Solve the simultaneous equation.
The value of a = -2 and b = 3.
What is a system of equations?
A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.
Here, we have
Given: 3a - 5b = -26, a + 2b = 6
We have to solve this equation.
3a - 5b = -26...(1)
a + 2b = 6...(2)
Now we multiply equation (1) by 2 and equation (2) by 5 and we get
6a - 10b = -52....(3)
5a + 10b = 30....(4)
After solving equations (3) and (4), we get
11a = -22
a = -2
Now we put the value of 'a' in equation(3) and we get
6(-2) - 10b = -52
-10b = -52 + 12
-10b = -30
b = 3
Hence, the value of a = -2 and b = 3.
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If You Answer This Then You Truly Deserve Brainliest,Star Rating ANDDDD a Thanks!
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1. What is the volume of cylinder A?
2. What is the volume of cylinder B?
3. Which cylinder is bigger?
Remember that the volume of a cylinder formula is V = π * r * r * h, and radius is half of the diameter, and π is 3.14.
(Please answer all )
3x - 5y = 15
x-intercept =
y-intercept =
Answer:
x-intercept is 5
y-intercept is -3
Step-by-step explanation:
For the x-intercept:
\(3x - 5(0) = 15\)
\(3x = 15\)
\(x = 5\)
For the y-intercept:
\(3(0) - 5y = 15\)
\( - 5y = 15\)
\(y = - 3\)
Answer:
Y intercept= -3
x-intercept = 5
Step-by-step explanation:
So you would want to get your y alone for it to be in slome intercept form (y=mx+b) so you would:
1. Subtract 3x from both sides to get -5y= -3x+15
2. then you would divide each side by -5 to get y= \(\frac{3}{5}\) x -3
And since in slope intercept form, b= the y-intercept, The y-intercept =-3 and to find the x-intercept you would have to solve for y=0 in your new-found equation.
sorry if this was long
Answer this math question for ten points :)
The trigonometric ratios are given as follows:
sin(A) = 4/5.cos(A) = 3/5.tan(A) = 4/3.sin(B) = 3/5.cos(B) = 4/5.tan(B) = 3/4.What are the trigonometric ratios?The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:
Sine of angle = length of opposite side to the angle divided by the length of the hypotenuse.Cosine of angle = length of adjacent side to the angle divided by the length of the hypotenuse.Tangent of angle = length of opposite side to the angle divided by the length of the adjacent side to the angle.5 is the hypotenuse length, while for angle A, we have that the sides are given as follows:
Opposite side of 4.Adjacent side of 3.Hence the ratios are given as follows:
sin(A) = 4/5.cos(A) = 3/5.tan(A) = 4/3.For angle B, we have that 4 is now the adjacent side, while 3 is the opposite side, hence:
sin(B) = 3/5.cos(B) = 4/5.tan(B) = 3/4.More can be learned about trigonometric ratios at brainly.com/question/24349828
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Andre and Elena are each saving money. Andre starts with 100$ in his savings account and adds 5$ per week. Elena starts with 10$ in her savings account and adds 20$ each week. after 4 weeks who has more money in their savings account
Step-by-step explanation:
let π be the person who has more money
solution
$100+$5+$10+$20
=135
135:π:4
5 1/4 x s + 9/14= if s equals 1 1/7
Answer: \(\frac{651}{98}\)
(please mark brainliest!)
Step-by-step explanation:
To evaluate the expression 5 1/4 x s + 9/14 when s is equal to 1 1/7, we first need to convert all mixed numbers to improper fractions:
5 1/4 = (4 x 5 + 1)/4 = 21/4
1 1/7 = (7 x 1 + 1)/7 = 8/7
So, we can substitute these values into the expression:
5 1/4 x s + 9/14 = 21/4 x 8/7 + 9/14
To simplify this expression, we first need to find a common denominator for the fractions:
The LCD of 4 and 7 is 28, so we can rewrite the expression as:
(21 x 7)/(4 x 7) x 8/7 + 9/14 = 147/28 x 8/7 + 9/14
Multiplying the fractions, we get:
(147 x 8)/(28 x 7) + 9/14 = 294/49 + 9/14
Now, we can find a common denominator of 98:
(294 x 2)/(49 x 2) + 9 x 7/(14 x 7) = 588/98 + 63/98
Adding the fractions, we get:
(588 + 63)/98 = 651/98
Therefore, the value of 5 1/4 x s + 9/14 when s is equal to 1 1/7 is 651/98.
explain how we can use the eigenvalue decomposition to define the square root of a diagonalizable matrix.
It appears to be a constant connection that the square matrix has n eigenvalues, where n is the dimensions (not dimensions as in Rank, but as in # of Column values) of the square matrix.
similar to: a 3x3 matrix square, which has 3 Eigenvalues and only permits eigenvalue decomposition in the event that the matrix is diagonasible.
I think it has to do with how mirror-reflective and inverse the dimensional features of the Matrix can be, and how its linear structure is strong enough to support a dimensional cube.
When it comes to interaction, eigenvalue decomposition can be used to systematically eliminate it.
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alan is saving money to buy a game. so far he has saved $30, which is 5/6 of the total cost of the game. how much does the game cost?
Please help quick!!!!
Find x.
Answer:
50
Step-by-step explanation:
angles in a triangle always add up to 180
Sum of all interior angles of triangle is 180°
⇛x + 40° + 90° = 180°
⇛x + 130° = 180°
⇛x = 180° - 130°
⇛x = 50°
HELP ME PLEASE ASAPPPPP! I HAVE TO TURN IT IN SOON! HELP WITH BOTH QUESTIONS
Answer: The first answer will be x + 2x = 21
Explain: Piper skated 2 times long, so it gives us the first clue to 2x.
And also, they said the total time spent walking and skating was 21 minutes. And we would also know that the x will be from Piper skated 2 times long so, we know that the x will go first.
Hope this helped. :)
I'm really sorry I could only know the first answer :(
first use the extended euclidean algorithm to find the greatest common divisor of 660 and 73 and express it as a linear combination of 660 and 73.
The greatest common divisor of 660 and 73 expressed as a linear combination of 660 and 73 is 1 = 4(63) - 37(73).
To find the greatest common divisor of 660 and 73, we will use the extended Euclidean algorithm.
Step 1: Begin by dividing 660 by 73.660 ÷ 73 = 9 R 63
Step 2: The remainder of the previous division becomes the divisor and the divisor becomes the dividend.73 ÷ 63 = 1 R 10
Step 3: The remainder of the previous division becomes the divisor and the divisor becomes the dividend.63 ÷ 10 = 6 R 3
Step 4: Repeat the process again by making the divisor the previous remainder and the dividend the previous divisor.10 ÷ 3 = 3 R 1
Step 5: Repeat the process again by making the divisor the previous remainder and the dividend the previous divisor.3 ÷ 1 = 3 R 0Since the remainder is 0, we have found the greatest common divisor, which is 1.
Now, we'll express it as a linear combination of 660 and 73. We need to work backwards using the remainders obtained from the division process.
We have:1 = 3 - 1(3)1 = 3 - 1(10 - 3(3))1 = 4(3) - 1(10)1 = 4(63 - 9(73)) - 1(10)1 = 4(63) - 37(73)
Therefore, the greatest common divisor of 660 and 73 expressed as a linear combination of 660 and 73 is:1 = 4(63) - 37(73).
The greatest common divisor of 660 and 73 expressed as a linear combination of 660 and 73 is 1 = 4(63) - 37(73).
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There is a basket containing 5 apples, how do you divide the apples among 5 children so that each child has 1 apple while 1 apple remains in the basket?
