Solve the following quadratic equation by factoring. If needed, write your answer as a fraction reduced to lowest terms
Answers
The given equation is
[tex]y^2-5y-36=0[/tex]For solving it we will factorize the number 36 as 9 x 4 which on subtraction gives 5 and on multiplication gives 36.
Then, we have
[tex]\begin{gathered} y^2-(9-4)y-36=0 \\ y^2-9y+4y-36=0 \\ y(y-9)+4(y-9)=0 \\ (y-9)(y+4)=0 \\ y-9=0\text{ and y+4=0} \\ y=p\text{ and y=-4} \end{gathered}[/tex]Hence, the values of y are 9 and -4.
Related Questions
Answer the following question by creating an exponential equation? 1. On the day a rumor was started, 4 people knew about the rumor. The next day, and onward, the number of people who knew about the rumor doubled. On what day did 800 people know about the rumor?
Answers
Given
Series of numbers
first day = 4
second day = 8
Third day = 16
4, 8, 16, ...
From the exponential sequence
First term a = 4
common ratio r = second term/first term
= 8/4 = 2
r = 2
[tex]undefined[/tex]REDUCE 48/96 TO THE LOWEST TERMS
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use the quadratic formula to find both solitions to the quadratic equation given below x^2+6×=16
Answers
Answer:
x1=4
x2=-8
Step-by-step explanation:
x^2+6x-16=0
a=1 b=6 c=-16
D=b^2 - 4ab= 36+64=100
D>0, 2 sqrt
x1= -b+sqrt{D} /2= -6+10/2= 4
x2= -b-sqrt{D} /2= -6-10/2= -8
(That's what we were taught!)
Solve the inequality. Express your answer using set notation or interval notation. Graph the solution set.
Answers
Answer:
(D) {xIx ≥ 5} or [5, ∞)
Explanation:
Given inequality: 5x - 11 ≥ 9 + x
By collecting the like terms, we have
5x - x ≥ 9 + 11
4x ≥ 20
Divide bothsides by 4
4x/4 ≥ 20/4
x ≥ 5
In set notation, we have {5, ∞}
The graph of the solution set is
How many flowers, spaced every 6 inches, are needed to surround a circular garden with a 50 foot radius? Round to the nearest whole number if needed
Answers
Given:
The radius of the circular garden is 50 feet.
First, find the circumference of the circle.
[tex]\begin{gathered} C=2\pi\times r \\ C=2\pi(50) \\ C=100\times3.14 \\ C=314 \end{gathered}[/tex]As we know that 6 inches equal 1/2 feet.
[tex]\frac{314}{\frac{1}{2}}=314\times2=628[/tex]Answer: There are 628 flowers will be needed for 314 feet circular garden.
how to calculate the amount compounded to 6 years not only one year1) $3000 deposit that earns 6% annual interest compounded quarterly for 6 years
Answers
Step 1
State the compound interest formula
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where;
[tex]\begin{gathered} A=\text{ amount} \\ P=Prin\text{cipal}=\text{\$3000} \\ r=\text{ rate= }\frac{\text{6}}{100}=0.06 \\ n=\text{ number of periods of compounding= 4} \\ t=\text{ time = 6 years} \end{gathered}[/tex]Step 2
Find the amount as required
[tex]\begin{gathered} A=3000(1+\frac{0.06}{4})^{6\times4} \\ A=3000(1+0.015)^{24} \\ A=3000(1.015)^{24} \\ A=\text{\$}4288.508436 \\ A\approx\text{ \$}4288.51 \end{gathered}[/tex]Hence the amount compounded quarterly for 6 years based on a principal of $3000 and a 6% annual interest rate = $4288.51
Trini bought some jeans that she had been saving up for. She purchased them for $88 but has wornthem 4 times already. So far, what is the cost of wear for the jeans?
Answers
In order to find the cost of wear for the jeans, we just need to divide the cost of the jeans by the number of times Trini worn it.
So we have:
[tex]\frac{88}{4}=22[/tex]Therefore the cost of wear so far is $22.
circumference of the back wheel=9 feet, front wheel=7 feet. On a certain distance the front wheel gets 10 revolutions more than the back wheel. What is the distance?
Answers
The distance would be 315 feet which is a certain distance the front wheel gets 10 revolutions more than the back wheel.
What is the Circumference of a circle?The Circumference of a circle is defined as the product of the diameter of the circle and pi.
