Answers
The step 2 should be m∠p + m∠o = 180 degrees(supplementary angles)
How to find the angles of a triangle?The external angle theorem states that the measure of each exterior angle of a triangle is equal to the sum of the opposite and non-adjacent interior angles(remote interior angles) .
Therefore,
Step 1
m∠m + m∠n + m∠o = 180°(sum of angles of a triangle)
It's very correct
Step 2
m∠p - m∠o = 90 degrees(Alternate angles)
This is incorrect.
It should be m∠p + m∠o = 180 degrees(supplementary angles)
The angles m∠p and m∠o are supplementary angles. This simply implies the angles add up to 180 degrees.
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Related Questions
If f(x) is given as an equation and g(x) is given as a table, how i can tell they are inverses
Answers
Answer: f(x) and g(x) both represent y of the equations
Step-by-step explanation: f(x) and g(x) both represent the y of the equation for example f(x)=mx+b or g(x)+mx+b both would be to find y of that specific equation and that would also make them inverses because you could use the table to label the inverses on a graph.
Solve each equation. Round to the nearest ten-thousandth. Check your answers.
25²x⁺¹=144
Answers
[tex]25^{2x+1}=144[/tex] => x = 0.272, by properties of logarithm.
What is Logarithm?The opposite of exponentiation is the logarithm.This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.Given: [tex]25^{2x+1}=144[/tex]
Taking logarithm on both sides:
log ([tex]25^{2x+1}[/tex]) = log (144)
=> (2x + 1) log (25) = log (144) (As [tex]log_b(a)^m = m (log_b(a))[/tex])
=> 2x + 1 = [tex]\frac{log144}{log25}[/tex]
=> 2x + 1 = [tex]\frac{2.158}{1.397}[/tex]
=> 2x + 1 = 1.544
=> 2x = 0.544
=> x = 0.272
Hence, [tex]25^{2x+1}=144[/tex] => x = 0.272, by properties of logarithm.
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Determine whether each logarithm is a common logarithm.
a. (log₂4)
Answers
the logarithm function ( log ₂ 4 ) is not a common logarithm function as it does not have a base 10.
In mathematics, the common logarithm is the logarithm with base 10.
It is also known as the decadic logarithm and as the decimal logarithm function.
Here, we have the logarithm function as:
( log ₂ 4 )
Now, we can see that:
It has a base of 2.
So, it will not be a common logarithm function as having base 10 is an important characteristic of a common logarithm function.
Therefore, we get that, the logarithm function ( log ₂ 4 ) is not a common logarithm function as it does not have a base 10.
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Can somebody simplify this? (−8) × (-6) − (−5)²
Answers
Answer:
23Step-by-step explanation:
Can somebody simplify this?
(−8) × (-6) − (−5)² =
48 - 25 =
23
Eli takes a typing test and types all 240 words in 1/12 hour. he takes the test a 2nd time and types all the words in 1/15 hour. was he faster or slower on the 2nd attempt.
Answers
Answer: he was faster the second time
Step-by-step explanation:
1/15 is a smaller fraction and 1/12, 1/15 of an hour is 4 minutes and 1/12 of an hour is 5 minutes, so he took it in 4 minutes the second time which was quicker
Using complete sentences describe the transformation from the parent function f(x)= |x| to g(x)=-2 |x+3|
Answers
Answer:
The transformation from the parent function is a translation of 3 units left, a vertical stretch of scale factor 2, and a reflection in the x-axis.
Step-by-step explanation:
Given function:
[tex]\text{g}(x) = -2|x+3|[/tex]
Parent function:
[tex]\text{f}(x) = |x|[/tex]
A parent function is the simplest form of a family of functions.
The graph of g(x) is related to the graph of f(x) by a series of transformations. To determine the series of transformations, work out the steps of how to go from f(x) to g(x).
Transformations
For a > 0
[tex]f(x+a) \implies f(x) \: \textsf{translated $a$ units left}[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated $a$ units right}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated $a$ units up}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated $a$ units down}[/tex]
[tex]a\:f(x) \implies f(x) \: \textsf{stretched parallel to the $y$-axis (vertically) by a factor of $a$}[/tex]
[tex]f(ax) \implies f(x) \: \textsf{stretched parallel to the $x$-axis (horizontally) by a factor of $\dfrac{1}{a}$}[/tex]
[tex]-f(x) \implies f(x) \: \textsf{reflected in the $x$-axis}[/tex]
[tex]f(-x) \implies f(x) \: \textsf{reflected in the $y$-axis}[/tex]
Step 1
Translation left by 3 units:
[tex]\implies f(x+3) =|x+3|[/tex]
Step 2
Stretch in the direction of the y-axis (vertically) with scale factor 2:
[tex]\implies 2f(x+3) =2|x+3|[/tex]
Step 3
Reflection in the x-axis:
[tex]\implies -2f(x+3) =-2|x+3|[/tex]
Conclusion
The transformation from the parent function is a translation of 3 units left, a vertical stretch of scale factor 2, and a reflection in the x-axis.
