Answer:
Solution : (15, - 11)
Step-by-step explanation:
We want to solve this problem using a matrix, so it would be wise to apply Gaussian elimination. Doing so we can start by writing out the matrix of the coefficients, and the solutions ( - 5 and - 2 ) --- ( 1 )
[tex]\begin{bmatrix}-4&-5&|&-5\\ -6&-8&|&-2\end{bmatrix}[/tex]
Now let's begin by canceling the leading coefficient in each row, reaching row echelon form, as we desire --- ( 2 )
Row Echelon Form :
[tex]\begin{pmatrix}1\:&\:\cdots \:&\:b\:\\ 0\:&\ddots \:&\:\vdots \\ 0\:&\:0\:&\:1\end{pmatrix}[/tex]
Step # 1 : Swap the first and second matrix rows,
[tex]\begin{pmatrix}-6&-8&-2\\ -4&-5&-5\end{pmatrix}[/tex]
Step # 2 : Cancel leading coefficient in row 2 through [tex]R_2\:\leftarrow \:R_2-\frac{2}{3}\cdot \:R_1[/tex],
[tex]\begin{pmatrix}-6&-8&-2\\ 0&\frac{1}{3}&-\frac{11}{3}\end{pmatrix}[/tex]
Now we can continue canceling the leading coefficient in each row, and finally reach the following matrix.
[tex]\begin{bmatrix}1&0&|&15\\ 0&1&|&-11\end{bmatrix}[/tex]
As you can see our solution is x = 15, y = - 11 or (15, - 11).
(20 points)Solve the equation cos x = sin (x + 22)
Answer:
[tex]\bold{x = 34^\circ}[/tex]
Step-by-step explanation:
Given:
[tex]cos x = sin (x + 22^\circ)[/tex]
To solve:
The given equation.
Solution:
First of all, let us consider an important property of sine and cosine.
[tex]sin(90^\circ-\theta )=cos\theta[/tex]
OR
[tex]cos(90^\circ-\theta )=sin\theta[/tex]
We can apply above property to solve for [tex]x[/tex] as per given equation.
[tex]cos x = sin (x + 22^\circ)[/tex]
Changing [tex]cosx[/tex] to sine form:
[tex]cosx=sin(90^\circ-x)[/tex]
[tex]cosx=sin(90^\circ-x) = sin(x+22^\circ)[/tex]
[tex]\therefore 90^\circ-x=x+22^\circ\\\Rightarrow 90^\circ-22^\circ=x+x\\\Rightarrow 2x=68^\circ\\\Rightarrow \bold{x = 34^\circ}[/tex]
So, solution to the equation [tex]cos x = sin (x + 22^\circ)[/tex] is:
[tex]\bold{x = 34^\circ}[/tex]
Simplify. (3 + 2) + (4 + 3) =
Answer:
5 + 7
Step-by-step explanation:
3 + 2 = 5, 4 + 3 = 7
Answer:
Simplified expression: 5 + 7
Answer: 12
Step-by-step explanation:
3 + 2 = 54 + 3 = 75 + 7 = 12HELP PLEASE.... Find the volume of this triangular pyramid Volume = 1/3(Area of Base)(Height) Enter only the numerical part of your answer in cubic units.
Answer:
[tex]96ft^{2}[/tex]
Step-by-step explanation:
Step 1: Find the area of the base
[tex]\frac{bh}{2} =\frac{(8)(6)}{2}=\frac{48}{2}=24ft^{2}[/tex]
Step 2: Find volume
[tex]=\frac{1}{3}(24)(12) \\=\frac{1}{3}(288)\\=96ft^{3}[/tex]
Which lines are parallel? Justify your answer.
Lines a and b are parallel because their corresponding angles are congruent.
Lines a and b are parallel because their same side exterior angles are congruent.
Lines e and f are parallel because their corresponding angles are congruent.
Lines e and f are parallel because their same side exterior angles are supplementary.
Answer:
Lines a and b are parallel because their corresponding angles are congruent
Step-by-step explanation:
The corresponding angle postulate states that Two lines are said to be parallel if when cut by a transversal, their corresponding angles are congruent.
Therefore given line a and line b which is cut by transversal e, both corresponding angles are equal to 110 (congruent), therefore according to the corresponding angle postulate, we can say that line a and line b are parallel to each other.
Answer: A
Step-by-step explanation:
Simplify -7x - (15y) + 3x - 2y
Answer:
Step-by-step explanation:
combine like terms
-7x + 3x - 15y - 2y
-4x - 17y
Mrs.Vega brought a new aquarium for her turtles. How much space will the turtles have in the aquarium if the length is 5.2 ft, the width is 1.8 ft and the height is 2 ft?
Answer:
18.72 cubic feet
Step-by-step explanation:
Volume of the aquarium = lwh
l = 5.2 ft,w = 1.8 fth = 2 ftV = 5.2*1.8*2 = 18.72 cubic feet
help me please!!!i rlly need it!
Answer:
7.5
Step-by-step explanation:
How long does it take a car to travel 1 mile if its average speed is 40 mph? The answer is 1/40 of an hour or 1.5 minutes. multiply this by 5
Answer:
0.1 hours to the nearest tenth (0.125 hours exact)
Step-by-step explanation:
For this problem, we simply need to do a conversion to find the length of time.
We are given the rate 40 miles per hour, and the distance of 5 miles. We simply need to know the amount of time.
5 miles * (1 hour per 40 miles) = 1 hour / 8
Note, the distance unit cancels out.
So, to travel 5 miles it will take 1/8 of an hour.
1/8 as a decimal is equal to 0.125. The answer rounded to the nearest tenth would be 0.1 hours, since the 2 rounds down.
Cheers.
Find the surface area. Leave your answers in terms of π. A. 32.5π ft² B. 105π ft² C. 90π ft² D. 65π ft²
The bottom face is a circle of area pi*r^2 = pi*5^2 = 25pi square feet
The lateral surface area is pi*r*L = pi*5*13 = 65pi square feet
Those two areas combine to 25pi+65pi = 90pi square feet
Answer: Choice CThe surface area of the cone is 65π square ft or 65π ft² option (D) 65π ft² is correct if the radius of the cone base is 5 ft and the slant height is 13 ft.
What is a cone?It is defined as a three-dimensional shape in which the base is a circular shape and the diameter of the circle decreases as we move from the circular base to the vertex.
[tex]\rm V=\pi r^2\dfrac{h}{3}[/tex]
We have a cone shown in the picture.
The radius of the cone r = 5 ft
The slant height l = 13 ft
As we know, the lateral surface is given by:
S = πrl
Here,
S is the surface area
r is the radius of the cone base
l is the slant height.
S = π(5)(13)
S = 65π square ft
Thus, the surface area of the cone is 65π square ft or 65π ft² option (D) 65π ft² is correct if the radius of the cone base is 5 ft and the slant height is 13 ft.
Learn more about the cone here:
brainly.com/question/16394302
#SPJ5
There is a triangle called XYZ the measurements are 12m 15m and 9m. What 2 kinds of a triangle is that? This would be helpful if someone answered this! UwU Tanks
Answer:
Right angle triangle
Step-by-step explanation:
12m
15m
9m
Assume the Longest side=15m
Using Pythagoras theorem
c^2=a^2 + b^2
Where,
c=hypotenuse
a=adjacent
b=opposite
Let a=9m
b=12m
c^2=a^2 + b^2
=9^2 + 12^2
=81 + 144
c^2=225
c=√225
=15m
Therefore, the triangle XYZ is a right angle triangle
What’s is the factor?
125 +27y^3
Answer:
[tex](3y+5)(9y^{2} -15y+25)[/tex]
Step-by-step explanation:
PLEASE help me. I am stuck on this question for a long time.
Answer:4th option
Step-by-step explanation:
Answer: D. Set B has a higher mean and a Higher standard deviation than Set A
Step-by-step explanation:
Set A and Set B has the same amount of data and all are identical except the maximum. In this scenario, the larger the numbers, the higher the mean. Since the maximum of Set B is greater that Set A, Set B has a higher, mean.
--------------------------------------------
The higher the standard deviation, the larger the gap between data sets. Since Set B has a larger maximum, this means it is further away from other data comparing to Set A, thus, Set B has a higher standard deviation
A positive number is 5 times another number, if 21 is added to both numbers, then one of the new numbers becomes twice the other new number, what are the numbers?
x - the first number,
y - the second number
We have:
[tex]\begin{cases}y=5x\\y+21=2(x+21)\end{cases}\\\\\\\begin{cases}y=5x\\y+21=2x+42\end{cases}\\\\\\\begin{cases}y=5x\\5x+21=2x+42\end{cases}\\\\\\\begin{cases}y=5x\\3x=21\quad|:3\end{cases}\\\\\\\begin{cases}y=5x\\\boxed{x=7}\end{cases}\\\\y=5x\\\\y=5\cdot7\\\\\boxed{y=35}[/tex]
So answer is 7 and 35.
Four penguins would satisfy a polar bear's appetite for 12 hours. A polar bear has a
territory of 10 square miles. There are 1000 penguins per square mile. What percent
of penguins (number eaten divided 1000 times 100) in the 10 square miles will a wild
polar bear eat?
Answer:
0.04%
Step-by-step explanation:
If there are 1000 penguins per square miles, the total number of penguins in a 10 square miles will be 1000*10 = 10,000 penguins/10square miles
Since a polar bear has a territory of 10 square miles, and can only eat four penguins within the 10square miles;
Percentage of penguins that the polar bear can eat will be expressed as;
number of penguin eaten per 10square miles/total number of penguin per 10square miles * 100
Percentage of penguins that the polar bear can eat = 4/10,000 * 100%
Percentage of penguins that the polar bear can eat = 4/100%
Hence, the percentage of penguins that the polar bear can eat in the 10 square miles is 0.04%
In triangle ABC we have angle C = 3 times angle A, a=27 and c=48 What is b? Note: a is the side length opposite A etc. please help
Answer:
35
Step-by-step explanation:
The law of sines tells us ...
sin(C)/c = sin(A)/a
a·sin(3A) = c·sin(A)
Using the identity sin(3x) = 3cos(x)·sin(x) -sin(x)^3 and sin(x)^2 +cos(x)^2 = 1, we can simplify this to ...
sin(A)(4cos(A)^2 -1) = (c/a)sin(A)
4cos(A)^2 = c/a +1 = (48+27)/27 = 75/27 = 25/9
cos(A)^2 = 25/36
cos(A) = 5/6
__
Now, the angle B will be the difference between 180° and the sum of the other two angles:
B = 180° -A -3A = 180° -4A
Using appropriate trig identities, we can write ...
sin(B) = 4cos(A)^3sin(A) -4sin(A)^3cos(A)
= 4sin(A)cos(A)(cos(A)^2 -sin(A)^2)
= 4sin(A)cos(A)(2cos(A)^2 -1)
Filling in our value for cos(A), this becomes ...
sin(B) = 4sin(A)(5/6)(2(5/6)^2-1) = sin(A)(35/27)
__
The law of sines tells us ...
b/sin(B) = a/sin(A)
b = a·sin(B)/sin(A) = 27(35/27)sin(A)/sin(A) = 35
The length of side b is 35 units.
Liz is using the distributive property to evaluate the expression 27 (36) by using friendlier numbers. Her work is shown below. Liz’s Work 27(36) Step 1 27 (3 + 12) Step 2 27 (3) + 27 (12) Step 3 81 + 324 Step 4 405 What was the first error that Liz made? PLZ HELP ME I DONT UNDERSTAND HELP ME PLZ!!!!!
Answer:
In step 1
Step-by-step explanation:
She has [tex]27(36)=27(3+12)[/tex]
this mean that 36=3+12
that's her mistake
Answer:
step 1
Step-by-step explanation:
Need Help ASAP algebra 2
Answer:
a = √10
Step-by-step explanation:
a² + b² = c²
a² + 9² = (√91)²
a² + 81 = 91
a² = 10
a = √10
hope this helps :)
Answer:
square root of 10
Step-by-step explanation:
a^2 + b^2 = c^2
=> a^2 + 9^2 = square root of 91^2
=> a^2 + 81 = 91
=> a^2 = 91 - 81
=> a^2 = 10
=> a = square root of 10
(3 x 105 ) x (2 x 103 )
Use the rules for division and multiplication to complete the questions below. Convert regular numbers to scientific notation to determine the answer.
Answer:
64,890
Step-by-step explanation:
105×3 =315
103×2= 206
315×206= 64,890
Answer:
6.489× 10⁴
Step-by-step explanation:
(3×105)×(2×103)
315× 206
64,890
6.489×10⁴
The mass of the part of a metal rod that lies between its left end and a point x meters to the right is 3x^2 kg. Find the linear density when is 1 m, Where is the density the highest? The lowest?
Answer:
6 kg/m
Step-by-step explanation:
mass m = 3x^2.
rho ρ= dm/dx =6x
ρ(1) =6 Kg/m
linear density is the derivative of mass (m) with respect to position(x)
that is how fast is the mass changing at that position.
A farmer has a field in the shape of a triangle. The farmer has asked the manufacturing class at your school to build a metal fence for his farm. From one vertex, it is 435 m to the second vertex and 656 m to the third vertex. The angle between the lines of sight to the second and third vertices is 49°. Calculate how much fencing he would need to enclose his entire field.
Answer:
Fencing required = 1586 m
Step-by-step explanation:
The given statements can be thought of a triangle [tex]\triangle ABC[/tex] as shown in the diagram attached.
A be the 1st vertex, B be the 2nd vertex and C be the 3rd vertex.
Distance between 1st and 2nd vertex, AB = 435 m
Distance between 2nd and 3rd vertex, AC = 656 m
[tex]\angle A =49^\circ[/tex]
To find:
Fencing required for the triangular field.
Solution:
Here, we know two sides of a triangle and the angle between them.
To find the fencing or perimeter of the triangle, we need the third side.
Let us use Cosine Rule to find the third side.
Formula for cosine rule:
[tex]cos A = \dfrac{b^{2}+c^{2}-a^{2}}{2bc}[/tex]
Where
a is the side opposite to [tex]\angle A[/tex]
b is the side opposite to [tex]\angle B[/tex]
c is the side opposite to [tex]\angle C[/tex]
[tex]\Rightarrow cos 49^\circ = \dfrac{656^{2}+435^{2}-BC^{2}}{2\times 435\times 656}\\\Rightarrow BC^2 = 430336+189225-2 (435)(656)cos49^\circ\\\Rightarrow BC^2 = 430336+189225-570720\times cos49^\circ\\\Rightarrow BC^2 =619561-570720\times cos49^\circ\\\Rightarrow BC \approx 495\ m[/tex]
Perimeter of the triangle = Sum of three sides = AB + BC + AC
Perimeter of the triangle = 435 + 495 + 656 = 1586 m
Fencing required = 1586 m
evaluate the following expression x^2+x when x=5
Answer:
30 will be the ans to this question
Step-by-step explanation:
5^2 +5
=25+5
=30
For all x, 5-3(x-4)=
Simplify
Let's simplify step-by-step.
x(5)−3(x−4)
Distribute:
=x(5)+(−3)(x)+(−3)(−4)
=5x+−3x+12
Combine Like Terms:
=5x+−3x+12
=(5x+−3x)+(12)
=2x+12
Answer:
=2x+12
Solve the inequality T > L plus D all divided by B for D.
Answer:
T > (L + D)/B...multiply by B
TB > L + D ... subtract L
TB - L > D
can you plz mark me brainiest ;<
tank chu hope this helps TwT
Given T(x, y)=(x+2, y+5), state the translation S(x, y) that would yield the identity transformation, I=S(T(x,y)).
Answer:
The translation S(x, y) for the identity transformation, I = ST(x, y) is S(x, y) = ( x - 2, y + 5)
Step-by-step explanation:
Identity transformation is the transformation that results in the copying of the source data to the destination data without change.
Given that T(x, y) = (x + 2, y + 5)
The identity transformation I = S(T(x, y)) that would allow a data (x, y) to remain the same at the destination after the transformation T(x, y) is given as follows;
Where S(x, y) = ( x - 2, y + 5), we have;
S(T(x, y)) = S(x + 2, y + 5) = (x + 2 - 2, y + 5 - 5) = (x, y)
Therefore the translation S(x, y) that would yield the identity transformation, I = ST(x, y) is S(x, y) = ( x - 2, y + 5).
How many feet per second is 1 mile/hour
Answer:
1.47 is the answer
Answer:
1.4666667 rounded off to 1.47
Step-by-step explanation:
Use the quadratic formula to solve the equation 3x^2+ 7x - 11 =0 You must show all your working and give your answers correct to 2 decimal places.
Answer:
Step-by-step explanation:
Hello, please consider the following.
[tex]3x^2+ 7x - 11 =0\\\\\Delta=b^2-4ac=7^2-4*3*(-11)=49+132=181\\\\x_1=\dfrac{-b-\sqrt{\Delta}}{2a}=\dfrac{-7-\sqrt{181}}{6}=-3.40894...\\\\x_2=\dfrac{-b+\sqrt{\Delta}}{2a}=\dfrac{-7+\sqrt{181}}{6}=1.075604...[/tex]
So, it gives -3.41 and 1.08
Thank you.
what is the product of (-1.5)(0.8)
Answer:
-1.2 Hope this helps!
Step-by-step explanation:
find the difference 3 d and 7 d
Answer:
[tex]-4d[/tex]
Step-by-step explanation:
We can subtract a term from another if they have the same variable. Both [tex]3d[/tex] and [tex]7d[/tex] have the variable [tex]d[/tex], so we can subtract them.
When subtracting these terms, we subtract the coefficients and keep the variable.
So:
[tex]3d - 7d = 3-7(d) = -4d[/tex]
Hope this helped!
Answer:
-4d
Step-by-step explanation:
3d - 7d
=> 3 x D - 7 x D
=> (3 - 7)(D)
=> -4 x D
=> -4d
A news site offers a subscription that costs $28.50 for 6 months. What is the
unit price per month? Show your work.
Answer:
The correct answer is $4.75/month.
Step-by-step explanation:
To find the unit price per month, or the amount that of the subscription that will be paid each month, we must divide the total price ($28.50) by the number of months covered (6 months).
$28.50/6 = $4.75
Therefore, the unit price per month is $4.75/month.
Hope this helps!
4(x + 4) = 4x + 16
One Solution No solutions or infinite number of solutions
Answer:
Infinite Number of Solutions
Step-by-step explanation:
Since 4*x= 4x
and 4*4= 16
its 4x+16
which is 4x+16=4x+16
Since there are the same, and both equal each other, there are an infinite number of solutions.
Answer:
infinite number of solutions
Step-by-step explanation:
4(x + 4) = 4x + 16
Distribute on the left side.
4x + 16 = 4x + 16
Subtract 16 from both sides.
4x = 4x
Divide both sides by 4.
x = x
x = x is a true equation for every value of x.
Answer: infinite number of solutions
I think of a number, multiply it by 4, add 1 and square the result
Step-by-step explanation:
Let the number be x
The number is multiplied by 4
That's
4 × x = 4x
One is added to it
= 4x + 1
The whole result is squared
That's
(4x + 1)²Hope this helps you
Answer:
[tex]\huge \boxed{(4x+1)^2 }[/tex]
Step-by-step explanation:
[tex]\sf Let \ the \ number \ be \ x.[/tex]
[tex]\sf x \ is \ multiplied \ by \ 4.[/tex]
[tex]x \times 4[/tex]
[tex]\sf 1 \ is \ added.[/tex]
[tex]4x+1[/tex]
[tex]\sf The \ result \ is \ squared.[/tex]
[tex](4x+1)^2[/tex]