Answer:
Triangle ABC is being enlarged using a scale factor of 2 and the origin as the center to give triangle A'B'C'. To find the coordinates of A' and B', we will have to multiply each of the x and y coordinates of A and B by the scale factor of 2.
The coordinates of A are (-5, -6) and the coordinates of B are (2, 3)
The coordinates of A' will be (-52, -62) = (-10, -12)
The coordinates of B' will be (22, 32) = (4, 6)
So the coordinates of A' are (-10, -12) and the coordinates of B' are (4, 6).
Determine weather the mean value theorem can be applied to f(x)= sqrt(5-x) on (-4,5) find all values of c in (-4,5) such that f’(c)= f(b)-f(a)/b-a if possible
Answer:2.75 (or 11/4, they are equal).
Step-by-step explanation: The graph of f(x) is continuous on the closed interval and differentiable on the open interval. Now we need to find the average slope over the interval, which is [0-3]/[5-(-4)] = -3/9 = -1/3. The goal is to find a place where f'(c) = -1/3, so basically anywhere where the derivative equals -1/3. First we need to find the derivative of the function which can be rewritten as (5-x)^(1/2). Differentiating this using the chain rule gives you -1/(2*sqrt(5-x)). Set this equal to -1/3. The numerator is -1, so really we just need to find where the denominator, 2sqrt(5-x), is equal to 3. Divide by 2 and get sqrt(5-x) = 3/2. Square both sides and get 5-x = 9/4. Subtract 5 and get -x = -2.75, so x = 2.75. This means c = 2.75.
Which of the sets of equations represent the two lines graphed?
Responses
A y = -x + 2 and y = -x - 4y = -x + 2 and y = -x - 4
B y = x - 2 and y = -x - 4y = x - 2 and y = -x - 4
C y = x + 2 and y = x - 4y = x + 2 and y = x - 4
D y = x + 2 and y = -x - 4y = x + 2 and y = -x - 4
E y = -x + 2 and y = x - 4y = -x + 2 and y = x - 4
The linear equations for the graph is obtained to be option D: y = x + 2 and y = -x - 4.
What is a linear equation?
A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.
The graph of two lines are given.
For the first line going from top left corner to bottom right corner, the point of coordinates are (-5, 1) and (-3,-1).
The slope-intercept form of an equation/function is - y = mx + b
To find the slope m use the formula -
(y2 - y1)/(x2 - x1)
Substituting the values in the equation -
[-1 - 1]/[-3 - (-5)]
(-2)/(2)
-1
So, the slope point is obtained as m = -1.
The equation becomes - y =-x + b
To find the value of b substitute the values of x and y in the equation -
-1 = -(-3) + b
-1 = 3 + b
b = -1 - 3
b = -4
So, the value for b is -4.
Now, the equation becomes -
y = -x - 4
Now, for the second line going from bottom left corner to top right corner, the point of coordinates are (-1, 1) and (-3,-1).
The slope-intercept form of an equation/function is - y = mx + b
To find the slope m use the formula -
(y2 - y1)/(x2 - x1)
Substituting the values in the equation -
[-1 - 1]/[-3 - (-1)]
(-2)/(-2)
1
So, the slope point is obtained as m = 1.
The equation becomes - y = x + b
To find the value of b substitute the values of x and y in the equation -
-1 = (-3) + b
-1 = -3 + b
b = -1 + 3
b = 2
So, the value for b is 2.
Now, the equation becomes -
y = x + 2
Therefore, the two equations are y = -x - 4 and y = x + 2.
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find two consecutive numbers whose cubes differ by 217
The two consecutive numbers whose cubes differ by 217 are n=-9 or n=8.
How can the two consecutive numbers be calculated?The concept that will be used here is factorization. Consecutive numbers are those that follow one another continually, from lowest to largest. For instance, the numbers 1, 2, 3, 4, 5, and so on are all consecutive.
The number can be arranged as
(n+1)^3 -n^3=217
We can simplified this as:
[n^3+3n^2 +3n+1 -n^3]=217
3n^2+3n+1=217
This can be simplified as :
3n^2+3n-216=0
This can be factorized as
(n+9)(n-8)=0
n=-9 or n=8
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Could someone please help! been struggling on these for a few mins !
The simplification of the logarithm expression are as shown below
How to simply logarithm expressions?A logarithm expression is a mathematical statement that involves logarithms. It is an expression that contains logarithmic functions, such as log, ln, logₐ, etc. These expressions can include logarithms with different bases, numbers in logarithm form, and exponents.
