(08.02 LC) Which description best describes the solution to the following system of equations? (1 point) y = −2x + 8 y = −x + 5 Line y = −2x + 8 intersects the origin. Lines y = −2x + 8 and y = −x + 5 intersect the x-axis. Lines y = −2x + 8 and y = −x + 5 intersect the y-axis. Line y = −2x + 8 intersects the line y = −x + 5.
Answer:
The solution to the system of equations is that line y = −2x + 8 intersects the line y = −x + 5.
Step-by-step explanation:
To see why, we can set the equations equal to each other and solve for x:
-2x + 8 = -x + 5
-x = -3
x = 3
Then we can substitute x = 3 into either equation to find the corresponding value of y:
y = -2(3) + 8 = 2
Therefore, the solution to the system of equations is the point (3, 2), which is where the two lines intersect.
A chord is 8 inches away from the center of its circle. This chord is 30 inches long. What, in inches, is the length of the radius?
Answer: The Length of the radius of the circle is 17 inches.
1. a) Write the prime factorization of 17 850
b) Determine the greatest common factor of 735 and 1715.
c) Determine the least common multiple of 450 and 180.
PLS HELP!
The prime factorisation of 17850 is 2 × 3 × 5² × 7 × 17. The Greatest common factor of 735 and 1715 is 245 and the Lowest common multiple of 180 and 450 is 900.
What is prime factorizationPrime factorization is a way of expressing a number as a product of its prime factors. A prime number is a number that has exactly two factors, which includes 1 and the number.
Using prime factorisation:
a). 17850 = 2 × 3 × 5² × 7 × 17
b). Greatest common factor of 735 and 1715 is;
735 = 3 × 5 × 7²
1715 = 5 × 7³
GCF = 5 × 7²
GCF = 244
c). Lowest common multiple of 180 and 450 is;
180 = 2² × 3² × 5
450 = 2 × 3² × 5²
LCM = 2 × 3² × 5³
LCM = 900
Therefore, the prime factorisation of 17850 is 2 × 3 × 5² × 7 × 17. The Greatest common factor of 735 and 1715 is 245 and the Lowest common multiple of 180 and 450 is 900.
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A baseball team played 154 regular season games. The ratio of the number of games they won to the number of
2/5
games they lost was g How many games did they win? How many games did they lose?
Answer: the team won 154g / (g + 1) games and lost 154 / (g + 1) games.
Step-by-step explanation: The mathematical equation "W/L = g" is expressed in a concise manner, wherein "W" refers to weight, "L" refers to the length, and "g" represents the gravitational acceleration. This equation can be utilized in various scientific and academic disciplines, particularly in the field of physics, engineering, and mechanics. The relationship between weight, length, and gravitational acceleration can be further explored and examined through research studies and experiments.
The equation in consideration may be rendered less intricate through the process of multiplication of both sides by L.
"The equation W = gL" can be expressed in an academic manner as follows: The equation denoted by W = gL can be deduced as the product of the gravitational acceleration (g) and the length (L) of an object in a given direction. This equation is commonly used in physics to determine the work (W) performed on an object as a result of a force acting on it, in correlation with the displacement it undergoes in the same direction.
It is understood that the summation of the games won and lost by the team is equivalent to the overall number of games that were played.
The equation denoting the sum of W and L yields a value of 154.
The first equation may now be replaced in the second equation, resulting in:
The mathematical equation GL + L = 154 represents an algebraic expression, where 'G' and 'L' are variables that denote unknown numerical values. The equation dictates that the sum of the values assigned to 'GL' and 'L' must equal to 154. Such equations are commonly used to solve numerical problems in mathematics and related disciplines.
One should perform the mathematical operation of factoring out the variable L on the left-hand side.
The equation L(g + 1) = 154 can be expressed with greater academic rigor.
The sides can be divided by (g + 1) to simplify the equation.
The equation L = 154 / (g + 1) represents a mathematical relationship wherein L is determined by dividing 154 by the sum of g and one.
The aforementioned equation can be utilized to derive a solution for W, ascertaining the relationship that W is equivalent to gL.
The presented expression, W = g(154 / (g + 1)), exhibits a mathematical relationship between the variables W and g, whereby W is a function of g. The numerator of the parenthetical expression, 154, is divided by the sum of g and one, then this ratio is multiplied by g to produce the value of W. The formula can be utilized in various disciplines, such as physics, engineering, and mathematics.
