the equation is
[tex]7x+22=1520[/tex]then solve for x
[tex]\begin{gathered} 7x+22-22=1520-22 \\ 7x=1498 \\ \frac{7x}{7}=\frac{1498}{7} \\ x=214 \end{gathered}[/tex]answer: the principal bought 214 t-shirts
Suppose that the edge lengths x, y, z of a closed rectangular box are changing at the following rates: dx/dt= 1m/s, dy/dt= -2 m/s, and dz/dt= 0.5 m/s.
At the instant x= 2m, y= 3m, z= 5m, find the rates of change:
a) volume of the box
b) surface area of the box
c) diagonal of the box
a) The rate of change of the volume of the box is 8m³/s.
b) The rate of change of the surface area of the box is -19m²/s.
c) The rate of change of the diagonal of the box is 1m/s.
Let the rate of change of the edge length x, y, and z of a closed rectangular box are:
dx/dt= 1m/s
dy/dt= -2 m/s
dz/dt= 0.5 m/s
a) The volume of the box
From the formula of the volume,
V=xyz
Then,
differentiate w.r.t t
[tex]\frac{dV}{dt} = xy\frac{dz}{dt} + yz\frac{dx}{dt} +xz\frac{dy}{dt}[/tex]
[tex]\frac{dV}{dt} = xy(0.5)+ yz(1)+xz(-2)[/tex]
put the value of x, y, z , then we get
[tex]\frac{dV}{dt} = 2.3.(0.5)+ 3.5.(1)+2.5.(-2)[/tex]
[tex]\frac{dV}{dt} = 3+ 15 - 10[/tex]
[tex]\frac{dV}{dt} = 8m^3/s[/tex]
The rate of change of the volume of the box is 8m³/s.
b) surface area of the box
surface area of the rectangular box is
s = 2xy + 2yz + 2zx
differentiate w.r.t t
[tex]\frac{ds}{dt} = 2(y + z)\frac{dx}{dt} + 2(z + x)\frac{dy}{dt} +2(x + y)\frac{dz}{dt}[/tex]
[tex]\frac{ds}{dt} = 2(y + z)(1) + 2(z + x)(-2)+2(x + y)(0.5)[/tex]
[tex]\frac{ds}{dt} = 2(3 + 5)(1) + 2(5 + 2)(-2)+2(2 + 3)(0.5)[/tex]
[tex]\frac{ds}{dt} = 16 -40 + 5[/tex]
[tex]\frac{ds}{dt} = -19m^2/s[/tex]
The rate of change of the surface area of the box is -19m²/s.
c) diagonal of the box
lengths of the boxes for the diagonal is
s = 2x² + y² + z²
differentiate equation w.r.t t
[tex]\frac{ds}{dt} = 4x\frac{dx}{dt} + 2y\frac{dy}{dt} +2z\frac{dz}{dt}[/tex]
[tex]\frac{ds}{dt} = 4.2.1+ 2.3.(-2) +2.5.(0.5)[/tex]
[tex]\frac{ds}{dt} = 8 -12 + 5[/tex]
[tex]\frac{ds}{dt} =1m/s[/tex]
The rate of change of the diagonal of the box is 1m/s.
a) The rate of change of the volume of the box is 8m³/s.
b) The rate of change of the surface area of the box is -19m²/s.
c) The rate of change of the diagonal of the box is 1m/s.
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Find the distance between the parallel lines. If necessary, round your answer to the nearest tenths.
The distance between the parallel lines is [tex]\frac{3}{5}}[/tex].
The given parallel lines are
[tex]y= $-$3x+4\\y= $-$3x+1[/tex]
We have to find the distance between the given parallel lines.
