The total amount Debra ended up paying for the equipment was $28,541.60 and the amount of interest Debra paid on the loan was $14,041.60
(a) To find the total amount Debra ended up paying for the equipment (including the down payment and monthly payments), we need to add the down payment to the total amount of the loan, and then add the total amount of the monthly payments made over the two years.
Total amount of the loan = $14,500 - $1,300 (down payment) = $13,200
Total amount paid = Down payment + Total amount of the loan + Total amount of monthly payments
Total amount paid = $1,300 + $13,200 + ($585.04 x 24) [since there are 24 monthly payments in 2 years]
Total amount paid = $1,300 + $13,200 + $14,041.60
Total amount paid = $28,541.60
Therefore, the total amount Debra ended up paying for the equipment (including the down payment and monthly payments) was $28,541.60.
(b) To find the amount of interest paid on the loan, we need to subtract the total amount borrowed from the total amount paid, and then subtract the down payment. This will give us the total amount of interest paid over the two years.
Total interest paid = Total amount paid - Total amount borrowed - Down payment
Total interest paid = $28,541.60 - $13,200 - $1,300
Total interest paid = $14,041.60
Therefore, the amount of interest Debra paid on the loan was $14,041.60.
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* (3) Find the area of the shaded area 2 of each rectangle. 7 cm 8 cm 12 cm
The area of the shaded region is 73.65 cm².
We have,
The shaded region is a triangle.
Base = x
Height = y
Now,
Using the Pythagorean theorem,
y² = 12² + 10²
y² = 144 + 100
y² = 244
y = √244
And,
x² = 8² + 5²
x² = 64 + 25
x² = 89
x = √89
Now,
Area of the shaded region.
= 1/2 x √89 x √244
= 1/2 x 9.43 x 15.62
= 73.65 cm²
Thus,
The area of the shaded region is 73.65 cm².
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Construct a polynomial function with the following properties: third degree, only real coefficients, −1 and 4+i are two of the zeros, y-intercept is −17 .
The polynomial function with the given properties is:[tex]f(x) = x^3 - 7x^2 + 9x - 17[/tex]
What do you mean by polynomial function?A polynomial function is a function that contains only non-negative integer powers or only positive integer exponents in the equation, such as a quadratic equation, a cubic equation, etc. For example, 2x + 5 is a polynomial whose exponent is 1.
Since the polynomial has real coefficients and one of its zeros is complex, the complex conjugate of 4+ i, which is 4-i, must also be zero. So the three zeros of the polynomial are -1, 4+i and 4-i. To form a polynomial with these zeros, we start by writing the factors of the polynomial:
(x + 1) (x - 4 - i) (x - 4 + i)
We can simplify this expression by multiplying the factors:
[tex](x + 1) (x^2 - 8x + 17)[/tex]
Expanding this, we get:
[tex]x^3 - 7x^2+ 9x - 17[/tex]
Thus, the polynomial function with the given properties is:
[tex]f(x) = x^3 - 7x^2 + 9x - 17[/tex]
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The polynomial function is p(x) = (-17/5)x³ + (34/5)x² + (33/5)x - 16
What do you mean by polynomial function?A polynomial function is a function that contains only non-negative integer powers or only positive integer exponents in the equation, such as a quadratic equation, a cubic equation, etc. For example, 2x + 5 is a polynomial whose exponent is 1.
If -1 is a zero of the polynomial function, then x+1 is a factor of the polynomial. Similarly, if 4+i is a zero, then 4-i is also a zero, because complex roots always occur in conjugate pairs. Therefore, (x+1) and (x - 4 - i)(x - 4 + i) = (x - 4)² + 1 are factors of the polynomial. We can then construct the polynomial function by multiplying these factors:
p(x) = A(x+1)(x - 4 - i)(x - 4 + i)
where A is a constant that we need to determine, and p(x) is the desired third-degree polynomial function.
To determine A, we can use the y-intercept given in the problem. The y-intercept is the value of p(0), so:
p(0) = A(0+1)(0 - 4 - i)(0 - 4 + i) = A(17+4i)
But we also know that p(0) = -17, so:
-17 = A(17+4i)
Solving for A:
A = -17/(17+4i) = (-17/5) + (68/5)i
Therefore, the polynomial function we seek is:
p(x) = [(-17/5) + (68/5)i](x+1)(x - 4 - i)(x - 4 + i)
Expanding the product and simplifying, we get:
p(x) = (-17/5)x³ + (34/5)x² + (33/5)x - 16
This is a third-degree polynomial with only real coefficients, -1 and 4+i are two of the zeros, and the y-intercept is -17.
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Someone please answer this question
Some forms of cardiovascular disease involve the buildup of plaque on the inside walls of blood vessels. The buildup can put added stress on the heart and vessels, reducing or preventing blood flow to vital organs of the body.
Imagine that the diagram is a circular cross section of a blood vessel. What is the area of the inside of the blood vessel (i.e., the yellow part) in square units? Round your answer to the nearest tenth. The equation for the area of a circle is A = πr2, where A is area, π ≈ 3.14, and r is the radius. Recall that the radius is half of the diameter.
Answer:
153.94 cm2
Step-by-step explanation:
Circle area = π * r² = π * 49 [cm²] ≈ 153.94 [cm²]
π ≈ 3.14159265 ≈ 3.14
d = r * 2 = 7 [cm] * 2 = 14 [cm]
MARK AS BRAINLIEST PLS I TOOK 3 HOURS THINKING ABOUT THIS
Please explain how to do this (Find the trig ratio) i have no idea :(
The cosine of angle B is: cos(B) = AC / AB = 20/29
Define the Pythagorean Theorem?
The Pythagorean Theorem, a well-known geometric theorem that states that the sum of the squares of the legs of a right-angled triangle is equal to the square of the hypotenuse (the opposite side of the right angle) - that is, in familiar algebraic notation. , a2 + b2 = c2 .
In a right triangle, the cosine of an angle is defined as the ratio of the adjacent side to its hypotenuse. In this case, angle B is the angle we are interested in, and the adjacent side is side AC. Using the Pythagorean theorem, we find the length of side AC:
AC² = AB²+ BC²
AC² = 29² - 21²
AC² = 400
AC = 20
Therefore, the cosine of angle B is:
cos(B) = AC / AB = 20/29
Other trigonometric ratios of angle B can be found using the following formulas:
sin(B) = BC / AB = 21/29
tan(B) = BC / AC = 21/20
csc(B) = AB / BC = 29 / 21
sec(B) = AB / AC = 29/20
bed (B) = AC / BC = 20 / 21
Thus, the trigonometric ratios of angle B are:
sin(B) = 21/29
cos(B) = 20/29
tan(B) = 21/20
csc(B) = 29/21
sec(B) = 29/20
crib(B) = 20/21
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If ƒ (x) = 3x²+1 — 1, what is the value of f(−1), to the nearest ten-thousandth (if necessary)?
Answer:
To find the value of f(-1), we need to substitute -1 for x in the given function:
f(x) = 3x² + 1 - 1
f(-1) = 3(-1)² + 1 - 1
f(-1) = 3(1) + 0
f(-1) = 3
Therefore, f(-1) is equal to 3.
Find sin(π/4). Round to 3 decimal places.
Step-by-step explanation:
sin (pi/4) = sqrt(2) / 2 = .707
you either just know this after a time or you can use a calculator (in RADIAN mode)
Answer:
sin(π/4) = sin(45°) = 0.707106781186548 ≈ 0.707 (rounded to 3 decimal places)
Step-by-step explanation:
here are the steps:
Convert π/4 to degrees: π/4 * (180/π) = 45°
Use the definition of sine to find the sine of 45°:sin(45°) = opposite/hypotenuse
In a right-angled triangle with an angle of 45°, the opposite and adjacent sides are equal, so we have:sin(45°) = opposite/hypotenuse = adjacent/hypotenuse = 1/√2
Rationalize the denominator by multiplying both the numerator and denominator by √2:sin(45°) = 1/√2 * √2/√2 = √2/2
Round to 3 decimal places: sin(45°) ≈ 0.707Therefore, sin(π/4) = sin(45°) = √2/2 ≈ 0.707 (rounded to 3 decimal places).
Suppose the odds for a bet are 11: 1. Your friend tells you that he thinks the odds are too generous. Select all of the odds that are less generous.
Answer
Select all that apply.
19:1
14:1
15:1
4:1
Answer:
The odds that are less generous are 19:1, 14:1, and 15:1.
Step-by-step explanation:
You have to see which numbers are greater than 11.
PLEASE HELP FOR 100 POINTS Polygon KLMN is drawn with vertices at K(0, 0), L(5, 2), M(5, −5), N(0, −3). Determine the image vertices of K′L′M′N′ if the preimage is rotated 270° clockwise.
K′(0, 0), L′(−2, 5), M′(5, 5), N′(3, 0)
K′(0, 0), L′(−2, −5), M′(−5, 5), N′(−3, 0)
K′(0, 0), L′(−5, −2), M′(5, −5), N′(3, 0)
K′(0, 0), L′(−5, −2), M′(−5, −5), N′(0, 3)
Answer: a
Step-by-step explanation:
Angle & segment relationship
Area & Arc Length
Angle & segment relationship
Area & Arc Length
Answer:
x = 81.5°
Step-by-step explanation:
the secant- tangent angle x is half the difference of the measures of the intercepted arcs.
the sum of the arcs in a circle = 360°, then
unknown intercepted arc = 360° - (215 + 93)° = 360° - 308° = 52°
then
x = [tex]\frac{1}{2}[/tex] (215 - 52)° = [tex]\frac{1}{2}[/tex] × 163° = 81.5°
Find the degree of the monomial. -3q4rs6
Therefore, the degree of the given monomial is 11.
What is monomial?In algebra, a monomial is an expression consisting of a single term. A term can be a constant, a variable, or the product of a constant and one or more variables. In other words, a monomial is a polynomial with only one term. The degree of a monomial is the sum of the exponents of its variables.
Here,
The degree of a monomial is the sum of the exponents of its variables.
For the monomial -3q⁴rs⁶, the degree would be:
4 + 1 + 6 = 11
Therefore, the degree of the monomial -3q⁴rs⁶ is 11.
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A suitcase is a rectangular prism whose dimensions are 2 3 foot by 1 1 2 feet by 1 1 4 feet. Find the volume of the suitcase.
The volume of the suitcase is 35/8 cubic feet or approximately 4.375 cubic feet.
What is rectangular prism?A rectangular prism is a three-dimensional solid object that has six faces, where each face is a rectangle. It is also called a rectangular parallelepiped. A rectangular prism is a type of prism because it has a constant cross section along its length.
According to question:A rectangular prism's volume V is determined by:
V = l × w × h
where l denotes the prism's length, w its width, and h its height. Here are the facts:
l = 2 3 ft
w = 1 1/2 ft
h = 1 1/4 ft
When we enter these values into the formula, we obtain:
V = (2 3 ft) × (1 1/2 ft) × (1 1/4 ft)
= (7/3 ft) × (3/2 ft) × (5/4 ft)
= 35/8 ft³
Therefore, the volume of the suitcase is 35/8 cubic feet or approximately 4.375 cubic feet.
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Please help me with the volume!! I beg‼️‼️‼️
Answer:
Option D) 400π cubic units.
Step-by-step explanation:
GIVEN :
Radius of cylinder = 5 unitsHeight of cylinder = 16 unitsTO FIND :
Volume of cylinderUSING FORMULA :
[tex]\quad\star{\underline{\boxed{\sf{V_{(Cylinder)} = \pi{r}^{2}h}}}}[/tex]
V = volume π = 3.14 or 22/7r = radius h = heightSOLUTION :
Substituting all the given values in the formula to find the volume of cylinder :
[tex]\quad{\sf{\dashrightarrow{V_{(Cylinder)} = \pi{r}^{2}h}}}[/tex]
[tex]\quad{\sf{\dashrightarrow{V_{(Cylinder)} = \pi{(5)}^{2}16}}}[/tex]
[tex]\quad{\sf{\dashrightarrow{V_{(Cylinder)} = \pi{(5 \times 5)}16}}}[/tex]
[tex]\quad{\sf{\dashrightarrow{V_{(Cylinder)} = \pi{(25)} \times 16}}}[/tex]
[tex]\quad{\sf{\dashrightarrow{V_{(Cylinder)} = \pi \times 25\times 16}}}[/tex]
[tex]\quad{\sf{\dashrightarrow{V_{(Cylinder)} = \pi \times 400}}}[/tex]
[tex]\quad{\sf{\dashrightarrow{V_{(Cylinder)} = 400 \pi}}}[/tex]
[tex]\quad\star{\underline{\boxed{\sf{\pink{V_{(Cylinder)} = 400 \pi \: {units}^{3}}}}}}[/tex]
Hence, the volume of cylinder is 400π cubic units.
—————————————————Is (-5, 3) a solution to this system of equations?
y = X-6
y = -2x - 7
yes
no
Answer:
No
Step-by-step explanation:
to determine if (- 5, 3 ) is a solution substitute the x- coordinate into both equations and if the value of y is equal to the y- coordinate then the point is a solution to the system.
y = x - 6 = - 5 - 6 = - 11 ≠ 3
y = - 2x - 7 = - 2(- 5) - 7 = 10 - 7 = 3
since both equations are not satisfied , then
(- 5, 3 ) is not a solution to the system
if a1 = 6 and an =5an-1 then find the value of a6
To find the value of a6, we need to first determine the value of a2, a3, a4, and a5 using the given recurrence relation:
a1 = 6
a2 = 5a1 = 5(6) = 30
a3 = 5a2 = 5(30) = 150
a4 = 5a3 = 5(150) = 750
a5 = 5a4 = 5(750) = 3750
Now, we can find a6 using the recurrence relation:
a6 = 5a5 = 5(3750) = 18750
Therefore, the value of a6 is 18750.
An entomologist writes an article in a scientific journal which claims that fewer than 20 in ten thousand male fireflies are unable to produce light due to a genetic mutation. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms. Be sure to address the original claim.
a) There is sufficient evidence to support the claim that the true proportion is less than 20 in ten thousand.
b) There is not sufficient evidence to support the claim that the true proportion is less than 20 in ten thousand.
c) There is not sufficient evidence to support the claim that the true proportion is greater than 20 in ten thousand.
d) There is sufficient evidence to support the claim that the true proportion is greater than 20 in ten thousand.
Mrs. Harris is making a fruit salad for the 6th grade picnic. She wants each person to get 25 of a cup of fruit. She made a total of 31 cups of fruit salad. Part A: How many complete servings of fruit salad will be served with the amount Mrs. Harris made? Part B: Each cup of fruit salad contains 14 of a banana. How many bananas does Mrs. Harris need to buy for the fruit salad?
Part A: Number of servings is 1.24 servings/person
What is the servings?Part A: To determine the number of complete servings of fruit salad, we need to divide the total amount of fruit salad Mrs. Harris made (31 cups) by the amount she wants each person to get (25 cup/person). Using the formula:
Number of servings = Total amount of fruit salad / Amount per serving
Number of servings = 31 cups / 25 cups/person
Number of servings = 1.24 servings/person
Since we cannot have a fraction of a serving, we round down to the nearest whole number, as we cannot serve a fraction of a fruit salad. Therefore, Mrs. Harris will be able to serve 1 complete serving of fruit salad with the amount she made.
art B:
If each cup of fruit salad contains 1/4 cup of fruit and each serving is 1/4 cup, then each serving contains 1 cup of fruit.
To calculate the number of bananas Mrs. Harris needs, we first need to determine how many cups of bananas are in 31 cups of fruit salad:
31 cups × 1/4 cup of banana per cup of fruit salad = 7.75 cups of bananas
Since each cup of banana contains 14 of a banana, we can multiply the number of cups of bananas by 14 to find the total number of bananas needed:
7.75 cups of bananas × 14 bananas per cup = 108.5 bananas
So Mrs. Harris needs to buy approximately 109 bananas for the fruit salad.
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4(x-1)-2x<6-5(x+2) so love and graph the inequality
The vertical line at x=0 represents the boundary of the inequality, and the shaded region to the left of the line represents the solution set of the inequality, x < 0.
Explain the term inequality
Inequality refers to the unequal distribution of resources, opportunities, and rewards among individuals or groups within a society. It can be based on factors such as race, gender, income, education, and social status, leading to disparities in outcomes and experiences.
According to the given information
Start by simplifying the inequality using the distributive property and combining like terms:
4(x-1) - 2x < 6 - 5(x+2)
4x - 4 - 2x < 6 - 5x - 10
2x - 4 < -5x - 4
2x + 5x < 4 - 4
7x < 0
x < 0
So the solution to the inequality is x < 0.
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HELP ASAP if ur good with non-linear and increasing lines and choose 2 of the letter A,B,C,D,E
(Please see the picture!)
Extra points nd brainlist!
Answer:
B and D
Step-by-step explanation:
A and C are linear because they are going in a straight line. E is going downwards, so it is decreasing. That leaves B and D, which have exponential growth.
