Randy is twice as old as his sister jane. together the sum of their ages is 15. how old is randy?

The measure of the angle is 30 degrees

A supplementary angle can be defined as an angle that sum up t0 180 degrees.

The two angles must add up to 180 degrees, that is, angles on a straight line.

The properties of supplementary angles are;

From the information given, we have that;

The angle measures 150 degrees less of supplementary angles

Then,

180 - 150

30 degrees

Hence, the value is 30 degrees

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The two supplementary angles in question measure 15° and 165° respectively, with one angle being 150° less than the other.

We are given that one angle measures 150° less than its supplementary angle. By definition, supplementary angles add up to 180°. Let's call the angle in question 'A', and its supplementary angle 'B'.

We thus have the following relationship:

A = B - 150°

and

A + B = 180°

Substituting the first equation into the second, we get:

(B - 150°) + B = 180°

This simplifies to:

2B - 150° = 180°

2B = 330°

B = 165°

Now that we know the measurement of B, we can find A:

A = 165° - 150°

A = 15°

So, the two angles are 15° and 165° respectively.

The statements are to be checked whether they are true or not.

The true statements are:

As Abigail’s time increases, her distance increases.

At 2 hours, Abigail has traveled 120 miles.

At 3 hours, Abigail has traveled 180 mile

Abigail is driving at a speed of 60 miles per hour for 3 hours.

The function representing the situation will be

[tex]y=60x[/tex]

where,

[tex]y[/tex] is the distance in miles

[tex]x[/tex] is the time in hours

If time increases this means [tex]x[/tex] increases so, distance [tex]y[/tex] will also increase.

At 2 hours [tex]x=2[/tex]

[tex]y=60\times 2=120[/tex]

The distance traveled is 120 miles.

At 1.5 hours [tex]x=1.5[/tex]

[tex]y=60\times 1.5=90[/tex]

The distance traveled is 90 miles.

At 3 hours [tex]x=3[/tex]

[tex]y=60\times 3=180[/tex]

The distance traveled is 180 miles.

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In this exercise we want to calculate the value of angle B, so we have to:

Letter A

So knowing the tangent formula as:

[tex]tan(x) = opposite / adjacent[/tex]

Knowing some information given in the exercise such as:

So we have:

[tex]tan(30)=5/b[/tex]

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To find two real numbers whose sum is 2 and product is -48, we form a quadratic equation x^2 - 2x - 48 = 0. Using the quadratic formula, we get two pairs of numbers (8, -6) and (-6, 8) that satisfy the given conditions.

To find two real numbers that satisfy the given conditions, namely their sum being 2 and their product being –48, we can set up a system of equations or use a . Let's denote the two numbers as x and y. We know:

We can express y in terms of x from the first equation: y = 2 - x. Substituting this into the second equation gives us:

x(2 - x) = -48

This simplifies to a quadratic equation:

x^2 - 2x - 48 = 0

Using the, x = (-b ± √(b^2 - 4ac)) / (2a), with a = 1, b = -2, and c = -48, we find the two possible values for x, which in turn gives us the corresponding values for y:

x = (2 ± √(4 + 192)) / 2

x = (2 ± √196) / 2

x = (2 ± 14) / 2

Therefore, the two solutions are x = 8 or x = -6. Since we were looking for two numbers, using x + y = 2, the corresponding y values are y = -6 and y = 8, respectively. Hence, the two pairs of numbers that satisfy the conditions are (8, -6) and (-6, 8).

Answer:

b. Rock Samples

Explanation:

Rock samples are obtained by drilling with special drills into the substance.

So, holes drilled several kilometers into Earth's crust provide direct evidence about Earth's interior in the form of a rock samples.

Answer:39

Step-by-step explanation:

130+30%=39

Answer:

Step-by-step explanation:

but what ab this one:  Find the length of the hypotenuse of a right triangle with legs of 5 ft and 12 ft.

A right triangle in which one angle is the right angle and the two sides are perpendicular to each other. Hence, the length of the hypotenuse is [tex]20ft[/tex].

What s the right triangle?

A right triangle or right-angled triangle, or more formally an orthogonal triangle, formerly called a rectangle triangle, is a triangle in which one angle is a right angle, i.e., in which two sides are perpendicular.

Here, the lengths of the triangle are [tex]12ft[/tex] and [tex]16ft[/tex] .

