Answer:
(2,-5)
Step-by-step explanation:
P(2,5)
(x,y)
Reflection over x-axis so the x coordinate stays the same while the y coordinate changes from a positive to a negative.
The point P(2, 5) reflected over the x-axis will have coordinates (2, -5), as the x-coordinate remains unchanged and the y-coordinate becomes negative.
Explanation:When the point P(2, 5) is reflected over the x-axis, the x-coordinate remains the same while the y-coordinate changes sign. Therefore, the coordinates of the resulting point, P', after reflection would be (2, -5). This is because reflecting over the x-axis means that we keep the horizontal position of the point the same (same x-coordinate), but flip the vertical position (change the sign of the y-coordinate).
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what is the fifth term of the geometric sequence? 5, 15 , 45, ...
The geometry sequence has the equation [tex]a(n)=5(3^{n-1})[/tex].
The 5 represents the first number of the sequence and the 3 represents the common ratio.
a(5) = [tex]5(3^{5-1})=5(3^{4})=5(81)=405[/tex]
answer: 405
Answer:
It is 405.
It is 405.
3. The product of 7/10 and another factor
is greater than 7/10. Which could be
the other factor?
A. 4/3
B. 5/9
C. 10/12
D. 7/7
Answer:
C
Step-by-step explanation:
product of 7 and 10 is 70
product of 10 and 12 is 120
a = 12
b =45
c =120
d =49
if 1/5 of the remaining blueberries is used to make muffins, how many pounds of blueberries are left in the container
To determine how many pounds of blueberries are left in the container after using 1/5 for muffins, calculate 4/5 of the initial amount, as this represents the remaining 80%. The ability to work with fractions and percentages is crucial here.
Explanation:The question involves understanding percentages and unit conversion. If 1/5 of the remaining blueberries is used to make muffins, that means 80% (or 4/5) of the blueberries are left in the container. To find out how many pounds of blueberries are left, we first need to know the total quantity before using any for muffins. Assuming we had a specific weight to begin with, we would calculate 4/5 of that weight to determine what remains.
For example, if there were 10 pounds of blueberries initially, 2 pounds (1/5) would be used for muffins, leaving 8 pounds (4/5) of blueberries in the container. It's essential to be comfortable with fractions and percentage calculations when dealing with such problems in mathematics.
a. Each bowl contains 1/12 of the total blueberries.
b. There were 72 ounces of blueberries in the full container.
c. There are 3 pounds of blueberries left in the container.
a. What fraction of the blueberries is in each bowl?
Initially, 1/6 of the blueberries are poured equally into two bowls. Therefore, each bowl receives 1/6 * 1/2 = 1/12 of the total blueberries.
b. If each bowl has 6 ounces of blueberries in it, how many ounces of blueberries were in the full container?
Since each bowl has 6 ounces of blueberries, and there are two bowls, the total amount of blueberries poured into the bowls is 6 * 2 = 12 ounces. Since this represents 1/6 of the total blueberries, we can set up the equation:
Total blueberries = 12 * 6 = 72 ounces
c. If 1/5 of the remaining blueberries are used to make muffins, how many pounds of blueberries are left in the container?
After pouring 1/6 of the blueberries into the bowls, 5/6 of the blueberries remain. Then, 1/5 of these remaining blueberries are used to make muffins. So, the fraction of blueberries remaining after making muffins is 5/6 * 4/5 = 20/30 = 2/3.
To convert the remaining blueberries to pounds, since 1 pound equals 16 ounces, we divide the total remaining ounces by 16:
Remaining blueberries in pounds = (72 ounces * 2/3) / 16 ounces/pound = (72 * 2) / (3 * 16) = 144 / 48 = 3 pounds
So, there are 3 pounds of blueberries left in the container.
