Answer:
See the explanation for the answer.
Step-by-step explanation:
[tex]2x^2+7x+2=0[/tex]
[tex]x=\frac{-7\pm \sqrt{49-16}}{4}=\frac{-7\pm \sqrt{33}}{4}[/tex]
Hope this helps!
Which is the best estimate for the average rate of change for the quadratic function graph on the interval 4 ≤ x ≤ 12? A) 1 B) 2 C) 3 D) 4
The average rate of change will be given by 16a + b
What is average rate?Average Rate: A single rate that applies to real estate at many locations and is calculated as the weighted average of the various rates that are appropriate at each site.
It is the average amount by which the function changed per unit throughout that time period. It is calculated using the slope of the line linking the interval's ends on the graph of the function.
Given:
A general quadratic function of x is given by f(x) = ax² +bx +c
Now, the rate of change of the function f(x) is given by df(x)/ dx.
Therefore, df(x)/ dx = 2ax+ b
Now, the value of x ranges between 4 ≤ x ≤ 12.
So, at x= 4
df(x)/ dx = 2a(4) + b= 8a+ b
and, x= 12
df(x)/ dx = 2a(12) + b= 24a+ b
Thus, the average rate of change will be given by
(8a+ b) + (24a+ b) / 2
= 32a+ 2b/ 2
= 16a + b
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Mandy paints four square walls that are ten feet on each side. Which expression represents the total square footage that Mandy painted?
4 × 10 squared
4 squared × 10
4 × 10 × 2
10 squared + 4
Answer:
i think its c
Step-by-step explanation:
Final answer:
The correct expression for the total square footage that Mandy painted is 4 × 10 squared, which totals 400 square feet when calculated.
Explanation:
The expression that represents the total square footage that Mandy painted when she paints four square walls that are ten feet on each side is 4 × 10 squared. To understand why, let us analyze a related problem where Marta has one square with a side length of 4 inches and another larger square with dimensions that are twice the first square, which means the side length of the larger square is 8 inches (4 inches × 2).
The area of a square is calculated by squaring its side length, so the smaller square has an area of 16 square inches (4 inches squared), and the larger square will have an area of 64 square inches (8 inches squared). This demonstrates that the area of the larger square is four times larger than the area of the smaller square, as the scale factor of the side lengths is squared to obtain the ratio of the areas.
Similarly, for Mandy's wall painting, each wall is 10 feet by 10 feet, so the area of one wall is 10 feet squared, which equals 100 square feet. Since there are four walls, the total area is 4 × 100 square feet, or 400 square feet in total. The correct expression for the total square footage Mandy painted is 4 × 10 squared.
What type of transformation is shown?
A) Dilation
Eliminate
B) Reflection
C) Rotation
D) Translation
Answer:
A Dilation
Step-by-step explanation:
your dilating the original shape to a new size
Answer:
A) Dilation
Step-by-step explanation:
I did this last year and when the original shape stays the same and another shape either grows or shrinks it's dilation.
kenneth drove 177.55 miles in 3 7/20 hours. what was his average speed
Kenneth's average speed, we divide the total distance by the total time traveled. In this case, Keneth's average speed was approximately 52.91 miles per hour.
Kenneth's average speed, you can use the formula:
Average Speed = Total Distance/Total Time.
In this case, Kenneth drove 177.55 miles in 3 7/20 hours.
First, convert the mixed number time to an improper fraction:
3 7/20 = 67/20.
Now, substitute the values into the formula:
Average Speed = 177.55 / (67/20).
To divide by a fraction, multiply by its reciprocal:
Average Speed = 177.55 * (20/67).
Average Speed ≈ 52.91 miles per hour.
Therefore, Keneth's average speed was approximately 52.91 miles per hour.
Can someone please find C for me
Which is the parametric form of the polar equation r=-3theta
A.x=3thats cos theta
Y=3theta sin theta
B.x=-3theta cos theta
Y=-3theta sin theta
C.x=-3cos theta
Y=-3 sin theta
D.x=-theta cos theta
Y=-theta sin theta
Answer:B
Step-by-step explanation:
Given
[tex]r=-3\theta [/tex]
so [tex]x=-3\theta \cos \theta \quad \ldots(i)[/tex]
and
[tex]y=-3\theta \sin \theta \quad \ldots(ii)[/tex]
squaring and adding [tex](i)[/tex] and [tex](ii)[/tex] we get
[tex]x^2+y^2=(-3\theta \cos \theta)^2+(-3\theta \sin \theta)^2[/tex]
[tex]x^2+y^2=r^2=9\theta ^2\cos ^2 \theta +9\theta ^2\sin ^2 \theta [/tex]
[tex]r^2=9\theta ^2[/tex]
[tex]r=-3\theta [/tex]
for [tex]r[/tex] to be negative both [tex]x[/tex] and [tex]y[/tex] must be negative
Subtract the equations.
Answer:
0x+2y=22
Step-by-step explanation:
Set them equal to each other, (5x+4y=25)-(5x+2y=3). Distribute the negative into the right equation, (5x+4y=25)(-5x-2y=-3). Then combine like terms to get your answer.
At the start of 2015, Barry's house was worth £270000.
The value of his house increased by 3% every year.
Work out the value of his house at the start of 2020
Answer:
£310500
Step-by-step explanation:
3% of 270000=8100
difference between 2020 and 2015=5 years
8100×5=40500
40500+270000=310500
pls give me brainliest
HELP NOW OR ELSE!
Which expressions are equivalent to 2(5)^4
2 times 5 times 4
2 times 5 times 5 times 5 times 5
2 times 4 times 4 times 4 times 4 times 4
10 times 10 times 10 times 10
2 times 5 times 4 is your answer
within a radius of 4.9 miles of a cell phone tower, 1483 people per square mile enjoy quality phone signals. what is the population of cell phones users within the towers converage area
Answer:
The population around the tower is 111,862 people.
Step-by-step explanation:
In order to solve this problem we first need to calculate the area surrounded by the tower, since it's a circle we can apply the following formula:
tower area = pi*r²
tower area = pi*(4.9)² = 75.4296 miles²
For every mile² there are 1483 people, therefore:
population = area*density
population = 75.4296*1483 = 111,862
The population around the tower is 111,862 people.
f(x)=x^2. What is g(x)
Answer:
D
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Having the line moving to the right we know that it has to be in parentheses. And
Can somebody please help me with this ?
Answer:
50
Step-by-step explanation:
the angles in a triangle will add up to 180 degrees
Determine the equation for the line of best fit to represent the data.
scatter plot with points going up from about zero comma negative 3 to the right to about 7 comma zero
y equals three sevenths times x minus 3
y equals negative three sevenths times x minus 3
y equals seven thirds times x minus 3
y equals three sevenths times x plus 3
Answer:
A) y equals three sevenths times x minus 3
God has a plan for everyone!!
Coach Chapman has 54 students signed up for a jump rope competition. He only has 18 jump ropes. What is the ratio of jump ropes to students?
brainliest
Answer:
1:3
Step-by-step explanation:
The question is asking what the ratio of jump ropes to students is.
The order of the question matters.
Since they ask for the jump ropes first and then the students, we
get a ratio of 18:54.
Find the GCF (Greatest Common Factor)
The GCF is 18.
Divide 18:54 by 18.
18/18=1
54/18=3
The answer is 1:3.
When Rachel puts gas in her car, she records the distance that she has driven since her last
fill-up and the number of gallons of gas that her car has used. She uses this information to
predict the amount of gas that her car will use to travel different distances,
g=0.04 times d
Step-by-step explanation:
if you multiply 0.04 with every number under the d column then you’ll get the outcome of each number under g
The relationship between the number of gallons of gas that the car uses g, and the number of miles the car has driven d, is given by the equation g=0.04d. Since the values of g and d are linearly connected.
Which is said to be a Linear equation?A linear equation is an algebraic equation that has the highest degree as 1.The general form of the linear equation is [tex]y=ax+c[/tex]. Where y is the dependent variable and x is the independent variable.So, as the value of x increases the value of y also increases linearly and forms a straight line.Given data:It is given that,
A table of content about the distance traveled by Rachel and the gas used for that distance.
