If the width (W) of the rectangle is 1 ft shorter than its length (L), then we can write the following equatiion:
W = L - 1
now since we know the formula for the area of a rectangle:
Area = length x width
Area = L * W
30 = L * (L - 1)
where we have substituted the width W using the expression in terms of the length in the first equation we wrote.
then we multiply as indicated:
30 = L^2 - L
and write all terms on one side of the equal sign:
L^2 - L - 30 = 0
we try solving this quadratic equation by grouping:
L^2 - 6 L + 5 L - 30 = 0
L (L - 6) + 5 (L - 6) = 0
(L - 6) * (L + 5) =0
then there are two possible solutions to make that product equal to zero:
L = 6
or
L= -5
We pick the POSITIVE answer since we are looking for a length
therefore the length of the rectangle is 6 feet.
Type a "6" in the blank of your question.
a Find the volume of the specified cone. Use 3.14 for x, and round your answer to the nearest whole number. Radius = 4 in., Height = 9 in. 301 cu. in. b. 226 cu. in. 75 cu. in. d. 151 cu. in. Please select the best answer from the choices provided ΟΑ OB с OD
volume of cone approximately is 151 cubic inch
please help asap! will give brainliest
Answer:
See below
Step-by-step explanation:
It'll look like this (but you will need to change the + - signs on the x and y axes !)
how do I do this question
The value of x can be determined as,
[tex]\begin{gathered} \tan 39^{\circ}=\frac{x}{15} \\ x=15\tan 39^{\circ} \\ x=12.15 \end{gathered}[/tex]Thus, the required value of x is 12.15.
Clara scores 24 points per coin. In all, how many coins does Clara have to collect to score a total of 48 points?
Here is a graph of the function g.4-3-2-1Use the graph to find the following.If there is more than one answer, separate them with commas.(a) All local maximum values of g:(6) All values at which g has a local maximut:X
Graphically, the local maximum can be localized by spotting the "highest value" inside a range. A local maximum point on a function is a point (x,y) on the graph of the function whose y coordinate is larger than all other y coordinates on the graph at points "close to'' (x,y).
We can see that in our g function at x= -2 and x = 3, with respective values y = 3 and y = -1.
The answer for item (a) is: -1, 3
For item (b): -2, 3
Hello, I really need help solving this. It is a practice problem from my ACT prep guide. The subject is trigonometry. The answer options are at the bottom, *one answer per box*
Answer:
To find the domain of the function f(x)=tanx restricted so that its inverse function exists
we know that,
Since the range of tan inverse x is (-π/2, π/2), the answer should lie in this interval. Assume that y = tan -1 x. Then by the definition of inverse tan, tan y = x. The value of y in the interval (-π/2, π/2) that satisfies the equation tan y = x .
The domain of tanx is restricted to (-π/2, π/2). The range of tanx is always real numbers.
we get that,
The domain of f(x)=tanx is restricted to (-π/2, π/2) so that the inverse function exists. This means that all functional values of f(x)=tan^-1 x are on the interval (-π/2, π/2).
8. Suppose that A, B, and C are sets. Prove or disprove that
(A − B) − C = (A − C) − B.
The equation be (A − B) − C = (A − C) − B. Then results exists different, so we contain disproven the hypothesis by counterexample.
Is (A − B) − C = (A − C) − B exists equivalent?Given: (A − B) − C = (A − C) − B.
First, we will attempt to show [tex]$A-(B-C) \subseteq(A-C)-C$[/tex]. Let [tex]$x \in A-(B-C)$[/tex]. Then [tex]$x \in A$[/tex] and [tex]$x \notin(B-C)$[/tex].
By De Morgan's law we have that
[tex]$$x \notin(B-C)=x \notin B \vee x \in C .$$[/tex]
We have that [tex]$x \in A \wedge(x \notin B \vee x \in C)$[/tex].
Then we have that [tex]$(x \in A \wedge x \notin B) \vee(x \in A \wedge x \in C)$[/tex].
So by definition of [tex]$\cup$[/tex] and [tex]$\cap$[/tex], we have [tex]$x \in(A-B) \cup(x \in(A \cap C))[/tex].
I can see a contradiction here in that LHS says x ∈ C but the RHS says x ∉ C.
For example, as longer as [tex]$C \neq 0$[/tex]. Let A = 4, B = 2, C = 1.
Then A - (B - C) = 4 - (2 - 1) = 4 - 1 = 3
On the other side (A - B) - C = (4 - 2) - 1 = 2 - 1 = 1.
The results exists different, so we contain disproven the hypothesis by counterexample.
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The first 19 terms of the arithmetic sequence 9, 2, -5, -12,...
9, 2, -5, -12,...
First let's find the common difference
Common difference= 2 - 9 = -7
So we will add - 7 to get the next term
9, 2, -5, -12, -19, -26, -33,-40, -47, -54, -61, -68, -75, -82, -89, -96, -103, -110, -117
PLS HELP ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!Which statement is true?A. 25-15×4-3×2=30B. 24-15×(4-3)×2=30C. (24-15)×4-3×2=30D. (24-15)×4-3×2=66
The correct statement is C.
To notice this, we need to remember the correct order of operations:
• Parentheses
,• Powers and roots
,• Multiplications and divisions
,• Additions and subtractions.
Using this ordering we have for each operation:
A.
[tex]\begin{gathered} 25-15\times4-3\times2=25-60-6 \\ =-41 \end{gathered}[/tex]B.
[tex]\begin{gathered} 24-15\times(4-3)\times2=24-15\times1\times2 \\ =24-30 \\ =-6 \end{gathered}[/tex]C.
[tex]\begin{gathered} (24-15)\times4-3\times2=9\times4-3\times2 \\ =36-6 \\ =30 \end{gathered}[/tex]D.
[tex]\begin{gathered} (24-15)\times4-3\times2=9\times4-3\times2 \\ =36-6 \\ =30 \end{gathered}[/tex]Hence the only correct result in the operations is the one given in option C.
Which of the following is equivalent to the expression below?
√28-√63+√112
The value of given expression is 3√7.
What is the expression?
An expression is a set of numbers or variables combined using the operations + , – , × or ÷ . Arithmetic expression that contains only numbers and mathematical operators and algebraic expression that contains variables, numbers and mathematical operators.
F(x) = √28 - √63 + √112
F(x) = 2√7 - 3√7 + 4√7
F(x) = 3√7
Option A is right answer.
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A bank deposit slip shows a total of $441 in $1 loonies and $2 coins. If the number of $2 coins was 3 times the number of $1 loonies, how many of each are there?
The number of $1 loonies are 63 and the number of $2 coins are 189
Let x be the number of $1 loonies and y be the number of $2 coins.
A bank deposit slip shows a total of $441 in $1 loonies and $2 coins.
so, we get an equation,
x + 2y = 441 .................(1)
The number of $2 coins was 3 times the number of $1 loonies.
so, we get an equation,
y = 3x .............(2)
Substitute the above value of in equation (1),
x + 2(3x) = 441
x + 6x = 441
7x = 441
x = 63
Substitute above value of x in equation (2),
y = 3 * 63
y = 189
Therefore, the number of $1 loonies are 63 and the number of $2 coins are 189
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You deposit $1,200 in an account that earns 5% interest compounded monthly. Estimate how long it would take for the investment to double.
17.5 years.
It takes 17.5 years to double the investment of $1200.
What is compound interest?Compound interest simply means that the interest on a bank account, loan, or investment grows exponentially over time rather than linearly.Given ,
P = $1200
r = 5 % = 0.05
n = 12
A = $2400( Since double of p)
Equation ,
A = [tex]P ( 1 + r / n)^{nt}[/tex]
2400 = [tex]1000 ( 1 + .05/ 12)^{12t}[/tex]
2.4 = [tex](1 + .05/12)^{12t}[/tex]
log both sides,
log 2.4 = log[tex]( 1 + .05/ 12)^{12t}[/tex]
log 2.4 = 12t . log ( 1 + .05/ 12)
(log 2.4) / (12 log (1 + .05/ 12)) = t
t = 17.5 years.
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What should be done to both sides of the equation in order to solve x = 4?Divide by 4.Multiply by 4.Divide by 1/3.Multiply by 1/3.
Given:
There are given that the equation:
[tex]\frac{1}{3}x=4[/tex]Explanation:
According to the question:
We need to find the value that orders to solve both sides of the equationn.
So,
From the equation:
[tex]\frac{1}{3}x=4[/tex]Then,
For the equation, divide by 1/3 on both sides of the equation:
So,
From the properties:
If,
[tex]\frac{a}{\frac{b}{\frac{c}{d}}}=\frac{a}{b}\times\frac{d}{c}[/tex][tex]\begin{gathered} \frac{1}{3}x=4 \\ \frac{\frac{1}{3}x}{\frac{1}{3}}=\frac{4}{\frac{1}{3}} \\ \frac{\frac{1}{3}x}{\frac{1}{3}}=4\times3 \\ \frac{1}{3}x\times3=12 \\ x=12 \end{gathered}[/tex]Final answer:
Hence, the correct option is C.
Water drips from a faucet at a rate of 41 drops a minute assuming there is a 15,000 drop in a gallon. How many minutes will it take for the dripping faucet to fill a 1 gallon bucket?
lynn is tracking the progress of her plants growth. today the plant is 5 cm high. the plant grows 1.5 cm per day. suppose Lynn's plant grewn to a height of 30.5 inches how many days will have passed
We have that the plant start with 5 cm high and it grows 1.5 cm per day, then the equation to model this situation is:
[tex]y=1.5x+5[/tex]where x represents the days that passes and y represents the height of the plant.
Now, let's convert 30.5 inches to cm:
[tex]\begin{gathered} 1in=2.54\operatorname{cm} \\ \Rightarrow(30.5)\cdot(2.54)=77.47\operatorname{cm} \end{gathered}[/tex]then, suppose that Lynn's plant grew to a height of 77.47 cm, then we have to make y = 77.47 and solve for x to get the following:
[tex]\begin{gathered} y=77.47 \\ \Rightarrow77.47=1.5x+5 \\ \Rightarrow77.47-5=1.5x \\ \Rightarrow72.47=1.5x \\ \Rightarrow x=\frac{72.47}{1.5}=48.3 \\ x=48.3 \end{gathered}[/tex]therefore, it will take approximately 48 days to the plant to grow to a height of 30.5 inches
an astronsut weighs 174 pounds on earth and 29 pounds on the moon if his daughter weighs 108 pounds on earth what is the daughters weight on the moon in pounds
Answer:
Step-by-step explanation:
18 pounds
A coin is flipped 2,500 times. It lands on heads 1,223 times and tails 1,277 times. What is the empirical probability of getting tails on this coin
Answer:
The empirical probability of getting tails on this coin is 50.08%.
Step-by-step explanation:
Sharon baked 72 cookies for herclassmates. Her brothers ate some ofthe cookies and 54 cookies remain.Find the percent of decrease.
Answer
Percent decrease = 25%
Explanation
Percent decrease is given as
[tex]\text{Percent decrease = }\frac{Amount\text{ decreased}}{\text{Original amount}}\times100\text{ percent}[/tex]For this question,
Amount decreased = (Original amount) - (Amount remaining)
Amount decreased = 72 - 54 = 18 cookies
Original amount = 72 cookies
Percent decrease = (18/72) × 100%
Percent decrease = 25%
Hope this Helps!!!
properties of chords. leave answer in simplest form. DONT TAKE FOREVER TO ANSWER
Let's put more details in the figure to better understand the problem:
To be able to determine DC, let's treat this as two similar triangles and apply ratio and proportion.
We get,
[tex]\text{ }\frac{\text{ AB}}{\text{ OB}}\text{ = }\frac{\text{ EF}}{\text{ OE}}[/tex][tex]\frac{18}{12}\text{ = }\frac{x}{\text{ 10}}[/tex][tex]\frac{18\text{ x 10}}{12}\text{ = }x[/tex][tex]\frac{180}{12}\text{ = }x[/tex][tex]15\text{ = }x[/tex][tex]\text{ FE = 15}[/tex]If a diameter or radius is perpendicular to a chord, then it bisects the chord and its arc. Therefore, we can say that FE = ED.
Determining the length of FD, we get:
[tex]\text{ FE + ED = FD}[/tex][tex]\text{ FE + FE = FD}[/tex][tex]\text{ 15 + 15 = FD}[/tex][tex]\text{ FD = 30}[/tex]Therefore, FD = 30
Marian purchased a home valued at $465,000. She purchased homeowner insurance for 75% of the value of the home. If the annual premium on the policyhundred-dollar unit, how much did she pay to the nearest whole cent)?$2,875.50$2,695.00$2,580.75$3,050.74None of these choices are correct.
Ok, so
Marian purchased a home valued at $465,000. If She purchased homeowner insurance for 75% of the value of the home, she paid:
$(465,000)*(75) / (100)
$348,750.
Now, we know that the annual premium on the policy was $0.74 per hundred-dollar unit. Then, this is:
0.74/100 dollar unit.
And, if we multiply, we obtain:
$348,750 * (0.74/100) = $2,580.75
Therefore, she paid $2,580.75
6.75 +3/8x=13 1/4 solve please
To solve this equation, we can proceed as follows:
[tex]6.75+\frac{3}{8}x=13\frac{1}{4}[/tex]1. Subtract 6.75 to both sides of the equation:
[tex]6.75-6.75+\frac{3}{8}x=13\frac{1}{4}-6.75\Rightarrow\frac{3}{8}x=13\frac{1}{4}-6.75[/tex]We can solve the right part of the equation using fractions as follows:
[tex]6.75=6+\frac{3}{4}[/tex]We also know that
[tex]13\frac{1}{4}=13+\frac{1}{4}[/tex]Then, we have:
[tex]\frac{3}{8}x=13+\frac{1}{4}-(6-\frac{3}{4})=13-6+\frac{1}{4}-\frac{3}{4}=7+\frac{1-3}{4}_{}[/tex][tex]\frac{3}{8}x=7+(-\frac{3}{4})=7-\frac{3}{4}=\frac{7\cdot4-3}{4}=\frac{28-3}{4}_{}=\frac{25}{4}[/tex]Now, the equation is:
[tex]\frac{3}{8}x=\frac{25}{4}[/tex]We need to multiply by 8/3 to both sides to solve for x as follows:
[tex]\frac{8}{3}\cdot\frac{3}{8}x=\frac{8}{3}\cdot\frac{25}{4}\Rightarrow x=\frac{8}{4}\cdot\frac{25}{3}\Rightarrow x=2\cdot\frac{25}{3}\Rightarrow x=\frac{50}{3}=16.6666666\ldots=16\frac{2}{3}[/tex]Therefore, the value for x is equal to:
[tex]x=16\frac{2}{3}=\frac{50}{3}=16.6666666\ldots[/tex]Answer:
The exact form, decimal form, and the mixed number form are down
Step-by-step explanation:
exact form ; x = 208/3
decimal form ; 69.33333..
Mixed number form ; 69 1/3
Need help ASAP thank you
Domain and range of a function is the set of values that we are allowed to enter into our function. This set consists of the x values for a function like f. (x). The set of values that a function can accept as input is known as its range.
answer -2< = x< = 3.
What are some illustrations of the domain and range of a function?
A simple function, such f(x) = x2, can only have the counting numbers 1, 2, 3, etc. as its domain (what goes in) and the set of numbers 1, 4, 9, etc. as its range (what comes out). Another function, g(x) = x2, may have a range of..., and an integer domain of..., -3, -2, -1, 0... 1, 2, 3.
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Convert 0.03 inches to days to grow 3 inches
Answer: 700
Step-by-step explanation:
i am smart
HELP ASAP PLEASE
Determine all real values of a.
a2 = 225
a = 112.5
a = ±112.5
a = 15
a = ±15
The real value of a is 15.
Given,
[tex]a^2 = 225[/tex]
Determine the real value of a
What is Perfect Square?
An integer that can be expressed as the square of another integer is called a perfect square. In other words, it is defined as the product of some integer with itself.
Here, find the square root of 225
Now,
[tex]a^2 = 225 \\\\a = \sqrt{225}[/tex]
a = 15 x 15 = 225
Hence, The real value of a is 15.
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Answer: the answer is the last option
Step-by-step explanation: I took the test and got it right
Can you help and explain what to do with practice question below?
Solution:
Given the figure below:
To solve for the missing angles,
Step 1: Solve for c.
The sum of the interior angles of a triangle equals 180 degrees.
Thus,
[tex]\begin{gathered} 48+58+c=180(sum\text{ of interior angles in a triangle\rparen} \\ \Rightarrow106+c=180 \\ subtract\text{ 106 from both sides,} \\ 106-106+c=180-106 \\ \Rightarrow c=74\degree \end{gathered}[/tex]Step 2: Solve for d.
The sum of angles on a straight line gives 180 degrees.
[tex]\begin{gathered} 58+d=180\text{ \lparen sum of angles on a straight line\rparen} \\ subtract\text{ 58 from both sides,} \\ 58-58+d=180-58 \\ \Rightarrow d=122\degree \end{gathered}[/tex]Step 3: Solve for a.
From the figure,
[tex]a=58\degree\text{ \lparen alternate angles\rparen}[/tex]Step 4: Solve for b.
From the figure,
[tex]\begin{gathered} b+c=d\text{ \lparen alternate angles\rparen} \\ \Rightarrow b+74=122 \\ subtract\text{ 74 from both sides,} \\ b+74-74=122-74 \\ \Rightarrow b=48\degree \end{gathered}[/tex]Hence, we have
[tex]\begin{gathered} a=58\degree \\ b=48\degree \\ c=74\degree \\ d=122\degree \end{gathered}[/tex]Sales are $500,00 and variable cost are $350,00. What is the contribution margin ratio
If Sales are $500,000 and variable cost are $350,000. The contribution margin ratio is 30%.
What is contribution margin ratio?Contribution margin ratio can be determine or find by substracting or deducting the variables cost form the sales and then dividing it by the sales.
Now let find the contribution margin ratio using this formula
Contribution margin ratio = Sales - Variable cost / Sales
Where:
Sales = $500,000
Variable costs = $200,000
Let plug in the formula
Contribution margin ratio = $500,000 - $350,000 / $500,000
Contribution margin ratio = $150,000 / $500,000
Contribution margin ratio = 0.3 × 100
Contribution margin ratio = 30%
Therefore we can conclude that 30% is the contribution margin ratio .
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The distribution of sale prices (online) for four-year-old Harley Davidson touring motorcycles is approximately Normally distributed with a mean
of $14,000 and a standard deviation of $4,000.
8. What proportion of available motorcycles are priced at or below $9,000? Show your work.
9. What proportion of available motorcycles are priced at or below $12,000? Show your work.
10. Mr. Kawasaki plans to spend between $9,000 and $12,000 on a motorcycle. What proportion of the available motorcycles of this type can he
afford?
11. What is the approximate z-score for the 30th percentile in the standard Normal distribution?
12. Hence, what is the 30th percentile for the prices of motorcycles of this type? Show your work.
Answer:
$2000
Step-by-step explanation:
you subtract 4000-2000=2000
If the measure of arc AB is 64 degrees, what is the measure of angle ADB?
Answer:
the answer is AB multi
Step-by-step explanation:
Is AB degrees
So can y’all help me please this is due at 5pm
Answer:
Variable terms: 4a and 6a
Constant terms: 4 and 11
Step-by-step explanation:
A constant term is one that is NOT multiplied by any variables.
At this level of math, think of constants as terms that are only numbers.
(for example: 1, 68.9, -42, etc.)
Note that a term in « a + bi » form can also be a constant.
A variable term is a one that IS multiplied by a variable.
(for example x, -3y, 8z, etc.)
In question 1, the variable terms are:
4a and 6a because they are multiplied by the variable a
The constant terms are:
4 and 11 because they are simply integers
Note that the constant terms could also be written as -4 and -11 depending on how the operations are viewed (subtracting vs adding a negative)
i have to find out if the triangles are similar and if so y
We will determine the height of the tree as follows:
*First: We take the height of Dave to just ft, that is:
We know that one feet has 12 inches, so:
[tex]x=\frac{4\cdot1}{12}\Rightarrow x=\frac{1}{3}[/tex]Now, we add that to the 6 feet:
[tex]6+\frac{1}{3}=\frac{19}{3}=6.333\ldots[/tex]So, his height is 19/3 ft.
Now, we determine the height of the tree as follows:
[tex]\frac{15}{(\frac{19}{3})}=\frac{y}{66+15}[/tex]Here y represents the height of the tree, now we solve for it:
[tex]\frac{45}{19}=\frac{y}{81}\Rightarrow y=\frac{45\cdot81}{19}\Rightarrow y=\frac{3645}{19}[/tex][tex]\Rightarrow y\approx191.8[/tex]So, the height of the tree is approximately 191.8 feet.
