Answer:
1) The total displacement vector is ((16 + √2)/2, -(6+11·√2)/2)
2) The number of miles they'd have to walk is approximately 13.856 miles
Step-by-step explanation:
1) The distance, direction, and location of the path of the walk the person takes, are listed as follows;
Start location, (0, 0)
6 miles East walk to location, (6, 0)
6 miles Southeast to location, (6 + 3·√2, -3·√2)
3 miles South to location, (6 + 3·√2, -3·√2 - 3)
5 miles Southwest to location, (6 + 3·√2 - 2.5·√2, -3·√2 - 3 - 2.5·√2)
2 miles East to location, (6 + 3·√2 - 2.5·√2 + 2, -3·√2 - 3 - 2.5·√2)
(6 + 3·√2 - 2.5·√2 + 2, -3·√2 - 3 - 2.5·√2) = ((16 + √2)/2, -(6+11·√2)/2)
Therefore the destination coordinates is ((16 + √2)/2, -(6+11·√2)/2)
The total displacement vector, [tex]\underset{d}{\rightarrow}[/tex] = ((16 + √2)/2, -(6+11·√2)/2)
d = (16 + √2)/2)·i - (6+11·√2)/2)·j
2) If the person walked straight home, the number of miles they'd have to walk, [tex]\left | \underset{d}{\rightarrow} \right |[/tex], is given as follows;
[tex]\left | \underset{d}{\rightarrow} \right | = \sqrt{\left(\dfrac{16 +\sqrt{2} }{2} \right)^2 + \left(-\dfrac{6 + 11 \cdot \sqrt{2} }{2} \right)^2 } = \sqrt{134 + 41 \cdot \sqrt{2} }[/tex]
Therefore;
If the person walked straight home, the number of miles they'd have to walk [tex]\left | \underset{d}{\rightarrow} \right | \approx 13.856 \ miles[/tex]
hurryyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy
Answer:
D. II & III
Step-by-step explanation:
II (x - 4)(2x + 9) = 2x² + x - 36
III (x - 4)(x - 6) = x²- 10x + 24
I has factors (x + 4)(x - 8)
IV has factors x(x - 16)
Angie used 4 apples and 5 strawberries in her fruit salad. Salim used 7 apples and 9 strawberries. Did Angie and Salim use the same ratio of apples to strawberries? If not, who used the greater ratio of apples to strawberries?
Answer:
We can write a ratio between two quantities, x and y, as:
x to y.
To find if two ratios:
"a to b" and "c to d" are equal, we need to see if the quotientes:
a/b and c/d are equal.
Here we know that the ratios are:
4 apples to 5 strawberries, this gives the quotient 4/5 = 0.8
7 apples to 9 strawberries, this gives the quotient 7/9 = 0.78
So the quotients are different, which means that the ratios are not equal.
Now we want to see who used a greater ratio of apples to strawberries.
notice that in the numerator we used the number of apples, so as larger is the quotient, larger is the ratio of apples to strawberries.
We can see that the quotient of Angie is larger, then Angie used the greater ratio of apples to strawberries.
What is 2:50 is simplest form
Answer:
0.04
Step-by-step explanation:
2 / 50 is the same as 1 / 25.
1 / 25 = 0.04
Answer:
0.04
Step-by-step explanation:
PLEASE HELP WILL GIVE BRAILNLIEST! Find the value of x
Answer:
x = 14.63
Step-by-step explanation:
Please help me ASAP I’m stuck on these questions
Answer:
4, yes through the middle 5, yes through the middle 6, yes through the middle all of them reflect from the center
Step-by-step explanation:
Any help, I would highly appreciate it
Answer:
B
Step-by-step explanation:
We are given the equation:
[tex]\displaystyle x(b-c) = y+x[/tex]
And that:
[tex]2b=3c=7[/tex]
And we want to find the value of y / x.
To start, subtract x from both sides in the first equation:
[tex]x(b-c) -x = y[/tex]
Divide both sides by x:
[tex]\displaystyle \frac{x(b-c)-x}{x}=\frac{y}{x}[/tex]
Simplify:
[tex]\displaystyle (b-c)-1 = \frac{y}{x}[/tex]
Next, in the second equation, divide everything by two:
[tex]\displaystyle b = \frac{3}{2} c = \frac{7}{2}[/tex]
Substitute:
[tex]\displaystyle \left(\frac{3}{2} c - c \right) - 1= \frac{y}{x}[/tex]
Simplify:
[tex]\displaystyle \frac{1}{2} c - 1 = \frac{y}{x}[/tex]
From the modified second equation, we can multipy both sides by 1/3:
[tex]\displaystyle \frac{1}{2} c = \frac{7}{6}[/tex]
Substitute:
[tex]\displaystyle \left(\frac{7}{6}\right) -1 = \frac{y}{x}[/tex]
Subtract:
[tex]\displaystyle \frac{y}{x} = \frac{7}{6} - \frac{6}{6} = \frac{1}{6}[/tex]
Therefore, our answer is B.
simplify (2^2×4^-2)×5^8+2+3^0
The average age of a preschool class is 4.5 years old. If there is one 3-year-old, five 5-year-olds, and two other children both of the same age, what is the age, in years, of the other two children?
Answer:
3.1
Step-by-step explanation:
5 x5 =25
25+3=28
the other children are 4 years old
Can someone help me with this
Answer:
Step-by-step explanation:
The formula for this, specific to our circle, is
∠RQP = [tex]\frac{1}{2}[/tex](arc SP - arc RP) and filling in:
∠RQP = [tex]\frac{1}{2}(170-86)[/tex] and
∠RQP = [tex]\frac{1}{2}(84)[/tex] so
∠RQP = 42°
volume of a cuboid whose edges are 4 cm, 5 cm and 6 cm
Answer:
120
Step-by-step explanation:
Formula for cuboid: L × W × H
Plug in:
L × W × H
4 × 5 × 6
^ ^
20 × 6
^ ^
120
Hope this helps.
The graph shows a probability distribution.
What is P(X < 3)?
Answer:
6/20 = 3/10 = 30%
Step-by-step explanation:
What is the equation of the line that is perpendicular to the line y = 2x + 5 and
passes through the point (-4, 2)?
Answer:
y = -1/2x
Step-by-step explanation:
If two lines are perpendicular to each other, they have opposite slopes.
The first line is y = 2x + 5. Its slope is 2. A line perpendicular to this one will have a slope of -1/2.
Plug this value (-1/2) into your standard point-slope equation of y = mx + b.
y = -1/2x + b
To find b, we want to plug in a value that we know is on this line: in this case, it is (-4, 2). Plug in the x and y values into the x and y of the standard equation.
2 = -1/2(-4) + b
To find b, multiply the slope and the input of x (-4)
2 = 2 + b
Now, subtract 2 from both sides to isolate b.
0 = b
Plug this into your standard equation.
y = -1/2x + 0 or y = -1/2x
This equation is perpendicular to your given equation (y = 2x + 5) and contains point (-4, 2)
Hope this helps!
equation of the line which passes through point (0,5) at gradient of - 1
Answer:
y = - x + 5
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here gradient (slope) = - 1 and (0, 5) ⇒ c = 5
y = - x + 5 ← equation of line
graph the equation y=5/7x
Answer:
Step-by-step explanation:
Which linear inequality is represented by the graph?
Answer:
D
Step-by-step explanation:
The correct answer is D
Answer:
D
Step-by-step explanation:
y<2/3 x-1 is the answer
You have $475 in your savings account that earns 3.25% simple interest each year. How much interest will you accumulate after 7 years?
Answer:
$613.45
Step-by-step explanation:
Multiply $475 by 3.25% of it and so on 7 times, which adds up to 613.4993293. Round that to 613.45
The triangle on the grid will be translated two units down.
On a coordinate plane, triangle A B C has points (2, 1), (0, negative 1), (2, negative 1).
Which shows the triangle when it is translated two units down?
On a coordinate plane, triangle A prime B prime C prime has points (0, negative 1), (0, negative 3), (2, negative 3).
On a coordinate plane, triangle A prime B prime C prime has points (0, 1), (negative 2, negative 1), (0, negative 1).
On a coordinate plane, triangle A prime B prime C prime has points (2, negative 1), (2, negative 3), (0, negative 3).
On a coordinate plane, triangle A prime B prime C prime has points (2, negative 1), (2, negative 3), (0, negative 1).
Given:
The vertices of the triangle ABC are A(2, 1), B(0,-1), C(2, -1).
To find:
The vertices of the image of triangle ABC if ABC is translated two units down.
Solution:
It is given that the triangle ABC is translated two units down. So, the rule of translation is:
[tex](x,y)\to (x,y-2)[/tex]
Using this rule, we get
[tex]A(2,1)\to A'(2,1-2)[/tex]
[tex]A(2,1)\to A'(2,-1)[/tex]
Similarly,
[tex]B(0,-1)\to B'(0,-1-2)[/tex]
[tex]B(0,-1)\to B'(0,-3)[/tex]
And,
[tex]C(2.-1)\to C'(2,-1-2)[/tex]
[tex]C(2.-1)\to C'(2,-3)[/tex]
The vertices of the image are A'(2,-1), B'(0,-3), C'(2,-3).
Therefore, the correct option is C.
Answer:
C.
Step-by-step explanation:
Rewrite the radical expression as an expression with rational exponents.
cube root of x to the power of 8
Answer:
Step-by-step explanation:
[tex]\sqrt[3]{x^8}=x^{\frac{8}{3}[/tex] The little number outside is called the index and that always serves as the denominator in the rational exponent. The power on the radicand (the radicand is whatever is inside the radical) serves as the numerator.
Lorraine writes the equation shown. x²+4-15=0 She wants to describe the equation using the term relation and the term function. The equation represents a relation and a function a relation but not a function a function but not a relation neither a relation nor a function
Answer:
Neither a relation nor a function
Step-by-step explanation:
A relation in mathematics is a relationship between two or more set of values in an ordered pair, such as related x and y-values
An equation is a statement that gives declare the equality between two expressions
A function is a mapping rule that maps each element in the domain set to only one element in the range set
Therefore, the given equation in one variable, x, that asserts the equality of the expressions on the left and right hand side, is neither a relation nor a function
A baker finds several new recipes to try. Of the new recipes, there are 11 for cookies, 10 for muffins, and 4 for cakes. If the baker selects a recipe at random, what is the probability the recipe is for a cake?
Answer:
4/25
Step-by-step explanation:
All the amount of recipes is 11+10+4=25 . There are 4 recipes for cakes
so probability is 4/25
The report "Digital Democracy Surveyt describes a large national survey. In a representative sample of Americans ages 14 to 18 years, 45% indicated that they usually use social media while watching
TV. Suppose that the sample size was 760.
(a) Is there convincing evidence that less than half of Americans ages 14 to 18 years usually use social media while watching TV? Use a significance level of 0.05.
State the appropriate null and alternative hypotheses.
O Hop 0.5 versus Hp > 0.5
O Moip 0.5 versus H: = 0.5
O Hp = 0.5 versus HP < 0.5
OH:P < 0.5 versus , p > 0.5
OHOD 0.5 versus H: 0.5
Find the test statistic and P-value. (Use a table or technology. Round your test statistic to two decimal places and your p-value to four decimal places.)
ZE
P-value
Answer:
H0 : p = 0.5 versus H1: P < 0.5
Test statistic = - 2.76
Pvalue = 0.0029
Step-by-step explanation:
The hypothesis :
We are to test if less Than half of the American population within the of 14 to 18 years usually use social media while watching TV :
Hence, population proportion, p = 0.5
H0: p = 0.5
H1: P < 0.5
Sample size, n = 760
Sample proportion, Phat = 45% = 0.45
The test statistic, Z :
Z = (Phat - P) / √[(P(1 - P)) /n]
Z = (0.45 - 0.5) / √[(0.5(1 - 0.5)) /760]
Z = - 0.05 / √0.0003289
Z = - 2.7568 ; Z = - 2.76 (2 decimal places)
The Pvalue :
Using technology :
Pvalue from Zscore calculator ; Pvalue = 0.0029
Decision region :
Reject H0 if Pvalue < α
α = 0.05
Since 0.0029 < 0.05 ; we reject the Null and conclude that less than half of American within age 14 to 18 years usually use social media while watching TV.
If cos(27) =p, express sin(27) in terms of p
Answer:
√(p²-1)
Step-by-step explanation:
sin (27°) = √(p²-1) / 1
= √(p²-1)
Find the 8th term of the geometric sequence 7,−21,63,
Answer:
8th term is -15309
Step-by-step explanation:
[tex]{ \boxed{ \bf{u_{n} = a( {r}^{n - 1} ) }}} \\ { \tt{u_{8} = 7( {( - 3)}^{8 - 1}) }} \\ { \tt{u_{8} = 7( - 2187)}} \\ { \tt{u _{8} = - 15309}}[/tex]
r is the common difference, r = -21/7 = -3
Answer:
a₈ = - 15309
Step-by-step explanation:
The nth term of a geometric sequence is
[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]
where a₁ is the first term and r the common ratio
Here a₁ = 7 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{-21}{7}[/tex] = - 3 , then
a₈ = 7 × [tex](-3)^{7}[/tex] = 7 × - 2187 = - 15309
A regular square pyramid has a slant height of 5 in and a base area of 49 in2. Find the surface area of the pyramid. ------------------------------------------------------------------------------------------- 171.5 square inches 70 square inches 119 square inches 245 square inches
Answer:
C: 119 square inches
Step-by-step explanation:
We are given;
Slant height; L = 5 in
Base area; B = 49 in²
Since it's a square pyramid, the base portion has a square shape.
Thus, area of base = x²
Where x is a side of the square.
Thus;
x² = 49
x = √49
x = 7
Perimeter of base = 7 × 4 = 28 in
Area of pyramid = ½PL + B
Plugging in the relevant values;
Area of pyramid = (½ × 28 × 5) + 49
Area of pyramid = 119 in²
In this activity, you will create an equation for a function represented by a verbal description.
Vicky charged her phone’s battery to 100 percent. Then she took the phone off the charger. When her phone is off the charger, it loses 5 percent of its battery life every hour. What function models the percentage of battery life left in terms of the number of hours since Vicky took it off the charger?
What is the initial value of the function? Is it positive or negative? Explain your answer.
What is the function’s rate of change? Is it positive or negative? Explain your answer.
Answer:
1) The initial value of the function is the y-value when the x-value is zero. The number of hours is the x-value and the percentage of battery life left is the y-value. When the number of hours, x, is 0, the percentage of remaining battery life, y, is 100 percent. So, the initial value of the function is 100. The initial value is positive because the percentage of remaining battery life cannot be negative.
2) The rate of change is the rate at which the y-value changes with respect to a change in the x-value. When off the charger, the phone loses its battery life at a constant rate of 5 percent per hour. So, the function’s rate of change is -5. The rate of change is negative because the rate indicates that the percentage of remaining battery life decreases as the number of hours increases.
Step-by-step explanation: I just did the tutorial right now i hope this helps
Answer:
part a = The number of hours since Vicky took the phone off the charger is the independent quantity, so the variable x should represent it.
part b = The percentage of battery life left in hours is the dependent quantity, so the variable y should represent it.
part c = The initial value of the function is the y-value when the x-value is zero. The number of hours is the x-value and the percentage of battery life left is the y-value. When the number of hours, x, is 0, the percentage of remaining battery life, y, is 100 percent. So, the initial value of the function is 100. The initial value is positive because the percentage of remaining battery life cannot be negative.
part d = The rate of change is the rate at which the y-value changes with respect to a change in the x-value. When off the charger, the phone loses its battery life at a constant rate of 5 percent per hour. So, the function’s rate of change is -5. The rate of change is negative because the rate indicates that the percentage of remaining battery life decreases as the number of hours increases.
part e = The rate of change of the function, m, is -5, and the initial value of the function, b, is 100. Substitute the values of m and b in the equation y = mx + b. The equation of the function that models the phone’s remaining battery life in terms of the number of hours from the time Vicky took it off the charger is y = -5x + 100.
Step-by-step explanation:
All edmentum answers :)
What is the equation of the sinusoid?
TI
21
Зп
47
Answer:
y = sin( x/2)
Step-by-step explanation:
The amplitude is 1
The period is 4pi
y = A sin ( Bx)
where A is the amplitude and B is 2pi/ period
y = 1sin (2pi/ 4pi x)
y = sin( x/2)
Answer:
Step-by-step explanation:
c
Jennifer invested $379 in a simple interest account. The account now has $554 in it. The money has been invested for 5 years. What interest rate (as a percentage) did this account have?
9514 1404 393
Answer:
9.23%
Step-by-step explanation:
The account balance for simple interest is given by ...
A = P(1 +rt) . . . . . principal P invested for t years at rate r
554 = 379(1 +r·5)
554 = 379 + 1895r . . . . eliminate parentheses
175 = 1895r . . . . . . . . . subtract 379
r = 175/1895 ≈ 0.092348 ≈ 9.23%
Jennifer's account had an interest rate of about 9.23%.
What is an
equation of the line that passes through the points (-3,-1) and (-4,-4)
Answer:
y= 3x+8
Step-by-step explanation:
not a 100% sure...
sry if its wrong
(try using Math-way, its rly helpful)
Answer:
Step-by-step explanation:
y=mx+b
To find slope: -4+1/-4+3
Slope=3
y=3x+b
Plug in either points ,as an example, i'll plug in (-3,-1)
-1=3(-3)+b
-1=-9+b
8=b
Finished formula: y=3x+8
According to the rules of Major League Baseball, the infield must be 30 feet by 30 feet in a diamond shape with perpendicular (90°) corners. Answer the following questions regarding the shape of the infield.
Answer:
No Major League ballparks are exactly alike, but certain aspects of the field of play must be uniform across baseball.
The infield must be a square that is 90 feet on each side, and the outfield is the area between the two foul lines formed by extending two sides of said square (though the dirt portion of the field that runs well past the 90-foot basepaths in all Major League parks is also commonly referred to as the infield). The field must be constructed so that the bases are the same level as home plate.
The rulebook states that parks constructed by professional teams after June 1, 1958, must have a minimum distance of 325 feet between home plate and the nearest fence, stand or other obstruction on the right- and left-field foul lines, and 400 feet between home plate and the nearest fence, stand or other obstruction in center field. However, some clubs have been permitted to construct parks after that date with dimensions shorter than those specified.
The pitcher's plate must be a 24-inch by 6-inch slab of whitened rubber that is 10 inches above the level of home plate and 60 feet, 6 inches away from the back point of home plate. It is placed 18 inches behind the center of the mound -- which is erected within an 18-foot diameter circle -- and surrounded by a level area that is 5 feet by 34 inches. The slope of the pitcher's mound begins 6 inches in front of the pitcher's plate and must gradually decrease by 1 inch every foot for 6 feet in the direction of home plate.
Home plate is a 17-inch square of whitened rubber with two of the corners removed so that one edge is 17 inches long, two adjacent sides are 8 1/2 inches each and the remaining two sides are 12 inches each and set at an angle to make a point. The 17-inch side faces the pitcher's plate, and the two 12-inch edges coincide with the first- and third-base lines. The back tip of home plate must be 127 feet, 3 and 3/8 inches away from second base.
The other bases must be 15-inch squares that are between 3 and 5 inches thick, covered by white canvas or rubber and filled with soft material.
Step-by-step explanation:
i have 17 coins. N of them are nickels and the rest are dimes. write an expression in two different ways for the amount of money that i have
Answer:
Step-by-step explanation:
(N)0.05 + (17-N)0.1 = M; M = amount of money I have.
Or 1.7-0.05N = M.
An expression two different ways to the amount of money is equals to
1. 5N + 10 (17 -N) = Y cents
2. N + 2(17 - N) = Y nickels
What is amount?
" Amount is defined as the total of any given quantity."
According to the question,
Total number of coins = 17
Number of nickels coins = N
Number of dimes coin = 17 - N
'Y' express the amount of money
Represent amount of money in cents
1 dime = 10 cents
1 nickel = 5 cents
Expression to represents amount of money in cents,
5N + 10 (17 -N) = Y cents
Expression to represents amount of money in nickels,
1 dime = 2 nickel
N + 2(17 - N) = Y nickels
Hence, an expression two different ways to the amount of money is equals to
1. 5N + 10 (17 -N) = Y cents
2. N + 2(17 - N) = Y nickels
Learn more about amount here
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