Answer: -7/1
Step-by-step explanation: When graphing both points and drawing a line through it, count how many times it goes up or down and then count how many times it goes left or right.
for what values of x and y are the triangles congruent by HL?
For the given congruent triangles, the values of x = -1 and y = 3.
What do you mean by congruence of triangle?Two triangles are congruent if all three corresponding sides are equal and all three corresponding angles are equal. These triangles can be moved, rotated, flipped, and flipped to look identical. When rearranged they match each other.
The congruence symbol is "≅".As both the triangles are congruent therefore their corresponding sides will be equal.
3y + x = y + 5 ...........(1)
y - x = x + 5 ..............(2)
Equation
1:3y + x = y + 5
3y - y = 5 - x
2y = 5 - x
x = 5 - 2y ..............(3)
Substitute this value of x in equation (2)
y - x = x + 5 y = x + x + 5y
= 2x + 5 y = 2(5 - 2y) + 5y
= 10 - 4y + 54y + y = 15
5y = 15 y = 15/ 5
y = 3
Substitute this value of y in equation (3) x = 5 - 2(3) = 5 - 6 = -1
Therefore, x = -1 and y = 3
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Explain how to solve 2^(x + 1) = 9 using the change of base formula log base b of y equals log y over log b. Include the solution for x in your answer. Round your answer to the nearest thousandth
The solution of the given expression is equal to 2.17.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression is [tex]2^{x+1} = 9[/tex]. The expression will be solved by using the logarithmic property below,
[tex]2^{x+1}=9[/tex]
Take logs on both sides,
(x+1) ln(2) = ln(9)
(x+1) = ln(9) / ln(2)
x + 1 = 3.17
x = 2.17
Hence, the expression will be solved by taking log on both sides.
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suppose a juice box contains 30% juice with the remaining portion of the drink composed of water. what is the solute in this type of juice box?
Suppose a juice box contains 30% juice with the remaining portion of the drink composed of water alcohol is the solute in this type of juice box.
Ethanol; Ethanol, a drab liquid with a pleasing scent this is produced evidently from fermentation through yeasts and different microorganisms. It is utilized in alcoholic beverages, as a solvent, and withinside the manufacture of different chemicals. Ethanol is a fairly poisonous and colorless compound.
Alcohol is the solute in this type of juice box is the solvent as alcohol is easily soluble as the solvent and has best property of a solute and csn pass through the semipermeable permeability and others solvent also. The alcohol is actually acting as the solute here to dissolve the solvent.
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Given f(x) = x² - 1 and g(x) = x + 5, find h(x) = (f. g)(x).
The function h(x) = (f.g)(x) would be x² + 10x + 24.
What are composite functions?
A composite function is generally a function that is written inside another function. The composition of a function is done by substituting one function into another function. For example, f [g (x)] is the composite function of f (x) and g (x). The composite function f [g (x)] is read as “f of g of x”.
To find h(x) = (f.g)(x), we need to find the composition of the functions f(x) and g(x).
The composition of two functions f(x) and g(x) is denoted by (f.g)(x) and is defined as (f.g)(x) = f(g(x)).
In this case, we have:
h(x) = (f.g)(x) = f(g(x)) = f(x + 5)
Substituting x + 5 for g(x) in the equation for f(x), we get:
h(x) = (f.g)(x) = f(x + 5) = (x + 5)² - 1
Simplifying this expression, we get:
h(x) = (f.g)(x) = x² + 10x + 24
Hence, the function h(x) = (f.g)(x) would be x² + 10x + 24.
