EX 2
QUAD ABCD is a rectangle with
diagonals that intersect at point P.
AC = 4x-13 and DP = x + 7. Find the
value of 'x'.

To convert the log2 to log10, we can use the convert of base formula for logarithms. The change of base formula for logarithms is as written:

log b(x)=logc(x) / logc(b)

By Using this formula, we can convert or find log base 2 to log base 10, where log base 10 is called the common logarithm, and we denote log10 (x) as log(x). The change of base formula gives the following:

log2(x)=log10(x)/log10(2) = log(x)/log (2)

This gives us the formula we can use to convert a logarithm with base 2 to a common logarithm with base 10.

The log function of e to the base 10 is denoted as “log 10 e”. Where the value of e is 2.7182818. The natural log function of e is presented as “log e e”.

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Answer: The vertex form of a parabola is:

y = a(x - h)^2 + k

Where (h, k) is the vertex of the parabola.

In this case, we are given that the vertex is (1, -2), so the equation of the parabola will be:

y = a(x - 1)^2 - 2

We know that the parabola passes through (0, -5), and it is given by the equation.

-5 = a(0 - 1)^2 - 2

so,

a = 1/3

The final equation of the parabola is :

y = 1/3(x-1)^2 - 2

so, the points that are on the parabola are:

A. (2,-3)

B. (-1,-14) is not true,

y = 1/3 (-1 -1)^2 - 2 = -1/3 + 2 = 1/3 ≠ -14

C. (3,2)

D. (2,-5)

E. (3,-14) is not true

y = 1/3 (3-1)^2 - 2 = -4/3 ≠ -14

F. (-2,7) is not true

y = 1/3 (-2-1)^2 - 2 = -7/3 + 2 = -1/3 ≠ 7

Therefore A, C and D are the correct answers.

Step-by-step explanation:

The value of the given expression 4x(3-x)+5x(x-2) when x = -3 is 3.

A phrase is considered a mathematical expression if it contains at least two numbers or variables and one or more mathematical operations.

A number is 6 more than half of the other number, which is x.

This statement is represented by the mathematical equation x/2 + 6.

So, we have the expression:

4x(3-x)+5x(x-2)

Now, the value of the expression when x = -3.

Insert values and calculate as follows:

4x(3-x)+5x(x-2)

4(-3)(3-(-3))+5(-3)((-3)-2)

-12(6)-15(-5)

-72 + 75

3

Therefore, the value of the given expression 4x(3-x)+5x(x-2) when x = -3 is 3.

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Correct question:

What is the value of the expression 4x(3-x)+5x(x-2) for x=(-3)​?

Answer:

[tex] \frac{7}{8} \times \frac{4}{5} = \frac{7 \times 1}{2 \times 5} \\ = \frac{7}{10} [/tex]

To solve the equation 5 = v + 29, you can subtract 29 from both sides of the equation. This will isolate the variable on one side of the equation and allow you to find its value.

The given equation is

5 = v + 29

Subtract 29 from both sides:

5 - 29 = v + 29 - 29

-24 = v

So the solution is v = -24.

So, we subtract 29 from both sides of the equation, this operation cancels out the addition of 29 from the variable v, and we get -24 = v. This means that -24 is the value that makes the equation true.

--The question is incomplete, answering to the question below--

"How do you solve 5 = v + 29?"

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The Law of Cosines can be used to calculate the angles of an isosceles triangle given three side lengths. Two of the angles are equal, while the third can be found by subtracting the two known angles from 180°.

Since you are given three sides of an isosceles triangle, you can use the Law of Cosines to calculate the angles of the triangle. The Law of Cosines states that for a triangle with side lengths a, b, and c and angle C opposite side c, the following equation holds:

c² = a² + b² - 2abcosC

Therefore, you can rearrange the equation to solve for angle C:

C = arccos((a² + b² - c²) / (2ab))

For an isosceles triangle, two of the angles will be equal, so you can calculate those two angles using the equation above, and the third angle can be found by subtracting the two known angles from 180°.

