Which of the following are solutions to the equation below?
Check all that apply.
x2 - 10x+ 25 = 17
I A. X = 17-5
B. x = --58-5
c. x= - - _17-5
D. x= 177 +5
E. x = 18 +5
F. x= -17 +5
Answer:
The answer is letter F po
Step-by-step explanation:
Use the formula
(b2)2 in order to create a new term. Solve for x
by using this term to complete the square.
Exact Form:x=±√17+5
22. Determine the value of c so that the line
segment with endpoints B(2, 2) and C(9,6)
BC
is parallel to the line segment with endpoints
D(c, -7) and E(5, -3).
help is appreciated !!!
Answer:
If the lines BC and DE are parallel, the value of c is c=-2
Step-by-step explanation:
We are given line segment BC with end points B(2, 2) and C(9,6) and line segment DE with endpoints D(c, -7) and E(5, -3).
Using slope formula: [tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex] we can find point c
When 2 lines are parallel there slope is same.
So, Slope of line BC =Slope of Line DE
[tex]\frac{y_2-y_1}{x_2-x_1}=\frac{y_2-y_1}{x_2-x_1}[/tex]
We have:
[tex]x_1=2, y_1=2, x_2=9, y_2=6 \ for \ line \ BC \ and \\\x_1=c, y_1=-7, x_2=5, y_2=-3 \ for \ line \ DE \[/tex]
Putting values and finding c
[tex]\frac{6-2}{9-2}=\frac{-3-(-7)}{5-c}\\ \frac{4}{7}=\frac{-3+7}{5-c} \\ \frac{4}{7}=\frac{4}{5-c} \\Cross \ multiply:\\4(5-c)=4*7\\20-4c=28\\-4c=28-20\\-4c=8\\c=\frac{8}{-4}\\c=-2[/tex]
So, If the lines BC and DE are parallel, the value of c is c=-2
x2 + 20x +__________
how solve these problem plssssss
Answer:
for the second question , all you have to do is substitute , the first point plotted is x and the second point is b , ploy those points in the equation and remember that to find x we make y= 0 and to find y we make x =0
The resultant of the vectors a = 3i - 2j and b = pi - 2pj is parallel to the vector c = 2i - 3j.
a) Find the value of p
b) Find the resultant of vectors a and b.
Please help me with this question, thank you
Part (a)
The resultant vector is the vector formed by adding the two vectors a and b. So we effectively add the corresponding components.
You can use the parallelogram law as a visual alternative.
Adding a and b leads to
a+b = (3i-2j) + (pi-2pj)
a+b = (3i+pi) + (-2j-2pj)
a+b = (3+p)i - (2+2p)j
Define vector d to be d = a+b so we can use it later below.
Recall that parallel vectors point in the same direction. This means the ratio of their components or coordinates are equal.
We can say the following
(x coord of d)/(x coord of c) = (y coord of d)/(y coord of c)
(3+p)/(2) = (-(2+2p))/(-3)
Let's solve for p
(3+p)/(2) = (-(2+2p))/(-3)
(3+p)/(2) = (2+2p)/3
3(3+p) = 2(2+2p) .... cross multiply
9+3p = 4+4p
4p+4 = 3p+9
4p-3p = 9-4
p = 5
Answer: p = 5========================================================
Part (b)
Since p = 5, from part (a), we can determine vector b
b = pi - 2pj
b = 5i - 2*5j
b = 5i - 10j
Then add vectors a and b to get
a+b = (3i-2j) + (5i - 10j)
a+b = (3i+5i) + (-2j - 10j)
a+b = (3+5)i - (2+10)j
a+b = 8i - 12j
Or we can say
a+b = (3+p)i - (2+2p)j .... from part (a)
a+b = (3+5)i - (2+2*5)j ... plugging in p = 5
a+b = 8i - 12j
Note the ratio of the components of vector d and vector c are such
(x coord of d)/(x coord of c) = (y coord of d)/(y coord of c)
8/2 = -12/(-3)
4 = 4
This helps confirm the answer
You could also graph the vectors c = 2i - 3j and d = 8i - 12j to note the two lines produce the same slope -3/2. We can see that -12/8 = -3/2. Lines of the same slope are parallel lines
Answer: 8i - 12ja.
The value of p is 5
Since vector a = 3i - 2j and vector b = pi - 2pj, the resultant of vectors a and b is R = a + b
= 3i - 2j + pi - 2pj
= (3 + p)i - 2(1 + p)j
Since R is aparallel to vector c = 2i - 3j, it implies that the cross product of R and c is zero.
The cross product of two vectors a and b is a × b = absinФ where a and b are the magnitudes of a and b and Ф is the angle between them.
So, R × c = [(3 + p)i - 2(1 + p)j] × [2i - 3j]
= (3 + p)i × 2i + (3 + p)i × (-3j) + (-2(1 + p)]j × 2i + (-2(1 + p)]j×(-3j)
= 0 - 3(3 + p)k - 4(1 + p)(-k) + 0
= -3(3 + p)k + 4(1 + p)k
= [-3(3 + p) + 4(1 + p)]k
= [-9 - 3p + 4 + 4p)]k
= [-9 + 4 - 3p + 4p)]k
= [-5 + p]k
[-5 + p]k = RcsinФ.
Since R and c are parallel, Ф = 0°
So, Rcsin0° = Rc × 0 = 0
So, [-5 + p]k = 0
-5 + p = 0
p = 5
The value of p is 5
b.
The resultant of vectors a and b is R = 8i - 12j
Since p = 5 and the resultant of vectors a and b is R = (3 + p)i - 2(1 + p)j
Substituting the value of p = 5 into r, we have
R = (3 + p)i - 2(1 + p)j
R = (3 + 5)i - 2(1 + 5)j
R = 8i - 2(6)j
R = 8i - 12j
So, the resultant of vectors a and b is R = 8i - 12j
Learn more about resultant of vectors here:
https://brainly.com/question/14358602
i need this asap, will give brainliest to fast answers!! :)
Answer: $22.50, but rounded to the nearest dollar its $23.00 Hope this helps :)
Step-by-step explanation: The unit rate it 1/0.75
9) Brenn has $60 in his savings account. His brother Chris has $135 in his. Brenn decides to save $5 of his allowance each week, while Chris decides to spend his whole allowance along with $10 of his savings each week. After how many weeks will Brenn and Chris have the same amount of money in their savings accounts?
Answer:
9) 15
Step-by-step explanation:
find the angle represented by x ( round the nearest tenth of a degree) A 16.2 B 16.4 c17.1 d17.4
Answer:
B. 16.4°
Step-by-step explanation:
reference angle = x = [tex] \theta [/tex]
Side length opposite to x = 20 ft = opp
Adjacent side length = 68 ft = adj
Apply the following trigonometric ratios formula:
[tex] tan(\theta) = \frac{opp}{adj} [/tex]
Plug in the values into the formula
[tex] tan(x) = \frac{20}{68} [/tex]
[tex] tan(x) = 0.2941 [/tex]
[tex] x = tan^{-1}(0.2941) [/tex]
[tex] x = 16.3886 [/tex]
x = 16.4° (nearest tenth)
Answer:
B. 16.4
Step-by-step explanation:
19 books on a shelf. 8 of these books are new. The rest of them are used. What is the ratio of new books to used books
Answer:
1:8
Step-by-step explanation:
You subtract 19 and 8, and you get 11 then you put them in ration form
Step-by-step explanation:
A police car drives 230 km in 2 1/2 hours. What is its average speed in kilometers per hour?
Answer:
92 km/h
Step-by-step explanation:
The larger of two numbers is two more than five times the smaller number.if the sum of the two numbers is 80 find both number
Answer:
the smaller number is 13 and the larger number is 67
A line intersects the points (3,-4) and (1,2).What is the slope intercept equation for this line
Answer:
y=-3x+5
Step-by-step explanation:
y=mx+b
m=(-4-2)/(3-1)=-3
b=y-mx
b =-4 - (3)(-3)
b=-4+9
b=5
HELP QUICKLY!!!
what is the y intercept of the line
Answer:
-23
Step-by-step explanation:
the equation of the line is y=-2/3x-23 so the b in the equation (y=mx+b) is the y int so that is -23
Solve 2c − 8f = 24 for f. Show your work.
Answer:
f=2 c=4
Step-by-step explanation:
8 times 2 equals 16 plus 2 times 4 equals 24 in total.
The number of tons of wheat the government can afford to buy if it spends total of $100 million, wheat costs $300 per ton, and it must buy 5 fighter planes at $15 million each.
Total amount, T = $100 million.
Cost of wheat per ton, C = $300 .
Price per fighter plane, c = $15 million.
Now,
Price of 5 fighter planes, P = $( 15 × 5 ) = $75 million.
Amount left = $( 100 - 75 ) = $25 million.
So,
Number of tons of wheat government can buy is :
[tex]n=\dfrac{25\times 1000000}{300}\\\\n = 83333.33\ tons[/tex]
Therefore, number of tons of wheat the government can afford is 83333.33 tons.
Hence, this is the required solution.
Help please uh thanks
help me, please it would get 15 points
Answer:
Here are 5 (2,4), (3,6), (1,2), (4,8), (5,10)
Step-by-step explanation:
What is the slope intercept form for this ?
Answer:
150
Step-by-step explanation:
Answer:
y = 150x + 400
Explanation:
Slope intercept form is : y = mx + b
B is the y intercept, you can also think of it like a starting value, in this case Susan starts with $400 dollars
M is the slope, you can also think of it like a value that is consistently changing over time, in this case Susan saves(or earns) $150 each month.
If you want to figure how much money she will have in a certain number of months, plug the number of months (x), into the x in y = 150x + 400.
PLZ HELP
12 yd = ___ ft
Answer:
12yd = 36ft
Why: For every 1 yard you have 3 feet
2 yards=6 3=9 and so on
Step-by-step explanation:
12 yards = 36 feet
if this answer is correct:
give a like and rate me 5
A rubber tree is 95 inches tall and growing at a rate of 4 inches per year. A cactus is 40 inches tall and growing at arate of 5 inches per year. After how many years will the rubber tree be shorter than the cactus tree
Select the better deal in the pair. Then give the unit rate for the better deal.
$56/25 gal
or
$32.05/15 gal
Answer:
The better deal is $32.05/15 gal
Step-by-step explanation:
Divide:
56/25
=2.24
32.05/15
=2.13666667
=2.14
A manufacturer has invested $120,000 in a new product and wants to set a price to earn a $80,000 profit. The variable cost per unit is $20 and the company sells the units at $100.
Answer: 500
Step-by-step explanation:
The remainder of the question is:
How many units does the company need to sell to reach the target profit?
The required sales to break even will be calculated as:
= (Fixed cost + Required profit) / ( Price per unit - Variable cost)
= (120000 - 80000) / (100 - 20)
= 40000/80
= 500
The company needs to sell 500 units.
What is 12.18 x 103 =
Answer:
1,254.54
Step-by-step explanation:
Answer:
1,254.54
Step-by-step explanation:
Megan bought 2 1/4 pounds of bananas for $0.80 per pound and 1 1/2 pounds of strawberries for $1.10 per pound. How much more did Megan spend on bananas than on strawberries?
Answer:
$0.15
Step-by-step explanation:
Cost of each pounds of banana = $0.80
Number of pounds of banana = 2 1/4 pounds
Total cost of banana = $0.80 × 2 1/4 pounds
= 0.80 × 9/4
= 0.80 × 2.25
= 1.8
Total cost of banana = $1.8
Cost of each pounds of strawberry = $1.10
Number of pounds of strawberry = 1 1/2 pounds
Total cost of strawberry = $1.10 × 1 1/2 pounds
= 1.10 × 3/2
= 1.10 × 1.5
= 1.65
Total cost of strawberry = $1.65
How much more did Megan spend on bananas than on strawberries?
Total cost of banana - Total cost of strawberry
= $1.8 - $1.65
= $0.15
Answer:
$0.15
Step-by-step explanation:
Cost of each pounds of banana = $0.80
Number of pounds of banana = 2 1/4 pounds
Total cost of banana = $0.80 × 2 1/4 pounds
= 0.80 × 9/4
= 0.80 × 2.25
= 1.8
Total cost of banana = $1.8
Cost of each pounds of strawberry = $1.10
Number of pounds of strawberry = 1 1/2 pounds
Total cost of strawberry = $1.10 × 1 1/2 pounds
= 1.10 × 3/2
= 1.10 × 1.5
= 1.65
Total cost of strawberry = $1.65
How much more did Megan spend on bananas than on strawberries?
Total cost of banana - Total cost of strawberry
= $1.8 - $1.65
= $0.15
Find the interest on an investment of $45,000
compound annually at 5.25% for 6 years
A = P(1 + r)t
Answer:
The interest on the investment is $16,170.93811
Step-by-step explanation:
The rule of the compound interest is [tex]A=P(1+\frac{r}{n})^{nt}[/tex], where
A is the new valueP is the initial valuer is the rate in decimaln is the number of periods in timet is the time∵ The investment is $45,000
∴ P = 45,000
∵ The interest on the investment is compounded annually at 5.25%
∴ r = 5.25% = 5.25 ÷ 100
∴ r = 0.0525
∴ n = 1 ⇒ compound annually
∵ It is for 6 years
∴ t = 6
→ Substitute them in the rule above
∵ [tex]A=45,000(1+\frac{0.0525}{1})^{1(6)}[/tex]
∴ [tex]A=45,000(1.0525)^{6}[/tex]
∴ A = 61,170.93811
∵ I = A - P, where I is the interest
∴ I = 61,170.93811 - 45,000
∴ I = 16,170.93811
∴ The interest on the investment is $16,170.93811
For any linear function f(x) = mx + b, when does 5f(x) = f(5x)?
a) always
b) when b = 0
c) when b = 5/4
d) when b = 5
Answer:
B
Step-by-step explanation:
Geometry 9th grade will give brainliest
Step-by-step explanation:
7.90.
can someone help plz
Answer:
6. a) 7/3
7. b) Y=20/3(x)
Which equation represents a line which is parallel to the line 3x + 8y = - 40 ?
Which ordered pair is a solution of the system of equations shown in the graph below?
Answer: A
Step-by-step explanation:
Answer:
(0,-1)
Step-by-step explanation:
because the line crosses through (0,-1) the vertex is (0,-4)