x-2y+z=9
2x + 3y - 2z = -12
x+y=3z = - 13

[tex] \bold{x_{1}=+9 \: or \: \: x_{2}=-9}[/tex]

This question is very simple because it asks us to solve the equation using square roots. We don't need to find any important information as this problem is quite simple. We just need to take into account some rules for moving terms from one member to another and we will get our answer.

Given the equation:

[tex] \bold{{x}^{2} - 81 = 0}[/tex]

Move -81−81 to the other member, this subtraction happens by doing the opposite operation, that is, it happens by adding.

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\bold{{x}^{2} = 81}[/tex]

We add square root to remove the exponent.

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\bold{{ {x}} = \sqrt{81}}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{x = ±9}[/tex]

∴ The solutions we have for this equation are both 9 and -9. And if we want to check our results, we can plug in the values into x and we'll see that both 9 and -9 are values that satisfy the equation, since negatives don't matter when we're squaring numbers.

Answer:

Step-by-step explanation:

x² - 81 = 0

x² = 81

x = √81

x = 9

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

9² = 81

81 = 81

the answer is good

The required solution of the equations is given as (2, 3, 0).

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

Here,
So we are given a system,
3x -2y + 3z = 0
-3x-5y-5z = -21

Substitute x =2, and we get the system,
-2y + 3z = -6
-5y -5z = -15

Multiply equation 1 by -5 and equation 2 by 2 we get the system,
10y - 15z = 30
-10y -10z = -30

Adding the above equations,
z = 0

Now,
-2y = -6
y = 3

Thus, the required solution of the equations is given as (2, 3, 0).

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The potential energy of the system to the conservative force acting on the particle is   [tex]U=\frac{Ax^2}{2} -\frac{Bx^2}{2}[/tex]

(a) The potential energy of the system to the conservative force acting on the particle, with Ui=0:

U=Uf−Ui=Uf−0

[tex]U=-\int\limits^x_0 {-Ax+Bx} \, dx \\\\U=\int\limits^x_0 {A\frac{x}{2}+B\frac{x}{2} } \, dx \\\\U=A\frac{x^2}{2} -B\frac{x^2}{2} \\\\[/tex]

(b) From (a), U(1.80m)=2A–2.67B, and U(3.40m)=4.5A–9B.

ΔU=(4.5A−9B)−(2A−2.67B)

ΔU=2.5A−6.33B

If we consider the particle alone as a system, the change in its kinetic energy is the work done by the force on the particle: W=ΔK.

For the entire system of which this Particle is a member, this work is internal work and equal to the negative of the change in potential energy of the system:

ΔK=−ΔU

ΔK=−2.5A+6.33B

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Here b is =0, According to the Zero Product Property, if ab=0, then either a=0 or b=0 (or both). If and only if one or more of the factors in a product are zero, the product is zero. This is very helpful when attempting to solve quadratic problems.

The product of two nonzero items is not zero, according to the algebraic definition of the zero product property. In other terms, the following claim:

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The range of the function y = -2x² + 12x - 13 will be [5, -∞). Then the correct option is A.

Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.

Then the equation of the parabola will be given as,

y = a(x - h)² + k

The domain means all the possible values of x and the range means all the possible values of y.

The equation is given below.

y = -2x² + 12x - 13

Convert the equation into a vertex form, then we have

y = -2x² + 12x - 13

y = -2x² + 12x - 18 + 18 - 13

y = -2(x² - 6x + 9) + 18 - 13

y = -2(x - 3)² + 5

The range of the function y = -2x² + 12x - 13 will be [5, -∞). Then the correct option is A.

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The parent function is the simplest form of the type of function in the graph is g(x) = 1/x

What is graph ?

In mathematics, a graph is a collection of points, called vertices, and lines, called edges, that connect the vertices. Graphs are used to represent networks of communication, data organization, computational devices, the flow of computation, and more. Graphs are one of the most fundamental concepts in mathematics, and they are used to model many real-world problems and situations.

The transformation from the first equation to the second one can be found by finding a, h and k for each equation.

y = a / x-h   +   k

Find  a, h and k for

g(x)= 1/x

a = 1

h=0

k = 0

The horizontal shift depends on the value of h and The horizontal shift is described as :

f(x) = f(x+h)  The graph is shifted to the left h units

f(x) = f(x-h) The graph is shifted to the right h units.

Horizontal shift depends on the value of k and The horizontal shift is described as :

f(x) = f(x+k)  The graph is shifted to up k units

f(x) = f(x-k) The graph is shifted down k units.

Vertical shift : none.

The sign of a describes the reflection across the x-axis. −a means the graph is reflected across the x-axis.

Reflection about the x-axis: None

To find the transformation, compare the two functions and check to see if there is a horizontal or vertical shift, reflection about the x-axis, and if there is a vertical stretch.

Parent Function: g(x) = 1/x

Horizontal Shift: None

Vertical Shift: None

Reflection about the x-axis: None

Hence, The parent function is the simplest form of the type of function g(x) = 1/x .

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Using exponential function, The total number of foxes that will remain after 4 years is 1534.

A mathematical function with the formula f (x) = an x is an exponential function. where an is a constant known as the function's base and x is a variable. The transcendental number e, or roughly 2.71828, is the exponential-function base that is most frequently encountered.

We employ the exponential function because...

In the biological sciences, exponential functions are frequently employed to simulate the evolution of a certain quantity over time, such as population number. Experimental data graphs are often created with the quantity on the y-axis and the time on the x-axis.

Using exponential function,

P(t) = A . b^t

Formulate: 3746 based on the provided conditions. (1 - 20%) ⁴

Analyze the following formula or expression: 1534.3616

he total number of foxes that will remain after 4 years is 1534

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Using the information given, select the statement that can deduce the line segments to be parallel. If there are none, then select none.

When m8 = m4, the line segments are parallel.

When two line segments have the same slope (m8 = m4), then the line segments are parallel. Therefore, the statement that the line segments are parallel can be deduced if m8 and m4 are equal.

When two line segments have the same slope, then they will be parallel to each other. This can be deduced when the slopes of both line segments are equal, which is represented by m8 = m4. If the two line segments have the same slope, then they will be parallel to each other and will never meet or intersect. This is because parallel lines always have the same slope and never touch each other. In conclusion, the statement that two line segments are parallel can be deduced if m8 and m4 are equal.

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The expression is A = (1/4 pi) * (C^2) when The area of a circle is the product of the number 1/4(pi) and the square of the circumference.

What is Area of circle?

Area of circle can be defined as the product of pi and square of radius of a circle.

Given ,

we have transform the sentence into a mathematical equation

so A is used to represent the area

and C is used to represent the circumference

And condition is

The area of a circle is the product of the number 1/4(pi) and the square of the circumference

SO,

A = (1/4 pi) * (C^2)

Hence, The expression is A = (1/4 pi) * (C^2) when The area of a circle is the product of the number 1/4(pi) and the square of the circumference.

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The measure of angle ∠B is 44°.

What is the measure of all angles in a triangle?

A triangle's angles add up to 180 degrees because one exterior angle is equal to the sum of the other two angles in the triangle. In other words, the other two angles in the triangle (the ones that add up to form the exterior angle) must combine with the third angle to make a 180 angle.

We have given,  

Triangle ΔABC,

and angles ∠ACB = 90°, ∠CAB= 46°, and ∠ABC = ?

We know that the sum of all angles in the triangle is 180°.

So,

∠ACB + ∠CAB + ∠ABC = 180°

90° + 46° + ∠ABC = 180°,

136 + ∠ABC = 180°,

∠ABC = 180° - 136

∠ABC = 44°,

Hence, the measure of angle ∠B is 44°.

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Answer:

lesser number: 9

greater number:41

Step-by-step explanation:

Given: a+b=50

Use the word problem to create equation: 5a-4=b

We can solve for either variables, we'll solve for b(greater number) first:

a=50-b

Plug a into other equation:

5(50-b)-4=b

250-5b-4=b

246-5b=b

246=6b

b=41

Plug what we found for b into equation to solve for a(lesser number):

a+41=50

a=9

Verify:

5(9)-4=41 ?

45-4=41

41=41 Checks out.

Hope this helps.

From the given data, using perimeter of rectangle, Length(L) = 6 × 11 - 7 of the rectangular field.

The length of a shape's outline is its perimeter. You must add the lengths of all four sides of a rectangle or square to determine its perimeter. In this instance, x represents the rectangle's length and y its width. P = x+x+y+y, where P is the perimeter.

Let length of the rectangular field = L

Width of rectangular field = W

Given,

length of a rectangular field is 7 feet less than six times its width

perimeter is 140 feet,

According to the question,

L = 6W - 7

Perimeter of the rectangle = 2 (L + W)

140 = 2 (6W - 7 + W)

140 = 2 (7W - 7)

70 = 7 W - 7

77 = 7 W

W = 11

L = 6 × 11 - 7

Length = 59

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Answer:

Circumference = 2π

Step-by-step explanation:

The formula for a circle's circumference is:

C = 2πr

Here is a quick breakdown:

C = circumference

r = radius

Since we are given that the radius is 1 mile, we can plug in r into the formula above:

C = 2π(1)

C = 2π

A cut parallel to the vertical axis, directly through the vertical axis. Option C is correct.

Axes for the figure are defined as the imaginary lines that toward which measurement of the figures are taken.

Here,
When cutting the pyramid through axis perpendicular axis to the vertical axis, the shape produced would be a quadrilateral. But when we cut the pyramid through the vertical axis it produces the triangle.

Thus, a cut parallels the vertical axis, directly through the vertical axis. Option C is correct.

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The volume of the sphereical globe is  1564in³

We know that when we talk about the volume we have to look at the volume of the box. Let us assume that the box in the problem that we have here is a cubic box, it the follows that the volume of the box is obtained from;

6l^3 = 2197in³

Where l is the length of each side in inches

l = ∛ 2197/6

l = 7.2 inches

This is the radius of the spherical globe

Volume of a sphere = 4/3πr^3

V = 4/3 * 3.142 * (7.2)^3

V = 1564in³

Hence 1564in³ is the volume of the globe.

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The initial number of people sick with the flu at time 0 is 100 and the rate of increase of the number of people sick with the flu is 120t - 3t^2 people per day.

P(t) = 100 + 120t - 3t^2

This formula can be used to calculate the number of people sick with the flu at time t, where time is measured in days from the beginning of the epidemic. The initial number of people sick with the flu at time 0 is 100 and the rate of increase of the number of people sick with the flu is 120t - 3t^2 people per day.

To calculate P(t), the initial number of people sick with the flu, 100, is added to the rate of increase of the number of people sick with the flu over t days, which is 120t - 3t^2. The sum of these two values is the number of people sick with the flu at time t.

For example, at t=2 days, P(2) = 100 + 120(2) - 3(2^2) = 100 + 240 - 12 = 328 people sick with the flu.

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Answer:

Step-by-step explanation 0% because there is more red markers

Answer: (Don't read this if this is a test)

Step-by-step explanation: I might get this wrong because I was kind of confused too (sorry if I am!)

Hello! The first thing you would want to do for these kinds of questions is to write the probability of a green, blue, or red marker being picked as a fraction.  To do this, add 12 + 4 + 20 which is 36.

The probability of picking a green marker - 12/36, partially simplified = 3/9

The probability of picking a blue marker - 4/36, simplified = 1/9

The probability of picking a red marker - 20/36, simplified = 5/9

G - 3/9
B = 1/9
R = 5/9

You know that the probability of picking a blue marker is 1/9.  Once you know this, you can figure out the new probability of picking a red marker since the blue marker won't be replaced.  The answer is 4/35.  Multiply 1/9 by 4/35 to find the probability of picking one after the other and you will get 4/315.  

Answer:

226.1 [tex]in^{2}[/tex]

Step-by-step explanation:

Answer: The truth value of a conditional statement can be determined by using the truth table for the conditional operator (->). The truth table for the conditional operator is as follows:

p q p -> q

T T T

T F F

F T T

F F T

To determine the truth value of a conditional statement r, you need to know the truth values of the individual propositions contained in r. Once you have the truth values of the individual propositions, you can use the truth table to determine the truth value of the entire conditional statement. If the conditional statement is true, then it is represented by "T", otherwise it is "F".

Step-by-step explanation:

Answer:

The work done by the constant unit force vector in moving the object 17 units in the positive x-axis direction is equal to the magnitude of the force multiplied by the displacement in the direction of the force. Since the force makes an angle of 30 degrees with the x-axis, the magnitude of the displacement in the direction of the force is equal to the displacement in the x-axis direction multiplied by the cosine of 30 degrees. Therefore, the work done is equal to the magnitude of the force multiplied by 17 multiplied by the cosine of 30 degrees. hope this helped

Answer:

375 square units

Step-by-step explanation:

Area = (1/2) h (a+b)

=1/2 × 10 (49+26)

= 5 × 75

= 375 square units

hope it helps you <3

Answer:

Va=4r³π

Step-by-step explanation:

Vb=(4/3)r³π, Vc=r²πh, h is the height of the cylindrical container.

h=12r.

So now the volume of the cylinder is:

Vc=r²π*12r=12r³π.

There are 6 balls so their total volume is:

6*Vb=6*(4/3)*r³*π=(24/3)*r³π=8r³π.

Now we subtract the volume of 6 balls from the volume of the cylinder to get the volume of air Va inside the cylinder:

Va=Vc-6*Vb=12r³π-8r³π=4r³π.

So the volume of air inside of the cylinder is Va=4r³π

Hope This Helps!

Answer:

Volume of air = 4πr³ (units cubed)

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{4 cm}\underline{Volume of a cylinder}\\\\$V=\pi r^2 h$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}[/tex]   [tex]\boxed{\begin{minipage}{4 cm}\underline{Volume of a sphere}\\\\$V=\dfrac{4}{3} \pi r^3$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}[/tex]

Model the squash ball as a sphere.

Assuming the six squash balls are packaged in a cylindrical container where each ball is one on top of the other, the height of the container is 6 times the height of a squash ball.  

The height of a squash ball is its diameter, which is twice its radius.  

Therefore, the height of the cylinder is 12 times the radius of the squash ball, and the radius of the cylinder is the radius of the squash ball.

Therefore:

[tex]\begin{aligned}\textsf{Volume of the cylinder}&=\pi r^2 \cdot 12 r\\&=12 \pi r^3\end{aligned}[/tex]

where r is the radius of the sphere (squash ball).

To find the volume of air inside the container, subtract 6 times the volume of a sphere from the volume of the cylinder.

[tex]\begin{aligned}\textsf{Volume of air}&=\textsf{Volume of cylinder}-\textsf{6 volume of sphere}\\&=12\pi r^3-6\left(\dfrac{4}{3} \pi r^3\right)\\&=12\pi r^3-8\pi r^3\\&=4\pi r^3\;\; \sf units \; cubed\end{aligned}[/tex]

Answer:

$139,200

Step-by-step explanation:

To find the total cost of the subsidized loan, we need to calculate the total amount of interest that will be added to the loan over the 10-year repayment period. We can use the formula for simple interest:

I = Prt

Where:

I = Interest

P = Principal (the original loan amount)

r = Interest rate (expressed as a decimal)

t = Time (in years)

In this case:

I = 80,000 * 0.074 * 10 = 59,200

The total cost of the loan would be the sum of the principal and the interest:

80,000 + 59,200 = $139,200

So the total cost of the subsidized loan is $139,200.

Answer:

4x + 7y = 27

Step-by-step explanation:

The slope-intercept form of the equation of a line is

y = mx + b

Here m = slope which is the rate of change of the y-value with respect to x and b is the y-intercept which is the y-value where the line crosses the x-axis. It is therefore the value of y when x = 0

We are given slope = -4/7

So equation of line is
y = (-4/7)x + b

To find b, notice that the given point is (5, 1) which indicates that at this point x = 5, y = 1

If we plug in x = 5 in the equation we should get a y0value of 1

We can rewrite y = (-4/7)x + b as

(-4/7)x + b  = y  

Substitute x=5 and y = 1

(-4/7)(5) + b = 1

-20/7  + b = 1

b = 1 + 20/7

b = 27/7

So the equation of the line in slope intercept form is

[tex]\quad y=-\dfrac{4}{7}x+\dfrac{27}{7} \cdots (1)[/tex]

The standard form of a line equation is
Ax + By = C

We can convert equation (1) to standard form by tweaking it

The area of the circle having a radius of 10 ft will be 100π.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the circle in a two-dimensional plane is called the area of the circle.

Given that the radius of the circle is 10 ft. The area of the circle is calculated by the formula written as below,

Area of the circle = πr²

Substitute the value of the radius in the formula and calculate the area of the circle.

Area of the circle = πr²

Area of the circle = π x ( 10 ) ²

Area of the circle = 100π square ft

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The pair of variables "laptop price ($) and memory capacity (GB)" are two different scales of measure.

What is the variable?

A variable is a quantity that may be changed according to the mathematical problem. The generic letters which are used in many algebraic expressions and equations are x, y, z. In other words, a variable is a symbol for a number where the value is not known. For example, x + 5 = 10. Here “x” is a variable.

This is because "laptop price" is measured in dollars, which is a monetary unit, and "memory capacity" is measured in GB (gigabytes), which is a unit of data storage.

These are two different types of measurement and cannot be directly compared.

On the other hand, "a number of goals scored" and "penalty minutes" are both measures of performance in a sport and can be directly compared.

"Height" and "IQ" are both measures of human characteristics, although they are different in nature, but they can also be compared.

"lipstick shades" and "brands of athletic shoes" are both consumer products, but they are not directly related and cannot be compared.

Hence, The pair of variables "laptop price ($) and memory capacity (GB)" are two different scales of measure.

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The conditional probability that the couple gives the correct answer if the husband and wife agree is p = .6 and if husband wife don't agree is p=0.5, and statement B is the better strategy.

Option B, have them both consider the question, and then either give the common answer if they agree or, if they disagree, flip a coin to determine which answer to give is the better strategy.

c.) The conditional probability that the couple gives the correct answer if the husband and wife agree is p = .6.

d.) The conditional probability that the couple gives the correct answer if the husband and wife disagree is 0.5. This is because in this case, they must flip a coin to decide which answer to give.

Since the probability of both parties giving the correct answer is p = .6, but the probability of either party giving the correct answer is only 0.5,

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