Hey there! I'm happy to help!
Let's look at all of the perfect squares (numbers with integer square roots) so that we can see where the square root of 12 lies.
√1=1
√4=2
√9=3
√16=4
√25=5
√36=6
√49=7
√64=8
√81=9
√100=100
We see that √12 would be in between √9 and √16 (3 and 4), so the square root of 12 is in between 3 and 4.
I hope that this helps! Have a wonderful day! :D
The square root of 12 lies between the whole numbers 3 and 4.
What is a square root?
The value of a number's power 1/2 is the number's square root. It is the number whose product by itself yields the original number, to put it another way.
Let's look at all of the perfect squares (numbers with integer square roots) so that we can see where the square root of 12 lies.
√1=1
√4=2
√9=3
√16=4
√25=5
√36=6
√49=7
√64=8
√81=9
√100=100
We see that √12 would be in between √9 and √16 (3 and 4), so the square root of 12 is in between 3 and 4.
Therefore, the square root of 12 lies between the whole numbers 3 and 4.
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Given point (-6, -2) and a slope of 5, write an equation in slope-intercept form.
a. y = 5x + 28
c. y + 2 = 5(x + 6)
b. y = -5x + 28
d. y - 2 = 5(x - 6)
Answer:
y=ax+b
y=5(-6)+28=-2
a
Given paralleogram ACDB-parallelogram FGHE, what
is the value of x?
O x= 40°
O x= 50°
O x= 65°
O x = 130°
The value of x will be 50 degrees. The correct option is B.
What is a parallelogram?A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure
The opposite angles of the parallelogram are equal and the sum of the adjacent angles of the parallelogram is 180 degrees.
Angle A is 130 degrees then angle F will also be 130 degrees. The angle E will be calculated as below:-
∠F + ∠ E = 180
130 + ∠E = 180
∠E = 180 - 130
∠E = 50
Therefore, the value of x will be 50 degrees. The correct option is B.
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1.
Harriet has deposited $693 in a savings account that earns interest at a rate of 4.6% compounded monthly. What will the account balance be in thirteen years? (2 points)
$1,258.77
$1,243.50
$724.88
$3,187.80
Answer:
Future amount (A) = $1,258.77 (Approx)
Step-by-step explanation:
Given:
Amount deposit (p) = $693
Rate of interest monthly (r) = 4.9% / 12 = 0.003833
Number of month (n) = 13 × 12 = 156
Find:
Future amount (A)
Computation:
[tex]A = p [1+r]^n \\\\ A = 693 [1+0.003833]^{156}\\\\ A= 693[1.8163]\\\\ A = 1258.77[/tex]
Future amount (A) = $1,258.77 (Approx)
The sum of two numbers is 167. The second number is 29 less than three times the first number. Fine the numbers. The two required numbers are:
Answer:
49 and 118
Step-by-step explanation:
Let the two numbers be x and y
x+y = 167
y = 3x-29
Substitute into the first equation
x+ 3x-29 = 167
Combine like terms
4x - 29 = 167
add 29 to each side
4x = 167+29
4x = 196
Divide by 4
4x/4 = 196/4
x = 49
x+y = 167
49+y = 167
y = 167-49
y =118
Answer:
[tex]\Huge \boxed{\mathrm{49 \ and \ 118}}[/tex]
Step-by-step explanation:
Let the first number be [tex]x[/tex]
Let the second number be [tex]y[/tex]
[tex]x+y=167[/tex]
[tex]y=3x-29[/tex]
Applying substitution method.
[tex]x+3x-29=167[/tex]
Combining like terms.
[tex]4x-29=167[/tex]
Adding 29 to both sides.
[tex]4x=196[/tex]
Dividing both sides by 4.
[tex]x=49[/tex]
Substituting x = 49 for the second equation.
[tex]y=3(49)-29[/tex]
Multiplying the numbers.
[tex]y=147-29[/tex]
Subtracting.
[tex]y=118[/tex]
The two required numbers are 49 and 118.
write another name for AE ? need asap
Answer:
EA, or s
Step-by-step explanation:
The line AE could also be named any of the following:
AC, EC, CE, CA, EA
If you’re only looking at the line segment AE, the only option is:
EA
Since I don’t know whether you need the line or line segment, you might want go with EA since it’s on both lists. It could also be line s.
20 points! Jason is 22, which is 6 years older than twice his sister Taylor’s age. How old is Taylor? Enter your answer in the box.
Answer:
8
Step-by-step explanation:
Jason = 22
Taylor = x
2x + 6 = 222x = 22 -62x = 16x = 16/2x= 8Taylor is 8
Find the standard form (ax + by + c = 0) of the line using the following information. Please show your work! Point: (6, -1) Slope: m is undefined I'll give brainliest!!!
Answer:
x - 6 = 0
Step-by-step explanation:
The only lines that have undefined slopes are vertical lines. Vertical lines are found in the form x = c where c is a constant. With vertical lines, it doesn't matter what the y value is because x will always be c. In this case, c = 6 because the x-coordinate of (6, -1) is 6. Therefore, our equation is x = 6. In standard form, that would be x - 6 = 0.
Answer:
[tex]\huge \boxed{x-6=0}[/tex]
Step-by-step explanation:
Vertical lines have undefined slopes.
The line crosses (6, -1), x = 6.
The equation of the vertical line is x = 6.
The equation of the line in standard form would be x - 6 = 0.
Find the greatest number of 5 digits which
when divided by 25, 30 and 40 leaves a
remainder 20,25, and 35 respectively.
Answer:
99,595
Step-by-step explanation:
We are looking at division and remainders. What do you do when a remainder is present? You usually add it when multiplying to get the final number, but since we are doing this backwards, we have to subtract the numbers divided by the remainder.
25 - 20 = 5
30 - 25 = 5
40 - 35 = 5
Look for the LCM (Least Common Multiple) for 20, 30, and 40 :
600
Now for the equation :
n + 5 = Multiple of all numbers and LCM =
n + 5 = 166 * 600 = 99,600
n = 99,600 - 5 = 99,595
The greatest 5 digit number which when divided by 25, 30 and 40 has a remainder of 20, 25, and 35 is 99,595
The reason why the above value arrived at is correct is as follows:
The required parameter;
To find a 5 digit number that with remainder of 20, remainder of 25 and a remainder of 35, when divided by 25, 30, and 40 respectively
Strategy;
Find the LCM of the divisor, then find the highest common multiple of the
LCM that is a 5 digit number, equate the expression for the required 5 digit
number to the highest common multiple of LCM of the divisors by adding
a value that will give a factor of the divisor as follows;
Let x represent the 5 digit number, from the question, we get;
x = 25·a + 20
x = 30·b + 25
x = 40·c + 35
x < 99,999
The 5 digit number is not a multiple of 25, 30, and 40, therefore, the number is not a multiple of the LCM of 25, 30, and 40 which is 600
The highest multiple of 600 which is a 5 digit number = 99,600
Therefore, we can write;
25·a + 20 + 5 = 30·b + 25 + 5 = 40·c + 35 + 5 = 99,600
However;
25·a + 20 + 5 = x + 5
By transitive property, we get
x + 5 = 99,600
∴ x = 99,600 - 5 = 99,595
The 5 digit number, x = 99,595
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solve:
[tex]\underset{x\rightarrow~3}{\lim}~\dfrac{2x^2-18}{x^2-3x}[/tex]
Hello, please consider the following.
[tex]\displaystyle \lim_{x\rightarrow3}~\dfrac{2x^2-18}{x^2-3x} \\ \\ \\ =\lim_{x\rightarrow3}~\dfrac{2(x^2-3^2)}{x(x-3)} \\ \\ \\ =\lim_{x\rightarrow3}~\dfrac{2(x-3)(x+3)}{x(x-3)} \\ \\ \\ =\lim_{x\rightarrow3}~\dfrac{2(x+3)}{x} \\ \\ \\=\dfrac{2(3+3)}{3}\\ \\ \\=\dfrac{2*3*2}{3} =\Large \boxed{\sf \bf \ 4 \ }[/tex]
Thank you
[tex]\\ \tt\longmapsto {\displaystyle{\lim_{x\to 3}}}\dfrac{2x^2-18}{x^2-3x}[/tex]
[tex]\\ \tt\longmapsto {\displaystyle{\lim_{x\to 3}}}\dfrac{2(x^2-9)}{x^2-3x}[/tex]
[tex]\\ \tt\longmapsto {\displaystyle{\lim_{x\to 3}}}\dfrac{2(x^2-3^2)}{x^2-3x}[/tex]
(a+b)(a-b)=a^2-b^2[tex]\\ \tt\longmapsto {\displaystyle{\lim_{x\to 3}}}\dfrac{2(x+3)\cancel{(x-3)}}{x\cancel{(x-3)}}[/tex]
[tex]\\ \tt\longmapsto {\displaystyle{\lim_{x\to 3}}}\dfrac{2x+6}{x}[/tex]
[tex]\\ \tt\longmapsto \dfrac{2(3)+6}{3}[/tex]
[tex]\\ \tt\longmapsto \dfrac{6+6}{3}[/tex]
[tex]\\ \tt\longmapsto \dfrac{12}{3}=4[/tex]
Use Stokes' Theorem to calculate . F = 5yi + 7xj + z3k; C: the counterclockwise path around the perimeter of the triangle in the x-y plane formed from the x-axis, y-axis , and the line y = 5 - 2x (Hint: n = k)
Answer:
hello your question is incomplete attached is the complete question
answer : 25/2 ( A )
Step-by-step explanation:
using Stokes' Theorem to calculate
F = 5yi + 7xj + [tex]z^3 k[/tex]
line y = 5 - 2x
attached below is the remaining part of the solution to the question
Which of the following is not an undefined term?
point
ray
line
plane
Answer:
ray
Step-by-step explanation:
ray is the answer because it starts with a startline but has no endpoint so it goes on for infinity.
1) write the equation of the
line in slope intercept form
that passes through (0,-2)
and (2,1).
Answer:
y=3/2x-2
Step-by-step explanation:
Find the slope first:
[tex]m=\frac{y_{2-y_{1} } }{x_{2}-x_{1} } =\frac{1-(-2)}{2-0}=\frac{3}{2}[/tex]
Then solve for y-intercept:
[tex]y=\frac{3}{2}x+b\\-2=\frac{3}{2}(0)+b\\-2=b[/tex]
Now, write out your complete equation:
y=3/2x-2
Manori’s bag has 10cent and 20cent coins. She has 202 coins with a total value of $31.90. How many 20cent coins does manori have?
a = 85 10cent coins
b = 117 20cent coins
Step-by-step explanation:a = 10c coins
b = 20c coins
$31.90 = c3190
a + b = 202 => a = 202 - b
10a + 20b = 3190
10(202 - b) + 20b = 3190
2020 - 10b + 20b = 3190
10b = 3190 - 2020
10b = 1170
b = 117 (20cent coins)
a = 202 - 117
= 85 (10cent coins)
(04.07A)
Two quantities are related, as shown in the table below:
x y
2 3
4 4
6 5
8 6
Which equation best represents the relationship?
Answer:
The equation that best represents the relationship is [tex]y=\frac{1}{2}x+2[/tex].
Step-by-step explanation:
We are given the following table representing the two quantities below;
x y
2 3
4 4
6 5
8 6
Firstly, we will find the two-point slope here, that is;
Consider two points; ([tex]x_1,y_1[/tex]) = (2, 3) and ([tex]x_2,y_2[/tex]) = (4,4)
Now, the formula for finding slope is;
Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{4-3}{4-2}[/tex] = [tex]\frac{1}{2}[/tex]
Similarly, finding the slope for the points (6,5) and (8,6);
Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{6-5}{8-6}[/tex] = [tex]\frac{1}{2}[/tex]
Now, the linear equation of the line having slope is given by;
[tex]y-y_1=m\times (x-x_1)[/tex] ; where m = slope and consider ([tex]x_1,y_1[/tex]) = (2, 3)
So, the equation of the line is;
[tex]y-3=\frac{1}{2} \times (x-2)[/tex]
[tex]y-3=\frac{1}{2}x-1[/tex]
[tex]y=\frac{1}{2}x+2[/tex]
Hence, the equation that best represents the relationship is [tex]y=\frac{1}{2}x+2[/tex].
Answer:
y = -1/2x + 11
Dave tried to evaluate 55 – 15 + 20 step-by-step.
55 - 15 + 20
Step 1: =40 + 20
Step 2: = 20
Find Dave’s mistake
Choose 1 answer:
A: step 1
B: step 2
C: Dave did not make a mistake
Answer:
Step 2
Step-by-step explanation:
In step 2 the expression was 40+20 which would have been 60 but he might have thought addition sign was subtraction so he did 40-20 which is 20 so he is wrong made mistake in step 2
pt 3 7/7 lasttt one helpppp
Answer:
2n+2
Step-by-step explanation:
-n + (-3) +3n + 5 -3
(-3+5) =2
-n +2+n+3n
3n-n = 2n
2n+2
Land in downtown Columbia is valued at $10 a square foot. What is the value of a triangular lot with sides of lengths 119, 147, and 190 ft?
Answer:
$87,461
Step-by-step explanation:
Given that the dimensions or sides of lengths of the triangle are 119, 147, and 190 ft
where S is the semi perimeter of the triangle, that is, s = (a + b + c)/2.
S = (119 + 147 + 190) / 2 = 456/ 2 = 228
Using Heron's formula which gives the area in terms of the three sides of the triangle
= √s(s – a)(s – b)(s – c)
Therefore we have = √228 (228 - 119)(228 - 147)(228 - 190)
=> √228 (109)(81)(38)
= √228(335502)
=√76494456
= 8746.1109071 * $10
= 87461.109071
≈$87,461
Hence, the value of a triangular lot with sides of lengths 119, 147, and 190 ft is $87,461.
I need help on this question, please stop by.
Answer:
last option from the left
Step-by-step explanation:
To find the price of one water bottle, we can calculate 6 / 24 because 24 bottles cost $6. Now, to find the price of 10 bottles, we can multiply the price of 1 bottle by 10 so the answer is 6 / 24 * 10.
PAPER II
Q1. Solve the equation 2r2 - 11r - 21 = 0.
Give the answer
Answer:
The values of r = -3/2 ,7
Step-by-step explanation:
2r2 - 11r - 21 = 0.
The is a quadratic equation in the form
2r²-11r -21= 0
Let's determine the value of r using factorization method
2r² -14r +3r -21= 0.
2r(r-7)+3(r-7)= 0
(2r+3)(r-7)= 0
2r+3= 0
2r= -3
r= -3/2
And
r-7= 0
r= 7
The values of r = -3/2 ,7
I don’t understand this?
Answer:
11.5 cm²
Step-by-step explanation:
We know that the triangle has a base of 3 + 4 = 7 and a height of 3 + 2 = 5. Therefore, the area of the triangle is 7 * 5 / 2 = 17.5. The area of the 3 by 2 rectangle is 3 * 2 = 6 so the shaded area is 17.5 - 6 = 11.5 square cm.
a companys product development division has 60 employees. Of these, 1/3 are engineers. If 40% of engineers are moved to another division. How many engineers will remain in the product development department?
Answer: There will be 12 engineers remaining in the product development department.
Step-by-step explanation:
So the givens are:
60 employees and 1/3 are engineers and if 40% of engineers are moved to another division and how many engineers will remain in the product development department?
So what we need to do:
60 * 1/3 = 60 / 3 = 20
There are 20 engineers.
20 * 40% = 8
There are 8 engineers that are going to be moved to another division.
20 - 8 = 12
12 engineers will remain in the development department.
Hence, your answer.
By calculations, 12 engineers will remain in the development department.
A companys product development division has 60 employees. Of these, [tex]\frac{1}{3}[/tex] are engineers.
The third part of a number is obtained by dividing a number by three, or what is the same, multiplying by a third ([tex]\frac{1}{3}[/tex]), thus dividing the number into a total of three equal parts.
In this case:
[tex]\frac{1}{3}[/tex]×60= 20
So, a companys product development division has 20 engineers.
40% of engineers are moved to another division.
The percentage is a way of referring to a proportion taking the number 100 as a reference. To calculate the percentage of a quantity, the quantity is multiplied by the percentage and divided by 100.
In this case:
40% of engineers= 40%×20=[tex]\frac{40x20}{100}[/tex]= 8
8 engineers are moved to another division.
The number of engineers who remain in the department is calculated by subtracting the total number of engineers in the department and the number of engineers who move to another division:
20 - 8= 12
12 engineers will remain in the development department.
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Use inductive reasoning to determine the next term in the sequence -2, 5, -4, 3, -6, ... *
Answer:1,-8
Step-by-step explanation: -2,5( add 7) 5,-4(sub 9),-4,3(add 7), 3,-6(sub 9)
Pattern of +7,-9,+7,-9
-6+7=1 and 1-9=-8
Which of the following presents can also be expressed as a mixed number 310% or 49% or 7.4% or 0.001%
Answer:
310%
Step-by-step explanation:
310% can be expressed as a mixed number because 150% would be 1 1/2.
310% would be 3 1/10.
which equation is equivalent to the given equation? x^2+16x=22
Answer:
[tex](x+8)^2 = 86[/tex]
Step-by-step explanation:
Given
[tex]x^2 + 16x = 22[/tex]
Required
Determine an equivalent equation
[tex]x^2 + 16x = 22[/tex]
Get the coefficient of x
[tex]Coefficient = 16[/tex]
Divide this by 2
[tex]Result = \frac{16}{2}[/tex]
[tex]Result = 8[/tex]
Take its square
[tex]Result = 8^2[/tex]
[tex]Result = 64[/tex]
Add this to both sides of the equation
[tex]x^2 + 16x + 64 = 22 + 64[/tex]
[tex]x^2 + 16x + 64 = 86[/tex]
Expand the expression on the right hand side
[tex]x^2 + 8x + 8x + 64 = 86[/tex]
Factorize
[tex]x(x+8)+8(x+8) = 86[/tex]
[tex](x+8)(x+8) = 86[/tex]
[tex](x+8)^2 = 86[/tex]
Hence, the equivalent equation is [tex](x+8)^2 = 86[/tex]
Define the following sequence recursively: 4, 4/3, 4/9, ....
Answer:
Step-by-step explanation:
[tex]a_n=\frac{1}{3} a_{n-1}[/tex]
please help! Please explain as well!!!!
Answer:
value of the variable: 3/2
perimeter: 84 feet
Step-by-step explanation:
Let's find the value of the variable first:
It is a square, so all 4 sides are the same (have the same length)
This means, 3(2f + 4) = 12f + 3
Simplify it,
6f + 12 = 12f + 3
6f = 9
f = 3/2
So, the variable f = 3/2!
Let's find the perimeter:
First, we find the value of one side of the square
12f + 3 is a side
because f = 3/2, we know that the one side of a square is 18 + 3 ft, which is 21 ft
Like I said, all 4 sides are the same in a square, so we can just calculate the length of 1 side, and multiply it by 4!
so 21 * 4 = 84!
The perimeter of this square is 84 feet!
I hope this helps! Please tell me if I did anything wrong, thank you and have a great day =D
c) Chairs are placed in equal rows and column of a squared room. If there are 144 chairs in the room, how many chairs are there in the first row?
Answer:
12
Step-by-step explanation:
144 chairs in total.
the room is square, this means that the number must be multiplied by the same number
12x12= 144
there are 12 chairs on the first row.
if there are two numbers on one side, do i have to add them together?
Answer:
YES
Step-by-step explanation:
For example, in the figure displayed in the attachment, the length of [tex] YM = MS + SY [/tex]
[tex] MS = 3 [/tex]
[tex] SY = 10 [/tex]
Therefore, [tex] YM = 3 + 10 = 13 [/tex].
The lengths of segments MS and SY sums up to give you the length of YM.
can someone please help me
Problem 6, part c)
The tickmarks indicate the sides are the same length. This triangle is isosceles.
The two base angles are always opposite the congruent sides. One base angle is 25, so the other base angle must be 25 as well (base angles are congruent for isosceles triangles).
The three angles of this triangle are
25, 25 and 4x+2
Add those three angles up, set the result equal to 180, and solve for x
4x+2+25+25 = 180
4x+52 = 180
4x = 180-52
4x = 128
x = 128/4
x = 32 is the answer====================================================
Problem 7, part a)
We use the same idea as with the last problem above. This works because this triangle is also isosceles (due to the tickmarks).
The three angles of this triangle are
(4x+1), (4x+1) and (5x-4)
note how (4x+1) shows up twice because it is a base angle
Add up those angles and set it equal to 180 to solve for x
(4x+1) + (4x+1) + (5x-4) = 180
13x - 2 = 180
13x = 180+2
13x = 182
x = 182/13
x = 14
Using this x value, we can find angle F
angle F = 5x-4
angle F = 5*14-4
angle F = 70-4
angle F = 66 degrees is the answer====================================================
Problem 7, part b)
We'll use the x value found back in part a) above.
angle D = 4x+1
angle D = 4*14+1
angle D = 56+1
angle D = 57 degrees is the answerAngle E is also 57, since D and E are congruent base angles
note how D+E+F = 57+57+66 = 180 to help confirm our answers
Help me please thank you
Answer:
135°
Step-by-step explanation:
Because the lines are parallel, <1 and <3 are the same.