The probable question maybe:
A container is filled with blueberries. 1/6 of the blueberries are poured equally into two bowls.
a. What fraction of the blueberries is in each bowl?
b. If each bowl has 6 ounces of blueberries in it, how many ounces of blueberries were in the full container?
c. If 1/5 of the remaining blueberries are used to make muffins, how many pounds of blueberries are left in the container?
The sum of the square of a positive number and the square of 3 more than the number is 89. What is the number?
The number is 5 which sum of the square of a positive number and the square of 3 more than the number 89.
What is a quadratic function?The quadratic function is defined as a function containing the highest power of a variable is two.
We have to determine the number which sum of the square of a positive number and the square of 3 more than the number 89.
Let the first number would be x
So second number = x + 3
According to the given condition,
⇒ x² + (x + 3)² = 89
⇒ x² + x² + 6x + 9 = 89
⇒ 2x² + 6x + 9 = 89
⇒ 2x² + 6x - 80 = 0
⇒ x² + 3x - 40 = 0
⇒ (x + 8)(x - 5) = 0
⇒ x + 8 = 0 or x - 5 = 0
⇒ x = -8 or x = 5
The answer is 5 because we are looking for a positive number.
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Final answer:
The positive number where the sum of its square and the square of 3 more than the number equals 89 is 5.
Explanation:
To determine the positive number where the sum of squares of the number and the square of 3 more than the number equals 89, we set up the following equation:
Let x be the positive number. Then:
x² + (x + 3)² = 89
Expanding the equation:
x² + x² + 6x + 9 = 89
Combining like terms, this becomes:
2x² + 6x + 9 = 89
Subtract 89 from both sides:
2x² + 6x - 80 = 0
We now have a quadratic equation. Dividing by 2 for simplicity:
x² + 3x - 40 = 0
Factor the quadratic equation:
(x + 8)(x - 5) = 0
Setting each factor equal to zero gives us two possible solutions for x:
x + 8 = 0, so x = -8 (which we can disregard as we are looking for a positive number)x - 5 = 0, so x = 5 (which is the positive number we're looking for)Therefore, the positive number is 5.
Dividing decimals
0.7 divided by 0.1995
Final answer:
When dividing 0.7 by 0.1995, it is crucial to perform the calculation accurately and round it according to the significant figures of the original numbers. Calculators will provide an exact answer, but understanding significant figures is necessary for a correctly rounded result.
Explanation:
Dividing Decimals
When we divide 0.7 by 0.1995, we have to handle decimals properly. It's similar to how a calculator operates but with an understanding of significant figures. The division of decimals can be tricky because calculators give an exact numerical value, which may not respect the precision of the input numbers.
For instance, if we divide 12.2 by 1.7 using a calculator, we get many decimal places. But based on the initial data's significant figures, we must round our answer appropriately. Similarly, if we divide 1.9436 by various powers of 10, we get:
1.9436 ÷ 100 = 0.019436
1.9436 ÷ 1000 = 0.0019436
When dividing by powers of 10, we move the decimal point to the left for each power. In more complex divisions or when your calculator presents more decimals than necessary, it is important to round the answer to the correct number of significant figures.
HELP
A gardener is planting two types of trees:
Type A is 2 feet tall and grows at a rate of 25 inches per year.
Type B is 10 feet tall and grows at a rate of 9 inches per year.
Algebraically determine exactly how many years it will take for these trees to be the same height.
Answer:
It will take 1/2 of a year or 6 months for these trees to be the same height.
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Type A is 2 feet tall and grows at a rate of 25 inches per year.
Type B is 10 feet tall and grows at a rate of 9 inches per year.
2. Algebraically determine exactly how many years it will take for these trees to be the same height.
x = Number of years
Type A = 2 + 25x
Type B = 10 + 9x
Let's solve for x, using the following equation:
Type A = Type B
2 + 25x = 10 + 9x
25x - 9x = 10 - 2
16x = 8
x = 8/16 = 1/2
It will take 1/2 of a year or 6 months for these trees to be the same height.
