38. For the following exercises, sketch a line with the given features.
38. An x-intercept of (-4,0) and y-intercept of (0,-2)

Rewriting the left hand side,

csc²t - cost sec t

= (1/sin²t)-(cost)(1/cost)

= 1/sin²t - 1

= 1/sin²t - sin²t/sin²t

= (1-sin²t)/sin²t

= cos²t/sin²t

= cot²t

Step-by-step explanation:

assuming this is correct, you can really manipulate either side and you should arrive eventually arrive to same sides. But in this case you usually manipulate the more complex side. So I'll manipulate the left side.

Original Equation:

[tex]csc^2(t)-cos(t)*sec(t)=cot^2(t)[/tex]

Rewrite csc and sec, using the reciprocal identities:

[tex](\frac{1}{sin(t)})^2-cos(t)*\frac{1}{cos(t)}=cot^2(t)[/tex]

multiply cos(t) and 1/cos(t) and also distribute the exponent:

[tex]\frac{1}{sin^2t}-1=cot(t)^2[/tex]

Multiply 1 by sin^2(t)/sin^2(t)

[tex]\frac{1}{sin^2(t)}-\frac{sin^2(t)}{sin^2(t)}[/tex]

subtract the numerator

[tex]\frac{1-sin^2(t)}{sin^2(t)}[/tex]

Pythagorean Identity:

[tex]sin^2(t)+cos^2(t)=1[/tex]

subtract sin^2(t) from both sides

[tex]cos^2(t)=1-sin^2(t)[/tex]

Use this to rewrite the numerator:

[tex]\frac{cos^2(t)}{sin^2(t)}[/tex]

Rewrite using the reciprocal identities:

[tex]cot^2(t) = cot^2(t)[/tex]

Answer:

(C) 496

Step-by-step explanation:

area = 100 yd × 372 yd = 37,200 yd²

37,200 yd² / 75 yd² = 496

Answer: (C) 496

The density is:

D = 10g/2mL = 5 g/mL

The correct option is the first one.

Remember that density is defined as the quotient between mass and volume.

We know that the mass of the solid is 10.0 grams.

And the volume of the solid is given by the difference between the volume of the water alone (15.0 mL) and the water with the solid (17 mL).

V = 17mL - 15mL = 2mL

Then the density is:

D = 10g/2mL = 5 g/mL

The correct option is the first one.

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A quadrilateral in which opposite sides are parallel is called a parallelogram. The correct option is D.

A quadrilateral in which opposite sides are parallel is called a parallelogram. Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.

For a parallelogram, the opposite sides are equal and parallel to each other. We can write,

AD ≅ BC

Since BX ≅ DY, therefore, we can write,

AB = CD

AX + XB = DY + YC

XB = DY, cancelling both the sides,

AX = YC.

Also, XY is the common side.

Since all the sides are equal also the angle are equal, therefore, it can be written,

AXDY ≅ CYXB

Given the area of CYXB is 71.5 square units. Therefore,

ABCD = CYXB + AXDY

ABCD = 2(CYXB)

ABCD = 143 square units.

Hence, the correct option is D.

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Answer:

- Please see the attached picture for full solution!:)

------------------ HappY LearninG<3 -------------

Answer:

x = -26

Step-by-step explanation:

[tex]5^7^x^+^5 =125^2^x^-^7\\\\5^7^x^+^5 =5^3^(^2^x^-^7^)\\\\5^7^x^+^5 =5^6^x^-^2^1[/tex]

∴ 7x + 5 = 6x - 21

7x - 6x + 5 = -21

x = -21 - 5

x = -26

Please find the question attached below.

The equation that models the decrease in water (in gallons) of the fish tank over time (in hours) is y = - 20x + 180.

We know that a linear equation with one variable is one that contains just one variable.

Here we have to find the appropriate equation that models the given chart.

For option A. :

y = - 40x + 140

At x = 2, y = - 40*2 + 140 = - 80 + 140 = 60 =/ 140

So this option is incorrect.

For option B.:

y = - 40x + 180

At x = 2, y = - 40*2 + 180 = - 80 + 180 = 100 =/ 140

So this option is incorrect.

For option C.:

y = - 20x + 140

At x = 2, y = - 20*2 + 140 = - 40 + 140 = 100 =/ 140

So this option is incorrect.

For option D.:

y = - 20x + 180

At x = 2, y = - 20*2 + 180 = - 40 + 180 = 140

So this option is correct.

Therefore, the equation that models the decrease in water (in gallons) of the fish tank over time (in hours) is y = - 20x + 180. So, the last option is correct.

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The system of inequality is y > 3 and 3x -2y < 1 these are the inequalities that represent the region.

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

We have a line showing the graph.

First, we have to calculate the equation of the line:

The horizontal line:

y = 3

The region represents the inequality:

y > 3

Second inequality line:

[tex]\rm \dfrac{x}{-2}+\dfrac{y}{3} < 1[/tex]

3x -2y < 1

Thus, the system of inequality is y > 3 and 3x -2y < 1 these are the inequalities that represent the region.

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The measure of angle QS based on the information given when Point R is between points Q and S is 11x + 35.

