Step-by-step explanation:
the scanned description is very hard to understand.
so I think what happened :
16x² - 9 = 16
then the first error :
sqrt(16x²) - sqrt(9) = sqrt(16)
that is wrong, as you cannot split a + or - operation inside a sqrt function into + or - separate sqrt results of the parts.
so, correctly, the only possible transformation involving sqrt for both sides :
sqrt(16x² - 9) = sqrt(16)
but it would be even easier to clean up the various constant numbers with each other.
so,
16x² - 9 = 16
16x² = 25
and now we trashes the square root
sqrt(16x²) = sqrt(25)
4x = 5
x = 5/4 or x = -5/4
and I cannot see or understand for my life what the second equation was, as Daniel did something wrong, so I cannot deduct the original equation out of a supposedly wrong
y³ - 1 = 7
1. Determine the sum of the first 53 terms of the following series: 179+173+167+...
2. Determine the sum of the first 19 terms of the following series: 6−12+24−48+...
(1) This series consists of terms of an arithmetic sequence:
179 - 173 = 6
173 - 167 = 6
and so on, so that the n-th term in the series is (for n ≥ 1)
a(n) = 179 - 6 (n - 1) = 185 - 6n
Then the sum of the first 53 terms is
[tex]\displaystyle\sum_{n=1}^{53}(185-6n) = 185\sum_{n=1}^{53}1-6\sum_{n=1}^{53}n[/tex]
[tex]\displaystyle\sum_{n=1}^{53}(185-6n) = 185\times53-6\times\frac{53\times54}2[/tex]
[tex]\displaystyle\sum_{n=1}^{53}(185-6n) = \boxed{1219}[/tex]
(2) This series has terms from a geometric sequence:
-12 / 6 = -2
24/(-12) = -2
-48/24 = -2
and so on. The n-th term is (again, for n ≥ 1)
a(n) = 6 (-2)ⁿ⁻¹
and the sum of the first 19 terms is
[tex]\displaystyle\sum_{n=1}^{19}6(-2)^{n-1} = 6\left(1 + (-2) + (-2)^2 + (-2)^3 + \cdots+(-2)^{19}\right)[/tex]
Multiply both sides by -2 :
[tex]\displaystyle-2\sum_{n=1}^{19}6(-2)^{n-1} = 6\left((-2) + (-2)^2 + (-2)^3 + (-2)^4 + \cdots+(-2)^{20}\right)[/tex]
Subtracting this from the first sum gives
[tex]\displaystyle(1-(-2))\sum_{n=1}^{19}6(-2)^{n-1} = 6\left(1 -(-2)^{20}\right)[/tex]
and solving for the sum, you get
[tex]\displaystyle3\sum_{n=1}^{19}6(-2)^{n-1} = 6\left(1 -(-2)^{20}\right)[/tex]
[tex]\displaystyle\sum_{n=1}^{19}6(-2)^{n-1} = 2\left(1 -(-2)^{20}\right)[/tex]
[tex]\displaystyle\sum_{n=1}^{19}6(-2)^{n-1} = 2\left(1 -(-1)^{20}2^{20}\right)[/tex]
[tex]\displaystyle\sum_{n=1}^{19}6(-2)^{n-1} = 2\left(1 -2^{20}\right) = 2-2^{21} = \boxed{-2,097,150}[/tex]
An airplane from Singapore to Melbourne takes about 7 1/2 hours to cover a distance of 6057 km. What is the average speed of the airplane.
Answer: 13.46 km/h
Step-by-step explanation:
7 1/2 hr= 450 min
6057/450= 13.46
please solve this please
Answer:
3
Step-by-step explanation:
An object is launched at 19.6 meters per second (m/s) from a 58.8-meter tall platform. The equation for the
object's height s at time t seconds after launch is s(t) = - 4.9t2 + 19.6t + 58.8, where s is in meters. Create a
table of values and graph the function. Approximately what is the maximum height that the object will get?
O 76.4 meters
113.5 meters
O 78.4 meters
58.8 meters
Answer:
Step-by-step explanation:
The easiest way to do this is to complete the square on the quadratic. This allows us to see what the vertex is and answer the question without having to plug in a ton of numbers to see what the max y value is. Completing the square will naturally put the equation into vertex form:
[tex]y=-a(x-h)^2+k[/tex] where h will be the time it takes to get to a height of k.
Begin by setting the quadratic equal to 0 and then moving over the constant, like this:
[tex]-4.9t^2+19.6t=-58.8[/tex] and the rule is that the leading coefficient has to be a 1. Ours is a -4.9 so we have to factor it out:
[tex]-4.9(t^2-4t)=-58.8[/tex] Now take half the linear term, square it, and add it to both sides. Our linear term is a -4, from -4t. Half of -4 is -2, and -2 squared is 4, so we add a 4 to both sides. BUT on the left we have that -4.9 out front there as a multiplier, so we ACTUALLY added on to the left was -4.9(4) which is -19.6:
[tex]-4.9(t^2-4t+4)=-58.8-19.6[/tex] and now we have to clean this up. The right side is easy, that is -78.4. The left side...not so much.
