The height of the triangle will be 14 cm.
What is a triangle?A triangle is a polygon that has three sides and three vertices. It is one of the basic figures in geometry.
The area of the triangle is the product of half the base and the height of the triangle.
The area of the triangle = 1/2 x b x h
so we will plug numbers into the equation and solve ;
Area = 6(x) 1/2
42 = 6(x) 1/2
42 = 3(x)
Now, divide each side by 3
14 = x
Therefore, the height of the triangle will be 14 cm.
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Express the set of real numbers between but not including 2 and 5 as follows.
If a car travels 23 miles on 1.0 gal of gas, how many liters of gasoline are needed for a 135 mile trip?
Loretta invested $1000 in a simple interest account yielding 5% paid annually. In 2 years, she will have $1100 in her account. From this example, we can conclude that 5% represents the:
Final answer:
The 5% represents the annual interest rate on Loretta's investment in a simple interest account.
Explanation:
The 5% represents the annual interest rate on Loretta's investment. In simple interest, the interest is calculated as a percentage of the initial investment. So, if Loretta invested $1000, and after 2 years her account has grown to $1100, the interest earned would be $100 (1100 - 1000).
To find the interest rate, we can use the formula:
Interest = Principal * Rate * Time
Using the given information, we can plug in the values and solve for the rate:
100 = 1000 * Rate * 2
Simplifying the equation, we get:
Rate = 100 / (1000 * 2) = 0.05 or 5%
Therefore, the 5% represents the annual interest rate in this scenario.
Which of the following is an odd function? f(x) = x3 + 5x2 + x mc023-1.jpg f(x) = x2 + x f(x) = –x
By evaluating each function in -x, we will see that the only odd one is:
f(x) = -x
What is an odd function?
We say that a function is odd if:
f(-x) = f(x)
Then we just need to check that for the given functions, let's see what we get:
1) f(-x) = (-x)^3 + 5*(-x)^2 + (-x) = -x^3 + 5x^2 - x ≠ -f(x)
2) f(-x) = (-x)^2 - x= x^2 - x ≠ -f(x)
3) f(-x) = -(-x) = x = -f(x)
So the only odd function is the third one, one useful thing that you may need to know is that usually when you see even exponents, that function will not be odd.
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The __________ is the score that occurs most frequently in a distribution.
The perimeter of a rectangle is 42 inches, and its area is 110 square inches. find the length and width of the rectangle.
What is negative three divided by zero fraction form should i just remove the zero?
Bethany sells roses and petunias. The expression 3r+2.5p gives the cost (in dollars) of r roses and p petunias.What is the cost of 7 roses and 8 petunias?
Which lines must be parallel if angle 10 is supplementary to angle 11?
Group A has an elevation of -282 feet. group B has an elevation of 279 feet. which is closer to sea level
Dustin has only nickels and quarters in his piggy bank. He has 49 coins total for a combined value of $8.85. How many of each does he have
Answer:
Dustin has 17 nickels and 32 quarters.
Explanation:
Let's denote the number of nickels as [tex]\(n\)[/tex] and the number of quarters as [tex]\(q\).[/tex]
We can set up a system of equations based on the given information:
1. The total number of coins: [tex]\(n + q = 49\)[/tex]
2. The total value of the coins: [tex]\(0.05n + 0.25q = 8.85\)[/tex]
We can solve this system of equations to find the values of [tex]\(n\) and \(q\).[/tex]
From equation (1), we can express [tex]\(n\)[/tex] in terms of [tex]\(q\):[/tex]
[tex]\[n = 49 - q\][/tex]
Now, substitute this expression for [tex]\(n\)[/tex] into equation (2):
[tex]\[0.05(49 - q) + 0.25q = 8.85\][/tex]
[tex]\[2.45 - 0.05q + 0.25q = 8.85\][/tex]
Combine like terms:
[tex]\[0.20q + 2.45 = 8.85\][/tex]
Subtract 2.45 from both sides:
[tex]\[0.20q = 6.40\][/tex]
Now, divide both sides by 0.20:
[tex]\[q = \frac{6.40}{0.20} = 32\][/tex]
So, Dustin has 32 quarters.
To find the number of nickels, we can substitute the value of \(q\) into the equation [tex]\(n + q = 49\):[/tex]
[tex]\[n + 32 = 49\][/tex]
[tex]\[n = 49 - 32\][/tex]
[tex]\[n = 17\][/tex]
So, Dustin has 17 nickels.
Approximately how many times greater is 9.75 * 10^6 than 1.25 * 10^2?
9.75 / 1.25 = 7.8
10^6 - 10^2 = 10^4
= 7.8 x 10^4 greater
Simplify 5x + 50/x+5 · 1/x+10
A. 5/x+5
B. 5x^{2}
C. x-3/x+7
D. x-2
A segment has an endpoint (14,-8) and (4,12) what are the coordinates of its midpoint
The coordinates of the midpoint of the segment that has endpoints as (14,-8) and (4,12) are (9,2).
What are the coordinates of the midpoint of the line segment AB?Midpoint, as the word suggests, means the point which lies in the middle of something. The midpoint of a line segment means a point which lies in the mid of the given line segment.
Suppose we've two endpoints of a line segment:
A(p,q), and B(m,n)
Then let the midpoint be M(x,y) on that line segment. Then, its coordinates are:
x = (p+m) / 2
and
y = (q+n) / 2
Given that a segment has an endpoint (14,-8) and (4,12). Therefore, The coordinates of the midpoint of the segment can be written as,
X- coordinate = (14+ 4)/2
= 18/2
= 9
Y- coordinate = (-8+12)/2
= 4/2
= 2
Hence, the coordinate of the midpoint of the segment that has endpoints as (14,-8) and (4,12) is (9,2).
