The property that justifies the step is the Commutative Property of Addition, which states that the order of addition does not affect the result.
Explanation:The property that justifies the illustrated step in solving the equation 3x + 4 - 2x + 5 = 6x + 2 as 3x - 2x + 4 + 5 = 6x + 2 is the Commutative Property of Addition.
This property states that the order in which numbers are added does not affect the result. So, we can rearrange the terms in any order without changing their sum.
In this step, we are rearranging the terms -2x and 5 so that like terms, namely 3x and -2x, and 4 and 5, are grouped together.
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The posted speed limit is 55 MPH. If you’re driving 1000 feet per minute, are you going too fast?
When making bread from scratch, the recipe calls for 2/4 cup of water. If you need to make a smaller portion of the recipe, how much water would you need in order to make only 1/6 of the recipe? Give your answer as a fraction, reduced to lowest terms
You would need 1/12 cups of water in order to make only 1/6 of the recipe
What is the fraction?A fraction is defined as a numerical representation of a part of a whole that represents a rational number.
What are Arithmetic operations?Arithmetic operations can also be specified by addition, subtraction, dividing, and multiplying built-in functions.
When making bread from scratch, the recipe calls for 2/4 cup of water. If you need to make a smaller portion of the recipe,
If a recipe requires 2/4 cup of water, then a fraction of the recipe requires 1/6 cup of water.
So the fraction of the recipe requires 1/6 cup of water as
⇒ 1/6×2/4
⇒ 2/24
⇒ 1/12
Hence, you would need 1/12 cups of water in order to make only 1/6 of the recipe.
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Someone please help me ?
a large bottle of dragon mouth was is 5.00 before tax and 5.30 after tax. What is the percentage of tax
PLEASE HELP! 10 POINTS!
Which algebraic expression represents the phrase below?
The quotient of the opposite of a number squared and three
*choices below*
True or false? To begin an indirect proof, you assume the converse of what you intend to prove is true.
A. True
B. False
Answer:
The statement is false.
Step-by-step explanation:
To begin an indirect proof, you assume the converse of what you intend to prove is true. This is false.
Rather the correct answer is that to begin an indirect proof, you assume the inverse of what you intend to prove is true.
The converse can be either true or false, depending on what the original statement is, so assuming the converse is pointless.
Is 0.33 bigger than 20/60?
Which of these shows the result of using the first equation to substitute for y in the second equation, then combining like terms?
y = 3x
2x + 3y = 55
A. 11x = 55
B. 5x = 55
C. 9x = 55
D. 5y = 55
Answer: A(11x=55)
Step-by-step explanation:
in the equation 2x + 3y = 55, subsitute 3y for 3x, because y = 3x. this will result in the equation 2x + 3(3x) which equals 11x. so 11x=55
Austin is watching a football game. His team loses 9 yards and then gains 5 yards. He doesn’t watch the next play, but afterwards he sees that his team now has a total loss of 1 yard. How many yards did the team gain or lose on the play Austin missed? Show your work.
Assume ABC DEF. If AB = 12, BC = 15, and AC = 17, what is the length of EF? A. 15 B. 17 C. Cannot be determined D. 10
Answer:
Option A) EF = 15 units.
Step-by-step explanation:
We are given the following information in the question:
ΔABC ≅ ΔDEF
AB = 12, BC = 15, and AC = 17
If two triangles are congruent then they have the following properties:
AB = DE
BC = EF
AC = DF
[tex]\angle A = \angle D \\\angle B = \angle E \\\angle C = \angle F[/tex]
Hence, by congruency:
BC = EF
EF = 15 units.
Thus, option A is the correct answer.
I have a right triangle they need an equation from me.the truangle is X,4,7 ... Please i need help
Final answer:
The question involves using the Pythagorean theorem to find the missing side 'X' in a right triangle with sides 'X', 4, and 7. 'X' is calculated by rearranging the theorem to X² = c² - b² and plugging in the known values. The equation simplifies to X = √33.
Explanation:
The student is asking for an equation to solve for the missing side of a right triangle, where the sides are given as 'X', 4, and 7. The Pythagorean theorem, which states that a² + b² = c², is the appropriate tool for solving this problem. Since the triangle is right-angled, we assume 'X' is one leg, 4 is the other leg, and 7 is the hypotenuse as it is the longest side.
To find 'X', we rearrange the theorem to solve for the unknown leg (X) as follows: X² = c² - b². Plugging the values into the equation gives us X² = 7² - 4² which simplifies to X² = 49 - 16, hence X² = 33. Consequently, X can be found by taking the square root of 33, which we rewrite as X = √33.
