The percentage increase is 50%
Here, we want to calculate the percentage increase or decrease
To know if it is a decrease or an increase, we use the following simple logic.
If new amount is greater than original amount, then it is an increase.
If new amout is less than original amount, then it is a decrease
For the first question, we can see that the new amount is greater than the old amount
This indicates an increase
Mathematically;
[tex]\text{percentage increase = }\frac{(new\text{ amount - original amount)}}{\text{old amount}}\text{ }\times\text{ 100 percent}[/tex]According to the first question, new amount = 45 while old amount = 30
so;
percentage increase = (45-30)/30 * 100%
= 15/30 * 100% = 100%/2 = 50%
If p(x) is a polynomial function where p(x) = 3(x + 1)(x - 2)(2x-5)a. What are the x-intercepts of the graph of p(x)?b. What is the end behavior (as x→ ∞, f(x)→?? and as x→ -∞, f (x)→ ??) of p(x))?c. Find an equation for a polynomial q(x) that has x-intercepts at -2, 3⁄4, and 7.
Hello there. To solve this question, we have to remember some properties about polynomial functions.
Given the polynomial function
[tex]p(x)=3(x+1)(x-2)(2x-5)[/tex]We want to determine:
a) What are the x-intercepts of the graph of p(x)?
For this, we have to determine the roots of the polynomial function p(x). In this case, we have to determine for which values of x we have
[tex]p(x)=0[/tex]Since p(x) is written in canonical form, we find that
[tex]p(x)=3(x+1)(x-2)(2x-5)=0[/tex]A product is equal to zero if at least one of its factors is equal to zero, hence
[tex]x+1=0\text{ or }x-2=0\text{ or }2x-5=0[/tex]Solving the equations, we find that
[tex]x=-1\text{ or }x=2\text{ or }x=\dfrac{5}{2}[/tex]Are the solutions of the polynomial equation and therefore the x-intercepts of p(x).
b) What is the end-behavior of p(x) as x goes to +∞ or x goes to -∞?
For this, we have to take the limit of the function.
In general, for polynomial functions, those limits are either equal to ∞ or -∞, depending on the degree of the polynomial and the leading coefficient.
For example, a second degree polynomial function with positive leading coefficient is a parabola concave up and both limits for the function as x goes to ∞ or x goes to -∞ is equal to ∞.
On the other hand, an odd degree function usually has an odd number of factors (the number of x-intercepts in the complex plane) hence the limits might be different.
In this case, we have a third degree polynomial equation and we find that, as the leading coefficient is positive and all the other factors are monoic, that
[tex]\begin{gathered} \lim_{x\to\infty}p(x)=\infty \\ \\ \lim_{x\to-\infty}p(x)=-\infty \end{gathered}[/tex]That is, it gets larger and larger when x is increasing arbitrarily, while it get smaller and smaller as x is decreasing.
c) To find the equation for a polynomial q(x) that has x-intercepts at -2, 3/4 and 7.
The canonical form of a polynomial of degree n with x-intercepts at x1, x2, ..., xn and leading coefficient equals a is written as
[tex]f(x)=a\cdot(x-x_1)(x-x_2)\cdots(x-x_n)[/tex]So in this case, there are infinitely many polynomials satisfying this condition. Choosing a = 1, we find that q(x) is equal to
[tex]\begin{gathered} q(x)=(x-(-2))\cdot\left(x-\dfrac{3}{4}\right)\cdot(x-7) \\ \\ \boxed{q(x)=(x+2)\cdot\left(x-\dfrac{3}{4}\right)\cdot(x-7)} \end{gathered}[/tex]These are the answers to this question.