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Find the point-slope form of the equation of the line passing through the points (–1, –3) and (4, 1).
Solve for y.
d = 5x + 5y
The solution for y of the given equation is y = (d - 5x)/ 5.
What are Arithmetic operations?Arithmetic operations can also be specified by the addition, subtract, divide, and multiply built-in functions.
The operator that performs the arithmetic operations are called arithmetic operators.
+ Addition operation: Adds values on either side of the operator.
For example 4 + 2 = 6
- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.
for example 4 -2 = 2
* Multiplication operation: Multiplies values on either side of the operator
For example 4*2 = 8
/ Division operation: Divides left-hand operand by right-hand operand
For example 4/2 = 2
Given that the equation as
⇒ d = 5x + 5y
Rearrange the terms in the above equation
⇒ 5y = d - 5x
Divided by 5 both sides of the equation
⇒ y = (d - 5x)/ 5
Hence, the solution for y of the given equation is y = (d - 5x)/ 5.
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What is the length of a rectangle with area 402 ft^2
and width 12 ft?
The length of the rectangle is 33.5 feet.
To find the length of the rectangle, we can use the formula for the area of a rectangle:
Area = length * width
Given:
Area = 402 ft^2
Width = 12 ft
Let's solve for the length:
402 ft^2 = length * 12 ft
To find the length, divide both sides by 12 ft:
length = 402 ft^2 / 12 ft
length = 33.5 ft
So, the length of the rectangle is 33.5 feet.
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A diver descends from an elevation of 6 feet below sea level to an elevation
of 98 feet below sea level in 4 equal intervals. What was the diver’s change in
elevation in each interval? Explain how you solved this problem.
the base of a pyramid has n sides write an expression for the number of faces of the pyramid
Which equation represents the line that passes through the points (–3, 7) and (9, –1)?
A) y = - 2/3 x + 5
B) y = - 2/3 x - 7
C) y = 2/3 x - 7
D) y = 2/3 x - 5
The equation represents the line that passes through the points (–3, 7) and (9, –1) will be A) y = - 2/3 x + 5.
What is the slope of a line which passes through points ( p,q) and (x,y)?Its slope would be:
[tex]m = \dfrac{y-q}{x-p}[/tex]
The slope of parallel lines are same. Slopes of perpendicular lines are negative reciprocal of each other.
The slope = (7 + 1)/(-3 - 9)
= 8 / -12
= -2/3
The equation of a line
[tex]y = mx + b\\7 = -2/3(-3) + b\\7 = 2 + b\\b = 5[/tex]
y = -2/3x + 5
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0.90 divided by 0.30 PLEASE SHOW WORK OR EXPLAIN YOUR REASONING!
If i multiply the numerator do i have to multiply the denominator
If 6 cats can kill 6 rats in 6 minutes, how many cats will it take to kill 100 rats in 50 minutes? previous next
A puzzle contains a triangular piece with a base of 3 in. and a height of 4 in. A manufacturer wants to make 80 puzzles. Find the amount of wood used if each puzzle contains 20 triangular pieces.
Answer:
9600 square inches.
Step-by-step explanation:
We have been given that a puzzle contains a triangular piece with a base of 3 in. and a height of 4 in.
The would used for each triangular piece would be equal to area of triangle.
[tex]\frac{1}{2}\times 3\text{ in}\times 4\text{ in}=3\text{ in}\times 2\text{ in}=6\text{ in}^2[/tex]
Each puzzle contains 20 triangular pieces, so wood used for each piece of puzzle would be 20 times 6 square inches.
[tex]\text{Wood used for each puzzle}=20\times 6\text{ in}^2[/tex]
[tex]\text{Wood used for each puzzle}=120\text{ in}^2[/tex]
[tex]\text{Wood used for 80 puzzles}=80\times 120\text{ in}^2[/tex]
[tex]\text{Wood used for 80 puzzles}=9600\text{ in}^2[/tex]
Therefore, 9600 square inches of wood is needed to make 80 puzzles.
Find all values of thetaθ, if thetaθ is in the interval [0degrees°, 360degrees°) and has the given function value cot thetaθ=1
Khalid invested $9500 in a savings account with a yearly interest rate of 3% for 8 years. How much simple interest did he earn?
Answer:
$2280
Step-by-step explanation:
for geometric sequence below, determine the explicit formula. be sure to enter your answer as a formula of the form a_n= a_1(r)^(n-1) with the correct a_1 and r values.
5/8, 25/8, 125/8, 625/8, . . ., a_n
Three orders are placed at a pizza shop. two small pizzas, a liter of soda, and a salad cost $14; one small pizza, a liter of soda, and three salads cost $15; and three small pizzas, a liter of soda, and two salads cost $22. how much does each item cost?
We can solve this problem by setting up a system of equations using the given information and using algebraic methods to solve for each variable, which represent the cost of the individual items.
Explanation:This question can be solved by using the method of linear equations. Let's denote the cost of a small pizza as P, a liter of soda as S, and a salad as A. From the given information, we can create three equations:
2P + S + A = $14 P + S + 3A = $15 3P + S + 2A = $22
By solving these equations, we can determine the prices of the individual items. The details of solving these equations may vary based on your level of comfort with algebra and systems of equations, but the general method involves isolating one variable in one equation and then substituting it into the other equations to eventually solve for each variable.
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At Susie's school, 5/8 of all students play sports. Of the students who play sports, 2/5 play soccer. What fraction of the students in Susie's school play soccer?
define a variable and write an inequality to model each situation. The school auditorium can seat at most 1200 people.