y = 7 + x
y = 3x + 9
To solve the simulataneous equation with subtraction,
Step 1: name the equations
y = 7 + x ---- equation 1
y = 3x + 9 ----- equation 2
Step 2: subtract equation 1 from 2
so that
y - y = (3 x -x ) + (9 - 7)
0 = 2x + 2
2x = - 2
divide oth sides by 2
x = -2/2
x = -1
To get y, substitute the value for x into equation 1
y = 7 + x
y = 7 + (-1)
y = 7-1 = 6
y = 6
hence the solution is (-1, 6)
find the exact value of cosine Pi / 3 express your answer with a rational denominator
it is given that,
the expression is
cosine Pi/3
we know that
so,
[tex]\cos \frac{\pi}{3}=\cos \frac{180}{3}=\cos 60=\frac{1}{2}[/tex]thus, the answer is 1/2
what is 7.950•100? and how to do it?
This problem uses the symbol •, which is another symbol to denote multiplication. Also, we are multiplying a decimal to 100. When multiplying such number, we move the decimal place to the right by two since we are multiplying the decimal by 100.
For this problem, we have
[tex]7.950\cdot100[/tex]We are multiplying 7.950 by 100. This means that we move the decimal point two times to the right. Hence, 7.950 multiplied by 100 will yield
[tex]7.950\cdot100=795.0[/tex]Answer: 795.0
hello can yoy help with this plane trigonometry question and in the question turn it into radians and thank you for your time for helping me
Answer:
The angle between 0 and 2 pie that is coterminal to the given angle is;
[tex]\frac{6}{7}\pi[/tex]Explanation:
We want to find the angle between 0 and 2 pie that is coterminal to;
[tex]\frac{34}{7}\pi[/tex]Angles that are coterminal with the given angle can be calculated using the formula;
[tex]x+n2\pi=\frac{34}{7}\pi[/tex]Where n=1,2,3...
and x is the coterminal angle.
At n = 1;
[tex]\begin{gathered} x+2\pi=\frac{34}{7}\pi \\ x=\frac{34}{7}\pi-2\pi \\ x=\frac{34}{7}\pi-\frac{14}{7}\pi \\ x=\frac{20}{7}\pi \end{gathered}[/tex]at n=2;
[tex]\begin{gathered} x+2(2\pi)=\frac{34}{7}\pi \\ x+4\pi=\frac{34}{7}\pi \\ x=\frac{34}{7}\pi-4\pi \\ x=\frac{34}{7}\pi-\frac{28}{7}\pi \\ x=\frac{6}{7}\pi \end{gathered}[/tex]At n=2;
The value of x is between 0 and 2pie;
So, the angle between 0 and 2 pie that is coterminal to the given angle is;
[tex]\frac{6}{7}\pi[/tex]Which of the following is the graph of the following system of equations? { 2x - 3y>12 {y< -1 x + 5 2
SOLUTION
The graph of the inequality
[tex]\begin{cases}2x-3y\ge12{} \\ y<-\frac{1}{2}x+5\end{cases}[/tex]is shown below
The darkest part is the required region
Comparing with the options,
the answer is the graph below
Yuson must complete 30 hours of community Service. She does two hours each day. Write a linear equation to represent the hours she has left after X days.
Yuson must complete 30 hours of community service.
She does two hours each day.
We are asked to write a linear equation to represent the hours she has left after x days.
We can write the following linear equation
[tex]30-2x=0[/tex]Where 30 represents the total hours of community service that Yuson has to complete.
2 represents the hours she works each day.
x represents the days.
We can also solve this equation to find how many days will it take her to complete the community service.
Graph the solution to the following inequality on the number line,(x + 6) (x-3) 20
If you have an equality of the form...
[tex](x+a)\cdot(x-b)\ge0[/tex]The inequality can be writen as...
[tex]a\leq x\leq b[/tex]I'll show you how it looks like on the graph
the graph indicates that x is any value less than or equal to -6 or greater than or equal to 3, which is the red area
[tex]\begin{gathered} x\leq-6 \\ x\ge3 \end{gathered}[/tex]Maria is using a meter stick to determine the height of a door. If the smallest unit on the meter stick iscentimeters, which measurement could Maria have used to most accurately record the height of thedoor?23 meters2 meters2.309 meters2.31 meters
The most accurate measure of the height in meters is in two decimal places
The most accurate measure for maria to use is 2.31meters
The Forth option is correct
-3v - 14> 3v+16 It’s for my final review and I’m so confused
The given inequality is
-3v - 14 > 3v + 16,
Add 3v on both side of the inequality
-3v -14 +3v > 3v +16 +3v
-3v +3v -14 > 3v + 3v + 16
0 - 14 > 6v + 16
Subtract 16 from both side of the equation,
-14 - 16 > 6v + 16 - 16
-30 > 6v + 0
Now subtract 6v from both side,
-30- 6v > 6v - 6v
-6v -30 > 0
Add 30 on both side,
-6v -30 + 30 > 30
-6v > 30
Divide both side by 6:
-6v/6 > 30/6
-v > 5
Multiply both side by (-1)
(-1) (-v) < (-1) 5
v < -5
Thus, v < -5
Answer : v < -5
Answer:
v < -5
Step-by-step explanation:
Add 14 to each side
[tex]-3v-14+14 > 3v+16+14[/tex]
Next, you need to simplify these additions by adding non-variable integers
[tex]16 + 14 = 30\\= 3v + 30\\= -3v > 3v + 30[/tex]
Now, subtract each side by 3v, the leading term in this equation.
[tex]-3v-3v > 3v+30-3v[/tex]
Again, we must simplify to get to the next step. This time we are dealing with a negative minus a negative. There on, things get trickier. In short words, a negative minus a positive is going to have a negative result, because both sides are treated as a negative plus a negative. In an equation, -a - b is the same as -a + -b.
[tex]-3v - 3v = -3v + -3v\\= -6v\\3v + -3v = 3v - 3v\\= 0\\= 0 + 30\\= 30\\= -6v > 30[/tex]
Next, we must multiply both sides by -1. The reason we're multiplying by a negative instead of a positive is because we are reversing the inequality.
[tex]= -6v\times -1 < 30\times 1[/tex]
Notice the change from greater than to less than.
IMPORTANT NOTE: A negative times a negative is a positive, a positive times a positive is also a positive. Lastly, a negative times a positive is a negative.
[tex]-6v\times -1 = 6v\\30\times -1 = -30\\= 6v < -30[/tex]
For the next step, we must divide by 6, because 6 can be divided by 6, and -30 can also be divided by 6 fairly.
[tex]\frac{6v}{6} < \frac{-30}{6}\\\frac{6v}{6} = \frac{6\times v}{6}\\Assume\:v=1!\\= \frac{6\times 1}{6}\\= \frac{6}{6}\\= 1\\= v[/tex]
[tex]\frac{-30}{6}\\\\(-a)/b = (-a/b)\\\\=-\frac{30}{6}\\= -5[/tex]
And therefore, v is less than -5.
If you need anything else, let me know!
Hope this helps!
Stats To quality for a police academy, applicants are given a lest of physical Itness. Ihe scores are normallyDistributed with a mean of 64 and a standard deviation of 9. If only the top 20% of the applicants are selected,Find the cutoff score.
Since we want just the top 20% applicants and the data is normally distributed, we can use a z-score table to check the z-score that gives this percentage.
The z-score table usually shows the percentage for the values below a certain z-score, but since the whole distribution accounts to 100%, we can do the following.
We want a z* such that:
[tex]P(z>z^*)=0.20[/tex]But, to use a value that is in a z-score table, we do the following:
[tex]\begin{gathered} P(zz^*)=1 \\ P(zz^*)=1-0.20=0.80 \end{gathered}[/tex]So, we want a z-score that give a percentage of 80% for the value below it.
Using the z-score table or a z-score calculator, we can see that:
[tex]\begin{gathered} P(zNow that we have the z-score cutoff, we can convert it to the score cutoff by using:[tex]z=\frac{x-\mu}{\sigma}\Longrightarrow x=z\sigma+\mu[/tex]Where z is the z-score we have, μ is the mean and σ is the standard deviation, so:
[tex]\begin{gathered} x=0.8416\cdot9+64 \\ x=7.5744.64 \\ x=71.5744\cong72 \end{gathered}[/tex]so, the cutoff score is approximately 72.
What is 0.6222... as. a fraction, and how do I solve?
The given number is
[tex]0.6222\ldots[/tex]This number is a repeating decimal number, which is a rational number because it has a pattern that repeats infinitely. That pattern or period is 2.
