Answer:
9m²-n²
Step-by-step explanation:
(3m+n)(3m-n)
This is so easy algebraic expression.
Just rewrite as,
[tex](3m) {}^{2} - n {}^{2} [/tex]Simplifying,
[tex]9m {}^{2} - n {}^{2} [/tex][Alternate method is there]
Eisha swims 18 ft from one side of her circular pool to the other, swimming straight through the center. she then swims one time around the entire edge of her swimming pool.
Answer: 74.52 if the question is how far she swims
Step-by-step explanation:
In the following exercises, multiply the binomials. Use any method.
266. (3rs − 7)(3rs − 4)
Answer:
Hence the expression [tex]$$(3rs-7)(3rs-4)=9r^2s^2-33rs+28$$[/tex]
Step-by-step explanation:
Explanation
The given expression is (3rs-7)(3rs-4).We have to multiply the given expression.Multiply the (3rs-7) by -4, multiply the (3rs-7) by 3rs then add like terms.[tex]$$\begin{matrix}{} & {} & {} & {} & 3rs & - & 7 \\ \times & {} & {} & {} & 3rs & - & 4 \\ \end{matrix}$$[/tex]
_________________
[tex]$$\begin{matrix}{} & {} & {} & - & 12rs & + & 28 \\ {} & {} & 9{{r}^2}{{s}^2} & - & 21rs & {} & {} \\ \end{matrix}$$[/tex]
________________
[tex]$$\begin{matrix}{} & {} & 9{{r}^2}{{s}^2} & - & 33rs & + & 28 \\ \end{matrix}$$[/tex]
how to convert whole number as fraction
To convert an integer to a fraction you must choose an expression that does not alter the numerical value. You can do this with multiples of the number, for example, for 100:
100/1 = 200/2 = 300/3 = 400/4 = 100
The numerical value is not altered and the result will always be 100
Another example, for 500:
500 = 500/1 = 1000/2 = 1500/3 = 2000/4
{ Pisces04 }Answer:
Step-by-step explanation:I actually depends on what your solving like if you are solving a question is says solving 16 times a random fraction, you just simply add one under 16. And it will make it 16/1
The black graph is the graph of y= f(x). Choose the equation for the red graph.
here is your answer
mark as brilliant and like pls in my answerif u want complete solution pls message meI need someone to solve this
The value of ? and X are 12 and 24 respectively
Similarity theorem of a triangleA triangles is 2D shape with three sides and angles.
From the given diagram, the ratio of similar sides is equal to a constant as shown;
15/20 = 9+15/20+x
Cross multiply
15/9+15 = 20/20+x
15/24 = 20/20+x
Comparing with the given ratio
? = 24
X = 20+x
Find x
15(20+x) = 480
300 + 15x = 480
15x = 180
x =12
Fro the given expression
x/32 = 9/?
12/32 = 9/?
12 ? = 32 * 9
? = 24
Hence the value of ?and x from the given diagram is 12 and 24 respectively
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PLEASE HELP
Triangle not drawn to scale
Given: measure of angle A = 51 degrees, b = 12, and c = 8. What is the length of a to the nearest tenth?
Select the correct answer.
This system of equations is shown on the graph:
2y - 4x = 6
y = 2x + 3
The equations are both the same with a slope of 2 and y-intercept of 3.
Solution to system of equationA line is the distance between two points. Given the equations below;
2y - 4x = 6
y = 2x + 3
___________
y - 2x = 3
y = 2x + 3
The equations are both the same with a slope of 2 and y-intercept of 3. The graph of the equation is plotted below.
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Use the properties of 30-60-90 and 45-45-90 triangles to solve for x in each of the problems below. Then decode the secret message by matching the answer with the corresponding letter/symbol from the exercises.
The trigonometric function gives the ratio of different sides of a right-angle triangle. The given problems can be solved as given below.
What are Trigonometric functions?The trigonometric function gives the ratio of different sides of a right-angle triangle.
[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}\\\\\\Cosec \theta=\dfrac{Hypotenuse}{Perpendicular}\\\\\\Sec \theta=\dfrac{Hypotenuse}{Base}\\\\\\Cot \theta=\dfrac{Base}{Perpendicular}\\\\\\[/tex]
where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.
1st.) x = 5 /Sin(30°)
x = 10
!) sin(45°) = 4/x
x = 4/sin(45°)
x = 4√2
I) Cos(45°) = √3 / x
x = √3 / Cos(45°)
x = √6
E) Tan(60°) = 3√3 / x
x = 3√3 / 3
W) For isosceles right-triangle, the angle made by the legs and the hypotenuse is always 45°.
x = 45°
N) x² + x² = (7√2)²
x = 7
V) Tan(60°) = 7 / x
x = 7√3/3
K) x² + x² = (9)²
x = 9/√2
Y) Sin(60°) = 7√3/x
x = 14
M) Sin(30°) = x/11
x = 11/2
T) Sin(45°) = x/√10
x = √5
A) x + 2x + 90° = 180°
x = 30°
O) Sin(45°) = √2 / x
x = 2
R) Tan(30°) = x / 4
x = 4/√3 = 4√3 / 3
S) Sin(60°) = x / (10/3)
x = 5√3 / 3
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Loralei's dance team wants to purchase new uniforms for their national dance competition. They will get 25% of their total cookie dough sales to add to the money they already raised in the car wash they held. Her team raised $356.00 during their car wash and sold a total of $2,973.00 in cookie dough. How much money will they have in total to spend on new uniforms?
The total money the dance team would have to spend on the new uniforms is $1099.25.
How much money would the dance team have?Percentage can be described as a fraction of an amount expressed as a number out of hundred.
Total amount = (25% of the amount raised at the sale) + amount raised during the car wash
$356+ ( $25% x $2,973) = $1099.25
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The function a(b) relates the area of a trapezoid with a given height of 12 and
one base length of 9 with the length of its other base.
It takes as input the other base value, and returns as output the area of the
trapezoid
a(b)=12
Which equation below represents the inverse function b(a), which takes the
trapezoid's area as input and returns as output the length of the other base?
OA 4(a)-+9
O B. o(a)-4-6
OC (a)-1-9
OD. (a)-+6
Complete the following proof.
Given: SW is diameter of R
m = 30°
Prove: m RTW = 15°
Using the circle theorems, we have proven that m ∠RTW = 15°
Circle theoremsFrom the question, we are to prove that m ∠RTW = 15°
In the given diagram,
measure of arc ST = 30°
∴ m ∠SRT = 30°
m ∠SRT = ∠T + ∠W ( Exterior angle of a triangle equals the sum of the two remote angles)
Also,
∠T = ∠W (Radii of the same circle)
∴ m ∠SRT = ∠T + ∠T
m ∠SRT = 2 × ∠T
30° = 2 × ∠T
∠T = 30° /2
∠T = 15°
∴ m ∠RTW = 15°
Hence, we have proven that m ∠RTW = 15°
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If a line has a slope of -3 and goes through the point (-4, 10), then the equation for the line in slope-intercept form is ______________.
a.)
y = 3x - 26
b.)
y = 3x + 2
c.)
y = -3x - 2
d.)
y = -3x + 26
Answer:
c.) y = -3x - 2
Explanation:
Given following:
slope (m): -3pass point: (-4, 10)Equation:
[tex]\sf y - y_1 = m(x - x_1)[/tex]
[tex]\sf y - 10 = -3(x - (-4))[/tex]
[tex]\sf y - 10 = -3(x + 4)[/tex]
[tex]\sf y = -3x -12 + 10[/tex]
[tex]\sf y = -3x -2[/tex]
3. Try It #3 Write the point-slope form of an equation of a line with a slope of -2 that passes through the point (-2,2). Then rewrite it in the slope-intercept form.
Answer:
Point-slope form of equation given as [tex]$y-2=-2(x+2)$[/tex].
Slope-intercept form of equation is given as [tex]$y=-2 x-2$[/tex].
Step-by-step explanation:
In the question, it is given that the slope of a line is -2 and it passes from (-2,2).
It is asked to write the point-slope form of the equation and rewrite it as slope-intercept form.
To do so, first find the values which are given in the question and put it in the formula of point-slope form. Simplify the equation to rewrite as slope-intercept form.
Step 1 of 2
Passing point of the line is (-2,2).
Hence, [tex]$x_{1}=-2$[/tex] and
[tex]$$y_{1}=2 \text {. }$$[/tex]
Also, the slope of the line is -2.
Hence, m=-2
Substitute the above values in point-slope form of equation given by [tex]$y-y_{1}=m\left(x-x_{1}\right)$[/tex]
[tex]$$\begin{aligned}&y-y_{1}=m\left(x-x_{1}\right) \\&y-2=-2(x-(-2) \\&y-2=-2(x+2)\end{aligned}$$[/tex]
Hence, point-slope form of equation given as y-2=-2(x+2).
Step 2 of 2
Solve y-2=-2(x+2) to write it as slope-intercept form given by y=mx+c.
[tex]$$\begin{aligned}&y-2=-2(x+2) \\&y-2=-2 x-4 \\&y=-2 x-4+2 \\&y=-2 x-2\end{aligned}$$[/tex]
Hence, slope-intercept form of equation is given as y=-2x-2.
The cube of the sum of a number and 3.
The word expression the cube of the sum of a number and 3 can be written as (x + 3)³ or x³ + 9x² + 27x + 27.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
It is given that:
Let x be the number:
The word expression is:
The cube of the sum of a number and 3.
The sum of a number x and 3 is:
x + 3
The cube of the number (x + 3)
= (x + 3)³
After expanding the cube of (a + b)
(a + b)³ = a³ + 3a²b + 3ab² + b³
Similarly,
(x + 3)³ = x³ + 3x²(3) + 3(x)(3)² + (3)³
(x + 3)³ = x³ + 9x² + 27x + 27
Thus, the word expression the cube of the sum of a number and 3 can be written as (x + 3)³ or x³ + 9x² + 27x + 27.
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Can someone help me out and show work please
The function is assigning to each element of one set exactly one element from the other set.
First table represent a function.
Second table not represent a function (for -1 are four different numbers).
Third table represent a function.
Fourth table not represent a function (for -6 are two differen numbers 5 and 9)
(3,3p) and (4,p²+1) has gradient -1 find p
[tex] \frac{p {}^{2} + 1 - 3p }{4 - 3} = -1[/tex]
[tex]p {}^{2} - 3p + 1 = -1[/tex]
[tex]p {}^{2} - 3p +2 = 0[/tex]
[tex](p-2)(p - 1) = 0[/tex]
[tex]p = 2 \: \: \: \: \: p = 1[/tex]
Pls help me with my hw.
I'm having difficulty in adjusting bases.
find x, here e is natural logarithm.
Answer:
See below
Step-by-step explanation:
7 + 15 e^(1-3x) = 10 start by subtracting 7 from both sides
15 e^(1-3x) = 3 now divide both sides by 15
e ^(1-3x) = .2 now take the ln of both sides
1-3x = -1.6094379 subtract 1 from both sides
-3x = = 2.6094379 divide both sides by -3
x = .869813
26) Jenny drove 48 mph for 65 minutes. Which is true? a. Jenny drove exactly 48 miles b. Jenny drove more than 48 miles c. Jenny drove less than 48 miles
Answer:
B- Jenny must have driven more than 48 miles.
Step-by-step explanation:
If Jenny rode for 60 at 48 mph, it would be exactly 48 miles. Though there is only 60 minutes in an hour, and Jenny rode 5 minutes longer than that, her drive being 65 minutes. To find how much she rode, 5 extra minutes into an hour would divide equally into 60, resulting in 12. Divide 48 by 12, and Jenny would have driven 4 miles in the 5 minutes drive after 60 minutes.
(Jenny basically driven 52 miles in 65 minutes).
PLEASE HELP QUICK!!
Question 1: About 80% of the packages on a delivery truck are internet orders. The driver delivered 644 packages that were internet orders. About how many total packages did the driver deliver that day?
Question 2: A librarian estimated that 60% of the books in the local library were fiction. She counted 8556 fiction books. About how many books are in the local library?
The total packages the driver delivered is 805.
The total number of books in the local library is 14,260.
What is the total packages delivered?Percentage can be described as a fraction out of an amount that is usually expressed as a number out of hundred.
Total packages delivered = total number of internet orders / percentage of internet orders
644 / 80%
644 / 0.8 = 805
Total number of books = total number of fiction books / percentage of fiction books
8556 / 60%
8556 / 0.6 = 14,260
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The floor of a moving van is 3 ft off the ground. The ramp into the van is 14.5 feet and makes an angle with the ground. Which of the angle measures below is approximately the angle of elevation made with the angle of the ground and the ramp?
Answer:
SHould be 11.6 degrees
if X+1/x = 4 find x-1/x
2 and 3/4 plus 3 and 2/4
Answer:
6 1/4
Step-by-step explanation:
ad 2 and 3 get 5 ad 3 and 2 get five now u have 5/4 uh oh the 4 is full
take 1 from the 5 over 4 and turn that one into 6 and turn the 4/4 to 1/4
boom 6 1/4
Make sure your answer is in
degrees. You should be able to
find this without a calculator.
-1
12/1/= = [?]°
sin-1
Answer:
210° , 330°
Step-by-step explanation:
using the sides of the 30- 60- 90 triangle
with legs 1, [tex]\sqrt{3}[/tex] and hypotenuse 2 , then
[tex]sin^{-1}[/tex] [tex]\frac{1}{2}[/tex] = 30° ← related acute angle
since [tex]sin^{-1}[/tex] - [tex]\frac{1}{2}[/tex]
then angle is in third / fourth quadrants , then required angles are
180° + 30° = 210° ← in third quadrant
360° - 30° = 330° ← in fourth quadrant
What are the domain and range of f(x)=logx-5
Hello and Good Morning/Afternoon:
Let's take this problem step-by-step:
Let's define some terms:
Domain: the set of inputs in the function (in this case, it is x)Range: the set of all of the possible outputs (in this case, it is y)Let's find the domain:
For log(x),
⇒ the only inputs that are accepted are nonnegative and nonzero
⇒ therefore: Domain is (0, ∞)
Now let's find out the range:
The biggest constraint of the output is log(x)
⇒ however log(x) has a range of (-∞,∞)
⇒ therefore the entire equation's range is
(-∞,∞)
Answer:
Domain: (0,∞)Range: (-∞,∞)Hope that helps!
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Greg walks 1/3 mile in 10 minutes
Answer:
Greg will walk 1 mile in 30 minutes, or 2 miles per hour.
Explanation:
Multiply the ratio of miles to minutes:
1/3 mi : 10 min
1 mi : 30 min
2 mi : 1 hr
Given: x//y
w is a transversal of x and y.
Prove: ∠4 ≅ ∠5
3) Vertical angles are congruent.
4) Corresponding angles tehorem
5) Transitive property of congruence
Let a=3/5 and let b=2/3. Compute a^2b^-3.
Answer: 81/100
Step-by-step explanation:
I don't guarantee you I am right but..
first, solve for the exponents after substituting the numbers in
3/5 x 3/5 is 9/25
since b's exponent is negative, you change the fraction into its reciprocal and then do it with the exponent but positive
2/3^-3 to 3/2^3 and 3/2 x 3/2 is 9/4
then you mutiply both numbers to get 9/4 x 9/25 is 81/100
help me solve this thanks
Answer:
The amount after 6 years is $25,533.34.
Step-by-step explanation:
Use the formula f(t)=P(1+b)^t.
Plug in the information.
f(6)=18000(1+0.06)^6
Plug in 18000(1.06)^6 into calculator.
25,533.344020608.
Round to 2 decimal places.
25,533.34
The amount after 6 years is $25,533.34.
Hope this helps!
If not, I am sorry.
Which property was applied to create this equivalent expression? 7 x (5 6 x) right-arrow (7 x 5) 6 x the commutative property only the associative property only the distributive property only both the commutative property and the associative property
Step-by-step explanation:
7×5×6×x
7×5×6×392
210×392
82320
The option (B) is correct. Associative property was applied to create the given expression.
Given expression is 7x+(5+6x) rightarrow (7x+5)+6x.
Firstly, check the given expression by commutative property.
The commutative property of addition is a+b=b+a and the commutative property of multiplication is a×b=b×a.
The commutative property didn't satisfy the given expression.
Now, check the given expression by associative property.
The associative property of addition is (a+b)+c=a+(b+c) and the commutative property of multiplication is (a×b)×c=a×(b×c).
The associative property of addition satisfy the given expression.
Further, check the given expression by distributive property.
The distributive property is a×(b+c)=ab+bc.
The distributive property didn't satisfy the given expression.
Hence, the given expression 7x+(5+6x) rightarrow (7x+5)+5x s created by the associative property.
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NEED HELP ASAP
what is the mode of the data
(A) 3
(B) no mode
(C) 17
(D) 40
QUESTION #2
what is the mean of the data
(A) 17
(B) 19.5
(C) 22
(D) 19
use the picture for both of these questions