The cartesian equation is y=x+1 for the parametric equations x(t)=−8t and
y(t)=−8t+1
What is Cartesian Equation?A cartesian equation for a curve is an equation in terms of x and y only
The two parametric equations are
x=-8t...(1)
y=-8t+1...(2)
Convert the second equation as below.
(1-y)/8=t
Now plug in t= (1-y)/8 in equation 1.
x=-8(1-y)/8=y-1
x=y-1 is one cartesian equation.
Now let us find the other cartesian equation
t=-x/8
Plug in t value in y.
y=-8(-x/8)+1
y=x+1
Hence the cartesian equation is y=x+1 for both parametric equations x(t)=−8t and y(t)=−8t+1
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1cm:10mm into a scale factor
One centimeter is equivalent to 10 millimeters.
Converting the cm to mm
10mm:10mm
The scale factor is 1:1 because the two are equal
Hope this helps :)
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- Jeron
You have invited g people to a party and expect 80% of them to attend. You estimate that your guests will
each eat p pieces of pizza. If each pizza has s slices, how many pizzas do you expect to be eaten?
The number of pizza expected to be eaten is equal to the number of persons that attends the party and this is equal to 0.8gp/s
How to find the number of pizzas that will be eatenFrom the problem it can be deduced that
number of people invited to the party = g
number of people attending
= 80% of people invited to the party
= 80% of g
and 80% = 80 / 100 = 0.8
therefore,
= 0.8g
You estimate that your guests will each eat p pieces of pizza
= 0.8g * p
= 0.8gp
and each pizza has s slices
the number of slices = s
the number of pizza to be taken is 0.8gp/s
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Represent the following sentence as an algebraic expression, where "a number" is the
letter x. You do not need to simplify.
5 is subtracted from the product of 3 and a number.
Answer:
3x -5
Step-by-step explanation:
You want the algebraic expression for "5 is subtracted from the product of 3 and a number".
Product"The product of 3 and a number" is represented by 3x.
SubtractionSubtraction is indicated by a minus sign. When 5 is subtracted from the product, the expression is written ...
3x -5
2
Select the correct answer from the drop-down menu.
A school administrator bought 6 desk sets. Each set consists of one table and one chair. He paid $48.50 for each chair. If he paid a total of $663
for the 6 sets, the cost of each table is
$
54.50
62.00
110.50
159.00
What is exactly 5/12 of a full rotation
Exactly 5/12 of a full rotation is 150, where full rotation is 360.
Define full rotation.A "full rotation," "revolution," "whole turn," or "full circle" describes this. It entails spinning around till you are once again pointing in the same direction. a rotational movement. In rotation, there is a fixed central point around which everything else revolves in a circle. 360° is a "Full Rotation." Each point in a figure is transformed into a rotation by rotating it a specific amount of degrees around another point.
Given,
Number = 5/12
Full rotation = 360
5/12 of full rotation
5/12 × 360
5 × 30
150
Exactly 5/12 of a full rotation is 150, where full rotation is 360.
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HELP ASAP PLS
Simplify the expression.
negative 15 plus the quantity negative 3 and seven tenths plus 9 and 15 hundredths end quantity divided by 5 all times 3 squared minus 4 and 7 tenths
−13.16
−9.89
0.49
20.11
The value of the given expression is -6.93.
How can make the expression simpler?The question's expression is as follows:
minus 15 plus the amount negative 3 and 7 tenths + 9 and 15 hundredths at the end of the number divided by 5 times 3 squared less 4 and 7 tenths results in the answer.
Correctly reformat the expression
Thus, we have
-15 - 3.7 + 9.15/5 * 3^2 - 4.7
Calculate the exponent and quotient.
Thus, we have
-15 - 3.7 + 1.83 * 9 - 4.7
Consider the product
-15 - 3.7 + 16.47 - 4.7
Analyze the difference and the total.
-6.93
Consequently, -6.93 is the value of the supplied equation (none of the options is correct)
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90000000000000000x900000000000000
Answer: 8.1e+31
Step-by-step explanation:
Solve the following equation using the quadratic formula.
3x² = -2x+4
The solution set is
-1±√√44 i 3
(Type an exact answer, using radicals and i as needed. Use a comma to separate answers as needed.)
Solution of equation 3x² = -2x+ 4 using the quadratic formula x = -1± √13/3.
Define quadratic formula.The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the general form ax² + bx + c = 0. where a, b, and c are numerical coefficients and x is an unknown variable. Due to the fact that the Latin word quadratum, which means "square," and the fact that the area of a square with side length x is equal to x², a polynomial equation with exponent two is referred to as a quadratic ("square-like") equation.
Given,
Equation
3x² = -2x+ 4
3x² + 2x - 4 = 0
Using quadratic formula,
x = -2 ± √2²- 4 × 3(-4)/ 2× 3
Simplifying:
x = -2 ± 2√13/6
Equations:
x = -2 + 2√13/6
x = -2 - 2√13/6
x = -1 + √13/3
x = -1 - √13/3
x = -1± √13/3
Solution of equation 3x² = -2x+ 4 using the quadratic formula x = -1± √13/3.
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A club collected $3,472 to buy computers. if each computer costs $680, estimate the number of computers that the club can buy explan
This is how I need to answer it:
Answer: 5 computers
Step-by-step explanation:
You would take the total amount collected and divide it by the cost of a computer.
3472/680=5.10
Since the number is not a whole number you would round down since you can not buy part of a computer. Therefore, the club can only buy 5 computers.
To raise money, the Boy Scouts bought 60 kg of caramels for $130.80. They sold the caramels in 300 g bags for $2.37 each. How much profit did they make?
Francine received a gift card to buy cell
phone apps. She says that the card’s value
is enough to buy any of the apps:
recipes-$9.50, W02 sports-$10.50, or
Remote desktop-$12.00. Let v be the dollar
value of the gift card. Write an inequality
that best describes the value of the gift
Card.
How many apps can Francine buy with the giftcard? Explain
The inequality that best describes the value of the gift card is v ≥ 12
What is inequality?
An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.
The inequality above states that the gift card, v could have $12 or possibly more on it because we know the most expensive app his gift card can buy is $12.
The inequality that best describes the value of the gift card is v ≥ 12
He can buy apps that are worth greater than or equal to $12
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Stefano owns a restaurant where his customers create their own pasta dishes. The customer chooses exactly one type of noodle, sauce, vegetable, and meat. The following table shows the options available to customers.
Create your own pasta
Noodle options Spaghetti, Penne, Linguine
Sauce options Tomato, Rosa, Alfredo
Vegetable options Mushroom, Onion, Green pepper, Tomato
Meat options Steak, Beef, Sausage, Chicken, Bacon
How many different pasta dishes can customers create
1
Given F (0, 2) and G (2,6), if point S lies 1/3 of the way along FG, closer to F than to G, find the
coordinates of S. Leave your answer in fraction form.
The coordinates of S(x₁, y₁)=(3/2 , 5) if F(0, 2) and G(2,6) and the lines divided in the ratio 1:3
What is a section formula?Finding the ratio by which a line segment is divided by a point internally or externally in coordinate geometry is done using the Section formula. The centroid, incenter, and ex center of a triangle are determined using it. Finding systems' centers of mass, equilibrium locations, etc. are all done using this method in physics. Finding the ratio by which a line segment is divided by a point internally or externally in coordinate geometry is done using the Section formula. The centroid, incenter, and ex center of a triangle are determined using it.
Given,
F(0, 2) and G(2, 6)
And also given that the points S lies on the way along FG then:
The lines divides the ratio,
1:3= m:n
Here we have to find the coordinates of S, we get:
S(x₁, y₁)=((mx₁+n x₂)/(m+ n), (my₁+n y₂)/(m+ n))
=((1(0)+3(2))/4 , (1(2)+3(6))/4)
=(6/4 , 20/4)
=(3/2 , 5)
S(x₁, y₁)=(3/2 , 5)
Therefore, the coordinates of S(x₁, y₁)=(3/2 , 5).
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Convert a housing price of $192/ft2 to euro/m². Use the fact that 1 meter (m) = 3.28 ft and assume that 1
euro = $1.225.
Answer:
1686 euro/m²
Step-by-step explanation:
$192/ft² × euro/$1.225 × (3.28 ft)²/(1 m)² = 1686 euro/m²
I will give Brainliest. 50 Point question when I give you Brainliest you will get 100 Points!
The equivalent expressions are:
1. C. 1/15x - 14y
2. B. 2x - 4 - 10x + 15
3. The expression we can use are:
64 + 64(0.015)
4. The expressions that represent the sale price are:
0.7p
p - 0.3p
(1 - 0.3)p
What are Equivalent Expressions?If the simplest form of two expressions have the same value, then they are equivalent expressions.
1. Simplify 2/5x - 3y - 1/5x - 11y by combining like terms to determine the expression that is equivalent to it:
2/5x - 1/5x - 3y - 11y
1/15x - 14y
The answer is: C. 1/15x - 14y
2. Simplify 2(x - 2) - 5(2x - 3), by first opening the parentheses:
2x - 4 - 10x + 15
The equivalent expression is: B. 2x - 4 - 10x + 15
3. The percentage error allowed is 1.5% = 1.5/100 = 0.015.
Therefore, the expression we can use are:
64 + 64(0.015)
4. 30% is, 30/100 = 0.3.
Original price = p = $100.
0.3 of $100 = 0.3(100) = $30
Sale price = 70% of original price = 0.7(100) = $70.
Therefore, the expressions of the sale price of the bicycle are:
0.7p
p - 0.3p
(1 - 0.3)p
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What is the amplitude of the graph of the
function f(x) = -5 cos (x + 2)-5?
Answer:
5
Step-by-step explanation:
The amplitude of the graph of a function of the form [tex]a\cos(bx+c)-d[/tex] is [tex]|a|[/tex].
What is an equation of the line that passes through the points (-8, 5) and (2, 0)?
Answer:
[tex]y=-\frac{1}{2}x+1[/tex]
Step-by-step explanation:
The slope of the line is [tex]\frac{5-0}{-8-2}=-\frac{1}{2}[/tex].
So, the equation is
[tex]y=-\frac{1}{2}(x-2) \\ \\ y=-\frac{1}{2}x+1[/tex]
Prime factorization of 64 + 144 as a product of the GCF and a sum of two numbers.
Answer: 402
Step-by-step explanation:
Use Newton's method to find the absolute maximum value of the function
f(x) = 7x cos(x), 0 ≤ x ≤ ,
correct to six decimal places.
Answer:
Step-by-step explanation:
Newton's method is an iterative method for finding the roots of a function, which means that it can be used to find the values of x that make a function equal to zero. It can also be used to find the maximum or minimum values of a function, but to do so you will need to find the derivative of the function and use that to determine where the maximum or minimum values occur.
The derivative of the function f(x) = 7x cos(x) is f'(x) = 7 cos(x) - 7x sin(x), and you can use this to find the maximum value of the function. To do this, you would need to find the values of x that make the derivative equal to zero, since the maximum or minimum values of a function occur at the points where the derivative is equal to zero.
To find the values of x that make the derivative equal to zero, you can use Newton's method, which involves starting with an initial guess for the value of x, and then using the derivative to find a better approximation for the value of x. This process is repeated until the desired level of accuracy is reached.
In your case, you could start by making an initial guess for the value of x that makes the derivative equal to zero. For example, you could start with x = 0 and then use the derivative to find a better approximation. This process would involve calculating the derivative at the initial guess, and then using that value to find a better approximation for the value of x. This process would be repeated until the desired level of accuracy is reached.
Once you have found the values of x that make the derivative equal to zero, you can plug those values back into the original function to find the maximum value of the function. This will give you the absolute maximum value of the function f(x) = 7x cos(x), 0 ≤ x ≤ , correct to six decimal places.
10. Find x . Round to the nearest tenths place.
11.3
10.7
10.4
11.7
In the given right angled triangle ABC, the value of x is equal to 10.7 (round to the nearest tenths place).
As given in the question,
In the triangle ABC,
Triangle ABC is right angled triangle with ∠C = 90°
Measure of angle A = 68degrees
AC = 4 units
AB = x units
Using trigonometric ratio,
cos 68° = AC / AB
⇒cos 68° = 4 / x
⇒ 0.3746 = 4 / x
⇒ x = 4 / 0.3746
⇒ x = 10.68
⇒ x = 10.7 ( round to the nearest tenths place)
Therefore, in triangle ABC , the value of x is equal to 10.7(round to the nearest tenths place).
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What is √75 in simplified form?
Answer:
The square root of 75 can be written as √75. To simplify this expression, we can use the property that the square root of a product is equal to the product of the square roots of the factors. In this case, we can factor 75 as the product of 25 and 3:
√75 = √(25 x 3)
We can then apply the property of the square root of a product to simplify the expression:
√75 = √(25 x 3) = √25 x √3
We can further simplify the expression by applying the property that the square root of a perfect square is equal to the number itself. Since 25 is a perfect square, we can simplify √25 to 5:
√75 = √(25 x 3) = √25 x √3 = 5 x √3
Therefore, the simplified form of √75 is 5 x √3. This means that the square root of 75 is equal to 5 times the square root of 3.
Step-by-step explanation:
Divide the polynomials.
Your answer should be a polynomial.
x² - 36
x − 6
Answer:
the answer to the division problem is `1x + 6` (a polynomial).
Step-by-step explanation:
To divide polynomials, we use the long division method. Here's how we can divide x² - 36 by x - 6:
x² - 36 |
--------
x - 6
First, we divide the leading coefficient of the numerator (which is 1) by the leading coefficient of the denominator (which is 1).
We get 1 / 1 = 1 as the first coefficient of our quotient.
x² - 36 |
--------
x - 6
1
Then, we multiply the quotient by the denominator and subtract it from the numerator.
We get (1 * (x - 6)) = x - 6, and x² - 36 - (x - 6) = x² - x - 30.
x² - 36 |
--------
x - 6
1
x - 6
----------
x² - x - 30
We repeat the process, dividing the leading coefficient of the new numerator (which is 1) by the leading coefficient of the denominator (which is 1).
We get 1 / 1 = 1 as the next coefficient of our quotient.
x² - 36 |
--------
x - 6
1
x - 6
----------
x² - x - 30
1
We multiply the quotient by the denominator and subtract it from the numerator.
We get (1 * (x - 6)) = x - 6, and x² - x - 30 - (x - 6) = x² - 2x + 24.
x² - 36 |
--------
x - 6
1
x - 6
----------
x² - x - 30
1
x - 6
---------------
x² - 2x + 24
We repeat the process one more time, dividing the leading coefficient of the new numerator (which is 1) by the leading coefficient of the denominator (which is 1).
We get 1 / 1 = 1 as the next coefficient of our quotient.
x² - 36 |
--------
x - 6
1
x - 6
----------
x² - x - 30
1
x - 6
---------------
x² - 2x + 24
1
We multiply the quotient by the denominator and subtract it from the numerator.
We get (1 * (x - 6)) = x - 6, and x² - 2x + 24 - (x - 6) = x² - 3x + 18.
x² - 36 |
--------
x - 6
1
x - 6
----------
x² - x - 30
1
x - 6
---------------
x² - 2x + 24
1
x - 6
------------------
x² - 3x + 18
Since the degree of the new numerator is less than the degree of the denominator, we have found the complete quotient.
So, the quotient is `1x + 6`, and the remainder is `x² - 3x + 18`.
Therefore, the answer to the division problem is `1x + 6` (a polynomial).
Answer:
x + 6
Step-by-step explanation:
[tex]\frac{x^{2} -36}{x-6}[/tex]
[tex]\frac{(x+6)(x-6)}{x-6}[/tex]
x + 6
Please help me this is due today
Answer:
x=20
Step-by-step explanation:
both of these angles equal each other
3x+50=6x-10
-3x. -3x
50= 3x-10
+10 +10
60=3x
/3. /3
20=x
hopes this helps please mark brainliest
Can you please help me from number 13 to 16?
Answer:
Step-by-step explanation:
sorry, i'm not a college student, so i don't know how to answer this.
The perimeter of a rectangle is 40 inches. Find the length and width if the length is an integer and the width is 2 times the next consecutive integer. Length = Width =
The values are;
Length = 6 inches
Width = 14 inches
How to determine the valuesThe formula for determining the perimeter of a rectangle is expressed as
P = 2( l + w)
Where;
P is the perimeterl is the lengthw is the widthFrom the information given, we have;
Length = x
Width = 2(x + 1) = 2x + 2
Now, substitute the values
40 = 2( x + 2x + 2)
expand the bracket
40 = 2(3x + 2)
40 = 6x + 4
collect like terms
6x = 40 - 4
6x = 36
x = 36/6
Divide the values
x = 6 inches
Length = 6 inches
Width = 2( 6 + 1) = 2(7) = 14 inches
Hence, the values are 6 and 14 inches
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The values are;
Length = 6 inches
Width = 14 inches
How to determine the values
The formula for determining the perimeter of a rectangle is expressed as
P = 2( l + w)
Where;
P is the perimeter
l is the length
w is the width
From the information given, we have;
Length = x
Width = 2(x + 1) = 2x + 2
Now, substitute the values
40 = 2( x + 2x + 2)
expand the bracket
40 = 2(3x + 2)
40 = 6x + 4
collect like terms
6x = 40 - 4
6x = 36
x = 36/6
Divide the values
x = 6 inches
Length = 6 inches
Width = 2( 6 + 1) = 2(7) = 14 inches
Hence, the values are 6 and 14 inches
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Which of the following is the most likely the next step in the series?
Answer: C is the correct answer!I don't feel like explaining. sorry.Please let me know if I am wrong.
y=−2x+4 (left parenthesis ,-2)
The equation y = 2x + 4 has the following missing value: 3.
What is an equation's solution?The x and y values of an ordered pair whose values, if substituted into the equation, would make it true are the answer to the given equation.
According to the Given information
If the value of x is the missing value in the solution to the equation y = -2x + 4, and the solution is (x, -2) Hence, by adding y = -2 to the equation and solving for x, the value of x can be found:
-2 = -2x + 4
Take 4 away from both sides.
-2 - 4 = -2x + 4 - 4 (subtraction property of equality)
-6 = -2x
Add -2 to both sides.
-6/-2 = -2x/-2
3 = x
x = 3
The equation y = 2x + 4 has the following missing value: 3.
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Suppose that the functions g and h are defined for all real numbers X as follows.
g(x)=x+2
h(x)=3x-3
Write the expressions for (h-g)(x) and (h+g)(x) and evaluate (h.g)(1).
Fehmen
If the two functions be g(x) = x + 2 and h(x) = 3x - 3 then
(h - g)(x) = 2x - 5
(h + g)(x) = 4x - 1
(h . g)(1) = 3x² + 3x - 6
What is meant by expression ?A phrase is considered a mathematical expression if it contains at least two numbers or variables and one or more mathematical operations. Mathematicians can multiply, divide, add, or subtract. An expression is structured as follows: (Math Operator, Number/Variable, Math Operator) is an expression.
Mathematical expressions are built using the addition, subtraction, multiplication, and division operations.
Let the two functions be g(x) = x + 2 and h(x) = 3x - 3
(h - g)(x) = h(x) - g(x)
substitute the value expressions in the above equation, we get
= (3x - 3) - (x + 2)
= 2x - 5
(h + g)(x) = h(x) + g(x)
= (3x - 3) + (x + 2)
= 4x - 1
(h . g)(1) = h(1) . g(1)
= (3x - 3) . (x + 2)
= 3x² + 3x - 6
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Mrs. Saunders bought a 19 pound turkey for Thanksgiving. The total cost of the turkey was $25.65. What was the cost of turkey per pound? Write an equation to represent the situation
The cost of turkey per pound is $1.35 and the equation which represents the situation is 19x - 25.65 = 0.
What is the linear equation?
An algebraic equation of the form y=mx+b is referred to as a linear equation. m is the slope, and b is the y-intercept, and all that is involved is a constant and a first-order (linear) term. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
We have,
19 turkey pound
$25.65
the cost of turkey per pound?
so,
25.65 / 19 = 1.35
the cost of turkey per pound is $1.35.
The equation becomes:
let's take x = $1.35
19x - 25.65 = 0
Hence, the cost of turkey per pound is $1.35 and the equation which represents the situation is 19x - 25.65 = 0.
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It takes 10 pounds of tomatoes to make 3 cups of tomato paste.
Type the answers in the boxes below.
1. At this rate, how many cups of tomato paste can be made with 25 pounds of tomatoes?
cups of tomato paste
2. At this rate, how many pounds of tomatoes are needed to make 14 cups of tomato paste?
pounds of tomatoes
7.5 cups of tomato paste can be made from 25 pounds and 14 cups can make 46.67 pounds.
What is unitary method?The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
Given, it takes 10 pounds to make 3 cups of tomato paste.
Thus, with 1 pound, number of cups can be made is equal to (3/10) cups
Thus, using 25 pounds, number of cups can be made is equal to
(3/10)*25
= 7.5 cups
3 cups of tomato paste can be made from 10 pounds
1 cup of tomato paste can be made from (10/3) pounds
14 cups of tomato paste can be made from
(10/3)*14
= 46.67 pounds
Thus, 7.5 cups of tomato paste can be made from 25 pounds and 14 cups can make 46.67 pounds.
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