Answer:
The missing term is 3x
Step-by-step explanation:
Given
-(x - 1) + 5 = 2(x + 3) - _
Required
Find _
For proper identification of the parameters, represent _ with Z
So, the equation becomes
-(x - 1) + 5 = 2(x + 3) - Z
Open bracket (start from the left hand side)
-x + 1 + 5 = 2(x + 3) - Z
-x + 1 + 5 = 2x + 6 - Z
Solve like terms
-x + 6 = 2x + 6 - Z
Subtract 6 from both sides
-x + 6 - 6 = 2x + 6 - 6 - Z
-x = 2x - Z
Subtract 2x from both sides
-x - 2x = 2x - 2x - Z
-3x = -Z
Multiply both sides by -1
-3x * -1 = -Z * -1
3x = Z
Reorder
Z = 3x
Hence, the missing term is 3x
Answer:
answer is 3x
Step-by-step explanation:
show that the straight line x+y does not intersect the curve x^2-8x+y^2-12y+6=0 if k^2-20k+8>0
Find the equation of the given parabola in vertex and standard form. Describe in words all transformations that have been applied to the graph of y=x^2 to obtain the given graph of the transformed function
Answer: [tex]a)\ \text{Vertex}:y=-\dfrac{3}{2}(x+1)^2+6[/tex]
[tex]b)\ \text{Standard}:y=-\dfrac{3}{2}x^2-3x=\dfrac{9}{2}[/tex]
c) Transformations: reflection over the x-axis,
vertical stretch by a factor of 3/2,
horizontal shift 1 unit to the left,
vertical shift 6 units up
Step-by-step explanation:
Intercept form: y = a(x - p)(x - q)
Vertex form: y = a(x - h)² + k
Standard form: y = ax² + bx + c
We can see that the new vertex is (-1, 6). Use the Intercept form to find the vertical stretch: y = a(x - p)(x - q) where p, q are the intercepts.
p = -3, q = 1, (x, y) = (-1, 6)
a(-1 + 3)(-1 -1) = 6
a (2)(-2) = 6
a = -6/4
a = -3/2
a) Input a = -3/2 and vertex (h, k) = (-1, 6) into the Vertex form to get:
[tex]y=-\dfrac{3}{2}(x+1)^2+6[/tex]
b) Input a = -3/2 into the Intercept form and expand to get the Standard form:
[tex]y=-\dfrac{3}{2}(x+3)(x-1)\\\\\\y=-\dfrac{3}{2}(x^2+2x-3)\\\\\\y=-\dfrac{3}{2}x^2-3x+\dfrac{9}{2}[/tex]
c) Use the Vertex form to identify the transformations:
[tex]y=-\dfrac{3}{2}(x+1)^2+6[/tex]
a is negative: reflection over the x-axis|a| = 3/2: vertical stretch by a factor of 3/2h = -1: horizontal shift left 1 unitk = +6: vertical shift up 6 unitsValentino sells ice cream cones and ice cream tubs. The ice cream flavours are chocolate, strawberry and vanilla. On Sunday, 120 people each bought one ice cream from Valentino. The two-way table shows some information about these ice creams. One of the 120 people is picked at random. Find the probability that this person bought a vanilla ice cream cone.
Answer:
11/60
Step-by-step explanation:
hello
in total there are 120 ppl
22 are vanilla cones
so the probability that this person bought a vanilla a ice cream cone is 22/120=11/60
hope this helps
The dimensions of a rectangle is 30cm x 20cm. When each dimension is
decreased by the same amount, the area of the new rectangle is
100cm^2. What are the new dimensions of the new rectangle (round to
one decimal place)? Hint: you will need to use the quadratic equation.
Answer:
The new dimensions are 6.18 cm by 16.18 cm.
Step-by-step explanation:
Original dimensions were 30 cm by 20 cm.
We decrease length and width by x and calculate the area:
Area = (length)(width)
= (30 - x)(20 - x) = 100
Performing the indicated multiplication, we get:
600 - 30x - 20x + x^2 = 100, or, after simplification,
x^2 - 50x + 500 = 0
Let's solve this by completing the square:
x^2 - 50x + 500 = x^2 - 50x + 625 - 625 + 500 = 0
This simplifies to (x - 25)^2 - 125 = 0, or (x - 25)^2 = 125
Taking the square root of both sides, we get:
x - 25 = ±√125, or
x = 25 ± 5√5
The two results are x = 36.18 (not possible, because we DECREASED the original dimensions) and x = 13.82 (possible)
The dimensions of the new rectangle are
(30 - 13.82) cm by (20 - 13.82) cm, or
16.2 cm by 6.18 cm
Check: With these dimensions is the area 100 cm^2, as expected?
