Answer:
Step-by-step explanation:
Multiplying two algebraic fractions produces a new algebraic fraction. Multiply the two numerators to get the new numerator and multiply the two denominators to get the new denominator. Then simplify by reducing the new fraction to lowest terms.
for example:
[tex]\frac{x}{y} \\[/tex]×[tex]\frac{a}{b}[/tex] = [tex]\frac{xa}{yb}[/tex]
Division of algebraic fractions
The procedure for dividing algebraic fractions is the same as the procedure for dividing common fractions. Replace the division by a fraction by the multiplication by the reciprocal of that fraction, like this. Then carry out the multiplication of the two fractions as described above.
for example:
[tex]\frac{\frac{a}{b} }{\frac{x}{y} }[/tex]
can be written as
[tex]\frac{a}{b}[/tex]×[tex]\frac{x}{y}[/tex]= [tex]\frac{ax}{by}[/tex]
hope this answer helped you. pls mark as brainliest.
A system of equations consists of two lines. line one passes through (-1,3) and (0,1). the other line passes through (1,4) and (0,2). determine if the pair has no solution, one solution, or an infinite number of solutions.
Final answer:
The two lines have different slopes, with the first line having a slope of -2 and the second line having a slope of 2. Since the slopes are different, the two lines intersect at exactly one point, indicating that there is one solution.
Explanation:
To determine if two lines have no solution, one solution, or an infinite number of solutions, we need to find the slopes of each line. If the slopes are different, the lines intersect at one point, indicating one solution. If the slopes are the same, but they have different y-intercepts, the lines are parallel and there is no solution. If the slopes and y-intercepts are the same, the lines coincide and there are an infinite number of solutions.
For the first line through (-1,3) and (0,1), the slope can be calculated using the formula slope (m) = (y2 - y1) / (x2 - x1). Plugging in the values, we get:
m = (1 - 3) / (0 + 1) = -2
The second line passes through (1,4) and (0,2). Using the same formula:
m = (2 - 4) / (0 - 1) = 2
Since the slopes of the two lines are different, they will intersect at exactly one point, indicating one solution.
The system of equations has one solution since the lines intersect at a single point, confirming a unique solution.
To determine if the system of equations has no solution, one solution, or an infinite number of solutions, we need to analyze the slopes and y-intercepts of the two lines.
Step 1:
Calculate the slope of each line using the formula [tex]\(m = \frac{{y_2 - y_1}}{{x_2 - x_1}}\).[/tex]
For the first line passing through (-1,3) and (0,1):
[tex]\[ m_1 = \frac{{1 - 3}}{{0 - (-1)}} = \frac{{-2}}{{1}} = -2 \][/tex]
For the second line passing through (1,4) and (0,2):
[tex]\[ m_2 = \frac{{2 - 4}}{{0 - 1}} = \frac{{-2}}{{-1}} = 2 \][/tex]
Step 2:
Calculate the y-intercept for each line using the slope-intercept form [tex]\(y = mx + b\)[/tex], where (b) is the y-intercept.
For the first line:
[tex]\[ 1 = -2 \cdot 0 + b_1 \][/tex]
[tex]\[ b_1 = 1 \][/tex]
For the second line:
[tex]\[ 2 = 2 \cdot 0 + b_2 \][/tex]
[tex]\[ b_2 = 2 \][/tex]
Step 3: Compare the slopes and y-intercepts.
Since the slopes are different (-2 for the first line and 2 for the second line), the lines are not parallel. Therefore, they will intersect at exactly one point, resulting in one solution for the system of equations.
Conclusion:
The system of equations has one solution.
The polynomial equation x4 - 6x3 + 10x2 + 2x - 15 = 0 has solution set _____.
{2 + i, 2 - i, -3, -1}
{2 + i, 2 - i, 3, -1}
{3 + i, 2 - i, 3, -1}
{3 + i, 3 - i, 3, -1}
Final answer:
The solution set of the polynomial equation can be found by testing the given sets of roots and verifying which set satisfies the polynomial equation.
Explanation:
To find the solution set of the polynomial equation x4 - 6x3 + 10x2 + 2x - 15 = 0, we need to factor the polynomial or use numerical methods to find roots. Polynomial equations of higher degrees such as quartics can often be simplified into quadratic equations or factored based on known roots or rational root theorem. Once a root is found, it can be used for polynomial division to reduce the degree of the polynomial and find other roots. One simple numerical method to guess and check roots would be to use synthetic division with possible rational roots.
However, since the question provides the sets of the roots, we only need to verify which set of roots satisfy the equation. We can use these sets as potential solutions and substitute the roots back into the equation to see if it satisfies the equation. Since complex roots always come in conjugate pairs for polynomials with real coefficients the only possible sets of roots that can be correct are {2 + i, 2 - i, -3, -1} or {2 + i, 2 - i, 3, -1}. Now we can substitute these roots into the original polynomial to determine which set is the actual solution
A right triangle has a base of 12 yards and a height of 7 yards. If you were to construct a similar but not congruent right triangle with a base of 26 yards, what would be the height of your new triangle rounded to the nearest tenth?
To find the height of a new right triangle similar to the original with a base of 26 yards, use the ratio of sides from the original triangle (7/12) to set a proportion. Solve the proportion to get the new height as 15.2 yards (or 45.5 feet).
Since the triangles are similar, the ratio of their corresponding sides must be the same. To find the height of the new triangle with a base of 26 yards, we set up a proportion using the corresponding sides of the original triangle:
7 yards / 12 yards = height / 26 yards
By cross-multiplying and solving for the unknown height, we get:
7 yards * 26 yards = height * 12 yards
182 y = height * 12 yards
height = 182 / 12 yards
height = 15.1666667 yards
Since 1 yard = 3 feet, we convert the height to feet:
15.1666667 yards * 3 feet/yard = 45.5 feet
Therefore, the height of the new right triangle is approximately 15.2 yards or 45.5 feet when rounded to the nearest tenth of a foot.
Which point is an x-intercept of the quadratic function f(x) = (x + 6)(x-3)?
Which point is an x-intercept of the quadratic function
f(x) = (x + 6)(x - 3)? THE ANSWER IS D.
If the width of a rectangle is 8 less than the length and the perimeter is 32, find the dimensions of the rectangle
Answer:
length = 12
width = 4
Step-by-step explanation:
Width = w
Length = l
w = l-8
l-8 + l-8 + l + l = 32
4l - 16 = 32
4l = 48
length = 12
width = 4
a:b=5:3 find the value of 3a+4b:5a+2b
Yo sup??
a:b=5:3
a/b=5/3
a=5x
b=3x
3a+4b:5a+2b
=15x+12x:25x+6x
=27x:31x
=27:31
Hope this helps.
Answer:
Step-by-step explanation:
a:b=5:3 the value of 3a+4b:5a+2b
(3*5)+(4*3):(5*5)+(2*3)
15+12:25+6
=27:31
find the equation of the line that passes through the point (2,6) and with a slope of 3
using yinterstep form
slope intercept form: y=mx+b
y=3x+6
y=3(2)+6
y=6+6
y=12
What is 3/4 times 8/9 equal
Answer:
2/3
Step-by-step explanation:
photomath bud
i believe the answer is 2/3
What is the area and perimeter of a heart
Area of the heart is 178.5 cm² and Perimeter is 51.4 cm
Step-by-step explanation:
Step 1:Total area of heart = Area of the square + 2 × area of the semi circle
Step 2:Calculate the area of the square where side = 10 cm
⇒ Area of the square = side² = 10² = 100 cm²
Step 3:Calculate the area of the 2 semicircles where radius = 10/2 = 5 cm
⇒ Area of the semicircle = 1/2 × π × r²
⇒ Area of the 2 semicircles = 2 × 1/2 × π × r² = 3.14 × 5² = 78.5 cm²
Step 4:⇒ Total area of the heart = 100 + 78.5 = 178.5 cm²
Step 5:Calculate the perimeter of the heart = length of 2 sides of the square + 2 × perimeter of the semicircle (since there are 2 semicircles)
⇒ Perimeter = 10 + 10 + 2 × π × r (since perimeter of semicircle = πr)
⇒ Perimeter = 20 + 2 × 3.14 × 5 = 20 + 31.4 = 51.4 cm
The area and Perimeter values of the figure are 178.5 cm² and 51.4 cm
How to calculate the Area and Perimeter of the figureThe area of the square portion
side length²We have;
Area of square = 10² = 100cm²Area of the Semicircle:
radius = 10/2 = 5 cmArea of Semicircle = 0.5×πr²
Area of Semicircle = 39.25
Since, we have 2 similar Semicircles :
2 × 39.25 = 78.5 cm²Total Area = 100 + 78.5 = 178.5 cm²
2.)
