What is the value of the discriminant in the equation shown below?
x^2+3x-6=0
...?
Discriminant = b^2 - 4ac
a = 1
b = 3
c = -6
3^2 - 4(1x-6)
9 - (4 x -6 )
9 - -24 = 33
Therefore it has 2 real roots
Jace walked a total of 5/6 of a mile to school this week how far did he walk for 5 days
Final answer:
To find how far Jace walked to school each day, divide the total distance (5/6 of a mile) by the number of days (5), resulting in 1/6 of a mile walked each day.
Explanation:
The question involves calculating the distance Jace walked to school each day if he walked a total of 5/6 of a mile over 5 days. To find out how far he walked each day, we need to divide the total distance by the number of days.
Here's the step-by-step calculation:
Total distance walked: 5/6 of a mile.
Number of days: 5 days.
To find the distance walked each day, divide the total distance by the number of days: (5/6) ÷ 5 = 5/6 ÷ 1/5 = 5/30 = 1/6.
So, Jace walked 1/6 of a mile to school each day.
Given g(x)=x^2-7x+1/4 show that the least possible value of g(x) is -12
"Find the constants m and b in the linear function f(x) = mx + b so that f(2) = 10 and the straight line represented by f has slope -5."
f(x) = mx + b m = slope = -5 f(2) = 10 = (-5)(2) + b b = 10 + 10 = 20 Ans. m=-5, b = 20
The difference between the square of two numbers is five. Twice the square of the second number is subtracted from three times the square of the first number is 19. Find the numbers. Please show work. The difference between the square of two numbers is five. Twice the square of the second number is subtracted from three times the square of the first number is 19. Find the numbers. Please show work.
The two possible pairs of numbers that fit the given equations are (√7, 2) and (-√7, -2). We find these by setting up two equations based on the provided conditions and solving them simultaneously.
Explanation:Let's denote the first number as 'x' and the second number as 'y'. We have two equations from the given information:
1. x² - y² = 5
2. 3x² - 2y² = 19
We can solve these equations simultaneously to find the values of 'x' and 'y'. The first step in solving a system of linear equations is to multiply the equations by what's needed to get the coefficients of one of the variables to match, so it can be eliminated when the equations are added or subtracted. Let's multiply the first equation by 3 and the second equation by 1. We then have:
3x² - 3y² = 15
3x² - 2y² = 19
If we subtract the second equation from the first, we get:
-y² = -4
which leads to y = 2 or y = -2 (squared numbers are always positive). Substituting '2' for 'y' in the first original equation, we find that x = √7 or x = -√7. Therefore, the possible pairs of numbers are (√7, 2) and (-√7, -2).
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The decimal number 0.66 is an example of a repeating decimal.
True
or
False
pls answer quick
Answer:
the anwser is FALSE
Step-by-step explanation:
(1.8 * 10^2) * (5 * 10^2)
Brandon has two 9 cookies. Natalie has 2 less than cookies than Brandon. How many cookies does Natalie have ?
For the fruit punch, keira needed 2 gallons of grape juice. she already had 2 quarts of grape juice. grape juice comes in bottles of 1 pint. how many bottles of grape juice does she need to buy? bottles
For all real numbers a and b, if ab=0, then a=0 or b=0. True or false?
If all four interior angles of quadrilateral P have the same measure, which of the following statements must be true?
1. All sides of P have equal length.
2. The diagonals of P are perpendicular.
3. The measure of each interior angle of P is 90 degrees.
Thanks in advance! ...?
Kevin, while calculating his tax adjustments, notes that he can make adjustments of $3,435 for contributions to his retirement plan, $3,393 for business losses, and $1,128 for business expenses. If Kevin’s gross income is $45,942, what is his adjusted gross income?
a. $53,898
b. $40,242
c. $41,421
d. $37,986
Answer: Option 'D' is correct.
Step-by-step explanation:
Since we have given that
Amount of Kevin's gross income = $45942
Amount he contribute to his retirement plan = $3435
Amount he lost in business losses = $3393
Amount he incurred in business expenses = $1128
So, His adjusted gross income will be
[tex]45942-(3435+3393+1128)\\\\=45942-(7956)\\\\=\$37986[/tex]
Hence, his adjusted gross income is $37,986.
Hence, Option 'D' is correct.
Geometry help please! ty
Can you explain to me how to find the area of rectangles and triangles on a coordinate plane? Images below...
the product of two integers is -21. the diference between the two integers is -10. the sum of the two integers is 4. what are the two integers
help :(
Which situations can be represented by a linear function?
Select each correct answer.
a. Every year, Luisa puts $10 into her savings account.
b. Every day, the number of bacteria in the dish is 3 times what it was the previous day.
c. A country's population increases by 0.8% each year.
d. The barrel leaks 0.5 L of water each day.
The barrel leaks 0.5 L of water each day.
Every year, Luisa puts $10 into her savings account.
If f(x) is an odd function and the graph of f(x) includes points in Quadrant IV, which statement about the graph of f(x) must be true?
a) It includes points in Quadrant I.
b) It includes points in Quadrant II.
c) It does not include points in Quadrant I.
d) It does not include points in Quadrant II.
Answer:
B) it includes points in quadrant ii
The graph of f(x) must include points in quadrants II and IV. Therefore, option B is the correct answer.
What is an odd function?A function is such that f(−x) =−f (x) where the sign is reversed but the absolute value remains the same if the sign of the independent variable is reversed.
So,
The points in quadrants II are in IV.
