If a conditional and its converse are always true, then the statement is a
A. converse.
B. conditional.
C. biconditional.
D. counterexample.
Can someone please help me
Noam walks home from school by walking 8 blocks north and then 6 blocks east. How much shorter would his walk be if there were a direct path from the school to his house? Assuming that the blocks are square.
To find out how much shorter Noam's walk would be if there were a direct path from the school to his house, we need to calculate the displacement using the Pythagorean theorem. Noam walks 8 blocks north and then 6 blocks east. The displacement is the straight-line distance from the starting point to the endpoint. Therefore, the displacement is the square root of (8² + 6²), which is the square root of 64 + 36, which is the square root of 100, which is 10 blocks. So, if there was a direct path, Noam's walk would be 10 blocks shorter.
Explanation:To find out how much shorter Noam's walk would be if there were a direct path from the school to his house, we need to calculate the displacement using the Pythagorean theorem. Noam walks 8 blocks north and then 6 blocks east. The displacement is the straight-line distance from the starting point to the endpoint.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Therefore, the displacement is the square root of (8² + 6²), which is the square root of 64 + 36, which is the square root of 100, which is 10 blocks. So, if there was a direct path, Noam's walk would be 10 blocks shorter.
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22:33 in its simplest form
Answer:
no its not
Step-by-step explanation:
simplest form for 22/33 is 2/3
I need help plz show work plz
What is 4(3m+4)=2(6m+8)
A right triangle has an acute angle measure of 22°. Which two numbers represent the lengths of the legs of this triangle?
1 and 5
2 and 5
3 and 5
4 and 5
The two numbers that represent the lengths of the legs of the right triangle are 2 and 5.
What is Trigonometry?Trigonometry is the study of the relationship between the ratios of the sides of a right-angled triangle and their angles. The trigonometric ratios used to examine this relationship are sine, cosine, tangent, cotangent, secant, and cosecant.
Given:
A right triangle has an acute angle measure of 22°.
Using Trigonometry
tan [tex]\theta[/tex] = opposite/adjacent
tan 22° = 2/5
= 0.40
Thus, the lengths of the legs of the right triangle are 2 and 5.
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Yoon Ki drove form Phoenix to Tucson in 1 1/2 hours. Then she drove form Tucson to El Paso in 4 3/4 hours. The second part of her trip was how many times as long as the first part?
A bag of marbles contains 7 blue marbles and 13 red marbles. what percent of the marbles are red?
The percentage of red marbles in a bag is 65%.
Given that, a bag of marbles contains 7 blue marbles and 13 red marbles.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Here, total number of marbles in a bag
= 7+13 =20
Now, percentage of red marbles
= 13/20 × 100
= 65%
Therefore, the percentage of red marbles in a bag is 65%.
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A rectangular park is 90 yards wide and 120 yards long.give the length and width of another rectangular park that has the same perimeter but a larger area.
Answer: 80x130
Step-by-step explanation:
FIND THE VALUE OF LOG 16 BASE 1/2
A work shift for an employee at a restaurant consists of 10 hours. What fraction of the employee's work shift is represented by 6 hours?
Final answer:
To calculate the fraction of a 10-hour shift that 6 hours represents, you divide 6 by 10 and simplify the resulting fraction, which is 6/10, to 3/5. Therefore, 6 hours is 3/5 of the work shift.
Explanation:
If an employee works a 10-hour shift, and you want to find out what fraction of the shift is represented by 6 hours, you divide 6 by the total hours in the shift which is 10. So, we write this as the fraction 6/10.
Now, simplifying the fraction, both the numerator (6) and the denominator (10) can be divided by 2. This gives us 3/5. Therefore, 6 hours represent 3/5 of the employee's 10-hour work shift.
To relate this to a concept you might already be familiar with, consider that 60 minutes make up 1 hour. If we write this as a ratio, it would be 60 minutes / 60 minutes, which simplifies to 1. Similarly, when we talk about fractions of an hour, like in the question, we're essentially looking for the number of parts of the shift that are being taken up by 6 hours in a 10-hour slot, which is 3/5.
