ANSWER
$1690000
EXPLANATION
A realtor sold 3 homes during her first month.
The average house price was $120,000.
During her second month, she sold 7 homes, at an average house price of $190,000.
We want to find the overall house price.
To do this, we must first state that average is gotten by adding up the data and dividing by the sum of data.
That is:
[tex]\text{Average = }\frac{Sum\text{ of data}}{Number\text{ of data}}[/tex]Therefore, for the first month:
[tex]\begin{gathered} 120000=\frac{Sum}{3} \\ \text{Cross multiply:} \\ \text{Sum = 120000 }\cdot\text{ 3} \\ \text{Sum = \$360000} \end{gathered}[/tex]The total price of houses in the first month is $360000
For the second month:
[tex]\begin{gathered} 190000=\frac{Sum}{7} \\ \text{Cross multiply:} \\ \text{Sum = 7 }\cdot\text{ 190000} \\ \text{Sum = \$1330000} \end{gathered}[/tex]The total price of houses in the second month is $1330000
Therefore, the total price of houses in both months is:
Total Sum = $360000 + $1330000
Total Sum = $1690000
The overall house price is $1690000.
Suppose the graph of a parent function f(x) is shifted to the left 1 unit, reflected vertically over the x-axis, and then shifted up three units. What equation models the transformed graph?o y = f (x - 1) + 3o y = -f (x- 1) + 3o y = f (x + 1) + 3o y = -f (x + 1) + 3
If it is shifted to the left by 1 unit, the function becomes:
[tex]y=f(x+1)[/tex]It is reflected vertically over the x-axis; the function becomes:
[tex]y=-f(x+1)[/tex]It is, then, shifted up 3units, thus we have:
[tex]y=-f(x+1)+3[/tex]Hence, the correct option is option D
When answering the question please use a areal model so I can completely understand! thank you in advance!
Using area model
Therefore,
[tex]5(6x-2)=30x-10[/tex]the expression 35+45x represents a trains distance in miles from a terminal after x hours of travel how far was the train from the terminal at the beginning of the journey1. 35mi2. 45mi3. 10mi4. 80mi
The expression is that of distance
The expression is
[tex]35+45x[/tex]x is the time in hours
We want the distance of the train from the terminal at the beginning of the journey.
This means at time = 0
We will plug in x = 0 and find the distance at the beginning.
Thus,
[tex]\begin{gathered} 35+45(0)_{} \\ 35+0 \\ =35 \end{gathered}[/tex]The train's distance was 35 miles from the terminal at the beginning of the journey
The correct answer is (1.)
A camera is originally $150 The store gives a discount and the camera is now priced at $112.50 Write the percentage discount for the camera
We are asked to determine the percentage of discount if the price for an item goes from $150 to $112.50. To do that we will use the following relationship:
[tex]150-\frac{150x}{100}=112.5[/tex]Where "x" is the percentage of the discount.
Now we solve for "x" first by subtracting 150 from both sides:
[tex]-\frac{150x}{100}=112.5-150[/tex]Solving the operations:
[tex]-\frac{150x}{100}=-37.5[/tex]Now we multiply both sides by 100:
[tex]\begin{gathered} -150x=-37.5\times100 \\ -150x=-3750 \end{gathered}[/tex]Now we divide both sides by -150:
[tex]x=-\frac{3750}{-150}[/tex]Solving the operations:
[tex]x=25[/tex]Therefore, the percentage of the discount is 25%.
A recent survey asked high school student their favorite type of music. The results are shown in the circle graph. Find the measure of arc FBD
Determine the measure of arc FBD.
[tex]\begin{gathered} \text{arc FBD=}360-arcFED \\ =360-(32+47) \\ =281 \end{gathered}[/tex]Si measure of arc FBD is 281
*Image of Graph and everything for this question in Jpeg image The tennis club is selling water bottles and hats to raise money for a tennis tournament. A water bottle costs $4 and a hat costs $6. The club wants to raise $1,200. 1. Write a linear equation that describes the problem.2. Graph the linear equation. Make sure to label both axes with appropriate titles. 3. Use the graph to approximate how many hats the tennis club must sell if it sells 150 water bottles are sold.
15.
Given:
The cost of a water bottle = $4.
The cost of a hat = $ 6.
The total amount = $ 1,200.
Aim :
We need to find the linear equation for the given model.
Explanation:
Let x be the number of water bottles.
Let y be the number of hats.
The cost of the x number of water bottles = x time 4.
The cost of the x number of water bottles = 4x.
The cost of the y number of hats = y times 6.
The cost of the y number of hats = 6y.
Addition of 4x and 6y = the total amount
[tex]4x+6y\text{ =1200}[/tex]Answer:
The linear equation is
[tex]4x+6y\text{ =1200}[/tex]16.
Aim:
We need to graph the line equation.
Set x =0 and substitute in the eqaution to find the value of y at x =0.
[tex]4(0)+6y\text{ =1200}[/tex][tex]6y\text{ =1200}[/tex]Divide both sides of the equation by 6.
[tex]\frac{6y}{6}=\frac{1200}{6}[/tex][tex]y=200[/tex]We get the point (0,200).
Set x =150 and substitute in the eqaution to find the value of y at x =150.
[tex]4\times150+6y\text{ =1200}[/tex][tex]600+6y\text{ =1200}[/tex]Subtract 600 from both sides of the equation.
[tex]600+6y-600=1200-600[/tex][tex]6y=600[/tex]Dividing both sides of the equation by 6.
[tex]\frac{6y}{6}=\frac{600}{6}[/tex][tex]y=100[/tex]We get the point (150,100).
Mark the points (0,200) and (150,100) on the graph and join them by ray.
The graph of the line equation is
17.
The number of water bottles that sold = 150.
From the graph, we get the point (150,100).
The number of hats =100.
Robyn invests $1500 at 4.85% compounded quarterly. Write an equation to represent the amount of money A she will have in tyears.
The amount of money A after t years, with a rate r, an initial investment P and a number of times n that the interest is compounded per year, is:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]If the initial investment is $1500, the rate is 4.85% anually compounded quarterly (n=4), then:
[tex]\begin{gathered} A=1500(1+\frac{4.85/100}{4})^{4t} \\ =1500(1+\frac{4.85}{400})^{4t} \end{gathered}[/tex]Therefore, the amount of money that she will have after t years, is:
[tex]A=1500(1+\frac{4.85}{400})^{4t}[/tex]Express the relation below as a graph i’m really having trouble some assistance would be nice thank you
Given: Table of values of x and y
To Plot the graph of the table given
The coordinate to plotted are
[tex]\begin{gathered} (-6,5) \\ (-5,4) \\ (2,-1) \end{gathered}[/tex]The third point is as shown below
Joining the lines give us
A marble is drawn randomly from a jar that contains 5 purple marbles, 2 blue balls, and 3 pink marbles. Find the probability of randomly selecting
Let's begin by identifying key information given to us:
Jar contains: 5 purple marbles, 2 blue balls, and 3 pink marbles
Total number of marbles = 5 + 2 + 3 = 10 marbles
Purple marbles = 5, Blue marbles = 2, Pink marbles = 3
[tex]P=\frac{No.\text{ of specific marbles colour}}{\text{Total number of marbles}}[/tex]Probability of selecting randomly without replacement:
a) Purple marble
[tex]\begin{gathered} P(P)=\frac{No.\text{ of purple marbles}}{\text{Total number of marbles}} \\ P(P)=\frac{5}{10}=0.5 \\ P(P)=0.5\text{ or 50\%} \end{gathered}[/tex]b) Blue marble
[tex]\begin{gathered} P(B)=\frac{No.\text{ of blue marbles}}{\text{Total number of marbles}} \\ P(B)=\frac{2}{10}=0.2 \\ P(BP)=0.2\text{ or 20\%} \end{gathered}[/tex]c) Pink marble
[tex]\begin{gathered} P(pi)=\frac{No.\text{ of pink marbles}}{\text{Total number of marbles}} \\ P(pi)=\frac{3}{10}=0.3 \\ P(pi)=0.3\text{ or 30\%} \end{gathered}[/tex]find the measure of PR given rectangle pqrs round answer to the nearest whole number
We can draw the following picture:
where we can see that triangle PSR is a right one. Then, we can apply Pytagorean theorem to find PR:
[tex](2.6)^2+4^2=PR^2[/tex]then, PR is given by
[tex]PR=\sqrt[]{(2.6)^2+4^2}[/tex]which gives
[tex]\begin{gathered} PR=\sqrt[]{6.76+16} \\ PR=\sqrt[]{22.76} \end{gathered}[/tex]therefore, PR is equal to 4.77 m. By rounding up to the nearest whole number, the answer is PR= 5 m.
