The length of a rectangle is 5 units and its width is 4 units. What is the approximate length of the diagonal of the rectangle?

A) 5 units
B) 6.4 units
C) 8.5 units
D) 9 units

Answer:

The difference of the original two-digit number and the number with reversed digits is 98 - 89 = 9

Step-by-step explanation:

Let the digit at unit(one's) place = y

Let the digit at ten's place =  x

So, the two-digit number will be: 10x +y

According to given condition:

Five times the sum of the digits of a two-digit number is 13 less than the original number. This statement can be written as:

5(x +y) = (10x +y) - 13

If you reverse the digits in the two-digit number, four times the sum of its two digits is 21 less than the reversed two-digit number.

if digits are reserved the two digit will be 10y + x

4(x + y) = (10y + x) -21

So, we have 2 equations, solving these 2 equations we can find the 2 digit number.

5(x +y) = (10x +y) - 13

5x + 5y = 10x +y -13

Rearranging:

5x -10x +5y -y = -13

-5x + 4y = -13 (eq1)

4(x + y) = (10y + x) -21

4x +4y = 10y +x =-21

4x -x +4y -10y = -21

3x -6y = -21 (eq2)

Solving:

Multiply eq 1 with 3 and eq 2 with 2

-15x + 12 y = -39

6x - 12y = -42

_______________

-9x = -81

x = -81/-9

x = 9

Putting in eq(1)

-5x + 4y = -13

-5(9) +4y = -13

-45 + 4y = -13

4y = -13 + 45

4y = 32

y = 32/4

y = 8

So, y =8 and x = 9

The 2 digit number is:

10x + y = 10(9) + 8 = 90+8 = 98

The reversed 2 digit number is:

10y + x = 10(8) + 9 = 80+9 = 89

The difference of the original two-digit number and the number with reversed digits is 98 - 89 = 9

Answer:

y=6(x+1)^(2)-16

Step-by-step explanation:

Use the formula x=-b/2a

Plug it in for x to get y. That will give you the vertex. Plug the numbers in where they go. There will be one number left that hasn't been filled out. The first number in the equation id 6, so it goes out front.

The equation is y = 6x2 + 12x – 10 rewritten in vertex form is y=6(x+1)²-16

By using the formula   x=-b/2a

simplify

y = 6x2 + 12x – 10

as y=6(x+1)²-16

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Answer:

[tex]\large\boxed{4\pi\ cm\approx12.56\ cm}[/tex]

Step-by-step explanation:

The formula of a length of an arc:

[tex]\dfrac{\pi\alpha r}{180^o}[/tex]

We have

[tex]\alpha=120^o\\\\r=6\ cm[/tex]

Substitute:

[tex][tex]\hat{MN}=\dfrac{\pi(120)(6)}{180}=4\pi\ cm\approx4(3.14)=12.56\ cm[/tex]

Answer:

x=35

Step-by-step explanation:

The angles are alternate interior angles.  Alternate interior angles are equal if the lines are parallel.

3x+16 = 5x-54

Subtract 3x from each side

3x -3x+16 = 5x-3x-54

16 = 2x-54

Add 54 to each side

16+54 = 2x-54+54

70 = 2x

Divide each side by 2

70/2 = 2x/2

35 =x

Answer:

Lets first subtract 35 from 22 since 35 is his total and the answer would be 13.

Step-by-step explanation:

I guess it would be 13 dollars left.

IF IT'S RIGHT PLZZ MARK BRAINLIST PLZZZ

Answer:

Step-by-step explanation:

Answer:

K = (e, d)

Step-by-step explanation:

We are given the coordinates of three vertices of a rectangle and we are to find the coordinates of the fourth point J.

H (0, 0)

I (0, d)

K (e, 0)

J = ?

We can find this using the following formula:

K = H + (I - H) + (K - H)

K = H + I - H + K - H

K = I + K - H

Substituting the given values in it to get:

K = [tex](0, d) + (e, 0) - (0, 0)[/tex]

K = [tex](0+e-0, d+0-0)[/tex]

K = (e, d)

Answer:

The probability that a student buys a drink  is 0.47

Step-by-step explanation:

The probability that a student buys a drink will be given by;

( the number of students who bought a drink)/(the total number of students)

We are told that;

Of the 100 students who came to the movie, 62 bought popcorn and 47 bought a drink. Therefore, the required probability is;

47/100= 0.47

The rate of change of the function can be determined by finding the slope of the function at different points in the table.

The rate of change of a function can be determined by finding the slope of the function at different points. In this case, we can use the values provided in the table to find the rate of change. The rate of change is equal to the difference in the y-values divided by the difference in the x-values.

