Rewrite each algebraic expression in an equivalent form with the fewest
number of terms possible.
a. 6(x + 7)(x + 2)
b. (2y – 5)
c. (5x + 4y)(2x - y)
d. (3x + 7)(3x – 7)
e. (t + 2) – (4t +9) – t
Answers
Answer:
Step-by-step explanation:
The terms will be multiplied in order to get the simplified polynomials.
a. 6(x + 7)(x + 2)
[tex]6(x + 7)(x + 2)\\=6[x(x+2)+7(x+2)]\\=6(x^2+2x+7x+14)\\=6(x^2+9x+14)\\=6x^2+54x+84[/tex]
The simplified form of 6(x + 7)(x + 2) is [tex]6x^2+54x+84[/tex]
b. (2y – 5)^2
Using the formula: [tex](a-b)^2 = a^2+b^2-2ab[/tex]
[tex]=(2y)^2+(5)^2-2(2y)(5)\\=4y^2+25-20y[/tex]
The simplified form is: [tex]4y^2-20y+25[/tex]
c. (5x + 4y)(2x - y)
[tex]=5x(2x-y)+4y(2x-y)\\=10x^2-5xy+8xy-4y^2\\=10x^2+3xy-4y^2[/tex]
The simplified form of (5x + 4y)(2x - y) is [tex]10x^2+3xy-4y^2[/tex]
d. (3x + 7)(3x – 7)
Using the formula: [tex](a+b)(a-b) = a^2-b^2[/tex]
[tex]= (3x)^2-(7)^2\\= 9x^2-49[/tex]
The simplified form of (3x + 7)(3x – 7) is [tex]9x^2-49[/tex]
e. (t + 2) – (4t +9) – t
[tex]=t+2-4t-9-t\\=t-4t-t+2-9\\= -4t-7[/tex]
The simplified form of (t + 2) – (4t +9) – t is [tex]-4t-7[/tex]
Hence,
a. The simplified form of 6(x + 7)(x + 2) is [tex]6x^2+54x+84[/tex]
b. The simplified form is: [tex]4y^2-20y+25[/tex]
c. The simplified form of (5x + 4y)(2x - y) is [tex]10x^2+3xy-4y^2[/tex]
d. The simplified form of (3x + 7)(3x – 7) is [tex]9x^2-49[/tex]
e. The simplified form of (t + 2) – (4t +9) – t is [tex]-4t-7[/tex]
Related Questions
PLEASE HELP!!
Find all missing angles
Answers
Answer:
m∠2= 52° (alt. ∠s)
m∠1 +m∠2= 180° (adj. ∠s on a str. line)
m∠1 +52°= 180°
m∠1= 180° -52°
m∠1= 128°
m∠3= 47° (alt. ∠s)
m∠4 +47°= 180°
m∠4= 180° -47°
m∠4= 133°
m∠5 +52° +47°= 180° (adj. ∠s on a str. line)
m∠5 +99°= 180°
m∠5= 180° -99°
m∠5= 81°
☆ The sum of the angles of a straight line is 180°.
you have $56 to spend on your family dinner each entree cost $8 and each cost $4
Answers
Answer:
ok I don't understand the problem.?
Step-by-step ex
There is no information here.
There isn't even a question. lol
a train covers 165km in 1.5 hours find the constant variation
Answers
Answer:
110 km/hour
Step-by-step explanation:
distance = 165 km
time = 1.5 hours
constant of variation = distance/time
constant of variation = 165 km / 1.5 hours = 110 km/hour
Kendall bought 6 notbooks and 3 pens for a total of $27. The cost of one notebook is $1.50 more than the cost of one pen. What is the combined cost of one notebook and one pen?
Answers
Answer:
$5.5
Step-by-step explanation:
6 * N (notebook) + 3 * P (pen) = 27
n = 1.5 +P
6 * (1.5 + P) + 3 * P = 27
9 +6p +3p = 27
9p = 18
p (pen): $2
N (notebook): $3.5
combined cost of 1 pen and 1 notebook: $2 + $ 3.5 = $ 5.5
Answer:
5.5
Step-by-step explanation:
^
The graph of the equation x – 2y = 5 has an x-intercept of 5 and a slope of StartFraction one-half EndFraction. Which shows the graph of this equation?
A coordinate plane with a line passing through (0, negative 2) and (4, 0).
A coordinate plane with a line passing through (0, 0.5) and (1, negative 1.5).
A coordinate plane with a line passing through (negative 2, 0) and (0, negative 1).
A coordinate plane with a line passing through (negative 3, negative 4) and (5, 0).
