Answer:
3 units and 4 units
Step-by-step explanation:
Given data
Volume of prism = 72 cubic units
Length of prism= 6 units
Width =????
The expression for the volume is
V= L*W*H
Also,
Volume = Area*L
72= Area*6
Area= 72/6
Area= 12 square units
Hence the possible width and Height is
3 units and 4 units
Because 4*3= 12 square units
Check
volume= 6*3*4= 72 cubic units
Write two expressions that are equivalent to x + 3 + 2x
Equivalent expressio
What are equivalent expressions?When two expressions can be reduced to a single third expression or when one of the expressions can be written in the same way as the other, they are said to be equivalent. When values are replaced for the variable and both expressions yield the same result, you may also tell if two expressions are equal.
Because both expressions have the same value for any value of x, 3(x + 2) and 3x + 6 are identical expressions. 3x + 6 = 3 × 4 + 6 = 18. Algebraic equations with equivalent solutions or roots are called equivalent equations.
An analogous equation is one that is created by adding or removing the identical quantity or expression from both sides of a given equation. Expressions that are equivalent do the same thing even when they have distinct appearances. In the event when two algebraic expressions.
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What is the length of the shorter side of a 30 60 90 triangle if the longer side is?
The shorter side of the triangle will be opposite to 30° angle and larger side will be opposite to 90° angle .
What is a right triangle ?A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or previously rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.
The side opposite the smallest angle is the one that is the shortest. The shortest side is opposite the angle that you already know to be the shortest.
The side opposite the right angle is always the hypotenuse of a right triangle. In a right triangle, it is the longest side.
So the shorter side will be opposite to 30° angle and larger side will be opposite to 90° angle .
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Nicole invests a sum of money in a retirement account with a fixed annual interest rate of 6 percent compounded continuously. After 17 years, the balance reaches $8,441.60. What was the amount of the initial investment?
Round your answer to the nearest TENs place.
Answer:
$3,040.00
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Continuous Compounding Formula}\\\\$ A=Pe^{rt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\\phantom{ww}$\bullet$ $P =$ principal amount \\\phantom{ww}$\bullet$ $e =$ Euler's number (constant) \\\phantom{ww}$\bullet$ $r =$ annual interest rate (in decimal form) \\\phantom{ww}$\bullet$ $t =$ time (in years) \\\end{minipage}}[/tex]
Given:
A =$8,441.60r = 6% = 0.06t = 17 yearsSubstitute the given values into the continuous compounding formula and solve for P:
[tex]\implies 8441.60=Pe^{0.06 \times 17}[/tex]
[tex]\implies 8441.60=Pe^{1.02}[/tex]
[tex]\implies P=\dfrac{8441.60}{e^{1.02}}[/tex]
[tex]\implies P=3043.99824...[/tex]
Therefore, the amount of the initial investment is $3,040.00 (rounded to the nearest tens place).
it’s due today help pls
You can only add or subtract radicals together if they are like radicals.
How to solve the problem?√28
Factor 4 out of 28.
√4(7)
Rewrite 4 as 22.
2 2.7
Pull terms out from under the radical.
217
The result can be shown in multiple forms.
Exact Form:
2√7
Decimal form:
5.29150262…
√63
Factor 9 out of 63.
/9 (7)
Rewrite 9 as 32.
Pull terms out from under the radical.
3√7
The result can be shown in multiple forms.
Exact form: 3√7
Decimal Form: 7.93725393...
Sqrt(24)
2√6
Pull terms out from under the radical.
√2^2.6
The result can be shown in multiple forms.
Exact Form:
2√6
Decimal Form:
4.89897948....
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The complete question is: Solve the following radicals:
a) 5 ± [tex]\sqrt{28}[/tex]
b) 4 ± [tex]\sqrt{63}[/tex]
c) 6 ± [tex]\sqrt{24}[/tex]
What is 7 power of 0?
Answer:
It equals one
Step-by-step explanation: Anything that has the exponent of 0 will always equal one
What is the area of a triangle with the base 4.8 cm and height 3.6 cm *?
