System of equations- does this have one solution, many solutions or no solution
y=4x+6
y=6-3x

Answer:

\(\boxed {\boxed {\sf D. \ 23.5}}\)

Step-by-step explanation:

The median is the number in the middle of a set of data. To find, we place the numbers in order from least to greatest and pick the middle number.

The data set is:

This is already in order from least to greatest, so we can begin removing numbers from each side of the list until the middle is reached.

Now we have 2 numbers that are in the middle. To find the median, we take the mean or average of these 2 numbers. Add them together, then divide by 2.

The median of this data set is 23.5 and choice D is correct.

Answer:

m=7, n=-1. (7, -1).

Step-by-step explanation:

4m+8n=20

-4m+2n=-30

---------------------

10n=-10

n=-10/10

n=-1

4m+8(-1)=20

4m-8=20

4m=20+8

4m=28

m=28/4

m=7

The midpoint has coordinates (19,19) as per the midpoint formula.

The statement is false.

The statement is false. The midpoint of the segment joining two points is determined by taking the average of their x-coordinates and the average of their y-coordinates. In this case, the two given points are (0,0) and (38,38).

To find the x-coordinate of the midpoint, we take the average of the x-coordinates of the two points:

(x1 + x2) / 2

= (0 + 38) / 2

= 38 / 2

= 19

Therefore, the x-coordinate of the midpoint is 19, which matches the statement. However, to determine if the statement is true or false, we also need to check the y-coordinate.

To find the y-coordinate of the midpoint, we take the average of the y-coordinates of the two points:

(y1 + y2) / 2

= (0 + 38) / 2

= 38 / 2

= 19

The y-coordinate of the midpoint is also 19. Therefore, the coordinates of the midpoint are (19,19), not 19 as stated in the statement. Since the midpoint has coordinates (19,19), the statement is false.

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Answer:

Statements A, C and D are true

Step-by-step explanation:

True statements:

A.) ∠AZB and ∠BZD are a pair of supplementary angles.

C.) The value of x is 17.

D.) ∠AZC and ∠CZD are a pair of complementary angles.

The spring will stretch 1.5 times further when the 0.60 kg block is added to the 1.2 kg block.

To determine how much further the spring will stretch when a 0.60 kg block is added to the 1.2 kg block, we need to consider Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position.

Let's assume that the spring is initially stretched by a certain amount x when only the 1.2 kg block is attached. The force exerted by the spring is given by F = kx, where k is the spring constant.

When the 0.60 kg block is added, the total mass becomes 1.2 kg + 0.60 kg = 1.8 kg. The force exerted by the spring remains the same, but the total mass affects the acceleration of the system according to Newton's second law, F = ma.

Using F = ma, we can find the acceleration of the system: F = (1.8 kg)(9.8 m/s^2) = 17.64 N.

Since F = kx, we can rearrange the equation to find x: x = F/k.

Now, if we assume the spring constant k remains constant, the displacement x will increase by a factor of 1.8 kg/1.2 kg = 1.5.

Therefore, the spring will stretch 1.5 times further when the 0.60 kg block is added to the 1.2 kg block.

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The expected value of z, e(z), is 12 and the variance of z, v(z), is 90. The expected value of the random variable z, defined as z = 2x - 3y + 5, can be determined using the properties of expected values. The value of e(z) is calculated as 2e(x) - 3e(y) + 5.

Similarly, the variance of the random variable z, denoted as v(z), can be determined using the properties of variances. The value of v(z) is calculated as 2^2v(x) + (-3)^2v(y), since x and y are independent random variables.

Given e(x) = 8, e(y) = 3, v(x) = 9, and v(y) = 6, we can calculate the expected value and variance of z.

e(z) = 2e(x) - 3e(y) + 5

    = 2(8) - 3(3) + 5

    = 16 - 9 + 5

    = 12.

