To find the coordinates of the midpoint of HX, we would apply the midpoint formula which is expressed as
[tex]\text{Midpoint = }\lbrack\frac{(x1\text{ + x2)}}{2},\text{ }\frac{(y1\text{ + y2)}}{2}\rbrack[/tex]From the information given,
[tex]\begin{gathered} x1\text{ = 4}\frac{1}{2}\text{ = 4.5, x2 = 2}\frac{3}{4}=\text{ 2.75} \\ y1\text{ = -4}\frac{1}{2}=-4.5,\text{ }y2=-2\frac{1}{4}=\text{ - 2.25} \\ \text{Midpoint = }\lbrack\frac{(4.5\text{ + 2.75)}}{2},\text{ }\frac{(-4.5\text{ - 2.25)}}{2}\rbrack \\ \text{Midpoint = (3.625, - 3.375)} \end{gathered}[/tex]The measures of the angles of a triangle are shown in the figure below. Solve for x.
44°
61°
(8x+11)°
Ninas math classroom is 6 and 4/5 meters long and 1 and 3/8 meters wide. What is the area of the classroom?
The most appropriate choice for area of rectangle will be given by -
Area of classroom = [tex]4\frac{27}{40}[/tex] [tex]m^2[/tex]
What is area of rectangle?
Rectangle is a four sided figure whose parallel sides are equal and whose every angle is 90°
The total space taken by the rectangle is called area of the rectangle.
If the length of the rectangle be l and the breadth of the rectangle be b, then area of the rectangle is given by
Area = [tex]l \times b[/tex]
Here,
Length of classroom = [tex]6\frac{4}{5}[/tex] m = [tex]\frac{34}{5}[/tex] m
Width of classroom = [tex]1\frac{3}{8}[/tex] m = [tex]\frac{11}{8}[/tex] m
Area of classroom = [tex]\frac{34}{5} \times \frac{11}{8}[/tex]
= [tex]\frac{187}{40}[/tex]
= [tex]4\frac{27}{40}[/tex] [tex]m^2[/tex]
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the length of a rectangle is 11 yd more than twice the width and the area of the rectangle is 63 yd squared. find the dimensions of the rectangle.
the length of a rectangle is 11 yd more than twice the width and the area of the rectangle is 63 yd squared. find the dimensions of the rectangle.
Let
L ------> the lenght
W ----> the width
we know that
the area of rectangle is
A=L*W
A=63 yd2
63=L*W -------> equation 1
and
L=2W+11 ------> equation 2
substitute equation 2 in equation 1
63=(2W+11)*w
2W^2+11w-63=0
solve the quadratic equation using the formula
a=2
b=11
c=-63
substitute
[tex]w=\frac{-11\pm\sqrt[]{11^2-4(2)(-63)}}{2(2)}[/tex][tex]\begin{gathered} w=\frac{-11\pm\sqrt[]{625}}{4} \\ \\ w=\frac{-11\pm25}{4} \\ \end{gathered}[/tex]the solutions for W are
w=3.5 and w=-9 (is not a solution, because is negative)
so
Find the value of L
L=2W+11 -------> L=2(3.5)+11
L=18
therefore
the dimensions are
Length is 18 yardsWidth is 3.5 yardsSimplify [tex]{({4e}^{ - 8x})}^{0.5} [/tex]with no negative exponents. thanks!
Explanation
Given the following expression
[tex]\begin{gathered} \text{Simplify (4 }e^{-8x})^{\frac{1}{2}} \\ \text{This expression can be written as} \\ (4\cdot\text{ }e^{-8x})^{\frac{1}{2}} \\ \text{Splitting the expression, we can have the below expression} \\ (4)^{\frac{1}{2}}\cdot(^{}e^{-8x})^{\frac{1}{2}} \\ \text{According to the law of indicies} \\ x^{\frac{1}{2}}\text{ = }\sqrt[]{x} \\ \text{Hence, we have the following expression} \\ \sqrt[]{4\text{ }}\cdot\text{ (}e^{-8x\cdot\text{ }\frac{1}{2}}) \\ 2\cdot\text{ }e^{-4x} \\ 2e^{-4x} \\ \text{Therefore, the simplified form is 2}e^{-4x} \\ \frac{2}{e^{4x}} \end{gathered}[/tex]I need a math wiz to explain this to me, are you a math wiz?
SOLUTION
The questions is outside scope
P is inversely proportional to Q. If P = 24 when Q = 3, then write the inverse variation equation that relates P and Q.
Inverse proportionality is when the value of one quantity increases with respect to a decrease in another, they behave opposite in nature.
