Answer:
(x - 6)(x + 4)(x - 2)
Step-by-step explanation:
since x = 6 is a root then (x - 6) is a factor
x³ - 4x² - 20x + 48 ÷ (x - 6)
= (x - 6)(x² + 2x - 8)
= (x - 6)(x + 4)(x - 2) ← factors of f(x)
By using the Remainder Theorem, all the factors of the function are,
⇒ (x - 6) (x + 2) (x - 4)
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
One root of function f (x) = x³ -4x² -20x + 48 is, x = 6.
Hence, (x - 6) is divide the function f (x) = x³ -4x² -20x + 48 as;
(x - 6) ) x³ -4x² -20x + 48 ( x² + 2x - 8
x³ - 6x²
--------------
2x² - 20x
2x² - 12x
-----------------
- 8x + 48
- 8x + 48
----------------
0
Hence, We get;
f (x) = x³ -4x² -20x + 48
f (x) = (x - 6) (x² + 2x - 8)
⇒ f (x) = (x - 6) (x² - 4x + 2x - 8)
⇒ f (x) = (x - 6) (x(x - 4) + 2(x - 4))
⇒ f (x) = (x - 6) (x + 2) (x - 4)
Thus., By using the Remainder Theorem, all the factors of the function are,
⇒ (x - 6) (x + 2) (x - 4)
Learn more about the function visit:
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Find the perimeter of triangle PQR if the vertices are P(3,0), Q(-1,3) and R(11,6).
[tex]\dag\bf\:P(x_1,y_1)=(3,0)[/tex]
[tex]\dag\bf\:Q(x_2,y_2)=(-1,3)[/tex]
[tex]\dag\bf\:R(x_3,y_3)=(11,6)[/tex]
❅ Distance between P and Q :
[tex]\sf\:PQ=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]\sf\:PQ=\sqrt{(-1-3)^2+(3-0)^2}[/tex]
[tex]\sf\:PQ=\sqrt{(-4)^2+(3)^2}[/tex]
[tex]\sf\:PQ=\sqrt{16+9}[/tex]
[tex]\sf\:PQ=\sqrt{25}[/tex]
[tex]\bf\:PQ=5\:unit[/tex]
❅ Distance between Q and R :
[tex]\sf\:QR=\sqrt{(x_3-x_2)^2+(y_3-y_2)^2}[/tex]
[tex]\sf\:QR=\sqrt{(11-(-1))^2+(6-3)^2}[/tex]
[tex]\sf\:QR=\sqrt{(12)^2+(3)^2}[/tex]
[tex]\sf\:QR=\sqrt{144+9}[/tex]
[tex]\sf\:QR=\sqrt{153}[/tex]
[tex]\bf\:QR=12.37\:unit[/tex]
❅ Distance between P and R :
[tex]\sf\:PR=\sqrt{(x_1-x_3)^2+(y_1-y_3)^2}[/tex]
[tex]\sf\:PR=\sqrt{(3-11)^2+(0-6)^2}[/tex]
[tex]\sf\:PR=\sqrt{(-8)^2+(-6)^2}[/tex]
[tex]\sf\:PR=\sqrt{64+36}[/tex]
[tex]\sf\:PR=\sqrt{100}[/tex]
[tex]\bf\:PR=10\:unit[/tex]
◈ Perimeter of Triangle :
➝ perimeter = PQ + QR + PR
➝ perimeter = 5 + 12.37 + 10
➝ Perimeter = 27.37 unit
I need help understanding the process of each formula. Each formula for each shape is different. I need help understanding the area and perimeter of the circled shapes and help answering them. **This is a homework I need help with** I answered the other uncircled questions unvirtually but need help with circled ones.
Answer:
See below.
Step-by-step explanation:
1)
Triangle
Perimeter = sum of lengths of the 3 sides
Area = base * height/2
Perimeter = 9 m + 10 m + 11 m = 30 m
Area = 10 m * 8 m /2 = 40 m^2
5)
Parallelogram
Perimeter = sum of lengths of 4 sides.
Hint: opposite side have equal lengths
Area = base * altitude
Perimeter = 9 m + 9 m + 7 m + 7 m = 32 m
Area = 9 m * 6 = 54 m^2
6)
Triangle
Do the same as for problem 1.
8)
Triangle
Do the same as for problem 1.
