A space shuttle is made using
a scale of 1 inch : 12 feet. If
the actual space shuttle has a
height of 84 feet, then the
model is inches tall.
we know that
the scale is 1 inch : 12 feet.
so
using proportion
1/12=x/84
solve for x
x=84/12
x=7 in
therefore
the answer is 7 inchesPart 2
please help I've been trying to get this for a really long time thank you
Let:
[tex]\begin{gathered} x=2y+2_{\text{ }}(1) \\ -3x+6y=-6_{\text{ }}(2) \end{gathered}[/tex]Replace the value of x into (2)
[tex]\begin{gathered} -3(2y+2)+6y=-6 \\ -6y-6+6y=-6 \\ -6y+6y=6-6 \\ 0=0 \end{gathered}[/tex]Therefore, the system has infinitely many solutions
The segment with endpoints (0,8) and (-6,0) is dilated to a segment with endpoints of (0,6) and (-4.5,0). What is the scale factor of the dilation?
To solve the exercise, we can first find the length of each segment using the formula for the distance between two points:
[tex]\begin{gathered} D=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \text{ Where }(x_1,y_1)\text{ and }(x_2,y_2)\text{ are the coordinates of the points} \end{gathered}[/tex]First segment:
[tex]\begin{gathered} (x_1,y_1)=(0,8) \\ (x_2,y_2)=\mleft(-6,0\mright) \\ D=\sqrt[]{(-6_{}-0)^2+(0-8)^2} \\ D=\sqrt[]{(-6)^2+(8)^2} \\ D=\sqrt[]{36+64} \\ D=\sqrt[]{100} \\ D=10 \end{gathered}[/tex]Second segment:
[tex]\begin{gathered} (x_1,y_1)=\mleft(0,6\mright) \\ (x_2,y_2)=\mleft(-4.5,0\mright) \\ D=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ D=\sqrt[]{(-4.5-0)^2+(0-6)^2} \\ D=\sqrt[]{(-4.5)^2+(-6)^2} \\ D=\sqrt[]{20.25+36} \\ D=\sqrt[]{56.25} \\ D=7.5 \end{gathered}[/tex]Now, we apply the following formula:
[tex]\frac{\text{image}}{\text{pre}-\text{image}}=\text{scale factor}[/tex]Then, we have:
[tex]\begin{gathered} \frac{\text{ length of second segment}}{\text{ length of first segment}}=\text{scale factor} \\ \frac{7.5}{10}=\text{ scale factor} \\ \text{ Simplify} \\ \frac{7.5\cdot10}{10\cdot10}=\text{ scale factor} \\ \frac{75}{100}=\text{ scale factor} \\ \frac{25\cdot3}{25\cdot4}=\text{ scale factor} \\ \frac{3}{4}=\text{ scale factor} \end{gathered}[/tex]Therefore, the scale factor of the dilation is 3/4.
e is a game where the outcome is a random integer from 1 to 50. If the outcome is odd, you win If the outcome is even, you win nothing. If you play the game, what is the expected payoff?
total possible outcomes: 50
odd outcomes: 25
even outcomes: 25
probability of an odd outcome = 25/50 = 1/2
probability of an even outcome = 25/50 = 1/2
return in case of an odd outcome = $26
return in case of an even outcome = $0
The expected payoff is computed as follows:
[tex]\begin{gathered} \text{ expected payoff=}p_{odd}\cdot r_{odd}+p_{even}\cdot r_{even} \\ \text{ expected payoff=}\frac{1}{2}\cdot26+\frac{1}{2}\cdot0 \\ \text{ expected payoff= \$13} \end{gathered}[/tex]Imagine reflecting triangle ABC across line MN. Then answer the questions about the reflected figure.(Look at picture?)What type of shape will the reflection figure be?
Reflection is a rigid transformation in which the shape, the size, and the angles remain the same. Therefore, the reflection will be a figure of the same shape, but an image that will be symmetrical to the preimage.
Something like this:
Find the mean, median, and mode of the list of values. Round to the nearest tenth if necess17, 9, 35, 26, 38, 33, 9,9
We have the following list of values:
17, 9, 35, 26, 38, 33, 9,9
rearrange them: 9,9,9,17,26,33,35,38
the population size is 8, so we can calculate the mean as it follows
[tex]\operatorname{mean}=\frac{9+9+9+17+26+33+35+38}{8}=22[/tex]mean = 22
using the list of values, we can find that the median is
[tex]\operatorname{median}=\frac{17+26}{2}=21.5[/tex]median = 21.5
and, mode = 9
because the value 9 is 3 times on the list
Use transformations of the graph of f(x) =x^3 to determine the graph of the given function.
Recall that the graph of a function l(x), reflected over the x-axis represents the function:
[tex]f(x)=-l(x)\text{.}[/tex]The graph of l(x) translated n units to the left is represented by the function:
[tex]l(x+n)\text{.}[/tex]Therefore, h(x) is f(x) translated 6 units to the left and reflected over the x-axis.
Answer:
X+YQuestion 24Page 1 of 4LineGuide?Every computer that a business owner purchases will lose most of its value after 5 years of use. The owner plans to purchase a computerfor $2,100 and replace it after 4 years.Part AMethod 1 of determining the computer's value is to reduce its value by a constant amount after each year of use. This method values thecomputer at $0 after 5 years of use.Which function, f(n), represents the value of the computer after n years of use for Method 1?f(n) = 420nf(n) = 525nf(n) = 2,100 - 420nd f(n) = 2,100 - 525n
EXPLANATION
Let's see the facts:
Useful life= 5 years
Computer Price = $2100
Replacing time = 4 years
Si, the initial price is $2,100 and we can assevere that we must subtract the depreciation component to this number in order ti reduce its value by a constant amount.
f(n) = 2,100 - ...
The next term to consider is constant decreasing amount is 420n or 525n. How can we get the right term?
It's simple, just replacing the variable n by 5 and looking if f(n) is equal to $0.
f(5) = 2,100 - 420*(5) = 0 Rigth reasoning!
f(5) = 2,100 - 525*(5) = -525 It's not equal to zero!
The function f(n) that represents the value of the computer after n years of uses is f(n) = 2,100 -420n
How far is Mr. Jones travel in 15 minutes if you continue driving at the same rate
Given:
The distance traveled by the Jones = 6 miles
Time is taken to travel the distance = 10 minutes
Required:
Find the distance traveled by Mr. Jones in 15 minutes if the speed rate is the same.
Explanation:
The speed is given by the formula:
[tex]speed\text{ = }\frac{Distance\text{ }}{Time}[/tex]Thus the speed of Mr. Jones car
[tex]\begin{gathered} s=\frac{6}{10} \\ s=0.6\text{ miles/minute} \end{gathered}[/tex]The speed rate is the same then the distance traveled by car in 15 minutes is:
[tex]\begin{gathered} distance\text{ = speed }\times time \\ distance\text{ = 0.6}\times15 \\ distance\text{ =9 miles} \end{gathered}[/tex]Final Answer:
The distance traveled by Mr. Jones travels in 15 minutes is 9 miles.
Thus the first option is the correct answer.
I need help to set up an equation the find the value of x. Then, to explain my reasoning.
the two horizontal lines are parallel so that mean that:
[tex]70=3x-14[/tex]and we can solve for x
[tex]\begin{gathered} 70-14=3x \\ 56=3x \\ x=\frac{56}{3} \\ x=18.66 \end{gathered}[/tex]Is Figure B a scale copy of Figure A? berhentian 6 2. 8 3 4 2 1 6 3 Figure A Figure B
If two figures are scale copies of each other, then the corresponding sides should have the same ratio.
Find the quotient of the sides of figure A to the corresponding sides of figure B. If they all have the same ratio, then figure B is a scale copy of figure A:
[tex]\begin{gathered} \frac{8}{4}=2 \\ \frac{4}{2}=2 \\ \frac{6}{3}=2 \\ \frac{2}{1}=2 \\ \frac{6}{3}=2 \end{gathered}[/tex]Since all the ratios are equal to 2, the answer is:
[tex]\text{Yes. Figure B is a scale copy of figure A.}[/tex]rite the following ratio as a fraction in lowest terms.54to56
We want to write the ratio of 54 to 56 as a fraction in lowest terms. To do this we have to factorize the numbers and simplify the equals factors:
[tex]\begin{gathered} \frac{54}{56}=\frac{2\cdot27}{2\cdot28}=\frac{27}{28}=\frac{3\cdot3\cdot3}{4\cdot7} \\ In\text{ the last, we cannot simplify the factors, so the lowest terms are:} \\ \frac{54}{56}=\frac{27}{28} \end{gathered}[/tex]Salma has completed 22 deliveries so far this week. She needs to make 55 deliveries for the week. What percentage of her deliveries has Salma completed?
The number of deliveries completed by Salma = 22.
Total deliveries to be completed = 55.
Percentage of delivery is calculated as,
[tex]\begin{gathered} \text{Percentage of delivery = }\frac{22}{55}\times100. \\ \text{Percentage of delivery = 20 \%} \end{gathered}[/tex]Thus the percentage of delivery completed is 20%.
When c is 21, what is the value of a?
ANSWER:
5
STEP-BY-STEP EXPLANATION:
We can determine the value of a by means of the table shown in the statement.
According to the table when x is equal to 21, the value of a is equal to 5.
which equation is the equation of the line, in point-slope form, that has a slope of 2 and passes through the point (-8,1)
y-1 = 2x +16
1) Gathering the data
m=2
(-8,1)
2) The equation of the line in point-slope form is obtained through a formula:
(y-y_1)=m(x-x_1)
3)Plugging into the formula the parameters.
(y-1) =2[x-(-8)]
(y-1)=2(x+8)
y-1 = 2x +16
write the equation for the line using the given information. Write the equation in slope intercept form Y=mx+b write the equation of the line with slope =6 and passing through the point (-4 -9)
m = 6 and the line passes through (-4,-9)
Then, we have: -9 = 6*(-4) + b
b - 24 = -9
b = 24 - 9 = 15
Therefore, the equation for the line is y = 6x + 15
1. It takes Keimon 36 minutes to ride his car 28 miles. At this rate, how longwill it take him to ride 38 miles? (YOUR ANSWER MUST BE IN HOURS)
it is given keimon travels 28 miles in 36 minutes
so its speed is = distance/ time
= 28 / 36
= 7/9 miles per minute
the time to travel 38 miles will be = distance/ speed
[tex]=\frac{38}{\frac{7}{9}}=\frac{38\times9}{7}=\frac{342}{7}[/tex]so the time is 342/7 minutes
now we will convert it into hours
60 minutes = 1 hours
1 minute = 1/60 hours
342/7 minutes =
[tex]\begin{gathered} =\frac{1}{60}\times\frac{342}{7} \\ =0.81 \end{gathered}[/tex]it will take 0.81 hours to ride 38 miles.
A teacher wants to buy graph paper and printer paper. The printer paper costs $2 a pack, while the graphing paper cost $3 a pack. She wants to buy at least 7 packs of paper, but wants to spend at most $30. Write a system of inequalities for the situation.
Given:
A teacher wants to buy graph paper and printer paper.
Let the number of packs of the graph paper = x
And the number of packs of the printer paper = y
The printer paper costs $2 a pack, while the graphing paper cost $3
so, the total cost will be: 2y+3x
She wants to buy at least 7 packs of paper
[tex]x+y\ge7[/tex]And wants to spend at most $30.
[tex]2y+3x\le30[/tex]so, the system of inequalities for the situation will be as follows:
[tex]\begin{gathered} x+y\ge7 \\ 2y+3x\le30 \end{gathered}[/tex]Galaxy A has 8 × 10^8 stars. Galaxy B has 6 x 10^10 stars. Choose which galaxy has more stars. Then fill in the blank with a number written in standard notation.
Given:
Galaxy A has 8 × 10^8 stars. Galaxy B has 6 x 10^10 stars.
We will write the numbers multiplied by ten raised to the same exponent
so,
[tex]\begin{gathered} 8\times10^8=8\times10^8 \\ 6\times10^{10}=6\times100\times10^8=600\times10^8 \end{gathered}[/tex]now, we will compare the numbers: 8 and 600
It is clear 600 is greater than 8
so, the answer will be option Galaxy B
Divide the number of stars of B by A
So,
[tex]\frac{6\times10^{10}}{8\times10^8}=\frac{600\times10^8}{8\times10^8}=\frac{600}{8}=75[/tex]
Galaxy B has 75 times as many stars as Galaxy A
Find the probability that a randomly chosen point is the figure lies in the shaded region. Give all answers in fraction and percent forms. help with #7
In order to determine the probability that a randomly chosen point lies in the shaded region of the figure we just have to divide the area of the shaded region by the total area.
As you can see in figure #7, the shaded area is the region bounded by the box and out of the two circles, then in order to determine the magnitude of the shaded resion we just have to subtract the area of the two circles from the area of the rectangle, like this:
Area of each circle
Each circle has a diameter of 2, then the radius of each circle is 1 (2/2), by replacing the radius r into the following formula, we can calculate the area of each circle:
[tex]\begin{gathered} A=\pi r^2 \\ A=\pi(1)^2 \\ A\approx3.14 \end{gathered}[/tex]Then the area of each circle is abot 3.14, by multiplying this area by 2 we can determine the total area of the two circles like this:
[tex]At=2\times3.14=6.28[/tex]Then the area of the two circles is 6.28.
The area of the rectangle can be calculated by multiplying the width and the length of the rectangle, to get:
[tex]Ar=4\times3=12[/tex]Then, the area of the shaded area is:
As = 12 - 6.28
As = 5.72
By dividing the area of the shaded area by the area of the rectangle we get the probability like this:
[tex]P=\frac{5.72}{12}=0.48[/tex]Then, the probability that a randomly chosen point lies in the shaded region is 0.48 (48%)
A line passes through (2, (2, – 1) and (4, 5) . Which answer is the equation of the line? 0-3x + 5y = 13 6 -3x + y = 17 0-3x + 5y = -13 0-3x + y = -7
A line passes through
(2, -1) and (4, 5)
We can say, given:
[tex]\begin{gathered} (x_1,y_1)=(2,-1) \\ \text{and} \\ (x_2,y_2)=(4,5) \end{gathered}[/tex]The equation of a line is given as:
[tex]y=mx+b[/tex]Where
m is slope and b is y-intercept
Now, finding the slope using the slope formula:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{5+1}{4-2} \\ m=\frac{6}{2} \\ m=3 \end{gathered}[/tex]So, the equation becomes:
y = 3x + b
Putting a point in (x,y), such as (4,5), we have:
y = 3x + b
5 = 3(4) + b
5 = 12 + b
b = 5 - 12
b = -7
Thus,
equation of the line >>> y = 3x - 7
Re-arranging in standard form >>> -3x + y = -7
Last Answer choice is right.
solve for x and y 5x+4y=9 x+2y=3
You have the following system of equations:
[tex]\begin{gathered} 5x+4y=9 \\ x+2y=3 \end{gathered}[/tex]In order to solve the previous equation, you first multiply by -2 the second equation:
[tex]\begin{gathered} (x+2y=3)(-2) \\ -2x-4y=-6 \end{gathered}[/tex]Next, you add the first equation of the system with the previous result:
5x + 4y = 9
-2x - 4y = -6
3x + 0 = 3
Next, you solve the previous result for x:
[tex]\begin{gathered} 3x=3 \\ x=\frac{3}{3}=1 \end{gathered}[/tex]Next, you replace the previous value of x into one of the equation of the system. For instance, you use:
[tex]\begin{gathered} x+2y=3 \\ 1+2y=3 \\ 2y=3-1 \\ 2y=2 \\ y=\frac{2}{2}=1 \end{gathered}[/tex]Hence, the solution to the given system of equations is:
x = 1
y = 1
What is a slope in math?
When comparing the variation between a variable and a result, the slope gives the relationship between the changes in both quantities.
It is mathematically defined as
[tex]\text{Slope = }\frac{Change\text{ in y}}{\text{Change in x}}\text{ = }\frac{\Delta y}{\Delta x}[/tex]What is the slope of the line?
Two points on the line are (3,0) and (0,-4.5)
The slope m of a line
= (y2 - y1)/(x2 - x1)
= (-4.5 - 0)/(0 - 3)
= -4.5/-3
= 1.5
The slope is 1.5
can u pls help me with this question i also want the answer
Given:
The graph show relationship between the length of hallway Denise covers in tiles (x)
And the number of tiles needed (y)
AS shown: the relation begins from the point (0,0)
And the relation is linear
so, the relation between x and y are proportional
So, the answer is yes
Now, we need to get the relation:
The general form of the proportional relationship is : y = kx
So, using one point from the line to get the value of k
so, the line passing through the point ( 4 , 20 )
when x = 4 , y = 20
so,
[tex]\begin{gathered} 20=k\cdot4 \\ \\ k=\frac{20}{4}=5 \end{gathered}[/tex]So, the relation between x and y is :
[tex]y=5x[/tex]So, the constant is 5
what is the value of x?(6x+38)
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[tex]\begin{gathered} 2(4x-55)+2(3x+25)=360 \\ 8x-110+6x+50=360 \\ 14x-60=360 \\ \text{Solve for x:} \\ 14x=420 \\ x=\frac{420}{14} \\ x=30 \end{gathered}[/tex]----------------------------------------------------------------------------------------------
[tex]\begin{gathered} 11x-54=3x+120 \\ 8x=174 \\ x=\frac{174}{8}=21.75 \end{gathered}[/tex]What are all x and y intercepts of the attached image?
From the given graph, let's find the x-intercept and y-intercept.
• x-intercept:
The x-intercept is the point where the line crosses the x-axis.
From the graph, the point where the line crosses the x-axis is at:
(x, y) ==> (2, 0)
x = 2
Therefore, the x-intercept is: (2, 0)
• y-intercept:
The y-intercept is the point where the line crosses the y-axis.
From the graph, the line does not cross the y-axis. Therefore, there is no y-intercept.
ANSWER:
(a). x-intercept: 2
(b). y-intercept: None
find the solution of this system of equations2x+7y=-31-4x-4y=-8
To find the solutions, we multiply the first equation by 2, then we sum the equations to solve for y.
[tex]\begin{gathered} \begin{cases}4x+14y=-62 \\ -4x-4y=-8\end{cases}\rightarrow10y=-70 \\ y=-\frac{70}{10} \\ y=-7 \end{gathered}[/tex]Then, we use y = -7 to find x
[tex]\begin{gathered} 2x+7y=-31 \\ 2x+7(-7)=-31 \\ 2x-49=-31 \\ 2x=-31+49 \\ 2x=18 \\ x=\frac{18}{2} \\ x=9 \end{gathered}[/tex]Hence, the solution is (9, -7).Can anyone help me with number 5 simplifying negative square roots
Use substitution in the system of equations. What is the value of x in both equations?A. 3B. -6C. 6D. 2
Given the following question:
[tex]\begin{gathered} 3x+2y=-12 \\ x=4y-18 \end{gathered}[/tex][tex]\begin{gathered} 3x+2y=-12 \\ x=4y-18 \\ \text{ Substitute x=4y - 18 into the first equation:} \\ 3(4y-18)+2y=-12 \\ 18-4=14y \\ 14y-54=-12 \\ -12+54=42 \\ y=3 \\ \text{ Substitute to find x} \\ x=4\times3-18 \\ 4\times3=12 \\ 12-18=-6 \\ x=-6,y=3 \\ x=-6 \end{gathered}[/tex]Option B is your answer.
Write an equation in each sentence. Analyze and solve.3. Find three consecutive integers whose sum is 99. Find the integers.
Given that the Sum of three consecutive integers is:
[tex]99[/tex]Let be:
- The first integer:
[tex]n[/tex]- The second integer:
[tex]n+1[/tex]- And the third integer:
[tex]n+2[/tex]By definition, the Sum is the result of an Addition.
Therefore, in this case, you can set up the following equation:
[tex]n+(n+1)+(n+2)=99[/tex]When you solve for "n", you get:
[tex]n+n+1+n+2=99[/tex][tex]3n+3=99[/tex][tex]3n=99-3[/tex][tex]3n=96[/tex][tex]\begin{gathered} n=\frac{96}{3} \\ \\ n=32 \end{gathered}[/tex]Now that you know that first integer, you can determine that the other consecutive integers are:
[tex]n+1=32+1=33[/tex][tex]n+2=32+2=34[/tex]Hence, the answer is:
[tex]\begin{gathered} 32 \\ 33 \\ 34 \end{gathered}[/tex]