Answer:
(P + 2)(p+ 16)
Step-by-step explanation:
Factor p 2 + 18p + 32.
Consider the form x² +bx +c. Find a pair of integers whose product is c and whose sum is b .
In this case, whose product is 32 and whose sum is 18 .
2,16 .
Write the factored form using these integers.
(P + 2)(p+ 16)
CHECK
(P + 2)(p+ 16)
distribute
p(p+16) + 2(p+16)
simplify
p² + 16p + 2p + 32
combine 16p + 2p = 18p
p² + 18p + 32
Please mark as brainliest
Answer:
(p + 2)(p + 16)
That's your answer!!
Write a system of equations and solve using elimination. Ricardo has two bills. The two bills together are $21. One bill is worth $19 more than the other. What are the two bills?
Answer:
The worth of one bill is $20 and the worth of the other bill is $1
Step-by-step explanation:
Let
x----> the worth of one bill
y ---> the worth of the other bill
I assume x > y
we know that
x+y=21 ----> equation A
x=y+19 ---> equation B
Solve the system by elimination
Multiply equation B by -1 both sides
-x=-y-19 ----> equation C
Adds equation A and equation C
x+y=21
-x=-y-19
------------
y=21-y-19
2y=2
y=1
Find the value of x
x=y+19 -----> x=1+19=20
therefore
The worth of one bill is $20 and the worth of the other bill is $1
what is the common difference for this arithmetic sequence? -6,-2,2,6,10 A.4 B.5 C.3 D.6
Answer:
A
Step-by-step explanation:
The common difference d is the difference between consecutive terms.
d = - 2 - (- 6) = - 2 + 6 = 4
d = 2 - (- 2) = 2 + 2 = 4
Answer:
4
Step-by-step explanation:
BIG BRAIN
Find the slope and the y-intercept of the line whose equation is negative 6 x plus y equals negative 7 −6x+y = −7.
Answer:
slope = 6, y- intercept = - 7
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Rearrange - 6x + y = - 7 into this form
Add 6x to both sides
y = 6x - 7 ← in slope- intercept form
with slope m = 6 and y- intercept c = - 7
A 43 degree angle can be classified as which angle type ?
Answer: Acute Angle
Step-by-step explanation:
Any angle 89 degrees or less will identify as an acute angle.
A 43 degree angle can be classified as an acute angle.
What type of angle is classified as 43 degrees?A 43 degree angle is classified as an acute angle which means it measures less than 90 degrees. Acute angles are commonly found in many geometric shapes.
They are also often associated with sharp corners or narrow angles. In the case of a 43 degree angle, it is smaller than a right angle (90 degrees) but larger than a zero or null angle.
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At the beginning of the season, MacDonald's had to remove 5 orange trees from his farm. Each of the remaining trees produced 210 oranges to a harvest of 41790 oranges.
Write a equation to determine the initial number of oranges on MacDonald farm.
Find the initial number orange trees on Macdonald farm.
Answer:
o = (41790/210)+5;0 = 204
Step-by-step explanation:
o = (41790/210)+5
o = 199+5
0 = 204
(pls give brainliest)
Answer: mcdonald Harvested oranges when there were 5 trees-210
So 1 tree is 210/5=42
41790 oranges come from _ trees
=41790/42
=995 trees
Step-by-step explanation:
At a competition with 7 runners, medals are awarded for first, second, and
third places. Each of the 3 medals is different. How many ways are there to
award the medals?
Decide if this is a permutation or a combination, and find the number of ways
to award the medals.
O
A. Permutation; number of ways = 210
O
B. Combination; number of ways = 210
O
c. Permutation; number of ways = 35
O
D. Combination; number of ways = 35
Answer:
Option A - Permutation; number of ways = 210
Step-by-step explanation:
Given : At a competition with 7 runners, medals are awarded for first, second, and third places. Each of the 3 medals is different.
To find : How many ways are there to award the medals?
Solution :
There are 7 runners but medals are three.
The first runner up got first medal as one is locked.
The second runner up got second medal as second is locked.
The third runner up got the third medal.
So, There is a permutation.
Number of ways to award the medals is [tex]^7P_3[/tex]
We know, [tex]^nP_r=\frac{n!}{(n-r)!}[/tex]
Substitute the values,
[tex]^7P_3=\frac{7!}{(7-3)!}[/tex]
[tex]^7P_3=\frac{7\times 6\times 5\times 4!}{4!}[/tex]
[tex]^7P_3=210[/tex]
Therefore, Option A is correct.
Permutation; number of ways = 210
which are the possible side lengths of a triangle?
Answer:
B) 4, 8, 10
Step-by-step explanation:
4+8 is greater than 10
4+10 is greater than 8
10+8 is greater than 4
7 ∙ 15 can be written as _____.
Answer:
7(10+5)
105
Step-by-step explanation:
Distributive property:
↓
A(B+C)=AB+AC
7*15=7(10+5)
7(10+5) is the correct answer.
105 is the correct answer.
I hope this helps you, and have a wonderful day!
By distributive property, 7·15 can be written as 7*(10 + 5) = 105 .
What is distributive property ?According to the distributive property, multiplying the sum of two or more variables by a number will give the same result as multiplying each variables individually by the number and then adding the products together.
Mathematically,
A*(B + C) = AB + AC
How to express the given expression ?Given expression is 7·15 .
By distributive property, the expression can be written as -
⇒ 7·15 = 7*(10 + 5)
⇒ 7*(10 + 5) = 7*10 + 7*5
⇒ 70 + 35 = 105 .
Thus, by distributive property, 7·15 can be written as 7*(10 + 5) = 105
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find a·b
a=<5,2>,b=<4,5>
Answer:
[tex]\large\boxed{\vec{a}\circ\vec{b}=30}[/tex]
Step-by-step explanation:
[tex]\text{Let}\ \vec{u}=\left<a,\ b\right>\ \text{and}\ \vec{v}=\left<c,\ d\right>,\ \text{then}\\\\\vec{u}\circ\vec{v}=ac+bd\\\\==========================\\\\\vec{a}=\left<5,\ 2\right>,\ \vec{b}=\left<4,\ 5\right>\\\\\vec{a}\circ\vec{b}=(5)(4)+(2)(5)=20+10=30[/tex]
find the value of x^3+y^3+15xy-125 if x+y=5
Answer:
0
Step-by-step explanation:
x+y=5
x^3+y^3+15xy-125
(x+y)(x^2-xy+y^2)+15xy-125
5(x^2-xy+y^2)+15xy-125
5x^2+5y^2-5xy+15xy-125
5x^2+5y^2+10xy-125
5[x^2+2xy+y^2]-125
5(x+y)^2-125
5(5)^2-125
125-125
0
which answer is a soultion to the equation lk+9l=4
Answer:
k=-5 or k= -13
Step-by-step explanation:
lk+9l=4
k+9=4 or k+9=-4
k=-5 or k= -13
The solutions for the equation |k+9| = 4 are k = -5 and k = -13. We got these results by considering separately the positive and negative cases for the absolute value.
Explanation:To find the solution to the equation |k+9| = 4, we need to think about what the absolute value operation represents. Absolute value takes the positive version of whatever is inside, no matter if it's positive or negative. So we actually need to consider two separate cases.
Case 1: k+9 = 4. Solving for k, we get k = 4 - 9 = -5.Case 2: -(k+9) = 4. Here, we first need to dissolve the negative sign by multiplying both sides by -1, which gives k + 9 = -4. Solving for k, we get k = -4 - 9 = -13.So the solutions to the equation are k = -5 and k = -13.
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How many four digit even numbers can be formed from digits 1,2,3,4,5 if repetition is allowed.
how can solve this using permutation formula
Answer:
Step-by-step explanation:
5*5*5*2
The number must end in 2 or 4.
1 3 and 5 will give you an odd number if either is at the end.
The permutation formula does not lend itself to this problem. That is because repetition is allowed. So 5554 is a possible answer.
You can choose any one of 1 to 5 for the first place.
1 to 5 in the second place independent of what you choose for the first place.
The only thing restricting you is the last place. It must be 1 of 2.
I suppose you could use 2P1 for that.
5 * 5 * 5 * 2P1
What transformations were applied to ABC to obtain A’B’C’
Answer: Im pretty sure it is D
Step-by-step explanation: I don't really know how to explain it.
I hope it helps tho ;)
Tell me if im wrong.
Answer: The correct option is
(D) rotation of 270 degrees counterclockwise and shifting 3 units up.
Step-by-step explanation: We are given to select the correct transformations that were applied to triangle ABC to obtain triangle A'B'C'.
From the graph, we note that
the co-ordinates of the vertices of triangle ABC are A(3, 4). B(5, 6) and C(8, 1).
And, the co-ordinates of the vertices of triangle A'B'C' are A'(4, 0), B'(6, -2) and C'(1, -5).
We see that
if a point (x, y) is rotated 270 degrees counterclockwise and then shifted 3 units up, then its co-ordinates becomes
(x, y) ⇒ (y, -x+3).
With this transformation rule,
A(3, 4) ⇒ (4, -3+3) = (4, 0),
B(5, 6) ⇒ (6, -5+3) = (6, -2)
and
C(8, 1) ⇒ (1, -8+3) = (1, -5).
Since the resulting co-ordinates are the vertices of triangle A'B'C', so the required transformations rare
rotation of 270 degrees counterclockwise and shifting 3 units up.
Option (D) is CORRECT.
Find the area of a 120° sector of a circle whose radius is 6.
4 sq. units
12 sq. units
24 sq. units
ANSWER
[tex] 12\pi[/tex]
EXPLANATION
The area of sector is calculated using
[tex] \frac{angle\:of \: sector }{360 \degree} \times \pi \: {r}^{2} [/tex]
The angle of the sector is 120° and the radius of the circle is 6 units.
We substitute the given values into the formula to obtain:
[tex] \frac{120 \degree}{360} \times \pi \times {6}^{2} [/tex]
[tex] = \frac{120 \degree}{360} \times \pi \times 36[/tex]
[tex]= \frac{120 \degree}{10} \times \pi = 12\pi[/tex]
Hence the area of the sector is [tex] 12\pi[/tex]
Choose the correct simplification of the expression 8 time b over a to the power of -5. a to the power of 5 time b all over 8 8 over a to the power of 5 times b 8a5b Already simplified
Expression to simplify: [tex]\frac{8b}{a^{-5} }[/tex]
Remember, when a number has a negative power, it reciprocates (flips over)
First lets write the expression so that the a is in a fraction by itself:
[tex]\frac{8b}{a^{-5} }[/tex] = [tex]8b[/tex] × [tex]\frac{1}{a^{-5} }[/tex]
So to simplify, all we do is reciprocate [tex]\frac{1}{a^{-5} }[/tex] and make the power positive:
[tex]8b[/tex] × [tex]\frac{1}{a^{-5} }[/tex] = [tex]8b[/tex] × [tex]a^{5}[/tex]
=[tex]8a^{5}b[/tex]
----------------------------------------------
Answer:
[tex]8a^{5}b[/tex]
The correct simplification Expression is [tex]8b/a^-5[/tex]
The correct simplification of the expression "8 times b over a to the power of -5" is [tex]8b/a^-5[/tex]. This can be simplified by using the following rule:
[tex]x^m \times x^n = x^ \ (m + n)[/tex]
Therefore, we can rewrite the expression as:
[tex]8b/a^-5 = 8b \times a^5[/tex]
We can then multiply the numerator and denominator by 8 to get:
[tex]8b \times a^5 = 64b \times a^5[/tex]
Finally, we can rearrange the factors to get:
[tex]64b \times a^5 = 8a^5 \times b[/tex]
Therefore, the simplified expression is [tex]8a^5 \times b.[/tex]
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Factor completely x2 + 20x + 99
[tex]x^2 + 20x + 99=x^2+9x+11x+99=x(x+9)+11(x+9)=(x+11)(x+9)[/tex]
80 POINTS!!! HELP PLEASE ASAP!!!!
The table and the graph below each show a different relationship between the same two variables, x and y:
A table with two columns and 5 rows is shown. The column head for the left column is x, and the column head for the right column is y. The row entries in the table are 4,100 and 5,125 and 6,150 and 7,175. On the right of this table is a graph. The x-axis values are from 0 to 10 in increments of 2 for each grid line. The y-axis values on the graph are from 0 to 300 in increments of 60 for each grid line. A line passing through the ordered pairs 2, 60 and 4, 120 and 6, 180 and 8, 240 is drawn.
