4. Solve the equation by factoring. 15 = 8x2 - 14x
X
3
5
or x =
4
2
0.
4
2
X=- orx
5
3
O
5
X=-3 or x =
8
3
x=-5 or x =
8
Answer:
1
5
=
8
2
−
1
4
15=8x^{2}-14x
15=8x2−14x
1
5
−
(
8
2
−
1
4
)
=
0
Step-by-step explanation:
=
−
3
4
=
5
2
The solution of equation is x =5/2 or x= -3/4.
What is Factorization?A number or other mathematical object is factored (or factorised, see variants in spelling in English) or factored when it is written as the product of numerous factors, typically smaller or simpler things of the same kind.
We have,
Equation: 15 = 8x² - 14x
Now, rearranging the equation as
8x² -14x -15 = 0
8x² - 20x + 6x -15=0
4x( 2x - 5) + 3 (2x-5)= 0
(2x-5)(4x +3)= 0
2x-5 =0 or 4x+ 3= 0
x =5/2 or x= -3/4
Learn more about Factorization here:
https://brainly.com/question/15615134
#SPJ7
9. Find the value of the trigonometric ratio tan C
Hi there!
[tex]\large\boxed{tanC = 40/9}[/tex]
tan = O / A, or the opposite side over the adjacent side.
From the diagram, we can see that the opposite side = 40 and the adjacent side = 9, so:
tan C = 40 / 9
Answer:
tan C = 40/9
Step-by-step explanation:
According to SOH - CAH - TOA, tan = opposite over adjacent.
In the picture, the opposite of tan C is 40 and the adjacent is 9.
So, tan C = 40/9
P.S. - Answer above is also correct.
Convert 2 1/3 into improper fraction: *
7/3
O 7/6
O 6/3
O 3/6
Answer:
7/3 is the answer
Step-by-step explanation:
Exercise science researchers collecting data within their state noticed that teens who spend more time streaming videos spend less time exercising.
What are the explanatory variable and response variable for this relationship?
Explanatory variable: time spent exercising
Response variable: state of teen’s residence
Explanatory variable: time spent streaming videos
Response variable: time spent exercising
Explanatory variable: time spent exercising
Response variable: time spent streaming videos
Explanatory variable: state of teen’s residence
Response variable: time spent streaming videos
I think it is (B):
Explanatory variable: time spent streaming videos
Response variable: time spent exercising
Answer:
It is (B) ED2021
Explanatory variable: time spent streaming videos
Response variable: time spent exercising
PLEASE HELP MIGHT GIVE BRAINLIEST!!!!! IM BEGGING YOU!!!!
Find the equation of the line with an x intercept of 4 and a y intercept of -1.5
Answer:
y = 4x -1.5
Step-by-step explanation:
The slope intercept form of a line is given by
y = mx+b where m is the slope and b is the y intercept
y = 4x -1.5
A sample of 1700 computer chips revealed that 35% of the chips do not fail in the first 1000 hours of their use. The company's promotional literature claimed that over 32% do not fail in the first 1000 hours of their use. Is there sufficient evidence at the 0.02 level to support the company's claim
Answer:
The p-value of the test is 0.004 < 0.02, which means that there is sufficient evidence at the 0.02 level to support the company's claim.
Step-by-step explanation:
The company's promotional literature claimed that over 32% do not fail in the first 1000 hours of their use.
At the null hypothesis, we test if the proportion is of at most 32%, that is:
[tex]H_0: p \leq 0.32[/tex]
At the alternative hypothesis, we test if the proportion is more than 32%, that is:
[tex]H_1: p > 0.32[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
0.32 is tested at the null hypothesis:
This means that [tex]\mu = 0.32 \sigma = \sqrt{0.32*0.68}[/tex]
A sample of 1700 computer chips revealed that 35% of the chips do not fail in the first 1000 hours of their use.
This means that [tex]n = 1700, X = 0.35[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.35 - 0.32}{\frac{\sqrt{0.32*0.68}}{\sqrt{1700}}}[/tex]
[tex]z = 2.65[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a sample proportion above 0.35, which is 1 subtracted by the p-value of z = 2.65.
Looking at the z-table, z = 2.65 has a p-value of 0.9960.
1 - 0.9960 = 0.004.
The p-value of the test is 0.004 < 0.02, which means that there is sufficient evidence at the 0.02 level to support the company's claim.
3) Consider the sequence -11 ; 2sin3x ; 15; ...
3.1.1) Determine the values of x in the interval [0 ; 90] for whichthe sequence will be arithmetic.
9514 1404 393
Answer:
x = 30
Step-by-step explanation:
In an arithmetic sequence, any given term is the average of the two terms that come before and after. The middle term of this sequence must be ...
2sin(3x) = (-11 +15)/2
sin(3x) = 1 . . . . . . . . . . simplify and divide by 2
Then the value of 3x must be 90°, so ...
x = 90/3 = 30
There is one value of x in the interval [0, 90] that makes this sequence arithmetic: x = 30.
What is the domain of the function
v=m***
O x2
O
O O xe3
o
X> 3
ASAP
Answer:
The function will be exist if and only if :
[tex] \frac{ - x + 3}{2} > 0 \\ = > - x + 3 > 0 \\ = > - x > - 3 \\ = > x < 3 \\ \\ \therefore \bf \: domain \: \: \green{x < 3}[/tex]
please help me with this on the image
Answer:
200 grams
Step-by-step explanation:
80 grams x grams
-------------- = -------------
6 people 15 people
Using cross products
80 *15 = 6x
1200 = 6x
Divide by 6
1200/6 = 6x/6
200 =x
Which is the following is equivalent to 16^3/4
Answer:
8
Step-by-step explanation:
8
Given the following coordinates complete the glide reflection transformation.
A(−1,−3)
B(−4,−1)
C(−6,−4)
Transformation: Reflection over the x-axis and a translation of shifting right 10 units.
Given:
The vertices of a triangle are A(−1,−3) , B(−4,−1) and C(−6,−4).
Transformation: Reflection over the x-axis and a translation of shifting right 10 units.
To find:
The image after glide reflection transformation.
Solution:
The vertices of a triangle are A(−1,−3) , B(−4,−1) and C(−6,−4).
If a figure is reflected over the x-axis, then
[tex](x,y)\to (x,-y)[/tex]
Using this, we get
[tex]A(-1,-3)\to A'(-1,3)[/tex]
[tex]B(-4,-1)\to B'(-4,1)[/tex]
[tex]C(-6,-4)\to C'(-6,4)[/tex]
If a figure is shifting 10 units right, then
[tex](x,y)\to (x+10,y)[/tex]
Using this we get
[tex]A'(-1,3)\to A''(-1+10,3)[/tex]
[tex]A'(-1,3)\to A''(9,3)[/tex]
Similarly,
[tex]B'(-4,1)\to B''(-4+10,1)[/tex]
[tex]B'-4,1)\to B''(6,1)[/tex]
And,
[tex]C'(-6,-4)\to C''(-6+10,4)[/tex]
[tex]C'(-6,-4)\to C''(4,4)[/tex]
Therefore, the vertices of the image are A''(9,3), B''(6,1) and C''(4,4).
tiếp tuyến của đồ thị hàm số x[tex]x^{3} -3x^{2} +2[/tex] tại điểm M(2,-2)
Answer:
what are you telling Id understand
Step-by-step explanation:
became
Five students sit at a circular table. Their chairs are number in order 1 through 5. Abby sits next to both Ben and Colin. Dalia sits next to both Ben and Sarah. The numbers on Abbys and Colins chairs add up to 6. Who is in chair number 3?
f(x)=4(2)^x
what would a graph of this look like?
9514 1404 393
Answer:
see attached
Step-by-step explanation:
A graphing calculator can do a nice job of showing you what the graph looks like.
The initial factor of 4 is the value when x=0, the y-intercept. The base of 2 tells you the function value is multiplied by 2 for each unit of x to the right, and divided by 2 for each unit of x to the left. (The curve quickly goes off the top of the graph.)
The horizontal asymptote is y=0, as it is for all exponential functions (that have not been translated).
A group of high school students were surveyed about their handedness and their favorite sport. The results are displayed below.
Which of the following statements is not true, according to the graph?
The left-handed group has a higher percentage of people who prefer baseball.
The right-handed group has a lower percentage of people who prefer basketball.
The percentage of people who prefer soccer has a lower percentage in the left-handed group.
The percentage of people who prefer football is approximately the same for the right- and left-handed groups.
Answer:
The percentage of people who prefer football is approximately the same for the right- and left-handed groups.
Step-by-step explanation:
The bar for the right-handed group representing soccer is between 10% and 20% (below 20%) while the bar for the left-handed group representing soccer is at 20%.
Percentage of left-handed group of people who prefer soccer is higher than the right-handed group who prefer soccer. Therefore, they don't have the same percentage.
Answer:
D
Step-by-step explanation:
;)
Which two statements are true
51.Tandin Dorji was married to five women. First woman had three
daughters and five sons and the youngest wife had two sons. Two
of the remaining wives had one son each. If the ratio of children of
5th wife was 1:3 with the children of other wives. How many
children does Tandin have
Answer:
Tandin has 16 children.
Step-by-step explanation:
Total of children:
3+5 = 8(first woman)
2(youngest wife)
1 + 1 = 2(two of the remaining wives)
So
8 + 2 + 2 = 12
If the ratio of children of 5th wife was 1:3 with the children of other wives.
Thus the 5th wife has 12/3 = 4 children.
How many children does Tandin have?
12 + 4 = 16
Tandin has 16 children.
Jerod hopes to earn $1200 in interest in 4.9 years time from $24,000 that he has available to invest. To decide if it's feasible to do this by investing In an account that compounds monthly, he needs to determine the annual interest rate such an account would have to offer for him to meet his goal. What would the annual rate of interest have to be? Round to two decimal places
Answer:
The annual interest rate would have to be of 0.1%.
Step-by-step explanation:
Compound interest:
The compound interest formula is given by:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.
Jerod hopes to earn $1200 in interest in 4.9 years time from $24,000 that he has available to invest.
This means that:
[tex]A(4.9) = 1200 + 24000 = 25200[/tex]
[tex]t = 4.9[/tex]
[tex]P = 24000[/tex]
Compounded monthly:
This means that [tex]n = 12[/tex]
What would the annual rate of interest have to be?
We have to solve for r, so:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]25200 = 24000(1 + \frac{r}{12})^{12*4.9}[/tex]
[tex](1 + \frac{r}{12})^{12*4.9} = \frac{25200}{24000}[/tex]
[tex](1 + \frac{r}{12})^{58.8} = 1.05[/tex]
[tex]\sqrt[58.8]{(1 + \frac{r}{12})^{58.8}} = \sqrt[58.8]{1.05}[/tex]
[tex]1 + \frac{r}{12} = (1.05)^{\frac{1}{58.8}}[/tex]
[tex]1 + \frac{r}{12} = 1.00083[/tex]
[tex]\frac{r}{12} = 0.00083[/tex]
[tex]r = 12*0.00083[/tex]
[tex]r = 0.001 [/tex]
The annual interest rate would have to be of 0.1%.
find the value of trigonometric ratio
Step-by-step explanation:
tan Z=p/b
=48/14
=24/7
Keep smiling and hope u are satisfied with my answer.Have a good day :)
WILL GIVE BRAINLISTAnother copy machine also has the ability to reduce image dimensions, but by a different percentage. This graph shows the results found when copying a design x times. Use the graph to write the equation modeling this relationship.
Answer:
f(x)=8 (0.5)^x
Step-by-step explanation:
Answer from plato
The Demand function for a product is given by:
D(q) = - 0.0003q^2 - 0.04q + 23.56
where q is the number of units sold and D(q) is the corresponding price per unit, in dollars. What is the average rate of change of Demand between 40 and 175 units sold?
Answer:
The average rate of change of Demand between 40 and 175 units sold is of -0.1045.
Step-by-step explanation:
Average rate of change:
The average rate of a function f(x) in an interval [a,b] is given by:
[tex]A = \frac{f(b) - f(a)}{b - a}[/tex]
In this question:
[tex]D(q) = -0.0003q^2 - 0.04q + 23.56[/tex]
What is the average rate of change of Demand between 40 and 175 units sold?
[tex]a = 40, b = 175[/tex]. So
[tex]D(40) = -0.0003*40^2 - 0.04*40 + 23.56 = 21.48[/tex]
[tex]D(175) = -0.0003*175^2 - 0.04*175 + 23.56 = 7.3725[/tex]
So
[tex]A = \frac{f(b) - f(a)}{b - a} = \frac{7.3725 - 21.48}{175 - 40} = -0.1045[/tex]
The average rate of change of Demand between 40 and 175 units sold is of -0.1045.
Use the discriminant to determine the number of solutions to the quadratic equation −40m2+10m−1=0
From the analysis of the discriminant, you obtain that the quadratic function has no real solutions.
In first place, you must know that the roots or solutions of a quadratic function are those values of x for which the expression is 0. This is the values of x such that y = 0. That is, f (x) = 0.
Being the quadratic function f (x)=a*x² + b*x + c, then the solution must be when: 0 =a*x² + b*x + c
The solutions of a quadratic equation can be calculated with the quadratic formula:
[tex]Solutions=\frac{-b+-\sqrt{b^{2} -4*a*c} }{2*a}[/tex]
The discriminant is the part of the quadratic formula under the square root, that is, b² - 4*a*c
The discriminant can be positive, zero or negative and this determines how many solutions (or roots) there are for the given quadratic equation.
If the discriminant:
is positive: the quadratic function has two different real solutions. equal to zero: the quadratic function has a real solution. is negative: none of the solutions are real numbers. That is, it has no real solutions.In this case, a= -40, b=10 and c= -1. Then, replacing in the discriminant expression:
discriminant= 10² -4*(-40)*(-1)
Solving:
discriminant= 100 - 160
discriminant= -60
The discriminant is negative, so the quadratic function has no real solutions.
Determine the equation for each of the following parabolas described with
a) zero values of -4 and 8 and a maximum value of 4
b) Vertex of (2,5) and through point A (7,2).
Answer:
honestly i dont know but i bet someone will
Question 1 and 2 plz explain
Answer:
1.D
2.B
Step-by-step explanation:
1. The x intercept is the value of x when y is zero. We know that the x intercept is 0.5 so we must find a value of k that will make our rational function equal zero when x=0.5
[tex]y = \frac{k}{x + 1} - 2[/tex]
Substitute x=0.5 and y=0.
[tex]0 = \frac{k}{0.5 + 1} - 2[/tex]
[tex]0= \frac{k}{1.5} - 2[/tex]
[tex]2 = \frac{k}{1.5} [/tex]
[tex]3 = k[/tex]
D is the Answer.
2. We need to consider the function
[tex] \frac{2x}{1 - {x}^{2} } [/tex]
Since the numerator is a linear term, it will have one zero to the equation using fundamental Theorem of Algebra so C is wrong.
This is a rational function because we are dividing two polynomials by each other and q(x) or the denominator isnt zero. So D is wrong.
The denominator is a quadratic term so it will have two vertical asymptote according to the fundamental Theorem of Algebra So A is Wrong.
B is Right, the equation isnt defined at x=0 because when we plug 0 into the denominator, it doesn't equate to zero.
Find the area of the shaded regions.
Answer: About 21.98 cm²
Step-by-step explanation:
First, find the area of the large shaded circle:
[tex]r^{2} \pi =3^{2} \pi =9\pi[/tex]
Find the area of the two small unshaded circles:
[tex]1) r^{2} \pi =1^{2} \pi =1\pi \\2) r^{2} \pi =1^{2} \pi=1\pi[/tex]
Subtract the area of the small circle from the large circle:
[tex]9\pi -1\pi -1\pi =9\pi -2\pi =7\pi[/tex]
Therefore, the area of the shaded region is:
[tex]7\pi =7*3.14=21.98[/tex]
2kg of chicken
61.5 g left
How many kg of chicken were eaten
Answer:
1.9385 kilograms were eaten
1.9385 kg
Step-by-step explanation:
because 2 kg=2000 g
Subtracting 2000
- 61.5
1938.5
Converting 1938.5 in kg is 1.9385 kg
complete the square to form a true equation;
x^2-3/4x+__ = (x-__)^2
172273-3-$=$==8399993939384888884-%"%/=%=%8%
Step-by-step explanation:
(x^2-3/4x+y^2)=(x-y)2
(x-3/4*1/2)2
(x-3/8)(x-3/8)
(x^2-3x/8-3x/8+9/64)
(x^2-6x/8+9/64)
(x-3/8)2
please help me with this
Answer:
2x-30 + x + 40 = 180
3x + 10 = 180
3x = 170
x = 56 [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
yesterday kofi earned 50cedis mowing lawns. today kofi earned 60% of what he earned yesterday mowing lawns.How much did kofi earned mowing lawns today?
Answer:
30 cedis
Step-by-step explanation:
todays earning = yesterdays earning * 60/100
50 * 60/100 =30
Help please. For the hign school basketball game, it costs $8 for every 4 tickets. Complete the table below showing the cost and the number of tickets.
Answer:
$2 for 1 ticket, 7 tickets for $14, $18 for 9 tickets, 10 tickets for $20
Step-by-step explanation:
Since we know that it $8 for 4 tickets, we can simplify the ratio down to 2:1, meaning that each ticket is $2.
You're welcome and good luck with your classes young one
