Use the substitution method to solve the system of equations. Choose the
correct ordered pair.
y = 7x + 8
y = x + 20
O A. (3, 29)
B. (7,8)
O C. (2,8)
O D. (2,22)

Answer:

5/15 is the probability of choosing a red marble from the box.

Step-by-step explanation:

We know that,

There are 5 red marbles and 10 green marbles in the box.

Divide the number of events by the number of possible outcomes. This will give us the probability.

P(red marble) = P(5)

Possible outcomes

5 red, 10 green -> 15 possibilities

Probability = [tex]\frac{5}{15}[/tex]

Please leave a 'thanks' if this helped!

The required probability of drawing a red marble the 6th time is 1/2.

Given that,

A box contains 10 red marbles and 10 green marbles.

Sampling at random from this box five times without replacement, you have drawn a red marble all five times.

Without replacing any of the marbles.

We have to determine,

What is the probability of drawing a red marble the 6th time?

According to the question,

There are 10 red marbles and 10 green marbles,

The initial condition is to the same state at every step, so the probability to get a red marble is the same in each sampling  and is equal to the ratio of the number of red marbles to the total number of samples.

Therefore,

The probability of drawing a red marble the 6th time is,

[tex]P = \dfrac{10}{10+10}\\\\P = \dfrac{10}{20}\\\\P = \dfrac{1}{2}[/tex]

Hence, The required probability of drawing a red marble the 6th time is 1/2.

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(x+2) + x + (x+4) = 2(1/2) + 2(x+3)

They are equal to each other and the rectangle has 2x more perimeter

The triangle would be divided in half from that rectangle.

Answer:

1).

A. Reflection across the y axis.

2).

A. Clockwise rotation about point B and a translation 20 units down.

The sequence of transformation that can be performed on quadrilateral

ABCD to show that is congruent to GHIJ is a B. 90 degree counter

clockwise rotation about point A  followed by a B. Reflection across the y-

axis and a translation 20 units down

Reasons:

The coordinates of the point (x, y) following a rotation of 90°

counterclockwise is the point (-y, x)

Taking point A as the origin

The coordinates of point A = (15, 10)

Coordinates of the points B, relative to the point A = (0, 10)

Coordinates of the points C, relative to the point A = (5, 5)

Coordinates of the points D, relative to the point A = (5, -5)

The location of the image of point B, following a rotation about the point A, is therefore;

B'(-10 + 15, 0 + 10) = B'(5, 10), C'(-5 + 15, 5 + 10) = C'(10, 15), D'(5 + 15, 5 + 10) = D'(20, 15)

The coordinates of the image of the point (x, y), following a reflection

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

A'B'C'D' following a reflection across the y-axis are the point B''(-5, 10),

C''(-10, 15), D''(-20, 15) A''(-15, 10). The coordinates of the quadrilateral GHIJ

are; G(-15, -10), H(-5, -10), I(-10 - 5), J(-20, -5)

The x-coordinates of the quadrilaterals A''B''C''D'', and GHIJ are the same,

therefore, we translate A''B''C''D'', 20 units down to get;

B'''(-5, -10), C'''(-10, -5), D'''(-20, -5) A'''(-15, -10)

Coordinates of A'''(-15, -10) = G(-15, -10)

Coordinates of B'''(-5, -10) = H(-5, -10)

Coordinates of C'''(-10, -5) = I(-10 - 5)

Coordinates of D'''(-20, -5) = J(-20, -5)

Therefore;

The sequence of transformation that can be performed on quadrilateral

ABCD to show that is congruent to GHIJ is a;

Followed by a;

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Answer:

$3.60

Step-by-step explanation:

Convert the percentage to a decimal.

2% = 0.02

Multiply the cost of the dress by the decimal to find the sales tax.

$180 × 0.02 = $3.60

The sales tax $3.60.

Answer:

3.60

Step-by-step explanation:

sales tax = cost * tax rate

                = 180 * 2%

                 = 180 * .02

                 =3.60

Answer:

2 should be distributed as 2y + 8; y = 4

Step-by-step explanation:

2(y + 4) = 4y

Distribute

2y + 8 = 4y

Step 2 is incorrect because the added instead of multiplied

Continuing on to correct the problem

Subtract 2y from each side

2y+8-2y = 4y-2y

8 = 2y

Divide by 2

8/2 = 2y/2

4 =y

Answer:

2 should be distributed as 2y + 8; y = 4

Step-by-step explanation:

Step 2 is wrong.

2(y + 4) = 4y

The step to solve is to expand brackets or distribute 2, not divide both sides by 2.

2y + 8 = 4y

Subtract both sides by 2y.

8 = 2y

Divide both sides by 2.

4 = y

Answer:

258.47

Step-by-step explanation:

v=πr²h/3

=π4.2 ×14/3

=258.615

Answer:

x=48

Step-by-step explanation:

The other angle is 66° because it's an isosceles triangle

so

180=66+66+x

180=132+x

x=48

Answer:

48 degrees

Step-by-step explanation:

Since the triangle is iscoceles because it has two sides with a length of 7, two angles will be 66 degrees and the missing angle will be the sum of total angles in a triangle minus the other two 66 degree angles. 180 - 66 - 66 = 48

Answer:

120

Step-by-step explanation:

Know that in a rotation, unless stated otherwise, it's always going clockwise. Knowing this, you'd only have to turn your triangle one time, and since its interior angles are 120 each, your answer is 120. Hope this helps!

Answer:

[tex] 162 cm^3 [/tex]

Step-by-step explanation:

Volume of a rectangular pyramid is given as = [tex] \frac{1}{3}lwh [/tex]

Where,

[tex] l = 9 cm [/tex]

[tex] w = 6 cm [/tex]

[tex] h = 9 cm [/tex]

Plug in the above values into the formula for volume of rectangular pyramid:

[tex] Volume = \frac{1}{3}*9*6*9 [/tex]

[tex] Volume = 3*6*9 [/tex]

[tex] Volume = 162 cm^3 [/tex]

Volume of the rectangular pyramid = [tex] 162 cm^3 [/tex]

Answer:

The shortest path to take is [tex]20\sqrt{3}\ cm[/tex] or [tex]34.64\ cm[/tex]

Step-by-step explanation:

This question requires an attachment (See attachment 1 for question)

Given

Cube Dimension: 20cm * 20cm

Required

Shortest path from A to B

For proper explanation, I'll support my answer with an additional attachment (See attachment 2)

The shortest path from A to B is Line labeled 2

But first, the length of line labeled 1 has to be calculated;

This is done as follows;

Since, the cube is 20 cm by 20 cm

[tex]Line1^2 = 20^2 + 20^2[/tex] (Pythagoras Theorem)

[tex]Line1^2 = 2(20^2)[/tex]

Take square root of both sides

[tex]Line1 = \sqrt{2(20)^2}[/tex]

Split square root

[tex]Line1 = \sqrt{2} * \sqrt{20^2}[/tex]

[tex]Line1 = \sqrt{2} * 20[/tex]

[tex]Line1 = 20\sqrt{20}[/tex]

Next is to calculate the length of Line labeled 2

[tex]Line2^2 = Line1^2 + 20^2[/tex] (Pythagoras Theorem)

Substitute [tex]Line1 = 20\sqrt{20}[/tex]

[tex]Line2^2 = (20\sqrt{2})^2 + 20^2[/tex]

Expand the expression

[tex]Line2^2 = (20\sqrt{2})*(20\sqrt{2}) + 20 * 20[/tex]

[tex]Line2^2 = 400*2 + 400[/tex]

Factorize

[tex]Line2^2 = 400(2+1)[/tex]

[tex]Line2^2 = 400(3)[/tex]

Take square root of both sides

[tex]Line2 = \sqrt{400(3)}[/tex]

Split square root

[tex]Line2 = \sqrt{400} * \sqrt{3}[/tex]

[tex]Line2 = 20 * \sqrt{3}[/tex]

[tex]Line2 = 20 \sqrt{3}[/tex]

The answer can be left in this form of solve further as follows;

[tex]Line2 = 20 * 1.73205080757[/tex]

[tex]Line2 = 34.6410161514[/tex]

[tex]Line2 = 34.64 cm[/tex] (Approximated)

Hence, the shortest path to take is [tex]20\sqrt{3}\ cm[/tex] or [tex]34.64\ cm[/tex]

Answer:

44.72 cm

Step-by-step explanation:

1. This was marked correct by RSM

2. Unfold the cube, so that points A and B and on points diagonal from each other on a 40 cm x 20 cm rectangle. Now draw a line connecting points A to B. That is the hypotenuse of both triangles. Now according to the pythagorean theorem, the hypotenuse is √2000, which is equal to 5√20.

3. The answer is 44.72 cm

Answer:

67 degrees

Step-by-step explanation:

alternate exterior angles are always congruent

Answer:

The value of y is 67°.

Step-by-step explanation:

Here, given that;

BD is parallel to XY. let EF be a transversal line meeting BD at O and XY at P.

now, angle XQF = 67°

now, angle XQF + angle YQF=180° (being linear pair)

or, 67°+angle YQF =180°

or, angle YQF=180°-67°

therefore angle YQF = 113°.

now, angle YQF + angle PQY=180° (being linear pair).

now, 113°+angle PQY = 180°.

or, angle PQY = 180°-113°.

therefore, angle PQY =67°.

again, angle EPD= angle PQY (being corresponding angles).

or, y°= 67°.

Therefore the value of y is 67°.

hope it helps...

Answer:

Step-by-step explanation:

First off:

multiply 1.7x103 and you get 175.1 then you multiply 2x103 and you get 206.

multiply 175.1x206 and you get 36070.6

Final answer is 36070.6

Answer:

36070.6

Step-by-step explanation:

Answer:

[tex]\large \boxed{\sf \ \ \text{The maximum profit is \$94 per day.} \ \ }[/tex]

Step-by-step explanation:

Hello,

The coefficient in [tex]x^2[/tex] is negative.

So, there is a maximum at the vertex point which is

[tex]x=-\dfrac{b}{2a}==\dfrac{-6}{-0.2}=\dfrac{6}{0.2}=30[/tex]

And then the maximum is f(30)=

[tex]-0.1\cdot 30^2+6\cdot 30 +4=-90 +180+4=94[/tex]

So the maximum profit is 94 $ per day.

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

2x^2+4x+11

Step-by-step explanation:

Answer:

288

Step-by-step explanation:

Answer:

[tex]V=72\pi ft^3[/tex]

Step-by-step explanation:

Recall the formula for the volume of a cone:

[tex]V=\frac{1}{3}\pi r^2h[/tex]

Where r is the radius and h is the vertical height.

We know that the diameter is 12ft. This means that radius must be 6ft.

And we are given that the vertical height is 6ft.

Plug in the numbers:

[tex]V=\frac{1}{3}\pi (6)^2(6)\\V=2(36)\pi\\V=72\pi ft^3[/tex]

Answer:

11√6

Step-by-step explanation:

5√6 +6√6 will equal to 11√6, because since √6 is the same, you just add the number on the outside

Answer:

48.

Step-by-step explanation:

[tex]\frac{24\sqrt{72} }{3\sqrt{2} }[/tex]

= (24 / 3) * [tex]\frac{\sqrt{72}} {\sqrt{2} }[/tex]

= 8 * [tex]\frac{\sqrt{72} * \sqrt{2}} {\sqrt{2} * \sqrt{2} }[/tex]

= 8 * [tex]\frac{\sqrt{144}} {2}[/tex]

= 8 * (12 / 2)

= 8 * 6

= 48.

Hope this helps!

Answer:

3 years

Step-by-step explanation:

I assume it's simple interest.

