The algebraic expression for the difference between the squares of the two numbers, supposing the two numbers to be a and b, is
a² - b² = (a + b)(a - b).
An algebraic expression is a combination of terms, where the terms are separated using mathematical operators like plus (+), minus (-), multiply (*), and divide (/).
The terms are combinations of numerals and variables.
Variables are represented alphanumerically, which can hold any value as per the expression they are used in.
In the question, we are asked to write the algebraic expression for the difference between the squares of two numbers.
We assume the two numbers to be a and b respectively.
Thus, we are asked to write an expression for the difference between the square of a and square of b, that is, we are asked to write an expression for a² - b².
We know that a² - b² is an identity, which can be shown as (a + b)(a - b).
Thus, the algebraic expression for the difference between the squares of the two numbers, supposing the two numbers to be a and b, is a² - b² = (a + b)(a - b).
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1/5n+3/5n=7/9
Can you help?
The value of n in 1/5n+3/5n=7/9 is 35/36
How to solve the equation?The equation is given as:
1/5n+3/5n=7/9
Multiply through by 5
n + 3n = 35/9
Evaluate the sum
4n = 35/9
Divide both sides by 4
n = 35/36
Hence, the value of n in 1/5n+3/5n=7/9 is 35/36
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Find the other endpoint of the line segment with the given endpoint -5, 2 and midpoint 2, -5
Answer:
( 9, -12 )
Step-by-step explanation:
Mario's Math Tutoring
you have the midpoint
2, -5
use the midpoint formula
(x1+x2)/2 , (y1+y2)/2
to get the endpoint
x :
(-5+x2)/2 = 2
(-5+x2) = 4
-5+x2 = 4
x2 = 9
y:
(2+y2)/2 = -5
(2+y2) = -10
2+y2 = -10
y2 = -12
Thank you Mario!
What is the y-intercept of the function f(x)=-2/9x + 1/3?
Answer:
y-intercept = [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
the coefficient is the slope (slope = -2/9x)
the constant is the y-intercept (y-intercept=1/3)
this is true for all functions like this
Answer:
The y-intercept is
c) 1/3
Step-by-step explanation:
Freddie had saved 231 pennies.
Which statement best describes
the number of pennies he had?
he has 231 pennies..............
A company designs microphones for use in conference rooms. a new microphone needs to focus on the person speaking and not the voices of other people in the room. which polar equation would best match the desired audible range of the microphone?
r = 3 + 3cos(θ) polar equation would best match the desired audible range of the microphone.
How do you know if an equation is polar?Determine the kind of polar equation. The polar equation has the shape of a limaçon, and is written as r = a - b cos. We just need to assess the equation throughout the range [0, 1] and then reflect the graph about the polar axis because the equation passes the condition for symmetry to the polar axis.What is a polar in math?The polar coordinate system in mathematics is a two-dimensional coordinate system in which the distance from a reference point and the angle from a reference direction are used to identify each point's location on a plane.What is the meaning of polar form?In addition to the rectangular form, a complex number can also be represented in polar form. Typically, we write complex numbers as z = x + iy, where I is an imaginary integer. However, in polar form, complex numbers are modeled as a union of argument and modulus.Learn more about polar form here:
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Answer:
D
Step-by-step explanation:
What is the slope of a line passing through (-4,-5)
and (-2,-9)?
Answer:
slope = - 2
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 ) = (- 4, - 5 ) and (x₂, y₂ ) = (- 2, - 9 )
m = [tex]\frac{-9-(-5)}{-2-(-4)}[/tex] = [tex]\frac{-9+5}{-2+4}[/tex] = [tex]\frac{-4}{2}[/tex] = - 2
In fig. 6.39, side QP and RQ of ΔPQR are produced to points S and T respectively, if ∠SPR = 135° and ∠PQT = 110°, find ∠PRQ.
Answer:
PRQ = 65 degrees
Step-by-step explanation:
Angles SPR and QPR and angles TQP and RQP form linear pairs, so they are supplementary (angle measures add up to 180 degrees).
SPR + QPR = 180
135 + QPR = 180
QPR = 45
TQP + RQP = 180
110 + RQP = 180
RQP = 70
Since interior angles of a triangle add up to 180 ...
QPR + RQP + PRQ = 180
45 + 70 + PRQ = 180
PRQ = 65
Can someone help me please
Answer: B. [tex]12log(x)-4log(y)[/tex]
Step-by-step explanation:
Properties of logs:
[tex]log_{a} (\frac{B}{C} )=log_{A}B-log_{A} C[/tex]
[tex]logA^B = BlogA[/tex]
So, [tex]log\frac{x^{12} }{y^4} =logx^{12} -logy^4 =12log(x)-4log(y)[/tex]
It would be 12 log x - 4 log y (B)
If the parabola of the form y = a(x – h)2 + k is always shifted horizontally h units and vertically k units, then its vertex is always
(–h, –k)
(h, k)
(–h, k)
(h, –k)
The vertex of the transformed parabola with the equation [tex]y=a(x-h)^2+k[/tex] is (h, k).
What are the transformation rules for horizontal and vertical shifts?The transformation rules are:
Translation: (x, y) → (x + a, y) or (x, y) → (x - a, y) (Horizontal shift)
Translation: (x, y) → (x , y + b) or (x, y) → (x , y - b) (Vertical shift)
Calculation:It is given that, the transformed parabola is [tex]y=a(x-h)^2+k[/tex]
This parabola has vertex at (h, k).
Since this equation is obtained by shifting h units horizontally and k units vertically.
So, the original vertex is at (h - h, k - k) = (0, 0)
Thus, the equation of the actual parabola is [tex]y=ax^2[/tex]
Therefore, the given transformed equation of parabola has vertex (h, k).
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Answer:
B] (h,k)
The next answer is Vertex (-5, -4)
☆
EDGE2022; Good luck :3!!!!
Which represents the inverse of the function f(x) = 4x?
O h(x) = x + 4
O h(x) = x -4
O h(x) = 3/4x
O h(x) = 1/4x
Answer:
last answer:
h(x) = 1/4 x
Step-by-step explanation:
First, change f(x) to y.
f(x) = 4x
y = 4x
Then switch the x and y.
y = 4x
x = 4y
Last, solve for y.
x = 4y
x/4 = 4y/4
x/4 = y
y = x/4
This is the same as:
y = 1/4 x
h(x) = 1/4 x
8 more than 3 times a number is the same as -5 times the number.
a. x = -1
b. x = 1
c. x = -2
Answer:
3x +8 = -5x
3x + 5x = -8
8x = -8x
x = -8 /8
x = -1
Hope it helps...
Please contact me for further explanation....
What is the area of a square with a perimeter of 44 mm?
Answer:
The area of the square is 121mm
Step-by-step explanation:
To solve this we need two basic formulas:
P = 4s
A = [tex]s^{2}[/tex]
P = perimeter
s = the length of the side
Since the shape is a square all the sides are the same length. To get the value of 's' we need to isolate:
P = 4s
44 = 4s
44 / 4 = 4s / 4
11 = s
Now plug in the answer for 's' to get the area:
A = [tex]s^{2}[/tex]
A = [tex]11^{2}[/tex]
A = 121
Hope this helps.
Solve the system of equations 4x+5y=-1 and -5x-8y=10 by combining the equations.
The solutions to the given system of equations are x = 6 and y = -5
Simultaneous linear equationsFrom the question, we are to solve the given system of equations
The given system of equation is
4x+5y=-1
-5x-8y=10
Multiply the first equation by 5 and the second equation by 4
5× (4x+5y=-1)
4× (-5x-8y=10)
20x + 25y = -5
-20x - 32y = 40
------------------------
0x + (-7y) = 35
-7y = 35
y = 35/-7
y = -5
Substitute the value of y into the first equation to find x
4x + 5y = -1
4x + 5(-5) = -1
4x -25 = -1
4x = -1 +25
4x = 24
x = 24/4
x = 6
Hence, the solutions to the given system of equations are x = 6 and y = -5
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Help me pleaseeeeeeeeeeeeeeeeeeeee
Answer:
a = 16.52 cmb = 23.85 cm=========================
Given AB = 22 cmm∠A = 42°m∠B = 75°To findSide length of a and bSolutionThe law of sines is:
a/sin A = b/sin B = c/sin CStep 1Find the value of ∠C using the angle sum theorem:
m∠A + m∠B + m∠C = 180°42° + 75° + C = 180°117° + C = 180°C = 180° - 117°C = 63°Step 2Find side a:
Note, the sides of a triangle are marked as:
a = BC, b = AC, c = AB (opposite to respective angle).Use two pairs with one unknown:
a/sin A = c/sin CSubstitute values and solve for a:
a/ sin 42° = 22/sin 63°a = 22*sin 42°/sin 63°a = 16.52 cm (rounded)Step 3Find side b, similar to finding side a:
b/ sin 75° = 22/sin 63°b = 22*sin 75°/sin 63°b = 23.85 cm (rounded)Answer:
a = 16.5 cm (nearest tenth)
b = 23.8 cm (nearest tenth)
Step-by-step explanation:
Definition
A, B and C are the angles and a, b and c are the sides opposite the angles.
