A) 9 cups of berries to 12 cups of juice
Explanation
to figure out this, we need to find the original ratio and then compare
Step 1
find the ratio:
ratio cups of berries to cups of juices
[tex]\text{ratio}=\frac{3\text{ cups of berries}}{4\text{ cups of juices}}=\frac{3}{4}[/tex]hence, the rario is 3/4
Step 2
now, check the ratio of every option
a)9 cups of berries to 12 cups of juice
[tex]\begin{gathered} \text{ratio}_a=\frac{9\text{ cups of berries}}{12\text{ cups of juice}}=\frac{3}{4} \\ \text{ratio}_a=\frac{3}{4} \end{gathered}[/tex]b) 12 cups of berries to 9 cups of juice
[tex]\text{ratio}_b=\frac{12\text{ cups of berries}}{9\text{ cups of juice}}=\frac{4}{3}[/tex]c) 6 cups of berries to 15 cups of juice
[tex]\text{ratio}_c=\frac{6\text{ cups of berries }}{15\text{ cups of juice}}=\frac{6}{15}=\frac{2}{5}[/tex]d) 15 cups of berries to 10 cups of juice
[tex]\text{ratio}_d=\frac{15\text{ cups of berries }}{10\text{ cups of juice}}=\frac{15}{10}=\frac{3}{2}[/tex]therefore, the option that haas the same ratio is a) 3/4
I hope this helps you
Subtract the following polynomials 1) (2x + 43) - (-3x-9)2) (f+9) - (12f 79)3) (75 X²)+ 23 + 13) - (15 X² - X + 40)
for 1.
2x+43+3x+9=5x+52
2.
f+9-12f+9=f-12f+9-9=-11f
3.
75x^2 +23x+13-15x^2+x-40=
=60x^2+24x-27
for 2)
23d^3+(7g^9)^13
remember that power to the power means that you need to multipy the exponents
=23d^3+7^13g^117
34x(2x-11)=68x^2-374x
2m(m+3n)=2 m^2+6mn
we have lenght
l=2x+5
w=x+7
area, A= lxw
A= (2x+5)(x+7)
this is the polynomial for the area
if we have x=12
l= (2*12)+5=24+5=29
w=12+7=19
A=29*19=551 ft^2
Find the prime factorization of the following number write any repeated factors using exponents
Notice that 100=10*10, and 10=2*5. 2 and 5 are prime numbers; therefore,
[tex]\begin{gathered} 100=10\cdot10=(2\cdot5)(2\cdot5)=2\cdot2\cdot5\cdot5=2^2\cdot5^2 \\ \Rightarrow100=2^2\cdot5^2 \end{gathered}[/tex]The answer is 100=2^2*5^2
So ABC and DEF are the same triangle, this question is asking me to write an equation between the relationships of DEF. How do I write that?
Explanation
The first step is to draw a representation of the given parameters.
Since this is a right-angle triangle, the Pythagorean theorem applies. This can be seen below;
[tex]\text{Longest Leg}^2=sum\text{ of the square of the short legs}[/tex]We can then apply it to the sides of the triangle.
DF is the longest side. Therefore,
Answer
[tex]DF^2=DE^2+EF^2[/tex]The relation between the number of batteries (n) and the maximum height reached by the drone (h) in feet (ft) is given. Complete the table and check the correct box(es) given below.
We use the equation: h = 100(n + 2), so:
For n = 1:
[tex]h=100(1+2)=100(3)=300[/tex]For n = 3:
[tex]h=100(3+2)=100(5)=500[/tex]We can see that this is the correct equation. Therefore, given h we find n:
For h = 700
[tex]\begin{gathered} 700=100(n+2) \\ \frac{700}{100}=\frac{100}{100}(n+2) \\ 7=n+2 \\ 7-2=n+2-2 \\ n=5 \end{gathered}[/tex]For h = 900
[tex]\begin{gathered} 900=100(n+2) \\ \frac{900}{100}=\frac{100}{100}(n+2) \\ 9=n+2 \\ 9-2=n+2-2 \\ n=7 \end{gathered}[/tex]Answer:
(n): 1 3 5 7
(h): 300 500 700 900
Correct equation: h = 100(n + 2)
Compute P(7,4)
From probability and statistics
The resultant answer from computing P(7,4) from probability and statistics is 840.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event could occur.So, P(7,4):
This is a permutation and can be calculated as:
ₙPₓ= n! / (n - x)!Here, n = 7 and x = 4Put the values in the given formula:
P(7, 4) = 7! / (7 - 4)!P(7, 4) = 7! / 3!P(7, 4) = 840Therefore, the resultant answer from computing P(7,4) from probability and statistics is 840.
To read more about probability:
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Write the slope-intercept form of the equation of each line.4) -3+y=2/5x
where
[tex]\begin{gathered} \text{slope}=\frac{2}{5} \\ y-\text{intercept}=3 \end{gathered}[/tex]Explanation
the equation of a line in slope-intercept form is given by:
[tex]\begin{gathered} y=mx+b \\ \text{where} \\ m\text{ is the slope} \\ b\text{ is the y-intercept} \end{gathered}[/tex]Step 1
then, isolate y
[tex]-3+y=\frac{2}{5}x[/tex]i) add 3 in both sides
[tex]\begin{gathered} -3+y=\frac{2}{5}x \\ -3+y+3=\frac{2}{5}x+3 \\ y=\frac{2}{5}x+3 \end{gathered}[/tex]Hence, the answer is
[tex]y=\frac{2}{5}x+3[/tex]where
slope=2/5
y-intercept=3
I hope this helps you
Determine the system of inequalities that represents the shaded area .
For the upper line:
[tex]\begin{gathered} (x1,y1)=(0,2) \\ (x2,y2)=(2,3) \\ m=\frac{y2-y1}{x2-x1}=\frac{3-2}{2-0}=\frac{1}{2} \\ \text{ using the point-slope equation:} \\ y-y1=m(x-x1) \\ y-2=\frac{1}{2}(x-0) \\ y=\frac{1}{2}x+2 \end{gathered}[/tex]For the lower line:
[tex]\begin{gathered} (x1,y1)=(0,-3) \\ (x2,y2)=(2,-2) \\ m=\frac{-2-(-3)}{2}=\frac{1}{2} \\ \text{ Using the point-slope equation:} \\ y-y1=m(x-x1) \\ y-(-3)=\frac{1}{2}(x-0) \\ y+3=\frac{1}{2}x \\ y=\frac{1}{2}x-3 \end{gathered}[/tex]Therefore, the system of inequalities is given by:
[tex]\begin{gathered} y\le\frac{1}{2}x+2 \\ y\ge\frac{1}{2}x-3 \end{gathered}[/tex]4. Betty Kusack and Theresa Peña together can do a job in 20 hours. Working alone,Betty can do the job in 60 hours. How long would it take Theresa, working alone, todo the job?AnswerH
Given:
Betty and Theresa together complete a job in 20 hours.
Betty alone does a work in 60 hours.
The aim is to find the time Theresa will take to complete the job alone.
Therefore,
Betty and Theresa's 1 day work:
[tex]=\frac{1}{20}[/tex]Betty's 1 day work when he works alone:
[tex]=\frac{1}{60}[/tex]Now, Theresa's 1 day work when he works alone is given by:
[tex]\begin{gathered} =\frac{1}{20}-\frac{1}{60} \\ =\frac{3-1}{60} \\ =\frac{2}{60} \\ =\frac{1}{30} \end{gathered}[/tex]Hence, Theresa can do the job in 30 hours working alone.
Subtract. Write fractions in simplest form. 12/7 - (-2/9) =
You have to subtract the fractions:
[tex]\frac{12}{7}-(-\frac{2}{9})[/tex]You have to subtract a negative number, as you can see in the expression, both negatives values are together. This situation is called a "double negative" when you subtract a negative value, both minus signs cancel each other and turn into a plus sign:
[tex]\frac{12}{7}+\frac{2}{9}[/tex]Now to add both fractions you have to find a common denominator for both of them. The fractions have denominators 7 and 9, the least common dneominator between these two numbers is the product of their multiplication:
7*9=63
Using this value you have to convert both fractions so that they have the same denominator 63,
For the first fraction 12/7 multiply both values by 9:
[tex]\frac{12\cdot9}{7\cdot9}=\frac{108}{63}[/tex]For the second fraction 2/9 multiply both values by 7:
[tex]\frac{2\cdot7}{9\cdot7}=\frac{14}{63}[/tex]Now you can add both fractions:
[tex]\frac{108}{63}+\frac{14}{63}=\frac{108+14}{63}=\frac{122}{63}[/tex]Given the matrices A and B shown below, find – į A+ B.89A=12 4.-4 -10-6 12B.=-3-19-10
Given:
[tex]\begin{gathered} A=\begin{bmatrix}{12} & {4} & {} \\ {-4} & {-10} & {} \\ {-6} & {12} & {}\end{bmatrix} \\ B=\begin{bmatrix}{8} & {9} & {} \\ {-3} & {-1} & {} \\ {-9} & {-10} & {}\end{bmatrix} \end{gathered}[/tex]Now, let's find (-1/2)A.
Each term of the matrix A is multiplied by -1/2.
[tex]\begin{gathered} \frac{-1}{2}A=\frac{-1}{2}\begin{bmatrix}{12} & {4} & {} \\ {-4} & {-10} & {} \\ {-6} & {12} & {}\end{bmatrix} \\ =\begin{bmatrix}{\frac{-12}{2}} & {\frac{-4}{2}} & {} \\ {\frac{4}{2}} & {\frac{10}{2}} & {} \\ {\frac{6}{2}} & {-\frac{12}{2}} & {}\end{bmatrix} \\ =\begin{bmatrix}{-6} & {-2} & {} \\ {2} & {5} & {} \\ {3} & {-6} & {}\end{bmatrix} \end{gathered}[/tex]Now let's find (-1/2)A+B.
To find (-1/2)A+B, the corresponding terms of the matrices are added together.
[tex]\begin{gathered} \frac{-1}{2}A+B=\begin{bmatrix}{-6} & {-2} & {} \\ {2} & {5} & {} \\ {3} & {-6} & {}\end{bmatrix}+\begin{bmatrix}{8} & {9} & {} \\ {-3} & {-1} & {} \\ {-9} & {-10} & {}\end{bmatrix} \\ =\begin{bmatrix}{-6+8} & {-2+9} & {} \\ {2-3} & {5-1} & {} \\ {3-9} & {-6-10} & {}\end{bmatrix} \\ =\begin{bmatrix}{2} & {7} & {} \\ {-1} & {4} & {} \\ {-6} & {-16} & {}\end{bmatrix} \end{gathered}[/tex]Therefore,
[tex]undefined[/tex]Please it’s due todayAre there any limitations on the inputs of the equation?Does the graph have any symmetry?If so, where? When will the graph point upward? When will it point downward?
We have the following:
1.
There is no limitation on the input values, the domain is all real numbers.
2.
Yes, it has an axis of symmetry at the point (0,0)
3.
The graph point upward in the interval:
[tex](0,\infty)[/tex]The graph point downward in the interval:
[tex](-\infty,0)[/tex]. . Read the problem and write your answer for each part. Make sure to label each part: , , .jasmine is tracking the growth of a specific bacteria bacteria for a science experiment. She assumes that there are bacteria () in a Perti dish at 12:00 midnight. Jamie observes that the number of bacteria increases by 25 every hour . write an equation that describes the relationship between total number of bacteria () and time () in hours, assuming there are () bacteria in the perti dish at = 0. . if Jamie starts with bacteria in the perti dish, how many bacteria will be present after 6 hours? . if Jamie starts with bacteria in the perti dish, draw a graph that displays the total number of bacteria with respect to time from 12:00 midnight ( = ) to 8:00 am. ( = ). Label each axis and label points on your graph at times = , , , .use the coordinate plane below to draw your graph.
Part A:
Let:
T(h)= Total Number of bacterias as a function of time
h = Number of hours
B = Initial number of bacterias
Since the number of bacteria increases by 25 every hour, we can defined the equation as:
[tex]T(h)=25h+B[/tex]Part B:
B = 5
h = 6
Evaluate the previous equation for those values:
[tex]\begin{gathered} T(6)=25(6)+5 \\ T(6)=150+5 \\ T(6)=155 \end{gathered}[/tex]there will be 155 baterias after 6 hours
Part C
Let's graph the equation:
[tex]T(h)=25h+5[/tex]2×+22=2(x+11)whats the property
Distributive property
In this property, multiplying the sum of two or more terms in that add up in a bracket by a number outside the bracket will be equal to multiplying each term in the bracket individually and then followed by sum of the product. In this question:
2x + 22 = 2(x + 11 ) in that when you perform product on the right side of the equation, the result is the same i.e 2x + 2*11 = 2x + 22
The number of bacteria in a culture increased from 27,000 to 105,000 in five hours. When is the number of bacteria one million if:a) Does the number increase linearly with time?b) The number increases exponentially with time?
We have the following situation regarding the growth of bacteria in a culture:
• The given initial population of bacteria is 27,000
,• After 5 hours, the population increases to 105,000.
Now, we need to find the moment when that population is one million if:
• The population increases linearly with time
,• The population increases exponentially with time
To find the time in both situations, we can proceed as follows:
Finding the moment when the population is one million if it increases linearly with time1. We need to find the equation of the line that passes the following two points:
• t = 0, population = 27,000
,• t = 5, population = 105,000
2. Then the points are:
[tex]\begin{gathered} (0,27000)\rightarrow x_1=0,y_1=27000 \\ (5,105000)\rightarrow x_2=5,y_2=105000 \\ \end{gathered}[/tex]3. Now, we can use the two-point form of the line equation:
[tex]\begin{gathered} y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1) \\ \\ y-27000=\frac{105000-27000}{5-0}(x-0) \\ \\ y-27000=\frac{78000}{5}x=15600x \\ \\ y=15600x+27000\rightarrow\text{ This is the line equation we were finding.} \end{gathered}[/tex]4. We can see that the population is given by y. Then if y = 1,000,000, then we need to solve the equation for x as follows:
[tex]\begin{gathered} 1000000=15600x+27000 \\ \\ 1000000-27000=15600x \\ \\ \frac{(1000000-27000)}{15600}=x \\ \\ x=62.3717948718\text{ hours} \\ \\ x\approx62.3718\text{ hours} \end{gathered}[/tex]Therefore, if the population increases linearly with time, the number of bacteria will be one million around 62.3718 hours.
Finding the moment when the population is one million if it increases exponentially with time1. In this case, we also need to find the equation that will give us the time when the number of bacteria is one million. However, since the equation will be exponential, we have:
[tex]\begin{gathered} y=a(1+r)^x \\ \\ a\rightarrow\text{ initial value} \\ \\ x\rightarrow\text{ number of time intervals that have passed.} \\ \\ (1+r)=b\text{ }\rightarrow\text{the growth ratio, and }r\rightarrow\text{ the growth rate.} \end{gathered}[/tex]2. Now, we can write it as follows:
[tex]\begin{gathered} a=27000 \\ \\ x=5\rightarrow y=105000 \\ \\ \text{ Then we have:} \\ \\ 105000=27000(b)^5 \\ \end{gathered}[/tex]3. We can find b as follows (the growth factor):
[tex]\begin{gathered} \frac{105000}{27000}=b^5 \\ \\ \text{ We can use the 5th root to obtain the growth factor. Then we have:} \\ \\ \sqrt[5]{\frac{105000}{27000}}=\sqrt[5]{b^5} \\ \\ b=1.31209447568 \end{gathered}[/tex]4. Then the exponential equation will be of the form:
[tex]\begin{gathered} y=27000(1.31209447568)^x \\ \\ \text{ To check the equation, we have that when x = 5, then we have:} \\ \\ y=27000(1.31209447568)^5=105000 \end{gathered}[/tex]5. Now, to find the time when the number of bacteria is one million, we can proceed as follows:
[tex]\begin{gathered} 1000000=27000(1.31209447568)^x \\ \\ \frac{1000000}{27000}=1.31209447568^x \end{gathered}[/tex]6. Finally, we need to apply the logarithm to both sides of the equation as follows:
[tex]\begin{gathered} ln(\frac{1000000}{27000})=ln(1.31209447568)^x=xln(1.31209447568) \\ \\ \frac{ln(\frac{1000000}{27000})}{ln(1.31209447568)}=x \\ \\ x=13.2974595282\text{ hours} \end{gathered}[/tex]Therefore, if the population increases exponentially with time, the number of bacteria will be one million around 13.2975 hours.
Therefore, in summary, we have:
When is the number of bacteria one million if:
a) Does the number increase linearly with time?
It will be 62.3718 hours
b) The number increases exponentially with time?
It will be around 13.2975 hours
Select all the equations that share a solution with this system of equations. (Hint: try adding and subtracting the equations.) 5x + 4y = 24 2x – 7y = 26 7x – 3y = 50 7x + 3y = 50 3x - 3y = -2 36 x+ 11y = -2
Select all the equations that share a solution with this system of equations. (Hint: try adding and subtracting the equations.)
5x + 4y = 24
2x – 7y = 26
____
a) 7x – 3y = 50
b) 7x + 3y = 50
c) 3x - 3y = -2
d) 3 x+ 11y = -2
_____________________________
Try adding and subtracting the equations
5x + 4y = 24
+(2x – 7y = 26)
_______________
7x -3y= 50
5x + 4y = 24
-2x + 7y = -26
______________
3x + 11y = -2
Do you have any questions regarding the solution?
. In a 30°-60-90° triangle, the hypotenuse is 7 yards long.Find the exact lengths of the legs?
ANSWER
The lengths of the legs of the triangle are 6.06 yards and 3.6 yards.
EXPLANATION
First, let us make a sketch of the problem:
To find the length of the legs, we have to apply trigonometric ratios SOHCAHTOA.
We have that:
[tex]\sin (60)=\frac{\text{opposite}}{\text{hypotenuse}}[/tex]From the diagram:
[tex]\begin{gathered} \sin (60)=\frac{x}{7} \\ \Rightarrow x=7\cdot\sin (60) \\ x\approx6.06\text{ yds} \end{gathered}[/tex]We also have that:
[tex]\sin (30)=\frac{\text{opposite}}{\text{hypotenuse}}[/tex]From the diagram:
[tex]\begin{gathered} \sin (30)=\frac{y}{7} \\ \Rightarrow y=7\cdot\sin (30) \\ y=3.5\text{ yds} \end{gathered}[/tex]The lengths of the legs of the triangle are 6.06 yards and 3.5 yards.
help me please.......
Let
x -----> the larger room
y -----> the smaller room
we have that
x=2y
we have
y=25 3/4 ft
Convert to an improper fraction
25 3/4=25+3/4=103/4 ft
Find the value of x
x=2y
x=2(103/4)
x=103/2 ft
Convert to mixed number
103/2=51.5=51+0.5=51 1/2 ft
the answer is51 1/2 fthe larger roomhe larger room
Solve triangle EFG with the given parts.f = 17.78, F = 27.3°, G = 102.1°
STEP - BY - STEP EXPLANATION
What to find?
g, E and e
Given:
Step 1
Find the measure of side g using the sine ratio.
[tex]\begin{gathered} \frac{sinF}{f}=\frac{sinG}{g} \\ \\ \frac{sin27.3}{17.78}=\frac{sin102.1}{g} \\ \\ gsin27.3=17.78sin102.1 \\ \\ g=\frac{17.78sin102.1}{sin27.3} \\ \\ g\approx37.9 \end{gathered}[/tex]Step 2
Find angle E.
[tex]E+F+G=180(sum\text{ of interior angle in a triangle\rparen}[/tex][tex]\begin{gathered} E+27.3+102.1=180 \\ \\ E=180-102.1-27.3 \\ \\ E=50.6° \end{gathered}[/tex]Step 3
Find side e using the sine ratio.
[tex]\begin{gathered} \frac{sinE}{e}=\frac{sinF}{f} \\ \\ \frac{sin50.6}{e}=\frac{sin27.3}{17.78} \\ \\ esin27.3=17.78sin50.6 \\ \\ e=\frac{17.78sin50.6}{sin27.3} \\ \\ e\approx29.96 \end{gathered}[/tex]ANSWER
g=37.9
E=50.6°
e = 29.96
Charlene and Gary want to make perfume. In order to get the right balance of ingredients for their tastes they bought 2ounces of rose oil at $4.36 per ounce, 5 ounces of ginger essence for $2.15 per ounce, and 4 ounces of black currant essence for $2.27 per ounce. Determine the cost per ounce of the perfume.
First, lets calculate how much the expended in the perfume:
[tex]2\times(4.36)+5\times(2.15)_{}+4\times(2.27)=28.55[/tex]So, for 11 ounces of perfume, they need $28.55, so the minimum that the perfume need to cost per ounce is:
[tex]\frac{28.55}{11}=2.5954\cong2.6[/tex]So, about $2.6 per ounce of perfume.
How many values does the expression 6+ (7 + 3)² have? Write down the values.
Answer:
3
Step-by-step explanation:
6
7
3
The values are the number that compose the expression
when graphed on a coordinate plane,Bumby Avenue can be represented by the equation y=-4x-7. primrose can be represented by the equation 8x+2y=17. Are these streets parallel ?
Answer:
The lines are not parallel because their slopes are opposite reciprocals.
Explanation:
The lines:
[tex]\begin{gathered} y=-4x-7 \\ \text{and} \\ 8x+2y=17 \end{gathered}[/tex]are not parallel because their slopes are not the same
Note:
Two straight lines are said to be parallel when their slopes are the same, and have different y-intercepts.
A. Determine the slope intercept equation of each line given two points on the line 1. (1, -3) and (-2, 6)
ANSWER
y = -3x
EXPLANATION
We have to determine the slope-intercept form of the equation of the line.
The slope-intercept form of a linear equation is given as:
y = mx + c
where m = slope
c = y intercept
First, we have to find the slope:
[tex]m\text{ = }\frac{y2\text{ - y1}}{x2\text{ - x1}}[/tex]where (x1, y1) and (x2, y2) are two points the line passes through.
Therefore:
[tex]\begin{gathered} m\text{ = }\frac{6-(-3)}{-2-1}=\frac{6+3}{-3}=\frac{9}{-3} \\ m=-3 \end{gathered}[/tex]Now, we have to use the point-slope method to find the equation:
y - y1 = m(x - x1)
=> y - (-3) = -3(x - 1)
y + 3 = -3x + 3
y = -3x + 3 - 3
y = -3x
That is the slope intercept form of the equation.
Two cyclists, 108 miles apart, start riding toward each other at the same time. One cycles 2 times asfast as the other. If they meet 4 hours later, what is the speed (in mi/h) of the faster cyclist?
Initial distance: 108 miles
We know that they start riding toward each other, and one of them is 2 times as fast as the other. Then, if the speed of the slowest is v, the speed of the faster cyclist is 2v. The combined speed is:
[tex]v_T=v+2v=3v[/tex]The speed and the distance are related by the equation:
[tex]V=\frac{D}{t}[/tex]They meet 4 hours later, thus:
[tex]\begin{gathered} D=108 \\ t=4 \end{gathered}[/tex]Finally, using the previous equation:
[tex]\begin{gathered} 3v=\frac{108}{4} \\ \Rightarrow v=9\text{ mi/h} \end{gathered}[/tex]The speed of the faster cyclist (2v) is 18 mi/h.
The first quartile of a data set is 32, and the third quartile is 52. Which of
these values in the data set is an outlier?
Answer: As we know that the formula of outlier is
IQR = Q3 - Q1
= 52 - 32
= 20
52 + 1.5(20) = 82...
so anything above 82 is an outlier
now
32 - 1.5(20) = 2.
..anything below 2 is an outlier
so...the 83 is outlier
so correct option is D
hope it helps
Step-by-step explanation:
3.2 Similar FiguresIf ASRT - ACBD, find the value of x.Show all work.Hint: Don't let your eyes deceive you pay attention tothe similarity statement.
Find the ratio of corresponding sides:
SRT to CBD =
70/50 = 1.4
SR / 60 = 1.4
SR = 60 x 1.4
SR = 84
84= 11x-4
Solve for x:
84+4 = 11x
88= 11x
88/11 = x
8=x
in a hurry! have to finish the practice test in 30mins, so I can take the real one!(CHECKING AWNSERS, SO ONLY NEED AWNSERS TO I CAN COMPARE)
The expression can be simplified as,
[tex]\begin{gathered} \frac{3}{x+2}+\frac{2}{x-3}=\frac{3(x-3)+2(x+2)}{(x-3)(x+2)} \\ =\frac{3x-9+2x+4}{(x-3)(x+2)} \\ =\frac{5x-5}{(x-3)(x+2)} \end{gathered}[/tex]Thus, option (D) is the correct option.
the vertex of the parabola below is at the point (3,2) and point (4,6) is on the parabola
By using the vertex and the given point, we conclude that the quadratic equation is:
y = 4*(x - 3)^2 + 2
How to find the equation of the parabola?A quadratic equation with a vertex (h, k) and a leading coefficient A can be written as:
y = A*(x - h)^2 + k
In this case, we know that the vertex is (3, 2), replacing that in the general equation we get:
y = A*(x - 3)^2 + 2
We also know that the curve passes through (4, 6), so when x = 4, the value of y must be 6, replacing that in the quadratic equation we can find the value of A.
6 = A*(4 - 3)^2 + 2
6 = A*(1)^2 + 2
6 - 2 = A*1
4 = A
So we conclude that the quadratic equation is:
y = 4*(x - 3)^2 + 2
Learn more about quadratic equations:
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(x - 5) (4x - 5) = 0 there are two answers
The solutions are the values of x that makes the expression equal to zero:
x-5 =0
Add 5 to both sides
x=5
4x-5=0
Add five to both sides
4x=5
Divide both sides by 4
x= 5/4
x=1.25
The confidence interval on estimating the heights of the students is given as (5.5, 6.5). Find the sample proportion of the confidence interval.
Answer:
Step-by-step explanation:
Which quadrant has ordered pairs (-x,-y)?
ANSWER
Quadrant III
STEP-BY-STEP EXPLANATION:
Firstly, we need to draw the cardinal points and label each quadrant on it
Looking at the ordered pair (-x, -y), you will see that the x and y-values both fall on the negative side of the x-ais and y-axis
Hence, it falls on the quadrant III
