Answer:
B is bigger
Step-by-step explanation:
a) 3^2 / 2^3
3*3 / 2*2*2
9/8
b) 9^4 / 4^6
9*9*9*9/4*4*4*4*4
6561 / 4096
1.601807
Identify the interval(s) on which each quadratic function is positive.
1. y= x^2 + 2x - 8
2. y= -x^2 +4x +12
3. y= 5x^2 - 3x - 8
Help on these three problems above would be greatly appreciated, thanks! ☜(ˆ▿ˆc)
Answer:
[tex]\textsf{1. \quad $x < -4$ or $x > 2$}[/tex]
[tex]\textsf{2. \quad $-2 < x < 6$}[/tex]
[tex]\textsf{3. \quad $x < -1$ or $x > \dfrac{8}[5}$}[/tex][tex]\textsf{3. \quad $x < -1$ or $x > \dfrac{8}[5}$}[/tex][tex]\textsf{3. \quad $x < -1$ or $x > \dfrac{8}{5}$}[/tex]
Step-by-step explanation:
The intervals on which a quadratic function is positive are those intervals where the function is above the x-axis, i.e. where y > 0.
The zeros of the quadratic function are the points at which the parabola crosses the x-axis.
If the leading coefficient of a quadratic function is positive, the parabola opens upwards.
If the leading coefficient of a quadratic function is negative, the parabola opens downwards.
Therefore, to find the intervals on which each quadratic function is positive:
Calculate the zeros.Determine if the parabola opens upwards or downwards.If the parabola opens upwards, the intervals are less than the smaller zero and greater than the larger zero.If the parabola opens downwards, the interval is between the zeros.Question 1Given function:
[tex]y=x^2+2x-8[/tex]
Factor the given function:
[tex]\implies y= x^2+4x-2x-8[/tex]
[tex]\implies y=x(x+4)-2(x+4)[/tex]
[tex]\implies y=(x-2)(x+4)[/tex]
Substitute y = 0 to find the zeros:
[tex]\implies (x-2)(x+4)=0[/tex]
[tex]\implies x-2=0 \implies x=2[/tex]
[tex]\implies x+4=0 \implies x=-4[/tex]
The leading coefficient is positive, so the parabola opens upwards.
Therefore, the interval on which the function is positive is:
Solution: x < -4 or x > 2Interval notation: (-∞, -4) ∪ (2, ∞)Question 2Given function:
[tex]y=-x^2+4x+12[/tex]
Factor the given function:
[tex]\implies y=-(x^2-4x-12)[/tex]
[tex]\implies y=-(x^2-6x+2x-12)[/tex]
[tex]\implies y=-(x(x-6)+2(x-6))[/tex]
[tex]\implies y=-(x+2)(x-6)[/tex]
Substitute y = 0 to find the zeros:
[tex]\implies -(x+2)(x-6)=0[/tex]
[tex]\implies (x+2)(x-6)=0[/tex]
[tex]\implies x+2=0 \implies x=-2[/tex]
[tex]\implies x-6=0 \implies x=6[/tex]
The leading coefficient is negative, so the parabola opens downwards.
Therefore, the interval on which the function is positive is:
Solution: -2 < x < 6Interval notation: (-2, 6)Question 3Given function:
[tex]y=5x^2-3x-8[/tex]
Factor the given function:
[tex]\implies y=5x^2-8x+5x-8[/tex]
[tex]\implies y=x(5x-8)+1(5x-8)[/tex]
[tex]\implies y=(x+1)(5x-8)[/tex]
Substitute y = 0 to find the zeros:
[tex]\implies (x+1)(5x-8)=0[/tex]
[tex]\implies x+1=0 \implies x=-1[/tex]
[tex]\implies 5x-8=0 \implies x=\dfrac{8}{5}[/tex]
The leading coefficient is positive, so the parabola opens upwards.
Therefore, the interval on which the function is positive is:
Solution: x < -1 or x > ⁸/₅Interval notation: (-∞, -1) ∪ (⁸/₅, ∞)Which estimate best describes the area under the curve in square units?
Responses
10 units²
10 units²
15 units²
15 units²
30 units²
30 units²
35 units²
35 units²
A curve is graphed on a coordinate plane. The horizontal x-axis ranges from 0 to 5 in increments of 0.5. The vertical y-axis ranges from 0 to 10 in increments of 1. The curve passes through begin ordered pair 0.5 comma 3 end ordered pair, begin ordered pair 2.5 comma 5 end ordered pair, begin ordered pair 3.5 comma 4 end ordered pair, and begin ordered pair 4 comma 2 end ordered pair. The region below the curve is shaded blue.
The estimate that best describes the area under the curve in square units is option B: 15 units².
What does the area under a curve represent?The area under a curve in calculus is a picture of an integral. It is frequently possible to interpret the area under a curve as the total amount of whatever the function is describing.
By performing a definite integral between the two locations, one can determine the area under a curve between two points. Integrate y = f(x) between the limits of a and b to tell about the area under the curve y = f(x) between x = a & x = b.
Therefore, each box:
0.5 × 1 = 0.5 units^2. Then add up the boxes, and it is about 30. So:
30×0.5 = 15 units².
Learn more about estimate from
https://brainly.com/question/11453377
#SPJ1
Which three of the following expenses can student aid cover
tuition
television
school supplies
parties and socializing
boarding/housing
The three of the following expenses which the student aid cover include the following below:
tuitionschool suppliesboarding/housing.What is Student aid?This is referred to as the type of funding which is required to cover the cost of post-secondary education and are usually in the form of scholarships, grants, etc. It is awarded by government or private institutions and most times the highest scorers in an exam determines who will get it.
This aid covers different types of school expenses which are the most important ones such as tuition, school supplies etc thereby making it the correct choice.
Read more about Student aid here https://brainly.com/question/26499492
#SPJ1
Mike took Jen bowling for the first time. He
bowled two games with scores of 157 and 175.
Jen had never bowled before and scored 78 and
98. What was Mike's average score?
Mike's average score is 166.
What is average?Divide the total by the number of numbers after adding up all the numbers.
Implying something that sits in the midst. The average is the ratio created by dividing the total number of figures in a set by the total number of figures. Averages are used to condense a vast number of data points into a single value. It is a visual depiction of all the data set's available numbers. By adding up all the data values and dividing them by the total number of data points, the average is calculated.
Given Data
Mike bowled two games with scores of 157 and 175.
Sum of scores = 332
Average = [tex]\frac{Sum of scores}{Totak number of bowling}[/tex]
Average = [tex]\frac{157 + 175}{2}[/tex]
Average = [tex]\frac{332}{2}[/tex]
Average = 166
Mike's average score is 166.
To learn more about average, visit:
https://brainly.com/question/24057012
#SPJ9
For a project in his Geometry class, Levi uses a mirror on the ground to measure the height of his school’s football goalpost. He walks a distance of 12.05 meters from the goalpost, then places a mirror flat on the ground, marked with an X at the center. He then walks 2 more meters past the mirror, so that when he turns around and looks down at the mirror, he can see the top of the goalpost clearly marked in the X. His partner measures the distance from his eyes to the ground to be 1.15 meters. How tall is the goalpost? Round your answer to the nearest hundredth of a meter.
Answer:
\text{ m} m
attempt 2 out of 2
Griffin Heaton
Word Problems, Similar Triangles (Level 2)
Oct 20, 9:06:20 PM
Watch help video
For a project in his Geometry class, Levi uses a mirror on the ground to measure the height of his school’s football goalpost. He walks a distance of 12.05 meters from the goalpost, then places a mirror flat on the ground, marked with an X at the center. He then walks 2 more meters past the mirror, so that when he turns around and looks down at the mirror, he can see the top of the goalpost clearly marked in the X. His partner measures the distance from his eyes to the ground to be 1.15 meters. How tall is the goalpost? Round your answer to the nearest hundredth of a meter.
The goalposts are 6.92m tall.
Angle of incidence Equals Angle of reflection, according to the physics principle of reflection.
Both angles ( θ) are equal, as seen in the attached image.
m<ABC = mADC = 90° - θ
m<ACB = mECD = 90°
detailed explanation?
Angle of incidence Equals Angle of reflection, according to the physics principle of reflection.
Both angles ( θ) are equal, as seen in the attached image.
m<ABC = mADC = 90° - θ
m<ACB = mECD = 90°
Thus, the ABC triangle and the EDC triangle will both be similar.
Their corresponding sides will also be proportionate due to the property of comparable triangles
AB/BD = CB/CD.
1.15/ED = 2.0/12.5
ED = 1.15 * 12.05 /2.0
ED= 6.92
ED = ED = 6.92 m
The goalposts are 6.92m tall.
To learn more about the problem refer to:
https://brainly.com/question/24174637
#SPJ13
Laqueta has a $50 gift card for an online music store. Each song costs ss dollars. Write an algebraic expression that represents the amount left on her card after Laqueta buys 7 songs. How much money will be left on her card if each song costs $1.25?
1. The algebraic expression that represents the amount left on her card after Laqueta buys 7 songs is 50 - 7s
2. The money that will be left on her card if each song costs $1.25 is $41.25.
How to illustrate the information?From the information given, Laqueta has a $50 gift card for an online music store and each song costs s dollars.
In this case, the algebraic expression that represents the amount left on her card after Laqueta buys 7 songs will be:
= Total amount - Cost of songs
= 50 - (7 × s)
= 50 - 7s
where s = number of songs
The money that will be left on her card if each song costs $1.25 will be:
= 50 - 7s
= 50 - (7 × 1.25)
= 50 - 8.75
= $41.25
Learn more about expressions on:
brainly.com/question/723406
#SPJ1
Which of the following are rational numbers?
5.48
78.541
97
42.111...
Answer:
5.48
78.541
97
42.111...
(all of above)
Step-by-step explanation:
because a rational number is a number that can be written as a fraction
a decimal number that ends can be written as a fraction (ex: 5/4 = 1.25)
a decimal number that has a repeating number after the decimal point can also be written as a fraction (ex: 10/3 = 3.33...)
Rick joined a bootcamp class at his gym that lasted two weeks. in each class, rick does cardio for c minutes and strength training for 30 minutes. rick went to the class 3 times the first week and 4 times the second week. pick all the expressions that represent how long rick worked out in all.
Answer: 7(30 + c) min
Step-by-step explanation:
Total time spent in gym = (30 + c)
Total day went to gym = (3 + 4) = 7 day
Net time = 7(30 + c) min
-) Written as products of their prime factors, N = 2^px5^qx7^r and 500=2² × 5³.
The highest common factor of N and 500 is 2^2 x 5²
The lowest common multiple of N and 500 is 2^3 x 5³ x7.
Find p, q and r.
The highest common factor of N and 500 is 2²x5² and The lowest common multiple of N and 500 is [tex]2^{3}[/tex]x[tex]5^{3}[/tex]x7. p, q and r is p =2 , q =2 , r =1
What is prime factorization ?Prime factorization is the technique of expressing a number as the product of prime numbers. The only two components in prime numbers are the number itself and the number itself. Prime numbers include, for instance, 2, 3, 5, 7, 11, 13, 17, 19, and so forth. Any number can be represented as a sum of prime numbers by "prime factorizing" it.
Given that : Written as product of their prime factors N= [tex]2^{p}[/tex] x[tex]5^{q}[/tex]x[tex]7^{r}[/tex] and 500= 2² x 5³ The highest common factor of N and 500 is 2² x 5³? The lowest common multiple of N and 500 is 2²x5²x7.
N= [tex]2^{p}[/tex] x[tex]5^{q}[/tex]x[tex]7^{r}[/tex]
500= 2² x 5³
highest common factor of N and 500 is 2²x5²
p ≥ 2
q = 2
r ≥ 0
The lowest common multiple of N and 500 is 2²x5²x7.
