Answer:
[tex]x = -2, \frac{12}{5}[/tex]
Step-by-step explanation:
We start with the equation:
[tex]5x^2-2x-24=0[/tex]
Factoring the equation gives us:
[tex](x+2)(5x-12)=0[/tex]
Thus we can derive:
[tex](x+2)=0\\x=-2[/tex]
or
[tex](5x-12)=0\\5x=12\\x=\frac{12}{5}[/tex]
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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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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Write a sentence for the equation.
4m=52
Multiple choice question.
A)
m multiplied by a number is equal to fifty-two.
B)
Four times m is equal to fifty-two.
C)
The sum of 4 and m is equal to fifty-two.
D)
Triple m is equal to fifty-two.
A sentence for the equation 4m=52 is,
B) Four times m is equal to fifty-two.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
Here, given that,
4m=52
i.e. we have,
4×m = 52
Hence, A sentence for the equation 4m=52 is,
B) Four times m is equal to fifty-two.
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Sketch the shape made with algebra tiles at right on your paper. Then answer parts (a) and (b) below.
A) Find the area and perimeter of the shape.
B) If the algebra tiles were rearranged into a different shape, how would the area change?
The evaluation of the algebra tiles are as follows;
A) The area of the algebra tiles is; 2·x² + 3·x
The perimeter of the tiles is; 6·x + 6
B) If the algebra tiles were rearranged, the area remains 2·x² + 3·x
What are algebra tiles?Algebra tiles are figures that can be manipulated to help explore and understand concepts such as expanding algebraic expressions, factoring expressions, and equations.
Please find attached the possible shape in the question created with MS Word.
A) The area of the of the shape is the sum of the areas of the individual shapes, which are found as follows;
The area = x² + x² + x + x + x = 2·x² + 3·xThe perimeter is the sum of the width and lengths of the rectangles as follows;
The width of the rectangle with area x = 1 unit
The width of the boxes with area x² = x
The length of the sides of each rectangle = x unit
The perimeter, P, of the figure is therefore;
P = x + x + 1 + 1 + 1 + x + 1 + 1 + 1 + x + x + x = 6·x + 6B) The area of the each of the algebra tiles remain the same when the tiles are rearranged, such that the area, of the new shape, which is the sum of the areas of the individual tiles remain the same.
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Find the perimeter. Simplify your answer.
Answer:
Pwede po b may pic
Step-by-step explanation:
para lang po maka answer kami
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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Why is 1111 a prime number?
1111 is not a prime number. It is a composite number, which means it can be factored into smaller integers. The factors of 1111 are 11 * 101. Prime numbers are numbers that are divisible by only 1 and itself. Only numbers that are greater than 1 and are not divisible by any other number except 1 and itself are prime numbers.
1, 11, 101, and 1111 are all divisors of the number 1111. A number must have exactly two elements in order to be deemed a prime number. 1111 is not a prime number since it has more than two components, namely 1, 11, 101, and 1111.
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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
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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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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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.
What are the types of triangles Class 7?
Answer:
Step-by-step explanation:
The six types of triangles are: isosceles, equilateral, scalene, obtuse, acute, and right.
PLEASE HELP!!! I NEED HELP WITH MY HOMEWORK!!!!
(GEOMETRY)
Answer:
3.here,tan45°=10/n
or,1=10/n
:.n=10
Now from Pythagoras theorem,
m²=(10)²+n²
or,m=√100+100
:.m=10√2
*mark me brainliest
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 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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In which quadrant would an angle x lie if cosx is negative and cotx is negative?.
When cosx is negative and cotx is negative, an angle x lies in Quadrant II. Hence, the correct answer is B.
The correct answer is Quadrant II because the cosine and cotangent of an angle are related to the x- and y-coordinates of a point on the unit circle, respectively.
In Quadrants I and IV, the cosine function is positive, while in Quadrants II and III, it is negative. In Quadrants I and III, the cotangent function is positive, while in Quadrants II and IV, it is negative. This means:
When cos x is negative, it means that the x-coordinate of the point on the unit circle corresponding to angle x is negative, which means the point is in Quadrant II or III.When cot x is negative, it means that the y-coordinate of the point on the unit circle corresponding to angle x is negative, which means the point is in Quadrant II or IV.Therefore, an angle x that satisfies both conditions of cos x being negative and cot x being negative must be in Quadrant II.
This question should be provided with answer choices, which are:
A. Quadrant IB. Quadrant IIC. Quadrant IIID. Quadrant IVThe correct answer is B.
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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
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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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
Which value of a makes 7+5(x-3) = 22 a true statement?
The statement 7+5(x-3) = 22 is true for x = 6.
Solving an equation:Finding the equation's solution is the concept of solving an equation. The value of the variable that may be used to verify the equation is known as a solution.
The same number added on both sides
Taking away the same amount from both sides
using the same integer on both sides when multiplying
using the same integer to divide into both sides
Here we have
7 + 5(x-3) = 22
The above expression can be solved as follows
7 + 5(x-3) = 22
Multiply 5 and (x - 3) terms
=> 7 + 5x - 15 = 22
=> 5x - 8 = 22 [ ∵ -15 + 7 = -8 ]
Add 8 on both sides
=> 5x - 8 + 8 = 22 + 8
=> 5x = 30
Divided by 5 into both sides
=> 5x/5 = 30/5
=> x = 6
Therefore,
The statement 7+5(x-3) = 22 is true for x = 6.
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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:
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:
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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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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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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Please review, Thank you!
The value of the expression will be:
9. 5(n + 5) = 5n + 25
10. -9(10 - 6r) = -90 + 54r
11. -6(m + 6) = -6m - 36
12. 3(4 - 6m) = 12 - 18m
How to calculate the expression?An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information.
The value of the expression will be:
9. 5(n + 5)
= (5 * n) + (5 × 5)
= 5n + 25
10. -9(10 - 6r)
= -90 -+ 54r
= -90 + 54r
11. -6(m + 6)
= -6m - 36
12. 3(4 - 6m)
= 12 - 18m
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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%.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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What is secant formula?
Therefore , the solution of the given problem of trigonometry comes out to be the reciprocal of both the cosine is the secant.
What is trigonometry?Trigonometry, a branch of mathematics, studies relationships between angles and sides of triangles. Trigonometric exists throughout all of geometry and can be reduced to a grouping of triangles from any horizontal form. Calculus, difficult or real trigonometry, algebra, and infinite series are only a few examples of the mathematics that are related to one another in a startlingly complex way.
Here,
The reciprocal of both the cosine is the secant. This is the fraction of a right triangle's hypotenuse towards the side closest to a particular angle.
The secant of slope in a right angled triangle is calculated by dividing the height of the y axis by the width of the neighboring side.
Thus, its fundamental formula is: sec X =[tex]\frac{Hypotenuse}{Adjacent Side}[/tex]
Additionally, it is the cosine value's reciprocal.
Therefore , the solution of the given problem of trigonometry comes out to be the reciprocal of both the cosine is the secant.
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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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