If the polynomial is having only two factors then the polynomial is a prime polynomial that is shown below.
[tex]\rm x^{2} +4\\\\ x^{2} -5x +2\\\\ x^{2} -x + 27 \\\\2x^{3} -4x + 5\\\\[/tex]
What is a prime polynomial?The polynomial that has only two factors is known as a prime polynomial.
The polynomials are
[tex]\rm 1. \ \ x^{2} +4\\\\2. \ \ x^{2} -5x +2\\\\3. \ \ x^{2} +10x -24 \\\\4. \ \ x^{2} -x + 27 \\\\5.\ \ 2x^{3} -4x + 5\\\\6. \ \ 5x^{2} - 10[/tex]
The factor of the given polynomial will be
1. [tex]\rm x^{2} + 4[/tex] is a prime factor. Because it has only two factors.
2. [tex]\rm x^{2} -5x + 2[/tex] is a prime factor. Because it has only two factors.
3. [tex]\rm x^2 + 10 x - 24[/tex] is not a prime factor. Because it has more than two factors.
4. [tex]\rm x^2 - x + 27[/tex] is a prime factor. Because it has only two factors.
5. [tex]\rm 2x^3 - 4x + 5[/tex] is a prime factor. Because it has only two factors.
6. [tex]\rm 5x^2 - 10[/tex] is not a prime factor. Because it has more than two factors.
More about the prime polynomial link is given below.
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three boys share R2100 in ratio 3:5:7 calculate how much each boy will get
The amount each boy receives from the R2100 is R420, R700 and R980 respectively
How to find ratioTotal amount = R2100
Ratio = 3 : 5 : 7
Total ratio = 3 + 5 + 7
= 15
First boy = 3/15 × 2100
= 0.2 × 2100
= R420
Second boy = 5/15 × 2100
= 0.33333333333333 × 2100
= R700
Third boy = 7/15 × 2100
= 0.46666666666666 × 2100
= R980
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The inverse of the logarithmic function f(x) = log0. 5x is f−1(x) = 0. 5x. What values of a, b, and c complete the table for the inverse function?.
The values of a, b, and c to complete the table for the inverse of the logarithmic function is 2,1 and -2 respectively.
What is the inverse of the logarithmic function?The Inverse of the logarithmic function is an exponential function.
The given logarithmic function is,
[tex]f(x) = \log_{0. 5}x[/tex]
The inverse of the given logarithmic function is,
[tex]f^{-1}(x) = 0.5^x.[/tex]
Put the value of x as -1 from the table attached below, to find the value of a.
[tex]f^{-1}(-1) = 0.5^{(-1)}\\f^{-1}(-1) = 2[/tex]
Similarly, put the value of x as 0 from the table attached below, to find the value of b.
[tex]f^{-1}(0) = 0.5^{(0)}\\f^{-1}(0) = 1[/tex]
Now, put the value of x as 2 from the table attached below, to find the value of c.
[tex]f^{-1}(2) = 0.5^{(2)}\\f^{-1}(2) = -2[/tex]
Thus, the values of a, b, and c to complete the table for the inverse of the logarithmic function is 2,1 and -2 respectively.
Learn more about the inverse of the logarithmic function here;
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The measures of the angles of a triangle are shown in the figure below. Solve for x.
Answer:
x = 2
Step-by-step explanation:
180= 90 + 57 + Z
Z = 180 - 90 - 57
Z = 33
33 = 7X + 19
7X = 33 - 19
7X = 14
X = 2
how manh solutions does the system have
Answer:
Step-by-step explanation:
To find how many solutions that this system equation has, we must solve it
since y equals to both '-5x +1' and '1-5x' we can set them equal to each other and get:
[tex]-5x+1 = 1-5x\\0 = 0[/tex]
So there are infinitely many solutions as we got 0 = 0
Hope that helps!
HELP IM TIMED PLEASE
Emesto tried to determine the solution for the system of equations using substitution. His work is shown below. x-y=7 3x – 2y = 8 Step 1: x= y + 7 Step 2: 3y + 7) – 2y = 8 Step 3: 3y + 7 – 2y = 8 Step 4: y + 7 = 8 Step 5: y = 1
in which step did Ernesto make the first error?
A. step 1
B. Step 2
C. step 3
D. step 4
Answer:
d step 4
Step-by-step explanation:
hope it helps you on what u are doing
Which function represents a reflection of f(x) = 5(0. 8)x across the x-axis? g(x) = 5(0. 8)–x g(x) = –5(0. 8)x g(x) = One-fifth(0. 8)x g(x) = 5(–0. 8)x.
The function which represents the reflection of provided function across the x-axis is,
[tex]g(x) = -5(0. 8)x[/tex]
What is reflection of function?The reflection of a function is flipping the original function with respect to a reference line.
The following steps used to for reflecting a the function-
Select the function which has to be reflected.Select a baseline or reference line over which the function has to be reflected.Mark the corners of the function at the equidistant from the reference line as the original function has, but in the opposite direction.The reflected function is now is facing the opposite direction.The function given in the problem is,
[tex]f(x) = 5(0. 8)x[/tex]
The function has the positive sign. Therefore, this function is located in the first quadrant.Now this function is reflected across the x-axis. This will lead this function in the fourth quadrant, with negative sign.
Therefore, the function become,
[tex]g(x) = -5(0. 8)x[/tex]
Hence, the function which represents the reflection of provided function across the x-axis is,
[tex]g(x) = -5(0. 8)x[/tex]
Learn more about the reflection here;
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Write the sentence as an equation.
249 is the product of m and 382, reduced by 110
i will give brainliest
Answer:
382 x m= 249 divided by 110
Step-by-step explanation:
:)
Answer:
249= 382m-110
Step-by-step explanation:
Please i need help, can someona explain how to solve the problems with the most easiest way to solve? Because this is so confusing
Answer:
Above your sheet, they give you formulas for the rectangular prism.
Method one;
V = L x W x H
Where "L" is length, "W" is width, and "H" is height.
Method 2;
V = B x H
Where "B" is the area of the base, and "H" is the height.
Now let's apply these formula to your questions:-
(Using method 2 for most of these problems)
1. If we look for the area of the base, we can see that 2 is the width and 4 is the length, so we would need to multiply those two to get the area of the base (2 x 4) = 8.
Now the height is 3.
So we plug this into our formula,
V = B x H
V = 8 x 3
V = 24 cubic feet
2. If we look at this question, we can see that this is a cube, meaning that all lengths are the same. To make this easier, we can use method 1 and just multiply the given lengths;
V = L x W x H
V = 4 x 4 x 4
V = 64 cubic inches
3. If we look for the area of the base, we can see that 5 is the width and the length is 20, so we would need to multiply those two to get the area of the base (5 x 20) = 100.
The height is 5.
So we plug this into our formula;
V = B x H
V = 100 x 5
V = 500 cubic yards
4) If we look for the area of the base, we can see that 3.2, if i'm correct, is the width and 5.4 is the length, so we would need to multiply those two to get the area of the base (3.2 x 5.4) = 17.28.
The height is 1.9.
So we plug this into our formula;
V = B x H
V = 17.28 x 1.9
V = 32.832, 32.83 cubic centimeters
What is an equation of the line that passes through the points (-4, -5) and
(-8, -2)?
To find the equation, First step is to find the slope which we can use in the formula and then we will find the equation using the specific formula...
Finding slope ⤵️[tex] \boxed{ \sf \:m = \frac{ y_{2} - y_{1} }{ x_{2} - x_{1}} }[/tex]
(x1,y1) = (-4,-5)(x2,y2) = (-8,-2)[tex] \tt \to \: m = \frac{ - 2-( - 5)}{ - 8 -(- 4)} [/tex]
[tex] \tt \to \: m = \frac{ -2+5}{ -8+4} [/tex]
[tex] \tt \to \: m = - \frac{3}{4} [/tex]
Now, Put the values in the formula used to find the equation ⤵️[tex] \boxed{ \sf \:y - y_{1} = m(x - x_{1}) }[/tex]
(x1,y1) = (-4,-5)[tex] \tt \nrightarrow \: y - ( - 5) = - \frac{3}{4} (x - ( - 4))[/tex]
[tex] \tt \nrightarrow \: y + 5 = - \frac{3}{4} (x + 4)[/tex]
[tex] \tt \nrightarrow \: y + 5 = - \frac{3}{4} x - 3[/tex]
[tex] \tt \nrightarrow \: y = - \frac{3}{4} x - 3 - 5[/tex]
[tex] \bf\nrightarrow \: y = - \frac{3}{4} x - 8[/tex]
The solution is, The equation the line is, y = -3x/4 -8
What is a straight line?A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.
Here, we have
two points (-4, -5) and (-8, -2)
So, by using the formula of equation of straight line of two-point form, we get,
(y-y_1)/(x-x_1 )=(y_2-y_1)/(x_2-x_1 )
=>(y+5)/(x+4)=(-2+5)/(-8+4)
=>(y+5)/(x+4)= 3/ -4
=>-4y - 20 = 3x +12
=> -4y = 3x + 32
=> y = -3x/4 -8
Hence, the required equation is, y = -3x/4 -8
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40/64 = 5/? what is the equivalent fraction
Answer:
40/64 = 5/8
Step-by-step explanation:
greatest commom dinaminator of 40 and 64 is 8 so,
divide each number by 8
40 divided by 8 =5
64 divided by 8 =8
Or you can do bc it gives you the 5 and the numerator you do 40 divided by 5 and get 8 so that means to get the second fraction you are divided the first one by 8 thats why 40 divided by 8 is 5 and youre going to do 64 divided by 8 which is 8. put the two numbers together and you get 5/8! :)
Please help with this
Answer:
2.5 feet per minute
Step-by-step explanation:
Rate of Change: [tex]\frac{75-25}{30-10}[/tex] = 50/20 or 5 feet every 2 minutes or
2.5 feet per minute
what is pi,
is pi 3.1415????
Answer:
Yes that's some of the digits
Step-by-step explanation:
You can round up pi to 3.14.
Actual digits of pi: 3.141592653589793238462...that's all I can memorize.
mathematical constant, approximately equal to 3.14159. It is defined in Euclidean geometry as the ratio of a circle's circumference to its diameter, and also has various equivalent definitions. The number appears in many formulas in all areas of mathematics and physics.
Answer: no its not 3.1415
Step-by-step explanation:
calculations included please
Answer:
[tex] \frac{ {r}^{ 3} + 25}{p(q + r)^{4} } = \frac{ {(3.5)}^{3} + 25}{5(6 + 3.5)^{4} } = \frac{42.875 + 25}{5 {(9.5)^{4} }} \\ \\ = \frac{67.875}{5(8145.0625)} = \frac{67.875}{40725.3125} \\ \\ = 0.00166665 = 0.002[/tex]
Step-by-step explanation:
(3.5^3 +25) ÷5(6+3.5)^4
(42.875 + 25) ÷5 (9.5)^4
(67.875) ÷ 5 (8145.0625)
(67.875) ÷ 203626.5625
=0.00033333078)
use the law of cosines to gind the value of x and y.
Answer: Answer:[tex]x = 49.8^\circ\\y = 54.6^\circ[/tex]Step-by-step explanation: Kindly refer to the image attached in the answer region for labeling of triangle.
Step-by-step explanation: u multiply the numbers
What is 0.7¯(the line is suppose to be ontop of the seven) expressed as a fraction in simplest form?
Answer:
the answer is just 7/9
I need help with this
Answer:
Since
4
4x
and
4
n
have the same denominator, add them by adding their numerators.
Step-by-step explanation:
Which statement is true?
Answer:
(b) Both vertical and horizontal reflection
Step-by-step explanation:
The figure will be a horizontal reflection of itself about any vertical line through two of the smaller 6-pointed stars.
The figure will be a vertical reflection of itself about any horizontal line through two of the smaller 6-pointed stars.
the pattern has both vertical and horizontal reflection
__
Additional comment
A pattern will have horizontal reflection if there exists a vertical line about which the pattern can be reflected to itself. That is, there exists one (or more) vertical lines of symmetry.
Similarly, the pattern will have vertical reflection if there is a horizontal line about which the pattern can be reflected to itself. Such a line is a horizontal line of symmetry.
Find the value of x. Justify your answer.
Answer:
x = 8
Step-by-step explanation:
Because the figure in the circle is a square, which has the property of possessing equal sides.
Therefore, the value of x is equal to 0.
1. Mateo plans to solve the system below using elimination. Which is a reasonable first step Mateo could take? -X + 6y=9 3x + 2y = 13 - A. Multiply the 2nd equation by 3 - B. Multiply the 2nd equation by -3 C. Multiply the 1st equation by - 3 D. Any of the above
Answer:
C
Step-by-step explanation:
multiply the 1st equation by -3
Solve for x.
7x/−10=−42/5
Answer:
x=12
Step-by-step explanation:
[tex]-\frac{7x}{10} =-\frac{42}{5}[/tex] multiply both sides by -10 as the first step to get x by itself
[tex]7x =84[/tex]. divide both sides by 7
x = 12
please help me with this
Factor the polynomial 3x4 – 2x2 15x2 – 10 by grouping. Which product is the factored form of the polynomial?.
The factors of the polynomial are [tex]\rm (x^2+5)(3x^2-2)[/tex].
What are the factors?These factors can be numbers, variables, or an algebraic expression.
Given
Factor the polynomial 3x4 – 2x2 + 15x2 – 10 by grouping.
The factors of the polynomial are;
[tex]\rm 3x^4-2x^2+15x^2-10\\\\x^2(3x^2-2)+5(3x^2-2)\\\\(x^2+5)(3x^2-2)[/tex]
Hence, the factors of the polynomial are [tex]\rm (x^2+5)(3x^2-2)[/tex].
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Graph the points (3,3) and (2,1) on the coordinate plane.
Answer:
1. Over three, up three
2. Over two, up one
Step-by-step explanation:
Given the following question:
Point A = (3, 3)
Point B = (2, 1)
To find the answer, please understand where the x and y axis is located. Remember that the x is the line intersecting the y axis.
