Answer:
y^-1 = (x + 4)/5
Step-by-step explanation:
To find the inverse equation of the function y=5x - 4, first we need to switch the x and y:
→ y = 5x - 4
→ x = 5y - 4
Now, solving for 'y':
→ x = 5y - 4
→ x + 4 = 5y
→ y = (x + 4)/5
therefore, the inverse equation is: y^-1 = (x + 4)/5
There is a mound of g pounds of gravel in a quarry. Throughout the day, 400 pounds of gravel are added to the mound. Two orders of 900 pounds are sold and the gravel is removed from the mound. At the end of the day, the mound has 1,500 pounds of gravel. Write the equation that best describes the situation.
Answer:
The equation that best describes the situation is:
[tex]g +400 -1800 = 1,500[/tex]
Step-by-step explanation:
The initial amount of gravel is g.
[tex]g[/tex]
Then we know that 400 pounds are added
[tex]g +400[/tex]
Two orders of 900 pounds are sold and the gravel is removed from the mound. This is:
[tex]g +400 -2 * 900[/tex]
[tex]g +400 -1800[/tex]
At the end of the day, the mound has 1,500 pounds of serious. This is:
[tex]g +400 -1800 = 1,500[/tex]
The equation that best describes the situation is:
[tex]g +400 -1800 = 1,500[/tex]
And
[tex]g= 1500 +1800 - 400\\\\g=2900[/tex]
The equation that best describes the given situation is[tex]\rm g + 400 - (2\times 900) = 1500[/tex] and this can be determined by forming the linear equation with the help of given data.
Given :
Throughout the day, 400 pounds of gravel are added to the mound.Two orders of 900 pounds are sold and the gravel is removed from the mound.At the end of the day, the mound has 1,500 pounds of gravel.Let the initial amount of gravel be 'g'. Then after the addition of 400 pounds of gravel, the total gravel becomes:
= g + 400
Given that two orders of 900 pounds are sold and the gravel is removed from the mound so, the total gravel now becomes:
[tex]\rm = g + 400 - (2\times 900)[/tex]
= g + 400 - 1800
= g - 1400
At the end of the day, the mound has 1,500 pounds of gravel, that is:
g - 1400 = 1500
g = 1500 + 1400
g = 2900
Therefore, the equation that best describe the given situation is:
g + 400 - 1800 = 1500
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A roll of fabric was 120 inches long. A customer bought 2 feet of the fabric.
How many feet of fabric were remaining?
(Hint: 1 foot = 12 inches)
OA. 12
OB. 7
OC. 118
OD.8
the correct answer is OB. 7.
What is the value of z in the equation 2(4z − 9 − 7) = 166 − 46?
Answer:
z = 19
Step-by-step explanation:
Given
2(4z - 9 - 7) = 166 - 46 ← simplify both sides
2(4z - 16) = 120 ← distribute parenthesis on left side
8z - 32 = 120 ( add 32 to both sides )
8z = 152 ( divide both sides by 8 )
z = 19
Answer:
z = 19.
Step-by-step explanation:
2(4z − 9 − 7) = 166 − 46
2(4z − 9 − 7) = 120
Divide both sides by 2:
4z − 9 − 7 = 60
4z = 76
z = 19.
Please help and thank you
Answer:
A
Step-by-step explanation:
Define each of the terms.
f(x) is the total level of radioactivity.
x is the total number of weeks.
[tex]\frac{1}{2}[/tex] is the weekly decay factor.
30 is the initial level of radioactivity.
Starting at the top of a square pyramid and make a vertical slice cutting pyramid in half what is the shape of the newly-exposed section
I really appreciate it if you can check my answer. I I think it’s a triangle.
Answer: Triangle
Step-by-step explanation: If you cut it vertically, the base is changed into a triangle.
Hope this helps!
Plz help me with this
Answer: D) at least 6mm
Step-by-step explanation:
95% confidence is 2 standard deviations.
5mm + 2(0.5) = 5 + 1 = 6
The oysters must be at least 6 mm
Quadrilateral ABCD is inscribed in a circle with m<A = (x2)°, m<B = (7x - 10)°,
and
m<C = (3x)°.
What is m<D?
Answer:
106°
Step-by-step explanation:
A quadrilateral inside a circle is a cyclic quadrilateral.
