The relationship representing the amount of water remaining in the pool when using the large hose to pump out is
a. 1200 - 60x = y
How to determine the equationThe amount of water to be pumped out = 1200 gallons
The rate of pumping out using the small hose 20 gallons of water per minute. = -20x
let each minute be x, hence every minute 20x volume of water leaves the pond
The equation is represented as
water remaining = 1200 - 20x
in 2 hours, we have 120 minutes, when will the water finish
water remaining = 0 = 1200 - 20x
20x = 1200
x = 1200 / 20
x = 60 minutes hence 1 hour
For the large hose the rate of pumping out is tripled hence
water remaining = 1200 - 60x
y = 1200 - 60x
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Kayla and Kevin have the same-size notebooks.
Kayla covered 5/6 of hers with stickers. Kevin covered 5/8 of his with stickers. Who covered more
8
of the notebook? Explain your answer.
if the second number is lower than that's the answer. so in this case kayla
-6 -5 across the x axis
The reflection of point (-6, -5) across the x-axis will give (-6, 5)
What is reflection?A reflection point occurs when a figure is constructed around a single point, known as the point of reflection or center of the figure.
Given is a point (-6, -5), we need to find the coordinates of the point when it is reflected across the x-axis,
The rule for a reflection across the x-axis -:
The rule for reflecting over the x-axis is to negate the value of the y-coordinate of each point, but leave the x-value the same.
i.e, (x, y) → (x, -y)
Therefore,
(-6, -5) → (-6, 5)
Hence, the reflection of point (-6, -5) across the x-axis will give (-6, 5)
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The question is incomplete, the question is solved for:
Reflect point (-6, -5) across x-axis
Marley surveyed the students in 7th grade to determine which type of social media they most commonly used. The data that Marley obtained is given in the table.
Type of Social Media Headbook Picturegram Tweeter VidTok
Number of Students 85 240 125 50
Which of the following circle graphs correctly represents the data in the table?
a circle graph titled social media usage, with four sections labeled headbook 17 percent, picturegram 48 percent, tweeter 25 percent, and vidtok 10 percent
a circle graph titled social media usage, with four sections labeled vidtok 17 percent, headbook 48 percent, picturegram 25 percent, and tweeter 10 percent
a circle graph titled social media usage, with four sections labeled tweeter 17 percent, vidtok 48 percent, headbook 25 percent, and picturegram 10 percent
a circle graph titled social media usage, with four sections labeled picturegram 17 percent, tweeter 48 percent, vidtok 25 percent, and headbook 10 percent
A circle graph titled social media usage, with four sections labeled vidtok 17 percent, headbook 48 percent, picturegram 25 percent, and tweeter 10 percent.
What is the division?
Division is an arithmetic operation that is the inverse of multiplication. It involves splitting a quantity into equal parts or determining how many times one quantity is contained within another.
If you add all of the numbers together you get 500, but you need to make it 100 percent so you divide the total number by five. to know what percent out of 100 you need to divide all of the variables by 5.
85 ÷ 5 = 17
240 ÷ 5 = 48
125 ÷ 5 = 25
50 ÷ 5 = 10
Hence, A circle graph titled social media usage, with four sections labeled vidtok 17 percent, headbook 48 percent, picturegram 25 percent, and tweeter 10 percent.
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Answer:
BBBBBBBBB
Step-by-step explanation:
• describe how to use bundled things to explain regrouping in the subtraction problem 231-67. Make math drawings to aid your explanation.
The information regarding the addition is explained below.
How to explain the additionAdding 29 + 46:
Student 1: May use the traditional column addition method, lining up the digits in the ones, tens, and hundreds place and carrying over if necessary.
Student 2: May use the breaking apart method, where they break apart the numbers into smaller parts (e.g. 20 + 40) and then add the pieces together.
Student 3: May use a number line, counting up from 29 by the increments of 46 until they reach the sum.
Subtracting 54 - 28:
Student 4: May use the traditional column subtraction method, lining up the digits in the ones, tens, and hundreds place and borrowing if necessary.
Using bundled things to explain regrouping in the addition problem 167 + 59:
First, separate the numbers into bundles of ten.
Next, show how you can regroup the ones as ten ones to make a bundle of ten.
Then add the tens and hundreds place to get the answer 226.
Using bundled things to explain regrouping in the subtraction problem 231 - 67:
First, separate the numbers into bundles of ten.
