Express 900 as a product of its prime factors in index form.
Write the prime factors in ascending order.

For given line segments RS = TR

In this question, we have been given two line segments QS and TU intersected at point R.

Also, we have been given QS = TU, QR = RU

We need to prove, RS = TR

We can observe that,

QS = QR + RS

and UT = UR + RT

QS = TU                               ................(Given)

QR + RS = UR + RT

QR + RS = QR + RT              .............(Given QR = RU )

QR + RS - QR = QR + RT - QR     .............(subtraction property of equality)

RS = TR

Hence proved.

Therefore, for given line segments RS = TR

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The maximum the company can expect for returned items is  $4190.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, The average daily profit of an electronics store is $27,235.

The company estimates that 15% is lost each day to returns.

∴ The amount of return is (15/100)×27135.

= 0.15×27125.

= $4068.

Now this has an error of ± 3%, therefore the maximum the company can expect for returned items is {(100 + 3)/100}×100

= 1.03×4068.

= $4190.

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By apply the law of cosine, the shortest length of wire needed is 180 feet.

In order to determine the shortest length of wire needed, we would apply the law of cosine because a mental image of the scenario described produces a right-angled triangle.

In Trigonometry, law of cosine (cos) is given by this mathematical expression:

C² = A² + D² - 2(A)(D)cosD

Note: Angle D = 90° + 32° = 122°

Substituting the given parameters into the formula, we have;

C² = 55² + 145² - 2(55)(145)cos122°

C² = 3,025 + 21,025 - 2(7,975)(-0.5299)

C² = 24,050 - (-8,451.905)

C² = 24,050 + 8,451.905

C² = 32,501.905

C = √32,501.905

C = 180.28 ≈ 180 feet.

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Answer: x=-1, y=2, z=-3

Step-by-step explanation:

[1]    2x + 3y - 4z = 16

  [2]    -x + 2y - z = 8

  [3]    2x - y - 2z = 2

Solve by Substitution :

Solve equation [3] for the variable  y

 [3]    y = 2x - 2z - 2

Plug this in for variable  y  in equation [1]

    2x + 3•(2x-2z-2) - 4z = 16

    8x - 10z = 22

Plug this in for variable  y  in equation [2]

    -x + 2•(2x-2z-2) - z = 8

      3x - 5z = 12

Solve equation [2] for the variable  x

 3x = 5z + 12

     x = 5z/3 + 4

Plug this in for variable  x  in equation [1]

   8•(5z/3+4) - 10z = 22

    10z/3 = -10

    10z = -30

Solve equation for the variable  z

    10z = - 30

   z = - 3

By now we know this much :

   x = 5z/3+4

   y = 2x-2z-2

   z = -3

Use the  z  value to solve for  x

   x = (5/3)(-3)+4 = -1

Use the  x  and  z  values to solve for  y

 y = 2(-1)-2(-3)-2 = 2

Answer:26.5

Step-by-step explanation:

There are 52 cards in the deck and so the probability of guessing the card right is 1/52.

Probability is simply the likelihood of something occurring. When we are uncertain about the result of an event, we might discuss the probabilities of several outcomes—how likely they are. Statistics is the study of occurrences guided by probability. The probability is a measure of the possibility that an event will occur. It assesses the event's certainty. P(E) = Number of Favourable Outcomes/Number of Total Outcomes is the probability formula.

Here,

We can find this probability by seeing that

=1/4×1/13

=1/52

Because there are 52 cards in the deck, the probability of correctly predicting the card is 1/52.

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Equation of the parabola with focus (-3,-3) and a directrix x=5 is given by x = (-1/16)(y² +6y -7).

As given in the question,

Focus of the parabola is equal to (-3, -3)

Directrix of the parabola is given by x = 5

Let (x, y) be the point on the parabola.

Distance between the (-3,-3) and (x, y) = Distance between (x, y) and x=5

⇒√(x +3)² + (y +3)² = | x -5|

⇒(x² +6x +9) +(y² + 6y +9) = (x-5)²

⇒x² +6x +y² +6y +18 = x² -10x +25

⇒y² +6y -7 = -16x

⇒x = (-1/16) (y² +6y -7) represents the equation of the parabola.

Therefore, equation of the parabola with focus (-3,-3) and a directrix x=5 is given by  x = (-1/16)(y² +6y -7).

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The required value of g(-4) = 1 in the given function is represented in the shown graph.

A graph can be defined as a visual representation or a diagram that represents data or values.

The function is given in the represented graph of g(x)

We have to determine the value of g(-4) of the given function in the graph

According to the given graph, we can see that the value of the domain of the given function g(x) when the value of variable x is -4 when the value of the variable y is 1. this means the value of g(-4) = 1.

Therefore, the required value of g(-4) = 1 in the given function is represented in the shown graph.

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Answer:

B (-2,-20)

Step-by-Step Explanation:

f(x)=3x^2 + 12x - 8

a=3 b=12

x=-12/2*3

x=-2

f(x)=3(-2)^2 + 12x - 8 , x=-2

f(-2) = -20

solution (-2,-20)

A statistically significant finding indicates that it is unlikely to just be explained purely by chance or random influences.

The notion that a set given observed data is not the result of random but can instead be linked to a specific cause is referred to as statistical significance.

Statistical significance indicates that a result is unlikely to be attributed purely by chance and random causes.

Thus, in other words, if there is no genuine effect in a research study, a statistically significant conclusion has an extremely low likelihood of occuring.

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The equation that represents this situation is t − 3 = 18. Tina is 21. The correct option is A.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Cole’s age is 3 years less than his sister Tina’s age, t. If Cole is 18.

The equation will be written as,

C = T - 3

18 = T-3

T = 18 + 3

T = 21 years

Therefore, the equation that represents this situation is t − 3 = 18. Tina is 21. The correct option is A.

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The standard form of a parabola passing through (1, 0), (2, -3), and (3,-10) is y = -2x² + 3x - 1

Define Parabola

The equation of parabola in standard form is y = ax² + bx + c

We have given the points,

(1, 0), (2, -3), and (3,-10)

Let's put each point in parabola equation and form three equation as,

Equation for point (1, 0)

0 = a * (1)² + b * 1 + c

a + b + c = 0                --------------------eq(i)

Now, equation for point(2, -3)

-3 = a * (2)² + b * 2 + c

4a + 2b + c = -3           --------------------eq(ii)

And, equation for point (3, -10)

-10 = a * (3)² + b * 3 + c

9a + 3b + c = -10         ---------------------eq(iii)

Now, we have three equation let's put them together

a + b + c = 0                --------------------eq(i)

4a + 2b + c = -3           --------------------eq(ii)

9a + 3b + c = -10         ---------------------eq(iii)

Now, form equation which is of two variable.

For that, we take first two equation and subtract eq(ii) from eq(i)

4a+2b+c = -3

a + b + c = 0

-    -     -      -

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

3a + b = -3                      ---------------eq(a)

Now, subtract eq(iii) from eq(ii)

9a + 3b + c = -10

4a + 2b + c = -3  

-     -        -      -

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

5a + b  = -7                   ------------------eq(b)

Now, we get eq(a) and eq(b) consist of two variable.

3a + b = -3                       ---------------eq(a)

5a + b  = -7                      ----------------eq(b)

Now, solve this equation simultaneously and find the value of a and b.

3a + b = -3

5a + b  = -7  

-     -        -

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

-2a = 4

a = -2

put a = -2 in eq(a) to find b

3a + b = -3

⇒3 * -2 + b = -3

⇒-6 + b = -3

⇒b = 3

We get the values of a and b. And, left with value of c for that just put the a and b value in eq(i) and find c

a + b + c = 0

-2 + 3 + c = 0

c = -1

Now, we get all the necessary values for equation.

Next, just put a, b and c values in parabola equation.

y = ax² + bx + c

y = -2x² + 3x - 1

Hence, the standard form of a parabola passing through (1, 0), (2, -3), and (3,-10) is y = -2x² + 3x - 1

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Answer: (X^3)*y

:) Hope this helps, I spent a lot of time on it!

Answer:

It's either 1:3 or 1:3

Step-by-step explanation:

A scale factor is times, calculate and, a reinduced PEMDAS

Linear Regression analysis has three key applications:

(1) evaluating predictor strength, (2) anticipating an effect, and as well (3) trend forecasting.

Linear regression is a fundamental and widely used method of predictive analysis. The overall goal of regression is to investigate two things:

Regression analysis has three key applications:

The formula y = c + b*x defines the simplest form of the regression equation with one dependent so one independent variable,

where,

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Answer:

x=-5/2

Step-by-step explanation:

x=-5/2

Answer:

12x+4=20x+24

Add negative 4 to both sides

6x+9=4x-3

Add -9 to both sides

-5x/4=4 Multiply both sides by 04

-4(5x-7)=-18 Distribute -4 on the left side

Step-by-step explanation:

12x+4=20x+24

Add negative 4 to both sides

6x+9=4x-3

Add -9 to both sides

-5x/4=4 Multiply both sides by 04

-4(5x-7)=-18 Distribute -4 on the left side

Yes, it is correct. (a) congruent by SSS

                             (b) congruent by SAS

                             (c) congruent by ASA

(a) Given in figure,

    MN = OP

    ∠MNO = ∠NOP

    ON = ON (Common)

   Hence, ΔMNO ≅ ΔNOP by SAS.

(b) Given in figure,

     UV = XY

    ∠UVW = ∠XYZ

    UW = XZ

   Hence, ΔUVW ≅ ΔXYZ by SAS.

(C) Given in figure,

     ∠ABC = ∠EDF

     BC = DE

    ∠ACB = ∠DEF

   Hence, ΔABC ≅ ΔDEF by ASA.

Therefore, all are congruent.

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As stated in the preceding statement the point R is collinear with points A and B.

An axis is a term used to describe a line upon whatever points are located, particularly if that line is connected to a triangle or other geometric shape. Since two factors determine a line, two points become trivially collinear.

Two lines may coincide if they have a same point and have the same slope. To put it another way, if A, B, as well as C are three points there in XY plane, they will all lie on a line, or three points will be collinear, but only if AB's slope and BC's slope are both equal.

then

m A B = m BC ( = m AC ).

The point is collinear with points A and B.

Therefore, the correct answer is option (d) R.

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For 8 pounds of weight, the charges be the same for both the companies.

Given, that To ship an overnight package

Shipping Company A charges $14 plus $2.25 per pound

Shipping Company B charges $20 plus $1.50 per pound

Let, the weight be w

And the cost of shipment by company A & B be A(w) & B(w) respectively.

According to the question,

A(w) = 14 + 2.25w

B(w) = 20 + 1.50w

Now, when charges be the same

A(w) = B(w)

14 + 2.25w = 20 + 1.50w

On subtracting 1.50w on both the sides, we get

14 + 2.25w - 1.50w = 20 + 1.50w - 1.50w

14 + 0.75w = 20

Now on subtracting 14 on both the sides, we get

14 + 0.75w - 14 = 20 - 14

0.75w = 6

On dividing both the sides by 0.75, we get

0.75w/0.75 = 6/0.75

w = 8

Hence, weight = 8 pounds.

For 8 pounds of weight, the charges be the same for both the companies.

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The value of x in the remote angles of the triangle  is 22.

The exterior angle theorem states that the measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles.  

In other words the sum of the remote interior angle is equals to the external angle.

Therefore,

110 = 3x + 2x

110 = 5x

divide both sides by 5

110 / 5 = 5x / 5

x = 22

Therefore, using exterior angle theorem, the value of x is 22.

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The simple interest on the loan of $600 at rate of 8% over a time period of 16 months is $664 and the interest generated is $64

The formula for simple interest helps you find the interest amount if the principal amount, rate of interest and time periods are given.

Simple interest formula is given as:

S.I = P(1 + rt)

Substituting the values into the formula

S.I = 600(1 + 0.08 * 16)

S.I = 664

The interest generated is $64

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Translation: What is the interest generated by $600, placed at 8% per year for 1 year 4 months?

The amount of water after x minutes is equal in both pools.

What is a Linear equation in one variable?

A univariate linear equation is an equation of the form ax + b = 0, where a and b are two integers, x is a variable, and there is only one solution.

For example, 2x+3=8 is a linear equation in one variable.

The given equation is 5000 - 50x = 4800 - 30x.

solving for 'x',

                        5000 - 50x = 4800 - 30x

                        5000 - 4800 = 50x - 30x

                        200 = 20x

                        x = 200/20

                        x = 10

The amount of water after 10 minutes in Pool A will be = 5000 - 50(10)

                                                                                           = 5000 - 500                                                                                                                                              

                                                                                           = 450 liters

The amount of water after 10 minutes in Pool B will be = 4800 - 30(10)

                                                                                           = 4800 - 300                                                                                                                                              

                                                                                           = 450 liters.

Hence, the amount of water will be the same in both pools.

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The train takes 6 hours to travel the same distance.

From the question, we have

A train with 20km per hour takes 3 hours  to travel the distance .

Another train with 10km per hour takes = (3*20)/10 hours

=6 hours

Multiplication:

Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.

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The possible value of x which the two triangles are similar is x=60°.

What do you mean by triangle?

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

Method:

Given that two angles of the triangle are specified, the triangles can be

similar for only one value of x.

According to the given data in the question,

The two triangles are similar when we have;

x + 10° = 2x - 50°

Which gives;

2x - x = 50° + 10° = 60°

x = 60°

Checking gives;

x + 10° = 2·x - 50° = 70°

Two angles of the first triangle are 70° and 60°

Then, the third angle of the first triangle is (180° - (70° + 60°)) = 50°

The three angles of the first triangle are therefore; 70°, 60° and 50°.

Two angles of the second triangle are 70° and 70°.

The third angle of the second triangle is (180° - (70° + 70°)) = 40°

The three angles of the second triangle are therefore; 70°, 70° and 40°

Therefore, the two triangles are similar by AAA similarity.

The two triangles are similar when, x = 60°

When x = 50°, we have;

x + 10° gives;

50° + 10° = 60°

∴ ∠(x + 10°) = 60°

The two angles of the first triangle are; 60° and 50°

The third angle on the second triangle is 180° - (60° + 50°) = 70°

On the second triangle, we have;

2·x - 50° gives;

2 × 50° - 50° = 50°

∴∠(2·x - 50°) = 50°

Therefore, the two angles of the second triangle are 70° and 50°

The third angle on the second triangle is 180° - (70° + 50°) = 60°

Therefore, the two triangles are not similar when x = 50°

Similarly, the two triangles are not similar when x + 10° = 50°

Hence, the possible value of x which the two triangles are similar is x = 60°.

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Answer:

40.5w + 118.37= 239.87; w=3

Step-by-step explanation:

You already saved 118.37.

239.87

118.37

111.50

40x3=120. So you'll need 3 more weeks to buy a gaming chair. And you also get 8.50 dollars extra in profit.

Answer:

40.5w + 118.37= 239.87; w=3

Step-by-step explanation:

Answer:

(-1,4) (-3,0)

picture below (im assuming you meant x^2.)

if you meant x2, please look at the second image

FIRST PHOTO = y=x^2 + 6x + 9 & y=2x+6

SECOND PHOTO = y=x2 + 6x + 9 & y=2x+6

Answer: The phone was £120 before the discount.