Let's prove it, this way:
2 + 25x = 10 + 9x
2 + 25 (1/2) = 10 + 9 (1/2)
2 + 25/2 = 10 + 9/2
29/2 = 29/2
14.5 = 14.5
Round to the nearest tenth, if necessary. Question: z2 = 361
options:
A.) 18, –18
B.) 180.5, –180.5
C.) 19, –19
D.) 19
The answer is option C) 19,-19
Step-by-step explanation:
Given, z² = 361
To eliminate the square of z, take square root on both sides
z = √361
The factor of 361 could not be an even number, since the last digit of 361 is odd. So, eliminate option A)The option B) is a larger number and it cannot be the answer. So, eliminate it.Try option C) works or not. (19)² = 19[tex]\times[/tex]19 = 361 and (-19)² = -19[tex]\times[/tex]-19 = 361.Therefore, z = √361 = ±19. option C) is the correct answer.[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{z^2 = 361}\\\\\large\text{Take the square root of the number 361}\\\\\mathsf{z = \pm \sqrt{361}}\\\\\large\text{Simplify it}\\\\\mathsf{z = -19\ or\ z = 19}\\\\\\\huge\text{Therefore your answer should be:}\\\huge\boxed{\mathsf{z = 19\ or\ z = -19 \ (Option\ C.)}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
What is the equation of the line that passes through the points (-4, 0.5) and (4, -0.5?
Answer:
y=-1/8x
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-0.5-0.5)/(4-(-4))
m=(-1)/(4+4)
m=-1/8
y-y1=m(x-x1)
y-0.5=-1/8(x-(-4))
y-0.5=-1/8(x+4)
y=-1/8x-4/8+0.5
y=-1/8x-1/2+1/2
y=-1/8x
if theres 56 docks and 20 of them join and then 5 of them leave how many ducks are left
Answer:
Step-by-step explanation:
Answer:
71 ducks
Step-by-step explanation:
1. 56 + 20 = 76
2. 76 - 5 = 71
6. Jefferson purchased a jacket originally priced at $129 on sale for $90.30. What
was the percent of discount?
A. 70%
B. 30%
C. 50%
D. 39%
Final answer:
To find the percent of discount, subtract the sale price from the original price, divide by the original price, and multiply by 100. The percent of discount is 30%.
Explanation:
To find the percent of discount, we need to calculate the difference between the original price and the sale price, and then divide it by the original price and multiply by 100.
Original price - Sale price = $129 - $90.30 = $38.70
Percent of discount = ($38.70 / $129) * 100 = 30%
Therefore, the percent of discount is 30%, which is option B.
How do you write 10+3x and 4x on a graph?
See the graph below
Explanation:First of all, let's rename those expressions as follows:
[tex]\left\{ \begin{array}{c}y=10+3x\\y=4x\end{array}\right[/tex]
So we we have two lines written in slope-intercept form. In order to graph those lines, let's find two points for each:
First line:
[tex]For \ x=0: \\ \\ y=10+3(0) \\ \\ y=10 \\ \\ \\ For \ x=-10/3: \\ \\ y=10+3(-10/3) \\ \\ y=10-10 \\ \\ y=0 \\ \\ \\ So \ the \ line \ passes \ through \ (0,10) \ and \ (-10/3,0)[/tex]
This line is the green one shown below.
Second line:
[tex]For \ x=0: \\ \\ y=4(0) \\ \\ y=0 \\ \\ \\ For \ x=1: \\ \\ y=4(1) \\ \\ y=4 \\ \\ \\ So \ the \ line \ passes \ through \ (0,0) \ and \ (1,4)[/tex]
This line is the red one shown below.
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Mr Patel is planning to drive 325 miles. He will stop one hour for lunch and take a 15 min rest break.
How many hours will the trip if he averages 65 mph?