It means that the angles opposite are supplementary (add up to 180).
If we draw the quadrilateral ABCD, the angles A and C are supplementary and the angles B and D are supplementary.
Since we know A and C, we can write:
A + C = 180
x^2 + 3x = 180
x^2 +3x - 180 = 0
(x+15)(x-12) = 0
x= -15, or x = 12
Now, if we put x = -15, some angles become negative, so we disregard it and take x = 12.
Now finding B:
B = 7x - 10
B = 7(12) - 10
B = 74
We also know that B + D = 180, so:
B + D = 180
74 + D = 180
D = 180 - 74 = 106
Find all solutions of the equation in the interval [0, 2 pi) 2 cos0-1=0
Answer:
θ = π/3, 5π/3
Step-by-step explanation:
2 cos θ - 1 = 0
2 cos θ = 1
cos θ = 1/2
θ = π/3, 5π/3
ANSWER
EXPLANATION
The given trigonometric equation is:
[tex]2 \cos( \theta) - 1 = 0[/tex]
[tex] \implies \: 2 \cos( \theta) = 1[/tex]
[tex]\implies \: \cos( \theta) = \frac{1}{2} [/tex]
The cosine ratio is positive in the first and fourth quadrants.
In the first quadrant,
[tex]\theta = \cos ^{ - 1} ( \frac{1}{2}) [/tex]
[tex]\theta = \frac{\pi}{3} [/tex]
In the fourth quadrant,
[tex]\theta =2 \pi - \cos ^{ - 1} ( \frac{1}{2}) [/tex]
[tex]\theta =2 \pi - \frac{\pi}{3} [/tex]
[tex]\theta = \frac{5\pi}{3} [/tex]
Therefore on the interval, [0,2π] the solution to the given trigonometric equation is:
[tex]\theta = \frac{\pi}{3} \: and \: \frac{5\pi}{3} [/tex]
Really need help with this!!!
Answer:
Principal Amount= $500
Formula for compound interest:
[tex]A = p (1 + \frac{r}{n} )^{nt}[/tex]
Formula for simple interest:
A = p(1 + r(t) )
need helpppppp thank you!!
Answer:
I would say 50%
Step-by-step explanation:
The answer is 50%. Hope that helps!
Given the following diagram, find the missing measure.
Answer:
∠4 = a + b
Step-by-step explanation:
Given ∠2 = a and ∠3 = b
The sum of the 3 angles in a triangle = 180°
Subtract the sum of the 2 given angles from 180 for ∠1
∠1 = 180 - (a + b) = 180 - a - b
Now
∠1 and ∠4 form a straight angle and are supplementary, hence
∠4 = 180 - (180 - a - b) = 180 - 180 + a + b = a + b
What is the amplitude, period, and phase shift of f(x) = −4 sin(2x + π) − 5?
Amplitude = −4; period = 2π; phase shift: x = -pie/2
Amplitude = −4; period = π; phase shift: x = pie/2
Amplitude = 4; period = π; phase shift: x = -pie/2
Amplitude = 4; period = 2π; phase shift: x = pie/2
Answer:
Amplitude = -4; period = π; phase shift: x = π/2
Step-by-step explanation:
* Lets revise the trigonometry translation
- If the equation is y = A sin (B(x + C)) + D
* A is the amplitude
- The amplitude is the height from highest to lowest points and
divide the answer by 2
* The period is 2π/B
- The period is the distance from one peak to the next peak
* C is the horizontal shift (phase shift)
- The horizontal shift is how far the function is shifted to left
(C is positive) or to right (C is negative) from the original position.
* D is the vertical shift
- The vertical shift is how far the function is shifted vertically up
(D is positive) or down (D is negative) from the original position.
* Now lets solve the problem
∵ f(x) = A sin (B(x + C)) + D
∵ f(x) = -4 sin (2x + π) - 5 ⇒ take 2 from the bract (2x + π) common factor
∴ f(x) = -4 sin 2(x + π/2) - 5
∴ A = 4 , B = 2 , C = π/2 , D = -5
∵ A is the amplitude
∴ The amplitude is -4
∵ The period is 2π/B
∴ The period = 2π/2 = π
∵ C is the horizontal shift (phase shift)
∴ The phase shift π/2 (to the left)
* Amplitude = -4; period = π; phase shift: x = π/2
The amplitude of the function f(x) = −4 sin(2x + π) − 5 is 4, its period is π, and it has a phase shift of x = -π/2.
Explanation:The amplitude of a trigonometric function like f(x) = −4 sin(2x + π) − 5 is the coefficient in front of the sine function which determines the maximum and minimum value of the function's graph. In this case, the amplitude is the absolute value of -4, which is 4.
The period of the function is found by taking 2π divided by the coefficient of x inside the sine function, which is 2 in this case, yielding a period of π.
The phase shift of the function is determined by solving the equation 2x + π = 0 for x, which gives us a phase shift of x = -π/2. Therefore, the correct description is amplitude of 4, a period of π, and a phase shift of x = -π/2.
Which choice is equivalent to the expression below? square root of negative 20
Answer:
B
Step-by-step explanation:
The expression can be written as
[tex]\sqrt{-20}[/tex]
The - can be taken out from under the radicand and a 2 can be factored out of the expression to leave you with the expression
[tex]2i\sqrt{5}[/tex]
Answer:
Correct option is:
B
Step-by-step explanation:
We have to find a expression which is similar to:
[tex]\sqrt{-20}[/tex]
Now we start solving
[tex]\sqrt{-20}[/tex] could also be written as:
[tex]\sqrt{-2\times 2\times 5}[/tex]
When we take - sign out of the square root it becomes i
i.e. [tex]\sqrt{-1}=i[/tex]
And there are two 2's inside the square root when we take square root it becomes 2
Hence, [tex]\sqrt{-20}=2i\sqrt{5}[/tex]
Hence, Correct option is:
B
Given right triangle XYZ, which correctly describes the locations of the sides in relation to ∠Y?
Answer:
Step-by-step explanation: a is adjacent, b is opposite, c is the hypotenuse
Answer:
D
Step-by-step explanation:
Shelly invested $1,000 at a rate of 5% interest per year. Which equation models the value of the investment, V, after t years?
Answer:
Step-by-step explanation:
You don't say whether this is compound interest or simple interest.
I will assume it's compounding that interests you.
The appropriate formula is
A = P(1 + r)^t, where r is the interest rate as a decimal fraction, t is the time in years, and P is the original amount. Thus:
A = $1000·(1 + 0.05)^t, or A = $1000·(1.05)^t
Please note: There were apparently possible answer choices. Next time, please be sure to list such choices. Thank you.
Final answer:
The equation modeling the value of an investment, V, after t years, for an initial investment of $1,000 at a 5% annual interest rate is V = 1000(1 + 0.05)^t, incorporating the principles of compounding interest.
Explanation:
The question asks about the equation modeling the value of an investment, V, after t years, given an initial investment of $1,000 at a 5% annual interest rate. Using the formula for the future value of a single sum, V = P(1 + r)^t, where P is the principal amount ($1,000), r is the annual interest rate (5% or 0.05), and t is the number of years, we can determine that the equation modeling the value of the investment is V = 1000(1 + 0.05)^t. This formula is applied to calculate the future value of the investment, taking into account the compounding interest over a period t years.
What is the volume of the pyramid 7x7x8
Answer:
The volume of the pyramid is [tex]130\frac{2}{3}\ units^{3}[/tex]
Step-by-step explanation:
we know that
The volume of the pyramid is equal to
[tex]V=\frac{1}{3}BH[/tex]
where
B is the area of the base
H is the height of the pyramid
Find the area of the base B
In this problem we have a square base
[tex]B=7^{2} =49\ units^{2}[/tex]
we have
[tex]H=8\ units[/tex]
substitute
[tex]V=\frac{1}{3}(49)(8)=\frac{392}{3}\ units^{3}[/tex]
Convert to mixed number
[tex]\frac{392}{3}=\frac{390}{3}+\frac{2}{3}=130\frac{2}{3}\ units^{3}[/tex]
you do length x width x be aight divided by 3 to get 392/3
which equation can you use to solve for x
As for a specific equation, I could not say. However, I can tell you how to find x!
The first thing to remember is that a straight line has a 180 degree angle.
You see on the bottom side that we have a 146 degree angle. Now look at the top side. Look closely, and you will see that the two sides are actually identical!
Don't see it? Look at the line on top between x and 56, and imagine it is not there. You see that we actually have the same 146 degree angle, just flipped right side up!
However, this angle does not say 146, but makes an extra line between them with x and 56. This means that x + 56 equals 146!
So we can find x by subtracting 56, from 146, which is... 90!
what is x in -2-3x=19
Answer:
x=-7
Step-by-step explanation:
Since you are solving for x, you need to work backwards. Add 2 to both sides: -2 and 2 cancel out, and 19 plus 2 is 21. Isolate the x by dividing both sides by -3. -3 cancels out, and 21 divided by -3 is -7.
Answer:
-7
Step-by-step explanation
−2−3x=19
−2+−3x=19
−3x−2=19
Step 2: Add 2 to both sides.
−3x−2+2=19+2
−3x=21
Step 3: Divide both sides by -3.
−3x
−3
=
21
−3
x=−7
Express 0.6239 as a fraction.
The value of 0.6239 as a fraction or proportion is
A fraction is a mathematical expression that represents a part or a division of a whole. It is used to represent numbers that are not whole numbers or integers. A fraction consists of two components:
1. Numerator: The numerator is the number on the top of the fraction. It represents the quantity or part of the whole being considered.
2. Denominator: The denominator is the number at the bottom of the fraction. It represents the total number of equal parts into which the whole is divided.
Multiply and divide 0.6239 by 10000,
0.6239 = [tex]\frac{0.6239}{10000} \times[/tex] 10000
= [tex]\frac{6239}{10000}[/tex].
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When Joe got out of bed, it was 58 in his room. He turned on the heater, and the temperature warmed up to 67 in five minutes. How many degrees per minute did the temperature rise?
Answer: 1.8
Step-by-step explanation:
Answer:
1.8
Step-by-step explanation:
(67 degrees - 58 degrees) / 5 minutes
1.8 degrees per minute
solve for b. -1/3b = 9
Answer:
B=-27
Step-by-step explanation:
Answer:
-27
-1/3b=9
Divide both sides by -1/3 to get b by itself
-1/3b=9
/-1/3 /-1/3
b=-27
A dog on intravenous fluids has received 40% of the 1000 mL initially in the i.v. bag. How many mL has it received?
Answer:
The dog should receive 400 mL of the i.v. bag.
Step-by-step explanation:
40% x 1000 = 400
Answer:
The dog received 400mLStep-by-step explanation:
Givens
A dog received 40% of 100 mL of intravenous fluids.To know how many mL the dog received, we just need to find the 40% of 100 mL.
We know that 40% equals 0.40, then we multiply it
[tex]0.40(1000mL)=400mL[/tex]
Therefore, the dog received 400mL
The formula gives the height of an object in free fall at time t and acceleration g.
[tex]h = \frac{1}{2}gt^{2} [/tex]
Solve for t.
[tex]t = (2gh)^{2} [/tex]
[tex]t = 2 \sqrt{gh} [/tex]
[tex]t = \frac{ \sqrt{gh} }{2} [/tex]
[tex]t = \frac{ \sqrt{2hg} }{g} [/tex]
t must equal √2h/g but I don't see that in the choices above
Answer:
t=2hg√g
Step-by-step explanation:
took the test!
which linear function has the same y -intercept as the one that is represented by the graph ?
Answer:
The answer is C: y = 2x + 3
Step-by-step explanation:
I took the test
Linear function is, y = 2 x + 3.
What does the y-intercept of this relationship represent?The slope and y-intercept values indicate characteristics of the relationship between the two variables x and y. The slope indicates the rate of change in y per unit change in x. The y-intercept indicates the y-value when the x-value is 0.Which is a y-intercept of the graphed function?The y -intercept of a graph is the point where the graph crosses the y -axis. (Because a function must pass the vertical line test , a function can have at most one y -intercept . ) The y -intercept is often referred to with just the y -value.How do you find the y-intercept of a graph?On a graph, the y-intercept can be found by finding the value of y when x=0. This is the point at which the graph crosses through the y-axis.According to the question:
From the points we can see the y-intercept of the line is 3 as it passes through point (0, 3).
y = 2 x - 4
y-intercept is -4 ≠ 3, incorrect.
y = 2 x - 3
y- intercept is -3 ≠ 3, incorrect.
y = 2 x + 3
y- intercept is 3 = 3, correct.
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Karoline has 16 marbles oneeight of them are blue how many of coroliens marbles are blue
Answer:
2
Step-by-step explanation:
Total Marbles = 16
Fractional amount blue marbles = 1/8
Number of blue marbles = fractional amount * Total marbles
Number of blue marbles = 1/8 * 16
Number of blue marbles = 2
Answer: 2
Step-by-step explanation:
16 divided by 1/8 = 2
Sarah got 16 out of 20 questions correct on a math quiz is each question was worth the same number of pints and the test was worth 50 points total, what was sarah’s score
The total points could be 50.
It has 20 questions, so each question is worth: 50/20 = 2.5 points each.
She got 16 correct, so her score was: 16 x 2.5 = 40
Apply the distributive property to factor out the greatest common factor.
30+42=
Answer:
[tex]30+42=6(5+7)[/tex]
Step-by-step explanation:
Let [tex]a,b,c\in \mathbb R[/tex], according to the distributive property:
[tex]a(b+c)=ab+ac[/tex]
The prime factorization of 30 is
[tex]30=2\cdot 3\cdot 5[/tex]
The prime factorization of 42 is
[tex]42=2\cdot 3\cdot 7[/tex]
The Greatest common factor is [tex]2\times 3=6[/tex]
[tex]\implies 30+42=6\times5+6\times7[/tex]
[tex]\implies 30+42=6(5+7)[/tex]
Answer:
Step-by-step explanation:
6(5+7
A principal of $3300 is invested at 8.5% interest, compounded anually. How much will the investment be worth after 11 years? Round your answer to the nearest dollar. Please help..
Answer:
[tex]\boxed{\$8378}[/tex]
Step-by-step explanation:
The formula for compound interest is:
A = P(1 + r)ⁿ
Data:
P = 3300
APR = 8.5 %
t = 11 yr
Calculations:
n = 11 × 12 = 132
r = 0.085/12 = 0.007 083
A = 3300(1 + 0.007 083)¹³²
= 3300 × 1.007 083¹³²
= 3300 × 2.5539
= 8378
[tex]\text{The investment will be worth }\boxed{\mathbf{\$8378}}[/tex]
what is x in 25-3x=40
Step 1: Subtract 25 to both sides. This will cancel 25 on the left side and bring it over to the right
(25 - 25) - 3x = 40 - 25
(0) - 3x = 15
-3x = 15
Step 2: Isolate x by dividing -3 to both sides (the opposite of multiplication is division).
-3x ÷ (-3) = 15 ÷ (-3)
x = -5
Check:
25 - 3(-5) = 40
25 + 15 = 40
40 = 40 ....................................Correct!
Hope this helped!
The value of x in this equation is -5.
What is an equation?A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation in algebra.
Equation given in the question:
25 - 3x = 40
25 - 40 = 3x
-15 = 3x
x = -5
The value of x in this equation is -5.
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A tourist has planned a trip to cover the distance of 640 miles, driving at some constant speed. However, when he already covered a quarter of the distance, he took a rest for 1.2 hours. Then, in order to arrive at the destination on time, he increased the speed by 20 mph. How long, actually, the trip lasted?
Answer:
The trip lasted for a total of 8 hours.
Step-by-step explanation:
Distance planned = S = 640 miles
Constant speed = V
Thus the time to be taken would be = T = V/S
We have an equation 640 = VT ----- eq (a)
Time For First Quarter = T/4
speed = V
Distance = 640/4 = 160
After first quarter, there is a rest of 1.2 hours and to complete his trip on time, he increased the velocity by 20 mph.
So, the remaining distance = 640 - 160 = 480 miles.
Speed = V + 20 mph
Time remaining = [(T-T/4) - 1.2] = 3T/4 - 1.2 hours
We have an equation for remaining distance s = vt
=> 480 = (V+20)(3T/4 - 1.2) ----- eq (b)
using eq (a), we have V = 640/T. Putting it in eq (b), we have:
[tex]480 = (\frac{640}{T} + 20)(3\frac{T}{4} - 1.2)\\480 = 480 - \frac{768}{T} + 15T - 24\\=> 15T - \frac{768}{T} -24 = 0\\=> 15T^{2} - 24T - 768 = 0\\[/tex]
Solving the equation, we get T = 8 or T = -32/5(which is not possible.
So, the right answer is T = 8 hours