a. <-13/2,-13/2>
Step-by-step explanation:The projection of a vector u onto another vector v is given by;
[tex]proj_vu[/tex] = [tex](\frac{u.v}{|v|^2})v[/tex] ----------------(i)
Where;
u.v is the dot product of vectors u and v
|v| is the magnitude of vector v
Given:
u = <-6, -7>
v = <1, 1>
These can be re-written in unit vector notation as;
u = -6i -7j
v = i + j
Now;
Let's find the following
(i) u . v
u . v = (-6i - 7j) . (i + j)
u . v = (-6i) (1i) + (-7j)(1j) [Remember that, i.i = j.j = 1]
u . v = -6 -7 = -13
(ii) |v|
|v| = [tex]\sqrt{(1)^2 + (1)^2}[/tex]
|v| = [tex]\sqrt{2}[/tex]
Substitute these values into equation (i) as follows;
[tex]proj_vu[/tex] = [tex][\frac{-13}{(\sqrt{2}) ^2}][i + j][/tex]
[tex]proj_vu[/tex] = [tex]\frac{-13}{2} [i + j][/tex]
This can be re-written as;
[tex]proj_vu[/tex] = [tex]\frac{-13}{2}i + \frac{-13}{2}j[/tex]
[tex]proj_vu[/tex] = [tex]<\frac{-13}{2}, \frac{-13}{2}>[/tex]
Activity 1 : Complete Me Directions write the statement or a reason and two column proof used two different definitions postulates theorems in geometry to support the given statement.
Paki ANSWER naman
Henry is buying orange juice to make punch for a party. He can buy the juice in 32-oz cartons for $2.56 each or 48-oz cartons for $3.36 each. Which is the better value? Use the drop-down menus to explain your answer.
Answer:
the 48
Step-by-step explanation:
fairly obvious
A bank account starts with $3.00. The amount in the account doubles every year .
Answer:
Step-by-step explana
multiply it by 2 or sdd itself to it
The account will have $1536.007 after 9 years.
Part A:
To express the total amount of money A(t) in the account after 7 years, we can use the formula:
A(t) = P[tex](2^t)[/tex]
where:
A(t) is the total amount in the account after t years,
P is the initial amount in the account (starting with $3.00 in this case),
t is the number of years.
Substituting the values into the formula, we get:
A(t) = 3 ([tex]2^7[/tex])
A(t) = 3 x 128
A(t) = 384
Therefore, the total amount of money in the account after 7 years is $384.
B) To find out after how many years the account will have $1536.007, we need to solve the equation:
1536.007 = 3 [tex](2^t)[/tex]
Dividing both sides of the equation by 3, we get:
512.0023333333 = [tex]2^t[/tex]
Taking the logarithm (base 2) of both sides, we have:
log2(512.0023333333) = t
t = 9.000317.
Therefore, the account will have $1536.007 after 9 years.
Learn more about Equation here:
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i will give brainliest if you wanttt!
Answer:
8 + 1.5x + 0.75y = pizza_cost
Step-by-step explanation:
It is given that every 10-inch cheese pizza costs ($8), meaning that this will be the constant.
Let (x) represent the number of inches added to the pizza. Since each extra additional inch costs ($1.5) thus one adds (1.5x) to the equation.
Let (y) represent the number of toppings. Every extra topping costs ($0.75) therefore one has to add (0.75y) to the equation.
Putting all of the elements together one gets the equation,
8 + 1.5x + 0.75y
Helppp quick! That’s the question^ please help guysss
Answer:
The slope represents the cost per gallon for heating oil while the y-intercept represents the fee for heating oil.
[tex]-a-\frac{7}{8} a[/tex]
paso a paso
Step-by-step explanation:
-a-7a/8
-8a-7a/8
-15a/8
Hope it helps you
Answer:
Step-by-step explanation:
WE have to find the least common denominator and it is 8
[tex]-a =\frac{-a*8}{1*8}=\frac{-8a}{8}\\\\-a -\frac{7}{8}a=-\frac{8}{8}a-\frac{7}{8}a\\\\=\frac{-8a-7a}{8}\\\\=\frac{-15a}{8}\\\\[/tex]
5 to the power -2 * 5x is equal to 1 solve for x
5^-2 * 5x = 1
Simplify:
5^-2 = 1/25
Now you have 1/25 * 5x = 1
1/25 x 5 = 1/5
1/5x = 1
Divide both sides by 1/5 ( when dividing by a fraction, flip the fraction over an multiply)
x - 1 x 5/1 = 5
X = 5
Answer:
x = 5
Step-by-step explanation:
This statement translates into 5^(-2)*5x = 1, which by rules of exponents simplifies to:
5x x
--------- = 1, or ----- = 1
5^2 5
Cross-multiplying, we get x = 5
4 out of every 12 children in a school are girls. What is the ratio of boys to girls in the school?
Answer:
1:3. That's the answer to this question.
Last question of the day :)
Answer:
yehshjdjejrdjjej3u Rudd ixjje
PLEASE HELP QUICKLY!!! Use the following image to answer the questions below:
Find the equation of the line with a slope of 2 and a point of (5,11)
PLEASE HELP !!!! THANKS !!!
Answer:
y=2x+1
Step-by-step explanation:
Hi there!
We are given the slope (m), which is 2, as well as the point (5,11).
We need to find the equation of the line.
There are 3 ways to write the equation of the line, but the most common type is slope-intercept form, or y=mx+b, where m is the slope and b is the y intercept
We're already given the slope (2), so we can substitute it into the equation right away
here's the equation so far:
y=2x+b
now we need to find b.
We can do this by plugging (5,11) into the equation, as the line passes through that point.
Substitute x as 5 and 11 as y
11=2(5)+b
multiply
11=10+b
subtract 10 from both sides
1=b
substitute 1 as b into the equation
y=2x+1
Hope this helps! :)
find -15(-8)
A. 120
B. 80
C. -23
D. -120
Answer:
A
Step-by-step explanation:
-15(-8)
=+(15*8)
=120
So, the ans is A
how do you translate "six more than x is equal to four." as a equation.
Answer:
6>x=4
hope that helps!
please mark brainiest<3
Which parallelograms have perpendicular diagonals
Answer: If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus. If one diagonal of a parallelogram bisects a pair of opposite angles, then the parallelogram is a rhombus. To prove a square, you must prove it is both a rectangle and a rhombus.
19. Which of the following are examples of segments
from the figure?
BCD
D
CA
BAD
DA
AB
BD
Answer:
BCD
Step-by-step explanation:
You can easily find out by the points at the end of line. These points indicate that this is line segment.
PLEASE HELP HURYYYYYYYYY
Answer:
273 - 153.94 = 119.1 [tex]in^{2}[/tex]
Step-by-step explanation:
area of a trapezoid - area of a circle = shaded area
which tessellation uses more than one type of regular polygon?
Answer:
semi-regular tessellations
Step-by-step explanation:
Find the measure of angle A
Answer:
This is an isosceles triangle, meaning it has 2 congruent angles and one other angle.
Looking at this triangle, we know that ∠B = ∠C.
∠B = 57 degrees
All the angles in a triangle add up to 180, so you need to subtract the two values from 180 to get ∠A.
∠A = 180 - 57 - 57
= 66 degrees
Hope this helps!
Find the measure of C to the nearest degree.
Let the ∠C be : θ
From the figure, We can see that the Side which is opposite to angle θ is measuring 7 units
Also, We can notice that Hypotenuse is 11 units
As we are dealing with opposite and hypotenuse, we can clearly use Sinθ to find out the angle θ
We know that :
[tex]\bigstar \ \ \boxed{\sf{Sin\theta = \dfrac{Opposite \ Side}{Hypotenuse}}}[/tex]
[tex]\implies \sf{Sin\theta = \dfrac{7}{11}}[/tex]
[tex]\implies \sf{\theta = Sin^{-1}\bigg(\dfrac{7}{11}\bigg)}[/tex]
[tex]\implies \sf{\theta = 39.52^{\circ}}[/tex]
Answer : The measure of ∠C to the nearest degree is 38°
HELP PLZZZZZZZ ITS FOR A TESTTT
Answer:
x = 9 , y = 27
Step-by-step explanation:
Given that the given polygons are similar , So their corresponding sides will be proportional .
Look at the base sides . They are 32 & 24. So the , ratio of sides is ,
=> Ratio = 32/24 = 4/3 .
This ratio will be same for all sides .
So that ,
=> x - 1 / 6 = 4/3
=> 3x - 3 = 24
=> 3x = 27
=> x = 9
Similarly ,
=> y + 1 / 21 = 4/3
=> 3y + 3 = 84
=> 3y = 81
=> y = 27
So the correct choice is last option .
Which is a quadratic function?
A y = X-9
B y = x² +9
C y = x + 2x -9
Answer:
B y = x² +9
Step-by-step explanation:
A quadratic function must have the highest power of x being x^2 and must have an x^2 term
A y = X-9 - linear
B y = x² +9 quadratic
C y = x + 2x -9 - linear
what is the a value of the vertex form...
y = (x - 3 )^2 - 36
Answer: I'm not smart or nun but u tryna find the graph? It's (3, -36)
Step-by-step explanation:
Kinda did it-
Which of the following equations correctly represents the distance between points (1, -1) and (-2, 2)?
Answer:
3√2
Step-by-step explanation:
d = √(x2 - x1)² + (y2 - y1)²
√(-2 - 1)² + [2 - (-1)]
√(-3)² + (3)²
√9 + 9
√18
= 3√2
George rolls a six sided die. What is the possibility that he rolls a 1 or a prime Number.
Answer:
1: 16.7%
prime number: 50%
Step-by-step explanation:
divide the numbers
Answer:
2/3
Step-by-step explanation:
There are 6 possible numbers
all of the prime numbers from 1 to 6 are
2, 3, 5 ( plus 1 because this problem is counting 1 along with the prime numbers)
That is 4 numbers
4 out of 6 numbers
so there is a 4/6 or 2/3 chance that George will roll a 1 or a prme number
Find the quotient of
x3−4x2−4x+16x−2
Answer:
x^2 - 2x - 8.
Step-by-step explanation:
Using long division:
x - 2)x^3 - 4x^2 - 4x + 16( x^2 - 2x - 8 <------ Quotient
x^3 - 2x^2
-2x^2 - 4x
-2x^2 + 4x
- 8x + 16
-8x + 16
............
Holly cuts 2 ribbons into tenths for a craft project how many 1/10 size ribbons does she have
Answer:
Holly would have 20 1/10 sized ribbons.
Step-by-step explanation:
One whole ribbon would equal out to 10, this number multiplied by 2 would be 20. Therefore meaning she should have 20 1/10 sized pieces of ribbon.
i need help with #2 and #6 pleaseeeeee
Answer:
Area of the rectangle = x² - 3x - 10
2019
Step-by-step explanation:
Length of the rectangle = x + 2
Width of the rectangle = x - 5
Area of the rectangle = length × width
= (x + 2) (x - 5)
= x² + 2x - 5x - 10
= x² - 3x - 10
Area of the rectangle = x² - 3x - 10
C = 20t² + 135t + 3050
Where
C = the number of new cars
t = year the number of new cars was purchased
t = 0 corresponds to 1998
Find the when c = 15,000
C = 20t² + 135t + 3050
15,000 = 20t² + 135t + 3050
20t² + 135t + 3050 - 15,000 = 0
20t² + 135t - 11,950 = 0
4t² + 27t - 2390 = 0
Solve using quadratic equation
t = -b ± √b² - 4ac / 2a
= -27 ± √27² - 4(4)(-2390) / 2(4)
= -27 ± √729 -(-38240) / 8
= -27 ± √729 + 38240 / 8
= -27 ± √38969 / 8
= -27/8 + √38969/8 or 27/8 - √38969/8
= -3.375 + 197.41/8 or -3.375 - 197.41/8
= -3.375 + 24.67625 or -3.375 - 24.67625
t = 21.30125 or - 28.05125
t cannot be negative
Therefore,
t = 21.30125
To the nearest whole number
t = 21
Recall,
t = 0 corresponds to 1998
Therefore
1998 + 21 = 2019
c = 15,000 in the year 2019
What is the length of the side opposite D?
units=
sin(D) =
Applying the Sine Ratio Warm up
Edge 2021
Answer:
5 units
sin(D)= 5/13
Step-by-step explanation:
i just did the question
What value of x will make the triangles similar by the
SSS similarity theorem?
Answer:
x=28
Step-by-step explanation:
Hi there!
SSS similarity theorem is a theorem that can determine similar triangles; the criteria for SSS~ is that the corresponding sides of the triangles create proportions which is the same as the ratio of similitude (k)
First, we need to find the ratio of similitude.
We need to assume that the triangles are similar.
15 corresponds with 20 (if you turn both triangles until they're titled the same way, you will see that 15 and 20 are the measures of the same sides on the triangles)
so that means 15/20 must make the ratio of similitude
15/20 is equal to 3/4
therefore k=3/4
as the triangle is already assumed similar, that means that 21/x will also give us a ratio that is equal to 3/4 (ratio of similitude)
therefore, 21/x=k
Since both ratios are equal to k, set 3/4 and 21/x equal to each other. This is possible via a property called transitivity (if a=b and b=c, then a=c)
3/4=21/x
cross multiply
3x=84
divide both sides by 3
x=28
So that means that 28 will make the triangles similar by SSS similarity
*you double check by doing 21/28 and see that it's also equal to 3/4
Hope this helps!
8. A warehouse 25 feet tall casts a shadow that is 15 feet long. At the same time of day, how
long is the shadow cast by an apartment building that is 90 feet?
Answer:
D
Step-by-step explanation:
