Answer:
[tex] 0.7287[/tex]
Step-by-step explanation:
Let $534.9=a$
Thus, given:
$\log a=2.7287$
Hence:
$\log \Big( \frac{a}{100}\Big)=\log a- \log 100$
$\implies \log \Big( \frac{a}{100}\Big)=2.7287-2=0.7287$
7. Assume two people, Swanson and Suzie, are standing 35 feet apart and are watching a boat
race. At a given moment, Swanson approximates the angle formed by the lead boat, himself, and
Suzie to be 30°. Suzie approximates the angle formed by the lead boat, herself, and Swanson to be
130. How far is the boat from Swanson?
130°
30"
35 feet
Swanson
Suzie
Part I: What is the missing angle in this triangle? (1 point)
Part II: Use the law of sines to find the distance from Swanson to the boat. (2 points)
Answer:
78.4 ft
Step-by-step explanation:
Part I:
Missing angle = 180° - (130 + 30) (sum of angles in a triangle)
= 180° - 160°
Missing angle = 20°
Part II: distance (d) from Swanson to the boat
Law of Sines is given as:
[tex] \frac{a}{sin(A)} = \frac{b}{sin(B)} [/tex]
Where,
a = d
A = 130°
b = 35 ft
B = 20°
Plug in the values and solve for d
[tex] \frac{d}{sin(130)} = \frac{35}{sin(20)} [/tex]
Multiply both sides by sin(130) to make d the subject of the formula
[tex] \frac{d}{sin(130)}*sin(130) = \frac{35}{sin(20)}*sin(130) [/tex]
[tex] d = \frac{35*sin(130)}{sin(20)} [/tex]
[tex] d = 78.4 ft [/tex]
If you apply the changes below to the absolute value parent function, f(x)=x, what is the equation of the new function? Shift 2 units to the right shift 3 units down
Answer:
f(x) = Ix - 2I -3
Step-by-step explanation:
f(x) = IxI
f(x) = Ix - 2I -3
The equation is f(x) = | x – 2 | + 3 Then the vertex of the absolute function will be at (2, 3).
What is an absolute function?The absolute function is also known as the mode function. The value of the absolute function is always positive.
The absolute function is given as
f(x) = | x – h | + k
If you apply the changes below to the absolute value parent function
f(x) = |x|
Then the equation of the new function will be
Shift 2 units to the right, shift 3 units down
f(x) = | x – 2 | + 3
Then the vertex of the absolute function will be at (2, 3).
More about the absolute function link is given below.
https://brainly.com/question/10664936
#SPJ5
PLEASE ANSWER ASAP The drama club is selling candles for a fundraiser. They spend $100 on the candles and sell them for $4.50 each. How many candles must they sell to make more than $125 profit? Let x represent the number of candles sold. Which inequality can you use to find x? 4.5x – 100 > 125 4.5x + 125 > 100 100 – 4.5x > 125 100 + 4.5x > 125
Answer: 4.5x-100 > 125
Step-by-step explanation: Each candle costs $4.50, which can be simplified to 4.5. To determine how much they will make from the candles, you want to multiply the cost of the candles (4.5) by how many candles are sold (x), and this is where the 4.5x comes from. We subtract 100, because that is how much they spent on the candles they are selling (profit means how much you make after expenses). Since they're trying to make MORE THAN $125 in profit, we use the > sign.
Answer:
So we know that they spend $100 on the candles. In order to make a $125 profit, they must sell $225 worth of candles. Each candle sells for $4.50, so: So we know that they spend $100 on the candles. In order to make a $125 profit, they must sell $225 worth of candles. Each candle sells for $4.50, so:
4.5x > 225 is the inequality for that. It just means $4.50 times the number of candles has to be more than the $225 we need. To simplify it, just divide both sided by 4.5:
x > 50
They have to sell more than 50 candles.
Santiago is eight years younger than Juan is today. If, in four years, Santiago will be half Juan’s age, how old is Santiago today? a) 1 b) 2 c) 3 d) 4
Answer:
d) 4.
Step-by-step explanation:
Let Santiago be x years old today.
Then Juan is x + 8 years old.
In 4 years Santiago will be x + 4 years.
In 4 years Juan will be x + 12 years.
From the given information:
x + 4 = 0.5(x + 12)
x = 0.5x + 6 - 4
0.5x = 2
x = 2 / 0.5
x = 4.
Lara is x years old and her two best friends are (x-2) and (x+2). Write an expression for the square of Lara’s age and the product of ages of Lara’s best friends.
Please help with a detailed step by step thanks
Answer: x^2 + (x+2)(x-2)
Step-by-step explanation:
The caret ^ before the 2 indicates that the 2 is an exponent. It means "x squared"
If the keyboard doesn't allow exponents the caret is the thing to use.
The expression for the square of Lara’s age and the product of ages of Lara’s best friends is x² + (x-2)(x+2)
The first thing to do is to calculate the square of Lara's age and this will be:
= x × x = x²
The product of the ages of Lara’s best friends will be (x-2)(x+2).
Therefore, the expression that can be used to calculate the square of Lara’s age and the product of ages of Lara’s best friends is x² + (x-2)(x+2)
Read related link on:
https://brainly.com/question/16592251
solve the following problem (1+5^2)-16(1/2)^3
Answer:
24
Step-by-step explanation:
Using PEMDAS, we know to solve exponents before everything else.
So:
[tex](1+5^2)-16(\frac{1}{2})^3 = (1+25) - 16(\frac{1}{8} )\\\\26 - 2\\24[/tex]
Hope this helped!
Answer:
24
Step-by-step explanation:
(1+5^2)-16(1/2)^3
simplify
(1+25)-16(1/8)
simplify
26-2
simplify
24
IM SO CONFUSED SOMEONE HELPP!! is it A? i honestly don’t even know anymore bc everytime it says i’m wrong :(((((
Answer:
it is option b
Step-by-step explanation:
pls mark me brainliest
Answer:
Hey there!
The answer is B, because the range is the possible y values.
Let me know if this helps :)
If you're good at angles of depression please help meeeeee and show full working out tyyyyyyyyyy
Answer:
236.9 m
Step-by-step explanation:
Let x and y represent the distances to the near and far cars, respectively. You know from the definition of the tangent of an angle that ...
tan(angle of depression) = building height/distance to car
tan(10°39') = 150/x
x = 150/tan(10°39')
and
tan(8°15') = 150/y
y = 150/tan(8°15')
The difference of these two distances is the distance between the cars:
y - x = 150/tan(8°15') -150/tan(10°39')
__
The minutes of arc can be converted to fractional degrees:
15' = 15'/(60'/1°) = (15/60)° = 0.25°
39' = 39'/(60'/1°) = (39/60)° = (13/20)° = 0.65°
So, the distance of interest is ...
distance between cars = (150 m)(1/tan(8.25°) -1/tan(10.65°)) ≈ 236.86 m
The cars are about 236.9 meters apart.
Directions: Calculate the percent increase or decrease between the starting and ending
quantities below. Round your answer to one decimal place.
1. Start: 3
End: 10
Answer:233.333%
Step-by-step explanation:
1. 10-3=7 subtract end by start
2.7/3=2.333 divide difference by absolute value of start
32.333x100=233.333% multiply by 100 if negative its decreasing if positive it increasing
hoped this helped
If f(x)=(2x^2)-1, find:
-f(3x-1)+2
Answer:
-f(3x - 1) + 2 = -18x² + 12x + 1
Step-by-step explanation:
Step 1: Find f(3x - 1)
f(3x - 1) = 2(3x - 1)² - 1
f(3x - 1) = 2(9x² - 6x + 1) - 1
f(3x - 1) = 18x² - 12x + 2 - 1
f(3x - 1) = 18x² - 12x + 1
Step 2: Plug in f(3x - 1)
-(18x² - 12x + 1) + 2
Step 3: Evaluate
-18x² + 12x - 1 + 2
-f(3x - 1) + 2 = -18x² + 12x + 1
PLease answer !!! Find constants $A$ and $B$ such that \[\frac{x + 7}{x^2 - x - 2} = \frac{A}{x - 2} + \frac{B}{x + 1}\] for all $x$ such that $x\neq -1$ and $x\neq 2$. Give your answer as the ordered pair $(A,B)$. and Find all values of $t$ such that $\lfloor t\rfloor = 2t + 3$. If you find more than one value, then list the values you find in increasing order, separated by commas.
Answer:
1. [tex](A,B) = (3,-2)[/tex]
2. The values of t are: -3, -1
Step-by-step explanation:
Given
[tex]\frac{x + 7}{x^2 - x - 2} = \frac{A}{x - 2} + \frac{B}{x + 1}[/tex]
[tex]|t| = 2t + 3[/tex]
Required
Solve for the unknown
Solving [tex]\frac{x + 7}{x^2 - x - 2} = \frac{A}{x - 2} + \frac{B}{x + 1}[/tex]
Take LCM
[tex]\frac{x + 7}{x^2 - x - 2} = \frac{A(x+1) + B(x-2)}{(x - 2)(x-1)}[/tex]
Expand the denominator
[tex]\frac{x + 7}{x^2 - x - 2} = \frac{A(x+1) + B(x-2)}{x^2 - 2x + x -2}[/tex]
[tex]\frac{x + 7}{x^2 - x - 2} = \frac{A(x+1) + B(x-2)}{x^2 - x -2}[/tex]
Both denominators are equal; So, they can cancel out
[tex]x + 7 = A(x+1) + B(x-2)[/tex]
Expand the expression on the right hand side
[tex]x + 7 = Ax + A + Bx - 2B[/tex]
Collect and Group Like Terms
[tex]x + 7 = (Ax + Bx) + (A - 2B)[/tex]
[tex]x + 7 = (A + B)x + (A - 2B)[/tex]
By Direct comparison of the left hand side with the right hand side
[tex](A + B)x = x[/tex]
[tex]A - 2B = 7[/tex]
Divide both sides by x in [tex](A + B)x = x[/tex]
[tex]A + B = 1[/tex]
Make A the subject of formula
[tex]A = 1 - B[/tex]
Substitute 1 - B for A in [tex]A - 2B = 7[/tex]
[tex]1 - B - 2B = 7[/tex]
[tex]1 - 3B = 7[/tex]
Subtract 1 from both sides
[tex]1 - 1 - 3B = 7 - 1[/tex]
[tex]-3B = 6[/tex]
Divide both sides by -3
[tex]B = -2[/tex]
Substitute -2 for B in [tex]A = 1 - B[/tex]
[tex]A = 1 - (-2)[/tex]
[tex]A = 1 + 2[/tex]
[tex]A = 3[/tex]
Hence;
[tex](A,B) = (3,-2)[/tex]
Solving [tex]|t| = 2t + 3[/tex]
Because we're dealing with an absolute function; the possible expressions that can be derived from the above expression are;
[tex]t = 2t + 3[/tex] and [tex]-t = 2t + 3[/tex]
Solving [tex]t = 2t + 3[/tex]
Make t the subject of formula
[tex]t - 2t = 3[/tex]
[tex]-t = 3[/tex]
Multiply both sides by -1
[tex]t = -3[/tex]
Solving [tex]-t = 2t + 3[/tex]
Make t the subject of formula
[tex]-t - 2t = 3[/tex]
[tex]-3t = 3[/tex]
Divide both sides by -3
[tex]t = -1[/tex]
Hence, the values of t are: -3, -1
Consider the function represented by the graph. What is the domain of this function?
Answer:
domain={8,7,6,5,4,3,2,1,0}
Answer:
[tex]\boxed{0 \leq x \leq R}[/tex]
Step-by-step explanation:
Well domain is the amount of x values on a graph,
so looking at the given graph we can tell the x values start at 0 and since it is a solid dot the x is greater than or equal to 0 then you can tell by the arrow that the line goes on forever.
0 ≤ x ≤ R
The R stands for all real numbers.
Hope this helps :)
What is the correct evaluation of x2 - y2 - z2, when x is equal to -2, y is equal to 3 and z is equal to 4?
Answer:
-18
Step-by-step explanation:
x2 - y2 - z2 if x=-2, y=3, and z=4
x2 - y2 - z2
(-2) 2 - (3)2 - (4)2
(-4) - (6) - (8)
-10 -8
-18
Answer:
18
Step-by-step explanation:
How would I solve this question? y = -1 1/8 - 7/8x -4x + 9y = -22 x = ?, y = ?
Answer:
(1.222, -2.444)
Step-by-step explanation:
I hope you can understand the question now
Help, show work please.
Answer:
A
Step-by-step explanation:
A: 0^2+8=8
B: 1^2+8=9
C: 2^2+8=12
D: 3^2+8=17
as 8 is the smallest, A is the answer
Michael just drank a cup of coffee to help him stay awake. The coffee had 110 milligrams of caffeine in it. If his body processes 5% of the caffeine every hour, how much will be left in 8 hours? A.74 B.72 C.56 D.73
Answer:C
Step-by-step explanation:
Ben deposited $2,700 in an account that pays 3.25% simple interest. He created a graph of his
account balance equation (A = Prt+P) with a slope of 8,775.
Step-by-step explanation:
His profit is 40%.
hope this helps
pls mark me brainliest
Answer:
40 percent i think
Step-by-step explanation:
hope its right
please put me brainlieeeeeeest
thxxx
Determine the graph transformation....
Answer:
I think its b
Step-by-step explanation:
Find an equation of the line with the slope m= 3 that passes through the point (2,2). Write the equation in the form Ax+By = C.
Answer:
[tex]y = 3x-4[/tex]
Step-by-step explanation:
We know that if we were to write an equation with the slope of 3, it would be [tex]y=kx[/tex], where k is the constant (in this case 3.)
So right now, we have [tex]y=3x[/tex].
However, this will not pass through the point (2,2). To do this, we need to add a y-intercept in which (2,2) will be crossed through.
If we have a y-intercept of -4, the points will be:
(0, -4)
(1, -1)
(2, 2)
So our final equation is [tex]y = 3x-4[/tex].
Hope this helped!
Answer: 3x-1y=4 in Ax+By=C form
Step-by-step explanation:
the intercept form is y=3x-4
subracting 3x from both sides would get -3x+y=-4
distributing -(-3x+y=-4) would get 3x-y=4.
4x = 2x + 2x + 5(x-x) does this have one solution, no solution or infinite solutions
Answer:
infinite solutions
Step-by-step explanation:
4x = 2x + 2x + 5(x-x)
Simplify
4x = 2x + 2x + 5*0
4x = 2x + 2x
4x = 4x
Divide by x
4 =4
This is always true so this has infinite solutions
If the degree measures of the angles of a triangle are in the ratio 3 : 3 : 4, what is the degree measure of the largest angle of the triangle? (Sum of all three angles is 180)
x=3k
y=3k
z=4k
x+y+z=180
3k+3k+4k=180
10k=180
k=180/10
k= 18
z=4*18
z=72
answer: 72
Answer:72 degrees
Step-by-step explanation:
3:3:4 is the ratio of the angles of a triangle and we have been asked the degree measure of the largest angle.
First of all...add the three ratios
3+3+4=10
;Ratio 10=180 degrees(the sum of all the angles;ratios add up to the sum of all three angles)
10=180 how about ratio 3?
Cross multiply...3 times 180 over 10= 54 degrees
Both angles with ratio 3 are 54 degrees
180-108=72
The angle with ratio 4 has 72 degrees which makes it the largest angle
help me plz can somewon help me
Answer:
The answer is 6x10^-4.
Step-by-step explanation:
Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the
10 .
If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.
How to get this answer:
Place the decimal point after the 6 to get 6.0
The question is now "how do we go from 6.0 to get back to 0.0006?"
The answer is "move the decimal point 4 spots to the left". This movement of "move 4 left" means the exponent is -4. The negative because we moved to the left. The 4 indicates how many spaces we moved.
So we get the scientific notation value of [tex]6.0 \times 10^{-4}[/tex] which is the same as [tex]6 \times 10^{-4}[/tex] because 6.0 simplifies to 6
Pllzzz help I’ll mark brainliest
Answer:
26°
Step-by-step explanation:
AC=tan 64
BC=x=sec 64
Using sine rule
(Sin 64)/tan 64 = (sin BAC)/sec 64
Cos 64 = (sin BAC)(cos 64)
Sin BAC= 1
BAC=90
ACB+ 64+90=180
ACB= 26°
Pls help me!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!please I’m begging u
Answer:
7. 36 8. 1 9. 21
Step-by-step explanation:
You plug in the variables in the equation.
7.[tex]5^{2} +-4^{2} = 41[/tex]
8. [tex](5-4)^{2} = 81[/tex]
9. [tex]5+4^{2} =21[/tex]
Answer:
See explanation
Step-by-step explanation:
1. 8^5 = 32768
2. a^6
3. 5^5*9^3 = 2278125
5. (-3)^5 = -243
6. (3/4)³ = 27/64
7. a² + b² = 5² + (-4)² = 25 + 16 = 41
8. (a + b)² = (5 + 4)² = 9² = 81
9. a + b² = 5 + 4² = 5 + 16 = 21
Please Help Will Mark as Brainlist
Answer:
Hey there!
We can write this equation: 2x+4x=180
6x=180
x=30
Hope this helps :)
The two angles are supplementary angles. When added together they equal 180 degrees.
2x + 4x = 180
Combine like terms:
6x = 180
Divide both sides by 6:
X = 180/6
X = 30
(08.01) Two lines, A and B, are represented by the following equations: Line A: y = x − 1 Line B: y = −3x + 11 Which of the following options shows the solution to the system of equations and explains why? (3, 2), because the point does not lie on any axis (3, 2), because one of the lines passes through this point (3, 2), because the point lies between the two axes (3, 2), because both lines pass through this point
Answer:
the answer is D
Step-by-step explanation:
y=x-1
2=3-1
2=2
y=-3x+11
2=-3(3)+11
2=-9+11
2=2
Answer:
Step-by-step explanation:
If both lines pass through the point (3, 2), we automatically know that (3, 2) is the soution of the system of linear equations given here, AND that (3, 2) is a solution of equation A and equation B both.
What is the expression in SIMPLEST radical form? (20)∧5/2
Answer:
The expression in the question can, and should, be written clearly as either 205(2)=8 or as 205(2)=2 . Relying on a left-to-right or right-to-left interpretation is not a good idea.
In cases of associative operators, like a⋅b⋅c , the parenthesis or other grouping can be omitted because any reasonable interpretation will yield the same result. But this isn’t true of division, which is not associative, nor is it true of mixed operators at the “same level” of precedence, like multiplication/division.
The other answers which say the result is 8 may not be wrong, but they are missing the main issue in that this expression should not be used because of the ambiguity
Step-by-step explanation:
Eli is driving on a long road trip. He currently has 12 gallons of gas in his car. Each
hour that he drives, his car uses up 1.75 gallons of gas. How much gas would be in the
tank after driving for 4 hours? How much gas would be left after t hours?
Gas left after 4 hours:
Gas left after t hours: 1
I
Submit Answer
attempt out of
Answer:
I would be 7 gallons used and 5 gallons left
Step-by-step explanation:
multyply 1.75 times 4 hours equal 7 then 12-7=5 is the total of gallons left
Hope this helps
Select the equation of the line that passes through the point (5.7) and is perpendicular to the line x = 4.
What's the perimeter of rectangle DEFG, shown? A) 17 B) 28 C) 40 D) 34
Answer:
[tex]\huge\boxed{Perimeter = 34\ units}[/tex]
Step-by-step explanation:
DE = 10 units
GF = 10 units
DG = 7 units
EF = 7 units
Perimeter of rectangle = Sum of all sides
P = DE + GF + DG + EF
P = 10 + 10 + 7 + 7
Perimeter = 34 units
Answer:
D) 34 units
Step-by-step explanation:
Coordinates:
D: (-5,4)
E: (5,4)
F: (5, -3)
G: (-5,-3)
Distance between points D and E = Distance between points F and G = 10
Distance between points E and F = Distance between points G and D = 7
Formula for perimeter of your rectangle:
2(x) + 2(y) =
2(10) + 2(7) =
20 + 14 = 34 units
That's your answer!
Hope that helps and maybe earns a brainliest!
Have a terrific day! > <
U