In modified boxplots, a data value is a(n) _______ if it is above q3plus+(1.5)(iqr) or below q1minus−(1.5)(iqr).
In modified boxplots, a data value is a potential outlier if it is outside the range of Q3 + (1.5)(IQR) or Q1 - (1.5)(IQR). The IQR is the spread of the middle 50% of the data, calculated as Q3 - Q1.
Explanation:In modified boxplots, a data value is a potential outlier if it is above Q3 + (1.5)(IQR) or below Q1 - (1.5)(IQR). The interquartile range (IQR) is crucial in this determination, representing the spread of the middle 50 percent of the data. It is found by subtracting the first quartile (Q1) from the third quartile (Q3). For example, if Q1 is 2 and Q3 is 9, the IQR is 7. Any data value greater than 9 + (1.5)(7) or less than 2 - (1.5)(7) would be considered a potential outlier.
Constructing a box plot involves identifying these five key values: minimum value, first quartile, median, third quartile, and maximum value. The box plot visually represents the data's spread, with whiskers extending to the most extreme values within the acceptable range, and separate marks for potential outliers.
Find the second and third term of the arithmetic sequence -7, _, _, -22, -27, ...
A. -12, -15
B, -17, -12
C. -10, -17
D. -12, -17
Final answer:
The second and third terms of the arithmetic sequence are -12 and -17, found by adding the common difference of 5 to each succeeding term in the sequence.
Explanation:
The question is asking to find the second and third terms of an arithmetic sequence. An arithmetic sequence is a sequence of numbers in which the difference between the consecutive terms is constant. This constant difference is known as the common difference. In the given arithmetic sequence (-7, _, _, -22, -27), we can find the common difference by subtracting two successive terms. For this sequence, the difference between -27 and -22 is -27 - (-22) = -27 + 22 = -5. This implies that to find the previous terms, we should add 5 to each term going backwards.
Starting with -22 and adding 5, we get -17 for the third term. Similarly, adding 5 again for the second term, we get -12. Therefore, the second and third terms of the arithmetic sequence are -12 and -17, respectively.
What is the length of leg s of the triangle below
Answer: The correct option is (B) 3.
Step-by-step explanation: We are given to find the length of the leg s in the triangle shown in the figure.
From the figure, we note that
the given triangle is a right-angled one, where
length of the hypotenuse, h = √18 units,
length of one leg, p = 3 units
and
length of the other leg, s = ?.
From Pythagoras theorem, we have
[tex]h^2=p^2+s^2\\\\\Rightarrow (\sqrt{18})^2=3^2+s^2\\\\\Rightarrow 18=9+s^2\\\\\Rightarrow s^2=18-9\\\\\Rightarrow s^2=9\\\\\Rightarrow s=3.[/tex]
Thus, the length of the leg s is 3 units.
Option (B) is CORRECT.
100/225 square feet of your bakery will be used as your storefront, where customers come to visit. the rest will be for storage and baking. In simplest form, what fraction of the space will be for storage and baking?
Someone's work
(225-110)/225
125/225
5/9
how did you get (225-110)? if it's 100/225
Answer: 5/9 will be the fraction of the space will be for storage and baking.
Step-by-step explanation:
Since area of bakery will be used as our storefront, where customers come to visit= 100/225
Thus, the total area of bakery = 225
And, the area will be used our storefront, where customers come to visit= 100
So, the remaining area which is used for storage and baking = 225 - 100 =125
So the part of area which is used for storage and baking= the remaining area which is used for storage and baking/ total area
=125/225= 5/9
which is the simplest form.
Why is x = 4 a solution to the proportion 14/x = 56/16
[tex]\large\text{Hey there!}[/tex]
[tex]\large\text{Step 1: You have to \underline{\bf{CROSS MULTIPLY}}}[/tex]
[tex]\mathsf{\dfrac{14}{x}=\dfrac{56}{16}}\\\\\mathsf{14\times16=56\times x}\\\\\mathsf{14(16)= \ \bf{\underline{224}}}\\\\\mathsf{56(x)=\underline{\bf{56x}}}[/tex]
[tex]\huge\text{We get: \bf{\underline{224 = 56x}}}[/tex]
[tex]\large\text{Step 2: }\large\text{\bf{\underline{FLIP}}}\large\text{ the new equation around}[/tex]
[tex]\huge\text{\bf{\underline{56x = 224}}}[/tex]
[tex]\large\text{Step 3: \bf{\underline{DIVIDE}}}\large\text{ both of your sides by 56}[/tex]
[tex]\mathsf{\dfrac{56x}{56}=\dfrac{224}{56}}\\\\\mathsf{Cancel\ out: \dfrac{56x}{56}\ because\ that\ gives\ us\ 1}\\\\\mathsf{Keep: \dfrac{224}{56}\ because\ it\ gives you\ the\ value\ of\ x }\\\\\mathsf{\dfrac{224}{56}=4}\\\\\mathsf{x=4}[/tex]
[tex]\boxed{\large\text{So, the reason why x = 4 for this equation is because } \mathsf{\dfrac{14}{4}}\ \& \ \dfrac{56}{16}\ \large\text{ are equal to each}}\\\boxed{\large\text{other. }}[/tex]
[tex]\mathsf{\dfrac{14}{4} = 3.5}[/tex]
[tex]\mathsf{\dfrac{56}{16} = 3.5}[/tex]
[tex]\huge\text{\bf{3.5 = 3.5}} \ \checkmark[/tex]
[tex]\large\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\dag\dfrac{\frak{LoveYourselfFirst}}{:)}[/tex]
Wilma and Betty are playing a number game. Wilma tells Betty, "I'm thinking of a number between 1 and 10. If I take the number and add 4 to it and then multiply that by 3, I get 30." What number is Wilma thinking of?
To find the number Wilma is thinking of, we create an equation and solve for x.
Explanation:To solve this problem, we need to create an equation based on the information given. Let's suppose the number Wilma is thinking of is x. According to the problem, if we add 4 to x and then multiply that result by 3, we get 30. We can write this as the equation 3(x + 4) = 30. To find the value of x, we need to isolate it. First, distribute the 3 to both terms inside the parentheses: 3x + 12 = 30. Next, isolate x by subtracting 12 from both sides of the equation: 3x = 18. Finally, solve for x by dividing both sides of the equation by 3: x = 6. Therefore, Wilma is thinking of the number 6.
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can someone please simplify 81^5 = 3^x
Answer:
20
Step-by-step explanation:
:D
The value of the x is 20.
We have given that,
[tex]81^5 = 3^x[/tex]
We have to determine the value of x.
3^4 = 81
What is the exponent?Exponentiation is a mathematical operation, written as bⁿ, involving two numbers, the base b, and the exponent or power n, and pronounced as b raised to the power of n.
exponent 4 x 5 = 20
so, 3^20 = 81^5
Therefore the value of the x is 20.
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If the volumes of two similar rectangular prisms are 40mm and 135mm find the scale factor of the two rectangular prisms.
(The answers are in fraction form)
A. 1/4
B. 8/27
C. 3/5
D. 2/3
The scale factor of the two rectangular prisms is 3/2 of the given problem the volumes of two similar rectangular prisms are 40 mm and 135 mm
To find the scale factor between two similar rectangular prisms, we can compare their volumes. The scale factor is the ratio of the cube root of the volumes.
Let's denote the volume of the first rectangular prism as V1 and the volume of the second rectangular prism as V2.
[tex]V1 = 40 mm^3\\V2 = 135 mm^3[/tex]
The scale factor (SF) can be calculated as follows:
[tex]SF = (V2)^{(1/3)} / (V1)^{(1/3)[/tex]
Plugging in the given values:
[tex]SF = (135)^{(1/3)} / (40)^{(1/3)[/tex]
To simplify the calculation, we can rewrite the values as prime factorization:
[tex]135 = 3^3 * 5\\40 = 2^3 * 5[/tex]
Now, let's calculate the cube roots:
[tex]SF = (3^3 * 5)^{(1/3) }/ (2^3 * 5)^{(1/3)}[/tex]
Using the property of exponents [tex](a^{(m/n) }= (a^m}^{(1/n)})[/tex]:
[tex]SF = (3^{(3/3)} * 5^{(1/3)}) / (2^{(3/3)} * 5^{(1/3)})[/tex]
Simplifying the fractions:
[tex]SF = 3 * 5^{(1/3)} / 2 * 5^{(1/3)[/tex]
The [tex]5^{(1/3)}[/tex] terms cancel out:
SF = 3/2
Therefore, the scale factor of the two rectangular prisms is 3/2 of the given problem the volumes of two similar rectangular prisms are 40 mm and 135 mm.
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Solve each system by substitution
y=-4x + 5
y= -2x + 1
Lorrae swims at a constant speed, s, for 2 hours. Create a formula for the distance she swims, d.
The formula for the distance Lorrae swims at a constant speed for 2 hours is d = 2s, where d is distance and s is her speed.
Explanation:The question is asking for a formula to calculate the distance that Lorrae swims. Since distance (d) is equal to speed (s) multiplied by time (t), and we know that Lorrae swims at a constant speed, s, for 2 hours, a formula for her distance would be d = s * t.
In this case, the time, t, is 2 hours. So, we can substitute t with 2 in our formula. Hence, the formula for the distance Lorrae swims is d = s * 2 or d = 2s. This is the equation you can use to compute the distance Lorrae swims for any given speed at a constant period of 2 hours.
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Find the value of x so that the function has the given value.
r(x)=−5x−1; r(x)=19
x=
To find the value of 'x' that makes the function r(x) = 19, we need to solve the equation -5x - 1 = 19 for 'x'. After doing so, we obtain x = -4.
Explanation:This question involves finding the value of 'x' in a mathematical function provided, in order to get a specific output. The function provided is r(x) = -5x - 1 and the question states that the output r(x) should be 19. We can setup the equation -5x - 1 = 19 and solve for 'x'.
Adding 1 to both sides of the equation, we obtain -5x = 20. Dividing both sides by -5 gives x = -4. So, the value of 'x' that makes the function r(x) = 19 is x = -4.
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Find the dimensions of the rectangular corral split into two pens (sharing a fence) of the same size producing the greatest enclosed area given 630 630 feet of fencing.
To find the dimensions of the rectangular corral split into two pens that produce the greatest enclosed area, use the perimeter and area formulas for a rectangle.
Explanation:To find the dimensions of the rectangular corral split into two pens that produce the greatest enclosed area, we can use the perimeter formula for a rectangle. Let L and W represent the length and width of each pen. The total fencing length will be 2L + 3W, and since it is given as 630 feet, we have 2L + 3W = 630. We can rearrange this equation to solve for one variable in terms of the other, substitute it into the area formula for a rectangle, and then find the maximum value using the first derivative test.
Using the equation 2L + 3W = 630, we can solve for L in terms of W: L = (630 - 3W) / 2. Substituting this into the area formula A = LW, we get A = (630 - 3W)W / 2. Taking the first derivative of A with respect to W, we have dA/dW = 630/2 - 3W/2. Setting this equal to zero, we find W = 105. Substituting this back into the equation 2L + 3W = 630, we can solve for L: 2L + 3(105) = 630, and simplifying gives L = 210/2 = 105.
Therefore, the dimensions of each pen that produce the greatest enclosed area are 105 feet by 105 feet.
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Through: (-4,4), perp. To y=4/5x-1
If you drive at 100km/hr for 6 hours, how far will you go
The distance covered by the vehicle in 6 hours will be 600 km.
What is speed?The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.
We know that the speed formula
Speed = Distance/Time
If you drive at 100km/hr for 6 hours.
Then the distance covered by the vehicle in 6 hours will be given as,
100 = Distance / 6
Distance = 100 x 6
Distance = 600 km
The distance covered by the vehicle in 6 hours will be 600 km.
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Suppose p = log n ( g ) p=logn(g). define an exponential relationship between p , n , p,n, and g g.
Paige made $1411.75 last year by investing a total of $15,250 in two accounts: one paying 8.5% annual interest and the other paying 10% annual interest. How much did she invest in each account?
Choose the correct answers for interest in dollars and the proceeds for the following problem. Sam Sounds received a $320 discount loan to purchase a stereo. The loan was offered at 16% for 90 days. Find the interest in dollars and the proceeds for the following problem.
The Interest is $12.595 while the value of the Proceeds is $307.405
How to find the interest and proceeds?The amount of loan; A = $320
The discount rate = 16%=0.16
Time = 90 days = 90/365 year = 0.246 year
The formula of interest is;
Interest = Amount × Discount rate × Time
Thus;
Interest = 320 × 0.16 × 0.246
Interest = $12.595
Proceed = Amount - Interest
Proceed = $320 - $12.595
Proceeds = $307.405
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Answer:
12.80
307.20
Step-by-step explanation:
You earned $23.10. You would like to buy some new T-shirts. Estimate the number of T-shirts you can buy if each one costs $5.75.
Which theorem could kari use to show the measure of angle qml is supplementary to the measure of angle snk? (1 point)?