The angle between vectors a = i - 5j and b = -5i + 12j is approximately 164 degrees to the nearest degree.
To find the angle between two vectors, we can use the dot product formula:
a · b = |a| |b| cosθ
where a · b is the dot product of vectors a and b, |a| and |b| are the magnitudes of vectors a and b respectively, and θ is the angle between the two vectors.
First, we need to calculate the magnitudes of vectors a and b:
[tex]|a| = sqrt(1^2 + (-5)^2) = sqrt(26)|b| = sqrt((-5)^2 + 12^2) = 13[/tex]
Next, we need to calculate the dot product of vectors a and b:
a · b = (1)(-5) + (-5)(12) = -65
Now we can substitute these values into the dot product formula to solve for the angle θ:
-65 = sqrt(26) * 13 * cosθ
cosθ = -65 / (sqrt(26) * 13) = -0.9765
Taking the inverse cosine of -0.9765, we get:
θ = 164.43 degrees
Therefore, the angle between vectors a = i - 5j and b = -5i + 12j is approximately 164 degrees to the nearest degree.
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An expression is given
4x + 5y + 7x
Identify the coefficient(s) and constant.
Coefficient: 4,5 and Constant: 7
Coefficient: 4,5,7 and Constant: None
Coefficient: None and Constant: 4,5,7
Coefficient: 4,7 and Constant: 5
Step-by-step explanation:
The coefficients are 4, 5 and 7
There is no constant
The second one is right
Answer:
Coefficient: 4,5,7 and Constant: None
Step-by-step explanation:
A coefficient can be defined as the number next to the variable or unknown numbers
This would be 4, 5, and 7
However, there does not seem to be a constant, which is a value that should not be the coefficient of a variable.
What is the y-intercept of the line shown?
−1
0
0.5
1
Answer:
-1
Step-by-step explanation:
It crosses the y axis at negative 1, the y axis is the vertical line
A triangle has side lengths of (6a-3b)(6a−3b) centimeters, (5a+5c)(5a+5c) centimeters, and (8c-b)(8c−b) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?
Answer:
P = a(61a - 36b + 50c) + 10b² + 89c² - 16bc
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Terms/CoefficientsExpand by FOIL (First Outside Inside Last)FactoringGeometry
Perimeter Formula [Triangle]: P = L₁ + L₂ + L₃
L₁ is one sideL₂ is another sideL₃ is the 3rd sideStep-by-step explanation:
Step 1: Define
L₁ = (6a - 3b)(6a - 3b)
L₂ = (5a + 5c)(5a + 5c)
L₃ = (8c - b)(8c - b)
Step 2: Find Perimeter
Substitute in variables [Perimeter - Triangle]: P = (6a - 3b)² + (5a + 5c)² + (8c - b)²Expand [FOIL]: P = (36a² - 36ab + 9b²) + (25a² + 50ac + 25c²) + (b² - 16bc + 64c²)Combine like terms (a²): P = 61a² - 36ab + 9b² + 50ac + 25c² + b² - 16bc + 64c²Combine like terms (b²): P = 61a² + 10b² - 36ab + 50ac + 25c² - 16bc + 64c²Combine like terms (c²): P = 61a² + 10b² + 89c² - 36ab + 50ac - 16bcRearrange variables: P = 61a² - 36ab + 50ac + 10b² + 89c² - 16bcFactor: P = a(61a - 36b + 50c) + 10b² + 89c² - 16bcAre the ratios 18:9 and 4:3 equivalent?
Answer:
No. (see below)
Step-by-step explanation:
If you match up the ratios like this:
18 : 9
4 : 3
Matching the two numbers (one on top of another, since they correspond to each other), you can see that these are not equivalent.
Here's why:
The top ratio is 18 to 9, which can be represented by 18 total people to 9 girls in the amount of total people.
We know that the number of boys will also be 9 because 9 is half of 18.
Let's look at the second ratio:
This can be represented by 4 total people to 3 girls in the amount of total people.
4 - 3 = 1
So there would be only 1 boy. Meaning that they're not equal because 1 is not half of 4. It would only be 1/4.
1/4 ≠ 1/2
If we make them similar denominators, you can really see it:
1/4 ≠ 2/4
-4x + 8x - 6x
i don’t know what x is and that’s all i have. if anyone can help it would be helpful. the other questions are-
-3n/8 + 2n/8 - n/8
-4a - a/3
5b/8 + -2b/3
Answer:
The answer are
[tex]34 = - 2x \\ 35 = - \frac{1}{4} n \\ 36 = - \frac{13}{3} a \\ 37 = - \frac{1}{24} b[/tex]
1. Dolores is on a bridge that is 42 feet above a lake. What is the distance from Dolores to the boat? G
Answer:
See answer below
Step-by-step explanation:
You are missing data such as the angle of the boat next to Dolores. I found an exercise similar to this, and I'm going to show it here and use the missing data to show you how to do it:
Dolores is on a bridge that is 45 feet above a lake. She sees a boat at a 30 degree angle of depression. What is Dolores' approximate horizontal distance from the boat?
According to that, I will use the angle of 30° to do this, but the distance of 42 feet.
Now, we can see this as a triangle. Dolores is on a bridge 42 feet above a lake, this 42 feet distance should be one side of the triangle (The vertical forming the 90° angle), and the boat that is on the lake, is seen with an angle of 30°. So the distance of the boat, to the spot where dolores is, under the bridge would be the horizontal side.
With this, we have the opposite side (a) and the adyacent side (b) of the triangle, and we have the angle, therefore:
tanα = a/b
Replacing we have:
tan30° = 42/b
b = 42 / tan30°
b = 72.75 feet
Hope this helps
How can you show that two figures are either congruent or similar to one another?
Answer:
By measuring the length of the sides and angles
Answer: If they are congruent, you'll see that they are exactly the same as one another. If there's measurements, they'll have the same numbers. If they are similar, they might be the same shape or just have similar measurements
Step-by-step explanation:
HELP HELP HELP HELP HELP HELP HELP HELP
Answer:
same to me HAHAHAawitawitWhich equation represents the total cost of a repair by an electrician after x hours?
An electrician charges $90 per hour plus a $50 travelling fee.
Answer:
y = 90x + 50
Step-by-step explanation:
In this situation, let's define the variable and the constant.
The variable is what changes, so in this case the wage ($90) changes with how many hours the electrician is hired for.
The constant is the number that stays the same, in this case it would be the $50 traveling fee because it remains the same every time.
The equation should be written in this form:
y = mx + b
m = slope (variable)
b = y-intercept (constant)
Therefore, you can write the equation like this:
y = 90x + 50
Hope this helps!!
- Kay :)
In 3 hours, Jim can walk 14 miles. To find the time
he would take to walk 25 miles, he wrote the proportion 3/14= 25/h.
Explain his error.
Answer:
He should have used the proportion:
3/14=h/25
h=5.36 hours
Step-by-step explanation:
He should have used the proportion:
3/14=h/25
14h=3(25)
14h=75
h=5.36
Among two supplementary angles the measure of the larger angle is 400 more than the
measure of the smaller. Find their measures.
9514 1404 393
Answer:
70° and 110°
Step-by-step explanation:
The sum of angles is 180°; their difference is 40°. So, the larger is ...
(180° +40°)/2 = 110°
The smaller is 180° -110° = 70°
The two angles are 70° and 110°.
_____
Above, we have "cut to the chase." If you let the larger be 'a' and 's' and 'd' represent the sum and difference, you have ...
a + (a-d) = s . . . . the sum of the larger and smaller angles
2a = s+d . . . . . . add d
a = (s+d)/2 . . . . the relation we used.
Complete or rewrite each equation using the property indicated (algebra).
Property: Associative
Equation: 5 x (3 x 4)
Rewrite 5 x (3 x 4) in associative property
Please explain.
Answer:
60
Step-by-step explanation:
Ok so,
in PEMDAS the first thing to do is parentheses so 3 times 4 = 12. now it should look like this
5x12 which equals 60
hope this helps! have a good day! please mark brainliest
What is the slope of the line
Answer:
[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
When finding the slope, pick two points on the linear line.
( -1.5, -1) (0.5, 0)
-1.5 is x1
-1 is y1
0.5 is x2
0 is y2
Place these numbers in a slop formula.
m = [tex]\frac{0 - (-1)}{0.5 - (-1.5)}[/tex] = [tex]\frac{1}{2}[/tex]
(m means slope)
Slope = [tex]\frac{1}{2}[/tex]
Answer:
1/2
Step-by-step explanation:
(7a^2 -a + 4) – (3a^2 - 4a - 3)
Step-by-step explanation:
Answer. in the attachment
Since my last question got reported ill give branliest + 20 points for like 2 mins of your time
Answer:
the diameter of the semi-circle is 5 in
the area of the shape is 79.63 in squared
Step-by-step explanation:
Solve the quadratic equation x2+8x−30=0 by completing the square.
What are the solutions to the quadratic equation, if any?
x=4±46−−√
This equation has no real solutions.
x=4±34−−√
x=±46−−√
Answer:
[tex]\bold{x=-4\pm\sqrt{46}}[/tex]
Step-by-step explanation:
[tex](a+b)^2=a^2+2ab+b^2\\\\\\x^2+8x-30=0\\\\\underbrace{x^2+2\cdot x\cdot 4+4^2}-4^2-30=0\\\\{}\qquad(x+4)^2\,-\,16-30=0\\\\{}\qquad\ \ (x+4)^2=46\\\\ {}\qquad\ \ x+4=\pm\sqrt{46}\\\\ {}\qquad\ \ x=-4\pm\sqrt{46}[/tex]
The solution to the quadratic equation by completing the square will be
x = -4 ± √46. The correct option is A.
What is a quadratic equation?It is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.
Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The given equation will be solved as below:-
x² + 8x − 30 = 0
Completing the square for the above equation.
( x + 4 )² - 16 - 30 = 0
( x + 4 )² = 46
x + 4 = ±√46
x = ±√46 - 4
Therefore, the solution to the quadratic equation by completing the square will be x = -4 ± √46. The correct option is A.
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Help pleaseee
The figure
Answer:
the 4th one pentagonal prism
Answer:
pentagonal prism
Step-by-step explanation:
it doesn't resemble a pyramid, so it could only be a prism, and it isn't a rectangular one, cause it has two pentagons, on top and bottom
The cost of tickets to a school play are $10 for adults and $6 for children under 12. If there were a total of 100 tickets sold to the play on a certain night, what equation would you use to represent the total ticket sales, T, if the number of adult tickets can be represented by a. Show and explain each step to create the equation.
Answer:
10a+6b=T------------2
Step-by-step explanation:
Given data
Let the number of adults be a
and the number of children be b
we are told that the total tickets is 100
hence
x+y=100-------------1
The cost of adult ticket = $10
The cost of children ticket = $6
since the total cost is T
Hence
10a+6b=T------------2
To rent a bike, Max pays a flat rate plus an hourly rental fee. The graph shows the amount, c dollars, he pays based on the number of hours, t, he uses the bike.
a) Find the vertical intercept of the graph and explain what information it gives about the situation.
b) Find the slope of the graph and explain what information it gives about the situation.
Answer:
The vertical intercept is 5y. The slope is 1/2
Step-by-step explanation:
Please mark Brainliest
Help!!!!!!!!!!!!! BRAINLIST WILL BE REWARDED
Answer:
135
Step-by-step explanation:
supplementary angles: either of two angles whose sum is 180°.
180 - 45 = 135
The area of a rectangle is 735 in squared. The ratio of the length to the width is 5 : 3. Find the length and the width.
Answer: Length = 35
Width = 21
Step-by-step explanation:
From the question, we are informed that the area of a rectangle is 735 in squared and that the ratio of the length to the width is 5 : 3.
To find the length and the width of the rectangle goes thus. We should note that the area of a rectangle is the length multiplied by the width.
Therefore, 5x × 3x = 735
15x² = 735
x² = 735/15
x² = 49
x = ✓49
x = 7
Recall that length = 5x = 5 × 7 = 35
Width = 3x = 3 × 7 = 21
A $50 item is discounted 30%. How much is the discount?
Answer:
$15
Step-by-step explanation:
Discount = $50 x 30% = $15
Step-by-step explanation:
❁ [tex] \underline{ \underline{ \large{ \tt{ \: G \: I \: V \: E \: N}}}} : [/tex]
Marked price ( MP ) = $ 50Discount % ( Dis % ) = 30 %❁ [tex] \underline{ \underline{ \large{ \tt{ T \: O \: \: F \: I \: N \: D}}}} : [/tex]
Discount amount = ?❁ [tex] \underline{ \underline{ \large{ \tt{S \: O \: L \: U \: T \: I \: O \: N}}}} : [/tex]
[tex] \boxed{ \sf{Discount \: amount = Dis\% \: of \:MP}}[/tex]
Plug the known values :
➝ [tex] \large{ \tt{30\% \: of \: 50}}[/tex]
Convert 30% to fraction. For that divide 30 by 100 and remove the percentage symbol.
➝ [tex] \large{ \tt{ \frac{30}{100} \times 50}}[/tex]
➝ [tex] \large{ \tt{ \bold{ \$ \: 15}}}[/tex]
[tex] \large{ \underline{ \pink {\boxed{ \boxed{ \tt{Our \: final \: answer : \boxed{ \underline{ \bold{ \tt{ \bold{ \$ \: 15}}}}}}}}}}}[/tex]
Hope I helped ! ♡
Have a wonderful day! ツ
# [tex] \underline{ \underbrace{\tt{ \pink{Carry \: on \: learning ! }}}}[/tex]
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1. Which of the following is equal to 10
A. (6-2)+3 B. (3+11) 4 C. 12-742 D. 6+5-2
2. Which of the following is NOT equal to 2?
A. 7+5-3 B. -84-941 C. 11-5-4 D. 55+2
3. If a=3, what is the value of a-5?
A.-5
B. -2
C, 2
D. 5
4. Which of the following equations is TRUE?
A (1+7)+3=20-9
C. 12-7-5+(7-6)
B. (6+9) 415-4-2
D. 4-5=3-(2+8)
5. Which of the following is equal to 22?
1. 14+15-5
il. (4)(5)+2
1. 54-24-8
iv. 16+5+10-9
A. i only B. li only C. i, ii, in only D. it, 1, iv only
6. What is the value of the algebraic expression x=3y-1? If y=-9
A.27
B. 28
C.-27
D. -28
7. If x=4, what is the value of the expression 5x+17
A 10
B. 21
C. 32
D. 55
8. Let y=10x-2, what is y when x=4?
A. X=3, y=4 B. X=-2, y=4 C. X=-3, y=2 D. X=4, y=-2
9. Which values of x and y will make the expression 4y-2x equal to -16?
A 10
B. 21
C. 32
D. 55
10. Which expression will snow the value 18 if x = 3?
A. 2x + 6 B. 12+
C. 8x4
D. 5x + 3
Step-by-step explanation:
noneexcept c-2A1+7)+3=20-9il. (4)(5)+2D. -283738D. X=4, y=-2A. 2x + 6Step-by-step explanation:
noneexcept c-2A (1+7)+3=20-9(4)(5)+2-2837389) X=4, y=-2
10) 2x + 6
state true or false :every natural number is a whole number
Answer:
true , because natural number is starte on no.1 to infinity but whole no. is started on 0 to infinity so it is true .
Step-by-step explanation:
Answer:
True
Step-by-step explanation:
The whole numbers are the numbers 0, 1, 2, 3, 4, and so on (the natural numbers and zero). Negative numbers are not considered "whole numbers." All natural numbers are whole numbers, but not all whole numbers are natural numbers since zero is a whole number but not a natural number.
25% of N is 12. Solve for N. Just put the number.
Answer:
25% of 48 = 12
Step-by-step explanation:
12 ÷ 25% = 12 ÷ 0.25 = 48
Answer: Divide each term by 25 % and simplify.
N = 48
Step-by-step explanation:
Which rate does not belong with the other three? 8 pounds for every 2 feet 12 pounds per 3 feet 20 pounds per 4 feet 24 pounds for every 6 feet
Answer:
20 pounds per 4 feet
all the others have the same proportion, 4 pounds per foot
Step-by-step explanation:
PLEASE HELP how do i solve (5-3i)^2
Answer:
16-30i
Step-by-step explanation:
This is what I got :)
Answer:
16−30i
Step-by-step explanation:
Use Square of Difference: {(a-b)}^{2}={a}^{2}-2ab+{b}^{2}(a−b)
2
=a
2
−2ab+b
2
.
{5}^{2}-2\times 5\times 3\imath +{(3\imath )}^{2}
5
2
−2×5×3+(3)
2
2 Simplify {5}^{2}5
2
to 2525.
25-2\times 5\times 3\imath +{(3\imath )}^{2}
25−2×5×3+(3)
2
3 Use Multiplication Distributive Property: {(xy)}^{a}={x}^{a}{y}^{a}(xy)
a
=x
a
y
a
.
25-2\times 5\times 3\imath +{3}^{2}{\imath }^{2}
25−2×5×3+3
2
2
4 Simplify {3}^{2}3
2
to 99.
25-2\times 5\times 3\imath +9{\imath }^{2}
25−2×5×3+9
2
5 Use Square Rule: {i}^{2}=-1i
2
=−1.
25-2\times 5\times 3\imath +9\times -1
25−2×5×3+9×−1
6 Simplify 2\times 5\times 3\imath2×5×3 to 30\imath30.
25-30\imath +9\times -1
25−30+9×−1
7 Simplify 9\times -19×−1 to -9−9.
25-30\imath -9
25−30−9
8 Collect like terms.
(25-9)-30\imath
(25−9)−30
9 Simplify.
16-30\imath
16−30
Tamika is ordering a taxi from an online taxi service. The taxi charges $3.50 just for the pickup and then an additional $0.75 per mile driven. How much would a taxi ride cost if Tamika is riding for 5 miles? How much would a taxi ride cost that is m miles long?
Answer:
m= 7.50
Step-by-step explanation:
0.75x5=4.00
4.00+3.50=7.50
A taxi ride cost if Tamika is riding for 5 miles will be $7.25.
What is Linear function?A linear function in mathematics is one that has either one or two variables and no exponents. It is a function with a straight line as its graph.
Given, Tamika is ordering a taxi from an online taxi service. The taxi charges $3.50 just for the pickup and then an additional $0.75 per mile driven.
Let "m" be the miles Tamika is riding along.
Total additional charges = m *0.75
pick up charges = 3.50
So, Total charges Tamika has to pay for m miles = 0.75*m + 3.50
For m = 5 miles
Tamika has to pay for 5 miles = 0.75 * 5 + 3.50
Tamika has to pay for 5 miles = 7.25
Therefore, 7.25$ would a taxi ride cost if Tamika is riding for 5 miles.
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math work pls help :)
Answer:
b. side angle side. hope this helps
A= bh;
A = 28, h = 4