It is represented by the following expression:
[tex]P=\frac{k}{Q}[/tex]Since P=24 when Q=3, we can substitute and solve for the constant k:
[tex]\begin{gathered} 24=\frac{k}{3} \\ k=24\cdot3 \\ k=72 \end{gathered}[/tex]Then, the equation that represents the inverse variation would be:
[tex]P=\frac{72}{Q}[/tex]9.5.35 Assigned Media An architect designs a rectangular flower garden such that the width is exactly two-thirds of the length. If 300 feet of antique picket fencing are to be used to enclose the garden, find the dimensions of the garden What is the length of the garden? The length of the garden is
Answer:
• The dimensions of the garden are 90 feet by 60 feet.
,• The length of the garden is 90 feet.
Explanation:
Let the length of the garden = l
The width is exactly two-thirds of the length, Width = (2/3)l
If 300 feet of antique picket fencing are to be used to enclose the garden, this means that the perimeter of the proposed garden is 300 feet.
[tex]\begin{gathered} \text{Perimeter}=2(\text{Length}+\text{Width)} \\ 300=2(l+\frac{2}{3}l) \end{gathered}[/tex]Next, solve the equation for the length, l:
[tex]\begin{gathered} \frac{300}{2}=l+\frac{2}{3}l \\ 150=\frac{5l}{3} \\ l=150\times\frac{3}{5} \\ l=90\text{ feet} \end{gathered}[/tex]The length of the garden is 90 feet.
Next, we determine the width.
[tex]\begin{gathered} \text{Width}=\frac{2}{3}l \\ =\frac{2}{3}\times90 \\ =2\times30 \\ =60\text{ feet} \end{gathered}[/tex]The dimensions of the garden are 90 feet by 60 feet.
Solve the following system of equation using substitution4x + 2y = 10x - y= 13What is the solution for y?
ANSWER
y = -7
EXPLANATION
To solve using the substitution method we have to clear x from one of the equations as a function of y. For example, for equation 2:
[tex]x=13+y[/tex]Then replace x in the first equation by this expression:
[tex]4(13+y)+2y=10[/tex]And solve for y:
[tex]\begin{gathered} 4\cdot13+4y+2y=10 \\ 52+6y=10 \\ 6y=10-52 \\ 6y=-42 \\ y=\frac{-42}{6} \\ y=-7 \end{gathered}[/tex]What is the product of V3 and 7V30 in simplest radical form?
Determine the product of two expressions.
[tex]\begin{gathered} \sqrt[]{3}\times7\sqrt[]{30}=7\sqrt[]{30\cdot3} \\ =7\sqrt[]{3\cdot3\cdot10} \\ =7\cdot3\sqrt[]{10} \\ =21\sqrt[]{10} \end{gathered}[/tex]So answer is,
[tex]21\sqrt[]{10}[/tex]Solve the system by graphing:2x – y= -14x - 2y = 6Solution(s):
To find the solution of the system by graphing we need to plot each line in the plane and look for the intersection.
First we need to write both equations in terms of y:
[tex]\begin{gathered} y=2x+1 \\ y=2x-3 \end{gathered}[/tex]now we need to find two points for each of this lines. To do this we give values to the variable x and find y.
For the equation 2x-y=-1, if x=0 then:
[tex]y=1[/tex]so we have the point (0,1).
If x=1, then:
[tex]y=3[/tex]so we have the point (1,3).
Now we plot this points on the plane and join them with a straight line.
Now we look for two points of the second equation.
If x=0, then:
[tex]y=-3[/tex]so we have the point (0,-3)
If x=1, then:
[tex]y=-1[/tex]so we have the point (1,-1).
We plot the points and join them wiith a line, then we have:
once we have both lines in the plane we look for the intersection. In this case we notice that the lines are parallel; this means that they wont intersect.
Therefore the system of equations has no solutions.
Hi, could you help me figure out why I got 8 points off in this problem?
In triangle PQR
Construction: Draw PX perpendicular to QR where x lies on QR
Since:
PX perpendicular to QR
In the 2 triangles PXQ and PXR
given
proved up
PX = PX ------- common side in the 2 triangles
Triangle PXQ congruent to triangle PXR by the AAS theorem of congruency
As a result of congruency
PQ = PR ------- proved
Which expression is equivalent to 8 - (-5) ?O 8+50 -8 +(-5)O 8+-5O -5 +8
Answer:
The first option is correct
[tex]8+5[/tex]Explanation:
[tex]\begin{gathered} 8--5 \\ \\ 8+5 \\ \end{gathered}[/tex]Two negatives makes a positive.
