The length of the base of a triangle with the given area and height is equal to [tex]8\ cm[/tex].
What is triangle?" Triangle is defined as the two dimensional geometric shape with three vertices, three sides, and three interior angles enclosed in it."
Standard formula
Area of the triangle [tex]\frac{1}{2} \times base \times height[/tex]
According to the question,
Given,
Given formula of the area of the triangle [tex]= bh[/tex]
[tex]'b'[/tex] represents the base of a triangle
[tex]'h'[/tex] represents the height of a triangle
Area of the triangle [tex]= 32 \ cm^{2}[/tex]
Height of the triangle [tex]= 4 \ cm[/tex]
Substitute the value in the given formula we get,
[tex]32= b\times 4\\\\\implies b = \frac{32}{4} \\\\\implies b = 8 \ cm[/tex]
From standard formula
[tex]32 = \frac{1}{2} \times base \times 4\\\\\implies base = \frac{32\times 2}{4}\\ \\\implies base = 16 \ cm[/tex]
Hence, Option(B) is the correct answer.
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Berta wants to plant 1,224 trees in 8 equal rows. How many trees will go in each row?
Answer: 153 trees in each row
Step-by-step explanation:
You would divide 1,224 by 8 to get 153 trees in each row.
What is the inverse of this given function?
to get the inverse of any expression, we start off by simply doing a quick switcheroo on the variables, and then solving for "y".
[tex]\bf g(x)=4y\implies \stackrel{switcheroo}{g(y)=4x}[/tex]
[tex]5.6 \div 1.682[/tex]
hi! I'm new to this type of math. i could really use some help understanding this. if you can help, that would help si much!
let f(x) = x^2 - 2x + 2 and g(x) = x - 3. find f(x) times g(x)
Answer:
x³ - 5x² + 8x - 6
Step-by-step explanation:
(x² - 2x + 2)(x - 3) ← product is required
Each term in the second factor is multiplied by each term in the first factor , that is
x²(x - 3) - 2x(x - 3) + 2(x - 3) ← distribute all 3 parenthesis
= x³ - 3x² - 2x² + 6x + 2x - 6 ← collect like terms
= x³ - 5x² + 8x - 6 → (b)
Answer:
g( x)^2=x^2-6x+9=f(x)-4x+7, f(x)=g(x)^2-4g(x)-5=(g(x)-2)^2-9=(g(x)+7)×(g(x)-11)
f(x)=x^2-2x+2=g(×)^2+4x-7
CAN SOMEONE HELP ME WITH THIS QUESTION?????????????????????????
The first one is Function 4. The y intercept is wherever the slope intercepts the Y axis, which would only be once if it is a true function. You can see that function 1's y intercept is 5. Function 2's is-4. Function 3's is -2. Function 4 tells you it's/ y intercept is 1. The one that's closest to 0 is number 4. As for the second one, the answer is function 1. I'm not positive on the third one, but can say function 4 is an answer.
Answer:
Step-by-step explanation:
Help me please!! 30 points
Answer:
1. 0.03
2. 0.066
3. 0.20833
4. 0.42105263157
Step-by-step explanation:
Use the commutative property to rewrite the following expression. x+13
Answer:
13+x
Step-by-step explanation:
1. Since its commutative property you can switch it around and you will still get the same answer.
2. Instead of x+13 you can write it as 13+x
The commutative property in mathematics tells us that the order in which you add or multiply numbers doesn't change the outcome. Therefore, using the commutative property, the expression 'x + 13' can be rewritten as '13 + x'.
Explanation:The commutative property in mathematics is a fundamental property that applies to both addition and multiplication. It states that the order in which you add or multiply numbers does not change the result. For example, 3 + 4 = 4 + 3 or 2 * 5 = 5 * 2.
So, when the question asks to use the commutative property to rewrite the expression x + 13, it simply means that you should reverse the order of the addition. Using the commutative property, the expression x + 13 changes to 13 + x.
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What is the solution to 8 + 9p = 9p - 7?
Answer:
15=0 not a real number
Step-by-step explanation:
8+9p=9p-7
+7 +7
15+9p=9p
-9p -9p
15=0
Which of the following lines has a zero slope?
It should be A because C cannot exist at the moment. B and D are clearly slopes, so it has to be A.
Am I right and if not what's the answer.
Answer:you are so right
Step-by-step explanation:
I need help Please!
Sally has 13 coins in her pocket. Nine of the coins are nickels, and the
rest of the coins are dimes. How many of the coins are dimes?
a.
Identify what is being asked.
b.
Strategize (What variable will you use to represent the unknown?)
c.
Set up (Write an equation)
d.
Solve (Find the solution)
e.
Check
(Does your answer make sense?)
Don't answer if you aren't going to answer all the questions!
Answer:
To solve, use a simple one-step equation
Known: Number of coins; Number of Nickles.
Unknown: Number of Dimes.
a) To find the number of Dimes
b) Use x (or virtually any letter) to represent the unknown number of dimes
c) 9+x=13
d) Subtract 9 from both sides to cancel out the 9 and isolate the variable on one side. x=4
e) 9+4=13, so yes, the answer is correct
Which three dimensional figure has double the number of edges than faces
Answer:cube
Step-by-step explanation:
Answer:
Cube
Step-by-step explanation:
Take a cube, or draw one. You can count the faces.
Knowing that a cube has 6 faces, we will count the edges.
There are 12 edges on a cube.
So, 12÷6=2.
Anything that you multiply by two is half the product.
Hugo received $100 for his birthday. He
then saved $20 per week until he had
a total of $460 to buy a printer. Use an
equation to show how many weeks it took
him to save the money.
Answer:
18 weeks
Step-by-step explanation:
Total amount of money saved up to buy the printer is T(w), where w is the number of weeks.
Then T(w) = $100 + ($20/wk)w
Setting this equal to $460, we solve the resulting equation for w to determine the number of weeks it took Hugo to save up $460 total:
$460 = $100 + ($20/wk)w, or
$360 = ($20/wk)w, or
w = $360/($20/wk) = 18 weeks
Hugo's savings over time can be represented by the equation 100 + 20w = 460. Here, w is the number of weeks saved. Solving this equation shows that Hugo saved for 18 weeks to have enough money for the printer.
Explanation:The problem can be solved by setting up an equation related to Hugo's savings. Hugo had $100 and he saved $20 per week until he had a total of $460. If we let w represent the weeks, we could represent this situation with the equation 100 + 20w = 460.
To solve the equation, we subtract 100 from both sides giving us 20w = 360. Then divide both sides by 20 to get w = 18. Therefore, it took Hugo 18 weeks to save enough money for the printer.
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Maricia has 412 bouquets of flowers for centerpieces.She uses 8 flowers for centerpiece.How many centerpieces can she make?
Interpet the remainder to solve?
Answer:
She can make about 51 centerpieces in total
List 3 things that you should consider when choosing a career.
Answer:
1.)Will this career choice be a good fit for you?
2.)Does choosing a profession in this field require you to relocate?
3.)Will this profession pay you what you want or need to survive?
Step-by-step explanation:
Decision-making involves balancing the pros and cons of what you have been researching and experimenting with. Will this career choice be a good fit for you? Does choosing a profession in this field require you to relocate? Will this profession pay you what you want or need to survive? Honest answers to these questions will help you make the best decision. Also, consider when you plan to enter the industry. If it is a job that requires a lot of training or years of education, this time may be far in the future, so you need to be flexible with your plans and make allowances for changes as they come.
Answer: salary, education requirements, work/life balance
Step-by-step explanation: edge 2022
Each grade level at Hooperville Schools has 298 students.
a. If there are 13 grade levels, how many students attend Hooperville Schools?
b. A nearby district, Willington, is much larger. They have 12 times as many students. How many students attend schools in Willington?
Answer:
(a) 3,874 students.
(b) 46,488 students.
Step-by-step explanation:
We have been given the each grade level at Hooperville Schools has 298 students.
(a) To find the number of students that attend Hooperville Schools, we will multiply the number of grades by 298.
[tex]\text{Students that attend Hooperville Schools}=13\times 298[/tex]
[tex]\text{Students that attend Hooperville Schools}=3,874[/tex]
Therefore, 3,874 students attend Hooperville Schools.
(b) We have been given that nearby district, Willington, is much larger. They have 12 times as many students.
To find the number of students that attend schools in Willington, we will multiply number of students at Hooperville schools by 12.
[tex]\text{Students that attend Willington Schools}=12\times 3,874[/tex]
[tex]\text{Students that attend Willington Schools}=46,488[/tex]
Therefore, 46,488 students attend schools in Willington.
What was built in Lowell, Massachusetts that helped change the lives of Americans?
A. Grain mills
B. Steel mills
C. Corn mills
D. Textile mills
Answer:
The Correct Answer is D
Textile mills
Step-by-step explanation:
Lowell's influence on industrialization in the United States was huge as his techniques were quickly replicated in different industries beyond the nation.By 1839, the facilities in Lowell hired at some measures more than 7,000 textile laborers, generally known as mill ladies or industry ladies. The Lowell mills were the primary reflection of the industrial revolution to happen in the United States, and with their achievement got two separate aspects of the facilities.What is the EXACT area of a circle that has a radius of 1/2 inch?
Answer:
π/4 in^2.
Step-by-step explanation:
The exact value = π r^2
= π * (1/2)^2
= π/4 in^2.
Factor the expression completely
[tex] { \times }^{2} - 2x - 63 [/tex]
show all work.
-5X - 16 = 8x - 3
Good evening ,
______
Answer:
x= -1
____________________
Step-by-step explanation:
-5X - 16 = 8x - 3
⇔-5x-8x = -3+16
⇔-13x = 13
⇔x = -1
Answer:
x = -1
Step-by-step explanation:
-5X - 16 = 8x - 3
add 5x on both sides
⇒ -5X - 16+5x= 8x -3 + 5x
⇒ -16 = 13x -3
add 3 on both sides
⇒-16 + 3 = 13x -3 +3
⇒ -13 = 13x
divide both sides by 13
⇒ -13/13 =13x/13
∴ -1 = x
Mitch is buying candy bars for his friends. He wants to give 2 bars to each friend, and wants to have 10 spare bars. He can afford to buy 36 candy bars. How many friends can he treat?
Answer:
Mitch can give 2 candy bars to 13 friends
Step-by-step explanation:
first, since he wants 10 left over, you subtract 36-10 which is 26. Then, since he wants to give each friend 2 candy bars, you divide 26 by 2 which equals 13.
- W2 - 11uv + 2v2
(if u = -1, v = 8, and w = -3)
The value of the given expression for the given variable values is 207.
The given expression is -w²-11uv+2v².
We need to find the value of the expression for u = -1, v = 8, and w = -3.
How to find the value of an expression?To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number. To evaluate an expression, we substitute the given number for the variable in the expression and then simplify the expression using the order of operations.
Now, substitute u = -1, v = 8, and w = -3 in the expression -w²-11uv+2v².
We get, -w²-11uv+2v²=-(-3)²-11(-1)(8)+2(8)²
=-9+88+128=207
Therefore, the value of the given expression for the given variable values is 207.
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A car salesperson is paid a base salary of
$35,000 plus 8% of sales. What are the
sales needed to have an annual income
greater than $65,000?
To have an annual income greater than $65,000, a car salesperson needs to achieve sales of at least $375,000.
Explanation:To determine the sales needed to have an annual income greater than $65,000, we need to set up an equation.
Let's represent the sales amount as 'x'.
The equation will be: $35,000 + 0.08x > $65,000.
To isolate 'x', subtract $35,000 from both sides: 0.08x > $30,000.
Finally, divide both sides by 0.08 to find the sales needed: x > $375,000.
Therefore, the sales needed to have an annual income greater than $65,000 is $375,000.
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What is the product?
(2x - 1)(x+4)
2x?-4
2x+4
2x+7-4
2x? - 7x-4
How to write 4÷873 show your work
You can write it as 4/873. This is the fraction form.
Hope this helped
Answer:
218.25
Step-by-step explanation:
Write the simplified expression.
Answer:
343
Step-by-step explanation:
Let's start simplifying with the numerator:
(15-8)⁹
=7⁹
=40353607
Now simplify the denominator :
[(5+2)³]²
=[(7)³]²
=[343]²
=117649
Now combine them :
(15-8)⁹/ [(5+2)³]²
=40353607 / 117649
=343
A woman traveled 2438.1 miles in 17 hours 20 minutes. Find the average speed of her light in miles per hour (Change 17 hours 20 minutes into hours and use the formula
d=rt)
Answer:
+140.68 m/h
Step-by-step explanation:
17.33 h
2438.1/17.33 = 140.68
+140.68 m/h
Final answer:
The woman's average flight speed is 140.7 miles/hour, calculated by using the formula for speed (v = d/t) on the provided distance (2438.1 miles) and the converted time (17 hours 20 minutes to 17.333 hours).
Explanation:
Calculating Average Speed
The question is asking to calculate the average speed of a woman's flight given the distance traveled and the time taken. To convert the time from hours and minutes to just hours, we use the fact that 20 minutes is ⅓ of an hour (20/60). Therefore, 17 hours 20 minutes is equivalent to 17 + ⅓ = 17.333 hours.
We use the formula for speed, v = d/t, which tells us that speed (v) is the distance (d) divided by the time (t). Plugging in the given values:
Distance (d) = 2438.1 miles
Time (t) = 17.333 hours
Applying these values to the formula gives us:
v = 2438.1 miles / 17.333 hours = 140.7 miles/hour.
So, the final answer is that the woman's average speed during her flight was 140.7 miles/hour.
Solve the equation for y.
23 = 5x – 2y
Answer:
Step-by-step explanation:
23 = 5x - 2y.
2y = 5x -23. Rearrange to make y the subject
y = (5/2)x - 23/2
23 = 5x – 2y
move 5x to the other side
sign changes from +5x to -5x
23-5x= 5x-5x-2y
23-5x= -2y
divide both sides by -2 to get y by itself
23/-2-5x/-2= -2y/-2
Answer:
y=-23/2+5x/2 or y=5x/2-23/2
Write an equation of a line in slope intercept form (y = mx + b) going through the points
(-2, 0) and (4, -3). Show your work for full credit.
Answer:
y = - [tex]\frac{1}{2}[/tex] x - 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + b ( m is the slope and b the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 2, 0) and (x₂, y₂ ) = (4, - 3)
m = [tex]\frac{-3-0}{4+2}[/tex] = [tex]\frac{-3}{6}[/tex] = - [tex]\frac{1}{2}[/tex], thus
y = - [tex]\frac{1}{2}[/tex] x + b ← is the partial equation
To find b substitute either of the 2 points into the partial equation
Using (- 2, 0 ), then
0 = 1 + b ⇒ b = 0 - 1 = - 1
y = - [tex]\frac{1}{2}[/tex] x - 1 ← in slope- intercept form
A freezer has a volume given by the trinomial y^3-2y^2-35y. What are the possible dimensions of the freezer? Use factoring.
Answer:
Step-by-step explanation:
[tex]y^{3} - 2y^{2} - 35y[/tex]
[tex]y(y^{2} - 2y - 35)[/tex]
[tex]y(y - 7)(y + 5)[/tex]
The possible dimensions of the freezer are given by the factors y, (y - 7), and (y + 5), representing the length, width, and height of the freezer respectively.
Explanation:The question is asking for the possible dimensions of a freezer with a volume represented by the trinomial y^3-2y^2-35y. To find the dimensions, we will factor this expression.
We can factor out the common factor y first:
y(y^2 - 2y - 35)
Next, we need to factor the quadratic equation. We look for two numbers that multiply to give -35 and add to give -2. These numbers are -7 and +5.
y(y - 7)(y + 5)
Now we have the factors of the trinomial. These factors represent the possible dimensions of the freezer: a length of y units, a width of (y - 7) units, and a height of (y + 5) units, where y is a positive real number because physical dimensions must be positive.