Find an equation of the line perpendicular to y=6x+4 that passes through the point (5,10) if possible write the equation in slope intercept form
Given:
y = 6x + 4
The slope of a perpendicular line, is the negative reciprocal of the slope of the original line.
Using the slope intercept form:
y = mx + b
Where m is the slope and b is the y-intercept
The slope of the origi line: y = 6x + 4 is = 6
The negative reciprocal of 6 is:
[tex]-\frac{1}{6}[/tex]Thus, the slope of the perpendicular line is
[tex]-\frac{1}{6}[/tex]To find the equation of the perpendicular line that passes through the point (5, 10), use the slope-intercept form:
y = mx + b
Substitute -1/6 for m, 5 for x and 10 for y to find b.
We have:
[tex]\begin{gathered} y=mx+b \\ \\ 10=-\frac{1}{6}\ast5+b \\ \\ 10=-\frac{5}{6}+b \\ \\ \text{Multiply through by 6:} \\ 10\ast6=-\frac{5}{6}\ast6+6b \\ \\ 60=-5+6b \\ \\ 60+5=-5+5+6b \\ \\ 65=6b \\ \\ \frac{65}{6}=b \end{gathered}[/tex]Therefore, the equation of the perperndicular line in slope intercept form is:
[tex]y=-\frac{1}{6}x+\frac{65}{6}[/tex]ANSWER:
[tex]y=-\frac{1}{6}x+\frac{65}{6}[/tex]Convert: 5 m = ________mm
Answer:
5,000 mm
Explanation:
To convert 5m to mm, we begin with the standard conversion rate between meters (m) and millimetres (mm).
[tex]1m=1000\operatorname{mm}[/tex]We then have:
[tex]\begin{gathered} 5m=5\times1000\operatorname{mm} \\ =5,000\operatorname{mm} \end{gathered}[/tex]Therefore, 5 m = 5,000 mm
What is another way to summarize the outcome of this proof?Given: AX || CY, BX || DY, AB || CDA ABX-ACDY2.Prove: Slope of AB = slope of CD1. AXDY. BX|DY. ABCDA ABDA DBCAX BXCY DY3. AX-DY=BX - CY4.StatementDY=DYCYBXAX5. Slope of AB= slope of CDBX-CY DY BXAXCY AX=slope of CDslope of AB1. GivenReason2. Definition of similar triangles: Correspondingsides of similar triangles are proportional.3. Multiplication property of equality4. Definition of slope5. Substitution
ANSWER:
B. Parallel lines have the same slope
STEP-BY-STEP EXPLANATION:
Two lines are parallel if they have the same direction vector or the same slope.
Two lines can have the same slope but different intercepts.
Therefore, the correct answer is and that summarizes the table is B. Parallel lines have the same slope
A principal designs a survey to determine whether students want to expand the school library or add a newscore board in the gym. He surveys every third student who enters the library. Which change would improvethe sample by providing data that is less likely to be biased?survey every third student who enters the band roomsurvey every third student who enters the cafeteriasurvey every third student who enters the basketball gamesurvey every third student who enters the theater room
The Solution:
The survey of every third student that enters the library is biased.
The option that is likely to make the survey less biased is:
(option 2) The survey of every third student who enters the cafeteria.
Explanation:
The students the enter the cafeteria are more representative of the whole students than those students that enter the library or others in the choiced options.
Thus, the correct answer is option 2.
3. If f(5)=35, Give an ordered pair that must be on the graph of the function
The Solution:
Given the function:
[tex]f(5)=35[/tex]This means that an ordered pair is
[tex](5,35)[/tex]Therefore, the correct answer is [option D]
Please help me !! 1. f(x) = -(x+2)*(x-4)A new parabola , g(x) , is translated from f(x) using the translation T (-3,7) . What is the vertex point of g(x) ? Explain how you know . What are the x intercepts of the g(x) ? How did you figure it out ?
ANSWER:
[tex]\begin{gathered} Vg(x)=(-2,16) \\ \text{The x intercept are:} \\ (2,0)\text{ and }(-4,0) \end{gathered}[/tex]STEP-BY-STEP EXPLANATION:
The first thing we must do is calculate the vertex of f (x)
1.
[tex]f(x)=-\mleft(x+2\mright)\cdot\mleft(x-4\mright)[/tex]the vertex of an open top-down parabola of the form y = a * (x-m) * (x-n) is the average of its zeros, just like that:
[tex]\begin{gathered} x=\frac{m+n}{2}=\frac{-2+4}{2}=1 \\ y=-1\cdot(1+2)\cdot(1-4)=9 \\ \text{The vertex is } \\ (1,9) \end{gathered}[/tex]Now the vertex of g (x) would then be to apply the translation of (-3, 7) to the vertex of f (x)
[tex]\begin{gathered} Vf(x)=(1,9)\rightarrow Vg(x)=(1-3,9+7)=(-2,16) \\ Vg(x)=(-2,16) \end{gathered}[/tex]Then for the intercepts with x we must first calculate the intercepts in f (x)
[tex]\begin{gathered} 0=-\mleft(x+2\mright)\cdot\mleft(x-4\mright) \\ 0=(x+2)\cdot(x-4) \\ x+2=0\rightarrow x=-2 \\ x-4=0\rightarrow x=4 \\ \text{Therefore, the x-intercept are:} \\ (-2,0)\text{ and}(4,0) \end{gathered}[/tex]In the case of the x intercept in g (x), the signs of f (x) are exchanged, like this:
[tex]\begin{gathered} (-2,0)\rightarrow(2,0) \\ (4,0)\rightarrow(-4,0) \end{gathered}[/tex]Bobby is designing a simulation to answer the question below.If 21% of the customers at a restaurant order fish, what is the probability that the next 3 customers in a row will order fish?Which design using red marbles to represent customers who order fish is BEST for the simulation?A. randomly select 3 marbles from 1 red marble and 99 green marblesB. randomly select 3 marbles from 7 red marbles and 93 green marblesC. randomly select 3 marbles from 21 red marbles and 79 green marblesD. randomly select 3 marbles from 63 red marbles and 37 green marbles
The probability of the second customer ordering a fish is independent of the first customer.
So, if the events are independent, the probability that the next three customers in a row will order a fish is (P):
[tex]P=P_1\cdot P_2\cdot P_3[/tex]Where P1, P2, and P3 are the probabilities of the first, second, and third customer ordering a fish.
Substituting the values:
[tex]\begin{gathered} P=0.21\cdot0.21\cdot0.21 \\ P=0.009261 \end{gathered}[/tex]Answer: The probability is 0.009261 = 0.9261%.
To represent the situation using red marbles:
Given that from 100 customers, 21 prefer fish, it is asked to calculate the probability of 3 customers in a row prefer fish.
From the options, randomly selecting 3 marbles from 21 red marbles and 79 green marbles is the best option, since there are 21 red marbles and a total of 100 (21 + 79) marbles.
Answer: C.
solve c=1/2 ab² for b
First we have to divide both sides of the equation by 1/2a:
[tex]\frac{c}{\frac{1}{2}a}=\frac{\frac{1}{2}a}{\frac{1}{2}a}b^{2}[/tex]And we get
[tex]\frac{2c}{a}=b^{2}[/tex]finally we have to take square root on both sides:
[tex]\sqrt[]{\frac{2c}{a}}=\sqrt[]{b^2}[/tex]And we get that b is:
[tex]b=\sqrt[]{\frac{2c}{a}}[/tex]What is 3x + 2y = 30 in slope intercept?
SOLUTION
Write out the equation
[tex]3x+2y=30[/tex]The equation of a line in slope intercept form is given by
[tex]\begin{gathered} y=mx+c \\ \text{Where} \\ m=\text{slope c=intercept} \end{gathered}[/tex]Hence
From the equation given, we make y the subject of the formula of the equation given.
[tex]\begin{gathered} 3x+2y=30 \\ \text{Subtract 3x from both sides } \\ 3x-3x+2y=30-3x \\ \text{Then} \\ 2y=-3x+30 \end{gathered}[/tex]Divide both sides by 2
[tex]\begin{gathered} \frac{2y}{2}=\frac{-3x+30}{2} \\ \text{Then} \\ y=-\frac{3x}{2}+\frac{30}{2} \end{gathered}[/tex]Hence
[tex]y=-\frac{3}{2}x+15[/tex]Therefore
The equation of the line in slope intercept form is
y=-3/2x + 15
Pleaseee help me I’m really bad at math and need all the help only help with you 100% have the correct answer
You have two expressions
(-6x-2)
and
(x+4)
You have to subtract the second expression from the first one so that:
[tex](-6x-2)-(x+4)[/tex]The minus sign in front of the second equation can be considered as a -1, so you can solve the parenthesis as:
[tex]\begin{gathered} (-6x-2)-1(x+4) \\ (-6x-2)-1\cdot x-1\cdot4 \\ -6x-2-x-4 \end{gathered}[/tex]Next you have to perform the corresponding operations:
[tex]\begin{gathered} -6x-x-2-4 \\ -7x-6 \end{gathered}[/tex]Determine whether the transformations of rectangle MNPQ described in the table would create animage that is congruent to rectangle MNPQ-For each transformation, select "Congruent" or "Similar but Not Congruent."TransformationCongruentSimilar but NotCongruenta translation 4 units up and 2 units righta 90°clockwise rotation, followed by a reflection over theX-axisa reflection over the y-axis, followed by a dilation by a scalefactor of 2 with the center at the origina dilation by a scale factor of 1.5 with the center at the origin,followed by a translation 5 units left
1)
a translation 4 units up and 2 units right
a 90°clockwise rotation, followed by a reflection over the
X-axis CONG
solve for x: X/2 = 3x+4 2x
the given expression is,
[tex]\frac{x}{2}=\frac{3x+4}{2x}[/tex][tex]\begin{gathered} 2x^2=6x+8 \\ 2x^2-6x-8=0 \end{gathered}[/tex][tex]2x^2-8x+2x-8=0[/tex][tex]\begin{gathered} 2x(x-4)+2(x-4)=0 \\ (x-4)(2x+2)=0 \end{gathered}[/tex]x-4 = 0
x = 4
2x + 2 = 0
2x = -2
x = -2/2
x = -1
thus, the answer is x = 4 , - 1
undefinedsimplify if possible.If an answer is undefinied, states so 5x4-3x6+9
Explanation
[tex]5\cdot4-3\cdot6+9[/tex]Step 1
remember the order of the operations
multiplication
addition, subtraction
then,
37 A cabin in the Catskills burns n gallons of oil each month in the winter. At this rate, g gallons of oil will supply c cabins for how many months? A. g/nc B.gnc C. (nc)/g D. (ng)/c
Given that, n gallons of oil is burnt in a month, then we can deduce that
[tex]\begin{gathered} ngallons=1\text{month} \\ 1\text{gallon}=\frac{1}{n}\text{month} \end{gathered}[/tex]Then g gallons will be
[tex]\begin{gathered} 1\text{gallon}=\frac{1}{n}\text{month} \\ g,gallons=g\times\frac{1}{n}month=\frac{g}{n}month \end{gathered}[/tex]Then c cabins would be
[tex]c,\text{cabins}=\frac{1}{c}\times\frac{g}{n}month=\frac{g}{nc}months[/tex]Hence, g gallons of oil will supply c cabins for g/nc months, OPTION A
Solve by substitutiony = 2x + 1y = 4x-1
1. y=2x+1
2. y=4x-1
We need to substitute 1 in 2:
2x+1=4x-1
1+1=4x-2x
2=2x
x=2/2
x=1
Now substituing x in 1:
y=2(1)+1
y=3
A car is travelling at speed of 30.0 m/s encounters an emergency and comes to a complete stop. how much time will it take for the car to stop it decelarates at -4.0 m/s2
To stop the car, the car would have a final velocity, v=0 m/s
We're going to use the first equation of motion i.e.
[tex]\begin{gathered} v=u+at \\ 0=30+(-4)\cdot t \\ -30=-4t \\ t=-\frac{30}{4} \\ t=7.5\text{ s} \end{gathered}[/tex]The car will need 7.5 seconds to stop.
374/×-10 is equivalent to -22, find the value of x.
Answer
x = -7
Explanation
The question asks us to solve for x in the equation
[tex]\frac{374}{x-10}=-22[/tex]To solve,
[tex]\begin{gathered} \frac{374}{x-10}=-22 \\ -22(x-10)=374 \\ -22x+220=374 \\ -22x=374-220 \\ -22x=154 \\ \text{Divide both sides by -22} \\ -\frac{22x}{-22}=\frac{154}{-22} \\ x=-7 \end{gathered}[/tex]Hope this Helps!!!
given: x is the midpoint of WY, WX= XZprove: XY 1/2XZ
Segment = WY
WX = XZ
angle 1 and angle 2 are vertical angles. If angle 1 = (5x + 12)° and angle 2 = (6x - 11), find angle 1.
Vertical angles are angles that are oposed by their vertex. When this happens their numerical value is equal, therefore to find the value of the angles we need to make them equal and solve the expression for the "x" variable.
[tex]\begin{gathered} \text{angle}1\text{ = angle2} \\ 5x\text{ + 12 = 6x - 11} \\ 5x\text{ - 6x = -11 -12} \\ -x\text{ = -23} \\ x\text{ = 23} \end{gathered}[/tex]We need to calculate the value of "angle 1", which obeys the following expression:
[tex]\text{angle 1 = 5x + 12}[/tex]Since x = 23, we have:
[tex]\begin{gathered} \text{angle 1 = 5}\cdot23\text{ + 12} \\ \text{angle 1 = }115+12 \\ \text{angle 1 = 127} \end{gathered}[/tex]The value of angle 1 is 127 degrees.
What fractional part of one semicircle does the labeled angle represent? Express your answer as a fraction in simplest terms. Then, express the labeled angle in radian measure.Please fill in the two blanks as fractions (if needed)
Remember that
A complete circle has 360 degrees
A semicircle has 180 degrees
so
Applying proportion
100/180=x/225
solve for x
x=(100/180)*225
x=22,500/180
x=125%
Convert to fraction
125/100
simplify
5/4
therefore
the labeled angle represents 5/4
Part b
Express the labeled angle in radian measure
Remember that
pi radian -------> represents 180 degrees
so
225 degrees
radians=225pi/180
5pi/4