Next, show how you can regroup the tens as ten tens to make a bundle of a hundred.
Then subtract the hundreds place and the tens place to get the answer 164.
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please help ):
Which triangle is NOT possible given the angle measures?
a
Triangle with angle measures: 26·, 19·, and 135·
b
Triangle with angle measures: 14·, 27·, and 139·
c
Triangle with angle measures: 9·, 18·, and 153·
d
Triangle with angle measures: 8·, 17·, and 152·
Answer: d. Triangle with angle measures: 8·, 17·, and 152·
Step-by-step explanation: i did the test
The triangle not possible is option
What is Triangle?A triangle is a two dimensional figure which consist of three vertices, three edges and three angles.
Sum of the interior angles of a triangle is 180 degrees.
Let us find the sum of the angles for each triangle given.
(a) Triangle with angle measures: 26°, 19°, and 135°·
Sum = 26° + 19° + 135° = 180°
(b)Triangle with angle measures: 14°, 27°, and 139°·
Sum = 14° + 27° + 139° = 180°
(c) Triangle with angle measures: 9°, 18°, and 153°·
Sum = 9° + 18° + 153° = 180°
(d) Triangle with angle measures: 8°, 17°, and 152°·
Sum = 8° + 17° + 152° = 177°, which is not equal to 180°.
Hence the option (d) is not possible.
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Help me please!!!
Unit 8: Right Triangles & Trigonometry
Homework 1: Pythagorean Theorem
and its Converse
The triangles given can be determined to be :
13. Right - angled14. Obtuse triangle 15. Obtuse triangle 16. Acute triangle How to determine the triangles ?You can use the Pythagorean Theorem and its Converse to determine the type of triangle.
The Pythagorean Theorem and its Converse are basically :
c ² = a² + b ² This is a right angled triangle
c ² > ( a² + b ² ) This is an obtuse triangle
c ² < ( a² + b ² )
The triangles are :
13 :
26 ² = 24 ² + 10 ²
676 = 676
Right - angled
14 :
20 ² = 13 ² + 6 ²
400 > 205
Obtuse triangle
15 :
17 ² = 16 ² + 3 ²
289 > 265
Obtuse triangle
16 :
32 ² = 29 ² + 24 ²
1, 024 < 1, 417
Acute triangle
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3x^3-2x^2+7x+9 divided by x^2-3x
The quotient is 3x + 7, and the remainder is (28x + 9) / (x^2 - 3x).
What is Division?A division is a process of splitting a specific amount into equal parts.
We have to find 3x³-2x²+7x+9 divided by x²-3x
3x³-2x²+7x+9 is the dividend and x²-3x is the divisor.
The steps to solve this are given below.
Step 1: Take the first digit of the dividend from the left. Check if this digit is greater than or equal to the divisor.
Step 2: Then divide it by the divisor and write the answer on top as the quotient.
Step 3: Subtract the result from the digit and write the difference below.
Step 4: Bring down the next digit of the dividend (if present).
Step 5: Repeat the same process.
Hence, the quotient is 3x + 7, and the remainder is (28x + 9) / (x^2 - 3x).
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Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
You have a credit card with a balance of $1,367.90 at a 9.5% APR. You pay $400.00 each month on the
due date until the card is paid off. How many months does it take to pay off the card, and what is the total
amount paid including interest?
Be sure to include in your response: answer and steps
Answer:
Step-by-step explanation:
The solution to this problem involves calculating the monthly interest and reducing the balance accordingly each month until the balance reaches zero. Here are the steps:
Calculate the monthly interest: First, we need to calculate the monthly interest rate. We can do this by dividing the APR by 12. The monthly interest rate is 9.5% / 12 = 0.7917%.
Calculate the interest charge for the first month: The interest charge for the first month is the balance multiplied by the monthly interest rate. In this case, the interest charge is $1,367.90 x 0.7917% = $10.87.
Calculate the new balance: Next, we need to subtract the payment from the balance and add the interest charge to determine the new balance. The new balance after the first payment is $1,367.90 - $400.00 + $10.87 = $978.87.
Repeat the steps for subsequent months: Repeat the process of calculating the monthly interest charge and the new balance for each subsequent month until the balance reaches zero.
Keep track of the number of months: As we repeat the steps, keep track of the number of months it takes to pay off the card.
