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.
is the algebraic expression t^2/t^4 equivalent to t^2?
Answer: no
Step-by-step explanation:
t^2/t^4 is 1/t^2 which is not t^2
7-(-4) is__units from 7 in the ____ direction
7-(-4) is 4 units from 7 in the negative direction. See the explanation and the linear scale attached.
What direction is being referred to in the above Question?The direction being referred to is the direction of the number on a numerical scale or Linear Scale.
In the attached linear scale, we can see that the arrow stops at 11. This is arrived at by expanding the bracket:
7 - (-4)
the subtraction signs cancel out each other creating a positive sign. Hence we have:
7 + 4
= 11.
Hence, 11 is 4 units away from 7 in the negative direction. That is going toward zero is negative or a reduction hence, to get to 7 you need to go toward the negative section of the scale.
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Consider the function f(x) = x3 − 6x2 + 11x − 6.
PART A: One factor of the function f(x) = x3 − 6x2 + 11x − 6 is (x − 3). Use that factor to divide and further factor the polynomial and find the x-intercepts without using technology.
PART B: Describe key characteristics of the graph of the function such as the number of x-intercepts, the y-intercept, and the end behavior without using technology. Explain with complete sentences using components of the function to support your answer.
For the function x³ - 6x² + 11x - 6, we have that:
a) The x-intercepts are: x = 1, x = 2, x = 3.
b) The y-intercept is of y = -6, while the end behavior is that it decreases to the left and increases to the right.
What are the x-intercepts of the function?The function is given as follows:
f(x) = x³ - 6x² + 11x - 6
x - 3 is a factor of the function, meaning that x = 3 is a x-intercept and the function can be written as follows:
x³ - 6x² + 11x - 6 = (x - 3)(ax² + bx + c)
Then we have to build a system of equations to find the coefficients as follows:
x³ - 6x² + 11x - 6 = ax³ + (b - 3a)x² + (c - 3b)x - 3c.
Then the coefficients are given as follows:
a = 1.b - 3a = -6 -> b = -3.-c = -6 -> c = 2.Then the factor is given by:
x² - 3x + 2.
Hence the other intercepts of the polynomial are found when:
x² - 3x + 2 = 0
(x - 2)(x - 1) = 0.
x - 2 = 0 -> x = 2.
x - 1 = 0 -> x = 1.
What is the y-intercept and the end behavior?The y-intercept is the value of f(x) when x = 0, that is, f(0), hence:
f(0) = 0³ - 6(0)² + 11(0) - 6 = -6.
For the end behavior, we need to find the limits as x goes to infinity, hence:
Positive infinity = (∞)³ = ∞. -> increases to right.Negative infinity = (-∞)³ = -∞. -> decreases to left.When the limit goes to infinity, we consider only the term with the highest exponent of the polynomial.
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P=1000 r=0.85% t=4 annually
Based on the given parameters, the amount of the investment after 4 years is $1030
How to determine the amount?The given parameters about the compound interest are
Principal Amount, P = $1000
Interest Rate, R = 0.85%
Time, t = 4
Number of times, n = 1 i.e. annually
Compound interests are different from simple interest, and they are calculated using the following compound interest formula
CI = P(1 + R/n)^nt - P
To calculate the amount, we have:
A = P + CI
So, the equation becomes
A = P + P(1 + R/n)^nt - P
Evaluate the like terms
A = P(1 + R/n)^nt
Substitute the known values in the above equation
A = 1000 * (1 + 0.85%/1)^(1 * 4)
Express 0.85% as decimal
A = 1000 * (1 + 0.0085/1)^(1 * 4)
Evaluate the sum
A = 1000 * (1.0085/1)^(1 * 4)
Evaluate the exponent
A = 1000 * 1.03
Evaluate the product
A = 1030
Hence, the value of the investment is $1030
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pls help ASAP
./././././././././././././././././././././././././././././././././././././././././././././././././././././././
Answer: the second one
Step-by-step explanation:
commutative is like
A+b=b+A
So 4+(-6)=-6+4
Which is like 4-6=-6+4
Find x ifwrewrijqeowehj
3x+x+(x+12)=152
<AOD =<COB(VERTICAL OPPOSITE ANGLES)
[tex]5x+12=152\\5x=152-12\\5x=140\\\frac{5x}{5} =\frac{140}{5} \\x=28[/tex]
x=28°
be reminded that <COB IS MADE OF ALOT OF BRANCH ANGLES THAT WE HAD TO ADD TO GET IT
i.e <COE,<EOF AND <FOB
Write a quadratic function in standard form containing the point (-7, 5) and
vertex (1, 9)
The quadratic function in the standard form containing the point (-7, 5) and vertex (1, 9) is y = (-1/16)(x - 1)² + 9.
How is a quadratic function formed with a vertex and a point?The vertex form of a quadratic function with vertex (h, k) is written as
y = a(x - h)² + k, where (x, y) denotes a point on the parabola. Real integers a, h, and k are also included.
Given:
Point (x, y) = (-7, 5)
Vertex (h,k) = (1, 9)
The general equation of quadratic function in vertex form is:
y = a(x - h)² + k
To solve for a, substitute the given point (x,y) = (-7,5) into the equation.
5 = a(-7 - 1)² + 9
a(-8)² = -4
a = -4 /64
a = -1/16
Therefore, the required quadratic function is,
y = (-1/16)(x - 1)² + 9
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Solve the quadratic equation by completing the square.x²-12x+30=0
In order to solve this quadratic equation by completing the square, let's analyse the coefficient b by comparing the equation with the standard form:
[tex]y=ax^2+bx+c[/tex]We have b = -12. In order to be a perfect square, the coefficient c needs to be (-12/2)^2 = (-6)^2 = 36
We already have 30, so we just need to add 6:
[tex]\begin{gathered} x^2-12x+30=0 \\ x^2-12x+30+6-6=0 \\ x^2-12x+36-6=0 \\ (x-6)^2-6=0 \\ (x-6)^2=6 \\ x-6=\pm\sqrt[]{6} \\ x_1=6+\sqrt[]{6} \\ x_2=6-\sqrt[]{6} \end{gathered}[/tex]plss solve this having big trouble will give brainiest n 55points
Considering that a transversal line cuts two parallel lines, the relations between the angles are given as follows:
1. Corresponding angles.
2. Alternate exterior angles.
3. Consecutive interior angles.
What is the relationship between angles 1 and 3?Angles 1 and 3 are corresponding angles, as they are both at the same position relative to their lines, j for angle 1 and m for angle 3, being cut by the transversal line t.
What is the relationship between angles 8 and 4?Angles 4 and 8 are alternate exterior angles, as:
Angle 4 is to the left of the transversal line t and below it's line m.Angle 8 is to the right of the transversal line t and above it's line m.Inverse positions in both senses, left/right and up/down, hence alternate exterior angles.
What is the relationship between angles 2 and 3?Angles 2 and 3 form a supplementary pair inside the same region, between the two lines being cut by the transversal, hence they are consecutive interior angles.
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reciprocal of b-1/b
FOR A RECIPROCAL OF FRACTION WE SWAP POSITIONS. WHATEVER WAS IN THE NUMERATOR BECOMES THE DENOMINATOR AND WHAT WAS IN THE DENOMINATOR BECOMES THE NUMERATOR.
THIS MEANS THAT AS A RESULTS WE HAVE
[tex] \frac{b}{b - 1} [/tex]
ATTACHED IS THE SOLUTION.
Sandeep is making fruit dip for a party. His recipe calls for 1/2 of a teaspoon of cinnamon and 3/4 of a cup
of yogurt. Using this ratio, how much cinnamon does Sandeep need if he uses 3 cups of yogurt?
2 teaspoon of cinnamon need if he uses 3 cups of yogurt
What is ratio ?By comparing two amounts of the same units, the ratio can be used to calculate how much of one item is included in the other. There are two different categories for ratios. The first is a part to part ratio, whereas the second is a part to whole ratio. The relationship between two separate entities or organizations is shown by the part-to-part ratio. For instance, a class has a 12:15 boy-to-girl ratio, whereas the part-to-whole ratio describes how one group compares to another. For instance, five people enjoy reading books out of every ten persons. Since the ratio of the component to the total is 5:10, 5 out of every 10 persons enjoy reading.
Given that :Sandeep is making fruit dip for a party. His recipe calls for 1/2 of a teaspoon of cinnamon and 3/4 of a cup
of yogurt.
[tex]0.5 : 0.75 = x : 3[/tex]
x = 2
2 teaspoon of cinnamon need if he uses 3 cups of yogurt
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What’s the relationship between the number of
$4 lunches
you buy with a $100 school
lunch card and the money remaining on
the card
The relationship will be a solid line .
How to find the relationship between the given amounts?
Given:
The amount of one lunch =$4
The amount of the school lunch card=$100
Let, the amount remaining on the card= b
Let the number of lunches to buy = a
The equation is given by,
b = 100 - 4a
When 1 lunch is bought ,a= 1 ;
b= 100 - 4(1) = 96
When 2 lunches are bought ,a= 2;
b= 100 - 4 (2)= 92
When 3 lunches are bought ,a= 3;
b= 100 - 4 (3)= 88
When 4 lunches are bought ,a= 4;
b= 100 - 4 (4)= 84
Since ,the decrease is gradual and same, the relationship will be a solid line.
The complete question is:
What is the relationship between the number of $4 lunches you buy with a $100 school lunch card and the money remaining on the card. Is the relationship a solid line or a set on unconnected points?
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katie is studying the polynomial and determines the polynomial has three real roots. do you agree or disagree with katie's statement? explain your reasoning.
Katie is studying the polynomial f(x) =(2x-3) (x-4) (x^2-3) and determines the polynomial has three real roots. you disagree with Katies statement because the function has four real roots
Katie is studying the polynomial and determines the polynomial has three real roots. Do you agree or disagree with Katie's statement? Explain your reasoning.
the complete question is
Katie is studying the polynomial f(x) =(2x-3) (x-4) (x^2-3) and determines the polynomial has three real roots. Do you agree or disagree with Katies statement? Explain your reasoning.
Write properties of function:
x intercept/zero: [tex]x_{1}[/tex] = 3/2 ; [tex]x_{2}[/tex] = 4 ; [tex]x_{3}[/tex] = -[tex]\sqrt{3}[/tex] ; [tex]x_{4}[/tex] = [tex]\sqrt{3}[/tex]
Katie is studying the polynomial f(x) =(2x-3) (x-4) (x^2-3) and determines the polynomial has three real roots. you disagree with Katies statement because the function has four real roots
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Please! Help me find the range of this graph as an inequality :((
Answer: [tex]\text{y} \ge 2[/tex]
Reason:
The lowest point on the graph occurs when y = 2. This is a closed endpoint so it's included with the graph. So either y = 2 or y > 2, both of which combine to get the answer shown above.
How many was the phone before the discounted price?
Answer: depends how many you have with you
Step-by-step explanation:
does not matter how many you have
convert -20°C to degrees Fahrenheit using the formula F = 9/5C + 32. (F=9/5(-20)+32)
Answer:
- 4° F
Step-by-step explanation:
substitute C = - 20 into the formula
F = ([tex]\frac{9}{5}[/tex] × - 20 ) + 32 = (9 × - 4) + 32 = - 36 + 32 = - 4° F
need help pls
#i love brainly
Answer:
x=10
Step-by-step explanation:
48=6x-12
60=6x
x=10
(-4s–3)+(6s–1) what is the sum
Answer:
=2s−4
Step-by-step explanation:
−4s−3+6s−1
=−4s+−3+6s+−1
Combine Like Terms:
=−4s+−3+6s+−1
=(−4s+6s)+(−3+−1)
=2s+−4
Answer:
=2s−4
At a health camp the number of children was three times the number of men.the number of men was 240 less than the number of women. if the number of children x give an equation that can be used to get the number of men if the total number of people who attended was 2400
The equation that can be used to get the number of men if the total number of people who attended was 2400 is x + 3x + x + 240 = 2400.
How to illustrate the information?It should be noted that from the information given, in the health camp the number of children was three times the number of men and the number of men was 240 less than the number of women.
Number of men = x
Number of children = 3x
Number of women = x + 240
Total number of people = 2400
The appropriate equation will be:
x + 3x + x + 240 = 2400
5x + 240 = 2400
Collect like terms
5x = 2400 - 240
5x = 2160
Divide
x = 2160 / 5
x =432
Therefore, the total number of men is 432 men.
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A leaky faucet drips 1/4 fluid ounce of water every 20 minutes. How many Gallons of water will leak from this faucet in 1 year? (Round to the nearest gal.)
Answer:
51
Step-by-step explanation:
I may have made a mistake somewhere along the way but if not then it is 51 gallons.
The way i did this was to multiply 20 minutes by 3 to equal an hour, then multiply that by 24 to equal a day, then multiply that by 365 to equal a year.
That gives you the numbers you need to multiply the ounce by. So first multiply 1/4 by 3 to get 3/4. Next you multiply 3/4 by 24 to get 72/4 or 18. Then you multiply 18 by 365 to get 6570 ounces in a year. Finally you translate that to gallons and you get 51.328125, which rounds down to 51.
Alsooo, i wouldnt mind a good old brainliest if im correct :)
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Answer:
d
Step-by-step explanation:
Pythagorean theorem : a2 + b2 = c2
Here, ‘a’ is the vertical side i.e. wall
‘b’ is the base side i.e. bottom = 5 m
‘c’ is the hypotenuse i.e. the ladder = 10 m
If b = 5 m, c = 10 m
Then, a2 = c2 - b2 = (10 x 10) - (5 x 5) = 75
a = √75 = 8.66 m
The the top of the ladder is at 8.66 m.
Which fractions are equivalent to 0.48? Select all that apply.
Answer:
Number
Step-by-step explanation:
48 divided by 100 equals .48
Which scale is equivalent to 1 cm to 1 km?
1 to 1,000
10,000 to 1
1 to 100,000
100,000 to 1
1 to 1,000,000
Answer:
1 to 100,000
Step-by-step explanation:
There are 100,000 cm in a km
Find an equation in point-slope form for the line having the slope m = -4 and containing the point (7,2)
Answer: y=-4x+30
Step-by-step explanation: put into point slope form y-y1=m(x-x1). M is out slope with the given point (7,2) 7 is out x and 2 is our y. Give us y-2=-4(x-7) once done distribute yo get y-2=-4x+28. Add the 2 from the left to the right. to get y=-4x+30
Determine the solution to p/4=12.2
Ruby has $0.86 worth of pennies and nickels. She has 4 more nickels than pennies. Determine the number of pennies and the number of nickels that Ruby has.
86 = 1p + 5n
n = p + 4
86 = 1p + 5(p + 4)
86 = 1p + 5p + 20
66 = 6p; p = 11
86 = 1(11) + 5n
86 = 11 + 5n
75 = 5n; 15 = n
11 pennies, 15 nickels
11(1) + 15(15) = 11 + 75 = 86
Activity 2: Which are not quadratic equations? How do you describe quadratic equation?
Answer:
A quadratic equation is an equation of the second degree, meaning it contains at least one term that is squared.
Complete the sentence below.
35 280 is ten times bigger than
Answer:
3528
Step-by-step explanation:
35280 divided by 10 is 3528. To check your work, multiply 3528 by 10. The answer is 35280.
Hope this helps! :)
Hey need help with this problem! Will give brainliest if right
Answer: 9,800
Step-by-step explanation:
She should save 9,800 yearly.
2/10 = 20/100 ; 20%
20% = 0.2
0.2 x 49,000
(which is 20% of 49,000)
= $9,800
Find the zeros of the functions:
f(x)=3x+7
f(x)=1/5x-7
Answer: x= -5
Step-by-step explanation: Zero is x
f(-5)= -15 +7= -8
f(-5)= -1 - 7 = -8
Answer is -8