Please help, I think its D but I know that things are usually the opposite of what you think when doing these types of problems.
Answers
Answer:
A. The graph of g(x) is the graph of f(x) vertically stretched by a factor of 5.
Step-by-step explanation:
The only thing that has changed is that x^2 is multiplied by 5.
If the x^2 is multiplied by a constant that has an absolute value less than 1, the parabola will undergo a vertical compression.
If the x^2 is multiplied by a constant that has an absolute value more than 1, the parabola will undergo a vertical stretch.
Since the absolute value of 5 is more than 1, A. The graph of g(x) is the graph of f(x) vertically stretched by a factor of 5.
Hope this helps!
Related Questions
Simplify 5 + 2{x - 4[3x + 7(2 - x)]}
Answers
Answer:
34x - 107.
Step-by-step explanation:
5 + 2{x - 4[3x + 7(2 - x)]}
= 5 + 2[x - 4(3x + 14 - 7x)]
= 5 + 2[x - 4(-4x + 14)]
= 5 + 2(x + 16x - 56)
= 5 + 2(17x - 56)
= 5 + 34x - 112
= 34x - 107
Hope this helps!
Answer
34x - 107
Let me know if it was correct please.
HURRY I NEED IT NOW!!! What is the solution to this system of equations? x + 2 y = 4. 2 x minus 2 y = 5. (3, Negative 5 and one-half) (3, one-half) no solution infinitely many solutions
Answers
Answer:
(3, 1/2)
Step-by-step explanation:
set the equation up
x+2y=4
2x-2y=5
then solve
The correct option is B.[tex](3,\frac{1}{2})[/tex]
Given equations,
[tex]x+2y=4.....(1)\\2x-2y=5.....(2)[/tex]
The standard form for linear equations in two variables is [tex]Ax+By=C[/tex].
On comparing equation 1 and equation 2 with the standard form we get,
[tex]a_{1}=1, b_{1}=2, c_{1}=4\\a_{2}=2, b_{2}=-2,c_{2}=5[/tex]
Here,
[tex]\frac{a_{1} }{a_{2} } =\frac{1}{2} \\[/tex] and [tex]\frac{b_{1} }{b_{2} } =\frac{2}{-2} =-1[/tex]
Since [tex]\frac{a_{1} }{a_{2} } \neq \frac{b_{1} }{b_{2} }[/tex], So the given system of equation has a unique solution.
Now Adding equation 1 and 2 we get,
[tex]3x=9\\x=3[/tex]
putting the value of x in equation 1 we get,
[tex]3+2y=4\\2y=1\\y=\frac{1}{2}[/tex].
Hence the required solution of equation is [tex](3,\frac{1}{2})[/tex]. the correct option is B.[tex](3,\frac{1}{2})[/tex]
For more details follow the link:
https://brainly.com/question/11897796
Sarah serves at a restaurant and makes 20% of what she sells as tips. Her base salary is $10.20an hour. Each hour she sells an average of $60 of food and drinks. She also makes time and a half when she works over 8 hours during a single shift. Her work week contains three 10-hour shifts, one 5-hour shift, and one 11-hour shift. Using the same income deductions as stated in the previous question, what is Sarah’s annual gross income and annual net income.
Answers
Sara works 46 hours per week
9 hours are overtime and 37 hours are regular time
pay rate at time and a half: 10.20∗1.5=15.30
regular hours plus overtime pay
37∗10.20=377.40
9∗15.30=137.70
Income due to tips
Total hours worked∗60per hour∗20%
46∗60∗.20=552
Weekly Income=Hourly income + tips
Weekly Income=377.40+137.70+552.00
Weekly Income=1067.10
Annual income=Weekly income∗52
Annual income=55489.20
List the coordinates of FOUR vertices that create the feasible region on the graph. Submit your answer in the form of FOUR ordered Pairs (x, y)
Answers
Answer:
(500,0) , (300,0), (200,200) and (300,200)
Step-by-step explanation:
The region of the graph we are concerned with is that small portion which is shaded.