To transform this decimal number into a fraction, we need to do it as follows
[tex]0.6\bar{2}=\frac{62-6}{90}[/tex]Notice that the difference is form by the complete number without a decimal point (62), and the digits before the repeating decimal (6). The denominator is formed by nines and zeros, in this case, we use one 9 because there's only one repeating digit, we use one 0 because there's only one digit between the decimal points and the repeating digit.
Now, we solve the fraction and simplify
[tex]0.6\bar{2}=\frac{62-6}{90}=\frac{56}{90}=\frac{28}{45}[/tex]Therefore, the fraction 28/45 is the one that represents the repeating decimal 0.6222...What is the prime factorization of 72?
A. What is the prime factorization of 72?
A.
Answer:
2 3 ⋅ 3 2
Step-by-step explanation:
Answer:23·32
Step-by-step explanation:72 divided by 32 will give you 23 and 32 multiplied by 23 equals 32
15 percent of a certain company's life insurance policy holders are smokers. For each nonsmoker the probability of dying during the year is 0.011. For each smoker the probability of dying during the year is 0.04. Find the probability that a policy holder who died last year was a smoker.
Percentage of Smoker Policy Holders = 15% / 100% = 0.15
Probability of Smokers Dying = 0.04
Let's substitute the values to the equation, we get,
[tex]\text{ P = (0.15)(0.04) = 0.006}[/tex]The probability that a policy holder who died last year was a smoker = 0.006
35,876 rounded to nearest 100 and 1000
EXPLANATION:
To round a figure we must look specifically at what place value is the number immediately after the comma.
for example:
35,876 rounded round to the nearest thousand:
ANSWER:
As the figure that follows after the comma approaches 9, immediately add one unit to 5, transforming the number into an approximate value of 36,000
Now rounded to nearest 100:
35,900
to round to 100 we only look at the three-unit figures that correspond to the hundred, that is, the place value of the figure after the comma.
cosx-sin^2x-1how do I write the expression in factored form as an algebraic expression of a single trigometric function?
You use the next trigonometric inentities:
[tex]\begin{gathered} \sin ^2x+\cos ^2x=1 \\ \\ \sin ^2x=1-\cos ^2x \end{gathered}[/tex][tex]\begin{gathered} \cos x-\sin ^2x-1 \\ \\ =\cos x-(1-\cos ^2x)-1 \\ =\cos x-1+\cos ^2x-1 \\ =\cos x+\cos ^2x-2 \\ \end{gathered}[/tex]Common factor cosx:
[tex]=\cos x(1+\cos x)-2[/tex]write an equation in slope intercept form of the line that is perpendicular to the line Y equals 1/4 x -9 and passes through 1, 1
For perpendicularity
[tex]\begin{gathered} \text{slope of line 1 =}\frac{-1}{slope\text{ of line 2}}_{} \\ \text{slope of line 1 = m}_1 \\ \text{slope of line 2 =m}_2 \end{gathered}[/tex][tex]\begin{gathered} \text{Hence,} \\ m_1=\frac{-1}{m_2} \end{gathered}[/tex][tex]\begin{gathered} \text{From the question} \\ m_1=\text{ }\frac{1}{4} \end{gathered}[/tex][tex]undefined[/tex]ine TrackerWhat additional piece of information is needed in order to say thatthese two triangles are congruent by AAS postulate?BO BC DEO AB DEO BC EFO AB DF
Answer
Option B is correct.
AB ≅ DE
Explanation
The key to two triangles being similar according to AAS is that they have two angles and an excluded side in common.
An excluded side does not reside between the two congruent angles.
So, for these two triangles to be congruent according to AAS,
Angle C = Angle F
Angle B = Angle E
And
Side AB ≅ Side DE
Hope this Helps!!!
enter each answer as a whole number the ratio of United States gold-medal to Russia gold medal was about _________ to 1 b about _________ %of Australia's total medals were gold.
the ratio of United States gold-medal to Russia gold medal was about 46/24=23/12 to 1
about %of Australia's total medals were gold.
PLEASE HELP!!
An ice cube is freezing in such a way that the side length s, in inches, is s of t equals one half times t plus 4 comma where t is in hours. The surface area of the ice cube is the function A(s) = 6s2.Part B: Find the surface area as a function of time, using composition, and determine its range. (4 points)
Answer:
A(t) = 3/2t² + 24t + 96
Range = (96, ∞)
Explanation:
The equation for the side length of the cube s is given by
[tex]s(t)=\frac{1}{2}t+4[/tex]Where t is the number of hours. In the same way, the equation for the surface area is:
[tex]A(s)=6s^2[/tex]Then, the surface area as a function of time will be the composite function A(s(t)). So, replacing s by the equation of s(t), we get:
[tex]\begin{gathered} A(s(t))=6s(t)^2 \\ A(s(t))=6(\frac{1}{2}t+4)^2 \\ A(t_{})=6(\frac{1}{4}t^2+2(\frac{1}{2}t)(4)+4^2) \\ A(t)=6(\frac{1}{4}t^2+4t+16) \\ A(t)=6(\frac{1}{4}t^2)+6(4t)+6(16) \\ A(t)=\frac{3}{2}t^2+24t+96 \end{gathered}[/tex]Then, the range is the set of all the possible values that A(t) can take. Since t takes values greater than or equal to 0, the minimum value that A(t) will take is 96 because:
A(0) = 3/2(0)² + 24(0) + 96 = 96
Therefore, the range for the surface area will be (96, ∞)
Pretty please help!!!If x= -3, which number line shows the value of |x|?
it is given that
x = -3
now
IxI = I-3I = 3
so
IxI = 3
so the correct answer is option C
What do the expanded form and a place- value chart tell you about a number such as 25,049?How are they alike and different
The expanded form of a number is written out in such a way that you would be able to see the math value of individual digits.
The number 25,049 which reads "twenty five thousand and forty nine," can be written in expanded form as follows;
2 x 10000 = 20,000
5 x 1000 = 5,000
0 x 100 = 0
4 x 10 = 40
9 x 1 = 9
So, as you can see the expanded form shows that the digit 2 (for example) in this number has a value of 20,000.
The place value chart groups the number in threes starting from the right to the left. That is, you count three numbers from the end (right hand side) insert a coma, and take the next three set of digits and so on. You can now tell the value of each digit by starting from the left (the begining) to the right (the end). Usually starting with billions, the chart now tells you the value of each digit. So in this question, you can read from left to right and by using the expanded form, you can tell the value of the 2, the 5, and so on till the last digit.
They are alike because the expanded form helps you determine the actual value of each digit without mistake, and the place value also tells you which number carries what value.
They are different because an expanded form gives you details of how each number gets its place value, while the place value chart simply tells you the value of each digit simply by arranging and inserting comas.
On a local sports team, 20% of 50 players are left-handed. How many left-handed are on the team?There is/are ____ left-handed player(s) on the team. (Type a whole number.)
Answer:
10 left-handed players
Explanation:
The total number of players on the team = 50
We are told that 20% of 50 players are left-handed.
Therefore, the number of left-handed players will be:
[tex]\begin{gathered} =20\%\text{ of 50} \\ =\frac{20}{100}\times50 \\ =\frac{20}{2} \\ =10\text{ players} \end{gathered}[/tex]There are 10 left-handed players on the team.
Estimating which integers are between square roots- please explain the steps!
Hello there. To solve this question, we want to determine how to find the square root of a value using estimations.
Given a number m, we want to determine an estimation for its square root:
[tex]\sqrt{m[/tex]In this case, we have to find the closest integers to m, considering it is not a perfect square and is positive (greater than zero).
Of course, zero is the trivial case, since every square root is bounded below by zero.
For this, consider the function:
[tex]\lfloor m\rfloor[/tex]It is the floor function and it gives us the nearest integer that is less than or equal to m.
We do the same to fi
Give the domain of the following rational function using (a) set-builder notation and (b) interval notation.f(y) = y —— y-1 ——————————————————(a) Select the correct choice below and, if necessary, fill in the answer box to complete your choice.A. The domain of the given function is {yly is a real number, y # ____}(Type an integer or a simplified fraction. Use a comma to separate answers as needed.)B. The domain of the given function is {yly is a real number).
ANSWER:
(a)
A. The domain of the given function is {yly is a real number, y ≠ 1}
(b)
[tex]\begin{equation*} D=\left(-\infty\:,\:1\right)\cup\left(1,\:\infty\:\right) \end{equation*}[/tex]STEP-BY-STEP EXPLANATION:
We have the following function:
[tex]f(y)=\frac{y}{y-1}[/tex]The domain of a function, are the input values of the function, in this case, it corresponds to the values that y can take.
Since it is a rational function and it cannot take values that make the denominator zero, so we set the denominator equal to zero, like this:
[tex]\begin{gathered} y-1=0 \\ \\ y\ne1 \end{gathered}[/tex](a)
That means that y can take the value of all reals except 1.
So the correct answer is:
A. The domain of the given function is {yly is a real number, y ≠ 1}
(b)
In its interval form it would be:
[tex]D=\left(-\infty\:,\:1\right)\cup\left(1,\:\infty\:\right)[/tex]find X and Y so that the quadrilateral is a parallelogram 5y 5x 25
x=31
y=5
Explanation
Step 1
if the green angles are equal and the blue angles are equal, then
is is a parallelogram, then
[tex]\begin{gathered} green\text{ angle} \\ 5y=25 \\ \\ y=\frac{25}{5} \\ \\ y=5 \end{gathered}[/tex]Step 2
blue angles
we do not have the value for the last angle, but we know
" the sum of the internal angles of a quadrilateral = 360
replacin
2 green angles +1 blue angle+5x=360
2*5y+5x+5x=360
[tex]\begin{gathered} 10y+10x=360 \\ 10x=360-10y \\ x=36-y \\ \text{replace }y=5 \\ x=36-5 \\ x=31 \end{gathered}[/tex]I hope this helps you
what's the simplest form to represent the area of a rectangular building that's 2y feet and the length to be 9y-4
The area of a rectangle is given by the formula:
[tex]A=lw[/tex]Where
A is area
l is length
w is width
We find the expression for the area by multiplying the two "lengths" given:
[tex]\begin{gathered} A=2y(9y-4) \\ A=18y^2-8y \end{gathered}[/tex]The answer is:
[tex]A=18y^2-8y[/tex]Select the values that make the inequality m≥7 true.
(Numbers written in order from least to greatest going across.)
Step-by-step explanation:
every number greater than or equal to 7.
just as the expression says.
are we taking only about integer values ?
so,
7, 8, 9, 10, ... +infinity
if we aim for radical or real values, then starting with 7 everything between these numbers.
the interval definition is
[7, +infinity)
please note the different brackets.
"[" or "]" means the interval end value is included.
"(" or ")" means the interval end value is excluded.
which is the normal thing for infinity, because infinity is only a concept and never a number. so, it cannot be included.
Which of the following is true about a kite?a.All angles are rightb.The diagonals have the same lengthc.All four sides are equald.Adjacent sides are congruent
In a kite, there is always an angle that is not right, otherwise, it would have a rectangular shape.
The diagonals are not of the same length because that would mean it would have a rectangular shape as well.
The sides are not equal, because that would mean it would have a rhomboid shape, to which a square belongs to.
The top edges are congruent with each other, as well as the bottom ones. This is because you can turn one into the other by reflecting them using an isometry, so D is true.
Provide the correct reason for the statement in line 4.
We have to prove x = -16/3.
The steps are:
[tex]1)3(x+5)=-1\longrightarrow\text{Reason: Given}[/tex][tex]2)3x+15=-1\longrightarrow\text{Reason: Distributive property}[/tex][tex]3)3x=-16\longrightarrow\text{ Reason: substracting 15 from both sides}[/tex][tex]4)x=-\frac{16}{3}\longrightarrow\text{ Reason: divide both sides of the equation by 3}[/tex]GIVING 100 POINTS!!
1.) Angles A and B are supplementary. Determine the measure of angle A if the measure of angle B is 115.2°.
A) 244.8°
B) 64.8°
C) 25.2°
D) 11.5°
2. Find the sum of the interior angles of a 22-sided polygon.
A) 1,980°
B) 2,160°
C) 3,360°
D) 3,600°
HELP! ME PLS!! TWO QUESTIONS!
Answer:
Step-by-step explanation:
1. The answer is C because 180-115.2=64.8
2. The answer is D.
Please give me brainliest!
Answer:
1. C
2. D
Step-by-step explanation:
Because
What is the measure of angle J in the triangle below? *Hint: Law of Sines*
SOLUTION:
Using the sine rules;
The equations developed;
[tex]\frac{15}{sin102}=\frac{12}{sinJ}[/tex]Making sinJ the subject;
[tex]\begin{gathered} sinJ=\frac{12sin102}{15} \\ sinJ=0.7825 \\ J=51.49^o \end{gathered}[/tex]Thus, the angle is 51.5 degrees.