The required answer would be (24 -3x - 4x²) / 4x = 0 which is the lcm of the rational algebraic equation 6/x+x-3/4=2.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
The given equation below as:
⇒ 6/x + x - 3/4 = 2
We have to determine the lcm of the rational algebraic equation
⇒ 6/x + x - 3/4 = 2
Rearrange the term of 2 in the equation,
⇒ 6/x + x - 3/4 - 2 = 0
Take LCM in the above equation,
⇒ [tex]\dfrac{6\times4+x\times4x-3\times x -2 \times 4x}{4\times x}[/tex]
⇒ (24 + 4x² -3x - 8x²) / 4x = 0
Combine the likewise terms in the numerator,
⇒ (24 -3x - 4x²) / 4x = 0
Therefore, the required answer would be (24 -3x - 4x²) / 4x = 0.
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Solve for xx and graph the solution on the number line below
-2 > -5+ x
Answer:
x< 3 this is for inequality and interval (inf,3)
I need to Know how to find the maximum and the minimum values of a function?
Answer:
Step-by-step explanation:
first you need to figure out what your solving for We will set the first derivative of the function to zero and solve for x to get the critical point. If we take the second derivative or f''(x), then we can find out whether this point will be a maximum or minimum. If the second derivative is positive, it will be a minimum value.
Sketch the graph of the equation. Label the vertex and the intercepts.
Given,
The expression of the function is,
[tex]y=x^2+4x+3[/tex]Required
The graph of the function.
Take x = 1 then the value of y is,
[tex]y=1^2+4(1)+3=8[/tex]Take x = 2 then the value of y is,
[tex]y=2^2+4(2)+3=15[/tex]Take x = 0 then the value of y is,
[tex]y=(-1)^2+4(-1)+3=0[/tex]Take x = -1 then the value of y is,
[tex]y=1^2+4(1)+3=8[/tex]Take x = -2 then the value of y is,
[tex]y=(-2)^2+4(-2)+3=-1[/tex]The graph of the function is,
The vertex of the graph is (-2, -1).
The x - intercept of the graph is -1 and -3.
The y - intercept of the graph is at 3.
Hence, the graph of the function is obtained.
Given the graph of a function f. Identify function by name. Then graph the indicated functions. State the domain and the range in set notation.A) f(x-1) -3B) -f(x)
Answer:
For f(x);
The domain is;
[tex]D\colon x=(-\infty,\infty)[/tex]The range is;
[tex]R\colon y=\lbrack0,\infty)[/tex]Graphing those points for function A, we have;
The domain and range of the given function A is;
[tex]\begin{gathered} \text{Domain}\colon x=(-\infty,\infty) \\ \text{Range}\colon y=\lbrack-3,\infty) \end{gathered}[/tex]Graphing those points for function B, we have;
The domain and range of the given function B is;
[tex]\begin{gathered} \text{Domain}\colon x=(-\infty,\infty) \\ \text{Range}\colon y=(-\infty,0\rbrack \end{gathered}[/tex]Explanation:
Given the function in the attached image;
The function is a square function and can be written as;
[tex]f(x)=x^2[/tex]The domain is;
[tex]D\colon x=(-\infty,\infty)[/tex]The range is;
[tex]R\colon y=\lbrack0,\infty)[/tex]A.
[tex]f(x-1)-3=(x-1)^2-3[/tex]B.
[tex]-f(x)=-x^2[/tex]Graphing the functions;
For A;
[tex]\begin{gathered} f(1-1)=(1-1)^2-3=-3 \\ (1,-3) \\ f(3-1)=(3-1)^2-3=1 \\ (3,1) \\ f(-1-1)=(-1-1)^2-3=1 \\ (-1,1) \end{gathered}[/tex]Graphing those points for function A, we have;
The domain and range of the given function A is;
[tex]\begin{gathered} \text{Domain}\colon x=(-\infty,\infty) \\ \text{Range}\colon y=\lbrack-3,\infty) \end{gathered}[/tex]For B;
[tex]\begin{gathered} -f(x)=-x^2 \\ -f(0)=-0^2 \\ (0,0) \\ -f(2)=-2^2=-4 \\ (2,-4) \\ -f(-2)=-(-2)^2=-4 \\ (-2,-4) \end{gathered}[/tex]Graphing those points for function B, we have;
The domain and range of the given function B is;
[tex]\begin{gathered} \text{Domain}\colon x=(-\infty,\infty) \\ \text{Range}\colon y=(-\infty,0\rbrack \end{gathered}[/tex]Can you help me complete the proof and also correct any mistakes in my work.
The given information is:
ABCD is a rhombus.
1 Statement: Rhombus ABCD
Reason: given
2. Statement: AB=AD
Reason: Definition of rhombus (all four sides are congruent)
3. Statement: AE=AE
Reason: Reflexive property
4. Statement: BE=DE
Reason: Diagonals bisect each other
5. Statement: Triangle ABE=Triangle ADE
Reason: SSS congruency (Side-Side-Side).
please help this is for my study guide thanks! (no rounding)
Answer:
The volume of the cylinder is;
[tex]653.45\text{ }in^3[/tex]Explanation:
Given the figure in the attached image;
[tex]\begin{gathered} r=4\text{ in} \\ h=13\text{ in} \end{gathered}[/tex]Recall that the volume of a cylinder can be calculated using the formula;
[tex]V=\pi r^2h[/tex]Substituting the given values;
[tex]\begin{gathered} V=\pi r^2h \\ V=\pi(4)^2\times13 \\ V=653.45\text{ }in^3 \end{gathered}[/tex]Therefore, the volume of the cylinder is;
[tex]653.45\text{ }in^3[/tex]Curious about people's recycling behaviors, Franco put on some gloves and sifted through some recycling and trash bins. He kept count of the plastic type of each bottle and which bottles are properly dispensed. Correctly placed Incorrectly placed Plastic #2 3 Plastic #4 3 3 What is the probability that a randomly selected bottle is made of plastic #2 or is correctly placed? Simplify any fractions.
Solution
Note: The event here is Mutually Exclusive,, meaning the 2 events can happen at the same time
Total number = 4 + 3 + 3+3 = 13
[tex]\begin{gathered} P\mleft(A\mright)+P\mleft(B\mright)-P\mleft(AnB\mright) \\ \frac{7}{13}\text{ + }\frac{7}{13}-\frac{4}{13} \\ \frac{7+7-4}{13} \\ \frac{10}{13} \end{gathered}[/tex][tex]F\text{inal Answer = }\frac{10}{13}\text{ }[/tex]Looking back on your History class, you discovered something interesting. On your first test, you received a score of 65 points with no additional study time, other than doing your homework and attend lectures. On the second test, you decided to put in two additional hours of study time and receive a score of 85. After you have studied some mathematical modeling in math 49, you suspect that there is a relationship between your test score and the number of additional study time. Let S be your test score and T is your additional study time.
A. Assuming S and T have a linear relationship, find a formula for the linear function S=f(T).(12pts)
B. If you want a score of 98. How many hours of additional time of study would you have to put in? (3pts)
Answer:
A. S = 65 + 10x
B. 3.3 hours
Step-by-step explanation:
A. S=f(T)
65 = f(0)
85 = f(2)
S₂ - S₁
85 - 65 = 20
T₂ - T₁
2 - 0 = 2
20 / 2 = 10
For every hour you study, you will score an additional 10 points with a baseline of 65 points.
S = 65 + 10x where x is the amount of time (in hours) that you studied for.
B. S = 65 + 10x
Since we want a specific score of 98, we plug it in for S and solve for x.
98 = 65 + 10x
33 = 10x
3.3 = x
If we wanted a score of 98, we would need to study for 3.3 hours.
3 c) and 10 d) - and 12 9draw a diagram for each pair of fractions. Which pairs are equivalent? Circle them
Drawing the diagram of option D we have
Which means that 5/6 and 10/12 are equivalent fractions.
What is the slope of the line represented by 4x-2y=10?
ANSWER:
2
STEP-BY-STEP EXPLANATION:
We have the following equation of line:
[tex]4x-2y=10[/tex]The equation of the line in its slope and intercept form is like this:
[tex]\begin{gathered} y=mx+b \\ \text{where, m is the slope and b is the y-intercept} \end{gathered}[/tex]Therefore, we must solve for y to know the value of the slope (m), like this:
[tex]\begin{gathered} 4x-2y=10 \\ 2y=4x-10 \\ y=\frac{4x-10}{2} \\ y=\frac{4x}{2}-\frac{10}{2} \\ y=2x-5 \\ \text{therefore,} \\ m=2 \end{gathered}[/tex]The slope is 2
hat is the expected share return given the following macro-economic probabilities? Probability of recession 20% - Share return 5%; Probability of steady state 60% - Share return 10%; Probability of boom 20% - Share return 15%
Based on the probability of the macro-economic probabilities and the share returns, the expected share return can be found to be 10%.
How to find the expected share return?The expected share return based on the economic probabilities can be found by the formula:
= (Probability of recession x Share return in recessions) + (Probability of steady state x Share return in steady state) + (Probability of boom x Share return in boom)
Solving for the expected share return gives:
= (20% x 5%) + (60% x 10%) + (20% x 15%)
= 1% + 6% + 3%
= 10%
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Find the Slope of the line through the points (4, -5) and (2, 2) then graph it.Slope =
The Slope of the line through the points (4, -5) and (2, 2) then graph it. Slope [tex]m=-\frac{7}{2}$$[/tex]
Slope between two points: [tex]$\quad$[/tex]Slope [tex]$=\frac{y_2-y_1}{x_2-x_1}$[/tex]
[tex]$$\begin{aligned}&\left(x_1, y_1\right)=(4,-5),\left(x_2, y_2\right)=(2,2) \\&m=\frac{2-(-5)}{2-4}\end{aligned}$$[/tex]
Refine
[tex]m=-\frac{7}{2}$$[/tex]
A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.
Any two different points on a line can be used to calculate the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula.
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the store purchased a produce for 1 dollar and sells it for 6 what is the mark up as a precent?
Pls help asap
Answer:
[tex]1 \div 6 = 0.16 \times 100 = 16.6 percent[/tex]
that's all I know
how much of a 2 gram sample of silver-105 would remain after 86 days? round to three decimal places
We know that the half life of this element is 41.3 days.
We have to find how much will remain of a sample of 2 grams after 86 days.
The half life of 41.3 days means that the mass after 41.3 days will become half of what it was.
We can express this as:
[tex]\frac{M(t+41.3)}{M(t)}=\frac{1}{2}[/tex]As this is represented with an exponential model like this:
[tex]M(t)=M(0)\cdot b^t[/tex]we can use the half-life to find the parameter b:
[tex]\begin{gathered} \frac{M(t+41.3)}{M(t)}=\frac{1}{2} \\ \frac{M(0)\cdot b^{t+41.3}}{M(0)\cdot b^t}=\frac{1}{2} \\ b^{t+41.3-t}=\frac{1}{2} \\ b^{41.3}=\frac{1}{2} \\ b=(\frac{1}{2})^{\frac{1}{41.3}} \end{gathered}[/tex]Then, knowing that the initial mass M(0) is 2 grams, we can express the final model as:
[tex]M(t)=2\cdot(\frac{1}{2})^{\frac{t}{41.3}}[/tex]We then can calculate the mass after t = 86 days as:
[tex]\begin{gathered} M(86)=2\cdot(\frac{1}{2})^{\frac{86}{41.3}} \\ M(86)\approx2\cdot0.236 \\ M(86)\approx0.472 \end{gathered}[/tex]Answer: the mass after 86 days will be 0.472 grams.
Refer to the number line. Find the coordinate of point X such that the ratio of BX to XF is 3:2
Coordinate of point X such that the ratio of BX to XF is 3:2 is 1 i.e. point D.
What is Coordinate?
A combination of numbers that use the vertical and horizontal separations out from two reference axes to define a point's location on a coordinate plane. Typically expressed by the x-value & y-value pair (x,y).A group of variables that accurately depict a stance.The first number on a graph represents the distance along, while the second number represents the distance upward or downward.Total coordinates son number line from -7 to +7 =15
Number line ratio that has to be provided = 3:2
Let the coordinate be provided is x.
Therefore, 3x+2x=15
⇒5x=15
⇒x=3
Coordinate X
3x=3(3)=9
9th coordinate from -7 = 1 i.e. D
Coordinate of point X such that the ratio of BX to XF is 3:2 is 1 i.e. point D.
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You have a solution that is 18.5% methyl alcohol. If the bottle contains 1.43 L of solution, what is the volume in milliliters of methyl alcohol?
We have the next given information:
-18.5% is the percentage of methyl alcohol
- The bottle contains 1.43 L
Now, we need to convert the percentage into a decimal.
Then 18.5% = 0.185
We need to determinate the volume in millimeters for methyl alcohol:
If 143L of solution contains 18.5% of methyl alcohol. Therefore:
The volume of methyl alcohol = 1.43 * 0.185
= 0.26455 L
Then, we need to convert Liters to milliliters:
1L ---------------------------- 1000ml
0.26455 L ------------------ x
Where x = (0.26455 L*1000ml)/1L
x =264.55ml
Sammy's teacher gives partial credit on quizzes if students show all of their work. Sammy earned the following points on his last quiz. Arrange the questions in order from least points earned to the greatest points earned.Questions- points1. 2 1/22. 1 2/53. 1 3/44. 2 2/35. 3 1/4
First, express all the mixed numbers as decimals:
2 1/2 = (2x2+1)/2 = 5/2 = 2.5
1 2/5 = (5x1+2)/5 = 7/5 = 1.4
1 3/4 = (1x4+3)/4 = 7/4 = 1.75
2 2/3 = (2x3+2)/3 = 8/3 = 2.67
3 1/4 = (3x4+1)/4 = 13/4 = 3.25
Now, we have
1. 2.5
2. 1.4
3. 1.75
4. 2.67
5. 3.25
From least to greatest.
2. 1.4
3. 1.75
1. 2.5
4. 2.67
5. 3.25
Translate Pre Image coordinates using the rule (x + 18) and (y - 12).
We need to translate the points under the rule (x+18) and (y-12).
The points are given by the x-coordinate and y-coordinate following the form (x,y).
Now, let us use this rule for each point:
A.(-6,15)
Under the translation rule (-6+18,15-12) = (12,3)
So, A'=(12,3)
For B(-8,7)
Under the translation rule (-8+18,7-12)= (10,-5).
Then, B'=(10,-5)
For C(-11,12)
Under the translation rule (-11+18,12-12)=(7,0).
Then, C'(7.0)
When you mix two colors of paint in equivalent ratios, the resulting color is 1 po always the same. ***How many cups of yellow paint should you mix with 1 cup of blue paint to make the same shade of green?*** cups of cups of blue paint yellow paint 2 10 1 Your answer
Since question is incomplete, I will try my best to complete it my way:
It is given that 2 cups of blue with 10 cups of yellow make up green.
Question asks how many cups of yellow would i need to mix with 1 cup of blue to make same shade of green.
So,
2 cup with 10 cup
We divide each by 2, to get:
2/2 = 1
10/2 = 5
This means:
1 cup with 5 cup
Or,
1 cup blue with 5 cup yellow.
So, we arrive at our answer:
with 1 cup of blue, we need to fix 5 cups of yellow to get same shade of green.
14 socks in a drawer . Four of them are navy blue and 10 white What’s the probability that the second sock is navy blue if the first one was white
The Solution:
Given:
We are required to find the probability that the second sock is navy blue if the first one was a white sock.
Step 1:
The probability of the first sock being a white is:
[tex]P(first\text{ }W)=\frac{Number\text{ of white}}{Total\text{ number of socks}}=\frac{10}{14}=\frac{5}{7}[/tex]Step 2:
The probability of the second sock being a Navy blue is:
Note:
One sock has been taken out without replacement. So, the total number of socks is now 13.
[tex]P(second\text{ Navy Blue\rparen}=\frac{Number\text{ of navy blue socks}}{Current\text{ Total number of socks}}=\frac{4}{13}[/tex]Thus, the probability of the first being White and the second being Navy Blue is:
[tex]P(W\text{ NB})=P(W)\times P(NB)=\frac{5}{7}\times\frac{4}{13}=\frac{20}{91}=0.2198\approx0.22[/tex]Therefore, the correct answer is 20/91 or 0.22
What’s the correct answer answer asap for brainlist
Answer: Maybe B
Step-by-step explanation:
The ratio of white roses to red roses in a garden is 8:7 . Check all statements that must be true based on the statement above. If none of the statements is true, check "None of the above".
A. There are exactly 8 white roses and exactly 7 red roses in the garden.
B. For every 7 white roses in the garden, there are 8 red roses.
C. Fer every 8 white roses in the garden, there are 7 red roses.
D. There are 8 white roses to every 7 roses in the garden.
E. None of the above.
The true statement is for every 8 white roses in the garden, there are 7 red roses.
What is the true statement?
Ratio is used to compare two or more numbers together. It shows the relationship that exists between two or more numbers. In this question, for every 8 white roses, there would be 7 red roses.
This ratio does not mean that there are exactly 8 white roses and 7 red roses. It means that regardless of the number of white roses and red roses, when expressed in its simplest form the ratio would be 8 : 7. For example, there can be 56 : 49 white roses and red roses.
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i need help plsssssssssss ill put 20 points
The common differences of arithmetic sequence are;
For a) -3
For b) - 20
For c) - 30
For d) - 10
What is Arithmetic sequence?
An arithmetic sequence is ordered set of numbers that have common difference between each consecutive term.
Given that;
The Arithmetic sequence are;
a) 35, 32, 29, 26 ...
b) - 3, -23, - 43, -63
c) -34, -64, -94, - 124
d) - 30, - 40, - 50, -60
Now, The common difference of an arithmetic sequence is calculated by the difference between each consecutive term.
For Arithmetic sequence a;
Common difference = 32 - 35 = -3
And, For Arithmetic sequence b;
Common difference = - 23 - (-3)
= - 23 + 3
= - 20
For Arithmetic sequence c;
Common difference = - 64 - (-34)
= - 64 + 34
= - 30
For Arithmetic sequence d;
Common difference = - 40 - (-30)
= - 40 + 30
= - 10
Thus, The common differences of arithmetic sequence are;
For a) -3
For b) - 20
For c) - 30
For d) - 10
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A group of 45 people attended a ball game. There were twice as many children as adults in the group. Set up a system of equations that represents the numbers of adults and children who attended the game and solve the system to find the number of children who were in the group. A. system15 adults, 30 children B. system30 adults; 22 children C. system22 adults; 30 children D. system30 adults, 15 children
Answer:
A
Step-by-step explanation:
45/2
A couple has two children. Let A be the event that their first child is a boy, and note that P(A) = 51.2%. Let B be theevent that their second child is a girl, with P(B) = 48.8%.A and B are independent events. What is the probability that the couple has a first child that is a boy and a second childthat is a girl?Give your answer as a decimal rounded to two decimal places.
Answer:
P(A and B) = 0.25
Step-by-step explanation:
Since P(A) and P(B) are independents events, The probability P(A) and P(B) occurs consecutively is P(A)*P(B):
P(A and B) = P(A)*P(B)
P(A and B) = 0.512*0.488
P(A and B) = 0.25
A 240 horsepower automobile engine delivers only 210 horsepower to the driving wheels of the car. What is the efficiency of the transmission and drive mechanism
The efficiency of the transmission and drive mechanism is 87.5%
Given,
The power of the automobile engine = 240 horsepower
The power that the automobile engine delivers to the driving wheels of the car = 210 horsepower
We have to find the efficiency of the transmission and drive mechanism:
Efficiency of the transmission and drive mechanism = (power that delivers / power of engine) × 100
= (210 / 240) × 100 = 2100 / 24 = 700/8 = 87.5%
That is the efficiency of the transmission and drive mechanism is 87.5%
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A number divides equally into another number called ______. A.Remainder
B.divisible
C.Multiplier
D.Divisor
Answer: Divisor
Step-by-step explanation:
The the answer to a division problem is called the quotient. The number that is doing the dividing is called the divisor. The number that gets divided up is called the dividend.
Example: If 3 boys ask to mow your yard for $24, then each boy would get $8.
24 divided by 3 is 8. (24 / 3 = 8 )
24 is the dividend (the number getting divided up)
3 is the divisor (the number that is doing the dividing)
8 is the quotient.
i dont really get what it means by pattern can u help me understand
Well the principals patterns are that the equations are quadratic equations, and the graphs are parables and that the equations and the graphs are related.
graph the polygon and it’s image after a dilation centered C with scale factor k
We plot and join the given ordered pairs.
Graphing the image of the polygon after the dilationThe formula of dilation when it is not centred at the origin is:
[tex]\begin{gathered} (x,y)\rightarrow(k(x-a)+a,k(y-b)+b) \\ \text{ Where} \\ k\text{ is the scale factor} \\ (a,b)\text{ is the center of the dilation} \end{gathered}[/tex]Then, we can find the coordinates of the image:
[tex]\begin{gathered} k=\frac{2}{3} \\ (a,b)=C(-2,4) \\ T(7,1)\operatorname{\rightarrow}T^{\prime}(\frac{2}{3}(7-(-2))-2,\frac{2}{3}(1-4)+4) \\ T(7,1)\operatorname{\rightarrow}T^{\prime}(\frac{2}{3}(7+2)-2,\frac{2}{3}(-3)+4) \\ T(7,1)\operatorname{\rightarrow}T^{\prime}(\frac{2}{3}(9)-2,\frac{2}{3}(-3)+4) \\ T(7,1)\operatorname{\rightarrow}T^{\prime}(6-2,-2+4) \\ T(7,1)\operatorname{\rightarrow}T^{\prime}(4,2) \end{gathered}[/tex][tex]\begin{gathered} k=\frac{2}{3} \\ (a,b)=C(-2,4) \\ U(4,4)\operatorname{\rightarrow}U^{\prime}(\frac{2}{3}(4-(-2))-2,\frac{2}{3}(4-4)+4) \\ U(4,4)\operatorname{\rightarrow}U^{\prime}(\frac{2}{3}(4+2)-2,\frac{2}{3}(4-4)+4) \\ U(4,4)\operatorname{\rightarrow}U^{\prime}(\frac{2}{3}(6)-2,\frac{2}{3}(0)+4) \\ U(4,4)\operatorname{\rightarrow}U^{\prime}(4-2,0+4) \\ U(4,4)\operatorname{\rightarrow}U^{\prime}(2,4) \end{gathered}[/tex][tex]\begin{gathered} k=\frac{2}{3} \\ (a,b)=C(-2,4) \\ V(1,13)\operatorname{\rightarrow}V^{\prime}(\frac{2}{3}(1-(-2))-2,\frac{2}{3}(13-4)+4) \\ V(1,13)\operatorname{\rightarrow}V^{\prime}(\frac{2}{3}(1+2)-2,\frac{2}{3}(13-4)+4) \\ V(1,13)\operatorname{\rightarrow}V^{\prime}(\frac{2}{3}(3)-2,\frac{2}{3}(9)+4) \\ V(1,13)\operatorname{\rightarrow}V^{\prime}(2-2,6+4) \\ V(1,13)\operatorname{\rightarrow}V^{\prime}(0,10) \end{gathered}[/tex][tex][/tex]-3(x+3)+11=14
(steps included)
Answer:
-4
Step-by-step explanation:
-3(x+3)+11=14
-3·x-3·3+11=14
-3x-9+11=14
-3x+2=14
-3x=14-2
-3x=12
x=12÷(-3)
x=-4