Answer:
Step-by-step explanation:
Solving for x means you have to factor. First factor out the GCF of 2 to get:
[tex]2(3x^2+x-6)[/tex] and now we'll factor using the regular old method of ac and then factoring by grouping. In our polynomial, a = 3, b = 1, c = -6. Therefore, a times c is 3 * -6 which is -18. We need some combinations of the factors of 18 that will add to give us 1, the b term in the middle. The factors of 18 are:
1, 18
2, 9
3, 6 and that's it. Hm...it seems that won't work, so let's throw this into the quadratic formula, going back to the original and a = 6, b = 2 and c = -12:
[tex]x=\frac{-2+/-\sqrt{2^2-4(6)(-12)} }{2(6)}[/tex] and
[tex]x=\frac{-2+/-\sqrt{4+288} }{12}[/tex] and
[tex]x=\frac{-2+/-\sqrt{292} }{12}[/tex] and
[tex]x=\frac{-2+/-\sqrt{4*73} }{12}[/tex] and
[tex]x=\frac{-2+/-2\sqrt{73} }{12}[/tex] which finally simplifies to
[tex]x=\frac{-1+/-\sqrt{73} }{6}[/tex] No wonder that didn't factor using the traditional method of factoring! We could have found that out by finding first the value of the discriminant, but oh well!
Uncle Frank has a paddock on his farm. The paddock is a right angled isosceles triangle and has area 16m2. What is the length of fence enclosing the paddock
Answer:
8 m
Step-by-step explanation:
Applying,
A = bh/2................ Equation 1
Where A = Area of the triangle, b = base of the triangle, h = height of the triangle.
Since the triangle is an isosceles triangle.
Then, b = h
Assuming, b = y m
Given: A = 16 m²
Substitute these values into equation 1
16 = (y×y)/2
16 = y²/2
y² = 16×2
y² = 32
y = √32
y = 4√2 m
Therefore,
b = 4√2 m and h = 4√2 m
Applying pythagoras theorem, to get the length of the fence enclosing the paddock
a² = b²+c²
a² = (4√2)²+(4√2)²
a² = 32+32
a² = 64
a = √64
a = 8 m
Hence the length of the fence enclosing the paddock is 8 m
ABCD and EFGH are rectangles with AB=10cm ,BC=7cm ,EF=7cm and FG =4cm ,all figures accurate to the nearest cm . Find the largest possible value of the shaded area . *
Answer:
42 cm^2
Step-by-step explanation:
Please find attached an image showing the diagram
area of shaded part = area of larger rectangle - area of smaller rectangle
Area of a rectangle = length x width
larger rectangle = 10 x 7 = 70 cm^2
smaller rectangle = 7 x 4 = 28cm^2
Area of shaded part : 70 - 28 = 42cm^2
A 16-foot ladder is leaning against a wall and the bottom of the ladder is 7 feet from
the bottom of the wall. How high up the wall is the ladder touching?
round to the nearest tenth
Answer:
13.23 feet^2
Step-by-step explanation:
What is the reciprocal of -3 2/7 ? -3 7/2 -23/7 -7/23 3 2/7
Reciprocal of -32/7 = -7/32
Answer:
-32/7 = -7/32
Step-by-step explanation:
Vince's birthday party is going to be at his favorite science museum next weekend. He has 8 friends who want to see the Dinosaur Discovery show and 4 friends who want to see the Wild Weather show. Typically, the Dinosaur Discovery show costs d dollars per ticket, and the Wild Weather show costs w dollars per ticket. But next weekend, all tickets are half price! Pick all the expressions that represent the total cost of his friends' tickets.
Answer:
See explanation
Step-by-step explanation:
Dinosaur Discovery show = 8 friends
Wild Weather show = 4 friends
Cost of Dinosaur Discovery show = $d
Cost of Wild Weather show = $w
At regular price:
Total cost of his friends' tickets = 8 * d + 4 * w
= 8d + 4w
At half price
Total cost of his friends' tickets =
8 * 1/2d + 4 * 1/2w
= 8/2d + 4/2w
= 4d + 2w
Total cost of his friends' tickets = 4d + 2w
Quadrilateral ABCD is inscribed in a circle. If angle B measures 112°, what is the measure of angle D?
