Answer:
Step-by-step explanation:
The formula for the dot product of vectors is
u·v = |u||v|cosθ
where |u| and |v| are the magnitudes (lengths) of the vectors. The formula for that is the same as Pythagorean's Theorem.
[tex]|u|=\sqrt{14^2+9^2}[/tex] which is [tex]\sqrt{277}[/tex]
[tex]|v|=\sqrt{3^2+6^2}[/tex] which is [tex]\sqrt{45}[/tex]
I am assuming by looking at the above that you can determine where the numbers under the square root signs came from. It's pretty apparent.
We also need the angle, which of course has its own formula.
[tex]cos\theta=\frac{uv}{|u||v|}[/tex] where uv has ITS own formula:
uv = (14 * 3) + (9 * 6) which is taking the numbers in the i positions in the first set of parenthesis and adding their product to the product of the numbers in the j positions.
uv = 96.
To get the denominator, multiply the lengths of the vectors together. Then take the inverse cosine of the whole mess:
[tex]cos^{-1}\theta=\frac{96}{111.64676}[/tex] which returns an angle measure of 30.7. Plugging that all into the dot product formula:
[tex]u*v=\sqrt{277}*\sqrt{45}cos(30.7)[/tex] gives you a dot product of 96
The path followed by a roller coaster as it climbs up and descends down from a peak can be modeled by a quadratic function, where h(x) is the height, in feet, and x is the horizontal distance, also in feet. The path begins and ends at the same height, covers a total horizontal distance of 100 feet, and reaches a maximum height of 250 feet. Which of the functions could be used to model this situation? A. h(x)=-0.1x^2-50x+250 B. h(x)=-0.1(x-50)^2+250 C. h(x)=-0.1(x-100)^2+250 D. h(x)=-0.1x^2+100x+250
Answer:
C
Step-by-step explanation:
0.1(x - 100)² + 250
0.1[(x - 100)(x - 100)] + 250
0.1(x² -200x + 10000) + 250
0.1x² - 20x + 1000 + 250
0.1x² - 20x + 1250
0.1x² - 25x + 5x + 1250
0.1x(x - 250) + 5(x + 250)
∴ (0.1x + 5)(x - 250) or (0.1x + 5)(x + 250)
There are 39 chocolates in a box, all identically shaped. There 16 are filled with nuts, 13 with caramel, and 10 are solid chocolate. You randomly select one piece, eat it, and then select a second piece. Find the probability of selecting a nut chocolate followed by a caramel chocolate.
Answer:
16/117Step-by-step explanation:
Probability is the likelihood or chance that an event will occur.
Probability = expected outcome of event/total outcome of event
Given the total amount of chocolate in a box = 39chocolates
Amount of nuts = 16
Mount of caramel = 13
Amount of solid chocolate = 10
If he randomly selects a nut chocolate and eat, the probability of selecting a nut chocolate = Amount of nuts/total chocolate in the box = 16/39
IF he selects a seconnd piece (caramel chocolate) and eat, the probability of selecting a caramel chocolate = Amount of caramel/total chocolate in the box = 13/39 = 1/3
The probability of selecting a nut chocolate followed by a caramel chocolate will be 16/39*1/3 = 16/117
What did you multiply together to find the sales tax?
Answer:
Step-by-step explanation:
To find the sales tax on a purchased or sold item, first convert the sales tax percentage into the equivalent decimal fraction. If the sales tax rate is 5.5%, then the desired decimal fraction is 0.055. Next, multiply the selling price of the purchased or sold item by this decimal fraction. If, for example, the selling price is $100, the sales tax is 0.055($100) = $5.50
Rewrite the expression 4+[tex]\sqrt{16-(4)(5)}[/tex]/2 as a complex number in standard form,a+bi .
Answer:
[tex]2+i[/tex]
Step-by-step explanation:
Given the expression:
[tex]\dfrac{4+\sqrt{16-(4)(5)}}{2}[/tex]
To find:
The expression of above complex number in standard form [tex]a+bi[/tex].
Solution:
First of all, learn the concept of [tex]i[/tex] (pronounced as iota) which is used to represent the complex numbers. Especially the imaginary part of the complex number is represented by [tex]i[/tex].
Value of [tex]i =\sqrt{-1}[/tex].
Now, let us consider the given expression:
[tex]\dfrac{4+\sqrt{16-(4)(5)}}{2}\\\Rightarrow \dfrac{4+\sqrt{16-(4\times 5)}}{2}\\\Rightarrow \dfrac{4+\sqrt{16-20}}{2}\\\Rightarrow \dfrac{4+\sqrt{-4}}{2}\\\Rightarrow \dfrac{4+\sqrt{(-1)(4)}}{2}\\\Rightarrow \dfrac{4+\sqrt{(-1)}\sqrt4}{2}\\\Rightarrow \dfrac{4+\sqrt4i}{2} \ \ \ \ \ (\because \sqrt{-1} =i) \\\Rightarrow \dfrac{4+2i}{2}\\\Rightarrow 2+i[/tex]
So, the given expression in standard form is [tex]2+i[/tex].
Let us compare with standard form [tex]a+bi[/tex] so we get [tex]a =2, b =1[/tex].
[tex]\therefore[/tex] The standard form of
[tex]\dfrac{4+\sqrt{16-(4)(5)}}{2}[/tex]
is: [tex]\bold{2+i}[/tex]
Pls ASAP help me with number 14
Answer:
D. 19
Step-by-step explanation:
because they are parallel bases you can compare
63/57 = 21/x
x = 19
Answer: D. 19
Let x by the length of CG. Since the two bases are parallel, we can create the following equation using proportions:
[tex]\dfrac{63}{21}=\dfrac{57}{x}[/tex]
Simplify left side of equation
[tex]3=\dfrac{57}{x}[/tex]
Multiply both sides by x
[tex]3x=57[/tex]
Divide both sides by 3
[tex]x=19[/tex]
Let me know if you need any clarifications, thanks!
One day at a school 70% of the students wore a polo shirt.
80% of the students wearing polo shirts were boys.
What percentage of students were girls who wore polo shirts?
Answer:
14%
Step-by-step explanation:
If the percentage of boys wearing polo shirts were boys, then the rest has to be girls. So 100%-80%=20%. However, we are not done here.
We have only figured out the percentage of girls out of the total number of people wearing polo shirts. We want to find the percentage of girls wearing polo shirts out of the whole school. To do that, we multiply 20% by 70%, since 20% of the polo shirt wearers were girls, and 70% of the entire student body is wearing a polo shirt.
Multiplying those two together gets you 14%.
Answer:
14%
Step-by-step explanation:
NEED HELP ASAP I believe the answer is C but I’m not sure
Find the value of x.
A) 7
b) 17
c)49
d)61
Answer:
x=17
Step-by-step explanation:
7x and 2x+27 are supplementary meaning they add up to be 180 degrees.
so, 7x + 2x + 27 = 180
9x + 27 =180
9x = 153
x = 17
hope this helped
A particular zebra is the 10th fastest animal in its herd and also
the 10th slowest animal in its hard. If every zebra in the herd is
of a different speed, then how many zebra are there in the herd?
Answer:
19
Step-by-step explanation:
The zebra is the 10th fastest, so there are 9 zebras that are faster.
It's also the 10th slowest, so there are 9 zebras that are slower.
The total number of zebras is therefore 9 + 1 + 9 = 19.
What is the approximate circumference of the circle shown below?
Answer:
[tex]\boxed{\sf 43.35 \ cm}[/tex]
Step-by-step explanation:
Apply formula for the circumference of a circle.
[tex]\sf C=\pi d[/tex]
The diameter [tex]\sf d[/tex] is 13.8 cm.
