Let |r| = 6 at an angle of 30° and |s| = 11 at an angle of 225°. Which expression represents |r – s|?
The resultant of subtraction of both vectors is
|r - s| = √(r² + s² - 2rscos{15})
What are vectors?A vector is an object that has both a magnitude and a direction.
Given is that |r| = 6 at an angle of 30° and |s| = 11 at an angle of 225°.
For the subtraction of vectors, we can write its magnitude as -
|r - s| = √(r² + s² - 2rscos{15})
Therefore, the resultant of subtraction of both vectors is
|r - s| = √(r² + s² - 2rscos{15})
To solve more questions on vectors, visit the link below -
https://brainly.com/question/29740341
#SPJ1
You need to give 250 mcg of adrenaline, and you have a 1 mL ampoule of 1:1000 adrenaline. How many mL do you want?
The volume of adrenaline you want is 0.25mL
How to determine the volume you wantFrom the question, we have the following parameters that can be used in our computation:
Amount to give = 250 mcg of adrenaline
Available = 1 mL of 1 : 1000 of adrenaline
The expression 1 mL of 1 : 1000 of adrenaline means that
1:1000 contains 1 mg in 1 mL (i.e. 1000 microgram/mL)
So, we have
Available = 1 mL * 1000 microgram/mL
Evaluate
Available = 1000 micrograms
This can be expressed as
Available = 1000 mcg
So, we have
Amount to give = 250 mcg of adrenaline
Available = 1000 mcg of adrenaline
When converted to mL, we have
Available = 1 mL of 1 : 1000 of adrenaline
Divide by 4
Amount = 1 mL of 1/4 : 1000/4 of adrenaline
Evaluate
Amount = 1 mL of 1/4 : 250 of adrenaline
This implies that
Amount = 1 mL of 1/4
Evaluate
Amount = 0.25 mL
So, the amount is 0.25 mL
Read more about ratio at
https://brainly.com/question/1781657
#SPJ1
100 POINTS!!! Please help.
Answer:
[tex]\dfrac{1}{a^{20}c^2d^2e^{6}}[/tex]
Step-by-step explanation:
Given expression:
[tex](a^{10}b^{0}cde^{3})^{-2}[/tex]
[tex]\textsf{Apply the exponent rule} \quad a^{-n}=\dfrac{1}{a^n}:[/tex]
[tex]\implies \dfrac{1}{(a^{10}b^{0}cde^{3})^{2}}[/tex]
[tex]\textsf{Apply the exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies \dfrac{1}{a^{(10 \times 2)}b^{(0 \times 2)}c^2d^2e^{(3 \times 2)}}[/tex]
Simplify:
[tex]\implies \dfrac{1}{a^{20}b^{0}c^2d^2e^{6}}[/tex]
[tex]\textsf{Apply the exponent rule} \quad a^0=1:[/tex]
[tex]\implies \dfrac{1}{a^{20}(1)c^2d^2e^{6}}[/tex]
[tex]\implies \dfrac{1}{a^{20}c^2d^2e^{6}}[/tex]
please help asap
will give brainliest
Answer:
m<D should also be 98° due to the congruent angles theorem
Answer:
98
Step-by-step explanation:
Sides AB and DC are parallel.
Sides AD and BC are parallel.
Quadrilateral ABCD is a parallelogram.
Opposite angles of a parallelogram are congruent.
m<D = m<B = 98°
Answer: 98
Given it was not a strike, what is the probability it was a knuckle
ball? Enter the answer as a percent (%)to the nearest tenth.
On solving the provided question, we can say that - here in the percentage obtained = 500 => so, 500/1000X100 = 50%
What is percentage?A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.
here,
total is = 1000
obtained = 500
so, 500/1000X100 = 50%
To know more about percentage visit:
https://brainly.com/question/29306119
#SPJ1
hello i need help with ym math today please and thanks
The annual cost if she chooses to make monthly payment is $1920 and money saved is $170
How to determine the incomes?The given parameters that will help us to determine the incomes are
Mindley switching to insurance comapnyAnnual premium $1750/ yearMonthly premium $160*12 = $1920a) Annual cost if she chooses to make one annual monthly installment is $1920
b) Money saved is she makes one annual payment is $(1920-1750)= $170
3) Volume of gas = 60 L
Efficiency rating = 10.2km/L
Average drive = Volume / Efficiency = 60/10.2 = 5.9km/L
b) Cost of gas = 149.9⊄⊄/L
Number of liters =60
= 60*149.9
=$8994
c) Constant gas price = $149.9⊄/L
Number of weeks /year = 52
=52*149.9
= $7795
4) Morgan pay $15/hr
Number of hours per week = 40
Gross monthly income = 40*15*4
=$2400
b) Monthly income $2400
Amount left after deduction = 85%
=0.85*2400
Net income = $2040
In conclusion Mindley receives $1920 monthly and saves $170
Study more about income determination on https://brainly.com/question/14617337
#SPJ1
If you shift the cubic parent function, F(x)=x^3, down 9 units, what is the equation of the new function
Therefore the table values of which represents a linear function are table 2 and table 3
What is linear equation?A linear equation is a first-order (linear) term and a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. A "linear equation of two variables" is what is sometimes referred to here, where y and x are the variables.
Here,
The values shown in table 2 have same constant rate of change of 3 units.
where as,
The values shown in table 3 have same constant rate of change of 5 units.
Therefore the table values of which represents a linear function are table 2 and table 3
To know more about linear equation , visit
brainly.com/question/12974594
#SPJ1
Which expression is equivalent to -3(x+4)(x-6)-(x^2+8x-10)?
Answer:-4x^2-2x+46.
Step-by-step explanation:
To simplify this expression, you can start by distributing the negative sign to the first set of parentheses:
(-3)(x+4)(x-6)-(x^2+8x-10)
Then, you can distribute the -3 to the terms inside the first set of parentheses:
(-3x-12)(x-6)-(x^2+8x-10)
Then, you can combine like terms:
-3x^2+6x+36-x^2-8x+10
This simplifies to:
-4x^2-2x+46
Therefore, the expression that is equivalent to -3(x+4)(x-6)-(x^2+8x-10) is -4x^2-2x+46.
Further reference to solve algebraic expression;
https://brainly.com/question/27807105
On her to her grandmothers house, Jackie traveled three times as many miles by train as by bus. She traveled four times as many miles by bus as by foot. If Jackie traveled 34 miles in all, how many miles did she travel by train?
She traveled 6.375 miles by train.
What is the speed of an object?Speed is the rate at which an object's position changes, measured in meters per second. For example, if an object starts at the origin, and then moves three meters in three seconds, its speed is one meter per second. The equation for speed is simple: distance divided by time
Given here as per question the formula is x × (4+3×4)=34
∴ x×16=34
x= 6.375
Hence, She traveled 6.375 miles by train.
Learn more about speed here:
https://brainly.com/question/28224010
#SPJ1
list this from least to greatest -$25.18,$48.12,-$24.72,$47.72,-$24.12,$25.12
The listing of the given values from the least to the greatest = -$25.18, -$24.72, -$24.12, $25.12, $47.72 and $48.12.
What is a number line?A number line is defined as the expression that represents the location of real numbers as being a positive number or a negative number.
The negative values which are the least in the number line are usually higher in value than the greater numbers, while the greater values are higher for positive numbers.
Therefore,the arrangement of the given values from least to the greatest = -$25.18, -$24.72, -$24.12, $25.12, $47.72 and $48.12.
Learn more about number line here:
https://brainly.com/question/24644930
#SPJ1
The measures of the angles of a triangle are shown in the figure below. Solve for x.
(5x-17)®
(7x-3)
56°
The measurement of three angles in the triangle are 43°, 81°, 56°.
What are the angles of a triangle?A triangle's interior angles always add up to 180°, whereas its exterior angles are equal to the sum of the two interior angles that are not adjacent to it.
Given three angles,
∠A = (5x - 17)°
∠B = (7x - 3)°
∠C = 56°
We know that in a triangle ∠A + ∠B + ∠C = 180°
By substituting values,
(5x - 17) + (7x - 3) + 56 = 180
12x -20 + 56 = 180
12 x + 36 = 180
12x = 180 - 36
12x = 144
x = 144/12
x = 12
By substituting values of x we get,
∠A = (5x - 17)°
= 5 x 12 - 17
= 60 - 17
= 43
∠A = 43°
∠B = (7x - 3)°
= 7 x 12 - 3
= 84 - 3
= 81
∠B = 81°
To learn more about triangle refer to :
https://brainly.com/question/25215131
#SPJ1
Here is a graph of the function h.
Use the graph to find the following
If there is more than one answer, separate them with commas
(a)
All local minimum values of
h
(b) All values at which h has a local minimum:
The graph also shows two other local maxima, at x=0.5 and x=1.5.
The local minimum(a) -4, -2, 0, 2 (b) The local minimum values of h occur at x = -4, -2, 0, and 2.These values can be seen on the graph as points at which the graph of h changes from decreasing to increasing.At each of these points, the value of h is at a minimum compared to the values of h on either side of the point.All values at which h has a local maximum: 0.5, 1.5All local maximum values of h: 2.5, 4.5.The graph of the function h is a parabola that opens upwards, with a turning point at x=1.This indicates that the function has a local maximum at this point.The local maximum values of h at these points can be determined by looking at the y-values at these points, which are 2.5 and 4.5 respectively.To learn more about All local minimum values refer to:
https://brainly.com/question/2437551
#SPJ1
Find the value of x that makes the quadrilateral a parallelogram?
Answer:
5
Step-by-step explanation:
since the sides of parallelogram are parallel
then 3X+3 = 4X-2 (they are equal because they are alternating angles )
3X+3 = 4X-2 subtract 3X from both sides
3 = X-2. add 2 to both sides
X= 5
Answer:
x = 5
Step-by-step explanation:
As the diagonals of a parallelogram bisect each other (divide into two equal parts):
[tex]\implies 2x+1=x+6[/tex]
[tex]\implies 4x-2=3x+3[/tex]
Solve the first equation for x:
[tex]\implies 2x+1-1=x+6-1[/tex]
[tex]\implies 2x=x+5[/tex]
[tex]\implies 2x-x=x+5-x[/tex]
[tex]\implies x=5[/tex]
Solve the second equation for x:
[tex]\implies 4x-2+2=3x+3+2[/tex]
[tex]\implies 4x=3x+5[/tex]
[tex]\implies 4x-3x=3x+5-3x[/tex]
[tex]\implies x=5[/tex]
Therefore, the value of x that makes the quadrilateral a parallelogram is:
x = 5All exponential functions can be written in many forms. Write the function f(t)=90,000(1.3)^t in the form f(t)=ab^t/5. Round all coefficients to four decimal places.
The expression can be written as [tex]90,000(3.71)^{\frac{t}{5} }[/tex]
What is an exponential function?A function whose value is a constant raised to the power of the argument, especially the function where the constant is e.
Given that, we have to express the function [tex]f(t) = 90,000(1.3)^t[/tex] in the form of [tex]f(t) = ab^{\frac{t}{5} }[/tex]
Comparing both the functions,
[tex]b^\frac{t}{5} = (1.3)^t[/tex]
We can write, [tex](1.3)^t[/tex] as
[tex](1.3)^t = (1.3^5)^\frac{t}{5}[/tex]
[tex]= 3.71^\frac{t}{5}[/tex]
Therefore, the equation ca be written as, [tex]90,000(3.71)^{\frac{t}{5} }[/tex]
Hence, the expression can be written as [tex]90,000(3.71)^{\frac{t}{5} }[/tex]
For more references on exponential function, click;
https://brainly.com/question/14355665
#SPJ1
HELLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLP
Write a letter to your friend describing your hobbies. (80 words)A2/32, Chengal Nagar
Tambaram
Chennai – 600023
May 5, 2021
Dearest Malu,
I hope this letter finds you in the best of health. I received your letter the other day asking how I am spending my leisure time these days.
I have developed many hobbies over the years but collecting stamps and embroidery have been my favourite so far. Stamp collection is something I started as a kid. I had just taken a few pages off my notebook and made it my stamp book. I get so excited every time I see the postman. I wait to see what kind of stamp I will get. Knowing that I have a liking for collection of stamps, my cousins have been sending it across to me every time they find a different stamp. I can’t wait to show you my collection.
Embroidery is another hobby I picked up recently. I always liked embroidered clothes. I just started trying out different stitching patterns. Slowly, I learned almost everything, and now I am selling embroidered frames and dresses. It is so fulfilling to see a piece of work come out so well. I am sending you a gift along with this letter, something I made, as your birthday is fast approaching.
Hope to meet you soon.
Your dearest friend,
Renitaالسلام عليكماخوي عارض شريطPandemic
3 Dylan needs to buy new contact lenses. His ophthalmologist sells 8-lens boxes in
packs of 2 for $52 and 10-lens boxes in packs of 4 for $120. Which option is the
better deal?
Answer:
Dylan should purchase the 10-lens boxes in packs of 4 for $120, as this is the better deal. This option provides 40 lenses for $120, which works out to be $3 per lens. The 8-lens boxes in packs of 2 for $52 only provides 16 lenses for $52, which works out to be $3.25 per lens Therefore, the 10-lens boxes in packs of 4 is the better deal.
Step-by-step explanation:
Answer:
he should buy the 10-lens boxes in packs of 4 for $120
Step-by-step explanation:
Is the set of rational expressions closed under division
Answer:
Step-by-step
Closure property is true for division except for zero.
Hannah simplified the radical below and wants someone to check the work (view image)
Answer:
4|x|y²√(3yz)
She forgot the absolute value sign on x, and she left out the exponent on y.
Step-by-step explanation:
Step 1 is correct.
x may be positive, zero, or negative.
√x is always non-negative. To assure that √x² is non-negative, √x² = |x|.
√16 = 4
√3 = √3
√x² = |x|
√y² × √y² = √y^4 = y²
Since y² is always non-negative, there is no need for absolute value sign.
√y^4 = y²
Answer should be
4|x|y²√(3yz)
draw and divide a rectangle to show each product use a distributive property to find the product 5×14
The product of 5 and 14 using the distributive property is 70.
What is Multiplication?Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.
a × b means that a is added to itself b times or b is added to itself a times.
For three numbers a, b and c, Distributive property states that,
a (b + c) = a b + a c
We have to find the product 5 × 14 using distributive property.
5 × 14 = 5 (12 + 2)
Using distributive property,
5 × 14 = (5 × 12) + (5 × 2)
= 60 + 10
= 70
Hence using distributive property, we can find the product of 5 and 14 as 70.
To learn more about Multiplication, click on the link given below :
https://brainly.com/question/28335468
#SPJ1
Find the value of x.
30°
105°
xo
Exterior angle of triangle x has a value of 135 in this sentence.
What is the simplest technique to measure angles?A protractor can be used to measure angles precisely. Angles are measured in degrees, hence the term "degree measure." Since one full revolution is equivalent to 360 degrees, it is divided into 360 segments.
What exactly is the triangle rule?According to the "sides of a triangle rule," any two sides of a triangle must add up to be longer than the third side.
By extending one side of the triangle, an external angle is formed. An exterior angle is the angle formed by the stretched side and the side that is immediately adjacent.
Practice. Triangle Angle Measurement
via the triangle's external angle characteristic, x = 105 + 30 = 135.
To know more about triangle visit:-
https://brainly.com/question/2773823
#SPJ1
Combine the like terms to create an equivalent expression.
4r + 14 - r - 6 =
[tex]4r + 14 - r - 6[/tex]
Combine Like Terms:
[tex](4r-r)+(14-6)[/tex]
[tex]=\fbox{3r + 8}[/tex]
D. Maria collects postcards. The table gives the
number of each type of postcard she has in her
collection. Use the data to write each ratio in
three different ways.
A. U.S. Landmarks to European Landmarks:
Answer: A. U.S. Landmarks to European Landmarks
Maria has 25 U.S. landmark postcards and 20 European landmark postcards. The ratio of U.S. landmarks to European landmarks can be written as 25:20 or as 25/20.
Alternatively, we can express the ratio as a fraction. If we divide the number of U.S. landmark postcards by the total number of U.S. and European landmark postcards, we get 25/(25+20)=25/45
The last way we can express the ratio as a decimal. By dividing the number of U.S. landmark postcards by the total number of U.S. and European landmark postcards, we can find that the ratio of U.S. landmarks to European landmarks is 25/45 =0.555 or 55.5%
Step-by-step explanation:
Which of the following points best represents the location of -1;
15.
ос
OD
Ов
ОА
+
-2
в с
0
on the number line?
D
2 +
2
value of y please help me
You are going to run at a constant speed of 6.5 miles per hour for 30 minutes. You calculate the distance you will run. What mistake did you make in your calculation? [Use the formula S = dt.]
Answer:
Below
Step-by-step explanation:
S = dt S = distance d = rate = 6.5 m/ hr t = time = 30 min = 1/2 hr
S = (6.5 m/hr) *(1/2 hr) = 3.25 miles
The value of distance you will run will be;
⇒ Distance = 3.25 miles
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
You are going to run at a constant speed of 6.5 miles per hour for 30 minutes.
Here,
Speed = 6.5 miles per hour
Time = 30 minutes
= 30/60 hour
= 1/2 hour
We know that;
⇒ Speed = Distance / Time
Substitute all the values we get;
⇒ 6.5 = Distance / (1/2)
⇒ 6.5 × 1/2 = Distance
⇒ Distance = 3.25 miles
Thus, We get;
⇒ Distance = 3.25 miles
Learn more about the divide visit:
https://brainly.com/question/28119824
#SPJ1
Find the greatest common factor of the
following monomials:
gh5
OOHO
Clear all
10g5h4
Enter the correct answer.
?
DONE
To find the greatest common factor (GCF) between monomials, take each monomial and write it's prime factorization. Then, identify the factors common to each monomial and multiply those common factors together.
What is monomial?Monomial is defined as an expression that has a single non-zero term. It consists of different parts like the variable, the coefficient, and its degree. The variables in a monomial are the letters present in it. The coefficients are the numbers that are multiplied by the variables of the monomial. The degree of a monomial is the sum of the exponents of all the variables. Let us consider an expression 6xy2. The variables, the coefficient, and the degree of this monomial are shown in the table given below. Observe the table to learn the various parts of the monomial 6xy2.In algebra, a monomial is an expression that has a single term, with variables and a coefficient. For example, 2xy is a monomial since it is a single term, has two variables, and one coefficient. Monomials are the building blocks of polynomials and are called 'terms' when they are a part of larger polynomials. In other words, each term in a polynomial is a monomial.To learn more about coefficients refer to:
https://brainly.com/question/1038771
#SPJ1
Graph the linear equation.
4x+6y=−12
Plot two points on the line to graph the line.
Answer: (-3,0) and (0,-2)
Step-by-step explanation:
factor each square root
0.7 times square root of 300
-0.125 times square root of 192
Answer:
To factor the first expression, "0.7 times square root of 300", we can rewrite it as:
0.7 * sqrt(300)
The prime factorization of 300 is 2 * 2 * 3 * 5 * 5, so we can rewrite the expression as:
0.7 * sqrt(2 * 2 * 3 * 5 * 5)
Since the square root of a number is the same as the square root of that number's prime factorization, we can rewrite the expression as:
0.7 * sqrt(2) * sqrt(2) * sqrt(3) * sqrt(5) * sqrt(5)
Combining like terms, we get:
0.7 * 2 * sqrt(2) * sqrt(3) * sqrt(5)
= 1.4 * sqrt(2) * sqrt(3) * sqrt(5)
This is the fully factored form of the expression "0.7 times square root of 300".
To factor the second expression, "-0.125 times square root of 192", we can rewrite it as:
-0.125 * sqrt(192)
The prime factorization of 192 is 2 * 2 * 2 * 2 * 2 * 2, so we can rewrite the expression as:
-0.125 * sqrt(2 * 2 * 2 * 2 * 2 * 2)
Since the square root of a number is the same as the square root of that number's prime factorization, we can rewrite the expression as:
-0.125 * sqrt(2) * sqrt(2) * sqrt(2) * sqrt(2) * sqrt(2) * sqrt(2)
Combining like terms, we get:
-0.125 * 6 * sqrt(2)
= -0.75 * sqrt(2)
This is the fully factored form of the expression "-0.125 times square root of 192".
Answer:
for the second one the answer is - square root of 3
Step-by-step explanation:
i could only solve the second one sorry
(5 x 7) + (n x 4) = 5 x (7+ 4) write each missing number
The missing number in the expression (5 x 7) + (n x 4) = 5 x (7+ 4) is 5.
What are GCF and distributive property?The GCF of two or more than two numbers is the highest number that divides the given two numbers completely.
We also know that distributive property states a(b + c) = ab + ac.
Given, An expression (5 × 7) + (n × 4) = 5 × (7 + 4).
Now, If we expand the RHS we have,
5×(7 + 4).
= (5 × 7) + (5 × 4).
Now, Writing the obtained RHS with LHS we have,
(5 × 7) + (n × 4) = (5 × 7) + (5 × 4).
So, The missing number is 5.
learn more about the distributive property here :
https://brainly.com/question/5637942
#SPJ2
[-12] + [4] find the absolute value of each integer then add them
Hello there!
Answer:
16
Step-by-step explanation:
[tex] |x| = x \: \: \: if \: \: x \: \geqslant 0 \\ |x| = - x \: \: \: if \: \: \: x \: \leqslant 0[/tex]
-12 < 0 so |-12| = -(-12) = 12
4 > 0 so |4| = 4
|-12| + |4| = 12 + 4 = 16
Answer:
16
Step-by-step explanation:
Hello! This question is looking for the absolute value of integers. The absolute value is the distance the number has from zero. For example, -12 as twelve numbers away from zero, twelve away in the negative direction. The absolute value of -12, then, is just twelve. An easy way to remember this is to take away the negative sign when taking the absolute value, since an absolute value can never be negative. The absolute value sign is represented by a squarish bracket [ and ].
This question says to find the absolute value of each integer and then add the two. First we have [-12]. This is 12 away from zero, and we can take away the - sign from the asked integer and we get 12.
The second integer given is 4, and when we take the absolute value of 4, [+4], we get positive four. This is because four is four spaces away from zero on the number line.
Thus, we have +12 and +4 as are values to add since they are the absolute values and we can form this equation
12+4=16
Thus, the answer is 16.
Hope this helps! Remember the hint, when something has brackets like that or asks for the absolute value, take away a negative sign and make it positive! Have a great day!