The logarithm expressions can be simplified as follow:
1. since logₐa = 1,
log₄4 = 1
2. Since logₐ1 = 0,
log₁₀1 = 0
3. since logₐ(M × N) = logₐM - logₐN and logₐa = 1
log₃4 × 3 = log₃4 + log₃3 = log₃4 + 1
4. since logₐxⁿ = n logₐx and logₐa = 1
log₄4³ = 3 log₄4 = 3 × 1 = 3
5. since logₐxⁿ = n logₐx and logₐa = 1
logₓx⁰ = 0 logₓx = 0 × 1 = 0
6. since logₐxⁿ = n logₐx and logₐa = 1
logₓx³ = 3 logₓx = 3 × 1 = 3
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What is the value of f(m) = 55?
Answer:
Step-by-step explanation:The exponent of a number shows how many times the number is multiplied by itself.
According to the rules of exponents,
We know that, am ÷ an = am − n
(5m ÷ 5−3) = 55
5m−(−3) = 55
5m + 3 = 55
The bases are the same on both the sides, so their exponents must be equal.
∴ m + 3 = 5
⇒ m = 5 − 3
⇒ m = 2
Choose the expression that is equivalent to fraction with 5 raised to the negative tenth power in the numerator and 5 raised to the fourth power times 5 raised to the zero power in the denominator.
negative 1 divided by 5 raised to the fourteenth power
−514
1 divided by 5 raised to the fourteenth power
514
The equivalent expression is 1 divided by 5 raised to the fourteenth power 5^14. Option B
What are index forms?The index form of a number is described as the number written as an exponential expression, or even a single number that is raised to another number.
This exponent, or index form, of an exponential expression tells us the number of multiple times to multiply the base by itself to simply the expression.
Other names for index forms are scientific notation or standard forms.
From the information given, we have that;
5 raised to the negative tenth power in the numerator = 5⁻¹⁰ 5 raised to the fourth power times 5 raised to the zero power in the denominator = 5⁴ × 5⁰This is represented as;
5⁻¹⁰/5⁴ × 5⁰
Any number raised to zero = 1
5⁻¹⁰/5⁴
subtract the exponents
5⁻¹⁰⁻⁴
5⁻¹⁴
Hence, the value is 5⁻¹⁴
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x+2=4(2x + 3)-3
X = ?
Answer:
x= 3x/7 - 10/7
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Answer:
x = -1Step-by-step explanation:
x+2=4(2x + 3)-3
x+2=8x+9
2=8x+9−x
2=7x+9
2-9=7x
-7=7x
-7/-7=7x/-7
-1 = x
x=-1
Angel read 1 3 of a book in the morning, and he read some more at night. By the end of the day, he still had 1 4 of the book left to read. How much of the book did Angel read at night?
The Angel read 5/12 of the book at night if Angel read 1/3 of a book in the morning, and he read some more at night. By the end of the day, he still had 1/4 of the book left to read.
What is ratio ?
Ratio can be defined as the given value divided by the total value.
The easiest thing to do first is convert all of these fractions to common denominators, and figure out the rest of the problem from there.
So the common denominator between 1/3 and 1/4 is 12, so convert these to fractions to /12 and continue on.
Think of the whole book being 12/12, and Sarah read 4/12 of it in the morning, so we know she has 8/12 left of it. Since we know she still has 3/12 left to read by the end of the day, we can subtract 8/12 - 3/12 to find out how much she read at night, which is 5/12. This makes sense because when we add all the fractions up (4/12 + 3/12 + 5/12) it comes out to 12/12, which is the whole book.
Therefore, The Angel read 5/12 of the book at night if Angel read 1/3 of a book in the morning, and he read some more at night. By the end of the day, he still had 1/4 of the book left to read.
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suppose you have a column of experimental data in column j and a column of positions for each experimental point in column k. what formula would you put in cell location h10 to find the numerical derivative at position 10 of column k of the data found in j? write your answer in your word document.
The formula would you put in cell location h10 to find the numerical derivative at position 10 of column k of the data found in j is =DERIVXY(h10, k10, j)
The term called derivative is defined as the process to determine the rate of change of a quantity with respect to another changing quantity
Here we have to write the formula for the cell location h10 to find the numerical derivative at position 10 of column k of the data found in j.
As from the definition, the general form derivative function is written as,
=> =DERIVXY(x, y, p, [options])
where x a vector of the points x-coordinates and y corresponding vector of the points y-values and p the point at which to compute the derivative.
Here we have the values of x as h10, y as k10 and p as j
Then the formula is written as,
=> =DERIVXY(h10, k10, j)
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How would paying off the lowest outstanding balance credit card first be beneficial over paying off the one with the highest?
