A tate government borrow $2,000,000 at imple annual interet. Some of the money i borrowed at 6%, ome at 7. 5%, and ome at 8. 5%. Ue a ytem of linear equation to determine how much (in dollar) i borrowed at each rate given that the total annual interet i $137,000 and the amount borrowed at 7. 5% i four time the amount borrowed at 8. 5%. Solve the ytem of linear equation uing matrice

Answer:

Below

Step-by-step explanation:

Break into components

1.5  + 2 cos 10 = 3.4696 hr     for the 'x' components

2 sin 10 = .347296  hr                the 'y' component

Use Pythag theorem to find hrs from start

  sqrt (3.4696^2 + .347296^2 ) = 3.478295   hr

3.478295 hr  *   645 mi/hr = 2243.5 mi from start position

A parallelogram is a type of quadrilateral which has opposite sides to be equal. So that the value of LP required is 26 units.

Generally, all four sided shapes or figures can be classified as quadrilateral. Some of these examples are; cube, square, rectangle, rhombus, trapezoid, parallelogram etc.

A parallelogram is a form of shape which has four sides with two opposite sides to have equal length.

From the parallelogram LMNO, it can be deduced that;

LP = PN

So that;

8x - 19 = 7x - 13

8x - 7x = -13 + 19

x = 6

Thus,

LP = 8x - 19

LP = 8(6) - 19

LP  = 48 - 19

LP = 29

Therefore, the value of LP is 26 units.

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Answer:

Step-by-step explanation:

The first step is combining like terms 3000 and 3000. The next step is to use the distributive property of equality. After that, combining like terms is the next step, and the last step will be the division property of equality to get the final answer.

hope this helps!! :3

Rectangles are plane figures with common length of opposite sides. Thus the required value of ED is 14 units.

A rectangle is a family of quadrilateral which has two equal opposite sides, with two adjacent sides at right angle to each other. Some properties of a rectangle are:

From rectangle ABCD, it can be deduced that:

AB = DC

AD = BC

AC = BD

So that;

9x + 1 = 13x - 11

11 + 1 = 13x - 9x

12 = 4x

x = [tex]\frac{12}{4}[/tex]

  = 3

Therefore, we have;

BD = 13x - 11

     = 13(3) - 11

BD = 39 - 11

     = 28

But ED = [tex]\frac{BD}{2}[/tex]

So that;

ED = [tex]\frac{28}{2}[/tex]

     = 14

ED = 14 units

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The x-intercept of both the functions is 0. Therefore, option A is the correct answer.

The given functions are f(x)=2x/(x+4) and g(x)= -log3(x+3)+1.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Find the horizontal asymptotes by comparing the degrees of the numerator and denominator.

For f(x)=2x/(x+4)

Vertical Asymptotes: x=-4

Horizontal Asymptotes: y=2

No Oblique Asymptotes

For g(x)= -log3(x+3)+1

An asymptote is a line that a curve approaches, but never touches. Find the horizontal, vertical, and oblique asymptotes.

No Vertical Asymptotes

No Horizontal Asymptotes

To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.

x-intercept(s): (0,0)

y-intercept(s): (0,0)

The x-intercept of both the functions is 0. Therefore, option A is the correct answer.

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Answer:

Step-by-step explanation:

Answer:

250

Step-by-step explanation:

We can approximate that the scientists counted [tex]\frac{18}{30}=\frac{3}{5}[/tex] of the elk.

So, the best estimate of the elk population is [tex]150(5/3)=250[/tex].

Answer:1,250

Step-by-step explanation:

Answer:

Locate the given point in the coordinate plane: for example; (−9,4)

Ans: Given that the x and y coordinate of the point are −9 and 4, respectively.

Here, the given point (−9,4) is located in the coordinate plane.  It will be located on the top left side of the coordinate plane if you drew it out.