The figure shows rectangle PQRS in the first quadrant of the coordinate plane?
The quadrants of a coordinate plane are:
Then, we can say that the rectangle PQRS is in the first quadrant.
- 2/3 (x+12)+2/3 x=-5/4 x+2
We will have the following:
[tex]-\frac{2}{3}(x+12)+\frac{2}{3}x=-\frac{5}{4}x+2\Rightarrow-\frac{2}{3}x-8+\frac{2}{3}x=-\frac{5}{4}x+2[/tex][tex]\Rightarrow-\frac{2}{3}x+\frac{2}{3}x+\frac{5}{4}x=2+8\Rightarrow\frac{5}{4}x=10[/tex][tex]\Rightarrow5x=40\Rightarrow x=8[/tex]So, the value of x is 8.
Let the graph of f(x) be given below. Find the formula of f(x), a polynomial function, of least degree.
To detrmine the formula of the polynomial, we check for the roots on the graph:
when y = 0, x = -2
when y = 0, x = 4
We have two roots.
x = -2
x + 2 = 0
x = 4
x - 4 = 0
3rd factor is x = 0
Hence, we have two factors: x(x + 2) and (x - 4)
The polynomial function using the factors:
[tex]f(x)\text{ = ax(x + 2)(x - 4)}[/tex]Next, we find the value of a:
To get a , we pick a point on the graph. let the point be (0, -4)
substitute the point in the function above:
[tex]\begin{gathered} f(x)\text{ = y = -4, x = 0} \\ -4\text{ = a(0 + 2) (0 - 4)} \\ -4\text{ = a(2)(-4)} \\ -4\text{ = -8a} \\ a\text{ = -4/-8} \\ a\text{ = 1/2} \end{gathered}[/tex]The formula of the polynomial becomes:
[tex]f(x)\text{ = }\frac{1}{2}x(x\text{ }+2)(x-4)[/tex]Use the formula for compound amount:$14,800 at 6% compounded semiannually for 4 years
SOLUTION
Given the question in the question tab, the following are the solution steps to answer the question.
STEP 1: Write the formula for calculating compound amount
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where
A = final compounded amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
STEP 2: Write the given data
Semiannually means that n will be 2
[tex]P=14,800,r=\frac{6}{100}=0.06,n=2,t=4[/tex]STEP 3: Calculate the compound amount
[tex]\begin{gathered} A=14800(1+\frac{0.06}{2})^{2\times4}\Rightarrow A=14800(1+0.03)^{2\times4} \\ A=14800(1.03)^8 \\ A=14800\times1.266770081 \\ A=\text{\$}18,748.1972 \end{gathered}[/tex]Hence, the compounded amount after 4 years is $18,748.1972
Earl Miller, a customer of J. Crew, will pay $400 for a new jacket. J. Crew has a 60% markup on selling price. What is the most that J. Crew can pay for this jacket?
If Earl Miller, a customer of J. Crew, will pay $400 for a new jacket. J. Crew has a 60% markup on selling price. The most that J. Crew can pay for this jacket is $160.
How to find the total payment?Given parameters:
Cost of new jacket = $400
Markup = 60%
Now let find the amount that was paid for the jacket using this formula
Amount = Cost of new jacket × ( 1- markup)
Let plug in the formula
Amount = $400 × ( 1 - .60 )
Amount = $400 × .40
Amount = $160
Therefore we can conclude that the amount of $160 was paid the most.
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Solve the following system of linear equations using elimination. x-y=5 -x-y=-11
Elimination Method : In the elimination method you either add or subtract the equations to get an equation in one variable. When the coefficients of one variable are opposites you add the equations to eliminate a variable and when the coefficients of one variable are equal you subtract the equations to eliminate a variable.
The given system of equation :
x - y = 5 ( 1 )
- x - y = - 11 ( 2 )
Add the equation ( 1 ) & ( 2 )
x - y + ( -x - y ) = 5 + ( -11 )
x - y -x - y = 5 - 11
x - x - y - y = -6
0 - 2y = - 6
y = -6/( -2)
y = 3
Substitute the value of y = 3 in the equation ( 1)
x - y = 5
x - 3 = 5
x = 5 + 3
x = 8
Answer : x = 8, y = 3
Passes through (8,8) with slope 11/6
Given:
point (8,8).
slope 11/6
The slope intercept form is,
[tex]y=mx+b[/tex]where m is the slope and b is the y-intercept.
we know that m=11/6 so subistute in the equation.
[tex]y=\frac{11}{6}x+b[/tex]Now, let us plug in the point in the equation to find the value of b that is the y-intercept.
[tex]undefined[/tex]How to solve this problem? (the answer is 262 Hz). i want to know the step by step on how to solve the equation given. if it helps, i am a grade 10 student. (YES, this is a MATH problem)
The frequency of middle C = 262 Hz
Explanation:The formula for calculating the frequency, F hertz, of a note n seminotes above the concert pitch is:
[tex]F\text{ = 440(}\sqrt[12]{2})^n[/tex]This can be re-written as:
[tex]F=440(2^{\frac{n}{12}})[/tex]Middle C is 9 semitones below the concert pitch
That is, n = -9
To find the frequency of middle C, substitute n = -9 into the equation for F
[tex]\begin{gathered} F=440(2^{\frac{-9}{12}}) \\ F\text{ = 440(}0.5946) \\ F\text{ = }261.62\text{ Hz} \\ F\text{ = 262 Hz (to the nearest hertz)} \end{gathered}[/tex]The frequency of middle C = 262 Hz
An elevator car starts on the second floor of a building 27 feet above the ground. The car rises 4.2 feet every second on its way up to the 15th floor. Assuming the car doesn’t slow down or make any stops , how long will it take the car to reach a height of 102 feet above the ground?
17.86 seconds
Explanation:The starting point of the elevator car = 27 feet above the ground
The endpoint point of the elevator car = 102 feet above the ground
The total distance traveled by the elevator car = 102 feet - 27 feet
The total distance traveled by the elevator car = 75 feet
Time taken by the elevator car to rise 4.2 feet = 1 second
Time taken by the elevator car to rise 75 feet = 75/4.2 seconds
Time taken by the elevator car to rise 75 feet = 17.86 seconds
Therefore, it takes the car 17.86 seconds to reach a height of 102 feet above the ground
James is putting a frame around a rectangular photograph. The photograph is 12 inches long
and 10 inches wide, and the frame is the same width all the way around. What will be the
area of the framed photograph? (Hint: use "x" as your variable.)
Polynomial:________
=_________
=_________
=_________final answer in standard form.
PLEASSEEEEEE i need know this asap
Answer:
The area is 4x² + 44x + 120Step-by-step explanation:
GivenDimensions of rectangle are 12 in and 10 in,Width of the frame is x.To find The area of the framed photographSolutionDimensions of the framed photograph are:
12 + 2x and 10 + 2xArea of the framed photograph is:
A = lwA = (12 + 2x)(10 + 2x) = 12*10 + 12*2x + 10*2x + 2x*2x = 120 + 24x + 20x + 4x²= 4x² + 44x + 120in a public opinion poll 624 people from a sample of 1100 indicated they would vote for specific candidate how many votes can the candidate expect to receive from a population of 40000
Hello!
In a sample of 1100 people, the specific candidate got 624 votes. So, we can write it as 624/1100.
And if the total of voters is 40,000, how many votes this specific candidate will receive? We can write it as x/40,000.
Now, let's equal both fractions look:
[tex]\begin{gathered} \frac{624}{1100}=\frac{x}{40000} \\ \\ 1100x=624\times40000 \\ 1100x=24960000 \\ x=\frac{24960000}{1100} \\ \\ x\cong22691 \end{gathered}[/tex]Answer:Approximately 22691 votes.
a company loses $5,400 as the result of manufacturing defect. each of the 8 owners have agreed to pay an equal amount, x, to pay for the loss. How much each owner paid?
Explanation:
If 'x' is the amount each owner will pay, there are 8 owners and the total amount to pay is $5,400 the equation to solve is:
[tex]8x=5,400[/tex]Solving for x:
[tex]x=\frac{5,400}{8}=675[/tex]Answer:
Each owner has to pay $675
4. The temperature in Baguio is 18.6℃, while Manila the temperature is 31.5℃. How much warmer is it in Manila than Baguio?A. 12.6℃B. 12.7℃C. 12.9℃D. 13℃
Given:
The temperature in Baguio is 18.6℃.
The temperature in manila is 31.5℃.
To find:
The differene bin temperature etween imanila and aguio.
Explanation:
The difference between manila and Baguio's temperature s
[tex]31.5^{\circ}C-18.6^{\circ}C=12.9^{\circ}C[/tex]Thus, manila is 12.9 degrees Celcius warmer than Baguio.
Final answer:
anila is 12.9 degrees Celcius warmer than Baguio.
Write the rate as a fraction in the simplest form $1680 for 8 weeks 236 miles on 12 gallons of gasoline
The question asked to write the rate as a fraction in simplest form
[tex]\text{ \$1,680 for 8 w}eeks[/tex]To write the above relation in a fraction, we will have
[tex]\begin{gathered} =\frac{1680}{8} \\ \end{gathered}[/tex]Dividing to the lowest term, we will have
[tex]\begin{gathered} =\frac{210}{1} \\ whichis\text{ \$210 for 1 we}ek \end{gathered}[/tex]The question asked to write the rate as a fraction in simplest form
[tex]236\text{ miles on 12 gallons of gasoline}[/tex]To write the above relation in a fraction, we will have
[tex]=\frac{236}{12}[/tex]To express as a fraction in its lowest terms will be
[tex]\begin{gathered} =\frac{59}{3} \\ \text{which represents 59 miles for 3 gallons} \end{gathered}[/tex]Please I really need help. I just need the answer no steps
Explanation
The question wants us to obtain the margin of error
A margin of error tells you how many percentages points your results will differ from the real population value.
The formula to be used is
To do so, we will have to list out the parameters to be used
[tex]\begin{gathered} standard\text{ deviation=}\sigma=13.8 \\ sample\text{ size=n=18} \\ confidence\text{ level=}\gamma=80\text{ \%} \end{gathered}[/tex]The next step will be to find the z-score value for a confidence level of 80%.
From the statistical table, we have
[tex]Z_{\gamma}=1.28[/tex]So, we can input the given data obtained into the formula
So we will have
[tex]\begin{gathered} MOE=1.28\times\sqrt{\frac{13.8^2}{18}} \\ \\ MOE=1.28\times\frac{13.8}{\sqrt{18}} \\ \\ MOE=1.28\times3.2527 \\ \\ MOE=4.16344 \end{gathered}[/tex]So the margin of error (M.E.) = 4.163 (To 3 decimal places)
what are the three terms and 4x - 2y + 3
Solution
We have the following expression:
[tex]4x-2y+3[/tex]Here we have 3 terms:
[tex]4x,\text{ -2y and 3}[/tex]Variable terms:
[tex]4x,-2y[/tex]Constant term
[tex]3[/tex]The diameter of a circle has endpoints P(-12, -4) and Q(6, 12).
ANSWER
[tex](x+3)^{2}+(y-4)^{2}=145[/tex]EXPLANATION
The equation of a circle is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex]where (h, k) = center of the circle
r = radius of the circle
The center of a circle is the midpoint of the endpoints of the diameter of the circle. Hence, to find the center of the circle, we have to find the midpoint of the diameter:
[tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]where (x1, y1) and (x2, y2) are the endpoints of the diameter.
Hence, the center of the circle is:
[tex]\begin{gathered} M=(\frac{-12+6}{2},\frac{-4+12}{2}) \\ M=(\frac{-6}{2},\frac{8}{2}) \\ M=(-3,4) \end{gathered}[/tex]To find the radius of the circle, we have to find the distance between any endpoint of the circle and the center of the circle.
To do this apply the formula for distance between two points:
[tex]r=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Therefore, the radius of the circle is:
[tex]\begin{gathered} r=\sqrt{(6-(-3))^2+(12-4)^2}=\sqrt{9^2+8^2} \\ r=\sqrt{81+64}=\sqrt{145} \end{gathered}[/tex]Hence, the equation of the circle is:
[tex]\begin{gathered} (x+3)^2+(y-4)^2=(\sqrt{145})^2 \\ (x+3)^2+(y-4)^2=145 \end{gathered}[/tex]Using the completing-the-square method, rewrite f(x) = x2 − 8x + 3 in vertex form. (2 points)
A) f(x) = (x − 8)2
B) f(x) = (x − 4)2 − 13
C) f(x) = (x − 4)2 + 3
D) f(x) = (x − 4)2 + 16
By using the completing the square method, f(x) = x² − 8x + 3 in vertex form is: B. f(x) = (x − 4)² − 13.
The vertex form of a quadratic equation.In this exercise, you're required to rewrite the given function in vertex form by using the completing the square method. Mathematically, the vertex form of a quadratic equation is given by this formula:
y = a(x - h)² + k
Where:
h and k represents the vertex of the graph.
In order to complete the square, we would have to add (half the coefficient of the x-term)² to both sides of the quadratic equation as follows:
f(x) = x² − 8x + 3
f(x) = x² − 8x + (8/2)² - 13
f(x) = x² − 8x + (4)² - 13
f(x) = x² − 8x + 16 - 13
f(x) = (x² − 8x + 16) - 13
f(x) = (x − 4)² − 13
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