Final answer:
To solve the quadratic equation 2x² + 9x - 5 = 0, the quadratic formula is used, and after calculating the discriminant and applying the formula, one of the roots is found to be 1/2, which is option C.
Explanation:
To solve the quadratic equation 2x2 + 9x - 5 = 0, we can use the quadratic formula which is x = (-b ± √(b2 - 4ac)) / (2a). In this equation, a equals 2, b equals 9, and c equals -5.
Firstly, we need to calculate the discriminant: b2 - 4ac which is 92 - 4 * 2 * (-5) = 81 + 40 = 121.
Since the discriminant is a perfect square, we can proceed with the formula: x = (-9 ± √(121)) / (2*2). The square root of 121 is 11, so we have:
x1 = (-9 + 11) / 4 = 2 / 4 = 0.5 or 1/2x2 = (-9 - 11) / 4 = -20 / 4 = -5Thus, one of the roots of the equation is 1/2, which corresponds to option C.
Find the equation for the circle with center (4,-5) and passing through (5,-4)
Answer:
(x -4)^2 +(y +5)^2 = 2
Step-by-step explanation:
The equation of a circle centered at (h, k) through point (p, q) is ...
(x -h)^2 +(y -k)^2 = (p -h)^2 +(q -k)^2
Filling in your given numbers gives ...
(x -4)^2 +(y +5)^2 = (5-4)^2 +(-4+5)^2
(x -4)^2 +(y -5)^2 = 2
The equation of the circle is (x - 4)² + (y + 5)² = 2.
The center of the circle is (4, -5). The circle passes through the point (5, -4).
The general formula for the equation of a circle is: (x - h)² + (y - k)² = r² where (h, k) is the center of the circle and r is the radius.
The radius is the distance between the center (4, -5) and the point (5, -4).
Use the distance formula: Distance = √ [(x2 - x1)² + (y2 - y1)²]
Distance = √ [(5 - 4)² + (-4 - (-5))²]
Distance = √ [(1)² + (1)²]
Distance = √ [1 + 1]
Distance = √ [2]
So, the radius r = √ [2].
Substitute the center (4, -5) and radius √ [2] into the circle equation: (x - 4)² + (y + 5)² = (√ [2])² (x - 4)² + (y + 5)² = 2
Which of the following options could represent a possible set of interior angles of a triangle?
60°, 150° and 150°
15°, 35°, and 40°
35°, 65°, and 80°
45°, 105°, and 120°
Answer:
35+65+80=180
Step-by-step explanation:
the total interior angle of a triangle is 180
Answer:
its the third answer
[tex]35 \: \: 65 \: \: 80[/tex]
Step-by-step explanation:
because the addition of a interior angles has to be 180.'
How is selective boarding school will only admit students who plays at least 2 .5 standard deviation above the mean on a standardized test that has a mean of 100 and a standard deviation of 24. What is the minimum score that an applicant must make on the test to be accepted?
Answer:
I'd don't now
Step-by-step explanation:
ok am sorry
QUESTION 10
The park manager wants to conduct a survey to determine how people like the park facilities. Which would give her the most representative sample for the survey?
conducting the survey at the softball diamond
conducting the survey at a shopping mall
conducting the survey as visitors leave the park
conducting the survey at the playground
conducting the survey as visitors leave the park
The park manager wants to figure out how people like the park so she will conduct the survey as people leave the park.
Final answer:
The most representative sample for a survey on park facilities satisfaction would be obtained by conducting the survey as visitors leave the park, ensuring a broad and unbiased cross-section of park users are included.
Explanation:
The question asks which method would provide the most representative sample for a survey about how people like the park facilities. The most representative sample would be achieved by conducting the survey as visitors leave the park. This method ensures a wide cross-section of park users are surveyed, capturing various interests and usage patterns of the park facilities, from those who come for leisure activities at the softball diamond or playground to those seeking quiet contemplation or exercise.
Conducting the survey in other locations like a shopping mall or specific areas within the park, such as the softball diamond or playground, would likely bias the results. Surveying at a shopping mall doesn't guarantee participants have visited or are familiar with the park, and focusing solely on one area within the park would not capture the diverse usage and opinions of all park visitors. Therefore, surveying as visitors leave the park is the most inclusive and unbiased approach to understanding how the facilities meet the needs of the community.
What is 245 and 7/50 in decimal form
Answer:
245=2.45
7/50=0.14
Step-by-step explanation:
divide by 100
USE MATHAWAY DOT COM!!
How would you solve 8(6-k)+2k ≥-15-(-3k) ( please show each step)
Answer:
Step-by-step explanation:
8(6-k)+2k ≥-15-(-3k)
Opening bracket
48 - 8k + 2k ≥ -15 + 3k
-8k - 3k + 2k ≥ -15 - 48
-9k ≥ -63
k ≤ -63/-9
k ≤ 7
Answer:
k ≤ 7
Step-by-step explanation:
8 (6 - k) + 2k ≥ - 15 -(-3k)
Let's simplify this by solving each side.
First side:
8 (6 - k) + 2k ≥ - 15 -(-3k)
48 - 8k + 2k ≥ - 15 -(-3k)
48 - 6k ≥ - 15 -(-3k)
Second side:
48 - 6k ≥ - 15 -(-3k)
48 - 6k ≥ -15 + 3k
DONE SIMPLIFYING!
Now solve for "k" algebraically (transitions are in bold):
48 - 6k ≥ -15 + 3k
-6k ≥ -15 - 48 + 3k
-6k ≥ -63 + 3k
-6k - 3k ≥ -63
-9k ≥ -63
-k ≥ -63 ÷ 9
-k ≥ -7
k ≤ 7
Are the magnetic North Pole and the geographic North Pole always the same distance apart
Are 10(e+0.5g) and 10e+5g not equivalent or equivalent?
Are 6(p+q) and 6p+q not equivalent or equivalent?
Are 7y-15+2y and 9y-15 not equivalent or equivalent?
Are 1+(8r+9) and (2+8)+8r not equivalent or equivalent?
Are 0x11+5n and 5n not equivalent or equivalent?
Are 16s-4+s and 12s not equivalent or equivalent?
Are 11dx2 and 22d not equivalent or equivalent?
Are 8m+(9m-1) and 8m-8 not equivalent or equivalent?
Please help me...
(1) 10(e + 0.5)g
Using distributive property, a × (b + c) = a × b + a × c
10(e + 0.5)g = 10 eg + 10 × 0.5g
Therefore, 10(e + 0.5g) and 10e + 5g are not equivalent.
(2) 6(p + q)
Using distributive property,
6(p + q) = 6p + 6q
Therefore, 6(p + q) and 6p + q are not equivalent.
(3) 7y – 15 + 2y
Using commutative property, a + b = b + a
7y – 15 + 2y = 7y + 2y – 15
= 9y – 15
Therefore 7y – 15 + 2y and 9y – 15 are equivalent.
(4) 1 + (8r + 9)
Using associative property, a + (b + c) = (a + b) + c
1 + (8r + 9) = (1 + 9) + 8r
= 10 + 8r
= (2 + 8) + 8r
Therefore 1 + (8r + 9) and (2 + 8) + 8r are equivalent.
(5) 0 × 11 + 5n
Using multiplicative identity property: a × 0 = 0
0 × 11 + 5n = 0 + 5n
= 5n
Therefore, 0 × 11 + 5n and 5n are equivalent.
(6) 16s – 4 + s
Using associative property, a + (b + c) = (a + b) + c
16s – 4 + s = 16s + s – 4
= 17s – 4
Therefore, 16s – 4 + s and 12s not equivalent.
(7) 11d × 2 = 22d
Therefore, 11d × 2 and 22d are equivalent.
(8) 8m + (9m – 1)
Using associative property, a + (b + c) = (a + b) + c
8m + (9m – 1) = (8m + 9m) – 1
= 17m – 1
Therefore, 8m + (9m – 1) and 8m – 8 not equivalent.
Lauryn grew p tomato plants. Padma grew 5 fewer than 3 times the number Lauryn grew. Kent grew 6 more than 4 times the number Lauryn grew. Choose an expression and a simplified expression to represent the total number of tomato plants that Lauryn, Padma, and Kent grew. Select all that apply.
A. p + (3p – 5) + (4p + 6)
B. p + (5 – 3p) + (6 + 4p)
C. p + 11
D. 8p + 1
E. 7p – 1
Answer:
the anwser is a
Step-by-step explanation:
The expression represents the total number of tomato plants is [tex]\rm p + (3p - 5) + (4p + 6)[/tex].
Given that
Lauryn grew p tomato plants.
The Padma grew 5 fewer than 3 times the number Lauryn grew.
Kent grew 6 more than 4 times the number Lauryn grew.
We have to determine
Choose an expression and a simplified expression to represent the total number of tomato plants that Lauryn, Padma, and Kent grew.
According to the question
Let the number of tomato plants be p.
Lauryn grew p tomato plants.
[tex]\rm = p[/tex]
The Padma grew 5 fewer than 3 times the number Lauryn grew.
[tex]\rm= 3p-5[/tex]
Kent grew 6 more than 4 times the number Lauryn grew.
[tex]\rm = 4p+6[/tex]
Therefore,
An expression to represent the total number of tomato plants = Lauryn + Padma + and Kent grew.
[tex]\rm p + (5 - 3p) + (6 + 4p)[/tex]
Hence, the expression represents the total number of tomato plants is [tex]\rm p + (3p - 5) + (4p + 6)[/tex].
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Every day, Bert spends an hour commuting to and from his office, driving at an average speed of 50 mph and taking the same route each way. How far does Bert live from his office?
When speed and time are known, distance can be calculated using the formula 'distance = speed x time'. Given Bert's speed of 50 mph and travel time of 0.5 hours each way, the distance from his home to the office is calculated to be 25 miles.
Explanation:The subject of this problem is fundamentally about understanding the relationship between speed, time, and distance. In this particular case, Bert is spending a total of an hour commuting to and from office. However, this total time includes both the journey to work and the journey back home so each journey takes half an hour or 0.5 hours. Given that his average speed is 50 mph, we can calculate the distance he travels one way using the formula "Distance = Speed x Time."
So, for Bert:
Distance = 50 mph x 0.5 hours = 25 miles
Therefore, "Bert lives 25 miles from his office."
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when would you use a negative number to describe a real world amount? Give an example.
Answer:
Debt
Step-by-step explanation:
Let's say someone uses debit instead of credit and they don't have any money in their account. If used multiple times you could potentially end up owing the bank (be in debt) .
Negative numbers are used in real-world contexts to describe temperatures below zero, financial debts, or elevations below sea level, helping to clearly indicate quantities that are less than a referenced zero point.
You would use a negative number to describe a real-world amount when talking about temperatures below zero, debts, or elevations below sea level, among other scenarios. For example, if the temperature is 5 degrees below zero, it could be represented as -5°C. This indicates that it is 5 degrees colder than the point at which water freezes (0°C). Another example is financial: if you owe $100, you could represent your account balance as -$100, indicating a debt. Similarly, a town located 100 meters below sea level could have its elevation represented as -100 meters.
These examples show how negative numbers can effectively convey quantities less than zero in various real-world contexts, providing a clear understanding of situations where values are lacking or in deficit compared to a reference point.
what is 6times40///////////////////////
Answer:
the answer is 240
Answer:
240
Step-by-step explanation:
i used a calculator
Solve the following system of equations by using the method of your choice
3x-y=-28
-5x-4y=-10
Answer:
(x, y) =(-6,4)
Step-by-step explanation:
3x-y=-28
-5x-4y=-10
y=3x+28
-5x-4(3x+28)=-10
y=3x+28
-5x-12x-112=-10
y=3x+28
-17x=-10+112
y=3x+28
-17x=102
y=3x+28
x=102/(-17)
y=3x+28
x=-6
y=3*(-6)+28
x=-6
y=-24+28
x=-6
y=4
x=-6
(x,y)=(-6,4)
simpilfy -19+4k-15k+k-9
Answer:
-10k-28
Step-by-step explanation:
-19+4k-15k+k-9
-28-11k+k
-10k-28
Answer:
12k+ -10
im not truely sure if this is correct... but i went off my knowlage
Which expression is equivalent to 7/2h-3(5h-1/2)?
Answer:
-23/2h+3/2
Step-by-step explanation:
7/2h-3(5h-1/2)
7/2h-15h+3/2
7/2h-30/2h+3/2
-23/2h+3/2
Answer:
(-23h+3)/2
Step-by-step explanation:
7/2h-3(5h-1/2)=
7/2h-3*5h+3*1/2=
7/2h-15h+3/2=
7/2h-30/2h+3/2=
-23/2h+3/2 or
(-23h+3)/2
Where will her cut be located? Round to the nearest tenth. Genevieve is cutting a 60-inch piece of ribbon into a ratio of 2:3. Since 2 inches are frayed at one end of the ribbon, she will need to start 2 inches in. This is indicated as 2 on the number line. 25.2 in. 29.4 in. 35.1 in. 40.7 in.
Answer:
25.2 in
Step-by-step explanation:
The short piece will have a length that is 2/(2+3) = 2/5 of the entire usable length. The usable length is 60-2 = 58 inches long, so the cut will be ...
(2/5)(58 in) = 23 1/5 in
from the beginning of the usable part. Since the usable part of the ribbon starts 2 inches in, the cut will be 23 1/5 + 2 = 25 1/5 inches from the frayed end of the ribbon.
Answer:
25.2
Step-by-step explanation:
Correct on Edge 2020
W+(-4)=37 solve for w
Answer:
W=41
Step-by-step explanation:
You have to isolate the W, so you have to carry the -4 to the other side. You do the opposite, so for a -4, you have to +4 to cancel it out. Whatever you do to one side, you have to do to the other and 37+4=41
Answer:
41
Step-by-step explanation:
What is the value of the expression below?
(9-3)+4(6-7)
-7
-1
7
20
Final answer:
The expression (9-3)+4(6-7)-7 is calculated following PEMDAS, resulting in a value of -5 after simplifying the operations within the expression.
Explanation:
The value of the expression (9-3)+4(6-7)-7-1720 seems to have a typo, and it should probably read (9-3)+4(6-7)-7. To evaluate this expression, you follow the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
First, calculate the parentheses: (9-3) = 6 and (6-7) = -1.
Next, perform the multiplication: 4 * (-1) = -4.
Finally, add and subtract from left to right: 6 + (-4) - 7 = 6 - 4 - 7 = 2 - 7 = -5.
The value of the expression is -5.
Evaluate (3x-1) + 2 when x = 5
Answer:
16
Step-by-step explanation:
(3x - 1) + 2
(3(5) - 1) + 2
(15 - 1) + 2
14 + 2
16
Answer:
16
Step-by-step explanation:
Start by plugging in 5 for x in the equation.
(3 x 5 - 1) + 2
Next do the multiplication.
15 - 1 + 2
Add and subtract.
16
You have your answer.
Hope this helped.
Which choice is equivalent to the expression below ?
The answer is B, 7i.
sqrt(-49)
Pull out an i.
i*sqrt(49)
Take the square root to get 7i.
⭐ Answered by Hyperrspace (Ace) ⭐
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Tickets for a school carnival cost 10$ for adult and 5 for children. last Saturday carnival sold 170 tickets worth a total of $1200 . How many adults and childeren attended the carnival
70 adults and 100 children attended the carnival.
Step-by-step explanation:
Given,
Cost of each adult ticket = $10
Cost of each child ticket = $5
Total tickets sold = 170
Total revenue generated = $1200
Let,
Number of adults = x
Number of children = y
According to given statement;
x+y=170 Eqn 1
10x+5y=1200 Eqn 2
Multiplying Eqn 1 by 10
[tex]10(x+y=170)\\10x+10y=1700\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 2 from Eqn 3
[tex](10x+10y)-(10x+5y)=1700-1200\\10x+10y-10x-5y=500\\5y=500[/tex]
Dividing both sides by 5
[tex]\frac{5y}{5}=\frac{500}{5}\\y=100[/tex]
Putting y=100 in Eqn 1
[tex]x+100=170\\x=170-100\\x=70[/tex]
70 adults and 100 children attended the carnival.
Keywords: linear equation, elimination method
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james says that 5 fithes is greater than 9 tenthes is he correct?
Answer:
yes
Step-by-step explanation:
Answer:
No
Step-by-step explanation:
9 tenths is 90. 5 fifths is 25.
Y = -1/3 x + 2
Y= x + 2
What is the solution to the system of equations?
A. (0, 2)
B. (2, 0)
C. (-1, 3)
D. (0, -2)
Answer:
X = 0
Y = 2
so Option A (0,2) IS CORRECT
Step-by-step explanation:
Y = -1/3 x + 2 equation 1
Y = x+ 2 equation 2
from equation 2 we have
y = x+ 2 Put in equation 1
x + 2 = -1/3 x + 2
x +1/3x = 2 -2
0.67 x = 0
X = 0
so put x =0 in equation 2 then we have
y = x +2
Y = 0+ 2
Y = 2
Can someone please help me with this also
Answer:
Step-by-step explanation:
each is divided into 8 sections.
So1 1/2 =1 1*4/2*4 =1 4/8 . plot in the 4 th point after 1
2 3/4
3*2/4*2 = 6/8
2 3/4 = 2 6/8. so plot in the 6th point after 2
Two numbers are respectively twenty percent and ten percent more than the third number. How many percent is the first number more than the second ?
Answer:
10%
Step-by-step explanation:
Let the third number is X.
then first number = (100-30)% of X
= 70% of X = 7X/10
Second number is (63X/100)
Difference = 7X/10 - 63X/100 = 7X/10
So required percentage is, difference is what percent of first number
=> (7X/100 * 10/7X * 100 )% = 10%
-8|4k-10|=-48 okay y'all can you help me out with this?
Answer:
k = 4
Step-by-step explanation:
-8|4k-10|=-48
|4k-10|=-48/-8
|4k-10|= 6
4k = 6+10
4k = 16
k = 4
one number is 6 more than another. the sum of the numbers is 30. find the numbers.
To find the numbers, we can set up a system of equations and solve for the variables.
Explanation:Let's represent the numbers as x and y. According to the problem, one number is 6 more than the other. This can be written as:
x = y + 6
The sum of the numbers is 30. This can be written as:
x + y = 30
We can solve this system of equations by substituting the value of x from the first equation into the second equation:
(y + 6) + y = 30
Combining like terms:
2y + 6 = 30
Subtracting 6 from both sides:
2y = 24
Dividing by 2:
y = 12
Now, we can substitute the value of y back into the first equation to find the value of x:
x = 12 + 6
x = 18
Therefore, the two numbers are 12 and 18.
What is the area of this trapezoid? 86 in² 112 in² 148 in² 184 in² Trapezoid A B C D with parallel sides D C and A B. Point F and E are on side D C. Point F is connected to point A by a dotted segment. Point E is connected to point B by a dotted segment. A B E F is a rectangle. D F is 3 inches. E C is 6 inches. E B is 8 inches. A B is 14 inches.
Option C: [tex]$148 \mathrm{in}^{2}$[/tex] is the area of the trapezoid.
Explanation:
The image of the trapezoid having these descriptions is attached below:
Now, we shall determine the area of the trapezoid using the formula,
[tex]$A=\frac{a+b}{2} h$[/tex] where a and b are the base of the trapezoid and h is the height of the trapezoid.
Thus, we shall find the value of a and b from the diagram given below.
[tex]a= AB=14in[/tex]
[tex]b=DC\\b=DF+FE+EC\\b=3+14+6\\b=23in[/tex]
It is given that the height of the trapezoid [tex]h=8in[/tex]
Thus, substituting the values of a,b and h in the formula [tex]$A=\frac{a+b}{2} h$[/tex], we get,
[tex]A=\frac{14+23}{2}(8)\\ A=\frac{37}{2} (8)\\A=148in^2[/tex]
Thus, the area of the trapezoid is [tex]$148 \mathrm{in}^{2}$[/tex]
Hence, Option C is the correct answer.
A play train travels around a Christmas
tree in a circle. The train track measures 6
feet in diameter. What is the distance that
the train travels?
The distance that the train travels is 18.84 feet
Solution:
Given that,
A play train travels around a Christmas tree in a circle
The train track measures 6 feet in diameter
To find: distance that the train travels
The distance the train travels is equal to the circumference of circle
The circumference of circle is given as:
[tex]C = \pi d[/tex]
Where, "d" is the diameter of circle
From given,
d = 6 feet
[tex]C = 3.14 \times 6\\\\C = 18.84[/tex]
Thus the train travels 18.84 feet
At the beginning of the year,
Shelby could run 2 miles. Now
she can run 3.5 miles. What is
the percent increase in the
distance she can run?
Answer:
175% increase
Step-by-step explanation:
(3.5 / 2) * 100 = 175%