(x+?)(x+3)=x squared+5x+6
The given expression is :
(x + ) (x + 3) = x² + 5x + 6
The polynomial is factorize and then written in the form of (x + ) (x + 3)
Let the missing number is "b" substitute in the equation and simplify :
(x + b ) (x + 3) = x² + 5x + 6
x² +bx + 3x + 3b = x² + 5x + 6
x² +x(b +3) + 3b = x² + 5x + 6
Comparing the constant term together :
3b = 6
Divide both side by 3
3b/3 = 6/3
b = 2
Since b is the missing term so, Missing term is 2
(x + 2 ) (x + 3) = x² + 5x + 6
Answer :(x + 2 ) (x + 3) = x² + 5x + 6
Let f(x) = 2x-1 and g(x) = x2 - 1. Find (f o g)(-7).
Answer: (f o g)(-7) = 95
Step by step solution:
We have the two functions:
[tex]\begin{gathered} f(x)=2x-1 \\ g(x)=x^2-1 \end{gathered}[/tex]We need to find (f o g)(-7) or f(g(-7)), first we evaluate g(-7):
[tex](f\circ g)(-7)=f(g(-7))[/tex][tex]g(-7)=-7^2-1=49-1=48[/tex]Now we evaluate f(48):
[tex]f(48)=2\cdot48-1=96-1=95[/tex]Solve for t. If there are multiple solutions, enter them as a
we have the equation
[tex]\frac{12}{t}+\frac{18}{(t-2)}=\frac{9}{2}[/tex]Solve for t
step 1
Multiply both sides by 2t(t-2) to remove fractions
[tex]\frac{12\cdot2t(t-2)}{t}+\frac{18\cdot2t(t-2)}{(t-2)}=\frac{9\cdot2t(t-2)}{2}[/tex]simplify
[tex]12\cdot2(t-2)+18\cdot2t=9\cdot t(t-2)[/tex][tex]24t-48+36t=9t^2-18t[/tex][tex]\begin{gathered} 60t-48=9t^2-18t \\ 9t^2-18t-60t+48=0 \\ 9t^2-78t+48=0 \end{gathered}[/tex]Solve the quadratic equation
Using the formula
a=9
b=-78
c=48
substitute
[tex]t=\frac{-(-78)\pm\sqrt[]{-78^2-4(9)(48)}}{2(9)}[/tex][tex]t=\frac{78\pm66}{18}[/tex]The solutions for t are
t=8 and t=2/3
therefore
the answer is
t=2/3,8
identify the terms ,coefficients constants in 5c2 + 7d
Algebraic expressions are compound by algebraic terms that are compound by a signed number or coefficient, one or more variables and one or more exponents.
In the given expression:
[tex]5c^2+7d[/tex]There are 2 terms which are 5c^2 and 7d, its coefficients are 5 and 7 respectively and there is not any constant, which are independent terms.
Scatter PlotWhich statement best describes the association betweenvariable X and variable Y?.moderate negative association. Perfect negative association. Moderate positive association. Perfect positive association
It's moderate negative association
what is the slope of a line perpendicular to this linewhat is the slope of a line parallel to this line
Answer:
• Slope perpendicular to the line: 8/5
,• Slope parallel to the line: –5/8
Explanation
Given
[tex]5x+8y=7[/tex]To know the result, it is better if we work with the slope-intercept form:
[tex]y=mx+b[/tex]Then, to get this kind of form we have to isolate y from the given equation:
[tex]8y=7-5x[/tex][tex]y=\frac{7-5x}{8}[/tex][tex]y=-\frac{5}{8}x+\frac{7}{8}[/tex]Thus, in this case, m = –5/8 and b = 7/8.
Perpendicular lines have negative reciprocal lines:
[tex]m_2=-\frac{1}{m_1}[/tex]where m₁ is the slope of line 1 and m₂ is the line perpendicular to line 1.
Then, replacing the values:
[tex]m_2=-\frac{1}{-\frac{5}{8}}[/tex][tex]m_2=\frac{8}{5}[/tex]Finally, the slopes of parallel lines are the same, meaning:
[tex]m_2=m_1[/tex]where m₁ is the slope of line 1 and m₂ is the line parallel to line 1.
the variable w varies inversely as the cube of v. if k is the constant of variation, which equation represents this situation?a: qv^=kb: q^3 v= kc: q/v^3=kd: q^3/v=k picture listed below
Solution
Given that:
[tex]\begin{gathered} q\propto\frac{1}{v^3} \\ \\ \Rightarrow q=\frac{k}{v^3} \\ \\ \Rightarrow k=qv^3 \end{gathered}[/tex]Option A.