10)
Parallelogram
Do the same as for problem 5.
Try problems 6, 8, 10 on your own. Write the answers for each in the comments, and I will tell you if you're correct and will help you if you need help.
A television set that retails for $600 is markdown by 20%. at checkout, an additional 20% is marked off the price of the tv. Find the final selling price of the television set.
Answer:
$360
Step-by-step explanation:
i added 20%+20%=40% so you turn 40% into.40 then you multiply 600×.40 to get 240 since it is discounted you have to subtract so you subtract 600-240 to get 360 which is your final product
Given f(x)= 18x + 12, find f(5).
Answer:
102
Step-by-step explanation:
Given f(x) =18x+12
F(5)=18(5)+12
=90+12
=102
“Y to the fourth Power” is what mathematical Expression? PLZ HELP ASAP 12 pts & Brainliest!
Answer:
[tex]Y^4[/tex]
Step-by-step explanation:
Given:
Y to the fourth Power
Required
Express using mathematical expression
In mathematics;
To the nth power means raise to the power of n
In this case;
to the fourth Power means raise to the power of 4
Hence;
Y to the fourth Power = Y raise to the power of 4
And this can be represented mathematically as:
[tex]Y^4[/tex]
What is the Standard form of five and three hundred fifty-two thousandths?
5.352
Hoped this helped.
Please add brainliest :)
Good luck mate ;) !
What is f(1/3
F(1/3)=-3x+7
Answer:
6
Step-by-step explanation:
-3(1/3)+7
6...this is it
solve for c: a(c−b)=d
The answer to this D=A(c-B)
In the 2010 Winter Olympics, American Tim Burke aspired to win an Olympic medal in the biathlon, an event that combines cross-country skiing and target shooting. Unfortunately, he wasn’t as successful as he’d hoped. After the 20K race, where he only hit 15 of his 20 targets, he criticized himself, saying his shooting was way below his average of 85% on the season so far. What does it mean if we claim that Burke’s ability to hit a target is 85%?
Answer:
If we claim that his ability to hit a target is 85% it means that he normally hits 17 out of 20 targets or 85 out of every 100 targets
Step-by-step explanation:
Percentage is the mathematics term for a ratio of numbers expressed in terms multiple of 100 and denoted by the symbol %. The percentage value has no unit and is used to compare proportion of items or to serve as a visible guide to the relative proportion event occurrence or prevalence of a characteristics within a population.
In the question, we have, the athlete's hitting average given as 85% of targets which means when presented with 20 targets, he is expected to hit 85% of the targets which is 0.85 × 20 = 17 hits.
Jorge needs 27 ounces of sugar for a recipe. He has 2 pounds of sugar. If he
makes the recipe, how much sugar will he have left over?
Answer:
he won't, he will need more
Step-by-step explanation:
Point O is on line segment NP. Given OP = 10, NP = 2x, and NO = x +7,
determine the numerical length of NO.
Answer:
17.
Step-by-step explanation:
We know that NP = NO + NP because all the points are on the same line.
So 2x = 10 + (x + 7),
x = 17.
Answer: Its 8
Step-by-step explanation:
Describe the 4 cases to look out for when dealing with adding or subtracting integers
Answer:
Step 1: Take the absolute value of each number. Step 2: Subtract the number with a smaller absolute value from the number with bigger or larger absolute value. Step 3: Copy the sign of the number with the bigger or larger absolute value.
Step-by-step explanation:
Which of the following must be true?
А
If (d) = 58 then d = 58 only
B
If yl = 11 then y = 11 and y = -11
C
If [x] = 18 then r = -18 only
D
If [n] = -49 then n = -49 and n = 49
Answer:
A
Step-by-step explanation:
58=58
1. Describe two ways the numbers in each proportion are related.
a) 5:20 = 125:500 b) 10:1 = 120:12 c) 75:25 = 300: 100
d) 1:3 = 16:48
2. Multiply between ratios to determine each value of n.
a) 2:5 = 8:n b) 2:n = 6:9 c) n:5 = 12:20
d) 8:n = 4:15
Need
Read
the lo
3. Multiply within ratios to determine each value of z.
a) 4:8 = 3:2 b) 5:2 = 6:18 c) z: 14 = 10:20
d) 3:21 = z:56
Answer:
Each value has been identified below.
