The solution of the given system of equations is x = -1 and y = 4.
The given system of equations is 4x + 8y = 40 and 6x + 3y = 6.
To solve this system of equations, we need to use elimination method. We can subtract 6x from both sides of the second equation and subtract 4x from both sides of the first equation. We get:
8y = 40 - 4x and 3y = 6 - 6x
We can now divide both sides of the second equation by 3 to obtain y = 2 - 2x.
We can substitute the value of y from the second equation into the first equation to get 4x + 8(2 - 2x) = 40, which simplifies to -8x = 8. We can solve this equation for x by dividing both sides by -8, resulting in x = -1.
Substituting the value of x into either equation, we can obtain y = 4. So, the solution of the given system of equations is x = -1 and y = 4.
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Math question 12 help
Answer:
It's neither of them. The function is neither odd nor even
what equivalent expression for (32 • 54)3?
Answer:
5,184 from my knowledge
The sum of the digits of a certain two-digit number is 3. Reversing its digits decreases the number by 27. Find the number.
The number is 30.
What is Addition?Addition is one of the basic mathematical operations where two or more numbers is added to get a bigger number.
The process of doing addition is also called as finding the sum
Given that,
The sum of the digits of a certain two-digit number is 3.
Since it is a two digit number, there will be a tens place and a ones place.
Let x be the digit in tens place and y be the digit in ones place.
x + y = 3
The number can also be written as 10x + y, since x is in the tens place.
When the number is reversed, tens place changed to ones place and vice versa.
The reversed number is 10y + x.
Given that the value of the number is decreased by 27 when the digits is reversed.
Original number - 27 = Reversed number
10x + y - 27 = 10y + x
9x - 9y = 27
x - y = 3
Also, we have,
x + y = 3 [Equation 1]
x - y = 3 [Equation 2]
Adding the equations,
2x = 6
x = 6/2 = 3
Substituting in equation 1, y = 0
Hence the number is 30.
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Karen invested her savings in two investment funds. The amount she invested in Fund A was 4 times as much as the amount she invested in Fund B. Fund A returned a 4% profit and Fund B returned a 7% profit. How much did she invest in Fund B, if the total profit from the two funds together was $1380?
Karen invested $6000 in Fund B, and $24000 in Fund A, as the weighted average of the two funds' returns is 5%, yielding a total profit of $1380, and we can use a system of equations to solve for the amounts invested in each fund.
To solve this problem, we can set up a system of equations using the information given.
Let x be the amount invested in Fund B, then the amount invested in Fund A is 4x. The total amount invested is the sum of these two amounts, so we have:
x + 4x = 5x = total amount investedThe total profit from the two funds is given as $1380, which is the sum of the profits from Fund A and Fund B.
We can express these profits using the amounts invested and the respective return rates:
0.04(4x) + 0.07(x) = 0.16x + 0.07x = 0.23x = $1380Solving for x, we find that x = $6000, which is the amount invested in Fund B. Therefore, the amount invested in Fund A is 4x = $24000.
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3. John wants an average bowling score of 215. If he scored 159, 182, 225, 240, 198,
200 and 230 on his first seven games, what must he score on his 8th game to achieve
this average?
John must score 286 on his 8th game to achieve an average score of 215.
What is an Average?
Average, also known as the mean, is a mathematical concept that represents the central value of a set of numbers. It is found by dividing the sum of the numbers by the total count of the numbers.
To find out what John must score on his 8th game to achieve an average score of 215, we need to use the formula for calculating the average or mean:
Average = (Sum of Scores) / (Number of Scores)
We can use this formula to solve for the unknown score:
215 = (159 + 182 + 225 + 240 + 198 + 200 + 230 + x) / 8
Multiplying both sides by 8, we get:
1720 = 159 + 182 + 225 + 240 + 198 + 200 + 230 + x
Simplifying, we get:
1720 = 1434 + x
Subtracting 1434 from both sides, we get:
x = 286
Therefore, John must score 286 on his 8th game to achieve an average score of 215.
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Two angles in a triangle measure 102 and 54. What measure of the third angle?
Answer:
24
Step-by-step explanation:
The sum of the three angles in a triangle is always 180 degrees.
Let x be the measure of the third angle.
Then we have:
102 + 54 + x = 180
Simplifying the left side:
156 + x = 180
Subtracting 156 from both sides:
x = 180 - 156
x = 24
Therefore, the measure of the third angle is 24 degrees.
Rewrite the logarithmic expression as a single logarithm with the same base. Assume all expressions exist and are well-defined. Simplify any fractions. 9log_(4)2-log_(4)40
The logarithmic expression can be rewritten as a single logarithm with the same base as [tex]log_{4} (12.8)[/tex].
To rewrite the logarithmic expression as a single logarithm with the same base means that we have to do logarithmic expression simplification.
To do so, we can use the logarithmic properties:
[tex]log_{b} (a)[/tex] + [tex]log_{b} (c)[/tex] = [tex]log_{b} (ac)[/tex]
[tex]log_{b} (a)[/tex] - [tex]log_{b} (c)[/tex] = [tex]log_{b} (a/c)[/tex]
b · [tex]log_{a} (x)[/tex] = [tex]log_{a} (x^{b} )[/tex]
Using these properties, we can rewrite the given expression:
9 · [tex]log_{4} (2)[/tex] - [tex]log_{4} (40)[/tex] = [tex]log_{4} (2^{9} )[/tex] - [tex]log_{4} (40)[/tex]
= [tex]log_{4} (512)[/tex] - [tex]log_{4} (40)[/tex]
= [tex]log_{4} (512/40)[/tex]
= [tex]log_{4} (12.8)[/tex]
So the logarithmic expression can be rewritten as a single logarithm with the same base as [tex]log_{4} (12.8)[/tex]
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The angle of elevation of the sun is 41°. The shadow of a building is 32 feet long. How tall is the building? Round your answer to the nearest hundredth.
This is an EMERGENCYYY
The height of the building is approximately 27.62 feet. Rounded to the nearest hundredth, the answer is 27.62 feet.
What connection exists between height and separation?In arithmetic, we use angles and distance to determine an object's height. The distance between the items is measured horizontally, and the height of an object is determined by the angle of the top of the object with respect to the horizontal.
What use do height and distance serve in everyday life?Trigonometry includes heights and distances, and it has numerous uses in practical daily life. It is used to determine the distance between any two objects, including heavenly bodies or other objects, as well as the height of towers, buildings, mountains, etc. Astronauts, surveyors, architects, and navigators are the main users.
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FRACTIONS Additive property of equality with fractions and mixed numbers Solve for u. u-(3)/(4)=5(1)/(3) u
The solution for u-(3)/(4)=5(1)/(3) u is 2(5)/(12).
The additive property of equality states that if the same amount is added to both sides of an equation, the equation remains true. In this case, we can use the additive property of equality to solve for u by isolating the variable on one side of the equation.
Step 1: Add (3)/(4) to both sides of the equation to cancel out the subtraction on the left side of the equation.
u-(3)/(4)+(3)/(4)=5(1)/(3)+(3)/(4)
Step 2: Simplify the left side of the equation.
u=5(1)/(3)+(3)/(4)
Step 3: Find a common denominator for the fractions on the right side of the equation and combine them.
u=20(1)/(12)+(9)/(12)
Step 4: Simplify the right side of the equation.
u=29/(12)
Step 5: Convert the improper fraction to a mixed number.
u=2(5)/(12)
Therefore, the solution for u is 2(5)/(12).
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Using the formula for finding the simple interest, I = Prt, find the Interest earned in a savings account by depositing $9,800 for 15 months at 5% simple interest
let's recall that a year has 12 months, thus 15 months is really 15/12 of a year.
