The sides of the triagle have lengths:
1.1 p + 9.5 q
4.5 p - 5.2 r
5.3 r + 5.4 q
Or:
1.1 p + 0 r + 9.5 q
4.5 p - 5.2 r + 0 q
0 p + 5.3 r + 5.4 q
If we want to calculate the perimeter of the triangle, we just need to sum the three lenghts:
(1.1 + 4.5) p + (-5.2 + 5.3) r + (9.5 + 5.4) q
= 5.6 p + 0.1 r + 14.9 q
A window washer drops a tool from their platform 155ft high. The polynomial -16t^2+155 tells us the height, in feet, of the tool t seconds after it was dropped. Find the height, in feet, after t= 1.5 seconds.
Write 3.25% as a fraction in simplest form. Can you explain step by step please?
From the problem, we have 3.25% to convert into fraction.
Note that percentage a% can be written as a/100
So 3.25% will be :
[tex]3.25\%=\frac{3.25}{100}[/tex]From here, we can multiply the numerator and the denominator by 100 to make 3.25 a whole number.
[tex]\frac{3.25\times100}{100\times100}=\frac{325}{10000}[/tex]Next step is to simplify the fraction by getting the factors of the numerator and the denominator.
325 = 25 x 13
10000 = 25 x 400
Rewriting it again :
[tex]\frac{325}{10000}=\frac{25\times13}{25\times400}[/tex]Cancel the common factor (25)
[tex]\frac{\cancel{25}\times13}{\cancel{25}\times400}=\frac{13}{400}[/tex]The answer is 13/400
Find the missing rational expression.382x + 6(x-3)(x + 1)X-332x + 6(x-3)(x + 1)(Simplify your answer.)X-3
A pound of rice crackers cost 42.88 Jacob purchased a 1/4 pound how much did he pay for the crackers?
Answer:
10.72
Step-by-step explanation:
The price per pound is 42.88
We are getting 1/4 pound.
Multiply 42.88 by 1/4
42.88 * 1/4 =10.72
Answer:
So you know that a pound of rice crackers cost $42.88. You also know that Matthew bought 1/4 or 25% or 0.25 of a pound. This means that by 42.88 divided 4 will equal the answer.
42.88 ÷ 4 = 10.72
Therefore, Matthew paid or $10.72 for 1/4 pound of rice crackers.
Find the formula for an exponential function that passes through the 2 points given
The form of the exponential function is
[tex]f(x)=a(b)^x[/tex]a is the initial value (value f(x) at x = 0)
b is the growth/decay factor
Since the function has points (0, 6) and (3, 48), then
Substitute x by 0 and f(x) by 6 to find the value of a
[tex]\begin{gathered} x=0,f(x)=6 \\ 6=a(b)^0 \\ (b)^0=1 \\ 6=a(1) \\ 6=a \end{gathered}[/tex]Substitute the value of a in the equation above
[tex]f(x)=6(b)^x[/tex]Now, we will use the 2nd point
Substitute x by 3 and f(x) by 48
[tex]\begin{gathered} x=3,f(x)=48 \\ 48=6(b)^3 \end{gathered}[/tex]Divide both sides by 6
[tex]\begin{gathered} \frac{48}{6}=\frac{6(b)^3}{6} \\ 8=b^3 \end{gathered}[/tex]Since 8 = 2 x 2 x 2, then
[tex]8=2^3[/tex]Change 8 to 2^3
[tex]2^3=b^3[/tex]Since the powers are equal then the bases must be equal
[tex]2=b[/tex]Substitute the value of b in the function
[tex]f(x)=6(2)^x[/tex]The answer is:
The formula of the exponential function is
[tex]f(x)=6(2)^x[/tex]If you select one card at random from a standard deck of 52 cards, what is the probability of that card being a 5, 6 OR 7?
To solve this question we will use the following expression to compute the theoretical probability:
[tex]\frac{\text{favorable cases}}{total\text{ cases}}.[/tex]1) We know that there are 4 fives, 4 sixes, and 4 sevens in a standard deck of 52 cards, then, the probability of selecting a 5, 6, or 7 is:
[tex]\frac{4+4+4}{52}\text{.}[/tex]2) Simplifying the above expression we get:
[tex]\frac{12}{52}=\frac{3}{13}\text{.}[/tex]Answer:
[tex]\frac{3}{13}\text{.}[/tex]Angle RQT is a straight angle. What are m angle RQS and m angle TQS? Show your work.