We need the coordinates that bounds this portion of the graph.
These coordinates are four in number and they are as identified by noticing the four points that surround the portion then making tracings from these points to the x and y axes respectively.
We proceed as follows;
The four points we are looking at in no particular order are;
(500,0) , (300,0), (200,200) and (300,200)
The points having coordinates that have y = 0 are those that are domiciled on the x-axis
We have two of these points which are on the x-axis.
Please help ASAP. Determine an equation of a quadratic function with the characteristics of its graph. Coordinates of the vertex: V(5,4) ; y intercept 79
Answers
Answer: y = 3(x - 5)² + 4
Step-by-step explanation:
Use the Vertex form: y = a(x - h)² + k to find the a-value
Given: (x, y) =(0, 79) and (h, k) = (5, 4)
79 = a(0 - 5)² + 4
79 = 25a + 4
75 = 25a
3 = a
Input a = 3 and (h, k) = (5, 4) into the Vertex form:
y = 3(x - 5)² + 4
12/31/2020: During 2020, $10,000 in accounts receivable were written off. At the end of the second year of operations, Yolandi Company had $1,000,000 in sales and accounts receivable of $400,000. XYZ's management has estimated that $17,000 in accounts receivable would be uncollectible.
Answers
12/31/2020: During 2020, $10,000 in accounts receivable were written off. At the end of the second year of operations, Yolandi Company had $1,000,000 in sales and accounts receivable of $400,000. XYZ's management has estimated that $17,000 in accounts receivable would be uncollectible.
For the end of 2020, after the adjusting entry for bad debts was journalized, what is the balance in the following accounts:
Bad debt expense: Allowance for doubtful accounts:
For the end of 2020, what is the company's net realizable value?
Answer:
Bad debt expense = $17000
Allowance for doubtful accounts = $17000
Company's net realizable value of accounts receivable at end of 2020 is
= $383,000
Step-by-step explanation:
From the information given :
Accounts written off in 2020 = $10,000
Accounts receivable expected to be uncollectible = $17,000
The Bad debt expense and Allowance for doubtful accounts can be computed as follows:
12/31/2020
Adjustment entry :
Debit Credit
Bad debt expense $17000
Allowance for doubtful accounts $17000
Company's net realizable value of accounts receivable at end of 2020 = Closing accounts receivables - Allowance for Doubtful accounts =
Company's net realizable value of accounts receivable at end of 2020 is:
= $400,000 - $17,000
= $383,000
Factorise (7x+19)/(x+1)(x+5)
Answers
Answer:
[tex] \frac{7x + 19}{ {x}^{2} + 6x + 5 } [/tex]Step-by-step explanation:
[tex] \frac{7x + 19}{(x + 1)(x + 5)} [/tex]
Multiply each term in the first parentheses by each term in second parentheses ( FOIL)
[tex] \frac{7x + 19}{x(x + 5) + 1(x + 5)} [/tex]
Calculate the product
[tex] \frac{7x + 19}{ {x}^{2} + 5x + x + 5} [/tex]
Collect like terms
[tex] \frac{7x + 9}{ {x}^{2} + 6x + 5 } [/tex]
Hope this helps...
Best regards!!
Segment BD is parallel to segment CE. If AB = 4, AC = 6, and AD = 7, what is AE?
Answers
Answer:
B. 10.5Step-by-step explanation:
If BD║CE then ΔADB and ΔAEC a similar triangles
so:
[tex]\frac{AE}{AD}=\frac{AC}{AB}\\\\\frac{AE}{7}=\frac{6}{4}\\\\AE=\frac32\cdot7\\\\AE=\frac{21}2\\\\AE=10.5[/tex]
What is the answer to 99,200 + 10(18/2)?
Answers
Answer:
99,290
Step-by-step explanation:
99,200 + 10(18/2)
= 99,200 + 10(9)
= 99,200 + 90
= 99,290
A container weighs 78.1 kg when it is filled with some cement. The same container weighs 25.5 kg when it is filled with some sand. The mass of the cement is 5 times as heavy as the mass of the sand. Find the mass of the container
Answers
Container + cement = 78.1
Container + sand = 25.5
Difference( cement - sand) = 78.1 -25.5 = 52.6
4 x Sand = 52.6
Sand = 52.6/4 = 13.15
Container = 25.5 - 13.15 = 12.35 kg
f(x) =
- 6x5 + 4x3
Which characteristic is correct for the function
Answers
Complete question:
[tex] F(x) = -6x^5 + 4x^3 [/tex]
Which characteristic is correct for the function
a) odd
b) neither even nor odd
c) both even and odd
d) even
Answer:
a) odd
Step-by-step explanation:
Given the equation:
[tex] F(x) = -6x^5 + 4x^3 [/tex]
To test for even or odd let's perform the following:
F
Replace "x" with "-x"
Thus,
[tex] F(x) = -6x^5 + 4x^3 [/tex]
[tex] = -6(-x)^5 + 4(-x)^3 [/tex]
[tex] = 6x^5 + -4x^3 [/tex]
Since [tex] -6x^5 + 4x^3 [/tex] ≠ [tex]-6(-x)^5 + 4(-x)^3[/tex] the equation is not even.
Also, the signs changed, the equation is considered to be odd.
I.e f(x) = -f(x)
Correct answer is option (a) odd
Answer:
odd
explanation:
Eight people are going for a ride in a boat that seats eight people. One person will drive, and only three of the remaining people are willing to ride in the two bow seats. How many seating arrangements are possible?
Answers
Answer:
720 seating arrangments
Step-by-step explanation:
There are eight people but driver is always the same so we only have to deal with combinations of the other 7 seats.
the combination of the five seats has 5! times 2 combinations for each of the 3 passengers willing to ride in the two boat seats thus the total number of different seating arrangements is 5! times 3! or 720
hope this helps :)
Using the Fundamental Counting Theorem, it is found that there are 5760 possible seating arrangements.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
In this problem:
For the driver, there are 8 outcomes, hence [tex]n_1 = 8[/tex].For the bow seats, there are [tex]n_2 = 3 \times 2 = 6[/tex] outcomes.For the other 5 seats, there are [tex]n_3 = 5![/tex] possible outcomes.Hence:
[tex]N = 8 \times 6 \times 5! = 5760[/tex]
There are 5760 possible seating arrangements.
More can be learned about the Fundamental Counting Theorem at https://brainly.com/question/24314866
Select the correct answer. Write (21 − 4i) − (16 + 7i) + 28i as a complex number in standard form. A. 5 + 39i B. 5 + 17i C. 5 − 39i D. 5 − 17i
Answers
Answer:
b. 5 + 17i
Step-by-step explanation:
Corey owns a 50 acre vineyard and every year, depending upon conditions, worries about flooding. Corey wants rainfall amounts to be at most 12 inches per year. Which model is correct?
A: X Greater than or equal to 12?
B: X less than or equal to 12?
C: X less than 12?
Answers
Answer:
B: X less than or equal to 12
x≤12
Step-by-step explanation:
Corey owns a 50acre vineyard
Corey wants rainfall amounts to be at most 12 inches per year
Let rainfall=x
Corey wants amount of rainfall (x) to be at most 12 inches per year
x is at most 12 inches per year
In inequality, the appropriate symbol representing “at most” is the “less than or equal to”
(≤) symbol
So, substituting the symbol
We have,
x≤12
B: X less than or equal to 12
Find the point Q along the directed line segement from point R (-3, 3) to point S(6, -3) that divides the segment in the ratio 2:1.
Answers
Answer:
Step-by-step explanation:
m : n = 2 : 1
R (-3, 3 ) ; x1 = -3 & y1 = 3
S(6 , -3) ; x2 = 6 & y2 = -3
Formula for the point that divides a line m:n = [tex](\frac{mx_{2}+nx_{1}}{m+n} , \frac{my_{2}+ny_{1}}{m+n})[/tex]
[tex]Q(\frac{2*6+1*(-3)}{2+1}, \frac{2*-3 + 1*3}{2+1})\\\\\\Q(\frac{12-3}{3} , \frac{-6+3}{2+1})\\\\\\Q(\frac{9}{3} , \frac{-3}{3})\\\\[/tex]
=Q(3, -1)
Answer:
D.) (3,-1)
Step-by-step explanation:
I got it correct on founders edtell
4.3) Consider the following function. (If an answer does not exist, enter DNE.) f(x) = ln(4 − ln(x)) (a) Find the vertical asymptote(s). (Enter your answers as a comma-separated list.) x =
Answers
Answer: [tex]x=0\text{ and }x=e^4[/tex]
Step-by-step explanation:
The vertical asymptote is at the zero of the argument and at points where the argument approaches to ∞ .Given function: [tex]f(x) = \ln(4 - \ln(x))[/tex]
Since, [tex]\ln 0=\infty[/tex]
Here, if
[tex]f(x)\to \infty\\\Rightarrow\ 4-\ln x=0\Rightarrow\ln x=4\Rightarrow\ x=e^4\\\text{OR}\ln x=\infty\Rightarrow\ x=0[/tex]
Hence, the vertical asymptotes of f(x) are:
[tex]x=0\text{ and }x=e^4[/tex].
Using it's concept, it is found that the vertical asymptotes of the function are: [tex]\mathbf{x = 0, x = e^4}[/tex]
A vertical asymptote of a function f(x) are the values of x for which the function is outside it's domain.
For the ln function, that is, [tex]\ln{g(x)}[/tex], they are the values of x for which:
[tex]g(x) = 0[/tex]
In this problem, the function is:
[tex]f(x) = \ln{(4 - \ln{(x)})}[/tex]
For the inner function, x = 0 is a vertical asymptote, as [tex]\ln{0}[/tex] is outside the domain.
For the outer function:
[tex]4 - \ln{(x)} = 0[/tex]
[tex]\ln{(x)} = 4[/tex]
[tex]e^{\ln{(x)}} = e^4[/tex]
[tex]x = e^4[/tex]
A similar problem is given at https://brainly.com/question/23535769
this is 69 points if you answer please help
Answers
Answer:
see below
Step-by-step explanation:
Angle C is equal to the 1/2 the difference of the two arcs
C = 1/2 ( large DC - small DC)
Large DC = ( 360 - 5x - 2) sum of a circle is 360 degrees
Small DC = 5x-2 the central angle is equal to the intercepted arc
C = 1/2 ( 360 - 5x-2 - ( 5x -2)) Angle Formed by Two Intersecting Chords
C = 1/2 ( 360 - 2 ( 5x-2))
Distributing the 1/2
C = 180 - (5x-2)
Replacing the C with 2x+7
2x+7 = 180 - (5x-2)
Add 5x-2 to each side
2x+7 +5x-2 = 180
Antonio is correct
Combine like terms
7x +5 = 180
7x = 175
Divide by 7
x =25
Then solve for A = 5x-2
A = 5*25-2
= 125-2
= 123
4x-5 - 2x-1
___ ____
2 6
Reduce the following expression into a single fraction.
Answers
Answer:
[tex]\frac{5x - 8}{3}[/tex]
Step-by-step explanation:
Find the LCM of the denominators and then solve:
[tex]\frac{4x - 5}{2} - \frac{2x - 1}{6} \\\\[/tex]
[tex]\frac{4x - 5}{2} - \frac{2x - 1}{6} \\\\\frac{3(4x - 5) - 2x - 1}{6} \\\\\frac{12x - 15 - 2x - 1}{6}\\\\\frac{10x - 16}{6}\\\\ \frac{2(5x - 8)}{2 * 3} \\\\ \frac{5x - 8}{3}[/tex]
Look at photo please don't understand
Does anyone understand this
Please answer quickly!
Answers
Answer:
a) 18.6%
b) 598,230
Step-by-step explanation:
a) In the first part of the question, you are given two population values and asked to find the percentage difference between them. A formula you can use for that is ...
percentage difference = (difference)/(original value) × 100%
The difference of interest is the difference between the 2011 population and the 2001 population
difference = 510,000 -430,000 = 80,000
The original value is the 2001 population, so the percentage difference is ...
percentage difference = 80,000/430,000 × 100% = 0.1860 × 100% = 18.6%
This is a positive value, so represents an increase.
The percentage increase in population from 2001 to 2011 was 18.6%.
__
b) In the second part, you are given the percentage difference and asked to find the new value. We can rearrange the above formula to find the difference:
difference = (percentage difference)/100% × original value
Then the difference between the 2021 population and the 2011 population will be ...
difference = (17.3%)/100% × 510,000 = 0.173 × 510,000 = 88,230
So, the population in 2021 is expected to be 88,230 more than in 2011:
2021 population = 520,000 +88,230 = 598,230
The predicted population in 2021 is 592,230.
Which is the length of the hypotenuse of the right triangle? Round your answer to the nearest tenth of a centimeter.
Hint: Pythagorean Theorem: a^2+ b^2 = c^2
Answers
Answer:
Length of hypotenuse of given triangle
= sqrt(356) (exact value)
= 18.87 (to 2 decimal places)
Step-by-step explanation:
Using the pythagorean Theorem,
The hypotenuse
c = sqrt(a^2+b^2)
= sqrt(16^2+10^2)
= sqrt(356) (exact value)
= 18.87 (to 2 decimal places)
The length of the hypotenuse of the right triangle is approximately
18.9 cm.
What is the Pythagorean theorem?Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
We can apply this theorem only in a right triangle.
Example:
The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.
Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm
We have,
The length of the hypotenuse of a right triangle can be found using the Pythagorean theorem:
c² = a² + b²
where c is the length of the hypotenuse, and a and b are the lengths of the other two sides (the base and the height in this case).
Plugging in the given values, we get:
c² = 16² + 10²
c² = 256 + 100
c² = 356
c ≈ 18.9
Rounding the answer to the nearest tenth of a centimeter, we get:
c ≈ 18.9 cm
Therefore,
The length of the hypotenuse of the right triangle is approximately
18.9 cm.
Learn more about the Pythagorean theorem here:
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HELP!!!!!
Find the slope of the line on the graph.
Write your answer as a fraction or a whole
number, not a mixed number or decimal.
Enter the correct answer.
Answers
Answer:
1
Step-by-step explanation:
identify two points on the graph:
1. (0, 4)
2. (-2, 2)
use slope formula: (y² - y¹) / (x² - x¹)
1. (2 - 4) / (-2 - 0) = -2 / -2 = 1
slope = 1
solve the simultaneous equation
y=x+3
y=7x+1
I'll mark you BRAINLIEST
Answers
Answer:
x = 1/3 , y = 10/3
Step-by-step explanation:
Solve the following system:
{y = x + 3 | (equation 1)
y = 7 x + 1 | (equation 2)
Express the system in standard form:
{-x + y = 3 | (equation 1)
-(7 x) + y = 1 | (equation 2)
Swap equation 1 with equation 2:
{-(7 x) + y = 1 | (equation 1)
-x + y = 3 | (equation 2)
Subtract 1/7 × (equation 1) from equation 2:
{-(7 x) + y = 1 | (equation 1)
0 x+(6 y)/7 = 20/7 | (equation 2)
Multiply equation 2 by 7/2:
{-(7 x) + y = 1 | (equation 1)
0 x+3 y = 10 | (equation 2)
Divide equation 2 by 3:
{-(7 x) + y = 1 | (equation 1)
0 x+y = 10/3 | (equation 2)
Subtract equation 2 from equation 1:
{-(7 x)+0 y = -7/3 | (equation 1)
0 x+y = 10/3 | (equation 2)
Divide equation 1 by -7:
{x+0 y = 1/3 | (equation 1)
0 x+y = 10/3 | (equation 2)
Collect results:
Answer: {x = 1/3 , y = 10/3
Answer:
[tex]\boxed{x=\frac{1}{3} }[/tex]
[tex]\boxed{y=\frac{10}{3} }[/tex]
Step-by-step explanation:
[tex]y=x+3\\y=7x+1[/tex]
Plug y as x+3 in the second equation.
[tex]x+3=7x+1\\7x-x=3-1\\6x=2\\x=\frac{1}{3}[/tex]
Plug x as 1/3 in the second equation.
[tex]y=7(\frac{1}{3} )+1\\y=\frac{7}{3}+1\\y=\frac{10}{3}[/tex]
Joe earned x dollars the first day he worked in December, where x is an integer. For each day after the first that he worked in December, Joe earned twice the amount he earned on the previous day. Did Joe earn less than $35 on the 4th day he worked in December?
(1) Joe earned more than $120 in total for the first five days he worked in December.
(2) Joe earned less than $148 on the 6th day he worked in December.
Answers
Answer:
1. Always translate the question stem, set up equations (limit the number of variables) and breakdown the question stem of possible
2. Never overlook the constraints the question provides.
Now the question stem tells us that on the
1st day Joe earned = x
2nd day = 2x
3rd day = 4x
4th day = 8x
Question stem: Did Joe earn less than $35 on the 4th day -----> 8x < 35 ----> x < 4.375
Since x is an integer, the question becomes 'Is x <= 4
Statement 1 : Joe earned more than $120 in total for the first five days he worked in December.
x + 2x + 4x + 8x + 16x > 120
31x > 120 ---> x > 3.9....
This gives us both a YES and a NO since x can be 4 or any integer greater than 4
Statement 2: Joe earned less than $148 on the 6th day he worked in December
32x < 148 ----> x < 4.625
Since x is an integer, x <=4. Sufficient.
hope this helps
-lvr
I'LL GIVE BRAINLIEST AND THANKS -SOLVE THE QUADRATIC EQUATION
Answers
Answer:
x = -1.47, 1.14
Step-by-step explanation:
Quadratic Formula: [tex]x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}[/tex]
We are given a = 3, b = 1, and c = -5. Simply plug it into the Quadratic Formula:
Step 1: Plug in variables
[tex]x=\frac{-1+/-\sqrt{1^2-4(3)(-5)} }{2(3)}[/tex]
Step 2: Solve
[tex]x=\frac{-1+/-\sqrt{1+60} }{6}[/tex]
[tex]x=\frac{-1+/-\sqrt{61} }{6}[/tex]
Step 3: Plug into calculator to evaluate into decimals
You should get x = -1.46837 and 1.13504
Answer:
1.13 and -1.46
Step-by-step explanation:
Our quadratic equation is: 3x²+x-5=0
The method we will use is te dicriminant method
let Δ be the discriminant:
a= 3b= 1c= -5Δ = b²-4*a*c
Δ= 1²-4*3*(-5)Δ= 1+60Δ=6161 is a positive number so we have solutions x and x':
x= (-b-√Δ)/2*a = (-1-√61)/2*3 = [tex]\frac{-1-\sqrt{61} }{6}[/tex] = -1.46 x'= (-b+√Δ)/2*a = (-1+√61)/2*3 =[tex]\frac{-1+\sqrt{61} }{6}[/tex] = 1.13so the two solutions are :
-1.46 and 1.13
Help me pls, it’s for right now
Answers
Answer:
c
Step-by-step explanation:
Which number lint represents the solution set for the inequity -1/2x>4
Answers
Answer:
B. x < -8
Step-by-step explanation:
Well first we need to get x by itself.