The distance is given in miles as d and the gas is given in gallons as g
The values of d given in the table are 14, 70, 109, and 140. Here the order is increasing.
The values of g given in the table are 0.56, 2.8, 4.36, and 17.6. Here also the order is increasing.
Finding the relationship between g and d:Since the values of g and d are increasing linearly and g is depending on d, consider a linear equation as follows:
[tex]g=ad+c[/tex]
Finding a and c from the obtained equation:
From the table, when d=14, g=0.56 and d=70, g=2.8
On substituting these values in the equation we get
0.56=14a+c
2.8=70a+c
Subtracting 1st equation from the 2nd equation,
2.8-0.56=(70a+c)-(14a+c)
⇒ 2.24=56a
⇒ a=0.04
On substituting a value in any of the equations we get
0.56=(0.04)(14)+c
⇒ c=0
Thus, the required equation becomes g=0.04d. This says that the g and d values are linearly related to each other.
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A piano teacher charges students $20.25 each month, plus $5.25 per hour for lessons.
Which expression and value represent the total the instructor will charge a student for x hours of lessons in a month and the amount the instructor would charge a student for 15 hours of lessons in a month?
$20.25 – x; $15
$20.25 + x; $25.50
$20.25 – $5.25x; $58.50
$20.25 + $5.25x; $99
Answer:
suppose the number of 2 hours lessons are x and 1 hour lessons are y; thus,
2x+y=25
50x+30y=690
to get the values of x and y we solve the quadratic equation given;
from the top equation:
y=25-2x.......i
substituting i in our second equation we get:
50x+30(25-2x)=690
50x+750-60x=690
-10x=-60
thus;
x=6
hence we conclude that the number of 2 hours classes are 6 hours
Step-by-step explanation:
The expression representing the total charge for x hours of piano lessons is $20.25 + $5.25x, and for 15 hours, the total charge would be $99.
Explanation:The correct expression to represent the total charge for a student who takes x hours of piano lessons in a month at $20.25 per month and $5.25 per hour is $20.25 + $5.25x. To calculate the amount the instructor would charge for 15 hours of lessons, we substitute x with 15:
Total charge for 15 hours = $20.25 + $5.25(15) = $20.25 + $78.75 = $99.
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Sanjay has 59 toy cars. 12 of the cars are blue and 23 of the cars are red. The rest of the cars are white.
How many more toy cars are white than blue? Enter the answer in the box.
toy cars
Answer: 12
Step-by-step explanation: 12+23 = 35
59-23 is 24
24 is the number of white cars so if 12 of the cars are blue, you just subtract 12 from 24 giving you 12 as the difference between white and blue cars
Final answer:
Sanjay has 12 more white toy cars than blue. There are 24 white cars in total after subtracting the number of blue and red cars from the total.
Explanation:
Sanjay has a total of 59 toy cars, of which 12 are blue and 23 are red. To find out how many toy cars are white, we need to subtract the number of blue and red cars from the total number of cars.
Total number of cars = 59
Number of blue cars = 12
Number of red cars = 23
Subtract the number of blue and red cars from the total:
59 - 12 - 23 = 59 - 35 = 24
So, there are 24 white cars.
To find out how many more white cars there are than blue cars, subtract the number of blue cars from the number of white cars:
24 (white cars) - 12 (blue cars) = 12
Therefore, there are 12 more white toy cars than blue toy cars.
True or false: the Pythagorean theorem can be applied to every triangle
The Pythagorean theorem can only be applied to right triangles.
Explanation:The Pythagorean theorem can be applied to right triangles only.
It states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
So, while the Pythagorean theorem cannot be applied to every triangle, it can be used to find the length of one side of a right triangle given the lengths of the other two sides.
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What is the value of a+b?
the answer is c
Step-by-step explanation:
because I was working on it
If sound travels 2 miles and 10 seconds how far does sound travel in 2 minutes
Answer:
24 miles
Step-by-step explanation:
2 miles:10 seconds
? miles: 120 seconds
120 divided by 10 =12
12 x 2 =24
Final answer:
Sound travels 2 miles in 10 seconds, giving it a speed of 0.2 miles per second. In 2 minutes, which equals 120 seconds, sound will travel 24 miles.
Explanation:
If sound travels 2 miles in 10 seconds, we can calculate the speed of sound by dividing the distance traveled by the time it took. To find out how far sound would travel in 2 minutes, we must first calculate its speed:
Speed = Distance / Time
Speed = 2 miles / 10 seconds
Speed = 0.2 miles/second
Now, let's convert 2 minutes to seconds since the speed is in miles per second:
2 minutes = 2 x 60 seconds = 120 seconds
Finally, we calculate how far sound travels in 2 minutes:
Distance in 2 minutes = Speed x Time
Distance in 2 minutes = 0.2 miles/second x 120 seconds
Distance in 2 minutes = 24 miles
Therefore, sound travels 24 miles in 2 minutes.
Factor the polynomial using the pattern.
x2 - 9x + 20
Answer: To factorize the quadratic expression
x2−9x+20, one must find the two numbers that add together to give 9, and multiply together to give 20. Those two numbers are 4 and 5, which factor into the expression
(x−4)(x−5). The signs are due to the fact that the first sign in the expression is a positive, which tells us that both signs must be the same, and the first sign is a negative, which means that, due to the positive sign in the expression, both signs are negative. To do the opposite, expanding, one must multiply
x by x, to get x2, add together 4 and 5 to get 9, and multiply them to get 20.
Answer:
Answer: To factorize the quadratic expression
x2−9x+20, one must find the two numbers that add together to give 9, and multiply together to give 20. Those two numbers are 4 and 5, which factor into the expression
(x−4)(x−5). The signs are due to the fact that the first sign in the expression is a positive, which tells us that both signs must be the same, and the first sign is a negative, which means that, due to the positive sign in the expression, both signs are negative. To do the opposite, expanding, one must multiply
x by x, to get x2, add together 4 and 5 to get 9, and multiply them to get 20.
Step-by-step explanation:
Which of the following functions generates the sequence 0, 2, 4, 6, ...?
Answer:
F(n) = 2n – 2
Step-by-step explanation:
The sequence 0, 2, 4, 6
First, let us determine if the sequence is arithmetic progression (A.P) or geometric progression (G.P)
This is illustrated:
Let us calculate the common difference (d)
Common difference (d) = 2nd term – first term
Common difference (d) = 3rd term – 2nd term
=> 2 – 0 = 2
=> 4 – 2 = 2
The common difference (d) = 2.
Common ratio (r) = 2nd term /1st term
Common ratio (r) = 3rd term /2nd term
=> 2/0 = undefined
=> 4/2 = 2
There is no common ratio.
Since we have a common difference, therefore the sequence is arithmetic progression.
Now, let us obtain an expression for the sequence.
This can be obtained by using the arithmetic progression formula as shown below:
F(n) = a + (n – 1)d
a is the first term
n is the number of term
d is the common difference.
The sequence 0, 2, 4, 6
The first term (a) = 0
Common difference (d) = 2
F(n) = a + (n – 1)d
F(n) = 0 + (n – 1)2
F(n) = 2n – 2
What is the length of line segment CD with endpoints (Negative 3 2) and (2, 2) as shown on the coordinate plane? On a coordinate plane, line C D goes from (negative 3, 2) to (2, 2). 2 units 3 units 4 units 5 units
Answer:
5 units
Step-by-step explanation:
im taking the test rn
If two triangles are congruent, which of the following statements must be
true? Check all that apply.
A. The triangles have the same shape, but not the same size.
B. The corresponding angles of the triangles are congruent.
C. The triangles have the same shape and size.
D. The corresponding sides of the triangles are congruent.
SUBM
Answer:
C. The triangles have the same shape and size.
B with C together also is accepted.
Two triangles are congruent if their corresponding sides are equal in length, and their corresponding angles are equal in measure.
Step-by-step explanation:
All the rest are wrong.
Emilio has worn a gray shirt on 7 of the last 14 days. What is the experimental probability that Emilio will wear a gray shirt tomorrow?
Answer:
Step-by-step explanation:
7/14
Step-by-step explanation:
Which transformations are needed to change the parent cosine function to the cosine function below?
On a coordinate plane, a curve crosses the y-axis at y = 1. It has a maximum of 1 and a minimum of negative 3. It goes through 2 cycles at 2 pi.
vertical stretch of 2, horizontal stretch to a period of 2 pi, phase shift of StartFraction pi Over 2 EndFraction units to the right, vertical shift of 1 unit up
vertical compression of 2, horizontal stretch to a period of StartFraction pi Over 4 EndFraction, phase shift of StartFraction pi Over 4 EndFraction units to the left, vertical shift of 2 units down
vertical compression of 2, horizontal compression to a period of 4 pi, phase shift of StartFraction pi Over 3 EndFraction units to the left, vertical shift of 1 unit down
vertical stretch of 2, horizontal compression to a period of StartFraction pi Over 2 EndFraction, phase shift of Pi units to the right, vertical shift of 1 unit down
Answer:
vertical stretch of 2, horizontal compression to a period of StartFraction pi Over 2 EndFraction, phase shift of Pi units to the right, vertical shift of 1 unit down
Step-by-step explanation:
If you stretch cosine function by a factor of 2, maximum will be y = 2 and minimum will be y = -2, and after that you shift it 1 unit down maximum will be y = 1 and minimum will be y = -3
Answer:
vertical stretch of 2, horizontal compression to a period of StartFraction pi Over 2 EndFraction, phase shift of Pi units to the right, vertical shift of 1 unit down
Step-by-step explanation:
On a coordinate plane, a parabola opens up. It goes through (negative 6, 0), has a vertex at (negative 4, negative 4), and goes through (negative 2, 0). The graph of the function f(x) = (x + 6)(x + 2) is shown. Which statements describe the graph? Check all that apply. The vertex is the maximum value. The axis of symmetry is x = –4. The domain is all real numbers. The function is increasing over (–∞, –4). The function is negative over (–6, –2).
Answer:The axis of symmetry is x=-4
The domain is all real numbers
The function is negative over (-6,-2)
Step-by-step explanation:
Its right
The statement that described the graph should be
The axis of symmetry is x=-4
The domain is all real numbers
The function is negative over (-6,-2)
What is a parabola in the graph?A parabola refers to the U-shaped curve that should be drawn for a quadratic function. The graph of the parabola should be considered downward at the time when the value of a should be less than 0, a < 0.
So based on this, we can conlcude that the above 3 statements should be considered and the other statements should be incorrect.
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Bernie drove from his house to his cousin's house in 6 hours at an average rate of 52 miles per hour he drove home at an average rate of 60 miles per hour how long did it take him to drive home
Answer:
7.5
Step-by-step explanation:
You have to divide the miles by the hours drived and then divide 60 per the miles per hour
Answer:
5.2 hours, or 5 hours 12 minutes
Step-by-step explanation:
The distance is the same in both cases. Since distance = rate (time),
time = distance / (rate).
Here, (6 hr)(52 mph) = (time)(60 mph, or
312 mi = (60 mph)(time), which gives us
(time) = (312 mi) / (60 mph) = 5.2 hours, or 5 hours 12 minutes
Hi xevysxvuiwhcusvidbufbicdbidvudbusviw
Answer:
29
Step-by-step explanation:
i know my math
the perimeter of an equilateral triangle is 150cm. If the length of the altitude of the triangle is x√3cm, what is the value of x?
Answer:
X = 25
Step-by-step explanation:
To solve this question, we'll first of all find determine the side length of the triangle from the perimeter.
Perimeter of an equilaterial triangle = 3 * s
S = side length
Perimeter = 150cm
150 = 3s
S = 150 / 3
S = 50cm
The side lengths are 50cm each since they are all equal.
To find x,
We have to divide the triangle equally into two different part.
Check the first attachment for better illustration on how the equilaterial triangle is.
Check the second attachment for better illustration on the triangle when its divided into a right angle triangle.
From the right angle triangle, we can use pythagorean theorem to solve for x
a² = b² + c²
a = 50cm
b = 25cm
c = x√(3)
50² = [x√(3)]² + 25²
2500 = x² * 3 + 625
2500 - 625 = 3x²
1875 = 3x²
X² = 1875 / 3
X² = 625
X = √(625)
X = 25