Answer:
To solve the above riddle, you just need to think creatively and not take the question literally. The answer to the above riddle is, "Four kids get an apple and the fifth kid gets an apple still in the basket." This way, everyone gets an apple and the last apple still stays inside the basket.
Answer:
well,4 kids will get 4 apples and the last kid will get the last apple but it will still remain in the basket.
Which shows a way to group the figures?
A 1 square, 1 rectangle, and 4 rhombuses
B 2 hexagons and 4 quadrilaterais
C1 octagon, 1 hexagon, and 4 quadrilaterals
D 1 hexagon, 1 pentagon, and 4 quadrilaterals
two containers are used to hold liquid. these containers have exactly the same shape. the first container has a height of 20 cm, and it can hold 320 m3 of liquid. if the second container has a height of , how much liquid can it hold?
The second container can hold approximately 1715 m³ of liquid.
Two containers have exactly the same shape, we can use their height ratio to determine the liquid capacity ratio.
Let's denote the height of the first container as H1 = 20 m and its liquid capacity as C1 = 320 m³.
We want to find the liquid capacity of the second container, C2, given its height H2 = 35 m.
The ratio of the heights is H2 / H1 = 35 m / 20 m = 7/4.
The ratio of the liquid capacities is equal to the ratio of the volumes, since the containers have the same shape. Therefore, we have:
C2 / C1 = (H2 / H1)³
Substituting the given values:
C2 / 320 m³ = (7/4)³
Simplifying the exponent:
C2 / 320 m³ = 343 / 64
To find C2, we can cross-multiply:
C2 = (343 / 64) × 320 m³
Calculating the result:
C2 ≈ 1715 m³
Therefore, the second container can hold approximately 1715 m³ of liquid.
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The question is incomplete the complete question is :
two containers are used to hold liquid. these containers have exactly the same shape. the first container has a height of 20 m, and it can hold 320 m³ of liquid. if the second container has a height of 35 m, how much liquid can it hold?
You have $6 and earn $0.50 for each cup of orange juice you sell. Write an equation in two variables that represent the total amount A (in dollars) you have after selling j cups of orange juice.
A=
Can you help me plz ASAP
Answer:
A = 0.50j + 6.......u r correct
he started with 6....and he is selling each cup (j) for 0.50
so lets say he sold 10 cups...u would sub in 10 for j
A = 0.50(10) + 6
A = 5 + 6
A = 11......and he would have $ 11
question 1what is the number of 6-card hands with three hearts and three spades?
The probability of a 6-card hand with three hearts and three spades is 0.001862, or 1/535
Probability is the mathematics of chance; it is the study of calculating the likelihood of certain outcomes in any given situation.
Here we have to find the probability of a particular 6-card hand consisting of three hearts and three spades is determined first by the fact that there are 13 hearts and 13 spades in a standard deck of 52 cards.
To calculate the probability of a 6-card hand consisting of three hearts and three spades, one must first consider that the order of the cards in a hand does not matter.
The total number of combinations of three hearts and three spades that can be drawn from a standard deck of cards is
=> 4,824.
This number can be calculated by an equation that uses the number of hearts, spades, and cards in a standard deck
=> (13 x 13 x 52).
Then the probability of a 6-card hand consisting of three hearts and three spades is calculated by dividing the number of combinations of three hearts and three spades
=> (4,824) / (2,598,960).
This equation yields a probability of 0.001862, or a 1 in 535 chance of getting a 6-card hand with three hearts and three spades.
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I need help. What does n equal.
\(5n^{2}=7n-2\)
Answer:
\(\boxed{\sf n= \dfrac{2}{5} ,\: n=1}\)
Step-by-step explanation:
\(\rightarrow 5n^2 = 7n -2\)
\(\rightarrow 5n^2 - 7n +2=0\)
\(\rightarrow 5n^2 - 5n -2n+2=0\)
\(\rightarrow 5n(n - 1) -2(n-1)=0\)
\(\rightarrow (5n-2)(n-1)=0\)
\(\rightarrow 5n-2= 0,\: n-1=0\)
\(\rightarrow 5n= 2,\: n=1\)
\(\rightarrow n= \dfrac{2}{5} ,\: n=1\)
Step-by-step explanation:
\(\hookrightarrow\sf{5n^2 = 7n -2}\\\\\hookrightarrow\sf{5n^2 - 7n +2=0}\\\\\hookrightarrow\sf{5n^2 - (5+2)n +2=0}\\\\\hookrightarrow\sf{5n^2 - 5n -2n+2=0}\\\\\hookrightarrow\sf{ 5n(n - 1) -2(n-1)=0}\\\\\hookrightarrow\sf{ (5n-2)(n-1)=0}\\\\\hookrightarrow\sf{ 5n-2= 0\:or~ n-1=0}\\\\\hookrightarrow\sf{ 5n= 2\:or~n=1}\\\\\hookrightarrow\bold{ n= \dfrac{2}{5} \:or~ n=1}\)
SOMEONE HELP!!!! EASY POINTS!!!! ANSWER ALL!!!
Answer:
1. 20x+8=48 2. x=2 3. the area of the square is 144units^2
Step-by-step explanation:
assuming its a perfect 4 sides square the total perimeter would be 5x + 2 units multiplied by 4 = the perimeter so 20x+8 = 48
20x+8=48
subtract 8 from both sides
20x=40
divide 20
x = 2 units
For area plug x back into 5x+2 and you will get 12 units for one side and all sides here should be 12 units so multiply one side with another
12 x 12 = 144 units^2
Answer:
Well I answered in the comments, but I need points so the answers are (in order) 12, 2, and 144
Step-by-step explanation:
Since it's a square, the sides will be the same length. If the perimeter is 48, then you divide 48 by 4 and you will have 12- your answer.
For x, subtract 2 from 12 to get ten, then divide that by five to get your answer which would be 2.
If the side length is 12, you square that and 12 squared is 144.
Jenny polled her 35 co-workers to find out which type of candy they liked best. She found that 10 like chocolate, 8 like gumdrops, 2 like hard candy, and 3 like taffy. There were 5 people who said they like BOTH hard candy and taffy and the remaining co-workers said they like BOTH chocolate and gum drops. How many of Jenny’s co-workers enjoy gumdrops or chocolate?
a.
10
d.
7
b.
8
e.
25
c.
18
The number of co-workers that like gumdrops and chocolate is 7 (option b).
How many like chocolate and gumdrops?The mathematical operations that would be used to determine the answer are addition and subtraction.
Addition is determining the total value or summing two or more numbers. The sign used to represent addition is +. Subtraction is the process of determining the difference between two or more numbers. The sign used to denote subtraction is -.
The first step is to add the total number of people who like a particular type of candy : 10 + 8 + 2 + 3 + 5 = 28
The second step is to subtract that number gotten in the previous step from the total number of co-workers.
Co-workers that like both chocolate and gum drops = 35 - 28 = 7
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solve for x. (round your answer to three decimal places.) log x = −1.8
To solve the equation log x = -1.8, we'll first convert it to exponential form using the properties of logarithms.
Step 1: Understand the base of the logarithm.
Since no base is specified, we assume it is base 10 (common logarithm).
Step 2: Convert the logarithmic equation to an exponential equation.
Using the properties of logarithms, we can rewrite the equation as:
10^(-1.8) = x
Step 3: Calculate the value of x.
Using a calculator, find the value of 10^(-1.8):
x ≈ 0.015848
Step 4: Round the answer to three decimal places.
x ≈ 0.016
So, when solving the equation log x = -1.8, we find that x ≈ 0.016 when rounded to three decimal places.
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A constant force of 56 pounds is applied at an angle of 35º to pull a 16 foot metal door shut. How much work is done?
a
513.9 ft-lbs
b
734.0 ft-lbs
c
−383.7 ft-lbs
d
−809.7 ft-lbs
(b) 734.0 ft-lbs of work is done.
To find the work done by the force, we need to use the formula:
Work = force x distance x cos(θ)
where:
force = 56 pounds (the given constant force)
distance = 16 feet (the distance the door is being pulled)
θ = 35 degrees (the angle between the force and the displacement of the door)
We need to convert the angle to radians to use it in the formula:
theta = 35 degrees x (pi/180) = 0.6109 radians
Now we can substitute the values into the formula:
Work = 56 pounds x 16 feet x cos(0.6109 radians)
Work = 734.0 ft-lbs (rounded to one decimal place)
Therefore, the answer is (b) 734.0 ft-lbs.
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Annie is having her birthday party at the Circus Fest party venue this year. The carnival party package costs $235 and covers the entrance fee for the guests, a private party room, and face painting. Annie's parents ungraded her package to include a favor for each of her guests, bringing the total to $277.
what is the equation to use?
The equation is written as 235 + 6x = 277. Then the cost of each faxor will be $7.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Annie is having her birthday celebration at the Carnival Fest party scene this year. The festival party bundle costs $235 and covers the extra charge for the visitors, a confidential party room, and face painting.
Annie's folks ungraded her bundle to incorporate some help for every one of her 6 visitors, carrying the absolute to $277.
Let 'x' be the cost each faxor. Then the equation is given as,
$235 + 6x = $277
6x = $42
x = $7
The equation is written as 235 + 6x = 277. Then the cost of each faxor will be $7.
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Let Z
26
={0,1,…,25} be the set of remainders modulo 26 . Define the function f:Z
26
→Z
26
as f(x)=3x
5
−9x
3
−5x+1(mod26) Consider the following encryption scheme which can encrypt messages consisting of lowercase letters (a to z ) only. To encrypt an ℓ-character message m=m
1
m
2
⋯m
ℓ
: - Interpret every letter m
i
as an element of Z
26
. That is, a↔0,b↔1, and so on. - Compute the values f(m
1
),f(m
2
),…,f(m
ℓ
). - Re-interpret these values as letters and output the concatenation as the ciphertext. For example, the encryption of "helloworld" is "ghaadvduae". Your task is to decrypt the following ciphertexts. a) Decrypt the ciphertext "gbshbjuhbwxhzhxwhu" b) Decrypt the ciphertext "ahwxhbwefmmbwdebn" c) Explain your methods. Note: it is recommended to use a computer program in this problem.
The decryption of ciphertext "gbshbjuhbwxhzhxwhu"
The function f: Z26→Z26 is defined as f(x) = 3x5−9x3−5x+1(mod 26).The decryption is calculated as f−1(y)=(7y+15)(−3)(mod26)Step-by-step solution: Using the formula for decryption:
f-1(y) = (7y+15)(-3)(mod 26)
Calculating the decryption:
=> f-1(g) = (7 * 6 + 15) * (-3) = -159= -159 + 4 * 26 = 49
=> f-1(b) = (7 * 1 + 15) * (-3) = -72= -72 + 3 * 26 = 6=> f-1(s) = (7 * 18 + 15) * (-3) = -333= -333 + 13 * 26 = 55
=> f-1(h) = (7 * 7 + 15) * (-3) = -138= -138 + 6 * 26 = 24
=> f-1(j) = (7 * 9 + 15) * (-3) = -198= -198 + 8 * 26 = 10
=> f-1(u) = (7 * 20 + 15) * (-3) = -483= -483 + 18 * 26 = 15
=> f-1(h) = (7 * 7 + 15) * (-3) = -138= -138 + 6 * 26 = 24
=> f-1(b) = (7 * 1 + 15) * (-3) = -72= -72 + 3 * 26 = 6
=> f-1(w) = (7 * 22 + 15) * (-3) = -534= -534 + 20 * 26 = 46
=> f-1(x) = (7 * 23 + 15) * (-3) = -561= -561 + 22 * 26 = 39
=> f-1(h) = (7 * 7 + 15) * (-3) = -138= -138 + 6 * 26 = 24
=> f-1(x) = (7 * 23 + 15) * (-3) = -561= -561 + 22 * 26 = 39
=> f-1(w) = (7 * 22 + 15) * (-3) = -534= -534 + 20 * 26 = 46
=> f-1(h) = (7 * 7 + 15) * (-3) = -138= -138 + 6 * 26 = 24
=> f-1(u) = (7 * 20 + 15) * (-3) = -483= -483 + 18 * 26 = 15
Decrypted text: gbshbjuhbwxhzhxwhu → gszwjeitjpkotixibq
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Jeremy is taking a photography class, but he doesn't own a camera. The class organizers will rent him a camera for $6 per day. Jeremy can spend up to $50 for the class, but he has to pay $15 to register for the class as well as rent the camera. The number of days, d, that Jeremy can rent the camera is represented by the inequality 6d + 15 < 50. Select the number of days Jeremy can rent the camera with the money he has.
