Answers
The formula to calculate the area of a triangle is given to be:
\(A=\frac{1}{2}\cdot b\cdot h\)where b is the length of the base of the triangle and h is the height.
From the triangle in the question, we have the following parameters:
\(\begin{gathered} b=20\text{ in} \\ h=14\text{ in} \end{gathered}\)Therefore, we can calculate the area to be:
\(A=\frac{1}{2}\times20\times14=140\)Therefore, the area of the triangle is 140.00 cubic inches.
Related Questions
1. The Rock has an 88-gallon fish tank. When it needs to be cleaned, it can be drained at a rate of 6 gallons per minute. Handwritten. Show all work. Complete sentence for each question. (a) Assuming the tank was full, write a function in the form y=mx + b that represents the amount of water in the tank, Y, after X minutes. You will need to know the initial value and the rate of change. (b) How long has the tank been draining for if it has 34 gallons left?
Answers
Using linear function concepts, it is found that:
a) The function is y = 88 - 6x.
b) The tank has been draining it for 9 minutes.
What is a linear function?
A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.Item a:
The full volume of the tank is of 88 gallons, hence the y-intercept is of b = 88.The volume can be drained at a rate of 6 gallons per minute, hence the slope is of m = -6.Thus, the equation is given by:
y = 88 - 6x.
Item b:
This is x for which y = 34, hence:
y = 88 - 6x
34 = 88 - 6x
6x = 54
x = 9.
The tank has been draining it for 9 minutes.
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The amount of water in the tank is given by y = -6x + 88, it would take 9 minutes for the water to remain 34 gallons.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let y represent the amount of water after x minutes.
The Rock has an 88-gallon fish tank which can be drained at a rate of 6 gallons per minute. Hence:
m = -6, b = 88
y = -6x + 88
For 34 gallons:
34 = -6x + 88
x = 9
The amount of water in the tank is given by y = -6x + 88, it would take 9 minutes for the water to remain 34 gallons.
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Need help with this will give branliest to the first who answers
Answers
First, find the equation
y = F(x) = x +3
Then plug in 2 for x ( you could also go to 2 on the x-axis to find the Y)
F(2) = (2)+3
F(2) = 5
refer to functions s and t. find the indicated function and write the domain in interval notation. write your answer as a single fraction.
s(x)= x-5/x^2-64 t(x)= x-8/5-x
(s-t)(x)=
write the domain in interval notation for part 2
Answers
The domain of (s - t)(x) in interval notation is (-∞, -8) U (-8, 5) U (5, 8) U (8,
∞).
To find (s - t)(x), we subtract the function t(x) from s(x).
s(x) =\((x - 5)/(x^2 - 64)\)
t(x) = (x - 8)/(5 - x)
To subtract the functions, we need a common denominator. In this case, we can use (x^2 - 64) as the common denominator.
(s - t)(x) =\([(x - 5)/(x^2 - 64)] - [(x - 8)/(5 - x)]\)
To simplify the expression, we need to factor the denominators and simplify further:
\((x^2 - 64) = (x - 8)(x + 8)\)
(5 - x) = -(x - 5)
Substituting these into the expression, we get:
(s - t)(x) = [(x - 5)/(x - 8)(x + 8)] - [(x - 8)/-(x - 5)]
Next, we need to find a common denominator for the two fractions. The common denominator will be (x - 8)(x + 8)(x - 5).
(s - t)(x) = [(x - 5)(-(x - 5))/((x - 8)(x + 8)(x - 5))] - [(x - 8)(x + 8)/((x - 8)(x + 8)(x - 5))]
Simplifying further:
(s - t)(x) = \([-(x - 5)^2 - (x - 8)(x + 8)]/[(x - 8)(x + 8)(x - 5)]\)
The domain of the function (s - t)(x) is the set of values for which the denominator is non-zero, since division by zero is undefined.
The denominator (x - 8)(x + 8)(x - 5) will be non-zero as long as x is not equal to 8, -8, or 5.
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Find the area of the figure.
(Sides meet at right angles.)
Answers
Answer:
16
Step-by-step explanation:
A of rectangle = L x W
= 3 x 4
= 12
A of square = L x W
= 2 x 2
= 4
The result is 16 squared
These box plots show daily low temperatures for a sample of days in two different towns.
Town A. 10,15,20,30, and 55
Town B. 5,20,30,40, and 55
Answers
*The question is incomplete. Attached below is the diagram of the box plots being referred to followed by the complete question and options.