I = Prt

132 = 800 * 0.055 * t

t = 132/(800 * 0.055)

t = 132/44

t = 3

Answer: 3 years

Answer:

The answer is f(x) = -sin(x) as you can see in the graph below

Step-by-step explanation:

Answer:

x is 45 degrees

Step-by-step explanation: The corresponding angles theorem states that if two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. In this case, the 45 degree angle and x are congruent, meaning that x is 45.

Answer:

45

Step-by-step explanation:

Answer:

From Plato

30e-0.12t less than or equal to M

40e-0.18t less than or equal to M

Step-by-step explanation:

It is given that compound A decays at a rate of 12% per week, and compound B decays at a rate of 18% per week. Since the rates represent decay, the r-value is negative. A decay rate of 12% is represented by an r-value of -0.12, and a decay rate of 18% is represented by an r-value of -0.18.

The initial amount of compound A is 30 grams and the initial amount of compound B is 40 grams. Substitute the initial amounts of each compound and their respective decay rates into the system of inequalities.

The following system of inequalities can be used to determine when the remaining mass of the two compounds, M, will be the same, after t weeks.

Answer:

[tex]y = - \frac{2}{5} x + 2[/tex]

Answer:

2x²+5x+2=(2x+1)(x+2)

Answer:

See details below

Step-by-step explanation:

in ax^2+bx+c = 2x^2+5x+2,

a=2,b=5,c=2.

1. a*c = 2*2 = 4

2. factor 4 to get 1,2,4,  Factors that add to b=5 are 1 & 4.

3. (2x^2+x) + (4x+2)

4. x(2x+1) + 2(2x+1)

5. (2x+1)

6. (2x+1) ( x+2)

Some of the details may not be the same as what is expected as we do not know the format expected.

Answer:

$149.66

Step-by-step explanation:

Step 1

Calculate Total Amount payable to the bank using compound interest

Total Amount payable (A) =

P(1 + r/n)^nt

P = Principal = $2000

r = Interest rate = 9% = 0.09

n = compounding interest = quarterly = 4

t = time in years = 2

Total Amount payable

= 2000(1 + 0.09/4)^0.09 × 2

A = $ 2,389.66

Interest = A - Principal

= $ 2,389.66 - $ 2,000.00

I (interest) = $ 389.66

Step 2

Calculate the Total amount payable to his uncle using simple interest.

Total Amount (A) = P(1 + rt)

P = Principal = $2000

r = Interest rate = 6% = 0.06

t = time in years = 2

A = 2000(1 + 0.06 × 2)

A = $2,240

A - Principal

= $ 2,240 - $ 2,000.

I (interest) = $240

Step 3

The amount of money you will save by borrowing the money from your uncle is calculated as:

Amount payable to the bank - Amount payable to your uncle

= $ 2,389.66 - $2,240

= $149.66

Therefore, the amount of money you will save by borrowing the money from your uncle is $149.66

Answer:

No

Step-by-step explanation:

0.99 is not a repeating decimal because it terminates, meaning that it "ends". We know this because there are no more digits after 9 and there is no "..." at the end of the decimal.

Answer:

366 minute

Step-by-step explanation:

first divide 15000 by 41 since there are 41 drops per minute and you get 365.85 so then you round it and get 366

Step-by-step explanation:

Hello!!!

Given, VXW is a Right angled triangle where WV =4 and XV =5.

now, by taking reference angle as angle W, and using tangent we get;

p=5

b=4

again,

tan thita =p/b

tan thita = 5/4

so, tan thita =1.25.

now, to find angle W, we should do tan thita inverse;

or, (tan thita)-1= tan thita-1(1.25)

or, (tan thita) -1 =51.3401°.

Now, by rounding off we get,

tan thita (angle W )= 51°.

Hope it helps....

Answer:

x^3/2 - 6x^1/2

Step-by-step explanation:

f(x) = x - 6

g(x) = x^1/2

g(x) * f(x) = x^1/2(x - 6)

g(x) * f(x) = x^3/2 - 6x^1/2