Answer:
C. 5x²-7x-8
Step-by-step explanation:
(-3x²-5x +1 ) + (8x²-2x-9)
Grouping like terms:
(- 3x² + 8x²) + (- 5x - 2x) + (1 - 9)
=> (5x²) + (-7x) + (-8)
=> 5x² - 7x - 8
Diana wants to build a rectangular
pen for her goats. The length of the pen
should be at least 50 feet, and the perimeter
of the pen should be no more than 190 feet.
What is a viable solution for the dimensions
of the pen? (Lesson 6-5)
A. 29 feet by 40 feet
B. 29 feet by 76 feet
C. 29 feet by 65 feet
D. 29 feet by 29 feet
Copyright © McGraw Hill
Answer:
29 feet by 40 feet to get a viable dimension for the goats pen
which number line shows the solution to x + 8 > 15
7 is not included and hence it is depicted on the number line using an open dot. Hence, solution to the inequality is option B.
What is inequality?In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign (≠)" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.
The given inequality is:
x + 8 > 15
Subtracting 8 on both sides of the equation:
x + 8 - 8 > 15 - 8
x > 7
Here, 7 is not included and hence it is depicted using an open dot.
Hence, option B is the correct answer.
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4x
Store A $25 for a 45 minute lesson
Store B. $30 for a 1 hour lesson
Store C $45 for a 1.5 hour lesson
Store D. $80 for three 1 hour lessons
Julle wants to purchase swim lessons for her son. There are four different stores that offer swim lessons. Based on the lowest cost per minute, which store has the BEST dea
4x A
4x B
x
C
4x D
Store B
Store A
Store D
Store C
The store with the best deal is given as follows:
Store D.
How to obtain the store with the best deal?The store with the best deal is obtained applying the proportions in the context of the problem.
The best deal is the store with the lowest cost per hour, and the cost per hour is obtained dividing the total cost by the number of hours.
Hence the hourly cost for each store is obtained as follows:
Store A: 25/0.75 = $33.3 per hour. (45 minutes = 45/60 hour = 0.75 hour).Store B: $30/1 = $30 per hour.Store C: $45/1.5 = $30 per hour.Store D: $80/3 = $26.7 per hour -> best deal.More can be learned about proportions at https://brainly.com/question/24372153
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Write an equation of the circle graphed below
Answer:
Below
Step-by-step explanation:
Center (h,k) is - 2, -2 radius is 1
Equation for a circle with center (h,k) and radius r is :
(x-h)^2 + (y- k )^2 = r^2 <====you have to learn/remember this
Plug in the values above to get
(x+2)^2 + (y+2)^2 = 1
Answer:
(x+2)^2+(y+2)^2=0.5625
Step-by-step explanation:
trust
What is the volume 
Answer:
384 cm
Step-by-step explanation:
The terminal side of θ in standard position contains the point (–14, 0). Find the exact values of the six trigonometric functions of θ.
sin(θ) =
cos(θ) =
tan(θ) =
csc(θ) =
sec(θ) =
cot(θ) =
The exact values of the six trigonometric functions of θ are:
sin(θ) = 0
cos(θ) = -√2/2
tan(θ) = 0
csc(θ) = undefined
sec(θ) = -√2
cot(θ) = undefined
The given point (-14,0) lies on the x-axis in the negative x-axis direction. Drawing a line from the origin to this point creates a right triangle with the hypotenuse being the line from the origin to (-14,0), the opposite side being the y-coordinate of (-14,0), and the adjacent side being the x-coordinate of (-14,0). The length of the hypotenuse can be found using the Pythagorean theorem:
h^2 = (-14)^2 + 0^2
h^2 = 196
h = 14√2
Using the definitions of the six trigonometric functions in terms of the opposite, adjacent, and hypotenuse sides of a right triangle, we can find the exact values of these functions for θ:
sin(θ) = opposite/hypotenuse = 0/14√2 = 0
cos(θ) = adjacent/hypotenuse = -14/14√2 = -√2/2
tan(θ) = opposite/adjacent = 0/-14 = 0
csc(θ) = 1/sin(θ) = undefined (since sin(θ) = 0)
sec(θ) = 1/cos(θ) = -√2
cot(θ) = 1/tan(θ) = undefined (since tan(θ) = 0)
Therefore, the exact values of the six trigonometric functions of θ are:
sin(θ) = 0
cos(θ) = -√2/2
tan(θ) = 0
csc(θ) = undefined
sec(θ) = -√2
cot(θ) = undefined
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hand consists of 3 cards from a well-shuffled deck of 52 cards.
a. Find the total number of possible 3-card poker hands.
b. A black flush is a 3-card hand consisting of all black cards. Find the number of possible black flushes.
c. Find the probability of being dealt a black flush.
a)
The total number of possible 3-card poker hands is 22100
b)
The number of possible black flushes is 2600
c)
The probability of being dealt a black flush is 0.1176
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
We have,
Number of cards = 52
Number of cards in hand = 3
Combination formula.
[tex]^nC_r[/tex] = n! / r! (n -r)!
a)
The total number of possible 3-card poker hands.
= [tex]^{52}C_3[/tex]
= (52 x 51 x 50) / (3 x 2)
= 22100
b.
Number of black cards (spades and clubs) = 13 + 13 = 26
The number of possible black flushes.
= [tex]^{26}C_3[/tex]
= (26 x 25 x 24) / (3 x 2)
= 2600
c.
The probability of being dealt a black flush.
From (a) and (b)
= 2600/22100
= 0.1176
Thus,
The total number of possible 3-card poker hands = 22100
The number of possible black flushes = 2600
The probability of being dealt a black flush = 0.1176
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A sprinter starts from rest, and accelerates at 1.87 m/s^2 over a distance of 14.0 m. What is a her final velocity?
6 There are 2 blue chips for every 3 red chips. If there are 20 total chips, how many blue chips and red chips are in the bucket?
Answer:
12 blue chips 8 red chips.
Step-by-step explanation:
Let's call the number of blue chips "b" and the number of red chips "r". We know that 2 blue chips for every 3 red chips, so we can set up the following equation:
2b = 3r
And we know that there are 20 total chips, so:
b + r = 20
Now we can use substitution to find the value of b. We'll substitute the expression for r from the first equation:
2b = 3(20 - b)
Expanding the right side:
2b = 60 - 3b
Combining like terms:
5b = 60
And finally, solving for b:
b = 12
So there are 12 blue chips and 20 - 12 = 8 red chips.
The ratio 1500:1200 in its lowest terms is
Answer:
Step-by-step explanation:
To put a ratio in its lowest terms, we need to divide both terms of the ratio by their greatest common divisor (GCD). The GCD of 1500 and 1200 is 300, which is the largest number that divides both numbers evenly.
Dividing both terms of the ratio by 300, we get:
1500 / 300 : 1200 / 300 = 5 : 4
So, the ratio 1500:1200 in its lowest terms is 5:4.
Question 4 of 10
Which of the following is a root of the polynomial shown below?
f(x) = x³ + 2x²-x-2
OA. 0
OB. 2
O C. 1
OD. 3
SUBMIT
Answer:
1
Step-by-step explanation:
f(x)=x3+2x2-x-2
...................
The Roots of the given polynomials shown below f(x) = x^3+2x^2-x-2 are -1, 1, -2.
What is a polynomial?They are mathematical expressions involving variables raised with non negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and nonnegative exponentiation of variables involved.
Example: x² + 3x + 3 is a polynomial.
Since, The given polynomials is,
f(x) = x³ + 2x²-x-2
Now, Solve as;
f(x) = x³ + 2x²-x-2
f (x) = x² (x + 2) - 1 (x + 2)
f (x) = (x² - 1) (x + 2)
Hence, The Roots of the polynomials : -1, 1, -2
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A flower garden is shaped like a circle. Its diameter is 30yd. A ring-shaped path goes around the garden. The width of the path is 5yd. The gardener is going to cover the path with sand. If one bag of sand can cover 6yd, how many bags of sand does the gardener need? Note that sand comes only by the bag, so the number of bags must be a whole number. (Use the value 3.14 for pi.)
The number of bags of sand that has to be used would be 92
How to solve for the bags of sanddiameter = 30 yards
width of path = 5 yards
diameter with path
30 + 2 * 5
= 40 Yd
area of path = area of garden with path - ara of garden
= 3.14 * 40² / 4 - 3.14 * 30² / 4
= 1256 - 706.5
= 549.5
area covered by bag = 549.5 / 6
= 91.58
= 92 bags
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If X and Y are independent and identically distributed uniform random variables on (0, 1), compute the joint density of
(a) U = X + Y, V = X/Y
(b) U = X, V = X/Y
(c) U = X + Y, V = X/(X+Y)
If X and Y are independent and identically distributed uniform random variables on (0, 1), then the joint density of
(a) U = X + Y, V = X/Y is u/v² for v > 1 and 0 ≤ u ≤ 1.
(b) U = X, V = X/Y is 1/v for v > 1 and 0 ≤ u ≤ 1.
(c) U = X + Y, V = X/(X+Y) is v/(1+v)² for v > 0 and v/(1+v) ≤ u ≤ 1.
In probability theory, joint density is a mathematical function that describes the probability distribution of two or more random variables. It represents the probability of occurrence of different values of those variables in a particular region of space. In this problem, we have to calculate the joint density of U and V, where U and V are functions of X and Y.
(a) For U = X + Y and V = X/Y, we can find the joint density as follows:
First, we need to find the distribution of U and V separately. Since X and Y are independent and identically distributed uniform random variables on (0, 1), their individual probability density functions are f(x) = 1 for 0 ≤ x ≤ 1.
To find the density of U, we can use the convolution formula, which states that the density of the sum of two independent random variables is the convolution of their individual densities. Thus,
fU(u) = ∫ fX(u - y)fY(y) dy
= ∫ 1 dy
= u for 0 ≤ u ≤ 1.
Next, to find the density of V, we need to transform X and Y using the change of variables formula. Let Z = X/Y, then
fV(v) = fZ(z)|dz/dv|
= fX(vz)/(z²) |z|
= 1/(v²) for v > 1.
Therefore, the joint density of U and V is given by the product of their individual densities:
fUV(u,v) = fU(u) fV(v)
= u/v² for v > 1 and 0 ≤ u ≤ 1.
(b) For U = X and V = X/Y, we can similarly find the joint density as:
fUV(u,v) = fX(u) fV(v)
= 1/v for v > 1 and 0 ≤ u ≤ 1.
(c) For U = X + Y and V = X/(X+Y), we can use the same method as in (a) to find the individual densities of U and V:
fU(u) = u for 0 ≤ u ≤ 1,
fV(v) = v/(1+v)² for v > 0.
Then, the joint density of U and V is given by:
fUV(u,v) = fU(u) fV(v) |du/dx|
= v/(1+v)² for v > 0 and v/(1+v) ≤ u ≤ 1.
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Which decimal is represented by the red portion of the picture?
Answer:
D
Step-by-step explanation: I did it
Only using positive exponents, what is the simplified form of the expression p−6q7r/p2q−2
Step-by-step explanation:
Here is it. I hope it will help
Looking for answer key to Gina Wilson All Things Algebra Unit 3 Parallel and Perpendicular Lines Homework 5 Slopes of lines; Parallel and Perpendicular Lines
It's important to work through the problems yourself to improve your understanding and problem-solving skills.
For the unit 3 homework on parallel and perpendicular lines, you should have learned about the slope of lines, how to find the slope of a line given two points, and the relationship between parallel and perpendicular lines.
To find the slope of a line given two points, you can use the slope formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are the coordinates of the two points on the line.
To determine if two lines are parallel, you can compare their slopes. Parallel lines have the same slope.
To determine if two lines are perpendicular, you can use the fact that the product of their slopes is -1. That is, if m1 and m2 are the slopes of two lines, and m1 * m2 = -1, then the lines are perpendicular.
It's important to practice working through problems using these concepts and formulas to develop your skills and understanding. Additionally, you can seek assistance from your teacher or tutor if you have specific questions or concerns.
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Let (8,-6) be a point on the terminal side of an angle 0 in standard position. Find the exact value of cos 0.
The exact value of cosine is 4/5
How to determine the exact value of cosineFrom the question, we have the following parameters that can be used in our computation:
(8,-6) be a point on the terminal side of an angle
Using the above as a guide, we have the following:
Cos(angle) = x/(√x² + y²)
In this case
x = 8 and y = -6
substitute the known values in the above equation, so, we have the following representation
Cos(angle) = 8/(√8² + (-6)²)
So, we have
Cos(angle) = 8/10
Simplify
Cos(angle) = 4/5
Hence, the value is 4/5
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Simplify this radical.
O 13√x
O 6x√x
O x√√x¹2
O x√x
6. Part D
Another method of proving diagonals of a parallelogram bisect each other
uses a coordinate grid.
A.
P (r, t)
S (0, 0)
R (s, 0)
What could be shown about the diagonals of parallelogram PQRS to com
the proof?
PR and SQ have the same length.
PR is a perpendicular bisector of SQ.
PR and SQ have the same midpoint.
D. Angles formed by the intersection of PR and SQ each measu
B.
Q
(r+s, t)
Answer:
PR and SQ have the same midpoint.
Step-by-step explanation:
PR and SQ have the same midpoint.
A function is given.
g(x) =
2
x
; x = 1, x = a
(a) Determine the net change between the given values of the variable.
(b) Determine the average rate of change between the given values of the variable.
According to the given function net change and average rate of change between the given values of the variable.
A. 2
B. 2/a
What is the net change?A rate of change's integral is taken into account by the net change theorem. According to this, a quantity's new value equals its initial value plus the integral of its rate of change whenever it changes. There are two methods to formulate the equation. The second is more widely known and is just the definite integral.
What does a function's net change look like?The (definite) integral of a function's derivative, in other words, represents the overall change in a function. In specifically, the integral of velocity is the net distance travelled (final position minus initial position). The integral of acceleration is the difference between the final velocity and the starting velocity.
According to the given information:g(x) =2/x
x = 1
x = a
A.
g(x) =2/x
g(1) =2/x
g(1) =2
B.
g(x) =2/x
g(a) =2/x
g(a) =2/a
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Mary plans to buy a kettle for R180-00, excluding vat.vat is charged at 15%.what is the total cost of the kettle vat is added
Answer:
R207
Step-by-step explanation:
R180 times 15% =27
27+180=207, therefore, R270 ir correct
Multiply. (Simplify your answer
(-5y4z)(-7y6z³)
Answer:
35y^(10)z^(4)
Step-by-step explanation:
Solution Given:
(-5y^(4)z)(-7y^(6)z³)
Here while opening bracket
If their is like terms they can be multiplied ,divided,subtracted as well as added.
So
Here
opening bracket and keeping in serially
-5*-7*y^(4)*y^(6)*z*z^(3)
here if their is like terms their power is added.
And solving remaining one.
35y^(4+6)z^(1+3)
Here -5*-7=35
Again
Solving it.
35y^(10)z^(4)
Answer:
[tex]35y^{10}z^4[/tex]
Step-by-step explanation:
Given expression:
[tex](-5y^4z)(-7y^6z^3)[/tex]
Apply the rule: (-a) · (-b) = ab
[tex]\implies 5y^4z \cdot 7y^6z^3[/tex]
Multiply the numbers: 5 · 7 = 35
[tex]\implies 35y^4zy^6z^3[/tex]
Collect like terms:
[tex]\implies 35y^4y^6z^3z[/tex]
[tex]\textsf{Apply exponent rule:} \quad a^b \cdot a^c=a^{b+c}[/tex]
[tex]\implies 35y^{(4+6)}z^{(3+1)}[/tex]
Simplify the exponents:
[tex]\implies 35y^{10}z^4[/tex]
The inequality of the form |x-a| k that has the solution set (5,13) is
The inequality is |x-9| ≥ 4, and its solution set is (5,13).
What is inequality?An Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
The inequality of the form |x-a| ≥ k means that the distance between x and a is greater than or equal to a certain value, k.
If the solution set is (5,13), it means that x is a number between 5 and 13, but not including 5 or 13. In other words, 5 < x < 13.
To find the value of a and k, we need to look for the midpoint of the solution set, which is (5+13)/2 = 9.
The distance between 9 and either endpoint (5 or 13) is 4, which is the value of k.
Thus, the inequality is |x-9| ≥ 4, and its solution set is (5,13).
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Solve the quadratic equation by the square root method and write the solution in radical form. simplify the solution. 4y^2=80
Answer:
[tex]y=\pm2\sqrt{5}[/tex]
Step-by-step explanation:
[tex]4y^2=80\\y^2=20\\y=\pm\sqrt{20}\\y=\pm2\sqrt{5}[/tex]
The square root method for solving a quadratic equation involves isolating the squared term, and then taking the square root of both sides of the equation.
Starting with the equation 4y^2 = 80, we can isolate the squared term by dividing both sides of the equation by 4:
y^2 = 20
Next, we take the square root of both sides of the equation:
y = ±√20
The solution in radical form is y = ±√20. To simplify the radical, we can factor 20 into 2 * 10. Then, we can simplify the square root as follows:
y = ±√2 * √10 = ±2√10
So, the simplified solution is y = ±2√10.
A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 65% salt and Solution B is 90% salt. She wants to obtain 130 ounces of a mixture that is 70% salt. How many ounces of each solution should she use?
On solving the provided question we can say that equations are = .60x + .85y = .75(180)
What is equation?A mathematical equatiοn is a formula that joins two statements and uses the equal symbol (=) tο indicate equality. A mathematical statement that establishes the equality of twο mathematical expressiοns is known as an equation in algebra. Fοr instance, in the equatiοn 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart.
The relationship between the twο sentences on either side of a letter is described by a mathematical formula. Often, there is οnly one variable, which also serves as the symbοl. for instance, 2x – 4 = 2.
t x = the number of ounces of Sοlution A
y = the number of ounces of Sοlution B
x + y = 180
y = 180 - x
Solving equation -
0.60 + 0.85y = 0.75(180)
0.60 + 0.85y = 135
60x + 85y = 13500
60x + 85(180-x) = 13500
60x + 15300 - 85x = 13500
-25x = -1800
x = 72ounces
y = 180 - 72
y = 108 ounces
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Solve 4 x + 16 = y for x if y = 35
Answer:
Below
Step-by-step explanation:
So you have this:
4x + 16 = 35 subtract 16 from both sides of the equation
4x = 19 Divide by 4
x = 19/4
Answer:
The value of x is
[tex]x = 4.75[/tex]
Step-by-step explanation:
Greetings!!!
Given expression [tex]4x + 16 = y[/tex]Thus, the value of y is given as 35, substitute known value of y in expression and solve for x.
[tex]4x + 16 = 35[/tex]
Move the constant to the right
[tex]4x = 35 - 16 \\ 4x = 19[/tex]
Divide both sides of the expression by 4
[tex] \frac{4x}{4} = \frac{19}{4} [/tex]
solve
[tex]x = \frac{19}{4} [/tex]
or
[tex]x = 4 \frac{3}{4} [/tex]
or
[tex]x = 4.75[/tex]
Hope it helps!!!
Line CD passes through points (0, 2) and (4, 6). Which equation represents line CD?
Oy=2x-2
Oy = 2x + 2
Oy=x+2
Oy=x-2
The required equation of the line representing line CD is y = x + 2. Option C is correct.
The equation of the line passing through two points is given by the equation,
y - y₁ = (y₂ - y₁) / (x₂ - x₁) (x - x₁) - - - -- -(1)
Here,
Line CD passes through points (0, 2) and (4, 6)
Let (0, 2) and (4, 6) equal to (x₁, y₁) and (x₂, y₂) respectively.
Substitute this point in equation 1 to get the equation of the line representing CD,
So,
y - 2 = (6 - 2)/(4-0) (x - 0)
y = x + 2
Thus, the required equation of the line representing line CD is y = x + 2. Option C is correct.
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show that the following function are continuos and discontinuos
A.(f×)={×+1 ,for×less than or equai to 2
{ 2×–1 ,for 1<×<2
{×–1 ×<1
f(x) is discontinuous.
Since LHS ≠ RHS ≠ f(x).
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
f(x) = x + 1, for x ≤ 2
f(x) = 2x - 1, for 1 < x < 2
f(x) = x - 1, for x < 1
Now,
A x = 1
LHS of f(x) = [tex]\lim_{x\to1^-}[/tex] f((h - 1)) = [tex]\lim_{h \to 0}[/tex] (h - 1 - 1) = 0 -2 = -2
RHS of f(x) = [tex]\lim_{x\to1^+}[/tex] f(h + 1) = [tex]\lim_{h \to 0}[/tex] (2(h + 1) - 1) = 2h + 2 - 1 = 0 + 1
f(1) = x + 1 = 1 + 1 = 2
We see that,
LHS ≠ RHS ≠ f(x)
So,
f(x) is not continuous, it is discontinuous.
Thus,
f(x) is discontinuous.
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The complete question.
Show that the following functions are continuous or discontinuous at x = 1.
f(x) = x + 1, for x ≤ 2
f(x) = 2x - 1, for 1 < x < 2
f(x) = x - 1, for x < 1
At the 2022 Winter Olympics, one country won a total of 150 medals. A circle graph of the medals is shown.
a circle graph titled 2022 Winter Olympic Medals, with three sections labeled gold 20 percent, silver 30 percent, and bronze 50 percent
How many gold and bronze medals were won?
50
70
105
120
Answer:
120
Step-by-step explanation:
The total number of medals won is 150, and the circle graph shows that the proportion of medals won as gold is 20 percent, as silver is 30 percent, and as bronze is 50 percent.
To find the number of gold and bronze medals won, we need to calculate the total number of medals won in each category by multiplying the total number of medals by the proportion of medals won in each category.
Gold medals: 150 * 20% = 30
Bronze medals: 150 * 50% = 75
So, a total of 30 + 75 = 105 medals were won as gold and bronze.
DATE
10. If you laid the radius end to end around the circumference of a circle A, how many radii would
it take to fit exactly?
Answer:
Step-by-step explanation:
Step 1: Understand the formula for the circumference of a circle
The formula for the circumference of a circle is given by:
C = 2 * π * r
where C is the circumference of the circle, π (pi) is a mathematical constant approximately equal to 3.14, and r is the radius of the circle. This formula expresses the relationship between the radius and the circumference of a circle.
Step 2: Substitute the radius of the circle for "r" in the formula
Let's say the radius of the circle is "r". Substitute "r" for "r" in the formula for the circumference:
C = 2 * π * r
Step 3: Divide the circumference by the radius
Now that you have the formula for the circumference, divide the circumference by the radius:
C/r = 2 * π
Step 4: Simplify the expression
The expression on the right side of the equation can be simplified to 2 times pi:
C/r = 2 * π
C/r = 2 * 3.14 = 6.28
Step 5: Conclusion
Therefore, it would take 6.28 radii laid end to end to fit exactly around the circumference of the circle.
Note: This answer is only an approximation, as the value of π is an irrational number that cannot be expressed exactly as a fraction or a decimal.
