Sketch the lines through the point with the indicated slopes. Make the sketches on the same set of coordinate axes
Point
Slopes
(1, 1)
(a) 3 (b) -3 (c) -5/2 (d) Undefined
The sketch for slope is attached below.
What is slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
Point Slopes
(1, 1) (a) 3
_ (b) -3
_ (c) -5/2
_ (d) Undefined
a) Now, using slope intercept form
y - 1= 3 (x-1)
y- 1= 3x- 3
y= 3x - 2
(b) Equation of a line has a slope -3 is given by
y - 1= (-3) (x-1)
y-1 = 3- 3x
y = -3x + 4
(c) Equation of a line has a slope -5/2 is given by
y - 1= (-5/2) (x-1)
y-1 = -5/2x + 5/2
y= -5/2x + 7/2
(d) The line parallel to y axis and passes through given point : x=1
"undefined" means the line is vertical.
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Solve x2 – 8x + 15 < 0. Select the critical points for the inequality shown. –15 –5 –3 3 5
Answer: To solve the inequality x^2 - 8x + 15 < 0, we first want to find the critical points, which are the points where the quadratic function changes direction (from increasing to decreasing or vice versa). To find the critical points, we need to set the quadratic equal to zero and solve for x. In this case, we have:
x^2 - 8x + 15 = 0
To solve this equation we should factor it or use the quadratic formula.
(x - 5)(x - 3) = 0
x = 5, x = 3
This means that the critical points for the inequality are x = 5 and x = 3. To find the solution set of the inequality, we test the signs of the function at the critical points and in the intervals between them.
The solution of the inequality is x < 3 or x > 5.
Step-by-step explanation:
what is 36 percent of 128
Answer:
Step-by-step explanation:
36 percent can be written as 36/100. So now the question is 36/100 x 28.
Its easier if you simplify 100 and 28 by a common factor, which im going to use 4 for. So instead you get 36/25 x 7.
36x7=252
252/25=10.08
Answer:
46.08
Step-by-step explanation:
Remember that a percent is always a fraction out of 100, in this case 36/100, so it can also be written as a decimal number, in this case 0.36. Now all you need to do is multiply 128*0.36
Solve for x. -2x + 1 = 3x + 16
Answer:
x=-3
Step-by-step explanation:
I showed my work in the picture
Answer:
[tex]\boxed{\sf x=-3}[/tex]
Step-by-step explanation:
[tex]\sf -2x+1=3x+16[/tex]
Subtract 3x from both sides:-
[tex]\sf -2x+1-3x=3x+16-3x[/tex]
[tex]\sf -5x+1=16[/tex]
Subtract 1 from both sides:-
[tex]\sf -5x+1-1=16-1[/tex]
[tex]\sf -5x=15[/tex]
Divide both sides by -5:-
[tex]\sf \cfrac{-5x}{-5}=\cfrac{15}{-5}[/tex]
[tex]\sf x=-3[/tex]
Therefore, x = -3!
______________________
Hope this helps!
Have a great day!
It is estimated that wireless soil monitors could save up to 6 trillion gallons of
water per year by reporting precise information needed to irrigate crops
properly. Using this data, express the number of gallons of water saved in two
years, in scientific notation.
Hint:
1Million=6 zeros
1billion=9 zeros
1trillion=12 zeros
____x10____
Using scientific notation, the number of gallons of water saved in two years by the wireless soil monitors is 1.2 x 10^12.
What is scientific notation?Scientific notation is a shorthand way of writing very large numbers or very small numbers in a simpler form.
The parts of a scientific notation are coefficient, base, and exponent.
We state that a number is written in standard notation when the number is between 1 and 10 and it is multiplied by a power of 10.
The number of gallons of water per year saved by wireless soil monitors = 6 trillion
The number of gallons of water saved by wireless soil monitors in 2 years = 12 trillion
In scientific notation, 12 trillion = 1.2 x 10^12.
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A landscaping business is purchasing plants from a nursery to finish a project. It will
cost $14 each to buy each tree and $7 each to buy each bush. The landscaper wishes to
keep the spending to no more than $870. Let t be the number of trees and b be the
number of bushes.
Select the inequality that describes the situation.
14t+7b> 870
O 14t+ 76 2 870
O 14t+7b < 870
O 14t+7b ≤ 870
I think it is the third answer.
Because your problem says 'no more than' so it can't be the fourth one,because it has '≤' which means that the number is lower or equal.
So it is the third one.
Hope I helped you!
Nicole cycled 9 laps on a bicycle path around the lake. If each lap was 9540ft long, what was the total distance she cycled? Write your answers in miles.
Answer:
162 miles.
Step-by-step explanation:
To find the total distance Nicole cycled, we can multiply the number of laps by the length of each lap.
The total distance Nicole cycled is:
9 laps * 9540 ft/lap = 858,600 ft
To convert this distance to miles, we can use the conversion factor that there are 5280 feet in a mile.
858,600 ft / 5280 ft/mile = 162 miles
So the total distance Nicole cycled is 162 miles.
A student says the expression 4+3(2x+2) is equivalent to the expression 6x+10 . As your answer, explain/show why the student is correct. Name each property that you use as you simplify the longer expression.
if im not wrong
4+3(2x+2) multiply since its in parenthesis first
property of mulitplication i think
4+6x+6
property of addition
6x+10
(this should be right)
GEOMETRY HELPPPP PLS
The new equation is y=-1/2x+5. An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used.
What is mathematical equation?An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal." The link between two expressions on either side of the sign is represented by a mathematical equation. One variable and an equal sign are typically present. For instance, 2x – 4 = 2. The smallest equivalent fraction of the number is considered to be its simplest form. What to do to discover the simplest form? Investigate the numerator and denominator for shared factors. To see if a fractional number is a prime number, check it.Our first line in this equation is y=2x-1. By applying the equation y=mx+b, where "m" stands for the slope, we can see that our "m" in this instance is 2. then negate 2. It turns into -2.
Change the denominator and numerator after that. Since -2 is actually -2/1, let's change it to -1/2. The perpendicular line's slope is that.
We must now make it pass through (-2,6). We just have a line like this to work with at the moment: y=-1/2x
Plugging in the x-coordinate of our target location, -2, yields y=-1/2(-2), or 1. But hold on, because the y-coordinate we were given is 6, shouldn't y be equal to 6 as well? Yes! The only thing left to do is to add 5 to get from 1 to 6!
The complete question is,
Write an equation for a line perpendicular to y = 2 x − 1 and passing through the point (-2,6)
Write an equation for a line perpendicular to y=2x−1 and passing through the point (-2,6)
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Can someone help me with this math problem? The answer is 7/2, but does anyone know how to get that answer?
Answer:
see explanation
Step-by-step explanation:
[tex]\frac{5}{x}[/tex] - [tex]\frac{2}{x^2}[/tex] = 2
multiply through by x² ( x ≠ 0 ) to clear the fractions
5x - 2 = 2x² , that is
2x² = 5x - 2 ( subtract 5x - 2 from both sides )
2x² - 5x + 2 = 0 ← in standard form
(2x - 1)(x - 2) = 0 ← in factored form
equate each factor to zero and solve for x
2x - 1 = 0 ⇒ 2x = 1 ⇒ x = [tex]\frac{1}{2}[/tex]
x - 2 = 0 ⇒ x = 2
since x₁ < x₂ , then
x₁ = [tex]\frac{1}{2}[/tex] and x₂ = 2
Then
3x₁ + x₂
= 3 × [tex]\frac{1}{2}[/tex] + 2
= [tex]\frac{3}{2}[/tex] + 2
= [tex]\frac{3}{2}[/tex] + [tex]\frac{4}{2}[/tex]
= [tex]\frac{7}{2}[/tex]
3. Line DG is the perpendicular bisector of chord El.
EF = 7, EI = 9.5, and DG = 1.8.
What is the diameter of the circle? Show your work.
The diameter of the circle would be given as = 10
What is a diameter?Diameter is defined as the length of a line through the center that touches two points on the edge of the circle.
The diameter of the circle can be found through finding first the radius of the circle.
The radius of the circle is half of the diameter. it is the line DI which is also the longer line of the triangle DGI.
Using the Pythagorean formula c² = a² + b²
The lines that represents ;
a= DG
b= EI/2 = 4.8
C= DI = ?
C² = DI
a² = 1.8²
b² = (9.5/2)² = 4.8²
c² = 2.24 + 23.04 = 25.28
C =√25.28
C = 5
Therefore the diameter of the circle = 5×2 = 10
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Solve for n. 7n - 2 = 5n + 6
Answer:
n = 4
Step-by-step explanation:
Pre-SolvingWe are given the equation 7n - 2 = 5n + 6, ans we want to solve it for n.
To do this, we need to isolate n one one side.
SolvingLet's start by adding 2 to both sides.
7n - 2 = 5n + 6
+2 +2
_______________
7n = 5n + 8
Now, subtract 5n from both sides.
7n = 5n + 8
-5n -5n
_______________
2n = 8
Divide both sides by 8 to get the value of n.
2n = 8
÷2 ÷2
________
n = 4
1. The sum of two three-digit numbers is a four-digit number.
Answer:
Step-by-step explanation:
What are the possible combinations of three-digit numbers that could add up to a four-digit number?
There are many possible combinations of three-digit numbers that can add up to a four-digit number. Here are some examples:
1. 100 + 900 = 1000
2. 200 + 800 = 1000
3. 300 + 700 = 1000
4. 400 + 600 = 1000
5. 500 + 500 = 1000
6. 600 + 400 = 1000
7. 700 + 300 = 1000
8. 800 + 200 = 1000
9. 900 + 100 = 1000
10. 111 + 889 = 1000
11. 222 + 778 = 1000
12. 333 + 667 = 1000
13. 444 + 556 = 1000
14. 555 + 445 = 1000
15. 666 + 334 = 1000
16. 777 + 223 = 1000
17. 888 + 112 = 1000
18. 999 + 001 = 1000
19. 123 + 877 = 1000
20. 234 + 766 = 1000
In triangle ABC, M is the midpoint of AB and N divides CB such as NB:NC = 1:5. Find the area of triangle MNB, MNC and ABC
The area of triangle MNB, MNC and ABC 6 in.², 60 in.², and 30 in.² respectively
How to find the area of the triangle?The ratio of the base of the triangles ΔMNB and ΔCBM, that shares a common vertex, is the ratio of their areas.
M is the midpoint of side AB in ΔABC
NB:CB = 1:5
Area of ΔCAM = 30 in.²
The area of ΔMNB and ΔABC
Area = 1/2 * base * height
Height of ΔCAM = Height of ΔCBM = Altitude of point C above line AB
MA = MB by definition of midpoint
MA is the base of ΔCAM, and MB is the base of ΔCBM
Therefore; Area of ΔCAM = 1/2 AM * Height of ΔCAM
= 1/2 * AM* height of ΔCAM
Which gives;
Area of ΔCAM = Area of ΔCBM = 30 in.²
Area of ΔABC = Area of ΔCAM + Area of ΔCBM = 30 + 30 = 60
Area of ΔABC = 60 in.²
Taking CB as the base of ΔCBM, we have;
Height of ΔMNB = Height of ΔCBM from line CB
Base length of ΔCBM = 5 × Base length of ΔMNB
Therefore; Area of ΔMNB = 30/5 = 6 in²
Area of ΔCBM = 30 in.² = 5 × The area of ΔMNB
Conclusively, the Area of ΔMNB = 6 in.²
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Correct question:
In a triangle ABC, M is the mid point of the side AB and N is the mid point of the side AC. Find the lenght of the segment MN if AB =18, BC = 10 and AC = 20
Please help, I’ll mark brainlest
g(x) = 2(x+3)^2 - 1
Value of g(x) with given values of x:
x -5 -4 -3 -2 -1
g(x) 7 1 -1 1 7
Given: the functional equation:
g(x) = 2(x + 3)^2 – 1
Solution:
Value of g(x), when x= -5
g(x) = 2 (-5 +3)^2 – 1
= 2 (-2)^2 – 1
= 2* (-2)* (-2) – 1
= 8 – 1
= 7
Value of g(x), when x= -4
g(x) = 2 (-4 +3)^2 – 1
= 2 (-1)^2 – 1
= 2* (-1)* (-1) – 1
= 2 – 1
= 1
Value of g(x), when x= -3
g(x) = 2 (-3 +3)^2 – 1
= 2 (0)^2 – 1
= 2* 0 – 1
= 0 – 1
= - 1
Value of g(x), when x= -2
g(x) = 2 (-2 +3)^2 – 1
= 2 (1)^2 – 1
= 2* (1)* (1) – 1
= 2 – 1
= 1
Value of g(x), when x= -1
g(x) = 2 (-1 +3)^2 – 1
= 2 (2)^2 – 1
= 2* (2)* (2) – 1
= 8 – 1
= 7
-
2 x
3
5
сл
6
The volume of a cuboid is 364cm³.
The length is 7cm and the width is 13cm.
Work out the height of the cuboid.
8
The height of the cuboid is 4 cm
What is a cuboid?
A cuboid is a solid shape or a three-dimensional shape in geometry. A cuboid is a convex polyhedron that has eight vertices, twelve edges, and six rectangular faces. A rectangular prism is another name for a cuboid. A cube is an object with six square faces on a cuboid.
volume of a cuboid = l *w*h
where, l= length, w=width, h= height
=> 364 = 7*13*h
=> h=364/(7*13) = 364/91
=> h= 4 cm
Thus, the height of the cuboid is 4 cm
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The area of the regular octagon is 10.15 cm².
1.45 cm
What is the measure of the apothem, rounded to the
nearest hundredth of a centimeter
The measure of the apothem is 1.75cm.
What is a regular octagon?
Eight equal sides and eight equal angles make up a normal octagon. Each side is the same length, and each angle is the same size. The total interior and external angles are 1080° and 360°, respectively. The inner angle at each vertex of a regular octagon is 135°.
Here, we have
Given: The area of the regular octagon is 10.15 cm².
We have to find the measure of the apothem.
The octagon can be divided into 8 congruent (identical) isosceles triangles. One of them is AOB.
Area (triangle AOB) = 10.15/8 = 1.27cm².
Area(triangle AOB) is also 1/2*MO*AB
1.27 = 1/2*MO*1.45
MO = 1.75cm
Hence, the measure of the apothem is 1.75cm.
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Arianys invests money in an account paying a simple interest of 3% per year. If m
represents the amount of money she invests, which expression represents her balance
after a year, assuming she makes no additional withdrawals or deposits?
Answer:
Step-by-step explanation:
The balance of an account after a year, when the interest rate is 3% per year and there are no additional withdrawals or deposits, can be represented by the formula:
Balance = Principal + Interest
where Principal is the initial amount of money invested (m) and Interest is the interest earned on that amount for the year.
Interest is calculated as the product of the principal, the interest rate, and the time period. In this case, the interest rate is 3% (or 0.03), and the time period is one year. Therefore the Interest can be represented by the following expression:
Interest = Principal * Interest Rate * Time
Substituting the given values:
Interest = m * 0.03 * 1
So the expression that represents Arianys balance after a year is:
Balance = m + (m*0.03)
= m + 0.03m
= 1.03m
This expression represents her balance after a year, assuming she makes no additional withdrawals or deposits.
HELP I NEED TO KNOW ANSWER! Determine if triangle QRS and triangle TUV are or are not similar and if they are state how you know
The given triangles are not similar because the sides given are not proportional.
What are Similar Triangles?Similar triangles are those triangles which has the same shape but different size.
The length of sides and angles are proportional in similar triangles.
Given are two triangles QRS and TUV.
Also given the measure of two sides of each triangle and an included angle of these sides of each triangle.
From the figure, given angles are equal.
If we prove that the sides including these angles are proportional, we can say the given triangles are similar by SAS similarity theorem.
7 / 35 = 1/5
But 13/55 ≠ 1/5
So they are not proportional.
Hence the given triangles are not similar.
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Pls help solve asap!!!!! I don’t understand
-2а + 3 ≥ 6а - 1 > 3а - 10
Answer:
00088n886668hb76u8y687440
pleasr help me out with this
Answer:
3π - π√2/2 or 7.2 cm-------------------------
According to the given we can state:
AD = BC = AB = 2AO = 2,EO is the perpendicular bisector of AB,Arc AC and arc BD are of equal length.Find arc AB, it is a semicircle of 1 cm radius:
arc(AB) = 1/2 × 2πr = πr = π cmΔAEO and ΔBEO are both isosceles, hence ∠A and ∠B are both 45°.
Find arcs ABD and BAC:
arc(ABD) + arc(BAC) = 2 × 45/360 × 2πr = 1/2 × πr = π cm∠AEB is a right angle since ∠AEO and ∠BEO are both 45°.
Hence ∠CED is also right angle as vertical angle with ∠AEB.
Find the length of EC and ED.
We know AD = BC = 2 cm and ΔAEO is 45° right triangle.
It gives us:
AE = √2Then:
ED = AD - AE = 2 - √2Find arc ECD:
arc(ECD) = 1/4 × 2πr = 1/2 × π(2 - √2) = π - π√2/2 cmThe perimeter is the sum of all the arc measures:
P = π + π + π - π√2/2 = 3π - π√2/2 or 7.2 cm (rounded)Answer:
[tex]\textsf{Perimeter}=3\pi-\dfrac{\pi}{\sqrt{2}}=7.20333649...\; \sf cm[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6.4 cm}\underline{Arc length}\\\\Arc length $=r \theta$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $\theta$ is the angle measured in radians.\\\end{minipage}}[/tex]
To convert degrees to radians, multiply the angle in degrees by π/180°.
Arc AB
As arc AB has center O, the radius of arc AB is OA = 1 cm.
As AB is a straight line, ∠AOB is 180° = π.
Therefore, the length of arc AB is:
[tex]\implies AB=r \:\theta=1 \cdot \pi = \pi[/tex]
Arc AC
Triangle BOE is a right triangle with base of 1 cm and height of 1 cm.
Therefore, ∠OBE is 45° = π/4
If arc AC has center B, then the radius is AB = 2 cm.
Therefore, the length of arc AC is:
[tex]\implies AC=r \:\theta=2 \cdot \dfrac{\pi}{4} = \dfrac{\pi}{2}[/tex]
Arc BD
Arc BD is the same as arc AC.
[tex]\implies BC= \dfrac{\pi}{2}[/tex]
Arc CD
As triangle BOE is a right triangle with base of 1 cm and height of 1 cm, the length of its hypotenuse BE is:
[tex]\implies BE=\sqrt{1^2+1^2}=\sqrt{2}[/tex]
As arc AC has center B and radius of AB = 2 cm, then BC is also its radius and therefore BC = 2 cm
Therefore:
[tex]\implies CE=BC-BE[/tex]
[tex]\implies CE=2-\sqrt{2}[/tex]
The arc CD has center E so its radius is CE = 2-√2.
As ∠BEO and ∠AEO are both 45° then ∠AEB is 90°.
According to the vertical angle theorem, ∠CED is also 90° = π/2.
Therefore, the length of arc CD is:
[tex]\implies CD=r \:\theta=(2-\sqrt{2}) \cdot \dfrac{\pi}{2} = \dfrac{(2-\sqrt{2})\pi}{2}[/tex]
Perimeter of the egg
The perimeter of the egg is the sum of the found arcs:
[tex]\implies \textsf{Perimeter}=AB+AC+BD+CD[/tex]
[tex]\implies \textsf{Perimeter}=\pi+\dfrac{\pi}{2}+\dfrac{\pi}{2}+\dfrac{(2-\sqrt{2})\pi}{2}[/tex]
[tex]\implies \textsf{Perimeter}=2\pi+\dfrac{(2-\sqrt{2})\pi}{2}[/tex]
[tex]\implies \textsf{Perimeter}=2\pi+\dfrac{2 \pi}{2}-\dfrac{\sqrt{2}\:\pi}{2}[/tex]
[tex]\implies \textsf{Perimeter}=3\pi-\dfrac{\sqrt{2}\:\pi}{2}[/tex]
[tex]\implies \textsf{Perimeter}=3\pi-\dfrac{\pi}{\sqrt{2}}[/tex]
[tex]\implies \textsf{Perimeter}=7.20333649...\; \sf cm[/tex]
The sides of MNPQ are represented by the expressions below. Find the perimeter of MNPQ.
MW=-2+37
QP= y+14
NP= x-5
MN=4y+5
perimeter: ? units
Answer:
Step-by-step explanation:
The perimeter of a polygon is the sum of the lengths of all its sides. To find the perimeter of MNPQ, we need to add up the lengths of MN, NP, PQ and PM.
Given that:
MW=-2+37 = 35
QP= y+14
NP= x-5
MN=4y+5
The perimeter can be calculated by adding up the above expressions:
Perimeter = MN + NP + QP + MW
= (4y + 5) + (x - 5) + (y + 14) + 35
= 4y + x + y + 54
= (4y + y) + (x + 54)
= 5y + x + 54
So the perimeter of MNPQ is 5y + x + 54 units.
Quick Help please
I don’t understand please answer all four.
Answer:
To find f(-3), substitute -3 for x in the equation for f(x):
f(-3) = 2(-3) + 5 = -6 + 5 = -1
Answer:
f(-3) = -1
To find g(x) - h(x), first substitute x into both g(x) and h(x) and then subtract h(x) from g(x):
g(x) - h(x) = -3x^2 + 2x - 6 - (-4 - x) = -3x^2 + 3x - 2
Answer:
g(x) - h(x) = -3x^2 + 3x - 2
To solve for x when f(x) = h(x), first substitute x into both f(x) and h(x), and then solve for x:
2x + 5 = -4 - x
3x = -9
x = -3
Answer:
x = -3
To determine which of the functions are linear, we need to look at the degree of the polynomials in each function. Linear functions have a degree of 1, while non-linear functions have a degree greater than 1.
f(x) = 2x + 5 is linear because it has a degree of 1
g(x) = -3x^2 + 2x - 6 is non-linear because it has a degree of 2
h(x) = -4 - x is linear because it has a degree of 1
Answer:
f(x) and h(x) are linear, while g(x) is non-linear.
factor: x^2 -x -2
plssss
Answer:
(x+1)(x-2)
Step-by-step explanation:
[tex](x+1)(x-2)=x^{2} -x-2[/tex]
Hope this helps
Jeremy analyses one of his parachute jumps.
He draws a graph showing his velocity up to the opening of his parachute.
The acccceleration will be 1m/s² and the average speed is 47m/s.
How to calculate the acceleration?For the acceleration problems, you must draw a tangent on curved velocity-time graphs. Since it requested acceleration at t = 10 seconds, we must create a straight line that only touches the graph once, at 10 seconds.
Now, when drawing tangents, you must be as precise as you can because they can only contact the line once.
Next, determine the gradient using the tangent. You can accomplish this by creating a triangle out of two additional lines drawn from the tangent, then dividing the rise by the run, or Y/X. The triangle that comes before the Y and the X simply denotes the Greek letter delta, which symbolizes change. Change in Y so prevails over Change in X. So 10/10 = 1. So 1m/s^2.
If we estimate the speed at 5 seconds intervals, then we have
Average speed = (36 + 46 + 49 + 50 + 50 +50 + 50) ÷ 7
Average speed = 331/7 = 47.29 m/s
Average speed = 47 m/s
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How does the use of internal rhyme affect the poem? A. It adds suspense by means of the steady repetition of similar sounds. B. It makes the speaker seem more sympathetic since he is so clever at rhyming. C. It helps create and maintain the poem's playful tone. D. It creates more emotional impact for the poem by emphasizing emotional words.
The use of internal rhyme affect the poem by: C. It helps create and maintain the poem's playful tone
What is internal rhymeInternal rhyme tend to occurs when words that are in the same line of a poem rhyme with one another.
The use of internal rhyme can tend to add more musical quality to a poem and it as well help to create cohesion within a line or stanza. Internal rhyme also help to a sense of playfulness in the poem.
Therefore we can conclude that the correct option is C.
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I need some help answering this question right here
The given expression can be as 2 + i as a complex number standard form.
Complex numbers:The combination of a number and an imaginary number is a complex number. Complex numbers are symbolized by the symbol z and have the form a + ib. a and b are said to be real numbers.
The imaginary portion of the complex number can be represented by the letter i called the iota.
Here i² = -1
Here we have
[tex]\frac{4 +\sqrt{16 - 4(5)}}{2}[/tex]
The above expression can be simplified as follows
=> [tex]\frac{4 +\sqrt{16 - 20}}{2}[/tex]
=> [tex]\frac{4 +\sqrt{- 4}}{2}[/tex]
As we know, [tex]i^{2} = -1[/tex]
=> [tex]\frac{4 +\sqrt{i^{2} (2)^{2} }}{2}[/tex]
=> [tex]\frac{4+2i}{2}[/tex]
=> [tex]\frac{2(2+i)}{2}[/tex]
= 2 + i
Therefore,
The given expression can be as 2 + i as a complex number standard form.
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If 7 more than twice a number is 5 less than three times the same number, what is the number?
Answer:
12
SolutionLet X be the unknown number we are supposed to find.
Given information from the question, we can form up an equation:
2X + 7 = 3X - 5
3X - 2X = 7 + 5
X = 12
Therefore the unknown number is 12
Sanjay is making two pumpkin pies for Thanksgiving, one to share with his family and one to share with his friends. He adds the same amount of cinnamon to both pies, but he adds more pumpkin puree to the pie he will share with his friends. Which pie will have a stronger cinnamon flavor?
Answer:
Step-by-step explanation:
Sanjay is making two pumpkin pies for Thanksgiving, one to share with his family and one to share with his friends. He adds the same amount of cinnamon to both pies, but he adds more pumpkin puree to the pie he will share with his friends. Which pie will have a stronger cinnamon flavor?
"The pie he will give to his parents"
More pumpkin flavor less cinnamon flavor
Understanding the meanings of words and phrases helps translate into algebraic expressions.
Example: 6 multiplied by the absolute value of 7 less than the cube of a number
6 · |n³ – 7|
? Question
What algebraic expression belongs with each verbal description?
the square root of the ____
of the ____ of a ____ and 11 → √x2² - 11 the ____ of __ times a number and -11 → -2x/11
the __ of the ____ ___ of two times a number and 11 → √2x + 11
Answer:
the square root of difference of the square of a number and 11the quotient of two times a number and -11the sum of the square root of two times a number and 11Step-by-step explanation:
