We have a direct proportionality between y and x.
If "k" is the constant of proportionality, the equation for this situation is:
[tex]y=kx[/tex]To find the constant of proportionality, we solve that equation for k:
[tex]k=\frac{y}{x}[/tex]And since when y=45, x=180, substituting these values to find k:
[tex]\begin{gathered} k=\frac{45}{180} \\ k=0.25 \end{gathered}[/tex]Now, we substitute the value of k into the equation of proportionality:
[tex]y=0.25x[/tex]And in this equation, we can substitute any value of the variables, and find the value of the other variable.
In this case, we have y=90, so we substitute that value and solve for x:
[tex]\begin{gathered} 90=0.25x \\ \frac{90}{0.25}=x \\ 360=x \end{gathered}[/tex]Answer: when y=90, x=360
What is the measure of EDH?EHFO 10°O 40°50°90
To find the measure of angle EDH we must solve for x first. Formulating an equation to find x, we have:
5x + 4x= 90 (Given that the sum of the angles EDH and HDG is equal to 90°)
9x = 90 (Adding like terms)
x= 90/9 (Dividing on both sides of the equation by 9)
x= 10
Replacing in the expression for angle EDH, we have:
m∠EDH = 5*(x) = 5*(10) = 50° (Multiplying)
The answer is m∠EDH =50°.
Solve and graph on a number line. 2(x-1) 4 or 2 (x-1)>4
The given inequality is:
2 (x - 1
Find the area of the circle. Use 3.14 or 227for π . thxQuestion 2
Step 1
State the area of a circle using the diameter
[tex]\frac{\pi d^2}{4}[/tex]Where d=diameter=28in
[tex]\pi=\frac{22}{7}[/tex]Step 2
Find the area
[tex]A=\frac{22}{7}\times\frac{28^2}{4}=616in^2[/tex]Answer;
[tex]Area\text{ = }616in^2\text{ when }\pi\text{ =}\frac{22}{7}[/tex]The profit of a cell-phone manufacturer is found by the function y= -2x2 + 108x + 75 , where x is the cost of the cell phone. At what price should the manufacturer sell the phone tomaximize its profits? What will the maximum profit be?
Hello!
First, let's rewrite the function:
[tex]y=-2x^2+108x+75[/tex]Now, let's find each coefficient of it:
• a = -2
,• b = 108
,• c = 75
As we have a < 0, the concavity of the parabola will face downwards.
So, it will have a maximum point.
To find this maximum point, we must obtain the coordinates of the vertex, using the formulas below:
[tex]\begin{gathered} X_V=-\frac{b}{2\cdot a} \\ \\ Y_V=-\frac{\Delta}{4\cdot a} \end{gathered}[/tex]First, let's calculate the coordinate X by replacing the values of the coefficients:[tex]\begin{gathered} X_V=-\frac{b}{2\cdot a} \\ \\ X_V=-\frac{108}{2\cdot(-2)}=-\frac{108}{-4}=\frac{108}{4}=\frac{54}{2}=27 \end{gathered}[/tex]So, the coordinate x = 27.
Now, let's find the y coordinate:[tex]\begin{gathered} Y_V=-\frac{\Delta}{4\cdot a} \\ \\ Y_V=-\frac{b^2-4\cdot a\cdot c}{4\cdot a} \\ \\ Y_V=-\frac{108^2-4\cdot(-2)\cdot75}{4\cdot(-2)} \\ \\ Y_V=-\frac{11664+600}{-8}=\frac{12264}{8}=1533 \end{gathered}[/tex]The coordinate y = 1533.
Answer:
The maximum profit will be 1533 (value of y) when x = 27.
