ANSWER
[tex]x = \sqrt{5} [/tex] units
EXPLANATION
Let the other leg be x units.
According to the Pythagoras Theorem, the sum of the squares of the two shorter legs should add up to the square of the hypotenuse.
This implies that,
[tex] {x}^{2} + {2}^{2} = {3}^{2} [/tex]
[tex]{x}^{2} + 4=9[/tex]
Group the constant terms,
[tex]{x}^{2}=9 - 4[/tex]
[tex]{x}^{2}=5[/tex]
Take square root.
[tex]x = \sqrt{5} [/tex]
There are 36 pencils in 6 packs. Igor wants to know how many pencils are in 1 pack. Elsa wants to know how many pencils are in 3 packs l.
In 1 pack there is 6 pencils cause you need to divide 36 by 6. In 3 packs there are 18 pencils because 6 pencils times 3 packs is 18 pencils!
Hope this helped!
Answer with step-by-step explanation:
We are given that there are 36 pencils in 6 packs and we are to find out how many pencils are there in one pack and three packs.
To find the number of pencils in one pack, we need to divide the number of pencils by the number of packs.
Number of pencils on 1 pack = 36/6 = 6 pencils
To find the number of pencils in 3 packs, we will multiply the number of pencils in one pack by 3.
Number of pencils in 3 packs = 6 * 3 = 18 pencils
c= [12 0 3/2 1 -6 7 ] What is 4C? its a 2x3 matrix so 12 0 3/2 on top and 1 -6 7 on bottom. The answer is also supposed to be a matrix.
Answer:
[tex]\left[\begin{array}{ccc}48&0&6\\4&-24&28\end{array}\right][/tex]
Step-by-step explanation:
4C implies that we multiply each element in C by the constant 4.
12*4 = 48
0*4 = 0
(3/2)*4 = 6
This will be the new elements on top
1*4 = 4
-6 * 4 = -24
7 * 4 = 28
This will be the new elements at the bottom. The required matrix 4C is thus;
[tex]\left[\begin{array}{ccc}48&0&6\\4&-24&28\end{array}\right][/tex]
Answer:
The required matrix is:
[tex]4C=\left[\begin{array}{ccc}48&0&6\\4&-24&28\end{array}\right][/tex]
Step-by-step explanation:
The matrix given is:
[tex]C=\left[\begin{array}{ccc}12&0&3/2\\1&-6&7\end{array}\right][/tex]
We need to find 4C which means we need to multiply the matrix C with 4. Every entry of matrix will be multiplied by 4.
[tex]4C=\left[\begin{array}{ccc}4*12&4*0&4*3/2\\4*1&4*-6&4*7\end{array}\right][/tex]
Solving:
[tex]4C=\left[\begin{array}{ccc}48&0&12/2\\4&-24&28\end{array}\right]\\4C=\left[\begin{array}{ccc}48&0&6\\4&-24&28\end{array}\right][/tex]
SO, the required matrix is:
[tex]4C=\left[\begin{array}{ccc}48&0&6\\4&-24&28\end{array}\right][/tex]
Help me answer this question please
Answer:
C
Step-by-step explanation:
g(x) - f(x)
= x - 3 - (3x + 2)
= x - 3 - 3x - 2 ← collect like terms
= - 2x - 5
This is defined for all real numbers → C
Examine the equation.
–2(–x + 9) = 2(x – 9) 2x – 18 = 2x – 18
This equation has:
A. one solution
B. infinitely many solutions
C. no solution
Answer:
B. infinitely many solutions
Step-by-step explanation:
–2(–x + 9) = 2(x – 9)
Distribute the -2 on the left side. Distribute the 2 on the right side.
2x - 18 = 2x - 18
Add 18 to both sides.
2x = 2x
The equation means two times a number x is equal to two times the same number x. This is true for all numbers x. Every number is a solution of this equation.
Answer: B. infinitely many solutions
The answer is B.
Hope this helps :)
Robert earns $300 every week. What equation show the relationship between salary per week (s), number of weeks worked (w),and total income (t)?