As we know,

[tex]H^{2}=P^{2}+B^{2}[/tex]      ..........[tex](1)[/tex]

Now, substituting the values in the equation [tex](1)[/tex], we get

[tex]H^{2}=(12)^{2}+(16)^{2}\\H^{2}=144+256\\H^{2}=400\\H=\sqrt(400)\\H=20ft[/tex]

Hence, the length of the hypotenuse is [tex]20ft[/tex].

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Answer:

[tex]25.1\ inches[/tex]

Step-by-step explanation:

we know that

The circumference of a circle is equal to

[tex]C=2\pi r[/tex]

we have

[tex]r=4\ in[/tex]

substitute

[tex]C=2(3.14)(4)=25.1\ in[/tex] -----> one more decimal than the given radius (nearest tenth)

Part A: ∠SMB does not have a complementary angle

Part B: The angle measure of the supplement of ∠SMB is 54.65°

Part C: The angle measure of the angle complement to ∠SMB's supplement is  35.35°

The given angle is ∠SMB and m ∠SMB =125.35 °

Complementary angles are angles that sum up to 90°.

To determine the angle measure that is complement to  ∠SMB, we will find the angles that adds up to ∠SMB to give 90°. Since  ∠SMB is already greater than  90°, therefore,  ∠SMB does not have a complementary angle.

Supplementary angles are angles that sum up to 180°.

To determine the angle measure of the supplement of ∠SMB, we will find the angle that adds up to ∠SMB to give 180°. Let the measure of the angle be x, that is

x + 125.35° = 180°

∴ x = 180° - 125.35°

x = 54.65°

∴ The angle measure of the supplement of ∠SMB is 54.65°

To determine the angle measure of the angle complement to ∠SMB's supplement, we will determine the measure of the angle that adds up to ∠SMB's supplement to give 90°. Let the angle be y

Then,

y + 54.65° = 90°

(NOTE: ∠SMB's supplement is 54.65°)

∴ y = 90° - 54.65°

y = 35.35°

∴ The angle measure of the angle complement to ∠SMB's supplement is  35.35°

Hence,

Part A: ∠SMB does not have a complementary angle

Part B: The angle measure of the supplement of ∠SMB is 54.65°

Part C: The angle measure of the angle complement to ∠SMB's supplement is  35.35°

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percent error=100 times error/predicted

error=175-100=75

predicted=100

percent error=100 times 75/100=75

the answer si 75% error

The matrix represents the system of linear equations: -3x + 5y = 15 and 2x + 3y = -10.

The matrix represents the system of linear equations. Each row corresponds to an equation and each column to a coefficient of the unknowns. So, the given matrix:

-3  5  |  15
2  3  | -10

Represents the system of linear equations:

-3x + 5y = 15

2x + 3y = -10

Where x and y are the unknown variables that we are trying to solve for.

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Answer:

(B) Incenter

Step-by-step explanation:

From the given figure, it can be seen that PMN is a triangle where MQ is the angle bisector of ∠NMP, PQ is the angle bisector of∠NPM and NQ is the angle bisector of ∠MNP.

Also, It is equally distant from the three line segments forming the sides of the triangle. Thus, By the definition of incenter, Q can be named as the incedntre of the given triangle PMN.

Since, the centroid, circumcenter and orthocenter does not satisfy the conditions given in the figure, thus Q can not be considered as centroid, circumcenter and orthocenter.

Hence, option B is correct.

Answer:

the answer is incenter

Step-by-step explanation:

took the apex quiz got it correct !

The width that gives the maximum area of the rectangular pen is 12 feet, and the maximum area is 144 square feet.

To maximize the area of a rectangle with a fixed perimeter, you want to make the rectangle as close to a square as possible. This maximizes the area because it distributes the available fencing evenly among the sides, optimizing the area enclosed. The given function, A = 24x - x^2, represents the area of a rectangle with width 'x' and length 'L' where L = (48-2x) / 2.

Maximization or minimization of a function occurs at its turning point. For a quadratic function like ours, the maximum or minimum happens at the vertex. The x-coordinate of the vertex is given by -b/2a. So, in our function A = -x^2 + 24x (which is the same as 24x - x^2), a = -1, b = 24.

Substitution gives: x = -(24) / 2*(-1) = 12 feet. Therefore, the width that gives you the maximum area is 12 feet.

Substitute x = 12 into the function to find the maximum area: A = 24*12 - 12^2 = 288 - 144 = 144 square feet.

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