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Three points of a parrallelogram are (4,3)(-4,3)(-4,3) and (2,-3) what are the coordinates of the 4th point that would complete the parallelogram
Answers
The fourth point of the parallelogram is (10, -3).
What is Parallelogram?
A Parallelogram is a quadrilateral with opposite sides parallel.
Given that;
Three points of a parallelogram are (4,3), (-4,3) and (2,-3).
Now, Take Two points at one diagonal of parallelogram are (4, 3) and
(2, -3).
Let fourth point of a parallelogram is (x, y).
Take (-4,3) and (x, y) on the another diagonal of a parallelogram.
Since, Midpoint of both diagonal is same.
Hence, Midpoint of (4, 3) and (2, -3) is calculated as;
(4+2/2, 3+(-3)/2) = (6/2, 0/2) = (3, 0)
So, Midpoint of (4, 3) and (2, -3) = (3, 0)
And, Midpoint of (-4,3) and (x, y) = (-4+x/2, 3+y/2)
Since, Midpoint of both diagonal is same.
Hence, (-4+x/2, 3+y/2) = (3, 0)
Equating coordinates we get;
⇒-4+x/2 = 3
⇒ -4 + x = 6
⇒ x = 6 + 4
⇒ x = 10
And, 3+y/2 = 0
⇒3 + y = 0
⇒y = -3
So, The fourth point of the parallelogram is (10, -3).
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using a property of operations, what can you say about the sum of two expressions
Answers
Answer: Using a property of operations, what can you say about the sum of two expressions, Then the temperature changed more on Day 2.
Step-by-step explanation:
Using a property of operations, what can you say about the sum of the two expressions.
Let us assume the table of values is : Sunrise (F) = -11.31 -7.69
Sunset (F) = 13.49 25.25
Day 1 and Day 2
Sunrise Temperature (F) = -11.31 -7.69 (eq-1)
Sunset Temperature (F) = 13.49 25.25 (eq-2)
The sum of the two equations are:
Sunrise Temperature (F) = -11.31 -7.69
(F) = -19
Sunset Temperature (F) = 13.49+ 25.25
(F) = 38.74
Which day saw the greatest variation in temperature? Describe your thinking. To do this, we only compute the absolute difference in daily temperatures between the times of sunrise and sunset.
So, we can write
Day 1 = |-11.31 - 13.49|
Day 1 = 24.8
Day 2 = |-7.69 - 25.25|
Day 2 = 32.94
So, 32.94 is greater than 24.8
Therefore, Day 2 is greater than the Day 1
Hence, the temperature changed more on Day 2.
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Which operation would you do first in the following equation?
10-4÷1x 5
Answers
A scale drawing is to be made of a rectangular plot of land that is 120yd x 53yd. If it is drawn to a scale of 1in.:5yd, what are the dimensions of the drawing
Answers
The dimensions of the drawing of the rectangular plot using the scale of 1in.:5yd is; 24 inches by 10.6 inches
How to represent Scale Drawings?
We are told that the dimensions of the rectangular plot of land is 120yd x 53yd.
Now, you want to draw this rectangular plot on a scale of 1 inch : 5 yards. This means that 1 inch will represent 5 yards.
Thus, for the side of 120 yards, using the scale gives us;
1/5 * 120 = 24 inches
For the side of 53 yards, using the scale gives us;
1/5 * 53 = 10.6 inches
Thus, the dimensions of the drawing of the rectangular plot using the scale of 1in.:5yd is; 24 inches by 10.6 inches
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Evvie has these dight card 4 5 0 8 2 she makes them into 6 digit number larger than 300.000 and smaller than 400.000
Answers
Step-by-step explanation:
500.000 evvie was on the digit card
Please helppppppppp!!!!!!!!!