Answer:
sw=t
Step-by-step explanation:
300 times the number of weeks,equals the total income
A fish tank that is 5 feet long by 3 feet wide by 3 feet high has a 2 foot cubic stone placed in the bottom how much water will the tank hold
Answer:
37ft³
Step-by-step explanation:
Volume of the fish tank = length × width × height = 5ft × 3ft × 3ft = 45ft³
Volume of the cubic stone = length × length × length = (2ft)³ = 8ft³
Volume of the water = volume of the fish tank - volume of the cubic stone
i.e Volume of the water = 45ft³ - 8ft³ = 37ft³
Sara had 207 dollars to spend on 9 books. After buying them she had 18 dollars. How much did each book cost
Answer:
21
Step-by-step explanation:
207-18=189..then divide by 9
The problem involves subtracting Sara's remaining money from her initial amount to find the total spent on books, then dividing by the number of books, giving us that each book cost 21 dollars.
Explanation:This is a basic algebra problem where we need to find the cost of each book. Sara initially has 207 dollars and after buying 9 books, she has 18 dollars left. Therefore, we can calculate the total spent on books by subtracting the final amount from the initial.
The calculation is: 207 dollars - 18 dollars = 189 dollars.
Now, to find the cost of each book, divide the total spent by the number of books. So, 189 dollars divided by 9 books results in 21 dollars per book.
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what type of association is shown by the scatterplot?
A.linear,strong
B.linear,weak
C.nonlinear,strong
D.nonlinear,weak
Answer: A; Linear, Strong
Step-by-step explanation: A linear scatterplot is normally when most of the dots on the scatterplot board are quite close to each other in a line. When it is strong it when most of the dots seem to form an actual line.
I hope this info helps!
A scatterplot categorized as "A: Linear, Strong" indicates a distinct and well-defined linear relationship, with closely clustered data points along the trend line, highlighting a robust association between the variables.
The correct answer is option A.
The scatterplot's visual characteristics provide insights into the nature of the relationship between two variables. In this case, when the answer is categorized as "A: Linear, Strong," it implies that the scatterplot predominantly exhibits a linear trend, suggesting a consistent and directional association between the variables. In a linear scatterplot, most data points align closely along a straight line, indicating a systematic relationship.
The term "strong" further emphasizes the degree of correlation or association between the variables. A strong linear scatterplot implies that the points are tightly clustered around the line, indicating a robust and noticeable relationship. The strength of the association is a reflection of how well the data points conform to the linear pattern, emphasizing the reliability of the trend observed.
In summary, when a scatterplot is described as "A: Linear, Strong," it signifies a clear and well-defined linear relationship between the variables, with data points forming a closely packed arrangement along the trend line.
Pls help so confused
ANSWER
B.
[tex](f+g)(x) ={3}^{x} + 2x + 6[/tex]
EXPLANATION
The given functions are:
[tex]f(x) = {3}^{x} + 10[/tex]
and
[tex]g(x) = 2x - 4[/tex]
We want to find (f+g)(x).
[tex](f+g)(x) = f(x) + g(x)[/tex]
[tex](f+g)(x) ={3}^{x} + 10 + 2x - 4[/tex]
Combine similar terms,
[tex](f+g)(x) ={3}^{x} + 2x + 10- 4[/tex]
Simplify:
[tex](f+g)(x) ={3}^{x} + 2x + 6[/tex]
The correct answer is B
The answer is B. Hope this helped
Evaluate cube root of 2×4^2/3 divided by 128^1/3
Answer:
you can see the solution in the photo i have uploaded
Answer:
Step-by-step explanation:
If all we need to do is to evaluate this expression, a calculator is one way to go.
Here's what I'd type in for the first expression:
(2*4^(2/3))^1/3 = 1.7145
... and for the second expression:
128^(1/3) = 5.0397
Therefore, the first expression, divided by the second, is 0.3402.
Which is the graph of 3y-5x>-6
The graph of the inequality equation 3y-5x>-6 will have a dotted line and shaded left wards (Option D).
How to graph the inequality equation?
The graph of the inequality equation given is sketched by simplifying the equation as shown below;
The given inequality equation;
3y - 5x > - 6
3y > 5x - 6
y > 5x/3 - 2
when x = 0, the value of y becomes;
3y - 5x > - 6
3y - 0 > - 6
y > - 2
when y = 0, the value of x is calculated as;
3y - 5x > - 6
0 - 5x > - 6
x < 6/5
The graph of the inequality equation 3y - 5x > - 6 is shown in the image attached.
35.
Elfa Beta
Alfa Beta's Objective Book
Any four vertices of a regular pentagon line on a
c) parallelogram d) None
a) circle b) square
36. If two circles touch, the point of contact line on a:
b) quadrilateral c) square .
a) St. line
d) None
37. The domain of the Relation R where R = {(x,y): y = x + x ; x,
and x < 9} will be
a) {x, 2, 3} b) {1, 2, 4, 8; c) {1, 0, 4, 8; d) None
38. A sum of money is divided between Mary and David in the rat
If Mary's Share is Rs. 225, then the total amount of money wil
a) 300 b) 400
c) 585
d) None
39. The angle between the vectors 2î + 39 + k and 29 - 39 - k is
a) "1a 6)" 13
d) None
160-11.27
c)"12
39 ko question solve gara
question no 39 isnot correct. they should be in i j k form
35. c)parallelogram, 36.a) straight line, 37.d) none, 38.d) None, 39.d)None
Question 35
Any four vertices of a regular pentagon will form a parallelogram. This is because the internal angles and lengths are such that selecting any four vertices will always result in the formation of a closed, opposite sides being equal, and opposite angles being equal shape, which is a parallelogram.
Question 36
If two circles touch, the point of contact lies on a straight line. Hence, the correct answer is a straight line.
Question 37
The domain of the relation R where R = {(x,y): y = x + x ; x ≥ 0 and x < 9} will be as follows: we are given that y = x + x^2 and x ranges from 0 (inclusive) to 9 (exclusive). Thus, the possible values for x within these constraints are all integers from 0 to 8. Therefore, the correct domain is
{0, 1, 2, 3, 4, 5, 6, 7, 8} and correct option is d. None
Question 38
If Mary's share is Rs. 225 and it is divided between Mary and David in the ratio 3:2, we first find the portion that represents Mary’s share. Here, Mary’s share is 3 parts and David’s is 2 parts. Together, their shares add up to 5 parts. If 3 parts equate to Rs. 225, then 1 part is Rs. 75. The total amount of money, which is 5 parts, will be 5 * 75 = Rs. 375. Hence, the correct total is Rs. 375.
Question 39
The angle between the vectors 2î + 3ĵ + k and 2î - 3ĵ - k can be found using the dot product formula.
The dot product of A and B, A.B = |A| |B| cos θ. First, compute A.B:
A = 2î + 3ĵ + kB = 2î - 3ĵ - kA.B = (2)(2) + (3)(-3) + (1)(-1) = 4 - 9 - 1 = -6Next, find |A| and |B|:
|A| = √(([tex]2^2) + (3^2) + (1^2)[/tex]) = √(4 + 9 + 1) = √(14)|B| = √(([tex]2^2) + (-3^2) + (-1^2[/tex])) = √(4 + 9 + 1) = √(14)Therefore,
cos θ = A.B / (|A| |B|) = -6 / (√(14) × √(14)) = -6 / 14 = -3 / 7Taking the inverse cosine:
θ = [tex]cos^(-1) (-3 / 7)[/tex]The approximate answer to the angle is around 116 degrees. However, because most multiple-choice sets would give their answers in radians, you would need to adjust accordingly. None of the provided answers exactly match this calculated result, therefore correct option is d. None
5) radius = 2.6 in
How do I find the circumference?
Answer:
[tex]\large\boxed{C=5.2\pi\ in\approx16.328\ in}[/tex]
Step-by-step explanation:
The formula of a circumference of a circle:
[tex]C=2\pi r[/tex]
r - radius
We have r = 2.6 in. Substitute:
[tex]C=2\pi(2.6)=5.2\pi\ in[/tex]
[tex]\pi\approx3.14\to C\approx(5.2)(3.14)=16.328\ in[/tex]
Mary is 21 years old. Her age is 9 years more than 3 times Henry’s age. Which equation can be used to determine x, Henry’s age in years?
Answer:4
Step-by-step explanation:
21=3x+9
12=3x
X=4
Final answer:
To find Henry's age, use the equation 21 = 3x + 9, where x represents Henry's age which is 4.
Explanation:
The question asks to find the equation to determine Henry's age. Given that Mary is 21 years old and her age is 9 years more than 3 times Henry's age, we set up the equation as follows: Let x represent Henry's age. The equation then becomes 21 = 3x + 9. This equation can be used to solve for x, Henry's age which is 12 = 3x; x = 4.
What’s the answers for this question please help me thank you
[tex]\text{Hey there!}[/tex]
[tex]\text{a will automatically equal one because it is unknown}[/tex]
[tex]\text{First you have to distribute your negative sign}\downarrow[/tex]
[tex]\text{Like: 2a - 5+ (-1)(3a+1)}[/tex]
[tex]\text{We get: 2a+(-5)+(-1)(3a)+(-1)(1)}[/tex]
[tex]\text{-1(3a)= -3a}[/tex]
[tex]\text{-1(1)= -1}[/tex]
[tex]\text{Our new equation becomes: 2a + (-5) + (-3a) + -1}[/tex]
[tex]\text{After solving that COMBINE YOUR LIKE TERMS}[/tex]
[tex]\text{\underline{2a}+ -5 + \underline{-3a} + -1 }[/tex]
[tex]\text{(2a + -3a)+ (-5 + -1)}[/tex]
[tex]\text{2a + -3a = -1a}[/tex]
[tex]\text{-5 + -1 = -6}[/tex]
[tex]\text{Now we can replace -1 with the value of -a}[/tex]
[tex]\boxed{\boxed{\text{Thus, your answer is: D. -a - 6}}}}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
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There are 3000 people at a concert you survey a random sample of 200 people and find that for 35 of them this is their first concert they have ever attended estimate how many total people are attending their first concert that night
35 out of 200 = 35/200 = 0.175 = 17.5% of the people surveyed are attending their first concert.
Now multiply all the people at the concert by 17.5%
3000 x 0.175 = 525
There are about 525 people total attending their first concert.
Musiclover is right give it to them it’s 525
if the pattern below follows the rule "starting with 10,every consecutive line has a number one less than the previous line." how many marbles must be in the sixth line?
I believe 5 marbles on the 6th line.
Line 1: 10
2: 10-1=9
3: 9-1=8
4; 8-1=7
5: 7-1=6
6: 6-1=5
For the pattern given, the number of marbles in the sixth line is 5.
Given that:
"Starting with 10, every consecutive line has a number one less than the previous line."
This is the pattern of the positions of the marbles.
The first line has 10 marbles.
The second line has 10 - 1 = 9 marbles.
The third line has 9 - 1 = 8 marbles.
The fourth line has 8 - 1 = 7 marbles
The fifth line has 7 - 1 = 6 marbles
The sixth line has 6 - 1 = 5 marbles.
The number of marbles in any line will be 10 - (n - 1) marbles for any nth line.
Hence the number of marbles is 5.
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Distance between (4,1) and (10,8)
See attachment for solution steps and answer.
if the ratio of the length of a rectangle to its width is 3 to 2 . what length of a rectangle whose width is 4 inches?
Answer:
6 in.
Step-by-step explanation:
So first you do 4 divided by 2 to find how much is 1 in the ratio.
4/2 = 2
Then you times 3 by 2
3 x 2 = 6 in.
Answer:
6
Step-by-step explanation:
I did it on plato :))
58:35
Compare the given dimensions of four triangles. Which triangle is possible to construct?
• side lengths of 5 ft, 12 ft, and 13 ft
O side lengths of 2 ft, 11 ft, and 15 ft
O side lengths of 3 ft, 7 ff. und 11 ft
O side lengths of 4 ft 8 ft, and 15 ft
Based on my calculations the answer is B
Answer:
D
Step-by-step explanation:
greast common factor of 52 and 12
Answer:
4 = GCF
Step-by-step explanation:
52/12 = 4.333
52/11 = 4.7272727
52/10 = 5.2
52/9 = 5.77777778
52/8 = 6.5
52/7 = 7.42
52/6 = 8.6666667
52/5 = 10.4
52/4 = 13 --> 4 works but does it work with 12
**check it.
12/4 = 3
**YES** So 4 is the GCF
Hello There!
The Greatest Common Factor Between "12" And "52" Is 4
Given y = 4x + 3, what effect does changing the equation to y = 4x - 3 have on the y-intercept?
Answer:
The y-intercept changes from (0, 3) to (0, -3)
Step-by-step explanation:
The y-intercept refers to the point where the graph of a function crosses or intersects with the y-axis. At this point, the value of x is usually 0.
