The option A is correct. A circle is the shape of the cross section taken parallel to the base of a cylinder.
According to the statement
We have given that the cylinder and we have to tell that the which shape required for the cross section taken parallel to the base of a cylinder.
So, For this purpose,
We know that the
A cylinder is a three-dimensional solid, one of the most basic geometric shapes.
In this shape the surface formed by the points at a fixed distance from a line segment, which is known as the axis of the cylinder.
As the bases of cylinder are two identical circles which are parallel to the curved surface.
The curved surface when we open will be circle rather than the circle.
So, Due to this reason the answer is a circle.
Therefore, a circle is the shape of the cross section taken parallel to the base of a cylinder.
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PLEASE HELP IM STUCK PLS
Answer:
y is equal to -16
Answer:
y = 8
Step-by-step explanation:
We can use proportions for this question since y varies directly with x. This means that if x changes, y changes along with the x, and vice versa.
When y = -8, x = 4, so the proportion will be -8 : 4.
We need to find the y when x is 4, so our equation will be:
-8 : 4 = y : -4
Since the proportion will be the same.
Next, we multiply the inner two numbers, and the outer two numbers, saying that the values are the same.
4y = 32
y = 8
So y = 8 will be our answer!
A company currently pays a dividend of $2.6 per share (d0 = $2.6). it is estimated that the company's dividend will grow at a rate of 24% per year for the next 2 years, and then at a constant rate of 8% thereafter. the company's stock has a beta of 1.8, the risk-free rate is 7.5%, and the market risk premium is 4.5%. what is your estimate of the stock's current price?
The stock's current price is 53.413455.
What is CAPM ?
The capital asset pricing model (CAPM) is an idealized portrayal of how financial markets price securities and thereby determine expected returns on capital investments. The model provides a methodology for quantifying risk and translating that risk into estimates of expected return on equity.The capital asset pricing model (CAPM) to know the value of the stock
[tex]Ke = rf + \beta ( r_{m} - r_{f} )[/tex]
risk free = 0.085
premium market =(market rate - risk free) = 0.045
beta(non diversifiable risk) 1.3
Ke = 0.085 + 1.3(0.045)
Ke = 0.14350
Now we need to know the present value of the future dividends:
D0 = 2.8
D1 = D0 × ( 1 +g ) = 2.8 = 2.8 * 1.23 = 3.444
D2 3.444 x 1.23 = 4.2361200
The next dividends, which are at perpetuity will we solve using the dividned grow model
[tex]\frac{divends}{return - growth} = Intrinsic value[/tex]
In this case dividends will be:
4.23612 x 1.07 = 4.5326484
return will be how return given by CAPM and g = 7%
plug this into the Dividend grow model.
[tex]\frac{4.5326484}{0.1435 - 0.07} = Intrinsic value[/tex]
value of the dividends at perpetity: 61.6686857
Finally is important to note this values are calculate in their current year. We must bring them to present day using the present value of a lump sum:
[tex]\frac{principal}{(1 + rate)^{time} } = PV[/tex]
[tex]\frac{3.444}{(1 + 1. 1435)^{1} } =PV[/tex]
3.011805859
[tex]\frac{4.23612}{( 1 + 0.1435)^{2} } = PV[/tex]
3.239633762
[tex]\frac{61.6686857}{(1 + 0.1435)^{2} } = PV[/tex]
47.16201531
We add them and get the value of the stock is 53.413455.
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The difference of the means is found and then compared to each of the mean absolute deviations. which is true?
The difference between the mean times is about 2 times the absolute deviation of the data sets.
Given that the difference of the means is found.
The difference in the means is basically the absolute difference between the mean of two groups. It explains the mean of two groups. It explains how much difference that exists between the average between two groups.Calculating mean difference is significant during clinical trials where we have the experimental group and the control group. The mean absolute deviations is basically the variation of each data value from the mean. It tells us how much the values in a set of data differ from the mean value. It explains the reach of values in a data set. There is a relationship that exists between the difference of the mean absolute deviations.
Hence the difference between the mean times is about 2 times the absolute deviation of the data sets.
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Which linear function represents the line given by the point-slope equation y – 8 = y minus 8 equals startfraction one-half endfraction left-parenthesis x minus 4 right-parenthesis.(x – 4)?
The linear function which represents the line given by the point-slope equation is (B) [tex]f(x)=\frac{1}{2} x+6[/tex].
What is a linear function?The word linear function in mathematics refers to two distinct but related concepts. A linear function in calculus and related fields is a function whose graph is a straight line, that is, a polynomial function of degree zero or one.To find the linear function which represents the line given by the point-slope equation:
Given: [tex]y-8=\frac{1}{2} (x-4)[/tex]
Distribute the right side:
[tex]y-8=\frac{1}{2} (x)-\frac{1}{2} 4\\y-8=\frac{1}{2} x-2[/tex]
Adds 8 on both sides:
[tex]y=\frac{1}{2}x-2+8\\y=\frac{1}{2}x+6[/tex]
Convert to function notation:
[tex]f(x)=y\\f(x)=\frac{1}{2} x+6[/tex]
Therefore, the linear function which represents the line given by the point-slope equation is (B) [tex]f(x)=\frac{1}{2} x+6[/tex].
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The complete question is given below:
Which linear function represents the line given by the point-slope equation y – 8 = y minus 8 equals start fraction one-half end fraction left-parenthesis x minus 4 right-parenthesis. (x – 4)?
A) F(x) = f(x) equals StartFraction one-half EndFraction x plus 4.X + 4
B) f(x) = f(x) equals StartFraction one-half EndFraction x plus 6.
C) X + 6 f(x) = f(x) equals StartFraction one-half EndFraction x minus 10.X –10
D) f(x) = f(x) equals StartFraction one-half EndFraction x minus 12.X – 12
8x + 2y =16
standard form
1) m=
2 y - intercept x - intercept
Answer:
m=-4
y-intercept=8
x-intercept=2
Step-by-step explanation:
Please see attachment.
y-intercept=8
The y-intercept is where the line crosses the y-axis.
x-intercept=2
The x-intercept is where the line crosses the x-axis.
m=-4
If you do not know how to find slope by looking at graph, use slope formula.
(y2-y1)/(x2-x1)
Choose 2 points. You may use the x and y intercepts.
(2,0) and (0,8)
(8-0)/(0-2)=8/-2=-4
Hope this helps!
Pls help 15. Find the exact area of the shaded region of the circle shown in the diagram.
Answer:
The shaded region is 9.83 cm²Step-by-step explanation:
Refer to attached diagram with added details.
GivenCircle O with:
OA = OB = OD - radiusOC = OD = 2 cmTo findThe area of segment ADB.SolutionSince r = OC + CD, the radius is 4 cm.
Consider right triangles OAC or OBC:
They have one leg of 2 cm and hypotenuse of 4 cm, so the hypotenuse is twice the short leg.Recall the property of 30°x60°x90° triangle:
a : b : c = 1 : √3 : 2, where a- short leg, b- long leg, c- hypotenuse.It means OC: OA = 1 : 2, so angles AOC and BOC are both 60° as adjacent to short legs.
In order to find the shaded area we need to find the area of sector OADB and subtract the area of triangle OAB.
Area of sector:
A = π(θ/360)r², where θ- central angle,A = π*((mAOC + mBOC)/360)*r²,A = π*((60 + 60)/360))(4²) = 16.76 cm².Area of triangle AOB:
A = (1/2)*OC*(AC + BC), AC = BC = OC√3 according to the property of 30x60x90 triangle.A = (1/2)(2*2√3)*2 = 4√3 = 6.93 cm²The shaded area is:
A = 16.76 - 6.93 = 9.83 cm²BRAINLIEST!
On a number line, the coordinates of P and Q are 8 and 48, respectively. The midpoint of PQ is B, the midpoint of BQ is C, and the midpoint of PC is D. What is the coordinate of D?
Answer:
23 is the answer
Write as a single term from Pascal's Triangle in the form t_nr(1 mark)
t_13,8 + t_13,9
¹³C₈ + ¹³C₉ as a single term from Pascal's Triangle is ¹⁴C₉
What is Pascal's triangle?
Pascal's triangle is a triangle written in such a way that it forms the coefficients of a binomial expansion. The coefficients of the terms are gotten through combination.
What is combination?Combination is the number of ways r in which n objects can be selected. It is given by ⁿCₓ = n!/x!(n - x)!
How to write a single term from Pascal's Triangle in the form t_nr = t_13,8 + t_13,9.Since we have ¹³C₈ + ¹³C₉ and we want to write it as a single term, we have that
¹³C₈ = 13!/8!(13 - 8)! = 13!/8!5! and ¹³C₉ = 13!/9!(13 - 9)! = 13!/9!4!So, ¹³C₈ + ¹³C₉ = 13!/8!5! + 13!/9!4!
= 13!/(8! × 5 × 4!) + 13!/(9 × 8! × 4!)
= 13!/8!4![1/5 + 1/9]
= 13!/8!4! × [(9 + 5)/45]
= 13!/8!4! × 14/45]
= 13!/8!4! × 14/(9 × 5)]
= 14 × 13!/8! × 9 × 4! × 5)]
= 14!/9!5!
= 14!/9!(14 - 9)!
= ¹⁴C₉
So, ¹³C₈ + ¹³C₉ as a single term from Pascal's Triangle is ¹⁴C₉
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Pretest: Unit 3
Question 12 of 28
A ladder leans against a 15-foot-tall building to form a right triangle. The
ladder is placed so it is 8 feet from the base of the building. What is the
length of the ladder?
A. 289 ft
OB. 17 ft
O C. 13 ft
D. 161 ft
←BREMQU
Building
15 ft
Ladder
8 ft
42
XA
18
Complete the ratio table to convert the units of measure from ounces to grams or grams to ounces.
Ounces Grams
111 282828
333
140140140
The ratio illustrates that the values will be 3146.7945 gram, 9440.3835 gram, and 3968.93 grams.
How to illustrate the information?It should be noted that 1 ounce is equivalent to 28.3495 gram.
Therefore, 111 ounces will be:
= 111 × 28.3495 gram
= 3146.7945 gram
333 ounces will be:
= 333 × 28.3495 gram
= 9440.3835 gram
140 ounces will be:
= 140 × 28.3495 gram
= 3968.93 grams
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The lifeguards at the beach post information of surfers by placing 3 flags, one above the other, on a flag pole. If there are 8 different flags available, how many possible signals can be flown?
Answer:
336
Step-by-step explanation:
They can place 1 of 8 frags on the bottom.
Now they have 7 flags left.
They can place 1 of 7 flags in the middle.
Now they have 6 flags left.
The can place 1 of 6 flags on top.
8 × 7 × 6 = 336
Find the first four partial sums, s1,s2,s3,s4, and the nth partial sum of the squence an=log(nn+1).
The first four partial sums of the sequence are S₁ = 0.3010, S₂ = 0.9999, S₃ = 2.447, S₄ = 4.8569.
In this question,
A sequence is a set of things (usually numbers) that are in order. A partial sum is the sum of part of the sequence.
The sequence is [tex]a_{n} =log(n^{n}+1 )[/tex]
The first four partial sum S₁, S₂, S₃, S₄ can be calculated by substituting n = 1,2,3,4 in the sequence.
S₁ can be calculated as
S₁ = a₁
⇒ [tex]a_{1} =log(1^{1}+1 )[/tex]
⇒ [tex]a_{1} =log(1+1 )[/tex]
⇒ [tex]a_{1} =log(2 )[/tex]
⇒ [tex]a_{1} =0.3010[/tex]
Now, S₁ = 0.3010
S₂ can be calculated as
S₂ = a₁ + a₂
⇒ [tex]a_{2} =log(2^{2}+1 )[/tex]
⇒ [tex]a_{2} =log(4+1 )[/tex]
⇒ [tex]a_{2} =log(5 )[/tex]
⇒ [tex]a_{2} =0.6989[/tex]
Now, S₂ = 0.3010 + 0.6989
⇒ S₂ = 0.9999
S₃ can be calculated as
S₃ = a₁ + a₂ + a₃
⇒ [tex]a_{3} =log(3^{3}+1 )[/tex]
⇒ [tex]a_{3} =log(27+1 )[/tex]
⇒ [tex]a_{3} =log(28)[/tex]
⇒ [tex]a_{3} =1.4471[/tex]
Now, S₃ = 0.3010 + 0.6989 + 1.4471
⇒ S₃ = 2.447
S₄ can be calculated as
S₄ = a₁ + a₂ + a₃ + a₄
⇒ [tex]a_{4} =log(4^{4}+1 )[/tex]
⇒ [tex]a_{4} =log(256+1 )[/tex]
⇒ [tex]a_{4} =log(257 )[/tex]
⇒ [tex]a_{4} =2.4099[/tex]
Now, S₄ = 0.3010 + 0.6989 + 1.4471 + 2.4099
⇒ S₄ = 4.8569
Hence we can conclude that the first four partial sums of the sequence are S₁ = 0.3010, S₂ = 0.9999, S₃ = 2.447, S₄ = 4.8569.
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If amy cuddy and her research team originally established a sample size of n=200 (100 in each group) and then discovered that 86% of the high-power group (86 of 100) took a gambling risk while 60% of the low-power group (60 of 100) took the risk, then the p-value would have been much lower than that originally found in question 1. this p-value would have been less sensitive and would have provided stronger evidence for the researcher's hypothesis. state the p-value, rounding to 5 decimal places.
The p-value that would be given as the evidence would be given as p-value = 0.00002 and also P value = 0.00003
How to solve for the p valueThe sample size of the first sample = 100
x1 = success 0f 86%
We have to find the proportion of this = 0.86
The sample size of the second sample n2 = 100
x12 = success 0f 60%
We have to find the proportion of this = 60/100
= 0.6
The difference = 0.86-0.6= 0.26
Next we have to find the pooled proportion. This is taken given as p = (x1+x2)/(n1+n2) this gives us 0.73
Next we have to find the standard error
= √(p*(1-p)*(1/n1+ 1/n2)= 0.06279
Z stat = (0.26-0)/0.0628= 4.1411
From here the p value would have to be
p-value = 0.00002 and also
P value = 0.00003
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The following data are the temperatures of effluent at discharge from a sewage treatment facility on consecutive days: Sample No.1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Temperature 40 45 49 47 52 45 51 46 44 48 51 50 56 44 48 50 49 50 46 46 49 49 51 50 Use the data above to calculate the descriptive statistics.
The descriptive statistics for the above data is given as follows:
X = 12.5
What is Descriptive Statistics?
A set of concise descriptive coefficients that describe a particular data set indicative of a whole or sample population is known as descriptive statistics.
For X (mean) = [tex]{\displaystyle X={\frac {1}{n}}\sum _{i=1}^{n}X_{i}[/tex]
= 300/24
= 12.5
For sample variance = [tex]s^2 = \frac{1}{n-1}\biggl[\, \sum_{i=1}^n X_i^2 - \frac{\Bigl(\,\sum\limits_{i=1}^n X_i\Bigr)^{\!2}}{n} \biggr][/tex]
= (1/(24-1) (4,900 - (300²/24)
= 50
Standard deviation s = √s²
= √50
= 7.0711
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Jamie is 6 years older than tyrion now. in 2 years, jamie will be one year less than twice tyrion's current age. what is jamie's current age?
Answer:
Jamie is currently 15.
Step-by-step explanation:
A portion of the Quadratic Formula proof is shown. Fill in the missing statement.
x²+x+
X+
a
X+
2a
b
2a
Statements
2a
2a
= ±₁
==
4ac b²
+
4a² 4a²
b²-4ac
4a²
b²-4ac
4a²
b²-4ac
4a²
?
Reasons
Find a common denominator on the right side of the equation
Add the fractions together on the right side of the equation
Rewrite the perfect square trinomial on the left side of the equation as a binomial squared
Take the square root of both sides of the equation
Simplify the right side of the equation
[tex]x+\frac{b}{2a}=\pm \frac{\sqrt{b^2 -4ac}}{2a}[/tex]
Which term is not possible in the domain of a sequence?
The term that is not possible in the domain of a sequence is:
-5
What is the domain of a function?The domain of a function is the set that contains all possible input values for the function. For a sequence, the domain is the set that contains all the indexed of the terms, starting at 0 and going until the nth term.
For example, suppose we have the following sequence: 3, 5, 7, ...
The term with index 0 is 3.The term with index 1 is 5.The term with index 2 is 7.From what was explained above, which also can be visualized with the example, an index term of a sequence cannot be negative, hence the term that is not possible in the domain of a sequence is:
-5.
Which is the only negative number of the options.
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I dont know this, please can someone help
The table of values for y=1/2x-1 is completed as follows:
x y
-2 -2
-1 -3/2
0 -1
1 -1/2
2 0
3 1/2
Exactly one value from the set of second components of the ordered pair is connected with each value from the set of first components of the ordered pairs in a relation known as a function.
Given function: y=1/2x-1
For x = -2
Value of y = -2
For x = -1
Value of y = 1/2(-1)-1 = -3/2
For x = 0
Value of y = 1/2(0)-1 =-1
For x = 1
Value of y = 1/2(1)-1 = -1/2
For x = 2
Value of y = 0
For x = 3
Value of y = 1/2(3)-1 = 1/2
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What is the measure of 28?
O 90⁰
O 60°
O 180°
O 120°
Answer: 120
Step-by-step explanation:
Answer:
B. 60°
Step-by-step explanation:
Angle 4 and angle 8 are equal. Find the measure of angle 4 to know the measure of angle 8.
∠4=∠8
180-120=60
∠4=60°
Since angle 4 equals 60 degrees, angle 8 also equals 60 degrees.
Hope this helps!
Complete the equation.
2 x 4 =
x 2
2x4=8
8x2=16
the answer is 16
_______ 2. Find the length of PQ
A. 4.5π units
B. 9π units
C. 54π units
D. 12π units
Answer:
D
Step-by-step explanation:
Pq=opp/hyp
(135+12)=180
Can anyone help me solve these linear systems using substitution?
1. 3x-y=4
x+2y=6
2. 2x-y= -39
x+y= -21
3. 2x+y =11
6x-5y =9
The system of the linear systems of equation using substitution is;
x = 2, y = 2 x = -20, y = -1Linear equation3x-y=4
x+2y=6
from (2)
x = 6 - 2y
substitute into (1)
3x-y=4
3(6 - 2y) - y = 4
18 - 6y - y = 4
- 6y - y = 4 - 18
-7y = -14
y = 2
Substitute into
x+2y=6
x + 2(2) = 6
x + 4 = 6
x = 6 - 4
x = 2
2. 2x-y= -39
x+y= -21
From (2)
x = -21 - y
substitute into
2x-y= -39
2(-21 - y) - y = -39
-42 - 2y - y = -39
- 2y - y = -39 + 42
- 3y = 3
y = 3/-3
y = -1
substitute into
x+y= -21
x + (-1) = -21
x - 1 = -21
x = -21 + 1
x = -20
3. 2x+y =11
6x-5y =9
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Consider this function. f ( x ) = 1 /2 x + 1 /4 Which graph represents the inverse of function f? Which graph represents the inverse of function f?
The inverse function of f(x) = 1/2x + 1/4 is f-1(x) = 2x - 1/2
How to determine the graph of the inverse function?The function is given as:
f(x) = 1/2x + 1/4
Rewrite the function as
y = 1/2x + 1/4
Swap the positions of x and y
x = 1/2y + 1/4
Multiply through by 4
4x = 2y + 1
Subtract 1 from both sides
2y = 4x - 1
Divide by 2
y = 2x - 1/2
Rewrite as an inverse function
f-1(x) = 2x - 1/2
Hence, the inverse function of f(x) = 1/2x + 1/4 is f-1(x) = 2x - 1/2
See attachment for the graph of the inverse function
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Answer:
Step-by-step explanation:
e graph opens upward, and it has a vertex of (0,0)
What is vertex?
The vertex of an equation is the minimum or the maximum point on the graph of the equation
The equation of the graph is given as:
The above equation represents an absolute value function
An absolute value function is represented as:
So, by comparison, we have:
This means that the graph opens upward, and it has a vertex of (0,0)
See attachment for the graph of
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Find the volume v of the solid obtained by rotating the region bounded by the given curves about the specified line. y = x + 1, y = 0, x = 0, x = 2; about the x-axis
The volume of a solid is [tex]\frac{26}{3} \pi[/tex].
Given
The given curves about the specified line. y = x + 1, y = 0, x = 0, x = 2; about the x-axis
Curve is y = x + 1
Line is y = 0
We have to find out the volume v of the solid obtained by rotating the region bounded by these curves.
If the region bounded above by the graph of f, below by the x-axis, and on the sides by x=a and x=b is revolved about the x-axis, the volume V of the generated solid is given by [tex]V = \pi \int\limits^b_a {(f(x))^{2} } \, dx[/tex]. We can also obtain solids by revolving curves about the y-axis.
Volume of a solid:
According to washer method:
[tex]V = \pi \int\limits^b_a {(f(x))^{2} } \, dx[/tex]
Using washer method, where a=0 and b=2, we get
V = [tex]\pi \int\limits^2_0 {(x+1)^{2} } \, dx[/tex]
= [tex]\pi[ \frac{(x+1)^{3} }{3} ]0 \ to \ 2[/tex]
= [tex]\pi [\frac{(3+1)^{3} }{3} -\frac{(0+1)^{3} }{3}][/tex]
= [tex]\pi [\frac{27}{3} -\frac{1}{3} ][/tex]
= [tex]\pi [\frac{26}{3}][/tex]
= [tex]\frac{26}{3} \pi[/tex]
Therefore the volume of a solid is [tex]\frac{26}{3} \pi[/tex].
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Jason left a bin outside in his garden to collect rainwater. he notices that 1 over 5 gallon of water fills 2 over 3 of the bin. write and solve an expression to find the amount of water that will fill the entire bin
The amount of water that will serve the entire container exists 3/10 gallons.
What is an expression?An expression exists a sentence with a minimum of two numbers or
variables and at least one math function.
Given: 1 over 5 gallons of water serve 2 over 3 of the container.
(1/5) gallon / (2/3) container = x gallons / 1 container
cross-multiplying the above equation, we get
1/5 = (2/3)x
multiply both sides by the reciprocal of 2/3 = 3/2
(3/2) (1/5) = x = 3/10 gallons serve the total container
Each 1/10 of a gallon serve 1/3 of the container
So 3(1/10) gallons serve 3(1/3)bins
3/10 gallons serve a whole container.
The amount of water that will serve the entire bin container exists 3/10 gallons.
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The
is the z-score right at the edge of the rejection region.
A. Critical value
B.crucial value
C. Critical region
D.vital statistics
The critical value is the z-score right at the edge of the rejection region option (A) is correct.
What is a normal distribution?It's the probability curve of a continuous distribution that's most likely symmetric around the mean. On the Z curve, at Z=0, the chance is 50-50. A bell-shaped curve is another name for it.
It is given that:
The z-score is right at the edge of the rejection region.
As we know, the rejection zone is the area in which we have sufficient data to reject the null hypothesis if our test statistic falls within it.
Thus, the critical value is the z-score right at the edge of the rejection region option (A) is correct.
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Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Answer:
[tex]\textsf{A. } y=3x^2+10x-8[/tex]
Step-by-step explanation:
We are given the information that a function has zeros at x = ⅔ and x = -4. In order to find the function that has those zeros, we can substitute the value of the zeros into each function. If the value of a function equates to zero with both values, then that is the function we are looking for.
..................................................................................................................................................
Standard Form of a Quadratic: ax² + bx + c = 0.
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[tex]\large \text{$y = 3x^2+10x-8 \implies 0=3x^2+10x-8$}[/tex]
[tex]\boxed{\begin{minipage}{15 em}{\text{$x=\dfrac{2}{3}$}} \\ \\\implies 0=3\left(\dfrac{2}{3}\right)^2+10\left(\dfrac{2}{3}\right)-8\\\\\implies 0=3\left(\dfrac{4}{9}\right)+10\left(\dfrac{2}{3}\right)-8\\\\\implies 0=\not{3}\left(\dfrac{4}{\not{9}\ 3}\right)+\dfrac{20}{3}-8\\\\\implies 0=\dfrac{4}{3}+\dfrac{20}{3}-8\\\\\implies 0=\dfrac{24}{3}-8\\\\\implies 0=0\ \checkmark\end{minipage}}[/tex] [tex]\boxed{\begin{minipage}{15 em}{\text{$x=-4$}} \\ \\\implies 0=3(-4)^2+10(-4)-8\\\\\implies 0=3(16)-40-8\\\\\implies 0=48-48\\\\\implies 0=0\ \checkmark\end{minipage}}[/tex]
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[tex]\large \text{$y = 2x^2-5x-12 \implies 0=2x^2-5x-12$}[/tex]
[tex]\boxed{\begin{minipage}{15 em}{\text{$x=\dfrac{2}{3}$}} \\ \\\implies 0=2\left(\dfrac{2}{3}\right)^2-5\left(\dfrac{2}{3}\right)-12\\\\\implies 0=2\left(\dfrac{4}{9}\right)-\dfrac{10}{3}-12\\\\\implies 0=\dfrac{8}{9}-\dfrac{10}{3}-12\\\\\implies 0=\dfrac{8}{9}-\dfrac{10\times3}{3\times3}-\dfrac{12\times9}{9}\\\\\implies 0=\dfrac{8}{9}-\dfrac{30}{9}-\dfrac{108}{9}\\\\\implies0=-\dfrac{22}{9}-\dfrac{108}{9}\\\\\implies 0=-\dfrac{130}{9}\ \textsf{X}\end {minipage}}[/tex] [tex]\boxed{\begin{minipage}{15 em}{\text{$x=-4$}} \\ \\\implies 0=2(-4)^2-5(-4)-12\\\\\implies 0=2(16)+20-12\\\\\implies 0=32+20-12\\\\\implies 0=40\ \textsf{X}\end{minipage}}[/tex]
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[tex]\large \text{$y = 2x^2+5x-12 \implies 0=2x^2+5x-12$}[/tex]
[tex]\boxed{\begin{minipage}{15 em}{\text{$x=\dfrac{2}{3}$}} \\ \\\implies 0=2\left(\dfrac{2}{3}\right)^2+5\left(\dfrac{2}{3}\right)-12\\\\\implies 0=\dfrac{8}{9}\right)+\dfrac{10}{3}-12\\\\\implies 0=\dfrac{8}{9}\right)+\dfrac{10\times3}{3\times3}-\dfrac{12\times9}{9}\\\\\implies 0=\dfrac{8}{9}+\dfrac{30}{9}-\dfrac{108}{9}\\\\\implies0=\dfrac{38}{9}-\dfrac{108}{9}\\\\\implies 0=-\dfrac{70}{9}\ \textsf{X}\end{minipage}}[/tex] [tex]\boxed{\begin{minipage}{15 em}{\text{$x=-4$}} \\ \\\implies 0=2(-4)^2+5(-4)-12\\\\\implies 0=2(16)-20-12\\\\\implies 0=32-32\\\\\implies 0=0\ \checkmark\end{minipage}}[/tex]
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[tex]\large \text{$y = 3x^2-10x-8 \implies 0=3x^2-10x-8$}[/tex]
[tex]\boxed{\begin{minipage}{15 em}{\text{$x=\dfrac{2}{3}$}} \\ \\\implies 0=3\left(\dfrac{2}{3}\right)^2-10\left(\dfrac{2}{3}\right)-8\\\\\implies 0=3\left(\dfrac{4}{9}\right)-\dfrac{20}{3}-8\\\\\implies 0=\not{3}\left(\dfrac{4}{\not{9}\ 3}\right)-\dfrac{20}{3}-8\\\\\implies 0=\dfrac{4}{3}-\dfrac{20}{3}-\dfrac{8\times3}{3}\\\\\implies 0=-\dfrac{16}{3}-\dfrac{24}{3}\\\\\implies 0=-\dfrac{40}{3}\ \textsf{X}\end{minipage}}[/tex] [tex]\boxed{\begin{minipage}{15 em}{\text{$x=-4$}} \\ \\\implies 0=3(-4)^2-10(-4)-8\\\\\implies 0=3(16)+40-8\\\\\implies 0=48+40-8\\\\\implies 0=80\ \textsf{X}\end{minipage}}[/tex]
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Therefore, the function whose zeros are ⅔ and -4 is [tex]y=3x^2+10x-8[/tex].
Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
[tex]y = mx + n[/tex]
[tex]m = \frac{y - y}{x - x} = \frac{5 - ( - 1)}{ - 5 - ( - 3)} = \frac{6}{ - 2} = - 3[/tex]
[tex]y = - 3x + n \\ [/tex]
Since both ( -3 , -1 ) and ( -5 , 5 ) pass through the line, they both satisfy its equation. Substitute any point in the new equation, I will choose ( -5 , 5 )[tex]5 = - 3( - 5) + n \\ n = 5 - 15 = - 10[/tex]
[tex]y = - 3x - 10[/tex]
HALP
What is the range of possible sizes for side xxx?
Answer:
See below
Step-by-step explanation:
Using triangle side rule : The sum of any two sides must be greater than the third side
.5<x<16.5
The range of possible sizes for side x for given triangle is 0.5<x<16.5.
In the given triangle, one side measures 8.5 units, other side is 8.0 units and third side is x units.
The length of one side of a triangle must be greater than the difference and less than the sum of the lengths of the other two sides.
Here, the range of x is 8.5-8.0<x<8.5+8.0
0.5<x<16.5
Therefore, the range of possible sizes for side x for given triangle is 0.5<x<16.5.
To learn more about the triangle inequality theorem visit:
https://brainly.com/question/1163433.
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The difference of two numbers is 3/4. The sum of the two numbers is 9 1/4. Find the number