Step-by-step explanation:

1. You have to draw two perpendicular lines, \ (x-\)axis and \ (y-\)axis.

2. From the point of origin, you have to move 5 units to the right side along the positive \ (x-\)axis.

3. Now, you have to move \ (6\) units up, parallel to the positive \ (y-\)axis

4.  Here, you mark the point of intersection and mark it as \ ((-9, 4).\)

The percentages of compact and subcompact cars the division should plan to manufacture to maximize the expected number of cars demanded each week are 24.5% and 24.5%.

The Latin word per centum, which means "hundred" or "by the hundred," is the source of the word "percent." The Italian term per cento, which means "for a hundred," gradually shrank to become the sign for "percent," which is now used globally. It eventually vanished entirely. The word "per" was frequently shortened to "p."

Given,

If the oil price increases at a higher than normal state,

Demand for the compact cars=1400

Demand for the sub-compact cars=2600

If the oil price increases at a normal rate,

Demand for the compact cars=3500

Demand for the sub-compact cars=2300

Assuming that the probability of price increases at higher than the normal rate is 50% and at a normal rate is 50%.

Then,

Demand for compact cars=50%(1400)+50%(3500)

=(50/100)×1400+(50/100)×3500

=700+1750

=2450

Demand for the sub-compact cars=50%(2600)+50%(2300)

=(50/100)×2600+(50/100)×2300

=1300+1150

=2450

Therefore, the percentages of compact and subcompact cars the division should plan to manufacture to maximize the expected number of cars demanded each week are 24.5% and 24.5%.

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Answer:

y = 6.08871x + 63.9274

Step-by-step explanation:

You can use Desmos a free graphing calculator to do this.  

Answer: Tonya's house is 2.37 miles farther from the school than Jamal's house.

Step-by-step explanation: To solve this problem using a quick picture, we can draw a line segment to represent the distance from the school to Tonya's house, and another line segment to represent the distance from the school to Jamal's house. We can then use a ruler to measure the length of each line segment and subtract the length of the line segment representing the distance to Jamal's house from the length of the line segment representing the distance to Tonya's house.

For example, if we draw a line segment that is 3.64 inches long to represent the distance from the school to Tonya's house and a line segment that is 1.27 inches long to represent the distance from the school to Jamal's house, then we can use a ruler to measure the lengths of the line segments and find that the line segment representing the distance to Tonya's house is 3.64 - 1.27 = 2.37 inches longer than the line segment representing the distance to Jamal's house. This means that Tonya's house is 2.37 miles farther from the school than Jamal's house.

Ordered pairs of graphs III and IV represents a function.

How do you find out if a set of ordered pairs is a function or not?

For a set of ordered pairs to be a function, there must not be any two points that have the same first elements.

This means that, the x-coordinates must not repeat for any two given points.

According to the given question:

Graph I - Clearly x coordinate repeats for the ordered pairs (-8, 12) and (-8, -8). Therefore ordered pairs of Graph I does not represents a function.

Graph II - Clearly x coordinate repeats for the ordered pairs (9, 2) and   (9, -10). Also for (18,4) and (18, -14) Therefore ordered pairs of Graph II does not represents a function.

Graph III - Every ordered pair of this graph is unique hence the ordered pairs of the graph III represents a function.

Graph IV - Every ordered pair of this graph is unique hence the ordered pairs of the graph IV represents a function.

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Answer:

Look at the attached image below

Step-by-step explanation:

[tex]\tt 3x-8\ge \:7[/tex]

Add 8 to both sides:-

[tex]\tt 3x\ge 7+8[/tex]

Add 7 and 8 to get 15:-

[tex]\tt 3x\ge 15[/tex]

Divide both sides by 3:-

[tex]\tt \cfrac{3x}{3}\ge \cfrac{15}{3}[/tex]

[tex]\tt x\ge \:5[/tex]

Yes Data can be modeled by a cubic function

Using finite differences to determine the degree of the polynomial function that fits the data, you know when a set of data could be modeled by a cubic function if you obtain a third difference that is nonzero and constant.