The Perimeter of the figure ;
For the 2 Semicircles ;
Perimeter = πrPerimeter = 31.4 cm
Perimeter of the square ;
2 × side length = 2(10) = 20Total Perimeter = 20 + 31.4 = 51.4 cm
Learn more on area : https://brainly.com/question/25292087
#SPJ3
What is the measure of angle ABC 4x+2, angle DBE, 5x-13, angle CBE angle ABD
The values are [tex]m\angle \mathrm{ABC}=62^{\circ}[/tex], [tex]m\angle \mathrm{DBE}=62^{\circ}[/tex], [tex]m\angle \mathrm{CBE}=118^{\circ}[/tex] and [tex]m\angle \mathrm{ABD}=118^{\circ}[/tex]
Explanation:
It is given that [tex]\angle \mathrm{ABC}=4x+2[/tex] and [tex]\angle \mathrm{DBE}=5x-13[/tex]
The image having these measurements is attached below:
The angles ABC and DBE are vertically opposite.
Since, vertically opposite angles are equal, [tex]\angle \mathrm{ABC}=\angle \mathrm{DBE}[/tex]
Equating the values, we have,
[tex]\begin{aligned}4 x+2 &=5 x-13 \\2+13 &=5 x-4 x \\15 &=x\end{aligned}[/tex]
Thus, the value of x is 15. Let us substitute x in the equation to find [tex]\angle \mathrm{ABC}[/tex] and [tex]\angle \mathrm{DBE}[/tex]
Thus,
[tex]\begin{aligned}\angle A B C &=4(15)+2 \\&=60+2 \\&=62\end{aligned}[/tex]
Thus, [tex]m\angle \mathrm{ABC}=62^{\circ}[/tex]
Also, substituting x = 15 in [tex]\angle \mathrm{DBE}[/tex]
We have,
[tex]\begin{aligned}\angle DBE &=5(15)-13 \\&=75-13 \\&=62\end{aligned}[/tex]
Thus, [tex]m\angle \mathrm{DBE}=62^{\circ}[/tex]
Hence, the measure of [tex]\angle \mathrm{ABC}=62^{\circ}[/tex] and [tex]\angle \mathrm{DBE}=62^{\circ}[/tex]
To find the measure of [tex]\angle \mathrm{CBE}[/tex] and [tex]\angle \mathrm{ABD}[/tex]:
Since, the angles in a straight line add up to 180°
To find [tex]\angle \mathrm{CBE}[/tex], let us add the angles and equals to 180°
[tex]\angle \mathrm{CBE}+\angle \mathrm{DBE}=180[/tex]
Substituting the value of DBE, we have,
[tex]\angle \mathrm{CBE}+62=180[/tex]
Subtracting both sides by 62,
[tex]\angle \mathrm{CBE}=118[/tex]
Thus, the measure of [tex]\angle \mathrm{CBE}[/tex] is 118°
Since, [tex]\angle \mathrm{CBE}[/tex] and [tex]\angle \mathrm{ABD}[/tex] are vertically opposite, they are equal.
Thus, [tex]\angle \mathrm{ABD}=118[/tex]
Thus, the measure of [tex]\angle \mathrm{ABD}[/tex] is 118°
Hence, the values of the angles are [tex]m\angle \mathrm{ABC}=62^{\circ}[/tex], [tex]m\angle \mathrm{DBE}=62^{\circ}[/tex], [tex]m\angle \mathrm{CBE}=118^{\circ}[/tex] and [tex]m\angle \mathrm{ABD}=118^{\circ}[/tex]
How many integers between 10 and 50 (inclusive) meet the following conditions? 1. The sum of the digits is odd. 2. The number is a perfect square.
a) 3
b) 4
c) 5
d) 6
There are only a handful of perfect squares in the given range: 16, 25, 36, and 49
The sum of their digits wil be odd if one digit is odd and the other is even, which is the case for 16, 25, and 49. So the answer is A.
I REALLY NEED HELP!!! I WILL MARK BRAINLIEST TO WHOEVER GETS IT FIRST!!!
You make 3 quarts of tomato sauce from two baskets of tomatoes. How much tomato sauce can you make from five baskets of tomatoes
Answer:
7.5 quarts
Step-by-step explanation:
2 baskets ------> make 3 quarts
1 basket ---------> makes 3/2 quarts
5 baskets -------> makes 3/2 x 5 = 15/2 = 7.5 quarts
The problem involves calculating ratios or proportional relationships. We find from a known ratio that 2 baskets yield 3 quarts of tomato sauce, and using cross-multiplication, we determine that 5 baskets would produce 7.5 quarts of tomato sauce.
Explanation:This is a ratio problem. Here, we see that 2 baskets of tomatoes yield 3 quarts of tomato sauce. Hence, the ratio of baskets to quarts is 2:3. Likewise, if we increase the number of baskets to 5, the amount of tomato sauce will also increase according to the ratio. To determine how much sauce that would be, use the principle of equivalent ratios, also known as cross-multiplication.
So, (2 baskets / 3 quarts) = (5 baskets / x quarts), where x is the quantity of sauce from 5 baskets. By cross-multiplying and simplifying, you get x = (5 baskets * 3 quarts) / 2 baskets, which simplifies to x = 7.5 quarts.
So, you can make 7.5 quarts of tomato sauce from 5 baskets of tomatoes.
Learn more about Ratio and Proportions here:https://brainly.com/question/26974513
#SPJ12
An arrangement of marbles has 12 marbles in the first row and 10 rows in all. In each successive row one marble is added.What is the explicit rule for this situation, and how many marbles will be in the 10th row?Drag and drop the answers into the boxes to match the situation.Explicit ruleNumber of marbles in the 10th rowAn = 11 + 11n, An = 12 + n, An = 11 + n, An = 12 + 10n, 19, 20, 21,
The explicit rule for the number of marbles in 10th row is An= 12+ n-1.
Step-by-step explanation:
Total number of rows = 10 rowsThe number of marbles in the 1st row = 12 marblesOne marble is added to each successive rowTherefore, for the remaining 9 rows out 10 rows ⇒ 9 marbles are added.
The number of marbles in the 10th row = 12+9 = 21 marbles.The explicit rule is An = 12 + n-1For n= 10, then
⇒ A10 = 12 + (10-1)
⇒ A10 =12+9 = 21
Answer:
A(n)=11+n
Step-by-step explanation: took test
What's the common denominator for 3/8 and 3/10?
Mark spent $79 on 3 shirts and a package of socks. If each shirts cost $24, how much did the package of socks cost?
Answer:7
Step-by-step explanation:
Gotta get rid of the shirts so 24x3 shirts is 72 and 79-72=7 which is the socks price
Answer:$7
Step-by-step explanation:3 Shirts at $24 each 24×3=$72 then subtract $72- from total cost for shirts and socks $72-$79=$7✔
Normal Distribution
Using the graph as a reference, select all
statements that are true about a normal distribution
of data.
Normal distributions are symmetrical about
the mean, m.
The total area under the curve is 100.
Ninety-five percent of the data lies within 1
standard deviation of the mean.
The probability that an event is within 1
standard deviation above the mean is 34%.
All data sets are normally distributed
Answer:
1 and 4.
Step-by-step explanation:
i just did it
Keisha drinks 15 quarts of water in 12 days what is the average amount of water that she drinks per day
Keisha drinks 1.25 quarts of water per day
Solution:
Given that,
Keisha drinks 15 quarts of water in 12 days
To find: Average amount of water that she drinks per day
Average amount of water that she drinks per day is found by dividing 15 quarts by 12 days
The formula used is:
[tex]Amount\ of\ water\ drank\ per\ day = \frac{\text{15 quarts of water}}{12\ days}[/tex]
Therefore,
[tex]Amount\ of\ water\ drank\ per\ day = \frac{15}{12}\\\\Amount\ of\ water\ drank\ per\ day = 1.25[/tex]
Thus she drinks 1.25 quarts of water per day
You deposit $7500 in an account that pays 5.2% interest compounded continuously. Find the balance after 10 years.