C = πd
where 'd' is the diameter of the circle
Given that the circumference of the back wheel=9 feet, the front wheel=7 feet. At a certain distance, the front wheel gets 10 revolutions more than the back wheel.
Both wheels must move at the same distance. If the number of revolutions taken by the back wheel is x, then the number of revolutions taken by the front wheel is x+10.
Because the distance traveled is the same as:
⇒ 9x = 7(x+10)
⇒ 9x = 7x+70
⇒ 9x - 7x = 70
⇒ 2x = 70
⇒ x = 35
We obtain x = 35 revolutions.
So the total distance traveled is 35×9=315 feet or 45×7=315 feet.
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Dave and his brother. Theo, are selling cookies by the pound at the school bake sale Dave sold 14 84 pounds of cookies and Theo sold 21.45 pounds of cookies How many pounds did they sell altogether? A 35 29 OB 36 39 C36 25 0 D. 36 29
Answers
For tis problem we have that Dave sold 14.84 pounds of cookies and Theo sold 21.45 pounds of cookies.
If we want to find the total of pounds that they sold together we just need to add the two values and we have:
[tex]14.84+21.45=36.29\text{pounds}[/tex]The reason is because 0.84+0.45=1.29
14+21=35. And finally 35+1.29=36.29
And the best answer for this case would be D. 36.29
The rate of growth of a particular population is given by dP/dt=50t^2-100t^3/2, where P is population size and t is fine and years. Assume the initial population is 25,000. a) determine the population function, P(t)b) estimate to the nearest year how long it will take for the population to reach 50,000
Answers
SOLUTION
Step1: write out the giving equation
[tex]\frac{dp}{dt}=50t^2-100t^{\frac{3}{2}}[/tex]Step2: Integrate both sides of the equation above
[tex]\int \frac{dp}{dt}=\int 50t^2dt-\int 100t^{\frac{3}{2}}dt[/tex]Then simplify by integrating both sides
[tex]p(t)=\frac{50t^{2+1}}{2+1}-\frac{100t^{\frac{3}{2}+1}}{\frac{3}{2}+1}+c[/tex][tex]p(t)=\frac{50}{3}t^3-40t^{\frac{5}{2}}+c[/tex]since the initial value is 25,000, then
the Population function is
[tex]\begin{gathered} p(t)=\frac{50}{3}t^3-40t^{\frac{5}{2}}+25000\ldots\ldots..\ldots\text{.. is the population function} \\ \text{where t=time in years} \end{gathered}[/tex]b). For the population to reach 50,000 the time will be
[tex]\begin{gathered} 50000=\frac{50}{3}t^3-40t^{\frac{5}{2}}+2500 \\ 50000-25000=\frac{50}{3}t^3-40t^{\frac{5}{2}} \\ 25000=\frac{50}{3}t^3-40t^{\frac{5}{2}} \\ \text{Then} \\ \frac{50}{3}t^3-40t^{\frac{5}{2}}-25000=0 \\ \end{gathered}[/tex]Multiply the equation by 3, we have
[tex]\begin{gathered} 50t^3-120t^{\frac{5}{2}}-75000=0 \\ \end{gathered}[/tex]To solve this we rewrite the function as
[tex]14400t^5=\mleft(-50t^3+75000\mright)^2[/tex]The value of t becomes
[tex]\begin{gathered} t\approx\: 15.628,\: t\approx\: 9.443 \\ t=15.625\text{ satisfy the equation above } \end{gathered}[/tex]Then it will take approximately
[tex]16\text{years}[/tex]
# 8 Write an equation in slope-intercept form to represent the line parallel to y = -3/4 x + 1/4 passing through the point (4, -2). O y = -3/4x + 1 O y y = 4/3x + 20/3 O y = -3/4 - 2 O y=-3x - 2
Answers
If the line is parallel to y = -3/4 x + 1/4 then the slope is -3/4
the form of an equation is y = mx +b
In this case m = -3/4
Using the point given (4, -2) we will find the value of b:
y = mx + b
y = -3/4 x + b
Using the values of the point (4, -2).... x = 4 and y = -2
-2 = (-3/4)(4) + b
Solving for b:
-2 = -3 + b
-2 + 3 = b
1 = b
b = 1
Therefore the equation would be:
y = (-3/4)x + 1
Answer:
y = (-3/4)x + 1
Find the area and the perimeter of the following rhombus. round to the nearest whole number if needed.
Answers
ANSWER
[tex]\begin{gathered} A=572 \\ P=96 \end{gathered}[/tex]EXPLANATION
To find the area of the rhombus, we have to first find the length of the other diagonal.
We are given half one diagonal and the side length.
They form a right angle triangle with half the other diagonal. That is:
We can find x using Pythagoras theorem:
[tex]\begin{gathered} 24^2=x^2+16^2 \\ x^2=24^2-16^2=576-256 \\ x^2=320 \\ x=\sqrt[]{320} \\ x=17.89 \end{gathered}[/tex]This means that the length of the two diagonals is:
[tex]\begin{gathered} \Rightarrow2\cdot16=32 \\ \Rightarrow2\cdot17.89=35.78 \end{gathered}[/tex]The area of a rhombus is given as:
[tex]A=\frac{p\cdot q}{2}[/tex]where p and q are the lengths of the diagonal.
Therefore, the area of the rhombus is:
[tex]\begin{gathered} A=\frac{32\cdot35.78}{2} \\ A=572.48\approx572 \end{gathered}[/tex]The perimeter of a rhombus is given as:
[tex]P=4L[/tex]where L = length of side of the rhombus
Therefore, the perimeter of the rhombus is:
[tex]\begin{gathered} P=4\cdot24 \\ P=96 \end{gathered}[/tex]simplifying with like terms; 2(m+10)
Answers
In order to simplify the expression, we would multiply the terms inside the bracket by the term outside. It becomes
2 * m + 2 * 10
= 2m + 20
In 2019, the USDA reported that acreage for wheat was approximately 45.6 million acres;this is down 5% from 2018. Which of the following can you conclude?a) The 2018 wheat acreage was 47.88 million acres.b) The 2018 wheat acreage was 48.0 million acres.c) The 2019 wheat acreage was 43.43 million acres.d) The 2019 wheat acreage was 43.32 million acres.
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Given that the USDA reported the acreage for wheat in 2019 was approximately 45.6 million acres; and was down 5% from 2018. We were asked to pick an option that would represent the right conclusion to the given statement.
To do this, we would assume that the acreage for wheat in 20 18 is x. Since 2018 differs from 2019 by 5%
This implies that the representation of 2019 acreage would be;
[tex]100\text{\%-5\%=95\%}[/tex]Therefore, we can have
[tex]\begin{gathered} \frac{95}{100}\times x=45.6 \\ \text{Cross multiply} \\ 95x=45.6\times100 \\ \text{Divide both sides by 95} \\ \frac{95x}{95}=\frac{45.6\times100}{95} \\ x=48 \end{gathered}[/tex]Therefore the 2018 acreage was;
Answer: Option B
Suppose theta is an angle in the standard position whose terminal side is in quadrant 1 and sin theta = 84/85. find the exact values of the five remaining trigonometric functions of theta
Answers
we know that
The angle theta lies in the I quadrant
[tex]sin\theta=\frac{84}{85}[/tex]step 1
Find out the value of the cosine of angle theta
Remember that
[tex]sin^2\theta+cos^2\theta=1[/tex]substitute given value
[tex]\begin{gathered} (\frac{84}{85})^2+cos^2\theta=1 \\ \\ cos^2\theta=1-\frac{7,056}{7,225} \\ \\ cos^2\theta=\frac{169}{7,225} \\ \\ cos\theta=\frac{13}{85} \end{gathered}[/tex]step 2
Find out the value of the tangent of angle theta
[tex]tan\theta=\frac{sin\theta}{cos\theta}[/tex]substitute given values
[tex]\begin{gathered} tan\theta=\frac{\frac{13}{85}}{\frac{84}{85}}=\frac{13}{84} \\ therefore \\ tan\theta=\frac{13}{84} \end{gathered}[/tex]step 3
Find out the cotangent of angle theta
[tex]cot\theta=\frac{1}{tan\theta}[/tex]therefore
[tex]cot\theta=\frac{84}{13}[/tex]step 4
Find out the value of secant of angle theta
[tex]sec\theta=\frac{1}{cos\theta}[/tex]therefore
[tex]sec\theta=\frac{85}{13}[/tex]step 5
Find out the value of cosecant of angle theta
[tex]csc\theta=\frac{1}{sin\theta}[/tex]therefore
[tex]csc\theta=\frac{85}{84}[/tex]Transform y f(x) by translating it right 2 units. Label the new functiong(x). Compare the coordinates of the corresponding points that makeup the 2 functions. Which coordinate changes. x or y?