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2(l+w) + 4a and 2l+2w + 2(2a) are two equivalent expressions which represent the total fencing material required to surround the playground and flower beds.

Mathematical expressions are a way of representing mathematical ideas, concepts, and operations using symbols and notation. They can take many forms, including numbers, variables, and operators. They can also be combined to create more complex expressions, equations, and formulas.

Explain:

The total fencing material required to surround the playground and flower beds would be the sum of the fencing material for the playground and the fencing material for the flower beds.

So, one possible expression for the total fencing material required to surround the playground and flower beds would be: 2(l+w) + 4a

Another possible expression for the total fencing material required to surround the playground and flower beds would be: 2l+2w + 2(2a)

Please note that these expressions are based on the information provided, and the actual total fencing material required will depend on the specific dimensions of the park and playground, and may differ from these expressions.

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Therefore, for x = 45 and y = 20, the quadrilateral is a parallelogram.

In geometry a quadrilateral is a four-sided polygon, having four edges and four corners.

A polygon is a closed polygonal chain made up of a limited number of straight-line segments and is a type of planar figure in geometry. A polygon is an area that is bordered by a bounding circuit, a bounding plane, or both.

We know opposite sides of a parallelogram are equal in length and parallel. Given opposite sides of a parallelogram are:

(4x - 35) and (3x + 10)

(y + 15) and (2y - 5)

Now, setting those opposite sides equal to each other:

4x - 35 = 3x + 10 = >x = 45

y + 15 = 2y - 5 => y = 20

Therefore, x = 45 and y = 20, the quadrilateral is a parallelogram.

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Answer:

[tex]x=11[/tex]

Step-by-step explanation:

[tex]6x-3(x+8)=9\\6x-3x-24=9\\3x-24=9\\3x=33\\x=11[/tex]

Answer:

X=11

Step by step:

6x-3(x+8)=9

=6x-3x-24=9

=3x-24=9

      +24   +24

=3x=33

=3x/3=33/3

X=11

Answer: The first three odd prime numbers are 3, 5, and 7. A number is a multiple of two but not three of these prime numbers if it is divisible by two of them, but not the third.

To find the number of numbers between 1000 and 2000 that are multiples of two but not three of the first three odd prime numbers, we can count the number of multiples of each pair of prime numbers and subtract the number of multiples of all three prime numbers.

There are 200 multiples of 3 and 5 between 1000 and 2000 (200 numbers for each, for a total of 200 * 2 = 400). There are 133 multiples of 3 and 7 between 1000 and 2000 (133 numbers for each, for a total of 133 * 2 = 266). There are 80 multiples of 5 and 7 between 1000 and 2000 (80 numbers for each, for a total of 80 * 2 = 160). There are no multiples of all three prime numbers between 1000 and 2000.

Thus, the total number of numbers between 1000 and 2000 that are multiples of two but not three of the first three odd prime numbers is 400 + 266 + 160 = 826.

Step-by-step explanation:

Answer:

? ≈ 20°

Step-by-step explanation:

using the cosine ratio in the right triangle

cos ? = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{16}{17}[/tex] , then

? = [tex]cos^{-1}[/tex] ( [tex]\frac{16}{17}[/tex] ) ≈ 20° ( to the nearest degree )

Answer: x=4

Step-by-step explanation: x+3=2x-1, then you do simple algebra

The domain and range of function Y = 4x² are:

Domain: (-∞, ∞) {x | x ∈ R}

Range: [0, ∞) {y | y ≥ 0}

Now, According to the question:

What are the domain and range?

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

We have,

Y = 4x²

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation: (-∞, ∞)

Set-Builder Notation:  {x | x ∈ R}

The range is the set of all valid y values: [0, ∞)

Set-Builder Notation: {y | y ≥ 0}

Hence, the domain and range of function Y = 4x² are:

Domain: (-∞, ∞) {x | x ∈ R}

Range: [0, ∞) {y | y ≥ 0}

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The complete question is this:

What is the domain of the function Y = 4x²

According to the pattern Brett receives points as follows 5,10,15,20,25,30,35 and according to the pattern of Yolanda, Yolanda receives points as 25,60,95,130,165,200,235 .

