Answer:
Step-by-step explanation:
Given that 3 apples and 4 pears cost $1.95, 4 pears and 1 orange cost $1.60, and 1 orange and 3 apples cost $1.15, what is the cost of 1 apple?
Let us represent
Number of apples = x
Number of pears = y
Number of oranges = z
Given that
3 apples and 4 pears cost $1.95
3x + 4y = 1.95
4 pears and 1 orange cost $1.60
4y + z = 1.60
z = 1.60 - 4y
1 orange and 3 apples cost $1.15
z + 3x = 1.15
z = 1.15 - 3x
what is the cost of 1 apple?
Determine the equation of the line giving the point (86,125) and the slope m = -18
The required equation of the line is y = -18x + 1673.
Slope-intercept form of a line:One of the most common ways to represent a line's equation is in the slope-intercept form of a line. When the slope of the straight line and the y-intercept are known, the slope-intercept formula can be used to determine the equation of a line.
Slope-intercept form of a line is y = mx + c
where m = slope and c - y-intercept of the line.
Here we have
Given points (86, 125) and
Slope of the line m = -18
As we know
Slope intercept form of a line is y = mx + c
Given m = - 18
=> y = (-18)x + c
=> y = -18x + c
Given points (86, 125) substitute in the above line
=> 125 = -18(86) + c
=> 125 = -1548 + c
=> c = 1673
Therefore,
The required equation of the line is y = -18x + 1673.
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How do you write exponential 4?
Exponential 4 can be written as x^4. This is an exponential expression and is used to represent a repeated multiplication of the base, 4, by itself.
In this case, the base is 4, and the exponent, x, represents the number of times 4 is multiplied by itself. For example, 4^3 can be written as 4x3, which is equal to 4*4*4. This is the same as saying “4 multiplied by itself 3 times.”
Exponential notation is a useful way to express large numbers. For example, 4^10 can be written as 4x10, which is equal to 4,096. The exponential form of this expression allows us to quickly calculate the result without having to write out the entire equation.
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jacks computer prints 36 pages in 2 minutes and 24 sec At that rate how many more seconds will it take for 5 more pages
The time taken to print the 5 more pages will be 1.25 seconds.
Define the unitary method?The unitary strategy involves calculating the value of an individual unit, from which we can derive the values of the appropriate number of units.For the stated question-
The printer at Jack's prints 36 pages in 2 minutes and 24 seconds.
This can be written as;
2*60 + 24 seconds ---> 36 pages
120 + 24 seconds ---> 36 pages
144 seconds ---> 36 pages
Time taken to print 1 page.
1 page ---> 36 / 144 seconds.
Thus, to print 5 more pages.
5 page ---> 36 / 144 * 5 seconds.
5 page ---> 1.25 seconds.
Thus, the time taken to print the 5 more pages will be 1.25 seconds.
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Which of the following is the nature of the roots of the quadratic equation if the value of its discriminant is positive and a perfect square?A. The roots are not real.B. The roots are rational and equal.C. The roots are irrational and not equal.D. The roots are rational and not equal.
D) if the value of its discriminant is positive and a perfect square the The roots are rational and not equal.
Nature of roots of quadratic equation:b2 – 4ac > 0 Real and the value of roots are unequal
b2 – 4ac = 0 Real and value of roots are equal
b2 – 4ac < 0 Distinct and Imaginary roots
b2 – 4ac > 0 (is a perfect square) Real, rational and value of roots are Distinct
These are the four conditon for the nature of root and the condition which is driving force for the loop .
so form the above statement conditon 4 satisfies and hence the quadratic equation have real rational and distinct or not equal root.
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A triangle has side lengths of (9f+g)(9f+g) centimeters, (5f+9h)(5f+9h) centimeters, and (2h+7g)(2h+7g) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?.
The expression that represents the perimeter of the triangle is P = (106f² + 50g² + 85h² + 18fg + 90fh + 28gh) centimeters. This result is obtained by adding up the lengths of the three sides of the triangle.
What is the perimeter of a triangle?A perimeter of a triangle is the sum of the side lengths of the triangle. It can be expressed as
P = a + b + c
Where
P is perimeter.a, b, and c are the side lengths of a triangle.The side lengths of a triangle are
a = (9f+g)(9f+g) cmb = (5f+9h)(5f+9h) cmc = (2h+7g)(2h+7g) cmFind the perimeter!
P = a + b + c
P = (9f+g)(9f+g) cm + (5f+9h)(5f+9h) cm + (2h+7g)(2h+7g) cm
P = (81f² + 9fg + 9fg + g² + 25f² + 45fh + 45fh + 81h² + 4h² + 14gh + 14gh + 49g²) cm
P = (106f² + 18fg + 50g² + 90fh + 85h²+ 28gh) cm
P = (106f² + 50g² + 85h² + 18fg + 90fh + 28gh) centimeters
Hence, the perimeter's expression is P = (106f² + 50g² + 85h² + 18fg + 90fh + 28gh) centimeters.
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Answer:
8g+11h+14f
Step-by-step explanation:
Fair Game Review what you
Tell whether x and y show direct variation.
If so, find the constant of proportionality. 28.) x = 2y
29.) y - x = 6
30.) xy = 5
28) The constant of proportionality is (k = 2)
29) x and y do not change in the same way
30) The constant of proportionality (k = 5/xy)
What is direct variation?x = 2y shows direct variation because as x increases, y also increases and as x decreases, y also decreases. The constant of proportionality, also known as the "k" value, is 2, it represents the ratio of x to y. (k = 2)
y - x = 6 does not show direct variation because the relationship between x and y is not constant, x and y do not change in the same way.
xy = 5 shows direct variation because as x increases, y also increases and as x decreases, y also decreases. To find the constant of proportionality, we can divide both sides by xy.
k = 5/xy
In this case, the constant of proportionality is not a fixed value, it is a variable depending on the values of x and y. It represents the ratio of xy to the product of x and y.
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Write in radical form. Do not simplify. 15x^1/4
The radical form of the given expression 15x^(1/4) is equal to ( 15 ) × [tex]\sqrt[4]{x}[/tex].
As given in the question ,
Given expression is written as :
15x^(1/4)
Using th formula to conversion of the exponential form into the radical form in general form is given by:
( z )^ ( m / n ) = [tex]\sqrt[n]{z^{m} }[/tex]
in the given expression the value of :
z is equal to x
m is equal to 1
n is equal to 4
Now, Substitute the values of the given variables in the formula of radical form we get,
15 x^(1/4)
= ( 15 ) × [x^(1/4) ]
= ( 15 ) × [tex]\sqrt[4]{x^{1} }[/tex]
Raising any variable or the number to the power one is always equal to same variable or the number itself.
= ( 15 ) × [tex]\sqrt[4]{x}[/tex]
Therefore, the radical form of the given exponential form of the expression 11x^(1/4) is written as : ( 15 ) × [tex]\sqrt[4]{x}[/tex].
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The length of a rectangle is 4 inches shorter than it’s width. The perimeter of the rectangle is 80 inches. what are the length and width of the rectangle?
Answer:
Suppose that x is the length and y the width of the rectangle. Then we have 2x+2y=80 and x=y+4. Therefore, 2(y+4)+2y=80 or 4y+8=80 or 4y=72 or y=18 and x=22
Step-by-step explanation:
What is the solution set of the given systems? 5x + 2y = 7 and y = x + 1
The solution set of the given system is (5/7, 12/7).
Now, According to the question:
The given equations are:
5x + 2y = 7 …. (1)
y = x + 1 ….. (2)
Let us solve the system of linear equations using the substitution method.
Substituting equation (2) in (1)
5x + 2(x + 1) = 7
By further calculation
5x + 2x + 2 = 7
So we get
7x = 7 - 2
7x = 5
Divide both sides by 7
x = 5/7
Substitute the value of x in equation (2)
y = 5/7 + 1
Taking LCM
y = (5 + 7)/7
y = 12/7
Therefore, the solution set of the given system is (5/7, 12/7).
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How do you find m1 and m2 in coordinate geometry?
In coordinate geometry, the slope of a line, m, is defined as the ratio of the change in y to the change in x of any two distinct points on the line. It can also be written as the ratio of the rise to the run.
What is meant by coordinate geometry?
Coordinate geometry (or analytic geometry) is defined as the study of geometry using the coordinate points. Using coordinate geometry, it is possible to find the distance between two points, dividing lines in m:n ratio, finding the mid-point of a line, calculating the area of a triangle in the Cartesian plane, etc.
To find the slope of a line, we can use the two-point form of the equation of a line, which is:
y = mx + b
Where m is the slope and b is the y-intercept.
To find the slope, we can use any two distinct points (x1, y1) and (x2, y2) on the line. To find m1 and m2, we use the following formulas:
m1 = (y2-y1) / (x2-x1)
m2 = (x2-x1) / (y2-y1)
It is important to note that m1 and m2 are the same value, just in different forms. m1 is the slope and m2 is the reciprocal of the slope.
In cases when x2-x1=0 (parallel to y-axis) or y2-y1=0(parallel to x-axis) the slope would be undefined and undefined respectively.
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What are the solutions of the inequality 2x² x 6 0?
The solutions of the inequality [tex]2x^{2} + x - 6 = 0[/tex] are 3/2, -2. This can be found by using the Quadratic Formula, which states that for any quadratic equation of the form [tex]ax^{2} +bx + c = 0[/tex], the solutions are [tex]x = -b +/-\sqrt{b^{2} -4ac} /2a[/tex].
Discriminant: b² - 4 a c = 1 - 4(2)(-6) = 1 + 48 = 49
Solution 1: x = [tex]-b + \sqrt{b^{2} -4ac} /2a[/tex] = (-1 + √49)/(2×2) = (-1 +7)/4 = 6/4 = 3/2
Solution 2: x = [tex]-b-\sqrt{b^{2} -4ac} /2a[/tex]= (-1 - √49)/(2×2) = -8/4 = -2
So, the two solutions are 3/2 and -2.
The equation can also be written as,
[tex]2x^{2} +4x -3x-6=0[/tex]
[tex]2x(x+2) -3(x+2) = 0[/tex]
[tex](2x-3)(x+2) = 0[/tex]
x = 3/2, -2
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Is 152 a multiple of 8?
Yes , the given statement is true. Number 152 is representing as multiple of 8.
As given in the question,
Given number is equal to 8:
Given multiple is equal to 152:
Multiple is the number which we get after multiplying the given number by any integer.
Multiple of 8 are given by :
8 , 16, 24, 32, 40, 48, 56, 64, ......., so on
Here 152 represents the multiple of 8.
When we multiply 8 by 19 we get a number equals to 152.
The given statement is true.
Therefore, the given statement is true as 152 is one of the multiple of 8.
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What are the 2 most common errors that people make when creating while loops?
The two most common errors that people make when creating while loops are infinite loops and off-by-one errors.
What is error in math?Error in math is when an incorrect result is obtained from a mathematical calculation. It can be caused by a mistake made in the calculation (such as a wrong formula or an incorrect use of a calculator) or by a misunderstanding of the problem being solved. Error in math can also be caused by a wrong assumption about the data being used. Regardless of the cause, an error in math can have serious consequences, as incorrect results can lead to incorrect decisions and actions.
An infinite loop is when a while loop is created that never ends, as the condition that the loop checks for never becomes false. An off-by-one error is when the loop is written in such a way that the loop will run one iteration too many or too few. This can lead to incorrect results and cause the loop to miss or repeat certain parts of the loop. To prevent these errors, it is important to have a clear understanding of the loop's condition and to always test the loop thoroughly before using it.
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Equivalents are things that are equal or have the same value. in mathematics, for example, the fraction 3/4 and the decimal ______________ are the same value
Equivalents are things that are equal or have the same value. in mathematics, for example, the fraction 3/4 and the decimal 0.75 are the same value
Any 2 terms in mathematics are said to be equivalent if the are identical in terms of values. They do not necessarily have to be "equal"
For example, 8 can be said to be equal to 8 but 8 is "equivalent" to
4 + 4
1 + 7
10 - 2 etc.
This can also be considered for conversion systems.
For example- 1 kg is equvalent to 1000 grams.
Just like in all the examples we considered before, equivalency can be drawn when fractional forms are converted into decimal forms.
1/2 is equivalent to 0.5
Hence for 3/4, we need to write a decimal value for the same
3/4 = 75/100 = 0.75
Hence 3/4 will be equivalent to 0.75
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The lateral surface area of a cylinder of length 14m is 220m². Find the volume of the cylinder.
The volume of the cylinder is 275m³.
We have given that,
Lateral surface of cylinder = 220m²
Height (h) = 14m
Let radius of cylinder = r
Then 2πrh = 220m²
⇒ × 22/7 × r × 14 = 220m²
[tex]$ \Rightarrow \text r = \frac{220 \times 7}{2 \times 22\times 14}[/tex]
[tex]$ \Rightarrow \text r = \frac{220 \times 7}{2 \times 22\times 14}[/tex]
[tex]$ \Rightarrow \text r = \frac{5}{2} = 2.5[/tex]
Now we can find the volume,
Volume of cylinder = πr²h
= 22/7 × (2.5)² × 14
= 22 × 6.25 × 2
= 275m³
Thus, the volume of the cylinder is 275m³.
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The volume of the cylinder is 274.75 cubic meter.
What is lateral surface area?All of the sides of the object are the lateral p of an object, except its base and top (when they exist). The lateral surface area is the lateral surface zone. This is to be distinguished from the overall surface area, which, along with the base and top areas, is the lateral surface area.
Given that, the lateral surface area of a cylinder of length 14m is 220 m².
We know that, the lateral surface area of a cylinder is 2πrh.
Here, 2πrh=220
2×3.14×r×14=220
87.92r=220
r=220/87.92
r=2.5 meters
We know that, the volume of a cylinder is πr²h
Here, volume = 3.14×2.5²×14
= 3.14×6.25×14
= 274.75 cubic meter
Therefore, the volume of the cylinder is 274.75 cubic meter.
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Ms. Higgins has 28 students in her gym class. She puts them in 4 equal groups. How many students are in each group?
Answer:
each group will have 7 students in it.
Step-by-step explanation:
Ms. Higgins has 28 students in her gym class and wants to put them in 4 equal groups.
divide the total number of students by the number of groups.
28 students / 4 groups = 7 students per group.
So, each group will have 7 students in it.
What is 2x2 aspect ratio?
2x2 aspect ratio means that the width is twice the height, which is commonly used in computer graphics, video and image processing.
The aspect ratio of an image or a display refers to the ratio of the width to the height of the image or display. A 2x2 aspect ratio means that the width of the image or display is twice the height. This aspect ratio is commonly used in computer graphics, video, and image processing. It is also known as a "square aspect ratio" because the width and height have the same ratio (1:1).
For example, a 2x2 aspect ratio is used in the QR Code standard, which is used for storing small amounts of data in a two-dimensional barcode. In this case, the width of the QR code is twice the height, making it square.
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Arun is driving on a long road trip. He currently has 9 gallons of gas in his car. Each
hour that he drives, his car uses up 1 gallon of gas. How much gas would be in the
tank after driving for 5 hours? How much gas would be left after t hours?
Gas left after 5 hours:
Gas left after t hours:
Please hurry
Answer:
9
Step-by-step explanation:
After driving for 5 hours, Arun's car would have used up 5 gallons of gas (1 gallon per hour for 5 hours). Therefore, the amount of gas left in the tank after driving for 5 hours would be 9 gallons - 5 gallons = 4 gallons.
To find the amount of gas left after t hours, we can use the formula:
Gas left after t hours = 9 - (1 x t)
Where t is the number of hours driven.
So, the amount of gas left after t hours would be 9 - t gallons.
After driving for 5 hours, Arun would have 4 gallons of gas left in his tank. If he drives for t hours, he would have (9 - t) gallons of gas left in his tank. The calculations are based on the fact that Arun's car uses 1 gallon of gas per hour of driving.
Explanation:To answer this question, we must understand that Arun's car uses 1 gallon of gas for every hour of driving. So, if he drives for 5 hours, his car will use 5 gallons of gas. Arun starts with 9 gallons of gas, so we subtract the 5 gallons of gas used from the 9 gallons of gas he started with. The result is:
9 - 5 = 4 gallons
So, after driving for 5 hours, Arun would have 4 gallons of gas left in his tank.
Similarly, if he drives for t hours, his car will use t gallons of gas. So, to find how much gas would be left after driving for t hours, we subtract t gallons from the 9 gallons he started with:
9 - t = (9 - t) gallons
Thus, after driving for t hours, Arun would have (9 - t) gallons of gas left in his tank.
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A friend has a 85% average before the final exam for a course. That score includes everything but the final, which counts for 30% of the course grade.
What is the best course grade your friend can earn?
What is the minimum score your friend would need on the final to earn a 75% for the course?
(Give answers accurate to at least one decimal place.)
Your friend's 80% average now represents 85% of the overall grade. This is because we are aware that the final, which is worth 15%, is the only thing left.
SOLUTIONIf your friend receives a 100 on the final, they will receive the highest possible course grade:
0.85(80%) + 0.15(100%) = 83%. The course's highest achievable grade is 83%.The following equation must be solved for "f," the result of the final test, in order to obtain a score of 75:
0.85(80%) + 0.15(f) = 75%68% + 0.15f = 75%0.15f = 7%f = 46.67%A final grade of 46.67% is required in order to receive a course passing grade of 75%.The sum of two numbers is 36 and the difference is 12. What are the numbers?
Answer:
x=24, y=12. (24, 12).
Step-by-step explanation:
Let x and y be the two numbers that we seek.
Then x+y=36 and x-y=12.
x+y=36
x-y=12
----------
2x=48
x=48/2
x=24
24+y=36
y=36-24=12
What is 3 to the 3rd exponent?
The expression "3 to the 3rd exponent" means that the number 3 is multiplied three times and is represented as 3³ and the value of this expression is 27 .
The expression is given as ; "3 to the 3rd exponent" ;
we have to represent it in exponential form and find the value ,
The number 3 to the 3rd exponent means that , the number 3 is multiplied three times , which is denoted as : ⇒ [tex]3\times 3 \times 3[/tex] ;
Since the base of all the numbers is same that is 3 , So , by the Law Of Exponents , the exponents/powers gets added ;
So , the expression becomes ⇒ [tex]3^{1+1+1}[/tex] ;
On adding the exponents ,
we get ;
⇒ [tex]3^{3}[/tex] ;
and the value of this exponential form is 27 .
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A set of 3 cards, spelling the word ADD, are placed face down on the table. Determine P(A, A) if two cards are randomly selected with replacement.
one third
one ninth
two thirds
two sixths
The probability of the two cards being A and A, P(A, A), is 1/9.
The correct option is the second option, one ninth.
What is the probability?The Probability in mathematics is the possibility of an event in time. In simple words, how many times that incident is happening in any given time interval.
Given:
A set of 3 cards, spelling the word ADD, are placed face down on the table.
And we have to determine P(A, A) if two cards are randomly selected with replacement.
From the formula for probability, we have that
P(A) = Number of favorable outcomes / Total number of possible outcomes
P(A) = 1/3
Then,
The probability of selecting two cards that have A and A with replacement is,
P(A, A) = P(A) × P(A)
P(A, A) = 1/3 × 1/3
P(A, A) = 1/9
Therefore, the probability is 4/9.
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here is a long division calculation of 917 ÷ 7 in words, explain the steps used to solve.
Step-by-step explanation:
Step 1: Create a division problem with the numbers being divided lined up one above the other.
Step 2: Divide the first digit of the dividend (917) by the divisor (7), and write the quotient (130) above the dividend.
Step 3: Multiply the divisor (7) by the quotient (130) and write the product (910) below the dividend (917).
Step 4: Subtract the product (910) from the dividend (917) and write the difference (7) below the product.
Step 5: Bring down the next digit of the dividend (917), making the next number to divide (7).
Step 6: Divide the new number by the divisor, and write the quotient, this case 0 (since 7 doesn't divides into 7) above it, and add the remainder, which is still 7.
Step 7: The remainder is the final result of the division. 917 divided by 7 is 130 with a remainder of 7, so the final answer is 130 remainder 7, this can be represented as 130 R 7.
Note: Even though it is not shown in the explanation above, to check the solution is correct, you could also multiply the quotient (130) by the divisor (7) and add the remainder (7) to get back to the dividend (917)
It's also worth to note that the final remainder could be seen as the number we couldn't divide and the quotient as the result of the division.
Find the perimeter. Simplify your answer.
Answer:
Pwede po b may pic
Step-by-step explanation:
para lang po maka answer kami
Find Overtime and Gross
Pay per week.
Pay Rate: $9.58/hour
Total hours worked last
week: 48
Answer:no
Step-by-step explanation:
1. N
2. O
Geometry : Parallelogram
Can I get help with this question?
Answer:
15° & 75°
Step-by-step explanation:
An equilateral triangle is one in which all three sides are congruent. It also has the property that all three interior angles are equal. In other words, all three angles of an equilateral triangle are always 60°.
So ∠ABE = 90+60=150.
because ABCD is square so AB = BC
because BEC is equilateral triangle, so BC = BE = AB
so we know in ABE triangle the 2 sharp angles are the same
so ∠AEB = (1/2) * (180-150) = 15
so ∠DAE = 90-15 =75
What is the value of exponential 1?
The term exponential 1 is represented as e¹ and the value of exponential 1 is 2.71828... .
The term Exponent can be defined as the method of expressing the large numbers in terms of powers.
For Example : if 2 is multiplied 4 times then , its exponent form is [tex]2^{4}[/tex]
According to the rule of exponent ; any number that is raised to the power of (1)one is equal to the number itself.
Thus , e to power of 1 can be written as e¹ .
and we know that value of e is 2.7182818284..... .
So , exponent to the power 1 is [tex]e^{1} = 2.7182818284...[/tex] .
Therefore , the value of exponent 1 is 2.7182818284... .
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If you have a rewards card at Biggby, you earn a free drink after every 12 drinks you buy. Can the total amount of money spent at Biggby after ordering n drinks be considered arithmetic? Why or why not?
What is substitution technique?
The substitution technique includes simplifying the given equation, solving one of the equations for any unknown value, substituting the step 2 solution in another equation, solving the new equation, and finally solving the equation to find the second variable.
The substitution method is the algebraic method to solve different linear equations. In this technique, the value of one variable from either of the equation is substituted in the other equation.
In this technique the following steps are used to solve an equation by substitution method:
Step 1. Simplify the given equation by removing the parenthesis.
Step 2. Solve one of the equations for any unknown value.
Step 3. Substitute step 2 result in the other equation.
Step 4. Now solve the equation which gets from step 3 obtained using elementary arithmetic operations.
Step 4. Finally, solve the final equation for the second variable.
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What are the domain and range of f(x) = -24?
Domain: All real numbers
Range: {-24}
Domain: {-24}
Range: {-24}
Domain: All real numbers
Range: All real numbers
Domain: {-24}
Range: All real numbers
For the function:
f(x) = -24
The domain and range are:
Domain: all real number.
Range: {-24}
What is the domain and range of the function?For a function:
y = f(x)
The domain is the set of possible inputs, this is, possible values of x.
The range is the set of possible outputs, this is, possible values of y.
Here the function is:
f(x) = -24
Notice that the input can be any value, we don't have any restrictions, and the output can only be -24, then we have:
Domain: all real number.
Range: {-24}
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