The formula is used to solve the distance between two parallel lines [tex]ax+by+c_{1}=0[/tex] and [tex]ax+by+c_{2}=0[/tex] is
[tex]d=|c_{2} $-$c_{1}|\frac{1}{\sqrt{a^{2}+b^{2}}}[/tex]
The first given line is [tex]y= $-$3x+4[/tex]
We can write that line as [tex]3x$-$y $-$4=0[/tex]
The second given line is [tex]y= $-$3x+1[/tex]
We can write that line as [tex]3x$-$y $-$1=0[/tex]
Comparing the both given parallel lines with the standard equation of line.
After comparing we get
[tex]a=3, b= $-$1, c_{1}= $-$4, c_{2}= $-$1[/tex]
Putting the value in the formula
[tex]d=|(-1) -(-4)|\frac{1}{\sqrt{(3)^{2}+(-4)^{2}}}\\d=|-1+4|\frac{1}{\sqrt{9+16}}\\d=|3|\frac{1}{\sqrt{25}}\\d=\frac{3}{5}}[/tex]
Hence, the distance between the parallel lines is [tex]\frac{3}{5}}[/tex].
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A. The measure of the angle can not be determined B. 70 degreesC. 110 degreesD. 180 degrees
Okay, here we have this:
Considering the provided graph, we are going to find the measure of the angle "3", so we obtain the following:
Since angle 3 and 4 form a straight angle, that is to say that these two angles are supplementary, then we have:
[tex]\begin{gathered} m\angle3+m\angle4=180 \\ m\angle3+70=180 \\ m\angle3=180-70 \\ m\angle3=110\text{ degre}es \end{gathered}[/tex]Finally we obtain that the correct answer is the option C.
A) 14x + 7y > 21 B) 14x + 7y < 21 C) 14x + 7y 5 21 D) 14x + 7y 221match with graph
As all the options are the same equation
so, we need to know the type of the sign of the inequality
As shown in the graph
The line is shaded so, the sign is < or >
The shaded area which is the solution of the inequaity is below the line
So, the sign is <
So, the answer is option B) 14x + 7y < 21
Which equation is equivalent to - 2x + 5 - 3x = 5x + 25?A. -5 = -30B. -6x + 5 = 5x + 25C. - 10x = 20D. 20x - 5 = 25
In order to determine which is the equivalent equation, simplify the given expression:
-2x + 5 - 3x = 5x + 25 simplify like terms left side
-2x - 3x + 5 = 5x + 25
-5x + 5 = 5x + 25 subtract 5x both sides and subtract 5 both sides
-5x - 5x = 25 - 5 simplify both sides
-10x = 20
Hence,the equivalent expression is -10x = 20
A line passes through the point (-2,-7) and has a slope of 4
Answer:
y= 4x +1
Step-by-step explanation:
The equation of a line, in slope-intercept form, is given by y= mx +c, where m is the slope and c is the y-intercept.
Given that the slope is 4, m= 4.
Substitute m= 4 into y= mx +c:
y= 4x +c
To find the value of c, substitute a pair of coordinates the line passes through.
When x= -2, y= -7,
-7= 4(-2) +c
-7= -8 +c
c= -7 +8
c= 1
Substitute the value of c into the equation:
Thus, the equation of the line is y= 4x +1.
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1. flight 1007 will hold 300 passengers the airline has booked 84% of the plane already. How many seats are open for the last-minute Travelers?2.Carly interviewed students to ask their favorite kind of television programs. 12 students claimed that they preferred comedies, 18 like drama 13 enjoy documentaries, and 7 voted for news programs what percentage of the students selected comedies?
The total passengers in the flight is P=300.
Determine the passenger who booked the seat in the flight.
[tex]\begin{gathered} Q=\frac{84}{100}\cdot300 \\ =252 \end{gathered}[/tex]The number of seats booked by passenger is 252.
Determine the seats available for last-minutes travelers.
[tex]\begin{gathered} S=300-252 \\ =48 \end{gathered}[/tex]So 48 seats available for the last minute travelers.