From the information given,

PR = 3x + 7

QR = 8x + 28

The value of QS will be:

PR + QR

= (3x + 7) + (8x + 28)

= 11x + 35

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Considering the given data-set, the dot plot is incorrect for the number 1.

The dot plot shows the number of times each measure appears in the data-set.

In this problem, number 1 appears only twice on the data-set, but has 3 dots, hence it is incorrect, it should be 2 dots.

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Answer: A pair of congruent, corresponding sides

Step-by-step explanation:

This will make the triangles congruent by either AAS or ASA.

A pair of congruent, corresponding sides will make the triangles congruent by either AAS or ASA property.

Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.

Consider it is given that two triangles ΔABC ≅ ΔDEF

Then that means ΔABC and ΔDEF are congruent. A Congruent triangles are exact same triangles, but they might be placed at different positions.

The order in which the congruency is written.

For ΔABC ≅ ΔDEF, since all of their corresponding elements like angle and sides congruent.

The ASA congruent rule state that If corresponding two angles and one corresponding side of two triangles are of same measurement, then the considered pair of triangles are congruent.

This will make the triangles congruent by either AAS or ASA property.

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Answer:

The side length of the blocks is 5 inches.

The total surface area of the 27 blocks is 4050 square inches.

This is 3 times the surface area of the box.

Step-by-step explanation:

Surface area of a cube

SA = 6s²  (where s is the side length)

Given the side length of the box is 15 inches:

⇒ SA of box = 6 · 15² = 1350 in²

Surface Area of blocks with 3 inch side lengths:

⇒ SA = 6 · 3² = 54 in²

⇒ SA of 27 blocks = 27 · 54 = 1458 in²

Surface Area of blocks with 4 inch side lengths:

⇒ SA = 6 · 4² = 96 in²

⇒ SA of 27 blocks = 27 · 96 = 2592 in²

Surface Area of blocks with 5 inch side lengths:

⇒ SA = 6 · 5² = 150 in²

⇒ SA of 27 blocks = 27 · 150 = 4050 in²

Therefore, from the given answer options for the total surface area of the 27 blocks, the side length of the blocks must be 5 inches.

To calculate how many times the total surface area of the 27 blocks is to the surface area of the box:

[tex]\implies \dfrac{\textsf{SA of 27 blocks}}{\textsf{SA of box}}=\sf \dfrac{4050}{1350}=3[/tex]

Summary

The side length of the blocks is 5 inches.

The total surface area of the 27 blocks is 4050 square inches.

This is 3 times the surface area of the box.

Answer: D

Step-by-step explanation:

See attached image.

There are 84 possible student body governments

The given parameters are:

Senior = 7

Junior = 3

Sophomore = 4

The number of student body governments is calculated as:

n = Senior * Junior * Sophomore

This gives

n = 7 * 3 * 4

Evaluate

n = 84

Hence, there are 84 possible student body governments

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The intersection of lines y=-14x+3 and y=-32x+3 is (0, 3)

The lines are given as:

y = -14x + 3 and y = -32x+3

Substitute y = -32x+3 in

-32x+3 = -14x + 3

Evaluate the like terms

-18x = 0

Divide by -18

x = 0

Substitute x = 0 in y = -14x + 3

y = -14(0) + 3

Evaluate

y = 3

Hence, the intersection of lines y=-14x+3 and y=-32x+3 is (0, 3)

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Answer:

Hence the expression [tex]$$(m+11)(m-4)=m^2+7m-44$$[/tex]

Step-by-step explanation:

Explanation

[tex]$$\frac{\begin{matrix}{} & {} & m & + & 11 \\ \times & {} & m & - & 4 \\ \end{matrix}}[/tex]

_____________

[tex]{\frac{\begin{matrix}{} & - & 4m & - & 44 \\ {{m}^2} & + & 11m & {} & {} \\ \end{matrix}}{\begin{matrix}{{m}^2} & + & 7m & - & 44 \\ \end{matrix}}}$$[/tex]

30 mph would be a safe speed for you to drive.

Collisions are much more likely to occur when one driver travels greater speedy or more slowly than the alternative motors on the road. You have to input a throughway at or near the velocity of visitors except if the speed of site visitors exceeds the prison speed restrict.

A pedestrian has a 90 percent threat of survival if hit by a vehicle transferring at 30 km ph (18.64 mph). This decreases to 70 percent at 40 kmph (24. eighty five mph) and much less than 20 percent at 50kmph (31 mph). driving at decreased speeds also enables drivers to stop within a shorter distance.

Retaining high speeds on highways is straightforward, as roads are wider and traffic is usually mild. If there are signs that show a pace restriction of 80kph, use them as a guide and stick near them. it's also an excellent exercise to assess road situations and set your pace thus.

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Answer:

200.96 m^2

Step-by-step explanation:

The formula for the area of a circle is πr^2, where r is the radius of the circle and π is approximately 3.14. We know that the diameter is 16 meters, and the radius is always half of the diameter (the diameter connects two ends of the circle, while the radius connects one point to the center). Therefore, the radius of this circle is 8m. Now we have all the information we need. The area of this circle is (3.14)(8)^2 = 3.14*64 = 200.96 m^2 (area is always in squared units)

Answer:

200.96m²

Step-by-step explanation:

Area of a Circle: Pi×r²

where:

pi = 3.14

r = diameter / 2

= 16÷2

= 8

Area = 3.14 × 8 × 8

= 200.96m²

The area of sector POR is approximately equal to 68.76 square centimeters, and the perimeter of sector POR is approximately equal to 34.92 centimeters.

In Mathematics, if you want to calculate the length of an arc formed by a circle, you will divide the central angle that is subtended by the arc by 360 degrees and then multiply this fraction by the circumference of the circle.

Mathematically, the length of an arc formed by a circle is given by:

Length of an arc = 2πr × θ/360

Substituting the given parameters into the formula, the radius of this circle is given by;

12 = 2 × 3.142 × r × 60/360

12 = 2 × 3.142 × r × 1/6

72 = 6.284r

Radius, r = 72/6.284

Radius, r = 11.46 centimeters.

Now, we can calculate the area of sector POR:

Mathematically, the area of a sector can be calculated by using this formula:

Area of sector = πr² × θ/360

Where:

Substituting the given parameters into the formula, we have;

Area of sector = 3.142 × 11.46² × 60/360

Area of sector = 3.142 × 131.3316 × 1/6

Area of sector = 68.76 square centimeters.

Next, we would calculate the perimeter of sector POR:

Perimeter of sector POR = 2r + Length of an arc

Perimeter of sector POR = 2(11.46) + 12

Perimeter of sector POR = 22.92 + 12

Perimeter of sector POR = 34.92 centimeters.

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The flow rate of the given fluid in the pipe is gotten as; 3/2 liters per minute

We are told that a pipe fills 11/15 liters in 22/45 minutes.

Now, to get the flow rate of this pipe, we will use the formula;

Flow rate = Quantity of fluid/Time

Thus;

Flow rate = 11/15 ÷ 22/45

⇒ 11/15 * 45/22

⇒ 3/2 liters per minute

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Answer:

y = 3x - 6

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 )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, - 6) and (x₂, y₂ ) = (2, 0) ← 2 points on the line

m = [tex]\frac{0-(-6)}{2-0}[/tex] = [tex]\frac{0+6}{2}[/tex] = [tex]\frac{6}{2}[/tex] = 3

the line crosses the y- axis at (0, - 6 ) ⇒ c = - 6

y = 3x - 6 ← equation of line L

Answer:

pretty 5

Step-by-step explanation:

5

hahaha

got it on khan

A scale factor is defined as the ratio between the scale of the new object and the original object.

If the original measurements and a scale factor for a figure are given, we can easily visualize the scaled figure measurement by multiplying the scale factor with the original figure measurement.

A scale factor is defined as the ratio between the scale of the new object and the original object.

We have,

The original measurement = x

The scale factor = m

The scale factor figure measurement = y

Now,

A scale factor is defined as the ratio between the scale of a given original object and a new object,

This means,

m = y/x

y = mx

This means,

The scaled figure measurement is the multiplication of the scale factor with the original measurement

Thus,

If the original measurements and a scale factor for a figure are given, we can easily visualize the scaled figure measurement by multiplying the scale factor with the original figure measurement.

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Answer:

yes

Step-by-step explanation:

she is right because if he had did as she said it could have been better

Answer: [tex]6.2 *10^9[/tex]

Step-by-step explanation:

Scientific notation is large numbers expressed as products consisting of a number between 1 and 10 multiplied by an appropriate power of 10

So the first number cannot be 6200 or 62 or 0.6, it has to be 6.2 because 6.2 > 1 and 6.2 < 10

count your numbers right of the decimal and you should get:

[tex]6.2 *10^9[/tex]

Answer:

B and D

Step-by-step explanation:

check where the points are. If they are in shaded triangle they are solutions

By using the concepts of direct and inverse trigonometric expressions, the angles that represents the trigonometric function cos 5/6 are θ₁ ≈ 33.557° and θ₂ ≈ 326.443°.

Cosine are trigonometric functions whose period is 360°. Cosine is positive both for the first and fourth quadrants. Thus, the two angles associated to the given trigonometric expression are by inverse trigonometric functions:

θ₁ ≈ 33.557°, θ₂ ≈ 326.443°

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Answer: 6

Step-by-step explanation:

    We will set up a proportion to solve. Let x be equal to ?.

[tex]\displaystyle \frac{3}{5} =\frac{x}{x+4}[/tex]

    Now, we will cross-multiply.

3 * (x + 4) = 5 * x

3x + 12 = 5x

12 = 2x

6 = x

The value of the probability P(AnB) is 0.11

The given parameters are:

P(a|b)=0.55 and P(b)=0.2

The value of P(AnB) is calculated using:

P(AnB) = P(a|b) * P(b)

Substitute the known values

P(AnB) = 0.55 * 0.2

Evaluate the product

P(AnB) = 0.11

Hence, the value of the probability P(AnB) is 0.11

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Answer:

6

Step-by-step explanation:

2+2+2