Answer:
(x + 2)(4x - 2).
Step-by-step explanation:
(x+2)(2x+1)+(x+2)(2x-3)
Note that (x + 2) is common to 2 parts of the expression. So we have:
(x + 2)(2x + 1 + 2x - 3)
= Ix + 2)(4x - 2)
The graph of $y=ax^2+bx+c$ passes through points $(0,5)$, $(1,10)$, and $(2,19)$. Find $a+b+c$.
Answer:
[tex]a+b+c=10[/tex]
Step-by-step explanation:
We are given that the graph of the equation:
[tex]y=ax^2+bx+c[/tex]
Passes through the three points (0, 5), (1, 10), and (2, 19).
And we want to find the value of (a + b + c).
First, since the graph passes through (0, 5), its y-intercept or c is 5. Hence:
[tex]y=ax^2+bx+5[/tex]
Next, since the graph passes through (1, 10), when x = 1, y = 10. Substitute:
[tex](10)=a(1)^2+b(1)+5[/tex]
Simplify:
[tex]5=a+b[/tex]
The point (2, 19) tells us that when x = 2, y = 19. Substitute:
[tex](19)=a(2)^2+b(2)+5[/tex]
Simplify:
[tex]14=4a+2b[/tex]
This yields a system of equations:
[tex]\begin{cases} 5 = a + b \\ 14 = 4a + 2b\end{cases}[/tex]
Solve the system. We can do so using elimination (or any other method you prefer). Multiply the first equation by negative two:
[tex]-10=-2a-2b[/tex]
Add the two equations together:
[tex](-10)+(14)=(-2a+4a)+(-2b+2b)[/tex]
Combine like terms:
[tex]4 = 2a[/tex]
Hence:
[tex]a=2[/tex]
Using the first equation:
[tex]5=(2)+b\Rightarrow b=3[/tex]
Therefore, our equation is:
[tex]y=2x^2+3x+5[/tex]
Thus, the value of (a + b + c) will be:
[tex]a+b+c = (2) + (3) + (5) = 10[/tex]
Bruce drove 25 km and his car used 4 L of gas. How many km can Bruce drive with 30 L of gas? Round your answer to the nearest km.
Answer:
188km
Hi there!!
I hope this answer helps.
Step-by-step explanation:
You can solve this with simple cross multiplication. (proportion)
Step-by-step explanation:
what is the value of x?
Explanation:
The adjacent angle to the right of the (6x+1) angle is 180-(6x+1). Simply subtract it from 180 to get its supplementary counterpart.
The three inner angles of any triangle must add to 180, so,
(inner angle 1) + (inner angle 2) + (inner angle 3) = 180
[ 180-(6x+1) ] + (79) + (2x+10) = 180
180 - 6x - 1 + 79 + 2x + 10 = 180
(-6x+2x) + (180-1+79+10) = 180
-4x+268 = 180
-4x = 180 - 268
-4x = -88
x = -88/(-4)
x = 22
Answer:
x = 22
Step-by-step explanation:
2x + 10 + 79 = 6x + 1
Think alternate interior angles
2x + 10 + 79 makes up one of the alternate interior angles
6x + 1 is the other.
Combine like terms.
Subtract 2x both sides.
Subtract 1 from both sides.
Divide by 4 both sides.
TRIANGLES please help!! :)
Answer:
A
Step-by-step explanation:
First, the list of congruence theorems are:
SSS
SAS
ASA
AAS
HL
SSA is not on the list, so we can cross that out
Next, ASA implies that two angles are congruent, but we only know that one pair of angles (the right angles) are congruent, so we can cross that out
After that, the angle is not connecting the congruent sides, so D is not an option
Finally, we know that the longest sides (AD / AC) are congruent to each other, one other pair of legs/sides are congruent, and the triangles are both right triangles. Therefore, we can apply HL here
(–4c2 + 7cd + 8d) + (–3d + 8c2 + 4cd) =
Answer:
4c² + 11cd + 5d
Step-by-step explanation:
(–4c2 + 7cd + 8d) + (–3d + 8c2 + 4cd)
-4c² + 7cd + 8d - 3d + 8c² + 4cd (opening bracket)
8c²-4c²+7cd + 4cd + 8d - 3d
= 4c² + 11cd + 5d
Because of a manufacturing error, three cans of regular soda were accidentally filled with diet soda and placed into a 12-pack. Suppose that two cans are randomly selected from the 12-pack. (a) Determine the probability that both contain diet soda. (b) Determine the probability that both contain regular soda. Would this be unusual
Answer:
1 /22
6/11
Step-by-step explanation:
Total number of soda = 12
Number of diet soda in pack = 3
Number of regular soda = 12 - 3 = 9
Suppose selection is done without replacement ;
Recall : probability = required outcome / Total possible outcomes
P(selecting diet soda on 1st pick) = number of diet soda / total Number of soda in pack = 3 / 12
Diet soda left = 3 - 1 = 2
Total sodas left in pack = 12 - 1 = 11
P(selecting diet soda on 2nd pick) = 2 /11
Probability(diet soda on both picks) =
3/12 * 2/11 = 6 / 132 = 1 / 22
B.)