Answer:
68°
Step-by-step explanation:
If a quadrilateral is inscribed in a cirle, the sum of its opposite angles is 180°. Angles B and D are opposite => B+D=180° => D=180°-B=180°-112°=68°
Answer:
68°
Step-by-step explanation:
Since angles B and D are opposite each other, they are supplementary.
A test has several multiple choice questions, each with 5 choices. If you guess on 4 questions, what is the probability that you get all 4 correct
Answer:
4/20 or 1/5
Step-by-step explanation:
number of guesses/total possible outcomes (formula for this question since it is an independent event)
total possible outcomes: 4(# of questions) x 5(# of possible answers in 1 question)
total possible outcomes: 20
number of guesses: 4 x 1(there are 4 questions and you guess 1 answer for each question)
number of guesses: 4
number of guesses/total possible outcomes = 4/20 or 1/5
(I might be wrong lol, I haven't learned it in a long time)
On a unit circle, the terminal point of 0 is (sqrt3/2,1/2)
What is 0?
Answer:
The measure of [tex]\theta[/tex] is 30°.
Step-by-step explanation:
In the statement, the angle has been misrepresented. The corrected statement is described below:
"On a unit circle, the terminal point of [tex]\theta[/tex] is [tex]\left(\frac{\sqrt{3}}{2}, \frac{1}{2} \right)[/tex]. What is [tex]\theta[/tex]?"
The measure of the angle ([tex]\theta[/tex]), in radians, is in standard form, that is, it is done with respect to the +x semiaxis. The measure of the angle whose terminal point is of the form [tex](x,y)[/tex] is determined by the following inverse trigonometric function:
[tex]\theta = \tan^{-1}\left(\frac{y}{x} \right)[/tex] (1)
If we know that [tex]x = \frac{\sqrt{3}}{2}[/tex] and [tex]y = \frac{1}{2}[/tex], then the measure of [tex]\theta[/tex] is:
[tex]\theta = \tan^{-1} \frac{\sqrt{3}}{3}[/tex]
[tex]\theta = 30^{\circ}[/tex]
The measure of [tex]\theta[/tex] is 30°.
Answer:
its 60 degrees
Step-by-step explanation:
a p e x 2021
PLZ HELP WILL GIVE BRAINLIEST IF RIGHT!!!
Christian goes out to lunch. The bill, before tax and tip, was $10.40. A sales tax of 6% was added on. Christian tipped 17% on the amount after the sales tax was added. How much tip did he leave? Round to the nearest cent.
Answer:
$12.89
Step-by-step explanation:
value of tax:
6 : 100 = x : 10.40
x = (10.40 * 6)/100 = $0.624
new amount
10.40 + 0.624 = $11.02
value of tip
17 : 100 = x : 11.02
x = (11.02 * 17)/100 = $1.8734
Final amount
11.02 + 1.8734 = $12.89
what is the y-intercept of this quadratic?
Answer:
The y-intercept is the value at which the graph of the function intersects the y-axis. Every quadratic has a (single) y-intercept. The reason for this is that the y-intercept is the function value at x = 0, and we can always substitute x = 0 into the quadratic.
Which of the following graphs is described by the function given below?
y = x^2 - 6x - 16
A. Graph A
B. Graph B
C. Graph C
D. Graph D
Answer:
(C).Graph C
Step-by-step explanation:
The function f(x) = –x2 – 4x + 5 is shown on the graph. On a coordinate plane, a parabola opens down. It goes through (negative 5, 0), has a vertex at (negative 2, 9), and goes through (1, 0). Which statement about the function is true? The domain of the function is all real numbers less than or equal to −2. The domain of the function is all real numbers less than or equal to 9. The range of the function is all real numbers less than or equal to −2. The range of the function is all real numbers less than or equal to 9.
Answer:
A≈1075.21
d Diameter
37
d
r
r
r
d
d
C
A
Using the formulas
A=
π
r
2
d=
2
r
Solving forA
A=
1
4
π
d
2
=
1
4
π
37
2
≈
1075.21009
Step-by-step explanation:
PLSSS HELPP ASAP
Each of the following data sets has a mean of 5. Which has the greatest variability? (no calculations are necessary)
Α.{1, 3, 5, 7, 9}
В. {1, 1, 1, 1, 21}
с. {3, 4, 5, 6, 7}
D. {5, 5, 5, 5, 5)
Answer:
choose B is the greatest variablity
a article cost$1424 it may be purchased by depositing$560 and making monthly payment of 48 how many months are required to complete payment
Answer:
18months
Step-by-step explanation:
1424-560=864
864÷48=18
Answer:
18
Step-by-step explanation:
$1424-$560= $864
$864 divided by $48 = 18 months
Two mechanics worked on a car. The first mechanic worked for 5 hours, and the second mechanic worked for 15 hours. Together they charged a total of $1025. What was the rate per hour by each mechanic if the sum of the two rates was $105 per hour?
Answer:
The mechanic who worked 5 hours charged $115 per hour, the one who worked 15 hours charged $120 per hour.
Step-by-step explanation:
x = rate of mechanic who worked 5 hours
y = rate of mechanic who worked 15 hours
Then
x + y = 235
5x + 15y = 2375
Just solve these 2 equations above for x and y.
x + y = 235 ⇒ x = 235 - y
Substitute into second equation to find y.
5(235 - y) + 15y = 2375
1175 - 5y + 15y = 2375
10y = 1200
y = 1200/10 = 120
x = 235 - y = 235 - 120 = 115
please help me im in need of serious help or ill flunk :(
Answer:
1. Interest: 15%
Amount owed: $500
2. Interest: 6%
Amount owed: $1,500
3. Interest: 18%
Amount owed: $12,500
4. Interest: 6%
amount owed: $5,000
Step-by-step explanation:
What two numbers sum up to 11 and multiply to 18
Answer:
9 and 2
Step-by-step explanation:
9+2=11
9×2=18
Answer:
9 and 2
Step-by-step explanation:
can anyone help with this? find st and rt
Answer:
ST= 5.2
RT= 23.6
Step-by-step explanation:
Answer:
ST= 5.2
RT= 23.6
Step-by-step explanation:
What is the slope of the line?
7x+2y=5
Answer:
- 7/2
Step-by-step explanation:
Please answer this!!!
Answer:
so a = -1 b = -1/4 and c = 7
Step-by-step explanation:
-x^2 - 1/4x +7
This is in the form
ax^2 + bx +c
so a = -1 b = -1/4 and c = 7
Answer:
[tex]a=-1[/tex]
[tex]b=-\frac{1}{4}[/tex]
[tex]c=7[/tex]
Step-by-step explanation:
Hope this helps:)
Jane bought 6 dozen banana at $250per dozen. She sells four and a half dozen at $35 each and the other were sold at $20 each. Determine if she made a profit or loss state her profit or loss as a percentage. Show working
Answer:
87.5% loss
Step-by-step explanation:
6 • 250 = 1500
4.5 • 35 = 157.5
6 - 4.5 = 1.5
1.5 • 20 = 30
157.5 + 30 = 187.5
1500x = 187.5
x = 0.125
12.5% is an 87.5% decrease
Find the middle point, M, of ab
Distance from A to B = B-A = 18-0 = 18
M is the midpoint which means it is equal distance between A and B
M = distance between A and B divided by 2:
M = 18/2 = 9
Answer: M = 9
Answer:
9
Step-by-step explanation:
If m is a midpoint of AB
then
M = 1/2AB
If AB = 18
Then M = 1/2 of 18
18/2 = 9
Hence M = 9
Need urgent help for this math question will give brainliest
Answer:
1st box: 6x - 3 = 9
2nd box: 6x = 12
3rd box: x = 2
4th box: y = 4(2) - 3
5th box: y = 8 - 3
6th box: y = 5
Step-by-step explanation:
Part A-
1) 4x-3 = -2x+9
2) 4x+2x -3 = -2x+2x + 9
3) 6x -3 = 9
4) 6x -3+3 = 9+3
5) 6x = 12
6) 6x/6 = 12/6
7) x = 2
Part B-
1) y=4x-3
2) y=4(2)-3
3) y=8-3
4) y= 5
Therefore, x = 2 and y = 5.
I really hope this helps, good luck!
Given the points A(-3, -2) and B(6, 1), determine the coordinates of point P on directed line segment that partitions in the ratio 2/1.
