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If we take the vector A and rotate it till it reaches 270° we would have the following figure
As we can see there's no horizontal component, the horizontal component is zero, and the vertical component is the vector magnitude.
Related Questions
Solve for n.25n−3=5n+8 Enter your answer in the box.n =
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Solution:
Consider the following equation:
[tex]25n\text{ - 3 = 5n +8}[/tex]putting together like terms, this equation is equivalent to:
[tex]25n\text{ -5n = 8}+3[/tex]this is equivalent to:
[tex]20\text{ n = 11}[/tex]solving for n, we get:
[tex]n\text{ = }\frac{11}{20}=0.55[/tex]so that, we can conclude that the correct answer is:
[tex]n\text{ = }0.55[/tex]what is the measure of
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For the propertie of similar angles we know that the angle J is equal to angle H so:
[tex]\angle H=67[/tex]then we can use the propertie of the sum of the internal angles of a triangle to dind x so:
[tex]x+67+46=180[/tex]and we solve for x
[tex]\begin{gathered} x=180-67-46 \\ x=67 \end{gathered}[/tex]can you pls help me i am unsure of how to solve this
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Since the profit in the first week is $70
Since it increases by $15 each week, then
We can solve it as an arithmetic progression
P = a + (n -1)d, where
a is the profit in the 1st week
d is the value of increasing each week
n is the number of the week
a = 70, d = 15, and n = 12 (12th week)
Substitute these values in the rule above
P = 70 + (12 - 1)(15)
P = 70 + 11(15)
P = 70 + 165
P = 235
The profit during the 12th week is $235
a1=-4; an= an-1+11What is the iterative rule for the arithmetic sequence above?
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a1 = -4, means the first term of the sequaence = -4
In the arithmetic sequence, there is a common difference between each two consecutive terms
We can find this difference from the given rule
an = a n-1 + 11
an-1 is the previous term of an
11 is the common difference
The rule of the sequence is
[tex]a_n=a+(n-1)d[/tex]a is the first term
d is the common difference
n is the position of the term
Substitute a by -4
d by 11
[tex]a_n=-4+(n-1)11[/tex]Multiply the bracket by 11
[tex]\begin{gathered} a_n=-4+n(11)-1(11)_{} \\ a_n=-4+11n-11 \end{gathered}[/tex]Add the like terms -4 and -11
[tex]a_n=11n-15[/tex]The rule of the sequence is a(n) = 11n - 15
what is the equation of the line that passes through the points (2,-2) and has a slope of -1/2
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Given the point (2,-2) and the slope m = -1/2, we can find the equation of the line using the point-slope formula:
[tex]\begin{gathered} (x_0,y_0)=(2,-2)_{} \\ m=-\frac{1}{2} \\ Equation\colon \\ y-y_0=m(x-x_0) \\ \Rightarrow y-(-2)=-\frac{1}{2}(x-2)=-\frac{1}{2}x+\frac{2}{2}=-\frac{1}{2}x+1_{} \\ \Rightarrow y+2=-\frac{1}{2}x+1 \\ \Rightarrow y=-\frac{1}{2}x+1-2=-\frac{1}{2}x-1 \\ y=-\frac{1}{2}x-1 \end{gathered}[/tex]therefore, the equation of the line is y = -1/2x -1
You have a frame that holds 8 pictures.you fill 1/4 of the frame.how many pictures do you put in the frame?explained
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2 pictures.
1) Considering that a frame is rectangular as well as each picture. We're dealing with the area of a rectangle and proportionality.
2) If I fill 1/4 and the whole frame holds 8, then I can state that:
[tex]8\times\frac{1}{4}=2[/tex]Therefore I put into the frame 2 pictures because 2 pictures are equivalent to 1/4 of the area of that frame.
Can I have help with this pleasehow would I make a graph
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The Solution:
We are required to make a graph of the situation.
The above graph is the required graph.
what is the y intercept of the equation? -10x -15y =60
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Let's begin by listing out the information given to us:
[tex]-10x-15y=60[/tex]We will proceed by making y the subject of the equation so as to conform it to the general linear equation formula
[tex]\begin{gathered} y=mx+b \\ where\colon b=y-intercept \\ \\ -10x-15y=60 \\ \text{Add 15y to both sides, we have:} \\ -10x-15y+15y=60+15y \\ -10x=15y+60 \\ \text{Subtract 60 from both sides, we have:} \\ -10x-60=15y\Rightarrow15y=-10x-60 \\ 15y=-10x-60 \\ \text{Divide through by 15, we have:} \\ \frac{15y}{15}=-\frac{10}{15}x-\frac{60}{15} \\ y=-\frac{2}{3}x-4 \\ \text{Comparing }y=-\frac{2}{3}x-4\text{ with }y=mx+b \\ b=-4 \\ \therefore\text{The }y-intercept\text{ is }4 \end{gathered}[/tex]Two angles are supplementary. One angle measures 9x+9 degrees and the other measures 7x-5 degrees. Determine the measure of both angles.
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108º and 72º
1) If two angles are supplementary then
α+β =180º
2) So we can write out:
(9x +9) + (7x -5) = 180º
9x+7x +9-5 = 180º
16x +4 = 180º
16x = 176º
16x/16 =176/16
x= 11
2.2) If x= 11 then we can plug into that and find out the measures of those angles this way:
9(11) +9 = 99 +9 = 108º
7(11) -5 = 77 -5 = 72º
3) Hence, the angles are 108º and 72º, note that 108 +72 = 180º
1)How many ounces are equal to 7 pounds?
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We are asked to find out how many ounces are there in 7 pounds?
Answer:
112 ounces are equal to 7 pounds.
Explanation:
Recall that 1 pound is equal to 16 ounces.
[tex]1lb=16oz[/tex]Please note that lb is the short form for pounds and oz is the short form for ounces.
To convert the 7 pounds into ounces, multiply the 7 pounds by 16.
[tex]7\cdot16oz=112oz[/tex]Therefore, 112 ounces are equal to 7 pounds.
x=_-b+_√b2-4ac -2a i need help
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solution
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}\text{ (1)}[/tex]When we have a quadratic equation in the following form:
[tex]ax^2+bx+c=0[/tex]And we want to find the roots we can use the quadratic formula given by (1)
I’m doing math homework for summer school and I don’t get this . I provided a picture so you can see the problem. Thanks so much -Chris
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Solution:
Given the table;
Thus;
[tex]f(-2)=1[/tex]Do you know the Distance formula?
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The distance between two points (x1, y1) and (x2, y2) is given by the formula below:
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]For example, the distance between the points (2, 4) and (3, 8) is given by:
[tex]undefined[/tex]You have a cup with 17 coins inside. The total inside the cup is $5.50. Determine how many half dollars and quarters are inside the cup.
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Let x be the number of half dollar and y, the number of quarter dollar
Thus,
[tex]x+y=17\text{ -----eq i)}[/tex]Half dollar is 50cent, quarter dollar is 25cents,
Thus,
[tex]0.5x+0.25y=5.50\text{ -----eq i}i)[/tex]Solving the two(2) equations simultaneously; we have:
From eq i)
[tex]\begin{gathered} x+y=17 \\ x=17-y\text{ -----eq }iii) \end{gathered}[/tex]Put eq iii) into ii), we have:
[tex]\begin{gathered} 0.5x+0.25y=5.50 \\ 0.5(17-y)+0.25y=5.50 \\ 8.5-0.5y+0.25y=5.50 \\ 8.5-0.25y=5.50 \\ 8.5-5.50=0.25y \\ 0.25y=3 \\ y=\frac{3}{0.25} \\ y=12 \end{gathered}[/tex]From eq iii)
[tex]\begin{gathered} x=17-y \\ x=17-12 \\ x=5 \end{gathered}[/tex]Hence, there are 5 half dollars and 12 quarter dollars inside the cup
EsparThe shorter leg of a right triangle is 7 m shorter than the longer leg. The hypotenuse is 7 m longer than the longer leg. Findthe side lengths of the triangle.entsLength of the shorter leg:Length of the longer leg:ImLength of the hypotenuse:Х$?
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In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
length of the shorter leg = ?
length of the longer leg = ?
length of the hypotenuse = ?
Step 02:
We must analyze the problem to find the solution.
x = length of the shorter leg
y = length of the longer leg
z = length of the hypotenuse
System of equations:
x = y - 7 (eq.1)
z = y + 7 (eq.2)
z² = x² + y² (eq.3)
eq.2 in eq.3
[tex]\begin{gathered} (y+7)^2=x^2+y^2\text{ } \\ y^2+14y+49=x^2+y^2 \\ 14y+49=x^2 \\ \\ \\ \end{gathered}[/tex]14y + 49 = x²
y - 7 = x * (-14) (eq.1)
14y + 49 = x²
-14y + 98 = -14x (eq.1)
__________________
147 = x² - 14x
x² - 14x - 147 = 0
Step 03:
Quadratic equation:
x² - 14x - 147 = 0
[tex]x=\frac{-(-14)\pm\sqrt[]{(-14)^2-4\cdot1\cdot(-147)}}{2.1}[/tex][tex]\begin{gathered} x1\text{ = }\frac{-(-14)+28_{}}{2}\text{ = 21} \\ x2=\frac{-(-14)-28}{2}\text{ }=\text{ -7} \end{gathered}[/tex]x = 21 (positive solution)
x = y - 7
21 + 7 = y
28 = y
z = y + 7 = 28 + 7 = 35
The answer is:
length of the shorter leg = 21
length of the longer leg = 28
length of the hypotenuse = 35
polygon abcde shown in the coordinate plane find the area of the figure Answer choices: 32466072
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We have to calculate the area of the polygon.
To do that we divide the polygon in known figures of which we can calculate the area.
Then, the area of the polygon will be the sum of the areas of its parts.
We can then divide the polygon as:
We can add the areas of the three figures as:
[tex]\begin{gathered} A=A_1+A_2+A_3 \\ A=\frac{3*4}{2}+\frac{6*4}{2}+4*\frac{9+5}{2} \\ A=\frac{12}{2}+\frac{24}{2}+4*7 \\ A=6+12+28 \\ A=46 \end{gathered}[/tex]Answer: the area is 46 square units.
if Teresa used five and a third gallons of gas on Sunday and two and a quarter gallons of gas on Monday how many more gallons of gas did she use on Sunday
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Hence the difference is
[tex]5\frac{1}{3}-2\frac{1}{4}=3\frac{4-3}{12}=3\frac{1}{12}[/tex]Hence she used 3 1/12 more gallons of gas on Sunday
how tall is Raj? Round answer to two decimal places.Raj is ____ feet tall.
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Given the information on the picture, we have the following right triangle:
then, to find the height, we can use the tangent function to get the following:
[tex]\begin{gathered} \tan (32)=\frac{\text{opposite side}}{adjacent\text{ side}}=\frac{h}{10} \\ \Rightarrow h=10\cdot\tan (32)=6.25 \\ h=6.25 \end{gathered}[/tex]therefore, Raj is 6.25 feet tall
Garrett needs a baseball coach. Coach A is offering her services for an initial $4,800 in addition to $550per hour. Coach B is offering her services for an initial $4,500 in addition to $700 per hour. When will thetwo coaches charge the same amount of money?The two coaches will charge the same amount of money afterhours.
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Let's define
x: time is hours
Coach A services costs 4800 + 550x dollars
Coach B services costs 4500 + 700x dollars
If both coaches charge the same:
4800 + 550x = 4500 + 700x
4500 is adding on the right, then it will subtract on the left
550x is adding on the left, then it will subtract on the right
4800 - 4500 = 700x - 550x
300 = 150x
150 is multiplying on the left, then it will divide on the left
300/150 = x
2 = x
The two coaches will charge the same amount of money after 2 hours.
Solve. Remember to use the order of operations, radical36 radical16
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Shena, this is the solution to question 15:
√25 √9
5 * 3
15
In case there is a minus sign, this is the answer:
√25 - √9
5 - 3
2
However, I do not see 15 as one of the available options, but I do see 2.
The current student population of Tucson is 2500. If the population increase at a rate of 15% each year. What will the student population be in 10 years?Write an exponential growth model for the future population (y) in terms of time x: y=What will the population be in 10 years? (Round to nearest student)
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Let's assume that we have a certain quantity y that increases at a rate of p% every x years. If the initial quantity (i.e. the quntity at x=0) is "a" then the value of y after x years is given by:
[tex]y=a\cdot(1+\frac{p}{100})^x[/tex]We are told that the current student population of Tucson is 2500 and that it will increase at a rate of 15% per year. Then the student population after x years is given by:
[tex]\begin{gathered} y=2500\cdot(1+\frac{15}{100})^x \\ y=2500\cdot1.15^x \end{gathered}[/tex]Then the student population after 10 years is given by:
[tex]y=2,500\cdot1.15^{10}=10113.89[/tex]AnswerThen the answers are:
[tex]y=2500\cdot1.15^x[/tex]The population will be 10114.
what is the length of segment AB in the triangle shown below?
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Given:
BC = 8 inches
AC = 17 inches
Let's solve for length of segment AB.
To solve for AB, apply Pythagorean theorem.
We have:
[tex]AC^2=BC^2+AB^2[/tex]Now, rewrite the equation for AB:
[tex]AB^2=AC^2-BC^2[/tex]Plug in the values:
[tex]\begin{gathered} AB^2=17^2-8^2 \\ \\ AB^2=289-64 \\ \\ AB^2=225 \end{gathered}[/tex]Take the square root of both sides:
[tex]\begin{gathered} \sqrt{AB^2}=\sqrt{225} \\ \\ AB=15 \end{gathered}[/tex]Therefore, the length of AB is 15 inches.
ANSWER:
15 inches
Fill in the blanks so the left side is a perfect square trinomial. That is, complete the square.x² + 8/9x+__ = (x+__)^2
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Given:
There are given the equation:
[tex]x^2+\frac{8}{9}x+()=(x+())^2[/tex]Explanation:
According to the question:
We need to find the missing terms:
So,
From the equation:
[tex](x+\frac{4}{9})^2=x^2+\frac{2.x.4}{9}+(\frac{4}{9})^2[/tex]Then,
[tex]\begin{gathered} (x+\frac{4}{9})^2=x^2+\frac{2.x.4}{9}+(\frac{4}{9})^2 \\ =x^2+\frac{8x}{9}+\frac{16}{81} \\ =x^2+\frac{8}{9}x+\frac{16}{81} \end{gathered}[/tex]Final answer:
Hence, the missing value is shown below:
[tex]x^2+\frac{8}{9}x+\frac{16}{81}=(x+\frac{4}{9})^2[/tex]What do I do next? Long division 459 divided by 2?
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Answer:
To divide 459 by 2 by long division method.
we have that,
Division is one of the four basic mathematical operations. In math, long division is a method for dividing large numbers into steps or parts, breaking the division problem into a sequence of easier steps. It is the most common method used to solve problems based on division.
we get,
we get,
229.5 as the quotient.
Answer is: 229.5
Divide the monomials 20m^5n^2/30m^3n^9
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Answer
[tex]\frac{2m^2}{3n^7}[/tex]Explanation
Given monomials:
[tex]\frac{20m^5n^2}{30m^3n^9}[/tex]Using division law of indices:
[tex]\begin{gathered} \frac{20}{30}\times\frac{m^5}{m^3}\times\frac{n^2}{n^9}=\frac{2}{3}\times m^{5-3}\times n^{2-9} \\ =\frac{2}{3}\times m^2\times n^{-7} \\ \end{gathered}[/tex]Now, using the negative exponent law of indices, we have:
[tex]\frac{2}{3}\times m^2\times\frac{1}{n^7}=\frac{2\times m^2\times1}{3\times n^7}=\frac{2m^2}{3n^7}[/tex]
Solve (-2,5) and (2,1) as an equation in point slope form for the second point
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Slope - Intercept Form of a Line:
y = mx + b
where m is the slope and b the y - intercept.
Given the points: (-2, 5) and (2, 1):
To find m:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{1-5}{2+2} \\ m\text{ = -1} \end{gathered}[/tex]To find b:
1 = -1(2) + b
b = 1 + 2
b = 3
EQUATION OF THE LINE:
y = -x + 3
How many solutions does the equation (2 sin x + 1)(sin x – 1) = 0 have over the interval 0 ≤ x < 2π?
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The initial equation is
[tex](2\sin x+1)(\sin x-1)=0[/tex]We can expand this expression as shown below
Which function of x would have zeros of 1/3 and -5?
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The functions of x with zeros of 1/3 and -5
[tex]\begin{gathered} x\text{ = }\frac{1}{3}\text{ and x = -5} \\ (x\text{ - }\frac{1}{3})\text{ and (x + 5)} \\ \end{gathered}[/tex][tex]\begin{gathered} (x\text{ -}\frac{1}{3})(x\text{ + 5)} \\ x^2\text{ + 5x - }\frac{x}{3}\text{ - }\frac{5}{3} \\ \text{ multiply through by 3} \\ 3x^2\text{ + 15x - x - 5} \\ 3x^2\text{ + 14x - 5} \\ F(x)\text{ = }3x^2\text{ + 14x - 5} \end{gathered}[/tex]Hence the functions of x with zeros of 1/3 and -5 = 3x² + 14x - 5
3 + 0.1 + 0.006 make it into a decimal
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Explanation:
To add the decimal we can rewrite the number 3 and 0.1 as:
3 = 3.000
0.1 = 0.100
Because we can add zeros after the decimal point without change the number.
Now, we can add the decimals as follows:
Find the measure of angle A for the triangle shown.oThe value of angle A is
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The sum of the internal angles of a triangle must be equal to 180 degrees. We were given two of the angles and need to calculate the last one, to do that we will solve the following equation:
[tex]\measuredangle A+\measuredangle B+\measuredangle C=180[/tex]Applying the data from the triangle we have:
[tex]\begin{gathered} \measuredangle A+100+47=180 \\ \measuredangle A+147=180 \\ \measuredangle A=180-147 \\ \measuredangle A=33 \end{gathered}[/tex]The angle A measures 33 degrees.