Answer: The system of equations has no solutions.
Step-by-step explanation:
Identify the equation as:
[tex]x + 2y - z=3[/tex] [Equation 1]
[tex]2x -y + 2z=6[/tex] [Equation 2]
[tex]x - 3y + 3z=4[/tex] [Equation 3]
Multiply [Equation 1] by -2 and add this to [Equation 2] :
[tex](-2)(x + 2y - z)=3(-2)[/tex]
[tex]\left \{ {{-2x - 4y +2z=-6} \atop {2x -y + 2z=6}} \right.\\ ..........................\\-5y+4z=0[/tex]
Find another equation of two variables: Multiply [Equation 3] by -2 and add this to [Equation 2]:
[tex](-2)(x - 3y + 3z)=4(-2)[/tex]
[tex]\left \{ {{2x -y + 2z=6} \atop {-2x +6y -6z=-8}} \right.\\........................\\5y-4z=-2[/tex]
Then you get this new system of equations. When you add them, you get:
[tex]\left \{ {{-5y+4z=0} \atop {5y-4z=-2}} \right.\\..................\\0=-2[/tex]
Since the obtained is not possible, the system of equations has no solutions.
The solution to the system of equations x + 2y - z = 3, 2x - y + 2z = 6, and x - 3y + 3z = 4 is (-1, 1, 2) utilizing substitution method.
Explanation:The subject of this question is to find a solution to the system of linear equations. We can solve this system by methods of either substitution, elimination or matrix - but let's use substitution. First, let's isolate x in the first equation: x = 3 - 2y + z. Then we substitute x into the second and the third equation:
2(3 - 2y + z) − y + 2z = 6(3 - 2y + z) − 3y + 3z = 4
After simplifying these equations, we find y = 1 and z = 2. Plugging these back into x = 3 - 2y + z, we get x = -1. Therefore, the solution to the system is (-1, 1, 2).
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An Internet and cable-television supplier surveyed a random sample of their customers. The results are shown in the table.
Which statement about the two-way frequency table is true?
Answer:
Step-by-step explanation:
the survey represents quantative data
The statement which is true about the frequency is About one-fourth of the cable-television customers are not satisfied.
The correct option is (D).
What is frequency?Frequency refers to the number of times an event or a value occurs. A frequency table is a table that lists items and shows the number of times the items occur.
The first statement doesn't satisfy.
The second statement is wrong because the greatest customers of cable television are not satisfied.
The third statement is also wrong because the customers surveyed for the cable television is less than half the total customers surveyed
The fourth statement is correct because,
=[tex]\frac{1}{4}[/tex] * 1109
= 277.25 which is very close to 285.
Hence, About one-fourth of the cable-television customers are not satisfied.
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Which equation represent the line show on the graph
[tex]f(x)=2x\Rightarrow y=2x[/tex]
Hope this helps.
Brainly would help me.
Answer:
y=2x
Step-by-step explanation:
the slope-intercept formula is y=mx+b, where m is the slope(rise over run) and b is the y-intercept, which then becomes y=2(2/1 because it goes up by 2 and right by 1)x+0, or simply y=2x, hope this helps! :D
Estimate the square root to the nearest integer.
2. 39
A : 5
B: 8
C: 6
D: 7
Answer:
C
Step-by-step explanation:
The square root of 39 is ~6.25 so 6 is closest
Answer:
2
Step-by-step explanation:
Think: 2.39 is sandwiched between the perfect squares 1 and 4.
The difference between 1 and 4 is 3. From 1 to 2.39 is a step of 1.39; from 2.39 to 4 is a step of 1.61. Therefore, 2.39 is closer to 1 than to 4, and we estimate 2.39 to be 2 (to the nearest integer).
solve the equation x + 3 x + 5 equal 21
Answer:
x = 4
Step-by-step explanation:
Combining like terms, we get 4x = 16, and so x = 4.
Answer: The answer is 4.
Step-by-step explanation: The way I got my answer was by isolating the variable by dividing each side by factors that don't contain the variable. I also have a website that you can use to help you! (if you want it, just ask me and I can provide it to you!)
I hope this info helps you! :D
Not sure what to do here
neither tbh lol and yea ok
How many subsets can be made from a set of six elements including the null set and the set itself
A) 84
B) 64
C) 32
Answer:
c. 32
Step-by-step explanation:
You are trying to dunk a basketball. You need to jump 2.5 feet. In the air to dunk the ball. The height that your feet are above the ground is given by the function h (t)=-16ft+12. What is the maximum height your feet will be above the ground? Will you be able to dunk the basketball
Answer:
1)he maximum height your feet will be above the ground is 12
2)Will you be able to dunk the ball= yes
Step-by-step explanation:
Given:
In order to dunk the basket ball, height needed to jump= 2.5 feet
The height that your feet need to be of the ground is given by the function h(t)= -16t^2+12
1) the maximum height your feet will be above the ground=?
Given function of height,h(x)=-16t^2+12
finding maximum of the above function
The maximum of any function written in form of ax^2+bx+c is given by
max= c - (b2 / 4a)
Putting values c=12, b=0 and a=16, we get
max= 12-(0^2/4(-16))
= 12 -0
=12 feet
he maximum height your feet will be above the ground is 12 feet.
2) Will you be able to dunk the ball=?
As the maximum height the feet will be above the ground is 12 feet which is greater than the height needed to jump in the air to dunk the ball 2.5 feet i.e.
12>2.25
hence yes you will not be able to dunk the ball !
A particular computer takes 78 nanoseconds to carry out seven sums and ten products. Another computer takes 55 nanoseconds to carry out 4 sums and eight products. How long does the computer take to carry out one sum? One product?
Answer:
The time that the computer take to carry out one sum is 4.63 nanoseconds and the time that the computer take to carry out one product is 4.56 nanoseconds
Step-by-step explanation:
Let
x----> the time that the computer take to carry out one sum
y----> the time that the computer take to carry out one product
we know that
7x+10y=78 ------> equation A
4x+8y=55 -----> equation B
Solve the system of equations by graphing
Remember that the solution of the system of equations is the intersection point both graphs
The solution is the point (4.625,4.563)
see the attached figure
therefore
The time that the computer take to carry out one sum is 4.63 nanoseconds
The time that the computer take to carry out one product is 4.56 nanoseconds
In Galveston, Texas there is a beautiful attraction called the Rainforest Pyramid which contains man plants and a variety of rainforest animals. The builders needed to calculate the volume of the squar pyramid to plan the climate control system. The length of the base is approximately 69.6 yards and the height is 33 yards. Which of the following is the closest estimate of the volume?
Answer:
53,286 yards
Step-by-step explanation:
69.6x69.6x33/3
The volume of the square pyramid is [tex]53,286[/tex] yards.
What is volume of the square pyramid?
The volume of a square pyramid is one-third of the product of the area of the base and the height of the pyramid.
[tex]V=\frac{1}{3} b^{2} h[/tex]
From the given,
The length of the base [tex]b[/tex] is [tex]$69.6\,\text{yards}$[/tex].
Height [tex]h[/tex] is, [tex]$33\,\text{yards}$[/tex].
We have to find [tex]V[/tex].
So,
[tex]$V=\frac{1}{3}{{\left( 69.6 \right)}^{2}}\cdot 33$[/tex]
[tex]$\therefore V=53286$[/tex]
Hence, the volume of the square pyramid is [tex]53,286[/tex] yards.
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What is the surface area using integrals of these two lines. Y=10-x^2 and Y=x^2+2 from the bounds x=2 and x=-2.
Check the picture below.
[tex]\bf \displaystyle\int\limits_{-2}^{2}~[\stackrel{\textit{above function}}{(10-x^2)}~~-~~\stackrel{\textit{below function}}{(x^2+2)}]dx\implies \int\limits_{-2}^{2}~(10-x^2-x^2-2)dx \\\\\\ \displaystyle\int\limits_{-2}^{2}~(8-2x^2)dx\implies \left. 8x\cfrac{}{} \right]_{-2}^{2}-\left. \cfrac{2x^3}{3} \right]_{-2}^{2} \\\\\\ ([16]-[-16])~~-~~\left( \left[ \cfrac{16}{3} \right]-\left[ -\cfrac{16}{3} \right]\right)\implies (32)~~-~~\left( \cfrac{32}{3} \right) \\\\\\ \cfrac{64}{3}\implies 21\frac{1}{3}[/tex]
Find the surface area of the following figure
Answer:
510.4 ft²Step-by-step explanation:
We have:
two trapezoids with bases 15ft and 7ft and height 5ft.
four rectangles 5ft × 11ft, 15ft × 11ft, 9.4ft × 11ft and 7ft × 11ft.
The formula of an area of a trapezoid:
[tex]A_t=\dfrac{b_1+b_2}{2}\cdot h[/tex]
b₁, b₂ - bases
h - height
Substitute:
[tex]A_t=\dfrac{15+7}{2}\cdot5=\dfrac{22}{2}\cdot5=(11)(5)=55\ ft^2[/tex]
The formula of an area of a rectangle:
[tex]A_r=lw[/tex]
l - length
w - width
The dimensions of rectangle l × w
Subtitute:
[tex]A_1=(5)(11)=55\ ft^2\\\\A_2=(15)(11)=165\ ft^2\\\\A_3=(9.4)(11)=103.4\ ft^2\\\\A_4=(7)(11)=77\ ft^2[/tex]
The surface area of the figure:
[tex]S.A.=2A_t+A_1+A_2+A_3+A_4\\\\S.A.=2(55)+55+165+103.4+77=510.4\ ft^2[/text]
Volume with cubes with fraction lengths
Answer:
[tex]\large\boxed{24\ cubes}[/tex]
Step-by-step explanation:
[tex]\bold{METHOD\ 1}\\\\\text{Calculate the volume of a prism:}\\\\V_{p}=(1)(2)\left(\dfrac{3}{2}\right)=3\ cm^3\\\\\text{Calculate the volume of a cube:}\\\\V_c=\left(\dfrac{1}{2}\right)^3=\dfrac{1}{8}\ cm^3\\\\\text{Calculate how many times the volume of the prism is greater}\\\text{than the volume of the cube:}\\\\\dfrac{V_p}{V_c}=\dfrac{3}{\frac{1}{8}}=3\cdot8=24[/tex]
[tex]\bold{METHOD\ 2}\\\\1cm:\dfrac{1}{2}m=1\cdot2=2\\\\2cm:\dfrac{1}{2}cm=2\cdot2=4\\\\\dfrac{3}{2}cm:\dfrac{1}{2}cm=\dfrac{3}{2}\cdot\dfrac{2}{1}=3\\\\2\cdot4\cdot3=24\ (cubes)[/tex]
PLEASE HELP!!!!!!! Solve for x. Use the completing the square method. 5x2−2x−10=0 Round decimals to the nearest tenth.
Answer:
0
Step-by-step explanation:
0 times anything is zero
ANSWER
x=-1.2 or x=1.6
EXPLANATION
The given equation is:
[tex] 5{x}^{2} - 2x - 10 = 0[/tex] Group and combine the constant terms:
[tex]5{x}^{2} - 2x = 10 [/tex]
Divide through by 5
[tex]{x}^{2} - \frac{2}{5} x = 2[/tex]
Add the square of the coefficient of x to both sides:
[tex]{x}^{2} - \frac{2}{5} x + \frac{1}{25} = 2 + \frac{1}{25} [/tex]
The left hand side is now a perfect square
[tex]( {x - \frac{1}{5} })^{2} = \frac{51}{25} [/tex]
Take square root:
[tex]{x - \frac{1}{5} }=\pm \sqrt{\frac{51}{25}} [/tex]
[tex]{x = \frac{1}{5} }\pm \frac{ \sqrt{51} }{5}[/tex]
[tex]{x = \frac{1}{5} } - \frac{ \sqrt{51} }{5} \: or \: \: {x = \frac{1}{5} } + \frac{ \sqrt{51} }{5}[/tex]
x=-1.2 or x=1.6
Solve this problem using the substitution method 2y-1/2y=2
Answer:
y=3/2and x =2
Step-by-step explanation:
Find the value of m23-m21.
Answer:
M2
Step-by-step explanation:
duh
PLEASE HELP ME NOW!!
Answer:
[tex]x=4+-2\sqrt{7}[/tex]
Step-by-step explanation:
To solve, we need to take square root of both sides first:
[tex](x-4)^2=28\\\sqrt{(x-4)^2} =+-\sqrt{28} \\x-4=+-\sqrt{28}[/tex]
Now we use the property of radical shown below to simplify square root of 28:
Property: [tex]\sqrt{x*y}=\sqrt{x} \sqrt{y}[/tex]
Now, we have:
[tex]x-4=+-\sqrt{28}\\x-4=+-\sqrt{4*7}\\x-4=+-\sqrt{4}\sqrt{7}\\x-4=+-2\sqrt{7}[/tex]
Now we take 4 to the other side and isolate x:
[tex]x-4=+-2\sqrt{7} \\x=4+-2\sqrt{7}[/tex]
first answer choice is right.
The answer is:
The correct answer is the first option.
[tex](x-4)^{2}=4+-2\sqrt{7}[/tex]
Why?To solve the problem, we must remember the following square root property:
[tex]\sqrt{ab}=\sqrt{a}\sqrt{b}[/tex]
So,
We are given the expression:
[tex](x-4)^{2}=28[/tex]
Now, isolating we have:
First, applying square root to both sides of the equation in order to simplify the quadratic term, we have:
[tex]\sqrt{(x-4)^{2} }=\sqrt{28}\\(x-4)=\sqrt{4*7}\\\\x=4+-(\sqrt{4}*\sqrt{7})\\\\x=4+-2\sqrt{7}[/tex]
Hence, the correct answer is the first option.
[tex](x-4)^{2}=4+-2\sqrt{7}[/tex]
Have a nice day!
Solve and show your work for each question.
What is 0. 45 expressed as a fraction in simplest form?
What is 0.45 expressed as a fraction in simplest form?
What is 0.45 expressed as a fraction in simplest form?
SHOW YOUR WORK
Answer:
9/20
Step-by-step explanation:
You set the fraction up at first as 45/100. Then you know that 5 goes into each so you divide by 5 [tex]\frac{45}{100} /5[/tex]
45/5=9
100/5=20
You get 9/20, and this is in simplest form.
0.45/1
Then multiply top and bottom by 100.
45/100
Then simplify!
45/100 divide top and bottom by 5.
9/20
The difference between the two numbers is 48. The ratio of the two number is 7:3, what are the two numbers?
Answer:
84 and 36
Step-by-step explanation:
The ratio of two numbers is 7:3.
We don't know what the numbers are, but since their ratio is 7:3, we can let the numbers be 7x and 3x. Notice that the ratio between 7x and 3x is 7x/3x = 7/3, so we still have the same ratio, 7:3.
The difference between the numbers is 48.
7x - 3x = 48
4x = 48
x = 12
7x = 7(12) = 84
3x = 3(12) = 36
The numbers are 84 and 36.
Check:
7/3 = 2.333...
84/36 = 2.333...
84 and 36 are int he same 7:3 ratio as 7:3.
84 - 36 = 48
The difference between 84 and 36 is 48 like the problem states.
This shows our answer, 84 and 36, is correct.
Hi, hope you’re having a good day today!!!
Answer:
84:36
(The explanation is really really long, so you may want to skip it, unless this is a test or you want a better understanding then, yeah)
So first, you have 7:3
Then, you have to multiply both by the same number to get an equal ratio to 7:3,
Let’s try 7*10=70 and 3*10=30 70-30=40, so you know that the answer is close,
Then, let’s try 7*11=77 and 3*11=33, subtract and you get 44. Nope, not the answer
So, finally let’s try 7*12=84 and 3*12=36, and 84-36=48!!!!
So, the answer is explained! Wait, but you still have to put them like ratios (if this chapter is ratios and proportions)
84:36 or 84 to 36, either way.
Have a great day!! ❤️❤️Find the perimeter of this figure.
Answers choices
40 m
20 m
100 m
80 m
4 congruent sides, each 10 m, so perimeter 10+10+10+10 =
Answer: 40 m
What is the area of the gray triangle shown?
Answer:
The area of the triangle is basically half the area of the square, so we only need to find the area of the square and divide it by 2:
S = (15 · 15)/2 = 112.5 (square units)
Answer:
112.5 square units
Step-by-step explanation:
Area = 1/2bh
where b = 15 and h = 15 (you can look at the graph)
So A = 1/2(15)(15) = 225/2 = 112.5 square units
Answer
112.5 square units
HELP FAST PLEASE!!!!! Which of the following is an equation of the translation y = sin x, shifted π units up?
y = sin (x + π)
y = sin x + π
y = sin (x − π)
y = sin x − π
to translate a graph up you need to add the amount you want to move it to the end of the equation, not to the variable.
The answer would be y = sin x + π
Answer:
B
Step-by-step explanation:
y=sinx+pi
helped needed! 20 points and brainliest of answered right !
Answer:
1. Cluster sampling
2. When finding a fair sample
3. Simple random sampling
The areas of the square and the rectangle are equal.
What is the value of x?
Answer:
x=12
Step-by-step explanation:
Area of the square
A = x^2
Area of the rectangle
A = (2x-8) (x-3)
Foil
A = 2x^2 -6x -8x +24
= 2x^2 -14x+24
The areas are equal
x^2 = 2x^2 -14x+24
Subtract x^2 from each side
x^2 - x^2 = 2x^2-x^2 -14x+24
0 = x^2 -14x -24
Factor
0 = (x-12) (x-2)
Using the xero product property
x-12= 0 x-2 =0
x=12 x=2
But looking at the rectangle
x-3 is a side length
2-3 is negative so x cannot equal 2
x=12
What is the exact volume of the cylinder? Enter your answer, in terms of π , in the box. 5cm 15cm
radius is half the breadth of box ie 2.5 cm height of cylinder is length ie 15 cm
so volume of cylinder =pi(r^2)h
ie 93.75pi cm^3
The exact volume of the cylinder is 93.75pi cm^3.
The question is incomplete the complete question is,
What is the exact volume of the cylinder? Where radius is 5cm and height is 15cm. Enter your answer, in terms of π, in the box.
We have given that,
The radius is half the breadth of the box ie 2.5 cm height of the cylinder is length ie 15 cm.
We have to determine the volume of a cylinder
What is the formula of the volume of a cylinder?Volume of the cylinder =pi(r^2)h
Use the given value in the above formula so we get,
[tex]V=\pi (2.5)^2(15)\\[/tex]
V= 93.75pi cm^3
Therefore the exact volume of the cylinder is 93.75pi cm^3.
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Question 2 options: 2(3x + 5 ) = 6x + 10
Answer:
Infinitely many solutions / All real numbers
Step-by-step explanation:
2(3x+5)=6x+10
Then, Distribute
6x+10=6x+10
Therefore, it is infinitely many solutions / all real numbers
For this case we must solve the following equation:
[tex]2 (3x + 5) = 6x + 10[/tex]
We apply distributive property to the left side of the equation:
[tex]6x + 10 = 6x + 10[/tex]
It is observed that we have an identity, that is, the terms on the right side are equal to the terms on the left side of the equation. Then, the equation has infinite solutions
Answer:
Infinite solutions
Monique planted seeds to grow pansies, Snapdragons, and petunias. After several weeks, 18 out of 40 pansy seeds, 21 out of 50 snapdragon seeds, and 12 out of 30 petunia seeds grew into plants. Write the named of the plants in order from least percentage of plants that grew to the greatest percentage of plants that grew.
Answer:
petunias, snapdragons, then pansy
Step-by-step explanation:
Ok first, lets find the percentage of 18 out of 40: 18/40= 0.45
The 21 out of 50= 21/50= 0.42
Lastly, 12/30= 0.40
And its very simple to put from least to greatest:
0.40, 0.42, 0.45
Hope this helped ;)
The answer is petunias, snapdragons, then pansies.
Hope this helps!
what happens when you subtract a fraction with the same denominators and numerators
Answer:
0
Step-by-step explanation:
Example : [tex]\frac{2}{5} - \frac{2}{5}[/tex] = 0
find the equation!!!!!! asap
Answer:
[tex]y=\frac{1}{36}x^2[/tex]
Step-by-step explanation:
The focus of the parabola is (0,9)
and the directrix is y=-9.
The equation of this parabola is given by:
[tex]x^2=4py[/tex]
The vertex of this parabola is at the origin.
The value of p is the distance from the vertex to the focus.
p=9-0=9
The equation of the parabola is
[tex]x^2=4(9)y[/tex]
[tex]x^2=36y[/tex]
Or
[tex]y=\frac{1}{36}x^2[/tex]
Is this relation a function?
Please help! This is 6th grade math on surface area.
Answer:
144
Step-by-step explanation:
Ok. I love problems like this.
You just have to find the surface are of each part and add it up!
To find the surface area of a rectangle, you multiple the base and the height. To find the surface area of a triangle, you multiple the base and height, and divide by 2 (because its half of a rectangle).
Left rectangle: 3*ll=33
Middle rectangle: 4*ll=44
Right rectangle: 5*ll=55
Top triangle: 3*4=12
12/2=6
Bottom triangle: 3*4=12
12/2=6
ADD THEM ALL!!! 33+44+55+6+6=144
(Also can I please please please have brainliest? I need it to level up!)