Another engineer is tiling a new building. A square tile is cut along one of its diagonals to form two triangles with two congruent angles. What are the measurements of the interior angles of the triangles? Explain how you calculated them.

For this case we have by definition, the GFC of two numbers is given by the largest factor that divides both numbers without leaving residue.

We have the following expression:

[tex]3p ^ 4[/tex] and [tex]4p[/tex]

So, we look for the factors of 3 and 4:

3: 1.3

4: 1, 2, 4

Thus, the GFC of both numbers is "1".

The GFC of both expressions is: [tex]1p = p[/tex]

Answer:

p

its y-axis for the first answer and the other one its, y=-x

The line of reflection which maps the point K to K' and L to L' is Y axis.

Reflection is the transformation where the image is flipped.

Line of reflection is the line for which a figure has a mirror image over that line.

Given a triangle JKL.

Let the coordinate of the triangle be J(4, 5), K(5, 2) and L(2, 3).

When a coordinate (x, y) is reflected over the X axis, then the coordinates changes to (x, -y).

When a coordinate (x, y) is reflected over the Y axis, then the coordinates changes to (-x, y).

Here,

K(5, 2) changes to K'(-5, 2).

Here x coordinate changes sign.

So the line of reflection is Y axis.

Similarly, the line of reflection for the other transformation is also Y axis.

Hence the line of reflection is Y axis.

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Answer:

54

Step-by-step explanation:

234-126 = 108

108/2 = 54

Answer:

4 integers

Step-by-step explanation:

We are given with two fractions

3/2 = 1.5  and 21/4 = 5.25

Let us draw a number line first and then we plot these two numbers on them.

Please refer to the picture attached. Here we see the number line in black line , where the integers are starting with 0. We have plotted the numbers 1.5  and 5.25  in red.

We are asked to determine the number of integers that lies between 1.5 and 5.25.

The definition of integer says , the whole numbers which be negative also including 0.

Hence we can see that there are 4 whole numbers between 1.5 and 5.25 ,

2,3,4,5

Hence our answer is 4 integer

Answer:

24 units

Step-by-step explanation:

As we can see in the attached picture. The area will be given by the sum of the area of the rectangle and the area of the triangle in the bottom.

The rectangle has a base of 6 units and a height of 3 units. Therefore:

A1 = bh = 6*3 = 18 units.

The triangle has a base of 6 units and a height of 2 units. Therefore:

A2 = (1/2)bh = (6*2)/ 2 = 6 units

Then, the total area is:

A = A1 + A2 = 6 + 18 = 24 units

Answer:

18, 5, 2

Step-by-step explanation:

its pretty much X times 2 to find Y and to find X with Y you must divide Y by 2

Answer:

18, 5, and 2

Step-by-step explanation:

#1 Plug in 9 for x

y = 2(9)

y = 18

#2 Plug in 10 for y

10 = 2x

Divide by 2 on Both sides

5 = x or x = 5

#3 Plug in 1 for x

y = 2(1)

y = 2

Hope this helps!

Answer:x=1

Step-by-step explanation: 2x+8-6=4

                                              2x+2=4

                                                2x=2

                                                  x=1

Answer:

[tex]x = 1[/tex].

Step-by-step explanation:

Apply the associative property of addition to rewrite the left-hand side of the equation.

The two addition operators on the left-hand side are typically evaluated from left to right.

[tex](2x + 8) - 6 = 4[/tex].

However, by the associative property of addition, the second addition can be evaluated before the first:

[tex]2x + (8 - 6) = 4[/tex].

[tex]2x + 2 = 4[/tex].

Move all terms with the unknown ([tex]x[/tex] in this case) to one side of the equation and move all numbers to the other side. For example, add [tex]-2[/tex] to both side of this equation will move the number [tex]2[/tex] to the right-hand side.

[tex]2x +2 -2 = 4 - 2[/tex].

[tex]2x = 2[/tex].

Multiply both sides of the equation by [tex]1/2[/tex] to find the value of [tex]x[/tex].