Let's take the first two points in the table as an example. The first point is (12/5, 5) and the second point is (5, 25/2). The difference in the y-values is 25/2 - 5 = 15/2, and the difference in the x-values is 5 - 12/5 = 23/5. Therefore, the rate of change is (15/2) / (23/5) = 15/2 * 5/23 = 75/46. So, the rate of change of the function for these two points is 75/46.

Answer:

A

Step-by-step explanation:

If the corresponding parts of the triangles are congruent then the triangles are congruent.

Here there are 2 corresponding congruent angles, that is 51° and 80°

The non- included corresponding sides are congruent both 10

Then by AAS postulate the triangles are congruent- True

Answer:

True

Step-by-step explanation:

A pex

For this case we must solve the following inequality:

[tex]8x-5 \geq27[/tex]

We add 5 to both sides of the inequality:

[tex]8x\geq27 + 5\\8x\geq32[/tex]

DIviding between 8 on both sides of the equation:

[tex]x \geq \frac {32} {8}\\x \geq4[/tex]

Thus, the solution is given by all the numbers greater than or equal to 4

Answer:

[tex]x \geq4[/tex]

Answer: [tex]x\geq4[/tex]

Step-by-step explanation:

Given the inequality [tex]8x-5\geq27[/tex], you need to solve for the variable "x".

You must follow these steps to solve for the variable "x":

- First, you need to add 5 to both sides of the inequality. Then:

[tex]8x-5+(5)\geq27+(5)\\\\8x\geq32[/tex]

- And finally, you need to divide both sides of the inequality by 8.

Therefore, you get:

[tex]\frac{8x}{8}\geq\frac{32}{8}\\\\x\geq4[/tex]

Answer:

864 sq.in.

Step-by-step explanation:

Given:

Prism with each leg of length 12

hence given prism is cube

Formula for Area of cubic prism= 6a^2

where a is length of a side

Area=6(12)^2

        =6(144)

         =864 !

Answer:

B

Step-by-step explanation:

volume = length x width x height

For the top half i use the formula for the area of a triangle (area = base x height ÷ 2), which results in 45. times it 10 and you have 450³ which is the volume of the top part.

For the bottom half it is just 10 x 10 x 10 = 1000³

450³+1000³=1450³

The Volume of the frozen figure is C. 1,000 cm³.

To calculate the volume of the frozen figure, we need to determine the shape of the mold first. Assuming the mold is a rectangular prism, we can use the volume formula for a rectangular prism:

Volume = length × width × height

Given that the dimensions of the mold are:

Now, let's calculate the volume:

Volume = 10 cm × 9 cm × 10 cm = 900 cubic centimeters (cm³)

The correct answer to the question C. 1,000 cm³

if its diameter is 8 cm, then its radius is half that, or 4 cm.

[tex]\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=4\\ h=13 \end{cases}\implies V=\cfrac{\pi (4)^2(13)}{2} \\\\\\ V=104\pi \implies \stackrel{\pi =3.14}{V=326.7}[/tex]

[tex]\bf (\stackrel{x_1}{3}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{4}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{4-(-2)}{1-3}\implies \cfrac{4+2}{1-3}\implies \cfrac{6}{-2}\implies -3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-2)=-3(x-3) \\\\\\ y+2=-3x+9\implies y=-3x+7[/tex]

Your answer will be 13,331 because you add up all the asset and subtract all the liabilities

Answer:

Option D.

Step-by-step explanation:

To calculate the net worth we subtract the liabilities from the assets.

Total assets

Checking and savings   $6432

Automobile                     $8345

Apartment contents       $5242

Valuables                        $867

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

                Total               $20886

Total Liabilities

Auto loan                       $2820

Credit card                     $1181

Other loans                    $3554

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

                 Total              $7555

Net worth = Assets - liabilities

                = $20886 - $7556

                = $13331

Option D is the answer.  

Answer:

Answer: There are 21 eggs left.

Step-by-step explanation:

One carton has 12 eggs.

2 cartons are two times one carton, so two cartons have 2 times 12 eggs.

2 * 12 = 24

There are 24 eggs in two cartons.

Margot uses 3 eggs. We subtract 3 eggs from 24 eggs.

24 - 3 = 21

Answer: There are 21 eggs left.

There are 21 eggs are left if each carton 12 eggs. There are 2 full cartons in the refrigerator. Margot uses 3 eggs to make a quiche.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

Each carton contains = 12 eggs

Number of carton = 2

Number of total eggs = 12×2 = 24

Margot uses 3 eggs to make a quiche.

