Leeann wants to buy a new tablet that costs $500. She has already saved 25% of the money. How much additional money does Leeann need to save to
have enough money to buy her tablet?

a.125$
b.150$
c.350$
d.375$

Matrix B and AB both are invertible implies that A is invertible as a matrix C such that AC = CA = I.

For matrix A to be invertible,

Show that there exists a matrix C such that AC = CA = I,

where I is the identity matrix.

Since B and AB are both invertible,

There exist matrices D and E such that ,

BD = DB = I

And ABE = EAB = I.

Multiplying both sides of the equation ABE = I by D on the left and E on the right, we get,

ADEBE = DE

Since BD = I, we can simplify this to,

ADE = DE

Multiplying both sides of this equation by B on the left and B^(-1) on the right, we get,

AD = DB^(-1)

Now, let C = DB^(-1).

Then we have,

AC

= ADB^(-1)

= ABEB^(-1)

= AI

= A

and

CA

= DB^(-1)A

= DB^(-1)ABE

= DI

= I

Therefore, A is invertible as a matrix C such that AC = CA = I.

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Answer:

3750

Step-by-step explanation:

3000 + 25% = 3750

as 25% of 3000 = 750, so 3000 + 750 = 3750

Answer:

q=24

Step-by-step explanation:

the opposite of division is multiplication so 4x6=24. then you check this by of course imputing your answer into the equation. 24 ÷ 6 =4

The width of the field is 95 feet

The length of the field is 950 feet

EXPLANATION

The perimeter of a rectangle can be calculated using the formula;

p = 2l + 2w

where P is the perimeter, l is the lenngth and w is the width.

Let l be the length of the rectangular field and w to represent the width of the rectangular field.

From the given question;

l= 10w

P =2090

Substitute the values into the formula given.

2090= 2(10w) + 2w

2090 = 20w + 2w

2090 = 22w

Divide both-side of the equation by 22.

Substitute the value of w into l=10w and evaluate.

l = 10(95)

l = 950

Hence, width is 95 feet and length = 950 feet.

Answer:

(2,-1)

Step-by-step explanation:

We can use substitution to solve this system of equations. Since x is already solved for in the second equation, we can substitute 2y + 4 for x in the first equation:

4(2y + 4) + 2y = 6

Simplifying the left side:

8y + 16 + 2y = 6

Combining like terms:

10y + 16 = 6

Subtracting 16 from both sides:

10y = -10

Dividing both sides by 10:

y = -1

Now that we know y, we can use the second equation to find x:

x = 2y + 4

x = 2(-1) + 4

x = 2

Therefore, the solution to the system of equations is (x, y) = (2, -1).

The correct answer choice is (2, -1).

The image you described features a number line that goes from 0 to 6.5 in increments of 0.5.

On this number line, there is an arrow that starts at 0 and extends to 2.5, and then continues from 2.5 to 5.

This image can be visualized as follows:

0        1        2        3        4        5        6        6.5

|--------|--------|--------|--------|--------|--------|--------|

        |------------------------|------------------------|

             0 to 2.5                 2.5 to 5

The vertical lines represent the increments of 0.5 on the number line, and the arrow indicates the segments from 0 to 2.5 and from 2.5 to 5.

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Answer: 22.4402

Step-by-step explanation:

Answer:

84.4% of 23 is 19.412.

Step-by-step explanation:

Let the unknown number be x.

Now, 84.4% of x = 19.412.

∴ (84.4 ÷ 100) × x = 19.412.

By simplifying the equation,

x = (19.412 × 100) ÷ 84.4

x = 1941.2 ÷ 84.4

∴ x = 23

Thus, 84.4% of 23 is 19.412.

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Answer:

  9.2

Step-by-step explanation:

You want the distance between A(2, 0) and B(0, 9).

The distance formula is based on the Pythagorean theorem. It tells you the distance between (x1, y1) and (x2, y2) is ...

  d = √((x2 -x1)² +(y2 -y1)²)

For the given points, this becomes ...

  d = √((0 -2)² +(9 -0)²) = √(4+81) = √85

  d ≈ 9.2

The distance between A and B is about 9.2 units.

The magnitude and direction of the force C are 93.853 pounds-force and  281.237°, respectively.

In this problem we find the case of a system at equilibrium and formed by 3 vectors, of which we must determine the magnitude and direction of a force must be determined. Vectors are described by two features: (i) Magnitude, (ii) Direction.

The magnitude is obtained by Pythagorean theorem:

F = √(x² + y²)

The direction is determined by inverse trigonometric functions:

θ = tan⁻¹ (y / x)

Besides, the system can be described physically by Newton's laws and mathematically by vector sum:

F₁(x, y) + F₂(x, y) + F₃(x, y) = (0, 0)

First, determine the vector associated to force C:

F₃(x, y) = - F₁(x, y) - F₂(x, y)

F₃(x, y) = - (- 92 · cos 45°, 92 · sin 45°) - (54 · cos 30°, 54 · sin 30°)

F₃(x, y) = - (- 46√2, 46√2) - (27√3, 27)

F₃(x, y) = (46√2, - 46√2) - (27√3, 27)

F₃(x, y) = (46√2 - 27√3, - 46√2 - 27)

Second, calculate the magnitude of force C:

F₃ = √[(46√2 - 27√3)² + (- 46√2 - 27)²]

F₃ ≈ 93.853

Third, determine the direction of force C:

θ = tan⁻¹ [(- 46√2 - 27) / (46√2 - 27√3)]

θ ≈ 281.237°

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Answer:

  F₃ = 94 lb at 78.8° below the +x axis

Step-by-step explanation:

You want the magnitude of force F₃ that makes the sum of forces be zero.

As you have already noted, the sum of forces is zero when the system is at equilibrium.

  F₁ +F₂ +F₃ = 0

  F₃ = -(F₁ +F₂)

The forces F₁  and F₂ can be added by adding their horizontal and vertical components.

  F₁ = 92(cos(135°), sin(135°)) ≈ (-65.0538, 65.0538)

  F₂ = 54(cos(30°), sin(30°)) ≈ (46.7654, 27)

Then the sum of forces is ...

  F₁ +F₂ ≈ (-18.2884, 92.0538) . . . . . sum of corresponding parts

As we noted above, F₃ is the opposite of the sum, so is ...

  F₃ = (18.2884, -92.0538)

The magnitude is found using the Pythagorean theorem:

  |F₃| = √(18.2884² +(-92.0538)²) ≈ √8808.3677 ≈ 93.8529

The magnitude of F₃ is about 94 lb.

The components of F₃ tell you the force is in the 4th quadrant. The ratio of the x- and y-components is the tangent of the angle:

  θ = arctan(y/x) = arctan(-92.0538/18.2884) = arctan(-5.03345)

  θ ≈ -78.763°

In the first attachment, the sum of forces F₁ +F₂ is shown by the black arrow. The direction of F₃ will be the opposite of that arrow's direction, so will be down to the right, about 78.8° below the +x axis. The second attachment shows the magnitude and direction of F₃, where 0° is the direction of the +x axis.

__

Additional comment

For finding the magnitude of the sum of two forces, the Law of Cosines is another way to do it. To use that, you need to know the angle between the two forces. That's the angle at lower right inside the triangle shown in the first attachment. It is 75°. Then the magnitude is ...

  |F₃| = √(54² +92² -2·54·92·cos(75°)) ≈ √8808.37 ≈ 93.853 . . . . lb

This math can be simpler than working with the x- and y-components of the forces.

The angle of F₃ is another matter. Finding that requires solving the force triangle for one of the other interior angles, then adding the angles in the appropriate way.

For example, the angle at the origin can be found from the Law of Sines as ...

  α = arcsin(92/93.853·sin(75°)) ≈ 71.237°

Adding this to the angle of the red vector (30°) gives the resultant angle relative to the +x axis of 101.237°. The direction of F₃ is opposite this, so is ...

  101.237° -180° = -78.763° . . . . as above

As you can see from the attachments, a vector calculator or spreadsheet is a useful tool for finding sums of forces from their magnitude and direction.

Just to be clear, the conversion between polar and rectangular forms is ...

  (x, y) = r(cos(θ), sin(θ))

  r = √(x² +y²)

  θ = arctan(y/x) . . . . . with attention to quadrant

Spreadsheets and some calculators have an ATAN2(x, y) function that takes the signs into account when it computes the angle. When working with angles, make sure the calculator's angle mode is set to degrees or radians appropriately. (Spreadsheets usually use radians.)

Step-by-step explanation:

well, what does the word "constant" tell you ?

e.g. "this is a constant reminder of ..."

a constant is steady and unchanging. always the same.

so, what could be the constant part/term in the expression ?

-3xy ? is that always the same value ? no matter what values you assign to x, y (and whatever other variables there might be in the system)?

or

10 ? is that always the same value, no matter what values are assigned to x, y, ... ?

there are no other parts/terms I can see here.

so, please use your common sense and pick the right one. you can do that !

this is so simple. to outright write the answer to this feels like an offense. also against your own intelligence.

Answer: The probability of choosing an ace or a club is 16.

Step-by-step explanation:

The number of strides the runner will make during 1 hour run will be =

10,800.

To calculate the distance or number of strides made by the runner in an

hour, the graph given above is considered as follows;

The y-axis which represents the number of strides is plotted against the x-axis which is the number of hours.

From the graph

20 minutes= 3600 strides

60 minutes = X strides

make X the subject of formula;

x= 3600×60/20

= 216000/20

= 10,800

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Answer:

Y=KX so its 10=K2

Step-by-step explanation:

Plug in the Number OR K=y/x

we can interpret the value of   \(m'(12) = -15\) as the instantaneous rate of change of the amount of milk in the tanker truck, which is decreasing by 15 gallons per minute at time  \(t = 12\) minutes.

The expression "m'(12)" represents the derivative of the function m(t) with respect to time t, evaluated at t=12. Geometrically, the derivative represents the instantaneous rate of change of the function at the point t=12.

In this case, m'(12) = -15 means that at the time t=12 minutes, the rate of change of the number of gallons of milk in the tanker truck is -15 gallons per minute. This indicates that the amount of milk in the truck is decreasing at a rate of 15 gallons per minute at time t=12.

To calculate m'(12), you need to take the derivative of the function m(t) with respect to t and then evaluate the result at t=12. Assuming you have the expression for m(t), the steps are as follows:

Differentiate m(t) with respect to t:

\(m'(t) = d/dt [m(t)]\)

Evaluate  \(m'(t) at t=12:\)

\(m'(12) = m'(t=12)\)

Therefore, we can interpret the value of   \(m'(12) = -15\) as the instantaneous rate of change of the amount of milk in the tanker truck, which is decreasing by \(15\) gallons per minute at time t = 12 minutes.

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Answer:

The range is 34!

Step-by-step explanation:

87-53=34

Answer:

34

Step-by-step explanation:

Hope this helps.

The values of a and b using the factor theorem for the polynomial f(x), we set f(1) and f(-1) equal to zero. Solving the resulting system of equations, we find that a = 12 and b = -1.

To find the values of a and b using the factor theorem, we need to use the given factors (x - 1) and (x + 1) and the fact that they are roots of the polynomial f(x).
The factor theorem states that if (x - c) is a factor of a polynomial, then f(c) = 0. Therefore, we can set x = 1 and x = -1 in the polynomial f(x) to get two equations.
First, let's substitute x = 1 into f(x):
f(1) = (1)^3 + a(1)^2 + b(1) - 12
f(1) = 1 + a + b - 12
Next, let's substitute x = -1 into f(x):
f(-1) = (-1)^3 + a(-1)^2 + b(-1) - 12
f(-1) = -1 + a - b - 12
Since (x - 1) and (x + 1) are factors, f(1) and f(-1) must equal zero. Therefore, we can set the two equations equal to zero and solve for a and b:
1 + a + b - 12 = 0
-1 + a - b - 12 = 0
Rearraning the equations, we have:
a + b = 11
a - b = 13
Now, we can solve this system of equations. Adding the two equations, we get:
2a = 24
a = 12
Substituting the value of a into one of the equations, we find:
12 - b = 13
b = -1
Therefore, the values of a and b are 12 and -1 respectively.

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Answer:

The square root of 22667121 is 69.

Step-by-step explanation:

can i get brainliest plz

Answer:

1st one x = BC/5 +9/5

2nd one x = AB/2 - 21/2

Step-by-step explanation:

If the length of the rectangle be (3x+2) units and width (4x+10)units then the area of the rectangle be \($x=-\frac{2}{3}, x=-\frac{5}{2}$$\).

The region enclosed by an object's shape is referred to as the area. The area of the shape is the area that the figure or any other two-dimensional geometric shape occupies in a plane.

A rectangle's sides determine its area. In essence, the length and breadth of the rectangle multiplied together gives the area of the rectangle.

Let the length of the rectangle be (3x + 2) units and width of the rectangle be (4x + 10)units.

Area of rectangle = length × breadth

= (3x +2) × (4x +10)

simplifying the above equation, we get

= (3x) × (4x +10) + 2(4x +10)

= 12x² + 30x +8x +20

12x² + 38x + 20 = 0

simplifying the above equation, we get

By using quadratic equation, then

\($x_{1,2}=\frac{-38 \pm \sqrt{38^2-4 \cdot 12 \cdot 20}}{2 \cdot 12}$$\)

simplifying the above equation, we get

\($$\begin{gathered}x_{1,2}=\frac{-38 \pm 22}{2 \cdot 12}\end{gathered}$$\)

Separate the solutions, we get

\($$\begin{aligned}& x_1=\frac{-38+22}{2 \cdot 12}, x_2=\frac{-38-22}{2 \cdot 12} \\& x=\frac{-38+22}{2 \cdot 12}:-\frac{2}{3} \\& x=\frac{-38-22}{2 \cdot 12}:-\frac{5}{2}\end{aligned}$$\)

The solutions to the quadratic equation are:

\($x=-\frac{2}{3}, x=-\frac{5}{2}$$\)

The complete question is:

Find the area of rectangle with length (3x+2) units and width (4x+10)units.

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i certify this question as an official h moment

Using the hypergeometric distribution, the probabilities are given as follows:

a) All 13 hearts: \(1.57 \times 10^{-12}\)

b) 13 cards of the same suit: \(6.30 \times 10^{-12}\)

c) Seven spades and six clubs: \(5.4 \times 10^{-9}\)

The formula is:

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are:

The general parameters in this problem are given as follows:

In item i, there are 13 hearts in a standard deck, hence k = 13 and the probability is P(X = 13), hence:

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}\)

\(P(X = 13) = h(13,52,13,13) = \frac{C_{13,13}C_{39,0}}{C_{52,13}} = 1.57 \times 10^{-12}\)

For item ii, we consider the same context of item i, just now we can consider any of the four types of cards, hence:

\(p = 4 \times 1.57 \times 10^{-12} = 6.30 \times 10^{-12}\)

For item iii, we want:

Hence the probability is given as follows:

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}\)

\(P(X = 7) = h(7,52,13,13) = \frac{C_{13,7}C_{13,6}}{C_{52,13}} = 5.4 \times 10^{-9}\)

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Answer:

13 units

Step-by-step explanation:

(8, -4) and (3,8)

To find the distance of two points, we use the distance formula:

\(d = \sqrt{(x_{2}-x_1)^2 + (y_2-y_1)^2 }\)

Let's plug in what we know.

\(d = \sqrt{(3 -8)^2 + (8 - (-4))^2 }\)

Evaluate the double negative.

\(d = \sqrt{(3 -8)^2 + (8 + 4)^2 }\)

Evaluate the parentheses.

\(d = \sqrt{(-5)^2 + (12)^2 }\)

Evaluate the exponents.

\(d = \sqrt{(25) + (144) }\)

Add.

\(d = \sqrt{(169)}\)

Evaluate the square root.

\(d = 13\)

13 units

Hope this helps!

Answer:

12

Step-by-step explanation:

a⋅(a+b)=  c⋅(c + d)                formula

9⋅(9+x)=  3⋅(3+60)

81+9x=3(63)

81+9x=189

-81       -81

9x=108

x=12

x = y² - 7 is the simplified inverse equation of the equation y = x² - 7.

Inverse function is a function which reverse one function to another.

If a function f takes the variable x to y, then the inverse of a function must takes y to x.

To get the inverse of the function, we have to interchange the variables.

Given equation is y = x² - 7

Now interchange the variable x to y and y to x,

we get  x = y² - 7

Hence, the required equation is x = y² - 7

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Answer:

False, x=6

Step-by-step explanation:

5x=30

Divide 5 on both sides

5/5 leaves x

30/5=6

Bring down x

x=6

Answer:

10 is your r

Step-by-step explanation:

The option (B) represents the derivative of y with respect to x option (B) is the correct choice.

The derivative of a function of a real variable in mathematics describes the sensitivity of the function value to a change in its argument.

We have:

\(\rm y= \dfrac{ln}{x^7}\right)\)

To find the derivative of y with respect to x differentiate with respect to x.

\(= \rm \dfrac{d}{dx}\left(\dfrac{ln}{x^7}\right)\)

Applying the divide rule:

\(\rm =\dfrac{\frac{d}{dx}\left(\ln \left(x\right)\right)x^7-\dfrac{d}{dx}\left(x^7\right)\ln \left(x\right)}{\left(x^7\right)^2}\)

\(\rm =\dfrac{\dfrac{1}{x}x^7-7x^6\ln \left(x\right)}{\left(x^7\right)^2}\)

\(\rm =\dfrac{1-7\ln \left(x\right)}{x^8}\)

Thus, the option (B) represents the derivative of y with respect to x option (B) is the correct choice.

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Answer:

But the 2lbs.

Step-by-step explanation:

Divide $9.19 by 2 and you get 4.595 which would be the cheapest option out of the 3 because the 1lb is $7.05 and the 3lb is $5.13.

You're welcome.

Answer:

system a

1)x=6

yh that's all I know srry

Answer:

D) X-12

Step-by-step explanation:

imagine that X = 2 or any number less than 12

A) 12 - X = 12 - 2 = 10

B) 12X = 12 ×2 = 24

C) X + 12 = 2 + 12 = 14

D) X - 12 = 2 - 12 = -10

So, the smallest number is (D)

Hope it's help.