The area of a triangle with the base 4.8 cm and height 3.6 cm is 8.64 cm².
The area of a triangle can be easily calculated by keeping the values of base and height in the formula -
Area of triangle = 1/2 × base × height of triangle. We know the values of base and height which are in same units. Hence, directly keeping the values -
Area = 1/2 × 4.8 × 3.6
Performing division on Right Hand Side of the equation
Area = 2.4 × 3.6
Performing multiplication on Right Hand Side of the equation
Area = 8.64 cm²
Therefore, the area of triangle is 8.64 cm².
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What is the additive inverse of negative 4X -8
The additive inverse of the expression is 4x + 8
How to determine the additive inverse of the expression?From the question, the expression is given as
negative 4X -8
Express properly
So, we have the following representation
-4x -8
For an expression y, the additive inverse is -y
Using the above as a guide, we have the following:
Additive inverse of -4x -8 = -(-4x -8)
Open the bracket
Additive inverse of -4x -8 = 4x + 8
Hence, the additive inverse is 4x + 8
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In a scatter diagram, a line that provides an approximation of the relationship between the variables is known as
In a scatter diagram, a line that provides an approximation of the relationship between the variables is known as trend line.
Explain what a scatter diagram is?
In a scatter diagram, pairs of numerical data are graphed with one variable on each axis in an effort to find a correlation between them. The points will fall along a line or curve if the variables are correlated. The points will hug the line closer the more highly correlated the data is.
Why are scatter plots employed?
The relationship between two different types of data is displayed using a scatter diagram. The connection between a cause and an effect, between two causes, or even between three causes, could be the subject of the analysis.
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How do you solve the factor theorem step by step?
The Factor Theorem states that if a polynomial is divided by (x-a) then the remainder is equal to zero if and only if (x-a) is a factor of the polynomial.
To solve the Factor Theorem, first you need to determine the polynomial and the value of (x-a).
Then you divide the polynomial by (x-a). To do this, use synthetic division. Synthetic division is a shorthand way of dividing a polynomial by a linear factor.
If the remainder is 0, then the polynomial is divisible by (x-a). If the remainder is not 0, then (x-a) is not a factor of the polynomial.
To summarize, the Factor Theorem states that if the remainder is 0 after dividing a polynomial by (x-a), then (x-a) is a factor of the polynomial. The Factor Theorem can be solved by using synthetic division.
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How do you find the area of a triangle in square units?
The area of a triangle can be calculated using the formula A=1/2*b*h, where b is the base of the triangle and h is the height.
The area of a triangle can be found by using the formula A = 1/2bh, where b is the base of the triangle and h is the height of the triangle. To find the area of a triangle in square units, you would need to multiply the base and the height of the triangle and then divide the result by 2.Once you have these two measurements, simply plug them into the formula and calculate the area.
To calculate the area, we need to first measure the base and the height. Once we have the measurements, we can calculate the area by multiplying the base by the height and then dividing by two. For example, if the base is 8 units and the height is 6 units, the area of the triangle will be 24 square units (A = 1/2*8*6 = 24).
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Explain how to reason with the diagram to find the weight of a piece with a letter.
The weight of a piece can be found through the letter because the diagram is made up of balanced hangers which means that the weight of one side is equal to the weight of the other side.
How to calculate the weights of the given diagram?For diagram A = X+3 = 8
X = 8-3 = 5
The weight of the letter piece X = 5
For diagram B = 12= 2y
y = 12/2 = 6
The weight of the letter piece y = 6
For diagram C = 11 = 4z
z = 11/4 = 2.75
The weight of the letter piece z = 2.75
For diagram D = 13⅘ = w + 3⅘
w = 13⅘ - 3⅘ = 10
The weight of the letter piece w = 10
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CALC HELP PLEASE!!!!
Step-by-step explanation:
[tex]2\mathbf{u}=\langle 10,6 \rangle \\ \\ 3\mathbf{v}=\langle -12, 0 \rangle \\ \\ 2\mathbf{u}-3\mathbf{v}=\langle 10,6 \rangle -\langle -12,0 \rangle =\langle 22,6 \rangle[/tex]
The lengths of two sides of a triangle are 5 and 14. Find the lengths that the third side must be greater than and less than.
Answer:
The third side of the triangle must be greater than 4 and less than 19. This follows from the Triangle Inequality Theorem, which states that the sum of any two sides of a triangle must be greater than the third side, and the difference between any two sides of a triangle must be less than the third side. Therefore, the third side must be greater than 4 (5 + 4) and less than 19 (14 - 4).
rectangular garden has a walkway around it. The area of the garden is 6(4.5x+2.5). The combined area of the garden and the walkway is 6.5(8x+6). Find the area of the walkway around the garden as the sum of two terms.
I got a similar one too. It was 6(4.5x+1.5) ..
Step-by-step explanation:
What are the 3 sides of a triangular prism?
A polyhedron with 3 rectangular faces and triangular shaped bases is called a triangular prism. It is a three-dimensional shape with three side faces, two base faces, and edges connecting them to one another.
Nine different nets make up the pentahedron known as Triangular Prism. The bases are connected at their vertices and edges by three rectangular sides. The triangular prism's rectangular-shaped sides are joined to one another side by side.
Triangles have all cross-sections that are perpendicular to their base faces. In contrast to a triangular prism, a triangular pyramid has four triangular bases that are all congruent with one another and connected together.
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Coach Smith purchases sports equipment.
Golf balls cost $25 per pack and lacrosse balls
cost $10. He has $250 dollars in the budget for
golf balls and lacrosse balls.
Part A. Write an inequality where g is the number
of golf balls purchased and I is the number of
lacrosse balls.
Part B. Given the coaches budget, which of the
following is a viable option for the equipment he
can purchase?
Therefore , the solution of the given problem of inequality comes out to be the inequality is: 25g + 10l ≤ 250.
Inequality: What is it?In mathematics, an inequality is a connection that does not have an equal sign between equations or values. Inequality precedes imbalance, therefore. When two numerical values are not equal, an inequality establishes a connection between them. Difference between equality and inequality Have used the not equal symbol, which is most often used, when values are not similar (). No issue how little or huge the values, variable inequalities are employed to contrast them.
Here,
Given:
Lacrosse balls cost $10 per pack
while golf balls price $25 per pack.
Total funds equal $250.
In order to create an inequality,
we must multiply g by the quantity of golf balls you bought and I by the quantity of lacrosse balls.
So, the inequality is:
25g + 10l ≤ 250
Therefore , the solution of the given problem of inequality comes out to be the inequality is: 25g + 10l ≤ 250.
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y=8x-2 y=8x+2 I don’t understand please help
Answer:
No solution
Step-by-step explanation:
y=8x-2
y=8x+2
8x - 2 = 8x + 2
8x = 8x + 4
0x = 4
We know any number multiplied by 0 will be equal to 0.
So, there is no solution.
What is the value of 3 exponent of 1?
The expression "value of 3 exponent of 1" is denoted as 3¹ ,and the value of this expression is 3 .
The Exponent is defined as how many times to use that number in a multiplication .
It is written as a small number to right above the base of the number.
we have to find the value of the exponent expression " value of 3 exponent of 1" ,
the given expression can be represented as ⇒ 3¹ ,
we know that the value of any number with an exponent of 1 is the number itself .
So , the value of 3¹ is ⇒ 3 .
Therefore , the value of 3 exponent of 1 is 3 .
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What is the formula for factor form?
Therefore , the solution of the given problem of factor comes out to be
Ax²+Bx+C= (x-a)(x-b) is the formula for factor form.
Define factor.It appears that a factor is a parameter that is combined by another to achieve an outcome. A product is the solution to a multiplication puzzle. Think of mixing the factors in an arithmetic problem to get the product. 8 has the elements 2 and 4, for instance: There could be just two parts to a number or many more.