What is recursion  ?

It is a process in which it calls itself to solve the given problem is called as recursion.

The recursive formula to find the nth term of a geometric sequence is:

an = an-1 * r for n ≥ 2

In Brett's case,

if n=2

a2 = a1 * r  

given a2 = 10 a1 =5

10 = 5 *d

d=2

a4 = a3 * d = 20*2 = 40

a5 = a4*d = 40*2 = 80

a6 = a5*d = 80*2 = 160

a7 = a6 * d = 160*2 = 320

In Yolanda case,

The recursive formula to find the nth term of an arithmetic sequence is:

an = an-1 + d for n ≥ 2

if n=2

a2 = a1 + d

60 = 25 + d

d = 35

a4 = a3+d = 95 + 35 = 130

a5 = a4+d = 130 + 35 = 165

a6 = a5+d = 165 + 35 = 200

a7 = a6 +d = 200 + 35 = 235

Hence the pattern in Brett's case could be 5,10,15,20,25,30,35 and in Yolando's case could be 25,60,95,130,165,200,235 .

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According to the pattern Brett receives points as follows 5,10,15,20,25,30,35 and according to the pattern of Yolanda, Yolanda receives points as 25,60,95,130,165,200,235 .

It is a process in which it calls itself to solve the given problem is called as recursion.

The recursive formula to find the nth term of a geometric sequence is:

an = an-1 * r for n ≥ 2

In Brett's case,

if n=2

a2 = a1 * r  

given a2 = 10 a1 =5

10 = 5 *d

d=2

a4 = a3 * d = 20*2 = 40

a5 = a4*d = 40*2 = 80

a6 = a5*d = 80*2 = 160

a7 = a6 * d = 160*2 = 320

In Yolanda case,

The recursive formula to find the nth term of an arithmetic sequence is:

an = an-1 + d for n ≥ 2

if n=2

a2 = a1 + d

60 = 25 + d

d = 35

a4 = a3+d = 95 + 35 = 130

a5 = a4+d = 130 + 35 = 165

a6 = a5+d = 165 + 35 = 200

a7 = a6 +d = 200 + 35 = 235

Hence the pattern in Brett's case could be 5,10,15,20,25,30,35 and in Yolando's case could be 25,60,95,130,165,200,235 .

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The exact value of secθ in simplest radical for is 1.083

Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.

We are Given θ is an angle in standard position.

Its terminal side passes through the point (12, -5).

To find the exact value of secθ in simplest radical form.

When θ is an angle in standard position and its terminal side passes through the point (x,y), then the exact value of secθ is:

So, we have x = 12 and y = -5 which is in the first quadrant.

Therefore,

r² = x² + y²

r² = ( 12 )² + ( -5 )²

r² = 144 + 25

r² = 169

r = 13

Then,

sec θ = 1/cosθ

sec θ = [ 1/(x/r) ]

sec θ = r/x

sec θ = 13/12

sec θ = 1.083

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Answer: We know that the trainer earns $2,456.75 every month, and she earns an extra $4.75 every time she sells a gym membership.

And last month she sold 32 gym memberships

We can calculate the total amount of money the trainer earned from selling gym memberships by multiplying the number of memberships sold by the amount earned per membership:

32 memberships * $4.75 per membership = $152.00

To find the total amount of money the trainer earned last month, we can add the amount earned from selling gym memberships to the amount earned from her salary:

$2,456.75 + $152.00 = $2,608.75

So, the total amount of money the trainer earned last month is $2,608.75

Step-by-step explanation:

To know if a triangle is a 30-60-90 triangle, you must check if the triangle's angles measure 30°, 60°, and 90°. Additionally, the sides of a 30-60-90 triangle will have a specific ratio. The longest side of the triangle is always double the length of the shortest side, and the side opposite the 60° angle is always the square root of 3 times the shortest side.