The expression can be simplified to yield:
The expression W can be denoted as 154g / (g + 1) in accordance with the commonly recognized conventions of formal academic writing.
Mary will need to pay National Insurance on her new salary at a rate of 12.5% per month and she also contributes to her pension at a monthly rate of 3.4%
How much will Mary have to pay in National insurance?
The amount of money that Mary has to pay in National insurance with salary X will be 0.125X.
Given that:
Mary must pay National Insurance on her new salary at a rate of 12.5% per month, and she must also make pension contributions at a rate of 3.4% per month.
Assuming Mary's monthly salary is X, then her National Insurance contribution would be:
National Insurance = 0.125X
The amount of money that Mary has to pay in National insurance with salary X will be 0.125X.
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Find the measure of each angle in the triangles shown.
The measure of each angle in the triangle is 60 degrees each
How to determine the measure of the angleTo determine the measure of the angles, we need to note that the sum of the angles in a triangle is equal to 180 degrees.
This is represented as;
<A + <B + <C = 180
From the information given in the diagram, we have;
Then, we have that;
2x - 120 + x - 30 + 1/2x + 15 = 180
add the like terms
2x + x + x/2 = 180 + 120 + 30 - 15
Add or subtract the like terms
3x + x/2 = 315
6x + x/2 = 315
cross multiply the values
7x = 630
Divide both sides by the coefficient
x = 90
Then, the angles are;
2x - 120 = 60 degrees
x/2 + 15 = 60 degrees
x - 30 = 60 degrees
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The value of a waterfront property decreases at a steady rate of 10% each year. What is the total percentage gain (to the nearest integer) in the value of the property at the end of 3 years?
As a result, the overall percentage rise in the property's value after three years is -27.1% to the next integer, which is -27%. This suggests that the property's value has declined by 27% during the last three years.
Compute the overall percentage increase?
Subtraction of the selling price from the buying price. The outcome is the gain or loss. Divide the investment gain or loss by the original amount or purchase price of the investment. Finally, divide the figure by 100 to get the percentage change in investment.
If the property value drops at a consistent rate of 10% every year, the value of the property will be 90% of its previous year's worth at the end of each year. So, after one year, the property is worth 90% of its original value, and after two years, it is worth ninety percent of 90% of its original price, or 81% of its original value. After three years, the asset will be worth 90% at its initial cost, or 72.9 percent of its initial cost
To determine the entire percentage gain, we must first determine the percentage increase from the end number (72.9%) to the original value (100%).The percentage increase is computed as follows:
((Final value - Original value) / Original value) / Original value) x 100%
Substituting the values yields:
((72.9% - 100%) / 100%) x 100% = (-0.271) x 100% = -27.1%
As a result, the overall percentage rise in the property's value after three years is -27.1% to the next integer, which is -27%. This suggests that the property's value has declined by 27% during the last three years.
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the set of odd integer Integer
The set of odd integers between three and five can be found to be D. A null set.
What are odd integers ?An odd number is defined as an integer that cannot be split exactly by two. For example: 1, 3, 5, 7, and so on.
We are asked about the set of odd integers ranging from 3 to 5. Because the question asks for odd numbers between 3 and 5, 3 and 5 will not be considered in the set.
This indicates that 3 and 5 are out. We are left with only one even number, four.
As a result, the set of odd integers between 3 and 5 is a Null Set (it contains no numbers).
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The full question is:
What is the set of odd integers between three and five?
4
3,4,5
all reall numbers
null set
Number graph ranging from negative four to four on the x and y axes. A line with a positive slope is drawn on the graph, passing through the labeled point A at (zero, two) and the labeled point B at three, three). What is the slope of the line passing through points A and B? Responses −3 − 3 , −15 − 1 5 14 1 4 13
The slope of the line passing through points A and B is 1/3.
The formula for the slope of a line to find the slope passing through points A and B. The formula is:
slope = (change in y) / (change in x)
Let's label the coordinates of point A as (x₁, y₁) and the coordinates of point B as (x₂, y₂).
Then, substitute the values and calculate the slope:
slope = (y₂ - y₁) / (x₂ - x₁)
slope = (3 - 2) / (3 - 0)
slope = 1 / 3
Therefore, the slope of the line passing through points A and B is 1/3.
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the expression negative 1 plus tangent x over 1 plus tangent x can be rewritten as which of the following
[tex]\tan(\alpha + \beta) = \cfrac{\tan(\alpha)+ \tan(\beta)}{1- \tan(\alpha)\tan(\beta)} \qquad \tan(\alpha - \beta) = \cfrac{\tan(\alpha)- \tan(\beta)}{1+ \tan(\alpha)\tan(\beta)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{-1+\tan(x)}{1+\tan(x)}\implies \cfrac{-1+\tan(x)}{1-(-1)\tan(x)} \\\\\\ \cfrac{\tan\left( \frac{3\pi }{4} \right)+\tan(x)}{1-\tan\left( \frac{3\pi }{4} \right)\tan(x)}\implies \tan\left( \cfrac{3\pi }{4} + x\right)[/tex]
You owe $2,154.35 on your PBnJ credit card that has an interest rate of 9.85% APR. Rather than placing $435.00 into a savings account earning a 2.5% APR, you pay down the principal at the beginning of the month on the credit card. How much interest did you save? (Hint: Calculate the difference between the interest you would earn from the savings account and the interest you would pay on your credit card for the
Using the monthly interest rate and the principal given the interest saved is -$16.8 which shows that nothing was saved.
How much interest was saved?To find the interest saved, let's calculate the interest paid on the credit card.
Monthly interest = 9.85 / 12 = 0.82%
The monthly interest rate on the card is 0.82%
For that particular month, the interest charged will be;
Interest = 2154.35 * 0.0082 = $17.7
However, the interest earned on the savings account will be;
Interest = 2.5 / 12 = 0.21%
We can calculate the interest earned as;
Interest = 0.0021 * 435 = $0.91
The interest saved can be calculated as 0.91 - 17.7 = -16.8
This shows that nothing was saved as the interest earned is lower than the interest charged.
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find the composition and simplify your answer as much as possible. Write the domain using interval notation.
The composition f∘g is given by (13) / (x - 13).
The domain of the composition is all real numbers except for x = 13, which can be represented in interval notation as (-∞, 13) U (13, ∞).
To find the composition f∘g, we need to substitute g(x) into f(x) in the following way:
f(g(x)) = f(13/x) = (13/x) / ((13/x) - 1)
To simplify this expression, we can multiply both the numerator and denominator by x, which gives us:
f(g(x)) = (13) / (x - 13)
The domain of f(g(x)) is restricted by the domain of g(x), which is all real numbers except for x = 0. Therefore, the domain of f(g(x)) is the set of all real numbers except for x = 13.
Using interval notation, we can write the domain of f(g(x)) as:
(-∞, 13) U (13, ∞)
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The value of y varies directly with x. If x = 3 then y = 21 What is the value of x when y = 105
Answers 15.
Step-by-step explanation:
105 = 7x Now, we can solve for x: x = 105 / 7 x = 15 So, the value of x when y = 105 is 15.
Need help will give brainliest and 5 stars I have 5 minutes please help!
(Check picture for equation)
Write the domain of the rational function r(x) in INTERVAL NOTATION.
Answer: the domain of the given rational function in interval notation is (-∞, -5) U (-5, -2) U (-2, 3) U (3, ∞).
Step-by-step explanation:
The area of a triangle with vertices (6, 6), (2, 4), and (0, 8) is ________ square units.
the area of the triangle with vertices (6, 6), (2, 4), and (0, 8) is 2 square units.
Why is it?
To find the area of a triangle given its vertices, we can use the formula:
Area = 1/2 × |x1×(y2-y3) + x2×(y3-y1) + x3×(y1-y2)|
where x1: $x_1$
x2: $x_2$
y1: $y_1$ are the coordinates of the vertices.
Using this formula and plugging in the given coordinates, we get:
Area = 1/2 × |6×(4-8) + 2×(8-6) + 0×(6-4)|
Simplifying:
Area = 1/2 × |-8 + 4 + 0|
Area = 1/2 × 4
Area = 2 square units
Therefore, the area of the triangle with vertices (6, 6), (2, 4), and (0, 8) is 2 square units.
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The area of the triangle with vertices (6, 6), (2, 4), and (0, 8) is 4 square units.
What is triangle?
A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry. A triangle is defined by its three sides and the three angles formed by those sides.
To find the area of a triangle given its vertices, we can use the following formula:
Area = 1/2 * |(x1*(y2-y3) + x2*(y3-y1) + x3*(y1-y2))|
where (x1, y1), (x2, y2), and (x3, y3) are the coordinates of the three vertices.
Substituting the given coordinates, we get:
Area = 1/2 * |(6*(4-8) + 2*(8-6) + 0*(6-4))|
Area = 1/2 * |-12 + 4|
Area = 1/2 * 8
Area = 4
Therefore, the area of the triangle with vertices (6, 6), (2, 4), and (0, 8) is 4 square units.
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Based on the scatter-plot answer the question: What was the number of visitors when the temperature was 92 degrees? Round it to the whole number.
What is the value of variable 2 if variable 1 is equal 8?
Using Scatterplot, when the temperature is 92, then the number of visitors is 450.
What is a scatterplot?A scatter plot is a graph used to display the relationship between two continuous variables. It visualizes this connection through plotted points, representing one variable plotted against another on both x and y axes.
The x-axis functions as the independent variable, commonly manipulated or changed, while the y-axis acts as the dependent variable, usually observed or recorded.
In conclusion, using scatterplot, when the temperature is 92, then the number of visitors is 450.
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Pleaseee help meee
The sum of three lengths of a fence ranges from 45 to 60 inches. Two side lengths are 9 and 18 inches If the wngth of the third siden xcess compound inequality to show the possible lengths of the third side
Answer:
45 < 9 + 18 + x < 60
45 < 27 + x < 60
18 < x < 33
identify the number pattern and fill in the missing numbers
1) 5, 3, 9, 2, 13
2) 24, 23, 25, 26,
3) 14, 17, 13, 15, 12
1) the number pattern is obscure2) The number pattern seems to be alternating 3) The number pattern seems to be increasing
How to find the aforementioned questions1) The pattern of the numbers is obscure. The connections between the numbers are not immediately apparent.
2) The number pattern seems to be alternating between subtracting 1 and adding 2 to the previous number. The missing numbers are 27 and 28.
3) The number pattern seems to be increasing by 3, then decreasing by 4, then increasing by 2, and so on. The missing numbers are 19 and 16.
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I NEED HELP ASAP!!!!!! GIVING BRAINLIEST TO WHOEVER ANSWERS IT RIGHT!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
The correct pairs are 16 and 30, 26 and 38, 22 and 34.
PLEASE HURRY AND ANSWER
The figure shows a 1175-yard-long sand beach and an oil platform in the ocean. The angle made with the platform from one end of the beach is 85 deg and from the other end is 75 deg Find the distance of the oil platform, to the nearest tenth of a yard, from each end of the beach.
The amount of soda in a randomly selected bottle varies according to a normal distribution with mean 18 ounces and standard deviation 9.7 ounces. What is the probability that a randomly selected bottle will be less than 18 ounces? Enter your answer as a decimal.
Answer:
.05 is the decimal
Step-by-step explanation:
.05 is the decimal answer
Cuál es el resultado (5 3/4) (1/3) (2)
The answer to (5 3/4) (1/3) (2) is 23/6 or 3 5/6.
How to convert mixed fractions to fractions?To multiply fractions and mixed numbers, the mixed number must first be converted to an improper fraction. We can do this by multiplying the whole number by the fraction's denominator and then adding the numerator.
As a result, 5 3/4 can be written as:
5 3/4 = (4 x 5 + 3)/4 = 23/4
We may now multiply the three factors:
(5 3/4) (1/3) (2) = (23/4) * (1/3) * (2)
When we multiply the numerators and denominators together, we get:
(23/4) * (1/3) * (2) = (2312)/(431) = 23/6
As a result, the answer to (5 3/4) (1/3) (2) is 23/6 or 3 5/6.
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Answer:
It is B
Step-by-step explanation:
I just know :D
Theresa earned $120,163 during 2022. On her income taxes she is going to file single and take the standard deduction. Help Theresa calculate her total estimated Federal Taxes for 2022.
2022 Tax Tables:
Theresa's estimated federal income tax for 2022 is $20,430.12.
To calculate Theresa's estimated federal taxes for 2022, we need to use the tax tables provided by the IRS. Here are the steps you can follow;
Determine Theresa's taxable income; To calculate her taxable income, we need to subtract the standard deduction from her gross income. For tax year 2022, the standard deduction for single filers will be $12,950.
Taxable income=Gross income-Standard deduction
Taxable income = $120,163 - $12,950
Taxable income = $107,213
Determine Theresa's tax bracket; To determine Theresa's tax bracket, we need to refer to the tax tables for tax year 2022. According to the tax tables, Theresa's taxable income falls into the 24% tax bracket.
Calculate Theresa's federal income tax; To calculate Theresa's federal income tax, we need to use the formula for her tax bracket. For the 24% tax bracket, the formula is;
Federal income tax = (Taxable income - Lower limit) x Tax rate + Base tax
Using the values for Theresa's tax bracket, we get;
Federal income tax = ($107,213 - $86,375) x 0.24 + $14,605
Federal income tax = $20,430.12
Therefore, federal income tax for 2022 is $20,430.12.
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Pedro tiene 37 canicas más que Daniel y la suma de las canicas que tienen entre los dos es 143. ¿Cuántas canicas tiene cada uno ?
Answer:
53
Step-by-step explanation:
x + (x + 37) = 143
Resolviendo para "x":
2x + 37 = 143
2x = 143 - 37
2x = 106
x = 53
Smashed Pumpkins Company paid $80 in dividends and $519 in interest over the past year. The company increased retained earnings by $432 and had accounts payable of $510. Sales for the year were $16,020 and depreciation was $692. The tax rate was 21 percent. What was the company's EBIT?
The company's EBIT is $1,065.84.
What was the company's EBIT?EBIT, fully known as earnings before interest and taxes is a company's net income before income tax expense and interest expenses are deducted. It is used to analyse performance of core operations without the costs of the capital structure and tax expenses impacting profit.
The net income equals to:
= $80 + $432
= $512
EBT = 432 * (1 - 21%)
EBT = 432 / 0.79
EBT = $546.84
EBIT = $546.84 + $519
EBIT = $1065.84
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if sales tax certain county is 7.2% of the price how much is sales tax on an item the price is $27.30 Round to 2 decimal places
27.30 round to the 2nd decimal place is 27.30.
Now we have to find 7.2% of $27.30.
7.2% of $27.30 is 1.9656.
If you mean that we have to round the answer bt 2 decimal place then the answer is 1.97.
You have 9 gallons of lemonade to sell. You use cone-shaped cups that are 10 centimeters in diameter and 12 centimeters tall. Each customer uses one paper cup. How many paper cups will you need if you sell all of the lemonade? (1 gal ≈ 3785 cm3)
Answer:27 paper cups.
Step-by-step explanation:
The volume of each cone-shaped cup can be calculated using the formula:
V = (1/3)πr^2h
where r is the radius of the cone (half the diameter), and h is the height of the cone.
Substituting the given values, we get:
V = (1/3)π(10/2)^2(12) ≈ 1256.64 cubic centimeters
We can convert the 9 gallons of lemonade to cubic centimeters using the conversion factor given:
1 gallon ≈ 3785 cubic centimeters
Therefore:
9 gallons * 3785 cubic centimeters/gallon ≈ 34,065 cubic centimeters of lemonade
To find out how many paper cups are needed, we can divide the volume of the lemonade by the volume of one cone-shaped cup:
34,065 cubic centimeters / 1256.64 cubic centimeters ≈ 27 cups
Therefore, approximately 27 paper cups are needed to sell all of the lemonade.
when you translate,(x,y+6) will move .
When we translate (x, y) to (x,y+6), will move: 6 units upwards
What is the translation rule?There are different ways of carrying out transformation of objects and they are:
Reflection whereby all the points of an object are reflected or flipped on a line called the axis of reflection or line of reflection
Rotation whereby all points are rotated about a point.
Dilation where the object is reduced or increased by a scale factor.
Translation where the object is moved from one point to another.
Now, we are told about the translation given as (x, y + 6) which was translated from (x, y). Thus:
This tells us that the initial graph has moved upwards by 6 units.
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The equation of the line l passing through (4, 3) and parallel to d: 4x + 5y = 1 is l: 16x + by = c. What is the value of b? Please answer with steps.
Hi duasara! It is my pleasure to answer this question for you with step-by-step instruction.
Okay, two lines are parallel if they have the same slope. The equation of line d is 4x + 5y = 1. Solving for y, we get:
5y = -4x + 1
y = (-4/5)x + 1/5
So the slope of line d is -4/5.
Since line l is parallel to line d, it also has a slope of -4/5. The equation of line l is given as 16x + by = c. Solving for y, we get:
y = (-16/b)x + c/b
Comparing this with the equation y = (-4/5)x + 1/5 for line d, we see that the slope of line l is -16/b, which must equal -4/5. Therefore:
-16/b = -4/5
Multiplying both sides by -5b, we get:
80 = 4b
b = 20
Therefore, the value of b is 20.
