Select all the correct answers.

Select all of the expressions that are equivalent to the expression 3x − 12 − 2(x + 12)

Answer:

I belive it should be # 3 i might be wrong thow.

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Car one rotated 90 degrees counterclockwise would be to car 4
then, it rotated 180 degrees clockwise would be car 2.

the answer is Car 2

Answer:

r = 55.2 cm

Step-by-step explanation:

the arc length is calculated as

arc = circumference × fraction of circle

     = 2πr × \(\frac{\frac{23}{20}\pi }{2\pi }\) ( r is the radius )

given arc = 63.48π , then

2πr × \(\frac{\frac{23}{20}\pi }{2\pi }\) = 63.48π ( cancel 2π on numerator/ denominator )

r × \(\frac{23}{20}\) π = 63.48π ( divide both sides by π )

\(\frac{23r}{20}\) = 63.48 ( multiply both sides by 20 to clear the fraction )

23r = 1269.6 ( divide both sides by 23 )

r = 55.2 cm

Answer: 55.2

Step-by-step explanation:

got it correct on my test!

Answer:

4. SR= 17 (opposite angle of parallogram are equal)

The solution of BVP is:

y(x) = 9x³/6 + (C1/2)x² + 5x + 2 - 9(7)³/6 - (C1/2)(7)² - 5(7)

The boundary value problem (BVP) for the given function is "y'' = 9, y(0) = 5, y(7) = 2".

Let's integrate "y'' = 9" twice:

∫y'' dx = 9∫ dx

²y' = 9x + C1

∫y' dx = 9x²/2 + C1x + C2

Here, "C1" and "C2" are integration constants.

Now, let's apply the boundary conditions "y(0) = 5" and "y(7) = 2":

y(0) = 5

∫y' dx = 9x²/2 + C1x + C2 => ∫y' dx = 9x²/2 + C1x + 5

y(x) = 9x³/6 + (C1/2)x² + 5x + C3

Similarly, for y(7) = 2:

y(7) = 2

y(x) = 9x³/6 + (C1/2)x² + 5x + C3 => 2 = 9(7)³/6 + (C1/2)(7)² + 5(7) + C3

Therefore, we can solve for "C3":

C3 = 2 - 9(7)³/6 - (C1/2)(7)² - 5(7)

Thus, the solution of the given BVP is:

y(x) = 9x³/6 + (C1/2)x² + 5x + 2 - 9(7)³/6 - (C1/2)(7)² - 5(7)

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Answer:

x = -3

y = 1

z = -2

Step-by-step explanation:

-2x + 3y + z = 7

-4x - y -2z = 15

x + 2y +3z = -7

|-2 3 1|

|-4 -1 -2|

|1 2 3|

Determinant of this from online determinant calculator is;

D = 21

For Dx, we have;

|7 3 1|

|15 -1 -2|

|-7 2 3|

Determinant of this from online determinant calculator is;

Dx = -63

For Dy, we have;

|-2 7 1|

|-4 15 -2|

|1 -7 3|

Determinant of this from online determinant calculator is;

Dy = 21

For Dz, we have;

|-2 3 7|

|-4 -1 15|

|1 2 -7|

Determinant of this from online determinant calculator is;

Dz = -42

From creamers rule;

x = Dx/D

y = Dy/d

z = Dz/d

Thus;

x = -63/21

x = -3

y = 21/21

y = 1

z = -42/21

z = -2

Thus,

x = -3

y = 1

z = -2

Given:

A square base pyramid whose base length is 10 in. and height of triangular surface is 4 in.

To find:

The surface area of the pyramid to the nearest whole number.

Solution:

A square base pyramid contains square base with edge 10 in. and 4 congruent triangles with base 10 in. and height 4 in.

Area of a square is

\(A_1=(edge)^2\)

\(A_1=(10)^2\)

\(A_1=100\)

So, area of square base is 100 sq. in.

Area of a triangle is

\(A_2=\dfrac{1}{2}\times base\times height\)

\(A_2=\dfrac{1}{2}\times 10\times 4\)

\(A_2=20\)

So, area of each triangular surface is 20 sq. in.

Now, the total surface area of the pyramid is

Total area = Area of square base + Area of 4 congruent triangles.

\(A=A_1+4\times A_2\)

\(A=100+4\times 20\)

\(A=100+80\)

\(A=180\)

Therefore, the area of the pyramid is 180 sq. in.

Answer:

11

4m-28 = 16

4m = 44

m=11

Step-by-step explanation:

Bags of limes = 4

Total limes in each bag = m

Total limes = 4m

ATQ

4m - 7(4)= 16

4m = 16+28

4m = 44

m = 44/4

m = 11

Value of m = 11

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The value of x that makes m║n is 40°

In geometry, the line that intersects two straight lines at distinct points is known as a transversal.

The angles that are formed when two parallel lines are intersected by a third line i.e a transversal are corresponding angles.

Note:

Two corresponding angles are formed by a transversal with two parallel lines that are equal

Here we have

The angle made by the intersecting line with line m is 120°

And the angle made by the same line with line n is 3x°

Let us assume that m║n  

From above observations

The given angle are corresponding angles

=> 3x° = 120°

=> x° = 40°  

Therefore,

The value of x that makes m║n is 40°

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The lateral area of the pyramid is 320 inches squared.

The pyramid above is a square base pyramid. Therefore, the lateral area of the pyramid can be found as follows:

Lateral area of the pyramid = 2al

where

Therefore,

a = 16 inches

Using Pythagoras's theorem,

8² + 6² = l²

l = √64 + 36

l = √100

l = 10 inches

Therefore,

Lateral area of the pyramid = 2 × 16 × 10

Lateral area of the pyramid = 2 × 160

Lateral area of the pyramid = 320 inches²

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For the given function g(x) , the values at given points :

a. g(9) = 2

b. g(0) = -2.5

c. g(3) = -1

d. g(17) = 6

A function is a set of rules that assigns each element of a set a unique element of another set.

If f is a function and f(x) = x+2, then if we have to find value of at x= 1 ,put 1 in place of x,

Then f(1 ) = 1+2 =3

Given that a function g is such that

g(x) = (x -5)/2

This the values of the function g at given points:

a. g(9) = (9-5)/2 = 4/2 = 2

b. g(0) = (0-5)/2 = -5/2 = -2.5

c. g(3) = (3-5)/2 = -2/2 = -1

d. g(17 ) =  (17-5)/2 = 12/2 = 6

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Answer:

14 cm

Step-by-step explanation:

from the right triangle we know that:

- A leg is 8 cm

- B leg is 11 cm

- angle between A and B leg is 90'

If we have one angle which is 90' we can use the following formula:

\(c = \sqrt{a^{2} + {b^{2} }\)

\(c = \sqrt{8^{2} + {11^{2} }\)

\(c = 13.60147\)

The Area Ratio is 1.5. and Perimeter Ratio is 1.22. The estimated overall cost for the proposed 15,000 SF warehouse is $150,000.

To perform a line by line estimate for the proposed warehouse, we'll calculate the area and perimeter ratios between the existing and proposed warehouses. We'll then use these ratios to estimate the overall cost for the proposed 15,000 square feet (SF) warehouse.

Given: Existing Warehouse:

Area: 10,000 SF

Perimeter: 410 LF

Proposed Warehouse:

Area: 15,000 SF

Perimeter: 500 LF

First, let's calculate the area ratio:

Area Ratio = Proposed Area / Existing Area

Area Ratio = 15,000 SF / 10,000 SF

Area Ratio = 1.5

Next, let's calculate the perimeter ratio:

Perimeter Ratio = Proposed Perimeter / Existing Perimeter

Perimeter Ratio = 500 LF / 410 LF

Perimeter Ratio = 1.22 (rounded to two decimal places)

We'll now use these ratios to estimate the overall cost for the proposed 15,000 SF warehouse. Since we don't have specific cost figures, we'll assume a linear relationship between the area and cost.

Cost Estimate = Existing Cost * Area Ratio

Let's assume the existing cost is $100,000.

Cost Estimate = $100,000 * 1.5

Cost Estimate = $150,000

Therefore, the estimated overall cost for the proposed 15,000 SF warehouse is $150,000.

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The measure of angle a is 15 degrees and this can be determined by using the properties of the isosceles triangle.

In geometry, interior angles are formed in two ways. One is inside a polygon, and the other is when parallel lines cut by a transversal. Angles are categorized into different types based on their measurements.

Given:

The following steps can be used in order to determine the measure of angle a:

Step 1 - According to the given data, it can be concluded that triangle PQR and triangle PSR are isosceles triangles.

Step 2 - Apply the sum of interior angle property on triangle PQR.

\(\angle\text{Q}+\angle\text{P}+\angle\text{R}=180\)

\(\angle\text{Q}+2\angle\text{R}=180\)

\(2\angle\text{R}=180-60\)

\(\angle\text{R}=60^\circ\)

Step 3 - Now, apply the sum of interior angle property on triangle PSR.

\(\angle\text{P}+\angle\text{S}+\angle\text{R}=180\)

\(\angle\text{S}+2\angle\text{R}=180\)

\(2\angle\text{R}=180-90\)

\(\angle\text{R}=45^\circ\)

Step 4 - Now, the measure of angle a is calculated as:

\(\angle\text{a}=60-45\)

\(\angle\text{a}=15\)

The measure of angle a is 15 degrees.

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The number of electrons lost or gained by an atom when it forms an ion is determined by the atom's position in the periodic table and its valence electron configuration.

Atoms can gain or lose electrons to attain a stable electron configuration. The number of electrons gained or lost by an atom to form an ion is determined by the difference between the number of valence electrons (the electrons in the outermost energy level) in the neutral atom and the nearest noble gas configuration.

For example,

Formation of a chloride ion (Cl⁻) from a chlorine atom (Cl). Chlorine has 7 valence electrons (2, 8, 7) and needs 1 more electron to achieve a noble gas configuration (2, 8, 8).

Thus, it gains one electron to become a chloride ion, Cl⁻

Formation of a sodium ion (Na⁺) from a sodium atom (Na). Sodium has 1 valence electron (2, 8, 1) and needs to lose this electron to achieve a noble gas configuration of neon (2, 8).

Thus, it loses one electron to become a sodium ion, Na⁺.

In general, atoms in the left side of the periodic table tend to lose electrons to form cations, while atoms in the right side tend to gain electrons to form anions.

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B) 2 hours and 15 minutes

Jill spent 3 hours at the mall and it took Jack 45 minutes to get back home.

3.00 - 0.45 = 2.15

Have a luvely day!

The equation of this circle in standard form is x² + y² - 8x  - 16y + 73.75 = 0

From the question, we have the following parameters that can be used in our computation:

Endpoints of the longest chord on a circle are (4, 5.5) and (4, 10.5)

These endpoints represent endpoints of the diameter

So, we have the diameter to be

diameter = √[(x₂ - x₁)² + (y₂ - y₁)²]

Substitute the known values in the above equation, so, we have the following representation

diameter = √[(4 - 4)² + (5.5 - 10.5)²]

Evaluate

diameter = 5

So, we have

radius, r = 5/2

The midpoint is

(a, b)= 1/2[(4 + 4, 5.5 + 10.5)]

So, we have

(a, b)= (4, 8)

The circle equation is calculated as

(x - a)² +(y - b)² = r²

Substitute the known values in the above equation, so, we have the following representation

(x - 4)² +(y - 8)² = 2.5²

This gives

x² - 8x + 16 + y² - 16y + 64 = 6.25

Evaluate the like terms

x² + y² - 8x  - 16y + 73.75 = 0

Hence, the equation is x² + y² - 8x  - 16y + 73.75 = 0

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Probability that exactly 5 cars will enter the car wash in an hour = 0.1606

The mean rate = 3 cars per half an hour

The mean rate in 1 hour, λ = 3(2) = 6

Probability that exactly 5 cars will enter the car wash in an hour, P(X = 5)

Using the Poisson distribution formula:

Probability that exactly 5 cars will enter the car wash in an hour = 0.1606

Answer:

Step-by-step explanation:

The perimeter of a quarter circle can be calculated by adding the length of the arc and the two radii that make up the quarter circle.

The length of the arc of a quarter circle is given by (πr)/2, where r is the radius of the quarter circle and π is approximately 3.142 (as given in the question).

So, for a quarter circle with a radius of 7 cm, the length of the arc would be:

(πr)/2 = (3.142 x 7)/2 = 10.997 cm (rounded to 3 decimal places)

The two radii that make up the quarter circle are each equal to the radius of the quarter circle, so the total length of the two radii would be:

2r = 2 x 7 = 14 cm

Therefore, the perimeter of the quarter circle would be:

10.997 cm + 14 cm = 24.997 cm (rounded to 3 decimal places)

So the perimeter of the quarter circle is approximately 24.997 cm. The digits given by the calculator will depend on the specific calculator used.

Answer:

3 or 4

Step-by-step explanation:

Answer: its 3 exactly

Step-by-step explanation:

Answer:

- 15

Step-by-step explanation:

\( \frac{1}{3} a = - 5 \\ \\ a = - 5 \times 3 \\ \\ a = - 15\)

Answer:

-15

Step-by-step explanation:

As you can see, the denominator of 1/3 is 3. 1 third of a is -5. So what you do is, you multiply -5 * 3 and that'll give you -15. So, it is equal to -15.

There would be about 12 pieces of fruit in the bag.

Check the picture below.

\(\textit{area of a segment of a circle}\\\\ A=\cfrac{r^2}{2}\left( ~~ \cfrac{\pi \theta }{180}-\sin(\theta ) ~~ \right) \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=8\\ \theta =60 \end{cases} \\\\\\ A=\cfrac{8^2}{2}\left( ~~ \cfrac{\pi (60) }{180}-\sin(60^o ) ~~ \right)\implies A=32\left( ~~ \cfrac{\pi }{3}-\sin(60^o ) ~~ \right) \\\\\\ A=32\left( ~~ \cfrac{\pi }{3}-\cfrac{\sqrt{3}}{2} ~~ \right)\implies A=\cfrac{32\pi }{3}-16\sqrt{3}\implies A\approx 5.8~in^2\)

The triangle is constructed by performing the steps illustrated below.

To plan your shot in pool, we can use the concept of similar triangles. By constructing a triangle using the given information, we can determine the angle and direction in which to hit the cue ball to pocket it successfully. Let's go through each step in detail.

Step a: Label the cue ball as A

Start by labeling the cue ball as point A. This will serve as one vertex of the triangle we are constructing.

Step b: Identify the pocket and label the center as E

Identify the pocket where you want your ball to go in. Label the center of this pocket as E. It will be the endpoint of a line segment that we will draw later.

Step c: Draw a line segment from E to the other side of the table, labeling the other endpoint as C

Draw a line segment starting from point E, passing through the colored ball, and extending to the other side of the table. Label the endpoint on the other side as C. This line segment represents the path your ball will take to reach the other side.

Step d: Draw a line segment from C to A

Next, draw a line segment from point C to point A (the cue ball). This line segment will make the same angle with the bumper as the line segment CE. We can consider triangle CEA to be a right triangle.

Step e: Draw a perpendicular line segment from A to the same bumper, labeling the endpoint as B

Draw a perpendicular line segment from point A (the cue ball) to the same bumper (side of the table). Label the endpoint where this line segment intersects the bumper as B. This line segment AB is perpendicular to the bumper and forms a right angle with it.

Step f: Complete triangle ABC by drawing the line segment BC

Finally, complete triangle ABC by drawing the line segment BC. This line segment connects point B to point C, forming the third side of the triangle.

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Complete Question:

The cue ball is 18 inches from the top bumper (side of pool table) and 50 inches from the right bumper. The dimensions of the pool table are 96 inches in the horizontal direction by 46 inches in the vertical direction.

Use the illustration of the table and what you know about similar triangles to plan your shot.

Construct a triangle by performing each of these steps (6 points: 1 point for each step)

a. Label the cue (white) ball A

b. identify the pocket (hole) that you want your ball to go in. Label the center of this pocket E (Hint: Click on the ball in the image on the Pool Table Problem page to see the bow to make this shot)

Draw a line segment that starts at E goes through the colored ball, and ends at the other side of the table Label the other endpoint of segment C.

d. Draw a line segment from C to A (the cue ball). This segment will make the same angle with the bumper as CE

e. Draw a perpendicular line segment from A to the same bumper (side of the table on Label the endpoint B.

f. Complete triangle ABC by drawing the line segment 80

Answer:

4

Step-by-step explanation:because 6022 is the sig figs, and 00000000000000000000 doesnt work because it is zero

Answer:

4/5-1/3=

12/15-5/15=7/5

Step-by-step explanation:

7/5

Hope this helps! =D

Answer:

25 Ft

Step-by-step explanation:

you multiply it's so the square root is 25 ft

Responder:

y = -6X + 36

Explicación paso a paso:

Dados los datos:

CANTIDADES __PRECIO

5 ___ 6

4 ___ 12

3 ___ 18

2 ___24

1 ___ 30

Usando una calculadora de modelo lineal:

La ecuación del modelo lineal obtenida con una calculadora de regresión es:

y = -6X + 36

Donde y = precio; - 6 = pendiente; Intercepción = 36

Se pudo observar que como reducción en la cantidad demandada puede ser como resultado de un aumento en el precio.

Answer:

x^2

Step-by-step explanation:

The greatest common factor of 5x^2, 10x^3, 6x^5:

For the numbers, there is no greatest common factor except for 1.

For the variables, the furthest we can go is x^2.

In conclusion, the greatest common factor of 5x^2, 10x^3, 6x^5 is x^2.