Here is a summary of the calculations:
Month Balance Interest Payment New Balance
1 $1,367.90 $10.87 $400.00 $978.87
2 $978.87 $7.74 $400.00 $586.61
3 $586.61 $4.62 $400.00 $191.23
4 $191.23 $1.50 $400.00 $-208.27
It takes 4 months to pay off the card, and the total amount paid including interest is $1,367.90 + $10.87 + $7.74 + $4.62 + $1.50 = $1392.73.
Write an expression: j with a coefficent 4 - 9
The Expression with coefficient 4 and -9 is 4j and -9j.
What is Expression?
A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:
An absolute numerical number is referred to as a constant.Variable: A symbol without a set value is referred to as a variable.Term: A term can be made up of a single constant, a single variable, or a mix of variables and constants multiplied or divided.Coefficient: In an expression, a coefficient is a number that is multiplied by a variable.Given:
We have to write the coefficient as 4 and -9.
As, coefficient is the number which is just before the variable like in 2x 'x' is the variable and '2' is the coefficient.
So, with coefficient 4 the expression is 4j
and, with coefficient -9 the expression is -9j.
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* Please help, I will mark brainest! *
A farmer can buy 2 types of plant food, mix A & Mix B.
Each cubic yard of mix A contains 20 pounds of acid, 30 pounds of nitrogen & 5 pounds of potash.
Each cubic yard of mix B contains 10 pounds acid, 30 pounds nitrogen & 10 pounds potash.
The minimum monthly requirements are 460 pounds of acid, 939 pounds of nitrogren & 200 pounds of potash.
If mix A costs $25 per cubic yard & mix B costs $49 per cubic yard, how many cubic yards of each mix should the farmer meet the MINIMUM monthly requirements?
Fill in the blank: If mix A costs $25 per cubic yard and mix B costs $40 per cubic yard, the farmer should blend _ yd of mix A & _ yd of mix B to meet the minimum monthly requirements at a minimum cost.
Answer:
Let's call the number of cubic yards of mix A that the farmer buys "x", and the number of cubic yards of mix B that the farmer buys "y".
We can write the following constraints based on the minimum monthly requirements:
20x + 10y >= 460 (for acid)
30x + 30y >= 939 (for nitrogen)
5x + 10y >= 200 (for potash)
We also want to minimize the cost, which is given by 25x + 49y.
This is a linear programming problem, which can be solved using simplex method or the graphical method.
By using the graphical method, we find that the optimal solution occurs at x = 11.75 and y = 4.5. This means that the farmer should buy 11.75 cubic yards of mix A and 4.5 cubic yards of mix B to meet the minimum monthly requirements at a minimum cost.
So, the answer to the question is: If mix A costs $25 per cubic yard and mix B costs $40 per cubic yard, the farmer should blend 11.75 yd of mix A & 4.5 yd of mix B to meet the minimum monthly requirements at a minimum cost.
A differentiable function f(x,y) has the property that f(5,4)=7 and fx(5,4)=-3 and fy(5,4)=7. Find the equation of the tangent plane at the point on the surface z=f(x,y) where x=5, y=4
The equation of the tangent plane at the point (5,4,7) on the surface z=f(x,y) is z = -3x + 7y + 8.
In 3-space, the plane tangent to a surface at a point can be imagined similarly to how we can see the line perpendicular to a curve at a point in 2-space.
The equation of the tangent plane at the point (5,4,7) on the surface z=f(x,y) can be found using the following formula:
z - [tex]z_{0}[/tex] = fx([tex]x_{0}[/tex],[tex]y_{0}[/tex])(x - [tex]x_{0}[/tex]) + fy([tex]x_{0}[/tex],[tex]y_{0}[/tex])(y - [tex]y_{0}[/tex])
where ([tex]x_{0},y_{0},z_{0}[/tex]) is the point on the surface at which we want to find the tangent plane, and fx([tex]x_{0}[/tex],[tex]y_{0}[/tex]) and fy([tex]x_{0}[/tex],[tex]y_{0}[/tex]) are the partial derivatives of f with respect to x and y, respectively, evaluated at ([tex]x_{0}[/tex],[tex]y_{0}[/tex]).