I need help with my algebra
We have the next equation line:
[tex]3x-y\text{ = 5}[/tex]We need to solve the equation for y to get the equation form
[tex]-y\text{ =5-3x}[/tex]Multiply the equation by -1
[tex](-1)-y\text{ =(-1)(5-3x)}[/tex][tex]y\text{ = -5+3x}[/tex]Where the y-intercept is -5 and the slope is 3x.
To find the line parallel we need to know that the parallel lines have the same slope.
The parallel line also intercepts y at point (0,-7).
[tex]y=mx+b[/tex]Replace the slope=m = 3
and the y-intercept is -7.
So the parallel line is:
[tex]y=3x-7[/tex]what is the image of -3 -7 after a reflection over the x-axis
Given the point (-3, -7)
We need to find the image after a reflection over the x-axis
The rule of reflection over the x-axis is:
[tex](x,y)\rightarrow(x,-y)[/tex]So, the image of the given point will be:
[tex](-3,-7)\rightarrow(-3,7)[/tex]so, the answer is option D. (-3, 7)
Three cities, A, B, and C, are located so that city A is due east of city B. If city C is located 35° west of north from city B and is 100 miles from city A and 70 milesfrom city B, how far is city A from city B?City Ais 20 miles due east of city B.City A is 35 miles due east of city B.City A is 42 miles due east of city B.City A is 122 miles due east of city B.
Given:
City A is due east of city B.
City C is located 35° west of north from city B.
Distance between city C and city A is 100 miles.
Distance between city C and city B is 70 miles.
The objective is to find the distance between city A and city B.
The above situation can be represented as,
Thus the total angle of ∠B = 90°+35° = 125°.
Now the measure of angle A can be calculated by law of sines.
[tex]\begin{gathered} \frac{AC}{\sin B}=\frac{BC}{\sin A} \\ \frac{100}{\sin125\degree}=\frac{70}{\sin A} \\ \sin A=70\cdot\frac{\sin 125\degree}{100} \\ \sin A=0.573 \\ A=\sin ^{-1}(0.573) \\ A\approx35\degree \end{gathered}[/tex]By the angle sum property of triangle the value of angle C can be calculated as,
[tex]\begin{gathered} \angle A+\angle B+\angle C=180\degree \\ 35\degree+125\degree+\angle C=180\degree \\ \angle C=180\degree-35\degree-125\degree \\ \angle C=20\degree \end{gathered}[/tex]Now, the distance between A and B can be calculated by,
[tex]\begin{gathered} \frac{AB}{\sin C}=\frac{BC}{\sin A} \\ \frac{AB}{\sin20\degree}=\frac{70}{\sin 35\degree} \\ AB=\sin 20\degree\cdot\frac{70}{\sin 35\degree} \\ AB\approx42\text{ miles} \end{gathered}[/tex]Thus, the distance of city A is 42 miles due east of city B.
Hence, option (C) is the correct answer.
two parallel lines are intersected by a transversal one angle is 100 degrees, more info on the picture
Obtuse angles (90°–180°) are those that fall within this range. Right angles are those that have a 90 degree angle ( = 90°). Straight angles are those that have a 180 degree ( = 180°) angle.
Explain about the obtuse angle?Any angle more than 90 degrees is deemed obtuse: A straight angle is one with a 180° measurement. A zero angle is one with a measurement of 0°: Angles with measures that add up to 90 degrees are said to be complementary angles: Angles with measures that add up to 180° are referred to as supplementary angles.
We now understand that an obtuse angle is one that is greater than 90 degrees but less than 180 degrees. Obtuse angle examples include 110°, 135°, 150°, 179°, 91°, and more. As a result, all angles between 90° and 180° are obtuse angles.
Hence obtuse angle is one of the angle which is not correct 100 degree angle
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The first three terms of a sequence are given. Round to the nearest thousandth (if necessary). 6 36 1, 5' 25 . Find the 10th term
The first three terms of a sequence are given. Round to the nearest thousandth (if necessary)
1, 6/5, 36/25, Find the 10th term
__________________________________________________________________
1, 6/5, 36/25
(6/5)^(n-1)
n= 1
(6/5)^(1-1) = (6/5)^0 = 1
n= 2
(6/5)^(2-1) = (6/5)^1 = 6/5
n= 3
(6/5)^(3-1) = (6/5)^2 = 36/25
_______________________
n= 10
(6/5)^(10-1) = (6/5)^9 = 5. 1598
_______________________
Answer
Round to the nearest thousandth
The 10th term is 5.160
what is the substitution for f7=3(x)^2+2(x)-9
Given a function f(x), whenever you want to evaluate the function, you simply change the variable for the value you where you want to evaluate the function at, and then perform the mathematical operations the function tells you to do.
In our case f(x) = 3x^2 + 2x -9
If we evaluate f(x) at x=7, then
[tex]f(7)=3(7)^2+2(7)\text{ -9 = 3 }\cdot\text{ 49 + 2}\cdot\text{ 7 - 9 = 152}[/tex]So f(7) = 152.
Given that events A and B are independent with P(A) = 0.08 and P(B) = 0.25,determine the value of P(A and B), rounding to the nearest thousandth, ifnecessary.
To find: P(AandB)
P(AandB)=P(A)*P(B)
P(AandB)=0.08*0.25
P(AandB)=0.02
Thus the required answer is 0.02
Determine whether the ratios are equivalent.
2:3 and 24:36
O Not equivalent O Not equivalent
We can conclude that the given ratios 2:3 and 24:36 are equivalent.
What are ratios?A ratio in math displays how many times one number is contained in another. The ratio of oranges to lemons, for instance, is eight to six if there are eight oranges and six lemons in a bowl of fruit. The proportions of oranges to the total amount of fruit are 8:14 for oranges and 6:8 for lemons, respectively.So, ratios are equivalent or not:
2:3 and 24:362/3 = 24/362/3 = 2/3 (Divide by 12)Then, 2:3 :: 2:3
Therefore, we can conclude that the given ratios 2:3 and 24:36 are equivalent.
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A number divisible by 2, 5 and 10 if the last digit is _______.
A. An even number
B. O
C. 0 or 5
D. An odd number
Answer :- B) 0
Only a number ending with the digit 0 is divisible by 2,5 and 10
Example :-
20 ÷ 2 = 10
20 ÷ 5 = 4
20 ÷ 10 = 2
Here, 20 is the number that ends with 0.
R'Find the composition of transformationsthat map APQR to APQ'R'.QT RRotate [?] degrees aboutthe origin and then translate(unit(s) [ ].90180
For a transformation like the one shown in the graph, note that the points have switched as follows;
[tex]P(x,y)\Rightarrow P^{\prime}(-y,x)[/tex]This is a 90 degree anticlockwise rotation about the origin.
That means point P would now be translated as follows;
[tex]\begin{gathered} P(1,1)\Rightarrow P^{\prime}(-1,1) \\ Q(2,1)\Rightarrow Q^{\prime}(-1,2) \\ R(2,3)\Rightarrow R^{\prime}(-3,2) \end{gathered}[/tex]After this rotation, the coordinates have now moved from their position one unit upwards. That now makes the final coordinates;
[tex]undefined[/tex]A rocket is shot off from a launcher. The accompanying table represents the height of the rocket at given times, where x is time, in seconds, and y is height, in feet. Write a quadratic regression equation for this set of data, rounding all coefficients to the nearest tenth. Using this equation, find the height, to the nearest foot, at a time of 3.8 seconds.
Given
The data can be modeled using a quadratic regression equation.