Substitute x = 0 in both equations to determine how the y-intercept changes;
The original equation is given as y = 4x + 3,
when x = 0; y = 4(0) + 3 = 3
The y-intercept is thus (0, 3)
The new equation is given as y = 4x - 3
when x = 0; y = 4(0) - 3 = -3
The y-intercept is thus (0, -3)
Therefore, the y-intercept changes from (0, 3) to (0, -3)
Jay rides his bike 6 3/4 miles in 1/3 hour. What is his average speed?
There are three 1/3's in 1 hour: 1/3 +1/3 +1/3 = 3/3 = 1
Multiple the distance he rode by 3:
His speed is: 6 3/4 x 3 = 20 1/4 miles per hour
are 2/8 and 3/4 equivalent
Step-by-step explanation:
They are not equivalent because :
2/8=1/4 decimal: 0.25
3/4 decimal:0.75
3/4 is greater than 2/8 when they are decimals.
Answer: They are not equivalent.
The other person spelled the word equivalent wrong.
Answer: THEY ARE NOT EQUIVILENT
2/8= .25
3/4=.75
.75≠.25
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Question 1 (1 point)
Which of the equations listed below is equivalent to 48=-8(3b/4+2)
A. 48= -6b+2
B. 48= -6b-16
C. -384= -6b-16
D. -384= 3b+16
Answer: OPTION B.
Step-by-step explanation:
Given the equation [tex]48=-8(\frac{3b}{4}+2)[/tex] you can find an equivalent equation by simplifying it.
You need to remember the multiplication of signs:
[tex](-)(-)=+\\(+)(+)=+\\(+)(-)=-[/tex]
Now you can apply the Distributive property:
[tex]48=\frac{(-8)(3b)}{4}+(-8)(2)\\\\48=\frac{-24b}{4}-16[/tex]
Simplifying the equation, you get:
[tex]48=-6b-16[/tex]
You can observe that this equivalent equation matches with the equation provided in option B.
Use the data set below to answer the following question.
2, 4, 7, 2, 3, 7, 9, 3, 1,7
What is the mean of this data set?
Answer:
5
Step-by-step explanation:
Mean is the Average of all the observations.
Here there are 10 observations.
And The total sum of these observations is: 1+2+2+3+3+4+7+7+7+9=45
So mean = Total sum/ Total no: of observations
-> Mean =45/10= 4.5
Hope it helps...
Regards;
Leukonov/Olegion.
Evaluate 5x + (-2x) for x= 3.
0 21
0
-3
Answer:
9
Step-by-step explanation:
5x + (-2x)
Combine like terms
5x -2x
3x
Let x =3
3(3)
9
For a given input value x, the function g outputs a value y to satisfy the following equation. -4x-6=-5y+2. Write a formula for g(x) in terms of x.
Answer:
[tex]g(x)=0.8x+1.6[/tex]
Step-by-step explanation:
we have
[tex]-4x-6=-5y+2[/tex]
Solve for y
That means-----> isolate the variable y
Subtract both sides -2
[tex]-4x-6-2=-5y+2-2[/tex]
[tex]-4x-8=-5y[/tex]
Divide by -5 both sides
[tex](-4x-8)/(-5)=y[/tex]
Rewrite
[tex]y=(-4x-8)/(-5)[/tex]
[tex]y=\frac{4}{5}x+\frac{8}{5}[/tex]
[tex]y=0.8x+1.6[/tex]
Convert to function notation
Let
g(x)=y
[tex]g(x)=0.8x+1.6[/tex]
wll what is the value of y
(105)
A 58
B 122
C
D
142
155
Answer:
D
Step-by-step explanation:
10x - 5 and 7x + 4 are vertical angles and congruent, hence
10x - 5 = 7x + 4 ( subtract 7x from both sides )
3x - 5 = 4 ( add 5 to both sides )
3x = 9 ( divide both sides by 3 )
x = 3
7x + 4 and y are same side interior angles and are supplementary, thus
y + 7x + 4 = 180 ← substitute x = 3
y + 21 + 4 = 180
y + 25 = 180 ( subtract 25 from both sides )
y = 155 → D
A architecture has a blueprint his scale of the lobby is 13 ft : 5 in. The lobby is 65 feet high. What is the height of the lobby in the blueprint
Answer:64
Step-by-step explanation: