-4x+1=0 subtract 1 from both sides

3*2-4x=-1 multiply 3 and 2

6-4x=-1 Subtract 6 from both sides

-4x=-7 divide both sides by -4

x=1.75

If this helped, please consider giving me brainliest, it will help a lot :)

Have a good day

Answer:

803.84yd²

Step-by-step explanation:

Surface Area of A Sphere: [tex]A=4\pi r^2[/tex]

We are given the radius of 8 yards.

Using 3.14 for pi:

[tex]A=4*3.14*8^2\\\\A=4*3.14*64\\\\A=12.56*64\\\\\boxed{A=803.84}[/tex]

The correct answer should be 803.84yd².

Brainilest Appreciated.

Answer:

803.84 yd^2

Step-by-step explanation:

4*3.14*8^2

12.56*64

803.84

brainliest pls

hope i helped

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▹ Answer

You can use a graphing calculator. Attached is a picture of it graphed.

Hope this helps!

CloutAnswers ❁

Brainliest is greatly appreciated!

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Step-by-step explanation:

c^2( c^2-10c+25)

=c^4 - 10c^3 + 25c^2

Answer:

(5,-6)

Step-by-step explanation:

ONE WAY:

If [tex]f(x)=x^2-6x+3[/tex], then [tex]f(x-2)=(x-2)^2-6(x-2)+3[/tex].

Let's simplify that.

Distribute with [tex]-6(x-2)[/tex]:

[tex]f(x-2)=(x-2)^2-6x+12+3[/tex]

Combine the end like terms [tex]12+3[/tex]:

[tex]f(x-2)=(x-2)^2-6x+15[/tex]

Use [tex](x-b)^2=x^2-2bx+b^2[/tex] identity for [tex](x-2)^2[/tex]:

[tex]f(x-2)=x^2-4x+4-6x+15[/tex]

Combine like terms [tex]-4x-6x[/tex] and [tex]4+15[/tex]:

[tex]f(x-2)=x^2-10x+19[/tex]

We are given [tex]g(x)=f(x-2)[/tex].

So we have that [tex]g(x)=x^2-10x+19[/tex].

The vertex happens at [tex]x=\frac{-b}{2a}[/tex].

Compare [tex]x^2-10x+19[/tex] to [tex]ax^2+bx+c[/tex] to determine [tex]a,b,\text{ and } c[/tex].

[tex]a=1[/tex]

[tex]b=-10[/tex]

[tex]c=19[/tex]

Let's plug it in.

[tex]\frac{-b}{2a}[/tex]

[tex]\frac{-(-10)}{2(1)}[/tex]

[tex]\frac{10}{2}[/tex]

[tex]5[/tex]

So the [tex]x-[/tex] coordinate is 5.

Let's find the corresponding [tex]y-[/tex] coordinate by evaluating our expression named [tex]g[/tex] at [tex]x=5[/tex]:

[tex]5^2-10(5)+19[/tex]

[tex]25-50+19[/tex]

[tex]-25+19[/tex]

[tex]-6[/tex]

So the ordered pair of the vertex is (5,-6).

ANOTHER WAY:

The vertex form of a quadratic is [tex]a(x-h)^2+k[/tex] where the vertex is [tex](h,k)[/tex].

Let's put [tex]f[/tex] into this form.

We are given [tex]f(x)=x^2-6x+3[/tex].

We will need to complete the square.

I like to use the identity [tex]x^2+kx+(\frac{k}{2})^2=(x+\frac{k}{2})^2[/tex].

So If you add something in, you will have to take it out (and vice versa).

[tex]x^2-6x+3[/tex]

[tex]x^2-6x+(\frac{6}{2})^2+3-(\frac{6}{2})^2[/tex]

[tex](x+\frac{-6}{2})^2+3-3^2[/tex]

[tex](x+-3)^2+3-9[/tex]

[tex](x-3)^2+-6[/tex]

So we have in vertex form [tex]f[/tex] is:

[tex]f(x)=(x-3)^2+-6[/tex].

The vertex is (3,-6).

So if we are dealing with the function [tex]g(x)=f(x-2)[/tex].

This means we are going to move the vertex of [tex]f[/tex] right 2 units to figure out the vertex of [tex]g[/tex] which puts us at (3+2,-6)=(5,-6).

The [tex]y-[/tex] coordinate was not effected here because we were only moving horizontally not up/down.

Answer: 3 x minus 3 + 4 = 2 minus x minus 3

              3 x + 1 = negative x minus 1

Step-by-step explanation:

             A and D. Edge 2020

The required equation that Samuel used is 3x -3 + 4 =2- x -3. option A is correct.

Samuel is solving the equation 3 (x minus 1) + 4 = 2 minus (x + 3). Which equivalent equations might Samuel use, is to be determined.

The equation is the relationship between variables and represented as[tex]y = ax +b[/tex]  is an example of a polynomial equation.

Given equation is [tex]3(x-1) +4 =2 -(x+3)[/tex]
Simplification of the above equation,
opening the parenthesis on both sides
step 1⇒ 3x - 3 + 4 = 2 - x - 3
step 2⇒ 3x + 1 = -x - 1
Transposition of -x to the left side and +1 to the right side
step 4 ⇒ 3x +x = -1 -1
                  4x = -2
Transposition of 4 to the denominator of -2.
step 5⇒ x = -2/4
               x = -1/2

Thus , Step 1 3x -3 + 4 =2- x -3 is the equivalent equation used by the samuel.

Learn more about the equation here:

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Answer:

7.5 jars

Step-by-step explanation:

There are 25 students in the art class.

Mr Jones is planning that for the project, each of the 25 students will need 0.3 jar of paint.

The amount of paint Mr Jones needs for this project is therefore the product of the number of students in the class by the amount of paint each student needs.

That is:

25 * 0.3 = 7.5 jars of paint

Mr Jones needs 7.5 jars of paint for the art project.

Answer:

6:00 p.m.

hope this helps :)

Answer:

The answer is 21.25cm

Step-by-step explanation:

Hope i am marked as brainliest

hey mate, here is ur answer in the attachment!

Answer:

25 children

So , each child will get 25 pens and 7 pencils

You have to find the highest common factor of 125 and 175 which is 25 and then you have to multiply it by those two numbers to find how may pens and pencils will be given to 1 child

Hope this helps and pls mark as brianliest :)

Answer:

y = -8

Step-by-step explanation:

Start by filling 8 in place of x

y = 8 - 2(8)

Multiply -2(8)

y = 8 - 16

Subtract 16 from 8

y = -8

Answer:

The 1st selection is appropriate.

_____

2nd: the rotation would need to be 90° CCW

3rd, 4th: rotation or double reflection will give the original orientation. This figure is reflected an odd number of times, so has its orientation reversed.

Hope it helps.. Mark brainliest

The sequence of transformations are reflection over the y-axis and then a rotation 90 clockwise about the origin.

Here are the rotation rules: 90° clockwise rotation: (x, y) becomes (y, -x) 90° counterclockwise rotation: (x, y) becomes (-y, x) 180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y).

Given that, figure G is rotated 90° clockwise about the origin and then reflected over the x-axis, forming figure H.

Vertices of triangle G are (-3, 1), (-1, 2) and (-2, 5).

The reflection of point (x, y) across the y-axis is (-x, y).

On reflection over x-axis, we get coordinates as (3, 1), (1, 2) and (2, 5)

90° clockwise rotation: (x, y) becomes (y, -x)

On 90° clockwise rotation, we get coordinates as (1, -3), (2, -1) and (5, -2)

Triangle H has points (2, -1), (1, -3), (5, -2).

Hence, the sequence of transformations are reflection over the y-axis and then a rotation 90° clockwise about the origin.

Learn more about the rotation of 90° counterclockwise here:

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Answer:

30°, 60° and 90°

Step-by-step explanation:

Given the expression Arccos (√3/2)=β, we can use the expression to calculate one of the acute angles in a right angled triangle.

Note that a right angled triangle is made up of two acute angles and a right angled (90°)

Let's get one of the acute angles first

If Arccos (√3/2)=β

β = cos^-1 √3/2

β = 30°

This shows that one of the acute angles is 30°

To get the third angle, we know that sum of angles in a triangle is 180° and since we already know two of the angles, i.e 90° and 30°, we can get the third angle.

90+30+x = 180

120+x = 180

x = 180-120

x = 60°

All the angle measurement for the right angled triangle are 30°, 60° and 90°

Answer:

The answer to this question can be defined as follows:

Step-by-step explanation:

Following are the description of the given points:

(a) This is a system of probability, which possibility occurs inside an intended manner whenever they choose this specific point of origin from 1 to 100 with no one reserve the possibility about who gets throughout the survey.  

(b) Its method is different from the random sampling technique with the base available. For example, two individuals whose names identical to both the list have no chance to join within the survey.  

(c) its sample is objective to its everyone can enter the test in equal measure.

Answer:

[tex]\overline{DF}[/tex] could be a midsegment of ∠ABC.

Step-by-step explanation:

A midsegment of a triangle must be two things:

1. Parallel to the 3rd side, in this case, [tex]\overline{AD}[/tex].

2. Half the length of the 3rd side, in this case, [tex]\overline{AD}[/tex].

Since we don't know the lengths, we can only go off of 1. There is only one line that is parallel to  [tex]\overline{AD}[/tex] and it is [tex]\overline{DF}[/tex].

Hope this helped!

Answer:

The value of x is 35

Step-by-step explanation:

In order to calculate the value of x in the  following parallelogram:  2x - 10  

2x + 50, we would have to calculate the following formula:

m<QPS+m<PQR=180°

According to the given data we have the following:

m<QPS=2x - 10  

m<PQR=2x + 50

Therefore, 2x - 10+2x + 50=180

4x+40=180

x=140/4

x=35

Answer:

A,C,D

Step-by-step explanation:

When b=0, there is a proportional relationship.

The slope in y=mx+b is the value next to x.

Using RISE/RUN when there is a change of 3 units in x, there is a change of 2 units in y.

Answer:

5/6π.

Step-by-step explanation:

The following data were obtained from the question:

Radius (r) = 12 cm

Area (A) = 60π cm²

Centre angle in radian (∅) =...?

Since we are to look for the centre angle in radian, the area of the sector will be given by:

A = ½r²∅

Inputting the values of the area, A and radius, r, the centre angle, ∅ can be obtained as follow:

A = ½r²∅

60π = ½ × 12² × ∅

60π = ½ × 144 × ∅

60π = 72 × ∅

Divide both side by 72

∅ = 60π/72

∅ = 5/6π

Therefore, the centre angle measured in radian is 5/6π.