P(selecting regular soda on 1st pick) = number of regular / total Number of soda in pack = 9 / 12
Diet soda left = 9 - 1 = 8
Total sodas left in pack = 12 - 1 = 11
P(selecting regular soda on 2nd pick) = 8 /11
Probability(regular soda on both picks) =
9/12 * 8/11 = 72 / 132 = 12 / 22 = 6/11
plz help me to do this
reciprocal of. 0×7/11
Answer:
it doesn't exist
Step-by-step explanation:
the expression 0×7/11 is equivalent to 0. 1/0 isn't possible, so its reciprocal doesn't exist.
What is the area of the parallelogram whose base is 50 mm long and whose height is 30 mm?
Answer:
A=1.5×10-3m² (This is the answer)
Step-by-step explanation:
Unit Conversion:
b=0.05m
h=0.03m
Solution
A=bh=0.05·0.03=1.5×10-3m²
(These here are just some add ins)
Which of the following statements does not prove that ABCD is a parallelogram.
Given: A(-4, 7), B(3,0), C(2,-5) and D(-5, 2).
Answer:
answer A
Step-by-step explanation:
A=(-4,7)
C=(2,-5)
midpoint = U=((-4+2)/2, (7+(-5))/2)=(-1,1))
B=(3,0)
D=(-5,2)
midpoint = V=((3+(-5))/2,(0+2)/2)=( -1,1)
Diagonals have the same middle, the quadrilater is a parallogram.
he manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in the sample to check out was 3.1 minutes. The population standard deviation is known to be 0.5 minute. We want to test to determine whether or not the mean waiting time of all customers is significantly more than 3 minutes. Refer to Exhibit 9-2. At a .05 level of significance, it can be concluded that the mean of the population is _____. a. significantly less than 3 b. significantly greater than 3.18 c. significantly greater than 3 d. not significantly greater than 3
What are ways using coordinate geometry, that I could determine that this is a trapezoid?
One method to see it's a trapezoid is to find the slope of lines BC and AD.
The slope formula is
m = (y2-y1)/(x2-x1)
You should find that BC and AD both have the same slope (of -1), so that means the lines are parallel. That proves we have a trapezoid.
-----------------------
To prove this trapezoid is isosceles, you can use the distance formula
[tex]d = \sqrt{ \left(x_1-x_2\right)^2 + \left(y_1-y_2\right)^2}[/tex]
to find the lengths of AB and CD (the two non-parallel sides). You should find that AB = CD.
Because AB and CD are horizontal and vertical respectively, this means you can simply count out the spaces to find that AB and CD are 3 units each. For any other rotated version of this trapezoid, use the distance formula instead.
tan(3x/7 - π/5)= -√3/3
Answer:
x is 7·π/30
Step-by-step explanation:
The given equation is presented as follows;
tan(3·x/7 - π/5) = (-√3)/3
We have that arctan (√3)/3 = π/6, and tangent of an angle is negative in the second quadrant, we get;
arctan (-√3)/3 = -π/6 = 5·π/6
∴ tan(-π/6) = -√3/3 = tan(3·x/7 - π/5)
-π/6 = 3·x/7 - π/5
x = (-π/6 + π/5) × 7/3 = (6·π - 5·π)/30 × 7/3 = π/30 × 7/3 = 7·π/30
x = 7·π/30
a + 1/a= p find a^3 + 1/a^3
(1) p^3 + 3p
(2) 3p
(3) p^3 - 3p
9514 1404 393
Answer:
(3) p^3 -3p
Step-by-step explanation:
(a +1/a) = p . . . . . . . given
(a +1/a)^3 = p^3 . . . . . . . . cube both sides
a^3 +3a^2(1/a) +3a(1/a)^2 +(1/a)^3 = p^3 . . . . . . expand
(a^3 +1/a^3) +3(a +1/a) = p^3 . . . . . . . . . . simplify, group
(a^3 +1/a^3) +3p = p^3 . . . . . . . . . . substitute p for a+1/a
(a^3 +1/a^3) = p^3 -3p . . . . . . subtract 3p from both sides
A rectangular swimming pool. Measures 16m by 20m. A path of uniform width is built around the pool. If the area of path is 100m^2, find the width of the path, giving your answer correct to 2 decimal places.
Answer:
not sure but good luck
Step-by-step explanation:
:))))
wat iz dis bul crup
i made the hardest math problem, lets see if you can figure it out
p.s. ingore the line right aside from the 7.
7×(15+7-4+(x+y×38))^3 when x = 4 and y = 9
7×(15+7-4+(4+9×38))^3
=> 7×(15+7-4+(4+342))^3
=> 7×(15+7-4+346)^3
=> 7×364^3
=> 7×48228544
=> 337599808
The graph of a function f(x) is shown below:
What is the domain of f(x)? (1 point)
integers from - 1< x <2
integers from -3 < y < 3
integers from -3 < y <3
integers from -1 < x < 2
Answer:
It's all integers x such that -1<=x<=2.
Step-by-step explanation:
The domain is the x values for which the relation exists.
Lets read from left to right.
First point I see from left exists at x=-1, next one at x=0, then x=1, and finally at x=2.
So it's all integers x such that -1<=x<=2.
*<= means less than or equal to
x-3(x-2)=3(2x) Solution
Step-by-step explanation:
x^2-2x-3x+6=6x
x^2-5x+6=6x
x^2+6=6x+5x
x^2+6=13x
x^2-13x=6
x(x-13)=6
Use the properties of logarithms to prove log, 1000 = log2 10.
Given:
Consider the equation is:
[tex]\log_81000=\log_210[/tex]
To prove:
[tex]\log_81000=\log_210[/tex] by using the properties of logarithms.
Solution:
We have,
[tex]\log_81000=\log_210[/tex]
Taking left hand side (LHS), we get
[tex]LHS=\log_81000[/tex]
[tex]LHS=\dfrac{\log 1000}{\log 8}[/tex] [tex]\left[\because \log_ab=\dfrac{\log_x a}{\log_x b}\right][/tex]
[tex]LHS=\dfrac{\log (10)^3}{\log 2^3}[/tex]
[tex]LHS=\dfrac{3\log 10}{3\log 2}[/tex] [tex][\because \log x^n=n\log x][/tex]
[tex]LHS=\dfrac{\log 10}{\log 2}[/tex]
[tex]LHS=\log_210[/tex] [tex]\left[\because \log_ab=\dfrac{\log_x a}{\log_x b}\right][/tex]
[tex]LHS=RHS[/tex]
Hence proved.
Find the coordinates of point X that lies along the directed line segment from Y(-8, 8) to T(-15, -13) and partitions the segment in the ratio of 5:2.
A. (-11.5, -2.5)
B. (-13, -7)
C. (-5, -15)
D. (-23, -5)
5894 divided by 14 step by step
(Please help. I just wanna know if I’m doing this right)
Answer:
421
Step-by-step explanation:
5894 divided by 14 in decimal = 421 • 5894 divided by 14 in fraction = 5894/14• 5894 divided by 14 in percentage= 42100%
YOUR WELCOME :)))
A jar contains four yellow balls, six red balls, and eight blue balls. One ball is selected at random.
What is the probability that it is yellow?
Answer:
Step-by-step explanation:
We are trying to see how likely we are to pick a yellow ball. So out of the total number of balls, we have 4 yellow balls (numerator). The total number of balls is 18 and so the probability of picking a yellow ball is 4/18
Answer:
4/18
Step-by-step explanation:
1. you would first take all the number of colored balls and add them together
2. next, you would take the number of yellow balls/ to the total number of balls.
Can someone help me with this math homework please!
Answer:
10
Step-by-step explanation:
f ( 1 ) = 18
First term ( a ) = 18
f ( n + 1 ) = f ( n ) - 2
When, n = 1
f ( 1 + 1 ) = f ( 1 ) - 2
f ( 2 ) = 18 - 2
f ( 2 ) = 16
f ( 2 ) - f ( 1 )
= 16 - 18
= - 2
Common difference ( d ) = - 2
f ( 5 )
= a + 4d
= 18 + 4 ( - 2 )
= 18 - 8
= 10
Please help me with this
Answer:
108
Step-by-step explanation:
Surface area = total area of net
The net is made up of 2 unique shapes
A square with a side length of 6
The area of a square can be calculated by squaring the side length
6^2 = 36
The area of the square = 36
The net is also made up of 4 triangles
The triangles have a base length of 6 and a height of 6
The area of a triangle can be calculated by using the formula A = (bh) / 2
Where b = base length and h = height
If the triangles have a base length of 6 then b = 6 and if they have a height of 6 then h = 6
So A = 6*6/2
6 * 6 = 32
32/2 = 18
We then multiply that by 4 to get the area of all four triangles
18 * 4 = 72
Finally we add the areas together
72 + 36 = 108
The surface area is 108
does anyone know this?