A) 3 3/4
B)5
C)6
D)6 1/4
E)6.5
Option D
The trip lasts for [tex]6\frac{1}{4}\ hours[/tex]
Solution:
Mr Patel is planning to drive 325 miles
Average speed is 65 mph
He will stop one hour for lunch and take a 15 min rest break
Let us first find the time taken
[tex]Time = \frac{distance}{speed}[/tex]
[tex]Time = \frac{325}{65}\\\\Time = 5[/tex]
Thus he covers 325 miles in 5 hours
Also, given that, he will stop one hour for lunch and take a 15 min rest break
Therefore, total time taken for trip is:
Total time = 5 hours + 1 hour + 15 minutes
Total time = 6 hours 15 minutes
We know that,
1 hour = 60 minutes
Therefore,
[tex]6\ hours\ 15\ minutes\ = 6 + \frac{15}{60}\ hours = 6 + \frac{1}{4} = 6\frac{1}{4}\ hours[/tex]
Thus the trip lasts for [tex]6\frac{1}{4}\ hours[/tex]
Mr. Patel's trip will last a total of 6.25 hours, including his driving time, lunch break, and rest break. The calculation was done using the formula Time = Distance / Speed, and factoring in the break times.
Explanation:First, we need to calculate how many hours Mr. Patel will spend driving. To do this, we use the formula Distance = Speed * Time. We rework this formula to find time, giving us Time = Distance / Speed. So, Mr. Patel’s total driving time is 325 miles divided by 65 mph (miles per hour), which equals 5 hours.
The next task is to factor in Mr. Patel’s lunch and rest breaks. He takes one hour for lunch and 15 minutes for a rest break. Note that 15 minutes is 0.25 of an hour. Add these two periods to our initial 5 hours of driving time, and we get a total of 6.25 hours. So, Mr. Patel's trip will last 6.25 hours, which corresponds to answer choice D).
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Find the 22nd term of the following sequence:
5, 8, 11, ...
63
71
14
68
68 is the 22nd term of the following sequence.
Step-by-step explanation:
The given sequence is with the same common difference between the two consecutive number in the series thus it is said to be the Arithmetic progression ( AP). For finding the nth term in the AP we have a formula tn = a + (n-1) × dHere a is the first term , n is the number of the term to be founded and d is the common difference between the two consecutive number in the series.Thus here tn = 5 + ( 22 - 1 ) × 3.On subtracting we get tn = 5 + (21 ) × 3 On multiplying we get tn = 5 + 63After adding we get tn = 68. It is the 22nd term in the given series.the twenty second (22) term of the sequence 5, 8, 11, ...... is: D. 68.
Given the following data:
First (1st) term = 5Second term = 8Third term = 11To find the twenty second (22) term of the sequence:
Mathematically, the [tex]n^{th}[/tex] term of a sequence is calculated by using the following formula;
[tex]a_n = a + (n - 1)d[/tex]
Where:
a is the first term.n is the term number.d is the common difference.First of all, we would determine the common difference.
[tex]d = 2^{nd} \; term - 1^{st}\;term\\\\d = 8 - 5 \\\\d = 3[/tex]
Substituting the given parameters into the formula, we have;
[tex]a_{22} = 5 + (22 - 1)3\\\\a_{22} = 5 + (21)3\\\\a_{22} = 5 + 63\\\\a_{22} = 68[/tex]
Therefore, the twenty second (22) term of the sequence is 68.
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Elena ate 2/8 of a pizza and Dylan ate 1/5. estimate how much of the pizza did they eat?
Pls Help need for tomorrow if u answer then i will give 10+ points and brainliest answer
Answer:
[tex]\frac{9}{20}[/tex]
Step-by-step explanation:
Given:
Elena ate 2/8 of a pizza.
Dylan ate 1/5 of a pizza.
Question asked:
How much of the pizza did they eat ?
Solution:
By simply adding.
Elena ate of a pizza. = [tex]\frac{2}{8}[/tex]
Dylan ate of a pizza = [tex]\frac{1}{5}[/tex]
Total of a pizza they ate = [tex]\frac{2}{8}[/tex] + [tex]\frac{1}{5}[/tex]
By taking LCM of 8 and 5 ; 40
[tex]\frac{10 + 8}{40} = \frac{18}{40} = \frac{9}{20}[/tex]
Thus, [tex]\frac{9}{20}[/tex] f the pizza they eat.
9(x + 8) +63
what is the answer?
Answer:
9x +135
Step-by-step explanation:
9(x + 8) +63 (by PEDMAS distribute 9 into parentheses first)
= x(9) + 8(9) +63
= 9x + 72 + 63
= 9x +135 [ =9(x+15) ]
Answer: 9x+135
Step-by-step explanation:
9(x + 8) +63
9x+72+63
9x+(72+63)
9x+135
Hope this helps, now you know the answer and how to do it. HAVE A BLESSED AND WONDERFUL DAY! As well as a great Valentines Day! :-)
- Cutiepatutie ☺❀❤
Write down two rational numbers between 4/5 & 5/6
⁶⁾4/5 = ¹⁰⁾24/30 = 240/300
⁵⁾5/6 = ¹⁰⁾25/30 = 250/300
Rational numbers between 4/5 & 5/6 :
241/300
242/300
243/300
.................
248/300
249/300
Yo sup??
There are infinite numbers possible but since we are asked to find only 2 we can say
4/5=0.8000
5/6=0.8334
Therefore the possible numbers are:
0.81=81/100
0.82=82/100=41/50
0.83=83/100
and so on
Hope this helps.
How to solve for-6g + 36 = 12
Answer:
4
Step-by-step explanation:
-6g+36=12
-6g=12-36
-6g=-24
6g=24
g=24/6
g=4
Answer:
g= - 8
Step-by-step explanation:
Simplifying
-6g + -36 = 12
Reorder the terms:
-36 + -6g = 12
Solving
-36 + -6g = 12
Solving for variable 'g'.
Move all terms containing g to the left, all other terms to the right.
Add '36' to each side of the equation.
-36 + 36 + -6g = 12 + 36
Combine like terms: -36 + 36 = 0
0 + -6g = 12 + 36
-6g = 12 + 36
Combine like terms: 12 + 36 = 48
-6g = 48
Divide each side by '-6'.
g = -8
Simplifying
g = -8
Calculate the surface area of the following triangular prism:
A. 156 cm^2
B. 240 cm^2
C. 336 cm^2
D. 288 cm^2
Answer:
B- 240 cm²
Step-by-step explanation:
Hope it can help you lovelots
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Every jump a game piece makes measures 8 9 . The piece starts at point A = 7 and jumps to the right. As soon as the piece jumps over B = 24, it switches direction and jumps to the left. The piece then stops at point A. How many jumps did the game piece take?
Answer:
The number of jumps that the game piece took, was 40.
Step-by-step explanation:
Every jump a game piece makes measures [tex]\frac{8}{9} = 0.889[/tex].
Now, the piece starts at point A = 7 and jumps to the right.
So, the number of jumps required by the piece to jump over B = 24 will be
[tex]\frac{24 - 7}{0.889} = 19.122[/tex] jumps ≈ 20 jumps {As the piece crosses the point B}
Now, as soon as the piece jumps over B = 24, it switches direction and jumps to the left. And the piece then stops at point A.
Therefore, the number of jumps that the game piece took, was (20 × 2) = 40. (Answer)
Final answer:
Calculating the jumps based on the jump size of 8 / 9 units, the piece makes 20 jumps to go from point A past point B, and then 23 jumps to return to point A, for a total of 43 jumps.
Explanation:
To solve the question, we must calculate the total number of jumps the game piece takes from the starting point A at 7, over point B at 24, and back to A. Each jump measures 8 / 9 units. To calculate the number of jumps to reach just past point B (24 units), we can set up a division problem to find the number of jumps it would take to first reach or pass 24 starting from 7. The formula for this is (B - A) / jump size.