In this case, we have [tex]x_{0}[/tex] = 5, [tex]y_{0}[/tex] = 4, [tex]z_{0}[/tex] = f(5,4) = 7, fx(5,4) = -3, and fy(5,4) = 7. Substituting these values into the formula, we get:
z - 7 = (-3)(x - 5) + (7)(y - 4)
Simplifying this equation, we get:
z = -3x + 7y + 8
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Hallar los primeros cuatro términos de la sucesión dado lo siguiente.
a=59-7(n-1),
n = 1, 2, 3 ...
Using the equation of the arithmetic sequence given, the first four terms are 59, 52, 45 and 38 respectively
What are the first four termsIn the sequence given, the progression is an arithmetic progression since it increases by a common difference.
The first term of the sequence is 59 while the common difference is -7.
A = 59 - 7(n - 1)
n = 1
a = 59 - 7(1 - 1)
a = 59
n = 2
a = 59 - 7(2 - 1)
a = 52
n = 3
a = 59 - 7(3 - 1)
a = 45
n = 4
a = 59 - 7(4 - 1)
a = 38
The terms are 59, 52, 45 and 38
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Translation: Find the first four terms of the sequence given the following
A grinding machine in an auto parts plant prepares axles with a target diameter
The mean of the sampling distribution is given as follows:
37.827 millimeters.
How to obtain the mean of the sampling distribution?The mean of the sampling distribution is obtained using the Central Limit Theorem.
The mean of the sampling distribution is the same as the population mean, hence it is given as follows:
37.827 millimeters.
(on the problem, we are given the population mean).
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10 less triple x is at least 12. Find all the values of x
The value of x for the given expression will be 22/3.
What is an expression?Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.
Given that the expression is triple x less by 10 is at least 12. The mathematical form of the expression can be written as below:-
3x - 10 = 12
3x = 10 + 12
3x = 22
x = 22 / 3
Hence, the value of x for the expression 3x - 10 = 12 is x = 22 / 3.
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The length of each side of an equilateral triangle having an area of square root of 243sq.cm is
Answer:
[tex]\textrm{Each side = 23.6893 cm}\\\\\\\textrm{Rounded to 2 decimal places = 23.69 cm}\\\\\textrm{Rounded to 1 decimal place = 23.7 cm}[/tex]
You can choose the level of precision as desired from the above
Step-by-step explanation:
The area of an equilateral triangle of side a
is
[tex]A = \dfrac{(a^2 \sqrt{3})}{4}[/tex]
We are given A = 243
Plugging in values we get
[tex]243 = \dfrac{a^2\sqrt{3}}{4}[/tex]
Switch sides so [tex]a^2[/tex] term is on the left
[tex]\dfrac{a^2\sqrt{3}}{4} = 243[/tex]
Multiply by 4 both sides to get rid of the denominator:
[tex]\dfrac{a^2\sqrt{3}}{4} \times 4 = 243 \times 4\\\\a^2\sqrt{3} = 972\\\\[/tex]
Divide by [tex]\sqrt{3}[/tex] both sides:
[tex]a^2 = \dfrac{972}{\sqrt{3}}\\\\a^2 = 561.18446\\\\a = \pm \sqrt{561.18446}\\\\[/tex]
Taking only positive square root:
[tex]a = \sqrt{561.18446}\\\\a = 23.6893\\\\[/tex]
helppp mee please ive been trying to get this for a while now
Answer:
[tex]sin(P)=\frac{\sqrt{55}}{10}[/tex]
Step-by-step explanation:
Sine Function:The sine function is defined as a ratio of sides: [tex]sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}[/tex]
where the "opposite" side is quite literally the opposite side, if you went straight from the angle, whatever side it's pointing towards is the opposite angle. The hypotenuse... is as the name implies, the hypotenuse. The symbol inside the parenthesis next to the sine is called theta and is just used to represent some angle.
We of course don't know the hypotenuse as it's not given, but we can use the Pythagorean Theorem to solve for the hypotenuse:
[tex]c^2=\sqrt{45}^2+\sqrt{55}^2\\c^2=45+55\\c^2=100\\c=10[/tex]
We do know the opposite side though, it's just the square root of 55, it's directly opposite of the angle P. Plugging in known values we get the following: [tex]sin(P)=\frac{\sqrt{55}}{10}[/tex] and we can't simplify this any further as 45 has no factors which are perfect squares.
just confusing can someone help due today
Step-by-step explanation:
It's a long answer. You have to find the area of the large triangle, the small triangle than subtract the two
A = 1/2(b)(h)
For the big triangle
A = 1/2(16)(4) = 1/2(64) = 32
For the small triangle
A = 1/2(8)(2)
We use 8 and 2 because that's half of 16 and 4, since at the bottom it says A and B are midpoints
A = 1/2(8)(2) = 1/2(16) = 8
Now we subtract
32-8 = 24 units
A textbook store sold a combined total of 426 math and sociology textbooks in a week. The number of math textbooks sold was 46 more than the number of sociology textbooks sold. How many textbooks of each type were sold?
Answer:
The number of books sold were:
Math textbooks: 426
Sociology textbooks = 46
Step-by-step explanation:
Let us use the variable [tex]m[/tex] to represent the number of math books sold
Let us use the variable [tex]s[/tex] to represent the number of math books sold
Combined total of 426 math and sociology books were sold is represented by the equation:
[tex]m + s = 426\quad\quad\quad(1)[/tex]
Number of math books sold was 46 more than the number of sociology textbooks sold is given by
[tex]m - s = 46\quad\quad\quad(2)[/tex]
Adding the equations (1) + (2):
[tex](m + s) + (m - s) = 426 + 46\\\\2m = 472\\\\m = \dfrac{472}{2}\\\\m = 236\\\\[/tex]
Using Equation (1): [tex]m + s = 426[/tex] we get
[tex]236 + s = 426\\\\s = 426 - 236\\\\s = 190[/tex]
I will give brainliest to whoever answers this correctly.
Answer:
1625
Step-by-step explanation:
You want the sum of the first 25 terms of the series 5 +10 +15 +....
General termThe first term is 5, the common difference is 5, so the general term is ...
an = a1 +d(n -1)
an = 5 +5(n -1)
Last termThe last term of the sum is ...
a25 = 5 +5(25 -1) = 125
SumThe sum of the series is the average of the first and last terms, multiplied by the number of terms:
S25 = (a1 +a25)/2 · 25 = (5 +125)/2 · 25 = 65·25 = 1625
The sum of 25 terms of the series is 1625.
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Which of the following equations are nonlinear? (Select all that apply)
Answer:
The 3rd and 6th equations
Step-by-step explanation:
Any equation that has a variable with an exponent is nonlinear and the 3rd and 6th equations follow this requirement.
A cell phone plan charges $47.35 per month plus $13.94 in taxes, plus $0.60 per minute for calls beyond the 400-minute monthly limit. Write a piecewise-
defined function to model the monthly cost C(x) (in S) as a function of the number of minutes used for the month.
CG)-{8
for (Choose one) ▼
for (Choose one)
X
The piecewise function for the given problem is;
C(x) = $61.29 x ≥ 400
C(x) = $61.29 + 0.6(x - 400) if x ≥ 400
How to identify the Piecewise Function?A piecewise function is defined as a function that has different definitions depending on which values of x are being used. Piecewise functions are called "piecewise" due to the fact that they are made of "pieces" with different function definitions. To evaluate a piecewise function for a given value of x, find which interval your value fits in, and then use that definition of the function to evaluate.
First, we will find the monthly cost if the 400-minute monthly limit is not exceeded. Then, the total cost would be;
47.35 + 13.94 = 61.29 with just the plan and taxes. So if x ≤ 400, then;
C(x) = 61.29
Now if the 400 minutes is exceeded, the bill will also include $0.60 per additional minute. To find the number of additional minutes, we can take the total number of minutes x and subtract 400. In general, the cost would be;
C(x) = $61.29 + 0.6(x - 400) if x ≥ 400
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The graph of a function is shown below. Describe the relationship between the number of gallons of gas and the cost in dollars. Explanation too please
The relationship between the number of gallons of gas and the cost in dollars is: C. The cost of gas is $3.75 per gallon.
What is a proportional relationship?In Mathematics, a proportional relationship is a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:
y = kx
Where:
x represent the number of gallons of gas.k is the constant of proportionality.y represent the cost of gas in dollars.Next, we would determine the constant of proportionality (k) for the relationship between the number of gallons of gas and the cost in dollars on this graph as follows:
Constant of proportionality, k = y/x
Constant of proportionality, k = 7.5/2
Constant of proportionality, k = $3.75.
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Please help me with this question
Answer:
120°
Step-by-step explanation:
360 / 12
30 X (5-1)
30 X 4= 120°
Figure 1 and figure 2 are right triangles.
two right triangles labeled figure 1 and figure 2, where the legs of figure 1 are 3 units long and the legs of figure 2 are 7 units long
What scale factor was used to produce Figure 2 from Figure 1?
Answer:
The answer
Step-by-step explanation:
Figure 1 figure
3/4
What is one unconventional use of word choice that Anaya employs in this passage?
What is one text structure that Anaya uses to create voice in this passage?
Tone is the feeling the author wants the reader to have when reading his or her work. Anaya employs tone to generate the texts "Take the Tortillas out of your poetry" and "Speaking Arabic."
Which of Anaya's word choices in this text stands out as being unusual?Both authors explore regional cuisine and make use of terminology from various languages.
The subject of heritage is covered by both writers.Both writers employ anecdotes.Pathos is used by both writers.Anaya makes use of logos.While Nye's tone is welcoming of mixed cultures, Anaya's tone is sincere towards culture and indignant towards suppression.
What voice does Ananya utilise throughout and why?The funny tone of Anaya's writing reflects his intention to draw attention to the subject. The laid-back nature of Anaya's delivery is evident.
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INDUSTRY Two identical right cylindrical steel drums containing oil need to be covered with a fire-resistant sealant. In order to determine how much sealant to purchase, George must find the surface area of the two drums.
The surface area, including the top and bottom bases, is given by the
formula S = 2πrh + 2πr^2
Note that the Polynomial Expression for to represent the total surface area of the two drums is: 4πrh + 4hr².
What is a polynomial expression?A polynomial expression is any expression that consists of variables, constants, and exponents and is combined using mathematical operators such as addition, subtraction, multiplication, and division.
According to the number of terms in the expression, polynomial expressions are classed as monomials, binomials, or trinomials.
Given that the total surface area of one cylinder is:
2πrh + 2πr²,
The total surface area of two drums will therefore be:
(2πrh + 2πr²) * 2
⇒ 4πrh + 4hr²
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XIII.4.11. Află două numere naturale care îndeplinesc simultan condiţiile:
a) diferenţa lor este egală cu sfertul sumei lor;
b) diferenţa dintre suma şi diferenţa lor este 108. VA ROG RAPIDDD DAU COROANA
Answer:B
Step-by-step explanation:
Find the value of x that will make L||m
Answer:
x=-13
Step-by-step explanation:
Since the two angles given are equivalent, you set up the equation as 7x+205=114.
7x+205=114
7x=114-205
7x=-91
7x/7=-91/7
x=-13
Hope this helps! Please give brainliest!
Inga is solving 2x2 + 12x – 3 = 0. Which steps could she use to solve the quadratic equation? Select three options. 2(x2 + 6x + 9) = 3 + 18 2(x2 + 6x) = –3 2(x2 + 6x) = 3 x + 3 = Plus or minus StartRoot StartFraction 21 Over 2 EndFraction EndRoot 2(x2 + 6x + 9) = –3 + 9
The steps that she could use to solve the quadratic equation is determined as 2(x² + 6x + 9) = 18 + 3.
Solution to the quadratic equation
The solution to the quadratic equation is determined as follows;
2x² + 12x - 3 = 0
2x² + 12x = 3
divide through by 2
x² + 6x = ³/₂
take half of coefficient of x, square it and add it both sides of the equation
(x + 3)² = ³/₂ + 3²
x² + 6x + 9 = 9 + ³/₂
2(x² + 6x + 9) = 18 + 3
Thus, the steps that she could use to solve the quadratic equation is determined as 2(x² + 6x + 9) = 18 + 3.
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A new coffee shop projects that its annual profit, p(t), in thousands of dollars, over the first 6 years in business can be
approximated by the function p(t) = 0.3t² +5.5t-8 where t is measured in years.
The amount of profit that the new coffee shop will make after 6 years is; 35.8 thousand dollars
How to solve Quadratic Equations?The quadratic equation that represents the annual profit made by the new coffee shop in thousands of dollars is;
p(t) = 0.3t² + 5.5t - 8
where;
t is the number of years for which the profit is measured
Thus, after 6 years, we will substitute 6 for t in the quadratic equation to get;
p(6) = 0.3(6)² + 5.5(6) - 8
p(6) = 10.8 + 33 - 8
p(6) = 35.8 thousand dollars
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