From inspection of the triangle:
A = 42°B = 75°c = 22 cmInterior angles of a triangle sum to 180°:
⇒ A + B + C = 180°
⇒ 42° + 75° + C = 180°
⇒ C = 180° - 117°
⇒ C = 63°
To find the missing side lengths a and b, use the Sine Rule:
[tex]\sf \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]
Substitute the given values into the Sine Rule formula:
[tex]\implies \sf \dfrac{a}{\sin 42^{\circ}}=\dfrac{b}{\sin 75^{\circ}}=\dfrac{22}{\sin 63^{\circ}}[/tex]
Finding side a:
[tex]\implies \sf \dfrac{a}{\sin 42^{\circ}}=\dfrac{22}{\sin 63^{\circ}}[/tex]
[tex]\implies \sf a=\dfrac{22\sin 42^{\circ}}{\sin 63^{\circ}}[/tex]
[tex]\implies \sf a=16.52162239...[/tex]
Therefore, side a is 16.5 cm (nearest tenth).
Finding side b:
[tex]\implies \sf \dfrac{b}{\sin 75^{\circ}}=\dfrac{22}{\sin 63^{\circ}}[/tex]
[tex]\implies \sf b=\dfrac{22\sin 75^{\circ}}{\sin 63^{\circ}}[/tex]
[tex]\implies \sf b=23.84984577...[/tex]
Therefore, side b is 23.8 cm (nearest tenth).
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Complete the congruence statement for the figure below.
"What is the y-intercept of the line that has a slope of- 4 and passes through the point (A)- 10 (B)-6 (C) 8 (D) 10
The y-intercept which is the point at which x = 0 is; A: -10
How to find the y-intercept?The general form of an equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
We are given the slope;
m = -4
Now, the line passes through the point 0, -10. Thus;
(y - y1)/(x - x1) = -4
(y + 10)/(x - 0) = -4
y + 10 = -4x
y = -4x - 10
Thus, the y-intercept which is the point at which x = 0 is; y = -10
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Line $m$ is parallel to line $n$ and the measure of $\angle 1$ is $\frac 18$ the measure of $\angle 2$. What is the degree measure of $\angle 5$?
The angle of m∠5 is 116 degrees.
How to find angles when parallel lines are cut by a transversal?When parallel lines are cut by a transversal, angle relationships are formed. This include corresponding angles, alternate angles , vertical angles etc.
Therefore, line m and n are parallel lines cut by the a transversal.
Hence,
m∠2 = 64 degrees
Therefore,
m∠5 = m∠4 (alternate angles)
Therefore,
m∠5 + m∠2 = 180
m∠5 = 180 - 64
m∠5 = 116 degrees.
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The degree measure of the angle labelled 5; m<5 = 116°.
What is the measure of the angle labelled 5 in the task content?The angle measure of the angle labelled 5 as in the complete task content in the attached image can be determined as follows;
It follows from the complete task content that; that the measure of angle 2 is; 64°.
On this note, it follows from the sum of angle measures on a straight line theorem that; m<4 = 180° - 64° = 116°.
Additionally, it follows from the congruence of alternate angles theorem that <4 and <5 are congruent and hence, their measures are equal.
Therefore, m<5 = 116°.
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Consider the function f(x)=x2 bx c. if the minimum of this function is located at point (2,0), then what are the values of b and c?
The values of b and c are -4 and 4 respectively
How to determine the values of b and c?The function is given as:
f(x) = x^2 + bx + c
Differentiate f(x)
f'(x) = 2x + b
Set to 0
2x + b = 0
Solve for b
b = -2x
The minimum is (2, 0).
So, we have:
b = -2 * 2
b = -4
Substitute b = -4 in f(x) = x^2 + bx + c
f(x) = x^2 - 4x + c
Substitute (2, 0)
0 = (2)^2 - 4(2) + c
This gives
0 = 4 - 8 + c
Evaluate
c = 4
Hence, the values of b and c are -4 and 4 respectively
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Identify the function with a period of 4 and an amplitude of 2.
Answer:
it's only 2pi/B because the period of sin and cos is 2pi. If we were dealing with tan it'd be pi/B, since the period of tan is just pi.
Use the distributive property to write an
addition sentence equivalent to:
8(5+2)
Answer:
8(5) + 8(2)
Step-by-step explanation:
8 (5 + 2) is 8 (7) or 56
If I distribute the 8 through the problem, I will get the same answer
8(5) + 8(2)
40 + 16
56
A teacher has 14 senior students, 7 junior students, 4 sophmore, 5 freshmen, what is the proabability that she chooses a senior?
Answer:
7/15
Step-by-step explanation:
To find the probability the student is a senior
P( senior) = number of seniors / total students
= 14 / ( 14+7+4+5)
= 14/30
= 7/15
Answer:
14/30 or 7/15
Step-by-step explanation:
probability = no. of senior students / total no. of students
probability = 14 / (14+7+4+5)
probability = 14/30
This can be simplified to 7/15.
Hope this helps!
2. Which of the following expressions is equivalent to 322?
01
08.1/1
032.2
08-2
Answer:
C. (32/4)*2
Step-by-step explanation:
C is the correct answer because when we divide 4/2 it equals 2.
Hope this helps!
Answer:
D
Step-by-step explanation:
Given expression:
[tex] \dfrac{32}{4} \times \dfrac{4}{2} \times 2 [/tex]
Evaluation of the given expression:
[tex] = 8 \times 2 \times 2 [/tex]
[tex] = 32 [/tex]
A. [tex] \dfrac{32}{\frac{16}{4}} = \dfrac{32}{4} = 8 [/tex]
B. [tex] 8 \times \dfrac{4}{2} = 8 \times 2 = 16 [/tex]
C. [tex] \dfrac{32}{4} \times 2 = 8 \times 2 = 16 [/tex]
D. [tex]8 \times \dfrac{4}{2} \times 2 = 8 \times 2 \times 2 = 32[/tex]
Only expression D evaluates to the same value as the given expression.
Answer: D
Bd=16 and ac is the perpendicular bisector of bd. 2x-14 37-x d 2y-2 3 y=[?] enter
The value of y from the given expression is 5
Perpendicular Bisector
Given:
BD = 16
BC = 2y - 2
CD = y + 3
Since AC is a perpendicular bisector of BD:
BC = CD
2y - 2 = y + 3
2y - y = 3 + 2
y = 5
Hence, the value of y from the given expression is 5
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Which is the graph of the function f(x) = x3 + x2 + x + 1?
Answer:
Step-by-step explanation:
the answer is on the graph
Find the area of the polygon formed whe these points are connected a(3,7)b(3,3)c(7,3)d(7,7)
Here, given
sides of polygon= a(3,7)b(3,3)c(7,3)d(7,7)
Let, 3 = x1 & 7= y1 , 3= x2 & 7= y2 , 7= x3 & 3= y3 , 7= x4 & 7= y4
[tex]\frac{1}{2}[/tex] [det.(9-21)+det.(9-21)+det.(49-21)+det.(49-21)] {we took determinants of all the given sides}
[tex]\frac{1}{2}[/tex] (32)
16cm^2
Hence, the area of the polygon is 16cm2.
The formula for calculating the area of a regular polygon is: area = (number of sides x 1 side length x apothem distance) / 2, where the value of the apothem is the formula apothem = [(1) Length side). / {2 × (tan (180 / number of sides))}].
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Find the seventh term of the sequence which has a first term of 1/2 and has a common ratio of three
The seventh term of the sequence is 364.5
Geometric progressionFrom the question, we are to determine the seventh term of the sequence
Using the formula,
[tex]a_{n} = ar^{n-1}[/tex]
Where [tex]a_{n}[/tex] is the nth term
a is the first term
and r is the common ratio
From the given information,
a = 1/2
r = 3
Thus,
[tex]a_{7} = (\frac{1}{2}) 3^{7-1}[/tex]
[tex]a_{7} = (\frac{1}{2}) 3^{6}[/tex]
[tex]a_{7} = \frac{1}{2} \times 729[/tex]
[tex]a_{7} = 364\frac{1}{2} \ OR \ 364.5[/tex]
Hence, the seventh term of the sequence is 364.5
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Which pair of complex numbers has a real-number product? (1 2i)(8i) (1 2i)(2 – 5i) (1 2i)(1 – 2i) (1 2i)(4i)
The third pair [(1+2i)(1-2i)] have a real number product and other pairs have complex number.
According to the statement
we have given Following are the pairs of the complex number:
(1+2i)(8i),
(1 + 2i)(2 – 5i)
(1+2i)(1-2i) and (1+2i)(4i)
We have to check which pair out of these is a real number product, which means which pair do not contain terms consisting of "i".
So, For this purpose
we have to multiply these pairs with each other.
So,
(1+2i)(8i) = 8i +16(i)^2
And
(1 + 2i)(2 – 5i) = 2 +4i - 5i +10(i)^2
And
(1+2i)(1-2i) = 1 -4(i)^2 -2i +2i = 1+4 = 5
And
(1+2i)(4i) = 4i + 6(i)^2
From these multiplication we found that the third pair have a real number product.
So, The third pair [(1+2i)(1-2i)] have a real number product and other pairs have complex number.
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Find the area of this circle
Answer:
[tex] {75ft}^{2} [/tex]
Step-by-step explanation:
[tex]a = \pi{r}^{2} = 3 {r}^{2} \\ a =3 ({ \frac{10}{2} })^{2} = 3 \times {5}^{2} \\ a = 3 \times 25 = 75[/tex]
First, we replace π with 3, since we were told to.We know 10 is the diameter and the radius is half of the diameter, so we divide 10 by 2.We get 5. 5 squared is the same as (5×5). Finally, we multiply 3 by 25.To start solving this exercise, we obtain as data:
π = 3r = 10 ft²a = ?To find the area of the circle. We apply the following formula: A =π r², where
a = areaπ = pir = radiusWe substitute our data in the formula and solve:
Substituting values into the equation:
[tex]\boldsymbol{\sf{A=3*(10 \ ft)^{2} }}[/tex]Taking the square root:
[tex]\boldsymbol{\sf{A=3*100 \ ft^{2} }}[/tex]Multiplying
[tex]\boxed{\boldsymbol{\sf{A=300 \ ft^{2} }}}[/tex]Therefore, the area of the circle is 300 ft².
Please help me! due today:(
Step-by-step explanation:
(π * r²) will give you are of entire circle
the multiply by 60/360 , to give the shaded part
Answer:
A ≈ 25.7 cm²
Step-by-step explanation:
the area (A) of the sector is calculated as
A = area of circle × fraction of circle
= πr² × [tex]\frac{60}{360}[/tex]
= π × 7² × [tex]\frac{1}{6}[/tex]
= [tex]\frac{49\pi }{6}[/tex]
≈ 25.7 cm² ( to the nearest tenth )
10. A drawer contains only green marbles. After
5 red marbles are added to the drawer, the
probability of picking a red marble is
How many marbles were there in the drawer
originally?
(A) 5
(B) 7
(C) 12
(D) 30
(8)
Answer:
(D) 30
Step-by-step explanation:
number of green marbles = x
number of red marbles = 5
total number of marbles = x + 5
p(red) = (number of red marbles)/(total number of marbles)
p(red) = 5/(x + 5)
p(red) = 1/7
5/(x + 5) = 1/7
(x + 5) × 1 = 5 × 7
x + 5 = 35
x = 30
Answer: (D) 30