(6.18)(16.18) = 99.9979 YES
Which polynomial is factored completely?
g^5-g
4g^3+18g^2+20g
24g^2-6g^4
2g^2+5g+4
Answer:
Option (4)
Step-by-step explanation:
To solve this question we will try to factor the expressions given in each option.
Option (1)
g⁵ - g = g(g⁴ - 1)
= g(g² - 1)(g² + 1)
= g(g - 1)(g + 1)(g² + 1)
Option (2)
4g³ + 18g² + 20g = 2g(2g² + 9g + 10)
= 2g[2g + 5g + 4g + 10]
= 2g[g(2g + 5) + 2(g + 5)]
= 2g(2g + 5)(g + 2)
Option (3)
24g² - 6g⁴ = 6g²(4 - g²)
= 6g²(2 - g)(2 + g)
Option (4)
2g² + 5g + 4
This expression is the in the completely factored form.
Answer:
yes its D :)
Step-by-step explanation:
other guy has the math, i just know the answer, sorry lol
A truck is to be filled with packages that weigh 5.8kg. If the maximum capacity of the truck is 48000 grams and there is a 5500 gram package already on the truck how many 5.8kg packages can be loaded?
Answer: 7 packages
Step-by-step explanation:
From the question, we are told that a truck is to be filled with packages that weigh 5.8kg. The maximum capacity of the truck is 48000 grams(48kg) and there is a 5500 gram(5.5kg) package already in the truck.
First, we need to subtract 5.5kg from 48kg to know the amount of space left. This will be:
= 48kg - 5.5kg
= 42.5kg
To get the number of 5.8kg packages that can be loaded, we divide 42.5kg by 5.8kg. This will be:
= 42.5kg/5.8kg
= 7.3
= 7 approximately
Therefore, 7 packages will be loaded.
N.B: 1000 grams = 1 kilogram
Suppose that you are seated next to a stranger on an airplane and you start discussing various topics such as where you were born (what state or country), what your favorite movie of all time is, your spouse's occupation, and so on. For simplicity, assume that the probability that your details match for any given topic is 1 50 and is independent from one topic to the next. If you discuss 17 topics, how surprising would it be to find that you match on at least one of them
Answer:
1/17 0r 6%
Step-by-step explanation:
the answer is rounded up for you
Bettina is measuring the food for her farm animals. She has 265 grams of corn, 500 grams of hay, and 495 grams of oats. What is the total weight in kilograms?
Answer
260 kilograms
Step-by-step explanation:
the correct answer is 260 kg
Answer: 12.6 kg
Step-by-step explanation: add the amounts of food for her farm, and just search for how many kg are in 1,260 grams
I really need help pls
Answer:
D.
Step-by-step explanation:
Original dimensions:
L = x
W = x
Now we reduce the width by 2 ft and increase the length by 2 ft.
L = x + 2
W = x - 2
The area is the product of the length and width.
A = LW = (x + 2)(x - 2)
The original length and width are 10 ft.
L = W = x = 10
A = LW = (10 + 2)(10 - 2) = 12 * 8 = 96
The new area is 96 sq ft.
Answer: D.
Someone Help me please !
Answer:
[tex] \sqrt{9} \times \sqrt{16} [/tex]
Step-by-step explanation:
[tex] \sqrt{9} \times 16 = \sqrt{9} \times \sqrt{16} = 3 \times 4 = 12[/tex]
Hope this helps ;) ❤❤❤
Answer:
sqrt(9) * sqrt(16)
Step-by-step explanation:
sqrt( 9*16)
We know that sqrt(a*b) = sqrt(a) sqrt(b)
sqrt(9) * sqrt(16)
3*4
12
Pleaseee hellllpp!!!!
How many grams of AuCl3, if the compound has 6.3 x10^23 atoms of Cl?
Answer:
105.86 grams of AuCl3, if the compound has 6.3 x10^23 atoms of Cl.
Step-by-step explanation:
We are given that the compound has 6.3 x10^23 atoms of Cl.
To find how many molecules of AuCl3 are in the given compound, we divide the compound by 3, i.e;
[tex]\frac{6.3 \times 10^{23} }{3}[/tex] = [tex]2.1\times 10^{23}[/tex] molecules of AuCl3.
Now, as we know that 1 mole of AuCI3 has [tex]6.022 \times 10^{23}[/tex] molecules.
So, the moles that our compound has is given by;
= [tex]\frac{2.1 \times 10^{23} }{6.022 \times 10^{23} }[/tex] = [tex]\frac{2.1}{6.022}[/tex] = 0.349 mole AuCI3
Also, the molar mass of AuCI3 = 303.33 g/mole
So, the molar mass of 0.349 moles AuCI3 = [tex]303.33 \times 0.349[/tex]
= 105.86 g
Hence, 105.86 grams of AuCl3, if the compound has 6.3 x10^23 atoms of Cl.
A: What are the solutions to the quadratic equation 9x2 + 64 = 0?
B: What is the factored form of the quadratic expression 9x2 +64?
Select one answer for question A, and select one answer for question B.
B: (3x + 81)(x - 1)
B: (x-8)(3x-8)
B:(3x8)(3x + 8)
B: (3x - 81)(3x + 81)
Ax = or x = -1
A:x =
A: x = i orx = -
O A x = 1
Answer:
B: (3x + 81)(x - 1)
Step-by-step explanation:
What is the equation of a line that is parallel to the line 2x + 5y = 10 and passes through the point (–5, 1)? Check all that apply.
Answer:
y = -[tex]\frac{2}{5}[/tex]x - 1
Step-by-step explanation:
First, we can put the equation into y = mx + b form:
2x + 5y = 10
5y = -2x + 10
y = -[tex]\frac{2}{5}[/tex]x + 2
Now, we know the slope is -[tex]\frac{2}{5}[/tex]. A parallel line will have the same slope.
So, we can plug in the point (-5, 1) into the equation y = -[tex]\frac{2}{5}[/tex]x + b to find b:
1 = -[tex]\frac{2}{5}[/tex](-5) + b
1 = 2 + b
-1 = b
So, the equation will be y = -[tex]\frac{2}{5}[/tex]x - 1
using Pythagoras theorem work out the length of AB
ABC is a triangle,
1 side is 22 cm 1 side is 8 cm
1 side is unknown the
1 unknown side is unknown
work out AB using Pythagoras theorem
Answer:
AB = 23.40 cmSolution,
Base ( BC ) = 22 cm
Perpendicular ( AC) = 8 cm
Hypotenuse (AB) = ?
Now,
Using the Pythagoras theorem:
[tex] {h}^{2} = {p}^{2} + {b}^{2} [/tex]
[tex] {h}^{2} = {(8)}^{2} + {(22)}^{2} [/tex]
[tex] {h}^{2} = 64 + 484[/tex]
[tex] {h}^{2} = 548[/tex]
[tex]h = \sqrt{548} [/tex]
[tex]h = 23.40 \: cm[/tex]
Hope this helps..
Good luck on your assignment...
3. Write an exponential equation for each coin that will give the coin's value, V, at any time, t. Use
the formula:
Vt) = P(1 + r) where V(t) is the value of the coin in t years, Please HELP! help on number three
Answer:
Coin A : [tex]V(t)=25(1.07)^t[/tex]
Coin B : [tex]V(t)=40(1.05)^t[/tex]
Step-by-step explanation:
Consider the given formula is
[tex]V(t)=P(1+r)^t[/tex]
where, P is current value, V(t) is the value of the coin in t years, and r is annual appreciation rate.
For coin A, current value is 25 dollars and annual appreciation rate is 7%.
[tex]V(t)=25(1+0.07)^t[/tex]
[tex]V(t)=25(1.07)^t[/tex]
For coin B, current value is 40 dollars and annual appreciation rate is 5%.
[tex]V(t)=40(1+0.05)^t[/tex]
[tex]V(t)=40(1.05)^t[/tex]
Therefore, the required equations for coin A and B are [tex]V(t)=25(1.07)^t[/tex] and [tex]V(t)=40(1.05)^t[/tex] respectively.
Angles C and D are complementary. The ratio of the measure of Angle C to the measure of Angle D is 2:3. What are the measures of both angles?
Answer:
36° and 54°
Step-by-step explanation:
Complementary angles are angles whose sum equals to 90°
Hence C +D = 90°
The ratio of C &D = 2:3 respectively
Sum of the ratio = 2+3 = 5
Hence we divide each of the ratio by the sum of the entire ratio and then multiply by 90°
For angle C :
2/5 × 90
2×18 = 36°
For angle D :
3/5× 90
3×18 = 54°
Hence the angles are 36° and 54° respectively
To proof that we are actually right
C+D = 90°
36+54 = 90°
Hence the answer is right.
Which relation is not a function?
a) y = 1x + 7
by=- 4(x + 3)2 + 10
c) -2y = - 3x + 9
d) x2 + y2 = 25
Answer:
x^2+y^2=25
Step-by-step explanation:
x^2+y^2=25 graphs a circle. A relation is a function if every x only has one y value. This is not true in a circle.
Answer:
d) x^2 + y^2 = 25.
Step-by-step explanation:
D is the equation of a circle so it fails the vertical line test for a function. If a relation is a function then any vertical line passing through it's graph will only intersect it once. This is not true of a circle.
Use SOHCAHTOA for this. Work out 'm' in 3sf, I need the working out.
Anwer:3.537m
STEP BY STEP EXPLANATIOND:using SOH CAH TOA
First find the opposite
Represent the opposite with x
Tan 33° =x\10
x=10Tan 33°
x=6.494
To find m
Sin 33°=m\6.494 Sin 33°
m=3.5368
m=3.537meteres
A system of linear equations contains two equations with negative reciprocal slopes. Select all of the correct statements. A. The system may have no solution B. The system will have one solution C. The system will have two solutions D. The system may have infinitely many solutions
Answer:
B.
Step-by-step explanation:
"negative reciprocal slopes" means the lines are perpendicular, so they will always intersect.
Hence there will be exactly one solution.
B. The system will have one solution.
What is a negative reciprocal slope?The slopes of perpendicular strains, or bisecting strains, are continually terrible reciprocals of each other. For instance, if the slope of a line is -five, then the slope of a line perpendicular to this line will be the negative reciprocal of -five.
What is the system of two linear equations that have different slopes?If the 2 traces have exclusive slopes, then they'll intersect as soon as. consequently, the gadget of equations has exactly one answer. If the two traces have the equal slope however of kind y-intercepts, then they're parallel strains, and they'll by no means intersect.
Learn more about the system of linear equations here: https://brainly.com/question/14323743
#SPJ2
Of a squirrel's hidden nuts, for every 555 that get found, there are 333 that do not get found. A squirrel hid 404040 nuts all together. How many of the nuts do not get found?
Answer:
151515 not found
Step-by-step explanation:
For every 555 nuts found, 333 are not. This gives a total of 888.
555 + 333 = 888
Divide the total number of nuts by this number.
404040/888 = 455
Multiply the number that get found and the number that don't by the number calculated above.
555 × 455 = 252525
333 × 455 = 151515
252525 nuts will be found and 151515 will not.
Answer:
15
Step-by-step explanation:
Which of the following is true?
A.
A ABC DEC by SAS
B. ABC EDC by SSS
C. BCA DCE by SAS
D. ABC DEC PLEASE HURRYYYYY
Here’s a graph of a linear function. Write the equation that describes that function.
Express it in slope-intercept form.
Answer:
The equation that describes the function is y = -6x-1
Step-by-step explanation:
Firstly we can see that the graph passes through the origin.
The general equation of a starlight line graph is;
y = mx + c
where m is the slope and c is the y-intercept
what’s left now is go find our slope
We need two points for this on the line.
Let’s identify these points;
The identifiable points are; (1,-7) and (-1,5)
So the formula for the slope is;
y2-y1/x2-x1 = (5-(-7))/(-1-1) = 12/-2 = -6
Thus, the equation of the line becomes
y = -6x + c
Looking at the graph again, we can see an obvious y-intercept at the point y = -1
So our intercept is -1
The equation of the line is thus;
y = -6x -1
Find all polar coordinates of point P = (2,14°)
Answer:
[tex](2,14^{\circ}+360^{\circ}n)\text{ and }(-2,194^{\circ} +360^{\circ}n)[/tex].
Step-by-step explanation:
If a point is [tex]P=(r,\theta)[/tex], the all polar coordinates are defined as
In radian : [tex](r,\theta +2n\pi)\text{ and }(-r,\theta +(2n+1)\pi)[/tex]
In degree : [tex](r,\theta +360^{\circ}n)\text{ and }(-r,\theta +(2n+1)180^{\circ})[/tex]
where, n is any integer.
The given point is
[tex]P=(2,14^{\circ})[/tex]
So, all polar coordinates are
[tex](2,14^{\circ}+360^{\circ}n)\text{ and }(-2,14^{\circ} +(2n+1)180^{\circ})[/tex]
[tex](2,14^{\circ}+360^{\circ}n)\text{ and }(-2,14^{\circ} +360^{\circ}n+180^{\circ})[/tex]
[tex](2,14^{\circ}+360^{\circ}n)\text{ and }(-2,194^{\circ} +360^{\circ}n)[/tex]
Therefore, the required polar coordinates are [tex](2,14^{\circ}+360^{\circ}n)\text{ and }(-2,194^{\circ} +360^{\circ}n)[/tex], where n is any integer.
describe the solution to the system of equations graphed below.
Answer:
Step-by-step explanation:
The answer is B, the solution to your equation is at (2,1). Your solution is where the two lines meet.
Answer:
The second option.
Step-by-step explanation:
When two lines intersect, they usually intersect at just one point (unless they are parallel, where they never intersect; or no solutions when they infinitely intersect).
According to the graph provided, the lines are intersecting at one point: (2, 1).
So, your answer will be the second option!
Hope this helps!
A sofa set costs $4800 and can be bought under a hire purchase plan. A 15% deposit is required and the remaining amount is to be paid in 24 monthly installments at a simple interest rate of 3% per annum. What is the amount to be paid in installment per month. *
Answer:
$180.20
Step-by-step explanation:
15% of $4800=$720
$4800-$720=$4080
6% of $4080=$244.8
$4080+$244.8=$4,324.80
$4,324.80/24=$180.20
so you would pay $180.20 a month
Factor the expression 4x + 32. Explain each step you take in the process. 100 points goes to brainliest
Answer:
4(x+8)
Step-by-step explanation:
4x+32
x+8 in parentheses
and put the 4 on the outside of the parentheses
like this 4(x+8)
Answer:
4(x+8)
Step-by-step explanation:
4x + 32
Rewriting
4*x + 4*8
Factor out 4
4(x+8)
Ruby is visiting San Francisco. From her hotel she walks 1 block west and 3 blocks south to a coffee shop. Then she walks 4 blocks east and 4 blocks south to a museum. Where is the museum in relation to her hote
Answer:
The Museum is 7 blocks south and 3 blocks east
Step-by-step explanation:
Since from the hotel Ruby went 1 block west (left) during the whole time traveled, you would go 3 east (from hotel to museum).
Then in total Ruby went south 7 blocks.
A rectangular driveway has the dimensions shown below. Concrete costs $49.75 per square yard to pour. How much will it cost to pour concrete for the entire driveway?
[tex]\boxed{ \bf The~answer~is~$2,350.69.}[/tex]The answer is $2,350.69.
Explanation:First, we must find the area of the rectangular driveway.
A = l × w
A = 15.75 × 3
A = 47.25
So, the area of the driveway is 47.25 yd².
Next, we need to multiply the cost of each square yard by the area.
49.75 × 47.25 = 2350.6875
This can be rounded to 2,350.69.
Find the coefficient of x^2 in the expression of (x - 7)^5. a. -3430 b. -3034 c. 3034 d. 3430
Answer:
let me know when you have the anwser
Step-by-step explanation:
The mean per capita income is 19,292 dollars per annum with a variance of 540,225. What is the probability that the sample mean would be less than 19269 dollars if a sample of 499 persons is randomly selected? Round your answer to four decimal places.
Answer:
The probability is 0.2423.
Step-by-step explanation:
Given mean per capita = 19292 dollars
Given the variance = 540225
Now find the probability that the sample mean will be less than 19269 dollar when the sample is 499.
Below is the calculation:
[tex]\bar{X} \sim N(\mu =19292, \ \sigma = \frac{\sqrt{540225}}{\sqrt{499}}) \\\bar{X} \sim N(\mu =19292, \ \sigma = 32.90) \\\text{therefore the probability is:} \\P (\bar{X}< 19269) \\\text{Convert it to standard normal variable.} \\P(Z< \frac{19269-19292}{32.90}) \\P(Z< - 0.6990) \\\text{Now getting the probability from standard normal table}\\P(Z< -0.6990) = 0.2423[/tex]