1. Measure the angles of the triangle.

2. Check if the angles measure 30°, 60° and 90°.

3. Measure the sides of the triangle.

4. Check if the longest side is double the length of the shortest side and if the side opposite the 60° angle is the square root of 3 times the shortest side.

To know if a triangle is a 30-60-90 triangle, you must check if the triangle's angles measure 30°, 60°, and 90°. Additionally, the sides of a 30-60-90 triangle will have a specific ratio. The longest side of the triangle is always double the length of the shortest side, and the side opposite the 60° angle is always the square root of 3 times the shortest side.

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Suzy randomly picks marbles from a bag containing 13 identical marbles. The possible outcomes of the given probability if she selects 9 marbles is:

259,459,200.

Randomness is commonly used to refer to an event's apparent or actual lack of pattern or predictability. Random events, symbols, or steps frequently occur in no particular order and do not adhere to any recognizable pattern or combination.

Germanic in origin, Randon is a name for boys. With a name that means "wolf shield," you can inspire baby Randon to embrace their sense of adventure. something or someone that is suspiciously out of the ordinary, unidentified, or unknown. a peculiar or erratic individual or thing. Something that is random lacks structure, direction, or intent. Like the random selection of lottery numbers or unplanned random events, it occurs entirely by chance.

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The percentage error is 16%

We know that the formula for the percentage error.

E = (absolute error / actual value) × 100

The formula for the absolute error is:

A = |actual value - experimental value|

A = |V1 - V2|

where V1 is the actual value

V2 is the experimental value

E is the percentage error

A is the absolute error

In this question, the experimental calculation of the specific heat of aluminum = 156 cal/g °C

And the actual specific heat of aluminum = 185 cal/g °C

Using above formula of absolute error,

A = |185 - 156|

A = 29 cal/g °C

And the percent error would be,

E = (absolute error / actual value) × 100

E = (29 / 185) × 100

E = 0.16 × 100

E = 16%

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By setting up the equation and solving we get the positive number is 2/5.

A positive number is a number greater than zero. In mathematical terms, it is a number that is greater than zero on the number line. Positive numbers are often represented with a "+" sign in front of them, but this is not always necessary as the positive sign is the default and is usually omitted.

An equation is a mathematical statement that asserts the equality of two expressions. It is a statement that asserts that the two expressions on either side of the "=" sign are equal and have the same value. The expressions on either side of the "=" sign are called the left-hand side (LHS) and the right-hand side (RHS) of the equation.

For example:

2x + 3 = 7

x(2x+x/2)=x

2x^2+x^2/2=x

5x^2/2=x

5x^2=2x

5x=2

x=2/5

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1(t) = 12(t) (2,2,4) +t(2,4,6) and Ia(t) = 12(t) (2,2,4) +t(2,4,6) represents the same line, as they are both equivalent to 12(t)(2,2,4) + t(2,4,6). So Option A is correct.

The equation of a line in 3-dimensional space can be represented in the form "r(t) = a + tb" where "r(t)" is a vector that represents any point on the line, "a" is a vector that represents a point on the line, and "b" is a vector that represents the direction of the line.

The given equations are:

1(t) = 12(t) (2,2,4) +t(2,4,6)

Ia(t) = 12(t) (2,2,4) +t(2,4,6)

As we can see that both equations are identical to equation 12(t) (2,2,4) +t(2,4,6) thus these three equations represent the same line.

The other given options B, C, and D are not equivalent to each other or to the original equation, thus they do not represent the same line.

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The slope of the line is 3 and the y-intercept is -5.

The slope of a line is the coefficient of the x term (in this case, 3). To calculate the y-intercept, we can plug in x = 0 and solve for y. Doing this, we get y = 0 + 3(0) + 5 = -5. Therefore, the slope is 3 and the y-intercept is -5.