The table shows Gillian’s Net worth. Assets are shown as positive numbers, and liabilities are shown as negative numbers. Gillian’s net worth is $90,500. Based on the information in the table, what is the number of money Gillian owes for student loan?
Answer:
Step-by-step explanation:
A rectangle has a perimeter of 36 feet. It is twice as long as it is wide. What are the dimensions of the rectangle??
Dimensions of the rectangle are 6 feet and 12 feet.
What is a Rectangle?Rectangle is a quadrilateral whose each pair of opposite sides are equal in length and each two consecutive sides are in right angle to each other. In rectangle one pair of equal opposite sides is called Length and another one is called Width.
What is the formula of Perimeter of a Rectangle?If length of a rectangle is L and width of rectangle is W then the perimeter of that rectangle will be = 2(L+W)
Let W be the rectangle's width.
Here according to question the rectangle is twice as long as it is wide.
So, length of rectangle = 2W
Perimeter will be = 2(W+2W) = 2*(3W) = 6W
So, according to question,
6W = 36
W = 36/6 = 6
Thus the width of the rectangle is = 6 feet.
Then the length = 2*6 = 12 feet.
Hence dimensions of the rectangle are 12 feet and 6 feet respectively.
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HELP! Showing all work, solve for x and y and round to nearest tenth
Answer:
x = 67.4°
y = 22.6°
Step-by-step explanation:
The tangent ratio is a trigonometric ratio that relates the ratio of the length of the side opposite an angle in a right triangle to the length of the side adjacent to that angle.
[tex]\boxed{\begin{minipage}{7 cm}\underline{Tangent trigonometric ratio} \\\\$\sf \tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle.\\\end{minipage}}[/tex]
Angle xThe side opposite angle x is 7.2, and the side adjacent angle x is 3.
Use the tangent trigonometric ratio to find the measure of angle x:
[tex]\begin{aligned}\tan(x)&=\dfrac{7.2}{3}\\x&=\tan^{-1}\left(\dfrac{7.2}{3}\right)\\x&=\vphantom{\dfrac12}67.380135...^{\circ}\\x&=67.4^{\circ}\;\sf (nearest\;tenth)\end{aligned}[/tex]
Therefore, x = 67.4°.
Angle yThe side opposite angle y is 3, and the side adjacent angle y is 7.2.
Use the tangent trigonometric ratio to find the measure of angle y:
[tex]\begin{aligned}\tan(y)&=\dfrac{3}{7.2}\\y&=\tan^{-1}\left(\dfrac{3}{7.2}\right)\\y&=\vphantom{\dfrac12}22.6198649...^{\circ}\\y&=22.6^{\circ}\;\sf (nearest\;tenth)\end{aligned}[/tex]
Therefore, y = 22.6°.
For each of the figures write an absolute value equation to satisfy the given solution set -5 and -1
the given solution set {-5, -1} can be obtained by substituting either of the possible solutions into the absolute value equation and verifying that it holds.
what is an equation ?
In mathematics, an equation is a statement that asserts the equality of two mathematical expressions. An equation typically consists of two expressions separated by an equal sign, with the expression on the left side of the equal sign equal to the expression on the right side of the equal sign.
In the given question,
To write an absolute value equation that satisfies a given solution set, we need to consider the definition of absolute value. The absolute value of a number is its distance from zero the number line. Therefore, an absolute value equation can be written as follows:
|expression| = distance
where the expression is the quantity whose absolute value is being taken, and distance is a non-negative value representing the distance from zero. The equation is satisfied if and only if the expression has a distance from zero that matches the given distance.
For the solution set {-5, -1}, we can write the following absolute value equations for the given figures:
A number line with -5 and -1 marked as solutions:
|x + 3| = 2
This equation is satisfied when x = -5 or x = -1, because |-5 + 3| = 2 and |-1 + 3| = 2.
A number line with -5 and -1 equidistant from zero:
|x| = 5
This equation is satisfied when x = -5 or x = 5, because |-5| = 5 and |5| = 5.
Note that for both figures, the given solution set {-5, -1} can be obtained by substituting either of the possible solutions into the absolute value equation and verifying that it holds.
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1. A contractor is building the base of a circular fountain. On the blueprint, the base of the fountain has a diameter of 40 centimeters. The blueprint has a scale of three centimeters to four feet. What will be the actual area of the base of the fountain, in square feet, after it is built? Round your answer to the nearest tenth of a square foot.
the actual area of the base of the fountain, in square feet, after it is built is approximately 1.3 square feet (rounded to the nearest tenth of a square foot).
How to solve the question?
To find the actual area of the base of the fountain, we need to convert the measurements from the blueprint to the actual measurements.
First, we need to find the radius of the circular base. The diameter of the base is given as 40 centimeters on the blueprint, so the radius is half of that, or 20 centimeters.
Next, we need to convert the scale of the blueprint from centimeters to feet. The scale is given as three centimeters to four feet, which can be simplified to a ratio of 3:4. To convert from centimeters to feet, we need to multiply by a conversion factor of 1 foot/30.48 centimeters, since there are 30.48 centimeters in a foot.
So, to find the actual radius of the circular base in feet, we multiply the blueprint radius (20 centimeters) by the conversion factor:
20 centimeters * (1 foot/30.48 centimeters) = 0.656168 feet
Now that we have the actual radius of the circular base, we can find the actual area of the base. The formula for the area of a circle is A = πr^2, where A is the area and r is the radius. Plugging in the actual radius we just found, we get:
A = π(0.656168 feet)^2 = 1.34977 square feet
Therefore, the actual area of the base of the fountain, in square feet, after it is built is approximately 1.3 square feet (rounded to the nearest tenth of a square foot).
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please help me solve the bonus question
Answer: a = 5 and k = 1/2
Step-by-step explanation:
We are given that the function is defined by:
f(x) = 16 + a(3^(kx))
We need to find the real numbers a and k such that f(0) = 21 and f(4) = 61. Using the given values of f(0) and f(4), we can form a system of two equations:
f(0) = 16 + a(3^(k(0))) = 21
f(4) = 16 + a(3^(k(4))) = 61
Simplifying the first equation, we get:
16 + a(3^0) = 21
16 + a = 21
a = 5
Substituting this value of a into the second equation, we get:
16 + 5(3^(4k)) = 61
5(3^(4k)) = 45
3^(4k) = 9
We know that 3^2 = 9, therefore
4k = 2
=> k = 2/4
=> k = 1/2
Therefore, the real numbers a and k that satisfy the given conditions are a = 5 and k = 1/2. So the function is:
f(x) = 16 + 5(3^(x/2))
The solution to the equation give us an approximate that x = 1.55.
What is the solution to the equation?To solve this equation, we can start by subtracting 4 from both sides to isolate the exponential term:
3.5^x + 4 - 4 = 11 - 4
This simplifies to:
3.5^x = 7
Next, we can take the logarithm of both sides with base 3.5 to eliminate the exponent:
log(3.5^x) = log(7)
Using the property of logarithms that log(a^b) = b*log(a), we can rewrite the left side as:
x*log(3.5) = log(7)
Now, we can solve for x by dividing both sides by log(3.5):
x = log(7) / log(3.5)
Plugging in the values, we get:
x = 0.84509804001 / 0.54406804435
x = 1.55329475566
x ≈ 1.55.
Answered question "Solve the equation 3.5^x + 4 = 11"
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What is the volume of a rectangular prism that is 120 centimeters by 2 meters by 1.5 meters in cubic centimeters? 3,600,000 cm 3 3,600 cm 3 36,000 cm 3 3.6 cm 3
The volume of the rectangular prism in cubic centimeters is 3,600,000
What is the volume of the rectangular prismFrom the question, we have the following parameters that can be used in our computation:
Dimension = 120 centimeters by 2 meters by 1.5 meters
The volume of the rectangular prism is the product of the dimensions
i.e.
Volume = Length * width * height
Substitute the known values in the above equation, so, we have the following representation
Volume = 120 * 2 * 1.5
Convert to cm
Volume = 120 * 200 * 150
Evaluate
Volume = 3600000
Hence, the volume in cubic centimeters is 3,600,000
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anyone know what the area of triangle ABC is?
The area of triangle ABC is 6cm²
What is a triangle?A triangle is a three-sided polygon that consists of three edges and three vertices. It is also known as the trigon and has special names such as the hypotenuse (opposite the right angle) and legs (the other two sides). It can also refer to a percussion instrument consisting of a rod of steel bent into the form of a triangle open at one angle.
The area of the triangle is given as
Area= 1/2absinC
But the CosB = Adj/Hypo
Cos60 = Adj/12
1/2 = Adj/12
corss and multiply to have
2A = 12
Therefore Adj = 6
Therefore base = 6*2 = 12
Applying the formula we have Area= 1/2acsinB
Area = 1/2* 12*12*Cos60
Area = 12*1/2 =6cm²
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Find the circumference of a child swimming pool that has a radius of 3 feet
The circumference of a child swimming pool is 6π.
What is circumference?
The circumference of a circle or ellipse in geometry is its perimeter. That is, if the circle were opened up and straightened out to a line segment, the circumference would be the length of the arc. The curve length around any closed figure is more often referred to as the perimeter.
Here, we have
Given: A child swimming pool that has a radius of 3 feet.
We have to find the circumference.
The circumference is diameter x π
The diameter is twice the radius
c = 2πr
c = 2π(3)
= 6π
Hence, the circumference of a child swimming pool is 6π.
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Consider the two-loop circuit shown below:
Ignore the red and pencil markings, just worry about the printed questions
The variables I₁ and I₂ using the matrix algebra and using the Cramer's rule are I₁ = 1 and I₂ = 1
Writing the system of equations in matrix formFrom the question, we have the following parameters that can be used in our computation:
15I₁ + 5I₂ = 20
25I₁ + 5I₂ - 30 = 0
Rewrite as
15I₁ + 5I₂ = 20
25I₁ + 5I₂ = 30
Rewrite as
I₁ I₂
15 5 20
25 5 30
From the question, the matrix form is
AI = b
Ths matrix A from the above is
[tex]A = \left[\begin{array}{cc}15&5&25&5\end{array}\right][/tex]
Ths matrix B from the above is
[tex]B = \left[\begin{array}{c}20&30\end{array}\right][/tex]
And, we have the matrix I to be
[tex]I = \left[\begin{array}{c}I_1&I_2\end{array}\right][/tex]
Finding I₁ and I₂ using the matrix algebraStart by calculating the inverse of A from
[tex]A = \left[\begin{array}{cc}15&5&25&5\end{array}\right][/tex]
So, we have:
|A| = 15 * 5 - 5 * 25
|A| = -50
The inverse is
[tex]A^{-1} = -\frac{1}{50}\left[\begin{array}{cc}5&-5&-25&15\end{array}\right][/tex]
Recall that
AI = b
So, we have
[tex]I = -\frac{1}{50}\left[\begin{array}{cc}5&-5&-25&15\end{array}\right] * \left[\begin{array}{c}20&30\end{array}\right][/tex]
Evaluate the products
[tex]I = -\frac{1}{50}\left[\begin{array}{c}5 * 20 + -5 * 30&-25 * 20 + 15 *30\end{array}\right][/tex]
[tex]I = -\frac{1}{50}\left[\begin{array}{c}-50&-50\end{array}\right][/tex]
Evaluate
[tex]I = \left[\begin{array}{c}1&1\end{array}\right][/tex]
Recall that
[tex]I = \left[\begin{array}{c}I_1&I_2\end{array}\right][/tex]
So, we have
I₁ = 1 and I₂ = 1
Finding I₁ and I₂ using the Cramer's rule,Recall that the determinant of matrix A calculated in (a) is
|A| = -50
Replace the first column in A with b
So, we have
[tex]AI_1 = \left[\begin{array}{cc}20&5&30&5\end{array}\right][/tex]
Calculate the determinant
DI₁ = 20 * 5 - 30 * 5
DI₁ = -50
Replace the second column in A with b
So, we have
[tex]AI_2 = \left[\begin{array}{cc}15&20&25&30\end{array}\right][/tex]
Calculate the determinant
DI₂ = 15 * 30 - 20 * 25
DI₂ = -50
So, we have
I₁ = DI₁ / |A| = -50/-50 = 1
I₂ = DI₂ / |A| = -50/-50 = 1
So, we have
I₁ = 1 and I₂ = 1
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Please help studying for next grade.
98+107÷(82-12)x122
Answer:
284.06
Step-by-step explanation:
To solve this expression using the order of operations (PEMDAS), we must first perform the operations inside the parentheses: 82-12 equals 70. Next, we must perform the multiplication and division from left to right: 107 divided by 70 equals approximately 1.53, and 1.53 times 122 equals approximately 186.06. Finally, we add 98 to get our answer. Therefore, the expression 98+107÷(82-12)x122 simplifies to approximately 284.06.
Answer:
284.06
Step-by-step explanation:
got it right on edge