Answer:
[tex]P = (3,0)[/tex]
Step-by-step explanation:
Given
[tex]A = (-3,-2)[/tex] ---- [tex](x_1,y_1)[/tex]
[tex]B = (6,1)[/tex] --- [tex](x_2,y_2)[/tex]
[tex]m:n =2:1[/tex]
Required
The coordinates of P
This is calculated as:
[tex]P = (\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n}][/tex]
So:
[tex]P = (\frac{2*6+1*-3}{2+1},\frac{2*1+1*-2}{2+1})[/tex]
[tex]P = (\frac{9}{3},\frac{0}{3})[/tex]
[tex]P = (3,0)[/tex]
If I have 75 oranges and I eat two and a half everyday for 30 days how many will I have eaten in one month
Answer:
all 75 of them
Step-by-step explanation:
2.5(30) = 75
4-2(2x-3)-(2x-4)=-2(x+3)
Answer:
x = 5
Step-by-step explanation:
Given
4 - 2(2x - 3) - (2x - 4) = - 2(x + 3) ← distribute parenthesis on both sides
4 - 4x + 6 - 2x + 4 = - 2x - 6
- 6x + 14 = - 2x - 6 ( add 2x to both sides )
- 4x + 14 = - 6 ( subtract 14 from both sides )
- 4x = - 20 ( divide both sides by - 4 )
x = 5
Answer:
[tex]x = 5[/tex]
Step-by-step explanation:
Let's solve:
[tex]4−2(2x−3)−(2x−4)=−2(x+3) \\ [/tex]
Step 1: Simplify both sides of the equation.
[tex]4−2(2x−3)−(2x−4)=−2(x+3) \\ 4−2(2x−3)+−1(2x−4)=−2(x+3) \\ (Distribute the Negative Sign)
\\ 4+−2(2x−3)+−1(2x)+(−1)(−4)=−2(x+3) \\
4+−2(2x−3)+−2x+4=−2(x+3)
4+(−2)(2x)+(−2)(−3)+−2x+4=(−2)(x)+(−2)(3) \\ (Distribute) \\
4+−4x+6+−2x+4=−2x+−6 \\(−4x+−2x)+(4+6+4)=−2x−6(Combine Like Terms) \\ −6x+14=−2x−6
\\ −6x+14=−2x−6[/tex]
Step 2: Add 2x to both sides.
[tex]−6x+14+2x=−2x−6+2x \\ −4x+14=−6[/tex]
Step 3: Subtract 14 from both sides.
[tex]−4x+14−14=−6−14 \\ −4x=−20[/tex]
Step 4: Divide both sides by -4.
[tex] \frac{ - 4x}{ - 4} = \frac{ - 20}{ - 4} \\ x=5[/tex]
Mindy puts a rectangular poster of her favorite singer on a wall in her bedroom. What is the perimeter of the poster?
Answer:
Step-by-step explanation:
If real estate agent earns a 3% commission and earned \$4,350 on the closing of a home What was the price of the home?
Answer:
Final price of house = $145,000 (Approx.)
Step-by-step explanation:
Given:
Rate of commission = 3%
Amount of commission = $4,350
Find:
Final price of house
Computation:
Final price of house = Amount of commission / Rate of commission
Final price of house = 4,350 / 3%
Final price of house = 4,350 / 0.03
Final price of house = 145,000
Final price of house = $145,000 (Approx.)
In a carnival game, players get 5 chances to throw a basketball through a hoop. If 7 out of 20 players made all 5 baskets, how many players out of 400 would you expect to make all 5 baskets?
=====================================================
Work Shown:
7/20 = 0.35 = 35% of the 20 players made all five baskets.
If this trend holds up, then we should expect 35% of the 400 people to make all five baskets.
35% of 400 = 0.35*400 = 140
We expect about 140 people will make all five baskets.
Note how 140/400 = 0.35 = 35%
-------------
Through another alternative method, we can solve like this
7/20 = x/400
7*400 = 20*x ... cross multiply
2800 = 20x
20x = 2800
x = 2800/20 ... dividing both sides by 20
x = 140 which is the same result as before
What is the value of x
A. 100 B.50 C.25 D.35
Answer:
D
Step-by-step explanation:
I believe this is correct