Help me with my schoolwork what is the slope of line /
The two points given on the line are
[tex]\begin{gathered} (x_1,y_1)\Rightarrow(-2,9) \\ (x_2,y_2)\Rightarrow(6,1) \end{gathered}[/tex]The slope of line that passes through (x1,y1) and (x2,y2) is gotten using the formula below
[tex]\begin{gathered} m=\frac{\text{change in y}}{\text{change in x}} \\ m=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{1-9}{6-(-2)} \\ m=-\frac{8}{6+2} \\ m=-\frac{8}{8} \\ m=-1 \end{gathered}[/tex]Therefore,
The slope of the line = -1
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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can I please getsome help with this question here, I can't really figure out how to find side PQ
SOLUTION
The following diagram will help us solve the problem
(a) From the diagram, the height of the parallelogram is given as TR, and it is 40 mm
Now we can use the area which is given to us as 3,600 square-mm to find the base of the parallelogram, which is PQ
So,
[tex]\begin{gathered} \text{Area }of\text{ a parallelogram = base}\times height \\ So\text{ } \\ 3600=PQ\times TR \\ 3600=PQ\times40 \\ 3600=40PQ \\ \text{dividing by 40, we have } \\ \frac{3600}{40}=\frac{40PQ}{40} \\ PQ=90 \end{gathered}[/tex]Hence PQ is 90 mm
(b) Now, note that the side
[tex]PS=QR[/tex]So, we will find QR
Also, since we have PQ, we can find TQ, that is
[tex]\begin{gathered} PQ=PT+TQ \\ 90=60+TQ \\ TQ=90-60 \\ TQ=30mm \end{gathered}[/tex]Note that triangle QRT is a right-angle triangle, and QR is the hypotenuse or the longest side
From pythagoras
[tex]\text{hypotenuse}^2=opposite^2+adjacent^2[/tex]So,
[tex]\begin{gathered} QR^2=TR^2+TQ^2 \\ QR^2=40^2+30^2 \\ QR^2=1600+900 \\ QR^2=2,500 \\ QR=\sqrt[]{2,500} \\ QR=50mm \end{gathered}[/tex]Now, since
[tex]\begin{gathered} PS=QR \\ \text{then } \\ PS=50mm \end{gathered}[/tex]Hence PS is 50 mm
Find the sum of the arithmetic series given a1 =2, an =35 an n = 12
Given:
[tex]a_1=2,a_n=35,n=12[/tex]Required:
Find the sum of the arithmetic series.
Explanation:
The sum of the arithmetic series when the first and the last term is given by the formula.
[tex]S_n=\frac{n}{2}(a_1+a_n)[/tex]Substitute the given values in the formula.
[tex]\begin{gathered} S_n=\frac{12}{2}(2+35) \\ =6(37) \\ =222 \end{gathered}[/tex]Final Answer:
Option D is the correct answer.
An airplane is taking off at angle of 9 degrees and traveling at a speed of 200 feet per second in relation to the ground. If the clouds begin at an altitude of 4,000 feet, how many seconds will it take for the airplane to be in the clouds?
ANSWER
[tex]\begin{equation*} 127.85\text{ }seconds \end{equation*}[/tex]EXPLANATION
First, let us make a sketch of the problem:
To find the time it will take the airplane to be in the clouds, we first have to find the distance flown by the airplane in attaining that height, x.
To do this, apply trigonometric ratios SOHCAHTOA for right triangles:
[tex]\sin9=\frac{4000}{x}[/tex]Solve for x:
[tex]\begin{gathered} x=\frac{4000}{\sin9} \\ x=25,569.81\text{ }ft \end{gathered}[/tex]Now, that we have the distance, we can solve for the time by applying the relationship between speed and distance:
[tex]\begin{gathered} speed=\frac{distance}{time} \\ \Rightarrow time=\frac{distance}{speed} \end{gathered}[/tex]Substitute the given values into the formula above and solve for time:
[tex]\begin{gathered} time=\frac{25569.81}{200} \\ time=127.85\text{ }seconds \end{gathered}[/tex]That is the number of seconds that it will take.
why does a cubic graph have both an x intercept and a y intercept
Answer:
All cubic function has domain (-∞,∞) and range (-∞,∞)
Step-by-step explanation:
3/5 ÷ 1/3 = ?????????
Change the division sign to multiplication and then invert 1/3
That is;
[tex]\frac{3}{5}\times3[/tex][tex]=\frac{9}{5}\text{ =1}\frac{4}{5}[/tex]Some airlines charge a fee for each checked luggage item that weighs more than 21,000 grams. How many kilograms is this?
The value of 21,000 grams to kilograms is 21 kilograms
How to convert kilograms to grams ?1000 grams = 1kg
The first step is to convert 21,000 grams to kilograms
It can be calculated as follows;
= 21000/1000
= 21
Hence the value of 21,000 grams in kilograms is 21 kilograms
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i need help, plotting the ordered pair (0, 0.5) and I need to state in which quadrant or on which axis the point lies.
The ordered pair:
[tex](x,y)=(0,0.5)[/tex]it is located at:
Since the point lies on the y-axis it doesn't not lie in any quadrant
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]Which of these would not produce a representative sample that determines the favoritesport of the students at the local high school?ask every tenth student from a list of names in the student directoryask every tenth student who arrives at school on Wednesdayask ten students wearing football jerseys each day for a weekask five students from each classroom chosen by picking numbersMy Progress >
Answer: ask ten students wearing football jerseys each day for a week
This sample wouldn't b representative because, the use of a footblla
match the system of equations with the solution set.hint: solve algebraically using substitution method.A. no solutionB. infinite solutionsC. (-8/3, 5)D. (2, 1)
We will solve all the systems by substitution method .
System 1.
By substituting the second equation into the first one, we get
[tex]x-3(\frac{1}{3}x-2)=6[/tex]which gives
[tex]\begin{gathered} x-x+6=6 \\ 6=6 \end{gathered}[/tex]this means that the given equations are the same. Then, the answer is B: infinite solutions.
System 2.
By substituting the first equation into the second one, we have
[tex]6x+3(-2x+3)=-5[/tex]which gives
[tex]\begin{gathered} 6x-6x+9=-5 \\ 9=-5 \end{gathered}[/tex]but this result is an absurd. This means that the equations represent parallel lines. Then, the answer is option A: no solution.
System 3.
By substituting the first equation into the second one, we obtain
[tex]-\frac{3}{2}x+1=-\frac{3}{4}x+3[/tex]by moving -3/4x to the left hand side and +1 to the right hand side, we get
[tex]-\frac{3}{2}x+\frac{3}{4}x=3-1[/tex]By combining similar terms, we have
[tex]-\frac{3}{4}x=2[/tex]this leads to
[tex]x=-\frac{4\times2}{3}[/tex]then, x is given by
[tex]x=-\frac{8}{3}[/tex]Now, we can substitute this result into the first equation and get
[tex]y=-\frac{3}{2}(-\frac{8}{3})+1[/tex]which leads to
[tex]\begin{gathered} y=4+1 \\ y=5 \end{gathered}[/tex]then, the answer is option C: (-8/3, 5)
System 4.
By substituting the second equation into the first one, we get
[tex]-5x+(2x-3)=-9[/tex]By combing similar terms, we have
[tex]\begin{gathered} -3x-3=-9 \\ -3x=-9+3 \\ -3x=-6 \\ x=\frac{-6}{-3} \\ x=2 \end{gathered}[/tex]By substituting this result into the second equation, we have
[tex]\begin{gathered} y=2(2)-3 \\ y=4-3 \\ y=1 \end{gathered}[/tex]then, the answer is option D
Given the conversion factor which cube has the larger surface area?
Given the surface area of a cube as
[tex]\begin{gathered} SA=6l^2 \\ \text{where l is the length} \end{gathered}[/tex]Given Cubes A and B
[tex]\begin{gathered} \text{Cube A} \\ l=19.5ft \end{gathered}[/tex][tex]\begin{gathered} \text{Cube B } \\ l=6m\text{ } \\ \text{ in ft}\Rightarrow\text{ 1m =3.28ft} \\ l=6\times3.28ft=19.68ft \end{gathered}[/tex]Find the surface area of the cubes and compare them to know which one is larger
[tex]\begin{gathered} \text{Cube A} \\ SA=6\times19.5^2=6\times380.25=2281.5ft^2 \end{gathered}[/tex][tex]\begin{gathered} \text{Cube B} \\ SA=6\times19.68^2=6\times387.3024=2323.8144ft^2 \end{gathered}[/tex]Hence, from the surface area gotten above, Cube B has a larger surface area than Cube A
name the three congruent parts shown by the marks on each drawing
In this case the aswer is very simple. .
The congruent parts are the equal parts in the 2 triangles.
Therefore, the congruent parts would be:
1. side AB and side XY
2. ∠ A and ∠ X
3. side AC and side XZ
That is the solution. .
The function is defined by h(x) = x - 2 . Find h(n + 1) .
SOLUTION:
Case: Functions
Method:
The function
[tex]\begin{gathered} h(x)=x-2 \\ Hence \\ h(n+1)=(n+1)-2 \\ h(n+1)=n+1-2 \\ h(n+1)=n-1 \end{gathered}[/tex]Final answer:
[tex]h(n+1)=n-1[/tex]A half-marathon has 53 runners. A first-, second-, and third-place trophy will be awarded. Howmany different ways can the trophies be awarded?
Let's use the combination formula:
[tex]\begin{gathered} C(n,k)=nCk=\frac{n!}{k!(n-k)!} \\ n=53 \\ k=3 \\ C(53,3)=53C3=\frac{53!}{3!(50)!}=23426 \end{gathered}[/tex]hannah paid 15.79 for a dress that was originally marked 24.99 what js the percent of discount
The percentage of discount is 37%
Here, we want to calculate the percentage of discount
The first thing we need to do here is to calculate the discount amount
Mathematically, we have this as;
[tex]24.99-15.79\text{ = 9.2}[/tex]Now, we find the percentage of 24.99 is this discount
We have this as;
[tex]\frac{9.2}{24.99}\text{ }\times100\text{ \% = 36.8\%}[/tex]The percentage of discount is approximately 37%
“Use the properties to rewrite this expression with the fewest terms possible:3+7(x - y) + 2x - 5y”
Expanding 7(x - y) in the above expression gives
[tex]-5y^{}+2x+7x-7y+3[/tex]adding the like terms (2x+ 7x) and (-5y-7y) gives
[tex](-5y-7y)+(2x+7x)+3[/tex][tex]\rightarrow\textcolor{#FF7968}{-12y+8x+3.}[/tex]The last expression is the simplest form we can convert our expression into.
If TW =6, WV =2, and UV =25, find XV to the nearest hundredth.
TW = 6
WV = 2
UV = 25
XV = ?
XV/UV = WV/TV
XV/25 = 2 /(6 + 2)
XV = 2(25)/7
XV = 50/7
XV = 7.1428
Rounded to the nearest hundredth
XV = 7.14
A psychology test has personality questions numbered 1, 2, 3, intelligence questions numbered 1, 2, 3, 4, and attitudequestions numbered 1,2. If a single question is picked at random, what is the probability that the question is an intelligence question OR has an odd number?
Answer:
7/9.
Step-by-step explanation?
Total number of questions: 3 + 4 + 2 = 9.
Number of Intelligence questions: 4
Number of questions that have an odd number: 5
The probability of a question is Intelligence questions = 4/9
The probability a question has an odd number = 5/9
The probability a question is Intelligence questions and has an odd number = 2/9
The probability a question is Intelligence question OR has an odd number is:
4/9 + 5/9 - 2/9 = 7/9.
The function f(x) = 40(0.9)^x represents the deer population in a forest x years after it was first studied. What was the deer population when it was first studied?a. 44b.40c. 36d.49
We are given the function that models a deer population:
[tex]f(x)=40(0.9)^x[/tex]Where x is the years since the study started. If we want to know the initial population, we want to find the population at x = 0 years.
