The following are three equivalent expressions for the submarine's final position:
-(5)(3) - (2)(4), -(5)(3) + (-2)(4) and -(5)(3) + (2)(-4)
What is defined as the equivalent expressions?Equivalent expressions have been expressions that perform the same function despite their appearance. If 2 algebraic expressions have become equivalent, they have the same value when the same value(s) for variable are used (s).Equivalent Expressions Examples:3(x + 2) and 3x + 6 have been equivalent expressions since their values remain constant for any value of x.Based on the question,
Each float advances by 5 units.Each group takes a two-unit step.As a result, the submarine's final position is:
Final = -(5)(3) - (2)(4)
The minus "-" symbol indicates that the submarine is sinking.
Thus, the following are equivalent expressions for the submarine's final position:
-(5)(3) - (2)(4), -(5)(3) + (-2)(4) and -(5)(3) + (2)(-4)
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What is the measure of the central angle that defines the shaded area below if the shaded area takes up 70% of the circle?
a sum of scalar multiples of two vectors (such as ab, where a and b are scalars) is called a linear combination of the vectors. let u, and v,. express , as a linear combination of u and v
The linear combination of u and v = <3,-27>=5U+4V.
What does linear combination in vectors mean?A linear combination of two or more vectors is the vector formed by multiplying two or more vectors (with distinct directions) by scalar values. The above equation demonstrates that the vector is produced by adding two vectors to three vectors.
What is the term "linear combination"?The term "linear" has two independent meanings: geometric and algebraic. Because linear combinations essentially linear in the both senses, the expression is accurate.
According to the given information:Let u= <3,3> and v= <-3,3>
<3,-27> = x< 3,3> + y<-3,3> = <3x - 3y, 3x + 3y>
3x - 3y = 3 => x - y = 1
3x + 3y = -27 => x + y = -9
Adding both, we get
2x = -8 => x = -4
y = -5
So <3,-27> = -4< 3, 3 > + (-5) < -3 , 3 >
The linear combination of u and v = <3,-27>=5U+4V.
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I understand that the question you are looking for is:
A sum of scalar multiples of two vectors (such as au + bv, where a and b are scalars) is called a linear combination of the vectors.
Let u= <3,3> and v= <-3,3>. Express <3,-27> as a linear combination of u and v.
Pls help me im stuck
Find the output (y) of the function y
20x + 38 if the input (2) is -9.
A function assigns the values. The output(y) of the function y=20x + 38 if the input is -9 is -142.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Given the function y=20x+38, therefore, if the input of the function is -9, then the output can be calculated by substituting the value of x as -9. Therefore, we can write the function as,
y = 20x + 38
y = 20(-9) + 38
y = -180 + 38
y = -142
Hence, the output(y) of the function y=20x + 38 if the input is -9 is -142.
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An urn contains 19 red marbles, 29 blue marbles, and 43 yellow marbles. one marble is to be chosen from the urn without looking. what is the probability of choosing a red marble?
The probability of choosing a red marble is 1/6.
What is probability ?Probability is the chance of occurring a certain event out of total possible events that can order in a given situation.
According to the given question an urn contains 19 red marbles, 29 blue marbles, and 43 yellow marbles.
So there are total of ( 19 + 29 + 43 ) = 85 marbles.
∴ No. of sample space N(s) = 85.
No. of red marble N(red) = 19.
One marble is to be chosen from the urn without looking the probability of choosing a red marble P(red) is N(red)/N(s) which is
P(red) = 19/85
P(red) = 1/5.
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Sal is selling two types of printed socks.he sells type a at r45 a pair.he sells type b at r30 if he sold 16 pairs in total,and had a total income of r585,how many pairs of sock did sal sell
Sal sold 7 pairs of type a socks and 9 pairs of type b socks
Let the number of type a socks sold by Sal be x
Let the number of type b socks sold by Sal be y
The selling price of type a socks = 45
The selling price of type b socks = 30
Total pairs sold = 16
Total income = 585
Therefore, the equations will be
x + y = 16-------(1)
45x + 30y = 585--------(2)
Multiplying equation (1) by 30 we get
30x + 30y = 480 ------(3)
Equating equations (2) and (3) we get,
15x = 105
x = 7
Putting x = 7 in (1) we get
y = 9
Sal sold 7 pairs of type a socks and 9 pairs of type b socks
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Look at the diagram and evaluate. Which of the statements below is TRUE?
A). EH < EF
B). F is the midpoint of EG
C). GH< EF
D). FH> EG
The correct statement regarding the segments on the number line is:
C). GH< EF
Why the third statement is correct?For the first statement, the lengths are EH = 19 - 6 = 13 and EF = 11 - 6 = 5, hence EF < EH.For the second statement, we have that EF = 5 and EG = 9, since 5 is not the half of 9, it is not the midpoint.For the third statement, GH = 19 - 15 = 4 < EF = 5, hence it is the correct statement.For the fourth statement, EG = 9 > FH = 8, hence it is also not correct.More can be learned about segments at https://brainly.com/question/18315903
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What is the answer to 1/4 times 2/3 times 4/3 equal?
Answer:
2/9
Step-by-step explanation:
To multiply fractions you just multiply the numerators with the numerators and the denominators with the denominators
1/4 * 2/3 = 2/12 which simplifies to 1/6
1/6 * 4/3 = 4/18 which simplifies to 2/9
:D
simplify fully
x^5-4x^3/ 3x-6
PLS HELP IM SO CONFUSED
The student says that the proof shows that AOM BOM because they are vertical angles.
Which statement best corrects the student's interpretation?
A. CON = BOM because they are vertical angles.
B. AOM = BOM because they are supplementary, not because they are vertical angles.
C. AOM = BOM because they are complementary, not because they are vertical angles.
D. AOM = BOM because they are both congruent to the same angle, not because they are vertical angles.
∠AOM ≅ ∠BOM because they are both congruent to the same angle, not because they are vertical angles.
How to Identify Congruent Angles?
From the image of the angles attached, we are given that;
∠AOM ≅ ∠DON
Now, from the vertical angle theorem, we can say that;
∠AOM ≅ ∠CON
Similarly, by vertical angles theorem, we can also say that;
∠BOM ≅ ∠DON
From transitive property of congruence, we can equally say that since ∠AOM and ∠BOM are equal to the same angle, then;
∠AOM ≅ ∠BOM
From transitive property of congruence, we can equally say that since ∠CON and ∠BOM are equal to the same angle, then;
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Answer: ∠AOM≅ ∠BOM because they are both congruent to the same angle, not because they are vertical angles.
Step-by-step explanation:
cause I did the mastery test
5. Using the data from question 2, you can compute the mean food and lodging
cost of a 10-day vacation by multiplying the per-day mean by 10. The
standard deviation for the 10-day vacation can be found by multiplying by
10 also.
a. What is the mean for food and lodging for a 10-day vacation?
Multiplying the underlying mean of $247 for a single day by 10 to account for the 10 days, the mean for food and lodging for a 10-day vacation is of $2470.
What is the mean per day cost?This problem is incomplete, but researching it on a search engine, it is found that the mean for a single day was of $247.
What is the mean for the entire trip?The entire trip was of 10 days, hence the mean is given as follows, multiplying the mean by the constant:
247 x 10 = $2,470.
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(-2+1)exponent2+5(12/3)-9=
Question :
(-2+1)exponent2+5(12/3)-9=
Answer:
The answer is : 12 po
Rewrite the polynomial in descending order. Identify the degree of the polynomial, the leading term, and the leading coefficient.
12 - 6b^6 + 4b - 3b^4
Answer:
Solution
12-6b6+4b-3b4, find Polynomial in descending order
Solution:
The Given Polynomial =12-6b6+4b-3b4
Descending order is basically when its terms are arranged in order from largest degree to smallest degree
Descending order of polynomial =-6x6-3x4+4x+12
Step-by-step explanation:
A recent report stated that less than 35 percent of adult residents in a certain city will be able to pass a physical fitness test. Consequently, the city's Recreation Department is trying to convince the City Council to fund more physical fitness programs. The council is facing budget constraints and is skeptical of the report. The council will fund more physical fitness programs only if the Recreation Department can provide convincing evidence that the report is true. The Recreation Department plans to collect data from a sample of 185 adult residents in the city. A test of significance will be conducted at a significance level of a= 0.05 for the following hypotheses.
H0:p=0.35
Ha:p<0.35
where p is the proportion of adult residents in the city who are able to pass the physical fitness test.
The Recreation Department recruits 185 residents who volunteer to take the physical fitness test. The test is passed by 77 of the 185 volunteers, indicating that more than 35 percent of the city is in shape. Describe the primary flaw in the study described in part and explain why it is a concern.
The primary flaw is that the sample will slightly overestimate the physical fitness of the people of the town.
The given hypothesis are,
[tex]H_0:p=0.35\\H_1:p < 0.35[/tex]
Type II error is accepted in null hypothesis when it is not actually true.
In the given question null hypothesis p= 0.35
The conclusion is that in the given sample proportion is not equal to 0.35, though we know that proportion is not equal to 0.35 we accept the null hypothesis, that is wrong.
Now given n=185,x=77 P=0.53 then Q=1-0.35=0.65
[tex]H_0:P=0.35\\H_1:P < 0.35[/tex]
Now test statistic [tex]Z=\frac{p-P}{\sqrt{\frac{PQ}{n}}}[/tex]
Solving for Z using the given values we get :
Z=1.99
Now 1.99>-1.65
So we accept [tex]H_0[/tex]
The primary flaw in the system is that the sample is not randomly selected rather they are volunteers. So it is reasonable to think that the physical fitness of the town will be slightly over estimated by the experiment.
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7 • 12 = 12 • 7 is an example of the ____ property of multiplication.
O commutative
O associative
O distributive
O multiplicative identity
Answer:
A, commutative
Step-by-step explanation:
Commutative property of Multiplication is when you can switch around the numbers when multiplying.
find x: -3 = 4x - 12x^2 + 7x^3
Answer:
x = 0.3384663
Step-by-step explanation:
Find the average rate of change for the function f(x)=3^x+17
Using the intervals x=3 to x=6
Answer:
234
Step-by-step explanation:
the average rate of change of f(x) in the closed interval [ a, b ] is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
here [ a, b ] = [3, 6 ] , then
f(b) = f(6) = [tex]3^{6}[/tex] + 17 = 729 + 17 = 746
f(a) = f(3) = 3³ + 17 = 27 + 17 = 44 , then
average rate of change = [tex]\frac{746-44}{6-3}[/tex] = [tex]\frac{702}{3}[/tex] = 234
Add. 5/7 + 1/2 + 3/4
please help
Answer: 1²⁷/₂₈
Step-by-step explanation:
[tex]\displaystyle\\\frac{5}{7}+\frac{1}{2}+\frac{3}{4} =\\\\\frac{5*4+1*14+3*7}{28} =\\\\\frac{20+14+21}{28} =\\\\\frac{55}{28} =\\\\1\frac{27}{28}[/tex]
4 (c) The high mountains of the world
. The expression 3x+1 is equal to 9 for a certain value of x. Which of the following is the value of the
expression 12x+4 for the same value of x?
(1) 18
(3) 36
(2) 28
(4) 112
Answer:
(3) 36
Step-by-step explanation:
3x + 1 = 9
Minus 1 from both sides.
3x = 8
Divide both sides by 3.
x = 2 2/3
Plug it in.
12 (2 2/3) + 4
32 + 4
36
Find a vector function r(t), that represents the curve of intersection of the two surfaces. the cylinder x2 y2=36 and the surface z=4xy
Given:
[tex]\begin{aligned}&x^2+y^2=16 \\&z=x y\end{aligned}[/tex]
Express 16 as [tex]4^{2}[/tex]: [tex]x^2+y^2=16[/tex]
[tex]x^2+y^2=4^2\\x^2+y^2=4^2 \times 1[/tex]
Trignometry,
[tex]\cos ^2(t)+\sin ^2(t)=1[/tex]
Now, substitute [tex]\cos ^2(t)+\sin ^2(t)[/tex] for 1:
[tex]\begin{aligned}&x^2+y^2=4^2 \times 1 \\&x^2+y^2=4^2 \times\left[\cos ^2(t)+\sin ^2(t)\right]\end{aligned}\\x^2+y^2=4^2 \times \cos ^2(t)+4^2 \times \sin ^2(t)[/tex]
Law of indicates:
[tex]\begin{aligned}&x^2+y^2=[4 \times \cos (t)]^2+[4 \times \sin (t)]^2 \\&x^2+y^2=[4 \cos (t)]^2+[4 \sin (t)]^2\end{aligned}\\x^2=[4 \cos (t)]^2 \text { and } y^2=[4 \sin (t)]^2[/tex]
Taking positive square roots as follows:
[tex]x=4 \cos (t), y=4 \sin (t)[/tex]
Recall that, z = xy.
Now, we have:
[tex]\begin{aligned}&z=4 \cos (t) \times 4 \sin (t) \\&z=16 \cos (t) \cdot \sin (t)\end{aligned}[/tex]
Now, substitute the values:
[tex]r(t)=x_t i+y_t j+z_t k[/tex]
So, the vector r(t) is: [tex]r(t)=(4 \cos (t)) i+(4 \sin (t)) i+(16 \cos (t) \cdot \sin (t)) i[/tex]
Therefore, the vector function r(t) is written as: [tex]r(t)=x_t i+y_t j+z_t k[/tex]
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1. Draw the graph of y = 3 – x/2 using a table of points from x = -3 to 3.
Answer:
Step-by-step explanation:
x = -3 to 3
means that they are asking for the graph from -3 to 3 on the x-axis
gradient is (-1/2) which means rise is -1 when run is 2
y-intercept is 3.
go to 3 on the y axis which means the coordinate (0,3) go downwards by 1 and to the right by 2. This will lead you to coordinate (2,-1). Now connect both points by a straight line.
Find the unit vectors that are parallel to the tangent line to the curve y = 2 sin(x) at the point 6 , 1 .
[1/2, sqrt(3)/2] and [-1/2, -sqrt(3)/2] are the unit vectors that are parallel to the tangent line to the curve.
Explain what a unit vector is?
A quantity with both magnitude and direction is referred to as a vector. A unit vector is one with a magnitude of 1. It also goes by the name Direction Vector.y=2sin(x)
dy/dx equals 2 cos x at pi/6 for x.
pi/6 = 2 cos pi/6 = 2 sqrt(3)/2 = sqrt = dy/dx(pi/6) (3)
the line sqrt(3) (x-pi/6) is the tangent to y at pi/6.
Atan Theta = sqrt is the angle with the x axis (3)
θ = pi/3 radians at 60 degrees
the vectors of units at (pi/6,1) [cos(60), sin(60)] and [-cos(60), -sin(60)] are parallel to this line.
[1/2, sqrt(3)/2] as well as [-1/2, -sqrt(3)/2]
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Is the following relation a function? Justify your answer.
Yes, because each output value has only one input value
Yes because each input value has only one output value
No, because there is an input value with more than one output value
No, because there is an output value with more than one input value
Answer:
No, because there is an output value with more than one input value.
Step-by-step explanation:
If you are using the same function equation, than you should not get the same output if you use two different inputs.
Question
Find the equation of the line with slope
1/4
and y-intercept (0, -2).
Answer:
y=1/4 -2
Step-by-step explanation:
y =mx + c
m= slope
c= y-intercept
putting the valves of x and y ( 0,-2)
-2 = 1/4(0) + c
solve for C
C = -2
substituting back to the general equation of
y= 1/4x + C
y = 1/4x - 2( ans).
The cost per unit of an item is called what?
Answer:
The cost per unit of an item is called unit cost
Evaluate the expression shown below and write your answer as a fraction in
simplest form.
17/23+3/23=
Answer:
17/23+3/23 = 10/23 =2.3
Step-by-step explanation:
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I have something on my page, please can you help me?
thankyou
_____ is the process of drawing conclusions about unknown characteristics of a population from which data were taken.
Answer:
Statistical inference
Step-by-step explanation:
a group of students is given a 10 by 10 grid to cut into individual unit squares. the challenge is to create two squares using all of the unit squares. their teacher states that after the two new squares are formed, one should have a side length two units greater than the other. which equation represents x, the side length of the greater square? x2 (x – 2)2
The correct option is C. x² + (x – 2)² = 100.
The equation which depicts x, the side length of the greater square is x² + (x – 2)² = 100.
What is square?In geometry, a square is a plane figure with 4 equal sides as well as 4 right (90°) angles. A square is a subset of a rectangle (an equilateral rectangle) and a subset of a parallelogram (an equilateral & equiangular one).
Now, as per the question;
Let x be the larger square's side length. Because it is two units larger than the relatively small square, the smaller square's side length would be (x-2).The side length squared, or the quantity of unit squares contained in the larger square, would give the quantity of unit squares within the larger square or x².The side length squared, or the number of unit squares in the smaller square, would give the number of unit squares within the smaller square or (x-2)².These total the quantity of unit squares in a 10 by 10 square, or 10² = 100.This is given by relation shown by expression;
x² + (x-2)² = 100
Therefore, the equation which represents x, the side length of the greater square is x² + (x-2)² = 100.
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The complete question is-
A group of students is given a 10 by 10 grid to cut into individual unit squares. The challenge is to create two squares using all of the unit squares. Their teacher states that after the two new squares are formed, one should have a side length two units greater than the other.
Which equation represents x, the side length of the greater square?
A. x² + (x – 2)² = 10
B. x² + 2x² = 10
C. x² + (x – 2)² = 100
D. x² + 2x² = 100
One more than the product of 14 and Mabel's age
Use the variable m to represent Mabel's age.
Answer: 14m + 1
Step-by-step explanation:
We will write an expression for this question.
One more➜ + 1
than the product of ➜ multiplication, *
Mabel's age ➜ m
One more than the product of 14 and Mabel's age
14 * m + 1, 14m + 1
