Answer:
2
Step-by-step explanation:
To find the slope, m, you use the equation:
[tex]m \: = \frac{y2 - y1}{x2 - x1} [/tex]
From our question, (x1 = 7, y1 = 5) ; ( x2 = 2, y2 = -5)
Substitute the values into the equation:
[tex]m \: = \frac{ - 5 - 5}{2 - 7} \\ = 2[/tex]
The slope, m is therefore 2
find the values of k for which the line y = 2x + k + 2 cuts the curve y = 2x^2 + (k + 2)x + 8 at two distinct points.
The values of k for which the line y = 2x + k + 2 cuts the curve y = 2x² + (k + 2) + 8 at two distinct points are; k > -12 or k < 4
What is the point of Intersection of the line and the curve?We are given the equation of the line as;
y = 2x + k + 2
Equation of the curve is;
y = 2x² + (k + 2) + 8
Now, to find the the values of k for which the line y = 2x + k + 2 cuts the curve y = 2x² + (k + 2) + 8 at two distinct points, we will just equate both equations to get;
2x + k + 2 = 2x² + (k + 2) + 8
2x + k + 2 = 2x² + kx + 2x + 8
2x² + kx + (-k + 6) = 0
Now, Two distinct solutions is the same as having a positive discriminant.
b² - 4ac > 0
k² - 4(2 * (-k + 6)) > 0
k² + 8k - 48 > 0
Solving using quadratic equation calculator gives;
k > -12 or k < 4
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simplify 3x + 5y - x + 2y
Answer:
2x + 7y
Step-by-step explanation:
3x + 5y - x + 2y ← collect like terms
= (3x - x) + (5y + 2y)
= 2x + 7y
By Simplifying 3x + 5y - x + 2y, we get 2x + 7y
More Explanation
The simplification here follows the basic method of addition and subtraction in algebra.
Given : 3x + 5y - x + 2y
Step 1: align the numbers with similar variables.
Therefore, we get, 3x - x + 5y + 2y
Step 2: Solve by addition and subtraction.
Therefore, we get, 2x + 7y
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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
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
subtract the quotiet of 70 divided by 2 from 60
The algebraic representation of the expression "subtract the quotiet of 70 divided by 2 from 60" is 60 - 70/2" which gives the result 25
Algebraic representation of expressionQuotient means the result obtained from the division of an expressionThe divisor is the expression or term used to divide the expressionThe dividend is the expression being divided by another expression.the quotiet of 70 divided by 2
= 70/2
subtract the quotiet of 70 divided by 2 from 60
= 60 - 70/2
= 60 - 35
= 25
In conclusion, the result of the expression "subtract the quotiet of 70 divided by 2 from 60" is 25
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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.
2. Find the parabola with equation y = ax² + bx whose tangent line at (1, 1) has equation y = 3x - 2.
Answer:
Step-by-step explanation:
Alyssa wants to play the game. Choose the statement below that is correct in all aspects. E(penny) = –0.33 and E(nickel) = 0.33, so she should play with the nickels. E(penny) = 0.5 and E(nickel) = 1.5, so she should play with the nickels. E(penny) = 1.75 and E(nickel) = 1.5, so she should play with the pennies. E(penny) = 2.38 and E(nickel) = 2, so she should play with the pennies
Using the expected value of a discrete distribution, the correct option is given as follows:
E(penny) = 1.75 and E(nickel) = 1.5, so she should play with the pennies.
What is the expected value of a discrete distribution?The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.
When 3 coins are tossed, the probabilities are given as follows:
All heads: (1/2)^3 = 0.125.All tails: (1/2)^3 = 0.125.At least one of each: 1 - 2(0.125) = 0.75.Hence the distribution for the penny points is:
P(X = -2) = 0.25.P(X = 3) = 0.75.The expected value for the penny points is:
-2 x 0.25 + 3 x 0.75 = 1.75.
When 2 coins are tossed, the probabilities are given as follows:
All heads: (1/2)² = 0.25.All tails: (1/2)² = 0.25.At least one of each: 1 - 2(0.25) = 0.50.Hence the distribution for the nickel points is:
P(X = -2) = 0.5.P(X = 5) = 0.5.The expected value of nickel points is:
E(X) = -2 x 0.5 + 5 x 0.5 = 1.5.
Due to the higher expected value, she should play with the pennies and the third option is correct.
What is the missing information?
The complete problem is given by the image at the end of the answer;
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Answer:
The answer is C
Step-by-step explanation:
edge
Evaluate the exponential expression: (y 3/xy 2)²=_______, if x = 2 and y = 6.
1. 9
2. 36/144
3. 6/144
4. 15
The value of the exponential expressions is 9. Option 1
What is an algebraic expressions?
An algebraic expression can be defined as an expression that is composed of coefficients, variables, terms, constants, and also factors.
These expressions may also consist of arithmetic or mathematical operations such as;
ParenthesesMultiplicationDivisionSubtractionBracketAddition, etcGiven the exponential expression as;
(y³/xy²)²
For when x = 2 and y = 6
We have to substitute the value into the expression, we have;
{(6³/(2)(6)²)}
Find the cube and square of the values, we have;
{ 216/2(36) }²
expand the bracket
{ 216/72}²
Find the quotient
{3}²
Find the square
9
Hence, the value is 9
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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.
a vendor sells hot dogs and bags of potato chips. a customer buys 3 hot dogs and 3 bags of potatochips for $8.25. another customer buys 5 hot dogs and 3 bags of potato chips for $11.25. find thecost of each item.
Cost of one hot dog is and potato chips is
As per the given problem a customer buys 3 hot dogs and 3 bags of potato chips for $8.25. we have to find the cost of each item.
let price of one hot dog is x nd price of potato chips is y.
Formulating the Equation we get
3x+3y=$8.25
another customer buys 5 hot dogs and 3 bags of potato chips for $11.25.
Formulting the Equation we get
5x+3y=$11.25.
we get two linear equation with two unknowns.
solving both equation we get $8.25-3x=$11.25-5x
or 2x=$3
x=$1.5
y=$1.25
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Three students were scheduled to give book reports in 1 hour.
After the first report, 2/3 hour remained (HINT: this means the first persons' report was 1/3 of an hour)
The next report took 1/6 hour. What fraction remained?
The fraction of hour that remained is 1/2 hour.
It is given in the question that three students were scheduled to give book reports in 1 hour.
After the first report, 2/3 hour remained. The next report took 1/6 hour.
We have to find the fraction of hour that remained.
We know that,
Total time for reports = time taken for first report + time taken for second report + time remained for third report
Hence, we can write,
Time taken for first report = 1-2/3 = 1/3 hour
Time taken for second report = 1/6 hour
1 = 1/3 + 1/6 + time remained for third report
1 = 2/6 + 1/6 + time remained for third report
1 = 3/6 + time remained for third report
1-3/6 = time remained for third report
3/6 = 1/2 = time remained for third report
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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! :)
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
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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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.
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
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
Q= (R-M) over 2
R-M/2
R= 21
M= 15
The image best explains, I cannot math and math cannot me, please I need help.
Answer:
3
Step-by-step explanation:
(21-15)/2
6/2
= 3
......
Answer:
3
Step-by-step explanation:
substitute the numbers into the equation Q= (21-15)/2
you then start with the numbers within the parathesis: 21 - 15 = 6
then divide it by 2: 6/2 = 3
answer: Q = 3
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
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 :)
The weather forecast for the weekend is a 35% chance of rain on Saturday and a 65% chance of rain on Sunday. Your friend says that means there is a 100% chance of rain this weekend. What error did your friend make?
Answer:
Because these probabilities are independent, the friend was supposed to multiply them, not add them. So the probability of rain this weekend is
.35 × .65, or .2275, meaning that the probability of rain this weekend is 22.75%
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
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 is 3 +7x(2+9x) simplify as a expression
are 5x^2 and -9x^2 like terms
true or false
Answer:
true
Step-by-step explanation:
when unlike terms are added, they cannot be "combined".
examples of unlike terms: [tex]2x +3[/tex] and [tex]5y - 2[/tex] and [tex]6y^2 - 4x^2[/tex]
[tex]5x^2 and -9x^2[/tex] are like terms because they both contain the variable x and have an exponent of 2.
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
56x raise to power minos 4 divided by 14x raise to power minos 8
56x raise to power minus 4 divided by 14x raise to power minus 8 has its answer calculated as 4[tex]x^2[/tex] by solving through formulas of exponents and powers.
What are exponents?A mark placed exactly or right above a mathematical equation or a numeral that helps to denote the action of raising to a power of something.
Exponent is also defined as one of the methods of expressing many large numbers in terms of powers. This means that exponent refers to how many times a single number or an equation is multiplied by itself.
The statement 56x raise to power minus 4 divided by 14x raise to power minus 8 can be simplified in equational terms as
[tex]\frac{56x^-{4}}{14x^{-8}}[/tex]
which can be further simplified as [tex]4x^{4}[/tex]
What does the term Exponentiation stand for?Exponentiation is a type of mathematical operation that can be written as bⁿ, involving two numbers. The base b and then the exponent or power n is included in it and pronounced as "b to the power n".
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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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A truck can be rented from Company A for $40 a day plus $0.40 per mile. Company B charges $20 a day plus $0.50 per mile to rent the same truck. Find the number of miles in a day at which the rental costs for Company A and Company B are the same.
The number of miles in day at which the rental cost for the company A and Company B are the same is 200 miles
The Company A rented the truck for $40 a day plus $0.40 per miles
The expression will be
40+0.40x
Where x is the number of miles
The company B rented the truck for $20 a day plus $0.50 per miles
20+0.50x
To find the number of miles in a day at which the rental costs for Company A and Company B are the same, the linear equation will be
40+0.40x = 20+0.50x
40-20 = 0.50x-0.40x
0.1x = 20
x = 200 miles
Hence, the number of miles in day at which the rental cost for the company A and Company B are the same is 200 miles
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