We'll use 3/8 cup of macadamia nuts.
Describe ratios.
A ratio is defined as a/b where b is not equal to 0. Since a and b are separate portions of the two values, the total combined amount is expressed as (a + b).
Given:
3/4 cup of macadamia nuts are used in a banana macadamia nut bread recipe that Vincent created. We are aware of this based on the information provided.
The quantity of nuts needed if he decides to make only half the recipe is:
used macadamia nuts = 1/2 * 3/4
used macadamia nuts =3/8
Therefore, there will be 3/8cup of Macadamia nuts utilized.
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The correct question is given below
"Vincent found a recipe for banana macadamia nut bread that uses 3/4 cup of macadamia nuts. If he only wants to make half the recipe, how many cups of macadamia nuts should be use?"
Solve each equation. Check for extraneous solutions. √x+4=√3 x
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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Old McDonald had a farm. And on that farm he had 38 animals, some
horses and some chickens. Altogether, there were 94 animal legs in the
farm. Solve for the number of Horses and Chickens.
Answer:
Heya, your answer would be 52 horses, and 42 chickens.
Step-by-step explanation:
By doing the long, long and I mean long process of adding 2 + 2 or 4 + 4 (due to the fact chickens have 2 legs and horses have 4), we get to 52 horse legs, and 62 chicken legs.
Adieu
Answer:
There are 9 horses and 29 chickens.
Step-by-step explanation:
a = animals
a = 38
h = horses
c = chickens
l = legs
l = 94
Equation 1: h + c = 38
Horses have 4 legs. Chickens have 2 legs.
Equation 2: 4h + 2c = 94
Manipulate the equations so that one of the coefficients are the same.
We will multiple Equation 1 by 2 so that both equations have 2c.
Equation 1: 2h + 2c = 76
Equation 2: 4h + 2c = 94
Subtract Equation 1 from Equation 2.
Equation 2 - Equation 1
(4h + 2c) - (2h + 2c) = 94 - 76
(4h - 2h) + (2c - 2c) = 94 - 76
2h = 18
h = 9
Substitute h into either equation to solve for c.
Equation 1: 2h + 2c = 76
Equation 1: 2(9) + 2c = 76
Equation 1: 18 + 2c = 76
Equation 1: 2c = 76 - 18
Equation 1: 2c = 76 - 18
Equation 1: 2c = 58
Equation 1: c = 29
Equation 2: 4h + 2c = 94
Equation 2: 4(9) + 2c = 94
Equation 2: 36 + 2c = 94
Equation 2: 2c = 94 - 36
Equation 2: 2c = 58
Equation 2: c = 29
There are 9 horses and 29 chickens.
If f(x) is given as an equation and g(x) is given as a table, how i can tell they are inverses
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.
Using complete sentences describe the transformation from the parent function f(x)= |x| to g(x)=-2 |x+3|
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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using a property of operations, what can you say about the sum of two expressions
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
How many 1/3 ounce spoonfuls of salt are in a filled 4 3/4 ounce Salt shakers
Answer:15 spoonfuls
Step-by-step explanation:
4 1/4 *-1/2= I really help on this it's for homework and I don't know if our teacher will be helping with it so please please please will somebody help me please.
Explain why the expansion at the right of log₄√t/s is incorrect. Then do the expansion correctly.
The correct expansion of log₄√t/s is 1/2 log₄(t/s).
Logarithms is another way of writing exponents. Logarithm is nothing but another way of expressing exponents and can be used to solve problems that cannot be solved using the concept of exponents only. Understanding logs is not so difficult. To understand logarithms, it is sufficient to know that a logarithmic equation is just another way of writing an exponential equation.
Logarithm and exponent are inverse forms of each other. One can understand this from the section below. Initially, a mathematician named John Napier introduced logarithms for making calculations in a simple way and this concept is quickly adopted by other scientists, engineers, etc.
Given that, log₄√t/s and we have to expand this logarithmic function having base 4 accordingly. So, let's proceed to solve this logarithmic expansion.
log₄√t/s = log₄((t/s)^(1/2))
= log₄((t/s)^(1/2))
Apply log rule, logₐ(xᵇ) = b.logₐ(x), assuming x ≥ 0
= 1/2 log₄(t/s)
Hence, log₄√t/s = 1/2 log₄(t/s) is the correct expansion.
Therefore, 1/2 log₄(t/s) is the required answer.
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Solve each equation. Round to the nearest ten-thousandth. Check your answers.
25²x⁺¹=144
[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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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.
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
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?
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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Confused on this entire problem i apoligize
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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Please helppppppppp!!!!!!!!!
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
Point t is on line segment \overline{su} su . given st=3x+2,st=3x+2, tu=3x+4,tu=3x+4, and su=5x+9,su=5x+9, determine the numerical length of \overline{su}. su .
Given that Point T is on line segment SU, T is collinear with S and U, and the numerical length of SU is 24.
Since Point T is on line segment SU, then S, T, and U are collinear.
Collinear points refers to the points that lies on the same straight line.
IF S, T, and U are collinear, then the sum of the numerical length of ST and the numerical length of TU is equal to the numerical length of SU.
ST + TU = SU
Given:
ST = 3x + 2
TU = 3x + 4
SU = 5x + 9
Substitute the expressions in the equation and solve for x.
ST + TU = SU
3x + 2 + 3x + 4 = 5x + 9
3x + 3x - 5x = 9 - 2 - 4
x = 3
Substitute the value of x in the expression for SU.
SU = 5x + 9
SU = 5(3) + 9
SU = 24
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If f(x)=3x+2 and g(x)=x(squared)−x, find the value.
f(-2)=______
Answer: f(-2) = - 4
Step-by-step explanation:
Determine whether each logarithm is a common logarithm.
a. (log₂4)
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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Simplify this please!
Answer:
Step-by-step explanation:
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
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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-46 decreased by the difference between -23 and -61
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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Is the expression 33x33^7 equivalent to (33x33)^7? Explain.
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
I need help with this.
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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Solve. Check for extraneous solutions. (x+5)¹/₂-(5-2 x)¹/₄=0
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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1.49 round to a whole number
Answer:
the answer is 1
Step-by-step explanation:
trust mehhhh
Can somebody simplify this? (−8) × (-6) − (−5)²
Answer:
23Step-by-step explanation:
Can somebody simplify this?
(−8) × (-6) − (−5)² =
48 - 25 =
23
someone help me please!!
Answer: Distance point is 8.
Step-by-step explanation:
You would do 2 by the power of 2 and double that (8)
What does x equal if log (1+3 x)=3 ?
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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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
Step-by-step explanation:
500.000 evvie was on the digit card
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
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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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
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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