Which inequality's solution is represented by the graph?A)-2x + 6 5 52B)-2x + 6 2 522x + 6 5 -52D)2x - 6 2 -52
Answers
From the graph, the inequality is
x ≤ -23
Multiplying by -2 at both sides we get:
-2x ≥ (-23)*(-2)
-2x ≥ 46
Adding 6 at both sides:
-2x + 6 ≥ 46 + 6
-2x + 6 ≥ 52
Related Questions
Another method is to add the parents’ heights in inches and then add an additional 5 inches if the child is a boy or subtract 5 inches if the child is a girl. This total is then divided by 2 to predict the child’s ultimate height.Use the variable D, height of dad) and M, height of mom Write a formula for a boy’s adult height. Write the formula for a girl’s adult height.
Answers
Concept:
Write the variables
Height of dad = D inches
Height of mum = M inches
Step 1:
Total parent's height = D + M
Step 2:
The formula for a boy's adult height
[tex]=\text{ }\frac{D\text{ + M + 5}}{2}\text{ inches}[/tex]Step 3:
The formula for a girl’s adult height.
[tex]=\text{ }\frac{D\text{ + M - 5}}{2}\text{ inches}[/tex]
with work please 2x -42 = -8x + 28
Answers
We first need to
Help meeee quickly, I will mark brainliest!
Answers
Answer:
adjacent and corrasopnding
Step-by-step explanation:
cos^2x(1+tan^2x)=1 simplify
Answers
After simplifying cos^2x(1+tan^2x)=1, we get LHS = RHS.
The given equation is a trigonometric equation, that includes trigonometric ratios which basically are the ratios of sides or lengths of a right angle triangle.
To simplify the given equation, we use the identity (sec^2 x - tan^2 x = 1)
that is further (sec^2 x = 1+tan^2 x)
Lets take LHS (left hand side) first,
cos^2x(1+tan^2x)
By putting the identity in LHS equation, we get
cos^2 x (1 + tan^2 x )
cos^2 x (sec^2 x)
As we know that sec^2 = 1/cos^2
Hence, cos^2 x *(1/cos^2 x)
cos^2 is eliminated by division,
= 1 which is equal to RHS
Hence, simplified and LHS = RHS
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After simplification, the trigonometric function becomes equal to each other i.e. LHS = RHS.
What are Trigonometric Functions ?
The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
What are Trigonometric Ratios used for ?In trigonometry, sin, cos and tan values are the primary functions we consider while solving trigonometric problems. These trigonometry values are used to measure the angles and sides of a right-angle triangle. Apart from sine, cosine and tangent values, the other three major values are cotangent, secant and cosecant.
To simplify the given equation, we would use the identity (sec^2x - tan^2x=1) which is (sec^2x = 1 + tan^2x)
Firstly we will solve the LHS side
cos^2x(1+tan^2x)
By inserting the identity in LHS equation, we get
cos^2x(1+tan^2x)
cos^2x(sec^2x)
As sec^2 = 1/cos^2
Therefore, cos^2x *( 1/cos^2x)
cos^2 is eliminated by division,
= 1
which is equal to RHS
Hence solved and LHS = RHS
After simplification, the trigonometric function becomes equal to each other i.e. LHS = RHS.
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1. Look at the figure, OJKLM. Find the length of JKM5x-114+ 2xK
Answers
Answer: 24
Explanation
Opposite sides of a parallelogram are congruent.
Thus, assuming JKLM as a parallelogram, then:
[tex]5x-1=14+2x[/tex]By solving we get:
[tex]5x-2x=14+1[/tex][tex]3x=15[/tex][tex]x=\frac{15}{3}[/tex][tex]x=5[/tex]Finally, replacing this value in the expression of JK to know the value of JK:
[tex]JK=14+2(5)[/tex][tex]JK=14+10[/tex][tex]JK=24[/tex]how do i find the zeros of y=6x^2-6
Answers
The given quadratic equation y = 6x² - 6 contains two zeros :
(x - 1) and (x + 1)
Solution:Steps to solve quadratic equation:
Transform the equation into standard form, with one side set to zero. Take into account the non-zero side. Make each factor equal to zero (Remember: a product of factors is zero if and only if one or more of the factors is zero). Solve each of the resulting equations.Given quadratic equation ,
y = 6x² - 6
To find the zeros we have to solve the equation ,
y = 6x² - 6
= 6( x² -1 )
= 6( x² + x - x -1)
= 6(x ( x + 1) - 1( x + 1 ))
= 6 ( x - 1) ( x + 1 )
The equation y = 6x² - 6 contains two zeroes
= (x-1) and (x + 1)
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Write a linear function that represents the depth of the pond at a given time
Answers
Let x represent the number of days
Let f(x) represent water depth
We can see that the water depth is a function of the number of days.
Water depth, f(x) is the dependent variable and number of days, x is the independent variable.
As the days go by, the water depth changes.
The function is therefore:
[tex]f(x)=54-0.5x[/tex]The domain is the set of values (number of days) for which the pond will have a valid depth, i.e. between 54'' and 0.
[tex]0\le x\le108[/tex]Because at 0 days,
[tex]f(x)=54-0.5(0)=54^{\doubleprime}[/tex]And at 108 days,
[tex]f\mleft(x\mright)=54-0.5\mleft(108\mright)=0[/tex]John connected three resistors in series. The equivalent resistance of series resistors is the sum of the values of the individual resistors. If John used resistors which were 2.2 × 102 ohms, 3.3 × 103 ohms, and 4.7 × 104 ohms, what was the equivalent resistance? Choice 'A'5.052 × 104 ohmsChoice 'B'50.52 × 103 ohmsChoice 'C'505.2 × 105 ohmsChoice 'D'5.052 × 103 ohms
Answers
Given resistors are:
[tex]\begin{gathered} 2.2\times10^2ohms \\ 3.3\times10^3ohms \\ 4.7\times10^4ohms \end{gathered}[/tex]The equivalent resistance is the sum which is obtained below
We can re-write the values given as follow
[tex]2.2\times10^2+33\times10^2+470\times10^2[/tex]=>
[tex]505.2\times10^2\text{ohms}[/tex]We can then convert this
We will get
[tex]\begin{gathered} 505.2\times10^2\text{ohms=}5.052\times10^4ohms=50.52\times10^3ohms \\ \end{gathered}[/tex]Hello, I need some assistance with this homework question please for precalculusHW Q44
Answers
SOLUTION:
Case: Logarithms
A logarithm is the opposite of power. In other words, if we take a logarithm of a number, we undo exponentiation.
We consider the log of power law below:
[tex]\begin{gathered} \log_aa^x=x\log_aa \\ =x \end{gathered}[/tex]Given:
[tex]\log_33^{66}[/tex]Required: Without using calculators, use log laws to answer
Method:
Applying the law above,
[tex]\begin{gathered} \log_33^{66} \\ =66\log_33 \\ =66\times1.(Remember\text{ same base law: }\log_33=1 \\ =66 \end{gathered}[/tex]Final answer:
66
If the figures are similar, use a proportion to find the missing side?
Answers
Given:
The figure is
Find-:
The value of "x"
Explanation-:
The ratio of sides is
Compared with angle sides is
[tex]\frac{28}{21}=\frac{8}{6}=\frac{30}{x}[/tex]So, the value of "x" is
[tex]\begin{gathered} \frac{8}{6}=\frac{30}{x} \\ \\ x=\frac{30}{8}\times6 \\ \\ x=\frac{30}{4}\times3 \\ \\ x=\frac{15}{2}\times3 \\ \\ x=\frac{45}{2} \\ \\ x=22.5 \end{gathered}[/tex]The value of "x" is 22.5
help me pleaseee!!!
thank you
Answers
The equation of the line is y = 800x + 294000 and the average price of a new home in 2014 is $302000.
What is the slope?The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
The line passes through the points:
(0, 294000) and (7, 288400)
The equation of the line:
y - 294000 = (288400 - 294000)/(7)[x]
y - 294000 = 5600/7 (x)
y = 800x + 294000
x = 2014 - 2004 = 10
Plug x = 10 in the above equation:
y = 800(10) + 294000
y = 302000
Thus, the equation of the line is y = 800x + 294000 and the average price of a new home in 2014 is $302000.
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can i get help on this?Number of digits in phone number is 7.
Answers
There are 7 digits in phone number. The first digit cannot be 0 and 1. So first digit can be filled by 8 numbers (from 2 to 9). Remaining 6 digits of the phone number can be filled by all 10 number (0 to 1).
The possible number of 7 digit phone numbers are,
[tex]8\cdot10\cdot10\cdot10\cdot10\cdot10\cdot10=8,000,000[/tex]So 8,000,000 different numbers are possible.
Answer: 8,000,000
two number cubes are rolled for two separate events event A is the event that the sum of the numbers on both cubes is less than 10 event B is the event that the sum of the numbers on both cubes is a multiple of 3 find the conditional probability of B given A occurs first enter your answer as a simplified fraction
Answers
We have two events:
A: sum of the numbers is less than 10.