How much more would the value of y be on the graph than its value in the table when x = 12?
20
30
60
70
Answer:
The answer D is incorrect
I'm sorry I don't know the answer but I wanted to warn you so you can at least have a better chance
Step-by-step explanation:
Answer:
60
Step-by-step explanation:
i took the test i got it right (:
Need help with 1-4.
Answer:
for number 4 the answer is 32 in (please read below)
Step-by-step explanation:
I will do one of them for now... how about number 4.
Similar triangles means we are going to setup a proportion:
Small triangle Big Triangle
Corresponding 12 15
Corresponding x 40
So the proportion is 12/x=15/40
cross multiply
12(40)=15(x)
Divide both sides by 15
giving x=12(40)/15=32
Try number 1... And I will check it for you (just post as a new question-I will be looking for it)
Answer:
1. 8 cm
2. 15 cm
3. 28 cm
4. 32 cm
Step-by-step explanation:
1. 12/6= 2
20/10= 2
Scale Factor= 2
16/2= 8cm
2. 30/18= 1.6666667
15/9= 1.6666667
Scale Factor= 1.6666667
25/1.6666667= 15cm
3. 16/12= 1.333333
32/24= 1.333333
Scale Factor= 1.333333
(21)(1.333333)= 28cm
4. 15/12= 1.25
25/20= 1.25
Scale Factor= 1.25
40/1.25= 32cm
Write an equation to solve the problem.
Jack has 5 trains. He gets 2 new trains every month for good behavior. How many months until Jack has 23 trains?
Answer:
5 + 2m = 23
Step-by-step explanation:
This equation can be solved as follows:
5 + 2m = 23
2m = 23 - 5
m = 18/2
m = 9 months
What is the slope-intercept form of a line that passes through points (2, 11) and (4, 17)?
[tex]\bf (\stackrel{x_1}{2}~,~\stackrel{y_1}{11})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{17}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{17-11}{4-2}\implies \cfrac{6}{2}\implies 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-11=3(x-2)\implies y-11=3x-6[/tex]
[tex]\bf y=3x+5\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
Answer:
[tex]y = 3x + 5[/tex]
Step-by-step explanation:
First, find the rate of change [slope]:
-y₁ + y₂\-x₁ + x₂ = m
[tex]\frac{-11 + 17}{-2 + 4} = \frac{6}{2} = 3[/tex]
Now, plug the coordinates into the Slope-Intercept Formula instead of the Point-Slope Formula because you get it done much swiftly. It does not matter which ordered pair you choose:
17 = 3[4] + b
12
5 = b
[tex]y = 3x + 5[/tex]
__________________________________________________________
11 = 3[2] + b
6
5 = b
[tex]y = 3x + 5[/tex]
You see? I told you it did not matter which ordered pair you choose because you will always get the exact same result.
I am joyous to assist you anytime.
X+3y=28 when x =28 find the value for y plz help
Answer:
y = 0
Step-by-step explanation:
Plug in 28 for x. Solve for the equation:
x + 3y = 28
(28) + 3y = 28
Isolate the variable, y. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS. First, subtract 28 from both sides:
28 (-28) + 3y = 28 (-28)
3y = 0
Isolate the variable, y. Divide 3 from both sides:
(3y)/3 = (0)/3
y = 0
y = 0 is your answer.
~
what is a linear function
Linear functions are "graphs with straight lines." The formula to solving a linear function is [tex]y=f(x)=a+bx[/tex] Linear functions also have one independent variable and one dependent variable.
Hope this helps.
Solve |x| + 7 < 4. {x | x < -11 or x > -3} {x | -3 < x < 3} Ø
Answer:
[tex]\large\boxed{\O}[/tex]
Step-by-step explanation:
[tex]|x|+7<4\qquad\text{subtract 7 from both sides}\\\\|x|+7-7<4-7\\\\|x|<-3\Rightarrow\ x\in\O\\\\\text{Because}\\\\|x|\geq0\ \text{for all real value of}\ x[/tex]
Answer: its the o with the line going diagonal through it
Step-by-step explanation:
In the diagram of circle C, what is the measure of 21?
O 17°
35°
70°
710
Answer:
The measure of angle 1 is 35°
Step-by-step explanation:
we know that
The measurement of the outer angle is the semi-difference of the arcs it encompasses.
∠1=(1/2)[106°-36°]=35°
some one help me please
For this case we have that by power properties it is fulfilled:
[tex](a ^ n) ^ m = a ^ {n * m}[/tex]
Now, we can rewrite the expression as:
[tex]\frac {64g ^ 9 * h ^ 6 * k ^ {12}} {8g ^ 3 * h ^ 2} -h ^ {25} k ^ {15} =[/tex]
We also have by definition of properties of powers that:
[tex]\frac {a ^ m} {a ^ n} = a ^ {m-n}[/tex]
So:
[tex]8g ^ {9-3} * h ^ {6-2} * k ^ {12} -h ^ {25} k ^ {15} =\\8g ^ 6 * h ^ 4 * k^{12} -h^{25} * k^{15}[/tex]
Answer:
Option D
Solve the following system of equations graphically. y - 4 = 0 2x - y - 2 = 0 What is the solution set?
Answer:
{[tex](x,y)|(x=3,y=4)[/tex]}
Step-by-step explanation:
The given system of equations is;
[tex]y-4=0...(1)[/tex]
and
[tex]2x-y-2=0...(2)[/tex]
We rewrite the equations in the standard form to get:
[tex]y=4...(3)[/tex]
[tex]2x-y=2...(4)[/tex]
We now substitute equation (3) into equation (4) to get:
[tex]2x-4=2[/tex]
Group similar terms:
[tex]2x=2+4[/tex]
[tex]2x=6[/tex]
Divide both sides by 2
[tex]\frac{2x}{2}=\frac{6}{2}[/tex]
This implies that:
[tex]x=3[/tex]
Therefore the solution set is:
{[tex](x,y)|(x=3,y=4)[/tex]}
A box that has a width of 32 inches and a length of 60 inches is used to ship
a part. The part lies along the diagonal of the bottom of the box. What is the
longest possible length of the part?
A. 28in
B. 88in
C. 92in
D. 68in
Answer:
68
Step-by-step explanation:
i just took the test.
Which shows the best path to find the number of centimiters in 1 yard
For this case we have by definition that one yard equals 91.44 centimeters.
We propose a rule of three that allows you to find the number of centimeters in any number of yards:
1yd ------------> 91.44cm
x ------------> y
[tex]y = \frac {x * 91.44} {1}\\y = x * 91.44[/tex]
Where:
y: It is the number of centimeters
x: It is the number of yards.
Answer:
one yard equals 91.44 centimeters.
The temperature measured in Kelvin (K) is the temperature measured in Celsius (C) increased by 273.15. This can be modeled by the equation K = C + 273.15. When solved for C, the equation is
Answer:
C=K-273.15
Step-by-step explanation:
Here we are given the relation between the measurements of temperatures in Celsius C and Kelvin K . The relationship is as under
K=C+273.15
now we have to rewrite this equation so that we can evaluate C in terms of K
In order to do so , we Subtract 273.15 from both sides.
K-273.15 = C + 273.15-273.15
K - 273.15=C
C=K-273.15
Find the surface are of this cube 8ft 8ft 8ft
Answer:
A=384
Step-by-step explanation:
For this case we have by definition, that the surface area of a cube is given by:
[tex]SA = 6l ^ 2[/tex]
Where:
l: It's the side of the cube
We have as data, according to the figure, that:
[tex]l = 8ft[/tex]
Substituting in the figure:
[tex]SA = 6 (8) ^ 2\\SA = 6 * 64\\SA = 384 \ ft ^ 2[/tex]
Thus, the surface area of the cube is [tex]384 \ ft ^ 2[/tex]
Answer:
[tex]384 \ ft ^ 2[/tex]