The image of the point (-9,0) under a translation is (-12, -4). Find the
coordinates of the image of the point (-1, -2) under the same translation.
we have
(-9,0) ------- >(-12,-4)
so
the rule of tye translation is
(x,y) -------> (x-3, y-4)
the translation is 3 units at left and 4 units down
Apply the rule point (-1, -2)
(-1, -2) --------> (-1-3, -2-4)
(-1, -2) --------> (-4, -6)
answer
(-4, -6)
Isaac Green Elimination (Level 1) Mar 17, 8:18:58 AM Find the solution of the system of equations. -10x+8y=-444x+8y=40
The given equations are:
[tex]\begin{gathered} -10x+8y=-44\ldots\ldots(1) \\ 4x+8y=40\ldots\ldots\text{.}\mathrm{}(2) \end{gathered}[/tex]Subtract equation 1 from 2, we get,
[tex]\begin{gathered} 4x+10x+8y-8y=40+44 \\ 14x=84 \\ x=\frac{84}{14}=6 \end{gathered}[/tex]Now, substitute the value of x in equation 2, we get
[tex]\begin{gathered} 4\times6+8y=40 \\ 8y=40-24=16 \\ y=\frac{16}{8}=2 \end{gathered}[/tex]Thus, the solution is x = 6 and y = 2
4472^73+10008×273÷6382
A professional baseball diamond is a square. Thedistance from base to base is 90 ft. To the nearest foot,how far does a catcher standing at home plate throwthe ball across the diagonal of the square to secondbase?
We have this diagram:
We have to calculate D, using the Pythagorean theorem:
[tex]\begin{gathered} D^2=A^2+A^2=2A^2 \\ D=\sqrt{2A^2}=\sqrt{2}\cdot A \\ D\approx1.414\cdot90=127.26\approx127 \end{gathered}[/tex]A catcher standing at home plate is at 127 ft across the diagonal from second base.
Find the general solution of the differential equation
[tex] \frac{dy}{dx} = (1 + {x}^{2} )(1 + {y}^{2} )[/tex]
[tex]{ \pink{ \tt{ { \tan }^{ - 1} y - \frac{ {x}^{3} }{3} = c }}}[/tex]
Step-by-step explanation:
This can be written as,
[tex]{ \green{ \tt \frac{dy}{1 + {y}^{2}}}} = { \green{ \tt{(1 + {x}^{2})dx}}}[/tex]
Integeare on both sides, then
[tex]{ \blue{ \tt{ ∫ \frac{1}{1 + {y}^{2}}}}}{ \blue{ \tt{dy}}} = { \blue{ \tt{ ∫ (1 + {x}^{2} )dx}}}[/tex]
[tex]{ \blue{ \tt{ { \tan }^{ - 1} y = \frac{ {x}^{3} }{3} + c}}}[/tex]
[tex]{ \huge{ \green{ \blue{ \tt{ { \tan }^{ - 1} y - \frac{ {x}^{3} }{3} = c}}}}}[/tex]
What is the amount in the account after 4 yrs , rounded to the nearest dollar
We have the next formula
[tex]f(x)=350(1+0.03)^x[/tex]where x us the number of years, in this case x= 4
[tex]f(4)=350(1+0.03)^4=393.92[/tex]rounded to the nearest dollar is $394 is the amount in the account after 4 years.
For a project in statistics class, a pair of students decided to invest in two companies, one that produces software and one that does biotechnology research. Kendall purchased 86 shares in the software company and 11 shares in the biotech firm, which cost a total of $2,056. At the same time, Audrey invested a total of $1,937 in 79 shares in the software company and 11 shares in the biotech firm. How much did each share cost?Each share in the software company cost $? and each share in the biotech firm cost $?
Answer:
[tex]\begin{gathered} \text{ Each share in the software company cost \$17.} \\ \text{ Each share in the biotech firm cost \$54.} \end{gathered}[/tex]Step-by-step explanation:
Use a system of linear equations to solve the situation. If Kendall purchased 86 shares in the software company and 11 shares in the biotech firm, which cost a total of $2,056.
[tex]86x+11y=2056[/tex]At the same time, Audrey invested a total of $1,937 in 79 shares in the software company and 11 shares in the biotech firm.
[tex]79x+11y=1937[/tex]Let x be the cost of each share in the software company cost.
Let y be the cost of each share in the biotech firm cost.
Solve using the substitution method, isolate one of the variables on one of the equations and plug it into the other equation;
[tex]\begin{gathered} x=\frac{1937}{79}-\frac{11}{79}y \\ Plug\text{ it into the first one:} \\ 86(\frac{1937}{79}-\frac{11}{79}y)+11y=2056 \\ \frac{166582}{79}-\frac{946}{79}y+11y=2056 \\ -\frac{77}{79}y=-\frac{4158}{79} \\ y=\frac{4158*79}{77*79} \\ y=\text{ \$54} \end{gathered}[/tex]Then, the cost of a share in the biotech firm cost $54. Substitute into the isolated ''x'' equation, and solve for x.
[tex]\begin{gathered} x=\frac{1937}{79}-\frac{11}{79}(54) \\ x=\text{ \$17} \end{gathered}[/tex]multi step equation -3x-2=-1
x = -1/3
Explanation:
-3x-2=-1
collect like terms by adding +2 to both sides:
-3x -2 + 2 = -1 + 2
-3x = 1
Divide both sides by the coefficient of x:
coefficient of x = -3
-3x/-3 = 1/-3
x = -1/3
7. If x = 8, which equation is true? A) 4x + 6 = 42B) 52 - 6x = 4 C×/2) + 20 = 16
The function table below is intended to represent the relationship y = 5x-1. However, one of the entries for y does not correctly fit the relationship with x.
Solution
We have the following info:
x y
1 4
2 8
3 14
4 19
The relationship is:
y= 5x-1
If we look for the second row we have this:
y= 5*2 -1 = 10 -1= 9
Then we can conclude that the incorrect value is:
x=2
The equation F = 9/5 C + 32 is used to convert Celsius temperature to Fahrenheittemperatures. C is the temperature in degrees Celsius. What is the temperature indegrees Fahrenheit when the temperature in 35 in Celsius?76596795Music offADdu1256 PM12/11/2020ORIeType here to search
The formula for converting from fahrenheit to celsius is given as
F = 9/5C + 32
Where
C represents Celsius
F represents Fahrenheit
If C = 35, then the temperature in fahrenheit is
F = 9/5 * 35 + 32
F = 63 + 32
F = 95
The correct option is 95
Solve the following inequality.45 < 9(x + 3) < 153
In order to solve this inequality, we can do the following steps:
[tex]\begin{gathered} 45<9(x+3)<153\\ \\ \frac{45}{9}Therefore the correct option is B.Find the x-intercepts and y-intercepts1) 3x + y = 3
The equation of a straight line is written as
y = mx + c
Where
m represents slope
c represents y intercept
The given equation is expressed as
3x + y = 3
y = 3 - 3x
y = - 3x + 3
Comparing the above equation with the slope intercept equation,
y intercept = 3
The x intercept is the value of x when y = 0
Putting y = 0 in the equation, it becomes
0 = - 3x + 3
3x = 3
x = 3x/3
x = 1
x intercept = 1
IExample 2 Reflection A trapezoid with the vertices W (-1.4) X(4.4) Y (4,1), and Z (-3 1) is reflected over the x-axisa.) Find the coordinates of the verticesof the image.b.) Graph trapezoid WXYZ and its
a) Reflection over the x-axis tranforms the point (x,y) into (x, -y). Then:
W (-1,4) → W' (-1,-4)
X (4,4) → X' (4,-4)
Y (4,1) → Y' (4,-1)
Z (-3,1) → Z' (-3,-1)
b) The graph is:
The area of OW is 2897 m2. Find the circumference of OW.A. C= 177 mB. C = 347 mC. C = 687 mD. C=2897 m
The formula to find the area of a circle is
[tex]\begin{gathered} A=\pi r^2 \\ \text{Where r is the radius and A is the area of the circle} \end{gathered}[/tex]So as you can see, if you have the area of the circle, you can see get the measure of its radius:
[tex]\begin{gathered} A=289\pi m^2 \\ A=\pi r^2 \\ 289\pi m^2=\pi r^2 \\ \text{ Divide by }\pi\text{ from both sides of the equation} \\ \frac{289\pi m^2}{\pi}=\frac{\pi r^2}{\pi} \\ 289m^2=r^2 \\ \text{ Apply square root to both sides of the equation} \\ \sqrt[]{289m^2}=\sqrt[]{r^2} \\ 17m=r \end{gathered}[/tex]Now that you have the measure of the radius of the circle, you can obtain its circumference using this formula:
[tex]\begin{gathered} C=2\pi r \\ \text{ Where C is the circumference and} \\ \text{r is the radius of the circle} \end{gathered}[/tex]So, you have
[tex]\begin{gathered} r=17m \\ C=2\pi r \\ C=2\pi(17m) \\ C=34\pi m \end{gathered}[/tex]Therefore, the correct answer is option B.
If 6 cups of rice will serve 14 people, howmany people can be served with 21/2cups of rice?
24 people
Explanations:Number of people that can be served with 6 cups of rice = 14
Number of people that can be served with 1 cup of rice = 14/6 = 7/3
Number of people that can be served with 21/2 cups of rice = 21/2 x 7/3
Number of people that can be served with 21/2 cups of rice = 147/6
Number of people that can be served with 21/2 cups of rice = 24.5
24 people can be served with 21/2 cups of rice
what's 2 over 5th plus 2 over 10th
The expression we need to solve is:
[tex]\frac{2}{5}+\frac{2}{10}[/tex]To solve this problem, we need to not that we can simplify the fraction 2/10 by dividing both number by 2:
If measure of angle P = (19x -5) degrees and x=4 find the measure of P.
Solution:
Given:
Angle P is measured in degrees.
[tex]P=19x-5[/tex]where x = 4
Substituting the value of x in the equation,
[tex]\begin{gathered} P=19x-5 \\ P=19(4)-5 \\ P=76-5 \\ P=71^0 \end{gathered}[/tex]Therefore, the measure of angle P is 71 degrees.
Suppose that Jupiter rotates on its axis once every 10 hours. The equator lies on a circle with a diameter of 88,846 miles.
1
(a) Find the angular speed of a point on its equator in radians per day (24 hours).
(b) Find the linear speed of a point on the equator in miles per day.
Do not round any intermediate computations, and round your answer to the nearest whole number.
a. The angular speed is 15.08 radians per day
b. The linear speed is v = 669899 miles per day
(a) Find the angular speed of a point on its equator in radians per day (24 hours).The angular speed is given by ω = 2π/T where T = period of rotation
Now, since Jupiter rotates on its axis once every 10 hours, its period T = 10 hours.
We now convert this to days.
10 h × 1 day/24 h = 5/12 days
Since the angular speed ω = 2π/T,
Substituting the value of the period into the equation, we have
ω = 2π/T
ω = 2π/5/12 days
ω = 2 × 12π/5 days
ω = 24π/5 days
ω = 75.4/5 days
ω = 15.08 radians per day
ω ≅ 15 radians per day
So, the angular speed is 15.08 radians per day
(b) Find the linear speed of a point on the equator in miles per day.The linear speed v = rω where
r = radius of equator and ω = angular speed of JupiterSince the equator lies on a circle with a diameter of 88,846 miles, its radius, r = 88,846 mi/2 = 44423 mi
So,
r = 44423 mi andω = 15.08 rad/daySubstituting the values of the variables into the equation for the linear speed, we have
v = rω
v = 44423 mi × 15.08 rad/day
v = 669898.84 miles per day
v ≅ 669899 miles per day
So, the linear speed is v = 669899 miles per day
Learn more about linear speed here:
https://brainly.com/question/15154527
#SPJ1
The first three terms of a sequence are given. Round to the nearest thousandth (if necessary).14,84,504Find the 6th term.
ANSWER
a6 = 108864
EXPLANATION
First, we have to find the rule to obtain the nth term of the sequence. For that, we have to decide if this sequence is an arithmetic sequence or a geometric sequence. Note that between the first and second term there's a difference of 70, but between the second and third terms the difference is 420. Therefore it can't be an arithmetic sequence.
Let's assume it is a geometric sequence. The formula for the nth term is:
[tex]a_n=a_1\cdot r^{n-1}[/tex]We have a1 = 14 and using the second term we can find r. a2 = 84:
[tex]\begin{gathered} a_2=a_1\cdot r^{2-1} \\ 84=14\cdot r^1 \\ r=\frac{84}{14} \\ r=6 \end{gathered}[/tex]The general formula for the nth term of this sequence is:
[tex]a_n=14\cdot6^{n-1}[/tex]To be sure, let's check if it works for the third term:
[tex]\begin{gathered} a_3=14\cdot6^{3-1} \\ a_3=14\cdot6^2 \\ a_3=14\cdot36 \\ a_3=504 \end{gathered}[/tex]Now, to find the 6th term, we just have to use this formula, with n = 6:
[tex]\begin{gathered} a_6=14\cdot6^{6-1} \\ a_6=14\cdot6^5 \\ a_6=108864 \end{gathered}[/tex]Hence, the 6th term of this sequence is 108864.
Can I get some help on this i got stuck
Given:
Given that
[tex]\tan\theta=\sqrt{5}[/tex]Required:
To find the other five trig ratio.
Explanation:
[tex]\begin{gathered} \tan\theta=\frac{opp}{adj} \\ \\ =\frac{\sqrt{5}}{1} \end{gathered}[/tex]Now the hypotenuse is,
[tex]\begin{gathered} hyp^2=opp^2+adj^2 \\ \\ hyp^2=5+1 \\ \\ =5+1 \\ \\ =6 \\ \\ hyp=\sqrt{6} \end{gathered}[/tex]Now,
[tex]\begin{gathered} \sin\theta=\frac{opp}{hyp} \\ \\ =\frac{\sqrt{5}}{\sqrt{6}} \end{gathered}[/tex][tex]\begin{gathered} \cos\theta=\frac{adj}{hyp} \\ \\ =\frac{1}{\sqrt{6}} \end{gathered}[/tex][tex]\begin{gathered} cot\theta=\frac{adj}{opp} \\ \\ =\frac{1}{\sqrt{5}} \end{gathered}[/tex][tex]\begin{gathered} sec\theta=\frac{hyp}{adj} \\ \\ =\frac{\sqrt{6}}{1} \end{gathered}[/tex][tex]\begin{gathered} cosec\theta=\frac{hyp}{opp} \\ \\ =\frac{\sqrt{6}}{\sqrt{5}} \end{gathered}[/tex]Final Answer:
The six trig ratio are
[tex]\begin{gathered} \sin\theta=\sqrt{\frac{5}{6}} \\ \cos\theta=\frac{1}{\sqrt{6}} \\ cot\theta=\frac{1}{\sqrt{5}} \\ sec\theta=\sqrt{6} \\ cosec\theta=\frac{\sqrt{6}}{\sqrt{5}} \end{gathered}[/tex]The volume of this cube is 125 cubic meters. What is the value of d?
EXPLANATION
The volume of a cube is equal to:
V= side*side*side
Let's call to the side: "d"
V = d*d*d = d^3
If the volume is equal to 125 m^3, then the value of d will be:
[tex]125=d^3[/tex]Isolating d:
[tex]\sqrt[3]{125}=5m^3[/tex]Answer: the value of d is 5 cubic meters.
A nonnative species of fish are taking over a lake in Florida. Each pair of fish creates 30 new fish each year. Scientists predict that there are currently 50 nonnative fish in the lake.
Create a table and graph to model this situation. How long will it take for the nonnative fish population to exceed 1,000,000?
Also please explain why you chose the multiplier you are using for your table/equations.
The table and the graph of the given model has been created and it will take 3 to 4 years for the nonnative fish population exceed 1000000
Number of nonnative fish in the lake = 50
Each pair of fish creates 30 new fish each year.
The population in one year = (50/2) ×30
= 25×30
= 750
The population in second year = (750/2) × 30
= 375 × 30
= 11250
The population in third year = (11250/2) × 30
= 5625 × 30
= 168750
The population in fourth year = (168750/2) × 30
= 84375 × 30
= 2531250
It will take 3 to 4 years for the nonnative fish population exceed 1000000
Create a table using the values and draw the graph
Hence, the table and the graph of the given model has been created and it will take 3 to 4 years for the nonnative fish population exceed 1000000
Learn more about graph here
brainly.com/question/17267403
#SPJ1
What type of function is the graph?Sqaue RootPiecewiseStepLinearQuadraticExponentialCube RootAbsolute Value
Let's begin by listing out the given information:
The graph is a curve that crossed the y-intercept
It cannot be a quadratic function. The graph does not cross the x-intercept twice
It cannot be a cube root function. The graph does not cross the x-intercept thrice
It cannot be a linear function because it is not a straight line
The graph is the graph of an exponential function (the graph has the x-axis as an asymptote on the left, and increases very fast on the right)
which answer best shows that is function is only decreasing
-2 < x < 0.5
By looking at the graph, we can see that from x = -2 to x = 0.5 the function is decreasing, from 0 to -7 ( olong the y axis)
17)
The table shows a linear relationship between x and y.
What is the rate of change of y with respect to x?
A -9/2
B 2/9
C -2/9
D 9/2
Explain in complete sentences why you chose this answer, make sure
to support your answer with the data above.
Answer:
A
Step-by-step explanation:
Slope is defined by [tex]\frac{y_2-y_1}{x_2-x_1} or \frac{rise}{run}[/tex]. Take 2 points from this table and plug into the formula to find the slope.
[tex]\frac{96-60}{-20--12} = \frac{36}{-8} = -9/2[/tex]
From a logical standpoint, since when x increases and y decreases, the slope must be negative, eliminating answering B and D. Because the y value changed more than the x value, the slope must be more than 1, eliminating option C and leaving you with option A.
A tree service company put logs in the shape of a rectangular prism.However, it is supposed to snow, and the owner wants to cover the logs tokeep them dry. If the pile of logs creates a rectangular prism with thesemeasurements: 30 cm long, 12 cm wide, and 40 cm high, what is theminimum amount of material needed to cover the pile of logs? *
An example of a rectangular prism is given below
To get the minimum amount of material needed to cover the pile of logs, we will get the volume of the rectangular prism
The volume is calculated as:
[tex]\text{Volume of prism = length}\times breadth\times height[/tex]Thus, the minimum amount of material will be
[tex]\begin{gathered} \text{Volume}=30\operatorname{cm}\times12\operatorname{cm}\times40\operatorname{cm} \\ \text{Volume}=14400\operatorname{cm}^3 \end{gathered}[/tex]The minimum amount of material needed to cover the pile of logs will be 14400cm³
Express the set in roster form.The set of natural numbers between and Question content area bottomPart 1Choose the correct answer below.A.B.C.D.E.F.G.
To express a set in roster form, we shall list all the elements of that set separated by comas, and enclosed on either side by braces.
For the set of all natural numbers between 18 and 161, we would have the answer as;
ANSWER:
[tex]\mleft\lbrace18,19,20,21,\ldots,161\mright\rbrace[/tex]The correct answer is option A
solve for f 8=6+2falgebra
Given the following question:
To find the answer we need to isolate the variable.
[tex]\begin{gathered} 8=6+2f \\ 2f+6=8 \\ 6-6=0 \\ 8-6=2 \\ 2f=2 \\ \frac{2f}{2}=f \\ 2\div2=1 \\ f=1 \end{gathered}[/tex]Your answer is f = 1.
Express the confidence interval (32.9%, 49.1%) in the form of ˆp ± ME
ANSWER
[tex]\text{ 41\%}\pm8.1\text{ \%}[/tex]EXPLANATION
The confidence interval is given as (32.9%, 49.19%)
Firstly, we need to find the value of P and ME
Assume, that the upper limit of the confidence interval is 49.19%, and the lower limit is 32.9%
P + ME = 49.1 ---------- 1
P - ME = 32.9 ------------2
The above equation can be solved simultaneously by using the substitution method
Isolate P in equation 1
P = 49.1 - ME
substitute the value of P = 49.19 - ME into equation 2
49.1 - ME - ME = 32.9
49.1 - 2ME = 32.9
subtract 49.1 from both sides of the equation
49.1 - 49.1 - 2ME = 32.9 - 49.1
-2ME = 32.9 - 49.1
-2ME = -16.2
Divide both sides by -2
-2ME/-2 = -16.2/-2
ME = 8.1
To find P, substitute the value of ME = 8.15 into the equation 1
P = 49.1 - 8.1
P = 41
From the above calculations, you will see that P = 41% and ME = 8.1%
Hence the confidence interval can be expressed as
[tex]\text{ 41\% }\pm\text{ 8.1\%}[/tex]400 ft 175 ft 550 ft What is the area of this trapezoid? square feet
Let's begin by listing out the information given to us:
[tex]b_1=400ft,h=175ft,b_2=550ft[/tex]The area of this trapezoid
[tex]\begin{gathered} A=\frac{1}{2}(b_1+b_2)h \\ A=\frac{1}{2}(400+550)\cdot175=\frac{1}{2}(950)\cdot175 \\ A=83125ft^2 \end{gathered}[/tex]