The area of a triangle is half the area of a parallelogram with the same base and height because a triangle's area is calculated using half the product of its base and height, while a parallelogram's area is the full product of its base and height.
The areas of a triangle and a parallelogram with the same base and height are related in that the area of the triangle is exactly half the area of the parallelogram. To understand this, recall that the area of a parallelogram is calculated by multiplying its base by its height ( extit{Base x Height}). A triangle sharing the same base and height will have half the area because the area of a triangle is given by half the product of its base and height ( extit{0.5 x Base x Height}).
Let's say we have a parallelogram and a triangle with the same base 'b' and height 'h'. The area of the parallelogram is extit{b x h}, while the area of the triangle will be extit{0.5 x b x h}. This relationship can be visualized by drawing a diagonal across the parallelogram, which cuts it into two equal triangles, each having the same area as the original triangle we're comparing it to.
evaluate the expression when a= 1/4 and b=6
Phil has 189 stamps to put into his stamp album he puts the same number of stamps on each of 9 pages. how many stamps does Phil put on each page?
An inequality is a statement that shows that two numbers are equal. TRUE OR FALSE?
Use the decimals 2.47,9.57 and 7.1 to write two different addition facts and two subtraction facts
We know 4 times 9 = 36
So, which of the following statements are also true?
Select all that apply.
9 is a multiple of 36
36 is a factor of 4
9 is a factor of 36
PLEASE HELP ASAP!!!
a machine takes 2.8 hours to make 9 parts at that rate,how many parts can machine make in 28.0
What is the answer to 15 divided by 1 2/3
To solve the problem '15 divided by 1 2/3', change the mixed number to an improper fraction, then multiply by the reciprocal. The answer to the operation is 9.
Explanation:The student's question is about division in Mathematics, specifically, 'What is the answer to 15 divided by 1 2/3?' To solve this division problem, one needs to remember to change the mixed number to an improper fraction. 1 2/3 is equivalent to 5/3. Then, to divide, we multiply by the reciprocal. The reciprocal of 5/3 is 3/5. Thus, the division operation 15 ÷ 1 2/3 turns into the multiplication operation 15 x 3/5.
Now, simplify by multiplying the two numbers: 15 x 3/5 = 9. So, 15 divided by 1 2/3 equals 9.
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The sea floor is 104 feet below sea level. Katy is 28 feet below sea level. She is moving downward at a rate of 4 feet per minute. Colin used the following calculation to determine how long it will take Katy to reach the sea floor. Is he correct? Explain.
104 – 28 ÷ 4 = 97 minutes
No, Colin is not correct. Katy requires 19 minutes to reach the sea floor.
What is Speed?
Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude.
Total distance between sea level and sea floor is 104 feet.
Katy is available 28 feet below sea level.
so, remaining distance katy needs to move = 104 - 28 feet
= 76 feet
Speed of Katy for moving downwards = 4 feet per minute
Time taken by Katy to reach sea floor = [tex]\frac{distance}{speed}[/tex]
= 76/4
= 19 minutes
Thus, Katy requires 19 minutes to reach the sea floor.
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Which of the following correctly simplifies the expression 2 to the power of 2 multiplied by 6 to the power of 0 whole over 7, the whole cubed.?
To simplify the expression, we calculate each part separately. Then, we multiply the numerator and simplify the denominator. Finally, we cube the expression by multiplying it by itself three times.
Explanation:To simplify the expression 2 to the power of 2 multiplied by 6 to the power of 0 whole over 7, the whole cubed, we need to calculate each part of the expression.
First, 2 to the power of 2 is 2 * 2 = 4.
Next, 6 to the power of 0 is 1, because any number raised to the power of 0 is always 1.
Now, we have 4 * 1 whole over 7. To simplify this, we can multiply the numerator and simplify the denominator. So the expression becomes 4 whole over 7 cubed.
To cube the expression, we need to multiply 4 by itself three times. So 4 * 4 * 4 = 64. Therefore, 4 whole over 7 cubed simplifies to 64.
Anthony has 36 bats evenly spread between 4 bags. He gave bats to players from one bag. The first player got three bats and the second player got 4 bats. How many bats are remaining in one bag. answer
On the track team, 3/5 of the members are boys. Of these boys, 4/7 are sixth graders. Of the sixth-grade boys on the team, 1/3 are runners. What fraction of the track team are sixth-grade boy runners?
By multiplying the fractions 3/5, 4/7, and 1/3, which represent the boys, sixth graders, and runners respectively, we find that 4/35 of the track team are sixth-grade boy runners.
To find the fraction of the track team that consists of sixth-grade boy runners, we'll need to multiply three fractions that represent different parts of the team:
The fraction of the team that are boys: 3/5
The fraction of these boys that are sixth graders: 4/7
The fraction of the sixth-grade boys that are runners: 1/3
Now, multiplying these numbers expressing common fractions gives us:
(3/5) × (4/7) × (1/3) = 12/105 = 4/35.
So, 4/35 of the track team are sixth-grade boy runners.
Find the slope of the line.
We can use the points (-2, 5) and (2, 0) to solve.
Slope formula: y2-y1/x2-x1
= 0-5/2-(-2)
= -5/4
Hope This Helped! Good Luck!
Mattie's house consists of two stories and an attic. the first floor is 8 5/6 feet tall, the second floor is 8 1/2 feet tall, and the entire house is 24 1/3 feet tall. how tall is the attic
First, change to improper fractions by:
multiplying whole number by denominator8×6=48
adding the numerator48+5=53 ---- this becomes new numerator
copying the denominator536
so
856 = 536 feet
Do the same for the other fractions.
812 = 172 feet
2413 = 733 feet
536+172 = height of two stories, excluding the attic
Let x = height of attic
x = 733 - (536+172)
Change to similar fractions by getting LCD=6
x = 733(22) - (536+172(33))
x=1466−(536+516)
x=1466−1046
x=426
x=7
The coordinates of a point on a coordinate grid are (−2, 6). The point is reflected across the x-axis to obtain a new point. The coordinates of the reflected point are
The correct answer is option C. (−2, −6). Hence the correct option is c.
Given the original point is (−2, 6), let's denote it as (x, y).
Identify the original point.
The original point is (−2, 6), where x = −2 and y = 6.
Reflect the point across the x-axis.
To reflect the point across the x-axis, we keep the x-coordinate the same and change the sign of the y-coordinate. This means that if the original y-coordinate is positive, it becomes negative, and if it's negative, it becomes positive.
So, for the reflected point:
[tex]\[ x_{\text{reflected}} = x_{\text{original}} = -2 \]\[ y_{\text{reflected}} = -y_{\text{original}} = -6 \][/tex]
Determine the coordinates of the reflected point.
So, the coordinates of the reflected point are (−2, −6).
Therefore, the correct answer is option C. (−2, −6). Hence the correct option is c.
Complete question:
The coordinates of a point on a coordinate grid are (−2, 6). The point is reflected across the x-axis to obtain a new point. The coordinates of the reflected point are A.(2, 6) B.(−2, 6) C. (−2, −6) D. (2, −6)
There are 26.2 miles in a marathon. Enter the number of miles using a mixed number in simplest form.
Answer:
[tex]26\frac{1}{5}[/tex] miles.
Step-by-step explanation:
We have been given that there are 26.2 miles in a marathon. We are asked to find the number of miles using a mixed number in simplest form.
First of all, we will convert our given number as a fraction by multiplying and dividing by 10 as:
[tex]26.2\times\frac{10}{10}=\frac{262}{10}[/tex]
[tex]\frac{262}{10}=26\frac{2}{10}[/tex]
[tex]26\frac{2*1}{2*5}[/tex]
[tex]26\frac{1}{5}[/tex]
Therefore, the number of miles in mixed number would be [tex]26\frac{1}{5}[/tex] miles.
write to explain how you can break apart 16×34 into four simpler multiplication problems.
The expression written in 4 simplified multiplication is
10×30 + 10×4 + 6×30 + 6×4. It is written using the distributive property.
What is multiplication?Multiplication is the process of adding a number up to a given number.
The given expression is 16 × 34.
Simplify the expression as follows:
16 × 34
= ( 10 + 6 ) × (30 + 4)
= 10×30 + 10×4 + 6×30 + 6×4
Hence, the expression written in 4 simplified multiplication is
10×30 + 10×4 + 6×30 + 6×4.
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in 2011, the population of Laos was about 6.586 x 10 to the 6 people. what is the number written in standard notation?
The population of Laos in 2011, given in scientific notation as 6.586 x 10 to 6, is equivalent to 6,586,000 in standard notation.
Explanation:The question is asking to convert the population of Laos in 2011, which is given in scientific notation, into standard notation. The scientific notation given is 6.586 x 10 to the 6. To convert this to standard notation, we simply move the decimal point 6 places to the right, as the exponent of 10 is positive. This results in the number 6,586,000; which is in standard notation.
This process of conversion is part of a larger mathematical concept known as scientific notation, which is commonly used to express very large or very small numbers.
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Juan plays little league baseball. In 24 at-bats, he had 8 hits. What is the ratio of at-bats to hits?
Describe two different methods you can use to graph the equation y=2x+4.
Which method do you prefer? Explain.
If you buy 12 pens for 22.20 dollars, how much does each pen cost?
12 is what % more than 6
if 1 out of 12 students at a school share a locker how many share a locker in a school of 456 students
You buy a pair of jeans at a department store.
Jeans 39.99
Discount -10.00
Subtotal 29.99
Sales tax 1.95
Total 31.94
a. What is the percent of discount to the nearest percent?
The percent of discount is ___%.
b. What is the percent of sales tax to the nearest tenth of a percent?
The percent of sales tax is ___%
c. The price of the jeans includes a 60% markup. After the discount, what is the percent of markup to the nearest percent?
The percent of markup is ___%
Answer
25%
Explanation
We know that original price of the jeans is $39.99 and the discount is $10, so we need to find what percentage of $39.99 is $10. To do it we can set up a proportion:
[tex]\frac{39.99---->100}{10---->x}[/tex]
Now we can express our proportion as a fraction and solve for [tex]x[/tex]:
[tex]\frac{39.99}{10}= \frac{100}{x}[/tex]
[tex]x=\frac{10*100}{39.99}[/tex]
[tex]x=25[/tex]
We can conclude that the percent of the discount to the nearest percent is 25%
b.Answer
6.5%
Explanation
Since the sales taxes is applied to the subtotal, this time we need to find what percentage of 29.99 is 1.95. To do it, we are going to set up a proportion, just like before:
[tex]\frac{29.99---->100}{1.95---->x}[/tex]
Now we can express our proportion as a fraction and solve for [tex]x[/tex]:
[tex]\frac{29.99}{1.95}= \frac{100}{x}[/tex]
[tex]x=\frac{1.95*100}{29.99}[/tex]
[tex]x=6.5[/tex]
We can conclude that the percent of sales tax to the nearest tenth of a percent is 6.5%
c.Answer
20%
Explanation
First, we need to find the cost of the Jeans; to do it, we are using the markup formula:
[tex]markup=(\frac{price-cost}{cost} )100[/tex]
We know that the price of the Jeans is $39.99 and the markup is 66%, so let's replace those values in our formula:
[tex]60=(\frac{39.99-cost}{cost} )100[/tex]
[tex]\frac{60}{100} =\frac{39.99-cost}{cost}[/tex]
[tex]0.6=\frac{39.99-cost}{cost}[/tex]
[tex]0.6cost=39.99-cost[/tex]
[tex]0.6cost+cost=39.99[/tex]
[tex]1.6cost=39.99[/tex]
[tex]cost=\frac{39.99}{1.6}[/tex]
[tex]cost=24.99[/tex]
Now that we have the cost now, we just need to use the markup formula again but this time using the price after discount ($29.99).
[tex]markup=(\frac{price-cost}{cost} )100[/tex]
[tex]markup=(\frac{29.99-24.99}{24.99} )100[/tex]
[tex]markup=(\frac{5}{24.99} )100[/tex]
[tex]markup=20[/tex]
We can conclude that the percentage of markup after the discount is 20%
Help with number 1-7
Which ordered pair is a solution to the system of linear equations -4x+y=8 and x-5y=17
how many tens and ones 63 and 9
(x÷(y÷z))÷((x÷y)÷z)
also the variables are not specified.
What is the prime factorization of 302 in exponent form?
Write an expression that represents the sum of b and 5 times 2
The mathematical expression for the sum of b and 5 times 2 is b + (5 × 2).
The expression that represents the sum of b and 5 times 2 is written as b + (5 × 2). The parentheses indicate that the multiplication should be done first, resulting in 5 times 2, which equals 10. Then, you add the value of b to this result. Therefore, the complete expression evaluates to b + 10.
It is important to understand the role of parentheses in mathematical expressions. Parentheses define the order of operations, ensuring that operations inside them are carried out first. Without the proper use of parentheses, expressions can yield different results.
Can someone help me in this thanks