Answers
If we translate y = f(x) 2 units to the right, we would have to sum and get g(x) =f(x+2).
That means the x-coordinates of g(x) are going to have 2 extra units than f(x).
[tex](x,y)\rightarrow(x+2,y)[/tex]Therefore, with the given transformation (2 units rightwards) the function changes its x-coordinates.Witch phrase best describes the position of the opposite of +4
Answers
To find the position that is opposite to +4, we need to consider 0 as a "mirror point", then we check which point has the same distance to 0 as the distance from +4 to 0:
The position which is opposite to +4 is the position -4.
This position is 4 units to the left of 0 and 8 units to the left of +4.
Looking at the options, the correct option is the second one.
27. If figure A and figure B are similar with a ratio of similarity of 2, and the perimeter of figure A is 28 units,what is the perimeter of figure B?
Answers
SOLUTION
Since the two shapes are similar, that is A and B similar with a ratio of 2, then we have that
[tex]\begin{gathered} \frac{length\text{ A}}{lemgth\text{ B}}=\frac{2}{1}=\frac{perimeter\text{ A}}{perimeter\text{ B}} \\ \frac{2}{1}=\frac{perimeter\text{ A}}{perimeter\text{ B}} \\ \frac{2}{1}=\frac{28}{perimeter\text{ B}} \end{gathered}[/tex]Cross multiplying we have
[tex]\begin{gathered} 2Perimeter\text{ B = 28} \\ Perimeter\text{ B = }\frac{28}{2} \\ =14\text{ units } \end{gathered}[/tex]hence the answer is 14 units
Personal Math Trainer Lesson 15.2 - Homework - Homework 112131415 5 16 17 8 Margo can purchase tile at a store for $0.69 per tile and rent a tile saw for $56. At another store she can borrow the tile saw for free if she buys tiles there for $1.39 per tile. How many tiles must she buy for the cost to be the same at both stores? Margo must buy tiles for the cost to be the same at both stores.
Answers
Let Margo buy x number of tiles, So total cost of tiles and tile saw at first store is,
[tex]y=0.69x+56[/tex]The total cost equation for tile and tile saw for second store (which provide tile saw for free).
[tex]\begin{gathered} y=1.39x+0 \\ =1.39x \end{gathered}[/tex]Determine the number of tiles for total cost of tiles and tile saw to be equal from both store is,
[tex]\begin{gathered} 1.39x+0.69x+56 \\ 1.39x-0.69x=56 \\ 0.70x=56 \\ x=\frac{56}{0.70} \\ =80 \end{gathered}[/tex]So Margo purchase 80 tiles, such that total cost is equal from both the stores.
RATIONAL FUNCTIONSSynthetic divisiontable buand write your answer in the following form: Quotient *
Answers
The given polynomial is:
[tex]\frac{2x^4+4x^3-6x^2+3x+8}{x\text{ + 3}}[/tex]Using the long division method:
The equattion can be written in the form:
Quotient + Remainder / Divisor
[tex](2x^3-2x^2\text{ + 3) +}\frac{-1}{x+3}[/tex]answer this question that stumbles tons of people around the world!!
Answers
The values of x and y in the angles formed by the straight lines are:
x = 18.5
y = 37
What are Angles on a Straight Line?If two or more angles lie on a straight line, they will have a sum of 180 degrees when added together. Therefore, all angles on a straight line have a sum of 180 degree.
Therefore:
16 + 90 + 2y = 180 [straight line angle]
Combine like terms
106 + 2y = 180
Subtract both sides by 106
106 - 106 + 2y = 180 - 106 [subtraction property of equality]
2y = 74
2y/2 = 74/2
y = 37
Also,
16 + 90 + 4x = 180
106 + 4x = 180
4x = 180 - 106 [subtraction property of equality]
4x = 74
4x/4 = 74/4
x = 18.5
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Explain how to translate the point (5, 2) with the transformations: D2 and r(180,0). Make sure toexplain, in words, how you got your final answer, including where the point was after the firsttransformation.Edit ViewInsertFormat Tools TableΑν12ptvParagraph | BIUTv
Answers
We will have the following:
First: We dilate by a factor of 2, then we would have:
[tex](10,4)[/tex]Second: We rotate by 180°:
[tex](-10,-4)[/tex]A person buys a 900-milliliter bottle of soda from a vending machine. How many liters of soda did the person buy?
Answers
Answer: 0.9 Liters.
Step-by-step explanation:
Divide the volume value by 1000.
900 ÷ 1000
Because 1000 mililiters are the same that one liter.
What is the value of x in the proportion2 1/4 = 1 1/2_________x = 3 3/5A. 2 2/5B. 5 2/5C. 8 1/10D. 12 3/20
Answers
First, we transform the mixed fractions
[tex]\begin{gathered} 2\frac{1}{4}=2+\frac{1}{4}=\frac{8}{4}+\frac{1}{4}=\frac{9}{4} \\ 1\frac{1}{2}=1+\frac{1}{2}=\frac{2}{2}+\frac{1}{2}=\frac{3}{2} \\ 3\frac{3}{5}=3+\frac{3}{5}=\frac{15}{5}+\frac{3}{5}=\frac{18}{5} \end{gathered}[/tex]Then, we use cross multiplication
[tex]\begin{gathered} \frac{\frac{9}{4}}{x}=\frac{9}{4}\times\frac{1}{x}=\frac{9}{4x} \\ \frac{\frac{5}{2}}{\frac{18}{5}}=\frac{3}{2}\times\frac{5}{18}=\frac{15}{36} \end{gathered}[/tex]so, we have
[tex]\frac{9}{4x}=\frac{15}{36}[/tex]Finally, we solve for x, we multiply x on both sides
[tex]\begin{gathered} \frac{9}{4x}x=\frac{15}{36}x \\ \frac{15}{36}x=\frac{9}{4} \\ x=\frac{\frac{9}{4}}{\frac{15}{36}} \\ x=\frac{9}{4}\times\frac{36}{15} \\ x=\frac{9\times9\times4}{15\times4} \\ x=\frac{81}{15} \\ x=\frac{27}{5} \end{gathered}[/tex]Since 27/5 = 5+2/5.Then,
[tex]x=5\frac{2}{5}[/tex]Then the answer is the second one.
perform the calculation then round to the appropriate number of significant digits
Answers
The given expression is,
[tex]\frac{308.45}{1.12}[/tex]On division we get,
[tex]\frac{308.45}{1.12}=275.4017[/tex]On rounding we get, 275.402.
The order in which you write the ratio is ____ to the meaning.
Answers
The ratio is defined as fraction in which one number is numertor and other number is denominator.
For example the ratio 2/3 has 2 in numerator and 3 in denominator, but if we write the ratio as 3/2 then it is different from previous ratio 2/3. So in ratio order is important in which you write the ratio.
Thus answer is,
The order in which you write the ratio is important to the meaning.
In the figure to the right, ABC and ADE are similar. Find the length of EC.
The length of EC is ___.
Answers
Answer:
ninety 90 feet or foot long
Reduce to lowest term10\25
Answers
Answer:
2/5
Step-by-step explanation:
10 and 25 can both be divided by 5
10 divided by 5 equals 2
25 divided by 5 equals 5
Two figures are similar. The smaller figure has dimensions that are 3:4 the size of the largerfigure. If the area of the larger figure is 100 square units, what is the area of the smallerfigure?
Answers
Answer:
56.25
Explanation:
We are told that the side lengths of the smaller figure are 3/4 the length of the larger figure.
[tex]S_{small}=\frac{3}{4}\times S_{large}[/tex]Now since the area is proportional to the equal of the side lengths, we have
[tex]A_{small}=S_{small}^2^[/tex][tex]A_{small}=(\frac{3}{4})^2\times S_{large}^2[/tex][tex]=A_{small}=(\frac{3}{4})^2\times A_{large}^2[/tex]The last is true since A_large = S^2_large.
Now we are told that A_large = 100 square units; therefore,
[tex]A_{small}=(\frac{3}{4})^2\times100[/tex][tex]\Rightarrow A_{small}=\frac{9}{16}\times100[/tex]which we evaluate to get
[tex]A_{small}=\frac{9}{16}\times100=56.25[/tex][tex]\boxed{A_{small}=56.25.}[/tex]Hence, the area of the smaller figure is 56.25.
CASSANDRA WENT FOR A JO9.SHE RAN AT A PACE OF 7.3 MILESPER HOUR. IF SHE RAN FOR 0.75HOURS, HOW FAR DID CASSANDRARUN?
Answers
We can use one simple formula, that is d=vt
d=distance
v=pace
t=time
So,
d=(7.3miles per hour)(0.75 hours)=5.475 miles
