solve the following system {y=x^2-3 and {y=3x-3 graphically and algebraicallyPLEASE HELP ME IM BEGGING

On dividing we get 69/2 or 34.5 as remainder.

In algebra, the factor theorem is a theorem linking factors and zeros of a polynomial. It is a special case of the polynomial remainder theorem. The factor theorem states that a polynomial f(x) has a factor if and only if f=0.

Long division is best suited for such expressions:-

On applying long division and factor theorem we get

2x²+7x-39 = (2x - 1/2)(x-7) + 69/2

Thus on dividing we get 69/2 or 34.5 as remainder.

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Answer:

15^6

Step-by-step explanation:

According to BODMAS

where;

B - Bracket ()

O - Off (*)

D - Division (/)

M - Multiplication (*)

A - Addition (-)

S - Subtraction (+)

Bracket should be solved first

therefore;

(3*5)^6

15^6 = 11390625

Which can be approximately in standard form written as 1.1*10^7

Answer:

[tex]154 $\ m^2[/tex]

Step-by-step explanation:

If 88 m of long rope is wrapped twice around the base of the drum, the circumference of the drum is 44m. We can use this information to find the radius of the base.

The equation for circumference is [tex]C=2\pi r[/tex]. We can substitute the value we found for circumference into the equation:

[tex]44=2\pi r[/tex]

Divide both sides by 2

[tex]22=\pi r[/tex]

Divide both sides by π

[tex]r=\frac{22}{\pi}[/tex]

The area of a circle is [tex]A=\pi r^2[/tex]. We can substitute the value we found for the radius into the equation:

[tex]A=\pi (\frac{22}{\pi})^2\\[/tex]

[tex]A=\pi (\frac{22}{\pi})(\frac{22}{\pi})[/tex]

[tex]A=22*\frac{22}{\pi}[/tex]

[tex]A=\frac{484}{\pi}[/tex]

[tex]A\approx154[/tex]

Based on the given parameters, the length of the missing length in the triangle is 12 units

The given triangle is an scalene triangle

Scalene triangles are triangles that have unequal three sides

The missing side is x, and the value of x is calculated using the following equivalent ratios

We have

4 : 8 = 6 : x

Express the above equation as a fraction

4/8 = 6/x

Evaluate the quotient

0.5 = 6/x

Solve for x

x = 6/0.5

Evaluate the quotient

x = 12

Hence, the length of the missing length is 12 units

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For sp3d hybridized central atoms, the only possible molecular geometry is trigonal bipyramidal.

Hybridisation (or hybridization) is a process of mathematically combining two or more atomic orbitals from the same atom to form an entirely new orbital different from its components and hence being called as a hybrid orbital.

In this case, if all the bonds are in place, the shape is also trigonal bipyramidal.

In chemistry, a trigonal bipyramid formation is a molecular geometry with one atom at the center and 5 more atoms at the corners of a triangular bipyramid.

Bond angle(s): 90°, 120°

Coordination number: 5

Point group: D3h

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By direct comparison and definition of line segment  we notice that the point (x, y) = (- 6, 0) lies on the line segment AB as each AP is a multiple of former. (Correct choice: C)

According to linear algebra, a point lies in a line segment if its vector is a multiple of the vector that generates the line segment itself, that is:

AB = k · AP        (1)

The vector that generates the line segment is:

AB = (2, 6) - (- 2, 3)

AB = (4, 3)

And the vectors related to each point are:

Case A

AP = (- 2, 12) - (- 2, 3)

AP = (0, 9)

Case B

AP = (6, 12) - (- 2, 3)

AP = (8, 9)

Case C

AP = (- 6, 0) - (- 2, 3)

AP = (- 4, - 3)

Case D

AP = (- 6, 6) - (- 2, 3)

AP = (- 4, 3)

By direct comparison and definition of line segment  we notice that the point (x, y) = (- 6, 0) lies on the line segment AB as each AP is a multiple of former. (Correct choice: C)

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There are only 13 multiples of both 3 and 5, since

[tex]200 = 3\cdot5\cdot13 + 5[/tex]

From these integers, we eliminate any that are also divisible by 4 or 7.

[tex]3\cdot5\cdot4 = 60 \implies \{60,120,180\}[/tex]

[tex]3\cdot5\cdot7 = 105 \implies \{105\}[/tex]

so there are 13 - 4 = 9 such integers.

Answer:

£13.75

Step-by-step explanation:

→ Call the charge x

x

→ Multiply by 16

16x

→ Equate to total

16x = 220

→ Divide both sides by 16

x = £13.75

[tex]m = \frac{ - 1}{a} = \frac{ - 1}{2} \\ y = \frac{ - 1}{2} x + b[/tex]

The points if the slope is 4 and the point is (1,-1) are (1,-1) and (2, 3)

Linear equations are equations that have constant average rates of change, slope or gradient

The given parameters are:

Slope = 4

Point = (1, -1)

The slope of 4 means that as x changes by 1, the value of y changes by 4

This means that, we have:

(x + 1, y + 4)

Substitute the known values in the above equation

(1 + 1, -1 + 4)

Evaluate

(2, 3)

Hence, the points if the slope is 4 and the point is (1,-1) are (1,-1) and (2, 3)

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Answer:

b 19.2

Step-by-step explanation:

a = [tex]\pi[/tex][tex]r^{2}[/tex] for a circle.  We do not want to find the area for a whole circle.  We only want to find the area for part of a circle.  a hole circle is 360 degrees.

a = [tex]\frac{88}{360}[/tex][tex]\pi[/tex][tex]r^{2}[/tex]

a = [tex]\frac{88}{360}[/tex][tex]\pi[/tex]([tex]5^{2}[/tex])

a = 19.2 rounded.

The area of the sector of circle is b. 19.20 square meter.

The space enclosed by the sector of circle is called area of the sector of circle.Mathematically,

Area of the sector of circle, A = θ/360πr²

where θ is the angle of the arc and r is the radius of the circle.

Now it is given that,

radius of the circle, r = 5m

Angle of arc, θ = 88°

Therefore, area ofsector of circle A = θ/360πr²

Put the values,

A = 88/360 π 5²

Solving the equation we get

A = 19.20 square meter.

Hence,the area of the sector of circle is b. 19.20 square meter.

So  the correct answer is b.) 19.20 square meter.

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Answer:

5/4

Step-by-step explanation:

(5/8)(2/1)

(Reciprocal of 1/2 is 2/1 as shown above)

(5)(2)/(8)(1)=10/8

10/8=5/4

The solution accurate to equation within [tex]10^{-2}[/tex] for [tex]x^{4}-2x^{3} -4x^{2} +4x+4=0[/tex] lies in [0,2].  

Given the equation  [tex]x^{4}-2x^{3} -4x^{2} +4x+4=0[/tex] and range is  [tex]10^{-2}[/tex].

We are required to find the interval in which the solution lies.

The attached table shows the iterations. At each step, the interval containing the root is bisected and the function value at the mid point of the interval is found. The sign of its relative to the signs of the function values at the ends of the interval tell which half interval contains the root. The process is repeated until the interval width is less than [tex]10^{-2}[/tex].

Interval:[0,2], signs [+,-],mid point:1, sign at midpoint +.

[1,2]                                                       3/2

[1,3/2]                                                    5/4

The rest is in the attachment. The listed table values are the successive interval mid points.

The final midpoint is 181/128=1.411406.

This solution is within 0.0002 of the actual root.      

Hence the solution accurate to equation within [tex]10^{-2}[/tex] for [tex]x^{4}-2x^{3} -4x^{2} +4x+4=0[/tex] lies in [0,2].

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Answer: 11 units

Step-by-step explanation:

We can say that [tex]\triangle TSQ\sim\triangle PSR[/tex] by AA Similarity Postulate. This is since [tex]\angle T\cong\angle P[/tex] and both ∠TSQ and ∠RSP are right angles, making them congruent.

Similar triangles have a property that corresponding sides are proportional. Hence, we can say that

[tex]\frac{ST}{PS}=\frac{SQ}{SR}\\\frac{15}{PS}=\frac{9}{12}\\\frac{15}{PS}=\frac{3}{4}\\60=3*PS\\PS=20[/tex]

We also know that PS is the combined length of PQ and QS. Since we know that QS is 9, let's substitute PQ + 9 in and solve.

[tex]PQ+9=20\\PQ=11[/tex]

The Distance - Time graph that represents that represents Charlie's trip is attached accordingly.

A distance-time graph can be used to illustrate the distance traveled by an item moving in a straight line.

The gradient of the line in a distance-time graph equals the speed of the item. The quicker the item moves, the higher the gradient (and the steeper the line).

Some of the uses of the distance-time graph are;

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Answer:

2

Step-by-step explanation:

The trick here is to reduce each of the bases to lowest form first

[tex]12 = 3.4 = 3 .2.2 = 3.2^{2}\\12^{3} = (3.2^{2} )^{3} = 3^{3}2^{6} \\6 = 3.2\\6^{5} = (3.2)^{5} = 3^{5} .2^{5} \\\\Numerator = 3^32^63^52^5 = 3^82^{11}\\Denominator computation\\9 = 3^2\\9^{4} = (3^{2} )^4 = 3^{8} \\Denominator = 3^82^{10} \\\\\frac{Numerator}{Denominator } =\frac{{3^8}{2^{11} }}{3^82^{10}} = \frac{2^{11}} {2^{10}} = 2^1 = 2[/tex]  

The measure of the angle <JKL is 56 degrees

The theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.

Given the following parameters

m<IL = 112 degrees

Since the measure of the vertex is half the measure of its intercepted arc, hence;

<JKl = 1/2(m<IL)

Substitute the given parameters into the formula to have;

<JKl = 1/2(112)

<JKL = 56 degrees

Hence the measure of the angle <JKL is 56 degrees

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Answer:

Option D is correct.

No solution

Step-by-step explanation:

2(x+7)=8

Apply 2 into bracket:

2x+14=8

2x=8-14

2x=-6

Divide both sides by 2:

x=-3

hence here is no option for x=-3, so answer is no solution.

Answer:

Jamie is currently 15.

Step-by-step explanation:

Answer:

127

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

We need to use a technique called dot multiplication. In this technique, we multiply the magnitude of two given vectors by the value of the angle between them.

In the question, the value of the angle between two vectors [tex]cos(45^0)[/tex] and the coordinates of the two vectors are given. Let's multiply them by the dot product to get the result.

Formula: [tex]u.v=|u||v|cos(a)[/tex]

[tex]u=3i+2j[/tex]
[tex]v=i+5j[/tex]
[tex]cos(a)=\frac{1}{\sqrt{2}}[/tex]

To find the magnitude of a vector, we square the coordinates, add them up and take the square root of the result.

Result: [tex]u.v=|\sqrt{(3^2)+(2^2)}||\sqrt{(1^2)+(5^2)}|.\frac{1}{\sqrt{2}}=(13\sqrt{2})\frac{\sqrt{2}}{2} =13[/tex]

I think it is 2, 0, 4 but it would be very helpful if you put in an image of the graph.

Have a great day :D

Answer:[tex]\Large\boxed{x=12~;~y=18}[/tex]

Step-by-step explanation:

Given a system of equations

[tex]1)~\frac{x}{y} =\frac{2}{3}[/tex]

[tex]2)~\frac{y}{24} =\frac{3}{4}[/tex]

Multiply 24 on both sides of 2) equation to isolate y-value

[tex]\frac{y}{24}\times24 =\frac{3}{4}\times24[/tex]

[tex]\Large\boxed{y=18}[/tex]

Substitute the y-value into the 1) equation

[tex]\frac{x}{18} =\frac{2}{3}[/tex]

Multiply 18 on both sides of 1) equation to isolate y-value

[tex]\frac{x}{18}\times18 =\frac{2}{3}\times18[/tex]

[tex]\Large\boxed{x=12}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

The table of values for y=1/2x-1 is completed as follows:

x               y

-2             -2

-1            -3/2

0               -1

1             -1/2

2                0

3              1/2

Exactly one value from the set of second components of the ordered pair is connected with each value from the set of first components of the ordered pairs in a relation known as a function.

Given function:  y=1/2x-1

For x = -2

Value of y = -2

For x = -1

Value of y = 1/2(-1)-1 = -3/2

For x = 0

Value of y = 1/2(0)-1 =-1

For x = 1

Value of y = 1/2(1)-1 = -1/2

For x = 2

Value of y = 0

For x = 3

Value of y = 1/2(3)-1 = 1/2

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Answer:

A square matrix whose determinant is equal to zero is called singular matrix.

[tex]\huge \mathbb{ \underline{ANSWER:}}[/tex]

[tex]\leadsto[/tex] So the square matrix that has its det zero and its inverse is not defined is called a singular matrix.

[tex]\bold{Example:}[/tex]

[tex]\begin{bmatrix} \sf{3} & \sf{6} \\ \sf{2} & \sf{4}\end{bmatrix} \\ \\ \sf and \\ \begin {bmatrix} \sf{ 1} & \sf2 & { \sf2} \\ { \sf1} & { \sf2} & \sf{2} \\ \sf{3} & \sf {2} & \sf{1}\end{bmatrix}[/tex]

[tex]\huge \mathbb{ \underline{EXPLANATION:}}[/tex]

A singular matrix is a square matrix if its determinant is O. i.e., a square matrix A is singular if and only if det A = 0. The formula to find the inverse of a matrix is

▪ [tex] \bold{ {A}^{1} = \dfrac{1 \: }{det \:A } adj[A] }[/tex]

So if det A = 0 then the inverse of A will be not defined.

The minimum value of f(4) - f(1) is 6.

The maximum value of f(4) - f(1) is 12.

In the question, we are given that, 2 ≤ f'(x) ≤ 4 for all values of x.

Taking the given inequality as (i).

We are asked to find the minimum and maximum possible values of f(4) - f(1).

We multiply (i) by dx throughout, to get:

4dx ≤ f'(x)dx ≤ 5dx.

To find this, we integrate (i) in the definite interval [4, 1] with respect to dx, to get:

[tex]\int_{1}^{4}2dx \leq \int_{1}^{4}f'(x)dx \leq \int_{1}^{4}4dx\\\Rightarrow [2x]_{1}^{4} \leq [f(x)]_{1}^{4} \leq [4x]_{1}^{4}\\\Rightarrow 2*4 - 2*1 \leq f(4)-f(1) \leq 4*4 - 4*1\\\Rightarrow 6 \leq f(4) -f(1) \leq 12[/tex]

Thus, the minimum value of f(4) - f(1) is 6.

The maximum value of f(4) - f(1) is 12.

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Answer:

1.09575e+11

Step-by-step explanation:

We have

[tex]\displaystyle \int_{-2}^2 f(x) \, dx - \int_{-2}^{-1} f(x) \, dx = \int_{-1}^2 f(x) \, dx[/tex]

so that

[tex]\displaystyle \int_{-2}^2 f(x) \, dx + \int_2^5 f(x) \, dx - \int_{-2}^{-1} f(x) \, dx \\\\ ~~~~~~~~~~~~ =  \int_{-1}^2 f(x) \, dx + \int_2^5 f(x) \, dx \\\\ ~~~~~~~~~~~~ = \boxed{\int_{-1}^5 f(x) \, dx}[/tex]