What is the area of a triangle with vertices at (−4, 1) , (−7, 5) , and (0, 1) ? Enter your answer in the box. ___units²
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you can pretty much count those lengths off the grid.
recall that A = 1/2 bh.
[tex] | - 4 - 0| = 4[/tex]
So b = 4 units
Now the height is the vertical distance from top to bottom, or the absolute value of the difference between y-values:
[tex] |5 - 1 | = 4[/tex]
So h = 4
Now a = 1/2 (b)(h) = 1/2 (4)(4) = 1/2 (16) = 8 units squared...
[tex]answer = 8 {units}^{2} [/tex]
Related Questions
Given the literal equation for the area formula of a trapezoid: A =12h(b1 + b2) solve for b1. Must show your work to receive full credit.
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[tex]\( b_1 = \frac{A}{12h} - b_2 \)[/tex] is the formula to solve for [tex]\( b_1 \)[/tex] in the trapezoid area equation.
To solve for [tex]\( b_1 \) in the equation \( A = 12h(b_1 + b_2) \), where \( A \)[/tex] is the area of the trapezoid, [tex]\( h \) is the height, \( b_1 \)[/tex]is one of the bases, and [tex]\( b_2 \)[/tex] is the other base, you can follow these steps:
1. Divide both sides of the equation by [tex]\( 12h \) to isolate \( (b_1 + b_2) \):[/tex]
[tex]\[ \frac{A}{12h} = b_1 + b_2 \][/tex]
2. Subtract [tex]\( b_2 \)[/tex] from both sides of the equation:
[tex]\[ \frac{A}{12h} - b_2 = b_1 \][/tex]
So, the equation for [tex]\( b_1 \) in terms of \( A \), \( h \), and \( b_2 \)[/tex] is:
[tex]\[ b_1 = \frac{A}{12h} - b_2 \][/tex]
Name the property the equation illustrated
8 + 3.4 = 3.4 +8
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commutative property of addition
Please can you help me
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Answer:
5 : 1
Step-by-step explanation:
From your second-grade memorization of multiplication tables, you recognize that 15 = 3×5, so you know 3 is a factor of both numbers in the ratio. To reduce the ratio to simplest form, you divide out all common factors:
15 : 3 = (15/3) : (3/3) = 5 : 1
300 yards / 1 minute find unit rate feet per wonds
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At city high school,the sophomore class has 60 more students than the freshman class.the junior class has 50 fewer students than twice the students in the freshman class.the senior class is three times as large as the freshman class.if there are a total of 1,424 students at the city high school,how many students are in the freshman class?
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J=Fx2-50
Senior=fx3
(f)+(f+60)+(fx2-50)+(fx3)=1424 (Parenthesis first)
f+f+60+2f-50+3f=1424 (rewrite)
2f+60+2f-50+3f=1424 (combine like variables)
7f+10=1424 (rewrite)
7f=1414 (isolate variable (take away 10 from each side))
1414/7
202=freshman
The number of students in the freshman class are:
202
Step-by-step explanation:Let the number of students in Freshman class = x
The sophomore class has 60 more students than the freshman class.This means that the number of students in sophomore class = x+60
The junior class has 50 fewer students than twice the students in the freshman class.This means that the number of students in junior class= 2x-50
The senior class is three times as large as the freshman class.This means that the number of students in senior class are: 3x
There are a total of 1,424 students at the city high school.This means that:
[tex]x+x+60+2x-50+3x=1424\\\\x+x+2x+3x+60-50=1424\\\\7x+10=1424\\\\7x=1424-10\\\\7x=1414\\\\x=\dfrac{1414}{7}\\\\x=202[/tex]
Please help me .......
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Answer:
[tex]9b+10u > 1,000[/tex]
What is 39ft/min to yd/s?
Please explain using dimensional analysis.
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In your problem, we're given ft/min and need to convert to yd/s. Start with feet and convert to yards for the numerator, then convert minutes to seconds for the denominator: (pretend the parentheses encompass the entire fractions - limitations of the answer box)
39 feet x ( 1 yard ) x (1 min)
1 min 3 feet 60 sec
Notice that feet cancel, and minutes cancel. We're left with yards in the numerator and seconds in the denominator.
Multiplying the numbers, we get 39/180, which simplifies to 0.217.
The final answer is ~0.22 yd/sec.
If y = 44 when x = –264, what is y when x = –486
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The value of 'y' when x equals -486 using the same ratio (1:6) as given in the original input is -81.
Explanation:To solve this problem, we're given a ratio of y to x (1:6) when x is -264 and y is 44. This ratio implies that y is one-sixth of x. Utilizing this information, we can determine y for a different x value (-486). By maintaining the 1:6 ratio, we divide -486 by 6, resulting in -81. Therefore, when x is -486, y equals -81. This solution stems from understanding the proportional relationship between y and x, allowing us to calculate y for any given x value based on the established ratio. In this case, the ratio of 1:6 guides the computation, ensuring the accurate determination of y as -81 when x is -486.
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i'm working at a distribution place and need help i'm supposed to be averaging 1000 units every hours if i do 4800 in a shift i'm 48 minutes behind schedule how many units per a hour am i averaging
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1000 units/h
Therefore the expected time for 4800 units is
(4800 units)/(1000 units/h) = 4.8 hours = 288 minutes
Because the worker is 48 minutes behind schedule, the actual time is
288 + 48 = 336 minutes = 5.6 hours
The actual average throughput is
(4800 units)/(5. h) = 857 units per hour.
Answer: 857 units per hour.
Cups are sold 5 to a package and plates are sold 10 to a package. If you want to have the same number of each item for the party, what is the least number of packages of each you need to buy?
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20, the LCM
(least common multiple) :)
1 package of plates = 10 plates and 2 package of cups = 10 cups
so 3 packages is least amount
The height of one square pyramid is 12 m. A similar pyramid has a height of 6 m. The volume of the larger pyramid is 400 m3. Determine each of the following, showing all your work and reasoning.
Scale factor of the smaller pyramid to the larger pyramid in simplest form
Ratio of the areas of the bases of the smaller pyramid to the larger pyramid
Ratio of the volume of the smaller pyramid to the larger
Volume of the smaller pyramid
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[tex]\bf \cfrac{smaller}{larger}\qquad \cfrac{\stackrel{height}{6}}{\stackrel{height}{12}}\implies \cfrac{1}{2}\impliedby \textit{scale factor of the pyramids}\\\\ -------------------------------\\\\ \cfrac{smaller}{larger}\qquad \cfrac{h}{h}=\cfrac{\sqrt{base}}{\sqrt{base}}\implies \cfrac{1}{2}=\sqrt{\cfrac{base}{base}}\implies \left( \cfrac{1}{2} \right)^2=\cfrac{base}{base} \\\\\\ \cfrac{1^2}{2^2}=\cfrac{base}{base}\implies \cfrac{1}{4}=\cfrac{base}{base}\\\\ -------------------------------\\\\[/tex]
[tex]\bf \cfrac{smaller}{larger}\qquad \cfrac{h}{h}=\cfrac{\sqrt[3]{volume}}{\sqrt[3]{volume}}\implies \cfrac{1}{2}=\sqrt[3]{\cfrac{volume}{volume}} \\\\\\ \left( \cfrac{1}{2} \right)^3=\cfrac{volume}{volume} \implies \cfrac{1^3}{2^3}=\cfrac{volume}{volume}\implies \cfrac{1}{8}=\cfrac{volume}{volume}\\\\ -------------------------------\\\\ \cfrac{smaller}{larger}\qquad \cfrac{1}{8}=\cfrac{\stackrel{volume}{v}}{\stackrel{volume}{400}}\implies \cfrac{1\cdot 400}{8}=v[/tex]
WHY is -2 3 8l9 1,476 -6.01 all rational numbers . have a separate explanation for each number
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All of these numbers are rational because a rational number is, or can be, turned into a fraction.
-2 = -2/1
3 = 3/1
819 = 819/1
1,476 = 1,476/1
-6.01 = -6 1/100 = -601/100
Is it true that |3-8| and |3+8|
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To determine if |3-8| is equal to |3+8|, we calculate the absolute values: |3-8|=5 and |3+8|=11. Since 5 is not equal to 11, the statement is false.
To solve the given problem, we need to understand the properties of absolute values. Absolute value measures the distance of a number from zero on the number line, regardless of direction.
First, calculate the absolute value of each expression: |3-8| and |3+8|.For |3-8|:3 - 8 = -5, and the absolute value of -5 is 5. Therefore, |3-8| = 5.
For |3+8|:3 + 8 = 11, and the absolute value of 11 is 11. Therefore, |3+8| = 11.
In conclusion, it is not true that |3-8| equals |3+8|, as |3-8| = 5 and |3+8| = 11.
here is the full question-Is it true that |3-8| and |3+8| are equal?
One out of two people entering the grocery store purchase soda. how many people out of 20 purchase soda?
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______________________
1/2 = x/20
(1*10) = (2*10) = 10/20 .
Note: 2*10 = 20.
1/2 = 10/20 .
10/20 = ? ; Cancel out the zeros to get: "1/2" ; "10/20 = 1/2" .
You went shopping and found a pair of shoes that were $45.00 on sale for $27.50. what was the percent of decrease of the shoes? your answer should go 1 decimal place)
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= (45 - 27.5) / 45.....* 100
= 17.5 / 45....* 100
= 0.3888 * 100
= 38.9 % decrease <== thats rounded
The LCD for the fraction 1/3 , 3/4 , 5/32 , and 8/9 Is?
A. 288
B. 24
C. 3,072
D. 64
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If the ratio between the radii of the two spheres is 3 5 what is the ratio of their volumes
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Answer:
The answer is 27:125
Cho welcome
If a line is perpendicular to a line segment, what angle do they form at their intersection
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Two ants walk on a line in a random fashion. they begin 10cm apart. at each time step, each ant has a probability of 1/2 to move 1cm to the left, and probability 1/2 to move 1cm to the right. what is the probability that after 7 time steps, the ants have met one another (i.e., passed through the same point)?
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I really need help on this problem can i get help on how to solve the problem please
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PLEASE ANSWER FAST!
Which statement best describes why the sale price is a function of the original price?
A:As the original price increases, the sale price also increases.
B:The sale price is always less than the original price.
C:For every original price, there is exactly one sale price.
D:The sales price is never less than zero.
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Answer:
I think B,not sure
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Got it right
Is it possible for a composite number to have more than one prime factorization?
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The commission of selling each iPhone is $30 and the commission of selling each iPad is $20. If you one day sold 4 more iPhones than iPads and earned a total commission of $520, how many iPhones and iPads did you sell respectively?
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By solving the system of equations which includes the total commission and difference in quantity of iPhones and iPads sold, we determine that the salesperson sold 8 iPads and 12 iPhones.
The student is tasked with solving a system of linear equations to determine how many iPhones and iPads were sold based on the commission earned. Let's define the number of iPads sold as x and the number of iPhones as x + 4.
The total commission for iPhones is $30 per iPhone and the total commission for iPads is $20 per iPad. The total commission earned from selling these products is $520.
We can set up two equations based on the given information:
Commission from iPhones: 30(x + 4)
Commission from iPads: 20x
Total Commission: 30(x + 4) + 20x = 520
By solving the equation 30(x + 4) + 20x = 520, we find:
30x + 120 + 20x = 520
50x + 120 = 520
50x = 400
x = 8
So, the number of iPads sold is 8. Since the number of iPhones sold is 4 more than iPads, we have:
Number of iPhones sold = x + 4 = 8 + 4
Number of iPhones sold = 12
Therefore, the salesperson sold 8 iPads and 12 iPhones respectively.
Neil and Jean each choose a number at random from the set 1,2,3,4,5,6,7,9,10 their numbers are allowed to be the same. What is the probability that the product of those two numbers is even?
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The probability that the product of the numbers selected by Neil and Jean is even is approximately 0.8889.
Explanation:To answer your question, let's first classify the numbers from the given set 1,2,3,4,5,6,7,9,10 into two categories: even numbers (2, 4, 6, 10) and odd numbers (1, 3, 5, 7, 9). Each of the people, Neil and Jean, can pick any number independently. Hence we have two scenarios which result in the product being even - either both pick even numbers or at least one of them picks even.
The probability of both picking an even number is (4/9)*(4/9) = 16/81. Also, there is no constraint on the second scenario, so, total probabilities = 1. Hence, the probability of at least one picking an even is 1 - probability(both picking odd) = 1 - (5/9)*(5/9) = 1 - 25/81 = 56/81.
Therefore, the total probability that the product of the numbers selected by Neil and Jean is even is the sum of the above two probabilities i.e., 16/81 + 56/81 = 72/81 = 0.8889 (approx).
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(−2+2i)⋅(5+5i)
Can you help me simplify
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FOIL
-10-10i+10i+10i²=-10+10i² this is the simplify answer
If you want the complete answer is
-10+10(-1)=-10-10=-20
A coin is flipped five times find the number of possible sets of heads and tails that have 0 heads
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The number of possible sets with 0 heads when flipping a coin five times is 1, represented by five consecutive tails (TTTTT).
When flipping a coin five times, the number of possible sets that have 0 heads (meaning all tails) is just one. This single microstate is TTTTT.
The reason for this is that each coin flip is an independent event with two possible outcomes: heads (H) or tails (T). When we are only concerned with the total head and tail count and not the order in which they appear, the only set with 0 heads is the set where every coin lands on tails.
Which equation below represents a vertical line? y = x + 0, y = x – 0, y = 4, x = 4
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so ur vertical line is : x = 4 <==
** and just so u know, a horizontal line is represented by y = a number.
hope this has helped you
Algebra Vocabulary Crossword help ?!
1. a relation described in word format? (17 letter)
9. a way to name a function identifying its input?
(16 letter)
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9. a way to name a function identifying its input (16 letter) is "f of x equals x square"
The student is looking for the terms 'Verbal Description' and 'Function Notation' for their Algebra Vocabulary Crossword. These refer to a relation described in word format and a way to name a function identifying its input respectively.
Explanation:Based on the number of letters you've indicated, it looks like you're looking for two vocabulary items in the field of Algebra.
First, a relation described in a word format is typically called a Verbal Description, which has 17 letters.
Second, a way to name a function identifying its input is called Function Notation, which has 16 letters.
In Algebra, Verbal Description is when you describe a mathematical relationship using words. For example, 'the sum of a number and three is seven.' This could be translated to the equation x+3=7.
Function Notation, on the other hand, is a way to name a function that is dependent on one or more inputs. For example, f(x) = x^2 is function notation, since the output 'f(x)' is dependent on the input 'x'.
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How many terms are in the expression a3 + 3a2b - 4ab - 11b + 7?
7
4
5
6
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Hope this helps
the answer is 5
1: a^3
2: 3a^2b
3: 4ab
4: 11b
5: 7
anything seporated by a + or - is a term
Michael has 4 lots of land to sell. He sells two of them at a loss of $1,200 each and sells the other two at a profit of $1,400 each. How much money does he make on his investment?
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1200*2= 2400
Subtract the two number 2800-2400= 400
Michael makes a total of $400 from his land investment after calculating the total losses and gains from the lands sold.
Explanation:In order to find out the total money that Michael has made from his land investment, you need to calculate the losses and the gains individually. Michael sells two of his lands at a loss of $1,200 each, hence his total loss is 2 * $1,200 = $2,400. On the other hand, he sells the other two lands at a profit of $1,400 each, hence his total profit is 2 * $1,400 = $2,800.
To get the total money that he made on his investment, you subtract the total loss from the total profit. That is $2,800 (total profit) - $2,400 (total loss) = $400. Hence, Michael makes $400 on his investment.
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