Here,
Take a look at the generic form:
=>Ax²+Bx+C= (x-a)(x-b),
where a & b are the polynomial's roots.
Here, b=2 and a=1
(x+1)(x2) (x + 1)(x 2) is the factored form.
Therefore , the solution of the given problem of factor comes out to be
Ax²+Bx+C= (x-a)(x-b) is the formula for factor form.
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Farmer Mei want to fence in a rectangular area that ha one ide bordered by a tream. If he
ha 250 m of fence, what are the dimenion and the maximum area he can encloe?
If the rectangular area has maximum area, the dimension of the rectangular area is 62.5 m×62.5 m. The area is 3,906.25 square meters.
To enclose a rectangular area with one side bordered by a stream, Farmer Mei can use the remaining 250 meters of fence to form the other three sides of the rectangle. Since the rectangle has two sides of equal length (the width and the height), we can set up the equation:
2L + 2W = 250
where L represents the length of the rectangle and W represents the width.
Solving for one variable in terms of the other:
W = 250/2 - L
The area of the rectangle is given by the formula:
A = L×W
Now, we can substitute the value of W from the above equation into this one to get:
A = L × (250/2 - L)
A = 125L - L²
To find the maximum area, we need to take the derivative of A with respect to L and set it equal to 0.
dA/dL = 250/2 - 2L = 0
Which gives us the value of L = 125/2 = 62.5m
Now, we can substitute this value of L back into the equation for W to find the width of the rectangle:
W = 250/2 - 62.5 = 62.5m
Therefore the dimensions of the rectangle is 62.5m x 62.5m and the maximum area that can be enclosed is 62.5m x 62.5m = 3,906.25 sq m.
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How do you find the side lengths of a 45 45 90 triangle?
The side lengths of a 45-45-90 triangle can be found using side ratios or the formula that the length of hypotenuse is root two times the length of each leg which is equal.
A 45-45-90 triangle is a special type of right triangle that has two angles that measure 45 degrees and one angle that measures 90 degrees. This triangle has a unique relationship between its side lengths.
The length of the hypotenuse (the side opposite the 90-degree angle) is equal to √2 times the length of one of the legs (the two sides that are congruent and form the 45-degree angles).
The length of each leg is equal to the length of the hypotenuse divided by √2.
For example, if the hypotenuse of a 45-45-90 triangle measures 8 units, then one leg measures 8/√2 = 8/1.4142 = 5.6568 units, and the other leg measures also 8/√2 = 8/1.4142 = 5.6568 units.
Another way to find the side lengths of a 45-45-90 triangle is to use the side ratios. The ratio of the sides in a 45-45-90 triangle is 1:1:√2, so if you know the length of one side, you can find the length of the other sides using these ratios.
It's important to keep in mind that a 45-45-90 triangle is a special type of triangle and its side lengths can be found using the formulas and ratios mentioned above. Regular triangles, such as a 30-60-90 triangle, have also similar relationships between their sides.
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WHY IS lens formula used?
The lens formula is used in optics to calculate the position and size of the image formed by a lens.
A lens is a piece of glass or other transparent material that bends light to form an image. The lens formula relates the distance of the object from the lens, the distance of the image from the lens, and the focal length of the lens.
The lens formula is used to determine the position and size of the image formed by a lens in order to design and analyze optical systems. It is used in the design of camera lenses, telescopes, microscopes, and other optical devices.
It also allows us to determine the size and position of the image formed by a lens in a given situation, which is essential for the analysis and correction of optical aberrations.
The lens formula also allows us to determine the type of image formed by a lens, whether it is real or virtual, inverted or erect, and the size of the image compared to the object.
In conclusion, the lens formula is used in optics to calculate the position and size of the image formed by a lens. It is used in the design and analysis of optical systems such as camera lenses, telescopes, microscopes and other optical devices. It also allows us to determine the type of image formed by a lens and the size of the image compared to the object.
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1. The cost of having a carpet installed is $25.00 for the delivery plus $1.50 per square yard of carpet. Write a function that models the cost of having a carpet installed.
Answer:
C(x) = 25 + 1.5x
Step-by-step explanation:
A function is a mathematical equation that describes how two variables are related. To write a function that models the cost of having a carpet installed, we can use the information provided in the problem.
The cost of having a carpet installed is:
C(x) = 25 + 1.5x
Where C(x) represents the total cost of the carpet installation and x represents the number of square yards of carpet.
25 is a fixed cost for delivery , and $1.5 is cost per sq yard.
So, C(x) = 25 + 1.5x this function is representing the cost of having a carpet installed in x sq yard.
what is 3x +6.5 and how do you solve it step by step
Answer: already simplified
Step-by-step explanation:
You cannot solve an equation without an equal sign, you could only solve it if it were like 3x + 6.5 = 0.5
then you would put the x on one side of the equation and the numbers on the other by subtracting 6.5 with 0.5.
3x = -6
divide by 3
x = -2
THIS QUESTION IS ALREADY SIMPLE, THER IS NOTHIGN TO DO ABOUT IT! SORRY!
how many triangles can be formed with SSA? In △MNO, m = 20, n = 14, and m∠M = 51°. How many distinct triangles can be formed given these measurements?
Triangle MNO with sides m = 20, n = 14 and angle m ∠ M = 51° can have two possible configurations.
How many triangles can be formed by given information on angles and sides
In this problem we have the knowledge of two sides and an angle of triangle MNO, where angle M is opposite to side m. First, determine the possible values for angle N by law of sine:
n / sin (m ∠ N) = m / sin (m ∠ M)
14 / sin (m ∠ N) = 20 / sin 51°
sin (m ∠ N) = (14 / 20) · sin 51°
sin (m ∠ N) = 0.544
There are two possible values for angle N: m ∠ N₁ ≈ 32.957°, m ∠ N₂ ≈ 147.043°. The existence of two different angles indicates that two distinct triangles can be formed.
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Find the total amount given the original price and tax rate. Round to the nearest hundredth if necessary.
Original price: $123.28
Tax rate: 7.5%
Answer: 132.526
Step-by-step explanation:
How many minutes are in two days?
Answer:
2880
Step-by-step explanation:
Brittney had a debt of $52.60 to her mom, her mom promised her that if she could save $25.00 by the end of month, she would pay off $10 for her if brittisey meets her goal and her mom follows through on her promise how much more will Brittney need to eam to have a positive $15 balance
Answer:
To have a positive balance of $15, Brittney will need to save an additional $25 - $10 = $15. Therefore, she will need to earn an additional $15 to meet her goal.
Combine like terms to simplify the expression:
7x + 3y – 2 + 6x – 1 + y2
Answer: 13x + 5y - 3
Step-by-step explanation: 7x + 6x + 3y + 2y -2 -1
= 13x + 5y - 3
How do you find the center and radius of an endpoint?
To find the center and radius of a circle given the endpoints of its diameter, you can use the following steps:
Find the midpoint of the diameter: The midpoint of the diameter is the center of the circle. To find the midpoint, you can use the midpoint formula: (x,y) = ((x1 + x2)/2, (y1 + y2)/2), where (x1, y1) and (x2, y2) are the coordinates of the two endpoints of the diameter.Find the radius: The radius of a circle is half the length of its diameter. To find the radius, you can use the distance formula to find the distance between the two endpoints of the diameter: d = √((x2 - x1)^2 + (y2 - y1)^2) and divide the result by 2.For example, if the endpoints of a diameter are (-3, 4) and (7, -6), you can use the midpoint formula to find the center:
(x,y) = ((-3 + 7)/2 , (4 + -6)/2)
(x,y) = (2,-1)
The center of the circle is (2,-1)
To find the radius, you can use the distance formula:
d = √((7-(-3))^2 + (-6-4)^2)
d = √((10)^2 + (-10)^2)
d = √(100+100)
d = √200
d = 10√2
The radius of the circle is 10√2/2 units.
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