The slope of a linear equation is found by looking at the coefficient of the x term. In this case, the coefficient of the x term is 3, so the slope of the line is 3. To find the y-intercept, we can plug in x = 0 into the equation and solve for y. Doing this, we get y = 0 + 3(0) + 5 = -5, so the y-intercept is -5. Therefore, the slope of the line is 3 and the y-intercept is -5. This equation is therefore a linear equation with a slope of 3 and a y-intercept of -5.

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The ordered triplet (x, y, z) or the following system of equations: x+3y + 2z = 1, 03x+y+5z=10, -2x-3y+z=7 is (-170/127, -89/127, 282/127).

Start with the first equation:

x + 3y + 2z = 1

Isolate x by subtracting 3y and 2z from both sides:

x = 1 - 3y - 2z

Substitute this expression of x into the second equation:

0.3x + y + 5z = 10

Substitute the value of x found in step 2 into this equation:

0.3(1 - 3y - 2z) + y + 5z = 10

0.3 -0.9y -0.6z + y + 5z = 10

0.1y + 4.4z = 9.7

y + 44z = 97

Solve for y by isolating it:

y = 97 - 44z

Substitute this expression of y into the first equation:

x + 3(97 - 44z) + 2z = 1

x + 291 - 132z + 2z = 1

Solve for x:

x = 130z - 290

Substitute this expression of x into the third equation:

-2(130z - 290) - 3(97 - 44z) + z = 7

-260z + 580 - 291 + 132z + z = 7

Solve for z:

127z = 282

z = 282/127

Substitute this value of z into the expression of y:

y = 97 - 44(282/127)

= -89/ 127

Substitute the values of z into the expression of x:

x = 130(282/127) - 290

= - 170/ 127

So the solution of the system of equations is: x = -170/127, y = -89/127, z = 282/127.

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Answer:

2(3n^2-4) and 6n^2-8

Step-by-step explanation:

There are two different answers but try at least both of them.

27 2/10

   or

27 1/5

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

Answer:

For Option A, the function rule would be:

totalAmountEarned(days) = 100 + 10*days

For Option B, the function rule would be:

totalAmountEarned(days) = 2^days

Step-by-step explanation:

The probability that the product will last for at least 1 wee and at most 2 week is 0.30.

This independent transmission of characteristics phenomenon can be explained by the product rule of probability. It claims that multiplying the odds of each event occurring alone will yield the probability of two independent events occurring together.

P(E F) = P(E) P(F) is the product rule, where E and F are independent events. Explain that independence means that the likelihood of one event occurring has no bearing on the likelihood of the other.

The probability that the product will last for at least 1 wee and at most 2 week is 0.30.

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The key features of the quadratic function y = -x² + 4x - 3 include the following: D) x-intercepts: (1, 0) and (3, 0), y-intercept: (0, –3), vertex: (2, 1).

In Mathematics, the y-intercept of any graph such as a quadratic function, generally occur at the point where the value of "x" is equal to zero (x = 0).

When x = 0, the y-intercept is given by;

y = -x² + 4x - 3

y = -0² + 4(0) - 3

y = -3

Therefore, the y-intercept of this quadratic function y = -x² + 4x - 3 is given by the ordered pair (0, -3).

In Mathematics, the x-intercept can be defined as the point at which the graph of a quadratic function crosses the x-coordinate and the value of "y" is equal to zero (0).

By critically observing the graph of this quadratic function y = -x² + 4x - 3, the x-intercept include the following:

In conclusion, the vertex of this quadratic function y = -x² + 4x - 3 is (2, 1).

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Answer:

5 ( or ) - 5

Step-by-step explanation:

12/3 = 4

240/4 = 60

m² + 35 = 60

m² = 60 - 35

m² = 25

m = - 5 ( or ) 5

Because,

( - 5 )² = - 5 * - 5 = 25

5² = 5 * 5 = 25