Answer:
1. Yes
2. Yes
Step-by-step explanation:
Leah wrote 2 different fractions with the same denominator. Both fractions were less than 1.
1. Can their sum equal 1?
Let Leah fractions be [tex]\dfrac{6}{7}[/tex] and [tex]\dfrac{1}{7}.[/tex] Both these fractions have the same denominators and are less than 1. Find their sum:
[tex]\dfrac{6}{7}+\dfrac{1}{7}=\dfrac{7}{7}=1[/tex]
2. Can their sum be greater than 1?
Let Leah fractions be [tex]\dfrac{6}{7}[/tex] and [tex]\dfrac{5}{7}[/tex]. Both these fractions have the same denominators and are less than 1. Find their sum:
[tex]\dfrac{6}{7}+\dfrac{5}{7}=\dfrac{11}{7}=1\dfrac{4}{7}>1[/tex]
Two fractions with the same denominator can sum to 1 if their numerators add up to the denominator, or they can sum to more than 1 if their numerators together exceed the denominator. This is based on the concept of adding fractions where only the numerators are summed.
Leah wrote two different fractions with the same denominator, and both were less than 1. Can their sum equal 1? Can their sum be greater than 1? The answer to both questions depends on the value of the numerators. Fractions represent parts of a whole. For two fractions with the same denominator to have a sum of 1, the numerators must add up to the denominator. If their sum is greater than the denominator, then the total sum would be greater than 1.
For example, if we have fractions ½ and ¾, their sum is ½ + ¾ = ¾ which is less than 1. However, if we have ¾ and ¾, the sum equals 6/4, which reduces to 1½, a sum greater than 1.
In conclusion, two fractions with the same denominator and each less than 1 can sum to 1 if the numerators total the denominator, or can sum to greater than 1 if the numerators together exceed the denominator. An important aspect of adding fractions is that we only add the numerators and never the denominators.
the three points (3, -5) , (-a+2,3) and (2a+3, 2) lie on the same line. what is a?
Answer:
a = -7/23.
Step-by-step explanation:
For them to lie on the same line the slope of the line joining the first 2 points must equal the slope of the line joining the second and third points.
so (3 - -5) / (-a+2 - 3) = (2 - 3) /[(2a + 3) - (-a + 2)]
8 / (-a - 1) = -1 / (3a + 1) Cross multiply:
-1(-a - 1) = 8(3a + 1)
a + 1 = 24a + 8
-7 = 23a
a = -7/23.
To find the value of a, we can set the slopes between pairs of points equal to each other and solve for a. The value of a is 14/13.
Explanation:To determine the value of a such that the points (3, -5), (-a+2,3), and (2a+3, 2) lie on the same line, we can use the slope formula. The slope between two points (x1, y1) and (x2, y2) is given by the formula: m = (y2 - y1) / (x2 - x1). We'll calculate the slopes for the two pairs of points and set them equal to each other to find a.
Let's start by finding the slope between the first two points: (-a+2, 3) and (3, -5).
The slope is: m1 = (3 - (-5)) / (-a+2 - 3), which simplifies to m1 = 8 / (-a-1).
Next, let's find the slope between the second and third points: (2a+3, 2) and (3, -5).
The slope is: m2 = (2 - (-5)) / (2a+3 - 3), which simplifies to m2 = 7 / (2a).
Setting the two slopes equal to each other, we have: m1 = m2. Plugging in the expressions for m1 and m2, we get: 8 / (-a-1) = 7 / (2a). To solve for a, we'll cross-multiply and simplify the equation.
After simplifying, we find that a = 14/13.
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Help!! Marking branniest
Basically, we are trying to find the equation that goes through the two points shown in the table. The points are: (5,30) and (10,55). The equation of a line is y=my+b where m is the slope and b is the y intercept. To find slope look for the change in y over the change in x.
Slope = (55-30)/(10-5)=5
We can stop here because the only answer choice with a slope of five is choice A.
Answer: A
Pls help ASAP .....................