The entities that contain the measures and dimensions make up the relational graph that is the Cube data model. The term "cubes" for entities in Cube was adopted from OLAP cubes. They are essentially data tables with a semantic meta layer that describes the measures, dimensions, and connections between the cubes.

The basic primitives of dimensions and measurements are the basis on which Cube operates. These primitives can be combined to create metrics by the user.

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The equation that that model the number of 2-point shots, x, and the number of 3-point shots, y is x + y = 21, 2x + 3y = 38

Destiny scored 38 points during a recent basketball game. She only made 2-point shots and 3-point shots. In total, Farrah made 21 shots.

The unique equations that model the number of 2-point shots, x, and the number of 3-point shots, y, that Destiney made in the game is as follows:

where

Therefore, the equation that represent the situation is as follows:

x + y = 21

2x + 3y = 38

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Answer: 5

Step-by-step explanation:

Pythagorean theorem a^2 + b^2 = c^2

5^2 + x^2 = 5sqrt(2) ^ 2

25 + x^2 = 50

x^2 = 25

x = 5 square root both sides

The measure of angle B is 141 degrees

Given,

In the question:

There is a seven sided polygon ABCDEFG

The measure of angle BCD is 148 degrees,

The measure of angle DEF is 142 degrees,

The measure of angle EFG is 130 degrees,

The measure of angle FGA is 129 degrees,

and the measure of angle GAB is 120 degrees.

Angle CDE is a right angle.

To find the m∠B.

Now, According to the question:

The sum of angles in a polygon adds up to 180(n - 2), where n is the number of sides of the polygon

The angles are given as:

∠BCD = 148

∠DEF = 142

∠EFG = 130

∠FGA = 129

∠GAB = 120

∠CDE = 90

So, the measure of angle B is calculated using:

∠B + 148 + 142 + 130 + 129 + 120 + 90 = 180(n - 2)

∠B + 759 = 180(n - 2)

The value of n is 7

∠B + 759 = 180(7 - 2)

∠B + 759 = 180 x 5

∠B = 900 - 759

∠B = 141

Hence, the measure of angle B is 141 degrees

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The solution is Option C.

4cm , 6cm , 10 cm does not form a right angle triangle

What is a Triangle?

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

Given data ,

Let the triangle be ABC which is a right angle triangle

Now , the sides of the triangle is given as

a)

6cm , 8cm , 10cm

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

So , substituting the values in the equation , we get

hypotenuse² = base² + height²

10² = 8² + 6²

100 = 64 + 36

100 = 100

Therefore , it is a right angle triangle

b)

12 cm , 35 cm , 37 cm

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

So , substituting the values in the equation , we get

hypotenuse² = base² + height²

37² = 35² + 12²

1369 = 1225 + 144

1369 = 1369

Therefore , it is a right angle triangle

c)

4 cm , 6 cm , 10 cm

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

So , substituting the values in the equation , we get

hypotenuse² = base² + height²

10² = 6² + 4²

100 = 36 + 16

100 ≠ 52

Therefore , it is not a right angle triangle

d)

10 cm , 24 cm , 26 cm

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

So , substituting the values in the equation , we get

hypotenuse² = base² + height²

26² = 24² + 10²

676 = 576 + 100

676 = 676

Therefore , it is a right angle triangle

Hence , the triangle with sides 4cm , 6cm , 10 cm does not form a right angle triangle

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The standard deviation gives information about how values are distributed around the mean. The range between the lowest and highest number is more constrained when the standard deviation is low. Values will so tend to group together around the mean.

What is explained by the standard deviation?

The term "standard deviation" (or "") refers to the degree of dispersion of the data from the mean. Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.

                                     When comparing data sets that may have the same mean but a different range, it is helpful. The mean of the following two numbers, for instance, is the same: 15, 15, 15, 14, 16 and 2, 7, 14, 22, 30.