Therefore, the expected value of z, e(z), is 12.

v(z) = 2^2v(x) + (-3)^2v(y)

    = 2^2(9) + (-3)^2(6)

    = 4(9) + 9(6)

    = 36 + 54

    = 90.

Therefore, the variance of z, v(z), is 90.

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The circumference of the circle when A is a minimum is 65.2 cm (approx).

Given that: You have a wire that is 98 cm long. You wish to cut it into two pieces. One piece will be bent into the shape of a square. The other piece will be bent into the shape of a circle. Let A represent the total area of the square and the circle. A square requires a total of 4 sides and a circle requires only one side. So, let the length of the wire used to make a square be x and the length of the wire used to make a circle be y. So, the length of the wire used to make the square is 4x and the length of the wire used to make the circle is 2πr.

So,x + y = 98        ----(1)A = πr² + x²/16     [∵ Length of a side of the square will be x/4]A = π(r/2)² + x²/16    [∵ diameter = radius x 2]

So, we have to find the value of r in terms of x in order to minimize A. Now,2πr + 4x = 98r = (98 - 4x)/2πSubstitute this value of r in the equation of A. So, A = π(98 - 4x)²/4π² + x²/16So,dA/dx = - 2(98 - 4x)/4π² + 2x/16= 0(98 - 4x)/4π² = x/8Solve for x,x = 32.8 cm. So, the length of the wire used to make the circle is y = 98 - x = 65.2 cm. Now, the circumference of the circle is, C = 2πr = 2π(65.2/2π) = 65.2 cm.

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Answer:

The diagonal length is 10 miles.

Step-by-step explanation:

This is the work of the Pythagorean theorem : \(a^{2} + b^{2} = c^{2}\)

-------------------------------

\(8^2 + 6^2 = c^2\\100 = c^2\\10=c\)

Good Luck!!!

Answer:

10 miles

Step-by-step explanation:

pythagoras' Theorem

8^2 + 6^2 = c^2

64 + 36 = 100

c^2 = 100

c = √100

c = 10 miles

Answer:

its the second one because i think it is im not sure if u get it wrong dont blame me i said i think it is

Step-by-step explanation:

because i think it is

If the company wants to keep its production costs under $175,000, then  5.6 ≤ x ≤ 24.13 constraint is reasonable for the model given that the function C(x) = −0.74x² + 22x + 75 ,the production cost C, in thousands of dollars for a tech company to manufacture a calculator, where x is the number of calculators produced, in thousands. This can be obtained by using the given graph of the function.

A constraint is a condition of an optimization problem that should be satisfied the condition.

From the we have the function,

⇒ C(x) = −0.74x² + 22x + 75

the production cost C, in thousands of dollars for a tech company to manufacture a calculator, x is the number of calculators produced, in thousands.

In the graph the dotted line is the line where C(x) is $175,000. Above this line every the value is greater than $175,000.

The points where this line, that is C(x) = y = 175, intersect the graph of the given function C(x) = −0.74x² + 22x + 75 is (5.6, 175) and (24.13, 175).

Therefore, x ≥ 5.6 and x ≤ 24.13  

⇒ 5.6 ≤ x ≤ 24.13

Hence if the company wants to keep its production costs under $175,000, then  5.6 ≤ x ≤ 24.13 constraint is reasonable for the model given that the function C(x) = −0.74x² + 22x + 75 ,the production cost C, in thousands of dollars for a tech company to manufacture a calculator, where x is the number of calculators produced, in thousands.

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Answer:

0 ≤ x < 5.6 and 24.13 < x ≤ 32.82

Step-by-step explanation:

The area of the window is 305.12 square inches.

given that

jaylon created this stained glass window the upper two coners are quater ciecleseach with a radius of 4 inches.

The window's area is equal to the sum of the areas of a rectangle, two quarter circles, and the smaller square between the two upper corners.

