[tex]\text{Given that,}\\\\\vec{v} = 15 \hat{i} +8 \hat j\\\\ \\\text{Magnitude of the vector,}\\\\|\vec v| = \sqrt{15^2 +8^2}= \sqrt{289} = 17[/tex]
6 A clothing store paid $30 for a jacket, and sold the jacket for $48.
What was the percent increase?
Answer:
60%
Step-by-step explanation:
% increase = Increase ÷ Original Number × 100
Answer:
60%
Step-by-step explanation:
Total increase in cost = $(48 - 30) = $18
Now,
% increase = Increase/Original amount × 100
=> 18/30 × 100
=> 18/3 × 10
=> 6 × 10
=> 60%
13. Write the equation of the line perpendicular to
5y = 3x + 25 but passing through (-4,-1)
Answer:
y = -[tex]\frac{5}{3}[/tex]x - -[tex]\frac{23}{3}[/tex]
Step-by-step explanation:
First, let's divide both sides by 5 to get the first equation into the form y = mx + b. We get y = [tex]\frac{3}{5}[/tex]x + 5. The m value, [tex]\frac{3}{5}[/tex], is the slope and the b value, 5, is the y-intercept of this line.
When a line is perpendicular to another line, the slopes must multiply to get -1. In other words, the slopes must be a negative reciprocal of each other. Since the slope of the original line is [tex]\frac{3}{5}[/tex], we know that the slope of the line perpendicular to that is -[tex]\frac{5}{3}[/tex].
Then, since we know x, y, and m of the second equation, we can substitute those three values into the equation, y = mx + b, to find the y-intercept (b).
-1 = (-[tex]\frac{5}{3}[/tex])(-4) + b
-1 = [tex]\frac{20}{3}[/tex] + b
b = -[tex]\frac{23}{3}[/tex]
After plugging in the values of m and b we calculated, we get the equation for the line perpendicular to the original line: y = -[tex]\frac{5}{3}[/tex]x -[tex]\frac{23}{3}[/tex].
what is the slope of y-3=-2(x+5)
Answer: slope (m) = -2
Step-by-step explanation:
y-3=-2(x+5)
put it into y=mx+b
use PEMDAS-Parantheses, Exponents, Mult. Div. Add. Sub. for your order of operations.
first, parantheses.
-2(x+5)
-2 times x = -2x
-2 times 5 = -10
your new equation is y-3 = -2x-10
now, to get y by itself, cancel out the -3 by adding a positive 3 to both sides.
you final equation will be y=-2x-7
in the form y=mx+b, m is your slope.
therefore, -2 is your answer, or slope.
5 : 1/3 in its simplest form
Answer:
15 : 1
Step-by-step explanation:
5 : 1/3
Multiply both numbers in the ratio by 3.
5 × 3 : 1/3 × 3
15 : 1
[tex]5:\frac{1}{3} =5.\frac{3}{1} =\frac{15}{1} <=>15:1 (=15)[/tex]
ok done. Thank to me :>
After Lois picks a value for b, Clark must solve the equation 2x + 7 - x = 4x + 2b – 3x - 3b.
Clark uses Lois's b, then tries to solve the equation by repeatedly guessing values of x until he guesses
the right one. However, for every x he picks, the left side is always 3 more than the right side. What
value of b did Lois give Clark?
The value of b that Lois give Clark will be -7
Given the expression 2x + 7 - x = 4x + 2b – 3x - 3b.First, we need to find the value of b from the expression.Rearrange;
2x + 7 - x = 4x + 2b – 3x - 3b.
x + 7 = x + 2b - 3b
2b - 3b = 7
-b = 7
b = -7
Substitute b = -7 into the expression and find the value of x;
2x + 7 - x = 4x + 2(-7) – 3x - 3(-7)
x + 7 = 4x - 3x - 14 + 21
x + 7 = x + 7
Since for every x he picks, the left side is always 3 more than the right side, the equation becomes;
x + 7 = x + 3x + 7
x + 7 = 4x + 7
x - 4x = 0
-3x = 0
x = 0
Hence the value of b that Lois give Clark will be -7
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Help me pleaseeeeeeeeeeee
Answer: Third option
Here's the question.
Answer:
The value of T₂₀ - T₁₅ is -20.
Step-by-step explanation:
Given :
>> If for an A.P, d = -4To Find :
>> T₂₀ - T₁₅Using Formula :
General term of an A.P.
[tex]\star{\small{\underline{\boxed{\sf{\red{ T_n = a + (n - 1)d}}}}}}[/tex]
>> Tₙ = nᵗʰ term>> a = first term>> n = no. of terms>> d = common differenceSolution :
Firstly finding the A.P of T₂₀ by substituting the values in the formula :
[tex]{\dashrightarrow{\pmb{\sf{ T_n = a + (n - 1)d}}}}[/tex]
[tex]{\dashrightarrow{\sf{ T_{20} = a + (20 - 1) d}}}[/tex]
[tex]{\dashrightarrow{\sf{ T_{20} = a + (19)d}}}[/tex]
[tex]{\dashrightarrow{\sf{ T_{20} = a + 19 \times d}}}[/tex]
[tex]{\dashrightarrow{\sf{ T_{20} = a + 19d}}}[/tex]
[tex]{\star \: {\underline{\boxed{\sf{\pink{ T_{20} = a + 19d}}}}}}[/tex]
Hence, the value of T₂₀ is a + 19d.
[tex] \rule{190}1[/tex]
Secondly, finding the A.P of T₁₅ by substituting the values in the formula :
[tex]{\dashrightarrow{\pmb{\sf{ T_n = a + (n - 1)d}}}}[/tex]
[tex]{\dashrightarrow{\sf{ T_{15}= a + (15 - 1) d}}}[/tex]
[tex]{\dashrightarrow{\sf{ T_{15}= a + (14) d}}}[/tex]
[tex]{\dashrightarrow{\sf{ T_{15}= a + 14 \times d}}}[/tex]
[tex]{\dashrightarrow{\sf{ T_{15}= a + 14d}}}[/tex]
[tex]{\star{\underline{\boxed{\sf \pink{ T_{15}= a + 14d}}}}}[/tex]
Hence, the value of T₁₅ is a + 14d
[tex] \rule{190}1[/tex]
Now, finding the difference between T₂₀ - T₁₅ :
[tex]{\dashrightarrow{\pmb{\sf{T_{20} - T_{15}}}}}[/tex]
[tex]{\dashrightarrow{\sf{(a + 19d) - (a + 14d)}}}[/tex]
[tex]{\dashrightarrow{\sf{a + 19d - a - 14d}}}[/tex]
[tex]{\dashrightarrow{\sf{a - a + 19d - 14d}}}[/tex]
[tex]{\dashrightarrow{\sf{0+ 19d - 14d}}}[/tex]
[tex]{\dashrightarrow{\sf{19d - 14d}}}[/tex]
[tex]{\dashrightarrow{\sf{5 \times - 4}}}[/tex]
[tex]{\dashrightarrow{\sf{ - 20}}}[/tex]
[tex]{\star \: \underline{\boxed{\sf{\pink{T_{20} - T_{15} = - 20}}}}}[/tex]
Hence, the value of T₂₀ - T₁₅ is -20.
[tex]\underline{\rule{220pt}{3.5pt}}[/tex]
C. Because slope =
rise over run the slope of a "downhill" line must be
run
-12 + 2a = -6(1 + a) + 8a
Find the equation of the line.
y=[ ]x +[ ]
Help me please ******
Answer:
11 is B then 12 is D
Hoped that helped:P
5. What are the solutions to the equation (x - 1)(x + 2) = -2?
I hope this helps. Comment if any doubt.
The diameters of a circle is 7m. Find its area to the nearest tenth?? Help please
Area =[tex]\pi r^{2}[/tex]
The diameter is double the length of the radius
7 ÷ 2 = 3.5
3.5 × 3.5 = 12.25
[tex]12.25\pi[/tex] = 38.4845100064751
38.4845100064751 rounded to the nearest tenth is 38.5
Answer:
A = 38.5 sq meters
Step-by-step explanation:
A = πr²
since diameter is 7, then radius is 7/2
A = π(7/2)²
A = 38.48
A = 38.5 rounded to nearest tenth
Which account option is more convenient for frequent check or debit card withdrawals and purchases but gains no interest?
A. Checking
B. Certificate of deposit
C. Savings
D. Money market
The best account if one plans to make frequent withdrawals via check or debit card is A. Checking account
Checking accounts:
Are the least interest bearing accounts Allow for frequent withdrawals using a check or debt card Charge lower feesChecking accounts are best when a person wants easy access to their money because they can get to it via checks or debit cards. The drawback however, is that interest on these accounts are low.
In conclusion, option A is correct.
Find out more about checking accounts at https://brainly.com/question/21714367.
Solve: 4|x| = 32
–8 or 8
8
24
no solution
Answer:
-8 or 8
Step-by-step explanation:
We are given the absolute equation:
[tex]\displaystyle \large{4|x|=32}[/tex]
First, divide both sides by 4 which leaves [tex]\displaystyle \large{|x|=8}[/tex]
Absolute Value Definition
[tex]\displaystyle \large{|x|=\begin{cases} x \ \ \ (x\geq 0)\\ -x \ \ \ (x<0) \end{cases}}[/tex]
So from |x| = 8, break into two intervals/conditions.
(1) when x ≥ 0
x = 8
(2) when x < 0
-x = 8
x = -8
From (1) and (2), the solution to 4|x| = 32 is 8 or -8
z/3 <= 3
solve for z
Answer:
assuming <= is less than or equal to
then z/3 is less than or equal to 3
z had to be less than 9
What is the square root of 12a^3b^5 times the square root of 6ab^2?
Step-by-step explanation:
sqrt(12×a³b⁵) × sqrt(6×ab²)
the content of multiplied square roots can be combined into one square root :
sqrt(12×6×a³×a×b⁵×b²) = sqrt( 72a⁴b⁷) =
= sqrt(4×9×2 × a⁴ ×b⁶×b) = 2×3×a²×b³×sqrt(2b) =
= 6a²b³×sqrt(2b)
Which congruence criteria is met in the following scenario?
AAS
ASA
SAS
None, because the sides of one triangle are NOT congruent to the sides of the other triangle.
SSS
i really really hope can see this
Answer:
did u ever figure it out?
Step-by-step explanation:
Find the solutions to x2 = 24.
=
O A. x = +4,16
=
O B.
X =
< = +2.1/6
O C. X= = +62
O D. x= 1514
=
Answer:
[tex]x\approx\pm4.8989[/tex]
Step-by-step explanation:
[tex]x^2=24[/tex]
[tex]\sqrt{x^2}=\sqrt{24}[/tex]
[tex]x=\pm\sqrt{24}[/tex]
[tex]x\approx\pm4.8989[/tex]
Can someone please help me I will mark brainliest please.
Answer:
GE = 8 inches
Step-by-step explanation:
The diagonals of a parallelogram bisect each other, then
GE = 2 × GH = 2 × 4 = 8 inches
A zookeeper is monitoring the population of birds. The flock needs to have exactly three times more females than males to thrive, and the zoo only has room for a maximum of 20 male birds. Let x represent the number of male birds and y represent the number of female birds. Write the constraints to represent a thriving population of birds at the zoo. X > 0 and y > 0 0 < x ≤ 20 and y > 60 x > 0 and y < 20 0 < x ≤ 20 and 0 < y ≤ 60.
The correct option is D.[tex]0< x\leq 20[/tex] and [tex]0< y\leq 60[/tex].
Given, [tex]x[/tex] represent the number of male birds and [tex]y[/tex] represent the number of female birds.
The flock needs to have exactly three times more females than males to thrive.
So, in equation form we have,
[tex]y=3x[/tex]........(1)
Since, The zoo only has room for a maximum of 20 male birds.
So, we can write the inequality for [tex]x[/tex] as,
[tex]0< x\leq 20[/tex]......(2)
Since The maximum number of male birds is 20, so for [tex]x=20[/tex]
y will be,
[tex]y=3\times 20\\[/tex]
[tex]y=60[/tex]
Hence, The maximum number of female birds is 60.
So, we can write the inequality for [tex]y[/tex] as,
[tex]0< y\leq 60[/tex]
Hence the required constraints are [tex]0< x\leq 20[/tex] and [tex]0< y\leq 60[/tex].
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Answer:d
Step-by-step explanation: did the test
help me with this math question
Answer:
Its Answer is 13
Step-by-step explanation:
2y + 3 (x - y) + x2
Help. I can’t seem to figure out what to do
Answer: Both of the Givens go in the left top boxes, and then in the right top boxes you would put B is the midpoint of AD and CE and then AC is equal to DE. In the third and fourth boxes on the left, you would put CB = EB and then AB is equal to DB. In the third and fourth boxes on the right you put both of the Def. of Midpoints. Then, in the last box to the left, you would put triangle ABC = DBE. In the final box to the right you would put Side-Side-Side Congruency.
Step-by-step explanation:
1) ac≅de, given
2) b is the midpoint, given
3) ab≅db, defn midpoint
4) cb≅eb, defn midpoint
5) abc≅dbe, side side side
What is the slope of a line that is perpendicular to the line y = 1?
O-1
ОО
O 1
O undefined
Answer: D) Undefined
Explanation:
The equation y = 1 is the same as y = 0x+1
Match that to the form y = mx+b to see that the slope is m = 0
Any horizontal line has a slope of 0.
Notice that we cannot apply the negative reciprocal to this because 0 = 0/1 leads to 1/0 which is undefined
The slope of any vertical line is undefined because we have run = 0 and slope = rise/run = 1/0. The rise can be any number you want (it doesn't have to be 1) and we get the same result.
The slope of a line that is perpendicular to the line y = 1 is undefined.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The equation y = 1 is the same as y = 0x+1
Match that to the form y = mx+b to see that the slope is m = 0
Any horizontal line has a slope of 0.
y = 1 is an vertical line.
The slope of any vertical line is undefined because we have run = 0 and slope = rise/run = 1/0.
= Undefined
Hence, the slope of a line that is perpendicular to the line y = 1 is undefined.
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ANSWER 100 POINTS AND BRAINLY THIS IS MATH
Difference between relation and function?
Functions have unique range for each domain.Where as relation haven't.So
Check option A
2 is repeated in domain
Hence table A is a relation.
Table B is a function
Rachel baked a pie with an area of 94.985 square inches. She gave away a slice of pie with an area of 13.56 square inches. Find the central angle measure of the slice. Numerical answer round to the nearest degree.
It is 103.68 degrees :)
Kennedy made 12 3/8 cups of tea. She and her friends drank 7 1/4 cups. How much was left?
Answer: 5 1/8 cups
Step-by-step explanation:
Make 1/4 to 2/8 the. Subtract 3/8 by 2/8
1/4 = 2/8
3/8 - 2/8 = 1/8
Then subtract 12 and 7
12 - 7 = 5
Finally add 5 and 1/8
5 + 1/8 = 5 1/8 cups
IF ANYONE CAN ANSWER THESE 2 QUESTIONS I WILL GIVE YOU BRAINLIEST AND LOVE YOU FOREVER. SERIOUSLY, ILL NEVER FORGET U <3
Answer:
3. 314 student and 226 adult
4. x = 6.5, y = -0.5
Step-by-step explanation:
3. First we will take our information and make a system of equations:
[tex]2.4a+1.25s=934.9[/tex]
[tex]a+s=540[/tex]
[tex]a[/tex] is the number of adult tickets sold and [tex]s[/tex] is the number of student tickets sold.
From the second equation we can rearange it to be:
[tex]a=540-s[/tex]
Then we can plug in our new value of [tex]a[/tex] to our first equation
[tex]2.4(540-s)+1.25s=934.9[/tex]
[tex]1296-2.4s+1.25s=934.9[/tex]
[tex]1.15s=361.1[/tex]
[tex]s=314[/tex]
We can then find [tex]a[/tex] by plugging in s to our second equation
[tex]a+314=540[/tex]
[tex]a=226[/tex]
4. It is mostly solved already. We can take the value of y from the first equation and plug it into the second to get:
[tex]3x -5(-5x+32)=22[/tex]
[tex]3x+25x-160=22[/tex]
[tex]28x=182[/tex]
[tex]x=6.5[/tex]
Then plug our value of x into the first equation to get:
[tex]3(6.5)-5y=22[/tex]
[tex]19.5-5y=22[/tex]
[tex]5y=-2.5[/tex]
[tex]y=-0.5[/tex]
9. Which of the following is an example of the Commutative Property of Addition? (1 point)
O 12 + 4 = 4 + 12
O 12 + (3 + 2) = (12 + 3) + 2
O 2 + 7 + 0 = 2 +7
O 17+ (-17) = 0
V
10. If p = 8, evaluate 42+p:3. (1 point)
02.
03
06
08
Finish
Cancel
Answer:
9. the first one ( 12 + 4 = 4 + 12 )
Step-by-step explanation:
the commutative property of addition means that you can change the order of the numbers you add and the sum will still be the same. this is shown in the 12 + 4 = 4 + 12 because the order is switched, but they are still equal.
The example of the commutative property of addition is 12 + 4 = 4 + 12, the correct option is A.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
We are given that;
The four options
Now,
The commutative property of addition states that changing the order of the addends does not change the sum.
This is the only option that shows the same sum with different orders of addends.
Therefore, by algebra the answer will be 12 + 4 = 4 + 12.
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