Answer:
The volume is approximately 50 m^3
Step-by-step explanation:
The volume of a cylinder is given by
V = pi r^2 h where r is the radius and h is the height
The radius is 1/2 of the diameter r = 8/2 = 4
V = pi ( 4)^2 (1)
V = 16 pi
Letting pi be approximated by 3.14
V = 3.14 * 16
V = 50.24
The volume is approximately 50 m^3
what is the answer for 14a³ - 22a we have to Factorise it
Answer: 2a (7a² - 11).
Answer:
Step-by-step explanation:
Both numbers are even. You can take out a 2.
14/2 = 7
22/2 = 11
There is a limitation of one a on the 22. But you can take out 1 a
a^3/a = a^2
Combing you get
Answer: 2a(7a^2 - 11)
This is the reverse distributive property.
Find the angles of the triangles if they are proportional to the following: 3,4,5
WILL GIVE BRAINLIEST IF UR ANSWER IS RIGHT
Let the proportion be 3x, 4x and 5x .
We know that sum of all angles of a triangle measures 180°.
So, keeping the values equals to 180°.
⇒ 3x + 4x + 5x = 180°
⇒ 12x = 180°
⇒ x = 180°/12
⇒ x = 15°
Now, finding the each angle measure.
⇒ 3x = 3 × 15 = 45°
⇒ 4x = 4 × 15 = 60°
⇒ 5x = 5 × 15 = 75°
Hence, the measure of each angle is 45°, 60° and 75° respectively.
❒ Required Solution:
It is given that the three angles of the triangle are proportional to 3,4,5. And we are here to find the three angles with the help of the angle sum property (Sum of the angles of a triangle = 180°). So, using this property we can find all the angles.So, Let's assume the angles as 3x, 4x and 5x.
❍ According to the question :
[tex]\\ \tt \implies \: 3 x+ 4x + 5x = 180{}^{ \circ} \\[/tex]
[tex]\\ \tt \implies \: 12 x = 180{}^{ \circ} \\[/tex]
[tex]\\ \tt \implies \: x = \frac{180{}^{ \circ} }{12} \\ [/tex]
[tex]\\ \implies \tt \: x = 15{}^{ \circ} [/tex]
Hence,
[tex]\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \circ \: \: \: \: \tt \:1st \: \: \: angle \: \: \: \: \: = 3x=3 \times 15=45{}^{\circ} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \circ \: \tt \:2nd \: \: \: angle \: \: \: \: \: = 4x=4\times 15=60{}^{\circ} \: \: \: \: \: \\ \\ \circ \: \: \: \: \tt \:3rd \: \: \: angle \: \: \: \: \: =5 x=5\times 15=75 {}^{\circ} \: \: \\ \\[/tex]
❒ V E R I F I C A T I O N :
Sum of the angles of the triangle = 180°
[tex]\\ \tt \implies \: 3 x + 4x + 5x = 180{}^{ \circ} [/tex]
[tex]\\ \tt \implies \: 45 {}^{ \circ} + 60{}^{ \circ} + 75{}^{ \circ}= 180{}^{ \circ} [/tex]
[tex]\\ \tt \implies \: 180{}^{ \circ} = 180{}^{ \circ} [/tex]
[tex]\\ {\quad { \quad{ \quad{ \textbf{ \textsf{L.H.S = R.H.S}}}}}}[/tex]
i need the answer for this 2120 = 18x + 320
Answer:
100
Step-by-step explanation:
we need to swap sides so we take the 320 and put it in the other side but in negative form and that comes out to 1800 and then we divide that by 18
Answer:
x = 100
Step-by-step explanation:
2120 - 320 = 1800
1800 ÷ 18 = 100
PLEASE I NEED HELP!!
Find the value of x
Answer:
y=4sqrt 3 X=8sqr 3
Step-by-step explanation:
4/y=y/12 y^2=48 y= sqrt 48= sqrt 4 * sqrt 3 * sqrt 4 = y = 4sqrt 3 then X
(4sqrt3)^2+144=x^2
48+144=192
sqrt 192
8sqrt3
What is the distance from W to X?
Answer:
The answer is 35 miles.
Step-by-step explanation:
Let's assume that the distance from W to Y is x miles
Distance from W to X is 70 % of x =0.7*x
Given distance from X to Y is 15 miles.
x-15=0.7x
x-0.7x=15
0.3x=15
x=15/0.3
x=50miles
Thus the distance from W to Y is 50 miles and the distance from W to X is 50-15=35 miles
