the values of a that satisfy the inequality |a|≤5 are those that satisfy both a ≤ 5 and a ≥ -5. This is why the expression equivalent to |a|≤5 is a ≥ –5 and a ≤ 5.
What is expression ?
In mathematics, an expression is a combination of numbers, variables, and operators that can be evaluated to produce a value. It can be as simple as a single number or variable, or as complex as a long sequence of operations involving multiple variables and operators.
The expression |a|≤5 means that the absolute value of a is less than or equal to 5. The absolute value of a number is its distance from zero on the number line, regardless of whether the number is positive or negative.
So, if |a|≤5, then a must be between -5 and 5, including both.
To see why this is true, consider two cases:
If a is greater than or equal to zero, then |a| = a, and so we have a ≤ 5.
If a is less than zero, then |a| = -a, and so we have -a ≤ 5, which is equivalent to a ≥ -5.
Therefore, the values of a that satisfy the inequality |a|≤5 are those that satisfy both a ≤ 5 and a ≥ -5. This is why the expression equivalent to |a|≤5 is a ≥ –5 and a ≤ 5.
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Answer:
the values of a that satisfy the inequality |a|≤5 are those that satisfy both a ≤ 5 and a ≥ -5. This is why the expression equivalent to |a|≤5 is a ≥ –5 and a ≤ 5.
Step-by-step explanation:
What is expression ?
In mathematics, an expression is a combination of numbers, variables, and operators that can be evaluated to produce a value. It can be as simple as a single number or variable, or as complex as a long sequence of operations involving multiple variables and operators.
According to the given conditions :
The expression |a|≤5 means that the absolute value of a is less than or equal to 5. The absolute value of a number is its distance from zero on the number line, regardless of whether the number is positive or negative.
So, if |a|≤5, then a must be between -5 and 5, including both.
To see why this is true, consider two cases:
If a is greater than or equal to zero, then |a| = a, and so we have a ≤ 5.
If a is less than zero, then |a| = -a, and so we have -a ≤ 5, which is equivalent to a ≥ -5.
Therefore, the values of a that satisfy the inequality |a|≤5 are those that satisfy both a ≤ 5 and a ≥ -5. This is why the expression equivalent to |a|≤5 is a ≥ –5 and a ≤ 5.
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2. If \( \left[\begin{array}{rr}10 & 1 \\ -6 & -6\end{array}\right]=\left[\begin{array}{rr}1 & 2 \\ 3 & -3\end{array}\right]\left[\begin{array}{ll}a & b \\ c & d\end{array}\right] \), find \( a+b+c+d
The answer is \(a+b+c+d = 10\).
To find \(a+b+c+d\), we can use matrix multiplication to solve for each variable. Matrix multiplication is performed by multiplying the elements of each row of the first matrix by the corresponding elements of each column of the second matrix, and then summing the products.
So, we can set up the following equations:
\(10 = 1a + 2c\)
\(1 = 1b + 2d\)
\(-6 = 3a - 3c\)
\(-6 = 3b - 3d\)
Solving for each variable, we get:
\(a = 6 - 2c\)
\(b = (1 - 2d)/1\)
\(c = (6 + 3a)/(-3)\)
\(d = (3b + 6)/(-3)\)
Substituting the values of \(a\) and \(b\) into the equations for \(c\) and \(d\), we get:
\(c = (6 + 3(6 - 2c))/(-3)\)
\(d = (3((1 - 2d)/1) + 6)/(-3)\)
Solving for \(c\) and \(d\), we get:
\(c = -2\)
\(d = -1\)
Substituting these values back into the equations for \(a\) and \(b\), we get:
\(a = 6 - 2(-2) = 10\)
\(b = (1 - 2(-1))/1 = 3\)
So, \(a+b+c+d = 10 + 3 + (-2) + (-1) = 10\).
Therefore, the answer is \(a+b+c+d = 10\).
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The Kennedy high school cross country running team ran the following distances in recent practices 3.5, miles 2.5, miles 4 miles 3.25 miles, 3 miles, 4 miles and 6 miles find the mean and median of the team's distances
The result is the mean of 3.9 miles and median of the team's distances is 3.5 miles.
What is mean and median?Mean and median are two ways to measure the center of a set of numbers. Mean is the average of all the numbers in the set, while median is the middle number in the set. Mean is more affected by extreme values, while median is not. Mean is generally used when data is normal, and median when data is skewed.
Mean and median are both measures of central tendency, or measures of the center of a data set. Both measures are used to summarize a data set, but the mean is more affected by outliers, or extreme values, while the median is not.
The mean of the team's distances is 3.9 miles, and the median is 3.5 miles. To calculate the mean, add all the distances together (3.5 + 2.5 + 4 + 3.25 + 3 + 4 + 6) and divide by the number of distances (7). The result is the mean of 3.9 miles. To calculate the median, first order the distances from least to greatest (2.5, 3, 3.25, 3.5, 4, 4, 6) and take the middle number (3.5). The median of the team's distances is 3.5 miles.
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Use the properties of equality to find the value of x, in the equation 12(5x-4. 5)=36
Step-by-step explanation:
12(5x - 4.5) = 36
if that is really correct, then we solve this first by dividing both sides by 12
5x - 4.5 = 3
then we add 4.5 to both sides
5x = 7.5
and finally we divide both sides by 5
x = 1.5
A large wooden prism will be covered with spray paint for a prop in a school play. The prop must be painted on all sides. A can of spray paint costs $4.00 and will cover 40 square feet. What is the cost to paint the box ?
Part A: how many full cans of spray paint need to be purchased?
Part B What is the cost to paint the box
(a) The number of cans of spray paint that needs to be purchased is 3.
(b) The cost to paint the wooden prism is $12.00.
What is the cost of the painting?
To determine the cost of painting the wooden prism, we need to calculate the surface area of the prism and then divide it by the coverage of each can of spray paint.
Let's assume the wooden prism has dimensions of 6 feet by 4 feet by 3 feet.
Part A:
The surface area of the prism can be calculated as follows:
The top and bottom faces have an area of 6 ft x 4 ft = 24 ft² each
The two side faces have an area of 6 ft x 3 ft = 18 ft² each
The front and back faces have an area of 4 ft x 3 ft = 12 ft² each
Therefore, the total surface area of the prism is:
2(24 ft²) + 2(18 ft²) + 2(12 ft²) = 96 ft²
Since each can of spray paint covers 40 ft², we need:
96 ft² ÷ 40 ft²/can = 2.4 cans
We can't purchase a partial can of spray paint, so we need to round up to the nearest whole can.
Therefore, we need to purchase 3 cans of spray paint.
Part B:
The cost of painting the box will be the number of cans required multiplied by the cost per can.
Since we need to purchase 3 cans, the cost will be:
3 cans x $4.00/can = $12.00
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AB=AD and BC=DX
x = [?]
In the given figure by using the alternative angles rule we know that x = 82°.
What are alternate angles?Alternate angles are a unique type of angle in geometry.
The collection of non-adjacent angles on either side of the transversal is known as alternate angles.
Alternative Interior Angles: Angles are created on the inside, or interior, of two other lines when a third line known as the transversal crosses them. These other lines are typically parallel.
The alternate internal angles are those that are perpendicular to one another.
So, in the given figure:
∠ABD = ∠BDC = 35° (Alternate angles)
Then, ∠DBC will be:
82 + 35 + x = 180
117 + x = 180
x = 180 - 117
x = 63°
Then, ∠DBC = ∠BDA = 63° (Alternate angles)
Now, ∠DAB = 63 + 35 + x = 180
= 63 + 35 + x = 180
= 98 + x = 180
= x = 180 - 98
= x = 82°
Therefore, in the given figure by using the alternative angles rule we know that x = 82°.
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What is the image of the point (4,8)(4,8) after a rotation of 180^{\circ}180 ∘ counterclockwise about the origin?
After being rotated 180 degrees anticlockwise around the origin, the picture of the point (4,8) is (-4,-8).
After a 180-degree rotation, where is the image point?The fixed point is referred to as the rotational centre. The quantity of the rotation is described by the term "angle of rotation," which is measured in degrees. The equivalent of turning a figure 90 degrees anticlockwise is turning it 180 degrees clockwise. Hence, the resulting image of the point is (-1, 2).
How is a 180 degree anticlockwise rotation calculated?Below are the guidelines for rotation: rotation 90 degrees clockwise: (x,y) results in (y,-x) rotation of (x,y) at 90 degrees anticlockwise results in (-y,x) Rotating (x, y) 180 degrees both clockwise and anticlockwise results in (-x,-y).
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What are the coordinates of D1.5(ABCD) for A(2, 0), B(8, -4), C(4, -6), and D(-5, -10)?
Answer: To find the coordinates of D1.5(ABCD), we need to perform a dilation with center D and scale factor 1.5 on the coordinates of each point.
The coordinates of point D are (-5, -10). To dilate point A, we can subtract the coordinates of D from the coordinates of A, multiply by 1.5, and then add the coordinates of D back:
D1.5(A) = 1.5[(2, 0) - (-5, -10)] + (-5, -10) = 1.5(7, 10) + (-5, -10) = (6.5, 5)
Similarly, we can dilate points B and C:
D1.5(B) = 1.5[(8, -4) - (-5, -10)] + (-5, -10) = 1.5(13, 6) + (-5, -10) = (14.5, -4)
D1.5(C) = 1.5[(4, -6) - (-5, -10)] + (-5, -10) = 1.5(9, 4) + (-5, -10) = (7.5, 4)
Therefore, the coordinates of D1.5(ABCD) are A'(6.5, 5), B'(14.5, -4), C'(7.5, 4), and D(-5, -10).
Step-by-step explanation:
What is the 5th term of the sixth term of
the sequence A(n) = 6.3 + (n-1)(5)?
The given sequence is A(n) = 6.3 + (n-1)(5).
To find the 6th term of the sequence, we substitute n = 6 into the formula:
A(6) = 6.3 + (6-1)(5)
A(6) = 6.3 + 25
A(6) = 31.3
Now, to find the 5th term of this sequence, we need to substitute n = 5 into the formula:
A(5) = 6.3 + (5-1)(5)
A(5) = 6.3 + 20
A(5) = 26.3
Therefore, the 5th term of the 6th term of the sequence A(n) = 6.3 + (n-1)(5) is 26.3.
What's the expression of this?
Answer:
[tex](3m + 5n)(9m {}^{2} - 15mn + 25n {}^{2} )[/tex]
Step-by-step explanation:
Greetings!!!
Given expression
[tex]27m {}^{3} + 125n {}^{3} [/tex]
Apply exponents rule
Rewrite 27 as 3³
[tex] = 3 {}^{3} m {}^{3} + 125n {}^{3} [/tex]
Rewrite 125 as 5³
[tex] = 3 {}^{3} m {}^{3} + 5 {}^{3} n {}^{3} [/tex]
Apply exponent rule:
[tex]a {}^{m} b {}^{m} = (ab) {}^{m} \\ = 3 {}^{3} m {}^{3} = (3m) {}^{3} \\ = 5 {}^{3} n {}^{3} = (5n) {}^{3} [/tex]
Apply sum of cubes formula
[tex]x {}^{3} + y {}^{3} = (x + y) (x {}^{2} - xy + y {}^{2} )[/tex]
[tex](3m {}^{3}) + (5n {}^{3} ) = (3m + 5n)((3m) {}^{2} - 3m.5n + (5n {}^){2} ) \\ = (3m + 5n)((3m {}^{2} ) - 3m.5n + (5n {}^{2} ))[/tex]
simplify
[tex] = (3m + 5n)(9m {}^{2} - 15mn + 25n {}^{2} )[/tex]
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Write a formula for a linear function f(x) that models the situation, where x is the number of years after. In 2006 the average adult ate 56 pounds of chicken. This amount will increase by 0. 6 pounds per year until 2011
The required linear function is (f(x) = 0.6(x - 2006) + 56) and this can be determined by using the arithmetic operations.
Given :
In 2006 the average grownup ate fifty-six kilos of birds.
the amount will increase by means of zero.6 pounds in step with yr till 2011.
To determine the linear feature f(x) following steps can be used
Let 'x' be the number of years.
Then the total number of years since 2006 will be:
= x - 2006
The amount boom in kilos in line with 12 months could be:
= 0.6(x - 2006)
Now, add 56 to the above equation.
= 0.6(x - 2006) + 56
It is a type of function that has a constant rate of change between the independent variable (usually denoted as x) and the dependent variable (usually denoted as y). The general form of a linear function is y = mx + b, where m is the slope or the rate of change, and b is the y-intercept.
Linear functions are commonly used in mathematics, economics, physics, and engineering to model real-world phenomena that have a linear relationship between two variables. For example, the cost of producing a certain number of units of a product may be modeled by a linear function, where the slope represents the cost per unit and the y-intercept represents the fixed costs.
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Write an equation for a line parallel to y = 2 x + 1 and passing
through the point (1,5)
To find the equation for a line parallel to y = 2x + 1 and passing through the point (1,5), we need to remember that parallel lines have the same slope.
Since the slope of y = 2x + 1 is 2, the slope of the parallel line will also be 2.
Using the point-slope form of a linear equation, we can plug in the given slope and point to find the equation of the parallel line:
y - y1 = m(x - x1)
y - 5 = 2(x - 1)
Simplifying this equation gives us the equation for the parallel line:
y = 2x + 3
So, the equation for the line parallel to y = 2x + 1 and passing through the point (1,5) is y = 2x + 3.
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Lynn had 1(5)/(8) yards of ribbon. She made 6 identical bows and had 1(1)/(4) yards of ribbon left. How many yards of ribbon did Lynn use to make a bow?
The number of yards of ribbon Lynn used to make a bow is 1/16 yards.
To find out how many yards of ribbon Lynn used to make a bow, we need to subtract the amount of ribbon she had left from the amount she started with and then divide by the number of bows she made. We can do this using the following steps:
1. Convert the mixed numbers to improper fractions: 1(5)/(8) = 13/8 and 1(1)/(4) = 5/4
2. Subtract the two fractions: 13/8 - 5/4 = 13/8 - 10/8 = 3/8
3. Divide the result by the number of bows: (3/8) / 6 = 3/8 x 1/6 = 3/48 = 1/16
Therefore, Lynn used 1/16 yards of ribbon to make a bow.
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A track runner ran for 15 minutes, walked for 15 minutes, ran for another 20 minutes, and then walked for 10 minutes.
Which graph describes the relationship between runner's total distance and time?
graph with the x axis labeled time in hours and the y axis labeled total distance in miles, with a line segment from 0 comma 0 to 0.25 comma 1.25, a horizontal line segment from 0.25 comma 1.25 to 0.5 comma 1.25, a line segment from 0.5 comma 1.25 to 0.8 comma 2.4, and a horizontal line segment from 0.8 comma 2.4 to 1 comma 2.4
graph with the x axis labeled time in hours and the y axis labeled total distance in miles, with a line segment from 0 comma 0 to 0.25 comma 1.25, a line segment from 0.25 comma 1.25 to 0.5 comma 1.75, a line segment from 0.5 comma 1.75 to 0.8 comma 2.95, and a horizontal line segment from 0.8 comma 2.95 to 1 comma 2.95
graph with the x axis labeled time in hours and the y axis labeled total distance in miles, with a line segment from 0 comma 0 to 0.25 comma 1.25, a horizontal line segment from 0.25 comma 1.25 to 0.5 comma 1.25, a line segment from 0.5 comma 1.25 to 0.8 comma 0.1, and a horizontal line segment from 0.8 comma 0.1 to 1 comma 0.1
graph with the x axis labeled time in hours and the y axis labeled total distance in miles, with a line segment from 0 comma 0 to 0.25 comma 1.25, a line segment from 0.25 comma 1.25 to 0.5 comma 1.75, a line segment from 0.5 comma 1.75 to 0.8 comma 2.95, and a line segment from 0.8 comma 2.95 to 1 comma 3.15
Answer:
Step-by-step explanation:
graph with the x axis labeled time in hours and the y axis labeled total distance in miles, with a line segment from 0 comma 0 to 0.25 comma 1.25, a line segment from 0.25 comma 1.25 to 0.5 comma 1.75, a line segment from 0.5 comma 1.75 to 0.8 comma 2.95, and a horizontal line segment from 0.8 comma 2.95 to 1 comma 2.95
It's B.
Explanation: I took the test
given the growth population model 12000/3+e^-.02(t), what is the initial population and what is the maximum population?
The initial population for this model is 12,000 and the maximum population is 24,000. The equation 12000/3+e^-.02(t) is used to model population growth.
The initial population and maximum population can be found by examining the growth population model.
The initial population is represented by the term before the exponential function, which in this case is 12000/3. This means that the initial population is 4000.
The maximum population is represented by the term in the denominator of the fraction with the exponential function. In this case, the maximum population is 3. This means that the population will never exceed 3, even as time (t) increases.
In conclusion, the initial population is 4000 and the maximum population is 3 according to the given growth population model.
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The Grade 8 learners decided to start training more. They will either box or grid. There
are 125 Grade 8 learners, and they box and grid in the ratio 3:2. Calculate how many
learners participate in each sport?
justin wants to create a rectangular garden whose area is 81x^(2)-126x square units. If one dimension of the garden is 9x-14 units, what is the length of the other dimension?
The final answer length of the other dimension of the garden is 9x units.
To find the length of the other dimension of the garden, we need to use the formula for the area of a rectangle:
Area = Length x Width
We are given the area and one dimension, so we can plug those values into the formula and solve for the other dimension:
[tex]81x^2-126x[/tex] = (9x-14)(Length)
To solve for the length, we need to divide both sides of the equation by (9x-14):
Length =[tex](81x^2-126x)/(9x-14)[/tex]
Now we can simplify the right side of the equation by factoring out a common factor of 9x:
Length = (9x)(9x-14)/(9x-14)
The (9x-14) terms cancel out, leaving us with:
Length = 9x
So the length of the other dimension of the garden is 9x units.
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Can someone answer this, please? I need the help
Answer:
Proofs attached to answer
Step-by-step explanation:
Proofs attached to answer
How does the concept of conservation of mass apply to chemical reactions?
1.The reactants and products have exactly the same atoms.
2.The reactants and products have exactly the same molecules.
3.The change in the amount of matter is equal to the change in energy.
4.The change in the amount of matter is only a small percentage of the total mass.
Since the elements in the reactants and products are identical, the principle of conservation of mass is applicable to chemical processes. Choice (b) is accurate.
What is the short meaning of a chemical reaction?chemical reaction, the transformation of one or even more substances (the reactants) into one or more distinct substances (the products). Chemical components or chemical combinations make up substances.
How does a chemical reaction start?When atoms create or break molecular bonds, chemical processes take place. Reactants are the substances that begin a chemical reaction, and products are the substances that are created as a result of the reaction.
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what x-value makes the set of ratios equivalent
The following values of x, makes the set of ratios equivalent:
2: 3 = 6: 9
4: 7 = 24: 42
(6*2)12: 48 = 3: 12
12: 15 = 16: 20
What are ratios?The ratio can be used to determine how much of one item is contained in the other by comparing two sums of the same units. Ratios fall into two different groups.
Whereas the second is a part to whole ratio, the first is a part-to-part ratio. The part-to-part ratio demonstrates the link between two independent entities or organisations.
Now here in the 1st set:
2:3 = 6:x
Now, x = 6×3/2
⇒ x = 9
Similarly,
4:7=x:42
⇒ x = 24
The next ratio we have:
2x:48= 3:12
⇒ x = 6
Now, the last ratio,
12:15 = x:20
⇒ x = 16
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(B) 5 (C) 6 (D) 9 What is the solution set for the absolute value equation |2x-4|=20?
The solution set for the absolute value equation |2x-4|=20 is {-14, 14}.
Absolute Value EquationAn absolute value equation is one that contains an absolute value expression, such as ||x| - 1| = 2.
These types of equations are solved by breaking them down into two separate equations and solving each one separately:
one with the original absolute value expression and a positive value for the other side, and the other with the negated absolute value expression and a negative value for the other side.
The steps to solving an absolute value equation are as follows:
1. Write the equation in the form |expression| = value, where expression is the absolute value expression and value is the constant on the right-hand side.
2. Separate the equation into two equations: expression = value and expression = -value.
3. Solve each equation for the variable.
4. Check the solution(s) to ensure that they satisfy the original equation.
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Let f and g be polynomials of degree 3. Is it true that f ∘ g = g ∘ f?
A. Yes, always
B. No, it's only with polynomials with a degrees of 1
C. It is true in some cases
D. No, never
The true statement about the polynomials is (b) No, it's only with polynomials with a degrees of 1
How to determine the true statementGiven that the polynomials f and g have a degree of 3
The composition of two functions, f ∘ g (read as "f composed with g"), is not commutative in general, meaning that f ∘ g is not necessarily equal to g ∘ f.
This holds true for polynomials of degree 3 as well.
In fact, if f and g are two different polynomials of degree 3, then f ∘ g and g ∘ f will be different polynomials in general.
The equation f ∘ g = g ∘ f holds true is when f and g are constant polynomials, that is, polynomials of degree 0 or 1.
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Evaluate. Write your answer as a fraction or whole number without exponents. 10^-3
10⁻³ is equal to 1/1000 or 0.001.
What are Exponents?
Exponents are a shorthand way of representing repeated multiplication of a number by itself. They are indicated by a superscript number placed to the right and above the base number.
The superscript number represents the number of times the base number is multiplied by itself. For example, 2³ means 2 multiplied by itself three times, which equals 8.
Exponents are used to simplify large and small numbers, and are fundamental to algebraic and mathematical calculations. Exponents have several rules, such as the power of a power rule, product rule, quotient rule, and negative exponents rule.
10⁻³ can be evaluated as:
1 / 10^3 = 1 / 1000
Therefore, 10⁻³is equal to 1/1000 or 0.001.
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In the next four problems find the VOLUME of
the shapes. Label each answer correctly. Remember that volume is measured in cubic units.
5) Square prism: 4 cm x 4 cm x 8 cm
6) rectangular prism: 3 cm x 4 cm x 5 cm
7) cylinder: radius 6 cm, height 5 cm (round the answer to the nearest whole cubic centimeters.)
8) cone: radius 6 cm, height 5 cm (round the answer to the nearest whole cubic centimeter.)
Volume of square prism = 128 cm³
Volume of rectangular prism is, V = 60 cm³
Volume of cylinder is, V = 565.2 cm³
Volume of cone is, V = 188.4 cm³
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
The dimensions of the shapes are,
Square prism: 4 cm x 4 cm x 8 cm
Rectangular prism: 3 cm x 4 cm x 5 cm
Cylinder: radius 6 cm, height 5 cm
Cone: radius 6 cm, height 5 cm
Now, We know that;
Volume of square = Side² × Height
Hence, We get;
Volume of square = 4² × 8
= 128
And, Volume of rectangular prism is,
V = 3 cm x 4 cm x 5 cm
V = 60 cm³
Volume of cylinder is,
V = πr²h
V = 3.14 × 6² × 5
V = 565.2 cm³
Volume of cone is,
V = πr²h/3
V = 3.14 × 6² × 5/3
V = 565.2 /3
V = 188.4 cm³
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New Bread Bakery purchased new equipment by making a down payment of $2000 and agreeing to make payments of $458 at the end of each month for five years. Interest is 9.2% compounded monthly.
(a) What was the purchase price of the new equipment?
(b) How much interest will have to be paid?
a) The purchase price of the new equipment is $20,531.76.
b) The amount of interest that will have to be paid is $6,948.24.
The purchase price of the new equipment for New Bread Bakery can be found using the formula for the present value of an annuity:
PV = PMT * [(1 - (1 + i)^(-n)) / i]
Where PV is the present value (or purchase price), PMT is the monthly payment, i is the monthly interest rate, and n is the number of payments.
Plugging in the given values:
PV = 458 * [(1 - (1 + 0.092/12)^(-5*12)) / (0.092/12)]
PV = 458 * [(1 - (1 + 0.00767)^(-60)) / 0.00767]
PV = 458 * [(1 - 0.6887) / 0.00767]
PV = 458 * 40.4624
PV = 18,531.76
The purchase price of the new equipment is $18,531.76. However, this does not include the down payment of $2000. So, the total purchase price is:
PV + Down Payment = 18,531.76 + 2000 = $20,531.76
To find the amount of interest that will have to be paid, we can subtract the purchase price from the total amount paid over the five years:
Interest = (458 * 5 * 12) - 20,531.76 = 27,480 - 20,531.76 = $6,948.24
Therefore, the amount of interest that will have to be paid is $6,948.24.
(a) The purchase price of the new equipment is $20,531.76. (b) The amount of interest that will have to be paid is $6,948.24.
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help asap pls!! What should be reason 6 in the following proof?
Answer:
Step-by-step explanation:
alternate interior angles
More formally:
If two lines and a transversal form alternate interior angles that are congruent, then the two lines are parallel (Since ∠1 = ∠4)
Answer: Alternate Interior Angles Converse
Step-by-step explanation:
If two lines are cut by a transversal so the alternate interior angles are congruent, then the lines are parallel.
A product received discounts of 33%, 25%, and 5%. A markup on
cost of 50% was then applied to arrive at the regular unit selling
price of $349.50. What was the original list price for the
product?
The original list price for the product was $487.09.
To find the original list price for the product, we need to reverse the discounts and markup that were applied to it. Here is a step-by-step explanation:
Start with the regular unit selling price of $349.50.Reverse the 50% markup by dividing by 1.50. This gives us the cost before the markup: $349.50 / 1.50 = $233.00.Reverse the 5% discount by dividing by 0.95. This gives us the price before the 5% discount: $233.00 / 0.95 = $245.26.Reverse the 25% discount by dividing by 0.75. This gives us the price before the 25% discount: $245.26 / 0.75 = $326.35Reverse the 33% discount by dividing by 0.67. This gives us the original list price: $326.35 / 0.67 = $487.09.Therefore, the original list price for the product was $487.09.
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Verify the identity. 2 sec? y - 2 cot? = cot(" - y) = 2 - 2 cot'( % - y) = 2 (sec?y- 2 sec? y - 2 2 ) X = 2 Need Help? Read it Watch It
2(cot2 y + tan2 y) = 2(1) Verified
Verify the identity:
2 sec2 y - 2 cot2 y = cot(2y) - 2 cot(2y) = 2 - 2 sec(2y)
To prove the identity, start by applying the identity:
cot2 y = 1 - tan2 y
Substitute this in the left side of the equation:
2 sec2 y - 2(1 - tan2 y) = 2 sec2 y - 2 + 2 tan2 y
Simplify the equation by factoring out a 2 from the right side:
2 sec2 y - 2 + 2 tan2 y = 2(sec2 y - 1 + tan2 y)
Next, apply the identity:
sec2 y - 1 = cot2 y
Substitute this in the equation and simplify:
2(sec2 y - 1 + tan2 y) = 2(cot2 y + tan2 y)
Finally, apply the identity:
cot2 y + tan2 y = 1
Substitute this in the equation and simplify:
2(cot2 y + tan2 y) = 2(1)
The identity is thus verified.
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HELP ASAPP!
The parallel lines are marked with "feathers". Find the measures of the angles located at positions a, b, c, d, e, & f.
Answer:
Step-by-step explanation:
a=70
b=45
c=65
d=45
e=70
f=110
make sure to add degree symbol
Enjoy :)
what is 3/8 divided by 1/4
Answer:[tex]1\frac{1}{2}[/tex]
Every pyramid is a prism, is it True? and why?
No, it is not true that every pyramid is a prism, because they have different properties.
A pyramid is a solid shape that has a base and triangular faces that meet at a point called the apex. The base of a pyramid can be any polygon, such as a square, triangle, or rectangle. A pyramid is named according to the shape of its base. For example, a pyramid with a square base is called a square pyramid.
A prism, on the other hand, is a solid shape that has two identical bases that are parallel to each other and rectangular faces that connect the bases. The bases of a prism can also be any polygon, and a prism is named according to the shape of its bases. For example, a prism with a rectangular base is called a rectangular prism.
So, while both pyramids and prisms are three-dimensional shapes with bases and faces, they have different properties and are not the same. Therefore, it is not true that every pyramid is a prism.
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