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If A=45° B = 30°, prove that
Sin (A-B) = sinAcos B - Cos Asin B
To prove that Sin (A-B) = sinAcos B - Cos Asin B, we can use the angle subtraction formula for sine:
Sin (A-B) = Sin A Cos B - Cos A Sin B
This formula is derived from the identity:
Sin (A-B) = Sin A Cos B - Cos A Sin B
which can be derived by using the double angle identities for sine and cosine:
Sin (2A) = 2 Sin A Cos A
Cos (2A) = Cos^2 A - Sin^2 A = 2 Cos^2 A - 1 = 1 - 2 Sin^2 A
Substituting these identities into the identity above, we get:
Sin (A-B) = Sin A Cos B - Cos A Sin B
What is an angle subtraction?Angle subtraction formulas is otherwise known as angle subtraction identities. This angle subtraction formulas permit us to find the exact values of less common trigonometric angles by expressing the less common angle as the difference of two common angles. For example, 15 degrees = 45 degrees - 30 degrees.
Therefore, Sin (A-B) = sinAcos B - Cos Asin B.
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What i cot of tiling a rectangular plot of land 500m long and 200m wide at the rate r 8 per q m
The cost of tilling a rectangular plot of land 500m long and 200m wide at the rate of rs 8 per sq m is Rs. 8,00,000.
Area of rectangle = length × breadth
Area of rectangular plot = 500× 200 = 1,00,000 sq m
Cost of tilling 1 sq m of land = Rs. 8
Cost of tilling 1,00,000 sq m of land = 8 × 1,00,000 = Rs. 8,00,000
Thus, The cost of tilling a rectangular plot of land 500m long and 200m wide at the rate of rs 8 per sq m is Rs. 8,00,000.
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Deposited (dollars)
12,500
10,000
7,500
$5,000
rate of change=
2,500 initial value=
Time (years)
y
dollars per year
dollars
The rate of change is $2500 per year.
The initial amount is $5000.
What is slope?The value of the steepness or the direction of a line in a coordinate plane is known as the slope of a line, often known as the gradient. Given the equation of a line or the coordinates of points situated on the straight line, slope can be determined using a variety of techniques.
The formula for slope between two points (x₁, y₁) and (x₂, y₂) is,
m = (y₂ - y₁)/(x₂ - x₁)
In the given graph,
The initial value that deposited at x = 0 is $5000.
To find the rate of change in amount per year,
Find slope of the line, because rate of change will be equal to slope.
Let two points are (0, 5000) and (1, 7500)
The slope = (7500 - 5000 / 1 - 0) = 2500
The rate of change is $2500 per year.
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What is the value of 24 + x ÷ 12 when x = −180?
17
9
−13
−178
If you don't know the answer please do not type random stuff or you'll see what ima do
The value of the expression 24 + x ÷ 12 when x = −180 is (b) 9
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to determine the value of the expression?From the question, we have the following parameters that can be used in our computation:
24 + x ÷ 12
Also, we have the value of the variable to be
x = −180
Substitute the known values in the above equation, so, we have the following representation
24 - 180 ÷ 12
Evaluate the quotient in the above equation
So, we have the following representation
24 - 180 ÷ 12 = 24 - 15
Evaluate the difference in the above equation
So, we have the following representation
24 - 180 ÷ 12 = 9
Hence, the value of the expression is (b) 9
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Find the perimeter and total area of the composite shape shown below. All measurements are given in inches. Use = 3.14 in
any formulas used.
The area of the composite shape is 292.96 in² and the perimeter of the composite shape is 65.12 inches
Area of Half circle:The quantity of surface contained within a semicircle's perimeter is known to as its area.
The formula for the Area of a half circle with a Radius (r) is given by
Area of Half circle = πr²/2
The formula for the perimeter of a half circle with a radius (r) is given by
Perimeter of Half circle = πr
Here we have
A picture of a Rectangle with a half circle
Dimensions of Rectangle = 16 in × 12 in
=> Area of rectangle = 16 in × 12 in = 192 in²
=> Perimeter of rectangle shape = 12 + 16 + 12 = 40 inches
[ Here we only take one side of the rectangle since one of the sides is connected with a Half circle ]
The radius of half circle = 8 inch
=> Area of Half circle = π(8)² = (3.14)(64)/2 = 100.96 in²
=> Perimeter of Half circle = πr =(3.14)(8) = 25.12 in
Area of the composite shape
= Ractangle's Area + Half circle's Area
= 192 in² + 100.96 in²
= 292.96 in²
The perimeter of the composite shape
= Ractangle perimeter + Half circle perimeter
= 40 inches + 25.12 inches
= 65.12 inches
Therefore,
The area of the composite shape is 292.96 in² and the perimeter of the composite shape is 65.12 inches
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2. How many points of inflection will f(x) = 3x5+2x4 - 5x - 12 have?
5
3
2
4
2 points of inflection will f(x) = 3x5+2x4 - 5x - 12 have.
What is Inflection points definition?
An inflection point is a point on the graph at which the second derivative is equal to zero or undefined and changes sign.
The characteristic that every input is associated to exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs. A mapping from A to B will only be a function if every element in set A has one end and only one image in set B. Let A & B be any two non-empty sets.
If [tex]$f^{\prime \prime}(x) > 0$[/tex]then f(x) concave upwards.
If [tex]$f^{\prime \prime}(x) < 0$[/tex]then f(x) concave downwards.
[tex]$$f^{\prime \prime}(x)=126 x^5+40 x^3$$[/tex]
Show Steps
Find intervals: Concave Downward: [tex]-\infty < x < 0$, Concave Upward: $0 < x < \infty$[/tex]
Plug x=0 into [tex]$3 x^7+2 x^5-5 x-12: \quad-12$[/tex]
(0,-12)
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a study is conducted to see if a daily exercise intervention affects blood pressure among people with pre-hypertension. one hundred participants are recruited to participate, and half are randomly assigned to participate in the intervention while the others serve as a control group. what study design is being used?
A study is conducted to see if a daily exercise intervention affects blood pressure among people with pre-hypertension. The study design being used is a randomized controlled trial (RCT).
What is a randomized controlled trial?Generally, In an RCT, the study participants are randomly assigned to either the intervention group or the control group. This helps to ensure that any differences between the two groups are not due to preexisting differences between them, but rather are due to the intervention being tested.
In this case, the intervention is a daily exercise intervention, and the outcome being measured is blood pressure among people with pre-hypertension.
The control group serves as a comparison group, and any changes in blood pressure observed in the intervention group can be attributed to the intervention rather than other factors.
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Last winter, a store sold 408 coats in
3 months. This winter, the store plans to sell
coats for 4 months. Based on the average
number of coats sold each month last winter,
how many total coats should the store plan to
sell this winter?
Total coats should the store plan to sell this winter is 952.
Last winter, a store sold 408 coats in 3 months. This winter, the store plans to sell coats for 4 months.
What is sell?
Determine the total cost of all the purchased units. To find the cost price, divide the total cost by the quantity of units purchased. To get the final price, use the formula for selling price (SP), which is: SP = CP + Profit Margin. The cost of the commodity will then be increased by the margin to determine the proper pricing. Retail math describes the mathematical techniques or formulae utilised in the sales industry. It is earning money or receiving change in the most basic sense. Business owners, retailers, managers, and sales representatives all utilise retail math in their daily work.
3month = 408 coats
1 month = 408/3 =136 coats
Then, 4 months = 136*4 = 544 coats
Total coats should the store plan to sell this winter = 544+408 = 952.
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Find the y intercept y = – 17 x + 12.
Answer: 12
Step-by-step explanation:
The y-intercept in the equation that is in slope-intercept form is the constant.
Simplify 4x - 7 + 12x - 3.
Answer:2(8x-5)
Hope this helps!
∠A and \angle B∠B are complementary angles. If \text{m}\angle A=(2x-13)^{\circ}m∠A=(2x−13)
∘
and \text{m}\angle B=(2x+7)^{\circ}m∠B=(2x+7)
∘
, then find the measure of \angle A∠A.
The measure of ∠A is 29.
What is an angle?
An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.
Given that,
m∠A = (2x−13)° and m∠B = (2x+ 7)° and ∠A and ∠B are complementary angles.
Therefore
m∠A + m∠B = 90°
(2x−13)° + (2x+ 7)° = 90°
4x + 6 =90
Subtract 6 from both sides:
4x = 84
Divide both sides by 4:
x = 21
Putting x = 21 in m∠A = (2x−13)°:
m∠A = (2 × 21−13)°
m∠A = 29°
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Justin is going to invest $90,000 and leave it in an account for 19 years. Assuming
the interest is compounded quarterly, what interest rate, to the nearest hundredth of
a percent, would be required in order for Justin to end up with $216,000?
Answer:
4.63%
Step-by-step explanation:
You want the interest rate that, compounded quarterly, will result in a balance of $216,000 for an investment of $90,000 after 19 years.
Compound interestThe formula for the balance of an account earning compound interest is ...
A = P(1 +r/n)^(nt)
where P is the principal invested, r is the annual interest rate, n is the number of times per year interest is compounded, and t is the number of years.
ApplicationFilling in the given values, we can solve for r:
216000 = 90000(1 +r/4)^(4·19)
2.4 = (1 + r/4)^76 . . . . . divide by 90,000
2.4^(1/76) = 1 +r/4 . . . . . . take the 76th root
(2.4^(1/76) -1) = r/4 . . . . . . subtract 1
r = 4(2.4^(1/76) -1) ≈ 0.0463437 ≈ 4.63%
The required interest rate is about 4.63%.
Seven days a year, Tiger Stadium becomes the fifth largest city in the state of Louisiana. Over 92,000 fans pack the stadium to watch the Tigers play. After the game, if the fans leave at a rate of 10% per minute, how long will it take before the stadium is half empty?
It will take 5 minutes before the stadium is half empty
Given that:
Over 92,000 fans pack the stadium to watch the Tigers play
The fans leave at a rate of 10% per minute
The number of fans that leave per minute will be:
10% of 92,000 = 10/100 × 92, 000 = 9,200
The stadium will be fully empty in:
time = 92,000/9,200 = 10 minutes
The stadium will be half empty in:
time = 10 minutes / 2 = 5 minutes
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What is an equation of a line that passes through the points (1, 4) and (2, 9) in
5)
point-slope form? Analyze the steps and fill in the blanks. (4pts)
First, use the two given points to find the slope.
m=
Уг-У1
Use the slope and one point to write an equation of the line in
point-slope form.
Point-slope form of a linear equation.
Substitute
The equation of line in point-slope form of the line, is y = 5x - 1.
What is point - slope form of the line?
The general form of a linear equation is y - y1 = m(x - x1).
It draws attention to the line's slope and one of the line's points (that is not the y-intercept).
Given:
The line passes through the points (1, 4) and (2, 9).
We have to find the equation of line in point - slope form.
First to find the slope from the given points.
Since,
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
Here, [tex](x_1, y_1) = (1, 4), (x_2, y_2) = (2, 9)[/tex]
So, [tex]m = \frac{9-4}{2-1} = 5[/tex]
Now consider, the point slope form of the line
[tex]y-y_1=m(x-x_1)[/tex]
Plug [tex]m = 5, (x_1, y_1) = (1, 4)[/tex]
⇒
[tex]y - 4=5(x-1)\\y-4=5x-5\\y=5x-5+4\\y=5x-1[/tex]
Hence, the equation of line in point-slope form of the line, is y = 5x - 1.
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One of the tallest ferris wheels in the world is in las vegas. It has a diameter, , of 520 feet. The circumference of the ferris wheel represents the distance traveled by a passenger after one full rotation. The circumference can be determined using the expression. What is the distance traveled, in feet, by passengers on each rotation of the ferris wheel? record your answer to the nearest tenth of a foot.
Answer:
Below
Step-by-step explanation:
Circumference of a circle = pi * diameter
circumference of ferris wheel = 3.14159 * 520=1633.6 ft
two thirds of a number b is no more than 12.
two thirds of a number b which is no more than 12, is b ≤ 18
What is inequality ?
In mathematics, an inequality represents the connection between two values in an imbalanced algebraic statement. A sign of inequality can be used to show that one of the two variables is larger than, greater than or equal to, less than, or equal to another value.
According to question
two thirds of a number b = (2/3)b
Given two thirds of number b is no more than 12
⇒ (2/3)b ≤ 12
⇒ 2b ≤ 12*3
⇒ b ≤ (12*3)/2
⇒ b ≤ 36/2
⇒ b ≤ 18
hence the number b whose 2/3 is no more than 12 is, b ≤ 18
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an item is regularly priced at . it is on sale for off the regular price. how much (in dollars) is discounted from the regular price?
An item is regularly priced at, 1.98$ is discounted from the regular price.
A percentage is a portion of a whole expressed as a number between 0 and 100 rather than as a fraction. All of something is 100 percent, half of it is fifty percent, none of something is zero percent. To determine a percentage, you divide the portion of the whole by the whole itself and multiply by 100.
Given that,
First, change the percentage into decimal:
Let us assume,
Sale of regular price = 1%
1% = 1/100 = 0.01
Assume, item regular price is = 2$
Multiply 2 with 0.01:
2 * 0.01 = 0.02
Note that this number 0.02 (0.01 of 2) is the amount off from the original price (2). Subtract 2 from 0.02
2 - 0.02 = 1.98
Therefore,
An item is regularly priced at, 1.98$ is discounted from the regular price.
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3. The vertices for A LML are L(-4,0), M(-2,0) and N(-3,-3). Its image is L'(1,1), M'(3,1) and
N'(2,-2). What is the translation rule that maps the preimage to the image?
The translation rule that maps the preimage to the image is (x, y) ⇒ (x + 5, y + 1)
How to determine the translation rule of the transformationFrom the question, we have the following parameters that can be used in our computation:
Pre-image: L(-4,0), M(-2,0) and N(-3,-3)
Image: L'(1,1), M'(3,1) and N'(2,-2)
The translation rule is calculated as
(x, y) = L' - L
Substitute the known values in the above equation, so, we have the following representation
(x, y) ⇒ (x + 1 + 4, y + 1 - 0)
Evaluate
(x, y) ⇒ (x + 5, y + 1)
Hence, the translation is (x, y) ⇒ (x + 5, y + 1)
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lonzo borrowed 15000$ at 1.2% simple interest to buy a car . after 9 months how much will lonzo owe the bank in interest
The simple interest implies that Lonzo owes $1513.5
How to determine the amount Lonzo owes?The given variables can be represented as:
Loan amount P = $1500
Rate of interest, R = 1.2%
Time to pay back the loan, t = 9 months i.e. 0.75 year
The amount from a simple interest can be calculated using:
A = P(1 + RT)
Substitute the known values in the above equation, so, we have the following representation
A = 1500 * (1 + 1.2% * 0.75)
Evaluate
A = 1513.5
Hence, the amount owed is $1513.5
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Write an equation of the line that passes through the points.
4.(-3,0), (-2, 3)
5. (-6, 10), (6, -10)
4.
find slope;
3 - 0/-2 -(-3) = 3/1 = 3
y = 3x + b
0 = (3)(-3) + b
0 = -9 + b
b = 9
y = 3x + 9
what is the value of the expression 3^{2}*(2^{3} +4)-22
Answer:
86
Explanation:
3² × (2³ + 4) - 22
9 × (8 + 4) - 22
9 × 12 - 22
108 - 22
86
find the least commmon multiple (LCM) for each pair of numbers.To solve the riddle the letters to the numberd lines below 2,5 3,15 6,12 2,15 2,3 8,24 4,10 6,9 7,9
The LCM of the given pairs are 10, 15,12,30,6,24,20,18, and 63 respectively.
What is LCM?The least common multiple (LCM) of two numbers is the lowest possible number that can be divisible by both numbers.
There are 9 pairs, so let's name them using the letters A to I.
The LCM of the first pair A (2, 5) is 10.
The LCM of the pair B (3, 15) is 1*3*5 = 15.
The LCM of the pair C (6, 12) is 3*2*1*2 = 12.
The LCM of the pair D (3, 15) is 2*3*1*5 = 30.
The LCM of the pair E (2, 3) is 1*3*2 = 6.
The LCM of the pair F (8, 24) is 2*2*2*1*3 = 24.
The LCM of the pair G (4, 10) is 2*2*5 = 20.
The LCM of the pair H (6, 9) is 3*2*3 = 18.
The LCM of the pair I (7, 9) is 7*9 = 63.
Hence, 10,15,12,30,6,24,20,18,63 are the LCM of the given pairs.
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Fatimah ate f cookies. Satvinder ate six fewer than two times the number that Fatimah ate. If Satvinder ate 4 cookies, write and solve an equation to find f, the number of cookies Fatimah ate.
If Satvinder ate 4 cookies, then the number of cookies that Fatimah ate will be 5.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Fatimah ate f treats. Satvinder ate six less than twice the number that Fatimah ate.
Let 's' be the number of cookies eaten by Satvinder. Then the equation is given as,
s = 2f - 6
If Satvinder ate 4 cookies, then the number of cookies that Fatimah ate will be given as,
4 = 2f - 6
2f = 10
f = 5
On the off chance that Satvinder ate 4 treats, the number of treats that Fatimah ate will be 5.
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Which is equal to 1/58^8 ? a.58^-8 b.-1/58^-8 c.58^8 d.1/(58)^-8
a) 58^-8 is the same as 1/58^8. we can also simplify the expression by applying the rule for negative exponents to the entire fraction.
How to evaluate this expression ?To evaluate this expression, we can use the rule that any number raised to a negative exponent is equal to the reciprocal of the same number raised to the same positive exponent. In other words, x^-n = 1/x^n.
Applying this rule to the expression 1/58^8, we get:
1/58^8 = 1/(58^8) = 58^-8
Therefore, the correct answer is 58^-8.
It is important to note that the exponentiation operator (^) has higher precedence than the division operator (/), so we need to use parentheses to indicate that the exponent should be applied to the entire denominator before the division is performed. In this case, we can also simplify the expression by applying the rule for negative exponents to the entire fraction:
1/58^8 = (1/58)^8 = 58^-8
This simplification shows that the correct answer is still 58^-8.
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Tabatha and Horatio each leave their separate houses and drive to a restaurant to meet for dinner. Tabatha lives 15 miles from the restaurant, and she drives at a rate of 3 miles every 2 minutes. The graph represents Horatio’s distance, in miles, y, from the restaurant after driving for x minutes.
Tabatha drives 1/12 mile more per minute than Horatio drives.
Tabatha drives 1/6 mile more per minute than Horatio drives
Tabatha drives 3 miles more per minute than Horatio drives.
Tabatha drives 9 miles more per minute than Horatio drives.
Answer:
Tabatha drives 1/6 mile more per minute than Horatio drives
Step-by-step explanation:
Which equation, when paired with y = 2x 5, creates an inconsistent system? 2x y = 5 y = 2x 5 2x – 4y = 10 2y – 4x = –10
The equation that creases an inconsistent system when paired with y = 2x + 5 is given as follows:
2y - 4x = -10.
What is an inconsistent system?A system of equations is called inconsistent when the number of equations of the system is of zero.
The system in this problem is composed by linear equations, which have the following format:
y = mx + b.
In which:
m is the slope.b is the y-intercept.For inconsistent system, we have that the equations:
Have the same slope.Have different intercepts.The function in this problem is given as follows:
y = 2x + 5.
Hence the inconsistent system is formed with:
2y - 4x = -10.
Which is simplified by 2 as follows:
y - 2x = -5.
y = 2x - 5.
Having the same slope of 2, but a different intercept.
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Answer: 2y – 4x = –10
Step-by-step explanation: trust.