Remaining eggs = 24 - 3 = 21

Thus, there are 21 eggs are left if each carton 12 eggs. There are 2 full cartons in the refrigerator. Margot uses 3 eggs to make a quiche.

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For this case we must simplify the following expression:

[tex](3 ^ {-2}) ^ 4[/tex]

By definition of power properties we have to:[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]

So, rewriting the expression we have:

[tex](\frac {1} {3 ^ 2}) ^ 4 = \frac {1 ^ 4} {(3 ^ 2) ^ 4} = \frac {1} {(3 ^ 2) ^ 4}[/tex]

By definition of power properties we have:

[tex](a ^ n) ^ m = a ^ {n * m}[/tex]

So:

[tex]\frac {1} {(3 ^ 2) ^ 4} = \frac {1} {3 ^ 8}[/tex]

Answer:

Option D

Answer:

(4, 5)

Step-by-step explanation:

Answer:

New x-coordinate: 4

New y-coordinate: 5

New point: (4,5)

Step-by-step explanation:

You know that the coordinates of a point of this triangle are the following:

[tex]x_1=8\\y_1=10[/tex]

And you know that it is dilated with a scale factor of [tex]\frac{1}{2}[/tex], then, to find the new coordinates of the point, you need to multiply the original coordinates by the scale factor:

New x-coordinate:

[tex]x_2=\frac{1}{2}x_1[/tex]

[tex]x_2=\frac{1}{2}(8)[/tex]

[tex]x_2=4[/tex]

New y-coordinate:

[tex]y_2=\frac{1}{2}y_1[/tex]

[tex]y_2=\frac{1}{2}(10)[/tex]

[tex]y_2=5[/tex]

The new point is (4,5)

Answer:

Addition of two vectors Will make an resultant vector or a third vectors

Step-by-step explanation:

When two vectors represents in both magnitude and direction as two sides of triangle then resultant will represent as both as third side of triangle but in opposite order

ANSWER

See below

EXPLANATION

The given function is

[tex]f(x)= {x}^{2} + 2x - 3[/tex]

We complete the square to rewrite this function in the vertex form.

[tex]f(x)= {x}^{2} + 2x + 1 - 1- 3[/tex]

[tex]f(x)= {(x + 1)}^{2} - 4[/tex]

The vertex is (-1,-4).

The axis of symmetry is x=-1

To find x-intercepts , put f(x)=0.

[tex]{(x + 1)}^{2} = 4[/tex]

[tex]x + 1 = \pm \sqrt{4} [/tex]

[tex]x = - 1\pm2[/tex]

[tex]x = - 3 \: or \: x = 1[/tex]

The x-intercepts are (-3,0), (1,0)

To find y-intercept , put x=0.

[tex]f(x)= {0}^{2} + 2(0) - 3 = - 3[/tex]

The graph is shown in the attachment.

Answer:

B

Step-by-step explanation:

The volume (V) of a triangular prism is

V = area of triangular end × length

area of Δ = [tex]\frac{1}{2}[/tex] bh

where b is the base and h the perpendicular height

here b = 8 and h = 5, so

area = 0.5 × 8 × 5 = 20 units²

the length of the prism is 10, hence

V = 20 × 10 = 200 units³

The Volume of the Triangular prism is 200 units³

The correct option is (B)

The volume of a triangular prism is the space inside it or the space occupied by it.

Volume (V) of a triangular prism,

V = base area × length

area of Δ =  bh

where b =base and h =perpendicular height

Given that,  b = 8 and h = 5, so

Area = 0.5 × 8 × 5

= 20 units²

The length of the prism is 10. So,

V = 20 × 10

  = 200 units³

volume of the triangular prism 200 units³

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Answer:

Step-by-step explanation:

pyramids have 5 surfaces and a point. a cube has 6 surfaces and is a square

Answer:

The correct answer option is B. [tex]1[/tex], [tex]\frac{1}{2}[/tex], [tex]\frac{1}{4}[/tex].

Step-by-step explanation:

We are given the following geometric sequence and we are to find its 8th term:

[tex]16, 8, 4, 2,...[/tex]  

Here [tex]a_1=16[/tex] and common ratio [tex](r) = \frac{2}{4}=0.5[/tex].

The formula we will use to find the next three terms is:  

nth term = [tex]a_1 \times r^{(n-1)}[/tex]  

5th term = [tex]16 \times 0.5^{(5-1)} = 1[/tex]

6th term = [tex]16 \times 0.5^{(6-1)}[/tex] = [tex]\frac{1}{2}[/tex]

7th term = [tex]16 \times 0.5^{(7-1)}[/tex] = [tex]\frac{1}{4}[/tex]

Examples of Quadratic Equation. A quadratic equation is an equation of the second degree, meaning it contains at least one term that is squared. The standard form is ax² + bx + c = 0 with a, b, and c being constants, or numerical coefficients, and x is an unknown variable.

Final answer:

A real-life example of a quadratic model is a ball's trajectory when thrown upwards, described by the quadratic equation h(t) = -4.9t^2 + v0t + h0, with -4.9 representing the acceleration due to gravity.

Explanation:

A common example of a quadratic model in real life is the path of a projectile. For instance, when you throw a ball, its trajectory can be described by a quadratic equation. Let's say a person throws a ball upwards with an initial velocity, and we want to model the ball's height above the ground over time.

The quadratic equation for the ball's height h at time t can be written as: h(t) = -4.9t2 + v0t + h0, where -4.9 is the acceleration due to gravity (in meters per second squared), v0 is the initial velocity (in meters per second), and h0 is the initial height (in meters).

For example, if the initial velocity is 14.3 m/s and the ball is thrown from the ground (initial height is 0), the equation becomes h(t) = -4.9t2 + 14.3t. To find when the ball hits the ground, we solve for t when h(t) = 0 using the quadratic formula.

Answer:

C [tex]4\log_w(x^2-6)-\dfrac{1}{3}\log_w(x^2+8)[/tex]

Step-by-step explanation:

First use the property of logarithms

[tex]\log _ab-\log_ac=\log_a\dfrac{b}{c}.[/tex]

For the given expression you get

[tex]\log_w\dfrac{(x^2-6)^4}{\sqrt[3]{x^2+8} }=\log_w(x^2-6)^4-\log_w\sqrt[3]{x^2+8}=\log_w(x^2-6)^4-\log_w(x^2+8)^{\frac{1}{3}}[/tex]

Now use property of logarithms

[tex]\log_ab^k=k\log_ab.[/tex]

For your simplified expression, you get

[tex]\log_w(x^2-6)^4-\log_w(x^2+8)^{\frac{1}{3}}=4\log_w(x^2-6)-\dfrac{1}{3}\log_w(x^2+8).[/tex]

Answer: C

Step-by-step explanation:

Answer: Option D

D. $108

Step-by-step explanation:

We must calculate the expected cost per patient to use treatment method B.

The expected cost for a discrete random variable x is:

[tex]C = \sum x_i * P (x_i)[/tex]

Where [tex]x_i[/tex] is the cost associated with the probability [tex]P(x_i)[/tex]

In this case, the random variable x is represented by the cost of each treatment.

For treatment B there is a possibility that antibiotic 2 works, in that case the cost x would be $ 100 and [tex]P (x) = 0.9[/tex]

There is also the possibility that it does not work, in this case the cost x would be $180 and the probability [tex]P (x) = 0.10[/tex]

The expected cost  is:

[tex]C =\$100*0.9 + \$180*0.1\\\\C = \$108[/tex]

The answer is 96 you’re welcome

Final answer:

The Ishango bone, found in the Congo with scratches believed to represent counting, shows evidence of prehistoric mathematical activity 20,000 years ago. It suggests early numerical understanding and supports the theory that Stone Age humans engaged in proto-mathematics.

Explanation:

The Ishango bone is a significant archaeological find believed by many archaeologists to be evidence of prehistoric mathematical activity. Found 20,000 years ago in what is now the Democratic Republic of Congo, the bone has a series of noticeable scratches that many scholars interpret as a form of counting. The precise nature of these markings is still the subject of debate, but the prevailing theory is that they were used for arithmetic operations, such as keeping track of numbers or simple calculations.

The archaeological context of the Ishango bone, being from the Stone Age, highlights the early presence of numerical comprehension, which could suggest that the humans of that era had some sense of numbers and possibly even a form of proto-mathematics. This idea is reinforced not just by the Ishango bone, but also by the evidence from various archaeological sites across Africa, where other mathematical tools and representations, such as carved stones with depictions of animal figures, which date back tens of thousands of years, have been found.

The discovery of the Ishango bone adds to a growing body of evidence that early humans had the ability to count and perform simple mathematical operations long before the establishment of formal systems of writing or the development of modern number systems. Such artifacts are invaluable for understanding the cognitive abilities of our early ancestors and the origins of mathematical practices.

Hello There!

First let me say this. I did not like how this question was worded I am a tutor in math and I had to read this problem over and over 5 times. It was confusing but I managed to figure it out. The answer is 61%

My work is shown on paper