Bharat can type words in lengths of time as 100 words, 600 words, and 460 words in 5 minutes, 30 minutes, and 23 minutes respectively.
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.
* Multiplication operation: Multiplies values on either side of the operator
For example 12×2 = 24
Bharat types 20 words per minute which are given in the question.
To determine the number of words can he type in each length of time
We have to multiply the time by his typing speed.
The number of words that can be typed by Bharat in 5 minutes :
⇒ 20 × 5
⇒ 100
The number of words that can be typed by Bharat in 30 minutes :
⇒ 20 × 30
⇒ 600
The number of words that can be typed by Bharat in 23 minutes :
⇒ 20 × 23
⇒ 460
Therefore, He can type words in lengths of time as 100 words, 600 words, and 460 words in 5 minutes, 30 minutes, and 23 minutes respectively.
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Please help me with my calculus homework, only question 3****
I would start by stating the Fundamental Theorem of Calculus which states that;
If a function f is continuous on a closed interval [a,b] and F is an antiderivative of f on the interval [a,b], then
[tex]\int ^b_af(x)dx=F(b)-F(a)\text{ }[/tex]Let
[tex]\begin{gathered} f(x)=x^3-6x^{} \\ F(x)=\int f(x)dx=\int (x^3-6x)dx \end{gathered}[/tex]Recall that;
[tex]\int x^n=\frac{x^{n+1}}{n+1},n\ne-1[/tex]That implies that,
[tex]F(x)=\int (x^3-6x)dx=\int x^3dx-\int 6xdx=\frac{x^4}{4}-6(\frac{x^2}{2})=\frac{x^4}{4}-3x^2+C[/tex]Applying the Fundamental Theorem of Calculus, where a=0, b=3
[tex]\begin{gathered} \int ^3_0(x^3-6x)dx=F(3)-F(0) \\ F(3)=\frac{3^4}{4}-3(3)^2+C=\frac{81}{4}-27+C=-\frac{27}{4}+C \\ F(0)=\frac{0^4}{4}-3(0)^2+C=C \\ \Rightarrow\int ^3_0(x^3-6x)dx=-\frac{27}{4}+C-C=-\frac{27}{4} \end{gathered}[/tex]So the answer is -27/4
What is the slope of the line passing through (3, 0) and (4, 0) ?
A) 0
B) 3/4
C) 4/3
D) Undefined
[tex]m=\frac{y_{2}-y_{1} }{x_{2} -x_{1} } \\m=\frac{0-0}{4-1} \\m=\frac{0}{1} \\m=0[/tex]
⇒0 divided by any number is 0
OPTION A IS THE ANSWER.
Answer:
A
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (3, 0 ) and (x₂, y₂ ) = (4, 0 )
m = [tex]\frac{0-0}{4-3}[/tex] = [tex]\frac{0}{1}[/tex] = 0
Which of the expressions are equivalent to the one below? Check all that apply.
( 15 • 3) - 20
Answer:
I don't know your answer choices but...
Step-by-step explanation:
( 15 • 3) - 20 is equal to:
45-20
25
(5)(3)(3)-20
Find the length of the third side. If necessary, round to the nearest tenth.914
The given trinagle is a right angle triangle. let the missing side be x. To find x, we would apply the pythagorean theorem which is expressed as
hypotenuse^2 = one leg^2 + other leg^2
From the triangle,
hypotenuse = 14
one leg = 9
other leg = x
Thus, we have
[tex]\begin{gathered} 14^2=9^2+x^2 \\ 196=81+x^2 \\ x^2\text{ = 196 - 81 = 115} \\ x\text{ = }\sqrt[]{115} \\ x\text{ = 10.72} \end{gathered}[/tex]To the nearest tenth, the length of the third side is 10.7
A right triangle has an area of 54 ft2 and a hypotenuse of 25 ft long. What are the lengths of its other two sides?
By theorem we have the following:
[tex]h^2=a^2+b^2[/tex]And, we are given:
[tex]A=\frac{a\cdot b}{2}\Rightarrow2A=a\cdot b[/tex]Then:
[tex]\Rightarrow4A^2=a^2b^2\Rightarrow4A^2=a^2(h^2-a^2)[/tex][tex]\Rightarrow a^4-h^2a^2+4A^2=0[/tex]Now, we replace h and A:
[tex]a^4-(25)^2a^2+4(54)^2=0[/tex]And solve for a:
[tex]a^4-625a^2+11664=0[/tex]Then, the possible values for a are:
[tex]a=\begin{cases}a_1=-\frac{29}{2}-\frac{\sqrt[]{409}}{2} \\ a_2=\frac{29}{2}-\frac{\sqrt[]{409}}{2} \\ a_3=\frac{\sqrt[]{409}}{2}-\frac{29}{2} \\ a_4=\frac{29}{2}+\frac{\sqrt[]{409}}{2} \\ \end{cases}[/tex]We can see that a1, and a2 are not solutions, therefore a2 and a4 are.
So, the two possible b sides are then:
[tex]b_2=\sqrt[]{25^2-(\frac{29}{2}-\frac{\sqrt[]{409}}{2})^2}\Rightarrow b_2\approx24.99[/tex]and:
[tex]b_4=\sqrt[^{}]{25^2-(\frac{29}{2}+\frac{\sqrt[]{409}}{2})^2}\Rightarrow b_{4\approx}15.50[/tex]So, the lengths of the two sides can be:
a = 4.38 and b = 24.99
or
a = 24.61 and b = 15.50
mr. Morales mix for 4 4/5 pound of macaroni and cheese and brings it to the 5th grade party. the kids ate 3/4 of the total amount that mr. Morales brought. he took the rest home then gave 3/4 of a pound of the macaroni and cheese to Mr. kang the next day. how many pounds of macaroni and cheese is left over for mr. Morales to eat
Convert the Mixed number to an Improper fraction:
- Multiply the Whole number by the denominator.
- Add the product to the numerator.
- Use the same denominator.
Then:
[tex]4\frac{4}{5}=\frac{(4)(5)+4}{5}=\frac{20+4}{5}=\frac{24}{5}[/tex]Then, the total amount of macaroni and cheese Mr. Morales brought was:
[tex]\frac{24}{5}lb[/tex]After the kids ate macaronis and cheese, the amount he took home was:
[tex]\frac{24}{5}lb-(\frac{24}{5}lb)(\frac{3}{4})=\frac{6}{5}lb[/tex]After he gave some macaroni and cheese to Mr. Kang the next day, the amount of macaroni and cheese (in pounds) left for mr. Morales to eat, is the following:
[tex]\frac{6}{5}lb-(\frac{6}{5}lb)(\frac{3}{4})=\frac{3}{10}lb[/tex]The answer is:
[tex]\frac{3}{10}lb[/tex]Helppppp!!!! Please!!
n > 39/4 is value of quartic equation.
What does quartic equation mean?
A fourth-degree equation, often known as a quartic equation, is one that reduces a quartic polynomial to zero and has the formula: where a 0. A quartic function's derivative is a cubic function.
For a quadratic ax² + bx +c , the sign of its determinant, given by
Δ = b²- 4ac
"determines" the nature of its roots. In particular, if Δ<0 , then the quadratic has two distinct non-real roots.
Now, we have
3z² - 9z = n - 3
3z² - 9z - (n - 3) = 0
with determinant
Δ = (-9)² - 4 .3( n - 3 ) = 117 - 12n
Solve for such that Δ < 0
Δ = 117 - 12n < 0 ⇒ 12n > 117
n > 117/12
n > 39/4
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need help with this problem Its not the first one
Solution:
In geometry, a line segment is a part of a line that is bounded by two distinct endpoints and contains every point on the line that is between its endpoints. The angle of rotational symmetry or angle of rotation is the smallest angle for which the figure can be rotated to coincide with itself.
A rotation is a transformation in a plane that turns every point of a figure through a specified angle and direction about a fixed point. The fixed point is called the center of rotation
Rotation of a line does not change the length of the line segments
Reflection does not preserve orientation.
Dilation (scaling), rotation, and translation (shift) do preserve it.
Hence,
The final answer is the THIRD OPTION
These two equations look very similar at first. What is the difference in how you would solve them?
`\frac{x-2}{3}=5` `\frac{x}{3}-2=5`
The difference in how we would solve them is that there is a different order of steps.
We are given two equations.The two equations look similar, but there is a different order of steps in order to solve them.The first equation is :(x-2)/3 = 5Multiply both the sides by 3.x-2 = 15Add 2 on both sides.x = 17Hence, the solution of the first equation is x = 17.The second equation is :(x/3)-2 = 5Add 2 on both sides.x/3 = 7Multiply both the sides by 3.x = 21Hence, the solution of the second equation is x = 21.To learn more about equations, visit :
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2^3= 8 is equivalent to log, C = D.cand D
we have
2^3= 8
Applying log both sides
log(2^3)=log(8)
Apply property of log
3log(2)=log(8)
therefore
C=3 and D=log(8)
A true-false test contains 11 questions. In how many different ways can this test be completed. (Assume we don't care about our scores.)Your answer is :
Let's suppose that 1 = TRUE and 0 = FALSE, we want to find how many combinations we can do with 11 zeros and ones, in fact, it's:
[tex]\begin{gathered} \text{ 000 0000 0000} \\ \text{ 000 0000 0001} \\ \text{ 000 0000 0010} \\ \text{ 000 0000 0011} \\ ... \\ \text{ 111 1111 1111} \end{gathered}[/tex]To evaluate the number of combinations we can do:
[tex]C=2^{11}[/tex]2 because we can pick 2 different options (true or false) and 11 because it's the number of questions, then
[tex]\begin{gathered} C=2^{11} \\ \\ C=2048 \end{gathered}[/tex]We have 2048 different ways that this test can be completed.
I need help with problem 7.Use the figure to find the values of x, y, and z that makes triangle DEF similar to triangle GHF.
ANSWER
• x = 12
,• y = 16
,• z = 7
EXPLANATION
Because the triangles are similar, we have that:
• The ratio between corresponding sides is constant:
[tex]\frac{DE}{GH}=\frac{EF}{GF}=\frac{DF}{HF}[/tex]• Corresponding angles are congruent:
[tex]\begin{gathered} \angle D\cong\angle H \\ \angle E\cong\angle G \\ \angle F\cong\angle F \end{gathered}[/tex]We know that the measure of angle E is 16°, so the measure of angle G must be the same because they are congruent,
[tex]16\degree=2(x-4)\degree[/tex]With this equation, we can find x. First, divide both sides by 2,
[tex]\begin{gathered} \frac{16}{2}=\frac{2(x-4)}{2} \\ \\ 8=x-4 \end{gathered}[/tex]And then, add 4 to both sides,
[tex]\begin{gathered} 8+4=x-4+4 \\ \\ 12=x \end{gathered}[/tex]Hence, x = 12.
Now we know that the length of side EF is,
[tex]EF=x-5=12-5=7[/tex]To find y and z, we will use the proportions we got at the top of this explanation,
[tex]\frac{DE}{GH}=\frac{EF}{GF}=\frac{DF}{HF}[/tex]Replace with the known values and the expressions with y and z,
[tex]\frac{25}{6z+8}=\frac{7}{14}=\frac{24}{3y}[/tex]With the first two, we can find z,
[tex]\frac{25}{6z+8}=\frac{7}{14}[/tex]Simplify the right side,
[tex]\frac{25}{6z+8}=\frac{1}{2}[/tex]Rise both sides to the exponent -1 - i.e. flip both sides of the equation,
[tex]\frac{6z+8}{25}=2[/tex]Multiply both sides by 25,
[tex]\begin{gathered} 25\cdot\frac{(6z+8)}{25}=2\cdot25 \\ \\ 6z+8=50 \end{gathered}[/tex]Subtract 8 from both sides,
[tex]\begin{gathered} 6z+8-8=50-8 \\ 6z=42 \end{gathered}[/tex]And divide both sides by 6,
[tex]\begin{gathered} \frac{6z}{6}=\frac{42}{6} \\ \\ z=7 \end{gathered}[/tex]Hence, z = 7.
Finally, with the last two proportions, we can find y,
[tex]\frac{7}{14}=\frac{24}{3y}[/tex]The first two steps are the same we did to find z: simplify the left side and flip both sides,
[tex]2=\frac{3y}{24}[/tex]Multiply both sides by 24,
[tex]\begin{gathered} 24\cdot2=24\cdot\frac{3y}{24} \\ \\ 48=3y \end{gathered}[/tex]And divide both sides by 3,
[tex]\begin{gathered} \frac{48}{3}=\frac{3y}{3} \\ \\ 16=y \end{gathered}[/tex]Hence, y = 16.
13. Write an equation of the line that passes through the points (-7, 6) and (3, -4 )in slope-
intercept form.
Answer:
Firstly we need to find the gradient of give two points as follows;
M= y
Answer:
Answer: y = -x - 1
Step-by-step explanation:
- Consider a straight line passing through (x, y) from the origin (0, 0). That line with a positive gradient of m and meets at a point (0, c) [y-intercept]
- It has a general equation as below;
[tex]{ \rm{y = mx + c}} \\ [/tex]
- So, consider the line given in our question; Let's find its slope m first;
[tex]{ \rm{slope = \frac{y _{2} - y _{1} }{x _{2} - x _{1} } }} \\ [/tex]
- From the points given in the question, (-7, 6) and (3, -4)
x_1 is -7x_2 is 3y_1 is 6y_2 is -4[tex]{ \rm{m = \frac{ - 4 - 6}{3 - ( - 7)} }} \\ \\ { \rm{m = \frac{ - 10}{10} }} \\ \\ { \underline{ \rm{ \: m = - 1 \: }}}[/tex]
- Therefore, our equation so far is y = -x + c. Our line has a negative slope that means it slants from top to bottom, its origin is its y-intercept
- Consider point (3, -4);
[tex]{ \rm{y = - x + c}} \\ { \rm{ - 4 = - 3 + c}} \\ { \rm{c = - 1}}[/tex]
- y-intercept is -1
hence equation is y = -x - 1
[tex]{ \boxed{ \delta}}{ \underline{ \mathfrak{ \: \: beicker}}}[/tex]
Sydney purchased a $50.00 gift for a baby shower. She uses a coupon that offers 20% off. How much will Sidney spend on the gift after the coupon?
From the scenario, the following are the pieces of information being given:
Price of Gift = $50
Discount Coupon used = 20% Off
Let's compute how much will Sidney spend on the gift after the coupon.
Step 1: Let's determine the equivalent amount of the discount.
[tex]\text{ Amount to be Discounted = Price of Gift x }\frac{Percentage\text{ of Discount}}{100}[/tex][tex]\text{ = \$50 x }\frac{20}{100}\text{ = \$50 x 0.20}[/tex][tex]\text{ = \$10}[/tex]Step 2: Let's deduct the equivalent amount of 20% to the actual price of the gift.
[tex]\text{ = \$50 - \$10}[/tex][tex]\text{ = \$40}[/tex]Therefore, Sydney will spend $40 on the gift after the coupon.
The manager of a new restaurant plans on ordering place-mats for the maximum number of diners, which is 279. Suppose the place-mats come in boxes of 24. Write a division expression that could be used to determine the number of boxes he needs to order.\
The number of boxes he needs to place = 279÷ 24 = 11.625 ≈ 12.
What is meant by division ?Multiplication is the opposite of division. If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group.
Creating equal groups or determining how many people are in each group after a fair distribution is the basic objective of division.
In the aforementioned scenario, you would need to place four donuts in each group in order to divide 12 donuts into three similar groups. Thus, 12 divided by 3 will result in the number 4.
Dividend: Divisor x Quotient + Remainder
Given : Number of diners = 279
And the number of boxes = 24
Thus to find out the number of boxes he needs to place = 279÷ 24 = 11.625 ≈ 12.
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It took 12 men 5 hours to build an airstrip. Working at the same rate, how many additional men could have been hired in order for the job to have taken 1 hour less?
A) Two
B) Three
C) Four
D) Six
Answer:
B
Step-by-step explanation:
hello the question is if it took 12 men 5 hours to build an age is working at the same rate how many additional men could have been hired in order for the job to have taken 1 hour less ok so we have to find that how many extra may be required to complete the job for a strip 1 hour less than five hours that is 4 hours ok bye have to complete the airstrip in 4 hours and they have to find that how many experiment we have to required for that we will assume that let extra number of number of extra man bhi X show the number of men when we are finishing in it in 4 hours would be 12 + X ok
would be the number of men now and time required would be equal to 1 hour less than 5 hours that is 4 hours ok no from the given data we can say that one cares if strip x 12 men and fibres ok so all vacancy job correct so vacancy job per man are would be 1 divided by 12 in 25 this is the job or the amount of a strip that is completed when
one man works for one hour ok so this is the amount of the job that is done for men power and we have we have this number of men that are not want working and the number of hours that their working for so for one job we will need for one job would be best job per man per hour into number of men into number of hour ok and we have 1 equal to number of Doberman per Rs 1 by 2 11 25 and number of men we have already know that 12 + 6 is the number of men that we will require 12 + X number
forces were less than 5 that is 44 4312 so it would give us 12 + X / 3515 1 to 15 of this site it would give us 12 + X equal to 15 which implies X is equals to 15 - 12 and X is equals to 3 significant required 3 more men to complete the job in Porus dancer is 3 which is given is be in the question make you
Which number line shows all the values of x that make the inequality - 3x +1 <7 true?A2-5-4--3-2-10123B.5in-4-3-2-1012.34С5-5-4-3-2-1012345D-4-3-2.12345
First let's solve the given inequality:-
[tex]\begin{gathered} -3x+1<7 \\ -3x<6 \\ x>-2 \end{gathered}[/tex]So the correct option is (D).
A certain television is advertised as a 5-inch TV. If the width of the TV is 4 inches, how many inches tall is the TV
Answer:
The TV is 3 inches tall.
[tex]3\text{ inches}[/tex]Explanation:
Given that the width of the TV is
[tex]4\text{ inches}[/tex]And the TV is 5 inch TV, which means its diagonal is;
[tex]d=5\text{ inches}[/tex]The height of the TV can be calculated using the Pythagoras Theorem;
[tex]\begin{gathered} c^2=a^2+b^2 \\ b=\sqrt[]{c^2-a^2} \end{gathered}[/tex]substituting the diagonal and the width;
[tex]\begin{gathered} b=\sqrt[]{5^2-4^2} \\ b=\sqrt[]{25-16} \\ b=\sqrt[]{9} \\ b=3\text{ inches} \end{gathered}[/tex]Therefore, the TV is 3 inches tall.
[tex]3\text{ inches}[/tex]Simplify the expression by first transforming the radical to exponential form. Leave the answer in exact form as a radical or a power, not as a decimal approximation.
Answer:
[tex]\textsf{Radical form}: \quad \sqrt[4]{2}\\\\\textsf{Exponent form}: \quad 2^{\frac{1}{4}}[/tex]
Step-by-step explanation:
Given expression:
[tex]\sqrt{8} \div \sqrt[4]{32}[/tex]
[tex]\textsf{Apply the exponent rule} \quad \sqrt[n]{a}=a^{\frac{1}{n}}:[/tex]
[tex]\implies 8^{\frac{1}{2}} \div 32^{\frac{1}{4}}[/tex]
Rewrite 8 as 2³ and 32 as 2⁵:
[tex]\implies (2^3)^{\frac{1}{2}} \div (2^5)^{\frac{1}{4}}[/tex]
[tex]\textsf{Apply the exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies 2^{\frac{3}{2}} \div 2^{\frac{5}{4}}[/tex]
[tex]\textsf{Apply the exponent rule} \quad a^b \div a^c=a^{b-c}:[/tex]
[tex]\implies 2^{\frac{3}{2}-\frac{5}{4}}[/tex]
[tex]\implies 2^{\frac{6}{4}-\frac{5}{4}}[/tex]
[tex]\implies 2^{\frac{1}{4}}[/tex]
[tex]\textsf{Apply the exponent rule} \quad \sqrt[n]{a}=a^{\frac{1}{n}}:[/tex]
[tex]\implies \sqrt[4]{2}[/tex]
What is the end behavior of the polynomial function?
Drag the choices into the boxes to correctly describe the end behavior of the function.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
f(x)=6x9−6x4−6 f(x)=−3x4−6x+4x−5
The end behavior of each function is given as follows:
f(x) = 6x^9 - 6x^4 - 4, as x -> -∞, f(x) -> -∞ and as x -> ∞, f(x) -> ∞.f(x) = -3x^4 - 6x + 4x - 5, as x -> -∞, f(x) -> -∞ and as x -> ∞, f(x) -> -∞.End behavior of a functionThe end behavior of a function is given by the limits of the function as x goes to infinity, both negative and positive infinity, giving how the function behaves to the left and to the right of the graph.
For a polynomial function, only the term with the highest exponent is considered for the calculation of the limit, which is a standard rule for limits when x goes to infinity.
The first function is given by:
f(x) = 6x^9 - 6x^4 - 4.
Then the limits that define the end behavior of the function are given as follows:
lim x -> -∞ x^9 = (-∞)^9 = -∞.lim x -> ∞ x^9 = (∞)^9 = ∞.The second function is given by:
f(x) = -3x^4 - 6x + 4x - 5.
Then the limits that define the end behavior of the function are given as follows:
lim x -> -∞ -x^4 = -(-∞)^4 = -∞.lim x -> ∞ -x^4 = -(∞)^4 = -∞.A similar problem, also about the end behavior of a function, is presented at https://brainly.com/question/28884735
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Which answer choice shows two hundred and two thousandths?A) 200.02B) 200.202C) 202.02D) 202.002
Given
two hundred two and two thousandths.
Answer
202.002
Option D is correct
Using the distance formula, d = √(x2 - x1)2 + (y2 - y1)2, what is the distance between point (0, 5) and point (3, -1) rounded to the nearest tenth?
The distance between the points is 6.7 units
What is distance?The distance between two points is the number of points between them
How to determine the distance?The points are given as
(0, 5) and (3, -1)
The distance formula is given as
d = √(x2 - x1)^2 + (y2 - y1)^2
Substitute the given points in the above distance formula
So, we have
d = √(0 - 3)^2 + (5 + 1)^2
Evaluate the difference and the sum
d = √(-3)^2 + 6^2
Evaluate the exponents
d = √9 + 36
Evaluate the sum
d = √45
This gives
d = 6.7
Hence, the distance is 6.7 units
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Write a two-column proof.
4. Given: AB EF
AC DF
Prove: ABC ~ FED
Please help
Explanation:
The following is a proof that ∆ABC ~ ∆FED.
Statement . . . . Reason1. AB║EF, AC║FD . . . . given
2. ∠BCA ≅ ∠EDF . . . . alternate exterior angles theorem
3. ∠ABC ≅ ∠FED . . . . alternate interior angles theorem
4. ∆ABC ~ ∆FED . . . . AA similarity postulate
8/11 when rounded is closer to 1 than 0? True False
Answer: False?
Step-by-step explanation:
Answer:
It is closer to [tex]1[/tex] than [tex]0[/tex], so the statement is True.
Step-by-step explanation:
Step 1: Finding the decimal form of [tex]\frac{8}{11}[/tex]
Upon simplification on a calculator, we can see that the exact value of [tex]\frac{8}{11}[/tex] is:
[tex]0.7272727273[/tex]
Let's round this to [tex]0.73[/tex] for an easier time.
Step 2: Identifying the value's difference from 1 and 0
We have found the value of the fraction to be [tex]0.73[/tex].
If we subtract the value from [tex]1[/tex], we get:
[tex]1-0.73\\=0.27[/tex]
If we find the difference between it and [tex]0[/tex], we get:
[tex]0.73-0\\=0.73[/tex]
As we can see, the value is [tex]0.27[/tex] units away from [tex]1[/tex], but is [tex]0.73[/tex] units away from [tex]0[/tex].
We can clearly see that it is closer to [tex]1[/tex], so the statement is True.
which variable has a set of zero pairs as a coefficients? (x or y)2x + 3y=20-2x + y=4
Answer:
The variable that has a set of zero pairs as a coefficients is;
[tex]x[/tex]Explanation:
We want to find the variable that has a set of zero pairs as a coefficients.
Zero pair is a pair of number that sum up to give zero.
Given the system of equation;
[tex]\begin{gathered} 2x+3y=20 \\ -2x+y=4 \end{gathered}[/tex]The pair of coefficient of x is;
[tex]\begin{gathered} 2\text{ and -2} \\ 2+-2=2-2=0 \end{gathered}[/tex]The pair of coefficient of y is;
[tex]\begin{gathered} 3\text{ and 1} \\ 3+1=4 \end{gathered}[/tex]So, since the coefficient of x sum up to give zero.
The variable that has a set of zero pairs as a coefficients is;
[tex]x[/tex]write a point slope equation for the line that has a slope 5and passes the point (6,22).
Solution:
The general equation of a line of slope m passing through a point A is expressed as
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \text{where} \\ (x_1,y_1)\text{ is the coordinate of the point A through which the line passes through} \end{gathered}[/tex]Given that the line has a slope of 5, and passes through the (6, 22), we have
[tex]\begin{gathered} m=5 \\ x_1=6 \\ y_1=22 \end{gathered}[/tex]thus,
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \Rightarrow y-22=5(x-6) \end{gathered}[/tex]Hence, the point-slope equation for the line is expressed as
[tex]y-22=5(x-6)[/tex]
Given z1 = 5(cos 240° + isin 240°) and z2 = 15(cos 135° + isin 135°), what is the product of z1 and z2?
By multiplying z1 and z2, we get:
[tex]\begin{gathered} z1\times z2=5(cos240+isin240)15(cos135+isin135) \\ z1\times z2=75(cos240+isin240)(cos135+isin135) \end{gathered}[/tex]Applying the distributive property:
[tex]\begin{gathered} z1\times z2=75(cos240+\imaginaryI s\imaginaryI n240)(cos135+\imaginaryI s\imaginaryI n135) \\ z1\times z2=75(cos240\times cos135+cos240\times isin135+\mathrm{i}s\mathrm{i}n240\times cos135+\imaginaryI s\imaginaryI n240\times\imaginaryI s\imaginaryI n135) \\ z\times1z\times2=75(cos240\times cos135+cos240\times\imaginaryI s\imaginaryI n135+\imaginaryI s\imaginaryI n240\times cos135-s\imaginaryI n240\times s\imaginaryI n135) \end{gathered}[/tex]In order to simplify this, we can use the following trigonometric identities:
[tex]\begin{gathered} sin(\alpha+\beta)=sin(\alpha)cos(\beta)+cos(\alpha)sin(\beta) \\ cos(\alpha+\beta)=cos(\alpha)cos(\beta)-sin(\alpha)sin(\beta) \end{gathered}[/tex]By taking β as 135 and α as 240, we can write:
[tex]\begin{gathered} is\imaginaryI n(240+135)=isin(375)=is\imaginaryI n(240)s\imaginaryI n(135)+icos(240)s\imaginaryI n(135) \\ cos(240+135)=cos(375)=cos(240)cos(135)-s\imaginaryI n(240)s\imaginaryI n(135) \end{gathered}[/tex]Then, by grouping some terms of the expression, we get:
[tex]z\times1z\times2=75(cos(375)+isin(375))[/tex]375° is equivalent to 15° (375 - 360 = 15), then the product of z1 and z2 can be finally written as:
[tex]z1\times z2=75(cos(15)+\imaginaryI s\imaginaryI n(15))[/tex]Then, option A is the correct answer
4^5 x 4^3 x 4^2 x 4^3 / 4^2 x 4 x 4^2 simplify help
The simplification form of the given mathematical equation 4^5 x 4^3 x 4^2 x 4^3 / 4^2 x 4 x 4^2 is [tex]4^{8}[/tex]
In the given question, it is given
We know the simplification property of the division of numbers as,
Division in exponential form
[tex]\frac{a^{x} }{a^{y} }[/tex] = [tex]a^{x-y}[/tex] , and
Multiplication in exponential form
[tex]a^{x} . a^{y}[/tex] = [tex]a^{x+y}[/tex]
Similarly, we'll apply the same property to solve this question,
[tex]4^{5+3+2+3 + ( -2 -1 -2)}[/tex]
[tex]4^{5+3+2+3 - ( 2 + 1 + 2)}[/tex]
[tex]4^{13 - 5}[/tex]
[tex]4^{8}[/tex]
Hence, the simplification form of the given mathematical equation 4^5 x 4^3 x 4^2 x 4^3 / 4^2 x 4 x 4^2 is [tex]4^{8}[/tex]
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PLEASE HELP !!
When a right triangle with a hypotenuse of 1 is placed in the unit circle, which sides of the triangle correspond to the x- and y-coordinates?
The adjacent side of the central angle is the x-coordinate and the opposite side of the central angle is the y-coordinate
A pair of numbers that use the horizontal and vertical separations from the two reference axes to define a point's location on a coordinate plane. typically expressed by the x-value and y-value pair (x,y).
The hypotenuse is the radius of a unit circle whose origin serves as its center. Allow being the central angle.
x = Adjacent Side of the central angle
y = Opposite Side of the Central angle
The x-coordinate is the central angle's adjacent side, while the y-coordinate is its opposite side.
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1. m/ASN = 63°
m/GSN =
The measure of angle ∠GSN is 27°.
What do we mean by angles?An angle is a figure in plane geometry that is created by two rays or lines that have a common endpoint. The Latin word "angulus," which means "corner," is the source of the English word "angle." The common endpoint of two rays is known as the vertex, and the two rays are referred to as the sides of an angle.So, a measure of ∠GSN:
The given angle ASG is 90° (Given)∠ASN = 63°Then, ∠GSN will be:
∠ASN + ∠GSN = ∠ASG63 + ∠GSN = 90∠GSN = 90 - 63∠GSN = 27°Therefore, the measure of angle ∠GSN is 27°.
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