[tex]\sf C=\pi (13.8)[/tex]
[tex]\sf C= 43.3539786195...[/tex]
[tex]\sf{C} \approx \sf{43.35}[/tex]
Answer:
43.4 cm
Step-by-step explanation:
Circumference of the circle = 2πr
r = radius, π = [tex]\frac{22}{7}[/tex]
f = diameter÷2
=13.8 ÷ 2
= 6.9
circumference = [tex]2 * \frac{22}{7} * 6.9\\[/tex]
= [tex]\frac{303.6}{7}[/tex]
= 43.37 cm or 43.4 cm
MATH HELP ASAP BRAINLIEST!!!!
Answer:
first option
Step-by-step explanation:
Given
- 3x - 2y = 1 → (1)
- x + y = 3 → (2)
Rearrange (2) by adding x to both sides, that is
y = x + 3
Substitute y = x + 3 into (1)
- 3x - 2(x + 3) = 1 ← is the equation to be solved for x
naledi climbed up a mountain. Her initial altitude is 40 meters above sea level, and increased by 10 meters per hour. let g(n) be naledi altitude at the beginning of nth hour of her climb. g is a sequence. what kind of sequence is it. arithmetic or geometric sequence? complete the recursive formula for g(n). g(1)= ? g(n) = g(n-1) (+ or *) ?
Answer: [tex]U_{n} =(40)+(n-1)(10)[/tex]
Step-by-step:
[tex]U_{n} =a+(n-1)d[/tex]
a = 40
d = 10
[tex]U_{n} =(40)+(n-1)(10)[/tex] is the formula for nth hour
find the area of the quadrilateral ABCD in which ab=5cm,bc=4.5cm,cd=3.5cm,da=4cm and ac=6.5cm
Answer:
A(ABCD) ≈ 17.285 cm²
Step-by-step explanation:
Heron formulaA = √s(s - a)(s - b)(s - c)
s = (a + b + c)/2
a ; b ; c = the sides of the triangle
A(ABCD) = A(ABC) + A(ACD)A(ABC) = √s(s - AB)(s - BC)(s - AC)s = (AB + BC + AC)/2 = (5cm + 4.5cm + 6.5cm)/2 = 16cm/2 = 8 cm
A(ABC) = √8(8 - 5)(8 - 4.5)(8 - 6.5)
= √8×3×3.5×1.5
= √126
≈ 11.225 cm²
2. A(ACD) = √s(s - AC)(s - CD)(s - AD)
s = (AC + CD + AD)/2 = (6.5cm + 3.5cm + 4cm)/2 = 14cm/2 = 7 cm
A(ACD) = √7(7 - 6.5)(7 - 3.5)(7 - 4)
= √7×0.5×3.5×3
= √36.75
≈ 6.060 cm²
3. A(ABCD) = 11.225cm² + 6.060cm² = 17.285 cm²
How is the graph of y=(x+1)^2-9 transformed from the graph of y=x^2? a shifted 1 unit left and 9 units up b shifted 1 unit right and 9 units up c shifted 1 unit left and 9 units down d shifted 1 unit right and 9 units down
Answer:
Step-by-step explanation:
Due to the '+1', the graoph of x^2 is shifted 1 unit to the left. The '+9' results in the entire graph being shifted downward 9 units.
WILL GIVE BRIANLIEST Circle O is shown. Tangents B C and B A intersect at point B outside of the circle. The measure of the first arc formed is 146 degrees. In the diagram of circle O, what is the measure of ? 34° 45° 68° 73°
Answer: 34°
Step-by-step explanation:
The Arc formed by segment AC:
Total measure of an arc = 360°
Measure of Major arc AC = (360° - measure of minor arc)
Minor arc = 146°
THEREFORE,
Major arc AC = (360° - 146°) = 214°
A° = B° = (214° - 146°) / 2 ( tangent - tangent theorem)
Angle formed by tangent AB and BC = difference between major and minor arcs divided by 2 : (Major arc - minor arc) / 2
(214 - 146)° / 2 = 68° / 2 = 34°
The measure of ∠ABC as shown in the circle is 34°.
CircleA circle is the locus of a point such that all the points are equidistant from a fixed point known as the center.
∠OCB and ∠OAB = 90° (angle between a tangent and radius)
∠OCB + ∠OAB + ∠COA + ∠CBA = 360° (angles in a quadrilateral)
90 + 90 + 146 + ∠CBA = 360
∠CBA = 34°
The measure of ∠ABC as shown in the circle is 34°.
Find out more on Circle at: https://brainly.com/question/22965557
He Brought 10 packages of AA and AAA batteries for a total of 72 batteries.
The AA batteries are sold in packages of 6, and the AAA batteries are sold in packages of 8. Write a system of equations that can be solved to find how many packages of each type of battery Dan bought. Remember to define your variables.
Please answer in full! Thank you
Answer:
4 packages of AA batteries
6 packages of AAA batteries.
Step-by-step explanation:
Let the number of packages of AA batteries bought be x
Let
the number of packages of AAA batteries bought be Y
He Brought 10 packages of AA and AAA
thus,
x+y = 10 equation 1
Given
The AA batteries are sold in packages of 6, it means one packet contains 6 batteries
Thus,
Total number of AA batteries in x packages = 6x
The AAA batteries are sold in packages of 8, it means one packet contains 8 batteries
Thus,
Total number of AAA batteries in y packages = 8y
Given total no. of batteries is 72
thus
6x + 8y = 72 equation 2
x+y = 10
y = 10-x ---using this in equation 2
6x + 8(10 - x) = 72
=> 6x + 80 - 8x = 72
=> -2x = 72-80 = -8
=> x = -8/-2 = 4
y = 10 -x = 10 -4 = 6
y = 6
Thus,
he bought 4 packages of AA batteries
6 packages of AAA batteries.
Discussion Topic There are four basic operations: addition, subtraction, multiplication, and division. Do you think these four operations can be performed on polynomials? What would it look like to perform these operations on polynomials? Which operation do you think would be the simplest? Which do you think will be difficult?
Step-by-step explanation:
1. Yes addition, subtraction, multiplication, and division can be performed on polynomials. like our everyday arithmetic dealings with mathematical operators, polynomials are no exception when it comes to math operators, the four basic operations addition, subtraction, multiplication, and division can be performed on polynomials as well.
2. It can be less handy plus the operation can get messy if you do not have a good sense/understanding/hold of what you are doing things can get messy.
3. I personally know that the simplest is the addition of polynomials
4. I cant say which is difficult, but the operation that can get things messy for me most time is the division operation
Polynomial
Total Number
of Roots
Maximum
Number
of Complex Roots
603 - 8.02 +53 +1 = 0
-4,3 - 2 + 5 = 404
Answer:In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. An example of a polynomial of a single indeterminate, x, is x2 − 4x + 7.
Step-by-step explanation:
might help
ILL GIVE BRAINLIEST PLS HELP
A stick has a length of $5$ units. The stick is then broken at two points, chosen at random. What is the probability that all three resulting pieces are longer than $1$ unit?
Answer:
1/5
Step-by-step explanation:
The stick has a length of 5 units
The stick is broken at two points chosen at random
First break: the probability that you get a piece that is 1 unit or longer than 1 units= 1/5.
Second break, the probability that you get a piece that is 1 unit or longer than 1 units is 1/5.
Therefore,
The total probability =probability of first break * probability of second break * original stick unit
=1/5 * 1/5 * 5
= 1/25 *5
=5/25
=1/5
Are these fractions equivalent or
nonequivalent?
Answer:
no
Step-by-step explanation:
there is no factor to convert one into the other.
moreover, 19 is prime and 9 is not, so no way.
A bookcase has 3 shelves with a total of 24 books. The top shelf has 8 mystery books. The middle shelf has 10 math books. The bottom shelf has 6 science books. Two books are now taken off each shelf. What fraction of the books remaining on the three shelves are math books? Express your answer as a common fraction.
Answer:
4/9
Step-by-step explanation:
So, the ratio of the books is 8:10:6. After 2 books were taken off of each shelf, it became 6:8:4. All of these numbers added up is 18. So that means 8/18 of the books are math books, which can be simplified to 4/9.
Answer:
4/9
Step-by-step explanation:
−2(1 − 4x) = 3x + 8
Answer: x = 2
Step-by-step explanation:
First, Distribute
-2+8x=3x+8
Then, Subtract 3x
-2 + 5x=8
Then, Add 2
5x=10
Then, Divide by 5
x=2
Hope it helps <3
Answer:
-2(1-4x)=3x+8
distributive property
-2+8x=3x+8
subtract 8 on both sides
-2-8+8x=3x=-10+8x
now subtract 8x on both sides which equal: -10=-5x
now it part of the step and divide -5 on both sides to leave x or solve for x
-10/-5=x=2=x
x=2
Step-by-step explanation:
HALLLLPPP Let g(x) = 2x and h(x) = x^2 + 4. Evaluate each expression: g(-2) - h(4)
Answer:
-24
Step-by-step explanation:
g(-2) = 2(-2)
g(-2) = -4
h(4) = 4² + 4
h(4) = 16 + 4
h(4) = 20
g(-2) - h(4)
-4 - 20
= -24
Answer:
g(-2) - h(4) = - 24Step-by-step explanation:
g(x) = 2x
To find g( -2) substitute - 2 into g(x)
That's
g( -2) = 2(-2) = - 4
h(x) = x² + 4
To find h(4) substitute 4 into h(x)
That's
h(4) = (4)² + 4 = 16 + 4 = 20
So
g(-2) - h(4) is
- 4 - 20
= - 24
Hope this helps you
4(x − 7) = 0.3(x + 2) + 2.11
Step-by-step explanation:
[tex]4(x-7)=0.3(x+2)+2.11\\\\Distribute\\\\4x+28=0.3(x+2)+2.11\\\\Distribute\\\\4x+28=0.3x+0.6+2.11\\\\Combine\\like\\terms\\\\4x+28=0.3x+2.71\\\\Subtract\\\\3.7x+28=2.71\\\\Subtract\\\\3.7x=-25.29\\\\Divide\\\\x=\tex{ about }6.83513514[/tex]
Hope it helps <3
Answer:
x = 83/10=8^3/10=8.3
Step-by-step explanation:
4(x − 7) = 0.3(x + 2) + 2.11
Use the distributive property to multiply 4 by x−7.
4x−28=0.3(x+2)+2.11
Use the distributive property to multiply 0.3 by x+2.
4x−28=0.3x+0.6+2.11
Add 0.6 and 2.11 to get 2.71.
4x−28=0.3x+2.71
Subtract 0.3x from both sides.
4x−28−0.3x=2.71
Combine 4x and −0.3x to get 3.7x.
3.7x−28=2.71
Add 28 to both sides.
3.7x=2.71+28
Add 2.71 and 28 to get 30.71.
3.7x=30.71
Divide both sides by 3.7.
x= 3071/370
Expand 3.7/30.71≈8.3 by multiplying both numerator and the denominator by 100.
x = 83/10
Please answer this question now
Answer:
469.4ft²
Step-by-step explanation:
We have Triangle WXY
In the question, we are given already
Angle W = 27°
Angle X = ?
Angle Y = 40°
Side w =?
Side x = ?
Side y = 38ft
Area of the triangle= ?
Step 1
We find the third angle = Angle X
Sum of angles in a triangle = 180°
Third angle = Angle X= 180° - (27 + 40)°
= 180° - 67°
Angle X = 113°
Step 2
Find the sides w and x
We find these sides using the sine rule
Sine rule or Rule of Sines =
a/ sin A = b/ Sin B
Hence for triangle WXY
w/ sin W = x/ sin X = y/ sin Y
We have the following values
Angle W = 27°
Angle X = 113°
Angle Y = 40°
We are given side y = 38ft
Finding side w
w/ sin W= y/ sin Y
w/sin 27 = 38/sin 40
Cross Multiply
sin 27 × 38 = w × sin 40
w = sin 27 × 38/sin 40
w = 26.83879ft
w = 26.84ft
Finding side x
x / sin X= y/ sin Y
x/ sin 113 = 38/sin 40
Cross Multiply
sin 113 × 38 = x × sin 40
x = sin 113 × 38/sin 40
x = 54.41795ft
x = 54.42ft
To find the area of triangle WXY
We use heron formula
= √s(s - w) (s - x) (s - y)
Where S = w + x + y/ 2
s = (38 + 26.84 + 54.42)/2
s = 59.63
Area of the triangle = √59.63× (59.63 - 38) × (59.63 - 26.84 ) × (59.63 - 54.42)
Area of the triangle = √
Area of the triangle = 469.40772706541ft²
Approximately to the nearest tenth =469.4yd²
Given here is the price list of vegetables shown at a Mother Dairy vegetable Booth.
Mrs. Khanna brought the following vegetables:
potatoes
[tex]2 \frac{1}{2} [/tex]
onions
[tex]3 \: kg[/tex]
Peas
[tex]1 \frac{1}{2} kg[/tex]
Carrots
[tex]1 \frac{1}{2} kg[/tex]
She Gave a 500 - Rupee note to the man at the counter. How Much balance did she get?
Answer:
Total amount received by Mrs Khanna will be 182.5 Rs.
Step-by-step explanation:
Cost of the potatoes = 25 Rs per kg
Cost of [tex]2\frac{1}{2}[/tex] kg potatoes = Weight of the potatoes × Per kg cost of the potatoes
= 2.5 × 25
= 62.5 Rs
Cost of onions = 30 Rs per kg
Cost of 3 kg onions = 3 × 30
= 90 Rs
Per kg cost of Peas = 70 Rs
Cost of [tex]1\frac{1}{2}[/tex] kg Peas = 1.5 × 70
= 105 Rs
Per kg cost of Carrots = 40 Rs
Cost of [tex]1\frac{1}{2}[/tex] kg Carrots = 1.5 × 40
= 60 Rs
Total amount of the vegetables = 62.5 + 90 + 105 + 60
= 317.5 Rs
Since she gave a note of 500 Rs
Balance amount she got = 500 - 317.5
= 182.5 Rs
Therefore, total amount received by Mrs Khanna will be 182.5 Rs.
– 4 = 5(p – 2)
plz help me if you know this.
Answer:
p = 6/5
Step-by-step explanation:
-4 = 5(p - 2)
-4 = 5p - 10
-4 + 10 = (5p - 10) + 10
6 = 5p
6/5 = (5p)/5
6/5 = p
p = 6/5
Answer:
p = 6/5
Step-by-step explanation:
-4 = 5(p - 2) (DISTRIBUTE)
-4 = 5p - 10 (ADD 10 TO BOTH SIDES)
6 = 5p (DIVIDE BY FIVE ON BOTH SIDES)
p = 6/5
y + 2 = -3 (x - 4) Complete the missing value in the solution to the equation. (____, -2)
Answer:
( 4,-2)
Step-by-step explanation:
y + 2 = -3 (x - 4)
We are given y = -2
-2+2 = -3 (x-4)
0 = -3(x-4)
Divide by -3
0 = x-4
Add 4 to each side
4 = x-4+4
4 =x
Answer:4
Step-by-step explanation:
11/12-1/6q+5/6q-1/3 it says its wrong
Answer:
2/3q + 7/12
Step-by-step explanation:
If you are trying to simplify your expression
4/6q + 7/12
2/3q + 7/12
A pound is approximately 0.45 kilogram. A person weighs 87 kilograms. What is the person’s weight, in pounds, when rounded to the nearest whole number?
Answer:
193.33333 pounds
Step-by-step explanation:
Divide 87kg by 0.45
So, it's 87 ÷ 0.45 = 193.3333333
Answer: 190
Step-by-step explanation: