Hey there! :)
Answer:
x = -5.
Step-by-step explanation:
Solving for x from the equation:
[tex]\frac{2}{3}x - \frac{1}{2} = \frac{1}{3} +\frac{5}{6}x[/tex]
Begin by creating a common denominator for the terms involving x as well as the constants:
[tex]\frac{4}{6}x - \frac{3}{6} = \frac{2}{6} +\frac{5}{6}x[/tex]
Now that each term has a common denominator, we can begin solving for x by isolating the variable:
Subtract 5/6x from both sides:
[tex]\frac{4}{6}x-\frac{5}{6}x - \frac{3}{6} = \frac{2}{6}[/tex]
[tex]-\frac{1}{6}x - \frac{3}{6} = \frac{2}{6}[/tex]
Add 3/6 to both sides:
[tex]-\frac{1}{6}x = \frac{5}{6}[/tex]
Divide -1/6 from both sides. (Multiply by the reciprocal, or -6)
[tex]-\frac{1}{6}x(-6) = \frac{5}{6}(-6)[/tex]
x = -5.
Write a rule in function notation for each situation:
1. Sales tax is 7% of the total price
2. For f(x) = 1/4x + 10, find x such that f(x) = 14
Then,
3. Identify the independent and dependent variables.
"The essay instructions were to write three facts about each person listed."
Answer:
1. [tex]\bold{S=f(P) = 0.07P}[/tex]
2. x = 16
3. Part 1: P is the independent variable and S is the dependent variable.
Part 2: x is the independent variable and y is the dependent variable.
Step-by-step explanation:
1. To write the function notation for:
Sales tax is 7% of the total price.
Let the total price be [tex]P[/tex].
And sales tax be [tex]S[/tex].
As per the given statement:
[tex]S = 7\% \ of\ P\\\Rightarrow S =\dfrac{7}{100}P\\\Rightarrow S=0.07P[/tex]
Writing it in the function notation:
[tex]\bold{S=f(P) = 0.07P}[/tex]
2. To find the value of x such that [tex]f(x) = 14[/tex] and
[tex]f(x) = \dfrac{1}4x + 10[/tex]
Putting the value of [tex]f(x) = 14[/tex]
[tex]14 = \dfrac{1}4x + 10\\\Rightarrow \dfrac{1}4x =14-10\\\Rightarrow \dfrac{1}4x =4\\\Rightarrow x =4\times 4\\\Rightarrow \bold{x =16}[/tex]
3. To find the dependent and independent variable.
Independent variables are those whose value is not dependent on the other variable's values.
Dependent variables are dependent on the value of other variables.
In question 1:
[tex]\bold{S=f(P) = 0.07P}[/tex]
P is the independent variable.
S is the dependent variable.
In question 2:
If we write it as follows:
[tex]y=f(x) = \dfrac{1}4x + 10[/tex]
x is the independent variable and y is the dependent variable.
Finding the Area of a Trapezoid
Use the formula A= 1/2h(b^1+b^2)
What is the area of the trapezoid?_____ square units
Answer: 75 u²
Step-by-step explanation:
1/2(5)((14)+(16))
Add in parenthesis
1/2(5)(30)
Multiply
1/2(150)
Multiply
75
Hope it helps <3
Nadia built a robot to filter air and water efficiently. She expects the robot to filter more than 343 liters of
air and water while using less than 49 Joules of energy.
12A + 8W > 343 represents the number of minutes the robot filters air A and water IV to hiter more
than 343 liters of air and water.
3A +41V < 49 represents the number of minutes the robot hiters air and water while using less than 49
Joules of energy
Does the robot meet both of Nadia's expectations by filtering air for 20 minutes and filtering water for 15
minutes?
Choose 1 answer.
A. The robot meets both of Nadia's expectations.
B. The robot filters the expected amount of air and water, but it doesn't use the expected amount
of energy
C. The robot uses the expected amount of energy, but it doesn't filter the expected amount of air
and water.
D. The robot doesn't meet either of Nadia's expectations.
Answer:
The correct option is;
B. The robot filters the expected amount of air and water, but it doesn't use the expected amount of energy
Step-by-step explanation:
The given requirements are;
Volume of air and water to be filtered by the robot = 343 liters
The amount of energy consumed by the robot < 49 joules
The number of minutes the robot filters air and water to filter more than 343 liters = 12A + 8W > 343
The number of minutes the robot filters air and with less than 49 Joule of energy = 3A + 4W < 49
Given that filtering air takes 20 minutes, filtering water takes 15 minutes, we have;
To filter more than 343 liters, we have
12*20 + 8*15 = 360 > 343
The robot meets the amount of air and water requirement
To filter with less than 49 joules we have
3*20 + 4*15 = 120 > 49
Therefore, the robot does not meet the energy requirement
The correct option is the robot filters the expected amount of air and water, but it doesn't use the expected amount of energy.
Please answer it now in two minutes
Answer:
135.5
hope this helps :)
Pls answer QUICKLY I need this
Answer:
pretty sure this is right
-iota^5
[tex]{ - i}^{5} [/tex]
pls tell me the answer
ill mark it as the brainliest
Answer:
[tex]\boxed{-i}[/tex]
Step-by-step explanation:
[tex]-i^5[/tex]
Use identity : [tex]i^5 =i[/tex]
[tex]-(i)[/tex]
P(x) has factors (x-2), (x+1), and (x-3). Decide if there is only one polynomial that has these factors. Justify your answer.
Answer:
See explanation
Step-by-step explanation:
if multiply the 3 factors together you get
(x² - x - 2)(x - 3) - trinomial x binomial
x³ - 3x²- x² + 3x - 2x + 6 - polynomial
x³ - 4x² + x + 6, this is the polynomial with those factors.
Poly means many so it could be a bigger polynomial with more factors but if it is limited to only these factors than there is just the one polynomial.
The polynomial is x³ - 4x² + x + 6 with factors (x-2), (x+1), and (x-3)
What is polynomial?A polynomial is the defined as mathematical expression that have a minimum of two terms containing variables or numbers. A polynomial can have more than one term.
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.
Operators which let do a basic mathematical calculation
+ Addition operation: Adds values on either side of the operator.
For example 12 + 2 = 14
- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.
for example 12 -2 = 10
* Multiplication operation: Multiplies values on either side of the operator
For example 12*2 = 24
Given that ,
P(x) has three factors (x-2), (x+1), and (x-3).
Multiplying the 3 factors together, we get
⇒ (x-2)(x+1)(x-3)
⇒ [x(x-3) - 2(x+1)](x-3)
⇒ (x² - x - 2)(x - 3)
⇒ x³ - 3x²- x² + 3x - 2x + 6
Rearrange the terms likewise and apply arithmetic operations
⇒ x³ - 4x² + x + 6
Hence, the polynomial is x³ - 4x² + x + 6 with factors (x-2), (x+1), and (x-3).
Learn more about polynomial here:
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Which graph shows the solution to the system of linear inequalities?
y > 2x + 1
y < 2x - 2
y = 2x+1 and y = 2x-2 have the same slope, but different y intercepts. This means the lines are parallel. So the boundary lines are parallel.
y > 2x+1 indicates we'll shade above the y = 2x+1 boundary line
y < 2x-2 tells us to shade below the y = 2x-2 boundary line
Both boundary lines are solid lines (and not dashed line) because of the "or equal to" portion
What results is similar to what you see in choice A. However, the red boundary line should go through (0,1) and not (0,2). The blue boundary line should go through (0,-2) and not (0,-1)
Basically take the graph of choice A and shift everything down 1 unit and you'll have your final answer.
This graph shows the solution to the system of linear inequalities
y ≥ 2x + 1
y ≤ 2x - 2
What is graph?A graph can be defined as a pictorial representation or a diagram that represents data or values.
Graph is y ≥ 2x + 1 and is the red shaded area and dotted means inequality
Graph is y ≤ 2x - 2 and is the blue shaded area and dotted means inequality
Learn more about graph
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What is the approximate length of arc s on the circle below? Use 3.14 for Pi. Round your answer to the nearest tenth. A circle is shown. 2 rays form an angle of 45 degrees. The length of the rays is 8 inches. Arc s contains the angle measuring 45 degrees.
