Find the area of the given triangle. Round the answer to the nearest tenth.
A.
7.9 square units
B.
149.4 square units
C.
2,055.6 square units
D.
2,071.8 square units
Answer:
B) Area of triangle = 149.4 square units.
Step-by-step explanation:
Given : A triangle with sides 16 , 19, 27 .
To find : Area of a triangle.
Solution : We have given that triangle with sides 16 , 19, 27 .
Using heron's formula :
Area of triangle: [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex].
Where, s = [tex]\frac{a+b+c}{2}[/tex] and a,b,c are sides of triangle.
Then s = [tex]\frac{16+19+27}{2}[/tex].
s = 31 units.
Area of triangle = [tex]\sqrt{31(31-16)(31-19)(31-27)}[/tex].
Area of triangle = [tex]\sqrt{31(15)(12)(4)}[/tex].
Area of triangle = [tex]\sqrt{22320)}[/tex].
Area of triangle = 149.39 square units.
Area of triangle = 149.4 square units. ( nearest tenth)
Therefore, B) Area of triangle = 149.4 square units.
PLEASE HELP ASAP
EXTRA POINTS
Sheila places a 54 square inch photo behind a 12-inch-by-12-inch piece of matting.
The photograph is positioned so that the matting is twice as wide at the top and bottom as the sides.
Write an equation for the area of the photo in terms of x.
MEDAL!
This Chinese painting is composed small cliffs in the background and a small building with trees in the foreground. This composition reflects what Taoist and Buddhists principle or philosophy?
a) simplicity
b) perseverance
c) harmony
or...
d) balance
btw- I know this is in the wrong section but no one was answering it in the art history section
***mathtest timed***
Given the data set for the length of time a person has been jogging and the person's speed, hypothesize a relationship between the variables.
A) I would expect the data to be positively correlated.
B)I would expect the data to be negatively correlated.
C) I would expect no correlation.
D) There is not enough information to determine correlation.
Write the quadratic equation whose roots are −4 and 3 , and whose leading coefficient is 1 .
Final answer:
To write a quadratic equation with roots −4 and 3 and a leading coefficient of 1, we start with the factored form (x - root1)(x - root2) = 0, substitute the given roots, and simplify to x² + x - 12 = 0.
Explanation:
The question asks us to write the quadratic equation whose roots are −4 and 3, and whose leading coefficient is 1. To find a quadratic equation given its roots, we can use the factored form of a quadratic equation, which is (x - root1)(x - root2) = 0, where root1 and root2 are the roots of the equation.
Given that the roots are −4 and 3, we substitute these values into the equation to get (x - (−4))(x - 3) = 0. Simplifying this, we first eliminate the double negative to get (x + 4)(x - 3) = 0. Multiplying these two binomials gives us the expanded form, which is x² + x - 12 = 0. This is the quadratic equation with roots −4 and 3, and a leading coefficient of 1.
A car travels 3 times around a traffic circle whose radius is 80 feet. What is the distance the car will travel? Use 3.14 for π . Enter your answer in the box. ft
Answer : Distance will be 1507.2 feet .
Explanation :
Since we have given that
Radius of circle = 80 feet
So,
Circumference of circle is given by
[tex]2\pi r=2\times 3.14\times 80=502.4 \text{ feet}[/tex]
Since , a car travels 3 times around a traffic circle.
So,
[tex]\text{ Distance covered by the car will travel}= 3\times 502.4= 1507.2 \text{ feet }[/tex]
So, Distance will be 1507.2 feet .
Dominik paid three-quarters of a dollar for a newspaper. Which amount is equivalent to the cost of the newspaper?
need help so much ...
Look at the data in the table below
X Y
4. 9
12. 28
7. 14
9. 20
5. 9
12. 30
10. 22
Which graph shows the best fit for this data
Your assigned 32 math exercises for homework you complete 87.5of these before dinner how many do you hav to do after dinner.
Which foundation drawing matches this orthographic drawing? ( just tell me what picture)
How is locating -1.5 on a number line the same as locating 1.5 on a number line? How is it different?
Locating -1.5 and 1.5 on a number line involves measuring 1.5 units from the origin, but in opposite directions; -1.5 is to the left and 1.5 is to the right.
Locating -1.5 on a number line is similar to locating 1.5 in that you measure the same distance away from the origin (0 point), which is 1.5 units. The main difference is the direction in which you measure from the origin. For -1.5, you would move 1.5 units to the left of the origin since negative numbers are represented to the left on a number line. On the other hand, for 1.5, you would move 1.5 units to the right of the origin because positive numbers are placed to the right.
Another perspective of understanding this concept comes from the coordinate system. If you stand on a straight line and choose a point as the origin, moving to the left will give you the negative coordinates, whereas moving to the right will give you the positive coordinates. Regardless of which side you choose, the absolute value of your position from the origin remains the same; only the sign changes to reflect the direction.
A square is cut out of a circle whose diameter is approximately 14 feet. What is the approximate area of the remaining portion of the circle in square feet?
A square is cut from a circle with a 14-foot diameter. Remaining circle area ≈ 53.86 sq ft here nearest round off option is c. 50 square feet.
To find the area of the remaining portion of the circle after a square with a side of 10 feet is cut out,
Find the area of the square:
Area of square
= side × side
= 10 feet × 10 feet
= 100 square feet
Find the radius of the circle:
The diameter is approximately 14 feet, so the radius is half of that:
Radius = 14 feet / 2 = 7 feet
Find the area of the entire circle:
Area of circle = π × radius²
Area of circle
= π × (7 feet)²
≈ 153.86 square feet (using π ≈ 3.14)
Subtract the area of the square from the area of the circle to find the remaining portion:
Remaining area = Area of circle - Area of square
Remaining area
≈ 153.86 square feet - 100 square feet
≈ 53.86 square feet
Therefore, the approximate area of the remaining portion of the circle is approximately 53.86 square feet nearest option is c. 50 square feet.
learn more about area here
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The above question is incomplete , the complete question is:
A square is cut out of a circle whose diameter is approximately 14 feet. What is the approximate area of the remaining portion of the circle in square feet?
Attached figure
The function graphed approximates the height of an acorn, in meters, x seconds after it falls from a tree.
After about how many seconds is the acorn 5 m above the ground?
The equation of the parabola is y = – 5x² + 20. The time when an acorn is 5 m above the ground in 1.7 seconds. Then the correct option is C.
What is the parabola?It is the locus of a point that moves so that it is always the same distance from a non-movable point and a given line. The non-movable point is called focus and the non-movable line is called the directrix.
The function graphed approximates the height of an acorn, in meters, x seconds after it falls from a tree.
We know that the equation of the parabola will be given as
y = a(x - h)² + k
where (h, k) is the vertex of the parabola and a is the constant.
We have
(h, k) = (0, 20)
Then
y = ax² + 20
The parabola is passing through (2, 0), then we have
0 = 4a + 20
a = -5
Then we have
y = – 5x² + 20
The time in seconds when the acorn is 5 m above the ground.
–5x² + 20 = 5
–5x² = –15
x = 1.7
More about the parabola link is given below.
https://brainly.com/question/8495504
WILL MARK BRAINLIEST! - Miguel is calculating the slope of a line of best-fit in the scatterplot below.
(Graph Below)
Which pair of points would be best for Miguel to use?
A. P and W
B. Q and V
C. R and U
D. S and T
Answer:
I thing its B
Step-by-step explanation:
Just trust
Answer:
"Q and V" should be correct.
Step-by-step explanation:
The data points by themselves create a line formation, all the other choices no good.
In other-words~ "B"
o_o
Factor this expression completely, and, then, place the factors in the proper location on the grid. Place the binomial factor first. x 3 + y 3
Answer:
[tex]x^{3}+y^{3}=(a+b)(a^{2}-ab+b^{2})[/tex]
Step-by-step explanation:
The given expression is
[tex]x^{3}+y^{3}[/tex]
This expression represents the sum of two perfect cubes, which is factorize as this product
[tex]x^{3}+y^{3}=(a+b)(a^{2}-ab+b^{2})[/tex]
We can demonstrate this factorization by multiplying the product
[tex](a+b)(a^{2}-ab+b^{2})=a^{3}-a^{2}b+ab^{2}+a^{2}b-ab^{2}+b^{3}=a^{3}+b^{3}[/tex]
Therefore, the answer is
[tex]x^{3}+y^{3}=(a+b)(a^{2}-ab+b^{2})[/tex]
Will mark brainiest
According to the chart, from 1996-2006, unintentional drug overdose deaths per 100,000 population rose dramatically. The numbers for each year are, roughly, 3, 3, 3, 4, 4, 5, 6, 6, 7, 9, 9. What is the mean of these statistics?
5.36
59
59.36
5
The answer to your question is A) 5.36
Hope this helps :)
In a parking lot of 240 red and blue cars, the ratio of red cars to blue cars is 3 : 5.
How many red cars are in the parking lot?
3+5 = 8
240/8 = 30
30*3 = 90 red cars
A $250,000 home loan is used to purchase a house. The loan is for 30 years and has a 5.4% APR. Use the amortization formula to determine the amount of the monthly payments.
Check my answers? GIving medal:
7. What is the slope of the line that passes throught the pair of points (1, 7) and (10, 1)?
a. 3/2
b. -2/3
c. -3/2
d. 2/3 <--
8. What is the slope of the line that passes through the points (-5.5, 6.1) and (-2.5, 3.1)?
a. -1
b. 1
c. -3 <--
d. d
9. what is the slope of the line that passes through the pair of points (-7/3, -3) and (-5, 5/2)?
a. 6/22 <--
b. -6/22
c. 22/6
d. -22/6,
Number seven Is B. -2/3
If the expected adult of a 2 week old puppy is 20 pounds how many grams per day should they gain?
Bill and Greg are walking in opposite directions with speeds of 45 and 75 feet per minute. When they started, the distance between them was 20 feet. What will be the distance between them in 2.5 min?
Answer:
320 ft
Step-by-step explanation:
I'm not sure how the other person was awarded brainliest answer because that answer is pretty far off. But the work was good just they messed up. Also kinda sad he is a brainly teacher and still has incorrect answers.
A new car is purchased for 20700 dollars. The value of the car depreciates at 13.75% per year. What will the value of the car be, to the nearest cent, after 12 years?
Answer:
USD 3,508.16
Step-by-step explanation:
Hello
Let´s see what happens the first year when the car depreciates 13.75% of 20700 USD
[tex]depreciation=20700*\frac{13.75}{100} =2846.25 USD\\[/tex]
at the end of the first year the car will have a price of 20700-2486.25=17853.75 USD, and this will be the price at the beginning of the second year.
completing the data for the 12 years with the help of excel you get
depreciation New Value
end of year 1 USD 20,700.00 USD 2,846.25 USD 17,853.75
end of year 2 USD 17,853.75 USD 2,454.89 USD 15,398.86
end of year 3 USD 15,398.86 USD 2,117.34 USD 13,281.52
end of year 4 USD 13,281.52 USD 1,826.21 USD 11,455.31
end of year 5 USD 11,455.31 USD 1,575.10 USD 9,880.20
end of year 6 USD 9,880.20 USD 1,358.53 USD 8,521.68
end of year 7 USD 8,521.68 USD 1,171.73 USD 7,349.94
end of year 8 USD 7,349.94 USD 1,010.62 USD 6,339.33
end of year 9 USD 6,339.33 USD 871.66 USD 5,467.67
end of year 10 USD 5,467.67 USD 751.80 USD 4,715.87
end of year 11 USD 4,715.87 USD 648.43 USD 4,067.43
end of year 12 USD 4,067.43 USD 559.27 USD 3,508.16
after 12 years the car will ha a value of USD 3508.16
you can verify this by applying the formula
[tex]v_{2} =v_{1} (1-\frac{depreciatoin}{100} )^{n} \\\\v_{2} =20700 (1-\frac{13.75}{100} )^{12} \\v_{2} = 20700*0.1694\\v_{2} = 3508.16 USD[/tex].
Have a great day.
The value of a new car, originally priced at $20,700 and depreciating at 13.75% per year will be approximately $1446.63 after 12 years. This is calculated using a compound interest formula with a negative rate.
Explanation:In order to solve this, we are going to use the formula for compound interest. Although we're actually dealing with depreciation, the calculation is the same as for interest, we just use a negative rate. The formula is P(t) = P0 * (1 + r) ^t, where P(t) is the value of the car after time t, P0 is the initial price of the car, r is the rate of depreciation, and t is time.
Here P0 = $20,700, r = -13.75% = -0.1375 (remember to convert rate from percentage to a proportion), and t = 12 years.
Substituting these values into the formula, we get: P(t) = 20700 * (1 - 0.1375)^12. Using a calculator, the value of the car after 12 years, to the nearest cent, is approximately $1446.63.
Learn more about Depreciation here:https://brainly.com/question/33528280
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WILL GIVE A BRAINLESTTTT
What is the solution of 3x+8/x-4 >= 0
Answer:
The inequality is given to be :
[tex]\frac{3x+8}{x-4}\geq 0[/tex]
The inequality will be greater than or equal to 0 if and only if both the numerator and denominator of the left hand side will have same sign either both positive or both negative.
CASE 1 : Both positive
3x + 8 ≥ 0
⇒ 3x ≥ -8
[tex]x\geq \frac{-8}{3}[/tex]
Also, x - 4 ≥ 0
⇒ x ≥ 4
Now, Taking common points of both the values of x
⇒ x ∈ [4, ∞)
CASE 2 : Both are negative
3x + 8 ≤ 0
⇒ 3x ≤ -8
[tex]x\leq \frac{-8}{3}[/tex]
Also, x - 4 ≤ 0
⇒ x ≤ 4
So, Taking common points of both the values of x we have,
[tex]x=(-\infty,-\frac{8}{3}][/tex]
So, The solution of the equation will be the union of both the two solutions
So, Solution is given by :
[tex]x=(-\infty,-\frac{8}{3}]\:U\:[4,\infty)[/tex]
2. Consider this scatter plot.
(a) How would you characterize the relationship between the hours spent on homework and the test scores? Explain.
(b) Paul uses the function y = 8x + 40 to model the situation. What score does the model predict for 3 h of homework?
(c) What does the number 40 in Part (b) mean in the context of the situation?
(a) The relationship between hours spent on homework and test scores is a positive correlation, where more homework is generally associated with higher test scores.
(b) The model predicts a score of 64 for 3 hours of homework.
(c) The number 40 represents the baseline test score when no homework is done, according to the model.
Analyzing the Scatter Plot and the Model
(a) Characterizing the Relationship
The scatter plot depicts test scores in relation to the hours of homework. Here’s how we can characterize the relationship:
- Positive Correlation: There is a general upward trend, indicating that as the hours of homework increase, the test scores also tend to increase.
- Strength: The points are not perfectly aligned, but there is a noticeable positive correlation, suggesting that more homework hours are associated with higher test scores.
- Outliers: Most points follow the trend, although there are a few variations. For example, there are a couple of points with low homework hours but relatively high test scores.
(b) Predicting the Score for 3 Hours of Homework
Paul uses the function [tex]\( y = 8x + 40 \)[/tex] to model the relationship, where [tex]\( y \)[/tex] represents the test score and [tex]\( x \)[/tex] represents the hours of homework.
To predict the score for 3 hours of homework:
[tex]\[y = 8(3) + 40 = 24 + 40 = 64\][/tex]
So, the model predicts a score of [tex]\( \boxed{64} \)[/tex] for 3 hours of homework.
(c) Meaning of the Number 40 in the Model
In the context of the situation, the number 40 in the equation [tex]\( y = 8x + 40 \)[/tex] represents the y-intercept. This implies:
- Baseline Score: If a student spends 0 hours on homework, the model predicts that they would score 40 on the test. This serves as a baseline score, indicating the minimum test score a student could achieve without any homework.
Summary
(a) The relationship between hours spent on homework and test scores is a positive correlation, where more homework is generally associated with higher test scores.
(b) The model predicts a score of 64 for 3 hours of homework.
(c) The number 40 represents the baseline test score when no homework is done, according to the model.
Abit is planning a birthday party for his grandfather. He bought a cake for $18. He also wants to buy some balloons, which are $4 each. Abit has $35 to spend all together. How much money will Abit have left after he buys the cake and as many balloons as possible?
solve for t. use the quadratic formula.
d=−16t^2+12t
Answer:
[tex]t\,=\,\frac{-3+\sqrt{9+4d}}{-8}\:\:and\:\:\frac{3+\sqrt{9+4d}}{8}[/tex]
Step-by-step explanation:
Given: d = -16t² + 12t
To find: t using quadratic formula
If we have quadratic equation in form ax² + bx + c = 0
then, by quadratic formula we have
[tex]x\,=\,\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Rewrite the given equation,
-16t² + 12t - d = 0
from this equation we have,
a = -16 , b = 12 , c = d
now using quadratic formula we get,
[tex]t\,=\,\frac{-12\pm\sqrt{12^2-4\times(-16)\times d}}{2\times(-16)}[/tex]
[tex]t\,=\,\frac{-12\pm\sqrt{144+64d}}{-32}[/tex]
[tex]t\,=\,\frac{-12\pm\sqrt{16(9+4d)}}{-32}[/tex]
[tex]t\,=\,\frac{-12\pm4\sqrt{9+4d}}{-32}[/tex]
[tex]t\,=\,\frac{4(-3\pm\sqrt{9+4d})}{-32}[/tex]
[tex]t\,=\,\frac{-3\pm\sqrt{9+4d}}{-8}[/tex]
[tex]t\,=\,\frac{-3+\sqrt{9+4d}}{-8}\:\:,\:\:\frac{-3-\sqrt{9+4d}}{-8}[/tex]
[tex]t\,=\,\frac{-3+\sqrt{9+4d}}{-8}\:\:and\:\:\frac{-(3+\sqrt{9+4d})}{-8}[/tex]
[tex]t\,=\,\frac{-3+\sqrt{9+4d}}{-8}\:\:and\:\:\frac{3+\sqrt{9+4d}}{8}[/tex]
Therefore, [tex]t\,=\,\frac{-3+\sqrt{9+4d}}{-8}\:\:and\:\:\frac{3+\sqrt{9+4d}}{8}[/tex]
Answer:
[tex]\frac{3-\sqrt{9-d}} {8}\text{ or }t=\frac{3+\sqrt{9-d}} {8}[/tex]
Step-by-step explanation:
Here, the given expression,
[tex]d= -16t^2+12t[/tex]
[tex]\implies -16x^2+12t-d=0[/tex] ------(1)
Since, if a quadratic equation is,
[tex]ax^2+bx+c=0[/tex] ------(2)
By using quadratic formula,
We can write,
[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
By comparing equation (1) and (2),
We get, a = -16, b = 12, c = -d,
[tex]t=\frac{-12\pm \sqrt{12^2-4\times -16\times -d}}{2\times -16}[/tex]
[tex]t = \frac{-12\pm \sqrt{16\times 9-16\times d}}{-32}[/tex]
[tex]t = \frac{-12\pm \sqrt{16}\times \sqrt{9-d}} {-32}[/tex]
[tex]t = \frac{-12\pm 4\sqrt{9-d}} {-32}[/tex]
[tex]t = \frac{4(-3\pm \sqrt{9-d})} {4(-8)}[/tex]
[tex]t = \frac{-3\pm \sqrt{9-d}} {-8}[/tex]
[tex]t = \frac{-3+\sqrt{9-d}} {-8}\text{ or }t=\frac{-3-\sqrt{9-d}} {-8}[/tex]
[tex]\implies t = \frac{3-\sqrt{9-d}} {8}\text{ or }t=\frac{3+\sqrt{9-d}} {8}[/tex]
Which is the required solution.
Ella sold 37 necklaces for $20 each at the craft fair. She is going to donate half of the money she earned to charity. Use the Commutative Property to mentally find how much money she will donate. Explain the steps you used.
Ella sold 37 necklaces for $20 each at the craft fair. She is going to donate half of the money she earned to charity. Use the Commutative Property to mentally find how much money she will donate. Explain the steps you used.
Solution:
Earning from 1 necklace=$20
Earning from 37 necklaces=$20*37
Half of the earnings= [tex] \frac{20*37}{2} =\frac{20}{2}*37=10*37 [/tex]
Half of the earnings=$10*37
Now, Applying Commutative Propert, a*b=b*a
So, Money she need to donate= Half of the earnings= 10*37 =37*10
So, Money she donates=$370
money she will donate=$370
Whats the number if the prime factorization is 5x7x7x17?
Which quotient is equivalent to the mixed number
2
2---------- =
3
answer in fractions
Final answer:
To convert 2 2/3 to an improper fraction, multiply the whole number by the denominator and add the numerator, resulting in 8/3. The question lacks details to provide another specific quotient to compare this with. In dividing fractions, multiplication by the reciprocal is used to find equivalent quotients.
Explanation:
To find which quotient is equivalent to the mixed number 2 2/3, we must first convert the mixed number to an improper fraction. A mixed number is composed of a whole number and a fraction, which can be converted into an improper fraction by multiplying the denominator by the whole number and then adding the numerator to this product.
For the mixed number 2 2/3, we multiply the whole number 2 by the denominator 3, giving us 6, and then add the numerator 2, resulting in 8. Therefore, 2 2/3 as an improper fraction is 8/3.
However, without context, it's unclear what other quotient we are being asked to compare with the mixed number 2 2/3. Quotients can refer to the result of any division. Nonetheless, in contexts of dividing fractions, we use the multiplication of the inverse to find equivalent quotients. For example, if dividing by 3/1 (which is the same as dividing by 3), we would multiply by its reciprocal, 1/3.
In cases of conversion factors, we could use a factor that equals 1 to convert units without changing the value. For instance, 1 m / 100 cm is a conversion factor that equals 1, allowing us to convert meters to centimeters without changing the quantity.
Remember, multiplication and division in fractions can be seen as interconnected operations, where dividing by a number is the same as multiplying by its reciprocal.