Answers
Answer:
Graph D
Step-by-step explanation:
Look, I'm trying here, I tried the graphing calculator and it appeared as Graph D
The graph of the equation is a coordinate plane with a line passing through (-3, -4) and (5, 0). Option D is correct
Equation of a lineA line is the shortest distance between two points. The equation of a line in slope intercept form is expressed as y = mx + b
where:
m is the slopeb is the y-interceptGiven the equation x - 2y = 5
Write in slope-intercept form;
-2y = -x + 5
y = 1/2 x - 5/2
We need two points passing through the line, we will find the x and y-intercept
If x = -3
y = 1/2(-3) - 5/2
y = -3/2 - 5/2
y = -4
Hence one of the coordinate point is (-3, -4)
If x = 5
y = 1/2(5) - 5/2
y = 5/2 -5/2
y = 0
Hence one of the coordinate point is (5, 0)
Hence the graph of the equation is a coordinate plane with a line passing through (-3, -4) and (5, 0).
Learn more on equation of a line here: https://brainly.com/question/18831322
#SPJ9
which angle has its terminal side on the negative y-axis?
Answers
A positive [tex]\frac{3\pi }{2}[/tex] radians angle’s terminal side falls on the negative y-axis.
AngleThe starting side of the angle is the primary ray, whereas the end position of the ray following rotation is the terminal side of that angle.
How to find the angle that has its terminal side on the negative y-axis?A positive 270 degree angle’s terminal side falls on the negative y-axis as shown in the figure.
Hence, a positive [tex]\frac{3\pi }{2}[/tex] radians angle’s terminal side falls on the negative y-axis.
Thus, option (B) is correct.
Consider the following figure for this.
Learn more about the angle here-
https://brainly.com/question/13954458
#SPJ2
Answer: B
Step-by-step explanation:
which choice is equvalent to the expression below 5^9.96
a. 5^9 • 5^96/10 • 5^9/100
b. 5^9•5^9/10•5^6/100•5^9/1000
c. 5^9+5^9/10+6^6/100
d. 5^9+9/10+9/10+6/1000
Answers
Answer:
B
Step-by-step explanation:
5^9•5^9/10•5^6/100•5^9/1000 = 5^(9+0.9+0.06+0.009) = 5^9.969
Find the radius of the base of a cylinder with a volume of 1357.17 cm3 if the height of the cylinder is twice the length of the radius.
Answers
Answer:
6cm
I hope it will be useful.
Graph a line that has a slope of -3 and contains the point (4,-2)
Answers
Answer:
The equation of the line is:
[tex]y = -3x+10[/tex]
The graph is attached below.
Step-by-step explanation:
Given that the line has a slope of -3, so
m = -3
As the point contains the point (4, -2), so we can use the point-slope form of the line equation to determine the line.
Point slope form:
[tex]y-y_1=m\left(x-x_1\right)[/tex]
where m is the slope of the line and (x₁, y₁) is the point
so substituting the values m = -3 and the point (4, -2)
[tex]y-y_1=m\left(x-x_1\right)[/tex]
[tex]y - (-2) = -3(x-4)[/tex]
[tex]y+2 = -3x+12[/tex]
[tex]y = -3x+12-2[/tex]
[tex]y = -3x+10[/tex]
Therefore, the equation of the line is:
[tex]y = -3x+10[/tex]
The graph is attached below.
a hiker walks at a speed of 3 2/5 km per hour. how many km will he walk in 3/4 of an hour
Answers
Answer:
2.55
Step-by-step explanation:
Bir su deposunun 17/24 şu ile doludur depodaki suyun 80 litresi kullaninca deponun yarısı dolu oluyor buna göre deponun tamamı kaç litre su alir
Answers
Answer:
384 Litre
Step-by-step explanation:
Tankın alabileceği toplam su miktarı = x
(17/24) x - 80 Litre = 1 / 2x
Benzer terimleri toplayın
17 / 24x - 1 / 2x = 80 Litre
5 / 24x = 80 Litre
5x / 24 = 80 Litre
Çapraz Çarpma
5x = 80 Litre × 24
x = 80 Litre × 24/5
x = 384 Litre
Dolayısıyla tüm tankın alabileceği su miktarı 384 Litredir.
How could the numbers 2, 3, 4, and 5 be used to get 10?
es
1)
A
2(4) - 3 + 5
2 +3-4 + 5
5-2-3+ 4
B)
D)
5(3)- 2(4)
Answers
Answer:
2(4)-3+5
Step-by-step explanation:
8-3+5
13-3
10
Answer:
i would say a
Step-by-step explanation:
6. Given the function f(x) = 7x determine the equation of a new function, g(x), that is reflected over
the x-axis and then shifted 4 units down.
a. g(x) = 7x + 4
b. g(x) = -7x + 4
c. g(x) = 7x - 4
d. g(x) = -7x - 4
Answers
Answer:
d. g(x) = -7x - 4
Step-by-step explanation:
If it is reflected over the x-axis, there is a negative sign to the x term.
There is a shift of 4 units, so it is -4.
There were 40 swimmers on the team last year. This year, there are 20 swimmers. What is the percent decrease?
Answers
i agree it should be 50%
Step-by-step explanation:
half of 40 is 20
20 pts
The graph below shows the numbers of cups of mango juice that are mixed with different numbers of cups of lemon-lime soda to make servings of mango soda:
What is the ratio of the number of cups of mango juice to the number of cups of lemon-lime soda?
1:40
10:1
40:1
1:10
Answers
Answer:
It'a B. 10:1
Step-by-step explanation:
answer to be marked as brainlist
Answers
Answer:
The SF is 3
Step-by-step explanation:
The sides are 3x the length of the sides of ∆ABC
I’ll mark brainliest what’s 1228822882-1228822882?
Answers
0
Subtract
Answer is 0
Hope this helps
God bless!
Answer:
oofff
Step-by-step explanation:
PLZ HELP ASAP MARK BRAINLIEST VIEW PICTURE!!
Answers
Answer: The second option
Step-by-step explanation: 14mph times 5 equal 70. 5 hours after 6 am is 11 am. 70 divided by 20 is 3.5. 3.5 hours after 6 am is 9:30. Hence 9:30 to 11
Karl needs to build a stage that has an area of 84 square feet. The length of the stage should be longer than the width. What are the possible whole number measurements for the length and width of the stage? Complete the table with possible measurements of the stage. Length Width 1 2 3 4 6 7
Answers
Answer/Step-by-step explanation:
84 = L x w
84 = 84 x 1
84 = 42 x 2
84 = 28 x 3
84 = 21 x 4
84 = 14 x 6
84 = 12 x 7
Answer:
below is the answer
Step-by-step explanation:
84 = L x w
84 = 84 x 1
84 = 42 x 2
84 = 28 x 3
84 = 21 x 4
84 = 14 x 6
84 = 12 x 7
Given right triangle ABC with altitude BD drawn to hypotenuse AC. If AB = 3 and AC = 9, what is the length of AD? (Note: the figure is not drawn to scale.)
Answers
Answer:
The length of AD is 1 unit
Step-by-step explanation:
Let us solve the question
In Δ ABC
∵ ∠B is a right angle
∵ BD is perpendicular to the hypotenuse AC
∴ (AB)² = AD × AC ⇒ rule
∵ AB = 3 units
∵ AC = 9 units
∵ AD = x
→ Substitute them in the rule above
∴ (3)² = x × 9
∴ 9 = 9x
→ Divide both sides by 9
∵ [tex]\frac{9}{9}[/tex] = [tex]\frac{9x}{9}[/tex]
∴ 1 = x
∴ The length of AD is 1 unit
pls help in a rushhh will give points
Answers
Answer:
The answer is 120
Step-by-step explanation:
A triangle has 180 degrees in it total.
So all you have to do is 180 - 35 -25, and get your answer.
Help pls !!!!!!!!!!!!!
Answers
Answer:
WOAH hold up i may be able to help you
Step-by-step explanation:
SAS- side-angle-side
in a survey of 500 voters 430 said they would vote for the same candidate again what percent of the voters would vote the same way again
Answers
Answer:
86%
Step-by-step explanation:
430 × 100 = 430 = 86%
500 1 5
you are going to cancel. 100 divided by 100 leaves 1. 500 divided by 100 is 5.
430×1= 430. 5×1=5. divide 430 by 5 and you"ll get 86.
Choose Yes or No to tell if 14.3 will make each equation true.
19.05 + □ = 33.35
□ + 32.62 = 45.92
62.01 – □ = 47.71
□ – 4.88 = 9.42
Answers
2. No
3. No
4. Yes
What is the value of x in the equation 8 + x = 3? (4 points) −5 5 11 24
Answers
Answer:
-5 is the correct answer
Answer:
-5
Step-by-step explanation:
Linear Function #3!!!
Answers
Answer:
The bottom left table
Step-by-step explanation:
The only table that is a line is the bottom left
Please help me please
Answers
x-(y+z)
x=9
y=3
z=2
9-(3+2)
the answer is A.
1. Sharon used 3 cups of water with
every 2 cups of lemon juice to make
lemonade. Find the ratio of the amount
of lemon juice used to the amount
of water used
Answers
Answer:3:2 is the answer i am very sure
Step-by-step explanation:
please help me on this , tyyy :]
Answers
9514 1404 393
Answer:
(a) 1, 2
(b) 4
Step-by-step explanation:
(a) 9x +81 = 9·x +9·9 = 9(x +9) . . . . . . matches first and second choices
__
(b) 10 +14y -5 -y = (14y -y) +(10 -5) = 13y +5 . . . . . . matches fourth choice only
Using the order of operations, what should be done first to evaluate 12+(-6)(3)+(-2)?
Vx
O Divide 12 by 5.
O Multiply -6 and 3.
O Divide 12 by -6.
O Add 3 and -2.
Hurry pls
Answers
You need to multiply -6 and 3