Answer:
D. The median for town A, 20 degrees, is less than the median of town B, 30 degrees
Step-by-step Explanation:
From the given diagram of the box plots showing the daily low temperatures for town A and B, the median of town A and B is shown on the box plots by the line that divides the box. Therefore, the median of town A is where the line that divides the box is. Median for town A is 20⁰. Same applies for town B. Town B median is 30⁰.
Therefore, option D is the most appropriate comparison of the centers. Median of town A is less than median of town B.
Question provided in attachment.
Answers
We can be 99% confident that the true mean healing rate of newts falls within the interval of 22.919 to 30.415 micrometers per hour.
How to calculate the valueSample Mean: = (29 + 27 + 34 + 40 + 22 + 28 + 14 + 35 + 26 + 35 + 12 + 30 + 23 + 18 + 11 + 22 + 23 + 33) / 18
= 480 / 18
≈ 26.667
Sample Standard Deviation (s):
= ✓((Σ(29 - 26.667)² + (27 - 26.667)² + ... + (33 - 26.667)²) / (18 - 1))
≈ ✓(319.778 / 17)
≈ ✓(18.81)
≈ 4.336
Confidence level = 99%
Sample Size (n) = 18
Sample Mean = 26.667
Sample Standard Deviation (s) = 4.336
Degrees of Freedom (df) = n - 1 = 18 - 1 = 17
Using a t-table or statistical software, we find that the critical value for a 99% confidence level with 17 degrees of freedom is approximately 2.898.
Margin of Error (E) = 2.898 * (4.336 / ✓18))
≈ 3.748
Confidence Interval = (26.667 - 3.748, 26.667 + 3.748)
= (22.919, 30.415)
We can be 99% confident that the true mean healing rate of newts falls within the interval of 22.919 to 30.415 micrometers per hour. This means that if we were to repeat the study multiple times and construct confidence intervals, approximately 99% of those intervals would contain the true mean healing rate of the population.
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Find the value of x,given the area of the quadrilateral
Answers
Answer:
x = 9
Step-by-step explanation:
The quadrilateral given above is a parallelogram.
Area of the quadrilateral = area of parallelogram = base × height
Area = 63 cm²
base = 7 cm
height = x
Plug in the values into the equation:
x × 7 = 63
7x = 63
7x/7 = 63/7
x = 9
3x – 2y = -1
y = -x+ 3
Is (1, 2) a solution of the system?
Help Pls
Answers
Answer:
Yes
Step-by-step explanation:
If you plug (1, 2) into the system, the equation would be correct.
Original Equation:
3x - 2y = -1
Plug in (1, 2)
3 - 4 = -1
Original Equation 2:
y = -x + 3
Plug in (1, 2)
1 = -2 + 3
Hope I helped :)
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i need help with my work asap
Answers
The area of the figure is 225 ft²
How to determine the valueFrom the figure shown, we have that it is made up of a triangle and a rectangle.
Now, the formula for calculating the area of a triangle is expressed as;
A = 1/2bh
Such that;
b is the baseh is the heightSubstitute the values
Area = 1/2 × 10 × 15
Multiply the values
Area = 75 ft²
Area of the rectangle is;
Area = length × width
Area = 10(15)
Area = 150 ft²
Total area = 225 ft²
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mations to Determine Similarity
What steps would you take to determine if these
figures are similar? Check all that apply.
Use a scale factor of 2.
Multiply the vertices of polygon ABCD by
O Translate the intermediate image 4 units down.
Perform two different dilations.
Reflect the intermediate image.
Answers
The steps which you would take to determine if these figures are similar include the following:
2. Multiply the vertices of polygon ABCD by 1/2.
5. Reflect the intermediate image.
What is a dilation?In Mathematics and Geometry, a dilation is a type of transformation which typically transforms the dimension (size) or side lengths of a geometric object, without affecting its shape.
Therefore, the dimension or side lengths of the dilated geometric object would be stretched or compressed (shrunk) depending on the scale factor that is applied.
By critically observing the graph representing polygon ABCD, we can logically deduce that a sequence of transformations that would polygon ABCD (pre-image) onto polygon A"B"C"D" (image) is a dilation by a scale factor of 1/2 and a reflection of intermediate image.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options.
The radius of the circle is 3 units.
The center of the circle lies on the x-axis.
The center of the circle lies on the y-axis.
The standard form of the equation is (x – 1)² + y² = 3.
The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Answers
The three statements that are true include the following:
A. The radius of the circle is 3 units.
B. The center of the circle lies on the x-axis.
D. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
What is the equation of a circle?In Mathematics, the standard form of the equation of a circle is represented by this mathematical expression;
(x - h)² + (y - k)² = r² .......equation 1.
Where:
h and k represents the coordinates at the center of a circle.
r represents the radius of a circle.
Based on the information provided, we have the following equation of a circle:
x² + y² – 2x – 8 = 0 ......equation 2.
In order to determine the true statements, we would rewrite the equation in standard form and then factorize by using completing the square method:
x² – 2x + y² = 8 = 0
x² – 2x + (2/2)² + y² = 8 + (2/2)²
x² – 2x + 1 + y² = 8 + 1
(x – 1)² + (y - 0)² = 9 .......equation 3.
By comparing equation 1 and equation 3, we have the following:
Center (h, k) = (1, 0)
Radius (r) = 3
Additionally, this line and the center of the given circle lies on the x-axis (x-coordinate) because the y-value is equal to zero (0).
(x - 0)² + (y - 0)² = 3²
x² + y² = 9.
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Subtract. Write your answer in simplest form.
6 3/4 - 2 3/20
Answers
Answer:
(6-2) (3/4-3/20)
4 ((3×20-3×4)/80)
4 48/80
4 3/5
Dividing by a Monomial
What is (9x^3-6x^2+15x) ÷ 3x^2?
Answers
Answer:
\(3x-2+\frac{5}{x}\)
Step-by-step explanation:
To divide the polynomial (9x^3 - 6x^2 + 15x) by the monomial 3x^2, we can write it as:
(9x^3 - 6x^2 + 15x) ÷ (3x^2)
To simplify the division, we divide each term of the polynomial by 3x^2:
(9x^3 ÷ 3x^2) - (6x^2 ÷ 3x^2) + (15x ÷ 3x^2)
To divide monomials with the same base, we subtract the exponents. So:
9x^3 ÷ 3x^2 = 9/3 * (x^3/x^2) = 3x^(3-2) = 3x
(-6x^2) ÷ (3x^2) = -6/3 * (x^2/x^2) = -2
15x ÷ 3x^2 = 15/3 * (x/x^2) = 5/x
Putting it all together, we have:
(9x^3 - 6x^2 + 15x) ÷ (3x^2) = 3x - 2 + 5/x
Therefore, the division of (9x^3 - 6x^2 + 15x) by 3x^2 is 3x - 2 + 5/x.
Benjamin bought a 3-pound bag of flour for $6.95. What is the unit price per ounce of flour? (1 pound = 16 ounces)
Answers
Answer:
The unit price per ounce of flour is
Step-by-step explanation:
We can first change the 3 pound bag into ounces which is just 3x16=48 we can do this because 1 pound=16 ounces. Now we know there are 48 ounces so we divide 6.95/48
Which is .144791666...
Classify each figure as stable or unstable.
Help please!!
Answers
A rectangular placemat is 18 inches long and 12 inches wide. What is the area of this tablecloth in square inches?
a. 216
b. 60
c. 54
d. 900
Answers
In a rectangle, there are 2 pairs of congruent sides. Therefore, the area of a rectangle can be found using:
\(\text{A}=\text{l} \times \text{w}\)
We know that the length is 18 and the width is 12, so we can multiply 18 in for l, and 12 in for w.
\(\text{A}=\text{18} \times \text{12}\)
Multiply the numbers together
\(\text{A}=216\)
So, the area is 216 inches.
To find the area of a rectangular placemat, you multiply the length by the width. In this case, the length is 18 inches and the width is 12 inches. Therefore, the area of the tablecloth is:
Area = Length × Width
Area = 18 inches × 12 inches
Area = 216 square inches
So, the correct answer is option a. 216.
A total of 27 students are in your class. There are nine more males than females.
How many females are in your class?
Answers
Sam had 5 fish. She ate 2 how many did she have left
Answers
Answer:
3
Step-by-step explanation:
Which of the following statements with respect to political risk is true?
Oa. Political risk premiums are added to the required rate of return to adjust for political risks.
b. Companies cannot take any steps to reduce the potential from loss from expropriation since a foreign
government is involved.
Oc. The risk of expropriation of U.S. assets abroad is high even in traditionally friendly and stable countries.
Od. A company can reduce political risk by structuring operations so that the subsidiary has value only as a part of the
integrated corporate system.
Answers
This statement is true. Political risk is the risk of loss in an investment due to political instability or changes in government policy. Companies can adjust for the potential impact of political risk by adding a political risk premium to their required rate of return. This premium compensates investors for the additional risk associated with the investment due to political factors. The size of the premium will depend on the specific country, the nature of the investment, and the perceived level of political risk. Companies can also take steps to reduce political risk, such as diversifying their operations, investing in political risk insurance, or structuring operations to minimize the value of a subsidiary that might be subject to expropriation.
16+[ 20+{16÷(25÷5-1)×2}-10]×2
Answers
Hello!
16 + (20 + (16 ÷ (25 ÷ 5 - 1) x 2) - 10) x 2
= 16 + (20 + (16 ÷ (5 - 1) x 2) - 10) x 2
= 16 + (20 + (16 ÷ 4 x 2) - 10) x 2
= 16 + (20 + (4 x 2) - 10) x 2
= 16 + (20 + 8 - 10) x 2
= 16 + (28 - 10) x 2
= 16 + 18 x 2
= 16 + 36
= 52Please help me I need to turn in tomorrow please help!!!!
Answers
Answer:
5/7 which is option c the correct answer.
Answer:
C. 5/7 is the correct answer
What is the solution to this equation
x^2+4x-12=0
Answers
Answer:
x = 2 or –6
Step-by-step explanation:
x² + 4x –12 = 0
x² +6x –2x –12 = 0
x(x + 6) –2( x + 6) = 0
(x–2)(x+6)= 0
x–2= 0
x= 2.
x+6= 0
x= –6
x = 2 or –6
(c) Figure 6 shows the triangle ABC, with all side lengths measured in centimetres.
side AB = 14.6 cm
side AC = 21.4 cm
side BC = 7.5 cm
(i) Find angle ABC, giving your answer correct to the nearest degree.
(ii) Find the area of triangle ABC, giving your answer correct to the nearest square centimetre.
Answers
Answer:
angle B ≈ 149°area ≈ 28 cm²Step-by-step explanation:
You want the largest angle and the area of a triangle with side lengths 7.5 cm, 14.6 cm, and 21.4 cm.
Law of cosinesThe law of cosines tells you ...
b² = a² + c² -2ac·cos(B)
Solving for angle B, we have ...
B = arccos((a² +c² -b²)/(2ac))
B = arccos((7.5² +14.6² -21.4²)/(2·7.5·14.6)) ≈ 149° . . . angle ABC
AreaThe area of the triangle can be found using the formula ...
Area = 1/2(ac·sin(B))
Area = 1/2·7.5·14.6·sin(149°) ≈ 28 cm² . . . area
__
Additional comment
Angle ABC is opposite side AC, which is the longest side. Hence, angle ABC is the largest angle.
We used the original (full precision) angle value to calculate the area. The rounded angle value would be inappropriate for that purpose. (Second attachment.) Note the calculator mode is set to DEGrees.
ab-c/d has a value of 24. write the values if :-
1- a, b, c, d are all positive.
2- a, b, c, d are all negative.
3- a, b, c, d are mixed of negative and positive.
WRITE ANSWERS FOR 1, 2 AND 3
Answers
The values of ab, b - c, and c/d are 6, -1, and 4 respectively when a = 2, b = 3, c = 4 and d = 1.Using BODMAS rule, we can simplify the given expression.ab - c/d = 24
Given ab-c/d has a value of 24.Now, we have to find the value ofab, b - c, and c/d.Multiplying d on both sides, we getd(ab - c/d) = 24dab - c = 24d...(1)Now, we can find the value of ab, b - c, and c/d by substituting different values of a, b, c and d.Value of ab when a = 2, b = 3, c = 4 and d = 1ab = a * b = 2 * 3 = 6.
Value of b - c when a = 2, b = 3, c = 4 and d = 1b - c = 3 - 4 = -1Value of c/d when a = 2, b = 3, c = 4 and d = 1c/d = 4/1 = 4Putting these values in equation (1), we get6d - 4 = 24dSimplifying, we get-18d = -4d = 2/9
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One shirt at H&M cost $7. what is the cost of 40 shirts
Answers
Answer:
$280
Step-by-step explanation:
7•40=$280
x^3 + 3x^2 -10x factor polynomial and find zero
Answers
Answer:
x(x - 2)(x + 5)x = 0, x = 2, x = -5Step-by-step explanation:
x^3 + 3x^2 - 10x
~Factor
x(x - 2)(x + 5)
Solve for the zero.
x(x - 2)(x + 5) = 0
We know that; x = 0, x - 2 = 0, and x + 5 = 0
x = 0
x - 2 = 0
x = 2
x + 5 = 0
x = -5
Best of Luck!
Here we are provided with an polynomial of degree 3 and we have to factorise it first and then we have to compute it's zeroes.
Given Polynomial:
x³ + 3x² - 10xTaking common x from all the 3 terms,
➝ x(x² + 3x - 10)
Factorising through Middle term factorisation,
➝ x(x² + 5x - 2x - 10)
➝ x{x(x + 5) - 2(x + 5)}
➝ x(x - 2)(x + 5)
Hence, Factorised !!
Now equating to 0 to find the zeroes of the poly.
➝ x(x - 2)(x + 5) = 0
That means,
x = 0x - 2 = 0x + 5 = 0So, the zeroes of the polynomial is 0, 2 or -5
And we are done....
Carry On Learning \(!\)
The functions f(x) and g(x) are shown on the graph. fx)=x2
What is g(x)
Answers
It’s a flip of the graph on the x-axis
Therefore f(x) = - x^2 (NOT IN PARENTHESIS that would be a reflection on the y axis)
It’s a shift 4 y values down therefore
g(x) = - x^2 - 4
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Which linear function has the same y-intercept as the one that is represented by the graph?
On a coordinate plane, a line goes through points (3, 4) and (5, 0).
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 3, negative 1, 1, 3. Column 2 is labeled y with entries negative 4, 2, 8, 14.
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 4, negative 2, 2, 4. Column 2 is labeled y with entries negative 26, negative 18, negative 2, 6.
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 5, negative 3, 3, 5. Column 2 is labeled y with entries negative 15, negative 11, 1, 5.
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 6, negative 4, 4, 6. Column 2 is lab
eled y with entries negative 26, negative 14, 34, 46.
Answers
The linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.
To determine the linear function with the same y-intercept as the graph, we need to find the equation of the line passing through the points (3, 4) and (5, 0).
First, let's find the slope of the line using the formula:
slope (m) = (change in y) / (change in x)
m = (0 - 4) / (5 - 3)
m = -4 / 2
m = -2
Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:
y - y1 = m(x - x1)
Using the point (3, 4) as our reference point, we have:
y - 4 = -2(x - 3)
Expanding the equation:
y - 4 = -2x + 6
Simplifying:
y = -2x + 10
Now, let's check the given options to find the linear function with the same y-intercept:
Option 1: The table with x-values (-3, -1, 1, 3) and y-values (-4, 2, 8, 14)
The y-intercept is not the same as the given line. So, this option is not correct.
Option 2: The table with x-values (-4, -2, 2, 4) and y-values (-26, -18, -2, 6)
The y-intercept is not the same as the given line. So, this option is not correct.
Option 3: The table with x-values (-5, -3, 3, 5) and y-values (-15, -11, 1, 5)
The y-intercept is the same as the given line (10). So, this option is correct.
Option 4: The table with x-values (-6, -4, 4, 6) and y-values (-26, -14, 34, 46)
The y-intercept is not the same as the given line. So, this option is not correct.
Therefore, the linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.
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Bobby put 1/3 of his lawn mowing money into his savings and uses the remaining 2/5 to buy a video game. If he has $12 left, how much did he have at first?
Answers
Given:
Bobby put 1/3 of his lawn mowing money into his savings
He uses the remaining 2/5 to buy a video game.
He has $12 left.
To find:
The amount did he have at first.
Solution:
Let x be the initial amount.
Bobby put 1/3 of his lawn mowing money into his savings. So, the remaining amount is
\(x-\dfrac{1}{3}x=\dfrac{2}{3}x\)
He uses the remaining 2/5 to buy a video game. Then the remaining amount is
\(Remaining=\dfrac{2}{3}x-\dfrac{2}{3}x\times \dfrac{2}{5}\)
\(Remaining=\dfrac{2}{3}x-\dfrac{4}{15}x\)
\(Remaining=\dfrac{10x-4x}{15}\)
\(Remaining=\dfrac{6x}{15}\)
\(Remaining=\dfrac{2x}{5}\)
It is given that the remaining amount is $12.
\(12=\dfrac{2x}{5}\)
\(12\times 5=2x\)
\(60=2x\)
Divide both sides by 2.
\(\dfrac{60}{2}=x\)
\(30=x\)
Therefore, Bobby have $30 at first.
HELP PLEASEEEEEEEEEEEEEEEEEEEEEEE WILL GIVE BRAINLISTTTTTTTTTTTTTTTTTTT
Answers
Answer:
Step-by-step explanation:
if we need to approximate,
the radius=125, the diameter is d=250
we estimate that pi=3
C=3*250=aprox 750
the closest number is 785
Answer:
I think it's D 785 meters.
Step-by-step explanation:
Circumference is 2nr
C=2πr=2·π·125≈785.39816
785.39816 is rounded to is 785