Answer:
The linear equation is;
[tex]f(x)=3x[/tex]Explanation:
Given that the function f(x) is a linear function;
[tex]f(x)=mx+b[/tex]let us derive the values of m and b.
At x=-1, f(-1)=-3;
[tex]\begin{gathered} f(-1)=m(-1)+b=-3 \\ -m+b=-3\text{ --------1} \end{gathered}[/tex]At x=2, f(2)=6;
[tex]\begin{gathered} f(2)=m(2)+b=6 \\ 2m+b=6\text{ ---------2} \end{gathered}[/tex]subtract equation 1 from 2;
[tex]\begin{gathered} 2m-(-m)+b-b=6-(-3) \\ 3m=9 \\ m=\frac{9}{3} \\ m=3 \end{gathered}[/tex]let's substitute the value of m into equation 2;
[tex]\begin{gathered} 2m+b=6 \\ 2(3)+b=6 \\ 6+b=6 \\ b=6-6 \\ b=0 \end{gathered}[/tex]Therefore, since we have the values of m and b we can substitute to get the equation f(x);
[tex]\begin{gathered} f(x)=mx+b \\ f(x)=3x+0 \\ f(x)=3x \end{gathered}[/tex]The linear equation is;
[tex]f(x)=3x[/tex]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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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.
Sole the following problem by using the 4 measurements given
The symbol Σ (called sigma) means "sum up". So, in this case, the expression indicates the sum of the (xᵢ)², where i goes from 1 to 4, which is 1, 2, 3 and 4. Then, we have:
[tex]\sum_{i\mathop{=}1}^4(x_i)^2=(x_1)^2+(x_2)^2+(x_3)^2+(x_4)^2[/tex]From the word problem, we know the value of each xᵢ.
[tex]\begin{gathered} x_1=5 \\ x_2=13 \\ x_3=19 \\ x_4=16 \end{gathered}[/tex]Finally, we operate.
[tex]\begin{gathered} \sum_{i\mathop{=}1}^4(x_i)^2=(x_1)^2+(x_2)^2+(x_3)^2+(x_4)^2 \\ \sum_{i\mathop{=}1}^4(x_i)^2=(5)^2+(13)^2+(19)^2+(16)^2 \\ \sum_{i\mathop{=}1}^4(x_i)^2=25+169+361+256 \\ \sum_{i\mathop{=}1}^4(x_i)^2=811 \end{gathered}[/tex]AnswerThe result of computing the given expression is 811.
Clara scores 24 points per coin. In all, how many coins does Clara have to collect to score a total of 48 points?
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
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?
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.
In ADEF below, mZD=3x+5, mZE = 4x-15, and mZF = 2x+10. Which statement is1) DF=FE2) DE = FE3) m
Therefore:
[tex]DF=FE[/tex]One option in a roulette game is to bet $20 on red. (There are 18 red compartments, 18 black compartments, and two compartments that are neither red nor black.) Ifthe ball lands on red, you get to keep the $20 you paid to play the game and youare awarded $20. If the ball lands elsewhere, you are awarded nothing and the $20that you bet is collected. Find the expected payback for this roulette game if you bet $20 on red.The expected payback is $ (Round to the nearest cent as needed.)
In order to calculate the expected value, we need to calculate the sum of products of every possibility (the product of its pr
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
Can someone help me asap
Answer:
A) 670
B) 192 and 670
C) 192
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)
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
what is the error and how do I explain it
When we do multiplications of polynomials we have to multiply every term of the first expression with every term of the second expression, then:
[tex]\begin{gathered} (k+4)^2=(k+4)(k+4) \\ =k\cdot k+4k+4k+4\cdot4 \\ =k^2+8k+4^2 \\ =k^2+8k+16 \end{gathered}[/tex]Now, the error in the expression given is that they did not do all the possible multiplications, they only squared the two terms.
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!!!
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
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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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).
I need help breaking it down to understand the answer.
SOLUTION
Each amount in the situation with the expression that represents it will be shown below
Situation Expression
The centimeters of rain on Thursday r
How many more centimeters of rain fell on Saturday 0.15r
than on Thursday
The centimeters of rain on Saturday 1.15r
solve for y y - 2x = 15
Starting with the equation:
[tex]y-2x=15[/tex]Add 2x to both sides of the equation:
[tex]y-2x+2x=15+2x[/tex]Since -2x+2x=0, then:
[tex]y=15+2x[/tex]Solve quadratic equations by finding square roots (2r-5)^2=81
r
=
7
r
=
−
2
Explanation:
(
2
r
−
5
)
2
=
81
or
2
r
−
5
=
±
√
81
or
2
r
−
5
=
±
9
or
2
r
=
5
±
9
or
r
=
5
±
9
2
or
r
=
5
+
9
2
or
r
=
14
2
or
r
=
7
-------------Ans
1
or
r
=
5
−
9
2
or
r
=
−
4
2
or
r
=
−
2
------------Ans
2
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How many liters each of a 55% acid solution and a 80% acid solution must be used to produce 50 liters of a 60% acid solution? (Round to two decimal places if necessary.)
Given:
Let x denote the number of liter solutions.
[tex]\begin{gathered} \text{acid}+\text{acid}=\text{acid} \\ 55\text{ \%x+80 \%( 50-x)=}60\text{ \%}\times50 \end{gathered}[/tex]Solve the equation for x,
[tex]\begin{gathered} 55\text{ \%x+80 \%( 50-x)=}60\text{ \%}\times50 \\ \frac{55}{100}x+\frac{80}{100}(50-x)=\frac{60}{100}\times50 \\ 0.55x+0.8(50-x)=30 \\ 0.55x+40-0.8x=30 \\ -0.25x=30-40 \\ x=-\frac{10}{-0.25} \\ x=40 \end{gathered}[/tex]It gives,
[tex]\begin{gathered} 40\text{ liters of 55 \% acid will be n}eeded \\ (50-x)=(50-40)=10\text{ liters of 80 \% acid will be n}eeded \end{gathered}[/tex]Answer: 40 liters of a 55% acid solution and 10 liters of 80% acid solution must be used to produce 50 liters of a 60% acid solution
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
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 !)
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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A can of beans has surface area 329 cm². Its height is 14 cm. What is the radius of the circular top?
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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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.
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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