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The length and width of the rectangular pen that optimizes the area are 400 feet and 200 feet, respectively, according to the perimeter of a rectangle.

The perimeter of a shape is the sum of the lengths of all its edges. For example, a triangle has three edges, hence its perimeter is equal to the sum of those three lengths.The perimeter of a form can be calculated by adding the lengths of all its sides. A perimeter example is what? A field with a length of 24 yards and a width of 15 yards, for instance, will have a perimeter of 78 yards.

calculation

In order to construct a hog pen, I have 800 feet of fencing.

Assume that "l" represents the rectangle's length and "w" its width.

One of your properties borders a river that I own.

I can secure my property with fencing on its three sides.

because of this, the fencing's necessary perimeter p = l + 2w

The fencing's perimeter is now equal to

⇒ l + 2w = 800

= l = 800 - 2w

now the  rectangle's area  = A = lw

Therefore,  A = l * w = w ( 800 - 2w ) = 800w - [tex]2w^{2}[/tex]

By diffusing the area equation, we can figure out the rectangle's greatest area.

Therefore, A' = 800 - 4w

Again, A" = -4

The rectangle has the largest area since the second order differentiation is constant negative.

Put simply, we obtain: A' = 0 , A' = 800- 4w

⇒800- 4w = 0

⇒ 4 w = 800

⇒ w = 200

So the rectangle has a 200-foot width.

The rectangle's length is currently:

l = 800 - 2w = 800 - 2 ( 200 ) = l = 400 feet

The length and width of the rectangular pen that optimizes the area are 400 feet and 200 feet, respectively, according to the perimeter of a rectangle.

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The percentage of population between 130 and 102 is 68%.

The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data distant from the mean. The normal distribution will show as a bell curve on a graph.

Given that the mean is 116 and the standard deviation is 14. Therefore, the approximate population between the given range of 102 to 130 is,

P(102 ≤ X ≤ 130) = P(X ≤ 130) - P(102 ≤ X)

                           [tex]= P(z \leq \dfrac{130-116}{14})- P(z \leq \dfrac{102-116}{14})[/tex]

                           = P(z ≤ 1) - P(z ≤ -1)

                           = 0.8413 - 0.1587

                           = 0.6826

Hence, the percentage is 68%.

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Answer:

-10

Step-by-step explanation:

When a problem asks you to find f("a number"), it's just telling you to replace x with "a number." So, substitute x with 72 to get the equation [tex]f(72)=-12+\frac{72}{36}[/tex]. The fraction simplifies to 2, and -12 plus 2 is just -10.

The amount of minute to reach a distance of 9 inches from the rock is 3 minutes

The complete question is added at the end of this solution

From the question, we have the equation to be

d = 3t

A distance of 9 inches from the rock means that

d = 9

So, we have

3t = 9

Divide both sides by 3

t = 3

Hence, the amount of time is 3 minutes

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Complete question

The equation d=3t represents the relationship between the distance (d) in inches that a snail is from a certain rock and the time (t) in minutes.

How many minutes does it take for the snail to reach a distance of 9 inches from the rock?

To write the equation of a line in slope-intercept form (y = mx + b), we need to find the slope of the line (m) and the y-intercept (the point where the line crosses the y-axis, which is represented by b).

We can use the point-slope formula to find the equation of the line that passes through the points (-2,-2) and (5,12):

y - y1 = m(x - x1)

Where (x1, y1) is a point on the line, and m is the slope of the line.

Plugging in the values for the given points and solving for m, we get:

m = (12 - (-2)) / (5 - (-2))

= 14 / 7

= 2

Now that we have the slope, we can use either of the given points to find the y-intercept (b). Let's use the point (-2,-2):

y = mx + b

-2 = 2(-2) + b

-2 = -4 + b

b = -2 + 4

b = 2

Therefore, the equation of the line in slope-intercept form is:

y = 2x + 2

This is the equation of the line that passes through the points (-2,-2) and (5,12).

