Simplify the rational expression. 16b2+40b+25/4b+5 Enclose numerators and denominators in parentheses. For example, (a−b)/(1+n).
Answers
Given the rational expression;
[tex]\frac{16b^2+40b+25}{4b+5}[/tex]We shall begin by factorizing the numerator as follows;
[tex]\begin{gathered} 16b^2+40b+25 \\ \text{Note that the coefficient of b}^2\text{ is greater than 1} \\ \text{Therefore we shall multiply the constant by the coefficient of b}^2 \\ \text{That gives us;} \\ 16\times25=400 \\ We\text{ shall now use the sum-product method, which is;} \\ \text{The factors of the constant 400} \\ S\text{hall also sum up to the coefficient of b } \\ \text{These factors are +20, +20} \\ \text{Therefore;} \\ 16b^2+40b+25\text{ becomes;} \\ 16b^2+20b+20b+25 \\ \text{Factorize by groups of two and we'll have} \\ 4b(4b+5)+5(4b+5) \\ \text{This becomes;} \\ (4b+5)(4b+5) \end{gathered}[/tex]The rational expression now becomes;
[tex]\frac{(4b+5)(4b+5)}{(4b+5)}[/tex]Related Questions
Calculate the quotient below and give your answer in scientific notation.0.000655 x 10-2= ?
Answers
A- what is R(300) interpret this result B- what is the revenue from the sale of 2,000 hats write in functional notation3 part question
Answers
Okay, here we have this:
Considering the provided information, and the given function we are going to calculate R(300) and then we will interpret the result, so we obtain the following:
[tex]\begin{gathered} R(x)=17x \\ R(300)=17\cdot300 \\ R(300)=5100 \end{gathered}[/tex]Considering that x corresponds to the number of hats sold, then it means that if 300 hats are sold, the total revenue will be equal to $5100.
can somebody please help me with my homework math by the way
Answers
Here, we want to subtract the mixed fraction from the whole number
To do this, we need to express the mixed fraction as an improper fraction
To do this, we will multiply the numerator by the whole number and add the numerator
We have this as;
[tex]5\frac{3}{4}\text{ = }\frac{(5\times4)+3}{4}\text{ = }\frac{20+3}{4}\text{ = }\frac{23}{4}[/tex]We can now perform the subtraction as follows;
[tex]17-\frac{23}{4}\text{ = }\frac{4(17)-23}{4}\text{ = }\frac{68-23}{4}\text{ = }\frac{45}{4}[/tex]To properly write the answer, we have to express 45/4 as a mixed fraction
What we have to do here is to divide 45 by 4, then place the quotient at the front, then, the remainder as the numerator
We have this as;
[tex]\frac{45}{4}\text{ = 11}\frac{1}{4}[/tex]Using the slope formula, find the slope of the line through the given points.(-3,-7) and (8,-7)
Answers
the slope of the line is 0
ExplanationThe slope of a line is a measure of its steepness of a line , The vertical change between two points is called the rise, and the horizontal change is called the run. The slope equals the rise divided by the run:
[tex]\begin{gathered} slope=\frac{rise}{run}=\frac{change\text{ in y}}{change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1} \\ where \\ P1(x_1,y_1\text{ \rparen and P2\lparen x}_2,y_2)\text{ are 2 points from the line} \end{gathered}[/tex]so
Step 1
given
[tex]\begin{gathered} P1=(-3,-7) \\ P2=(8,-7) \end{gathered}[/tex]replace in the formula
[tex]\begin{gathered} slope=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ slope=\frac{-7-(-7)}{8-(-3)}=\frac{-7+7}{11}=\frac{0}{11}=0 \end{gathered}[/tex]hence, the slope of the line is 0
I hope this helps you
Each person in a group of students was identified by year and asked when he or she preferredtaking classes: in the morning, afternoon, or evening, The results are shown in the table. Findthe probability that the student preferred afternoon classes given he or she is a junior. Roundto the nearest thousandth. When Do You Prefer to Take Classes?
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
Junior
Morning 17
Afternoon 20
Evening 3
Step 02:
Junior
probability afternoon = junior afternoon / total junior afternoon
total junior afternoon = 17 + 20 + 3 = 40
probability afternoon = 20 / (17 + 20 + 3) = 0.5
The answer is:
probability afternoon = 0.5
Joshua has $1.20 worth of nickels and dimes. He has 6 more nickels than dimes.
Graphically solve a system of equations in order to determine the number of nickels,
x, and the number of dimes, y, that Joshua has.
40
38
36
34
32
30
28
26
24
22
20
18
16
14
12
10
8
0
Click twice to plot each line. Click a line to delete it.
2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40
Answers
Answer:
12 nickels, 6 dimes
Step-by-step explanation:
0.05x + 0.1y = 1.20
x - 6 = y
0.05x + 0.1(x-6) = 1.20
0.05x + 0.1x - 0.6 = 1.20
0.15x = 1.80
x = 12
(12) - 6 = y
y = 6
Now graph y = x - 6 and y = (-1/2)x + 12
If you don't know how to graph the functions, then go to khan academy for help.
The formula for the volume of a rectangular prism is found by multiplying the width, length, and height of the prism. In other words, V = lwh. Solve the formula for the width, w.
Answers
The formula for the volume of a rectangular prism is
[tex]V=l\cdot h\cdot w[/tex]You need to write the formula for w, note that the width is being miltiplied by "lh"
to cancel this multiplication you have to divide it by "lh" and to keep the equality valid, what is done to one side of the expression must be done to the other, so divide V by "lh" too
[tex]w=\frac{V}{lh}[/tex]calculate the length of side AC
Answers
Answer:
×=12+5
×=144+25
×=169
×=13
I am doing an equation trying to figure out a formula for the volume of a box and I am so lost I will include a picture
Answers
The volume of any rectangular box is expressed as:
[tex]\text{Volume}=\text{length}\times\text{breadth}\times height[/tex]Now, for the box that will be formed from the figure shown in the question, we will have:
length = 37 - 2x
breadth = 37 - 2x
height = x
Thus, we have that:
[tex]\begin{gathered} \text{Volume}=\text{length}\times\text{breadth}\times height \\ \Rightarrow\text{Volume}=(37-2x)\times(37-2x)\times x \end{gathered}[/tex]We now simplify the above as:
[tex]\begin{gathered} \text{Volume}=(37-2x)\times(37-2x)\times x \\ \Rightarrow\text{Volume}=(1369-148x+4x^2)\times x \\ \Rightarrow\text{Volume}=1369x-148x^2+4x^3 \\ \Rightarrow\text{ V(x)}=1369x-148x^2+4x^3 \end{gathered}[/tex]Now that we have obtained the expression for the volume of the box, we now have to find the value of x that maximizes it.
This is done as follows:
Method
- Differentiate the function V(x) with respect to x, and equate to zero as follows:
[tex]\begin{gathered} \Rightarrow V^1\text{(x)}=1369-296x^{}+12x^2 \\ \text{Equating to zero:} \\ 1369-296x^{}+12x^2=0 \\ \text{The roots of the equation are:} \\ \Rightarrow x=6.167\text{ and x = }18.5 \end{gathered}[/tex]Now we have to find the second derivative of V(x) in order to confirm which value of x makes the function V(x) a maximum
Thus:
[tex]\begin{gathered} \Rightarrow V^{11}\text{(x)}=-296^{}+24x^{} \\ \text{when x = 6.167} \\ \Rightarrow V^{11}\text{(6.167)}=-296^{}+24(6.167)=-296+148.008=-148 \\ \text{when x = }18.5 \\ \Rightarrow V^{11}\text{(18.5)}=-296^{}+24(18.5)=-296+444=148 \end{gathered}[/tex]Now since the second derivative is a negative number when x = 6.167, we now know for sure that it is that value of x that maximizes the function V(x), and not x = 18.5.
Thus, we can conclude that the value of x that maximizes the volume of the box is:
x = 6.17 inches (to 2 decimal places)
If we had been asked to find the value of x that minimizes the volume, the answer will have been x = 18.5, because this value of x made the second derivative of V(x) positive.
Now, the maximum volume of the box is obtained by simply substituting the value of x that maximizes the function into the original expression for V(x), as follows:
[tex]\begin{gathered} V(x)=1369x-148x^2+4x^3 \\ \text{when x= 6.167} \\ \Rightarrow\text{ V(6.167)}=1369(6.167)-148(6.167)^2+4(6.167)^3 \\ \Rightarrow\text{ V(6.167)}=8442.623-5628.720+938.171 \\ \Rightarrow\text{ V(6.167)}=3752.074in^3 \\ \Rightarrow\text{ V(6.167)}=3752.07in^3\text{ (to 2 decimal places)} \end{gathered}[/tex]The cubic function f(x) = z3 - 6x2 + 11x - 6 has a root at z = 3. a What are the other roots of the function?O r = 3, x = 2O r =-3, x = -2O x = -1, x = -2O x = 1, r = 2
Answers
Given the function f(x) as follows:
[tex]f\mleft(x\mright)=x^3-6x^2+11x-6[/tex]The function has a root at x = 3
We will use the synthetic division to find the other roots:
We will divide the coefficients by 3
As follows:
So, the given function will be written as follows:
[tex]f(x)=(x-3)(x^2-3x+2)[/tex]Factor the term of the quadratic function
[tex]f(x)=(x-3)(x-2)(x-1)[/tex]So, there are three zeros x = 1, 2, 3
So, the answer will be option 4) x = 1, x = 2
3^9/3^6= answer in exponential form
Answers
To express this fraction in exponential form we have to remember the following property:
[tex]\frac{a^m^{}}{a^n}=a^{m-n}[/tex]Applying it to our problem we have:
[tex]\begin{gathered} \frac{3^9}{3^6}=3^{9-6} \\ =3^3 \end{gathered}[/tex]So the exponential form of our fraction is
[tex]3^3[/tex]Which exponential expressions are equivalent to the one below? Check allthat apply.(3.7) 10A. 310 + 710B. (3:7)10O .C. 2110O d. 310.710
Answers
Given the exponential expression:
[tex](3\cdot7)^{10}[/tex]The equivalent expressions are:
[tex]\begin{gathered} (3\cdot7)^{10}=3^{10}\cdot7^{10} \\ (3\cdot7)^{10}=21^{10} \end{gathered}[/tex]So, the answer will be options C, D
Write logaa=4x in exponential form and find x to evaluate logaa for any a>0, a≠1.
Answers
Given:
[tex]\log _aa=4x[/tex]To find the exponential form of the above, all we need to do is to raise the base a to the power of 4x.
That is;
[tex]a^{4x}=a[/tex]To find the value of x, we need to raise the power of the right - hand side so that we can equate the exponent
That is;
[tex]a^{4x}=a^1[/tex]4x = 1
Divide both-side by 4
[tex]x=\frac{1}{4}[/tex][tex]\text{Log}_aa=4(\frac{1}{4})[/tex][tex]\text{Log}_aa=1[/tex]
AC⌢ =84 ∘ , find m∠ADC.
Answers
The measure of minor arc is 84 degree
The expression for the an angle inscribed in a circle, then the measurement of the angle is equal to the half of the measure of its intercepted arc.
[tex]\text{Angle}=\frac{1}{2}m(arc)[/tex]here we have, arc length = 84 degree
[tex]\begin{gathered} m\angle ADC=\frac{1}{2}(mAC) \\ m\angle ADC=\frac{1}{2}\times84 \\ m\angle ADC=42^o \end{gathered}[/tex]Angle = 42 degree
A phone company offers two monthly charge plans. In Plan A, the customer pays a monthly fee of $30 and then an additional 9 cents per minute of use. In PlanB, the customer pays a monthly fee of $33.60 and then an additional 8 cents per minute of use.For what amounts of monthly phone use will Plan A cost less than Plan B?Use m for the number of minutes of phone use, and solve your Inequality for m.
Answers
Let m denote the number of minutes.
Plan A:
The customer pays a monthly fee of $30 and then an additional 9 cents per minute of use.
Mathematically,
[tex]30+0.09m[/tex]Plan B:
The customer pays a monthly fee of $33.60 and then an additional 8 cents per minute of use.
Mathematically,
[tex]33.60+0.08m[/tex]For what amounts of monthly phone use will Plan A cost less than Plan B?
[tex]30+0.09m<33.60+0.08m[/tex]Let us solve the above inequality for m
[tex]\begin{gathered} 30+0.09m<33.60+0.08m \\ 0.09m-0.08m<33.60-30 \\ 0.01m<3.60 \\ m<\frac{3.60}{0.01} \\ m<360 \end{gathered}[/tex]This means that for less than 360 minutes, plan A will cost less than Plan B.
Look for a pattern in the following list. Then use this pattern to predict thenext number. 2, -2, 3, -3, 4, ... *
Answers
Here, we are given the following numbers:
2, -2, 3, -3, 4.........
The pattern here is that a positive integer is followed by its negative value.
We can see that the number after 2 is its negative value -2
The number after 3 is its negative vaule -3
The number after 4 will be its negative which is -4
ANSWER:
-4
multiply and simplify (5x−4√5)(5x+4√5)
Answers
Answer::
[tex]25x^2-80[/tex]Explanation:
Given the product:
[tex]\left(5x−4\sqrt{5}\right)\left(5x+4\sqrt{5}\right)[/tex]First, expand the brackets:
[tex]\begin{gathered} =5x\left(5x+4\sqrt{5}\right)−4\sqrt{5}\left(5x+4\sqrt{5}\right) \\ =(5x)^2+20x\sqrt{5}-20x\sqrt{5}-(4\sqrt{5})^2 \\ =(5x)^2-(4\sqrt{5})^2 \end{gathered}[/tex]We then simplify:
[tex]\begin{gathered} =5^2x^2-4^2\sqrt{5}^2 \\ =25x^2-16(5) \\ =25x^2-80 \end{gathered}[/tex]The simplified form of the product is:
[tex]25x^2-80[/tex]can you help me with the 4th question which is marked b
Answers
we are given the following equation:
[tex]3x+2y=12[/tex]The slope-intercept form is the following:
[tex]y=mx+b[/tex]Therefore, we need to solve for "y" in the equation. To do that we will subtract "3x" to both sides:
[tex]\begin{gathered} 3x-3x+2y=12-3x \\ 2y=12-3x \end{gathered}[/tex]Now we will divide both sides by "2":
[tex]y=\frac{12-3x}{2}[/tex]Now we will separate the numerator:
[tex]y=\frac{12}{2}-\frac{3}{2}x[/tex]simplifying:
[tex]y=6-\frac{3}{2}x[/tex]And thus we get the slope-intercept form.
A triangle has sides with lengths of 12 yard, 13 yards, and 15 yards. Which numbers are representing the legs of a triangle?
Answers
ANSWER
None of these sides represent the legs.
EXPLANATION
The legs of a triangle are the sides that form the right angle in a right triangle. The legs are always the shortest sides, while the hypotenuse is the longest side.
In this case, the hypotenuse would be 15 yards, while the legs would be 12 yards and 13 yards. For this to be a right triangle, the Pythagorean Theorem must be satisfied,
[tex]\begin{gathered} 12^2+13^2=15^2 \\ 144+169=15^2 \\ 313=225\to false \end{gathered}[/tex]These side lengths do not satisfy the Pythagorean Theorem and, therefore, this is not a right triangle. If it is not a right triangle, then it does not have legs. Hence, none of these represent the legs.
Please help me to select the correct image for the representation of the function f(x) = 4 x3x?
Answers
Answer:
Explanation:
Given the below exponential function;
[tex]f(x)=4\cdot3^x[/tex]To be able to graph the above function, we'll go ahead and choose different values for x and determine the corresponding values of f(x).
When x = 0, we'll have;
[tex]f(0)=4\cdot3^0=4\cdot1=4[/tex]Looking at all the given four graphs, we can observe that only one of them has a y-interce
select the expression that will calculate how many eighths are in 2 bars
Answers
Answer:
Explanations:
Read the proof. Statement Reason 1. given Given: AE1 EC; BD 1 DC 1. AEI EC;BD IDC Prove: AAEC - ABDC A 2. ZAEC is a rt. 2; ZBDC 2. definition of is a rt. 2 perpendicular 3. ZAEC • ZBDC 3. all right angles are congruent 4. ? 4. reflexive property 5. AAEC - ABDC 5. AA similarity theorem. What is the missing statement in step 4? B D O ZACE = ZBCD O ZEAB DBC O ZEAC LEAC O ZCBD ZDBC
Answers
Answer:
(a) ∠ACE≅∠BCD
Step-by-step explanation:
You want to know the missing statement in the proof that goes with reason "Reflexive Property."
ProofYou are proving two triangles are similar by showing two corresponding angles are congruent. Corresponding angles in the two triangles are ...
EAC and DBCAEC and BDCACE and BCDThe proof already shows AEC is congruent to BDC in statement 3.
Reflexive propertyThe reflexive property says an angle is congruent to itself. Looking at the list of corresponding angles, the only angle that corresponds to itself is angle C, which can be named ∠ACE or ∠BCD.
The appropriate choice is ...
∠ACE≅∠BCD . . . . Reflexive property
<95141404393>
The missing statement in step 4 should be:ZACE = ZBCD
This statement is missing from the proof and should be included to establish the congruence between the angles in the two triangles.Let's go through the proof step by step and explain each statement and reason.
Given:
AE = EC; BD = DC
AEI = EC; BD = DC
Reason: Given
ZAEC is a right angle; ZBDC is a right angle
Reason: Definition of a right angle. This statement indicates that angle ZAEC and angle ZBDC are both right angles.
ZAEC ≅ ZBDC
Reason: All right angles are congruent. This statement asserts that angle ZAEC and angle ZBDC are congruent (have the same measure) because they are both right angles.
[Missing Statement]
Reason: Reflexive property. This statement is missing in the proof and should be included. The reflexive property states that any angle is congruent to itself. In this case, it implies that angle ZAEC is congruent to angle ZAEC.
AAEC ≅ ABDC
Reason: AA similarity theorem. This statement indicates that triangle AAEC is congruent to triangle ABDC. The AA similarity theorem states that if two pairs of corresponding angles in two triangles are congruent, then the triangles are similar.
So, to complete the proof, the missing statement in step 4 should be:
ZACE = ZBCD
Reason: Reflexive property. This statement establishes that angle ZACE is congruent to angle ZBCD, based on the reflexive property.
Learn more about statement here:
https://brainly.com/question/9048478
#SPJ8
Consider the line y=2x/3 - 7 Find the equation of the line that is perpendicular to this line and passes through the point (2, 6)Find the equation of the line that is parallel to this line and passes through the point (2, 6)Equation of perpendicular line: Equation of Parallel line:
Answers
The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m = slope
c = y intercept
The given equation is
y = 2x/3 - 7
By comparing both equations,
m = 2/3
If two lines are perpendicular, it means that the slope of one line is equal to the negative reciprocal of the slope of the other line. This means that the slope of the perpendicular line passing through the point (2, 6) is the negative reciprocal of 2/3. It is - 3/2
Thus, m = - 3/2
We would find the y intercept of the perpendicular line by substituting m = - 3/2, x = 2 and y = 6 into the slope intercept equation. We have
6 = - 3/2 * 2 + c
6 = - 3 + c
c = 6 + 3 = 9
By substituting m = - 3/2 and c = 9 into the slope intercept equation, the equation of the perpendicular line is
y = - 3x/2 + 9
Also,
If two lines are parallel, it means that the slope of one line is equal to the slope of the other line. This means that the slope of the parallel line passing through the point (2, 6) is 2/3
Thus, m = 2/3
We would find the y intercept of the perpendicular line by substituting m = 2/3, x = 2 and y = 6 into the slope intercept equation. We have
6 = 2/3 * 2 + c
6 = 4/3 + c
c = 6 - 4/3 = 14/3
By substituting m = 2/3 and c = 14/3 into the slope intercept equation, the equation of the parallel line is
y = 2x/3 + 14/3
The number line below represents which combined inequality? xs-6 orx 25 xs -6 and x 2 5 X2 -6 and x s 5 x2-6 or x s 5
Answers
Answer
Option C is correct.
x ≥ -6 and x ≤ 5
Explanation
In graphing inequality equations, the first thing to note is that whenever the equation to be graphed has (< or >), the circle at the beginning of the arrow is usually unshaded.
But whenever the inequality has either (≤ or ≥), the circle at the beginning of the arrow will be shaded.
Since the beginning of the blue mark is a shaded circle, the inequality is (≤ or ≥).
And considering that the region of the answer is between -6 and 5, it is evident that x is greater than or equal to -6 and less than or equal to 5. In mathematical terms,
x ≥ -6 and x ≤ 5
-6 ≤ x ≤ 5
Hope this Helps!!!
Ms. Wong wrote a test. Part A had true/false questions, each worth 7 points. Part B had multiple choice questions, each worth 3 points. She made the number of points for Part A equal the number of points for Part B. It was the least number of points for which this was possible.
Answer the following questions.
How many points was each part worth?
How many questions did Part A have?
How many questions did Part B have?
Answers
Considering the least common multiple of 7 and 3, it is found that:
Each part was worth 21 points.Part A had 3 questions.Part B had 7 questions;How to obtain the measures?The amount of points of each question in each part are given as follows:
Part A: 7 points.Part B: 3 points.Both parts have the same number of points, and this amount was the least number of points for which this was possible, hence this amount is the least common multiple of 7 and 3.
Both 3 and 7 are prime numbers, hence the least common multiple of 3 and 7 is given by their multiplication, as follows:
7 x 3 = 21.
Hence each part of the test was worth 21 points.
The number of questions of each part is given by the division of 21 and the worth of each question, hence:
Part A: 21/7 = 3 questions.Part B: 21/3 = 7 questions.More can be learned about the least common multiple at https://brainly.com/question/10749076
#SPJ1
n were to share the juice equally, how much would each child get?
Answers
Please let me know what is the amount of juice to be shared equally among n people.
Please share an image of the problem so I can see the values in question.
What is the amount of juice to be shared?
Whatever that value is, you divide it by the number of children present.
Another problem seems to be show which number is smaller and which one is larger between the following:
[tex]1\text{ }\frac{2}{3}\text{ and 3}[/tex]So, we proceed to write the mixed number as an improper fraction:
[tex]1\text{ }\frac{2}{3}=1+\frac{2}{3}=\frac{3}{3}+\frac{2}{3}=\text{ }\frac{5}{3}[/tex]and on the other hand, the number 3 can be written as 9/3 (nine thirds)
Therefore, since the mixed number is 5/3 and 3 is 9/3, we see clearly that 5/3 is smaller than 9/3 : One shows 5 of the "thirds" while the other one involves 9 of the "thirds".
Now it seems that you want to add the mixed number plus the 3. so, since they already are expressed with the same DENOMINATOR, we can easily add them:
[tex]1\frac{2}{3}+3=\frac{5}{3}+\frac{9}{3}=\frac{14}{3}=4\text{ }\frac{2}{3}[/tex]Please see attachment for question.Fill in the table and then graph the function
Answers
ANSWER
EXPLANATION
First, we have to fill in the table. To do so, we will plug the x-values into the function to find the corresponding value of y,
[tex]\begin{cases}y=-3\cdot3^{-3}=-\frac{3}{3^3}=-\frac{3}{27}=-\frac{1}{9} \\ \\ y=-3\cdot3^{-2}=-\frac{3}{3^2^{}}=-\frac{3}{9}=-\frac{1}{3} \\ \\ y=-3\cdot3^{-1}=-\frac{3}{3^1}=-\frac{3}{3}=-1 \\ \\ y=-3\cdot3^0=-3\cdot1=-3 \\ \\ y=-3\cdot3^1=-3\cdot3=-9 \\ \\ y=-3\cdot3^2=-3\cdot9=-27 \\ \\ y=-3\cdot3^3=-3\cdot27=81\end{cases}[/tex]So, the table is,
Next, we have to graph all of these points in the coordinate plane. The last one cannot be graphed because y = -81 does not fit in the given coordinate plane. Also, the first two values won't be very accurate because of the scale of the y-axis. The graphed points are,
And finally, to graph the function we join the dots with a line.
Solve the equation for y in terms of x. In other words, algebraicallyrearrange the equation so that the y variable is by itself one side of theequation. Type your answer in the form y = mx + b. If you have a valuethat is not an integer then type it rounded to the nearest hundredth. Donot put spaces between your characters.4x + 2y = 8y = ?
Answers
We can determine an expression of y in terms of x by isolating y on one side of the equation, we can do this by means of some algebraic operations to get:
4x + 2y = 8
1. Subtract 4x from both sides of the equation:
4x - 4x + 2y = 8 - 4x
0 + 2y = 8 - 4x
2y = 8 - 4x
2. Divide both sides by 2
2y/2 = (8 - 4x)/2
y = 4 - 2x
y = -2x + 4
Then, the equation of y in terms of x is y=-2x+4
32. What is the rate of change of y with the respect to x for 24x - 4y = 50
Answers
The equation for the graph is given as
[tex]24x-4y=50[/tex]Let us rearrange the equation into its Slope-Intercept form given as
[tex]y=mx+c[/tex]Where
m = rate of change
c = y-intercept
Therefore, we will have
[tex]-4y=-24x+50[/tex]Divide all terms by -4 to make y a standalone variable:
[tex]\begin{gathered} \frac{-4y}{-4}=\frac{-24x}{-4}+\frac{50}{(-4)} \\ y=6x-\frac{25}{2} \end{gathered}[/tex]Comparing with the Slope-Intercept equation, the rate of change is given as 6.
Please do this fast and quick I need to sleep
Answers
Given:
distance from sea level to top of hill = initial heeight = 73.5 meters
velocity = 9.8 m/s
[tex]\begin{gathered} For\text{ vertical movement:} \\ Final\text{ height = acceleration\lparen t}^2)\text{ + velocity\lparen t\rparen+ initial height} \\ Since\text{ it is reaching sea level, final height = 0} \\ acceleration\text{ = -9.8 m/s}^2 \\ \\ 0\text{ = -}\frac{1}{2}(9.8)t^2\text{ + 9.8t + 73.5m} \end{gathered}[/tex][tex]\begin{gathered} 0\text{ = -4.9t}^2\text{ + 9.8t + 73.5} \\ 4.9t^2\text{ - 9.8t - 73.5 = 0 \lparen quadratic equation\rparen} \\ \\ \text{Using formula method to find the value of t:} \\ t\text{ = }\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ t\text{ = }\frac{-(-9.8)\pm\sqrt{(-9.8)^2-4(4.9)(-73.5)}}{2(4.9)} \\ \text{ t = }\frac{-(-9.8)\pm\sqrt{1536.64}}{9.8} \\ t\text{ = }\frac{9.8\pm39.2}{9.8} \end{gathered}[/tex][tex]\begin{gathered} t\text{ = }\frac{9.8+39.2}{9.8}\text{ ot }\frac{9.8\text{ - 39.2}}{9.8} \\ \\ t\text{ = 5 or -3} \end{gathered}[/tex]Since we can't have t to be negative, t = 5
The cannonball will reach the sea level at 5 seconds