Answer:
You should add 4 to both sides because that would make the left side a perfect square which is what you are intending to do when you complete the square.
Answer:
4
Step-by-step explanation:
x² + 4x = 5
b = 4
We need to add (b/2)² to both sides to complete the square.
(4/2)² = 4
x² + 4x + 4 = 5 + 4
x² + 4x + 4 = 9
(x + 2)² = 9
Evaluate the following expression (-3)^-2
It is approximately equal to 0.1111
=================================
To get this answer, we use the rule
[tex]x^{-k} = \frac{1}{x^k}[/tex]
The negative exponent tells us to apply the reciprocal to get the exponent to be positive.
So,
[tex](-3)^{-2} = \frac{1}{(-3)^2}\\\\(-3)^{-2} = \frac{1}{9}[/tex]
Squaring -3 means you square the negative as well
[tex](-3)^2 = (-3)*(-3) = 9[/tex]
Answer:
1/9
Step-by-step explanation:
(-3)^-2 would be better written as (-3)^(-2).
1
(-3)^(-2) would be easier to evaluate if written as -------------
(-3)^2
The final answer is 1/9.
The local store where Tim shops charges a 7% sales tax for clothing. Complete the table by figuring the cost of the jeans after sales tax is applied. The first row has been done for you.
Answer:
[tex]A=P+P\times S\%[/tex]
Step-by-step explanation:
For calculating the sales tax of a product, it is required to first multiply the original cost price of the product by the sales tax percentage.
Once the sales tax has been computed add it to the original cost price in order to determine the total cost of the product.
The formula of final amount is:
[tex]A=P+P\times S\%[/tex]
Here,
A = final amount
P = original cost price
S = sales tax percentage
Answer:
1.$25.68
2.$51.36
3. 77.04
Step-by-step explanation:
I just took the test.
Samad's age and his father's age
are 12 years old and 40 years old
respectively. How many years later
will Samad's father be twice as old as
Samad?
Answer:
Step-by-step explanation:
let x= time period in years between age now and when father's age=2* the samad's age
in x years father's age will be 40 + x years old
in x years samad's age will be 12+x years old
at a certain point in time, the father's age = 2*the samad's age
40+x=2*(12+x)
or, 40 +x=24 + 2x
or, 40-24 = x
x=16
test:
father=40+16=56
son=12+16=28
hence , after 16 years samad's father will be twice as old as samad
The proportional relationship between the cost and duration of a phone call is shown in the following
Which statement about the graph are true
Answer:
None of the above
Step-by-step explanation:
the x coordinate tells us the duration, and the y-coordinate tells us the total cost of a phone call. The y coordinate of point aA represents the total cost of an 8 minutes phone call. not 8 phone calls. point a tells us that the cost is $2 for an 8-minute phone call, so the cost per minute is 2/8=$0.25, not $0.3.
Hope this helps!
How many complex and real roots are in the problem (x+10)^9.
Answer:
9 roots
Step-by-step explanation:
(x+10)^9 = 0
If you would multiply it out, the highest power is x^9 so the equation has 9 roots
Solving (x+10)^9 =0
Taking the 9th root of each sdie
x+10 = 0
x = -10
The root is -10 with multiplicity of 9
WILL GET BRAINLISET AND EXTRA POINTS Which is the approximate solution for the system of equations 8 x minus 10 y = negative 23 and 9 x + 10 y = negative 16? (–2.3, 0.5) (–2.5, 1) (–2.3, –0.5) (–2.5, –1)
Answer:
(-2.3, 0.5)
Step-by-step explanation:
Step 1: Write out systems of equations
8x - 10y = -23
9x + 10y = -16
Step 2: Elimination (add the 2 equations together)
17x = -39
x = -39/17 = -2.29412 ≈ -2.3
Step 3: Plug in x to find y
8(-39/17) - 10y = -23
-312/17 - 10y = -23
-10y = -79/17
y = 79/170 = 0.464706 ≈ 0.5
Answer:
(-2.3, 0.5)
Step-by-step explanation:
Step 1: Write out systems of equations
8x - 10y = -23
9x + 10y = -16
Step 2: Elimination (add the 2 equations together)
17x = -39
x = -39/17 = -2.29412 ≈ -2.3
Step 3: Plug in x to find y
8(-39/17) - 10y = -23
-312/17 - 10y = -23
-10y = -79/17
y = 79/170 = 0.464706 ≈ 0.5
Step-by-step explanation:
Determine which is NOT an arithmetic sequence
2.4.8.16
O -7,0.7.14
O 0..5.1.1.5
O 10.6.2.-2
Answer:
1st option
2,4,8,16
Step-by-step explanation:
1st option is not an Arithmetic sequence, it is geometric sequence. Because, the common ratio is 2
the 2nd option has a common difference of 7, so it is arithmetic
the 3rd option has a common difference of 0.5, so it is arithmetic
and 4th option has a common difference of -4. so it is arithmetic
Find the greatest common factor of 24, 36, and 48. help
Answer:
24, 36, and 48
Step-by-step explanation:
those numbers are the most high common factor of 24, 36, and 48.
Answer:
12
Step-by-step explanation:
1, 2, 3, 4, 6, 8, 12, 24
1, 2, 3, 4, 6, 6, 9, 12, 18, 36
1, 2, 3, 4, 6, 8, 12, 16, 24, 48
hopefully this helped :3
Which of the following is not a function?
A. {(4,5), (4,2), (5,4), (2,4)}
B. {(1,2), (2,3), (3,4), (4,5)}
C. {(1,2), (2,3), (3,3), (4,5)}
D. {(4,1), (5,1), (6,1), (7,1)}
Answer:
A
Step-by-step explanation:
it is A for for two outgoing (y)there is one in going(x)
Answer:
The answer is (A)
Step-by-step explanation:
A ladder is 8m long. It leans against a wall with one end on the ground 6m from the wall. How far up the wall does the ladder reach?
Step-by-step explanation:
Use pythagoras theorem
a^2=b^2+c^2
a^2=64+36
a=10m
The length up to the wall of the ladder will be around 5.2915.
What is Pythagoras theorem?The Pythagoras theorem is a theorem used to find out any length of a right-angle triangle.
Pythogoroous theorem is
Hypotenuse² = base² + perpendicular²
Given that a ladder leans against a wall so the ladder will act like a hypotenuse.
Let 6m be the base then we have to find the perpendicular.
Hypotenuse² = base² + perpendicular²
perpendicular² = Hypotaneous² - base²
perpendicular = [tex]\sqrt{ (Hypotenuse)^2 - (base)^2}[/tex]
Given hypotenuse is 8m and the base is 6m.
perpendicular² = 8² - 6²
perpendicular² = 28
perpendicular = √(28) = 5.2915 hence this much be far up the wall does the ladder reach.
For more information about Pythagoras theorem.
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A rectangular prism has a length of 4.2 cm, a width of 5.8 cm, and a height of 9.6 cm. A similar prism has a length of 14.7 cm, a width of 20.3 cm, and a height of 33.6 cm. The dimensions of the smaller prism are each multiplied by what factor to produce the corresponding dimensions of the larger prism? 3 4 4 5
Answer: 3.5
Step-by-step explanation:
Given: Dimensions of larger prism = length of 4.2 cm, a width of 5.8 cm, and a height of 9.6 cm.
Dimensions of smaller prism = length of 14.7 cm, a width of 20.3 cm, and a height of 33.6 cm.
Scale factor = [tex]\dfrac{\text{Size of image}}{\text{Size of original figure}}[/tex]
Since, smaller figure is the original figure and the bigger one is the image.
So, scale factor = [tex]\dfrac{14.7}{4.2}=3.5[/tex] [Taking lengths
Hence, the factor to produce the corresponding dimensions of the larger prism = 3.5
Answer:
A
Step-by-step explanation:
find the length of this
Answer:
Hey there!
We have tan 9= 21/BW
tan 9 (BW)=21
BW= 21/tan 9
BW= 132. 59
Hope this helps :)
Answer:
A- 132.59
Step-by-step explanation:
since we have to find the adjacent and already have the opposite we'll use tanθ = opp/adj
tan(9)= 21/WB
WB = 21/tan(9) (make WB the subject)
WB = 132.5887818 or 132.59
3) Equation 3 should represent a parabola that is a vertical stretch of the parent function and has a y-intercept greater than 3 and opens down. Equation 3:___________________________________________________________________ What strategy are you using to solve this equation and why? ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ Show your work and solution for solving this equation:
Answer:
The answer is given below
Step-by-step explanation:
The equation of a quadratic function is given by:
ax² + bx + c where a, b and c are the coefficients of the quadratic equation. The value of a determines whether the graph opens up or down (if a is positive opens up and if a is negative opes down), the value of c determines the y intercept (if c is positive, we have a positive intercept and if c is negative the intercept is negative).
The chosen equation is -x² -4x + 5. Since it has y-intercept of 5 and opens down (coefficient of x² is -1)
Let us assume a vertical stretch of 4, the new equation becomes:
4(-x² -4x + 5)
-4x² - 16x + 20
-4x² - 16x + 20 = 0
a = -4, b = -16 and c = 20
Using the quadratic formula:
[tex]x=\frac{-b \pm \sqrt{b^2-4ac} }{2a}\\ x=\frac{-(-16) \pm \sqrt{(-16)^2-4(-4)(20)} }{2(-4)}=\frac{16 \pm 24}{-8} \\x= -5 \ or \ x=1[/tex]
Imagine you are standing near a large rectangular pool and your friend asks you how far you think it is from one corner of the pool to the other, the long (diagonal) way. Explain how you could calculate that length (without getting wet) by only measuring the length and width of the pool. Then, make up a length and width (ex. 3 ft. by 4ft... etc.)... and perform the calculations to get the diagonal!
Answer:
See explanation below.
Step-by-step explanation:
A right triangle is a triangle that has a right angle (90º). In math, the Pythagorean theorem allows us to calculate the length of the sides of a right triangle.
In a right triangle, the legs are the two sides that meet at the 90º angle and the hypotenuse is the side that opposes the right angle. The Pythagorean Theorem tells us that the square of the hypotenuse equals the sum of the squares of the legs. In other words: [tex]c^2 =a^2 +b^2[/tex] where c is the hypotenuse and a and b are the legs.
Now, we can use this formula to calculate the diagonal of the pool if we just have the length and the width (these would be the legs of the triangle). We need to measure both the length and the width and then square both of them and sum up the squares: this would give us the square of the diagonal so we will only need to find its quadratic root and we will have the length of the diagonal.
For example, let's say we have a pool that is 3 ft by 4ft, using the formula we have:
[tex]Diagonal^2=3^2 +4^2 \\Diagonal^2 = 9+16\\Diagonal^2 = 25\\Diagonal = \sqrt{25} \\Diagonal =5[/tex]
Therefore, in this case the diagonal would be 5 ft long.
Answer:
a
Step-by-step explanation:
The area of a circle is 81pi in.squared. What is the circumference, in inches? Express your answer in terms of pi
Answer:
18π
Step-by-step explanation:
the area of a circle is :
A= r²*π where r is the radius
here r² =81⇒ r= 9
the circumference of a circle is :
P= 2*r*π
P= 18π
Answer:
18 pi inches
Step-by-step explanation:
The area of a circle is given by
A = pi r^2
81 pi = pi r^2
Divide by pi
81 = r^2
Take the square root of each side
sqrt(81) = sqrt (r^2)
9 = r
We want the circumference
C = 2 * pi * r
C = 2 * pi * 9
C = 18 pi
Can you please help me -3x-y=6
Answer:
(0,-6), (-2,0)
Step-by-step explanation:
-3x-y=6
-y=6+3x
y=-3x-6
when x=0, y=-6
when y=0 x=-2
Plz help I’ll mark Brainlynest
Answer:
36.00 units
Step-by-step explanation:
Lengths of horizontal and vertical segments are easily determined by subtracting coordinates or counting grid squares:
ST = 6 -1 = 5
TR = 5 -(-1) = 6
IP = 1 -(-6) = 7
PE = 2 -(-3) = 5
The lengths of the diagonal segments are found using the Pythagorean theorem. Those lengths are the root of the sum of the squares of the rise and run. As before, you can determine those from counting squares or subtracting coordinates.
RI = √(2^2 +5^2) = √29 ≈ 5.385
ES = √(3^2 +7^2) = √58 ≈ 7.616
Then the perimeter is the sum of segment lengths:
Perimeter = ST +TR +RI +IP +PE +ES
= 5 + 6 + 5.385 +7 +5 +7.616 = 36.001
Rounded to hundredths, the perimeter is 36.00 units.
Consider the following expression and the simplified expression. Expression Simplified Expression 3 x squared + 5 y squared box + 3 box + 4 y squared + 6 9 x squared minus y squared + 9 Which terms could be in the boxes to make the expressions equivalent? Positive 6 x squared and Negative 6 y squared Positive 6 x squared and Negative 10 y squared Positive 9 x squared and Negative 10 y squared Positive 9 x squared and Negative 6 y squared
Answer:
The correct answer is:
[tex]+6x^{2}\\-9y^2[/tex]
Step-by-step explanation:
We are given the term:
[tex]3x^{2} +5y^{2} [\text{ \ }] +3 [\text{ \ }] +4y^{2} +6 = 9x^{2} -y^{2} +9[/tex]
We have to fill in to the empty spaces such that the above equation gets satisfied.
First of all, let us simplify the LHS (Left Hand Side):
[tex]3x^{2} +5y^{2} [\text{ \ }] +3 [\text{ \ }] +4y^{2} +6\\\Rightarrow 3x^{2} +5y^{2} +4y^{2} [\text{ \ }] [\text{ \ }] +6 +3\\\Rightarrow 3x^{2} +9y^{2} [\text{ \ }] [\text{ \ }] +9[/tex]
Now, let us equate the LHS and RHS (Right Hand Side):
[tex]\Rightarrow 3x^{2} +9y^{2} [\text{ \ }] [\text{ \ }] +9 = 9x^{2} -y^{2} +9[/tex]
Equating the coefficients of [tex]x^{2}\ and\ y^{2}[/tex] in LHS and RHS:
One box will have value = [tex]9x^{2} -3x^{2} =+6x^{2}[/tex]
Other box will have value = [tex]-y^{2} -9y^{2} =-10y^{2}[/tex]
The correct answer is:
[tex]+6x^{2}\\-9y^2[/tex]
So, if we fill the boxes with above values, the expression will be simplified as given.
Answer:
The correct answer is B. Positive 6 x squared and Negative 10 y squared
Step-by-step explanation:
A kite is flying at an angle of elevation of about 55°. Ignoring the sag in the string, find the height of the kite if 85 m of string has been let out.
Answer: 69.6 m
Step-by-step explanation:
Sin 55 deg = opposite side/hypotenuse
0.819 = height/string length
0.819 * 85= height
height = 69.6 m
Which of these shapes is congruent to the given shape?
A.
B.
C.
D.
E.
Answer:
C
Step-by-step explanation:
Most of the times C is the answer on a test
Answer:
its D
Step-by-step explanation:
brainly tests
The diagonal of a square is x units. What is the area of the square in terms of x? One-half x squared square units x squared square units 2x square units One-half x square units
Answer:
[tex]\frac{x^2}{2}[/tex] square units [one-half x squared square units]
Step-by-step explanation:
As shown in the diagram attached to this response,
Since a square has all sides equal, let the sides of the square be each of a units.
The area, A, of the square = a x a = a²
i.e
A = a² --------------(i)
Now,
The diagonal is x units such that applying Pythagoras rule gives;
x² = a² + a²
x² = 2a²
a² = [tex]\frac{x^2}{2}[/tex] ----------------(ii)
Substitute the value of a² in equation (ii) into equation (i) to get;
A = [tex]\frac{x^2}{2}[/tex]
Therefore, the area of the square is [tex]\frac{x^2}{2}[/tex] square units
Answer:
1/2x^2 square units
Step-by-step explanation:
jane will run less than 32 miles this week. So far she has run 19 miles. what are the possible numbers of additional miles she will run ?use t for the number of additional miles she will run.
Answer:
Jane will run more than 30 miles this week, as thus far she ran 22.
Step-by-step explanation:
X + 22>30
X>8
She runs more than 8 miles.
Answer:
Well, it depends.
Step-by-step explanation:
In the problem, it doesn't specify if the miles she runs is a positive integer or not, but I will assume that it is.
There are number of miles: 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, and 31.
So t = 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, and 31
At a DBE lecture of 100 students, there are 29 women and 23 men. Out of these students, 4 are teachers and 24 are either men or teachers. Find the number of women teachers attending the lecture.
Answer:
We operate the principle of sets to solve the problem. We are given the number of women to be 28 and men to be 23. The intersection will be while the union of both sets will be 24. To calculate the number of women teachers attending the lecture we first sum up the number of women and men and subtract from the intersection of both sets which gives us 3. Therefore, the number of teachers that are men are 3 while the number of women teachers are 1.
Step by step explaination:
Given the following, Let the set for men be represented by MM, that of women be represented by WW and that of teachers represented by TT.
Therefore, number of men i.e n(MM)= 23,
number of women i.e n(WW)= 29
number of teachers i.e n(TT)=4
number of men or teachers i.e n(MM U TT)= 24
Therefore, we have:
n(MM U TT)=n(MM) + n(TT) - n(MM n TT)
Therefore:
n(MM n TT)=n(MM) + n(TT) -n(MM U TT)
n(MM n TT)= 23+ 4 - 24 = 3
There fore number of men that are teachers are n(MM n TT)= 3 .
Therefore, from the number of teachers n(TT)=4
the number of teachers that are men are 3 while the number of women teachers are 1.
n is an integer.
Write the values of n such that -15 < 3 < 6
Answer:
Step-by-step explanation:
n could be : -14, -13, -12... -1, 0 , 1, 2, 3 ,4,5
can someone help me with this question
Answer: a (see explanation below) .b.) rhombus .c) trapezoid in USA or trapezium elsewhere in the world
Step-by-step explanation:
For a.) Draw a horizontal from the bottom vertex, extending 2 units to the right. Then form a triangle by connecting a line from the right end of that line up to the right angle at the top of the original triangle
As per the given diagram
(a) represents a parallelogram not rectangle as shown in construction.
(b) Shape made by three congruent triangles on the grid below represents trapezium.
(c) Four congruent triangle in the grid below represents rhombus.
What are congruent triangles?"Two triangles are said to be congruent if the measure of all the three corresponding sides and angles of one triangle are equal to that of other triangle."
According to the question,
(a) First diagram we have to construct a triangle with given triangle in such a way it forms a parallelogram but not rectangle.
As shown in the constructed diagram.
(b) In the fourth diagram given quadrilateral having one pair of parallel line , therefore trapezium.
(c) In the second diagram all the four sides are congruent and parallel to each other and diagonals bisects each other at 90°, therefore it is rhombus.
Hence, (a) as shown in construction ,(b) trapezium and (c) rhombus is the correct answer.
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A straight line passes through the origin and has a gradient of 4. Find the equation
Answer:
y = 4x
Step-by-step explanation:
The slope is 4.
The line passes through (0, 0).
Equation of a line y = mx + b, m is the slope, and b is the y-intercept.
y = 4x + b
Put x and y as 0.
0 = 4(0) + b
0 = b
The y-intercept is 0.
The equation of the line is y = 4x.
The sum of the digits of a two-digit number is 7 .When the digits are interchanged the reversed number is five times the tens digit of the original number find the original number .
frnds pls help me
I want answer with full process pls help me
pls frnds do it fast pls help me
Answer:
Original number is 52.
Step-by-step explanation:
1) Two digit number xy,
it can be written as 10x + y.
2) The sum of the digits of a two-digit number is 7.
x + y = 7
3) The digits are interchanged the reversed number is yx,
the new number can be written as 10y + x.
4) The original number is 10x + y, so the tens digit of the original number is x.
5) Five times the tens digit of the original number is 5*x.
6) The reversed number is five times the tens digit of the original number:
10y + x = 5*x
7) We have system of two equations
x + y = 7 ----> x = 7 - y
10y + x = 5*x ---> 10y - 4x = 0
10y - 4x = 0
10y - 4(7 - y) =0
10y - 28 + 4y = 0
14y = 28
y = 2
x = 7 - y = 7 - 2 = 5
x = 5
Original number is 52.
New number 25.
Check:
Original number is 52, the tens digit is 5.
The reversed number (25) is five times the tens digit of the original number find the original number .
25 = 5*5 True
Instructions: Write the explicit rule. Remember to simplify and do not put spaces in your answer. Sequence: 30,0,−30,−60,… 30 , 0 , − 30 , − 60 , … = a n = Answer
Answer:
a(n)=60-30n
Step-by-step explanation:
Equation to use:
a(n) = a(1) + d(n-1)
where a(1) is the first term, d is the common difference between terms, and n is the nth term you are trying to find.
In this case, a(1) is 30, d is -30, and n is just n.
If you plug that into the equation and use the distributive property, you would get: a(n) = 30 -30n + 30.
Adding the two 30's gets you: a(n) = 60 - 30n, which is the solution.
please helpppppp please help please hellpppp
What is the product of 6x – y and 2x – y + 2? 8x2 – 4xy + 12x + y2 – 2y 12x2 – 8xy + 12x + y2 – 2y 8x2 + 4xy + 4x + y2 – 2y 12x2 + 8xy + 4x + y2 + 2y
Answer:
(6x – y) * (2x – y + 2) =12x2 – 8xy + 12x + y2 – 2y
Step-by-step explanation:
(6x – y) * (2x – y + 2)
= 6x*(2x – y + 2) - y*(2x – y + 2)
= 12x^2 - 6xy + 12x - 2xy + y^2 -2y
= 12x^2 + 12x - 8xy - 2y + y^2
Out of the answer choices:
8x2 – 4xy + 12x + y2 – 2y
12x2 – 8xy + 12x + y2 – 2y
8x2 + 4xy + 4x + y2 – 2y
12x2 + 8xy + 4x + y2 + 2y
the second choice is a correct answer.
Answer:
Step-by-step explanation:
B. 12x2 – 8xy + 12x + y2 – 2y