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$9800\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years\to \frac{15}{12}\dotfill &\frac{5}{4} \end{cases} \\\\\\ I = (9800)(0.05)(\frac{5}{4}) \implies I = 612.5[/tex]
Consider the following matrix.λ003λ+1201λFind the determinant of the matrix. Find the values ofλfor which the determinant is zero. (Enter your answers as a comma-separated list.)λ=
This equation has two solutions: λ = 0 and λ = -1
The determinant of a matrix is given by the formula:
det(A) = a11(a22a33 - a23a32) - a12(a21a33 - a23a31) + a13(a21a32 - a22a31)
In the given matrix, the values of a11, a22, and a33 are λ, (λ+1), and λ respectively. The values of a12, a13, a21, a23, a31, and a32 are all 0. Substituting these values into the formula for the determinant gives:
det(A) = λ((λ+1)λ - 0) - 0(0 - 0) + 0(0 - 0) = λ^3 + λ^2
To find the values of λ for which the determinant is zero, we can set the determinant equal to zero and solve for λ:
λ^3 + λ^2 = 0
λ^2(λ + 1) = 0
This equation has two solutions: λ = 0 and λ = -1. Therefore, the values of λ for which the determinant is zero are 0 and -1. The answer can be written as a comma-separated list as follows:
λ = 0, -1
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Solve the quadratic equation x2+8x+30=0 by completing the square.
Answer:
(x + 4)2 = -26 x = -4 ± √26
Step-by-step explanation: x2 + 8x + 30 = 0
x2 + 8x = -30
x2 + 8x + (8/2)2 = -30 + (8/2)2
(x + 4)2 = -22
x + 4 = ±√22
x = -4 ± √22
math sucks lol
Describe the transformation of the equation below from the parent function of y = I x I
y = -2 I x - 3 I + 3
The transformation of the equation y = -2 I x - 3 I + 3 from the parent function y = I x I includes a horizontal shift of 3 units to the right, a vertical stretch by a factor of 2, a reflection across the x-axis, and a vertical shift of 3 units up.
The transformation of the equation y = -2 I x - 3 I + 3 from the parent function y = I x I can be described as follows:
The parent function is shifted 3 units to the right. This is indicated by the "-3" inside the absolute value bars in the equation.
The parent function is vertically stretched by a factor of 2. This is indicated by the "-2" in front of the absolute value bars in the equation.
The parent function is reflected across the x-axis. This is indicated by the negative sign in front of the "2" in the equation.
The parent function is shifted 3 units up. This is indicated by the "+3" outside the absolute value bars in the equation.
In summary, the transformation of the equation y = -2 I x - 3 I + 3 from the parent function y = I x I includes a horizontal shift of 3 units to the right, a vertical stretch by a factor of 2, a reflection across the x-axis, and a vertical shift of 3 units up.
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Evaluate each expression using the values given in the table. X -3 -2 -1 0 1 2 3
F(x) 8 7 6 5 4 3 2
G(x) -7 -3 0 1 0 -3 -7
a. (f∘g)(1) b. (f∘g)(2) c. (g∘f)(2) d. (g∘f)(3) e. (g∘g)(1) f. (f∘f)(3)
Using the values given in the table to evaluate each expression, the value of each expression is (a) 5, (b) 8, (c) -7, (d) -3, (e) 1, and (f) 3.
To evaluate the expressions, we need to use the values given in the table for f(x) and g(x). The composition of functions (f∘g)(x) means that we plug the value of g(x) into the function f(x).
a. (f∘g)(1) = f(g(1)) = f(0) = 5
b. (f∘g)(2) = f(g(2)) = f(-3) = 8
c. (g∘f)(2) = g(f(2)) = g(3) = -7
d. (g∘f)(3) = g(f(3)) = g(2) = -3
e. (g∘g)(1) = g(g(1)) = g(0) = 1
f. (f∘f)(3) = f(f(3)) = f(2) = 3
Therefore, the answers are (a) 5, (b) 8, (c) -7, (d) -3, (e) 1, and (f) 3.
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Overview Question Progress Look at these three number cards. 44 45 46 Use each card once to make all these statements correct. 3 4 Homework Progress 2/12 5 6 I is a multiple of 2 is a multiple of 3 is a multiple of 4 7
The numbers in the cards are:
Multiple of 2: 44 and 48Multiple of 3: 45 and 48Multiple of 4: 48How to determine the numbers in the statementsFrom the question, we have the following parameters that can be used in our computation:
Cards = 45, 45 and 46
Next, we have
Multiples of 2, 3 and 4
Using the above as a guide, we have the following:
Multiple of 2: 44 and 48 (divisible by 2)Multiple of 3: 45 and 48 (divisible by 3)Multiple of 4: 48 (divisible by 4)Read more about multiples at
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f(x) = 2^x +2: shifts 2 units left
g(x)=
Exponential Functions
Answer:
g(x) = f(x + 2) = 2^(x + 2) + 2
Step-by-step explanation:
To shift the function f(x) = 2^x + 2 two units to the left, we need to replace x with (x + 2) in the equation. This will shift the graph horizontally to the left by two units.
So, the new function g(x) that represents the shifted graph is:
g(x) = f(x + 2) = 2^(x + 2) + 2
3 mi. and 10,000 ft.
is the same equal or different
Answer:
3 Miles
Step-by-step explanation:
3 mi = 15,840ft.
15,840 is greater than 10,000, so 3 miles is more
An equivalent expression for (3x+2)/(x-5) with a denominator of (3x+4)(x-5) can be ob
we can use the fact that anything multiplied by 1 results in the same value to simplify the expression:
(3x + 2)(x - 5) / (3x + 4)(x - 5) = (3x + 2)/(3x + 4)
To obtain an equivalent expression for (3x+2)/(x-5) with a denominator of (3x+4)(x-5), we can use the distributive property to expand the numerator and denominator:
(3x + 2) / (x - 5) = (3x + 2)(x - 5) / (3x + 4)(x - 5)
From here, we can use the fact that anything multiplied by 1 results in the same value to simplify the expression:
(3x + 2)(x - 5) / (3x + 4)(x - 5) = (3x + 2)/(3x + 4)
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A track runner ran for 15 minutes, walked for 15 minutes, ran for another 20 minutes, and then walked for 10 minutes.
Which graph describes the relationship between runner's total distance and time?
graph with the x axis labeled time in hours and the y axis labeled total distance in miles, with a line segment from 0 comma 0 to 0.25 comma 1.25, a horizontal line segment from 0.25 comma 1.25 to 0.5 comma 1.25, a line segment from 0.5 comma 1.25 to 0.8 comma 2.4, and a horizontal line segment from 0.8 comma 2.4 to 1 comma 2.4
graph with the x axis labeled time in hours and the y axis labeled total distance in miles, with a line segment from 0 comma 0 to 0.25 comma 1.25, a line segment from 0.25 comma 1.25 to 0.5 comma 1.75, a line segment from 0.5 comma 1.75 to 0.8 comma 2.95, and a horizontal line segment from 0.8 comma 2.95 to 1 comma 2.95
graph with the x axis labeled time in hours and the y axis labeled total distance in miles, with a line segment from 0 comma 0 to 0.25 comma 1.25, a horizontal line segment from 0.25 comma 1.25 to 0.5 comma 1.25, a line segment from 0.5 comma 1.25 to 0.8 comma 0.1, and a horizontal line segment from 0.8 comma 0.1 to 1 comma 0.1
graph with the x axis labeled time in hours and the y axis labeled total distance in miles, with a line segment from 0 comma 0 to 0.25 comma 1.25, a line segment from 0.25 comma 1.25 to 0.5 comma 1.75, a line segment from 0.5 comma 1.75 to 0.8 comma 2.95, and a line segment from 0.8 comma 2.95 to 1 comma 3.15
Answer:
Step-by-step explanation:
graph with the x axis labeled time in hours and the y axis labeled total distance in miles, with a line segment from 0 comma 0 to 0.25 comma 1.25, a line segment from 0.25 comma 1.25 to 0.5 comma 1.75, a line segment from 0.5 comma 1.75 to 0.8 comma 2.95, and a horizontal line segment from 0.8 comma 2.95 to 1 comma 2.95
It's B.
Explanation: I took the test
Graph the solution to the following system of inequalities.
v55x - 2
y>-28+5
Answer: See attached.
Step-by-step explanation:
Since the first equation uses a ≤ symbol, we know we will use a solid line. This is because it is less than and equal to. Then, we will graph it as a regular slope-intercept line.
This line has a slope of 5 and a y-intercept of -2. This means we will start at (0, -2) and move five units up for every unit right, or five units down for every unit left.
For the next equation, it uses a > symbol so we will use a dashed line. This is because it is not equal to, only greater than. Same as the previous. We will graph it as a slope-intercept line, but using a dashed line instead of a solid line.
This line has a slope of -2 and a y-intercept of positive 5. This means we will start at (0, 5) and move two units down for every unit right, or two units up for every unit left.
1) A 20 lb. BAG OF GRASS SEED WILL COVER AN AREA OF 10,000 ft2 . HOW MANY POUNDS WILL YOU NEED TO COVER AN AREA OF 140,000 ft2 . HOW MANY WHOLE BAGS OF SEED WILL YOU NEED TO BUY? WRITE THE EQUATION FOR A PROPORTION AND SOLVE IT.
2) SOLVE THE FORMULA FOR T2. ???????????????? ???????? = ???????????????? ????????
3) THE GILBERTS PURCHASED A CAR. IF THE TOTAL COST, INCLUDING A 5% SALES TAX, WAS $14,512, FIND THE COST OF THE CAR BEFORE TAX.
4) JIM MEYERS BOUGHT A NEW LAPTOP COMPUTER AT A 15% OFF SALE. IF THE SALE PRICE WAS $722.50, WHAT WAS THE LIST PRICE OF THE COMPUTER?
5) FIND THE x AND y INTERCEPTS FOR THE EQUATION 3x + 6y = 9.
1) 140
2) T2 = ?
3) $13,786.40
4) $835.88
5) x = 3, y=(0, 1.5)
1) To find the number of pounds of grass seed needed to cover an area of 140,000 ft2, you need to write a proportion and solve it. Set up the proportion using the given information:
20 lb/10,000 ft2 = x lb/140,000 ft2
To solve for x, multiply both sides of the equation by 140000:
20 lb * 140000/10,000 ft2 = x lb
x = 2800 lb
You will need 2800 lbs of grass seed to cover an area of 140,000 ft2. To find out how many whole bags of seed you will need to buy, divide the total number of pounds by the number of pounds in a bag, which is 20 lbs. You will need to buy 140 whole bags of seed.
2) To solve for T2 in the equation ???????????????? ???????? = ???????????????? ????????, divide both sides of the equation by ???????????????? :
T2 = ???????????????? ????????/????????????????
3) To find the cost of the car before the sales tax, subtract the 5% sales tax from the total cost. The formula is:
Cost before tax = Total Cost - (Total Cost * Sales Tax %)
Cost before tax = $14,512 - ($14,512 * 0.05) = $13,786.40
4) To find the list price of the laptop computer, add the 15% off sale to the sale price. The formula is:
List Price = Sale Price + (Sale Price * Discount %)
List Price = $722.50 + ($722.50 * 0.15) = $835.88
5) The x and y intercepts for the equation 3x + 6y = 9 can be found by setting x or y equal to 0 and solving for the other. To find the x intercept, set y = 0:
3x + 6(0) = 9
3x = 9
x = 3
The x intercept is (3, 0). To find the y intercept, set x = 0:
3(0) + 6y = 9
6y = 9
y = 1.5
The y intercept is (0, 1.5).
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Let r (t) = sin t i+ e^t j + ln ( t + 1 ) k
be a space curve. Which of the following vectors is perpendicular to the tangent vector of the curve at ( 0, 1, 0)?
a. < 0, 1, 0 >
b. < -1, 0, -1 >
c. < 1, 0, -1 >
d. < 1, - 1, 1>
e. <1, 0, 1 >
The vector that is perpendicular to the tangent vector of the curve at (0, 1, 0) is <1, 0, -1>, or option c
The space curve given is r(t) = sin t i + e^t j + ln(t+1) k. To find the tangent vector of the curve at a given point, we need to take the derivative of the curve with respect to t. The derivative of the curve is r'(t) = cos t i + e^t j + (1/(t+1)) k.
At the point (0, 1, 0), t = 0. So, the tangent vector at this point is r'(0) = cos 0 i + e^0 j + (1/(0+1)) k = <1, 1, 1>.
Now, we need to find which of the given vectors is perpendicular to the tangent vector. Two vectors are perpendicular if their dot product is equal to 0. So, we need to find the dot product of the tangent vector with each of the given vectors and see which one is equal to 0.
a. <1, 1, 1> • <0, 1, 0> = 0 + 1 + 0 = 1 (not perpendicular)
b. <1, 1, 1> • <-1, 0, -1> = -1 + 0 - 1 = -2 (not perpendicular)
c. <1, 1, 1> • <1, 0, -1> = 1 + 0 - 1 = 0 (perpendicular)
d. <1, 1, 1> • <1, -1, 1> = 1 - 1 + 1 = 1 (not perpendicular)
e. <1, 1, 1> • <1, 0, 1> = 1 + 0 + 1 = 2 (not perpendicular)
Therefore, the vector that is perpendicular to the tangent vector of the curve at (0, 1, 0) is <1, 0, -1>, or option c.
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Factor 36x^4 -25 completely
Answer: (6x²+5) (6x²- 5)
Please give me brainliest :)
Step-by-step explanation:
4. Write the function rule for g(x) from f(x) = √x. Shift up 5, then vertical stretch by a factor of 2, followed by a shift to the right 3 units.
This function rule represents the original function f(x) = √x, shifted up 5 units, vertically stretched by a factor of 2, and shifted to the right 3 units.
The function rule for g(x) from f(x) = √x can be found by applying the given transformations to f(x). First, we shift up 5 units by adding 5 to the function. Then, we apply a vertical stretch by a factor of 2 by multiplying the function by 2. Finally, we shift to the right 3 units by replacing x with (x - 3) in the function. The resulting function rule for g(x) is:
g(x) = 2√(x - 3) + 5
This function rule represents the original function f(x) = √x, shifted up 5 units, vertically stretched by a factor of 2, and shifted to the right 3 units.
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5 out of the 10 employees at the water slides are temporary employees. What percentage of the employees at the water slides are temporary?
Write your answer using a percent sign (%).
Answer: 50%
Step-by-step explanation: There are 5 out of 10 employees at the water slide. 10 in this situation is going to be 100%
since there is only 5 out of 10 employees that are temporary
it would be 50%
Answer: 50%
Step-by-step explanation:
Subtract.x2+3xy−4y26x−3y−x2+xy−2y25x+3yx2+3xy−4y26x−3y−x2+xy−2y25x+3y=(Simplify your answer. Type your answer in factored form.)
The factored form is 2y(x - y) - 11x.
What is factored form?Factored form of a polynomial is when the polynomial is written as a product of its factors. Each factor is either a polynomial or a number. Factored form is useful for identifying the zeros of a polynomial and for solving polynomial equations.
To simplify the given expression, we need to combine like terms and factor if possible.
First, let's combine the like terms:
x^2 + 3xy - 4y^2 - 6x + 3y - x^2 - xy + 2y^2 - 5x - 3y
= 2xy - 2y^2 - 11x
Next, let's see if we can factor the expression:
2xy - 2y^2 - 11x
= 2y(x - y) - 11x
Since we cannot factor any further, the simplified expression in factored form is:
2y(x - y) - 11x
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The number of blueberry muffins that a baker makes each day is 30% of the total number of muffins she makes.
A. On Monday, the baker makes 42 blueberry muffins. What is the total number of muffins that the baker makes on Monday?
B. On Tuesday, the baker makes a total of 60 muffins. How many blueberry muffins does the baker make on Tuesday?
The baker makes a total of 140 muffins on Monday.
The baker makes 18 blueberry muffins on Tuesday.
What are percentages?
Percentages are a way of expressing a fraction or proportion out of 100. The term "percent" literally means "per hundred." Percentages are commonly used in many areas of everyday life, including finance, science, and statistics.
To express a number as a percentage, it is multiplied by 100. For example, 0.75 is equivalent to 75 percent, since 0.75 x 100 = 75. Similarly, 50 percent is equivalent to 0.5 or 1/2.
Percentages are commonly used to express changes and comparisons. For example, if a product's price increases from $100 to $120, this represents a 20 percent increase in price. If a person scored 80 out of 100 on a test, this represents an 80 percent score.
Percentages are also used to calculate percentages of a total. For example, if a person earned $40,000 out of a total company income of $500,000, their income represents 8 percent of the total income. Similarly, if a person wants to calculate a 20 percent tip on a $50 meal, they would calculate 20 percent of $50, which is $10.
In summary, percentages are a way of expressing a fraction or proportion out of 100, and are commonly used to express changes, comparisons, and percentages of a total in everyday life.
A. Let's assume the total number of muffins the baker makes on Monday to be x.
According to the problem, the number of blueberry muffins that the baker makes is 30% of the total number of muffins.
So, 30% of x is equal to 42:
0.30x = 42
To solve for x, we can divide both sides by 0.30:
x = 140
Therefore, the baker makes a total of 140 muffins on Monday.
B. Let b be the number of blueberry muffins the baker makes on Tuesday.
According to the problem, the number of blueberry muffins is still 30% of the total number of muffins. So, we can set up the equation:
0.30(60) = b
Simplifying the left side:
18 = b
Therefore, the baker makes 18 blueberry muffins on Tuesday.
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find the measure of ycg
Answer:
59
Step-by-step explanation:
Opposite angles are equal
C or KCG isn121
Straight line angle is 180
YCG + GCK = 180
YCG = 180- 121
Another method
All the four angles at a point is 360
YCH + HCK + KCG +YCG is 360
C is 121
121 + X + 121 + X = 360
2X + 242 =360
Subract 242 from both sides
2X = 118
Divide both sides by 2 = 59
solve for x
help me pls
The value of x from the similar triangles is x = 4
What are similar triangles?If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.
Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides
Given data ,
Let the first triangle be ΔQRS
Let the second triangle be ΔLMN
Now , the measure of ∠QRS = measure of ∠NLM
And , the triangles are similar
Now , the corresponding sides of similar triangles are in the same ratio
On simplifying , we get
LM / RQ = LN / QS
( 2x + 4 ) / 8 = 9 / 6
Multiply by 8 on both sides , we get
2x + 4 = ( 3/2 ) 8
2x + 4 = 12
Subtracting 4 on both sides , we get
2x = 8
Divide by 2 on both sides , we get
x = 4
Therefore , the value of x is 4
Hence , the similar triangles are solved
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given the figure below with the provided measurements, what is PQ?
The requried measure of the PQ in the triangle PQT is 16 in.
What are Similar triangles?Similar triangles are those triangles that have similar properties,i.e. angles and proportionality of sides.
Here,
A figure of triangles has been shown, ΔPQT and ΔORS.
We have to determine the measure of side PQ.
Since the given triangle is similar to one another, we can apply the property of proportionality between the similar triangles. By which:
PR/PQ = RS/QT
PQ + 4 / PQ = 10/8
8PQ + 32 = 10PQ
2 PQ = 32
PQ = 16 in
Thus, the requried measure of the PQ in the triangle PQT is 16 in.
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