Answer:
The number of days that Jeremy can rent the camera is any value less than 5.83. Since d represents an integer value (the number of days), the number of days Jeremy can rent the camera is 5 days.
Step-by-step explanation:
To solve this inequality, you need to find the value of d that makes the inequality true. You can do this by isolating the d term on one side of the inequality. To do this, you need to subtract 15 from both sides of the inequality:
6d + 15 < 50
6d < 35
Then, divide both sides of the inequality by 6:
6d/6 < 35/6
d < 35/6
d < 5.83
Answer:
Step-by-step explanation:
17
You have $20 to spend on pizza. It costs $16 plus $1.25 for each additional topping, tax included.
a) Write an inequality to determine the maximum number of toppings the pizza can have.
b) Solve the inequality from part a.
c) Use your answer to decide how many toppings you can get on your pizza.
Sam can type 20 words in 30 seconds how many words can he type in 90 seconds
Answer:
60
Step-by-step explanation:
90 divided by 30 is 3, so you would multiply 20 by 3 to get your answer of 60.
Hope this helps :)
Answer:
He can type about 51 words in 90 seconds because...
Use proportion!
7x = 360
X = 51 3/7
X is ABOUT 51
Annie rounds 280.05 to the nearest hundred.
Bobby rounds 280.05 to the nearest ten.
Ciro rounds 280.05 to the nearest integer.
Denise rounds 280.05 to the nearest tenth.
What is the sum of Annie's answer, Bobby's answer, Ciro's answer, and Denise's answer?
Answer: 280.1
Step-by-step explanation: so the reason this is right is because any number under 5 would round it down but 5 and up and it would round up.
Select the correct answer from each drop-down menu.
The high temperature on a particular day was 68°F at city A, 58°F at city B, 64°F at city C, and 60°F at city D.
City was the warmest. City was the coolest.
through: (-1,0), parallel to y = 4x
Answer:
Find the slope of the original line and use the point-slope formula y−y1=m(x−x1)to find the line parallel to y=4x.
y=4x+4
Step-by-step explanation:
The straight line ny=3y-8 where n is an integer has the same slope (gradient ) as the line 2y=3x+6. Find the value of n.
Given that the straight line ny=3y-8 where n is an integer has the same slope (gradient ) as the line 2y=3x+6. We need to find the value of n. Let's solve the given problem. Solution:We have the given straight line ny=3y-8 where n is an integer.
Then we can write it in the form of the equation of a straight line y= mx + c, where m is the slope and c is the y-intercept.So, ny=3y-8 can be written as;ny - 3y = -8(n - 3) y = -8(n - 3)/(n - 3) y = -8/n - 3So, the equation of the straight line is y = -8/n - 3 .....(1)Now, we have another line 2y=3x+6We can rewrite the given line as;y = (3/2)x + 3 .....(2)Comparing equation (1) and (2) above.
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