Point P is in the interior of
∵ m< OZQ = m[tex]\because m\angle OZP=62[/tex]Substitute the measures of the given angles in the equation above
[tex]\therefore125=62+m\angle PZQ[/tex]Subtract 62 from both sides
[tex]\begin{gathered} \therefore125-62=62-62+m\angle PZQ \\ \therefore63=m\angle PZQ \end{gathered}[/tex]The measure of angle PZQ is 63 degrees
The half-life of radium is 1690 years. If 70 grams are present now, how much will be present in 570 years?
Solution
Given that
Half life is 1690 years.
Let A(t) = amount remaining in t years
[tex]\begin{gathered} A(t)=A_0e^{kt} \\ \\ \text{ where }A_{0\text{ }}\text{ is the initial amount} \\ \\ k\text{ is a constant to be determined.} \\ \end{gathered}[/tex]SInce A(1690) = (1/2)A0 and A0 = 70
[tex]\begin{gathered} \Rightarrow35=70e^{1690k} \\ \\ \Rightarrow\frac{1}{2}=e^{1690k} \\ \\ \Rightarrow\ln(\frac{1}{2})=1690k \\ \\ \Rightarrow k=\frac{\ln(\frac{1}{2})}{1690} \\ \\ \Rightarrow k=-0.0004 \end{gathered}[/tex]So,
[tex]A(t)=70e^{-0.0004t}[/tex][tex]\Rightarrow A(570)=70e^{-0.0004(570)}\approx55.407\text{ g}[/tex]Therefore, the answer is 55.407 g
What is the solution to the following equation?x^2+3x−7=0
Answer:
Explanation:
Given the equation:
[tex]x^2+3x-7=0[/tex]On observation, the equation cannot be factorized, so we make use of the quadratic formula.
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]Comparing with the form ax²+bx+c=0: a=1, b=3, c=-7
Substitute these values into the formula.
[tex]x=\dfrac{-3\pm\sqrt[]{3^2-4(1)(-7)}}{2\times1}[/tex]We then simplify and solve for x.
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2. Luis hizo una excursión de 20 km 75 hm 75 dam 250 m en tres etapas. En la primera recorrió 5 km 5 hm, y en la segunda 1 km 50 dam más que en la anterior. ¿Cuánto recorrió en la tercera etapa? Expresa el resultado de forma compleja
solve for x. then find the missing piece(s) of the parallelogram for #7
Let us find the angles of the parallelogram below
[tex]\begin{gathered} 2x+30 \\ x=40 \\ 2(40)+30 \\ 80+30 \\ 110^0 \end{gathered}[/tex][tex]\begin{gathered} 2x-10 \\ 2(40)-10 \\ 80-10 \\ 70^0 \end{gathered}[/tex]Theorem+: opposite angles of a parallelogram are the same
Hence the angles of the parallelogram are 110, 70, 110, and 70
17. 19yd. 28in.- 16yd. 31in.18. 61wk. 4da.- 18wk. 6da.21. 8tbsp. 2tsp. * 15
We need to solve the next expressions:
17. 19yd. 28in.- 16yd. 31in
We need to solve subtract each expression.
Then:
19yd. 28in.- 16yd. 31in =
19yd - 16yd and 28in-31in
3yd -3in
Then, we have the next equivalent.
1 yard = 36 in
So:
36 in - 3 in = 33 in
Therefore
19yd. 28in.- 16yd. 31in = 2 yard 33
18 61wk. 4da.- 18wk. 6da.
We need to subtract both expression:
Then
61wk - 18wk = 43kw
4da-6da = -2da
Where 1 week = 7 days
Then
7 da - 2da = 5 da
Hence, 43kw -1 wk = 42 wk.
The result is:
42 wk 5 da
21. 8tbsp. 2tsp. * 15
We need to convert 2ts into tbsp and then multiply the result by 15.
If
1 tsp ------- 0.333tbsp
Then
2tp ------ 2(0.333tbsp)= 0.66666 tbsp
Now
(8tbsp + 0.6666 ) * 15 = 130 tbsp
4 Use the sequence below to complete each task. -6, 1, 8, 15, ... a. Identify the common difference (a). b. Write an equation to represent the sequence. C. Find the 12th term (a) our Wilson (All Things Algebral. 2011 Enter your answer(s) here
we have
-6, 1, 8, 15, ...
so
a1=-6
a2=1
a3=8
a4=15
a2-a1=1-(-6)=7
a3-a2=8-1=7
a4-a3=15-8=7
so
the common difference is
d=7
Part 2
write an equation
we have that
The equation of a general aritmetic sequence is equal to
an=a1+(n-1)d
we have
d=7
a1=-6
substitute
an=-6+(n-1)7
an=-6+7n-7
an=7n-13
Part 3
Find 12th term
we have
n=12
a12=-7(12)-13
a12=71
a group orders three large veggie pizzas each slice represents eighth of an entire Pizza the group eats 3/4 of a piece of how many slices of pizza are left
1 pizza contain 8 slices, so we can state a rule of three as:
[tex]\begin{gathered} 1\text{ Pizza ------ 8 slices} \\ \frac{3}{4}\text{ pizza ------ x} \end{gathered}[/tex]then, x is given by
[tex]x=\frac{(\frac{3}{4})(8)}{1}\text{ slices}[/tex]which gives
[tex]\begin{gathered} x=\frac{3}{4}\times8 \\ x=\frac{3\times8}{4} \\ x=3\times2 \\ x=6\text{ slices} \end{gathered}[/tex]that is, 3/4 of pizza is equivalent to 6 slices. So, there are 8 - 6 = 2 slices left of one pizza.
However, they bought 3 large pizzas and ate almost one of them. So, there are 2x8 = 16slices plus 2 slices, that is, 18 slices are left.
The sum of 19 and twice a number
Answer:
2x+19
Step-by-step explanation:
Let x be the number
2x+19
(9 •10^9)•(2•10)^-3)
First, let's distribute the exponent -3 for 2 and ten, like this:
[tex]\begin{gathered} 9\times10^9\times(2\times10)^{-3}^{} \\ 9\times10^9\times2^{-3}\times10^{-3} \end{gathered}[/tex]Now, we can apply the next property when we have a number raised to a negative power:
[tex]a^{-b}=\frac{1}{a^b}[/tex]Then:
[tex]\begin{gathered} 9\times10^9\times2^{-3}\times\frac{1}{10^3} \\ 9\times2^{-3}\times\frac{10^9}{10^3} \end{gathered}[/tex]And when we have a division of the same number raised to different powers we can apply:
[tex]\frac{a^b}{a^c}=a^{b-c}[/tex]then:
[tex]\begin{gathered} 9\times2^{-3}\times\frac{10^9}{10^3} \\ 9\times2^{-3}\times10^{9-3} \\ 9\times2^{-3}\times10^6 \\ 9\times\frac{1}{2^3}^{}\times10^6 \end{gathered}[/tex]Now, as we know, having 10 raised to 6 means that we are multiplying ten by ten 6 times, when we do this we get:
[tex]10\times10\times10\times10\times10\times10=1000000[/tex]And with 2 raised to three we get:
[tex]2\times2\times2=8[/tex]Then we have:
[tex]\begin{gathered} 9\times\frac{1}{8^{}}^{}\times1000000 \\ \frac{9\times1000000}{8^{}}^{} \\ \frac{9000000}{8^{}}^{} \\ \frac{4500000}{4}^{}=11250000 \end{gathered}[/tex]I need help with this practice I am new to this subject of mathematics (algebra) Can you show me how to solve this STEP-BY-STEP?
Given:
[tex]4+x+8=24[/tex]Required:
To find the correct one.
Explanation:
The given quation is:
4 + x +8 =24
Subtract 8 on both sides
4 + x +8 - 8 = 24 -8
4 + x = 16
Final Answer:
Thus the first option is the correct answer.
An equation is incorrectly solved below.Equation: 2x+3=-4step 1: 2x+3-3=-4-3step 2: 2x=-1step 3: 2x/2=-1/2step 4: x=-1/2What is the first step that shows an error in the solution of the Equation? A. Step 1B. Step 2C. Step 3D. Step 4
To find the step where the error was made, we are going to correctly solve the equation:
[tex]2x+3=-4[/tex]We need to solve for x, first we subtract 3 from each side:
[tex]\begin{gathered} 2x+3-3=-4-3 \\ 2x=-7 \end{gathered}[/tex]We divide by 2 each side:
[tex]\begin{gathered} \frac{2x}{2}=\frac{-7}{2} \\ x=-\frac{7}{2} \end{gathered}[/tex]The first step that shows an error in the solution of the equation is the Step 2, because when we have two negative numbers, we add them, we do not subtract them.
Answer: B. Step 2
Drag the curve to the correct location on the graph. A small museum opened in 2004 with 80 pieces of art in its collection. In 2005, the number of pieces of art in the collection was 1.2 times the initial number of pieces of art. Then, in 2006, the number of pieces of art in the collection was 1.2 times the size of the previous year's collection. The directors of the museum plan to continue acquiring pieces of art at the same rate. Complete the graph of this relationship. 1207 ces of Art f(x) 3001 240 180 120
The most appropriate choice for geometric series will be given by
The equation is [tex]y = 80 (1.2)^x[/tex] and it is a geometric function.
What is geometric series ?
The series in which the ratio between consecutive terms of the series are same is called geometric series
For example, 2, 4, 8, 16, ... is a geometric series in which ratio between two consecutive terms is 2.
Number of pieces of art in 2004 = 80
Number of pieces of art in 2005 = [tex]80 \times 1.2[/tex]
Number of pieces of art in 2006 = [tex]80\times (1.2)^2[/tex]
Number of pieces of art after x years from 2004 = [tex]80 \times (1.2)^x[/tex]
The equation is [tex]y = 80 (1.2)^x[/tex]
This is a geometric function
The graph has been attached here.
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What is the length of the dotted line in the diagram below? Round to the
nearest tenth.
Answer:
12.1 units
Step-by-step explanation:
Percents build on one another in strange ways. It would seem that if you increased a number by 5% and thenincreased its result by 5% more, the overall increase would be 10%.7. Let's do exactly this with the easiest number to handle in percents.(a) Increase 100 by 5%(b) Increase your result form (a) by 5%.(C) What was the overall percent increase of the number 100? Why is it not 10%?
Answer:
a) 105
b) 110.25
c) Increase of 10.25%. It is not 100% because the second increase of 5% is over the first increased value, not over the initial value.
Step-by-step explanation:
Increase and multipliers:
Suppose we have a value of a, and want a increse of x%. The multiplier of a increase of x% is given by 1 + (x/100). So the increased value is (1 + (x/100))a.
(a) Increase 100 by 5%
The multiplier is 1 + (5/100) = 1 + 0.05 = 1.05
1.05*100 = 105
(b) Increase your result form (a) by 5%.
1.05*105 = 110.25
(C) What was the overall percent increase of the number 100? Why is it not 10%?
110.25/100 = 1.1025
1.1025 - 1 = 0.1025
Increase of 10.25%. It is not 100% because the second increase of 5% is over the first increased value, not over the initial value.
1. describe the end behavior. 2. determine whether it represents an odd degree or an even degree function.3. state the number of real zeroes
1. Quadratic curve
2. Odd degree function
3. TWO REAL ZEROS
Jan is looking at a mapof Roaring River. The map wascreated using the scale 1 inch :25 miles. If the river is 5.5inches long on the map, then itis actuallymiles long.
The map of Roaring River shows1 inch to be an equivalent of 25 miles. If therefore, the river is shown as 5.5 inches long on the map;
[tex]\begin{gathered} \text{Scale; 1 inch=25 miles} \\ 5.5\text{ inches=25 x 5.5 miles} \\ 5.5\text{ inches=137.5miles} \end{gathered}[/tex]The river is "actually" 137.5 miles long
Please answer last oneTo graph F using a graphing utility…Either A,B,C, or DLet me know which option
We have to graph the function F(x) defined as:
[tex]F(x)=\frac{x^2-11x-12}{x+6}[/tex]We can graph it as:
To see the complete graph we have to show the horizontal axis from x = -30 to x = 30 and the vertical axis from y = -80 to y = 80.
Answer: Option B
Add the rational expression as indicated be sure to express your answer in simplest form. By inspection, the least common denominator of the given factor is
Notice that the least common denominator is 9*2=18, therefore:
[tex]\begin{gathered} \frac{x-3}{9}+\frac{x+7}{2}=\frac{2(x-3)}{9\cdot2}+\frac{9(x+7)}{9\cdot2}, \\ \frac{x-3}{9}+\frac{x+7}{2}=\frac{2x-6}{18}+\frac{9x+63}{18}, \\ \frac{x-3}{9}+\frac{x+7}{2}=\frac{2x-6+9x+63}{18}, \\ \frac{x-3}{9}+\frac{x+7}{2}=\frac{11x+57}{18}\text{.} \end{gathered}[/tex]Answer:
[tex]\frac{x-3}{9}+\frac{x+7}{2}=\frac{11x+57}{18}\text{.}[/tex]Write an equation of variation to represent the situation and solve for the missing information The time needed to travel a certain distance varies inversely with the rate of speed. If ittakes 8 hours to travel a certain distance at 36 miles per hour, how long will it take to travelthe same distance at 60 miles per hour?
The time needed to travel a certain distance varies inversely with the rate of speed, so:
[tex]\begin{gathered} let\colon \\ t=\text{time} \\ v=\text{rate of speed} \\ t\propto\frac{1}{v} \end{gathered}[/tex]8hours----------------------------->36mi/h
xhours----------------------------->60mi/h
[tex]\begin{gathered} \frac{8}{x}=\frac{36}{60} \\ \text{ Since the it varies inversely:} \\ \frac{8}{x}=(\frac{36}{60})^{-1} \\ \frac{8}{x}=\frac{5}{3} \\ \text{solve for x:} \\ x=\frac{3\cdot8}{5} \\ x=4.8h \end{gathered}[/tex]4.8 hours or 4 hours and 48 minutes
Consider the following statement:
If Paul is older than Bill and Fred is younger than Bill, then Bill's age is between Paul's and Fred's.
Write the Given statement
Paul is the oldest and Fred is the youngest of the three.
What is mean by younger?Younger is a comparative adjective that generally indicates more youthful.
Similar to old, elder simply indicates older in age. It is a comparative version of old.
Given that x is a natural number, let Bill's age equal x years.
Paul's age is thus calculated as (x + a) Years, where an is any positive integer.
Fred is also younger than Bill.
So, Fred's age is equal to x - k, where k is any positive integer.
As a result, if we arranged Fred, Bill, and Paul's ages, they would be
Bill, Fred, and Paul
x-k < x < x+a
As a result, we can conclude that Paul is the oldest and Fred is the youngest of the three.
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Find the domain of the function f(x)=√100x²
The domain of the function √(100x²) will be (-∞,∞) as the definition of domain states that the set of inputs that a function will accept is known as the domain of the function in mathematics.
What is domain?The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the set of values it can take as input.
What is function?A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
Here,
The function is √(100x²).
The domain would be (-∞,∞).
The set of inputs that a function will accept is known as the domain of the function in mathematics, and the domain of the function √(100x²) will be (-∞,∞), according to the definition of domain.
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Hi dear how do I get to know you and
Given the picture, we have:
Enclosed area: A = x*y
Fence Length: F= 2x+y