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2 days ago

The function f(x) is given by the set of ordered pairs. {(1,0), (–10,2), (0,6), (3,17), (–2,–1)} Which equation is true?

Mathematics

2 answers:

Leona [9.2K]2 days ago

8 0

The answer is option C.

Leona [9.2K]2 days ago

7 0

The linear equation can be expressed as y = -6x + 6. First, identify the slope, calculated with the formula (y2 - y1) / (x2 - x1) which is equal to -6. Then, this value is substituted into the slope-intercept form y = mx + b. Finally, by inputting a coordinate, you can find the b value, resulting in the equation y = -6x + 6.

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A middle school took all of its 6th grade students on a field trip to see a ballet at a theater that has 1300 seats. The student

Leona [9271]

77%

I prefer using ratios and cross multiplication for scenarios like this. Divide the part (1001) by the whole (1300), and set that equal to x percent of 100 percent.

1001/1300 = x/100
100100 = 1300x
x = 77

3 0

11 days ago

W hich of these scales is equivalent to the scale 1 cm to 5 km? Select all that apply. (Lesson 1-11) A. 3 cm to 15 km D. 5 m

AnnZ [9104]

The corresponding scales are:

3 cm for 15 km translates to 1 cm for 5 km ⇒ answer A

5 mm for 2.5 km translates to 1 cm for 5 km ⇒ answer D

1 mm for 500 m translates to 1 cm for 5 km ⇒ answer E

Detailed explanation:

To engage with this problem:

1. Given that 1 cm is equivalent to 5 km, all provided answers must

be converted to cm and km

2. Determine the matching scales against the provided scale

Since 3 cm indicates 15 km

- Divide both values by 3

Thus, 1 cm indicates 5 km

3 cm for 15 km equates to 1 cm for 5 km

Since 1 mm signifies 150 km

- Convert mm to cm

Since 1 cm = 10 mm

Thus, 1 mm = $\frac{1}{10}$ cm = 0.1 cm

So, 0.1 cm indicates 150 km

- Then multiply both by 10

So, 1 cm indicates 1500 km

1 mm to 150 km does not match with 1 cm to 5 km

Since 5 cm signifies 1 km

- Divide both by 5

Thus, 1 cm signifies 0.2 km

5 cm to 1 km does not match with 1 cm to 5 km

Since 5 mm signifies 2.5 km

- Convert mm to cmSince 1 cm = 10 mm

Thus, 5 mm = $\frac{5}{10}$ cm = 0.5 cm

Therefore, 0.5 cm indicates 2.5 km

- Divide both by 0.5

Therefore, 1 cm represents 5 km

5 mm to 2.5 km corresponds to 1 cm to 5 km

Since 1 mm signifies 500 m

- Convert mm to cm

Since 1 cm = 10 mm

So, 1 mm = $\frac{1}{10}$ cm = 0.1 cm

- Convert m to km

Since 1 km = 1000 m

Thus, 1 m = $\frac{1}{1000}$ = 0.001 km

Thus, 500 m = $\frac{500}{1000}$ = 0.5 km

Thus, 0.1 cm indicates 0.5 km

- Multiply both by 10

Thus, 1 cm represents 5 km

1 mm to 500 m corresponds to 1 cm to 5 km

Learn more:

You can learn more about equivalent measurements in

3 0

3 days ago

Evaluate ∫SF⃗ ⋅dA⃗ , where F⃗ =(bx/a)i⃗ +(ay/b)j⃗ and S is the elliptic cylinder oriented away from the z-axis, and given by x2/

Inessa [9006]

Respuesta:

Por lo tanto, la integral de superficie es $\pi(a^2+b^2)c-0-0=\pi(a^2+b^2)c$ .

Explicación paso a paso:

La función dada es,

$\vec{F}=\frac{bx}{a}\uvec{i}+\frac{ay}{b}\uvec{j}$

Para encontrar,

$\int\int_{S}\vec{F}dS$

donde S=A=superficie del cilindro elíptico debemos aplicar el teorema de divergencia, así que,

$\int\int_{S}\vec{F}dS$

$=\int\int\int_V\nabla.\vec{F}dV$

$=\int\int\int_V(\frac{b}{a}+\frac{a}{b})dV$

$=\frac{a^2+b^2}{ab}\int\int\int_VdV$

$=\frac{a^2+b^2}{ab}\times \textit{Volume of the elliptic cylinder}$

$=\frac{a^2+b^2}{ab}\times \pi ab\times 2c=\pi (a^2+b^2)c$

Si el vector unitario $\cap{n}$ está dirigido en dirección positiva (hacia afuera), entonces z=c y,

$\int\int_{S_1}\vex{F}.dS_1=\int\int_{S_1}. dA$

$=\int\int_{S_1}.dA=0$

Si el vector unitario $\cap{n}$ está dirigido en dirección negativa (hacia adentro), entonces z=-c y,

$\int\int_{S_2}\vex{F}.dS_2=\int\int_{S_2}. -dA$

$=\int\int_{S_2}. -dA=0$

Por lo tanto, la integral de superficie sin el vector unitario de la superficie es,

$\pi(a^2+b^2)c-0-0=\pi(a^2+b^2)c$

5 0

1 month ago

In triangle JKL, sin(b°) = three fifths and cos(b°) = four fifths. If triangle JKL is dilated by a scale factor of 2, what is ta

Inessa [9006]

Answer:

Tan(b°) = 3/4, which is equivalent to three fourths (C).

Step-by-step explanation:

Triangle JKL is a right triangle with angle K being the right angle and angle L equal to b°.

We will employ SOHCAHTOA principles from trigonometry to calculate the sides' values.

For triangle ∆JKL:

Sin(b°) = opposite/hypotenuse

Sin(b°) = 3/5

Cos(b°) = adjacent/hypotenuse

Cos(b°) = 4/5

Tan(b°) = 3/4.

From the earlier information, we have the values for each side of triangle ∆JKL.

Please refer to the attached diagram for the triangle (1).

Triangle ∆JKL is scaled with a factor of 2.

This implies multiplying each side of ∆JKL by 2, resulting in:

Opposite side = 2(3) = 6

Adjacent side = 2(4) = 8

Hypotenuse = 2(5) = 10.

To find tan(b°) for the new triangle, we use the tangent ratio:

Tan(b°) = opposite/adjacent.

Tan(b°) = 6/8.

Tan(b°) = 3/4.

Find the diagram for the new triangle included (2).

Diagram 3 provides a depiction of both triangles.

As shown, the angle remains unchanged when a triangle is scaled by a factor.

Thus, we conclude that tan(b°) = three fourths (C).

6 0

21 day ago

Shannon manages a small zoo and she has been analyzing the attendance data. Shannon finds that the number of visitors increases

AnnZ [9104]

To plot the two functions, you need to assign values for x. By selecting various x values, corresponding y values are calculated. You then plot the points as shown. The blue line illustrates the function f(x) = 3x, while the orange line indicates f(x) = -x + 4.

These two lines intersect at the coordinates (1,3). To solve for this analytically, we establish the system of equations:

y = 3x
y = -x + 4

By setting these two equations for y equal to each other:

3x = -x + 4
4x = 4
x = 1

Next, substituting x into one of the original equations gives us: y = 3x = 3(1) = 3. Therefore, the solution is (1,3), meaning at a temperature of 3 units, the number of visitors entering matches those exiting the zoo, indicating a balance of one person entering for each one leaving.

3 0

16 days ago

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