To do that we do 4 / -1/2 = -8
And since a negative was divided the > changes to a <.
So x<-8.
If x is less than -8 the line starts at -8 and goes to the left.
Thus,
the answer is choice b.
Hope this helps :)
By visual inspection, determine the best-fitting regression model for the
scatterplot.
Need help ASAP please
Answers
Answer:
its a! sorry im so late
Step-by-step explanation:
Question 8 of 10
A T-shirt vendor is thinking about changing the number of T-shirts he brings to
an event. To make sure he doesn't run out, he plans to bring more of the size
most likely to be sold.
The table shows the number of T-shirts of each size sold at his last event and
the number he had for sale.
Sold
Number for sale
180
Small
126
Medium
220
270
284
315
Large
X-Large
95
135
Which size should he bring more of?
A. Small
B. Medium
C. Large
D. X-Large
Answers
Large-size shirts should be brought more of which is more likely to be sold.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Sales Sold
Small 180 126
Medium 220 270
Large 284 315
x-large 95 135
Now,
The percentage of small size sold.
= 126/180 x 100
= 70%
The percentage of medium size sold.
= 220/270 x 100
= 81.5%
The percentage of large size sold.
= 284/315 x 100
= 90%
The percentage of x-large size sold.
= 95/135 x 100
= 70%
Thus,
Large-size shirts are sold more.
Learn more about expressions here:
https://brainly.com/question/3118662
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If the quadratic formula is used to solve 2x^2 - 3x - 1 = 0, what are the solutions?
Answers
Answer:
[tex]x=-1[/tex]
Step-by-step explanation:
[tex]2x-3x-1=0\\(2x-3x)+(-1)=0\\-x-1=0\\-x-1+1=0+1\\-x=1\\\frac{-x}{1}=\frac{1}{-1}\\ x=-1[/tex]
To measure a stone face carved on the side of a mountain, two sightings 700 feet from the base of the mountain are taken. If the angle of elevation to the bottom of the face is 35degreesand the angle of elevation to the top is 38 degrees,what is the height of the stone face
Answers
Answer:
Height of stone face is : 56.7 ft
Step-by-step explanation:
Kindly refer to the attached image for the diagram of the given conditions and values.
Let C be the base of mountain.
D be the point from where two sightings are taken.
AB be the stone face.
Angle of elevations:
[tex]\angle BDC =35^\circ\\\angle ADC =38^\circ[/tex]
To find:
Height of stone face = ?
AB = ?
Solution:
We can use trigonometric function of tangent here in two triangles [tex]\triangle BCD\ and\ \triangle ACD[/tex]:
[tex]In\ \triangle BCD :[/tex]
[tex]tan(\angle BDC) = \dfrac{Perpendicular}{Base} = \dfrac{BC}{CD}\\\Rightarrow BC = 700 \times tan35 ..... (1)[/tex]
[tex]In\ \triangle ACD :[/tex]
[tex]tan(\angle ADC) = \dfrac{Perpendicular}{Base} = \dfrac{AC}{CD}\\\Rightarrow AC = 700 \times tan38\\\Rightarrow AB +BC = 700 \times tan38\\\\\text{Using equation (1):}\\\Rightarrow AB + 700 \times tan 35 = 700 \times tan 38\\\Rightarrow AB = 700 \times tan 38-700 \times tan35\\\Rightarrow AB = 700 \times (tan 38-tan35)\\\Rightarrow AB = 700 \times 0.081\\\Rightarrow AB = \bold{56.7}\ ft[/tex]
So, Height of stone face is : 56.7 ft