Using the general form of a quadratic equation:
[tex]y=ax^2\text{ + bx + c}[/tex]We should use a regression calculator to obtain the required coefficients. The graph of the equation is shown below:
The coefficients of the equation is:
[tex]\begin{gathered} a\text{ = -17.5 (nearest tenth)} \\ b\text{ = }249.0\text{ (nearest tenth)} \\ c\text{ = }-0.5 \end{gathered}[/tex]Hence, the regression equation is:
[tex]y=-17.5x^2\text{ + 249.0x -0.5}[/tex]We can find the height (y) at a time of 3.8 seconds by substitution:
[tex]\begin{gathered} y=-17.5(3.8)^2\text{ + 249}(3.8)\text{ - 0.5} \\ =\text{ }693 \end{gathered}[/tex]Hence, the height at time 3.8 seconds is 693 ft
4(y – 4) = 8 O A. -2 O B. 2 0 C. 4 D. 6
To find the value of y
4(y – 4) = 8
Divide both-side of the equation by 4
y - 4 = 2
Add 4 to both-side of the equation
y = 2 + 4
y = 6
D is the correct option
Graph the following inequality.Note: To graph the inequality:Select the type of line below (solid or dashed).Plot two points on the line.Click on the side that should be shaded.
Given:
[tex]-4x-y>2[/tex]Consider the line,
[tex]-4x-y=2[/tex]Find the points on the line,
[tex]\begin{gathered} x=0 \\ -4(0)-y=2\Rightarrow y=-2 \\ x=1 \\ -4(1)-y=2\Rightarrow y=-6 \\ x=-1 \\ -4(-1)-y=2\Rightarrow y=2 \end{gathered}[/tex]The graph of the line is,
Now, find the region for inequality.
Consider any point from the right and the left side of the line and check which side satisfies the inequality.
[tex]\begin{gathered} R=(2,0) \\ -4x-y>2 \\ -4(2)-0=-8\text{ >2 is not true.} \end{gathered}[/tex]And,
[tex]\begin{gathered} L=(-2,0) \\ -4x-y>2 \\ -4(-2)-0=8>2\text{ is true} \end{gathered}[/tex]Therefore, the graph of the inequality is,
Note that inequality does not contain boundary points.
Can someone help me with this geometry question?A.Triangular prismB.Hexagonal prismC.Triangular pyramidD.Hexagonal pyramid
B. Hexagonal Prism
1) One prism is defined, in terms of naming it by the base.
2) Counting the edges of the base in this net surface, we can tell that this is a Hexagonal Prism for the base is a hexagon.
Determine the minimum and maximum value for f(x) = -5x²-3x+7 over interval [-1, 3].
The maximum and minimum value of the equation "f(x) = -5x²-3x+7" over the interval [-1, 3] is 5 and -47.
What are equations?A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation. A number that can be entered for the variable to produce a true number statement is the solution to an equation. 3(2)+5=11, which states that 6+5=11, is accurate. The answer is 2, then. The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.So, the minimum and maximum values when x are -1 and 3:
(1) When x = -1:
f(x) = -5x²-3x+7f(x) = -5(-1)²-3(-1) +7f(x) = -5(1) + 3 +7f(x) = -5 + 10f(x) = 5(2) When x = 3:
f(x) = -5x²-3x+7f(x) = -5(3)² -3(3)+7f(x) = -5(9) -9 +7f(x) = -45 -9 +7f(x) = - 54 + 7f(x) = - 47Therefore, the maximum and minimum value of the equation "f(x) = -5x²-3x+7" over the interval [-1, 3] is 5 and -47.
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In a survey of 200 college students it is found that:61 like cooking32 like reading73 like video games19 like both cooking and reading23 like cooking and video games92 like reading or video games6 like all 3 hobbiesa. How many do not like any of these hobbiesb how many like reading onlyc how many like reading and video gamesd how many do not like cooking or video games
Given:
The number of total students = 200
The number of students like cooking = 61
The number of students who like reading = 32
The number of students who like both cooking and reading= 19
The number of students who like video games = 73
The number of students who like cooking and video games= 23
The number of students who like reading and video games = 92
The number of students who like all 3 hobbies = 6
Required:
(a)
Graph the solution set of each system of inequalities. Graph the solution set of each sx+2y ≤ 63x- 4y < 2
Given:
[tex]\begin{gathered} x+2y\le6\ldots\text{ (1)} \\ 3x-4y<2\ldots(2) \end{gathered}[/tex]We have to take the value of x as zero and to find the value of y in bothe the equations to plot the graph.
By taking the value of x as zero in the first equation,
[tex]\begin{gathered} 2y\le6 \\ y\le3 \end{gathered}[/tex]By taking the value of y as zero in the first equation,
[tex]x\le6[/tex]By taking the value of x as zero in the second equation,
[tex]\begin{gathered} -4y<2 \\ -2y<1 \\ y>-\frac{1}{2} \end{gathered}[/tex]By taking the value of y as zero in the second equation,
[tex]\begin{gathered} 3x<2 \\ x<\frac{2}{3} \end{gathered}[/tex]Plot the Trapezoid ABCD with vertices A(-8,-4),B(-5, -1), C(0, -2), and D(-4,-8) in the x-axis.
Let's begin by listing out the information given to us:
ABCD is a trapezoid
A (-8, -4); B (-5, -1); C (0, -2); D (-4, -8)
We will proceed to plotting this points on a Cartesian plane, we have:
The following are the distances (in miles) to the nearest airport for 13 families.10, 13, 15, 15, 20, 26, 27, 28, 30, 32, 34, 37, 39Notice that the numbers are ordered from least to greatest.Give the five-number summary and the interquartile range for the data set.
We have the next given set for distances (in miles) to the nearest for 13airport families:
10, 13, 15, 15, 20, 26, 27, 28, 30, 32, 34, 37, 39
The minimum is the least number value. Then:
Minimum =10
In this case, we have 13 data, so :
- The middle number is the median:
10, 13, 15, 15, 20, 26, 27, 28, 30, 32, 34, 37, 39
Now, the lower quartile is given by the next equation:
[tex]=(n+1)\ast\frac{1}{4}[/tex]Replacing:
[tex]\begin{gathered} =(13+1)\ast\frac{1}{4} \\ =14\ast\frac{1}{4} \\ =3.5=4 \end{gathered}[/tex]The lower quartile is in the fourth position:
Lower quartile = 15
The upper quartile is given by the next equation:
[tex]\begin{gathered} =(n+1)\ast\frac{3}{4} \\ =(13+1)\ast\frac{3}{4} \\ =10.5=11 \end{gathered}[/tex]The upper quartile is located in the 11th position:
Upper quartile = 34
The interquartile range is given by:
IQR=upper quartile - lower quartile
IQR=34-15
The interquartile range =19
A school debate team has 4 girls and 6 boys. A total of 4 of the team members will be chosen top participate in the district debate. What is the probaility that 2 girland 2 boys will be selected?
The probability that 2 girls and 2 boys are selected is given by:
[tex]P(\text{ 2 boys, 2 girls })=\frac{4C2\times6C2}{10C4}=\frac{6\times15}{210}=\frac{3}{7}[/tex]Therefore, the correct choice is option D) 3/7.
Please help me don't understand
Answer:
x=13
Step-by-step explanation:
50+3x=89
89-50=3x
39=3x
13=x
A population of a certain species of bird is 22,000 animals and is decreasing by 700 birds per year..Write an equation for y, the population at time t (in years), representing the situation.y= How many birds are in the population after 7 years?
We can solve that problem using a linear function, we know that
[tex]y=mx+y_0[/tex]Where y0 is the initial population and m is the rate of decreasing, we know that for each "x" years we have -700 birds, therefore
[tex]y=-700x+22000[/tex]Let's use t instead of x
[tex]y=-700t+22000[/tex]That's the equation that represents the population at time t
[tex]\begin{gathered} y=-700t+22000\text{ \lparen t = 7\rparen} \\ \\ y=-700\cdot(7)+22000 \\ \\ y=-4900+22000 \\ \\ y=17100 \end{gathered}[/tex]Therefore after 7 years, the population will be 17100 birds.