HCF x LCM = N * 500
=> 2²x5² x 2²x5²x7 = [tex]2^{p}[/tex] x[tex]5^{q}[/tex]x[tex]7^{r}[/tex] x 2² x5³
=> 2²x5x7 = [tex]2^{p}[/tex] x[tex]5^{q}[/tex]x[tex]7^{r}[/tex]
p = 2
q = 1 but q = 2 as per HCF
r = 1
There is mistake in data
As LCM should have [tex]5^{3}[/tex] atleast as 500 has 5^2
To learn more about prime factor visit :
brainly.com/question/24182713
#SPJ9
how many solution does 3(2x+1)=2(2x+1) have
Answer:
1 solution
Step-by-step explanation:
please help!! due tmr morning!!
Answer:
6, -2, and-1
Step-by-step explanation:
f(2) means that x is 2, so looking in the left column find x as 2, and then find the corresponding number beside it.
f(x)=0 so look for 0 in the right column and find the number corresponding to it in the left.
Answer:
#8 is equal to 6
#9 is equal to -2
#10 is equal to -1
Step-by-step explanation:
If you look in the x column for 2 the outcome is 6
If you look in the f(x) column for 0 the income is -2
If you look in the f(x) column for 1.5 the income is -1
Roger ran 13.2 miles in 1.6 hours. Ana ran 10.85 miles in 1.4 hours. In miles per hour, how much faster was Roger's average speed than Ana's?
Roger has a faster speed at 8.25 miles per hour compared to Ana who ran with a speed of 7.75 mph.
What is Average speed?
The average speed is the total distance traveled by any object in a particular time interval.
Given that;
Distance covered by Roger = 13.2 miles
Time is taken by Roger = 1.6 hours
Distance covered by Ana = 10.85 miles
Time is taken by Ana = 1.4 hours
Now, Calculate the speed of Roger and Ana as;
Speed = Distance / Time
For Roger,
Speed = 13.2/1.6 = 8.25 mph
For Ana,
Speed = 10.85/1.4= 7.75 mph
Hence, Roger has a faster speed at 8.25 miles per hour compared to Ana who ran with a speed of 7.75 mph.
A box of 24 ornaments contains 3/4 red ornaments. How many red ornaments are in the box? How many ornaments are another color than red?
Answer:
18 red and 6 other color
Step-by-step explanation:
A box of 24 ornaments contains 3/4 red ornaments. How many red ornaments are in the box? How many ornaments are another color than red?
3/4 × 24 = red ornaments
= 18 red
24 - 18 = 6 other color
solve for x
please huryy
Answer:
X = 31
Step-by-step explanation:
180 = 2x + 9 + 3x +16
180 = 5x + 25
180 + -25 = 5x
155 = 5x
5x/5 = 0 (Cancel out)
155 /5x = 31
X = 31
Check math by :
2 x 31 = 62 + 9 = 71
3 x 31 = 93 + 16 = 109
109 + 71 = 180
Therefore, X = 31
Therfore we can derive the equation:
[tex]2x+9+3x+16 = 180[/tex]Next, we group like terms.[tex]2x+3x+9+16 =180[/tex]
Now, we combine like terms.[tex]5x+25 = 180[/tex]
Then, we move 25 to the right side.5x = 155
Finally, we divide both sides by 5.[tex]x = 31[/tex]
Evaluate f(x) = x + 6 When x = -2,0, and 5
f(-2)= ?
f(0) = ?
f(5) = ?
Simplify these expressions
a) x x x x x xу ху
b) 2 xx x x x 3 ×ухуху
Answer:
a) x^7 y^2
b) 6 x^8 y^3
Step-by-step explanation:
Exponential expressions
a) x x x x x xу ху
There are 7 x 's in the expression and 2 y's The number of the x's is the exponent for x is the exponent and the same for y
x^7 y^2
b) 2 xx x x x 3 ×ухуху
Multiply the constants 2*3 = 6
Count the x's 8 x's = x^8
Do the same for y 3 y's = y^3
6 x^8 y^3
The zeros of a quadratic function are 1 and 4. How would you use this information to write the equation for the function? If the equation cannot be written, explain why. Use complete sentences in your answer.
Answer:
The quadratic function is x²-5x+4=0
Step-by-step explanation:
To find a quadratic equation whose roots are given we use
x²-(sum of roots)x + (product of roots) =0
x²-(4+1)x + (4×1)=0
x²-5x+4=0
let us check if it is correct
x²-5x+4=0
x²-1x-4x+4=0
x(x-1)-4(x-1)=0
(x-4)(x-1)=0
(x-4)=0 and (x-1)=0
x=4 and x=1
please rate as brainliest
A mother dog weighs 75 pounds. One of her puppies weighs
6 pounds. How many times greater is the mother dog's weight
than her puppy's weight?
Answer: 12.5 pounds
Step-by-step explanation:
How many times greater, 75=6x
divide by 6
help i will give 50 points
Answer:
Option 4, 8 1/3
Step-by-step explanation:
-2.5 * - 3 1/3 = 8.3 repeating
8.3 repeating = 75/9
75/9 = 8 1/3
To make bread, 2 teaspoons of yeast are needed for 500 grams of flour. How many teaspoons of yeast are needed for 750 grams of flour?
Answer:
3 teaspoons.
Step-by-step explanation:
500/2=250 grams per teaspoon
750/250=3
3 teaspoons
0.35x – 4.8 < 5.2 – 0.9x
The solution to the given linear inequality expression is equivalent to x < 8
Inequality expressionsInequality expressions are expressions that are not separated by an equal sign. They are separated by the signs <, >, ≤ and ≥.
Given the inequality below:
0.35x – 4.8 < 5.2 – 0.9x
Collect the like terms;
0.35x + 0.9x < 5.2 + 4.8
Simplify the result to have:
(0.35+0.9)x < 10.0
1.25x < 10.0
Divide both sides by 1.25
1.25x/1.25 < 10.0/1.25
x <8
This gives the solution to the linear inequality shown.
Learn more on inequality here: https://brainly.com/question/24372553
#SPJ1
7sufifiglhofsufigif7dufig
Using a proportional relationship, it is found that:
a) The independent variable is x.
b) The dependent variable is y = 12x.
c) The domain is of 0 ≤ x ≤ 25.
d) The range is of 0 ≤ y ≤ 300.
What is a direct proportional relationship?A direct proportional relationship is a function in which the output variable is given by the multiplication of the input variable and the constant of proportionality k, as shown below:
y = kx
In which:
x is the independent variable.y is the dependent variable.For this problem, Jennifer makes $12 an hour, hence the constant is of k = 12 and the equation is:
y = 12x.
She can work between 0 and 25 hours, hence:
The domain is 0 ≤ x ≤ 25, which is the set that contains all possible input values for the function.The range is 0 ≤ y ≤ 300, as 25 x 12 = 300, which is the set that contains all possible output values for the function.More can be learned about proportional relationships at https://brainly.com/question/10424180
#SPJ1
A liquid storage container is being filled at a constant rate. The container is being filled at a rate of 1
3
gallon per 1
4
minute.
As per unit rate of storing liquid in a container , the equivalent rate for 4 minutes is equal to (16/3) gallons.
As given in the question,
Liquid storage container is being filled at a constant rate.
Rate of filling a container = 1/3 gallon per 1/4 minute
Unit rate = (1/3 gallons)/ (1/4 minutes)
= (4/3) gallons per minute
Equivalent rate for 4 minutes is equal to
= [ ( 4 / 3) × 4 ] gallons per 4 minutes
= ( 16 / 3) gallons
Therefore, as per unit rate of storing liquid in a container , the equivalent rate for 4 minutes is equal to (16/3) gallons.
The complete question is :
A liquid storage container is being filled at a constant rate. The container is being filled at a rate of 1/3 gallon per 1/4 minute.
Unit rate = (1/3 gallons)/ (1/4 minutes)
= (4/3) gallons per minute
Find the equivalent rate for 4 minutes.
Learn more about equivalent here
brainly.com/question/14672772
#SPJ1
5. If the solution of an equation is a = -2, what could the original equation be?
-
OA. x+6=8
OB. x-6-8
O c. x+8 = 6
OD x 8-6
HELP PLEASEEEE
Answer:
C
Step-by-step explanation:
x + 8 = 6
x = 6-8
x = -2
.....
a cylindrical tank with a diameter 1.0m and height 1.5m is to be filled with water. How many liters of water are needed to fil the tank
375π litters of water is needed to fill the cylindrical tank with a diameter of 1.0m and height of 1.5m.
What is the volume of the given cylindrical tank?A cylinder is simply a 3-dimensional shape having two parallel circular bases joined by a curved surface.
The volume of a cylinder is expressed as;
V = π × r² × h
Where r is radius of the circular base, h is height and π is constant pi.
Given the data in the question;
Diameter d = 1.0mRadius r = d/1 = 1.0m/2 = 0.5mHeight h = 1.5mVolume V = ?Plug the given values into the formula above and solve for V, to determine the liters of water that will fill the tank.
V = π × r² × h
V = π × ( 0.5m )² × 1.5m
V = π × 0.25m² × 1.5m
V = 0.375π m³
Next, convert cubic meters to liters.
V = 0.375π m³ = ( 1000 × 0.375π )L
Volume V = 375π L
Therefore, a volume of 375π litters is needed to fill the tank.
Learn more about volume of cylinder here: brainly.com/question/16788902
#SPJ1
Solve: 3(x+4)= 3x+12
Ox=0
Ox=4
Oall real numbers
Ono solution
Correct option is C, The solution is set of all real numbers.
When x=0, 0=0 and 24 Equals 24 when x = 4.
This equation holds true for all real numbers since both sides of the equation are the same. When 0=0, the solution reveals that the equation is an identity, a specific kind of equation that is true regardless of the value of x.
Identity equation: What is it?Identity equations are described as equations that are true regardless of the value of the inserted variable.
3(x+4)=3x+12
3x+12=3x+12
When x = 0
3(0)+12=3(0)+12
12=12
When x = 4
12+12=12+12
The set of all real numbers is the answer as a result.
Y - = m is an equation for a line given a slope and a point ( x - )
or y - 7 = 1 ( x - 1) ( x - 1)
or y - 7 = x -1
or y = x + 6
Consequently, a line parallel to the line y = x + 4 has the equation y = x + 6.
To know more about identity equation, visit:
https://brainly.com/question/10832178
#SPJ9
please help and explain thank you
Find the value of f(4) for the function.
f(a) = 7(a + 2)-5
f(4) = (Simplify your answer.)
Answer:
f= 37 / 4
Step-by-step explanation:
I am using ( / ) to show a fraction
Let's solve your equation step-by-step.
f(4)=7(4+2)−5
Step 1: Simplify both sides of the equation.
f(4)=7(4+2)−5
4f=42+−5
4f=(42+−5)(Combine Like Terms)
4f=37
4f=37
Step 2: Divide both sides by 4.
4f / 4 = 37 / 4
f= 37 / 4
Answer:
f= 37 / 4
Hope this helps! :)
The algebraic expression of 9+11g
The mathematical statement of the expression 9 + 11g is the sum of 9 and 11g
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to determine the expression?The algebraic expression is given as
9 + 11g
The above mathematical representation is an algebraic expression that is already in its most simplified form
This means that the algebraic expression cannot be further simplified
However, the algebraic expression can be rewritten as a mathematical statement
Recall that, we have
9 + 11g
The pronunciation of the above expression is:
9 plus 11g
In expressions, plus represents sum
So, we have
9 + 11g can be represented as the sum of 9 and 11g
Hence, the representation of the algebraic expression given as 9 + 11g is the sum of 9 and 11g
Read more about expression at
brainly.com/question/4344214
#SPJ1
Hello I really need help with this and this would help me a lot
Answer:
1.divide
2.minus
3.times