A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 12 in. by 20 in. by cutting out equal squares of side x at each corner and then folding up the sides as in the figure. Express the volume V of the box as a function of x. v(x)

Answer:

m∠B = 83°

EF = 10

Step-by-step explanation:

Two triangles are similar if their corresponding angles are the same size.

Therefore if ΔABC ~ ΔDEF then:

Interior angles of a triangle sum to 180°:

⇒ m∠A + m∠B + m∠C = 180°

⇒ 24° + m∠B + 73° = 180°

⇒ m∠B + 97° = 180°

⇒ m∠B = 83°

In similar triangles, corresponding sides are always in the same ratio.

Therefore if ΔABC ~ ΔDEF then:

⇒ AB : DE = BC : EF = CA : FD

⇒ 12 : DE = 8 : EF = 16 : 20

Therefore, to find the length of EF:

[tex]\implies \sf 8 : EF = 16 : 20[/tex]

[tex]\implies \sf \dfrac{8}{EF} = \dfrac{16}{20}[/tex]

[tex]\implies \sf 8 \cdot 20= 16 \cdot EF[/tex]

[tex]\implies \sf160= 16 \cdot EF[/tex]

[tex]\implies \sf EF=\dfrac{160}{16}[/tex]

[tex]\implies \sf EF=10[/tex]

Answer:

Step-by-step explanation:

Final answer: Lily received 10 postcards from Thailand.

Explanation: Number of postcards=50

Percentage of postcards from thailand= 16

Number of postcards from Thailand= 16/100*50= 8

Now, he received some postcards from Thailand. Let the number of postcards received from Thailand be x. Therefore,

Number of postcards=50+x

Number of postcards from Thailand= 8+x

We know that the percentage of postcards from Thailand now is 30.

Therefore,

30=(8+x/50+x)*100

0.3(50+x)=8+x

15+0.3x=8+x

0.7x=7

x=10

Therefore, he received 10 postcards from Thailand.

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The annual interest rate that yields $31 from $600 in 10 months is 6.2%

An interest is the amount earned by placing a sum of money in a savings account or in an investment.

The principal amount you put in the account, P = $600

The amount (interest) earned in 6 months, I = $31

The duration over which the interest of $31 is earned, T = 10 months

The annual interest rate is found as follows;

The annual interest rate is the interest rate per year

The number of months in a year = 12 months

The formula for the simple interest, I, is presented as follows;

I = P·R·T

Where;

I = The simple interest earned

P = The principal amount saved in the account

R = The annual interest rate

T = The time duration the amount was saved in years

12 months = 1 year

Therefore; 10 months = (1/12) × 10 year = (5/6) year

The time, T, of 10 months = (5/6) year

31 = 600 × R × (5/6)

R = 31/(600 × (5/6)) = 0.062

0.062 in percentage is 0.062 × 100 = 6.2%

The annual interest rate, R = 6.2%

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Answer:

4,700,000 can be written as 4.7 × 10⁶ in scientific notation

For Example:

Here,

1200 can also be written as

12 × 100

we know that, 100 = 10²

so,

12 × 10²

Remember

1.2 × 10³

y = (-4/11)x + 5.27 is the equation that passes through each pair of points (9,2) (-2,6).

A group of numbers and variables without an equal sign are known as a numerical expression. A set of numbers and variables with an equal sign is referred to as an equation.

Once you are familiar with these terms, you will realise that an equation is just two expressions joined by an equal sign. You can also write expressions, equations, and simplify equations.

To find an equation of the line that passes through each pair of points (9,2) (-2,6) we need to find slope and convert it to y-intercept form

Slope formula = y - y₁ = m(x - x₁)

Putting the values in the formula we get

2 - 6 = m(9 - (-2))

-4 = m(11)

m = -4/11

As we have found slope, we can find the slope intercept form i.e.

y - 2 = -4/11(x -9)

y = (-4/11)x + 3.27 + 2

y =  (-4/11)x + 5.27

Thus, y = (-4/11)x + 5.27 is the equation that passes through each pair of points (9,2) (-2,6)

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The number of miles Sallu car will travel with 16 gallons fuel capacity if he travelled 28 miles per gallon is 448 miles.

If Sallu car can travel 28 miles using 1 gallon of fuel;

then, Sallu car will travel x miles using 16 gallons of fuel.

Based on the given task content; we can solve the task using the concept of ratio.

A ratio is a number representing a comparison between two named things.

It also refers to the relative magnitudes of two quantities usually expressed as a quotient.

Equate the ratio of miles travelled to gallons of fuel used

28 miles : 1 gallon = x miles : 16 gallons

28/1 = x / 16

28 × 16 = x × 1

448 = x

Therefore, Sallu car will travel 448 miles using 16 gallons of fuel.

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Therefore , the solution to the given problem of triangle comes out to be x =20 degree and y = 20 degree.

In a plane, any three points can be joined to form triangles, that have 3 components and three angles. They were among the first geometrical forms to be investigated. Because each polygon, regardless of its number of sides (four, five, six, or n), may be divided into a triangle, they are especially significant.

Here,

Given : 140 degree

Since it is a scalar triangle

two sides will have equal angle,

Thus ,

x=y

=> x+ x + 140 =180

=> 2x = 180-140

=> 2x =40

=> x =20

Therefore , the solution to the given problem of triangle comes out to be

x =20 degree and y = 20 degree.

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Ticket #1  ║  Ticket #2  ║  Ticket #3  ║  Ticket #4  ║  Ticket #5

  $150               $300             $450              $600              $750

Step-by-step explanation:

The table shows tickets #1-5, but if you want to go up to tickets #6 and #7, then Ticket #6 would be $900, and Ticket #7 would be $1,050. Due to each ticket being equivalent to $150, you get your answer by adding 150 for each ticket or multiplying 150 × 7.

Answer: m<5 = 142°

Step-by-step explanation:

On solving the provided question, we can say that - by prime factorization the factors of 5 are 5 and 1

A number that divides another number by itself with no residual is known as a factor. In other words, if multiplying two whole numbers results in the creation of a product, the numbers we are multiplying are factors of the product since the product is divisible by them. Division and multiplication are the two ways to discover factors. A number or other mathematical object is factorized or factored in mathematics by expressing it as the product of numerous factors, often smaller or simpler things of the same sort. One factorization of the polynomial x2 - 4 is 3 5, which is also a factorization of the number 15.

The factors of 5 are -

5and 1

as 5 = 5 X 1

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Answer:

x=-7/6, y=-8/3. (-7/6, -8/3).

Step-by-step explanation:

6x-3y=1

y=-2x-5

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

6x-3(-2x-5)=1

6x+6x+15=1

12x+15=1

12x=1-15

12x=-14

x=-14/12=-7/6

y=-2(-7/6)-5=7/3-5=7/3-15/3=-8/3

308 cubic yards of sand will be needed for 280 square yards of surface.

If 1.1 cubic yards of sand are needed for every 100 square yards of surface, we can find the amount of sand needed for 280 square yards of surface using the proportion:

1.1 cu yd / 100 sq yd = x cu yd / 280 sq yd

To find the value of x, we can cross-multiply and solve for x:

1.1 cu yd * 280 sq yd = x cu yd * 100 sq yd

x = 1.1 cu yd * 280 sq yd / 100 sq yd

x = 308 cu yd

So, 308 cubic yards of sand will be needed for 280 square yards of surface.

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On simplifying the values obtained for the fractions are - 3 / 3/4= 4, 5 / 3/4= 6.66, 8 / 4/7= 14, 6 / 3/5= 10, 2 / 5/8= 3.2 and 4 / 8/9= 4.5.

What is fraction?

In mathematics, a fraction is represented by a number that identifies a portion of a whole. A fraction is a component or section taken from a whole, which can be any number, a certain amount, or an object.

The first fraction is 3/(3/4).

The denominator will reciprocate.

Simplify, the fraction -

3 × 4/3 = 4

The second fraction is 5/(3/4).

The denominator will reciprocate.

Simplify, the fraction -

5 × 4/3

20/3 = 6.66

The third fraction is 8/(4/7).

The denominator will reciprocate.

Simplify, the fraction -

8 × 7/4 = 14

The fourth fraction is 6/(3/5).

The denominator will reciprocate.

Simplify, the fraction -

6 × 5/3 = 10

The fifth fraction is 2/(5/8).

The denominator will reciprocate.

Simplify, the fraction -

2 × 8/5

16/5 = 3.2

The sixth fraction is 4/(8/9).

The denominator will reciprocate.

Simplify, the fraction -

4 × 9/8

9/2 = 4.5

Therefore, the values of fractions are 4, 6.66, 14, 10, 3.2 and 4.5.

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The ratio for 5 / 15 based on the information is 1:3. The value of x is 1.

Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).

This simply indicates that you're dividing the variable A by B. Let us say for instance, the ratio will be 3/10 if A is 3 and B is 10.

The ratio for 5 / 15 will be:

= 5 / 15

= 1 / 3

= 1:3

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The following equations are equivalent:

2 + x = 5

x + 1 = 4

Negative 5 + x = negative 2

This is because, in each equation, x is the same variable, and it has the same value on both sides of the equation.

In the first equation, x is equal to 3.

In the second equation, x is equal to 3

In the third equation, x is equal to -3

Note that the equation 9 + x = 6 and x + (negative 4) = 7 are not equivalent as these equations have different values for x.

The equation of line segment AB, whose endpoints are A(x, y) = (2, 1) and B(x, y) = (1, - 1.5), is P(x, y) = (1 - k) · (2, 1) + k · (1, - 1.5), for 0 ≤ k ≤ 1.

In this problem we need to determine the equation that described the line segment AB, whose endpoints are points within other two line segments. The location of a point can be found by means of the following formula:

P''(x, y) = P(x, y) + k · [P'(x, y) - P(x, y)], 0 ≤ k ≤ 1

Where:

First, determine the locations of endpoints A and B:

A(x, y) = (- 2, 3) + 0.5 · [(6, - 1) - (- 2, 3)]

A(x, y) = (- 2, 3) + 0.5 · (8, - 4)

A(x, y) = (- 2, 3) + (4, - 2)

A(x, y) = (2, 1)

B(x, y) = (4, 3) + 0.75 · [(0, - 3) - (4, 3)]

B(x, y) = (4, 3) + 0.75 · (- 4, - 6)

B(x, y) = (4, 3) + (- 3, - 4.5)

B(x, y) = (1, - 1.5)

Second, derive the equation of line segment AB:

P(x, y) = A(x, y) + k · [B(x, y) - A(x, y)]

P(x, y) = (2, 1) + k · [(1, - 1.5) - (2, 1)]

P(x, y) = (1 - k) · (2, 1) + k · (1, - 1.5), for 0 ≤ k ≤ 1.

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540 yards should be purchased to enclose the deck and option B is correct.

A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides.

A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.

Pools dimension = 1:3

Length = 60 × 3

= 180

Breadth= 30 × 4

= 90

Perimeter of rectangle = 2(l+b) = 2(90+180)

P = 2(270) = 540 yards

Thus, 540 yards should be purchased to enclose the deck and option B is correct

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Answer: Slower

Step-by-step explanation:

Speed is a measure of how quickly an object moves, and it is calculated as distance traveled divided by time. Since Jorge and Zahara's dad traveled the same amount of time but Jorge traveled a shorter distance, it can be inferred that Zahara's dad traveled at a faster speed.

Another way to understand this is that, if Jorge and Zahara's dad were driving at the same speed, they would have traveled the same distance in the same amount of time. However, since Jorge traveled a shorter distance than Zahara's dad, it can be inferred that Jorge was driving at a slower speed.

Answer:

Step-by-step explanation:

Answer:

96

Step-by-step explanation:

Answer:

D. 10/3x^2+3x

Step-by-step explanation:

The product of the two rational expressions is:

(2/x+1) * (5/3x)

Multiply the numerator of the first fraction by the numerator of the second fraction and the denominator of the first fraction by the denominator of the second fraction:

(2*5) / (x+1) * (3x)

Which simplifies to:

10 / (x^2 + x)

So the correct answer is:

D. 10/3x^2+3x

Answer:

10c-4+11d Welcome :D

Step-by-step explanation:

The solution for the given decimal multiplication is 0.025.

To multiply two decimal numbers, first multiply the values without the decimal points.

The digits in the factors that follow the decimal point should now be added together.

Following that, the dot should be placed in the product so that it has the same number of digits as the total number of factors.

If there are more decimal places than digits in the number, place zeroes immediately after the dot.

If there are more decimal places present compared to digits in the product, fill the decimal places with zeroes immediately after the dot.

For the given question, multiply -5 * -5 = 25

Now the total digits after the decimal point in factors are 3.

But there are only 2 digits in 25.

So fill the decimal place with a zero.

Therefore the product of given decimal numbers is 0.025.

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Therefore , the solution of the given problem of congruent comes out to be in this case we have two side equal and one side common so it is sss

Two figures are said to be "congruent" if they can be positioned perfectly over one another. Both of the bread slices are the same size and shape when stacked one on top of the other. Congruent refers to things that are exactly the same size and shape.

SSS definitions. an autonomous government organization responsible for overseeing military conscription. Selective Service and Selective Service System are synonyms. independent agency kind. a federal agency that was established by a congressional act and is unrelated to the executive departments.

In this case we have two side equal and one side common so it is sss

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By applying pythagorean theorem and perimeter formula, The answer is D 9+[tex]\sqrt{2}[/tex] +[tex]\sqrt{5}[/tex]

The Pythagorean theorem is a fundamental result in mathematics named after the ancient Greek mathematician Pythagoras. It states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Perimeter is a measure of the distance around the outside of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape. The formula for perimeter depends on the shape. For example, the perimeter of a rectangle is twice the sum of its length and width, while the perimeter of a circle is equal to its circumference.

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Answer:

13009 is the best answer for this question

The equation in slope-intercept form of the line that passes through the point (0, -4) and has a slope of 5 is y = 5x - 4.

The form of a line's slope intercept is one of the most common ways to represent a line's equation. The slope intercept formula can be utilized to find a line's equation given its slope and y-intercept for a straight line ( the y-coordinate of the point where the line intersects the y-axis). For a line to exist, every point along the line must be satisfied by its equation. This straight line equation, which is represented as, can be resolved in a number of ways.

1. Slope-intercept form

2. Two-point form

3. Intercept form

4. Point slope form

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Answer: The interest rate is 0.16 or 16% ✅

Step-by-step explanation:

The interest rate is the percentage of the principal (the initial amount of money) that is paid as interest over a certain period of time. To find the interest rate in this scenario, we can use the formula:

Interest = Principal x Interest Rate x Time

In this case:

Interest = $12,800

Principal = $40,000

Time = 4 years

So we can set up the equation:

12800 = 40000 x Interest Rate x 4

To find the interest rate, we can divide both sides of the equation by 40000 x 4, which gives us:

12800 / (40000 x 4) = Interest Rate

We can simplify this fraction:

0.16 = Interest Rate

So the interest rate is 0.16 or 16%.

When Todd made $12,800 in interest by placing $40,000 in a savings account with simple interest for 4 years, the interest rate was 7.5%.

Simple interest is a formula for calculating the amount of interest that will be charged on a sum of money at a specific rate and during a specific time frame.

In contrast to compound interest, where the interest of one year's principal is added to the principal of the following year to calculate the interest, the principal sum in the case of simple interest stays the same.

Simple Interest = [tex]$ \frac{ \text P \times \text R \times \text T}{100}[/tex]

where,

P = Principal,

R = Rate of Interest in % per annum, and

T = Time, in years

Here given that,

Todd made $12,800 in interest, i.e. Simple Interest = 12,800

By placing $40,000 in a savings account, i.e. Principal = 40,000

with simple interest for 4 years, i.e. Time = 4 years

To find, interest rate

Substitute the data into the simple interest formula

[tex]$ \Rightarrow 12,800 = \frac{40,000 \times \text R \times 4}{100}[/tex]

[tex]$ \Rightarrow \text R = \frac{ 12,000 \times 100}{40,000 \times 4}[/tex]

[tex]$ \Rightarrow \text R = \frac{1,200,000}{160,000}[/tex]

⇒ R = 7.5%

Thus, the interest rate was 7.5%.

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Y-intercept linear 12 shows that the total cost will be $12.00 when the taxi travels 0 miles.

the connection between two variables that, when plotted on the coordinate plane, forms a straight line. The term "linear expression" refers to both the linear equation and the expression that depicts a linear relationship.

(2, 15), (5, 19.50), (7, 22.50), and (10, 27) are the coordinates (15, 34.50)

We will obtain a straight line if we plot the points on the XY coordinate system. The line crosses the Y axis at 12.00, as can be seen. As a result, the y-intercept is 12.00, and its coordinate is (0,12)

The y-intercept in this case is 12, which indicates that the total cost will be $12.00 even if the taxi travels 0 miles.

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Ann should have switched the inequality symbol to not include 16 as a possible choice. The correct answer would be an option (C).

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

As per the question, we have been given that Ed's birthday is less than 16 days

away and that Ann writes the inequality

d ≤ 16, where d equals the number of days, to represent this.

Thus, He should have switched the inequality symbol to not include 16 as a possible choice.

Hence, the correct answer would be an option (C).

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