Answer:$3900
Step-by-step explanation:
the list shows how much yarn mary has= 1/3 red yarn, 2/9 white yarn, 2/6 blue yarn what is the total amount of yarn mary has?
The total amount of yarn Mary has is [tex]\frac{8}{9}[/tex].
Step-by-step explanation:
Mary has;
Red yarn = [tex]\frac{1}{3}[/tex]
White yarn = [tex]\frac{2}{9}[/tex]
Blue yarn = [tex]\frac{2}{6}[/tex]
Total yarn = Red + White + Blue
Total yarn = [tex]\frac{1}{3}+\frac{2}{9}+\frac{2}{6}\\[/tex]
Taking LCM = 18
Total yarn = [tex]\frac{6+4+6}{18}[/tex]
Total yarn = [tex]\frac{16}{18}=\frac{8}{9}[/tex]
The total amount of yarn Mary has is [tex]\frac{8}{9}[/tex].
Keywords: fraction, addition
Learn more about fractions at:
brainly.com/question/2150928brainly.com/question/2154850#LearnwithBrainly
The total amount of yarn that Mary has is the sum of the fractions representing each color of yarn. After converting all fractions to like terms with denominator 9, we find that Mary has 8/9 in total.
Explanation:To calculate the total amount of yarn Mary has, you should add all the given fractions together. We have:
1/3 red yarn,
2/9 white yarn, and
2/6 (which can be simplified to 1/3) blue yarn.
To add these fractions, they need to have a common denominator. The lowest common denominator of 3 and 9 is 9. So, we get:
3/9 red yarn + 2/9 white yarn + 3/9 blue yarn = 8/9.
Therefore, the total amount of yarn Mary has is 8/9.
Learn more about Fraction Addition here:https://brainly.com/question/14427715
#SPJ12
Multiply.
6x^2 - 4x-5
2x^2 + 3x
A. 12x^4 + 18x^3 - 22x^2 - 15x
B. 12x^4 + 10x^3 – 22x^2 - 15x
c. 12x^4 + 18x^3 - 12x^2 - 15x
D. 12^4 + 10x^3 - 12x^2 - 15x
Answer:
its B
Step-by-step explanation:
i took the test the answer is B
please give me brainly
(6x² - 4x - 5)(2x² + 3x)
= 12x⁴ + 18x³ - 8x³ - 12x² - 10x² - 15x
= 12x⁴ + 10x³ - 22x² - 15x
so the answer is B
From 45 ft to 92 ft?
Answer:47
Step-by-step explanation:
Answer:
47 feet
Step-by-step explanation:
92 feet-45 feet= 47 feet
Answer is 47 feet
How many times does 33 go into 264?
Answer:
IT GOES 8 TIMES
Answer: 8 times
Step-by-step explanation:
There are 4000 sheets of paper in 8 reams. Which of the following expresses the ratio of sheets of paper to reams in simplest form?
A.
1 to 500
B.
1:500
C.
4000 to 8
D. 500 to 1
500 : 1 expresses the ratio of sheets of paper to reams in simplest form ⇒ D
Step-by-step explanation:
The given is:
There are 4000 sheets of paperThere are 8 reamsWe need to find the ratio between the sheets of paper to the reams in simplest form
∵ The number of the sheets is 4000
∵ The number of the reams is 8
→ sheet : ream
→ 4000 : 8
to simplify the ratio divide the two terms by the same number
∵ 4000 ÷ 2 = 2000 and 8 ÷ 2 = 4
∵ 2000 ÷ 2 = 1000 and 4 ÷ 2 = 2
∵ 1000 ÷ 2 = 500 and 2 ÷ 2 = 1
∴ 4000 and 8 can be divided by 8 to get the simplest form
of the ratio
→ sheet : ream
→ 4000 ÷ 8 : 8 ÷ 8
→ 500 : 1
∴ The ratio of sheets to reams is 500 : 1
500 : 1 expresses the ratio of sheets of paper to reams in simplest form
Learn more:
You can learn more about the ratio in brainly.com/question/4302397
#LearnwithBrainly
Which number is farther from 0: -7 or 5
Answer:
-7
Step-by-step explanation
[tex] {x}^{2} - 5x + 6 = 0 \: \: the \: numbers \: a \: lies \: between \: the \: roots[/tex]
Answer:
x is either 2 or 3
Step-by-step explanation:
[tex] {x}^{2} - 5x + 6 = 0 [/tex]
(x-3)×(x-2) = 0
x- 3 = 0 ➡x = 3
x -2 = 0➡ x = 2
15 POINTS!
IMAGE ATACHED
Answer:
Step-by-step explanation:
T think its the 3rd option down
Answer:
b
Step-by-step explanation:
A sports team is throwing an end-of-season party at the fitness club. The costs associated with the party include a $150 flat fee for the room rental and a $14 per person charge for the Italian buffet. An 18% tip must be added to the cost of the food. Express the total cost for the party as a function of the number of people attending
Answer:
[tex]c(x)=150+16.52x[/tex]
With x being the number of people attending the party, and c(x) the cost in dollars.Explanation:
The total cost is comprised of three costs, namely the flat fee for the room rental ($150), the charge person for the Italian buffet ($14 per person), and the tip (18% added to the cost of the food). With this you can build your equation:
[tex]Total\text{ }cost=$150+$14x+18\%\times (14x)[/tex]
Where x respresents the number of people attending the party.
Convert 18% to its decimal form, which is 0.18 and simplify the equation:
[tex]Total\text{ }cost=$150+$14x+0.18\times (14x)=150+14x+2.52x\\ \\ Total\text{ }cost=150+16.52x[/tex]
Hence, calling the function c(x), it is:
[tex]c(x)=150+16.52x[/tex], with x being the number of people attending the party, and c(x) the cost in dollars.
The function which representing the total cost of party is [tex]150+16.52x[/tex]
Total cost :Let us consider that number of people who attending part be x.
The room rental amount is $150.
The charge of the Italian buffet for per person = $14
For x number of people [tex]=14x[/tex]
Since, 18% tip added to the cost of the food.
Tip cost [tex]=14x*\frac{18}{100} =2.52x[/tex]
Total cost of the party [tex]=150+14x+2.52x=150+16.52x[/tex]
Learn more about the function here:
https://brainly.com/question/24380382
What number 0.2% of 50?
Answer:
0.2% of 50 = [tex]0.1[/tex]
Step-by-step explanation:
0.2% of 50
We have to find 0.2% of 50
[tex]50*0.2*\frac{1}{100}[/tex]
[tex]50*\frac{2}{10}* \frac{1}{100}[/tex]
=[tex]\frac{5*2}{100}[/tex]
=[tex]\frac{10}{100}\\\\ \frac{1}{10}\\\\0.1[/tex]
The 0.2% of 50 is 0.1
Answer:
0.1
Step-by-step explanation:
Two streets intersect at a 30 degree angle. At the intersection, there are four crosswalks formed that are the same length. what type of quadrilateral is formed by the crosswalks?
Answer:
rhombus
Step-by-step explanation:
A quadrilateral with equal-length sides is a rhombus.
_____
A square is a special case of a rhombus.
Determine whether the number could be the probability of an event. Explain your reasoning. − 0 . 25
Answer:
So the answer is NO, the probability of an event cannot be -0.25.
Step-by-step explanation:
i) The probability or likelihood of an event cannot be negative or less than zero.
ii) The probability of an event cannot be greater than 1.
iii) If the probability of an event is 0 then the event did not or does not happen
iv) If the probability of an event is one then the event did or does happen with 100% certainty.
v) If the probability is between 0 and 1 then the event occurs wit a certainty that is less than 100%.
vi) So the answer is NO, the probability of an event cannot be -0.25.
Final answer:
The number -0.25 cannot represent the probability of an event because probability values must be between 0 and 1, and negative values are not within this range.
Explanation:
The number -0.25 cannot be the probability of an event. In probability theory, the value assigned to the likelihood of an event occurring must be within a certain range, specifically between 0 and 1, inclusive.
A probability of 0 denotes an impossible event, whereas a probability of 1 represents an event that is certain to occur. Since -0.25 is a negative number, it falls outside of this acceptable range, therefore it cannot represent the probability of an event occurring in any valid probability distribution.