[tex]x = 1[/tex].

The value of y from the given equation with x=2+i is y= 7(i+2).

The given equation is y= x²+3x+5.

We need to evaluate y from the given equation for x= 2+i.

A complex number is the sum of a real number and an imaginary number. A complex number is of the form a + ib and is usually represented by z. Here both a and b are real numbers. The value 'a' is called the real part which is denoted by Re(z), and 'b' is called the imaginary part Im(z).  Also, ib is called an imaginary number.

The alphabet i is referred to as the iota and is helpful to represent the imaginary part of the complex number. Further the iota(i) is very helpful to find the square root of negative numbers.

Now, put x= 2+i in y= x²+3x+5 and simplify.

That is, (2+i)²+3(2+i)+5

=4+i²+4i+6+3i+5

=15-1+7i

=7i+14

=7(i+2)

Therefore, the value of y from the given equation with x=2+i is y= 7(i+2).

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Answer:

7/12

Step-by-step explanation:

If the probability of winning a race is 5/12, the odds in favor of winning the race is 7/12.

Probability of winning a race: 5/12 or a 5 out of 12 chance.

12 - 5 = 7

Numerator = 7

The denominator would stay 12.

Denominator = 12

Therefore, the odds of winning the race is 7/12.

Answer:

-10x+18

Step-by-step explanation:

combine like terms.

The expression 8−4x+10−6x can be simplified by adding and subtracting similar terms. Add 8+10 which gets 18. Subtract -4x - 6x which gets -10x. So, the simplified expression is 18 - 10x.

The expression given is 8−4x+10−6x. In this expression, similar terms are grouped together to simplify it. By similar terms, we mean terms that involve the same variable raised to the same power. In this case, the similar terms are -4x and -6x (the 'x' terms) and 8 and 10 (the constant terms). So let's add and subtract these similar terms.

First, add 8 and 10 to get 18.

Secondly, subtract -4x - 6x. This gives you -10x.

So, the simplified form of your expression (8−4x+10−6x) is 18 - 10x.

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Answer: First Option

[tex]\frac{x(x-4)(x-1)}{2(x+4)}[/tex]

Step-by-step explanation:

We have the following expression

[tex]\frac{x^2-16}{2x+8}*\frac{x^3-2x^2+x}{x^2+3x-4}[/tex]

First factorize the denominators:

[tex]\frac{x^2-16}{2(x+4)}*\frac{x^3-2x^2+x}{(x+4)(x-1)}[/tex]

Now we factor the numerators

[tex]\frac{(x-4)(x+4)}{2(x+4)}*\frac{x(x^2-2x+1)}{(x+4)(x-1)}[/tex]

[tex]\frac{(x-4)(x+4)}{2(x+4)}*\frac{x(x-1)^2}{(x+4)(x-1)}[/tex]

now we simplify the expression

[tex]\frac{(x-4)}{2}*\frac{x(x-1)}{(x+4)}[/tex]

[tex]\frac{x(x-4)(x-1)}{2(x+4)}[/tex]

The answer  is the first option

Answer:

A on Edge

Step-by-step explanation:

Good Luck!

Answer:

(x-5)

Step-by-step explanation:

factor the equation and the sign is x-5 because the equation has to be negative at the 25.

The width of the rectangle is found by dividing the area by the length, which simplifies to x - 5.

The area of a rectangle is given by the product of its length and width. Given the area is x² - 25 and the length is x + 5, you can find the width by dividing the area by the length.

So, the width = area / length = (x² - 25) / (x + 5).

Factoring the numerator gives us (x + 5) (x - 5), therefore, the width = [(x + 5) (x - 5)] / (x + 5). As you can see, (x + 5) is a common factor in the numerator and denominator so we can cancel them out.

The resulting expression for the width is x - 5.

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Answer:

B there were 4 ducks living in Anoops pond when he first built it

Step-by-step explanation:

The equation is in the form

y = a b^x

The a  is the initial value at time x =0

The b is the growth rate

x is the time

So

4 * 3^t

4 is the initial amount of ducks

3 is the growth rate, or the duck population increase by a factor of 3 each time period

t is the time period in years

Answer:

192

Step-by-step explanation:

12:49 - 12:17 = 32min

if 60min = 360°

32min = ?

32×360

60

=192°

Answer:

B. 192 degrees

Step-by-step explanation:

First, calculate how many degrees a minute equals.

The minute hand rotates 360 degrees every 60 minutes.

Thus, one minute is equivalent to dividing 360 degrees by 60 minutes, that is 360/60 = 6 degrees per minute.

Now, we subtract the minutes from the two hours given,

12:49 PM - 12.17 PM = 32 minutes

Finally, we calculate the angle traveled by the minute hand by multiplying 6 degrees by 32 minutes, that is

Angle = 6 * 32 = 192 degrees.

I hope this helps!

A box has six sides.

Using the dimensions of the box:

2 sides are 5 x 7

2 sides are 7 x 3

2 sides are 5 x 3

Now calculate the total area:

2 x 5 x 7 = 70

2 x 7 x 3 = 42

2 x 5 x 3 = 30

Total area = 70 + 42 + 30 = 142 square inches.

Answer:

The answer is 142 square inches.

Step-by-step explanation:

Let length be = 5

Let the width be = 7

Let the height be = 3

The gift box is a 3 D box with 6 faces.

So, we get three possible combinations, and each combination is multiplied by 2 for a parallel face.

Hence, we get;

[tex](5)(7)(2)=70[/tex] square inches

[tex](5)(3)(2)=30[/tex] square inches

[tex](7)(3)(2)=42 [tex] square inches

Therefore, the amount of gift wrap needed will be:

[tex]70+30+42=142[/tex] square inches.

Answer:

A) 760 ft³

Step-by-step explanation:

The surface area of the figure has to be calculated.

Step 1: Divide the figure

The figure is divided into the following parts to calculate the volume.

Part 1: Box without ledge

Formula for volume of rectangle = length x width x height

Volume = 14.3 x 7.8 x 6.6

Volume = 736.164 ft³

Part 2: Box with ledge-we will only calculate height and width since the length has already been included in part 1 therefore including it again would result in double counting and give the wrong answer.

Volume = height x width

Volume = 2.7 x 7.8

Volume = 21.06 ft³

Step 2: Add both volumes to find the total volume

Volume part 1 + Volume part 2 = 736.164 ft³ + 21.06 ft³

= 757.224 ft³ rounded off to nearest tenth = 760 ft³

Therefore, answer A is correct.

!!

There are 21 books Jason's have and 24 books Nathan's have.

Given

Six times Jason's collection of books and one-third of Nathan's collection add up to 134 books.

One-third of Jason's collection and Nathan's entire collection add up to 31 books.

Let the number of collection of books Jason's be x.

And the number of collection of books Nathan's be y.

Six times Jason's collection of books and one-third of Nathan's collection add up to 134 books.

[tex]\rm 6x+\dfrac{1}{3} y=134\\\\\dfrac{18x+y}{3} =134\\\\ 18x+y = 134\times 3\\\\18x+y=402[/tex]

One-third of Jason's collection and Nathan's entire collection add up to 31 books.

[tex]\rm \dfrac{1}{3}x+y=31\\\\\dfrac{x+3y}{3} =31\\\\x+3y=31\times 3\\\\x+3y=93[/tex]

On solving both the equations;

From equation 1;

[tex]\rm 18x+y=402\\\\y = 402-18x[/tex]

Substitute the value of y in equation 2

[tex]\rm x+3y=93\\\\x+ 3(402-18x)=93\\\\x+1206 -54x=93\\\\-53x = 93-1206\\\\-53x =-1113\\\\x = \dfrac{-1113}{-53}\\\\x=21[/tex]

Substitute the value of x in equation 2

[tex]\rm x+3y=93\\\\21+3y=93\\\\3y=93-21\\\\ 3y =72\\\\ y = \dfrac{72}{3} \\\\ y=24[/tex]

Hence, there are 21 books Jason's have and 24 books Nathan's have.

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Answer:

14x-11

Step-by-step explanation:

f(x) = 2x − 5

g(x) = 7x − 3

(f(g(x))=

Substitute g(x) into f(x) for every x

f(g(x) = 2 (g(x) -5

         =2 (7x-3) -5

 Distribute

         =14x-6 -5

        =14x-11

Answer:

Option B

Step-by-step explanation:

Given:

As per the contract "Notification of the Buyer’s intent to do so must be made by written letter or phone call to the phone number and address listed below within one business week of delinquency.”

So,buyer needs to only notify the bank about the monthly payments in case of delinquency and not about if payment is going to be late or not.

Option B is correct

Notify the bank if a payment is going to be late !

The buyer is not responsible for paying an additional $75.00 for payments made after the 15th of the month it was due; this is not specified in the contract's provided clauses.

According to the contract, the responsibility that is not a part of the buyer's obligations is option (c): Pay an additional $75.00 with a payment made after the 15th day of the month it was due. The contract stipulates that the buyer should pay the monthly payment on time (a), notify the bank if a payment is going to be late (b), and notify the bank of his or her intent to split a late payment into three partial payments (d) in the event of delinquency. However, there is no mention within the provided excerpt of the contract that indicates an additional fee of $75.00 is imposed for late payments. It is important for individuals facing financial difficulties, such as inability to make timely payments, to communicate effectively with their lenders to find potential solutions and avoid the repercussions of default.

Answer:

Step-by-step explanation:

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points (-1, 5) and (3, 5). Substitute:

[tex]m=\dfrac{5-5}{3-(-1)}=\dfrac{0}{4}=0[/tex]

It's a horizontal line y = 5.

Answer:

Explanation:

The exponential parent function is the most basic form of the exponential form, which is:

That is so because other expnential functions, named daughter functions, can be obtained as a stretching, compression, or translation of such parent function.

Let's see every option:

That is true: the end behavior of the function is y approaches zero from above, when x goes to negative infinite, never getting the zero value, and y increases indefintely as x goes to positive infinite, then y is always positive.

This is false: the origin is the point (0,0). When you make x = 0, you get y = a⁰ , which is 1. So instead of the origin it goes through (0, 1).

This is true: the function is defined for all the values of x, from negative infinity to positive infinity. which is all real numbers.

This is true as shown above.

Although exponential parent functions have characteristics such as a horizontal asymptote at y=0, positivity, and either exponential growth or decay, they do not have a constant slope or rate of change. This is unlike linear functions which maintain a consistent slope.

The characteristics of an exponential parent function, depicted in mathematical terms as f(x) = a*b^x, generally include several properties. Such properties include a horizontal asymptote at y=0, the function being always positive since it's above the x-axis, and it showing exponential growth if b is greater than 1, or exponential decay if b is between 0 and 1.

However, one feature that is not characteristic of an exponential parent function is having a constant slope or rate of change. The rate of change in exponential functions varies across the graph, which is contrary to linear functions that maintain a constant slope.

As an example: the function y = 2^x is an exponential one. The slope between any two points is not consistent. For instance, between x=0 and x=1, the slope would be 2, while between x=1 and x=2, the slope is 2, indicating that the rate is not constant.

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Answer:

2

Step-by-step explanation:

i got it right on the quiz

Points with opposite x-coordinates and the same y-coordinate are symmetrically placed with respect to the y-axis. Their distance from the y-axis is the absolute value of their x-coordinate.

If points A and B have opposite x-coordinates but the same y-coordinates, we can deduce that they are positioned symmetrically with respect to the y-axis. The distance of each point from the y-axis is equal to the absolute value of their x-coordinate. This is because the y-axis serves as a reference line where the x-coordinate is zero.

For example, if point A has coordinates (-5, 3) and point B has coordinates (5, 3), then both points are 5 units away from the y-axis. The only difference between their positions is the direction relative to the y-axis; point A is on the left side and B is on the right side.

So, the general rule is that no matter the y-coordinate, the distance of a point from the y-axis is simply the absolute value of its x-coordinate.

Answer:

A:A(6t)=πp^2

B: about 7234.56

Step-by-step explanation:

First find A[p(t)], Since this is a composite function so whenever you see p(t), you replace it with 6t, that is the value of p(t).

This is a simplified version of the area of the circle as a function of time A(6t)=πp^2

To find how large the area of paint spilled plug in 8 for t because t represents time.

A(48)≈3.14(48)^2

A(48)≈3.14*2304

A(48)≈7234.56

Final answer:

To find the area of spilled paint over time, we replace the time-dependent spread 'p(t)' in the area function 'A(p) = πp²' with '6t'. This results in the equation 'A[p(t)] = 36πt²'. After 8 minutes, the area is approximately 7233.76 square units when using 3.14 for π.

Explanation:

To solve for the area of the circle of spilled paint as a function of time, we need to use the given functions. We are given p(t) = 6t, which represents how far the paint spreads over time in minutes. The area of the circular pattern is given by A(p) = πp².

Part A

To find A[p(t)], we substitute the expression for p(t) into the equation for A(p):

A[p(t)] = π(6t)²
= π(36t²)
= 36πt²

Part B

After 8 minutes, the area of spilled paint can be calculated by substituting t=8 into the function A[p(t)]:

A[p(8)] = 36π(8)²
= 36π(64)
= 2304π
≈ 2304(3.14)
≈ 7233.76 square units

Answer:

Step-by-step explanation:

We can determine if the triangle is a right triangle by using the Pythagorean theorem

a^2 +b^2 = c^2  where a and b are the legs and c is the hypotenuse

25^2 + 27^2 = 48^2

625+729=2304

1354 ≠2304

This is not true, so this is not a right triangle

Answer:

Step-by-step explanation:

If a ≤ b < c are a length of sides of a right triangle, then

a² + b² = c²

We have a = 25, b = 27 and c = 48.

Substitute:

25² + 27² = 48²

625 + 729 = 2304

1354 = 2304            FALSE

Answer:

B = 60°; c = 30; b = 25.98

Step-by-step explanation:

1. Calculate ∠B

 ∠A + ∠B + ∠C =180°

30° + ∠B + 90° = 180°

       ∠B + 120° = 180°

                  ∠B = 60°

2. Calculate c

  sinA = a/c

sin30° = 15/c

      ½ = 15/c

       c = 2 × 15 = 30

3 .Calculate b

   sinB = b/c

sin60° = b/30

 √3/2 = b/30

       b = (30√3)/2 = 15√3 = 25.98

Step-by-step explanation:

Rectangles, rhombuses, and squares all have angles that add up to 360°.

Rectangles, rhombuses, and squares all have opposite angles that are congruent.

Rectangles and squares have four right angles.

the square has 4 right angles, the rectangle has both pairs of opposite angles that are congruent, and the rhombus has angles where the sum is 360 degrees.

Answer:

A

Step-by-step explanation:

The angle adjacent to 133 and 133 form a straight angle and are supplementary, hence

adjacent angle = 180° - 133° = 47°

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles. The angle 90 is an exterior angle, thus

p + 47 = 90 ( subtract 47 from both sides )

p = 43° → A

Answer:

18 since f(3)=18

Step-by-step explanation:

f(x)=2x^2 is give as our function. To find f(3) we need to replace x with 3.

f(3)=2(3)^2   (Replaced x with 3.)

f(3)=2(9)   (Did 3^2 which was 3*3=9)

f(3)=18    (Did 2(9) which was 18)

[tex]f(3)=2\cdot 3^2=18[/tex]

Answer:

Step-by-step explanation:

the graph of x + y = 4 is the line passes by the point A(2,2) and the slope -1

because 2+2 =4  and y = -x +4