Answer:
The wrong in Rafael reason is that 3/6 = 4/8 = 1/2 pizza
Step-by-step explanation:
* Lets explain how to solve the problem
- When we have a quantity we can divided it to many equivalent
fractions
- Equivalent fractions means fractions equal each other
- We can find the equivalent fraction by multiply or divide the two
terms of the fraction by the same number
- Ex: We can divide a circle into two equal parts each part is 1/2 the
circle, if we multiply each term of the fraction by 2 (up and down)
then we will have 2/4 which is equivalent to 1/2 the circle
- Then we can divide the circle by 2 parts with many equivalent fractions
1/2 = 2/4 = 3/6 = ..................
* Lets solve the problem
- Rafael wanted to order half a medium pizza
- The medium pizza could be cut into 6 or 8 slices
∵ The half of 6 is 3/6
∵ The half of 8 is 4/8
- Lets simplify the two fraction
∵ 3/6 = 1/2 by dividing up and down by 3
∵ 4/8 = 1/2 by dividing up and down by 4
∴ There is no difference between the two orders, both of them
equal half the pizza
∴ The wrong in Rafael reason is that 3/6 = 4/8 = 1/2 pizza
Matthew invested $3,000 into two accounts. One account paid 3% interest and the other paid 8% interest. He earned 4% interest on the total investment. How much money did he put in each account?
Answer:
Mathew invested $600 and $2400 in each account.
Solution:
From question, the total amount invested by Mathew is $3000. Let p = $3000.
Mathew has invested the total amount $3000 in two accounts. Let us consider the amount invested in first account as ‘P’
So, the amount invested in second account = 3000 – P
Step 1:
Given that Mathew has paid 3% interest in first account .Let us calculate the simple interest [tex](I_1)[/tex] earned in first account for one year,
[tex]\text {simple interest}=\frac{\text {pnr}}{100}[/tex]
Where
p = amount invested in first account
n = number of years
r = rate of interest
hence, by using above equation we get [tex](I_1)[/tex] as,
[tex]I_{1}=\frac{P \times 1 \times 3}{100}[/tex] ----- eqn 1
Step 2:
Mathew has paid 8% interest in second account. Let us calculate the simple interest [tex](I_2)[/tex] earned in second account,
[tex]I_{2} = \frac{(3000-P) \times 1 \times 8}{100} \text { ------ eqn } 2[/tex]
Step 3:
Mathew has earned 4% interest on total investment of $3000. Let us calculate the total simple interest (I)
[tex]I = \frac{3000 \times 1 \times 4}{100} ----- eqn 3[/tex]
Step 4:
Total simple interest = simple interest on first account + simple interest on second account.
Hence we get,
[tex]I = I_1+ I_2 ---- eqn 4[/tex]
By substituting eqn 1 , 2, 3 in eqn 4
[tex]\frac{3000 \times 1 \times 4}{100} = \frac{P \times 1 \times 3}{100} + \frac{(3000-P) \times 1 \times 8}{100}[/tex]
[tex]\frac{12000}{100} = \frac{3 P}{100} + \frac{(24000-8 P)}{100}[/tex]
12000=3P + 24000 - 8P
5P = 12000
P = 2400
Thus, the value of the variable ‘P’ is 2400
Hence, the amount invested in first account = p = 2400
The amount invested in second account = 3000 – p = 3000 – 2400 = 600
Hence, Mathew invested $600 and $2400 in each account.
you are designing a room for a house and are drawing a floor plan. The room is actually 18 feet wide. On your floor plan, you draw the room as 6 inches wide. what is the scale factor for the floor plan
Answer:
1:3
Step-by-step explanation:
18 / 6 = 3
Answer:
3 feet per inch
Step-by-step explanation:
trust me bro
Solve 23(3x+9)=−2(2x+6).
George has a mass of 65kg. What would George weigh on the Moon? (The gravitational field strength on the Moon is 1.6N/kg.)
George would weigh
65 kg × 1.6N /kg = 104 Newtons
That's compared to around 650 Newtons on earth.
Answer: Weight of George on Moon =104 N
Step-by-step explanation:
Given : George has a mass of 65 kg.
The gravitational field strength on the Moon is 1.6N/kg.
Then, the weight of George on Moon = George's Mass x Gravitational field strength
=[tex]65\times1.6=104\text{ Newtons}[/tex]
Hence, the weight of George on Moon =104 N
I am thinking of a number.Multply my number 5 and add 13
Hey!
-----------------------------------------------
[tex]\boxed{ \bf 5n~+~13}[/tex]
-----------------------------------------------
Solution:
Number = n
Multiply a number and five: 5n
Add thirteen: + 13
End Result: 5n + 3
-----------------------------------------------
Hope This Helped! Good Luck!
If your target number of calories is 1700 per day to lose weight, but you are consuming 2500 calories per day. Then, your target is to consume what percent of the calories you are consuming?
Answer:
32%
Step-by-step explanation:
We have been given that your target number of calories is 1700 per day to lose weight, but you are consuming 2500 calories per day.
First of all, we will find number of calories you should eat to lose weight by subtracting 1700 calories from 2500 calories.
[tex]2500-1700=800[/tex]
Now, we will find 800 is what percent of 2500.
[tex]\frac{800}{2500}\times 100=0.32\times100=32\%[/tex]
Therefore, your target should be consume 32% of the calories, you are consuming.
Rewrite the function f of x equals 4 times one third to the 2 times x power using properties of exponents. f of x equals 4 times one ninth to the x power f of x equals 4 times two sixths to the x power f of x equals 16 times one third to the x power f of x equals 16 times one ninth to the x power
Answer:
A
Step-by-step explanation:
Answer:
Option 1
Step-by-step explanation:
Given : Function f of x equals 4 times one third to the 2 times x power.
To find : Rewrite the function using properties of exponents ?
Solution :
Writing the function in numeric terms,
f of x equals 4 times one third to the 2 times x power
i.e. [tex]f(x)=4\times (\frac{1}{3})^{2x}[/tex]
Solve the expression,
[tex]f(x)=4\times (\frac{1}{3}^2)^{x}[/tex]
[tex]f(x)=4\times (\frac{1}{9})^{x}[/tex]
i.e. f of x equals 4 times one ninth to the x power.
Therefore, Option 1 is correct.
The polygon below is an irregular pentagon.
Answer:
○ D) Need more information
Step-by-step explanation:
We do not have have enough angle measures to know how to solve this, although each interior angle in a pentagon is 108°.
I am joyous to assist you anytime.
Round 19,837 to the nearest hundred.
The answer is 19,800
If you need a better explanation just as in the comments.
Happy to help! Please mark as BRAINLIEST! Thanks
Answer:
19,837 rounded to the nearest hundred is 19,800
Step-by-step explanation:
so we know that 4 and under we keep the number the same, so the 3 in the tens place means that we keep the 8 ind the hundreds place the same and so that leads us to our answer, 19,800
Hope I helped :)
How many times larger is 400 than 4
Answer:
It's 100x bigger.
Step-by-step explanation:
I divided 400 by 4 and got 100.
To check the work, you multiply 100 by 4.
The number 400 is 100 times greater than 4 when we divide the number 400 by 4.
What is a fraction?The fraction is defined as the division of the whole part into an equal number of parts. The fraction is defined as the representation of one number with respect to the other number. or one number is how many times the other number.
Given numbers are 400 and 4. To calculate the times divide the number 400 by 4. The division will be done as below:-
Divison = 400 / 4
Division = 100
Therefore, the number 400 is 100 times greater than 4.
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The slope of the line below is -1/7. Write a point slope equation of the line using the coordinates of the labeled point
Answer:
○ D. y - 3 = -⅐(x - 3)
Step-by-step explanation:
According to the Point-Slope Formula, y - y₁ = m(x - x₁), all the negative symbols give the OPPOSITE terms of what they really are, so be EXTREMELY careful inserting the coordinates into the formula with their CORRECT signs.
I am joyous to assist you anytime.
Equation of line is [tex]y = -\frac{x}{7} + \frac{24}{7}[/tex]
Formula for finding Equation of line?[tex]y - y_{1} = m ( x - x_{1} )[/tex]
where [tex](x_{1},y_{1})[/tex] are coordinates and m is slope.
How to solve?
Given:- Coordinate (3,3) and slope [tex]\frac{-1}{7}[/tex]
Equation of line:
[tex]y - y_{1} = m ( x - x_{1} )[/tex]
given : [tex]x_{1} = 3 , y_{1} = 3 , m = -\frac{1}{7}[/tex]
substituting values, Equation of line is:
y - 3 = [tex]-\frac{1}{7}[/tex] ( x - 3)
[tex]y = - \frac{x}{7} + \frac{3}{7} + 3[/tex]
[tex]y = -\frac{x}{7} + \frac{24}{7}[/tex]
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Keith has $500 in a savings account at the beginning of the summer. He withdraws $25 per week for food,clothing, and movie tickets. How many weeks can Keith withdraw money from his account?
Answer:
20 weeks.
Step-by-step explanation:
So, he has $500 in savings and he's taking out $25 each week. That would be $25 x ?. Which is the same as 500 divided by 25 which equals 20. I hope this helps!
Keith can withdraw $25 each week from his $500 savings account for 20 weeks.
Keith starts with $500 in his savings account and withdraws $25 every week. To determine how many weeks he can continue these withdrawals, we need to divide his initial amount by the weekly withdrawal amount.
Let's perform the calculation step by step:
Initial amount in the savings account: $500Weekly withdrawal amount: $25Number of weeks Keith can withdraw money = $500 / $25Perform the division: $500 ÷ $25 = 20 weeksSo, Keith can withdraw money from his account for 20 weeks.
the perimeter of a rectangle if the width is 3 centimeters and the length is 6 centimeters longer than the width.
Answer:
24
Step-by-step explanation:
Length 9 (3+6)
Width 3
Perimeter = 2 times length + 2 times width
18 + 6 = 24
What is the polynomial function of least degree whose only zeros are -3, ,-2, and 4 ?
The polynomial function of least degree with zeros -3, -2, and 4 is f(x) = (x+3)×(x+2)×(x-4), which is a cubic polynomial.
The polynomial function of least degree with given zeros of -3, -2, and 4 is derived from the fact that if a polynomial has zeros at x=a, x=b, and x=c, then it can be represented as f(x) = k×(x-a)×(x-b)×(x-c), where k is any non-zero constant. Given the zeros -3, -2, and 4, the polynomial function is:
f(x) = k×(x+3)×(x+2)×(x-4)
Because the question does not specify a leading coefficient, we can assume k=1 for the least degree polynomial. Thus, the final form of the polynomial would be:
f(x) = (x+3)×(x+2)×(x-4)
Expanding this would give us a cubic polynomial, which is the polynomial of least degree that satisfies the condition of having exactly these three zeros.
Essential Question How do the signs of
factors affect their product?
Answer:
If a negative number is multiplied with a positive number, the result will be negative. If two positive numbers are multiplied, the result will be positive. If two negative numbers are multiplied, the result will also be positive.
Mathematical signs are very important to take note of when multiplying factors.
The product of an addition and subtraction sign results in a negative sign. This is important as it affects the signs of factors affecting their product. For instance; -3 (2 + 5)According to distributive law, the negative sign will affect the positive sign in the bracket to have -3(2) -3(5) = -6 - 15
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Pd).
cot x/sec x
show that -=cos ecx -sin x
Answer:
see explanation
Step-by-step explanation:
Using the trigonometric identities
• cot x = [tex]\frac{cosx}{sinx}[/tex]
• sec x = [tex]\frac{1}{cosx}[/tex] and cosec x = [tex]\frac{1}{sinx}[/tex]
Consider the left side
[tex]\frac{cotx}{secx}[/tex]
= [tex]\frac{cosx}{sinx}[/tex] × cosx
= [tex]\frac{cos^2x}{sinx}[/tex]
= [tex]\frac{1-sin^2x}{sinx}[/tex]
= [tex]\frac{1}{sinx}[/tex] - [tex]\frac{sin^2x}{sinx}[/tex]
= cosec x - sin x
= right side ⇒ verified
i need the answer on number 8
Answer:
van: 18
bus: 59
Step-by-step explanation:
x: students per van
y: students per bus
Highschool A:
x + 6y = 372 / *(-2)
Highschool B:
4x + 12y = 780
-2x - 12y = - 744
2x = 36
x = 18
Replace x in 1 equation
18 + 6y = 372
y = 59
3. A scientist starts an experiment with 5 bacteria. The number triples every 30
minutes. How many bacteria are in the culture after 2 hours and 30 minutes?
Answer:
1215 bacteria
Step-by-step explanation:
5 x 3 = 15 (after 30 minutes)
15 x 3 = 45 (after 60 minutes)
45 x 3 = 135 (after 90 minutes)
135 x 3 = 405 (after 120 minutes)
405 x 3 = 1215 (after 150 minutes)
11 help cause I'm stuck
:3
11
let's say each restaurant has a container of soup which is the same size, let's say there is a total of "s" amount of soup in the container of each restaurant, so 5/4 of that much will just be (5/4)s and 7/4 of "s" is just (7/4)s.
well, one restaurant makes 20 servings from 5/4 of it and the other makes 25 from 7/4 of it,
[tex]\bf \cfrac{5}{4}s\div 20\implies \cfrac{5}{4}s\div \cfrac{20}{1}\implies \cfrac{~~\begin{matrix} 5 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{4}s\cdot \cfrac{1}{\underset{4}{~~\begin{matrix} 20 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}\implies \boxed{\cfrac{1}{16}}s \\\\[-0.35em] ~\dotfill\\\\ \cfrac{7}{4}s\div 25\implies \cfrac{7}{4}s\div \cfrac{25}{1}\implies \cfrac{7}{4}s\cdot \cfrac{1}{25}\implies \boxed{\cfrac{7}{100}}s[/tex]
now, which one is larger? well, we can simply put both fractions with the same denominator by multiplying one by the other's denominator,
[tex]\bf \cfrac{1}{16}\cdot \cfrac{100}{100}\implies \boxed{\cfrac{100}{1600}}\qquad \qquad \qquad \stackrel{\textit{\Large larger}}{\cfrac{7}{100}\cdot \cfrac{16}{16}\implies \boxed{\cfrac{112}{1600}}}[/tex]
7x = 2y solve for y in terms of x
Y=?
Answer:
7x/2
Step-by-step explanation:
7x=2y
1) Divide both sides by 2:
y=7x/2
10
TIME REMAINING
53:10
The functions f(x) and g(x) are graphed.
Which represents where f(x) = g(x)?
O f(2) = g(2) and f(0) = g(0)
O f(2) = g(0) and f(0) = g(4)
O f(2) = g(0) and f(4) = g(2)
O f(2) = g(4) and f(1) = g(1)
Answer:
first one. Since its X crosses or passes (2,0)
Step-by-step explanation:
The value of function represents with same domain f(x)= g(x) is f(2) = g(2) and f(0) = g(0).
We know that two functions f and g are said to be equal if:
(i) f and g have same domain D
(ii) for all x ∈ D, f(x) = g(x)
Thus, we must select the response that best captures the situation where f(x) = g. (x)
Considering the fact that f(x) and g(x) are defined on the same domain
If they are equivalent for all values of x in the domain, then f(x) = g(x).
Thus, f(2) = g(2) and f(0) = g(0)
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What digit is in the tens place in the number 35,176?
Answer:7
Step-by-step explanation:
Ten Thousands Thousands Tens
3 5 7
Answer:
7
Step-by-step explanation:
The ones place always starts on the left then it works it way up.
ones, Tens, hundreds, thousands, ten thousands and it goes on in the same ones tens hundreds pattern
A waitress sold 10 ribeye steak dinners and 45 grilled salmon dinners, totaling $591.99 on a particular day. Another day she sold 24 ribeye steak dinners and 15 grilled salmon dinners, totaling $583.39. How much did each type of dinner cost?
Answer:
The cost of a ribeye steak dinner is $18.68 and the cost of a grilled salmon dinner is $9.00
Step-by-step explanation:
Let
x ----> the cost of a ribeye steak dinner
y ----> the cost of a grilled salmon dinner
we know that
10x+45y=591.99 -----> equation A
24x+15y=583.39 ----> equation B
Solve the system by graphing
Remember that the solution is the intersection point both graphs
The solution is the point (18.68,9.00)
see the attached figure
therefore
The cost of a ribeye steak dinner is $18.68 and the cost of a grilled salmon dinner is $9.00
Find the equation of the line passing through the given point and perpendicular to the given equation write your answer in slope intercept form. (3,4) and y= -4/9x-3
Answer:
Step-by-step explanation:
To find the slope of a line perpendicular to y = (-4/9)x - 3, take the negative reciprocal of this slope -4/9. The slope of the new line is thus 9/4.
Now we have this data to work with: m = 9/4, y = 4 and x = 3. Subbing this info into y = mx + b, to obtain the value of b, we get:
4 = (9/4)(3) + b, or
4 = 3/4 + b. Thus, b = 3 1/4, or b = 13/4.
The desired equation is
y = (9/4)x + 13/4.
in this diagram below, the 2 line segments are congruent. Find the value of x
Answer:
Step-by-step explanation:
because the two line segments are the same length-->
12+10-x=18
x=22-18=4
The question aims to determine the value of x for two congruent line segments, typically involving algebraic and geometric methods; however, no specific solution can be provided without the diagram.
Explanation:The question involves finding the value of x when given two congruent line segments in a diagram. This typically requires the use of algebraic methods or the application of geometric theorems to establish relationships between the lengths represented in the diagram and solve for x.
Without the specific diagram, we cannot provide the direct steps to solve for x.
However, the context suggests the use of equations to calculate lengths. Common strategies include setting equations equal to each other when line segments are congruent and simplifying to find x.
The mention of bisectors and lines intersecting at right angles can also imply the use of properties related to parallel and perpendicular lines or the Pythagorean theorem.
Remember, when equations have two solutions for x, it's necessary to consider which solution is consistent with the geometric context of the problem.
Which expression is equal to [tex]2\sqrt{-27}[/tex] ?
−6i3√
63i−−√
6i3√
−63√
Answer:
6i3√ or 6i√3
Step-by-step explanation:
it takes away the - it is a trick question
Using root properties and complex numbers, it is found that the equivalent expression is:
[tex]6i\sqrt{3}[/tex]
----------------------------------
The most widely used definition in complex numbers is:
[tex]i^2 = -1 \rightarrow \sqrt{-1} = i[/tex]
The expression is:
[tex]2\sqrt{-27} = 2\sqrt{3 \times -9} = 2\sqrt{3 \times 9 \times -1}[/tex]
Applying the property:
[tex]2\sqrt{3 \times 9 \times -1} = 2\sqrt{3}\sqrt{9}\sqrt{-1} = 6i\sqrt{3}[/tex]
[tex]6i\sqrt{3}[/tex] is the equivalent expression.
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is -8 a solution to the equation 3x=16-5x
Answer: YEP
Step-by-step explanation: -8 makes it -24=16-40, which is -24
I HOPE THIS HELPS. HAVE THE MOST AMAZING WEEKEND EVER CHILD
༼ つ ◕_◕ ༽つ
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Divide the following polynomial and then place the answer in the proper location on the grid.
8y 7 ÷ 4y 5
Answer:
2y^2. 8/4 = 2 and y^7/y^5 is y^2 i don't know if this is what you completely asked for but here is the answer
Step-by-step explanation:
Division of the given polynomial [tex]8y^{7}[/tex] ÷ [tex]4y^{5}[/tex]is equal to [tex]2y^{2}[/tex].
What is division?" Division is defined as the distribution of a given quantity into equal parts as per the given condition."
Formula used
[tex]a^{m}[/tex] ÷ [tex]a^{n}[/tex] [tex]= a^{m-n} , m > n[/tex]
According to the question,
Given polynomial,
[tex]8y^{7}[/tex] ÷ [tex]4y^{5}[/tex]
Division of given polynomial also use the formula we get,
[tex]8y^{7}[/tex] ÷ [tex]4y^{5}[/tex]
[tex]= 2 y^{7-5} \\\\= 2y^{2}[/tex]
Hence, division of the given polynomial [tex]8y^{7}[/tex] ÷ [tex]4y^{5}[/tex]is equal to [tex]2y^{2}[/tex].
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Mario wants to put a rectangular fence around the pool in his backyard. Since one side is adjacent to the house, he will only need to fence three sides. There is one long side parallel to the house, and two shorter sides. He needs 130 feet of fencing to enclose the pool. The length of the long side is 10 feet less than twice the width. Find the length and width of the pool area to be enclosed.
Answer:
The length and width of the pool area is:
Length = 60 feet. Width = 35 feet.Step-by-step explanation:
Since the 130-foot fence should enclose only three parts of the pool (two wide and one long), equations are performed to express the information provided.
First an equation that says the total feet in the fence:
X + 2Y = 130 (where X is the length and Y is the width) X = 2Y-10 (since the length is 10 feet less than twice the width)With these equations, we proceed to replace the second equation in the first one and solve for Y:
X + 2Y = 130 2Y -10 + 2Y = 130 4Y - 10 = 130 4Y = 130 + 10 Y = 140/4 Y = 35 feetSince we already know that the width corresponds to 35 feet, we use the second equation to find the value of X:
X = 2Y-10 X = 2 (35) -10 X = 70 - 10 X = 60With which it is identified that the length is 60 feet.
To find the dimensions of the pool area, we can set up an equation using the given information. Solving the equation, we find that the width of the pool area is 35 feet and the length is 60 feet. Therefore, the dimensions of the pool area to be enclosed are 35 feet by 60 feet.
Explanation:To find the dimensions of the pool area, we will set up an equation based on the given information. Let's say the width of the pool area is 'w'. According to the problem, the length of the long side is 10 feet less than twice the width, so the length can be represented as 2w - 10. Since Mario needs to fence three sides, we can calculate the total length of the fence as follows:
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u=3a-1
Solve the equation for the indicated variable: a