A woodworking artist makes two types of carvings: type X and type Y. He spends 2 hours making each type X carving and 3 hours making each type Y carving, and he can spend up to 30 hours each week making carvings. His materials cost him $6 for each type X carving and $4 for each type Y carving, and he must keep his weekly cost for materials to $120 or less. If x is the number of type X carvings he makes in a week and y is the number of type Y carvings he makes in a week, which of the following systems of inequalities models this situation?

A. 2x + 3y ≥ 30, 6x + 4y ≤ 120

B. 2x + 3y ≥ 30, 6x + 4y ≥ 120

C. 2x + 3y ≤ 30, 6x + 4y ≤ 120

D. 2x + 3y ≤ 30, 6x + 4y ≥ 120

The area of the triangle ABC with the coordinates A(6,0) B(1,5) C(2,0) is 10 square units

The coordinates are given as:

A(6,0) B(1,5) C(2,0) D(4,2)

The area of the triangle is calculated using:

Area = 0.5 * |Ax(By - Cy) + Bx(Ay - Cy) + Cx(Ay - By)|

Using the above formula, we have:

Area = 0.5 * |6 * (5 - 0) + 1 * (0 - 0) + 2 * (0 - 5)|

Evaluate the sum of products

Area = 0.5 * |20|

Remove the absolute bracket

Area = 0.5 * 20

Evaluate the product

Area = 10

Hence, the area of the triangle ABC is 10 square units

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Answer:

B

Step-by-step explanation:

Answer: 2 inches

At 8 days there will be 8/4 = 2

Difference = 2 - 0 = 2 inches

The area of the given figure is 787.5 square centimeter

The area of Rectangle is length times of width.

The given figure has a rectangle whose length is 23 cm

width is 14 cm

Area of rectangle = 23×14

=322 square centimeter

Area = 15+34/2 ×19

=931/2

Total area = 322+931/2

=787.5 square centimeter

Hence, the area of the given figure is 787.5 square centimeter

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Answer:

1400

Step-by-step explanation:

i hope this helps u

Answer:

1,400

Step-by-step explanation:

It's closer to 400 than 300

Answer:

110°

Step-by-step explanation:

if we're looking for the bearing of C from A, the angle should be formed at A

then, starting from the north poles, move in a clockwise direction till you meet the line coming from C . then, sum up the angles involved.

which is = 45°+ 65° = 110°

therefore, the bearing of C from A is 110°

The sum of angle ∠FEC and angle ∠ECF is 90°. Then they are complementary angles.

It is the centre of an equidistant point drawn from the centre. The radius of a circle is the distance between the centre and the circumference.

DE is tangent to circle C, at point F.

Then prove that angle ∠FEC and angle ∠ECF are complementary angles.

We know that the radius of the circle and the tangent on the circle make a right angle at the circumference.

Then angle ∠EFC will be 90°.

The sum of all interior angles of the triangle is 180°. Then we have

∠FEC + ∠ECF + ∠EFC = 180°

  ∠FEC + ∠ECF + 90° = 180°

            ∠FEC + ∠ECF = 90°

The sum of angle ∠FEC and angle ∠ECF is 90°. Then they are complementary angles.

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Answer:

(2,8)

Step-by-step explanation:

2 units down means y is decreased by 2

3 units left mean x is decreased by 3

So

for

The translation is

Answer: The function h because the graphs of f and h are symmetrical about the line y=x.

Answer:

[tex]a_{n}[/tex] = - 8n + 10

Step-by-step explanation:

the sequence has a common difference between consecutive terms , that is

- 6 - 2 = - 14 - (- 6) = - 22 - (- 14) = - 8

this indicates the sequence is arithmetic with nth term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 2 and d = - 8 , then

[tex]a_{n}[/tex] = 2 - 8(n - 1) = 2 - 8n + 8 = - 8n + 10

Answer:

-33.2

Step-by-step explanation:

The measure of the other angle is 60°.

An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.

As given in the question

An angle that measures 125° is composed of three smaller angles.

Two of the smaller angles measure 25° and 40 degrees

Tom thinks he can use the equation 25 degrees + (40 degrees - 25 degrees) = s to find the measure of the unknown smaller angle, s

Tom is incorrect because the sum of the smaller angles will be equal to the bigger angle and the equation he has written is wrong.

The right equation and method will be

25 +40+x = 125

x = 125-40-25

x = 60°

Therefore the measure of the other angle is 60°.

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Answer:

The answer is 28 in

Step-by-step explanation:

I divided 392/14=28

hopefully it helps.

please mark brainliest.

Answer:

it is 28

Step-by-step explanation:

i took the exam

Answer:

32

P = 100 × 32%(0.32) = 32

Answer:

32

Step-by-step explanation: You multiply 100 by 0.32 which is 32% as a decimal

now, we're assuming she made the deposit at the child's birth, namely when year was 0, at the child's twenty-first birthday that'll be 21 years later.

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$6000\\ r=rate\to 9\%\to \frac{9}{100}\dotfill &0.09\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &21 \end{cases} \\\\\\ A=6000\left(1+\frac{0.09}{12}\right)^{12\cdot 21}\implies A=6000(1.0075)^{252}\implies A\approx 39437.11[/tex]

Answer:

b x h

Step-by-step explanation:

product of the base (b) and the height (h) just means b x h.

Answer:

n= -80

Step-by-step explanation:

Hope this helps! ;-)

Answer:

[tex]\huge\boxed{\sf n = -20}[/tex]

Step-by-step explanation:

Given Equation:

[tex]n=5(2k^2+2k-6)[/tex]

Put k = -2

[tex]n=5[2(-2)^2+3(-2)-6]\\\\n =5[2(4)-6-6]\\\\n=5(8-12)\\\\n= 5(-4)\\\\\boxed{n = -20}\\\\\rule[225]{225}{2}[/tex]

Answer:

2π - 4√5

(= -2.66 to nearest hundredth).

Step-by-step explanation:

√(2π - 4√5)^2

= 2π - 4√5             (by the definition of a square root)

If you want an approximate value it is

-2.66 to the nearest hundredth

Step-by-step explanation:

= 3x - 2x + 24x

= 3 × 4 - 2 × 4 + 24 × 4

= 12 - 8 + 96

= 12 + 96 - 8

= 108 - 8

= 100

Answer:

28

Step-by-step explanation:

the formula for finding the area of a triangle is 1/2×base×height. the height is the spot where you can create a right angle with the base, which here is 14 meaning the equation is 1/2(4)(14)

Answer:

I think it is D, if I am wrong I am sooooo sorry

Answer:

65 miles

Step-by-step explanation:

Given:

Equation:

5 × 7 + k = 100

Solving:

⇒ 5 × 7 + k = 100

⇒ 35 + k = 100

⇒ k = 100 - 35

⇒ k = 65

Answer:

See below ~

Step-by-step explanation:

The tracking number for the package is : 693840002

The number you have typed in is : 698340002

The place values of 8 and 3 in the tracking number have been switched. Therefore, as it is not the same tracking number, you get tracking information of a different package which corresponds to the number.

Answer:

4

Step-by-step explanation:

It is 4 because the point rises 4 units up from the graph and runs 1 unit to the right which is 4/1 = 4.

Answer:

B

Step-by-step explanation:

the biggest portion of the pie graph is labeled comedy, so that would be your answer.

Answer:

The correct answer is 1/4 gallon.

Step-by-step explanation:

If we add all the fractions from the line plot, we will get 10/8 gallon.

10/8 divided by 5 is .25.

.25 converted to a fraction would be 1/4.

Hope this helps:) Goodluck!

Caroline, Colin & Sarah share some money.Caroline will get [tex]\dfrac{2}{3}[/tex]  when Caroline, Colin & Sarah share some money.

The ratio defined as the sharing of the two or three things or it represent that one thing or number is how many times to the other.

One part is excluded in the problem. That part is:

"Caroline gets [tex]\dfrac{1}{9}[/tex] of the money."

If Caroline gets 1/9th, then remaining is:

[tex]1-\dfrac{1}{9}=\dfrac{8}{9}[/tex]

Colin and Sarah share in ratio 3 is to 1, that means 3 + 1 = 4 parts...

8/9th in 4 parts means, each part is:

[tex]\dfrac{\dfrac{8}{9}}{4}=\dfrac{2}{9}[/tex]

We know Colin gets "3" parts of the total, each part is (2/9)th, so 3 parts would be:

[tex]3\times \dfrac{2}{9}=\dfrac{6}{9}=\dfrac{2}{3}[/tex]

Colin gets  [tex]\dfrac{2}{3}[/tex] money when three of them share money.

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Answer:

Step-by-step explanation:

Equation

-6(1-4v) = 3v-8(-6-6v)                  Use the distributive property to get rid of the brackets.

Solution

-6 + 24v = 3v +48 +48v              Combine

-6 + 24v = 51v + 48                     Subtract 24v from both sides

-6 +24v-24v =51v-24v +48         Combine.

-6 = 27v + 48                              Subtract 48 from both sides.

-6-48 = 27v+48-48                     Combine

-54 = 27v                                    Divide by 27

-54/27=27v/27

-2 = v

Answer

v=-2