11x + 5 + 8x + 4 = 180
Simplifying like terms
11x + 8x = 180 - 5 - 4
19x = 171
x = 171/19
x = 9
RQS = 11(9) + 5
= 99 + 5
= 104°
TQS = 8(9) + 4
= 72 + 4
= 76°
12 = - 2/5 yI got -30 I want to see if I did the correct steps
Solution
[tex]12=-\frac{2}{5}y[/tex]Step 1: Simplify the expression
[tex]\begin{gathered} 12=-\frac{2}{5}y \\ \text{cross multiply} \\ 12(5)=-2y \\ 60=-2y \end{gathered}[/tex]Step 2: Divide the both side by -2
[tex]\begin{gathered} 60=-2y \\ \frac{60}{-2}=-\frac{2y}{-2} \\ y=-30 \end{gathered}[/tex]Therefore the correct value of y = - 30
helppppppppppppppppppp
Which of the following statements must be true based on the diagram below!(Diagram is not to scale)O JL is a segment bisector.JL is a perpendicular bisector.OJT is an angle bisectora Lis the vertex of a right angle,Jis the midpoint of a segment in the diagramNone of the above.
From the diagram, we notice that the line JL bisects the angle J into two equal angles. Hence, we can conclude that the correct statement is this:
JL is an angle bisector
An angle bisector are
you bought a car for $5000. each year it depreciates by 8.5%. Which equation can be used to find the value, v, of the car, x years after it was purchased?
We have the following:
In this case, we have the following formula:
[tex]v=C\cdot(1-r)^x[/tex]Where C is the original value of the car, r is the depreciation rate and x is the time in years
a janitor had 2/3 of a cleaning solution. he used 1/4 of the solution in an day. how much of the bottle did he use?
Answer:
5/12 of the cleaning solution.
Step-by-step explanation:
2/3 – 1/4
------------------------------------------
2 × 4
= 8/12
3 × 4
------------------------------------------
1 x 3
= 3/12
4 x 3
------------------------------------------
8 – 3
12
= 5/12
------------------------------------------
Hopefully this makes sense!
If each machine produces nails at the same rate, how many nails can 1 machine produce in 1 hour
Divide the number of nails by the number of minutes:
16 1/5 ÷ 15 = 1 2/25 per minute
48 3/5 ÷ 45 = 1 2/25 per min
59 2/5 ÷ 55 = 1 2/25 per min
We have the number of nails produced per minute, to calculate the number of nails in an hour multiply it by 60, because 60 minutes= 1 hour:
1 2/25 x 60 = 64 4/5
Need help with this question
Given: a quadratic function with vertex (2,3) opening upward .
Find: the given statement is true or false.
Explanation: if parabola has a vertex at (2,3) and opens upward, it has one real solution., (2,3) will be a lowest point. The vertex will be at lowest point, it will be minimum.
that means graph has no one real solution. hence it will never going to intersect. so this statement is false.
Final answer: the given statement is FALSE.
Don’t get part b of the question. Very confusing any chance you may help me with this please.
To solve this problem, first, we will solve the given equation for y:
[tex]\begin{gathered} x=3\tan 2y, \\ \tan 2y=\frac{x}{3}, \\ 2y=\arctan (\frac{x}{3}), \\ y=\frac{\arctan(\frac{x}{3})}{2}=\frac{1}{2}\arctan (\frac{x}{3})\text{.} \end{gathered}[/tex]Once we have the above equation, now we compute the derivative. To compute the derivative we will use the following properties of derivatives:
[tex]\begin{gathered} \frac{d}{dx}\arctan (x)=\frac{1}{x^2+1}, \\ \frac{dkf(x)}{dx}=k\frac{df(x)}{dx}. \end{gathered}[/tex]Where k is a constant.
First, we use the second property above, and get that:
[tex]\frac{d\frac{\arctan(\frac{x}{3})}{2}}{dx}=\frac{d\arctan (\frac{x}{3})\times\frac{1}{2}}{dx}=\frac{1}{2}\frac{d\arctan (\frac{x}{3})}{dx}\text{.}[/tex]Now, from the chain rule, we get:
[tex]\frac{dy}{dx}=\frac{1}{2}\frac{d\text{ arctan(}\frac{x}{3})}{dx}=\frac{1}{2}\frac{d\arctan (\frac{x}{3})}{dx}|_{\frac{x}{3}}\frac{d\frac{x}{3}}{dx}\text{.}[/tex]Finally, computing the above derivatives (using the rule for the arctan), we get:
[tex]\frac{dy}{dx}=\frac{1}{2}\frac{\frac{1}{3}}{\frac{x^2}{9}+1}=\frac{1}{6}(\frac{1}{\frac{x^2}{9}+1})=\frac{3}{2(x^2+9)}.[/tex]Answer:
[tex]\frac{3}{2(x^2+9)}.[/tex]f(x)A6X-868Which of the given functions could this graph represent?OA. f(t) = (x - 1)(x - 2)(x + 1)(x + 2)O B. f(x) = x(x - 1)(1 + 1)Oc. /(x) = x(x - 1)(x - 2)(x + 1)(x + 2)OD. (r) = x(x - 1)(x - 2)
The Solution:
Given the graph below:
We are required to determine the function that best describes the above graph.
Step1:
Identify the roots of the function from the given graph.
[tex]\begin{gathered} x=-2 \\ x=-1 \\ x=1 \\ x=2 \end{gathered}[/tex]This means that:
[tex]\begin{gathered} x+2=0 \\ x+1=0 \\ x-1=0 \\ x-2=0 \end{gathered}[/tex]So, the required function becomes:
[tex]f(x)=(x-1)(x-2)(x+1)(x+2)[/tex]Therefore, the correct answer is [option A]
the length of a rectangle is 13 centimeters less then four times it’s width it’s area is 35 centimeters find the dimensions of the rectangle
Solution:
The area of a recatngle is expressed as
[tex]\begin{gathered} \text{Area of rectangle = L}\times W \\ \text{where} \\ L\Rightarrow\text{length of the rectangle} \\ W\Rightarrow\text{ width of the rectangle } \end{gathered}[/tex]Given that the length of the rectangle is 13 centimeters less than four times its width, this implies that
[tex]L=4W-13\text{ ---- equation 1}[/tex]Tha area of the rectangle is 35 square centimeters. This implies that
[tex]36=L\times W\text{ --- equation 2}[/tex]Substitute equation 1 into equation 2. Thus,
[tex]\begin{gathered} 36=L\times W \\ \text{where} \\ L=4W-13 \\ \text{thus,} \\ 36=W(4W-13) \\ open\text{ parentheses} \\ 36=4W^2-13W \\ \Rightarrow4W^2-13W-36=0\text{ ---- equation 3} \\ \end{gathered}[/tex]Solve equation 3 by using the quadratic formula expressed as
[tex]\begin{gathered} W=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}_{} \\ \text{where} \\ a=4 \\ b=-13 \\ c=-36 \end{gathered}[/tex]thus, we have
[tex]\begin{gathered} W=\frac{-(-13)\pm\sqrt[]{(-13)^2-(4\times4\times-36)}}{2\times4}_{} \\ =\frac{13\pm\sqrt[]{169+576}}{8} \\ =\frac{13\pm\sqrt[]{745}}{8} \\ =\frac{13}{8}\pm\frac{\sqrt[]{745}}{8} \\ =1.625\pm3.411836016 \\ \text{thus,} \\ W=5.036836016\text{ or W=}-1.786836016 \end{gathered}[/tex]but the width cannot be negative. thus, the width of the recangle is
[tex]W=5.036836016[/tex]From equation 1,
[tex]\begin{gathered} L=4W-13 \\ \end{gathered}[/tex]substitute the obtained value of W into equation 1.
Thus, we have
[tex]\begin{gathered} L=4W-13 \\ =4(5.036836016)-13 \\ =20.14734-13 \\ \Rightarrow L=7.14734 \end{gathered}[/tex]Hence:
The width is
[tex]5.036836016cm[/tex]The length is
[tex]7.14734cm[/tex]What is the first step for finding the quotient of 3x^3 z^5/5y * x^2 z^6/20y^3
The initial expression is:
[tex]\frac{3x^3z^5}{5y}\text{ / }\frac{x^2z^6}{20y^3}[/tex]So the first step is to multiply the numerator of the second fraction with the denominator of the first franction and the denominator of the second fraction by the numerator of the first fraction so:
[tex]\frac{3x^3z^6}{5y}(\frac{20y^3}{x^2z^6})[/tex]So is option C)
For p(2) = 7 + 10x - 12x^2 - 10x^3 + 2x^4 + 3x^5, use synthetic substitution to evaluate
Answer:
p(-3) = -428
Explanations:Given the polynomial function expressed as:
[tex]p(x)=7+10x-12x^2-10x^3+2x^4+3x^5[/tex]Determine the value of p(-3)
[tex]\begin{gathered} p(-3)=7+10(-3)-12(-3)_^2-10(-3)^3+2(-3)^4+3(-3)^5 \\ p(-3)=7-30-12(9)-10(-27)+2(81)+3(-243) \\ p(-3)=-23-108+270+162-729 \\ p(-3)=-428 \end{gathered}[/tex]Hence the value of p(-3) is -428
Find the absolute maximum and minimum values of the following function on the given interval. f(x)=3x−6cos(x), [−π,π]
Answer:
Absolute minimum: x = -π / 6
Absolute maximum: x = π
Explanation:
The candidates for the absolute maximum and minimum are the endpoints and the critical points of the function.
First, we evaluate the function at the endpoints.
At x = -π, we have
[tex]f(-\pi)=3(-\pi)-6\cos (-\pi)[/tex][tex]\Rightarrow\boxed{f(-\pi)\approx-3.425}[/tex]At x = π, we have
[tex]f(\pi)=3(\pi)-6\cos (\pi)[/tex][tex]\Rightarrow\boxed{f(\pi)\approx15.425.}[/tex]Next, we find the critical points and evaluate the function at them.
The critical points = are points where the first derivative of the function are zero.
Taking the first derivative of the function gives
[tex]\frac{df(x)}{dx}=\frac{d}{dx}\lbrack3x-6\cos (x)\rbrack[/tex][tex]\Rightarrow\frac{df(x)}{dx}=3+6\sin (x)[/tex]Now the critical points are where df(x)/dx =0; therefore, we solve
[tex]3+6\sin (x)=0[/tex]solving for x gives
[tex]\begin{gathered} \sin (x)=-\frac{1}{2} \\ x=\sin ^{-1}(-\frac{1}{2}) \end{gathered}[/tex][tex]x=-\frac{\pi}{6},\; x=-\frac{5\pi}{6}[/tex]
on the interval [−π,π].
Now, we evaluate the function at the critical points.
At x = -π/ 6, we have
[tex]f(-\frac{\pi}{6})=3(-\frac{\pi}{6})-6\cos (-\frac{\pi}{6})[/tex][tex]\boxed{f(-\frac{\pi}{6})\approx-6.77.}[/tex]At x = -5π/6, we have
[tex]f(\frac{-5\pi}{6})=3(-\frac{5\pi}{6})-6\cos (-\frac{5\pi}{6})[/tex][tex]\Rightarrow\boxed{f(-\frac{5\pi}{6})\approx-2.66}[/tex]Hence, our candidates for absolute extrema are
[tex]\begin{gathered} f(-\pi)\approx-3.425 \\ f(\pi)\approx15.425 \\ f(-\frac{\pi}{6})\approx-6.77 \\ f(-\frac{5\pi}{6})\approx-2.66 \end{gathered}[/tex]Looking at the above we see that the absolute maximum occurs at x = π and the absolute minimum x = -π/6.
Hence,
Absolute maximum: x = π
Absolute minimum: x = -π / 6
Which number is greater in each set?
We have three set of numbers and we must choose the greater value in each set
1.
[tex]\frac{1}{3}or\frac{1}{4}or\frac{1}{5}[/tex]When the numerator is 1, the greater fraction is the one that has the small denominator.
So, in this case the greater number is
[tex]\frac{1}{3}[/tex]2.
[tex]\frac{1}{4}or\frac{4}{3}or\frac{5}{6}[/tex]In this case we can rewrite the fractions as fractions with the same denominator
[tex]\frac{1}{4}=\frac{3}{12}[/tex][tex]\frac{4}{3}=\frac{16}{12}[/tex][tex]\frac{5}{6}=\frac{10}{12}[/tex]Then, the greater number is the one that has the greater numarator
So, it is
[tex]\frac{16}{12}=\frac{4}{3}[/tex]in this case the greater number is
[tex]\frac{4}{3}[/tex]3.
[tex]\frac{16}{5}or3\frac{2}{5}or3.25[/tex]In this case we can rewrite the numbers as decimal numbers
[tex]\frac{16}{5}=3.2[/tex][tex]3\frac{2}{5}=3.4[/tex][tex]3.25=3.25[/tex]In this case the greater number is
[tex]3\frac{2}{5}[/tex]Can someone help with this question?✨
The equation of the line that is perpendicular with y = 4 · x - 3 and passes through the point (- 12, 7) is y = - (1 / 4) · x + 4.
How to derive the equation of a line
In this problem we find the case of a line that is perpendicular to another line and that passes through a given point. The equation of the line in slope-intercept form is described below:
y = m · x + b
Where:
m - Slopeb - Interceptx - Independent variable.y - Dependent variable.In accordance with analytical geometry, the relationship between the two slopes of the lines are:
m · m' = - 1
Where:
m - Slope of the first line.m' - Slope of the perpendicular line.If we know that m = 4 and (x, y) = (- 12, 7), then the equation of the perpendicular line is:
m' = - 1 / 4
b = 7 - (- 1 / 4) · (- 12)
b = 7 + (1 / 4) · (- 12)
b = 7 - 3
b = 4
And the equation of the line is y = - (1 / 4) · x + 4.
To learn more on equations of the line: https://brainly.com/question/2564656
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Find a polynomial f (x) of degree 3 that has the following zeros.6 (multiplicity 2), -7Leave your answer in factored form.
If a polynomial has a zero of "a" with multilicity b, the factor would be:
[tex](x-a)^b[/tex]So, accordingly the factors would be:
[tex]\begin{gathered} (x-6)^2 \\ (x-(-7))^1 \end{gathered}[/tex]They are
[tex]\begin{gathered} (x-6)^2 \\ (x+7) \end{gathered}[/tex]We can write out the polynomial, f(x), as:
[tex]f(x)=(x-6)^2(x+7)[/tex]What the answer to this to solve the problem
Answer:
25
Step-by-step explanation:
180-88=92
92+61=123
123+30+x=180
153+x=180
x=25
1. Sketch the graph of y = x that is stretched vertically by a factor of 3. (Hint: Write the equation first, then graph) Sketch both y = x and the transformed graph.
ANSWER and EXPLANATION
We want to stretch the graph of:
y = x
A vertical stretch of a linear function is represented as:
y' = c * y
where c is the factor
The factor from the question is 3.
So, the new equation is:
y' = 3 * x
y' = 3x
Let us plot the functions:
ur answer as a polynomial in standard form.=f(x) = 5x + 1g(x) = x2 – 3x + 12=Find: (fog)(x)
(fog)(x) = 5x² - 15x + 61
Explanation:The given functions are:
f(x) = 5x + 1
g(x) = x² - 3x + 12
(fog)(x) = f(g(x))
This means that we are substituting g(x) into f(x)
(fog)(x) = 5(x² - 3x + 12) + 1
(fog)(x) = 5x² - 15x + 60 + 1
This can be further simplified as:
(fog)(x) = 5x² - 15x + 61
Use the remainder theorem to find P(-2) for P(x) = x³ + 3x² +9,Specifically, give the quotient and the remainder for the associated division and the value of P(-2).QuotientRemainder =P(-2)=
Answer:
Quotient:
[tex]x^2+x-2[/tex]Remainder:
[tex]13[/tex]P(-2):
[tex]13[/tex]Step-by-step explanation:
Remember that the remainder theorem states that the remainder when a polynomial p(x) is divided by (x - a) is p(a).
To calculate the quotient, we'll do the synthetic division as following:
Step one:
Write down the first coefficient without changes
Step two:
Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).
Add the obtained result to the next coefficient of the dividend, and write down the sum.
Step 3:
Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).
Add the obtained result to the next coefficient of the dividend, and write down the sum.
Step 4:
Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).
Add the obtained result to the next coefficient of the dividend, and write down the sum.
Now, we will have completed the division and have obtained the following resulting coefficients:
[tex]1,1,-2,13[/tex]Thus, we can conlcude that the quotient is:
[tex]x^2+x-2[/tex]And the remainder is 13, which is indeed P(-2)
2x - 6(x-3) ≥ 5
solve for x.
Answer:
It’s siu
Step-by-step explanation:
Answer:x≤4.6
Step-by-step explanation: 2x-6(x-3)≥5. 1).combine the like terms. 2x+x=3x & -6+-3=-9. 2). isolate the "x". 3x-9≥5. 3x≥14. 3). divide both sides by your coefficient. 3x≥14/ 3
x≥4.6
4) flip your sign. x≤4.6
Need help !! Geometry unit 3 parallel and perpendicular lines
ANSWER;
Converse; Exterior alternate angles are equal
[tex]x\text{ = 3}[/tex]EXPLANATION;
Here, we want to get the value of x given that the lines l and m are parallel
From the diagram given, we can see that;
[tex]15x\text{ +29 = 26x-4}[/tex]The reason for this is that they are a pair of exterior alternate angles
Mathematically, exterior alternate angles are equal
From here, we can proceed to solve for the value of x;
[tex]\begin{gathered} 26x-15x\text{ = 29+4} \\ 11x=33 \\ x\text{ = }\frac{33}{11} \\ x\text{ = 3} \end{gathered}[/tex]The graph of f(x) is shown in black.Write an equation in terms of f(x) to match the redgraph.For example, try something like this:f(x)+3, f (x - 2), or 4f(x).
Notice that the red function is similar to the black function, which means the transformation applied was a translation.
The transformation is 5 units to the right, exactly.
Therefore, the function that represents the red figure is
[tex]f(x-5)[/tex]