Paying off the lowest outstanding balance credit card first will not be beneficial over paying off the one with the highest. Instead, it's beneficial to pay the highest outstanding balance first.
Actually, paying the one with the highest interest rate is logically the right thing to do because you can shorten the amount that you spend on interest or charges by month, but paying the lowest outstanding balance credit card first makes more sense if you could transfer the highest interest balance into a low or maybe no interest rate that is being offered to another card, only if you are so certain that you will pay the remaining balance or on before its due.
It should be remarked that paying off the lowest outstanding balance credit card first cannot be beneficial over paying off the one with the highest interest rate.
It's significant to pay the one that has the highest interest rate. This is because it'll assist in shortening the amount the person will pay as interest.
In conclusion, it's important to pay the highest Interest rate.
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5 5/7 divided by 1 3/5 times 4 2/3
Answer:
50/3
Step-by-step explanation:
5 5/7 divided by 1 3/5 times 4 2/3
5 5/7 = 40/7
1 3/5 = 8/5
4 2/3 = 14/3
40/7 divided by 8/5 = 40/7 times 5/8 = 200/56
200/56 times 14/3 = 2800/168 = 400/24 = 100/6 = 50/3
So, the answer is 50/3
Evaluate. −8+(6+4)÷(−2)
−13
negative 13
−4
negative 4
−3
negative 3
−1
The solution of the given expression is -13. The correct option is A.
PEMDAS stands for the sequence of operations for multi-step mathematical expressions. The letters PEMDAS stand for parentheses, exponents, multiplication, division, addition, and subtraction.
Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication and division.
Given the expression is −8+(6+4)÷(−2). The expression by using the PEMDAS will be solved as below,
E = −8+(6+4)÷(−2)
First, solve the bracket and then division,
E = -8 + ( 10 ) ÷ (−2)
E = -8 - 5
E = -13
Hence, the solution is -13.
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is f(x)=x+1/x+2 a function? Explain.
The equation represented as f(x) = x + 1/x + 2 is a function
How to determine if the equation is a functionFrom the question, we have the following parameters that can be used in our computation:
f(x) = x + 1/x + 2
The above equation is a rational equation whose numerator and denominator are linear functions
Equations with these properties are always functions
This is so because their x values do not have multiple y values
Hence, the equation f(x) = x + 1/x + 2 is a function
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On Thursday, the temperature in Spincich Lake, Michigan was 22F. By Friday, the temperature had dropped 35 degrees. What was the temperature on Friday?
Answer:
-13F
Step-by-step explanation:
since its negative, you could find the answer by doing 35-22
then, just adding a negative symbol in front!
this is because you are finding the difference by subtracting, and by doing this i find it a lot easier to get your answer
so, 35-22 is equal to 13. so, 22-35 is -13
i hope that makes sense
honestly, you can just use a calculator to figure it out too! just put 22-35
HELPPPPPPPPP
What is the value of x?
Enter your answer as a decimal in the box.
Check the picture below.
Find the missing angles measurements. Please show your steps.
If m∠DAC = 65°, m∠DAC and m∠BCA can be classified as alternate interior angles. And m∠BCA = 65°.
What is alternate interior angles of a rectangleAlternate interior angles of a rectangle are congruent, which implies they are equal in measure and are formed by the intersection of the opposite sides of the rectangle.
Considering the diagonal AC from one corner of the rectangle to the opposite corner, the angles formed at the intersection of the non-parallel sides will be congruent
Therefore, the angles m∠DAC and m∠BCA are alternate interior and m∠DAC = m∠BCA, which makes m∠BCA = 65°
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Maria is 5 feet 3 inches tall. Marla is 4 feet 11 inches tall, Mandy is 5 feet 2 inches tall
and Marilyn is 4 feet 8 inches tall.. What is the average height of these 4 friends? Explain
how you found your answer.
Answer:
the average height is 5 feet 0 inches
Step-by-step explanation:
To find the average height of Maria, Marla, Mandy and Marilyn, we need to add up their individual heights and divide by the number of people in the group.
First, we need to convert all the heights to a common unit of measurement. Since inches are the smallest unit of measurement, we will convert all the heights to inches.
Maria: 5 feet 3 inches = 63 inches
Marla: 4 feet 11 inches = 59 inches
Mandy: 5 feet 2 inches = 62 inches
Marilyn: 4 feet 8 inches = 56 inches
Now we can add up the heights:
63 inches + 59 inches + 62 inches + 56 inches = 240 inches
To find the average, we divide the total height by the number of people:
240 inches / 4 people = 60 inches
So the average height of these four friends is 60 inches or 5 feet, which is the same as 5 feet 0 inches.
Therefore, the average height of these four friends is 5 feet 0 inches.
20. MP MODELING REAL LIFE The plate for a microscope has a circumference of
100 millimeters. What is the area of the plate?
The area of the plate of the microscope with a circumference of
100mm is 2500/π mm².
What is the area of the circle?A circle is simply a closed 2-dimensional curved shape with no corners or edges.
The area of a circle is expressed mathematically as;
A = πr²
The circumference of a circle is expressed as 2πr.
Given the data in the question;
Circumference of the plate C = 100 mmRadius r = ?Area A = ?First, we determine the radius of the plate.
Circumference C = 2πr
100 = 2πr
r = 100/2π
r = 50/π
Now, calculate the area of the plate.
A = πr²
A = π ( 50/π )²
A = π × 2500/π²
A = 2500π / π²
A = 2500/π mm²
Therefore, the area of the plate is 2500/π mm².
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Evaluate 12.3v + 11.7w when v=3 and w=4.
Answer:
83.7
Step-by-step explanation:
Substitute v = 3 and w = 4:
[tex]\displaystyle{12.3 \cdot 3 + 11.7 \cdot 4}\\\\\displaystyle{= 36.9 + 46.8}\\\\\displaystyle{= 83.7}[/tex]
Therefore, the value is 83.7
a hybrid electric vehicle is a car with both a gasoline-powered motor and an electric motor. some hybrids achieve mileage ratings as high as 75 miles per gallon of gasoline. calculate this quantity in miles per liter and kilometers per liter.
The mileage rate of 75 miles per gallon is equal to 19.8 miles/liter or 31.9 km/liter. The result is obtained by converting the value of each unit.
How to convert the unit of mileage rate?The conversion value of
1 gallon = 3.785 L1 mile = 1.609 kmSome hybrids achieve mileage ratings as high as 75 miles per gallon of gasoline. Determine that quantity in:
Miles per literKilometers per literMultiply the number with the conversion value of each!
In miles per liter,
75 miles/gallon = 75 × 1/3.785 miles/liter
75 miles/gallon = 19.8 miles/liter
In kilometers per liter,
75 miles/gallon = 75 × 1.609 × 1/3.785 km/liter
75 miles/gallon = 31.9 km/liter
Hence, 75 miles per gallon is equal to 19.8 miles/liter or 31.9 km/liter.
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2x is greater than 5 + 2
Answer:
x = greater than or equal to 3.5 x = 3≥
Step-by-step explanation:
any number that is greater than or is 3.5 will make 2x greater than 5 + 2 which equals 7
how many inches is a feather
Answer: 4-6 inches
Step-by-step explanation: Hope this helps
Answer:
Feathers are 214 in or less
Step-by-step explanation:
For value of the variable does this expression make sense?
[tex]\sqrt{\frac{1+3a}{25}[/tex]
Answer: a ≥ -1/3
Step-by-step explanation:
If we want the result of the expression to end up as a real number, the fraction under the square root cannot be negative.
Therefore, we can make an equation like this:
(1+3a) / 25 ≥ 0
Multiply by 25
1 + 3a ≥ 0
Subtract 1
3a ≥ -1
Divide by 3
a ≥ -1/3
Which expression is equal to 3/square root of 7?
six thirty children had gallon of lemonade to share. if each child had the same amount, what portion of the gallon did each child have to drink?
If each child consumed the same quantity, then each would need to drink (63)x(4/n) of a gallon.
The US fluid ounce is equal to 1/128 of a US gallon since there are four quarts in a gallon, two pints in a quart, and 16 US fluid ounces in a US pint. The US gallon is accepted to be equivalent to around 3.785 L or 231 in inches, but the Imperial gallon is accepted to be equal to 4.54609 L. The liter is the unit of volume used by the great majority of people in the world. a volume measurement equal to eight pints.
An imperial gallon (Britain, Canada) is exactly 4.54609 liters. (US) 3.785 liters or around 231 cubic inches for liquids (a "U.S. liquid gallon")
Here gallon of lemonade to share = 63
let each children has 1 gallon of lemonade
so gallon=63
so portion =63/1
Formula = gallon to share x (4 parts of gallon shape / number of gallon)
which means if each one have n gallon then portion = (63)x(4/n)
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Each child would need to eat 63*4/n of a gallon if they all consumed the same amount.
Since there are four quarts in a gallon, two pints in a quart, and 16 US fluid ounces in a US pint, one US fluid ounce is equivalent to 1/128 of a US gallon. The Imperial gallon is acknowledged to be equal to 4.54609 L, but the US gallon is accepted to be about 3.785 L or 231 in. The vast majority of people in the world measure volume in litres. a volume that is eight pints in size.
In Britain and Canada, an imperial gallon equals precisely 4.54609 litres. 3.785 litres (US) or around 231 cubic inches (a "U.S. liquid")
Here, six thirty kids were sharing a gallon of lemonade.
each youngster should drink a gallon of lemonade.
Gallon = 63.
Hence part = 63/1
It indicates that the fraction is equal to 63*4/n if each has n gallons.
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Note: The complete question would be as bellow,
six thirty children had gallon of lemonade to share. if each child had the same amount, what portion of the gallon did each child have to drink?
Select the equivalent expression. (2^-10/4^2)^7
The equivalent expression for the given expression is 1/2⁹⁸.
What is an equivalent expression?Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
The given expression is (2⁻¹⁰/4²)⁷.
Now, (2⁻¹⁰/(2²)²)⁷
= (2⁻¹⁰/2⁴)⁷
= (1/2¹⁰×2⁴)⁷
= (1/2¹⁰⁺⁴)⁷
= (1/2¹⁴)⁷
= 1/2⁹⁸
Therefore, the equivalent expression for the given expression is 1/2⁹⁸.
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Please answer this question within 10 min! Information in the picture.
The area of triangle A(F) D is 42.44 units²
How to find the area of the triangle?
The formula to calculate the area of a triangle with base b and height h is given by:
Area = 1/2(bh)
In ΔA(F) D, the base is (F)D and A(F) is the height
Using trigonometric ratio:
sin 30° = A(F) /AD (opposite/hypotenuse)
0.5 = A(F) /14
A(F) = 7 units
(F)D = √(14²-7²) = 7√3 units (Pythagoras theorem)
Area of ΔA(F) D = 1/2 × (F) D × A(F)
Area of ΔA(F) D = 1/2 × 7√3 × 7
Area of ΔA(F) D = (49√3)/2
Area of ΔA(F) D = 42.44 units²
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Mia estimated 5/8 + 1/9 by replacing 5/8 with 1 and 1/9 with 0. Her
estimated sum was 1 + 0 = 1. Explain why Mia's estimate is Not accurate?
NOT accurate.
Estimation done by Mia is not accurate, as the accurate estimated sum of the given expression 5/8 + 1/9 is equal to ( 1/2).
Estimation done by Mia is not accurate:
Replaced 5 /8 with 1.
But accuracy represents:
0 < (1 /4 ) < ( 1 /2 ) < (5 /8 ) < ( 3 / 4 ) < 1
( 5 / 8 ) is more close to ( 1 /2 ).
Estimated value of ( 5 / 8 ) is ( 1 / 2 )
0 < ( 1 / 9 ) < ( 1 / 4 )
So , estimated value of ( 1 / 9 ) is 0
Estimated sum = ( 1 / 2 ) + 0
= ( 1 / 2 )
≠ 1
Therefore, accurate estimated sum of 5/8 + 1/9 is equal to ( 1 /2 ).
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Lorena and Karla are creating an art project in the shape of a right triangle. They have a 92 cm long piece of wood, which is to be used for the hypotenuse. The two legs of the triangular support are of equal length. Approximately how many more centimeters of wood do they need to complete the supports?
The amount of wood that they need to complete the supports is given as follows:
130.10 cm.
How to obtain the amount of wood needed?First we must obtain the side lengths of the right triangle.
The equal side lengths of the right triangle are obtained applying the Pythagorean Theorem, hence:
x² + x² = 92²
2x² = 92²
x² = 4232
x = square root of 4232
x = 65.05 cm.
They have two sides of 65.05 cm, hence the amount of wood needed is obtained as follows:
2 x 65.05 = 130.10 cm.
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After traveling 70 meters in its dive, the submarine is at a depth of 25 meters. About what will the submarine’s depth be if it continues its dive for another 110 meters? Round to the nearest whole number A) 40m
B) 64m
C) 18m
D) 4m
About 40 meters the submarine’s depth be if it continues its dive for another 110 meters. So the option A is correct.
Since it is essentially a ratio problem, we can use the information given and apply the Rule of Three assuming that the submarine is moving at a constant speed.
In this rule, the depth after 110 meters is obtained by simply multiplying the ratio's diagonal values and dividing by the last value.
70min = 25 m
110min = x m
x = (110 × 25)/70
x = 2750/70
x = 39.28
x = 40(approx)
We can see that at 110 minutes, the depth would have been approximately 40 meters, but since the submarine travelled further during this time, we must add this measurement to the original 25 meters to determine the submarine's total depth.
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