The Solution.
Assuming the radius is 1.
[tex]x=\cos (\frac{3\pi}{4})=-\sin (\frac{3\pi}{4})[/tex]Therefore,
[tex]\begin{gathered} x=-y \\ or \\ y=-x \end{gathered}[/tex]So, the correct answer is option D
c-884= -853solve for c
c-884= -853
solve for c
that means Isolate the variable c
so
step 1
Adds 884 both sides
c-884+884=-853+884
simplify
c=31You invested $5000 between two accounts paying 7% and 8% annual interest. If the total interest earned for the year was $380, how much was invested at each rate?
Let x be the amount invested in the account paying 7% and y the amount invested in the account paying 8%, then we can set the following system of equations:
[tex]\begin{gathered} x+y=5000 \\ 0.07x+0.08y=380 \end{gathered}[/tex]Solving the first equation for x and substituting it in the second equation we get:
[tex]0.07(5000-y)+0.08y=380[/tex]Solving for y we get:
[tex]\begin{gathered} 350-0.07y+0.08y=380 \\ 0.01y=30 \\ y=3000 \end{gathered}[/tex]Substituting y=3000 in the first equation and solving for x we get:
[tex]\begin{gathered} x+3000=5000 \\ x=2000 \end{gathered}[/tex]Therefore, $2000 was invested in the account paying 7%, and $3000 was invested in the account paying 8%.
HW Score: 77 Score: 0 of 1 pt 15 of 18 (15 complete) v X 7.3.43 On a world globe, the distance between Chy A and Cycles that are actually 10.730 kilometers apart, is 132 inches. The actual distance between City C and City Dis 1500 kilometers How far apart are this globe? chy C and Cny D are inches apart on this giebe (Type an integer ordenalpadd to the manded) More Enter you are All parts showing Type here to search
13.2 inches is. 10,730
1500 km , how far apart are
Find X= (1500/10,730) = 150/1073= 0.14
then multiply by 13.2
13.2X = 1.85
Then ,in a globe , distance between C and D cities is 1.85 inches
Answer is 1.85 inches
determine whether the equation below has a one solutions,no solutions, or an infinite number of solutions. afterwards, determine two values of x that support your conclusion.x-4=4-x
x - 4 = 4 - x
4 is subtracting on the left, then it will add on the right
x is subtracting on the right, then it will add on the left.
x + x = 4 + 4
2x = 8
2 is multiplying on the left, then it will divide on the right
x = 8/2
x = 4
So, there is only one solution
Evaluate the expression when a =3 and x = - 5-8a + x
We have an expression:
[tex]-8a+x[/tex]We have to evaluate it when a = 3 and x = -5. To do that we replace a and x by its values and calculate:
[tex]\begin{gathered} -8(3)+(-5) \\ -24-5 \\ -29 \end{gathered}[/tex]Answer: the expression value is -29
14. What property is used to show that 3(4-6) = 12-18?
Answer:
Distribution property method
Solve for a 76=4/5a+16
Answer:
a=75
Step-by-step explanation:
76=4/5a+16
first get the a term by itself on one side
76-16=4/5a
simplify
60=4/5a
now divide both sides by 4/5 or multiply by 5/4(its the same thing)
60*5/4=4/5a*5/4
now simplify
75=a
Let angle D be an acute angle and tan D = 0.72 . Use technology to approximate the measure of D to the nearest 10th of a degree.
D=35.8 °
Explanation
Acute angles measure less than 90 degrees, to solve this we need to use a calculator
Step 1
a) let
[tex]\begin{gathered} angle\text{ =D} \\ tan\text{ angle = }tan\text{ D=0.72} \end{gathered}[/tex], b) now, use the inverse tan function to isolate D
[tex]\begin{gathered} tan\text{ D=0.72} \\ inverse\text{ tan function in both sides} \\ \tan^{-1}(tan\text{ D\rparen=}\tan^{-1}(\text{0.72\rparen} \\ D=35.75388 \\ rounded \\ D=35.8\text{ \degree} \end{gathered}[/tex]so, the answer is
D=35.8 °
I hope this helps you
One number is five more than three times another. If their sum is increased by one, the result is twenty-six. Find the numbers.The smaller of the numbers is ? and the larger is ? .
Let:
x = The smaller number
y = The larger number
[tex]y=3x+5_{\text{ }}(1)[/tex][tex]x+y+1=26_{\text{ }}(2)[/tex]Replace (1) into (2):
[tex]x+3x+5+1=26[/tex]Add like terms:
[tex]4x+6=26[/tex]Solve for x:
[tex]\begin{gathered} 4x=26-6 \\ 4x=20 \\ x=\frac{20}{4} \\ x=5 \end{gathered}[/tex]Replace x into (1):
[tex]\begin{gathered} y=3(5)+5 \\ y=20 \end{gathered}[/tex]Answer:
The smaller number is 5
The larger number is 20
Which expression fits this description? • The expression is the quotient of two quantities. • The numerator of the expression is the product of 5 and the sum of x and y. • The denominator is the product of negative 8 and x. 5x + y 5(x + y) - (8 + x) 5x + y –8+x 5(x + y) -82 - 8x Done -
Given the word problem:
The numerator of the expression is the product of 5 and the sum of x and y and The denominator is the product of negative 8 and x.
The numerator will be the value on top in a fraction.
Here, the numerator is the product of 5 and the sum of x and y ==> 5(x + y)
The denominator is the value below in a fraction.
Here, the denominator is the product of negative 8 and x ==> -8x
Therefore, the expression that fits this description is:
[tex]\frac{5(x+y)}{-8x}[/tex]Suppose f(x)= 2+4x^2.Simplify as much as possible: f(1)/f(2)= ______
Given,
The expression is,
[tex]f(x)=4x^2+2[/tex]Taking x =1,
Subsituting the value of x in the given function then,
[tex]\begin{gathered} f(1)=4(1)^2+2 \\ =4\times1+2 \\ =4+2 \\ =6 \end{gathered}[/tex]Taking x =2,
Subsituting the value of x in the given function then,
[tex]\begin{gathered} f(2)=4(2)^2+2 \\ =4\times4+2 \\ =16+2 \\ =18 \end{gathered}[/tex]Divide f(1) by f(2) then,
[tex]\frac{f(1)}{f(2)}=\frac{6}{18}=\frac{1}{3}[/tex]Hence, the simplified value is 1/3.
I get 15 percent discount at a store if I find a I like for 40 how much will I have to pay for it
price: $40
Given that you get a 15% discount, you get a discount of $40*15% = $6.
Then, you have to pay $40 - $6 = $34
G is located at (0, 4)What are the coordinates of G' after G undergoes the translation (x,y)-> (x-5,y+2)?
Applying the translation rule:
G(0, 4) → (0-5, 4+2) → G'(-5, 6)
Consider the functions f(x)=4-X^2 and g(x)=3x+5.Find the value of f(g)g-2))).
Solution
First find the g(x)
g(-2)= 3(-2) +5
g(-2)= -6+5
g(-2)= -1
substitute for x in f(x) when x is -1
[tex]\begin{gathered} F(-1)=4-(-1)^2 \\ F(-1)\text{ = 4-1} \\ F(-1)\text{ =3} \end{gathered}[/tex]The correct option is the last option
Find the area of this circle please…Use 3 for pi
Given:
The radius of circle is 11 inch
The value for pi is 3
The objective is to find the area of the circle.
The area of the circle is given by the formula:
[tex]A=\pi\times r^2^{}[/tex]Substituting ,r = 11
[tex]\pi=3[/tex]We get:
[tex]\begin{gathered} A=\pi\times r^2 \\ =3\times(11)^2 \\ =3\times121 \\ =363 \end{gathered}[/tex]Hence, the area of the circle is 363 square inches
Help with this question please!!What are the coordinates of the vertex?
The coordinates of the vertex are:
[tex](-2,-4)[/tex]Debra brought a desk on sale for $438. This price was 73% of the original price. What was the original price
Let x = the original price of the desk.
It's known that 73% of the price is $438, thus:
[tex]\frac{73}{100}x=438[/tex]Multiplying by 100 and dividing by 73:
[tex]x=\frac{100\cdot438}{73}=600[/tex]The original price of the desk was $600
a shop sells on average 250 can's of juice a day there are 25500 cans in stock how many days will these stocks last
If a shop sells on average 250 can's of juice a day and there are 25500 cans, these stocks last for 102 days
A shop sells on average 250 can's of juice a day, it has, it has 25500 cans in stock. We need to find the number of days these stocks will last.
The number of days can be found by using unitary method
1 can of juice is being sold in 1/250 day
25500 can of juice will be sold in 1/250 (25500)
25500 can of juice will be sold in 102 days
Therefore, if a shop sells on average 250 can's of juice a day and there are 25500 cans, these stocks last for 102 days.
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Mrs. Peck is making school supply baskets. She purchased 27 composition booksand 9 packs of map pencils. Which shows the ratio of packs of map pencils tocomposition books.
Number of composition books: 27
Number of packs of map pencils: 9
The ratio of packs of maps pencils to composition books: 9 to 27
9/27 = 1/3
1:3
Find the distance between the points (2, – 5) and ( – 7, – 7)
Answer:
=[tex] \sqrt{85} [/tex]
Step-by-step explanation:
let, (x1,y1) = (2,-5) & (x2,y2) = (-7,-7)
now, for distance between two points,
D = [tex]\sqrt[]{(x_{1}-x_{2} )^{2} +(y_{1}-y_{2} )^{2} }[/tex]
=[tex]\sqrt[]{(2-(-7))^{2}+(-5-(-7))^2 }[/tex]
[tex]=\sqrt{(2+7)^2+(-5+7)^2}[/tex]
[tex]=\sqrt{9^2+2^2}[/tex]
[tex]=\sqrt{81+4}[/tex]
[tex]=\sqrt{85}[/tex]
Answer:
[tex] \huge{ \boxed{ \sqrt{85} \: \text{or} \: 9.219 \: \text{units}}}[/tex]
Step-by-step explanation:
The distance between two points say [tex] A(x_1,y_1) [/tex] and B(x_2,y_2) can be found by using the formula;
[tex] \bold{d = \sqrt{{x_2-x_1}^{2}+{y_2-y_1}^{2}}} [/tex]
From the question the points are (2, – 5) and ( – 7, – 7)
[tex] x_1=2 \\ y_1=-5 \\ x_2=-7 \\ y_2=-7 [/tex]
Substituting the values into the formula that is;
[tex]d = \sqrt{ {( - 7 - 2)}^{2} + {( - 5 - - 7)}^{2} } \\ d = \sqrt{ {( - 9)}^{2} + {(2)}^{2} } \\ d = \sqrt{81 + 4} \\ d = \sqrt{85} = 9.219[/tex]
We have the final answer as
√85 or 9.219 unitsTala Abarkowe NAME PERIOD Unit 2 Lesson 5 Cool Down An albatross is a large bird that can fly 400 kilometers in 8 hours at a constant speed. Using d for distance in kilometers and t for number of hours, an equation that represents this situation is d = 50t. = 1) What are two constants of proportionality for the relationship between distance in kilometers and number of hours? Due in this s cose lh sud
Given relation is
[tex]d=50t[/tex]Here, d is the distance in kilometers and t is the number of hours.
Since distance and time both vary, therefore, they are not constants.
The only value which is fixed is 50.
Therefore, the only constant of proportion is 50.
Since the ratio of two valus are constant, therefore, they are in direct proportional relationship.
From the given relation, we can write
[tex]t=\frac{d}{50}[/tex]Hence, another relationship between d and t is
[tex]t=\frac{d}{50}[/tex]The rectangular foor of a classrom is 30 feet in length and 24 feet in width. A scale drawing of the floor has a length of 5 inches. What is the perimeter, in inches, of the floor in the scale drawing?
The required perimeter of the scale drawing is given as 18 inches.
Given that,
The rectangular floor of a classroom is 30 feet in length and 24 feet in width. A scale drawing of the floor has a length of 5 inches. The perimeter, in inches, of the floor in the scale drawing, is to be determined.
Perimeter is the measure of the figure on its circumference.
Here,
According to the question,
L = 30 feet, W = 24 feet,
for Scaled drawing
l = 5 inch, w = x
Now,
30/5 = 24 / x
6 = 24 / x
x = 24 {1/6}
x = 4,
So the width of the scale drawing is 4 inches,
perimeter of the scaled drawing = 2[l + w]
= 2 [5 + 4] = 18 inches
Thus, the required perimeter of the scale drawing is given as 18 inches.
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There are approximately 2.54 cm in 1 inch. what is the distance in inches of 14 cm. use a proportion to solve and round your answer to the nearest 10th of an inch
We know that there are 2.54 cm in 1 inch
2.54 cm ⇔ 1 inch
We want to find what is the distance in inches of 14 cm:
14 cm ⇔ ?? inch
Then, we have the following equivalence:
14 cm ⇔ ?? inches
2.54 cm ⇔ 1 inch
If we divide both sides of the equivalence we would have the same proportion:
[tex]\frac{14}{2.54}=\frac{?\text{?}}{1}[/tex]Solving both sides of the equation:
[tex]\begin{gathered} \frac{14}{2.54}=\frac{?\text{?}}{1} \\ \downarrow \\ 5.51=\text{??} \end{gathered}[/tex]This means that:
14 cm ⇔ 5.51 in
Rounding the answerWe want to round our result to the nearest tenth. This is a number with one digit after the decimal point:
5.51 in ≅ 5.5 in
Answer: the distance in inches of 14 cm is 5.5 inThe picture that I sent to the app would not pick up the greater or less than signs. The instructions say solve the system of inequalities by graphing. I would like someone to walk me through the steps. I had an amazing tutor the last time but my connection got lost she sent me a graph to help me.
See graph below
Explanation:We have two inequalities:
y < 6
y > x + 3
To plot the inequalities on a graph, we change the inequality sign to equal to in order to get points to plot the graph:
y = 6
This means at y = 6, there will be an horizontal line for all values of x. But due to the less than sign, it means the horizontal line will be shaded down.
y = x + 3
We assign values to x inorder to get y values:
let x = -2, 0, 2, 4
when x = -2
y = -2 + 3 = 1
when x = 0
y = 0 + 3 = 3
when x = 2
y = 2 +3 = 5
when x = 4
y = 4 + 3 = 7
When we plot this points, we get a straight line. SInce the sign is greater than, the line will be shaded towards the positive side
plotting the graph:
First inequality
Both inequalities:
Write an inequality for the problem and answer the question about the inequality. The square of x is greater than or equal to 10. Is 3 a solution.
"The square of x..." translates to x²
"...is greater than or equal to 10." translates to ≥ 10.
To determine if 3 is a solution, substitute 3 to the inequality.
[tex]\begin{gathered} x^2\ge10 \\ \text{If }x=3 \\ (3)^2\ge10 \\ 9\ge10 \\ 9\ngeq10 \end{gathered}[/tex]The resulting number, 9 is not greater than 10. Therefore, 3 is not a solution.
8 people have to give a presentation in class today. How many different orders can theyspeak in?65,5364,09640,32013,440
Answer:
They can speak in 40, 320 different orders
Explanation:
Given that 8 people have to give a presentation in class.
They can speak in many different orders:
First could be second, second could be first, third could be eight, seventh could be fifth, and so on.
This number of ways result in factorial 8.
This is written as:
[tex]8![/tex]Which represents the multiplications of numbers on the number line from 8 down to 1.
That is:
[tex]\begin{gathered} 8!=8\times7\times6\times5\times4\times3\times2\times1 \\ \\ =40,320 \end{gathered}[/tex]who can solve this for me it's due next class period
Here, we want to get the value of x
As we can see, we have the interior angle as 45;
The other is 90; and that means the last angle will be 45
This mean that we have an isosceles right-triangle
The sides that face the angles are equal
These sides are x and 12
That means x = 12
To get the value of y, we have to use the Pythagoras' theorem
The square of the hypotenuse (the longest side and the side that faces the right angle) is equal to the sum of the squares of the two other sides
The side facing the right angle is y
So, the sum of the squares of x and 12 will give the square of y
Mathematically, we have this as follows;
[tex]\begin{gathered} y^2=12^2+x^2 \\ \sin ce\text{ x = 12} \\ y^2=12^2+12^2 \\ y^2\text{ = 144 + 144} \\ y^2\text{ = 288} \\ y\text{ = }\sqrt[]{288} \\ y\text{ = 12}\sqrt[]{\text{ 2}} \end{gathered}[/tex]Find the distance between (-5,3) and (-6,6).
When you convert a number from decimal notation to scientific notation, how do you know if the exponent will be positive or negative? Explain.
When converting a number from decimal to scientific notation,
The exponent is positive if the movement of the decimal point is to the left
The exponent is negative if the movement of the decimal point is to the right.
Examples :
[tex]1200\rightarrow1.2\times10^3[/tex]The decimal point moves from the right of the last digit to the place between 1 and 2. It moves to the left so the exponent is positive.
[tex]0.0012\rightarrow1.2\times10^{-3}[/tex]The decimal point will move 3 places to the right, so the exponent will be negative.
Which order pair makes both inequalities true? Y<-2x+3Y< x-2
The ordered pair which makes both inequalities true are (3, 0).
Inequalities are mathematical expressions where neither side is equal.
Contrary to equations, we compare two values in inequality.
Less than, greater than, or not equal to signs are used in place of the equal to sign in between.
Let us consider the ordered pair (3, 0)
In the first inequality
y > -2x + 3
Substituting the values of x and y
0 > -2(3) + 3
0 > -6 + 3
0 > -3
In the second inequality
y < x - 2
Substituting the value of x and y
0 < 3 - 2
0 < 1
Therefore, the ordered pair which makes both inequalities true are (3, 0).
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