Answer:
530.66 cm^2
Step-by-step explanation:
[tex]area \: of \: circle = \pi{r}^{2} [/tex]
Using the above formula,
Area of plate= 3.14(13)^2 = 530.66 cm^2
(I replaced pi with 3.14 since the question said to use 3.14 for pi)
Answer:
the area of a circle
[tex] \pi{r}^{2} [/tex]π= 3.14
r=13
3.14*13²3.14*169530.66cm²Use long division to write the fraction 2/9 as a decimal
Answer:
.2 repeating
The drawing will help
3x - 1 + 9x - 7 + 19 = 180 what does x equal
Answer: x≈ 14 . 08
Step-by-step explanation:
Given :
3x - 1 + 9x - 7 + 19 = 180
The first thing is to collect the like term , then we have
3x + 9x - 1 - 7 + 19 = 180
12x + 11 = 180
subtract 11 from both sides
12x = 180 - 11
12x =169
divide through by 12
x = 169/12
x = 14.083333333333
x≈ 14 . 08
I DO NOT KNOW HOW TO DO THIS. PLEASE PROVIDE AN EXPLANATION!
Simplify
Answer:
[tex]x^{4} -3x+2x^{3} y[/tex]
Step-by-step explanation:
use photo math and it will help with any math problem
do exponents first!
2x^5 = 32x
-6x^2 = -36x
4x^4y= 256xy
32x-36x+256xy/2x
Compare like terms, 32x-36x = -4x^2
-4x^2+256xy/2x
do, -4x^2=-16
-16+256xy/2x
Thats all, hope this is helpful!!!!!!!(:
Which equation is equivalent to 2x + 10 = 6?
A) 2x = 4
B) x + 5 = 3
C) x + 10 = 3
D) 2x + 6 = 10
Answer:
B
Step-by-step explanation:
Given
2x + 10 = 6 ( divide all 3 terms by 2 )
x + 5 = 3 ← equivalent equation
The equation which is equivalent to 2x + 10 = 6 from the given options is x + 5 = 3.
Which of the given equations is equivalent to 2x + 10 = 6?Given the equation in the question:
2x + 10 = 6
Options:
A) 2x = 4
B) x + 5 = 3
C) x + 10 = 3
D) 2x + 6 = 10
To find the equation that is equivalent to 2x + 10 = 6, we check each of the options.
For A) 2x = 4
2x + 10 = 6
2x = 6 - 10
2x = -4
Option A is wrong.
For B) x + 5 = 3
2x + 10 = 6
Divide each term by 2:
2x/2 + 10/2 = 6/2
x + 5 = 3
Option B is correct.
For C) x + 10 = 3
2x + 10 = 6
Divide each term by 2:
2x/2 + 10/2 = 6/2
x + 5 = 3
Option C is wrong.
For D) 2x + 6 = 10
2x + 10 = 6
Subtract 6 and 10 from both sides:
2x + 10 - 10 - 6 = 6 - 6 - 10
2x - 6 = -10
Option D is wrong.
Therefore, x + 5 = 3 is equivalent to the equation.
Option B) x + 5 = 3 is the correct answer.
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What is the slope of line a?
3/4
-4/3
-3/4
4/3
Answer:
The correct slope is 3/4
Step-by-step explanation:
If we take (0,1) and (4,4) as our points, we find (4-1)/(4-0)=3/4
Hope this helped!
Hello ! Do you know the ways of arranging the letters in the word TOY?
Answer:201525
Step-by-step explanation:
In permutations, the order of items matters. The word 'TOY' can be arranged in 6 different ways, calculated using the formula: n!/(n-r)!.
Explanation:The student is asking a mathematical question related to permutations. Permutations refer to the arrangements of items where the order is important. In this instance, the student is interested in arranging the letters in the word 'TOY'. To calculate the number of ways to arrange these letters, we use the formula: n!/(n-r)!. Here, 'n' is the total number of items and 'r' is the number of items to choose and arrange.
Since 'TOY' has three distinct letters, then 'n' would be 3 and 'r' would also be 3. Applied to the formula, this becomes 3!/(3-3)!. Once you calculate this, you get 6. Therefore, there are 6 possible arrangements of the word 'TOY'.
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Suppose you bought supplies for a party. Three rolls of streamers and fifteen party hats cost $30. Later, you bought two rolls of streamers and four party hats for $11. Write and solve a system of equations to determine the cost of streamers and party hats, find their costs.
Final answer:
To determine the cost of streamers and party hats, a system of linear equations is created and solved. The streamers cost $2.50 each, and the party hats cost $1.50 each after solving the system by the elimination method.
Explanation:
To find the cost of streamers and party hats, we need to set up a system of linear equations based on the information provided. Let's denote the price of one roll of streamers as s and the price of one party hat as h.
From the first purchase:
3s + 15h = $30
From the second purchase:
2s + 4h = $11
Now, we'll solve the system using substitution or elimination method. For simplicity, we'll use the elimination method.
First, let's multiply the second equation by 3.75 to match the number of hats in the first equation:
7.5s + 15h = $41.25
Subtract the first equation from this new equation:
7.5s + 15h - (3s + 15h) = $41.25 - $30
4.5s = $11.25
s = $2.50
With the cost of a streamer found, substitute s = $2.50 into the second original equation:
2($2.50) + 4h = $11
$5 + 4h = $11
4h = $6
h = $1.50
Therefore, the cost of one roll of streamers is $2.50 and the cost of one party hat is $1.50.
Final answer:To determine the cost of streamers and party hats, a system of linear equations is created and solved. The streamers cost $2.50 each, and the party hats cost $1.50 each after solving the system by the elimination method.Explanation:To find the cost of streamers and party hats, we need to set up a system of linear equations based on the information provided. Let's denote the price of one roll of streamers as s and the price of one party hat as h.From the first purchase:3s + 15h = $30From the second purchase: 2s + 4h = $11Now, we'll solve the system using substitution or elimination method. For simplicity, we'll use the elimination method.First, let's multiply the second equation by 3.75 to match the number of hats in the first equation:7.5s + 15h = $41.25Subtract the first equation from this new equation:7.5s + 15h - (3s + 15h) = $41.25 - $304.5s = $11.25s = $2.50With the cost of a streamer found, substitute s = $2.50 into the second original equation:2($2.50) + 4h = $11$5 + 4h = $114h = $6 h = $1.50Therefore, the cost of one roll of streamers is $2.50 and the cost of one party hat is $1.
BC is parallel to DE. What is the length of BC? 7 8 9 6
Step-by-step explanation:
The length of BC 7 8 9 6 would probaly wouldnt be parallel but most likely be perpendicular if not intersecting
The monthly revenue, f(x) for the Sweet Treats Ice Cream truck
can be modeled by the function f(x) = 2x^2+ 16x – 20, where x is the number
of months the truck has been in business.
Which statement is true for the situation? ALGEBRA NATION
Answer:
The vertex is (-4, -52), and it represents the minimum for the function.
Step-by-step explanation:
at the movies theater, the clayton family bought 4 fountain drinks and 3 bags of popcorn and paid 22.50. The Hanks family bought 5 fountain drinks and 2 bags of popcorn and paid 23.75. How much is an fountain drink
Answer:
Therefore the price of an foundation drink is $ 3.20(approx).
Step-by-step explanation:
Let the price of one fountain drink be x and one beg of popcorn be y.
The Clayton family bought 4 fountain drinks and 3 begs of popcorn and paid $22.50. The Hanks family bought 5 fountain drinks and 2 begs of popcorn and paid $23.75.
According to the problem,
4x+3y=22.50..............(1)
5x+2y=23.75..............(2)
Equation (1)×5 - Equation (2)×4
20x+15y-(20x+8y)=112.5-91
⇔20x + 15y -20 x-8y=21.5
⇔7y=21.5
⇔y = 3.07
putting the value of y in equation (1)
4x+3×3.07 =22.50
⇔4x=22.50 -9.21
⇔x=3.20
Therefore the price of an foundation drink is $ 3.20(approx).
Jimmy dean made 15 sausages in 3 hours. At this same rate , how many sausages did he make in 8 hours
Answer:
40
Step-by-step explanation:
15/3=5
5*8=40
Jimmy Dean would make 40 sausages in 8 hours, based on a calculation using his rate of sausage making determined from the 15 sausages he made in 3 hours.
Explanation:If Jimmy Dean made 15 sausages in 3 hours, we can calculate the rate at which he makes sausages and then use this rate to find out how many he would make in 8 hours. First, find the sausage-making rate by dividing the total sausages made by the total hours worked:
Rate = Total Sausages / Total Hours = 15 sausages / 3 hours = 5 sausages per hour
Next, we multiply this rate by the number of hours we are interested in, which is 8 hours:
Sausages in 8 hours = Rate * 8 hours = 5 sausages/hour * 8 hours = 40 sausages
Therefore, at the same rate, Jimmy Dean would make 40 sausages in 8 hours.
A football field is 120 yards long by 53 yards wide. What is the total area
Answer:
6360
Step-by-step explanation:
the steps is just 120 times 53 which equals 6360. area= length multiplied by width
The area of a football field that is 120 yards long and 53 yards wide is 98,304,000 square inches.
To calculate the total area of a football field that is 120 yards long and 53 yards wide, you can use the formula for the area of a rectangle, which is length× width.
Step 1: Identify the dimensions of the field. The football field is 120 yards long and 53 yards wide
Step 2: Convert the dimensions into a consistent unit of measure, such as feet. Since there are 3 feet in a yard, multiply each dimension by 3.
Length in feet: 120 yards× 3 feet/yard = 360 feet
Width in feet: 53 yards × 3 feet/yard = 159 feet
Step 3: Calculate the area in feet. Area = Length × Width.
Area = 360 feet × 159 feet = 57,240 square feet
Step 4: To get the area in square inches, recognize that there are 12 inches in a foot, so the area in square inch\
es is:
Area in square inches = 57,240 ft²× (12 inches/foot)² = 98,304,000 square inches.
This calculation shows that the total area of the football field is approximately 98,304,000 square inches.
fyf inch d yr xdr thg f iij fuh ft.
Answer:
next time please ask a real question
Thanks
Step-by-step explanation:
The question appears to explore historical texts or languages, likely suited for college-level English or History studies, focusing on linguistics, manuscript studies, or medieval literature.
Explanation:Given the fragments provided, it's challenging to decipher a coherent question or subject matter directly. However, the content suggests a possible exploration of historical texts or languages, particularly those relevant to English or linguistics studies at the college level.
Understanding or translating ancient or cryptic texts can be a significant part of higher education in English, where students might delve into Old English literature, manuscripts, or historical documents.
The various fragments hint at texts that might be from different periods or contexts, suggesting a study that spans a range of historical documents, potentially requiring translation or interpretation skills. Such a task would be well-suited for college-level English or History students focusing on linguistics, manuscript studies, or medieval literature.
What is the answer to this?
(2i-6)(3i-9)
Remember that i² = -1. Using FOIL...
(2i-6)(3i-9) = 6i²-36i+54
Now simplify by subbing in -1 for i².
6(-1)-36i+54 = 48-36i
answer: 48-36i
If f(x) = 2x^2 + 5 and g(x) = 6 + f(x) , what is the value of f(4) + g(3) ?
Answer: 66
Step-by-step explanation:see attachment.
If this helps you please rate brainest
Answer:
66
Step-by-step explanation:
Timed need answer ASAP
Answer:
6
4 squared= 16
16÷8=2
2×3=6
Answer: the answer is 6
Step-by-step explanation:
Which equation can be used to find V, the volume of the cylinder in cubic inches?
The formula to find the volume of a cylinder is V = hπr², where h is the height of the cylinder and r is the radius of its base.
Explanation:To find V, the volume of a cylinder in cubic inches, we can use the formula V = Ah, where A represents the cross-sectional area of the cylinder and h represents the height or depth of the cylinder. To find the cross-sectional area for a cylinder, the formula A = πr² can be used, where r is the radius of the cylinder's base. Substituting value of A in volume's formula will give V = hπr², which is commonly used formula to find the volume of a cylinder.
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To find the volume of a cylinder in cubic inches, use the formula V = πr²h, where r is the radius of the base of the cylinder and h is the height of the cylinder.
Explanation:The equation for finding the volume V of a cylinder in cubic inches can be derived from the basic principle that the volume of a shape is equal to the area of its base multiplied by its height. For a cylinder, the base is a circle, and the area of a circle is given by the formula πr², where r is the radius of the circle.
Therefore, the volume of the cylinder is the area of its base times its height, which can be written as V = πr²h, where h is the height of the cylinder. By using this formula, you can calculate the volume of a cylinder if you know the radius of its base and its height.
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Jane has 15 phone cards worth either $20 or $15. How many of each does she have if the phone cards total $245?
The correct answer is 12
Hope this helped!
Jane has 4 number of 20 phones and 11 number of 15 phone cards.
It is given that 15 phone cards worth either $20 or $15
lets Jane has x number of 20 phones and y number of 15 phone cards
Then by the problem we have
x+y=15....(1)
20x+15y=245....(2)
What is the substitution method for linear equation?Solve one of the equations either for the variable x or y. Now, substitute the solution from step 1 to the other equation.
So by using substitution method we have,
from equation 1 we get
y=15-x
use this value in equation 2
[tex]20x+15(15-x)=245\\\\20x+225-15x=245\\\\5x+225=245[/tex]
[tex]5x=20\\x=4\\y=15-4\\y=11[/tex]
Therefore we get x=4 and y=11
Therefore,Jane has 4 number of 20 phones and 11 number of 15 phone cards.
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Solve 9/4x-5/6=-13/12x
Answer:
4
Step-by-step explanation:
Cuzzzzz I know this stuff realy well
To solve this, you need to isolate/get x by itself in the equation:
[tex]\frac{9}{4}x-\frac{5}{6}=-\frac{13}{12} x[/tex] Subtract 9/4x on both sides
[tex]-\frac{5}{6} =-\frac{13}{12} x-\frac{9}{4} x[/tex] To combine fractions, the denominator has to be the same. They both have a least common denominator (LCD) of 12, so multiply -9/4x by 3/3 to make the denominator 12
[tex]-\frac{5}{6} =-\frac{13}{12}x -(\frac{3}{3})\frac{9}{4}x[/tex]
[tex]-\frac{5}{6} =-\frac{13}{12}x-\frac{27}{12} x[/tex]
[tex]-\frac{5}{6} =-\frac{40}{12} x[/tex] Multiply the reciprocal of -40/12 to get x by itself, which is -12/40 [basically flipping the fraction or switching the numerator and the denominator]
[tex](-\frac{12}{40})-\frac{5}{6} =(-\frac{12}{40})-\frac{40}{12} x[/tex] [two negative signs cancel each other out and become positive]
[tex]\frac{60}{240} =x[/tex] Simplify the fraction
[tex]\frac{1}{4} =x[/tex]
Explain how to evaluate a + b ÷ c, when a = 1 2/5, b = 2 2/5, and c = 3/4. You do not have to compute the values.
Answer:
The correct answer is: [tex]4\frac{3}{5}[/tex]
Step-by-step explanation:
According to the rule of BODMAS, division is done before addition.
So, in a + b ÷ c, we will first calculate, b ÷ c
Given b = [tex]2\frac{2}{5}[/tex] = [tex]\frac{12}{5}[/tex] , c = [tex]\frac{3}{4}[/tex] .
So, [tex]\frac{b}{c}[/tex] = [tex]\frac{12}{5}[/tex] ÷ [tex]\frac{3}{4}[/tex]
So, [tex]\frac{b}{c} = \frac{12}{5} \times\frac{4}{3}[/tex] , as the numerator and denominator gets reversed as division is changed to multiplication.
So, [tex]\frac{b}{c} = \frac{16}{5}[/tex] .
Next the value of a to [tex]\frac{b}{c}[/tex] , where, [tex]a = 1\frac{2}{5} = \frac{7}{5}[/tex], we get,
[tex]\frac{7}{5} +\frac{16}{5} = \frac{23}{5} = 4\frac{3}{5}[/tex].
How do you solve the problem 4 2/3×13 using common core math
3*4³ Simplify answer 30 points
Answer:
the answer is 192
Step-by-step explanation:
because 4^3 is 64
and if you multiply it by 3 it will give you 192
your welcome have a nice day!
Answer: 192
Step-by-step explanation:
3*4³
Since there is an exponent we have to do that first
4³
4*4*4=64
Plug 64 in 4³'s place
3*64
=192
Help me find out this prom or
Please I will do anything by btntntnthtjtbtjtjtitjtbt yjtntit titbybtititjybt
Answer:
80 percent
Step-by-step explanation:
Answer:
80 percent
Step-by-step explanation:
what is the square of half of a number is 32?
Answer:
16
Step-by-step explanation:
An item costs $310 before tax, and the sales tax is %15.50
What is the sales tax rate? I'll give a ton of points for this one.
Plz answer asap
Cost of item of $ 310 including the sales tax is $358.05.
Convert the percentage rate of sales tax to a decimal by dividing the percentage by 100.
A 15.50% sales tax rate becomes 0.155 when converted to a decimal.
After performing the multiplication, you will get the amount of sales tax that needs to be added to the item's price. So, $310 x 0.155 = $48.05.
Therefore, the total cost of the item after sales tax would be the original price plus the amount of sales tax, which is $310 + $48.05 = $358.05.
Parallelogram ABCD has coordinates A(-1,10) B(2, -1) C(5,4) and D(-4,5). Find the coordinates of where diagonals AC and BD intersect at. Enter your answers as numbers.
The coordinates of where diagonals AC and BD intersect at O(2,7).
Step-by-step explanation:
We are given coordinates as A(-1,10) and C(5,4).And we know that the diagonals of parallelogram always bisect each other.
Let us consider O is the intersection point among the diagonals AC and BD. So, the point O bisects the line AC into two equal parts, and also it is the mid-point of AC.
We can find point O using the midpoint formula as,
O (x,y) = ([tex]\frac{(x1+x2)}{2}[/tex] , [tex]\frac{(y1+y2)}{2}[/tex])
= ([tex]\frac{(-1+5)}{2}[/tex] , [tex]\frac{(10+4)}{2}[/tex])
= ([tex]\frac{4}{2}[/tex], [tex]\frac{14}{2}[/tex])
= (2,7)
So Diagonals AC and BD intersects at the point O (2,7).
(05.01 MC)
Which statement best describes the area of Triangle ABC shown below?
A triangle ABC is shown on a grid. The vertex A is on ordered pair 4 and 5, vertex B is on ordered pair 5 and 2, and the vertex C is on ordered pair 3 and 2.
It is one-half the area of a rectangle with sides 2 units × 3 units.
It is twice the area of a rectangle with sides 2 units × 3 units.
It is one-half the area of a square of side length 3 units.
It is twice the area of a square of side length 3 units.
Answer:
It is one-half the area of a rectangle with sides 2 units × 3 units.
Step-by-step explanation:
we have the coordinates of triangle ABC
A(4,5),B(5,2),C(3,2)
Plot the coordinates of triangle to better understand the problem
see the attached figure
step 1
Find the area of triangle ABC
The triangle ABC is an isosceles triangle `(AB=AC)
The area of triangle ABC is
[tex]A=\frac{1}{2}(BC)(AM)[/tex]
we have
[tex]BC=5-3=2\ units[/tex] ---> difference of the x-coordinates
[tex]AM=5-2=3\ units[/tex] ---> difference of the y-coordinates
substitute
[tex]A=\frac{1}{2}(2)(3)=3\ units^2[/tex]
step 2
Find one-half the area of a rectangle with sides 2 units × 3 units
[tex]A=\frac{1}{2} (2)(3)=3\ units^2[/tex]
therefore
The area of triangle ABC is one-half the area of a rectangle with sides 2 units × 3 units
Answer:
It is one-half the area of a rectangle with sides 2 units × 3 units.
Step-by-step explanation: