The value for c is 36 which completes the square for the quadratic x² + 12x + c.
What is a quadratic equation?The polynomial having a degree of 2 is termed as the quadratic equation.It means that the equation will have the maximum power of 2.
Here we have the equation
=x²+12x+c
=x^2+12x+36
=x^2+6x+6x+36
=x(x+6)+6(x+6)
=(x+6)(x+6
=(x+6)²
hence value for c is 36 which completes the square for the quadratic x² + 12x + c.
To know more about quadratic equation follow
https://brainly.com/question/1214333
#SPJ1
Connor is 6 feet tall and casts a shadow that is 2.5 feet long. He stands next to a tree that is 25 feet tall. How long is the shadow the tree casts? Round your numerical answer to the nearest whole number.
Answer:
10
Step-by-step explanation:
[tex]\frac{6}{2.5} =\frac{25}{x} \\6x=2.5*25\\6x=62.5\\x=10.417=10[/tex]
The Tree casts a height of 10.41 feet tall.
What is Proportion?In general, the term "proportion" refers to a part, share, or amount that is compared to a total.
According to the concept of proportion, two ratios are in proportion when they are equal.
According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.
Given:
Connor is 6 feet tall and casts a shadow that is 2.5 feet long.
He stands next to a tree that is 25 feet tall.
let the shadow of tree is x feet long.
Using proportion
6/ 2.5 = 25/x
6x = 62.5
x= 10.41 feet
Learn more about Proportion here:
https://brainly.com/question/26974513
#SPJ2
The length of time it takes a worker to assemble a large product is assumed to be normally distributed. a random sample of 25 workers a were selected, and their times to assemble the product were recorded. the mean and variance for this sample were 3 and 0.5 hours, respectively.
the 90 percent confidence interval for the mean length of time (in hours) it takes a worker to assemble the product _____ hours to ______ hours
Using the t-distribution, it is found that the 90% confidence interval is of 2.71 hours to 3.29 hours.
What is a t-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 25 - 1 = 24 df, is t = 2.0639.
The other parameters are given as follows:
[tex]\overline{x} = 3, s = \sqrt{0.5} = 0.707, n = 25[/tex]
Hence the bounds of the interval are given as follows:
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 3 - 2.0639\frac{0.707}{\sqrt{25}} = 2.71[/tex]
[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 3 + 2.0639\frac{0.707}{\sqrt{25}} = 3.29[/tex]
More can be learned about the t-distribution at https://brainly.com/question/16162795
#SPJ1
PLS ANSWER FOR MEEEE FAST TYYYYSMM
The following sphere has. A diameter of 18 cm.
Answer:
I think your answer is A, correct me if I'm wrong
Julianna has thirty two pieces of candy in a candy jar. Julianna only has two kinds of candy.
jolly rangers and twix. For every four twix bars, she has two pieces of jolly rangers. How many
pieces of each candy are in the candy jar?
The number of jolly rangers candy she has is 22. The number of twix bars she has is 11.
What are the linear equations that represent this question?
j + t = 33 equation 1
4t = 2j
j = 2t equation 2
Where:
j = number of jolly rangers
t = j = number of twix
How many twix candies does Julianna have?
Substitute for j in equation 1 using equation 2
2t + t = 33
3t = 33
t = 11
How many jolly candies does Julianna have?Subsitute for t in equation 2
j = 11 x 2 = 33
To learn more about simultaneous equations, please check: https://brainly.com/question/25875552
#SPJ1
Simplify the following expression. (3m-4)²+8(3m-2)
A. 8m/4
B. 9m/4
C. 3m+24/4
D. 3m+28/4
Step-by-step explanation:
(3m-4)² + 8(3m-2) = (3m-4)(3m-4) + 24m - 16 =
= 9m² - 3m×4 - 4×3m + 16 + 24m - 16 =
= 9m² - 24m + 16 + 24m - 16 = 9m²
so, there is seemingly something missing in your original expression.
going from 9m², the most likely solution would be 9m/4 and therefore B.
but we cannot be sure, because again, I don't know what you left out in the beginning.
We have a part-whole ratio of 2 : 10. How can we represent this ratio as a percent?
Answer:
20%
Step-by-step explanation:
2:10 = 2/10 = 20/100 = 20%
Find the mean of the data.
9, 56, 24, 59, 2
Answer:
24 because it is the middle number
Step-by-step explanation:
When Lillian goes bowling, her scores are normally distributed with a mean of 130
and a standard deviation of 11. Using the empirical rule, what percentage of the
games that Lillian bowls does she score between 119 and 141?
Using the Empirical Rule, it is found that she scores between 119 and 141 on 68% of the games that she bowls.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.In this problem, considering that the mean is of 130 and the standard deviation is of 11, the interval between 119 and 141 is within one standard deviation of the mean, hence she scores between 119 and 141 on 68% of the games that she bowls.
More can be learned about the Empirical Rule at https://brainly.com/question/24537145
#SPJ1
8. Higher Order Thinking There are points on a grid at (0, 0) and (3, 0).
a. What is a possible coordinate of the third vertex if the triangle has
a perimeter of 11 units? Explain.
b. Is there another point that could be the third vertex? Explain.
par poib
signe
Higher Order Thinking There are points on a grid at (0, 0) and (3, 0).
a. What is a possible coordinate of the third vertex if the triangle has
a perimeter of 11 units? Explain.
b. Is there another point that could be the third vertex? Explain.
par poib
signe
What are the period, phase shift, and vertical shift of y = csc[3(x 4)] 6?
The period of the given function is 2π/3, the phase shift is 4, and the vertical shift is 6 units.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a trigonometric function:
y = csc[3(x+ 4)]+ 6
Every each revolution of 2π the function repeats the same value for every x.
The period of the original function is 2π
For the given function plug 2π
y = csc[3(x+ 4)+2π]+ 6
y = csc[3(x+ 2π/3+4)]+ 6
The period of the function will be 2π/3
From the function, the phase shift = 4
And vertical shift = 6
Thus, the period of the given function is 2π/3, the phase shift is 4, and the vertical shift is 6 units.
Learn more about the function here:
brainly.com/question/5245372
#SPJ1
Option 3
Step-by-step explanation:
Given that ‘z’ is in set of complex number and ‘a’ is any real numbers. Solve the trigonometric equation sin(z) = a for all general solutions.
Recall that for all [tex]z\in\Bbb C[/tex],
[tex]\sin(z) = \dfrac{e^{iz} - e^{-iz}}{2i}[/tex]
so that
[tex]\sin(z) = a \iff e^{iz} - e^{-iz} = 2ia[/tex]
Multiply both sides by [tex]e^{iz}[/tex] to get a quadratic equation,
[tex]e^{2iz} - 2iae^{iz} - 1 = 0[/tex]
Solve for [tex]e^{iz}[/tex]. By completing the square,
[tex]e^{2iz} - 2ia e^{iz} + i^2a^2 = 1 + i^2a^2[/tex]
[tex]\left(e^{iz} - ia\right)^2 = 1 - a^2[/tex]
[tex]e^{iz} - ia = \pm \sqrt{1-a^2}[/tex]
[tex]e^{iz} = ia \pm \sqrt{1-a^2}[/tex]
[tex]iz = \log\left(ia \pm \sqrt{1-a^2}\right)[/tex]
[tex]iz = \ln\left|ia \pm \sqrt{1-a^2}\right| + i \left(\arg\left(ia \pm \sqrt{1-a^2}\right) + 2\pi n\right)[/tex]
[tex]\boxed{z = -i \ln\left|ia \pm \sqrt{1-a^2}\right| + \arg\left(ia \pm \sqrt{1-a^2}\right) + 2\pi n}[/tex]
where n is any integer.
We are given with:
[tex]{\quad \qquad \longrightarrow \sin (z)={\sf a}\:,\:z\in \mathbb{C}}[/tex]
Recall the identity what we have for the sine function of complex numbers
[tex]{\boxed{\bf{\sin (z)=\dfrac{e^{\iota z}-e^{-\iota z}}{2\iota}}}}[/tex]Put the values to thus obtain:
[tex]{:\implies \quad \sf \dfrac{e^{\iota z}-e^{-\iota z}}{2\iota}=a}[/tex]
[tex]{:\implies \quad \sf e^{\iota z}-e^{-\iota z}=2a\iota}[/tex]
Multiply both sides by [tex]{\sf e^{\iota z}}[/tex]
[tex]{:\implies \quad \sf e^{\iota z}\cdot e^{\iota z}-e^{-\iota z}\cdot e^{\iota z}=2a\iota e^{\iota z}}[/tex]
[tex]{:\implies \quad \sf (e^{\iota z})^{2}-2a\iota e^{\iota z}-1=0}[/tex]
Put x = [tex]{\sf e^{\iota z}}[/tex]:
[tex]{:\implies \quad \sf x^{2}-2a\iota x-1=0}[/tex]
Find the discriminant, here D will be, D = (-2ai)² - 4 × 1 × (-1) = 4 - 4a² = 4(1-a²)
Now, By quadratic formula:
[tex]{:\implies \quad \sf x=\dfrac{-(-2a\iota)\pm \sqrt{4(1-a^{2})}}{2}}[/tex]
[tex]{:\implies \quad \sf x=\dfrac{a\iota \pm \sqrt{1-a^{2}}}{2}}[/tex]
[tex]{:\implies \quad \sf e^{\iota z}=\dfrac{a\iota \pm \sqrt{1-a^{2}}}{2}}[/tex]
[tex]{:\implies \quad \sf \iota z=log\bigg(\dfrac{a\iota \pm \sqrt{1-a^{2}}}{2}\bigg)}[/tex]
Using the formula for logarithms, we have:
[tex]{:\implies \quad \sf \iota z=log(a\iota \pm \sqrt{1-a^{2}})-log(2)}[/tex]
[tex]{:\implies \quad \sf z=\dfrac{1}{\iota}log(a\iota \pm \sqrt{1-a^{2}})-\dfrac{1}{\iota}log(2)}[/tex]
The sine function is periodic on 2πn and zero on (π/2), and the logarithmic expression becomes undefined for all ia±√(1-a²) < 0, so we will take modulus of it
[tex]{:\implies \quad \boxed{\bf{z=\dfrac{1}{\iota}log\bigg|a\iota \pm \sqrt{1-a^{2}}\bigg|-\dfrac{1}{\iota}log(2)+\dfrac{\pi}{2}+2\pi n\:\:\forall \:n\in \mathbb{Z}}}}[/tex]
I need help PLEASE HELPP
Answer:
1 and 5 are corresponding angle
8 and 4 are corresponding angle
4 and 6 are alternate interior angle
2 and 8 are alternate exterior angle
7 and 3 are corresponding angle
2 and 6 are corresponding angle
3 and 5 are alternate interior angle
1 and 7 are alternate exterior angle
Use the order of operations to evaluate the numerical expression.
Answer:
I'm sorry but I need some numbers to solve. we just learned this in class so I'm new though
Step-by-step explanation:
Needs numbers
Work out the surface area of this cylinder
Answer:
in terms of pi: 24pi cm squared
substituting pi for 3.14: 75.36 cm squared
Step-by-step explanation:
8pi + 16pi = 24pi
There were 16 teams that competed in men's ice hockey at the Salt Lake City Olympics of 2002.
Find the number of permutations for the gold, silver, and bronze metals at the awards ceremony.
Answer:
3360.
Step-by-step explanation:
That would be the number of permutations of 3 from 16.
= 16P3
= 16!/(16-3)!
= 16*15*14
= 3360
Answer:
3 360 permutations
Step-by-step explanation:
the number of permutations :
16P3 = 16 × 15 × 14 = 3 360
(3x + 1) + 8 (2x - 3) = 4 (3x -1) -7 (x -4) ayúdenme
Step-by-step explanation:
[tex](3x + 1) + 8(2x - 3) = 4(3x - 1) - 7(x - 4) \\ 3x + 1 + 16x - 24 = 12x - 4 - 7x + 28 \\ 19x - 23 = 5x + 24 \\ 19x - 5x = 24 + 23 \\ 14x = 47 \\ x = \frac{47}{14} [/tex]
Below is the work a student completed with an error. Identify the step where the error first occured an
Step 1: (7 - 10) – 2(6y - 5) + 17
Step 2: (3) - 12y – 5 + 17
Step 3:3 - 12y + 12
Step 4: - 12y + 15
А
Step 2
B
Step 3
C
Step 4
D
Answer should be 12y - 9
E
Answer should be 12y + 9
C2022 Illuminate Education, Inc.
TM
Answer:
Step 2
Step-by-step explanation:
Solving
(7 - 10) - 2(6y - 5) + 17 [Step 1]3 - 12y + 10 + 18 [Step 2]3 - 12y + 28 [Step 3]-12y + 31 [Step 4]The error has occurred in Step 2.
The distribution of -2 to 6y and -5 gives -12y and 10 respectively.
Instead, the distribution has not happened between -2 and -5.
You decide to go to dinner with three friends. Before the check comes, the group decides to split the check evenly. The total
check is $134.50. As a group you decide to tip the waiter 20% on top of the total check amount. How much money should
you and each friend pay, including tip? Round your answer to the nearest cent.
Answer:
You each will pay $40.35
Step-by-step explanation:
First you take the total $134.50 and divide it by 4 which is you and your three friends.
This will give you 33.625 which is the amount each of you will pay without tip.
To find the tip you take 20% from $134.50 which will give you 26.9 and when you divide that by the four of you it will give you 6.725.
Then you take your amount 33.625 plus your tip 6.725 which will give you $40.35.
The total you all will pay will be $161.40 this is the total $134.50 plus the tip $26.90.
Hope this helped.
What is the solution of rootindex 3 startroot x 8 endroot = negative 4?
The solution to the equation [tex]\sqrt[3]{x + 8} = -4[/tex] is x = 72
How to determine the solution?The equation is given as:
[tex]\sqrt[3]{x + 8} = -4[/tex]
Take the cube of both sides
x + 8 = -64
Subtract 8 from both sides
x = 72
Hence, the solution to the equation [tex]\sqrt[3]{x + 8} = -4[/tex] is x = 72
Read more about equation solutions at:
https://brainly.com/question/2972832
#SPJ4
Which is an equation of an asymptote of the hyperbola? y = 3x 10 y = –3x 8 y = x 2 y = x
The equation of the asymptote of the hyperbola is y = 3x + 10
How to determine the asymptote?From the complete question the asymptote passes through the points:
(x,y) = (-1, 7) and (-3,1)
The slope of the line is calculated using:
[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]
So, we have:
[tex]m = \frac{7 - 1}{-1 + 3}[/tex]
This gives
m = 3
The equation is then calculated using:
y = m(x -x1) + y1
This gives
y = 3(x + 1) + 7
Evaluate
y = 3x + 3 + 7
y = 3x + 10
Hence, the equation of the asymptote is y = 3x + 10
Read more about asymptotes at:
https://brainly.com/question/4138300
#SPJ4
0.596 as a fraction and 0.596 as a percentage.
596/1000 and 59.6%
Step-by-step explanation:
because when we make 596/1000 is 0.596
8. (06.04 MC)
Find the total surface area of a cylinder with a height of 8 cm and radius of 4 cm. Leave your answer in terms of r. (1 point)
O 80 cm²
96 cm²
128 cm²
192 cm²
The total surface area of the cylinder in terms of π is 96π cm². The correct option is the second option 96π cm²
Calculating Total surface area of a CylinderFrom the question, we are to determine the total surface area of the cylinder
The total surface area of a cylinder can be calculated by using the formula,
T.S.A = 2πr² + 2πrh = 2πr(r +h)
Where r is the radius
and h is the height
From the given information,
h = 8 cm
r = 4 cm
Putting the parameters into the formula, we get
T.S.A = 2π×4(4 +8)
T.S.A = 8π(12)
T.S.A = 96π cm²
Hence, the total surface area of the cylinder in terms of π is 96π cm². The correct option is the second option 96π cm²
Learn more on Calculating Total surface area of a Cylinder here: https://brainly.com/question/15389804
#SPJ1
A small class has 10 students, 6 of whom are girls and 4 of whom are boys. The teacher is going to choose two of the students at random. What is the probability that the teacher will choose two girls? Write your answer as a fraction in simplest form.
Answer:
2
5
Step-by-step explanation:
fraction of girls in the class is 6
5
so........the total number of girls is 6 and only 2 are chosen,meaning you have to subtract 2 from 6 which is 4 and then 4
10(total number of students) is
2
5 when simplified
7!
——————-
————-
please help!!
——————
math geniuses where r uuuu
————
help!
Answer:
It is the fourth option, D.
What is the area of a triangle whose vertices are J(-2, 1), K(0, 3), and L(4,4)?
Answer: 3
Step-by-step explanation:
Using the identity sin? O + cos? O = 1, find the value of tan O, to the nearest
hundredth, if sin 0 = 0.27 and 0 < 0 < 7
Answer:
3.7
Step-by-step explanation:
Given
sin²θ + cos²θ = 1sinθ = 0.27Solving for cosθ
cos²θ = 1 - sin²θcos²θ = 1 - (0.27)²cos²θ = 0.0729Finding tanθ
tanθ = sinθ / cosθtanθ = 0.27 / 0.0729tanθ = 3.7Verifying it lies in the range
θ = tan⁻¹ (3.7)θ = 74.88° Range is : 0 < θ < π/2 [or 0 < θ < 90°]It lies in the range [Verified]!!100!! POINTS PLEASE HELP
Answer:
[tex]\sf x = 6\dfrac{2}{3} \ \ or \ \ 6.67 \ (rounded \ to \ nearest \ hundreth)[/tex]
Build a proportional equation:
[tex]\rightarrow \sf \dfrac{AB}{AD} = \dfrac{BC}{DE}[/tex]
[tex]\rightarrow \sf \dfrac{10}{x+10} = \dfrac{6}{10}[/tex]
[tex]\rightarrow \sf 10(10) = 6(x+10)[/tex]
[tex]\rightarrow \sf 100 = 6x+60[/tex]
[tex]\rightarrow \sf 40= 6x[/tex]
[tex]\rightarrow \sf x = 40/6[/tex]
[tex]\rightarrow \sf x = \dfrac{20}{3}[/tex]
[tex]\rightarrow \sf x = 6\dfrac{2}{3}[/tex]
Answer:
Step-by-step explanation:
1. Create a porportianal equation. ab/ad=bc/de
2. plug in the variables for each line segment. 10/x+10=6/10
3. multiply each side by x + 10. (6x+60)/10=10
4. Multiply each side by 10. 6x+60=100
5. simplify. 6x=40 3x=20
6. divide each side by 3. x=20/3
(Sorry about my last answer)
What is the greatest common factor of
21xy^3 6x^4y^2
A. 42x^4 y^3
B. 42x^5 y^5
C. 3x^4 y^3
D. 3xy^2
what is the surface area
Find the volume of the cone.
Either enter an exact answer in terms of π or use 3.14 for π and round your final answer to the nearest hundredth.
Answer:
[tex]V=12\pi\:\text{units}^3[/tex]
Step-by-step explanation:
[tex]\displaystyle V=\frac{\pi r^2h}{3}\\ \\V=\frac{\pi (3)^2(4)}{3}\\\\V=\pi(3)(4)\\\\V=12\pi[/tex]