Question 1
Identify the percent of change as an increase or a decrease.

50 pounds to 35 pounds

Answer: 94%

Step-by-step explanation:  

solution: 47/50 as a percent is 94%

If the perimeter of the isosceles triangle is 12 cm, then the base of the triangle (x), as well as the length of the triangle leg (x) is 4 cm.

An isosceles triangle is a type of triangle in which two sides have the same length. These two equal sides are referred to as the legs of the triangle, while the remaining side is known as the base.

The perimeter of a triangle is the sum of the lengths of all its sides. In this case, since the triangle is isosceles, the base and one leg have the same length (x), and the other leg also has the same length (x). Therefore, the perimeter of the triangle is 2x + x = 3x. Given that the perimeter of the isosceles triangle is 12 cm, then:

3x = 12

 x = 12/3

 x = 4

So, the base and legs of the isosceles triangle each have a length of 4 cm.

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Your question seems to be missing the value for the perimeter of the triangle, but I suppose the complete question was:

"The length of the base of an isosceles triangle is x. The length of a leg is x. The perimeter of the triangle is 12 cm. Find x."

The value of k in the equation is  3x + e^(x^2-3x/2)

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

y = 2ln(k - 3x) + x^2 - 3x

The x-axis is the set of points where y = 0. To find where the curve crosses the x-axis, we need to solve the equation y = 0 for x.

y = 2ln(k - 3x) + x^2 - 3x

so

0 = 2ln(k - 3x) + x^2 - 3x

We can re-arrange this equation to solve for x:

x^2 - 3x + 2ln(k - 3x) = 0

Now we can use the quadratic formula to find x.

x = (3 +/- sqrt(3^2 - 4(2ln(k - 3x))))/2

Now we know that there is only one root, we can pick the positive value and solve for k using k-3x = e^(x^2-3x/2)

k = 3x + e^(x^2-3x/2)

This is the final solution for k.

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Answer:

128 дней (days)

Step-by-step explanation:

5375/42 = 128 (округляем)

Answer:

128 days

Step-by-step explanation:

To solve this problem, we simply have to divide the total amount of oil in the tank by the amount of oil used each day.

[tex]5375 \textrm{ liters} \times \dfrac{1 \textrm{ day}}{42 \textrm{ liters}} = \dfrac{5375}{42} \textrm{ days} \approx 128 \textrm{ days}[/tex]

So, the tank will be empty after 128 days.

Note that the number of days is approximate; normally when measuring in the real world, whole numbers are used, as decimals in certain contexts (like in this situation) are confusing. So to simplify our answer, we can simply round up to 128 because by the end of the 128th day, the tank will be empty.

The ratio between the weights, giving how much Piglio is heavier than Whiskers, is given as follows:

1.5.

The ratio between two amounts a and b is obtained applying the proportion between these two amounts, that is, dividing a by b, as follows:

Ratio = a/b.

Which gives how many times greater the measure a is than the measure b, if the ratio is greater than 1.

The weight for each cat in this problem is given as follows:

The ratio between the weights of Piglio and Whiskers is given as follows:

Ratio = 4/2.67

Ratio = 1.5.

Meaning that Piglio is 1.5 times heavier than Whiskers.

Whisker's weight is given as follows: 2 and 2/3 kg.

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The set of properties for inequalities is as follows:

1. Additive characteristics of inequality

2. Inequality's subtraction property

3. The inequality's multiplication property

4. The unequal division property

5. Converse Property

An inequality is a relationship between two expressions that can be described mathematically and can be represented by any of the following symbols: >, <, ≤, ≥, =, and ≠.

The set of properties for inequalities is as follows:

1. Additive characteristics of inequality: The inequality remains the same even if both sides are given the same value.

2. Inequality's subtraction property: The inequality remains the same even after deducting the same amount from each side of it.

3. The inequality's multiplication property: Take p and q, two positive numbers. When p and q are both multiplied by the same positive value, the inequality stays the same. However, the inequality changes when p and q are both multiplied by the same negative value.

4. The unequal division property: Take p and q, two positive numbers. When p and q are both divided by the same positive number, the inequality is unaffected. However, the inequality is reversed when p and q are split by the same negative value.

5. Converse Property: According to the converse property, all we need to do to reverse the inequality symbol is flip the number.

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Answer: 96 and 97

Step-by-step explanation:

The system of Equation the tables represent are:

y = 11.5x + 22 and y = –13x + 218

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

Manuel:

slope = (33.50- 22)/ (1-0)

slope = 11.5

So, the Equation for Manuel

y- 22= 11.5 (x- 0)

y- 22 = 11.5x

y= 11.5x + 22

Ruben:

slope = (205- 218)/ (1-0)

slope = - 13

So, the Equation for Ruben

y- 218= -13 (x- 0)

y- 218 = -13x

y= -13x + 218

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Answer:

I= PTR/100 where P=Principal, T = Time period in years, R = Rate of interest per annum.

The area of the trapezium shown is 57.97 cm²

An equation is an expression that shows the relationship between variables and numbers.

The area for a two dimensional shape is the amount of space occupied for that shape.

The area of a trapezium is given by:

Area = (1/2)(sum opposite base) * height

For the trapezium shown, the parallel sides have a measure of 17 inches and 31 inches respectively. The height is 11.7 inches:

Area = (1/2)(7.9 + 10.8)(6.2) = 57.97 cm²

The area is 57.97 cm²

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Answer:

Perimeter = 162 units

Area = 1508 square units

Step-by-step explanation:

Given expressions:

If x = 10, then:

The formula for the perimeter of a rectangle is:

where w is the width and l is the length.

Therefore, the perimeter of the rectangle is:

[tex]\implies \sf P = 2(29 + 52)[/tex]

[tex]\implies \sf P = 2(81)[/tex]

[tex]\implies \sf P = 162\;units[/tex]

The formula for the area of a rectangle is:

where w is the width and l is the length.

Therefore, the area of the rectangle is:

[tex]\implies \sf A=29 \cdot 52[/tex]

[tex]\implies \sf A=1508\;square\;units[/tex]

Answer:

Area of rectangle = 1508

Perimeter of rectangle = 162

Step-by-step explanation:

Now we have to,

→ find the perimeter and area.

→ where x = 10.

Perimeter of rectangle is,

→ P = 2 × (L + W)

→ P = 2 × (5(10) + 2 + 3(10) - 1)

→ P = 2 × (50 + 2 + 30 - 1)

→ P = 2 × 81

→ [ P = 162 ]

Area of rectangle will be,

→ A = L × W

→ A = (5(10) + 2) × (3(10) - 1)

→ A = (50 + 2) × (30 - 1)

→ A = 52 × 29

→ [ A = 1508 ]

Hence, these are the values.

The length of diagonal AC is 54.8 inches when two sides are 29inches and 25 inches long.

To find the length of diagonal AC in the kite-shaped sandbox, we can use the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the length of the hypotenuse (the longest side) is equal to the square root of the sum of the squares of the other two sides.

Identify the right triangle. In this case, we can see that the right triangle is formed by diagonal DB and the two sides of length 25 inches, which we'll call side a.

Substitute the known values into the formula, where AC is the hypotenuse and a and DB are the other two sides of the triangle: AC^2 = a^2 + DB^2

Solve for AC by taking the square root of both sides: AC = √(a^2 + DB^2)

Substitute the given values for a and DB: AC = √(25^2 + 49^2) = √(625 + 2401) = √3016 = 54.8

It's important to note that the kite shape can be considered as two congruent right triangles. The sides 25 and 29 are the legs, and the diagonal DB (49 inches) is the hypotenuse of one of the triangles. Since the triangles are congruent, their hypotenuse will have the same length. Therefore, the diagonal AC, which is the hypotenuse of the other triangle, also has a length of 49 inches.

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Answer:

x = 35°

Step-by-step explanation:

AC is a straight line with the 3 angles lying on it summing to 180°, so

∠ E + ∠ D + ∠ G = 180°

55° + ∠ D + 90° = 180°

145° + ∠ D = 180° ( subtract 145° from both sides )

∠ D = 35°

then

x  and ∠ D are vertically opposite angles and are congruent, thus

x = 35°

To find the equation of the line, we can use the two points on the line.

An equation is a mathematical statement that expresses the relationship between two or more variables, or a condition that two or more expressions must satisfy. An equation typically involves an equal sign, with an expression on either side of the sign. The expressions on each side of the equation can contain constants, variables, functions, operations, and other mathematical symbols. Equations are used to solve problems in mathematics, physics, engineering, chemistry, economics, and other scientific and practical fields.

The distance between a point (P) and a line (L) can be found using the following formula:
d = |(ax + by + c)|/√(a^2 + b^2)

where (a, b, c) are the coefficients of the line equation, and (x, y) are the coordinates of the point.

To find the equation of the line, we can use the two points on the line. Let's say these two points are (x1, y1) and (x2, y2). We can calculate the equation of the line using the following formula:

a = (y2 - y1)/(x2 - x1)
b = -1
c = y1 - ax1

Using these equations, we can easily calculate the distance between the point and the line.

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Therefore , the solution of the algebraic expression is the value of 3b - 5c when b = 5 and c = 2 is 5

An algebraic expression is a mathematical phrase that can contain numbers, variables, and mathematical operations. It represents a mathematical relationship, but it does not have a specific value. Algebraic expressions can be simple or complex, and they can be used to represent mathematical concepts or to perform calculations.

Here,

To find the value of 3b - 5c when b = 5 and c = 2, we can substitute these values into the expression and simplify it.

Given 3b - 5c = 3(5) - 5(2) = 15 - 10 = 5

Hence, the value of 3b - 5c when b = 5 and c = 2 is 5

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Answer:

Step-by-step explanation:

If two right triangles share an acute angle measure, they are similar by angle-to-angle similarity. Corresponding side length ratios in the triangle are the same. The ratio of the side lengths of a right triangle depends only on the acute angle.

So on solving provided question we can say that the exponent will be as follows  [tex]e^{x^{-2y}} = e^{x^{3}} = e^{34}[/tex].

Exponentiation, often known as "b raised to the nth power," is a mathematical operation denoted by the symbol bn that involves two numbers: a base number, b, and an exponent, or power, n. Exponents show how many times a number has been multiplied by itself. As an illustration, 2-3 (written as 23) denotes: 2 x 2 x 2 = 8. 23 is not equivalent to 2 + 3 = 6. Recall that an integer raised to the power of one equals itself. A approach to express huge numbers as powers is through the use of exponents. Exponent, then, is the quantity that indicates how many times a number has been multiplied by itself. As an illustration, 6 is multiplied by 4 to provide 6 x 6 x 6 x 6. It may be expressed as 64. 4 is where

the given exponent is

[tex]e^{x^{-2y}} = e^{x^{3}} = e^{34}[/tex]

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The formula for the area of a rhombus is a = d1d2, where d1 and d2 are the lengths of the diagonals. The equivalent equation is d1 = 2A/d2 and d2 = 2A/d1.

The formula for rhombus area is as follows:

A= 1/2 d1d2

where d1d2 and are the rhombus's diagonals.

The comparable expressions must be found.

Because A =  1/2 d1d2

We must first eliminate the denominator 2, regardless of whether we need to construct the corresponding statement in terms of d1 or d2. When we multiply the two sides of the previous equation by two, we get

2A =  d1d2

So, the equivalent expressions are d1 = 2A/d2 and d2 = 2A/d1

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Answer:

The height is 32

Step-by-step explanation:

The ratio of width to height is

4:3

We know the height is 24  so to go from 3 to 24 is multiplying by 8.

Multiply all terms by 8

4 * 8  : 3 * 8

32: 24

The ratio of the width to height is

32:24

The height is 32

=================================================

Work Shown

width/height = 4/3

w/24 = 4/3

3w = 24*4

3w = 96

w = 96/3

w = 32 cm is the width

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

Another approach.

The ratio of width to height is 4:3, meaning a screen that has width 4 cm and height 3 cm is possible. Instead, we want the "height 3 cm" to be "height 24 cm". This is a jump of "times 8".

Multiply both parts of that ratio by 8 to get...

4:3

8*4:8*3

32:24

A screen that is 32 cm wide and 24 cm tall will give us a ratio 4:3 when simplifying fully.

The order of the numbers is important. We have the width listed first simply because it was listed first in the phrasing "ratio of width to height".

Using simple mathematical operations, we know that Adalyn can purchase 14 cans if she spends no more than $30.

An operation is a function in mathematics that transforms zero or even more input values into a clearly defined output value.

The firm's arity is influenced by the number of operands.

Most people believe that addition, subtraction, multiplication, and division are the four basic operations in mathematics.

So, we know that:

Money =30 + 3 = 33

Price per can 2.25.

Then, she can buy:

33/2.25 = 14.67

Round off to 14 cans.

Therefore, using simple mathematical operations, we know that Adalyn can purchase 14 cans if she spends no more than $30.

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The area of the figure, which has a triangle and a rectangle with the same height, is 275 cm2.

You may also refer to it as a quadrilateral that is equiangular, meaning that all of its angles are equal. The parallelogram could alternatively have a straight angle. Rectangles with four sides that are all the same size are called squares. Four 90-degree vertices and equal parallel sides make up a quadrilateral with the rectangular shape. A rectangle is also referred to as a parallelogram since its opposing sides are parallel and equal.

given

Area of Figure = Area of Rectangle + Area of Triangle 

= l*b+ 1/2*b*h 

= 10 * 20 * 1/2 * 15 * 10 

= 275cm2

The area of the figure, which has a triangle and a rectangle with the same height, is 275 cm2.

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Answer:

Drew is incorrect

Step-by-step explanation:

Let the number be x such that if the product of the number and 4 is 1.08 then

x * 4 = 1.08

Divide both sides by 4

x = 1.08/4

= 0.27

Drew is incorrect because the result (1.08) has 2 decimal places and not one like he concluded. The number of digits before the decimal point for the numbers being multiplied must be 2.

The length of side of the cube with 181 square inches surface area is 5.5 inches

The information that was provided indicates that the surface area of the cube is 181.5 square inches. A cube's surface area is calculated as the square of the length of each side multiplied by 6. The formula to use in order to get the total surface area of a cube is = 6a²

Where "a" represents the side of the cube.

As a result, 6a² = 181.5 square inches

a² = 181.5/6

a² = 30.25

a² = √30.25

a = 5.5 inches

Therefore, each face of the cube is 5.5 inches on a side.

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The slope of the green line is -4/3.

The correct option is C.

What is the slope of the line?

The slope of a line is a measure of how steep the line is and the direction it is going. It is defined as the ratio of the "rise" (the change in the y-coordinate) to the "run" (the change in the x-coordinate) between two points on the line.

The slope of a line is often represented by the letter "m" and can be calculated using the following formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are two points on the line.

It is given that the lines graphed below are parallel.

We know that if two line having slopes m₁ and m₂ are parallel, then

m1 = m2

In other words, the slopes of two parallel lines are the same.

The slope of the red line is -4/3 and it is parallel to the green line. It means the slope of red and green line are the same.

The slope of green line = Slope of the red line

The slope of the green line = -4/3

Hence, The slope of the green line is -4/3.

The correct option is C.

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The slope of the green line is -4/3. The correct option is C.

What is the slope of the line?

The slope of a line is a measure of how steep the line is and the direction it is going. It is defined as the ratio of the "rise" (the change in the y-coordinate) to the "run" (the change in the x-coordinate) between two points on the line.

The slope of a line is often represented by the letter "m" and can be calculated using the following formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are two points on the line.

It is given that the lines graphed below are parallel.

We know that if two line having slopes m₁ and m₂ are parallel, then

m1 = m2

In other words, the slopes of two parallel lines are the same.

The slope of the red line is -4/3 and it is parallel to the green line. It means the slope of red and green line are the same.

The slope of green line = Slope of the red line

The slope of the green line = -4/3

Hence, The slope of the green line is -4/3.

The correct option is C.

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The area of the triangle GHJ is 48 square units.

The area of a triangle can be found using the formula:

Area = (1/2) * base * height.

In this question, we are given that triangle GHJ has a base of 12 units and a height of 8 units. To find the area of the triangle, we simply substitute these values into the formula and solve.

Area = (1/2) * 12 * 8 = 48 square units

To be more specific, first, we multiply the base and height together to get 12*8 = 96. Then we divide 96 by 2 to get 48. Therefore, the area of triangle GHJ is 48 square units.

It's important to note that the base and height of a triangle must be perpendicular to each other in order for the formula to be accurate. Also, the unit of measurement used for the base and height must be consistent, otherwise, the area calculated will not be correct.

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The complete question is:

A triangle GHJ has a base of 12 units and a height of 8 units. What is the area of the triangle GHJ?

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The measure of the remaining angle is 71 degrees.

The measure of the remaining angle in a triangle can be found by subtracting the sum of the measures of the other two angles from 180 degrees.

Key points:

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Answer:

Step-by-step explanation:

[tex]\frac{a^{3}-2a^{2}-15a }{a^{3}+a^{2}-30a} =\frac{a^{2}-2a-15}{a^{2}+a-30}[/tex]

[tex]\frac{a^{2}-2a-15}{a^{2}+a-30}=\frac{(a-5)(a+3)}{(a-5)(a+6)}= \frac{(a+3)}{(a+6)}[/tex]

The part of the field would Roni mow will be 4 3/7 of the field.

To find out what part of the field Roni would mow if he and Allie worked together to mow the field, you would need to calculate their combined rate of mowing.

You can find the combined rate by adding the rates of each person working alone:

Combined rate = (Roni's rate) + (Allie's rate)

Combined rate = (1/30 hour) + (1/75 hour) = (5/150) + (2/150) = (7/150) hour

Then divide the rate of Roni by the combined rate to find the proportion of the field that Roni would mow:

(Roni's rate) / (Combined rate) = (1/30 hour) / (7/150 hour) = (30/7) / 1 = 4.2857142857142856

So Roni would mow about 4.29 or roughly 4.3/7 of the field if he and Allie worked together.

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