The quantity of space occupied by a flat surface with a specific shape is referred to as the area.

now, find the area of rectangle

A = length x breadth

A = 12 x (26-4)

A = 12 x 22

A = 264 square inches

find the area of the two quarter circle

\( A= 2( \frac{1}{4} (3.14) \times {4}^{2} ) \\ A = 25.12 {in}^{2} \)

Find the area of the smaller square between the two upper corners

A = (12-8) (4)

A = 4 x 4

A = 16 sq.in

now, find the total area

A = 264 + 25.12 + 16

A = 305.12 square inches

Hence, the area of the window is 305.12 square inches.

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Answer:

157.89 is the answer

Answer:

300

Step-by-step explanation:

5 or more raise the score 4 or less let it rest basically 5 or more up 4 or less down

=================================================

Explanation:

Sine is given to be negative, and so is tangent. This only happens in quadrant Q4

Recall that y = sin(theta), so if sin(theta) < 0, then we're below the x axis.

If tan(theta) < 0, then this means cos(theta) > 0

So we have y < 0 and x > 0 which places the angle somewhere in Q4.

--------------------------

Draw a right triangle as shown below in the attached image. We have AC = 25 and BC = 7. Use the pythagorean theorem to find that AB = 24

So this is what your steps may look like

a^2+b^2 = c^2

7^2+b^2 = 25^2

b^2+49 = 625

b^2 = 625-49

b^2 = 576

b = sqrt(576)

b = 24

So because AB = 24, we know that the cosine of the angle is adjacent/hypotenuse = 24/25

---------------------------

As an alternative, you could use the trig identity

sin^2(x) + cos^2(x) = 1

and plug in the given value of sine to solve for cosine. The cosine value result will be positive since we're in Q4.

So,

sin^2(x) + cos^2(x) = 1

(-7/25)^2 + cos^2(x) = 1

(49/625) + cos^2(x) = 1

cos^2(x) = 1 - (49/625)

cos^2(x) = (625/625) - (49/625)

cos^2(x) = (625-49)/625

cos^2(x) = 576/625

cos(x) = sqrt(576/625)

cos(x) = sqrt(576)/sqrt(625)

cos(x) = 24/25

This is effectively a rephrasing of the previous section since the pythagorean trig identity is more or less the pythagorean theorem (just in a trig form)

Answer: 6/49 positive not negative

Step-by-step explanation:

Answer:

x=9.3

Step-by-step explanation:

use SohCahToa

in this case u use cos

cos(41°)=7/x

x=7/cos(41)

x=9.275090953

x=9.3

Answer:

33/4=8.25

So the best way to do it is 33 divided by 4. That equals 8.25.

Therefore, the initial value of the function is $1,852 and the rate of change is $12.18 per shirt. The initial value represents the cost of the shirts before any were purchased,

In mathematics, a function is a rule that assigns to each element in a set called the domain, a unique element in another set called the range. In other words, a function is a mathematical object that takes an input and produces a specific output, according to a specific set of rules or operations.

by the question.

et the initial value be represented by a and the rate of change by r.

The given information can be represented by the following equation:

a + 150r = 1,852

Since the flat-rate shipping cost is $25, the cost of the 150 shirts alone would be:

a + 150r - 25 = 1,827

The initial value, a, represents the cost of the shirts before any shirts were purchased. In this case, it would be the cost of the shirts if no shirts were purchased plus the flat-rate shipping cost of $25.

So, a = 1,827 + 25 = 1,852.

The rate of change, r, represents the increase in cost for each additional shirt purchased. In this case, it would be the cost of one shirt.

So, r = (1,852 - 25)/150 = 12.18.

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The expression that represents the width is w = (P-2l)/2

Given the formula for calculating the perimeter of a triangle expressed as:

P = 2(l + w)

where

l is the length

w is the width

Make w the subject of the formula

Given

P = 2(l + w)

Expand

P = 2l + 2w

Subtract 2l from both sides

P - 2l = 2w

Divide both sides by2

2w/2 = (P-2l)/2

w = (P-2l)/2

Hence the expression that represents the width is w = (P-2l)/2

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The three extra squares that should be shaded to have a pattern with 4 lines of symmetry and a rotational symmetry of order 4 are E, H, N.

It is required for the new shape to have four lines of symmetry, which means that if the new shape is divided we can obtain four identical lines; moreover, it should have a rotational symmetry of order 4, which means that if we rotate the shape it will coincide with the original shape four times. Based on this, the squares that should be shaded are E, H, N.

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Answer:

\(r = \sqrt{ {(6 - 2)}^{2} + {(1 - ( - 3))}^{2} } \)

\(r = \sqrt{ {4}^{2} + {4}^{2} } = \sqrt{16 + 16} = \sqrt{32} \)

So the equation of the circle is

\( {(x - 2)}^{2} + {(y + 3)}^{2} = 32\)

The simplified form of equation 6x[(3x - 4) + (4x + 2)] is 42\(x^{2}\) - 12x.

To simplify the expression 6x[(3x - 4) + (4x + 2)], we need to apply the distributive property and combine like terms.

First, let's simplify the terms inside the parentheses:

(3x - 4) + (4x + 2) = 7x - 2

Now, we can rewrite the expression as:

6x(7x - 2)

Next, we distribute 6x to the terms inside the parentheses:

6x * 7x - 6x * 2 = 42x^2 - 12x

Therefore, the simplified form of the expression 6x[(3x - 4) + (4x + 2)] is 42\(x^{2}\) - 12x.

In summary, by applying the distributive property and combining like terms, we simplified the expression to 42\(x^{2}\) - 12x.

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The system of equations for x^3 - 2x^2 + 5x - 6 = -4x^2 + 14x + 12.

Carlos graphed the system of equations that can be used to solve the equation x^3 - 2x^2 + 5x - 6 = -4x^2 + 14x + 12.

To graph this system of equations, we need to set the equation equal to zero. So, the equation becomes:

x^3 - 2x^2 + 5x - 6 + 4x^2 - 14x - 12 = 0

Combining like terms, we get:

x^3 + 2x^2 - 9x - 18 = 0

To graph this equation, you can use a graphing calculator or plot points manually. Here are the steps to manually plot the graph:

1. Choose a range for x, for example, from -5 to 5.
2. Pick a few values for x within the chosen range and substitute them into the equation to find the corresponding y-values.
3. Plot the points (x, y) on a coordinate plane.
4. Connect the plotted points to create a smooth curve.

By following these steps, you can graph the system of equations for x^3 - 2x^2 + 5x - 6 = -4x^2 + 14x + 12.

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Answer:

D!

Step-by-step explanation:

a and b - we cant do translations, because the shapes size would be preserved

so its between c and d

c makes it smaller -  so even smaller than KLM

d makes KLM larger(into K'L'M'), and since it is the last option, D is correct

hope it helps

ask for any questions

Total volume of the shape is 124 cm³

A cuboid is a three-dimensional solid shape that has six rectangular faces or sides, where each face meets at a right angle with its adjacent faces.

The formula for the volume of a cuboid is:

Volume = Length x Width x Height

So, the Volume of first cuboid = 3 × 4 × 5 = 60 cm³

and the Volume of second cuboid = 2 × 4 × 8 = 64 cm³

Total volume of the shape = Volume of first cuboid + Volume of second cuboid

Total volume of the shape = 60 cm³ + 64 cm³

Total volume of the shape = 124 cm³

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Applying the cosine ratio, the value of x to the nearest tenth is: 11.9.

The cosine ratio is found using the formula, cos ∅ = adjacent length / hypotenuse length of a right triangle.

Given the following:

Plug in the values into the cosine ratio:

cos 32 = x/14

x = (cos 32)(14)

x = 11.9

Thus, applying the cosine ratio, the value of x to the nearest tenth is: 11.9.

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Answer:

An included angle is the angle between two sides of a triangle. It can be any angle of the triangle, depending on its purpose.

Step-by-step explanation: