Substitution Property of Equality:
If AB = 20, then AB + CD

Answer:70.2

Step-by-step explanation:

Answer:

Domain: All real numbers greater than or equal to 1.

Step-by-step explanation:

Answer 1: -14 is not in the domain

Answer 2: 4 is included in the domain

Answer:

70% increase

Step-by-step explanation:

51-30 = 21

21/30 = 0.7

0.7 x 100

The polynomial 18x³ - 2x² + 4x - 1 consists of four terms.

The number of terms in a polynomial helps when performing operations like simplification, factoring, or evaluating expressions.

The polynomial 18x³ - 2x² + 4x - 1 consists of four terms.

In order to determine the number of terms in a polynomial, we count the number of distinct algebraic expressions separated by addition or subtraction operations.

In this polynomial, we have:

Term 1: 18x³ (This is the term with the highest degree, which is 3 in this case, and it includes the coefficient 18.)

Term 2: -2x² (This term has a degree of 2 and a coefficient of -2.)

Term 3: 4x (This term has a degree of 1 and a coefficient of 4.)

Term 4: -1 (This is a constant term with a degree of 0.)

We can see that there are four distinct terms separated by addition and subtraction operations:

18x³, -2x², 4x, and -1.

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We can see here that the Pythagorean theorem can help one determine whether the roped off area is in the shape of a right triangle because the converse of Pythagorean Theorem is actually used to prove that a triangle is a right triangle.

Let's understand the definition and meaning of  Pythagorean Theorem.  Pythagorean Theorem is actually seen as the fundamental concept that is used to describe the relationship that exists  between all the sides of a right-angled triangle.

The theorem actually states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Mathematically, it can be expressed as a² + b² = c², where "a" and "b" are the lengths of the two shorter sides, and "c" is the length of the hypotenuse.

When we don't know that a triangle is a right-angle triangle, we use the converse to prove it.

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Answer:

20%

Step-by-step explanation:

2/10 cm are blue.

Answer:

Points scored in a basketball game vary directly with shots taken.

This means that this question can be solved

by proportions, using a rule of three.

How many would she have scored if she takes 60 shots?

Using a rule of three:

50 points - 40 shots

x points - 60 shots

Applying cross multiplication:

4x = 50 × 60

Divide from both sides

x = 50 × 1.25 = 75

Answer is 75

Step-by-step explanation:

Here is a easier explanation if you didn't understand clearly:

It asked for how many 60 shots would score.

You would look at the first time he scored which is 50 and took 40 shots. Divide them

50 ÷ 40 = 1.25 or 1.5

So now you know each point scores 1.25 or 1.5

Now you multiply 1.25 or 1.5 with how many shots to see how much was scored and in this case 60 shots.

60 × 1.25 or 60 × 1.5

& They both end up equaling just the same, 75.

Hope it made sense :)

The quadratic functions are: f(x) = 0.03x² for Design A and g(x) = 0.024x² for Design B.

A quadratic function is a type of polynomial function of the form f(x) = ax² + bx + c, where a, b, and c are constants and x is the variable. In a quadratic function, the highest power of the variable is 2.

The graph of a quadratic function is a parabola, which is a U-shaped curve that opens either upwards or downwards depending on the sign of the coefficient a. If a > 0, the parabola opens upwards, and if a < 0, the parabola opens downwards. The vertex of the parabola, which is the point where the curve changes direction, is given by the coordinates (-b/2a, f(-b/2a)).

Quadratic functions have a wide range of applications in various fields such as physics, engineering, economics, and finance. For example, they can be used to model the motion of projectiles, the trajectory of a rocket, the shape of a bridge arch, the optimization of business profits, and the behavior of financial markets.

Let's assume that each side of the cube has a length of x inches. Then, the surface area of the cube is 6x² square inches.

a. For Design A with a cost of $0.005 per square inch, the total cardboard cost can be calculated using the quadratic function:

f(x) = 0.005(6x²) = 0.03x²

b. For Design B with a cost of $0.004 per square inch, the total cardboard cost can be calculated using the quadratic function:

g(x) = 0.004(6x²) = 0.024x²

Therefore, the quadratic functions are:

f(x) = 0.03x² for Design A

g(x) = 0.024x² for Design B

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The complete question is:

volume of a cone

.

.

.

volume of sphere

.

.

number of spheres that can be made......

.

.

hence a hemisphere can be formed

The equation of the line in fully simplified slope-intercept form is y = x + 7.

We have,

From the graph,

The coordinates of the line are:

(0, 7), (-7, 0), and (-2, 5).

We can use any coordinates the line touches on the graph.

We will use,

(0, 7) and (-7, 0)

The equation can be written in the form y = mx + c

m = (0 - 7) / (-7 - 0)

m = -7/-7

m = 1 ______(1)

And,

(0, 7) = (x, y)

So,

y = mx + c ______(2)

7 = 1 x 0 + c

7 = c

c = 7 ______(3)

Now,

From (1), (2), and (3).

y = x + 7

Thus,

The equation of the line in fully simplified slope-intercept form is y = x + 7.

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Answer:

X = -29/22

Step-by-step explanation:

I used PEMDAS to solve the question

Answer:

1.61

Step-by-step explanation:

Answer:

Step-by-step explanation:

1.61

Answer:

cioè x ≥ 1; si avrà pertanto x > 0

Step-by-step explanation:

EXERCISE 2. Risolvere le seguenti disuguaglianze:

(1) | x−1 |< 3

(2) | x+1 |> 2

(3) | 2x+1 |< 1

(4) | x−1 |<| x+1 |

Caso: (a): | x−1 |< 3, risolvo

x−1 < 3

x ≥ 1

∪

−x+1 < 3

x < 1

, si avrà quindi

x < 4

x ≥ 1

cioè 1 ≤ x < 4 e

x > −2

x < 1

cioè −2 < x < 1. L’unione tra le due dà la soluzione −2 < x < 4

Caso: (b):

x+1 > 2

x ≥ −1

∪

−x−1 > 2

x < −1

, si avrà quindi

x > 1

x ≥ −1

cioè x > 1 e

x < −3

x < −1

cioè x < −3,

pertanto x < −3 ∪ x > 1

Caso: (c):

2x+1 < 1

x ≥ −1

2

∪

−2x−1 < 1

x < −

1

2

, si avrà quindi

x < 0

x ≥ −1

2

cioè −

1

2 ≤ x < 0 e

x > −1

x < −

1

2

cioè

−1 < x < −

1

2

. pertanto −1 < x < 0

Caso: (d): in questo caso,

−x+1 < −x−1

x < −1

∪

−x+1 < x+1

−1 ≤ x < 1

∪

x−1 < x+1

x ≥ 1

, si avrà quindi

0 < −2

x < 1

cioè non si hanno soluzioni e

x > 0

−1 ≤ x < 1

cioè 0 < x < 1 e

0 < 2

x ≥ 1

cioè x ≥ 1; si avrà pertanto x > 0

Answer:

The answer is

x equal -243

Answer:

-243 is yr correct answer.

Step-by-step explanation:

hope it helps

f(x) has a point of inflection at x = 0 and x = 1/2.To find the values of x where the graph of the function\(f(x) = x^4 - x^3\) has a point of inflection, we need to find where the second derivative of the function changes sign from positive to negative or vice versa.

The first derivative of the function is:

\(f'(x) = 4x^3 - 3x^2\)

The second derivative of the function is:

\(f''(x) = 12x^2 - 6x\)

Setting f''(x) equal to zero and solving for x gives:

\(12x^2 - 6x = 0\)

6x(2x - 1) = 0

This equation has two solutions:

x = 0, or x = 1/2

To determine whether these values of x correspond to points of inflection, we need to look at the sign of the second derivative on either side of each value.

When x < 0, f''(x) is positive because both \(12x^2\) and -6x are positive. When 0 < x < 1/2, f''(x) is negative because \(12x^2\)is positive but -6x is negative. When x > 1/2, f''(x) is positive again because both \(12x^2\) and -6x are negative.

Therefore, f(x) has a point of inflection at x = 0 and x = 1/2.

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Answer: 0.4419

Step-by-step explanation:

Given: The birth weights of full-term newborn infants in the U.S. have an approximately normal distribution with a mean weight of 6.8 lbs and a standard deviation of 1.7.

i.e. \(\mu=6.8\ \ \ \text{ and }\sigma= 1.7\)

Let X denotes the birth weight.

Then, the proportion of newborn babies will have a birth weight between 6 lbs and 8 lbs is given by :-

\(P(6<X<8)=P(\dfrac{6-6.8}{1.7}<\dfrac{X-\mu}{\sigma}<\dfrac{8-6.8}{1.7})\\\\=P(-0.47<Z<0.71)\ \ \ [Z=\dfrac{X-\mu}{\sigma}] \\\\=P(Z<0.71)-(1-P(Z-0.47))\\\\=0.7611-(1-0.6808)\ \ \ [\text{By z-table}]\\\\= 0.4419\)

Hence, the proportion of newborn babies will have a birth weight between 6 lbs and 8 lbs is 0.4419 .

The value of the test statistic is given as follows:

z = 4.47.

The equation to calculate the test statistic using the z-distribution is given as follows:

\(z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}\)

In which:

The parameters for this problem are given as follows:

\(\overline{p} = 0.59, p = 0.5, n = 618\)

p = 0.5 as the most term means that we are testing if the proportion is either less than or greater than 0.5.

Then the test statistic is obtained as follows:

\(z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}\)

\(z = \frac{0.59 - 0.5}{\sqrt{\frac{0.5(0.5)}{618}}}\)

z = 4.47.

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Answer:

21

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp/ adj

tan 60 = x / 7 sqrt(3)

7 sqrt(3)  tan 60 = x

7 sqrt(3) sqrt(3) = x

7*3 = x

21 = x

Convert 50 yards into meters.

A. 45.87 meters

C. 72.45 meters

B. 50 meters

D. 60 meters

It's actually 45.72 but A is the closest :)

Answer:

Hey there!

One yard is about 0.9144 m.

Thus, 50 yards would be about 45.87 meters.

Let me know if this helps :)

The roots of the given polynomial using the rational zero theorem are;  2, -4 and 6.

We are given the polynomial;

y = x³ - 4x² - 20x + 48

Since all coefficients are integers, we can apply the rational zeros theorem.

The trailing coefficient (the coefficient of the constant term) is 48

Find its factors (with the plus sign and the minus sign): ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±16, ±24, ±48.

These are the possible values for p.

The leading coefficient (the coefficient of the term with the highest degree) is 1.

These are the possible rational roots:

±1, ±2, ±3, ±4, ±6, ±8, ±12, ±16, ±24, ±48.

Checking the possible roots: if a is a root of the polynomial P(x), the remainder from the division of P(x) by x - a should equal 0 (according to the remainder theorem, this means that P(a)=0

Plugging in those values, the only ones that yield P(a) = 0 are; 2, -4 and 6.

Thus, these are the roots of the given polynomial.

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Answer:

According to this diagram, the tan 62 degrees, is the ratio of the opposite side and the adjacent side of the triangle which is equal to 1.875 units.

What is the right angle triangle property?

In a right-angle triangle ratio of the opposite side to the adjacent side is equal to the tangent angle between the adjacent side and the hypotenuse side.

Here, (b) is the opposite side, (a) is the adjacent side, and is the angle made between the adjacent side and the hypotenuse side.

The sides of the triangle are 8, 15, and 17 units long and the measure of the angles of the right angle triangle is 62, 90, and 28 degrees.

Re-draw, the  Here in the given triangle, the base is the side which is 15 units long. Re-draw the triangle as shown below.

In the attached triangle below, the opposite side of the triangle is 15 units and the adjacent side of the triangle is 8 units long.

The angle between the opposite side and the adjacent side is 62 degrees. Thus using the right angle triangle property as,

Thus, according to this diagram, the tan 62 degrees, is the ratio of the opposite side and the adjacent side of the triangle which is equal to 1.875 units.

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Answer:

x = 5

y = 1

Step-by-step explanation:

2x - y = 9

3x + 4y = 19

We multiply the first equation by 4

8x - 4y = 36

3x + 4y = 19

11x = 55

x = 5

Now we put 5 in for x and solve for y

2(5) - y = 9

10 - y = 9

-y = -1

y = 1

Let's Check the answer

2(5) - 1 = 9

10 - 1 = 9

9 = 9

So, x = 5 and y = 1 is the correct answer.

Answer:

11700

Step-by-step explanation:

The graph of the function y = 5|x - 4| is added as an attachment

From the question, we have the following parameters that can be used in our computation:

y = 5|x - 4|

The above function is an absolute value function that has been transformed as follows

Next, we plot the graph using a graphing tool by taking not of the above transformations rules

The graph of the function is added as an attachment

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Hey there! I'm happy to help!

We see that light travels 186,000 miles per second. How many miles is this per minute. Well, there are 60 seconds a minute, so we multiply by 60!

186,000×60=11160000

And there are 60 minutes in an hour, so we multiply by sixty again!

11160000×60=669600000

Now, we need to write this in scientific notation. To do this, we move the decimal back enough places to have a one digit number, and we multiply that one digit number by 10 to the power of how many places you moved the decimal back.

In the number 669600000 we can move the decimal point back 8 times which gives us 6.696 (we don't need the zeroes after a decimal) multiplied by 10 to the 8th power because we moved the decimal back eight places.

This can be written as 6.696×10^8, which is closest to the answer option 6.7×10^8 miles.

Have a wonderful day! :D

Answer:

Gina has 5 large shipping boxes and 6 small shipping boxes.

Step-by-step explanation:

32 items to ship and 11 shipping boxes.

Large=4 items

4 X 5 = 20

Small=2 items

2 X 6 = 12

20 + 12 = 32

Answer:

His rate would be 910.8 miles per hour

Step-by-step explanation:

This is division so divide 63756 by 70 and there’s your answer

Answer:

10.35 miles per hour

Step-by-step explanation:

63,756/5280 = 12.075 miles

12.075/70 = 0.1725 miles per minute

0.1725 x 60 = 10.35 miles per hour

Answer:

110/150

Step-by-step explanation:

125/500 is smallest, since you can imagine the difference from 125 to 500 is much larger compared to the others! Then, 90/270 is second smallest, because 9/27 is simply one third. You can tell that 125/500 is smaller than one third, because 125x3 is less than 500. After that, we only have 56/100 and 110/150. We need the denominators to be the same.

56/100

110/150

100 is two thirds of 150. This means that we must divide the numerator by 2 and multiply it by three to balance the common denominator. 56/2 then x3 is 84, which is less than 110.

56/100 = 84/150

84/150 < 110/150

Therefore the largest fraction is the 110/150 school.

Each silver bead costs $0.50, and each green bead costs $1.

Let's assume the cost of each silver bead is 's' dollars, and the cost of each green bead is 'g' dollars.

According to the given information, the necklace requires 25 silver beads and 15 green beads, and the bracelet requires 10 silver beads and 5 green beads.

The total cost of the necklace beads is $27.50, and the total cost of the bracelet beads is $10.

Using this information, we can set up the following system of equations:

25s + 15g = 27.50 (Equation 1)

10s + 5g = 10 (Equation 2)

We can solve this system of equations using any appropriate method, such as substitution or elimination.

Let's use the elimination method to solve the system:

Multiplying Equation 2 by 3, we get:

30s + 15g = 30 (Equation 3)

Subtracting Equation 3 from Equation 1:

25s + 15g - (30s + 15g) = 27.50 - 30

-5s = -2.50

s = 0.50

Now, substituting the value of s into Equation 2:

10(0.50) + 5g = 10

5 + 5g = 10

5g = 5

g = 1

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