So, in order to plot point A and B, we have to remember that the first value represents x, and the second represents the y value.
(3, 3) = (x, y)
(2, 1) = (x, y)
For the first point we will move over three on the x axis, and then up three on the y axis.
For the second point we will move over two on the x axis, and then up 1 on the y axis.
Hope this helps.
How many 1-in. cubes can fit into a 2 by 4 by 2 in. prism?
8 cubes
16 cubes
24 cubes
32 cubes
~Shoto Todoroki here~
Answer:
16 cubes
Step-by-step explanation:
Answer:
16 cubes B).
Step-by-step explanation:
If we find the volume for the prism we find that it is 16 in. overall.
And since each cube is 1 in. you can fit 16 cubes.
Hope this helped.
A brainliest is always appreciated.
omg help me pls and tysm
Answer:
33
Step-by-step explanation:
Alright, so, let's break it down.
We know that d = negative 6 (-6)
Lets start with -5d.
Since d = -6, we have to do -5 × -6, which is 30.
So, now, we are using fractions. -6 plus 15.
(Which is, negative 6 plus 15)
That is 9. Since we are adding a negative number to a positive number, it will be the same way as 15 minus 6.
Now, we know that we are using division (due to the fraction line, we know that we are using division). Let's divide 9 into 3. That's 3, because 3 times 3 is also 9. Now, if we add 30 plus 3, we get 33, Therefore, the answer is 33.
Answer:
33
Step-by-step explanation:
-5(-6) + (-6) + 15/3
30 + -6 + 15/3
30 + 9/3
30 + 3
33
Have an amazing day!!
PLEASE RATE AND MARK BRAINLIEST!!
Miguel's irrigation tank for his large garden held 45. 5 gallons before he began to fill it at a rate of 17 gallons per minute.
Before he started watering the plants in his garden, Miguel's friend Alejandro checked his irrigation tank and found it contained 425 gallons.
If Alejandro is irrigating his plants at rate of 11. 5 gallons per minute, how much water will be in each tank when both tanks have the same amount of water?
Answer:
year, subtract that amount from the 230,000 gallons of seasonal water use. 230,000 gallons – 150,000 gallons = 80,000 gallons use for irrigation per year .
Step-by-step explanation:
I took the test
A
B
E
D
С
Note: Figure is not drawn to scale.
In rhombus ABCD, segments AC and BD are diagonals. If mZDAB = 160°, what is the measure of ZABE?
OA. 190°
ОВ.
170°
OC
10°
D.
100
Answer:
The correct option is OPTION C.
Step-by-step explanation:
Recall that for a rhombus, the diagonals bisect the interior angles.
This means that if we are given that:
m∠DAB=160°
Then:
m∠EAB=m∠DAB/2=160/2=80°
Also, recall that the diagonals of a rhombus are perpendicular. Therefore:
m∠AEB=90°
Hence, we can have a triangle that looks like the one shown below:
Recall that the sum of angles in a triangle is 180°. Therefore, we have that:
m∠AEB+m∠ABE+m∠EAB=180°
Hence, we can calculate m∠ABE to be:
m∠ABE =180-80-90
m∠ABE=10°
The correct option is OPTION C.
Graph the function.
y = 3 square root x
Answer:
x=3×3
Step-by-step explanation:
ok it's fine if you don't mind
The Bridge Problem
A group of four people has to cross a bridge. It is dark, and they have to light the path with a flashlight. No more than two people can cross the bridge simultaneously, and the group has only one flashlight. It takes different time for the people in the group to cross the bridge:
Chris crosses the bridge in 1 minute,
Tracy crosses the bridge in 2 minutes,
Ashley crosses the bridge in 5 minutes,
Jalen crosses the bridge in 10 minutes.
How can the group cross the bridge in 17 minutes?
So, the first thing is that the group requires flashlight to cross the bridge. It also means that each time one person must return to bring back the flashlight.
Chris and Tracy cross the bridge in 2 minutes. ( The maximum time required by both of them would be 2 minutes)
Then Chris would return with flashlight in 1 minute.
Ashley and Jalen then cross the bridge in 10 minutes.
Now, Tracy will return with flash light in 2 minutes.
Then, Chris and Tracy will cross the bridge in 2 minutes.
Total time taken => 2+1+10+2+2 => 17 minutes.
Hope this helps :)
Answer:
Chris and Tracy cross the bridge together = 2 minutes
Chris goes back on his own (leaving Tracy across the bridge) = 1 minute
Chris gives the flashlight to Ashley
Ashley and Jalen cross the bridge together = 10 minutes
They give the flashlight to Tracy (who was waiting across the bridge)
Tracy goes back = 2 minutes
Chris and Tracy cross the bridge together = 2 minutes
Total 17 minutes
Solve for x, rounding to the nearest hundredth.