The length of the arc s is 6.283 inches.
Length of an ArcThe length of an arc is given by the formula,
[tex]\rm{ Length\ of\ an\ Arc = 2\times \pi \times(radius)\times\dfrac{\theta}{360}[/tex]
where
θ is the angle, which arc creates at the center of the circle in degrees.
Given to us,Radius, r = 8 in.
Angle, θ = 45°,
Length of the Arc[tex]\rm{ Length\ of\ an\ Arc = 2\times \pi \times(radius)\times\dfrac{\theta}{360}[/tex]
[tex]\rm{ Length\ of\ the\ Arc\ s = 2\times \pi \times(8)\times\dfrac{45}{360}[/tex]
[tex]\rm{ Length\ of\ the\ Arc\ s =6.283\ inches.[/tex]
Hence, the length of the arc s is 6.283 inches.
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The approximate length of arc s on the given circle is; 6.28inches
Length of an arc.The length of an arc is given by the formula;
L = (a/360) ×2πr.where, a = angle subtended by the arcr = radius of the circle.Therefore,
Length, L = (45/360) × 2 × 3.14 × 8
L = 50.24/8L = 6.28 inchesRead more on length of an arc;
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1. How many terms are in the polynomial?
2. What is the degree of the polynomial?
3. How would you classify the polynomial?
Answer:
Step-by-step explanation:
A term, loosely defined, is a product of numbers and variables. Terms are separated from one another with a + or a - sign. So we have 2 terms here.
The degree of the polynomial, because it is just in terms of x and no other variable, is the highest degree'd term. Our highest degree of x is 3, so this is a third degree polynomial.
It is classified by its number of terms:
1 term is a monomial, 2 terms is a binomial, 3 is a trinomial, and anything higher is just called a "polynomial". This has 2 terms so it is a binomial.
The answer is:
⇨ a third-degree binomial.Work/explanation:
Here's how we classify polynomials based on the number of terms:
monomial - has only one term
binomial - has two terms
trinomial - has three terms
polynomial - has four terms or more
As for degrees, those are the highest exponents the polynomial.
Now, [tex]\sf{14x^3+x^2}[/tex] has 2 terms so it's a binomial; the highest exponent is 3.
Hence, this is a third-degree binomial.A realtor uses a lock box to store the keys to a house that is for sale. The access code for the lock box consists of digits. The first digit cannot be and the last digit must be . How many different codes are available? (Note that 0 is considered an even number.)
Answer:
4,500 Codes
Step-by-step explanation:
Given that, the access code consists of 4 digits.
Since, the First digit cannot be zero, and the last digit has to be even.
Therefore, Locks can only use numbers (0-9), which means the first digit has 9 possible outcomes ( 1-9),
the 2nd has 10 possible outcomes (0-10),
the same with the 3rd (0-10) and
finally the 4th has only 5 possible outcomes (0,2,4,6,8),
which we assume that zero is not excluded.
Finally, Mulitply 9 x 10 x 10 x 5 = 4,500.
The bottom cup in a 73 cm tall stack of nested identical cups is 10 cm tall. If each additional cup adds 1.5 cm to the height of the stack, how many total cups are in the stack?
Answer:
43 cups
Step-by-step explanation:
Subtract the height of the one cup from the stack
73 - 10
63
The rest of the cup each add 1.5 cm to the stack
take the remaining height and divide by 1.5 for each cup
63 cm/ 1.5 cm per cup
42 cup
There are 42 cups in the remaining part of the stack
Plus the 1 cup that is 10 cm
42+1 = 43 cups total in the stack
Answer:
[tex]\boxed{\sf 43 \ cups}[/tex]
Step-by-step explanation:
The stack is 73 cm tall, one cup is 10 cm.
Let’s subtract the height of the one cup from the height of the stack.
[tex]\sf 73 - 10\\=63[/tex]
The cups left each add 1.5 cm.
Let x be the cups left.
[tex]\sf 1.5x=63\\x=\frac{63}{1.5} \\x=42[/tex]
Add the 1 to the cups left, because that first cup was subtracted from the height of the stack.
[tex]\sf 42+1\\=43[/tex]
What’s the slope???
(4, 1 2/3) and (-2, 2/3)
Answer:
1/6
Step-by-step explanation:
using this formula
[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
You get 0.1666666666666666666666666666666666666666
which is 1/6
Hope this helped, if it did, please consider giving me brainliest it will help me a lot
Have a good day! :)
Aiko is finding the sum (4 + 5i) + (–3 + 7i). She rewrites the sum as (–3 + 7)i + (4 + 5)i. Which statement explains the error Aiko made by using a mathematical property incorrectly?
Answer:
The error was made when they factored out the i, so this would be the distributive property they did not do correctly.
Factoring out the i was never needed.
Answer:
She shouldn't have factored out the i.
Step-by-step explanation:
In both parentheses, only one of the two additives had an "i" in it, so only one of them could have i factored out of it. If she wanted to factor out the i, the equation would look like this:
(4/i + 5)i + (-3/i + 7)i.
If anything, she should have done:
5i+7i + 4-3=
12i + 1.
Factoring out the i was unnecessary.
Hope this helps!
if you drop a tennis ball from the height of 100in and the rebound is 58in what is the height on the 10th bounce?
Answer:
0.431 inches
Step-by-step explanation:
We were given the following values:
Height the tennis ball was dropped = 100in
Rebound height = 58in
We have to find the rebound ratio
= 58in/100in = 0.58
The formula to be used
Height on nth bounce = Initial height × (Rebound ratio)ⁿ
Where n = number of bounce
Height on the 10th bounce = 100 × (0.58)^10
Height on the 10th bounce = 0.4308042069inches
Approximately, the height on the 10th bounce = 0.431 inches.
2.
Solve the equation.
2
3 x - 2 = 7
Answer:
4/ 3 = 7
Step-by-step explanation:
Answer: x=3
Step-by-step explanation:
first add two to each side
Simplify 7+2 to 9
3x=9
divide both sides by 3.
x=9/3
simplify 9/3 to 3
1)Determine que acción realiza la función definida como: f(x) = -7x - 7 a) Multiplica la variable independiente por -7 y luego resta 7 b) Multiplica la variable independiente por 7 y luego resta 7 c) Multiplica la variable dependiente por -7 y luego resta -7 d) Multiplica la variable dependiente por -7 y luego resta -7 2)Dada la funcion F(x) = -3x + 6 el valor de F(5) es
Answer:
a) Multiplica la variable independiente por -7 y luego resta 7
Step-by-step explanation:
Sea [tex]f(x) = -7\cdot x - 7[/tex], las acciones realizadas por la función sobre la variable independiente, esto es, [tex]x[/tex], son:
1) Multiplica la variable por 7.
2) Refleja el resultado anterior con eje de simetría en el eje x. (Multiplicación por -1).
3) Traslada vertical el resultado de 2) siete unidades en la dirección -y.
Por ende, la opción correcta es a).
1. Use words to write this expression:
9 + 7x
Answer:
nine added to seven times a number.
Step-by-step explanation:
''x'' is the unknown number which is being multiplied by 7. Than 9 is added to it.
Which statement is true of the function f(x) = Negative RootIndex 3 StartRoot x EndRoot? Select three options.
Answer:
Options (2), (3) and (4) are correct.
Step-by-step explanation:
The given function is f(x) = [tex]-\sqrt[3]{x}[/tex]
1). First derivative of the function = f'(x) = [tex]\frac{d}{dx}(-\sqrt[3]{x} )[/tex]
f'(x) = [tex]-\frac{1}{3}(x)^{-\frac{2}{3}}[/tex]
Since derivative is negative, function will be decreasing everywhere.
Therefore, Option (1) is incorrect.
2). Since value of the function is true for every value of all real values of x.
Domain of the function is (-∞, ∞).
Therefore, Option (2) is correct.
3). For the given domain, range of the function will be all real values of y Or (-∞, ∞)
Therefore, Option (3) is correct.
4). Function 'f' when reflected across x axis, equation of the reflected function will be g(x) = [tex]\sqrt[3]{x}[/tex].
Therefore, Option (4) is correct.
5). For a point (3, -27),
-27 = [tex]-\sqrt[3]{3}[/tex]
Therefore, Option (5) is incorrect.
Answer:
The answer is B, C, and D
Step-by-step explanation:
Hope this helps. :)
In Central City, Elm Street and Maple Street are parallel to one another. Oak Street crosses both Elm Street and Maple Street as shown.Tell whether each statement is True or False.
Answer:
a. True, because they are corresponding angles.
b. False, because angles 1 and 2 are supplementary, meaning that they add up to 180 degrees, but 125 + 65 = 190 degrees.
c. True, because they are corresponding angles.
d. True, becuase they are two angles that add up to 180 degrees.
e. True, because they are both interior angles on opposite sides of the transversal.
Answer:
a. True.
b. False.
c. True.
d. True.
e. True.
Step-by-step explanation:
a. This statement is true because angles 6 and 8 are vertical angles. That means they are congruent.
b. This statement is false because Elm Street is a straight line, which means that angles 1 and 2 are supplementary angles and their measures will add up to be 180 degrees. 65 + 125 = 190, which is not equal to 180.
c. This statement is true because angles 5 and 1 correspond to each other.
d. This statement is true because angles 7 and 8 form a straight line.
e. This statement is true because they are interior angles that are alternate.
Hope this helps!
A regular admission for a movie is k8 per ticket seniors only pay k6 per ticket if the revenue for a movie totaled k1440 for an audience of 190 how many seniors attended?
Answer:
Step-by-step explanation: wjbsgstexrczlkcidgxtftwdcwdkfmw,d,f
Sarah has a bag of green and yellow marbles. The number of yellow marbles is 2 less than double the number of green marbles. If you let g be the variable for the green marbles and y be the variable for the yellow marbles, which equation represents the relationship between yellow and green marbles? Sarah has a total of 16 marbles. Which equation represents the total number of marbles she has?Sarah has a bag of green and yellow marbles. The number of yellow marbles is 2 less than double the number of green marbles. If you let g be the variable for the green marbles and y be the variable for the yellow marbles, which equation represents the relationship between yellow and green marbles? Sarah has a total of 16 marbles. Which equation represents the total number of marbles she has?
Answer:
[tex]y = 2g - 2[/tex]
[tex]y + g = 16[/tex]
Step-by-step explanation:
Given
Let g represent the green marbles
Let y represent the y marbles
Required
Determine the relationship between both marbles
The question says that y is 2 less than twice of g
This implies that: [tex]y = 2g - 2[/tex]
The question further states that, Sarah has a total of 16 marbles;
This implies that [tex]y + g = 16[/tex]
So, the system of equation that defines the relationship between y and g are:
y = 2g - 2
y + g = 16
Answer:
edge 2021
Step-by-step explanation:
If you let g be the variable for the green marbles and y be the variable for the yellow marbles, which equation represents the relationship between yellow and green marbles?
✔ y = 2g - 2
Sarah has a total of 16 marbles. Which equation represents the total number of marbles she has?
✔ y + g = 16
please help me explain this correctly..
Answer:
Yes, the ordered pair is correct.
Explanation:
You can check the if the ordered pair by substituting the values into the equation. If you substitute the ordered pair (1, 3), then you can make sure the ordered pair is correct. The equation with the substitution will be 3 = 1 + 2, which results in the true equation 3 = 3, therefore the ordered pair is correct.
Please solve!!! Will make Brainliest!!
Answer:
Pretty Simple!
Step-by-step explanation:
So, according to similar triangles, all the measures of their corresponding angles are equal.
According to the picture, <A corresponds to <D. Thus:
m<D=32 degrees
Hope this helps!
Answer:
C. 32°
Step-by-step explanation:
If two triangles are similar, their corresponding angles must be equal.
∠D corresponds to ∠A, so
∠D = ∠A
∠A = 32°
∴ ∠D = 32°
Given: XY - tangent to circles k1(P) and k2(O) OX=16, PY=6 and OP=26 Find: XY
Answer:
the answer is XY = 24 units.
Step-by-step explanation:
Given:
XY is tangent to the circles with center P and O respectively.
OX=16 units
PY=6 units
OP=26 units
To find:
Side XY = ?
Solution:
As per given statement, the diagram of two circles and their tangent is shown in the diagram.
We need to do one construction here,
Draw a line parallel to tangent XY from P towards OX such that it meets OX at A .
Now, let us consider triangle [tex]\triangle OAP[/tex]. It is a right angled triangle.
With sides Hypotenuse, OP = 26 units
Perpendicular, OA = 16 -6 = 10 units
Base AP is equal to XY.
If we find the value of Base AP, the value of XY is calculated automatically.
Let us use pythagorean theorem in [tex]\triangle OAP[/tex]:
According to pythagorean theorem:
[tex]\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}\\\Rightarrow OP^{2} = AP^{2} + OA^{2} \\\Rightarrow 26^2=XY^2+10^2\\\Rightarrow XY^2 = 676- 100\\\Rightarrow XY = \sqrt{576}\\\Rightarrow XY = 24\ units[/tex]
Hence, the answer is XY = 24 units.
PLEASE HELP!! ASAP
The two square pyramids are similar. The side length of the smaller pyramid is 3/4 the side length of the larger pyramid. Which fraction represents the ratio of the base area of the smaller pyramid to the base area of the larger pyramid? Answer choices: 9/16 or 16/9
I need help with this question! solve “k” -19=b-6
k = b + 13
Step-by-step explanation:k - 19 = b - 6
k = b + 19 - 6
k = b + 13
Answer:
[tex]\boxed{k=b+13}[/tex]
Step-by-step explanation:
[tex]k-19=b-6[/tex]
Add 19 on both sides.
[tex]k-19+19=b-6+19[/tex]
[tex]k=b+13[/tex]
Solve this problem. Reduce to lowest terms.
John worked in his garden for 4 3/4hours on Saturday and 2 1/2 hours on Sunday. How
many hours did he work in all?
6 hours
O 74 hours
4 hours
5 hours
Answer:
7 1/4
Step-by-step explanation:
4 3/4 + 2 1/2 =
4 3/4 +2 2/4 =7 1/4
Answer:
7 1/4 hours
Step-by-step explanation:
4 3/4 + 2 1/2
Get a common denominator
4 3/4 + 2 2/4
6 5/4
Rewriting as
6 + 4/4 + 1/4
6 + 1 + 1/4
7 1/4 hours
The price of sugar increased by 20%. What percent of sugar would the family have to stop using so that they pay the same amount of money each month?
Answer:
9.16
Step-by-step explanation:
We know that
Total expense = price of sugar * consumption
let price of sugar was 100
So total expense = 100*10=1000
But now new expense =1100 (I,e.10% more than 1000)
and new price =120(i,e. 20% more than 100)
So new consumption = new expense/ new price=
1100/120
=110/12
=9.16
HOPE IT HELPS :)
PLEASE MARK IT THE BRAINLIEST!
Answer:
16 2/3 % or approx. 16.67%
Step-by-step explanation:
Original price = 100%
New price = 100+20% = 120%
To reduce back to 100%
we need to reduce 20% from 120 % = 20/120 = 1/6 = 16 2/3 % = 16.7% approx.
Identify the equation of the circle that has its center at (9,12) and passes through the origin
Answer:
(x -9)^2 +(y -12)^2 = 225
Step-by-step explanation:
The equation of a circle with center (h, k) that passes through point (a, b) is ...
(x -h)^2 +(y -k)^2 = (a -h)^2 +(b -k)^2
For your given points, the equation is ...
(x -9)^2 +(y -12)^2 = (0 -9)^2 +(0 -12)^2 = 81 +144
(x -9)^2 +(y -12)^2 = 225