Answer:x = {-4, 4}
explanation:
PLEASE HELP QUICK!! WILL MARK BRAILIEST!!
Question the formula (equation) for finding the VOLUME of a rectangular prism is?
A= 1/2 bh
A= lw
V= lwh
V= x + 3
Answer:
V = lwh
Step-by-step explanation:
The volume of a rectangular prism or a rectangle stretched is the basic rectangle area formula ( wh ) multiplied by the new factor, the length ( l ). This makes the formula V = lwh
Hope this helped
9. Jack recorded the number of different colored marbles he has in a pouch. The results are provided in the table below. Color blue 5 brown 4 green. 3 orange 5 red 4 yellow 4 Part B. Jack has another jar of 275 marbles that have the same distribution as the table above. Based on the information in the table, determine the number of yellow marbles
Based on the information provided in the table, Jack has 4h yellow marbles.
To determine the number of yellow marbles in the jar of 275 marbles, we can use the information from the table to find the proportion of yellow marbles in the first pouch.
According to the table, there are 4 yellow marbles out of a total of 25 marbles in the first pouch.
Therefore, the proportion of yellow marbles in the first pouch is 4/25.
To find the number of yellow marbles in the jar of 275 marbles, we can multiply this proportion by the total number of marbles in the jar.
Number of yellow marbles = (4/25) x 275 = 44
Therefore, there are 44 yellow marbles in the jar of 275 marbles.
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Will mark brilliant
14. What information below would be enough to prove ADEF = ARPQ?
E
The information which would be enough to prove the triangles to be congruent are either DE = RP or ∠F = ∠Q.
Given two triangles,
ΔDEF and ΔRPQ.
If ΔDEF is congruent to ΔRPQ, then the corresponding vertices of D, E and F are R, P and Q respectively.
Already we have from the figure,
∠D = ∠R
DF = RQ
Now, it is enough to prove either DE = RP or ∠F = ∠Q.
When DE = RP, by SAS congruence theorem, corresponding two sides and the included angle of each triangle are equal and thus triangles are congruent.
When ∠F = ∠Q, by ASA congruence theorem, corresponding two angles and the included side of each triangle are equal and thus triangles are congruent.
Hence the information required are either DE = RP or ∠F = ∠Q.
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Consider polygon ABCD, shown below.
B
C
E
A
G
F
D
Select all the ways that describe rigid transformations that take AEFD to CFEB.
The option that describes the rigid transformation that take AEFD to CFEB are:
Rotate AEFD 180 degrees counterclockwise around point GRotate AEFD 180 degrees clockwise around point G.What does it mean to rotate shape 180°?To rotate a form 180°, turn it about its center point such that it faces the opposite way. This is accomplished by tracing the form on a sheet of paper and then folding it in half so that the two sides of the shape line up. The form is now rotated 180 degrees.
A rigid transformation (also known as a Euclidean transformation or Euclidean isometry) in mathematics is a geometric transformation of a Euclidean space that retains the Euclidean distance between each pair of points.
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Full Question:
Although part of your question is missing, you might be referring to this full question:
See attached image.
A home decor store donated a percent of every sale to hospitals. The total sales were $8,400 so the store donated $672. What percent of $8,400 was donated to hospitals?
Answer:
8% of sales donated-----------------------
What percent of $8400 is $672?
672/8400 * 100% = 0.08 * 100% = 8%Answer:
8%
Step-by-step explanation:
To find the percentage that was donated to hospitals, we can set up the following equation:
[tex]\sf \dfrac{total\: donation}{ total \:sales} * 100 = percentage \:donated[/tex]
In this case, the total donation was $672 and the total sales were $8,400.
Substituting these values into the equation, we get:
[tex]\sf \dfrac{672}{8400} * 100 = percentage \:donated[/tex]
Simplifying this expression:
(0.08) * 100 = percentage donated
8% = percentage donated
Therefore, the home decor store donated 8% of $8,400 to hospitals.
2.2. Khensani received his pay slip for March which is summarized below: Name DS. MAJOLA ID NO. 28205235584057 Employee Gode::::7/203 Earnings Basic Salary Gross Earnings Monthly Payslip Amount R23 400 Deductions UIF Union Contribution Total Deductions R23 400 Net Salary 2.2.1. What does the abbreviation UIF stand for? 2.2.2. Calculate UIF at 1% of basic salary. 2.2.3. State one benefit of contributing UIF by employee. 2.2.4. Determine the values of B and C. QUESTION 3 3.1. A plan with a scale of 1: 100 was drawn. Amount A GRAND TOTAL = 50 R78,00 2.2.4. Khensani's claims that his monthly salary is more than US$1 000. Verify, by calculation, whether his claim is valid. US$1 = R19,85. B 3.1.1. Name the scale used. 3.1.2. If the dimension (length) of a kitchen is 3,6 cm. Determine the actual dimens of the floor in metres. Samsung Quad Camera Shot with my Galaxy A32 (2) (2) (2) (4) (4)
UIF at 1% of the basic salary is R234.
The actual dimension of the kitchen on the floor is 0.036 meters.
2.2.1. UIF stands for Unemployment Insurance Fund.
2.2.2. To calculate UIF at 1% of the basic salary, we multiply the basic salary by 1%:
UIF = 1% of Basic Salary
= 1/100 x Basic Salary
Given that the Basic Salary is R23,400, we can calculate UIF:
UIF = 1/100 x 23,400
= 234
Therefore, UIF at 1% of the basic salary is R234.
2.2.3. One benefit of contributing UIF by the employee is that it provides financial protection against unemployment. If an employee becomes unemployed, they may be eligible to receive UIF benefits, which can provide temporary financial support during the period of unemployment.
2.2.4. Unfortunately, the values of B and C are not provided in the given information. If you provide the values, I can assist you with determining them.
3.1.1. The scale used is 1:100.
3.1.2. If the dimension (length) of the kitchen on the plan is 3.6 cm, to determine the actual dimension in meters, we need to scale it up by the scale factor:
Scale factor = 1/100 (since it's a 1:100 scale)
Actual dimension = Dimension on the plan x Scale factor
= 3.6 cm x (1/100)
= 0.036 meters
Therefore, the actual dimension of the kitchen on the floor is 0.036 meters.
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you purchase a tight sealed container for your sugar cubes to keep the ants away. The container is a rectangular prism with dimensions 6 in by 4 in by 3. The sugar cubes have 0.5 in sides. Is your container big enough to store 560 sugar cubes?
The container is indeed big enough to store 560 sugar cubes.
To determine if the container is big enough to store 560 sugar cubes, we need to calculate the volume of the container and compare it to the total volume occupied by the sugar cubes.
The volume of a rectangular prism is given by the formula V = lwh, where l is the length, w is the width, and h is the height.
In this case, the dimensions of the container are:
Length (l) = 6 inches
Width (w) = 4 inches
Height (h) = 3 inches
Using the formula, the volume of the container is calculated as follows:
V = 6 inches * 4 inches * 3 inches
V = 72 cubic inches
Now, let's calculate the volume occupied by a single sugar cube:
The side length of a sugar cube is 0.5 inches, so the volume of a single sugar cube is:
V_cube = 0.5 inches * 0.5 inches * 0.5 inches
V_cube = 0.125 cubic inches
To determine the number of sugar cubes that can fit in the container, we divide the volume of the container by the volume of a single sugar cube:
Number of sugar cubes = V_container / V_cube
Number of sugar cubes = 72 cubic inches / 0.125 cubic inches
Number of sugar cubes = 576
Since the number of sugar cubes that can fit in the container is 576, which is greater than the required 560 sugar cubes, we can conclude that the container is indeed big enough to store 560 sugar cubes.
Therefore, the container can comfortably accommodate the desired quantity of sugar cubes while providing a tight seal to keep ants away.
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HELP IMAGE ATTACHED ANSWER FAST!! 6) Match the equations to the lines below:
Answer:
Step-by-step explanation:
In order from top to bottom:
3
2
1
4
Please help due !!!! Please asap !
Answer:
hello
the answer to (a) is:
y = kx ----> y = (1/8)x
and the answer to (b) is:
if x = 7
y = (1/8) × 7 = 7/8 or 0.875
HELP PLS
The equation for the area of a trapezoid is A equals one-half times h times the quantity of b subscript 1 plus b subscript 2 end quantity.. If A = 28, b1 = 6, and b2 = 8, what is the height of the trapezoid?
h = 2
h = 4
h = 6
h = 7
Answer:
h = 4 units
Step-by-step explanation:
Given equation:
[tex]\text{A}_{\text{trapezoid} } = \dfrac{1}{2}(h)(b_{1} + b_2)[/tex]
Given numerical values:
A = 28b₁ = 6b₂ = 8Plug in all values into the equation and simplify it to find the height:
[tex]\implies \text{28} = \dfrac{1}{2}(h)(6 + 8)[/tex]
[tex]\implies\text{28} = (h)(3 + 4) = 7h[/tex]
[tex]\implies h = \dfrac{28}{7} = 4[/tex]
Therefore, the measure of the height is 4 units.
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In a group of 150 kids 6 have green eyes 52% have brown eyes 16% have gray eyes and the rest have blue eyes what percentage of the kids have blue eyes.
Answer:
[tex]\boxed{\boxed{\sf{\:\:\: \green{Percentage = 28\%}\:\:\: }}}[/tex][tex]\\[/tex]
Step-by-step explanation:
We know that the total number of kids is 150. We can find the number of kids with green, brown, and gray eyes using the given percentages:
[tex]\sf\dashrightarrow Green\: eyes = 6\: kids[/tex]
[tex]\sf\dashrightarrow Brown\: eyes = 0.52 \times 150 = 78\: kids[/tex]
[tex]\sf\dashrightarrow Gray\: eyes = 0.16 \times 150 = 24\: kids[/tex]
[tex]\\[/tex]
To find the number of kids with blue eyes, we can subtract the number of kids with green, brown, and gray eyes from the total number of kids:
[tex]\sf\dashrightarrow Blue\: eyes = 150 - 6 - 78 - 24[/tex]
[tex]\sf\dashrightarrow Blue\: eyes = 42\: kids[/tex]
[tex]\\[/tex]
Finally, we can calculate the percentage of kids with blue eyes by dividing the number of kids with blue eyes by the total number of kids and multiplying by 100:
[tex]\sf\implies Percentage = \dfrac{42}{150} \times 100[/tex]
[tex]\sf\implies Percentage = \dfrac{4,200}{150}[/tex]
[tex]\sf\implies Percentage = \green{28\%}[/tex]
[tex]\\[/tex]
[tex]\\[/tex]
Therefore, 28% of the kids have blue eyes.
Which shows a true comparison? Select all that apply.
A. 32.03 > 32.3
B. 3.114 > 3.112
C. 4.003 < 3.996
D. 0.541 > 0.145
E. 0.141 < 0.19
The true comparisons are:
B. 3.114 > 3.112: In this case, the number 3.114 is greater than 3.112, as the digit in the thousandth place (4) is greater than the corresponding digit in 3.112 (1).
D. 0.541 > 0.145: Here, the number 0.541 is greater than 0.145 because the digit in the hundredth place (4) is greater than the corresponding digit in 0.145 (1).
E. 0.141 < 0.19: In this example, the number 0.141 is indeed less than 0.19, as the digit in the hundredth place (1) is less than the corresponding digit in 0.19 (9).
Option A is not a true comparison because 32.03 is actually less than 32.3. The digit in the hundredth place is 0 in both numbers, and the digit in the thousandth place is 3 in 32.03, while it is 0 in 32.3.
Option C is also not a true comparison since 4.003 is greater than 3.996. The digit in the thousandth place (4) is greater than the corresponding digit in 3.996 (3).
Answer: -D) 0.541 > 0.145
-B) 3.114 > 3.112
-E) 0.141 < 0.19
explanation: The number 3.114 is greater than 3.112, as the digit in the thousandth place (4) is greater than the corresponding digit in 3.112 (1). Here, the number 0.541 is greater than 0.145 because the digit in the hundredth place (4) is greater than the corresponding digit in 0.145 (1). In this example, the number 0.141 is indeed less than 0.19, as the digit in the hundredth place (1) is less than the corresponding digit in 0.19 (9).
PLEASE HELP ME ANSWER THIS QUESTION I NEED IT PLEASE.
Find ∫ x^5 √(2 - x^3) dx
Answer:
[tex]\displaystyle \frac{2}{15}(2-x^3)^{\frac{5}{2}}-\frac{4}{9}(2-x^3)^{\frac{3}{2}}+C[/tex]
Step-by-step explanation:
[tex]\displaystyle \int x^5\sqrt{2-x^3}\,dx\\\\=\int x^5(2-x^3)^{\frac{1}{2}}\,dx\\\\=\int x^3x^2(2-x^3)^{\frac{1}{2}}\,dx[/tex] <-- Breaking up [tex]x^5[/tex] into [tex]x^3x^2[/tex] helps us later
Let [tex]u=2-x^3[/tex] and [tex]du=-3x^2\,dx[/tex] so that [tex]2-u=x^3[/tex] and [tex]\displaystyle -\frac{1}{3}du=x^2dx[/tex]:
[tex]\displaystyle -\frac{1}{3} \int (2-u)u^{\frac{1}{2}}\,du\\\\=-\frac{1}{3} \int 2u^{\frac{1}{2}}-u^{\frac{3}{2}}\,du\\\\=-\frac{1}{3}\biggr(\frac{4}{3}u^{\frac{3}{2}}-\frac{2}{5}u^{\frac{5}{2}}\biggr)+C\\\\=-\frac{1}{3}\biggr(\frac{4}{3}(2-x^3)^{\frac{3}{2}}-\frac{2}{5}(2-x^3)^{\frac{5}{2}}\biggr)+C\\\\=-\frac{4}{9}(2-x^3)^{\frac{3}{2}}+\frac{2}{15}(2-x^3)^{\frac{5}{2}}+C\\\\=\frac{2}{15}(2-x^3)^{\frac{5}{2}}-\frac{4}{9}(2-x^3)^{\frac{3}{2}}+C[/tex]
Multiply
4 8/9 • 1 1/3
Answer:
Step-by-step explanation:
[tex]4\frac{8}{9} . 1\frac{1}{3}\\= \frac{44}{9}.\frac{4}{3} \\= \frac{176}{27}[/tex]
I need an equation for the line done in this graph
15. The volumes of two similar solids are 857.5 mm^3 and 540 mm^3. The surface area of the smaller solid is 108 mm^2. What is the surface area of the larger solid?
The surface area of the larger solid is approximately 172 mm sq. approx
Given
The volume of the smaller solid = 540 mm cube
The volume of the larger solid = 857.5 mm cube
The surface area of the smaller solid = 108 mm sq.
Required to find the surface area of the larger solid =?
Let the surface area of the larger solid be x.
(surface area of smaller solid) / (volume of smaller solid) = (surface area of larger solid) / (volume of larger solid)
Putting the values in the above formula we get the value of x.
108 mm^2 / 540 mm^3 = x / 857.5 mm^3
x = 171.5 mm sq
Thus, the surface area of the larger solid is approximately 172 mm sq
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3 2 points Find the height of a cone with a diameter of 12 m whose volume is 188 m³. Use 3.14 for 77 and round your answer to the nearest meter. Please record your work/justification on your paper or document
5m
6 m
2m
12 m
4 m
5m is the height of a cone with a diameter of 12 m whose volume is 188 m³.
To find the height of a cone, we can use the formula for the volume of a cone and solve for the height.
The formula for the volume of a cone is:
V = (1/3)× π × r² × h
Given that the diameter of the cone is 12 m, the radius (r) is half of the diameter, which is 6 m.
We are also given that the volume of the cone is 188 m³.
Using the formula, we can rearrange it to solve for the height (h):
h = (3V) / (πr²)
Plugging in the values:
h = (3 × 188) / (3.14 × 6²)
h = 564 / (3.14 × 36)
h = 564 / 113.04
h =4.9916
h=5
Therefore, the height of a cone with a diameter of 12 m whose volume is 188 m³ is 5 m.
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Find the circumference
The circumference of the circle is 88 units given the radius 14 units
What is Circumference of a circle?Circumference of a circle is the measurement of the boundary of the circle or the path or the boundary that surrounds the shape. It is also called Perimeter of a circle.
Howto determine this
Given the radius of the circle = 14
Circumference of a circle = 2πr
Where π = 22/7
Circumference of circle = 2 * 22/7 * 14
Circumference of circle = 44/7 * 14
Circumference of circle = 616/14
Circumference of circle = 88 units
Therefore, the Circumference of circle is 88 units
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Find the volume of a pyramid with a square base, where the side length of the base is
14.4
m
14.4 m and the height of the pyramid is
15.3
m
15.3 m. Round your answer to the nearest tenth of a cubic meter.
The volume of a pyramid with a square base is 3172.608 cubic meter.
Given that, the side length of the base is 14.4 m and the height of the pyramid is 15.3 m.
Formula to find the volume of the object is Volume = Area of a base × Height.
Here, volume = 14.4²×15.3
= 3172.608 cubic meter
Therefore, the volume of a pyramid with a square base is 3172.608 cubic meter.
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50 Points! Multiple choice algebra question. Photo attached. Thank you!
21. (1 point) Let y 00 −64y = 0. Find all values of r such that y = kerx satisfies the differential equation. If there is more than one correct answer, enter your answers as a comma separated list. r = help (numbers) Answer(s) submitted:
The values of r for which y = e^(rx) satisfies the differential equation y″ - 64y = 0 are r = 8 and r = -8.
How to calculate the valueFirst, differentiate y twice:
y' = [tex]re^{rx}[/tex]
y'' = r²[tex]e^{rx}[/tex]
y'' - 64y = r²[tex]e^{rx}[/tex] - 64[tex]e^{rx}[/tex] = 0
[tex]e^{rx}[/tex] * ([tex]r^{2}[/tex] - 64) = 0
[tex]r^{2}[/tex] - 64 = 0:
Solving this quadratic equation gives:
[tex]r^{2}[/tex] = 64
r = ±8
Therefore, the values of r that satisfy the differential equation are r = 8 and r = -8.
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Let y″−64y=0.
Find all values of r such that y=kerx satisfies the differential equation. If there is more than one correct answer, enter your answers as a comma separated list.
2. Observe the following triangles and answel (a) Find the value of 'a' in each triangle. (b) Find the measure of the unknown angles. 1. P 67° 48° R A 65° 55° C
The value of x that is measure of angle R from the given triangle PQR is 60°.
In the given triangle PQR, angle P is right angle and measure 90°, angle Q measures 30° and angle R measures x.
We know that, sum of the interior angles of triangle is 180°.
Here, ∠P+∠Q+∠R=180°
90°+30°+∠R=180°
120°+∠R=180°
∠R=180°-120°
∠R=60°
Therefore, the value of x that is measure of angle R from the given triangle PQR is 60°.
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The stemplot shows the snowfall, in inches, in US cities during December.
Use this graphic to answer the question.
Use the drop-down menus to complete the statements about the snowfall amounts shown in the stemplot.
This distribution of snowfall amounts is
. There appears to be one outlier in snowfall amount at
inches.
This distribution of snowfall amounts is skewed to the right
When are data skewed to the rightData is said to be skewed to the right or positively skewed, when the tail of the distribution extends more towards the right side of the data. This means that there are a few larger values or outliers that pull the mean or median towards the higher end of the scale, resulting in a longer tail on the right side of the distribution.
In a positively skewed distribution majority of the data is concentrated towards the lower values.
Considering the stemplot the majority of the data is in the lower values
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Answer:
to the second part
18.7 inches
Ms. Chung drives the same distance to go to work every Monday through Friday. On Saturday she drove g the distance she drives to work. The distance she drove on Saturday was 0.9 miles. Part A: In the first box, enter an equation to represent the distance, d, that Ms. Chung drives to work. Part B: In the second box, enter the distance Ms. Chung drives to work.
A) The algebraic expression will be 12d + 7 = 91
B) He drives 7 miles per day to work.
For 11 days straight, Ms. Chung drove the same distance every day going to and coming from work.
The distance she drove on Saturday was; 0.9 miles.
The number of miles she drives per day:
84 miles/12
= 7 miles per day
Let the number of miles she travels be day = d
12d + 7 = 91 miles
12d + 7 = 91
12d = 91 - 7
12d = 84
d = 84/12
d = 7 miles per day
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Here are the first five terms of a number sequence. 23 20 17 14 11 (a) Write down the 8th term of this sequence. *********
The 8th term of the sequence is 2.
To find the 8th term of the given number sequence, we can observe that the sequence is decreasing by 3 with each term.
Starting from the first term, which is 23, we subtract 3 repeatedly to get the subsequent terms:
23 - 3 = 20
20 - 3 = 17
17 - 3 = 14
14 - 3 = 11
We can see that each term is obtained by subtracting 3 from the previous term.
To find the 8th term, we continue this pattern:
11 - 3 = 8
8 - 3 = 5
5 - 3 = 2
Therefore, the 8th term of the sequence is 2.
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the radius of a sphere with a volume of 4.5π cubic centimeters.
hello
the answer to the question is:
volume of sphere = ⁴⁄₃πr³
4.5π = ⁴⁄₃πr³ ----> r³ = 3.375 ----> r = 1.5 cm
Find the equation of the line.
Use exact numbers
Answer:
y = [tex]\frac{2}{3}[/tex] x + 4
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 6, 0) and (x₂, y₂ ) = (0, 4) ← 2 points on the line
m = [tex]\frac{4-0}{0-(-6)}[/tex] = [tex]\frac{4}{0+6}[/tex] = [tex]\frac{4}{6}[/tex] = [tex]\frac{2}{3}[/tex]
the line crosses the y- axis at (0, 4 ) ⇒ c = 4
y = [tex]\frac{2}{3}[/tex] x + 4 ← equation of line
Find a dimensionless product relating the torque, (ML²T-²) produced by an automobile engine, the engine's rotation rate, (T-¹), the volume V of air displaced by the engine, and the air density p.
The dimensionless product relating the torque, rotation rate, volume, and air density is:
Pi = (torque) * (rotation rate)² * (volume)^(1/3)
To find a dimensionless product relating the torque (ML²T⁻²) produced by an automobile engine, the engine's rotation rate (T⁻¹), the volume V of air displaced by the engine, and the air density p, we can make use of the Buckingham Pi theorem.
The Buckingham Pi theorem states that in a physical problem involving n variables with k fundamental dimensions, there will be n - k dimensionless quantities that can be formed as products of powers of the original variables.
In this case, we have 4 variables with 3 fundamental dimensions: torque (M L² T⁻²), rotation rate (T⁻¹), volume (L³), and air density (M L⁻³). Therefore, we expect to have 4 - 3 = 1 dimensionless product.
Let's define the dimensionless product (Pi) as:
Pi = (torque)ᵃ * (rotation rate)ᵇ * (volume)ᶜ * (air density)ᵈ
To determine the powers (a, b, c, d), we equate the dimensions on both sides of the equation:
M L² T⁻² = (M)ᵃ * (T⁻¹)ᵇ * (L³)ᶜ * (M L⁻³)ᵈ
Equating the dimensions of mass (M):
1 = a + d
Equating the dimensions of length (L):
2 = 3c - 3d
Equating the dimensions of time (T):
-2 = -b
Solving these equations, we find:
a = 1
b = 2
c = 1/3
d = 0
This dimensionless product captures the relationship between these variables, independent of their specific units and scaling factors.
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Find the number that belongs
in the green box.
37⁰
64°
21.1
30
Round your answer to the nearest tenth.
The length of the third side, which is opposite the angle of 84°, is approximately 30.1 units.
Given is a triangle with angles 64° and 32°, and side 21.1 and 30, we need to find the third side,
So, according to the angle sum property of triangle,
Third angle = 180° - (64° + 32°)
Third angle = 84°
To find the length of the third side, which is opposite the angle of 84°, we can use the Law of Sines.
The Law of Sines states that the ratio of the length of a side to the sine of its opposite angle is constant for all sides of a triangle.
Let's label the triangle with angles A, B, and C, and sides a, b, and c, respectively.
In this case, angle A is 84°, angle B is 64°, and angle C is 32°. Side a is the side opposite angle A, side b is the side opposite angle B, and side c is the side opposite angle C.
Using the Law of Sines, we have the following equation:
sin(A) / a = sin(B) / b = sin(C) / c
We want to find the length of side a, so we can rearrange the equation as follows:
sin(A) / a = sin(B) / b
Now we can substitute the given values:
sin(84°) / a = sin(64°) / 30
To find side a, we can solve for it algebraically:
a = (sin(84°) × 30) / sin(64°)
Calculating this expression, we get:
a ≈ 30.1
Therefore, the length of the third side, which is opposite the angle of 84°, is approximately 30.1 units.
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If u⃗ =⟨3,9⟩ and w⃗ =⟨−3,1⟩, find 13u⃗ −2w⃗ .
The resultant vector of the operation 13u - 2w is given as follows:
13u - 2w = <45, 115>.
How to obtain the resultant vector?The vectors in the context of this problem are defined as follows:
u = <3,9>.w = <-3,1>.When we multiply a vector by a constant, each component of the vector is multiplied by the constant, hence:
13u = <39, 117>.2w = <-6, 2>.Then when the two vectors are subtracted, the equivalent components of each vector are subtracted, hence:
13u - 2w = <39, 117> - <-6, 2>
13u - 2w = <45, 115>.
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