Alexander purchased a computer on sale here is no price $1200 the sale price was 5/6of the original price how much did Alexander pay for the computer
Solve for x: the quantity of x plus 4 over 3 = 2.
A. x = −2
B. x = 2
C. x = 2 over 3
D. x = negative 10 over 3
If the length of the hypotenuse is 14 miles and the angle of reference is 30 degrees, what is the length of the opposite side to the angle?
Write an equation that says the length of a rectangle is 4 more than six times the value of x
is 4x-3=19 true, false, or open
True.
4x-3=19
4x=21 (add 3)
x=5.25 (divide both sides by 4)
Answer:
Open
Step-by-step explanation:
i just took the quick check
trust me
An electrician cut 36 feet of wire into sections that were each 8 feet long. After cutting, how many pieces of wire did the contractor have?
divide 36 by 8
36 / 8 = 4.5
so he had 4 pieces that were 8 feet long and he had 1 piece 4 feet long
so he had 5 pieces of wire
What is 2/3 of 8 please
Michael has a total of$4.40 in dimes (1 dime=$0.10) and quarters (1quarter=$0.25), and he has 20 coins in total. Which of the following systems of equations can be used to find the number of dimes, d, and the number of quarter,q, he has?
Final answer:
To solve for the number of dimes and quarters Michael has, we use two equations: 0.10d + 0.25q = 4.40 for the total value, and d + q = 20 for the total quantity of coins.
Explanation:
To find the number of dimes, d, and the number of quarters, q, Michael has, we need two equations to form a system. The first equation will represent the total amount of money in terms of dimes and quarters, and the second one will represent the total number of coins.
The value of a dime is $0.10 and the value of a quarter is $0.25. The total amount of money, $4.40, can be represented as 0.10d + 0.25q = 4.40. This is the value equation.
Since there are 20 coins in total, the second equation will simply be the count of both types of coins together: d + q = 20. This is the quantity equation.
The system of equations to find the number of dimes and quarters is:
0.10d + 0.25q = 4.40 (value equation)
d + q = 20 (quantity equation)
Given f(x)=6x^4, find f^-1(x). Then state whether f^-1(x) is a function.
The inverse function of f(x) = 6x^4 is f^(-1)(x) = (x/6)^(1/4), and f^(-1)(x) is a function.
To find the inverse function of f(x) = 6x^4, we can follow these steps:
1. Replace f(x) with y:
y = 6x^4
2. Swap x and y:
x = 6y^4
3. Solve for y:
Divide both sides by 6:
x/6 = y^4
4. Take the fourth root of both sides:
(x/6)^(1/4) = y
Now we have found the inverse function:
f^(-1)(x) = (x/6)^(1/4)
To determine if f^(-1)(x) is a function, we need to check if it passes the vertical line test. The vertical line test states that if a vertical line intersects a graph in more than one point, then the graph is not a function.
Let's imagine graphing f^(-1)(x) = (x/6)^(1/4). We see that for every x-value, there is only one corresponding y-value. Hence, each vertical line will intersect the graph at most once, confirming that f^(-1)(x) is indeed a function.
In conclusion, the inverse function of f(x) = 6x^4 is f^(-1)(x) = (x/6)^(1/4), and f^(-1)(x) is a function.
Gary said this model shows shaded. John said this model shows shaded.
Which student is correct?
A.
both Gary and John
B.
Gary
C.
John
The question is missing critical information as it lacks the proportion or number related to the shaded part of the model. Without this detail or a visual representation, it's not possible to determine the accuracy of Gary or John's statements.
Explanation:The question provided seems to be missing critical information, specifically the proportion or number that Gary and John are referring to when they mention how much of a model is shaded. In a typical mathematics problem regarding fractions or percentages, students would be asked to determine if statements about the shaded portion of a model are correct. Without the visual model or additional context indicating the proportion of the model that is shaded, it's impossible to conclude which student, Gary or John, is correct.
In order to answer correctly, we would need either a clear description of the model and its shaded parts or, preferably, a visual representation. Then, we would analyze the shaded portion to assess which statement about the fraction or percentage shaded is accurate. If we had this information, we could illustrate the process of comparing the given fraction or percentage with the actual shaded section of the model.
Unfortunately, without the necessary details, we can neither confirm if Gary, John, or both are correct, nor can we properly address the question.
Translate each phrase into a numerical expression.
The product of five and the sum of six and seven.
∠1 and ∠2 are supplementary and ∠1 ≅ ∠2. Which one of these statements will always be true?
∠1 and ∠2 are adjacent angles
∠1 and ∠2 are vertical angles
∠1 and ∠2 are right angles
∠1 and ∠2 are complementary angles
∠1 and ∠2 are right angles
What are Congruent Triangles?
Transformations change the size or position of shapes. Congruent shapes are identical, but may be reflected, rotated or translated. Scale factors can increase or decrease the size of a shape. Congruent Triangles simply mean the triangles that possess the same size and shape
• The three sides are equal (SSS: side, side, side)
• Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)
• Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)
• A right angle, the hypotenuse and a corresponding side are equal (RHS, right angle, hypotenuse, side)
Given data ,
∠1 and ∠2 are supplementary
So , ∠1 + ∠2 = 180°
∠1 ≅ ∠2
So , ∠1 and ∠2 are congruent
Since , we know that both of these angles are congruent and supplementary , both of the angles add up to 180°
So , each of the angle measures a total of ∠1 = 180° / 2
= 90°
And ∠2 = 90°
When the angle of a triangle is 90° , the angle is known as right angle
So ∠1 and ∠2 are right angles
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Which polynomial correctly combines the like terms and expresses the given polynomial in standard form? 8mn5 – 2m6 + 5m2n4 – m3n3 + n6 – 4m6 + 9m2n4 – mn5 – 4m3n3
Answer: n6 + 7mn5 + 14m2n4 - 5m3n3 - 6m6
Step-by-step explanation:
Kevin and Brittany write an equation to represent the following relationship, and both students solve their equation. Who found the correct equation and solution? Why is the other person incorrect?
5 times the difference of a number and 20 is the same as half the sum of 4 more than 4 times a number.
Kelvin found the correct equation and solution.
Brittany write incorrect equation because difference of a number and 20 can be written as, x - 20 where, x is a number; but Brittany can be written as 20 - x.
Here,
Kevin and Brittany write an equation to represent the following relationship, and both students solve their equation.
And, condition is given as,
5 times the difference of a number and 20 is the same as half the sum of 4 more than 4 times a number.
What is linear equation?
A linear equation only has one or two variables. No variable in a linear equation is raised to a power greater than 1.
Now, according to given condition,
5 times the difference of a number and 20 is written as,
[tex]5 ( x - 20 )[/tex]
And, half the sum of 4 more than 4 times a number, is written as
[tex]\frac{1}{2} ( 4x + 4)[/tex]
Now, both equation are equal
[tex]5 ( x - 20 ) = \frac{1}{2} ( 4x + 4)\\5x - 100 = 2x + 2\\3x = 102\\x = 34[/tex]
Hence, Kelvin found the correct equation and solution.
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Evaluate the expression. Drag the answer into the box to match the expression. 27⋅((33)−1)
27
3
1
1/9
Answer:
1
Step-by-step explanation:
[tex]27 \cdot ((3^3)^{-1})[/tex]
We need to evaluate the given expression
3^3 is 3 times 3 times 3= 27
[tex]27 \cdot ((3^3)^{-1})[/tex]
[tex]27 \cdot ((27)^{-1})[/tex]
Now we apply exponential property
[tex]a^{-m}= \frac{1}{a^m}[/tex]
[tex]27^{-1}= \frac{1}{27}[/tex]
[tex]27 \cdot ((27)^{-1})[/tex]
[tex]27 \cdot \frac{1}{27}=1[/tex]
What value of c makes the equation true? −3−34(c−4)=54
If PQ = PQ then PQ = PQ
What is the slope of the line through (1, -1) and (5, -7)? Your Answer Must Be Exact, Be sure to make the answer a fraction.