Which of the following equations will yield the surface area of a triangular prism?
A. SA = 2lw + 2lh + 2wh
B. SA = lwh
C. SA = 2B + Ph
D. SA = Bh
Final answer:
The correct formula for the surface area of a triangular prism is SA = 2B + Ph, where B is the area of one triangular base, P is the perimeter of this base, and h is the height of the prism.
Explanation:
To find the surface area of a triangular prism, we don't use any of the formulas mentioned for the area of a triangle or volume. The correct formula is one that combines the area of the base triangles and the rectangles formed by the sides of the prism. In this case, the correct formula is SA = 2B + Ph, where B represents the area of one of the triangular bases, P is the perimeter of the triangular base, and h is the height of the prism that is perpendicular to the bases.
Let's clarify the correct formula with an example: Imagine a triangular prism with a triangular base having sides of lengths 3m, 4m, and 5m, and a height of 6m. To find the base area B, you'd use the formula for the area of a triangle, which is B = bh/2, where b is the base and h is the height of the triangle. The perimeter P would simply be the sum of the sides of the triangular base. The surface area would then be calculated by plugging these values into the SA = 2B + Ph formula.
What is the perimeter of the triangle shown on the coordinate plane, to the nearest tenth of a unit?
14.6 units
15.5 units
21.0 units
21.6 units
HELP MATH!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
if an angle is acute then its measure is 30 degrees true or false
An acute angle is any angle less than 90 degrees, and while 30 degrees is an example of an acute angle, it is not accurate to say that all acute angles must be 30 degrees.
Explanation:The statement 'If an angle is acute then its measure is 30 degrees' is false. An acute angle is defined as any angle that is less than 90 degrees. While 30 degrees is indeed an example of an acute angle, an acute angle can be any value less than 90 degrees. For example, 45 degrees, 20 degrees, or 1 degree are also acute angles. Therefore, it is not accurate to say that an acute angle must be 30 degrees.
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The first three numbers in sequence are 1, 4, and 9. Marie determined that the fourth number in the sequence is 16. Marie’s rule involved multiplication. What rule did she use to determine the fourth number in the sequence? Specific please
Evaluate ab for a = 2 3/4 and b = 4/5
A. 1 1/15
B. 8/15
C. 2 1/5
D. 2/3
By the end of the school year, Terry had passed 80% of his science tests. If Terry failed 4 science tests, how many science tests did Terry pass?
Answer: Terry passed 16 science tests.
Step-by-step explanation: Given that by the end of the school year, Terry had passed 80% of his science tests and Terry failed 4 science tests.
We are to find the number of science tests that Terry passed.
Let x represents the total number of science tests that Terry appeared in.
Since he failed 4 science tests, so the number of science tests that Terry passes is given by
[tex](x-4).[/tex]
Since he passed 80% of his tests, so we get
[tex]80\%\times x=x-4\\\\\\\Rightarrow \dfrac{80}{100}\times x=x-4\\\\\\\Rightarrow \dfrac{4}{5}\times x=x-4\\\\\Rightarrow 4x=5x-20\\\\\Rightarrow 5x-4x=20\\\\\Rightarrow x=20.[/tex]
So, total number of science tests = 20.
Therefore, the number of science tests that Terry passed is given by
[tex]n=20-4=16.[/tex]
Thus, Terry passed 16 science tests.
Twenty-five members of the eighth grade class at Park Center Middle School are going to a museum and then to lunch. Each student must pay an entrance fee to the museum and $7.25 for lunch. The total cost for the trip is $443.75. What is the entrance fee for one student?
Answer: $17.75
Step-by-step explanation: $443.75 / 25 = $17.75
True or false? If four points are collinear, they are also coplanar
We have that the statement If four points are collinear, they are also coplanar is
True
From the Question we are told that
four points are collinear
Collinear
This occurs when three or more lines lines on the same plane or line
While
Coplanar is when simply means on the same plane
Therefore
If four points are collinear, they are also coplanar
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Which of the following is the linear parent function
Option: C is the correct answer.
C.) F(x)= x
Step-by-step explanation:We know that a linear parent function is a function whose graph is a straight line passing through the origin and the equation of such a function is given by:
y=F(x)=x
Since, it is the simplest form of the equation of all the linear functions that are known to us and hence known as the parent linear function.
what is the mass of an object that has a force of 100 Newtons and acceleration of 25 m/s2
What is the area of a rectangle with vertices at (−3, −1) , (1, 3) , (3, 1) , and (−1, −3) ?
Enter your answer in the box. Do not round any side lengths.
___units²
(−3, −1)(−3, −1) , (1, 3)(1, 3) , (3, 1)(3, 1) , and (−1, −3)(−1, −3) ?
Enter your answer in the box. Do not round any side lengths.
Answer: 16 Units
2.) What is the perimeter of the rectangle shown on the coordinate plane, to the nearest tenth of a unit?
Answer: 26.8 Units
3.) What is the area of a triangle with vertices at
(0, −2) , (8, −2) , and (9, 1) ?
Enter your answer in the box.
Answer: 12 Units(−2, 1) , (−2, 4) , (2, 7) , (6, 4) , and (6, 1) ?
Enter your answer in the box. Do not round any side lengths.
Answer: 24 Units
I really hope this helps! Let me know if it did... or anyone else that used this info!
he formula for a trapezoid relates the area A, the two bases, a and b, and the height, h.
A=1/2 h(a+b)
Solve for h.
What is the point slope form of a line with slope 4/5 that contains the points -2,1
Answer:
[tex]y-1= \frac{4}{5} (x+2)[/tex]
Step-by-step explanation:
Using point-slope intercept form:
The equation of line is given by:
[tex]y-y_1 = m(x-x_1)[/tex] .....[1]
where,
m is the slope of the line and [tex](x_1, y_1)[/tex] is the point on the line.
As per the statement:
A line with slope 4/5 that contains the points (-2,1)
⇒m = [tex]\frac{4}{5}[/tex] and [tex](x_1, y_1)=(-2, 1)[/tex]
Substitute these values in [1] we have;
[tex]y-1= \frac{4}{5} (x+2)[/tex]
Therefore, [tex]y-1= \frac{4}{5} (x+2)[/tex] is the point slope form of a line with slope 4/5 that contains the points (-2,1).
It takes 33 pounds of seeds to completly plant a 6 acre field. how many acres can be planted per pound of seed
The median of the values of the data set is h. If 625 were subtracted from each of the values in the data set what would be the median of the resulting data ?
A. H - 625
B.625 - h
C.h + 625
D.625 • h
The correct answer is A. H - 625.
Sure, let's go step by step to find the correct answer.
Given:
- Median of the original data set = h
- Subtracted 625 from each value in the data set
Let's represent the original data set as {x1, x2, x3, ..., xn} where n is the number of values in the data set.
1. Median of the original data set:
The median of a data set is the middle value when the values are arranged in ascending or descending order. Since the data set has been modified by subtracting 625 from each value, the new data set would be {x1 - 625, x2 - 625, ..., xn - 625}.
2. Median of the modified data set:
If we subtract 625 from each value, it doesn't affect the relative order of the values. Therefore, the median of the modified data set would also be h.
So, the correct answer is A. H - 625.
The median represents the middle value in a sorted data set. When we subtract a constant (625 in this case) from each value in the data set, it shifts the entire set downwards without changing the order of values relative to each other. Therefore, the position of the middle value, which determines the median, remains the same. This means the median of the modified data set will still be h.
complete question
The median of the values of the data set is h. If 625 were subtracted from each of the values in the data set what would be the median of the resulting data ?
A. H - 625
B.625 - h
C.h + 625
D.625 • h
A general contractor is constructing a building that requires a concrete foundation that is to be 20 feet by 12 feet and 4 inches thick. if the local home supply store sells concrete for $125 per cubic yard, what will be the cost of the concrete for the foundation?
First we calculate the volume of the foundation:
Volume (V) = 20 ft * 12 ft * 4 in (1 ft / 12 in)
V = 80 ft^3
Since the cost is in cubic yard (yard^3) so convert:
V = 80 ft^3 * (1 yard^3 / 27 ft^3) = 2.963 yard^3
So the total cost is:
cost = ($125 / yard^3) * 2.963 yard^3
cost = $370.37
Answer:
$370.37.
Step-by-step explanation:
We have been given that a general contractor is constructing a building that requires a concrete foundation that is to be 20 feet by 12 feet and 4 inches thick.
First of all, we will convert the given dimensions of foundation in yards.
[tex]\text{3 feet}=\text{1 yard}[/tex]
[tex]20\text{ feet}=\frac{20}{3}\text{ yards}[/tex]
[tex]12\text{ feet}=\frac{12}{3}\text{ yards}[/tex]
[tex]\text{36 inches}=\text{1 yard}[/tex]
[tex]\text{4 inches}=\frac{4}{36}\text{ yards}=\frac{1}{9}\text{ yards}[/tex]
Since the foundation of building is in form of cuboid, so volume of foundation will be the product of 3 sides.
[tex]\text{Volume of foundation}=\frac{20}{3}\text{ yards}\times \frac{12}{3}\text{ yards}\times \frac{1}{9}\text{ yards}[/tex]
[tex]\text{Volume of foundation}=\frac{20\times 12\times 1}{3\times 3 \times 9}\text{ yards}^3[/tex]
[tex]\text{Volume of foundation}=\frac{240}{81}\text{ yards}^3[/tex]
[tex]\text{Volume of foundation}=2.962962962962963\text{ yards}^3[/tex]
Since the local home supply store sells concrete for $125 per cubic yard, so the cost of the concrete for the foundation will be the volume of foundation times $125.
[tex]\text{The cost of the concrete for the foundation}=2.962962962962963\text{ yards}^3\times \frac{\$125}{\text{ yards}^3}[/tex]
[tex]\text{The cost of the concrete for the foundation}=\$370.37037\approx \$370.37[/tex]
Therefore, the cost of the concrete for the foundation is $370.37.
1. The equation of a circle is x ^2 + y ^2 – 4 x + 2 y = 11 .
What are the coordinates of the center of the circle?
Question 1 options
(2, –1)
(4, –2)
(–4, 2)
(–2, 1)
2. What is the equation of the circle with center (4, -3) and radius 2?
Question 2 options:
(x + 4)^2 + (y – 3)^2 = 4
(x + 4)^2 – (y – 3)^4 = 4
(x – 4)^2 + (y + 3)^2 = 2
(x – 4)^2 + (y + 3)^2 = 4
3. What is the equation of this circle? (has picture)
(x – 2)^2 + (y – 7)^2 = ½
(x + 2)^2 + (y + 7)^2 = ¼
(x + 7)^2 + (y + 2)^2 = ¼
(x + 2)^2 + (y + 7)^2 = ½
4. What are the center and radius of the circle described by the equation x2 + y2 – 18x + 12y + 68 = 0?
Question 4 options:
Center (-9, 6); radius 7
Center (9, -6); radius 7
Center (-6, 9); radius 7
Center (6, -9); radius 7
5. Select the equation of a circle with center (-3, 7) and radius 5.
Question 5 options:
(x - 3)^2 + (y + 7)^2 = 25
(x + 3)^2 + (y - 7)^2 = 25
(x + 3) + (y - 7) = 25
(x - 3) + (y + 7) = 25
the ordered pair (2 36) is a solution to which equation(s)
A. y=2x^2
B. y=(3x)^2
C. y=7x^2+2
D. y=(x+4)^2
(2, 36) → x = 2, y = 36
Substitute the value of x and y to the equations of the functions:
A. y = 2x^2
36 = 2(2)^2 → 36 = 8 FALSE
B. y = (3x)^2
36 = (3 · 2)^2 → 36 = 6^2 → 36 = 36 CORRECT
C. y = 7x^2 + 2
36 = 7(2)^2 + 2 → 36 = 7 · 4 + 2 → 36 = 30 FALSE
D. y = (x + 4)^2
36 = (2 + 4)^2 → 36 = 6^2 → 36 = 36 CORRECT
Answer: B. y = (3x)^2 and D. (x + 4)^2
The width of a poster is 4/5 of its length, It takes 36 ft. of metal framing to frame the poster. Find the dimensions of the poster.
What is the difference between 3/7 and 1/14
Classify the function as linear or quadratic and identify the quadratic, linear, and constant terms. f(x) = (3x + 2)(−6x − 3)
A) quadratic function; quadratic term: 6x^2; linear term: 24x; constant term: −6
B) linear function; linear term: −21x; constant term: −6
C) quadratic function; quadratic term: −18x^2; linear term: −21x; constant term: −6
D) linear function; linear term: −18x^2; constant term: −6
Answer:
The correct Option is C). quadratic function; quadratic term: −18x²; linear term: −21x ; constant term: −6
Step-by-step explanation:
Given : f(x) = (3x + 2)(-6x - 3)
Now, f(x) = -18x² -9x -12x - 6
⇒ f(x) = -18x² - 21x - 6
Now, since the highest degree of the given function f(x) is 2 so the function f(x) is quadratic.
Now, quadratic term is one which has highest power x = 2 So, quadratic term = -18x²
Linear term is one which has power x = 1 So, linear term = -21x
Constant term is one which has power of x = 0. So, constant term = -6
Hence, The correct Option is C). quadratic function; quadratic term: −18x²; linear term: −21x ; constant term: −6
What is the class rank if someone has the 40th best GPA in his class of 600?
Solve the inequality for x
20x > 8(4x - 5) - 20
Answer:
its -5 not five
Step-by-step explanation:
A prism is named for the shape of its bases.
True
False
true
Step-by-step explanation:
Hope is helps and good luck
Is 50 degrees celsius hotter than 50 degrees fahrenheit?
50 degrees Celsius is hotter than 50 degrees Fahrenheit because the Celsius scale rises at a faster rate of 1.8 times the Fahrenheit scale per degree, which measurably shows the greater warmth of 50°C compared to 50
Explanation:Yes, 50 degrees Celsius is hotter than 50 degrees Fahrenheit. To understand why, let's look at how temperature is measured on both scales. On the Celsius scale, the freezing point of water is 0°C and the boiling point is 100°C, whereas on the Fahrenheit scale, the freezing point is 32°F and the boiling point is 212°F. This means that 100 Celsius degrees cover the same range as 180 Fahrenheit degrees.
The rate at which temperature increases per degree is faster on the Celsius scale compared to the Fahrenheit scale. Specifically, each degree on the Celsius scale corresponds to a 1.8 times larger temperature change than one degree on the Fahrenheit scale. Therefore, a temperature of 50°C is significantly warmer than 50°F. so, 50°C is equivalent to 122°F, a fact made evident by the conversion formula: °F = (°C × 9/5) + 32.
3.Cornelia spends 2 2/3 hours studying for her big science test. She spent 2/3 of an hour finishing her writing assignment and 1/4 of an hour playing outside. How much time did she spend overall on the three activities?
One car rental company charges $30 per day plus $0.25 per mile driven. a car company charges $40 per day plus $0.10 per mile driven. how many miles must you drive for a one-day rental at the second company to be less expensive than the same rental at the first company? write an inequality to solve.
Answer:
66.667 miles
Step-by-step explanation:
Given: One car rental company charges $30 per day plus $0.25 per mile driven.
Second car company charges $40 per day plus $0.10 per mile driven.
To find: how many miles must you drive for a one-day rental at the second company to be less expensive than the same rental at the first company?
Solution: Let the distance driven on a day be x miles.
As per question,
The first rental company will charge [tex]=30+0.25x[/tex]
The second rental company will charge [tex]=40+0.10x[/tex]
Now, we want the rental charges of second company to be less expensive then the first.
So we get the inequality,
[tex]30+0.25x>40+0.10x[/tex]
[tex]0.25x-0.10x>40-30[/tex]
[tex]0.15x>10[/tex]
[tex]x>\frac{1000}{15}[/tex]
[tex]x>66.667[/tex] miles
Hence, at least 66.667 miles should be driven on a day.
Find two positive numbers such that the sum of one and the square of the other is 200 and whose product is a maximum.
If EG=40 and point F is 2/5 of the way between E and G, find the value FG.
The drawing is not to scale.
a. 32
b. 20
c. 16
d. 24