Answers
Answer:
Rate of change in y is -6
-3-6 = -9
-9-6=-15
-15-6=-21
Rate of change in x is 1
1+1=2
2+1= 3
3+1 = 4
4-1=5
........And so on
Confused on this entire problem i apoligize
Answers
The linear function f(x) with a slope of -8 and that f(1) = 2 is f(x) = 10 -8x
Equation of a lineFrom the question, we are find a linear function with slope of -8 and that f(1) = 2
If f(1) = 2, then the line passes through the point (1, 2)
Using the point-slope form of the equation of a straight line
y - y₁ = m(x - x₁)
Where m is the slope
Then,
y - 2 = -8(x - 1)
Simplify
y - 2 = -8x + 8
y = -8x + 8 + 2
y = -8x + 10
∴ f(x) = -8x + 10
f(x) = 10 - 8x
Hence, the linear function is f(x) = 10 -8x
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1.49 round to a whole number
Answers
Answer:
the answer is 1
Step-by-step explanation:
trust mehhhh
the number before the whole is the most important and if its below 5 then u round down
If f(x)=3x+2 and g(x)=x(squared)−x, find the value.
f(-2)=______
Answers
Answer: f(-2) = - 4
Step-by-step explanation:
Work out the following, giving your answers in their simplest form:
a) 4/7 / (1 3/4)
b) 5 3/5 / (2 2/3)
Answers
The simplest form of the following are -
a) 4/7 / (1 3/4) = 16/49
b) 5 3/5 / (2 2/3) = 21/10
The word simplify means to make something easier to do or understand. So, reducing or simplifying fractions means we make the fraction as simple as possible. We do this by dividing the numerator and the denominator by the largest number that can divide into both numbers exactly.
We have been given that
a) 4/7 / (1 3/4)
Rewrite as -
= (4/7) / (1× 3/4)
= (4/7) / (7/4)
= (4/7) × (4/7)
= 16/49
b) 5 3/5 / (2 2/3)
Rewrite as -
= (5× 3/5) / (2× 2/3)
= (5× 3/5) / (8/3)
= (28/5) / (8/3)
= (28/5) × (3/8)
= 7/5 × 3/2
= 21/10
= 2.1
Thus , the following are in order of simplicity:
a) 4/7 / (1 3/4) = 16/49
b) 5 3/5 / (2 2/3) = 21/10
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What does x equal if log (1+3 x)=3 ?
Answers
The required value of x using the properties of exponents and logarithm is 6.362.
What are the various properties of the logarithm?
Out of several properties of logarithms, some of the main properties are given below:
Product Rule
log (ab) = log a + log b
Change of base
log ₇ x = log x / log 7
Power Rule
log a² = 2 log a
Quotient Rule
log (a / b) = log a - log b
Solving the given equation for x
We are given a logarithmic expression: log (1 + 3x) = 3
On applying exponent both sides, we get,
e^[log (1 + 3x)] = e^3
Using the properties of exponents and logarithm, we get,
1 + 3x = 20.0855
3x = 19.0855
x = 6.362
Hence, the required value of x can be 6.362.
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Is the expression 33x33^7 equivalent to (33x33)^7? Explain.
Answers
Answer:
Step-by-step explanation:
no because perenthesis
Answer:
No it is not equivalent because the parenthesis
Step-by-step explanation: When it comes to parenthesis you have to do the problem in them, so you would do 33x33 rather than the whole problem at once. no idea if that makes sense bff it sounded right in my head
Phillis used the wrong metal in her experiment which had a very different density than the intended metal. As a result when calculating her results she found that the mass necessary was 612 grams instead of the theoretical 390 grams that was needed. What is her percent error?
Answers
The percent error is 56. 9%
What is percent error?Percent error is defined as the difference between the estimated value and the actual value in comparison to the actual value.
The formula for percent error is expressed as;
Percent error = [tex]\frac{|VA - VE|}{VE}[/tex] × 100/1
Where;
VA is the actual value = 612 gramsVE is the expected value = 390 gramsSubstitute the values
Percent error = | 612 - 390| / 390 × 100/ 1
Percent error = 222/ 390 × 100/ 1
Percent error = 0. 56 × 100
Percent error = 56. 9%
Thus, the percent error is 56. 9%
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To get to work each morning, Emily takes a horse 10.9810.9810, point, 98 kilometers and a bike 4.064.064, point, 06 kilometers.
Answers
Answer: Emily's in total journey is 15.045 kilometers.
Step-by-step explanation:
Given data,
Emily traveled a certain distance on a horse = 10.98 kilometers
Emily traveled a certain distance on a bike = 4.06 kilometers
The overall distance traveled by Emily on her horse and bike needs to be determined.
For "Total Distance" , we will use addition operation:
So, Total distance covered by Emily's journey is given by equal to
Emily traveled a certain distance on a horse + Emily traveled a certain distance on a bike
Let us assume,
Total distance covered by Emily's journey is represented by 'x'
Then we can write,
x = 10.981 kilometers + 4.064 kilometers
x = 15.045 kilometers
Therefore, Emily's in total journey is 15.045 kilometers.
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How many 1/3 ounce spoonfuls of salt are in a filled 4 3/4 ounce Salt shakers
Answers
Answer:15 spoonfuls
Step-by-step explanation:
Simplify this please!
Answers
Answer:
Step-by-step explanation:
Write each expression in simplest form. (x¹/₄ / y⁻³/₄)¹²
Answers
The given expression can be written in its simplest form by solving the exponents.
There are two types of exponent rules that will be applied to the expression. First, we will solve the negative exponent then we will multiply the exponents.
According to the negative exponent rule: x^-n=1/x^n.
Hence, applying the rule to the base term in the denominator, 1/y^⁻³/₄= y^³/₄
Therefore, x^¹/₄ / y^⁻³/₄= x^¹/₄ y^³/₄
According to the multiplication of exponent rule: (x^n)^m=x^nm
Hence, applying the rule to the expression,
(x^¹/₄ y^³/₄)^12=x^¹/₄*12 y^³/₄*12
Multiplying the powers and simplifying,
x^¹/₄*12 y^³/₄*12=x^3y^9
The simplest form of the expression (x^¹/₄/y^⁻³/₄)^12 is x^3y^9.
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The grid shows Figure Q and its image Figure Q′ after a transformation.
Figure Q is a pentagon drawn on a coordinate grid with vertices in clockwise order at point 2 comma 4, point 3 comma 7, point 7 comma 5, point 5 comma 4, and point 4 comma 2. Figure Q’ is a pentagon drawn with vertices in clockwise order at point negative 2 comma negative 4, point negative 3 comma negative 7, point negative 7 comma negative 5, point negative 5 comma negative 4, and point negative 4 comma negative 2.
Which of the following transformations could be used to prove that Figure Q and Figure Q′ are congruent?
Counterclockwise rotation of 90° about the origin
Counterclockwise rotation of 270° about the origin
Clockwise rotation of 90° about the origin
Clockwise rotation of 180° about the origin
Answers
The transformation of pentagon Q to pentagon Q' is a clockwise rotation of 180° about the origin.
What is transformation?A transformation is a general term for four specific ways to manipulate the shape or position of a point, a line, or a geometric figure.
We have,
Coordinates of a pentagon Q.
(2, 4), (3, 7), (7, 5), (5,4), and (4,2).
Coordinates of pentagon Q'.
(-2, -4), (-3, -7), (-7, -5), (-5,-4), and (-4,-2).
We see that the coordinates of each point of the pentagon Q have changed their position as negative coordinates in pentagon Q'
The coordinates of pentagon Q are in (x, y) which can be assumed to be in the first quadrant of the coordinate plane.
The coordinates of pentagon Q' are in (-x, -y) which is in the 3rd quadrant.
From the first quadrant to 3rd quadrant there is a rotation of 180°.
Thus the transformation of pentagon Q to pentagon Q' is a clockwise rotation of 180° about the origin.
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Solve. Check for extraneous solutions. (x+5)¹/₂-(5-2 x)¹/₄=0
Answers
No extraneous solution to the equation.
The equation is
[tex](x + 5)^{1/2}[/tex] - [tex](5 - 2x)^{1/4}[/tex] = 0
To know whether the equation is an extraneous solution we first need to find the value of x.
So we have,
[tex](x + 5)^{1/2} = (5 - 2x)^{1/4}[/tex]
Multiply both sides with the power of 4, then we have
[tex]((x+ 5)^{1/2})^{4}[/tex] = [tex]((5 - 2x)^{1/4} )^{4}[/tex]
[tex](x+ 5)^{2}[/tex] = 5 - 2x
[tex]x^{2}[/tex] + 10x + 25 = 5-2x
[tex]x^{2}[/tex] + 12x + 20= 0
[tex]x^{2}[/tex] + 10x + 2x + 20 = 0
x(x + 10 ) + 2(x + 10) = 0
(x + 10)(x+2) = 0
x = -10, -2
Now we have to put the value of x in the equation
x = -10
[tex](-10 + 5 )^{1/2}[/tex]-[tex](5 - 2 * -10)^{1/4}[/tex] = 0
[tex](-5)^{1/2}[/tex] - [tex]25^{1/4}[/tex]= 0
[tex](-5)^{1/2}[/tex] - [tex]5^{1/2}[/tex] = 0
Which has not possible as we don't have negative number in the square root.
x = -2
[tex](-2 + 5)^{1/2}[/tex] -[tex](5-2*-2)^{1/4}[/tex]=0
[tex]3^{1/2}[/tex]- [tex]9^{1/4}[/tex]=0
[tex]3^{1/2}[/tex]- [tex]3^{1/2}[/tex]=0
0 = 0
Therefore there is no extraneous solution to the equation
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I need help with this.
Answers
20 people likes movies, such that 12 of these also like music, then the probability is just the quotient between:
Q = 12/20 = 0.6
The probability that a person likes music given that he/she lies movies is 0.6 or 60%
How to find the probability P(movies|music)?Notice that there are 5 + 7 common elements between movies and music, and a total of 20 people likes movies, such that 5 + 7 = 12 of these also like music, then the probability is just the quotient between the numbers of total people that likes movies which we know is 20, and the people that likes movies and also music.
So the quotient between 12 and 20, that will gave us the probability we want to find.
The probability that a person likes music given that he/she lies movies is 0.6 or 60%
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If a person walks
mile in 1 hour, how far does that person walk
in 1 3/4 hours at that rate?
Answers
7/4 miles distance does that person walk.
What is distance?
The length or width between two objects, points, lines, etc. remoteness is the state or fact of something or someone being physically distant from another. A straight line in space It would take too long to walk seven miles in one hour. a distance; a space: The ship was encircled by a sizable body of water.We can use a ratio to solve
1 mile x miles
----------------= ---------------
1 hour 1 3/4 hours
Changing to improper fractions
1 mile x miles
----------------= ---------------
1 hour 7/4 hours
Using cross products
1 * 7/4 = 1 * x
7/4 = x
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Devon has 4 3/4 bags of soil to put in hs flower bed each bag will cover 15 ft2 how many squares will he be able to cover
Answers
Devon will be able to cover 71.25 ft² of flower bed.
The number of bags of soil Devon has = [tex]4\frac{3}{4}[/tex]
Converting mixed fraction to fraction
Number of bags of soil = (4×4+3)/4
Performing multiplication and addition in numerator to find the number of bags of soil with Devon
Number of bags of soil = 19/4
Now, it is stated that area covered by 1 bag = 15 ft²
So, 19/4 bags will cover area = 15×(19/4)
Performing multiplication and division to find the area covered by the bags of soil
Area covered by bags of soil Devon has = 71.25 ft²
Hence, the area covered by bags of soil Devon has is 71.25 ft²
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The complete question is -
Devon has 4 3/4 bags of soil to put in his flower bed. Each bag will cover 15 ft2. How many square feet will he be able to cover?
Solve each equation. Check for extraneous solutions. √x+4=√3 x
Answers
The solution to the equation √x+4=√3 x is x = 2(1 + √3) or x = 2(1 - √3).
Quadratic equationAny equation of the form [tex]\rm ax^2+bx+c=0[/tex] is called a quadratic equation.
The formula for the roots of the quadratic equation is found by:
[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]
It is given that:
The equation is:
√x + 4 = √3 x
√x = √3 x - 4
Squaring both sides:
x = (√3 x - 4)²
x = 3x² - 8√3 x + 16
2x² - 8√3 x + 16 = 0
x² - 4√3 x + 8 = 0
After solving with the quadratic formula:
[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]\rm x = \dfrac{-(-4\sqrt3) \pm\sqrt{(-4\sqrt3)^2-4(1)(8)}}{2(1)}[/tex]
x = 2(1 + √3) or x = 2(1 - √3)
Thus, the solution to the equation √x+4=√3 x is x = 2(1 + √3) or x = 2(1 - √3).
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-46 decreased by the difference between -23 and -61
Answers
When -46 decreased by the difference between -23 and -61, the number becomes -18.
What is the value of the subtraction?
Subtraction is the mathematical operation that is used to determine the difference between two or more numbers. The sign that is used to represent subtraction is -.
According to mathematical rules, when two negative signs are multiplied by each other, the number becomes positive.
The difference between -23 and -61: -61 - (-23)
-61 + 23 = -38
-46 - (-38)
-46 + 28 = -18
Here is the complete question:
-46 decreased by the difference between -23 and -61. What is the value of the number?
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