The measure of <Y: 40⁰,80⁰90⁰100⁰ are the complementary angles and their supplementary angles respectively which are 50⁰,10⁰,0⁰ and 70⁰ respectively

The measure of angles is defined as the complementary or or supplementary angle of the given angle.

Complementary angles add up to 90⁰

supplementary angles add up to 180⁰

The given angles are: 40⁰, 80⁰, 90⁰ and 100⁰

The measure of 40⁰

x+40=90⁰

x=90-40

x=50⁰

The measure of 80⁰ is

x+80=90

x=90-80

x=10⁰

The measure of 90⁰ is

x+90=90

x=90-90

x=0⁰

The measure of 100⁰ is

x+100=180

Since 100⁰ is an obtuse angle

x=180-100

x=80⁰

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The points on the line 2x - 6y = 12 is

x                y

0               -2

6                0

9                -1

12               2

What is equation of line in slope intercept form?

The most general form of equation of line in slope intercept form is given by y = mx + c

Where m is the slope of the line and c is the y intercept of the line.

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If  [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m =  [tex]tan \theta[/tex]

The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.

The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.

a)The equation is 2x - 6y = 12

For x = 0,

[tex]2 \times 0- 6y = 12\\6y = -12\\y = -\frac{12}{6}\\y = -2[/tex]

For x = 6,

[tex]2 \times 6 - 6y = 12\\6y = 0\\y = 0[/tex]

For x = 9

[tex]2 \times 9 -6y = 12\\18 - 6y = 12\\6y = 12 - 18\\6y = -6\\y = -\frac{6}{6}\\y = -1[/tex]

For x = 12

[tex]2 \times 12 - 6y = 12\\-6y = 12 - 24\\-6y = -12\\y = \frac{12}{6}\\y = 2[/tex]

x                y

0               -2

6                0

9                -1

12               2

b) The graph has been attached

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Answer:

20w

Step-by-step explanation:

If you have 20 bottles, and each contains w ounces, we can use the following example to solve.

If there were 4oz per bottle,

20 * 4 = 80

80oz

We have w oz per bottle,

20 * w = ?

20w

The value of m∠E is 120°

Define Congruent angles

Given,

The Δ ABC be congruent to Δ DEF.

Since, the triangles are congruent, B and E are automatically congruent, since they are corresponding angles.

First let's find the value of y,

To find y, equate the measure of y like this

95 + y = 6y - 30

95 + 30 = 6y - y

125 = 5y

y = 25

Now, substitute the value of y in ∠E

∠E = 6y - 30

∠E = 6* 25 - 30

∠E = 120°

Hence, the value of m∠E is 120°

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The true statement from the given options is C. If the mA does not equal 60, then ABC is not an equilateral triangle.

An equilateral triangle is one in which the angles and all three sides are equal. An equilateral triangle is also called an equiangular triangle since each of its angles has a value of 60 degrees.

The equal angle in an Equilateral triangle = 60°

Here we have 3 options

A. If the mA = 60, then ABC is an equilateral triangle.

B. If ABC is not an equilateral triangle, then the mA does not equal 60.

C. If the mA does not equal 60, then ABC is not an equilateral triangle.    

Here we need to justify which of the given point will be true in the case of Equilateral Triangles.

Given

Option A: If the mA = 60, then ABC is an equilateral triangle.  

With the measurement of A = 60°, here we can't conclude that  ABC is an equilateral triangle because there is a possibility that the remaining angles are not equal to 60°

Option B: If ABC is not an equilateral triangle, then the mA does not equal 60.

Any type of triangle can have an angle that is equal to 60° so the given statement is wrong.  

Option C. If the mA does not equal 60, then ABC is not an equilateral triangle.

As we know each angle of an equilateral triangle is 60°, So it is true that   If the mA does not equal 60, then ABC is not an equilateral triangle.

Therefore,

The true statement from the given options is C. If the mA does not equal 60, then ABC is not an equilateral triangle.

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