Thus:
[tex]f(0)=40(0.9)^0=40\cdot1=40[/tex]The correct answer is option b. 40
Use the Binomial Theorem to expand the expression.(x +6)^3
ok
[tex]\begin{gathered} (x+6)^3=^{}x^3+3(x)^2(6)+3(x)(6)^2+6^3 \\ \text{ = x}^3+18x^2\text{ + 3(36)x + 216} \\ \text{ = x}^3+18x^2\text{ + 108x + 216} \end{gathered}[/tex][tex]\begin{gathered} (a+b)^3\text{ } \\ first\text{ term = a} \\ \text{second term = b} \\ \text{theorem } \\ (a+b)^3=a^3+3a^2b+3ab^2+b^3 \end{gathered}[/tex]that is the rule
just identify a and b in your problem
a = x
b = 6
Substitute in the theorem, and simplify
One ton (2,000 pounds) is equivalent to 907 kilograms. A baby elephant weighs about 91 kilograms atbirth. Approximately how many pounds (lbs.) is this?A 200 lbs.B 400 lbs.C 600 lbs.D 1,000 lbs.
Since 2000 pounds = 907 kilograms, use the conversion factor:
[tex]\frac{2000\text{ pounds}}{907\operatorname{kg}}[/tex]To find out what 91 kg are equal to, measured in pounds:
[tex]91\operatorname{kg}=\frac{2000\text{ pounds}}{907\operatorname{kg}}=\frac{91\cdot2000}{907}\text{ pounds =200.66 pounds}[/tex]Therefore, a baby elephant weighs about 200 lbs.
What is the average rate of change from g(1) to g(3)?Type the numerical value for your answer as a whole number, decimal or fractionMake sure answers are completely simplified
The average rate of change from g(1) to g(3)
[tex]\frac{g(x)_3-g(x)_1}{X_3-X_1}_{}[/tex]where
[tex]g(x)_3=-20,g(x)_1=-8,x_3=3,x_1=\text{ 1}[/tex][tex]\begin{gathered} =\frac{-20\text{ --8}}{3-1}\text{ = }\frac{-20\text{ +8}}{2} \\ =\frac{-12}{2} \\ -6 \end{gathered}[/tex]Hence the average rate of change is -6
Raphael has an odd-shaped field shown in Figure 13-2. He wants to put a four-strand barbed wire fence around it for his cattle.A. What is the perimeter of the field?b. How many 80-rod rolls of barbed wire does he need topurchase?c. How many acres will be fenced?
Answer: Total perimeter = 9, 962.01 feet
The figure is a composite structure
It contains a rectangle and triangle
The perimeter of a rectangle is given as
Perimeter = 2( length + width)
length of the rectangle = 1500ft
Width of the rectangle = 1390 ft
Perimeter = 2( 1500 + 1390)
Perimeter = 2(2890)
Perimeter = 5780 ft
To calculate the perimeter of a triangle
[tex]\begin{gathered} \text{Perimeter = a + b + }\sqrt[]{a^2+b^2} \\ a\text{ = 1050ft and b = 1390 ft} \\ \text{Perimeter = 1050 + 1390 + }\sqrt[]{1050^2+1390^2} \\ \text{Perimeter = 2440 + }\sqrt[]{1,102,\text{ 500 + 1, 932, 100}} \\ \text{Perimeter = 2400 + }\sqrt[]{3,034,600} \\ \text{Perimeter = 2440 + 1,742,01} \\ \text{Perimeter = }4182.01\text{ f}eet \end{gathered}[/tex]The total perimeter of the field = Perimeter of the rectangle + perimeter of the right triangle
Total perimeter = 5780 + 4182.01
Total perimeter = 9, 962.01 feet
Which representation does not show y as a function of x?1.II.€9> 10III.x 1 3 5 7y -6 -18 -30 -42IV. {(-2,3), (-1,4), (0,4), (3, 2)}a) I and IIb) I, II, and IIIc) I and IVd) All of the above are functions
We can say that I is not a function because inputs can only have one output.
II it's not a function since if you draw an horizontal line through the function intersect in two points, then it's not a function.
The answer is A.