The reason we complete the square is to create a perfect square binomial, which is the [tex](x-h)^2[/tex] part from above. Completing the square does this naturally, now it's just up to us to write the binomial created during the process:
[tex]-4.9(t-2)^2=-78.4[/tex] Now, move the constant back over and set the equation back equal to y:
[tex]-4.9(t-2)^2+78.4=s(t)[/tex] and we see that the vertex is (2, 78.4). That means that 2 seconds after launch, the object reached its max height of 78.4 meters, the third choice down.
Mrs. Kennedy is teaching an 8th grade class. She is standing 7 meters in front of Catherine. Davis is sitting to Catherine’s left. If Davis and Mrs. Kennedy are 12 meters apart, how far apart are Davis and Catherine?
13.90 meters
5 meters
9.75 meters
4.36 meters
Answer:
9.75 meters
Step-by-step explanation:
Davis and Catherine are approximately 13.90 meters apart.
How to determine distance apartTo find the distance between Davis and Catherine, we can use the concept of right triangles and apply the Pythagorean theorem.
Let's consider a right triangle where the distance between Davis and Mrs. Kennedy is the base, the distance between Mrs. Kennedy and Catherine is the height, and the distance between Davis and Catherine is the hypotenuse.
According to the given information, Mrs. Kennedy is 7 meters in front of Catherine, and Davis and Mrs. Kennedy are 12 meters apart.
Using the Pythagorean theorem, we have:
(Base)² + (Height)² = (Hypotenuse)²
Substituting the given values:
(12)² + (7)² = (Hypotenuse)²
Simplifying the equation:
144 + 49 = (Hypotenuse)²
193 = (Hypotenuse)²
Taking the square root of both sides:
√193 ≈ 13.89 = 13.90
Therefore, Davis and Catherine are approximately 13.90 meters apart.
Learn more about distance at
https://brainly.com/question/26550516
#SPJ2
find the measure of acute angle of a right angle triangle when one angle is 60°
Answer:
30 degrees.
Step-by-step explanation:
Let the acute angle be x.
Then as the 2 acute angles in a right triangle sum to 90 degrees,
x = 90 - 60
= 30.
We used the information we know to give us this equation.
90°+60°+x=180°
We add 90° and 60° to give 150°
150°+x=180°
x must therefore be 30°ZEFG and ZGFH are a linear pair, mZEFG = 2n + 16, and mZGFH = 3n+24. What are mZEFG and mZGFH?
mZEFG =
Answer:
m<EFG = 72°
m<GFH = 108°
Step-by-step explanation:
m<EFG = 2n + 16
m<GFH = 3n + 24
Linear pairs are supplementary, therefore,
m<EFG + m<GFH = 180°
Substitute
2n + 16 + 3n + 24 = 180
Add like terms
5n + 40 = 180
5n + 40 - 40 = 180 - 40 (subtraction property of equality)
5n = 140
5n/5 = 140/5 (division property of equality)
n = 28
✔️m<EFG = 2n + 16
Plug in the value of n
m<EFG = 2(28) + 16 = 72°
✔️m<GFH = 3n + 24
Plug in the value of n
m<GFH = 3(28) + 24 = 108°
Pls help me this is my homework
Answer:
C) 840
C) 87
D) 3000-150n
Step-by-step explanation:
Answer:
c
c
d
Step-by-step explanation:
(8) The average daily temperatures in July of some cities in Texas are shown in the table. Which
of the following fiets the cities from greatest temperature to least temperatura
City
Average Daily
Temperature
Austin
84.52F
Dallas
85.9°F
San Antonio
85 F
Fort Worth
85.31°F
a. Dallas, Fort Worth, San Antonio, Austin
b. Austin, Dallas, San Antonio, Fort Worth
c. Austin, San Antonio, Fort Worth, Dallas
d. Dallas, San Antonio, Fort Worth, Austin
Answer:
A.
Step-by-step explanation:
85.9 > 85.31 > 85 > 84.52
Dallas, Fort Worth, San Antonio, Austin
b. Compare the similar triangle proof from question 3 with the inscribed square
proof. How are they different? Which method was easier for you to understand?
(1 point)
Answer:
i might be wrong but this is what i put
Step-by-step explanation:
In question 3 it was comparing three triangles where now it is using the triangles to find the area of a square instead of proving that they are the same.
Simplify each of the following:
a) root25 + root50 - root24 + root49
b) root2(2root8 – 3root32 + 4roor50)
Show your work
Answer:
a)
√25 + √50 - √24 + √49 =5 + 5√2 - 2√6 + 7 = 12 + 5√2 - 2√6b)
√2(2√8 – 3√32 + 4√50) =2√16 - 3√64 + 4√100 = 2*4 - 3*8 + 4*10 = 8 - 24 + 40 = 24Answer:
a.) 12 + 5√2 - 2√6
b.) 24
Step-by-step explanation:
a) √25 + √50 - √24 + √49
√25 + √50 - √24 + √49Calculate the square root .
5 + √50 - √24 + 7Simplify the radical expression.
5 + 5√2 - 2√6 + 7Combine like terms.
5 + 7 + 5√2 - 2√6 12 + 5√2 - 2√6b.) √2 ( 2√8 - 3√32 + 4√50 )
√2 ( 2√8 - 3√32 + 4√50 )Simplify the radical expression.
√2 ( 4√2 - 3 × 2²√2 + 20√2)Evaluate the power.
√2 ( 4√2 - 3 × 4√2 + 20√2)Calculate the products.
√2 ( 4√2 -12√2 + 20√2)Combine like terms.
√2 × (4 - 12 + 20 )√2√2 × 12 √ 2Multiply.
2 × 12 243. Rita is applying for a job as an engineer. Hier starting salary at Company will be $30,000 a $300 yearly
raise. Her starting salary at company will be $65.000 with a 5% increase sach year. If Rata is working at a
company for 5 years. Which company should she pick?
Answer:
The 65,000 salary
Step-by-step explanation:
Because the 30,000 salary after 5 years would be 31,500.
30,000+300=30,300
30,300+300=30,600
30,600+300=30,900
30,900+300=31,200
31,200+300=31,500
The 65,000 paying company
65,000x1.05=68,250
68,250x1.05=71.662.5
71,662.5x1.05=75,245.625
75,245.625x1.05=79,007.90625
79,007.90625x1.05=82,958.3015625
her salary after 5 years would be 82,958.3015625
Determine which equations have the same solution set as StartFraction 2 Over 3 EndFraction minus x plus StartFraction 1 Over 6 EndFraction equals 6 x. – x + = 6x by recognizing properties, rather than solving. Check all that apply.
Answer:
A, B, F
Step-by-step explanation:
2/3 - x + 1/6 = 6x
Collect like terms
2/3 + 1/6 = 6x + x
(4+1) / 6 = 7x
5/6 = 7x
x = 5/6 ÷ 7
= 5/6 × 1/7
x = 5/42
a) 4 - 6x + 1 = 36x
4 + 1 = 36x + 6x
5 = 42x
x = 5/42
Equivalent to the last step of the simplification above
b) 5/6 - x = 6x
5/6 = 6x + x
5/6 = 7x
This is equivalent to the third step of the simplification
c) 4 - x + 1 = 6x
4 + 1 = 6x + x
5 = 7x
x = 5/7
Not equivalent to any of the steps in the simplification above
d) 5/6 + x = 6x
5/6 = 6x - x
5/6 = 5x
x = 5/6 ÷ 5
= 5/6 × 1/5
x = 5/30
Not equivalent to any of the steps in the simplification above
e) 5 = 30x
x = 5/30
Not equivalent to any of the steps in the simplification above
f) 5 = 42x
x = 5/42
Equivalent to the last step of the simplification above
Tìm x, y sao cho: B=-x^2+2xy-4y^2+2x+10y-8
Answer:
Hello,
Step-by-step explanation:
All i can do is to show you the ellipse.
This Venn diagram shows the pizza topping preferences for 9 students.
What elements are in A and B?
(Look at picture)
Answer:
I think the answer is C.
pls help i need both blanks the options for the second one is left, right, up, down PLS HURRY ITS TIMED!!
Answer:
The graph is shifted 7 units right and 5 units up.
-2/3a+5/6a-1/5a-1/6
Answer:
[tex]\frac{-1}{30} a - \frac{1}{6}[/tex]
Step-by-step explanation:
Multiply. (Use photo). Enter your answer in simplest radical form.
Answer:
72√2
Step-by-step explanation:
3√2 × 2√8 × √3 × √6
The above can be simplified as follow:
3√2 × 2√8 × √3 × √6
Recall
a√c × b√d = (a×b)√(c×d)
3√2 × 2√8 × √3 × √6 = (3×2)√(2×8×3×6)
= 6√288
Recall
288 = 144 × 2
6√288 = 6√(144 × 2)
Recall
√(a×b) = √a × √b
6√(144 × 2) = 6 × √144 × √2
= 6 × 12 × √2
= 72√2
Therefore,
3√2 × 2√8 × √3 × √6 = 72√2
Wages and salaries
Kelly earns a salary of $68 430 pa how much does he earn each week, each fortnight and each month?
Answer:
Each week = $ 1311.41
Each fortnight = $ 2622.84
Each month = $ 5702.5
Step-by-step explanation:
Given that,
Annual salary of Kelly = $ 68,430
As we know,
There are 52.18 weeks in a year.
So,
Weekly income = Annual salary ÷ no. of weeks in the year
= $ 68,430 ÷ 52.18
= $ 1311.42
Fortnight income = 2 * weekly income
= 2 * $ 1311.42
= $ 2622.84
Each month's income = Annual income ÷ 12(no. of months)
= $ 68,430 ÷ 12
= $ 5702.5
Diagram shows triangle ABC.
Workout the size of angles x,y,z
x= 70*
y= 30*
z= *
WILL MARK BRAINLIEST
picture included^^^^
need help asap please n thank you!
^^^^
Answer:
14
Step-by-step explanation:
The a value is from the center to the maximum
We want from minimum to max so we need 2 times the amplitude
a = 7
2 *7 = 14
1)The sum of two consecutive multiples of 5 is55. Find these multiples.
2)The sum of three consecutive integers is 93. What are the integers?
3)If five is subtracted from three times a number, the result is 10. What is the number?
Part 1
Let the consecutive multiples be 5x and 5x + 5
ATQ
5x + 5x + 5 = 55
10x = 55 - 5
10x = 50
x = 5
Answer is 25 and 30
Part 2
Let the number be x , x + 1, x + 2
ATQ
x + x + 1 + x + 2 = 93
3x + 3 = 93
3x = 93 - 3
x = 90/3
x = 30
The integers are 30,31 and 32
Part 3
Let the number be x
ATQ
3x - 5 = 10
3x = 10 + 5
x = 15/3
x = 5
The number is 5
Answered by Gauthmath must click thanks and mark brainliest
What point lies on the line with point slope equation y-3=4(x+7)?
Answer:
(-7, 3)
General Formulas and Concepts:
Algebra I
Point-Slope Form: y - y₁ = m(x - x₁)
x₁ - x coordinate y₁ - y coordinate m - slopeStep-by-step explanation:
Step 1: Define
Identify
y - 3 = 4(x + 7)
↓ Compare to Point-Slope Form
Point (-7, 3)
Slope m = 4
What is the slope of the line passing through the points
(-3, - 5) and (-1,6)? (URGENT)
What is the answer? How to solve?
Answer:
a +73°=90°
a= 90°-73°
a =17°
d+18°=90°
d=90°-18°
d =72 °
What is the tangent ratio of angle x?
tan x= 20/21
tan x= 21/29
tan x= 20/29
tan x= 21/20
Answer:
[tex]\tan x=21/20[/tex]
Step-by-step explanation:
In any right triangle, the tangent of an angle is equal to its opposite side divided by its adjacent side. (o/a)
For angle [tex]x[/tex], its opposite side is 21 feet and its adjacent side is 20 feet. Therefore, we have:
[tex]\boxed{\tan x=21/20}[/tex]
What is the equation of the line of reflection? please help, due in 30 minutes!!!
Answer:
The line of reflection is usually given in the form y = m x + b y = mx + b y=mx+by, equals, m, x, plus, b.
Step-by-step explanation:
Answer:
The line of reflection in [tex]y=mx+b[/tex] form is [tex]y=\frac{1}{3} x-2[/tex]
Step-by-step explanation:
i need help. i don't understand this at all.
Answer:
Step-by-step explanation:
If this is in terms of angles, 4x+6 must be equal to 90 since it is half of the angle produced by a line (180°) So solving for 4x+6=90, x=21
Quick! HELP! THANK YOU SO MUCH!
If the difference between the interior and exterior angles of a regular polygon is 100°, how many sides does the polygon have?
Answer:
9 sides
Step-by-step explanation:
Sum of the measures of the interior angle of a polygon with n sides:
(n - 2)180
Measure of 1 interior angle of a regular polygon of n sides:
(n - 2)180/n
Sum of the measures of the exterior angles of a polygon, one per vertex:
360
Measure of 1 exterior angle of a regular polygon of n sides:
360/n
(n - 2)180/n = 360/n + 100
Multiply both sides by n.
(n - 2)180 = 360 + 100n
Distribute on left side.
180n - 360 = 360 + 100n
Subtract 100n from both sides.
80n - 360 = 360
Add 360 to both sides.
80n = 720
Divide both sides by 80.
n = 9
Answer: 9 sides
What is the explicit formula for this sequence?
-9, -3, 3, 9, 15,
Answer:
+6
Step-by-step explanation:Look at the trend of numbers and notice. Maybe put it in a table.