The points in quadrants I are in III.
From the question, we understand that graph includes the points in IV.
This means that these points are also in quadrant II.
Hence, the graph of f(x) must include points in quadrants II and IV.
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Find the distance between (4, 2) and (-4 ,-4).
A) 2
B)√10
C) 4
D) 10
. Help I can't find anyone who knows the answer to this!
A scientist sets up an experiment to see how colored lights affect the height of plant growth. He grows one group of plants in full sunlight, one group under red lights, one group under blue lights, and one group under green lights. All the plants are exactly that same type and all receive an equal intensity of life. At the end of the experiment he measures all the plants.
What is the independent and dependent variable in this equation?
(A) the color of the light
(B) the height of the plant
(C) sunlight
(D) The intensity of the light
In the image, point A is the center of the circle. Which two line segments must be equal in length?
AH¯¯¯¯¯ and BC¯¯¯¯¯
HI¯¯¯¯ and BC¯¯¯¯¯
EF¯¯¯¯¯ and HI¯¯¯¯
EF¯¯¯¯¯ and AI¯¯¯¯
Answer: [tex]\overline{EF}=\overline{HI}[/tex]
Step-by-step explanation:
Given: In the image, point A is the center of the circle.
Therefore every straight line segments passing from one to another point of circle through the center of circle A is the diameter of the circle.
Since, [tex]\overline{EF}[/tex] and [tex]\overline{HI}[/tex] are the line segments passing from side to side of circle through the center of circle A is the diameter of the circle, then both are representing diameter of the given circle.
Since, all the diameter of a circle has a unique length .
Hence, the line segments must be equal in length :
[tex]\overline{EF}=\overline{HI}[/tex]
Which of the following would you round and estimate to a sum of 11?
3.41 + 8.051
3.65 + 7.992
4.25 + 8.103
4.89 + 7.431
Answer:
3.41+8.051
Step-by-step explanation:
this year 90 students signed up for the group Talent contest if all the groups have the same number of students how many groups could be formed
a. 4 or 5 groups
b. 5 or 6 groups.
c. 4 or 6 groups
d. 4 or 9 groups
If the sum of the measures of the interior angles of a convex polygon is 2160o, how many sides does the polygon have?
It takes ten identical pieces to form a circular track for a pair of toy racing cars. If the inside arc of each piece is 3.4 inches shorter than the outside arc, what is the width of the track? ...?
To find the width of the track, add up the lengths of all the inside and outside arcs and subtract the total length of the inside arcs from the total length of the outside arcs.
Explanation:To find the width of the track, we first need to determine the difference between the inside and outside arcs of each piece. Let's assume the outside arc has a length of A inches. According to the question, the inside arc is 3.4 inches shorter than the outside arc. Therefore, the inside arc has a length of A - 3.4 inches.
Since there are ten identical pieces forming the circular track, we can add up the lengths of all the inside arcs and all the outside arcs to find the total distance covered by the track. The width of the track is then the difference between the total length of the outside arcs and the total length of the inside arcs.
Let's express the width of the track as a function of A. The total length of the outside arcs is 10A inches, and the total length of the inside arcs is 10(A - 3.4) inches. Therefore, the width of the track is:
Width = 10A - 10(A - 3.4) inches.
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whats 64 divided by 8
Answer: 8
Step-by-step explanation:
Step 1: eight times one equals eight. Eight times two equals 16, as you keep multiplying, you'll eventually get to 8 times 8 equals 64. To find 64 divided by 8, you find the other "piece" which be what makes 8 times the number equal to 64. :)
How to expand 5x(5 3x)?
Renna pushed the button for the elevator to go up, but it would not move. The weight limit for the elevator is 450 kilograms, but the current group of passengers weighs a total of 750 kilograms. Renna wants to determine how many 70-kilogram passengers need to get off the elevator.
Let p represent the number of excess passengers. Write an inequality to determine the number of passengers who need to get off the elevator to meet the weight requirement.
What is 117.28 rounded to the nearest 10 cents?
If a 16 in. by 24 in. picture has a wooden frame "x" in. wide surrounding it, what equation can be used to find the total area of the picture and frame? ...?
What is the range of possible values for x? The diagram is not to scale.?
Answer:
Range : 0° < x < 17°
Step-by-step explanation:
In any triangle, the smallest angle is opposite to the smallest side.
So, In ΔABD , the side which faces ∠ABD is AD whose length is 22 units.....(1)
And, in ΔCBD, the side which faces ∠CBD is CD whose length is 30 units....(2)
Now, from equations (1) and (2) We get,
∠ABD < ∠CBD
So, ∠ABD lies between 0° to 34°
[tex]\Rightarrow 0 < 2\cdot x<34\\\Rightarrow 0<x<\frac{34}{2}\\\Rightarrow0<x<17[/tex]
∴ Range of x is 0° to 17°
Answer:
Range : 0° < x < 17°
Step-by-step explanation:
In any triangle, the smallest angle is opposite to the smallest side.
So, In ΔABD, the side which faces ∠ABD is AD whose length is 22 units.....(1)
And, in ΔCBD, the side which faces ∠CBD is CD whose length is 30 units....(2)
Now, from equations (1) and (2) We get,
∠ABD < ∠CBD
So, ∠ABD lies between 0° to 34°
∴ Range of x is 0° to 17°
determine whether multiplication by A is one to one linear transformation
a)A=[ 1 -1
2 0
3 -4]
b) A=[ 1 2 3
-1 0 4] ...?