Answer:
Step-by-step explanation:
x⁴ + x² - 20
(x² + 5)(x² - 4)
(x² + 5)(x - 2)(x + 2)
The required factor of the given expression is given as (x² + 5)(x - 2)(x + 2).
Given that,
To determine the factor of the expression, x⁴ + x² - 20.
A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor.
Here,
Given expression,
= x⁴ + x² - 20
= x⁴ + 5x² - 4x² - 20
= x²[x² + 5] - 4 [x² + 5]
= [x² + 5][x²- 4]
Since (a² - b²) = (a + b)(a - b)
= (x² + 5)(x - 2)(x + 2)
Thus, the required factor of the given expression is given as (x² + 5)(x - 2)(x + 2).
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if there is a 1 4 chance that it will rain for your fourth of july brbeque what is the probability it wont rain
Answer:
86% chance
Step-by-step explanation:
there is an 86% chance it won't rain because 100%-14%=86%
Mr. Walthour is building a storage in a conical shape. The base of the shed is 4 meters in diameter and the height of the shed is 3.8 meters. What is the volume of the shed? Round to the nearest tenth.
Teddy has 23 boxes of juice packed and plans to pack 3 additional boxes each hour. Charley has 7 boxes packed and plans to pack 5 additional boxes each hour. The equation below represents when Teddy and Charley will have packed the same number of boxes, based on x number of hours.
23 + 3x = 5x +7
After how many hours will Charley have packed the same number of boxes of juice as teddy?
Answer:
8 hours
Step-by-step explanation:
23 + 3x = 5x + 7
- 3x -3x
23 = 2x + 7
-7 - 7
16 = 2x
16/2 = 2x/2
x = 8
Answer:
BillyBob got it right, well explained..
Step-by-step explanation:
Eduardo's teacher made the table shown here His teacher asked him to identify the missing value in the table Eduardo's answer was correct Which statement describes Eduardo's answer? A Eduardo s answer as 8. He added 6-2 Eduardo s answer was 12 He subtracted 2 from 14 Eduardo's answer was 10 He multiplied the number of cats by 2 Eduardo's answer was 15. He multiplied the number of cats by 3. USATestprep, LLC 2021, All Rights Reserved. Read Our Blog Privacy Policy PHONE 1 - 877 - 377- 9537 I FA
Answer:
Your Answer is C!
Step-by-step explanation:
2x2 = 4
3x2 = 6
5x2 = 10
7x2 = 14
Select the correct answer from each drop-down menu.
A machine cuts a strip of carpet into two pleces. The length of the smaller plece is 5 meters greater than 4 the length of the larger piece. If
the length of the smaller piece is 12 meters, the length of the bigger plece is meters and the total length of the carpet is
meters.
Length of larger piece be x
Smaller piece=4x+5x=12m
[tex]\\ \sf\longmapsto 4x+5=4(12)+5=60+5=65m[/tex]
Total length=65+12=77m
The length of the bigger piece is 1.75 meters and the total length of the carpet is 13.75 meters.
Given that length of the smaller piece is 12 meters.
The length of the smaller piece is 5 meters greater than 4 times the length of the larger piece.
Let's represent the length of the larger piece as "x."
Length of the smaller piece = 4 times the length of the larger piece + 5
12 = 4x + 5
Subtracting 5 from both sides:
12 - 5 = 4x
7 = 4x
Dividing both sides by 4:
7/4 = x
1.75 = x
So, the length of the bigger piece is 1.75 meters.
To calculate the total length of the carpet, we add the length of the smaller piece and the length of the bigger piece:
Total length of the carpet = Length of the smaller piece + Length of the bigger piece
Total length of the carpet = 12 + 1.75
Total length of the carpet is approximately 13.75 meters.
Therefore, the length of the bigger piece is 1.75 meters and the total length of the carpet is 13.75 meters.
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which option would be correct?
Answer:
similar by angle angle similarity property.
Step-by-step explanation:
they have the right angles, and then the two vertical angles.
:))
A rectangular tank is 54cm long, 29cm wide and 65cm deep.
Answer:
so what do i do
Step-by-step explanation:????????????
A small pizza at Little Italy pizzeria costs $9.50, and each topping is an additional $0.50. So the cost of ordering a pizza can be determined by the equation y=0.50x+9.50, where y represents the cost of the pizza and x represents the number of toppings.
Step 2 of 2 : Use the graph to estimate to the nearest quarter of a dollar ($0.25) the cost of a small pizza with 8 toppings.
Answer:
$13.50 for 8 toppings
Step-by-step explanation:
There are 163 girls and 157 boys in school. 27 girls and 33 boys play soccer after school. What percentage of students play soccer after school?
Answer: The answer is to this math question is 18.75% of the students play the soccer after school.
Step-by-step explanation: Here are the following steps in order to convert the given fraction to percentage of the students play the soccer after school:
Step 1. First I add the total of the students in school and then added the total of the students play the soccer after school that looks like this: [tex]163+157=320[/tex] and [tex]27+33=60.[/tex]
Step 2. Using the online fraction to percentage calculator, first I find The Greatest Common Factor of 60 and 320 that looks like this: GCF(60,320) = 20.
Step 3. I can reduce this fraction by dividing both the numerator and denominator by 20 that looks like this: 60÷20/320÷20=[tex]\frac{3}{16}.[/tex]
Step 4. I know that [tex]\frac{3}{16}[/tex] is the same as 3÷16, then using The Long Division for 3 divided by 16 that gives us: 0.1875.
Step 5. I multiply the given decimal number by 100% in order to convert the fraction to percentage of the total students play the soccer after school that looks like this: 0.1875×100=18.75%.
I hope that my given answer with my given step-by-step explanation is very helpful to your own math question about how to find the percentage of the total students play the soccer after school, please mark me as brainliest and have a great P.A. Day and weekend! :D
Sincerely,
Jason Ta,
The ambitious of Brainly and the role of The TDSB and WHCI Student of the high school.
What equipment is generally used to make lyophilized medications suitable for administering to the patient? a) Test tubes or sterile ampules b) Petri dishes and sterile droppers c) Sterile syringes or graduated cylinders d) Measuring cups and clean, warm water
Answer:
B. Petri dishes and sterile droppers
pls help its an image scroll down
Answer:
D. y = 3x + 9
Step-by-step explanation:
Use the point-slope formula to find the equation in slope-intercept form.
[tex]y-y_1=m(x-x_1)\\\\y-33=3(x-8)\\\\y-33=3x-24\\\\y=3x+9[/tex]
on a photograph an ant is enlarged at scale 25:1 In the photo the ant leg is 15 cm what is the actual length of the ants leg
Answer:
0.6 cm
Step-by-step explanation:
15/25=0.6
Answer:
0.6 Is the answer
Step-by-step explanation:
Hope this helped ¬∪ω∪¬
Will give brainliest!
We know that a + b + c = 7 and [tex]\frac{1}{a+b} + \frac{1}{b+c} +\frac{1}{a+c} =\frac{7}{10}[/tex]. What is the value of [tex]\frac{10a}{b+c} +\frac{10b}{a+c} +\frac{10c}{a+b}[/tex]?
Answer:
19
Step-by-step explanation:
Note that
[tex]\dfrac{10a}{b+c} + \dfrac{10b}{a+c} + \dfrac{10c}{a+b} = 10\left(\dfrac{a}{b+c} + \dfrac{b}{a+c} + \dfrac{c}{a+b} \right)[/tex]
and
[tex]\dfrac{7-b-c}{b+c}+\dfrac{7-a-c}{a+c}+\dfrac{7-a-b}{a+b}=\dfrac{a}{b+c} + \dfrac{b}{a+c} + \dfrac{c}{a+b}[/tex]
from [tex]a+b+c=7 \implies a=7-bc; b = 7-a-c; c = 7-a-b[/tex]
and
[tex]\dfrac{7-b-c}{b+c}+\dfrac{7-a-c}{a+c}+\dfrac{7-a-b}{a+b} = 7\left(\dfrac{1}{a+b}+\dfrac{1}{b+c}+\dfrac{1}{a+c}\right)-3[/tex]
because it is not difficult to note that
[tex]$\sum \dfrac a{b+c}=\dfrac a{b+c}+\dfrac b{c+a}+\dfrac c{a+b}$[/tex]
Therefore,
[tex]7\left(\dfrac{7}{10}\right)-3 = \dfrac{49}{10}-3 =\boxed{ \dfrac{19}{10}} = \dfrac{a}{b+c} + \dfrac{b}{a+c} + \dfrac{c}{a+b}[/tex]
Finally,
[tex]10\left(\dfrac{a}{b+c} + \dfrac{b}{a+c} + \dfrac{c}{a+b} \right) = 10 \cdot \dfrac{19}{10} = 19[/tex]
The function f(t) = t2 + 4t - 14 represents a parabola.
Part A: Rewrite the function in vertex form by completing the square. Show your
work.
Part B: Determine the vertex and indicate whether it is a maximum or a minimum on
the graph. How do you know?
Part C: Determine the axis of symmetry for f(t).
Answer:
a: [tex]f(t)=(t+2)^2-18[/tex]
b: vertex: (-2, -18)
minimum
c: x = -2
Step-by-step explanation:
Completing the square is difficult to explain in words. but I'll try my best. Let me know if you need any more information.
Part A ===============
Start with the given function in this form:
[tex]f(x)=ax^2+bx+c\\t^2+4t-14[/tex]
We need an additional number, d, and we'll calculate it like this:
[tex]d=(\frac{b}{2a})^2 \\\\d=(\frac{4}{2(1)} )^2\\d=2^2\\d=4[/tex]
d needs to be added and subtracted at the same time. That way we do not change the value of the expression:
[tex]ax^2+bx+d-d+c\\\\t^2+4t+4-4-14[/tex]
And you can separate them like this to make it easier to read:
[tex](t^2+4t+4) + (-4-14)\\(t^2+4t+4)-18[/tex]
Finally, we need to factor the trinomial in the parenthesis. Because we've completed the square, it's now a perfect square trinomial. The factored form is just:
[tex](x+e)^2[/tex]
where e is half of b, or the square root of c. That looks like this in our case, and you can also expand it to make sure.
[tex](t+2)^2\\\\(t+2)(t+2)\\t^2+2t+2t+4\\t^2+4t+4[/tex]
Put that all together and you get the answer:
[tex]f(t)=(t+2)^2-18[/tex]
Part B ===============
Vertex form is this:
[tex]f(x)=a(x-h)^2+k[/tex]
where (h, k) is the vertex and a is the scale factor.
In part A, we converted the given function into vertex form. Looking at that, you can see the vertex is at (-2, -18), and the scale factor is 1. When the scale factor is positive, the parabola faces upwards. When it's negative, the parabola faces downwards.
The scale factor is a positive 1 in this case, and if you picture that in your mind, the vertex is at the very lowest point, or the minimum, of the parabola.
Part C ==============
The axis of symmetry is always on the vertex, and that is because the vertex is the exact point where the parabola changes direction from positive to negative, or negative to positive.
The vertex of this parabola is (-2, -18), so the axis of symmetry is at x = -2.
Sorry if that got too long and hard to follow, I can clarify any part of it if needed.
What is the slope of the line y = -4?
Can someone check my work and show me where I went wrong?
Answer:
the part where it's 25 and 183 should be 5400 if you are rounding to the nearest 10 and then multiplying
Answer:
You made a wrong answer in 183 and 25.
It should be 5,400
Step-by-step explanation:
183 round to the nearest ten = 180
25 round to the nearest ten = 30
180 * 30 = 5,400
write an equation with the two given points (7, -2) (-1, 0)
Answer:
haha.A. Write True if the statement is correct and False if it is not true. 1. In active voice, the subject of the sentence is doing the action, 2. In passive voice, the action is done on/upon the subject. 3. The doer of the action is followed by the verb in active voice. 4. The doer of the action is preceded by the verb in active voice, 5. The receiver of the action in active voice is preceded by the verb. 6. The receiver of the action in passive voice is followed by the verb. 7. In passive voice, meaning is clearer and more direct. 8. In active voice, meaning can be confusing and indirect, 9. The tone is authoritative and subjective in active voice, 10. The tone is neutral or objective in passive voice.
The cost of producing key chains with the company logo printed on them consists
of a onetime setup fee of $265.00 plus $0.90 for each key chain produced. This
cost can be calculated using the formula C = 265.00 +0.90p, where p represents
the number of key chains produced and C is the cost. Use the formula to calculate
the cost of producing 2700 key chains.
Answer:
$2695
Step-by-step explanation:
$265 + $0.90p=C
To find out the value of C (cost), we must solve the equation by replacing P (number of keychains) with the given value, 2700.
265 + 0.90(2700) = C
Now, we use order of operations. (PEMDAS)
In this case, the parentheses stand for multiplication. Since multiplication comes first, we multiply 0.90 by 2700.
The product of 0.90(2700) is 2430.
Our new equation should look like this
265 + 2430=C
Adding those together you get 2695, to finish this off, C=$2695
(Side note: be sure to identify what the value is, for example 2695 is the cost of producing 2700 key chains, meaning it's $)
I hope this made sense and helped lol
The position of an object at any time t is given by
s(t)=3t4−40t3+126t2−9
.
1 Determine the velocity of the object at any time t.
2 Does the object ever stop changing?
3 when is the object moving to the right and when is the object moving to the left
Answer:
Step-by-step explanation:
I will ASSUME that your equation is
s(t) = 3t⁴ - 40t³ + 126t² - 9
1) velocity is the derivative of position
v(t) = s'(t) = 12t³ - 120t² + 252t
2) changing what? position? velocity? acceleration? gender? color?
position No the plot is continuous
velocity Yes both magnitude and direction. Zeros at t = 0, 3, and 7 s
acceleration Yes, both magnitude and direction. Zeros at approx. t = 1.306 and 5.361 s
gender? who knows
color? probably.
3) velocity is positive (moving to the right on a standard number line) for
0 < t < 3 and t > 7
Moves to the left for
t < 0 and 3 < t < 7
1. the velocity of the object at any time "t" is v(t) = 12t³ - 120t² + 252t.
2. the object stops changing at t = 6 and t = 3.5.
3. the object is moving to the right in the interval 0 < t < 3.5 and moving to the left in the interval t > 6.
To determine the velocity of the object at any time "t," we need to find the derivative of the position function "s(t)" with respect to "t."
1. Velocity of the object at any time "t":
The velocity is the rate of change of position with respect to time, which is given by the derivative of the position function, s(t).
s(t) = 3t⁴ - 40t³ + 126t² - 9
To find the velocity function, we take the derivative of s(t) with respect to t:
v(t) = d/dt (3t⁴ - 40t³ + 126t²- 9)
v(t) = 12t³ - 120t² + 252t
So, the velocity of the object at any time "t" is v(t) = 12t³ - 120t² + 252t.
2. Does the object ever stop changing?
The object stops changing when its velocity becomes zero. To find when the velocity is zero, we need to solve the equation v(t) = 0.
12t³ - 120t² + 252t = 0
Now, we can factor out common terms:
t(12t² - 120t + 252) = 0
Now, set each factor equal to zero and solve for "t":
1st factor: t = 0
2nd factor: 12t² - 120t + 252 = 0
To solve the quadratic equation, we can either factor it further or use the quadratic formula. Factoring the quadratic equation gives us:
(t - 6)(12t - 42) = 0
Setting each factor to zero:
1. t - 6 = 0
t = 6
2. 12t - 42 = 0
12t = 42
t = 3.5
So, the object stops changing at t = 6 and t = 3.5.
3. When is the object moving to the right and when is the object moving to the left?
The object is moving to the right when its velocity (v(t)) is positive, and it is moving to the left when its velocity (v(t)) is negative.
Let's analyze the velocity function
v(t) = 12t³ - 120t² + 252t
To find the intervals where the object is moving to the right or left, we need to determine when v(t) is positive or negative.
1. Find critical points by setting v(t) = 0 and solving for "t":
12t³ - 120t² + 252t = 0
As we already found earlier, the critical points are t = 6 and t = 3.5.
2. Test each interval created by these critical points using test points to determine the sign of v(t) in those intervals.
Pick a value of "t" in each of these intervals:
- When t < 3.5 (e.g., t = 0),
- When 3.5 < t < 6 (e.g., t = 4),
- When t > 6 (e.g., t = 7).
Now, substitute these test values into the velocity function v(t):
- v(0) = 12(0)³ - 120(0)² + 252(0) = 0
- v(4) = 12(4)³ - 120(4)² + 252(4) = 192
- v(7) = 12(7)³ - 120(7)² + 252(7) = -588
Based on the test points, we can conclude:
- The object is moving to the right when 0 < t < 3.5 (positive velocity).
- The object is moving to the left when t > 6 (negative velocity).
Therefore, the object is moving to the right in the interval 0 < t < 3.5 and moving to the left in the interval t > 6.
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A taxi service charges $1.00 for the first 1/10 of a mile and $0.10 for each additional 1/10 of a mile after that. fill in the table.
distance traveled
(miles)
9/10
2
3 1/10
10
price
?
(dollars)
Is this a proportional relationship?
Type yes or no
9414 1404 393
Answer:
$1.80, 2.90, 4.00, 10.90
not proportional
Step-by-step explanation:
For some distance d, we have a charge f(d) that is ...
[tex]f(d)=\begin{cases}1.00&0\le d\le0.1\\1.00+0.10\cdot\dfrac{(d-0.1)}{0.10}&0.1<d\end{cases}[/tex]
for d > 0.1, this simplifies to d +0.9.
Then the charges are ...
[tex]\begin{array}{cc}\underline{\text{miles}}&\underline{\text{charge}}\\9/10&1.80\\2&2.90\\3\ 1/10&4.00\\10&10.90\end{array}[/tex]
The different relation for the first 1/10 mile indicates ...
the relationship is not proportional.
7. Sid has a board that is 8 5/6
feet long. He cuts a piece off of the board that
is 3 1/4 feet long. How long is the remaining piece of board
Answer:
5 7/12 feet left
Step-by-step explanation:
Step 1: 8 5/6 - 3 1/4
Step 2: = 67/12 (Put into proper fraction)
Step 3: = 5 7/12
Hope that helps :)
Answer:
5 7/12
Step-by-step explanation:
Given that the board is 8 5/6 feet long.
Cuts off 3 1/4 feet.
8 5/6- 3 1/4
Change fractions into improper fractions.
8 5/6=53/6
3 1/4=13/4
-------------------------------------------------------------
53/6x2/2=106/12
13/4x3/3=39/12
106/12-39/12=67/12
=5 7/12
Hope this helps :)
the probability that a tin of paint is dented is 0.07 out of 3000 tins of paint,how many would you expect to be dented?
Answer:
3000×0.07=210 tins
Step-by-step explanation:
210 tins
Step-by-step explanation:
3000÷100×0.07
=2.1
MARK ME BRAINLIEST PLS!!why is upendrakishore roy chouwdhury remembered
Answer:
Upendrakishore Roy Chowdhury; 12 May 1863 – 20 December 1915) was a Bengali writer and painter. He was the first person who introduced the colour printing in bangal. He started the first color children's magazine Sandesh in 1913.
Step-by-step explanation:
history ig
Find the difference:
x+
x-1
-
- 8
x-1
O
9
x-1
2-7
X1
-7
1
2x+9
1
DONE
Answer: [tex]\frac{9}{x-1}[/tex]
Step-by-step explanation:
Since the denominators are the same, we can subtract the numerators.
[tex]\frac{x+1}{x-1}-\frac{x-8}{x-1}=\frac{(x+1)-(x-8)}{x-1}=\boxed{\frac{9}{x-1}}[/tex]
Find the equation of the line with slope m = 2 that contains the point (8,19).
Answer:
y = 2x + 1
Step-by-step explanation:
Pls mark as brainliest
The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
The equation of the line with slope m = 2 and point (8, 19) is
y = 2x + 3
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
Slope:
m = 2
Point = (8, 19) = (x, y) _____(A)
Now,
The equation of a line is given as,
y = mx + c ______(B)
Substitute (A) into (B)
From (A) we get,
19 = 2 x 8 + c
19 = 16 + c
c = 19 - 16
c = 3
Now,
The equation of the line with slope m = 2 and point (8, 19) is
y = 2x + 3
Thus,
The equation of the line with slope m = 2 and point (8, 19) is
y = 2x + 3
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Fill in the blank to make each equality true. _ divided by (1/2x^3)=16x^6y^4.
PLS HELP!
Answer:
(8x^9 x y^4) : (1/2x^3)=16x^6y^4
Step-by-step explanation:
8 : 1/2 = 16
x^9 : x^3 = x^6
Equation - [tex]8x^3y^4[/tex] divided by (1/2x^3)=16x^6y^4.
What is equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign. A mathematical equation is a formula that uses the equals sign to express the equality of two expressions. The meanings of the word equation as well as its cognates in other languages can vary slightly. For instance, in French, an equation is defined as having one or more variables, whereas in English, an equation is any well-formed formula that consists of two expressions linked by the equals sign.
Finding the values of the variables that result in the equality is the first step in solving an equation with variables. The unknown variables are also known as the variables for which the equation must be solved, and the unknown variable values that satisfy the equality are known as the equation's solutions.
Let the required term be z.
[tex]z/ (1/2x^3)=16x^6y^4[/tex]
[tex]z=(16x^6y^4) }{(1/2x^3)}[/tex]
[tex]z = 8x^3y^4[/tex]
Hence, [tex]8x^3y^4[/tex]
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Use the diagram below. What is the value of z?
(Picture included) it would mean sm if anyone could help
[tex]z = 29°[/tex]
Step-by-step explanation:
According to the triangle angle sum theorem, the sum of the interior angles of a triangle is 180°. So for [tex]\triangle{ABD},[/tex] the sum of its interior angles is
[tex]43 + 59 + x = 180[/tex]
[tex]\Rightarrow x = 78°[/tex]
But [tex]\angle{x}[/tex] is supplementary with [tex]\angle{y}[/tex] so that
[tex]x + y = 180 \Rightarrow y = 180 - 78 = 102°[/tex]
Now that we know the value of y, we apply the triangle angle sum theorem to [tex]\triangle{BDC}[/tex] and we get
[tex]49 + y + z = 180 \Rightarrow 49 + 102 + z = 180[/tex]
Solving for z, we finally get
[tex]z = 29°[/tex]
Write the prime factorization of 185.
Answer:
5 ⋅ 37
Step-by-step explanation:
185 has factors of 5 and 37.
Answer:
Step-by-step explanation:
All Factors of 185: 1, 5, 37 and 185.
Negative Factors of 185: -1, -5, -37 and -185.
Prime Factors of 185: 5, 37.
Prime Factorization of 185: 5^1× 37^1
Sum of Factors of 185: 228.
Select two answers from below. x=_ and then which theorem justifies your answer.
(2x + 2)
(3x -63)
m
a
x=63
x=64
Ob
c
roob.
X=65
X=66
Alternate Interior Angles
Alternate Exterior Angles
Corresponding Angles
Same Side Interior Angles
f
Answer:
c. x=65
f. Alternate Exterior Angles
Step-by-step explanation:
2x+2=3x-63
2x=3x-65
-x=-65
x=65
They would be Alternate Exterior Angles because, they are 1, both on the outside of the parallel lines, and they are on different sides of the intersecting line, making them alternate. So, Alternate Exterior Angles
Please Help Me, I don't understand this kind of math
Answer:
x = 9 cm
y = 4 cm
Step-by-step explanation:
The angle markings tell you the three angles of one triangle are equal to the three angles of the other triangle. That means the triangles are "similar", and the lengths of corresponding sides have the same ratio.
The bottom sides, between the angles with 1 mark and 3 marks, are shown as 3 cm in the green triangle and 6 cm in the blue triangle. This tells you all of the the green triangle dimensions are half those of the corresponding dimensions in the blue triangle:
x = (18 cm)/2 = 9 cm
It also tells you the blue triangle dimensions are 2 times those of the green triangle:
y = 2(2 cm) = 4 cm
_____
Additional comments
Corresponding sides having the same ratio means they are proportional (and vice versa). This can be expressed in equation form as ...
y/(2 cm) = (18 cm)/x = (6 cm)/(3 cm)
__
You may want to discuss this problem with your teacher. The side lengths shown in the figure do not form a triangle. The two short sides are too short to connect to the ends of the long side. The figure is impossible.