B: sum of the numbers is a multiple of 3.
We can calculate the probabilities as a quotient of the "success" events and all the possible events.
The conditional probability P(B | A) is equal to the probability of P(A intersection B) divided by P(A). That is because, if A is given, then if B happens, A had also happen.
The "success" events for intersection A and B are:
{1,2}, {2,1}, {1,5}, {5,1}, {2,4}, {4,2}, {3,3}, {3,6}, {6,3}, {4,5}, {5,4}
There are a total of 11 results that belong to the intersection of A and B (sum less than 10 and multiples of 3).
Now, we calculate the results that correspond to event A:
{1,1}, {1,2}, {2,1}, {1,3}, {3,1}, {1,4}, {4,1}, {1,5}, {5,1}, {1,6}, {6,1}
{2,2}, {2,3}, {3,2}, {2,4}, {4,2}, {2,5}, {5,2}, {2,6}, {6,2}
{3,3}, {3,4}, {4,3}, {3,5}, {5,3}, {3,6}, {6,3}
{4,4}, {4,5}, {5,4}
There are 30 results that correspond to event A (sum is less than 10).
Then we can calculate P(B | A) as:
[tex]P(B|A)=\frac{P(A\cap B)}{P(A)}=\frac{11}{30}[/tex]The conditional probability of B given A is P(B|A) = 11/30.
Cosh x = 25/7, x > 0
Answers
we have
cosh(x)=25/7 and x>0
Remember that
[tex]\cos h^2(x)-\sinh ^2(x)=1[/tex]
substitute the given function
[tex](\frac{25}{7})^2-\sinh ^2(x)=1[/tex][tex]\sinh ^2(x)=\frac{625}{49}-1[/tex][tex]\sinh ^2(x)=\frac{576}{49}[/tex]therefore
sinh(x)=24/7PLEASE HELP WITH NUMBER 16
Answers
Answer: C: Exam>=90
Step-by-step explanation:
The flaw you did was divided it by two, but you have to divide it by the number of numbers you have, which would be 4. that would give you 75, and then you have to figure out what score you would need to get on two tests (The question says it counts as 2 tests) which ends up being 90% to give you an 80%. So the answer is C! I hope this helps :)
Given f(x) = 1 - 2x with the range {-3, -5, -7}, find the domain.ОООО{2,3,4}{7, 11, 15){2, 15){-7,8}
Answers
Here is the answer: {2,3,4}
option A
The countries with the most widgets in the world are the United States and France. If the United States has 2006 more widgets than France and the total number of widgets is 8306. Find the number of widgets for each country.
Answers
Given:
a.) The United States has 2006 more widgets than France.
b.) The total number of widgets is 8306.
Let,
x = The number of widgets the United States has
y = The number of widgets France have
x = y + 2006 ; Since the United States has 2006 more widgets than France.
From the given scenario, we generate the following equation:
[tex]\text{ x + y = 8306}[/tex]Let's determine the value of x and y.
[tex]\text{ x + y = 8306}[/tex][tex]\text{ (}y+2006)\text{ + y =8306}[/tex][tex]\text{ }y+2006\text{ + y =8306}[/tex][tex]\text{ }y+\text{ y =8306 - }2006[/tex][tex]\text{ 2y = }6,300[/tex][tex]\text{ }\frac{\text{2y}}{2}\text{ = }\frac{6,300}{2}[/tex][tex]\text{ y = }3150[/tex]Therefore, France has 3150 Widgets.
Let's determine the number of fidgets the United States has. Use y = 3150 in the equation x + y = 8306.
[tex]x+y=8306[/tex][tex]x+3150=8306[/tex][tex]x=8306\text{ - }3150[/tex][tex]x=5156[/tex]Therefore, the United States has 5156 Widgets.
Gina has a box of red,blue,and green markers.The ratio of the number of red markers to the number of blue markers is 5:2.The ratio to the number of blue markers to the number of green markers is 3:5.What is the ratio of the number of red markers to the number of green markers?
Answers
Answer: 5:5
Step-by-step explanation:
Use the information to figure out how much you have of each color, then put in ratio.
AJ's Car used 3 1/4 gallons of gas on a trip to the beach assume one gallon equals 3.8 what is the best estimate of number of liters AJ's Car use
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Suppose 30% of Americans will take the flu shot this season. Consider a random sample of 50 people. Let X be the number of the people who will take the flu shot. What the average number of X? (Round your answer to the nearest whole number)
Answers
Using percentages we can conclude that the average number is x is 15.
What is the percentage?A percentage is a number or ratio expressed as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" is also used, the percent sign, "%," is frequently used to indicate it. A percentage is a number without dimensions and without a standard measurement. By dividing the value by the total value and multiplying the result by 100, one can determine the percentage. The percentage calculation formula is (value/total value)100%.So, an average number of x:
A random sample is 50 people and 30% will get the flu shot.So, get 30% of 50 as follows:50/100 × 30 = 15Therefore, using percentages we can conclude that the average number is x is 15.
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I'm having trouble answering this Simplifying Variable Expressions question I will have two pictures. One will be for the actual question and the other one is for the steps
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Given the expression:
[tex]-7(-15w+21)+3(18-27w)[/tex]We will simplify the expression as follows:
1) using the distributive property to expand the expression:
[tex](-7)\cdot(-15w)+(-7)\cdot21+3\cdot18+3\cdot(-27w)[/tex]2) using the commutative property:
[tex]\begin{gathered} 105w-147+54-81w \\ =105w-81w-147+54 \end{gathered}[/tex]3) Combine the like terms:
[tex]=24w-93[/tex]So, the answer will be 24w - 93
PLS HELP FAST!! Question due in 5 minutes!!!
Answers
Answer:
Leg 1: 4
Leg 2: 3
Hypotenuse: 5
Step-by-step explanation:
Pythagorean Theorem
a^2+b^2=c^2
4^2+3^2=c^2
16+9=c^2
25=c^2
5=c
Hope this helps :)
Answer: side c =5
Step-by-step explanation:
We can use Pythagorean Theorem.
a squared + b squared = c squared
We know leg a is 4 units and leg b is 3 units.
4^2+3^2=16+9=25
We square root both c and 25 to get our answer.
sqr 25= sqr c squared
5=c
Mr. Braid asks every 6th person entering the auditorium for the spring concert at school if they would approve of taking money from the school sports budget to pay for a school play.
a) State the objective
b) population
c) and sample of the survey.
d) Then share if there is any bias in the sample.5
Answers
a. The objective is to know if they will approve of taking money from the school sports budget to pay for a school play.
b. The population is the students entering the auditorium.
c. The sample of the survey is this 6th person entering the auditorium.
d. There is no bias.
What is population?It should be noted that population simply means the people that the researcher makes research on.
The sample are those selected.
It should be noted that the objective is the reason why the research is carried out.
In conclusion, there's no bias as it's not preferential but a random selection.
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Use the Law of Sines to solve the triangle. Round your answers to two decimal places.A = 8° 40', B = 13° 15', b = 4.8
Answers
Given
[tex]A=8°40^{\prime},B=13°15^{\prime},b=4.8[/tex]To find the value of a, c, C.
Explanation:
It is given that,
[tex]A=8°40^{\prime},B=13°15^{\prime},b=4.8[/tex]Since,
[tex]A=8°40^{\prime},B=13°15^{\prime}[/tex]Then,
[tex]\begin{gathered} A+B+C=180 \\ 8\degree40^{\prime}+13\degree15^{\prime}+C=180\degree \\ C=180\degree-21\degree55^{\prime} \\ C=(179-21)\degree(60^-55^)^{\prime} \\ C=158\degree5^{\prime} \end{gathered}[/tex]Therefore, by using Sine law,
[tex]\begin{gathered} \frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c} \\ \frac{\sin8\degree40^{\prime}}{a}=\frac{\sin13\degree15^{\prime}}{4.8}=\frac{\sin158\degree5^{\prime}}{c} \\ \Rightarrow\frac{\sin8\degree40^{\prime}}{a}=\frac{\sin13\degree15^{\prime}}{4.8} \\ \Rightarrow\frac{\sin13\degree15^{\prime}}{4.8}=\frac{\sin158\degree5^{\prime}}{c} \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} \begin{equation*} \frac{\sin8\degree40^{\prime}}{a}=\frac{\sin13\degree15^{\prime}}{4.8} \end{equation*} \\ \frac{0.14608}{a}=\frac{0.227501}{4.8} \\ a=\frac{0.14608}{0.047396} \\ a=3.08211 \\ a=3.1 \end{gathered}[/tex]Also,
[tex]\begin{gathered} \begin{equation*} \frac{\sin13\degree15^{\prime}}{4.8}=\frac{\sin158\degree5^{\prime}}{c} \end{equation*} \\ 0.047396=\frac{0.366501}{c} \\ c=\frac{0.366501}{0.047396} \\ c=7.73274 \\ c=7.7 \end{gathered}[/tex]Hence, the answer is
[tex]C=158\degree5^{\prime},a=3.1,c=7.7[/tex]Stephanie practiced the piano for 1 hour 15 min per day. If she practiced for 8 days, what was her total practice time?
Answers
convert 1 hour and 15 minutes into minutes, you should get 75 minutes.
multiply 75 by 8 (because 75 minutes for 8 days) and you should get 600 minutes
600 minutes is a fine answer, but if you want to simplify it, divided 600 minutes by 60 (because we’re converting it into hours and there are 60 minutes in an hour)
600/60 = 10
so she practiced for 10 hours in 8 days
Answer:
10 hours
Step-by-step explanation:
1 hour 15 mins = 75 minutes
75 minutes x 8 days = 600 total in minutes
600 minutes/ 60 minutes = 10 hours
Find an equation for the line with slope
m=5 and which goes through the point (8,−9).
Write your answer in the form y=mx+b
Answers
An equation of line with slope m = 5 and which goes through the point (8, -9) is y = 5x - 49
In this question, we have been given a slope of the line and a point (8, -9)
We need to find an equation of the line with slope m = 5 and which goes through the point (8, -9)
Let (x1, y1) = (8, -9)
Using the slope-point form of the line,
y - y1 = m(x - x1)
y - (-9) = 5(x - 8)
y + 9= 5x - 40
y = 5x - 40 - 9
y = 5x - 49
Therefore, an equation of line with slope m = 5 and which goes through the point (8, -9) is y = 5x - 49
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A company wants to decrease their energy bill by 14%. If their electric bill is currently $2,900 a month, what will their bill be if they are successful? Round your answer to the nearest dollar.$______
Answers
To solve this problem, first, we will determine the 14% of $2,900 and then we will subtract that amount from $2,900.
Recall that to compute the x% of y we can use the following expression:
[tex]y\cdot\frac{x}{100}\text{.}[/tex]Using the above expression, we get that the 14% of 2,900 is:
[tex]406.[/tex]Therefore, if they succeed the next month they should receive a bill for
[tex]2900-406=2494[/tex]dollars.
Now, if they pay less than the above amount they can consider it a success.
Answer:
$2494.
Yes, that is a success.
Options for the first time:increases, remains the same, decreases Options for the second box: increases, remains the same, decreases Options for the third box: reflects over the x-axis, remains the same, reflects over the y-axis
Answers
The general form of a trigonometric function is:
[tex]A\sin (B(x-C))+D[/tex]Where B is the frequency of the function.
In our problem, A=1, C=D=0.
Then, as the value of B increases, so the frequency does. The answer to the second gap is 'increases'.
On the other hand, let P be the period and f the frequency. Those two quantities are related by the formula:
[tex]f=\frac{1}{P}[/tex]Then, if the frequency increases, the period decreases. The answer to the first gap is 'decreases'.
Finally, if B is negative we have that:
[tex]\begin{gathered} B<0,A=-B,A>0 \\ \Rightarrow\tan (Bx)=\frac{\sin(Bx)}{\cos(Bx)}=\frac{\sin(-Ax)}{\cos(-Ax)}=-\frac{\sin(Ax)}{\cos(Ax)}=-\tan (-Bx) \end{gathered}[/tex]Therefore, the function is reflected over the x-axis.
A flagpole 95.2 ft. Tall is on top of a building. From a point on level ground, the angle of elevation of the top of the flagpole is 34.1° , while the angle of elevation of the bottom of the flagpole is 25.8° . Find the height of the building.
Answers
Let x be the height of the building
We will first make a sketch
[tex]\tan \theta=\frac{opposite}{\text{adjacent}}[/tex][tex]\tan 25.8=\frac{x}{y}[/tex][tex]y=\frac{x}{\tan 25.8}[/tex][tex]\tan 34.1=\frac{95.2+x}{y}[/tex]substitute the y-value in the above
[tex]\tan 34.1=\frac{95.2+x}{\frac{x}{\tan 25.8}}[/tex][tex]\tan 34.1=(95.2+x)\text{.}\frac{tan25.8}{x}[/tex][tex]x\tan 34.1=(95.2+x)\tan 25.8[/tex]x (0.677) = (95.2 + x)0.4834
open the parenthesis
0.677x = 46.01968 + 0.4834x
subtract 0.4834x from both-side of the equation
0.677x - 0.4834x = 46.01968
0.1936x = 46.01968
Divide both-side by 0.1936
x≈ 237.7 ft
[tex]x\approx238\text{ f}eet[/tex]
[tex] \sqrt{20} \times \sqrt{15} \times \sqrt{3} [/tex]
can you help me solve it