So, the calculation for jumps to point B is: (24 - 7) / 8 / 9 = 17 × 9 / 8 = 153 / 8 = 19.125. Since the game piece cannot make a partial jump, we must round up to 20 jumps to reach beyond 24 units.
After the piece switches direction, we perform a similar calculation to find how many jumps it takes to go back to point A (7 units).
Here, since the piece is already beyond 24, it only needs to jump back to the next integer value before 7 which is 6.
Now, the game piece is at (20 × 8 / 9) + 7 = approximately 24.222 + 7 = approximately 31.222 units along the path.
To calculate the jumps back to 6, we have (31.222 - 6) / 8 / 9 which is approximately 22.556 jumps, and rounding up gives us 23.
Therefore, the total number of jumps made is the sum of the jumps to point B and back to point A,
which is 20 + 23 = 43 jumps.
Simplify 12 × 10 ^8/ 4 × 10^5 and leave in ordinary form
Answer:
3 x 10^3
Step-by-step explanation:
The first is to identify the operation to be performed, it is a quotient between two potency.
Being two potency of the same base number (10), the property says that the quotient of two potency of the same base subtracts its exponent, and the base remains the same.
The corresponding exponents are 8 and 5.
The subtraction is 8-5 = 3.
The whole number that accompanies the base is divided in a current way, that is 12/4. Therefore, the result is 3.
Solve: 8y - 6x = 48 / 2y = 3/2x - 12
Three vertices of parallelogram WXYZ are X(–2,–3), Y(0, 5), and Z(7, 7). Find the coordinates of vertex W
Final answer:
The coordinates of vertex W of parallelogram WXYZ, given vertices X(-2,-3), Y(0, 5), and Z(7, 7), are W(9, 15). This is found by calculating vector ZW as equal to vector XY and adding ZW to the coordinates of Z.
Explanation:
The coordinates of vertex W of parallelogram WXYZ can be found by using the properties of parallelograms. In a parallelogram, opposite sides are equal in length and parallel. Given vertices X(-2,-3), Y(0, 5), and Z(7, 7), we can first find the vector representation from X to Y and from Y to Z:
XY = Y - X = (0 - (-2), 5 - (-3)) = (2, 8)YZ = Z - Y = (7 - 0, 7 - 5) = (7, 2)To find the vector from Z to W, which we'll call ZW, we use the fact that ZW must be parallel and equal in length to vector XY. Therefore:
ZW = XY = (2, 8)Now we add vector ZW to the coordinates of Z to find W:
W = Z + ZW = (7, 7) + (2, 8) = (9, 15)Thus, the coordinates of vertex W are (9, 15).
A bag contains 6 white marbles and 4 black marbles. A marble is drawn from the bag and then a second marble is drawn without replacing the first one.
What is the probability of drawing a white marble on the first draw, followed by a black marble on the second?
[tex]\frac{?}{?}[/tex]
Answer:
4/15
Step-by-step explanation:
P(drawing white marble and black marble)
= 6/10 × 4/9 [9 as there is no replacement]
= 4/15
Final answer:
The probability of drawing a white marble first and a black marble second without replacing the first one from a bag of 6 white and 4 black marbles is 12/45, which simplifies to 4/15.
Explanation:
The question is asking to find the probability of drawing a white marble first and then a black marble second from a bag of 6 white marbles and 4 black marbles, without replacing the first marble. To solve this, we calculate the probability of each event separately and then multiply them because the events are independent.
First, the probability of drawing a white marble is calculated by dividing the number of white marbles by the total number of marbles:
P(White first) = 6/10 or 3/5.
Since the first marble is not replaced, there are now only 9 marbles left in the bag, with 5 white and 4 black marbles. Next, the probability of drawing a black marble after drawing a white marble is the number of black marbles over the remaining total number of marbles:
P(Black second | White first) = 4/9.
To find the combined probability of both events happening in sequence, multiply the probabilities:
P(White first and Black second) = P(White first) × P(Black second | White first) = (3/5) × (4/9) = 12/45.
Therefore, the probability of drawing a white marble first followed by a black marble is 12/45, which simplifies to 4/15.
What is the equation of the line that is parallel to the given
line and passes through the point (-2, 2)?
y=1/5x+4
y =1/5x+12/5
y=-5+4
y=-5x12/5
Answer:
[tex]y=\frac{1}{5}x+\frac{12}{5}[/tex]
Step-by-step explanation:
Complete Question: What is the equation of line that is parallel to the line [tex]y=\frac{1}{5}+4[/tex] and passes through [tex](-2,2).[/tex]
[tex]Let\ the\ equation\ of\ line\ is\ y=mx+c\\\\Since\ it\ is\ parallel\ to\ the\ line\ y=\frac{1}{5}x+4,\ the\ slope\ of\ both\ the\ lines\ will\ be\ same.\\\\Slope\ of\ y=\frac{1}{5}x+4\ is=\frac{1}{5}\\\\m=\frac{1}{5}\\\\Equation: y=\frac{1}{5}x+c\\\\It\ passes\ through\ (-2,2),\ This\ point\ will\ satisfy\ the\ equation.\\\\2=\frac{1}{5}\times (-2)+c\\\\c=2+\frac{2}{5}\\\\c=\frac{12}{5}\\\\The\ Equation\ is: y=\frac{1}{5}x+\frac{12}{5}[/tex]
To find the equation of a line parallel to a given line and passing through a given point, use the point-slope form of a line.
Explanation:To find the equation of a line parallel to the given line, we need to remember that parallel lines have the same slope. The given line has a slope of 1/5. So, the parallel line will also have a slope of 1/5. We can use the point-slope form of a line to find the equation. The point-slope form is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Plugging in the values, we get:
y - 2 = 1/5(x + 2)
To simplify the equation, we can multiply through by 5 to get rid of the fraction:
5y - 10 = x + 2
Finally, we can rearrange the equation to the standard form:
x - 5y = -12
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Does the following table represent a proportional relationship, and if so what is the proportion of the cost for a box of cereal to the size of the box?
Cost for a box of cereal $2.20 $2.64 $3.30 $4.84
Size of box (in ounces) 10 12 15 22
yes, $0.22 per ounce
yes, $4.55 per ounce
yes, $0.44 per ounce
no it is not proportional
Answer:
A
Step-by-step explanation:
I'm not entirely sure but please let me know if I'm right
Answer: yes
Step-by-step explanation: 2.20 divided by 10 is .22, so one ounce is 22 cents. 2.64 divided by 12 is .22, 3.30 divided by 15 is .22, and 4.84 divided by 10 is .22. All the costs are the same per ounce, so it is a proportional relationship of .22.
Naomi solves a system of equations using substitution. The system has infinitely many solutions. Which of the following could be the last step in Naomi's solution? A. x = 0 B. 3 = –3 C. 2 = 2 D. 5 = y
Answer:
Option C) 2=2 is the last step of Naomi and it is the correct answer
Step-by-step explanation:
Given that Naomi solves a system of equation by Substitution method :
The given system has infinite many solutions
Naomi's last step is 2=2
For : A system of equations after solved then its constant value must be same in both the sidesThen the system of equations has infinite many solutions
Therefore it must be 2=2
Hence option C) 2=2 is the last step and it is the correct answer
The correct last step in a solution with infinitely many solutions is option C, '2 = 2,' which shows that the system of equations is dependent and represents an identity.
Explanation:When Naomi solves a system of equations using substitution and finds that the system has infinitely many solutions, this means that the two equations are essentially the same line. Therefore, the last step in her solution would demonstrate that the two expressions are identical. Option C, which states 2 = 2, would be the correct answer because it represents an identity, showing that the two sides of the equation are the same no matter what value is chosen for the variables. This is consistent with a situation where the system of equations is dependent, having an infinite number of solutions.
Find the missing value so that the two points have a
slope of -
(-2,y) and (0, -4)
Answer:
y = -2
Step-by-step explanation:
Use the formula for slope: [tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
"m" means slope, and we know it is -1.
Decide which points will be point 1 and point 2
Point 1 (-2, y) x₁ = -2 y₁ = y
Point 2 (0, -4) x₂ = 0 y₂ - -4
Substitute the "x" and "y" values into the formula
[tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m = \frac{-4-y}{0-(-2)}[/tex] Simplify
[tex]-1 = \frac{-4-y}{2}[/tex] Remember m = -1. Get rid of the fraction
[tex]2*-1 = 2*\frac{-4-y}{2}[/tex] Multiply both sides by 2
[tex]-2 = \frac{2(-4-y)}{2}[/tex] The "2"s cancel out on the right
[tex]-2 = -4-y[/tex] Start isolating "y"
[tex]-2 +4= -4-y + 4[/tex] Add 4 to both sides
[tex]2= -y[/tex]
[tex]2/-1= -y/-1[/tex] Divide both sides by -1 to isolate "y"
-2 = y Answer
y = -2 Variable on left side
Nicole has five times as many stickers in her sticker collection as her sister her sister has 32 stickers how do you stickers does Nicole have
Answer:
160 stickers
Step-by-step explanation:
32 x 5=160
Answer:
160
Step-by-step explanation:
Let x = sister's number of stickers
Then 5x = Nicole's number of stickers
x = 32
5x = 5 × 32 =160
Nicole has 160 stickers.
Jake has a rectangular garden that measures 12 feet by 14 feet. He wants to increase the area by 50% and plans to increase each dimension by equal lengths, x. Which equation could be used to determine the value of x?
In order to increase the area of a rectangular garden that measures 12 feet by 14 feet by 50% Jake must increase each dimension by equal lengths, x:
[tex]x\approx 2.9ft[/tex]
Explanation:First of all, let's calculate the area of the original rectangular garden:
[tex]A=b\times h \\ \\ b:base \\ \\ h:height \\ \\ \\ b=12ft \\ \\ h=14ft \\ \\ \\ A=12(14) \\ \\ A=168ft^2[/tex]
Jake wants to increase the area by 50%, so the new area would be:
[tex]A'=168(1.5) \\ \\ A'=252ft^2[/tex]
He wants to increase the area by 50% and plans to increase each dimension by equal lengths, x, so this is represented by the figure below, therefore:
[tex](12+x)(14+x)=252 \\ \\ 168+12x+14x+x^2-252=0 \\ \\ x^2+26x-84=0 \\ \\ \\ Using \ quadratic \ formula: \\ \\ x=\frac{-b \pm \sqrt{b^2-4ac}}{2a} \\ \\ a=1 \\ \\ b=26 \\ \\ c=-84 \\ \\ \\ x=\frac{-26 \pm \sqrt{26^2-4(1)(-84)}}{2(1)} \\ \\ x=\frac{-26 \pm \sqrt{1012}}{2} \\ \\ \\ Two \ solutions: \\ \\ x_{1}=-13+\sqrt{253} \approx 2.9\\ \\ x_{2}=-13-\sqrt{253} \approx -28.9 \\ \\ x_{2} \ is \ discarded \ because \ it \ can't \ be \ negatives[/tex]
Finally:
In order to increase the area of a rectangular garden that measures 12 feet by 14 feet by 50% Jake must increase each dimension by equal lengths, x:
[tex]x\approx 2.9ft[/tex]
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reduce 36/60 to simplest terms
Answer:3/6
Step-by-step explanation: