SOLUTION
We want to find which of the following is a solution to
[tex]2x-y=-1[/tex]Let's try the first option (2, -1)
So, the first value will be x, so if we get y as 1, then this option is correct
Now replacing x for 2 in the equation, we have
[tex]\begin{gathered} 2x-y=-1 \\ 2(2)-y=-1 \\ 4-y=-1 \\ y=4+1 \\ y=5 \end{gathered}[/tex]So, this is not correct. Let us try the next option (1, 2)
Let's put x to be 1 and see what y becomes
[tex]\begin{gathered} 2x-y=-1 \\ 2(1)-y=-1 \\ 2-y=-1 \\ y=2+1 \\ y=3 \end{gathered}[/tex]So, when x = 1, y =3, If you look at the 4th option, we can see (1, 3), which means x = 1 and y = 3, hence
the correct answer is (1, 3) the 4th option
Keegan fills a bucket of water, carries it to the flower bed and slowly pours the water over the new planted flowers. Select the graph that represents the height of the water in the bucket.
Answer:
The first graph shows the height of water in the bucket
Find the second derivative of the function.g(t) = 31t-2g"(t) =X
Let's find the first derivative of the function:
[tex]g^{\prime}(t)=\frac{dg}{dt}=\frac{d}{dt}(31t^{-2})=-2(31)t^{-3}=-62t^{-3}[/tex]Hence the first derivative is:
[tex]\frac{dg}{dt}=-62t^{-3}[/tex]Now, that we have the first derivative we can calculate the second derivative:
[tex]g^{\doubleprime}(t)=\frac{d^2g}{dt^2}=\frac{d}{dt}(-62t^{-3})=-3(-62)t^{-4}=186t^{-4}[/tex]Therefore:
[tex]g^{\doubleprime}(t)=186t^{-4}[/tex]I need help please it’s due today and I don’t want to fail please help!! I’m in 8th grade just so you know
Using distribution property:
5 (3m - 6) = 5(3m) + 5 (-6) = 15m - 30
(-6p + 7) (-4) = (-6p)(-4) + (7)(-4) = 24 p - 28
5 (b - 1) = 5 (b) + 5(-1) = 5b - 5
(x + 9) 5 = x(5) + 9 (5) = 5x + 45
The sum of the interior angles of a polygon with n sides is 1980°. Find n.
We can relate the sum of the interior angles of a polygon S with its number of sides n as:
[tex]S=(n-2)\cdot180[/tex]Then, if S=1980 degrees, we can find n as:
[tex]\begin{gathered} 1980=(n-2)\cdot180 \\ n-2=\frac{1980}{180} \\ n-2=11 \\ n=11+2 \\ n=13 \end{gathered}[/tex]Answer: the polygon has 13 sides (n=13)
What happens to the function when x gets close to zero?What happens to the function as y gets very large, we say x'"approaches infinity"?What happens as x gets very small (approaches -∞)?
According to the graph:
* Domain:
[tex](-\infty,0)\cup(0,\infty)[/tex]* Range:
[tex](-\infty,0)\cup(0,\infty)[/tex]* When x gets close to zero on the left, the function approaches negative infinity.
And when x gets close to zero on the right, the function approaches to infinity.
* When y gets very large x approaches zero.
* When x gets very small, y is close to zero.
The Chinese Postman Problem question! 60 points
Answer:
if it travels a longer distance it will clear up more than it is supposed to and maybe go the wrong direction
Step-by-step explanation:
Convert the angle π/9 from radians to degrees. Round your answer to one decimal place, if needed.
pi/9 to degress
pi rad ----------------------- 180°
pi/9 rad ------------------- x
x = (pi/9 x 180) / pi
x = (180 x pi) / 9pi
x = 180/9
x = 20°
Result = 20°
You randomly select one of the marbles from the jar shown below. What is the probability that you will select a red marble? R marbles red, G marbles are green, and B marbles are blue.3/101/21/53/7
In the jar, we have:
• # of R marbles = 3,
,• # of G marbles = 2,
,• # of B marbles = 5,
,• total # of marbles = 3 + 2 + 5 = 10.
The probability of randomly selecting a red marble is:
[tex]P(\text{red})=\frac{\#\text{ of R marbles}}{\text{total \# of marbles}}=\frac{3}{10}.[/tex]Answer
3/10
Describe the vertical asymptote(s) and hole(s) for the graph of y= (x+2) / (x^2+8x+15).a) asymptotes: x = 3 and 5 and hole: x = - 2b) asymptotes: x = 3 and 5 and no holesc) asymptotes: x = - 5, - 3 and hole: x = - 2d) asymptotes: x = - 5, - 3 and no holes
we have the function
[tex]y=\frac{x+2}{x^2+8x+15}[/tex]Simplify
[tex]x^2+8x+15=(x+5)(x+3)[/tex]substitute
[tex]y=\frac{x+2}{(x+5)(x+3)}[/tex]Remember that
The denominator cannot be equal to zero
so
The domain of the given function, are all real numbers, except for x=-5 and x=-3
that means
There are vertical asymptotes at x=-5 and at x=-3
No holes in the graph
therefore
The answer is the option DA slope of 2 and passes through (2,3)
The equation of a Straight Line can be found knowing a point and the slope, as follows:
y-yo=m(x-xo)
Where:
m=2
(2,3)=(xo,yo)
xo=2
yo=3
Therefore:
y-3=2(x-2)
y-3=2x-4
y=2x-1
Find the zeros of each function by factoring. F(x)=x^2+9x+18
We have the following:
[tex]F\mleft(x\mright)=x^2+9x+18[/tex]factoring:
[tex]\begin{gathered} \mleft(x+3\mright)\mleft(x+6\mright)=0 \\ x+3=0 \\ x=-3 \\ x+6=0 \\ x-6 \end{gathered}[/tex]If 1/4 + 1/8 + n + 1/2 = 1, find the value of n.
Given:
[tex]\frac{1}{4}|+\frac{1}{8}|+n+\frac{1}{2}|=1[/tex]To Determine: The value of n
Solution:
[tex]\begin{gathered} \frac{1}{4}|+\frac{1}{8}|+\frac{1}{2}|+n=1 \\ \frac{2+1+4}{8}|+n=1 \\ \frac{7}{8}|+n=1 \end{gathered}[/tex][tex]\begin{gathered} n=1-\frac{7}{8}| \\ n=\frac{8-7}{8}| \\ n=\frac{1}{8}| \end{gathered}[/tex]Hence, the value of n is
[tex]n=\frac{1}{8}|[/tex]A drug manufacturer produces 7,000,000mg of a certain drug. How many kg is thisequal to?
1 mg = 1/1,000,000 kg =10^-6 kg
multiply 7,000,000 by 1/1,000,000
7,000,000 x (1/1,000,000) = 7 kg
Simplify completely: 12x11y · 1848062" y? 16O 6x^y? V6xO 6x"y? 6xO 216'ya
Given:
[tex]\sqrt[]{12x^{11}y^6}.\sqrt[]{18y^8}[/tex]To simplify this, we can follow the steps below
[tex]\sqrt[]{12x^{11}y^6}.\sqrt[]{18y^8}=\sqrt[]{12\times18\times x^{11}\times y^6\times y^8}[/tex]This can be simplified further
[tex]\sqrt[]{216\times x^{11}\times y^{14}}[/tex]Then we will obtain
[tex]\sqrt[]{216\text{ }}\text{ x }\sqrt[]{x^{11}}\text{ x}\sqrt[]{y^{14}}[/tex]=>
[tex]6\sqrt[]{6}\times x^{\frac{11}{2}}\times y^{\frac{14}{2}}[/tex]=>
[tex]6\sqrt[]{6}\text{ }\times(x^{5+\frac{1}{2}})\times y^7[/tex]=>
[tex]6\sqrt[]{6}\text{ }\times x^5\times x^{\frac{1}{2}}\times y^7[/tex]=>
[tex]6\sqrt[]{6}\text{ }\times x^5\times\sqrt[]{x}\text{ }\times y^7[/tex]=>
[tex]6x^5y^7\sqrt[]{6x}[/tex]What is 6.43 x 10^7 in standard notation?A.643 x 10^5B.64,300,000C.6,430,000,000D.64.3 x 10^10
Step 1
Standard notation of a number is when a number is written with only number digits and not in scientific notation.
E.g 1235679 is in standard notation
1.235679 x 10^6 is in scientific notation
Step 2
Write 6.43 x 10^7 in standard notation
[tex]\begin{gathered} 10^7=\text{ 10000}000 \\ 6.43\text{ x 10000000= 64,300,000} \end{gathered}[/tex]Hence the answer is option B
Use the given function value and the trigonometric identities to find the exact value of each indicated trigonometric function. (I already have the csc I need the others)
b.
In order to calculate the cotangent of 60°, we can use the relation below:
[tex]\cot (90\degree-x)=\frac{1}{\cot x}=\frac{1}{\frac{1}{\tan x}}=\tan x[/tex]So we have:
[tex]\begin{gathered} \cot (90\degree-30\degree)=\frac{1}{\cot (30\degree)} \\ \cot (60\degree)=\frac{1}{\frac{1}{\tan30\degree}}=\tan 30\degree \\ \cot (60\degree)=\frac{\sqrt[]{3}}{3} \end{gathered}[/tex]c.
To calculate the cosine of 30°, we can use the relation below:
[tex]\tan x=\frac{\sin x}{\cos x}[/tex]So we have:
[tex]\begin{gathered} \tan 30=\frac{\sin 30}{\cos 30} \\ \frac{\sqrt[]{3}}{3}=\frac{\frac{1}{2}}{\cos 30} \\ \sqrt[]{3}\cos 30=\frac{3}{2} \\ \cos 30=\frac{3}{2\sqrt[]{3}}=\frac{\sqrt[]{3}}{2} \end{gathered}[/tex]d.
Calculating the cotangent of 30°, we have:
[tex]\cot (30\degree)=\frac{1}{\tan(30\degree)}=\frac{1}{\frac{\sqrt[]{3}}{3}}=\frac{3}{\sqrt[]{3}}=\sqrt[]{3}[/tex]Part A. 0.3 is 30% of what number ?
Let be "x" the number that represents 100%.
According to the information given in the exercise, 30% of the number "x" is:
[tex]0.3[/tex]Then, you can set up the following proportion:
[tex]\frac{0.3}{30}=\frac{x}{100}[/tex]Now you can solve for "x" in order to find the number:
[tex]\begin{gathered} (100)(\frac{0.3}{30})=x \\ \\ \frac{30}{30}=x \\ \\ x=1 \end{gathered}[/tex]Therefore, the answer is:
[tex]1[/tex]Write the first five terms of the sequence whose general term, a_n, is given as a_n= -3n+9
To find the terms, substitute n by the number of the term, according to the steps.
Step 01: Find a₁.
To do it, substitute n by 1.
[tex]\begin{gathered} a_n=-3n+9 \\ a_1=-3\cdot1+9 \\ a_1=-3+9 \\ a_1=6 \end{gathered}[/tex]Step 02: Find a₂.
[tex]\begin{gathered} a_2=-3\cdot2+9 \\ a_2=-6+9 \\ a_2=3 \end{gathered}[/tex]Step 03: Find a₃.
[tex]\begin{gathered} a_3=-3\cdot3+9 \\ a_3=-9+9 \\ a_3=0 \end{gathered}[/tex]Step 04: Find a₄.
[tex]\begin{gathered} a_4=-3\cdot4+9 \\ a_4=-12+9 \\ a_4=-3 \end{gathered}[/tex]Step 05: FInd a₅.
[tex]\begin{gathered} a_5=-3\cdot5+9 \\ a_5=-15+9 \\ a_5=-6 \end{gathered}[/tex]In summary:
a₁ = 6
a₂ = 3
a₃ = 0
a₄ = -3
a₅ = -6
3.Consider this dilation. (a)Is the image of the dilation a reduction or an enlargement of the original figure? Explain. (b)What is the scale factor? Explain.
a)
Image VMS is reduced to image M'V'S'.
b) the scale factor is 2/3
M(-3,3)
Multiply -3 and 3 with 2/3 your result = -2 and 2.
Scale factor for coordinate M = (-3,3) andN = (-2,2)
Since it is reduction, -2/-3 or 2/3
Therefore, scale factor = 2/3
x-(x+7) What is the simplified expression?
EXPLANATION
Given the expression x-(x+7), removing the parentheses give us:
= x - x - 7
Adding like terms:
= -7
The simplified expression is -7
A realtor sold 3 homes during her first month at an average house price of $120,000. During her second month, she sold 7 homes at an average house price of $190,000. What is the overall house price average for both months combined?
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.
A computer technician charges $35.00 per hour plus a $75.00 service charge. Your father's firm hires him to hook up his company's Internet service. The computer technician spends h hours to complete the job. Complete the function that represents the cost of the total bill, c(h), in terms of hours worked. c(h) =
Answer
c(h) = 35h + 75
Explanation
The computer technician charges 35 dollars per hour and a 75 dollar service charge.
So, if the computer technician spends h hours on a particular job.
Total charge = (Sevice charge) + (Charge based on number of hours)
Sevice charge = 75 dollars
Charge based on number of hours = (35) (h) = 35h dollars
Total charge = (Sevice charge) + (Charge based on number of hours)
Total charge = 75 + 35h
Total charge = c(h)
c(h) = 35h + 75
Hope this Helps!!!
A quadrilateral has two angles that measure 150° and 140°. The other two angles are in aratio of 3:4. What are the measures of those two angles?o ando
Solution
Let the quadrilateral be
From the above
[tex]\begin{gathered} x+y+140+150=360 \\ x+y+290=360 \\ x+y=360-290 \\ x+y=70 \\ \text{Multiply through by 4} \\ 4x+4y=280\ldots\ldots\ldots\text{.}(1) \end{gathered}[/tex]Without the loss of generality, let
[tex]\begin{gathered} x\colon y=3\colon4 \\ \frac{x}{y}=\frac{3}{4} \\ \text{cross multiply} \\ 4x=3y \end{gathered}[/tex]Substitute 4x = 3y into equation (1)
[tex]\begin{gathered} 4x+4y=280 \\ 3y+4y=280 \\ 7y=280 \\ y=\frac{280}{7} \\ y=40 \end{gathered}[/tex]From
[tex]\begin{gathered} x+y=70 \\ x=70-y \\ x=70-40 \\ x=30 \end{gathered}[/tex]Therefore, the two angles are
[tex]30^{\circ},40^{\circ}[/tex]express 24,010 in scientific notation
24,010 = 24.010 x 1000 = 2.4010 x 10000 = 2.401 x 10^4
[tex]2.401x10^4[/tex]Answer:
2.401x10(power4)
Using the information in the diagram, state the free fact needed and the theorem usedto prove that WZI WZY.ZFree fact: Select)Congruence Theorem: (Select)
WX = WZ (Given)
WY = WY (Reflexive property of equality)
angle XWY = angle YWZ
Hence triangle WXY = triangle WZY
SAS (Two sides and an included angle)
What is the shape of the cross section taken parallel to the base of a square pyramid? (1 point)
Since the cross-section is parallel to the base of the pyramid
Since the base of the square pyramid is shaped a square, then
The cross-section should be a square
The answer is C
(2 points) In the state of Indiana, 471700 people don't drive. If this is 8.9% of the population of Indiana residents aged 5 years and older, estimate the population of Indiana residents aged 5 years and older. Express your answer rounded to the nearest hundredth of a million.
You have that in the state of Indiana, 471700 people don't drive. And this population corresponds to the 8.9% of the total population of Indiana resident aged 5 years and older.
In order to calculate the Indiana residents aged 5 years and older, you can use the information about people don't drive and the percentage about it. You can write the given specification as follow:
x(8.9/100) = 471700
where the unknown value x is the total population. When this factor x is multiplied by 8.9/100 you are calculating the 8.9% of that value, which in this case is equal to 471700.
Then, you solve the last equation for x, just as follow:
x(8.9/100) = 471700
x(0.089) = 471700
x = 471700/0.089 = 5300000
Hence, the total population of Indiana resident aged 5 years or older are 5,300,000
estimate the probability that the next three songs to playare all country songs.Which simulation design could Carlos use to estimate the probability?O A. Number cubeLet even number = countryLet odd number = not countryRoll cube three times. Repeat.O B. Number cubeLet 1, 2 = classicalLet 3,4 = countryLet 5, 6 = popRoll cube three times. Repeat.O C. Random digitsLet 1,2,3 = classicalLet 4,5,6 = country17 On-OnPREVIOUS
Explanation
Since the personal music player have equal numbers of classical songs, country music, and pop songs.The probability must be symmetric that is;
[tex]\begin{gathered} pr(pop)=\frac{1}{3} \\ pr(country)=\frac{1}{3} \\ pr(classic)=\frac{1}{3} \end{gathered}[/tex]The above must hold regardless of the number of songs. The right answer that correlates to this is:
Answer: Option B
What is sin θ if cos θ= √2/2 And θ is in 0< θ< π /2?
Can someone help me with this geometry question?The first box has four options: cylinder, square pyramid, cone, triangular prism
Answer:
The shell is best modeled by a cone.
[tex]SA=32\pi=100.6\text{ square inches}[/tex]By the given choices, since the surface area is not a perfect cone, it has a small alteration at the bottom which increases the area. The approximate surface area of the shell is 107.4 square inches.
Step-by-step explanation:
The seashell is best represented by a cone. The surface area of a cone is represented by the following equation:
[tex]\begin{gathered} SA=\pi rs+\pi\cdot r^2 \\ \text{where,} \\ \\ r=\text{radius} \\ s=\text{ slant height} \end{gathered}[/tex]Then, use the Pythagorean theorem to find the slant height:
[tex]\begin{gathered} s=\sqrt[]{2.5^2+10^2} \\ s=\frac{5\sqrt[]{17}}{2} \end{gathered}[/tex]Now, solve for the surface area. If s=10.3, r=2.5
[tex]\begin{gathered} SA=\pi\cdot2.5\cdot\frac{5\sqrt[]{17}}{2}+\pi\cdot(2.5)^2 \\ SA=25.75\pi+6.25\pi \\ SA=32\pi=100.6\text{ square inches} \end{gathered}[/tex]By the given choices, since the surface area is not a perfect cone, it has a small alteration at the bottom which increases the area. The approximate surface area of the shell is 107.4 square inches.