Step-by-step explanation:
(1) We have to describe two ways the numbers in each proportion are related;
(a) 5 : 20 = 125 : 500
One way of describing that the given ratios are in proportion is;
Product of means = Product of extremes
20 [tex]\times[/tex] 125 = 5 [tex]\times[/tex] 500
2500 = 2500
This shows that the given proportion is related.
Another way of describing that the given ratios are in proportion is;
As 5 : 20 = 125 : 500
We will check that; [tex]\frac{5}{125}[/tex] is equal to [tex]\frac{20}{500}[/tex] or not.
[tex]\frac{5}{125} = \frac{20}{500}[/tex]
[tex]\frac{1}{25} = \frac{1}{25}[/tex]
This shows that the given proportion is related.
(b) 10 : 1 = 120 : 12
One way of describing that the given ratios are in proportion is;
Product of means = Product of extremes
1 [tex]\times[/tex] 120 = 10 [tex]\times[/tex] 12
120 = 120
This shows that the given proportion is related.
Another way of describing that the given ratios are in proportion is;
As 10 : 1 = 120 : 12
We will check that; [tex]\frac{10}{120}[/tex] is equal to [tex]\frac{1}{12}[/tex] or not.
[tex]\frac{10}{120} = \frac{1}{12}[/tex]
[tex]\frac{1}{12} = \frac{1}{12}[/tex]
This shows that the given proportion is related.
(c) 75 : 25 = 300 : 100
One way of describing that the given ratios are in proportion is;
Product of means = Product of extremes
25 [tex]\times[/tex] 300 = 75 [tex]\times[/tex] 100
7500 = 7500
This shows that the given proportion is related.
Another way of describing that the given ratios are in proportion is;
As 75 : 25 = 300 : 100
We will check that; [tex]\frac{75}{300}[/tex] is equal to [tex]\frac{25}{100}[/tex] or not.
[tex]\frac{75}{300} = \frac{25}{100}[/tex]
[tex]\frac{1}{4} = \frac{1}{4}[/tex]
This shows that the given proportion is related.
(d) 1 : 3 = 16 : 48
One way of describing that the given ratios are in proportion is;
Product of means = Product of extremes
3 [tex]\times[/tex] 16 = 1 [tex]\times[/tex] 48
48 = 48
This shows that the given proportion is related.
Another way of describing that the given ratios are in proportion is;
As 1 : 3 = 16 : 48
We will check that; [tex]\frac{1}{16}[/tex] is equal to [tex]\frac{3}{48}[/tex] or not.
[tex]\frac{1}{16} = \frac{3}{48}[/tex]
[tex]\frac{1}{16} = \frac{1}{16}[/tex]
This shows that the given proportion is related.
(2) Now we have to determine each value of n in the following given ratios;
(a) 2 : 5 = 8 : n
As we know that Product of means = Product of extremes
5 [tex]\times[/tex] 8 = 2 [tex]\times[/tex] n
40 = 2n
[tex]n=\frac{40}{2}[/tex] = 20
Hence, the value of n is 20.
(b) 2 : n = 6 : 9
As we know that Product of means = Product of extremes
n [tex]\times[/tex] 6 = 2 [tex]\times[/tex] 9
6n = 18
[tex]n=\frac{18}{6}[/tex] = 3
Hence, the value of n is 3.
(c) n : 5 = 12 : 20
As we know that Product of means = Product of extremes
5 [tex]\times[/tex] 12 = n [tex]\times[/tex] 20
60 = 20n
[tex]n=\frac{60}{20}[/tex] = 3
Hence, the value of n is 3.
(d) 8 : n = 4 : 15
As we know that Product of means = Product of extremes
n [tex]\times[/tex] 4 = 8 [tex]\times[/tex] 15
4n = 120
[tex]n=\frac{120}{4}[/tex] = 30
Hence, the value of n is 30.
(3) Now we have to determine each value of z in the following given ratios;
(a) 4 : 8 = 3 : z
As we know that Product of means = Product of extremes
8 [tex]\times[/tex] 3 = 4 [tex]\times[/tex] z
24 = 4z
[tex]z=\frac{24}{4}[/tex] = 6
Hence, the value of z is 6.
(b) 5 : z = 6 : 18
As we know that Product of means = Product of extremes
z [tex]\times[/tex] 6 = 5 [tex]\times[/tex] 18
6z = 90
[tex]z=\frac{90}{6}[/tex] = 15
Hence, the value of z is 15.
(c) z : 14 = 10 : 20
As we know that Product of means = Product of extremes
14 [tex]\times[/tex] 10 = z [tex]\times[/tex] 20
140 = 20z
[tex]z=\frac{140}{20}[/tex] = 7
Hence, the value of z is 7.
(d) 3 : 21 = z : 56
As we know that Product of means = Product of extremes
21 [tex]\times[/tex] z = 3 [tex]\times[/tex] 56
21z = 168
[tex]z=\frac{168}{21}[/tex] = 8
Hence, the value of z is 8.
Is it necessary to do all of the calculations to determine the sign of the product? Why or why not?
(-5) × (-5) x ... X (-5) = (-5)95
95 times
Please help I don’t understand
Answer:
= (- 475)
Step-by-step explanation:
Given:
(-5) × (-5) × ... × (-5) = (-5)95
Find:
Sign of the product
Computation:
(-5) × (-5) × ... × (-5) = (-5)95
= (- 475)
No, it is not compulsory to do all calculation to find sigh of product
Negative number × odd time = Negative number
Negative number × even time = Positive number number
smith math class has 40 students but students drop out at a rate of two students per week how much students will be in mr.smith class after 7 weeks of school
Answer this. Will give brainliest (that probably spelled wrong)
Answer:
He added the exponents instead of multiplying them
Step-by-step explanation:
When a power is raised to a power (in this case, -8 was raised to the -2) the exponents should be multiplied, not added. So instead of j^-10 it should be j^16.
The area of a blackboard is 1 1 third square yards. A poster’s area is 8 over 9 square yards. What is the unit rate of the blackboard's area to the poster's area? (plz dont take points)
Step-by-step explanation:
(1 ⅓ yd²) / (8/9 yd²)
(4/3 yd²) / (8/9 yd²)
(4/3) × (9/8)
3/2
1.5 / 1
Answer:
[tex]\qquad {:}\longrightarrow\tt 1\dfrac {1}{3}=\dfrac{4}{3}[/tex]
Now answer[tex]\qquad {:}\longrightarrow\displaystyle\tt \dfrac {\dfrac {4}{3}}{\dfrac {8}{9}}[/tex]
Simplify[tex]\qquad {:}\longrightarrow\tt \dfrac {4}{3}\times \dfrac {9}{8}[/tex]
[tex]\qquad {:}\longrightarrow\tt \dfrac {36}{24}[/tex]
[tex]\qquad {:}\longrightarrow\tt \dfrac {3}{2}[/tex]
[tex]\qquad {:}\longrightarrow\tt 1.5 \:per\:unit[/tex]
Help please ill paypal you!!!!!
Answer:
Step-by-step explanation:
The frequency table shows the results of tossing a ball 24 times into the four coloured sections on a carnival game Section | number of | Tosses Blue | 3 Green | 5 Red | 12 Yellow | 4 Based on the data on the table, how many times will the ball most likely land in the yellow section when it is tossed 200 times? A. 35 B. 40 C. 50 D. 65
Answer:
50
Step-by-step explanation:
you toss the ball 24 times, and of those 24 times, it lands 12 times on the yellow section, so 12/24= 0.5
Answer: 50
Step-by-step explanation:
HELP ASAP PLEASE!!!!
Simplify numbers to layman terms.
[tex]\frac{\pi}{2}[/tex] will be a little more than [tex]\frac{3}{2}[/tex], since [tex]\pi[/tex] is 3.14.
[tex]-\sqrt{18}[/tex] will be a little less than -4, since [tex]-\sqrt{18}<-\sqrt{16}[/tex].
[tex]\sqrt{18}[/tex] will be a little more than 4, since [tex]\sqrt{18}>\sqrt{16}[/tex]
[tex]-\sqrt{7}[/tex] will be a little less than -2, since [tex]-\sqrt{7}<-\sqrt{4}[/tex]
Now we can order them.
[tex]-\sqrt{18},-\sqrt{7},\frac{\pi}{2},\sqrt{18}[/tex]
Hope this helps.
頑張って!
Answer:
1: negative square root of 18 (-4.2)
2: negative square root of 7 (-2.6)
3: pi/2 (1.57)
4: square root of 15 (3.9)
some are approximate calculations, but you only need the order of from smallest to largest number
Manny has four pieces of carpet in the shape of a square like the one shown. He wants to use them together to carpet a portion of his basement. What is the area of the space he can cover with carpet?
Answer:
the area of the space he can cover with carpet = 16x⁴ yards²
Step-by-step explanation:
The shape of the square is not shown in this question.
Let assume that the base of the shape of the square is 2x² yards.
and Manny has four of that.
Then side we known the base, we can calculate for the area of the square.
Area of a square = l²
Area of a square = (2x² yards)²
Area of a square = 4x⁴ yards²
However, since Manny has four pieces of that carpet and wants to use them together to carpet a portion of his basement.
Let the pieces of the carpet be carpet A, B, C and D
where; their side is 2x² yards, then their area = 4x⁴ yards²
the area of the space he can cover with carpet = A+B+C+D
the area of the space he can cover with carpet = 4x⁴ yards² + 4x⁴ yards² + 4x⁴ yards² + 4x⁴ yards²
the area of the space he can cover with carpet = 16x⁴ yards²
ax + by = c
Solve for b
Answer:
[tex]b = \frac{c - ax}{y}[/tex]
Step-by-step explanation:
[tex]ax + by = c \\ by = c - ax \\ b = \frac{c - ax}{y} [/tex]
The girl loves to go shopping.
Inference:
Answer:
you can infer she likes to dress up in whatever style she likes.
Step-by-step explanation:
1) 116 = -2x - 3(1 + 5x)
Answer:
x = -7
Step-by-step explanation:
I hope this helps!
Hi there!
~
[tex]116 = -2x - 3(1 + 5x)[/tex]
= [tex]x = -7[/tex]
Hope this helped you!
Steve weighs 18 more pounds than Ryan. If their weight totals 144 pounds, how much does Ryan weigh?
Answer:
A) Steve = Ryan +18
B) Steve + Ryan = 144
A) Steve -Ryan = 18 then adding B
B) Steve + Ryan = 162
2 Steve = 162
Steve weighs 81 pounds
Ryan weighs (81 -18) pounds 63 pounds
Step-by-step explanation:
A basketball coach is interested in measuring a players vertical jumping ability. While standing and reaching up the players hand reaches the 4 inch mark on the scale. When jumping, the player can reachthe 19 inch mark. What is the players vertical jumping ability?
Answer:
3
Step-by-step explanation:
HELP FAST!
On a number line, suppose point E has a coordinate of - 4, and EG = 8. What are the possible coordinates of point G?
The possible coordinates for G are?
Answer:
G could be at either 14 or at -6.
Step-by-step explanation:
What’s the simplified expression for the expression below 7(x - 4) - 3(x + 5)
Answer:
4 x + -43
Step-by-step explanation:
Simplify the following:
7 (x - 4) - 3 (x + 5)
Hint: | Distribute 7 over x - 4.
7 (x - 4) = 7 x - 28:
7 x - 28 - 3 (x + 5)
Hint: | Distribute -3 over x + 5.
-3 (x + 5) = -3 x - 15:
7 x + -3 x - 15 - 28
Hint: | Group like terms in 7 x - 3 x - 28 - 15.
Grouping like terms, 7 x - 3 x - 28 - 15 = (7 x - 3 x) + (-28 - 15):
(7 x - 3 x) + (-28 - 15)
Hint: | Combine like terms in 7 x - 3 x.
7 x - 3 x = 4 x:
4 x + (-28 - 15)
Hint: | Evaluate -28 - 15.
-28 - 15 = -43:
Answer: 4 x + -43
Answer:
4x – 43
Step-by-step explanation:
What is the simplified form of this expression (8x^2-3x+1/3) - (2x^2-8x+3/5)
Answer:=6x2+5x + −4/15
Step-by-step explanation:Let's simplify step-by-step.
8x2−3x+13−(2x2−8x+3/5)
Distribute the Negative Sign:
=8x2−3x+13+−1(2x2−8x+3/5)
=8x2+−3x+13+−1(2x2)+−1(−8x)+−1(3/5)
=8x2+−3x+13+−2x2+8x+−3/5
Combine Like Terms:
=8x2+−3x+1/3+−2x2+8x+−3/5
=(8x2+−2x2)+(−3x+8x)+(1/3+−3/5)
=6x2+5x+−4/15