Answer:
[tex]y =-\frac{1}{2}(x +2)(x - 3)[/tex]
Step-by-step explanation:
Given
[tex]x_1 = -2[/tex]
[tex]x_2 = 3[/tex]
[tex](x,y) = (-1,2)[/tex] --- a point on the parabola
Required
The equation
First, calculate the equation from the zeros
[tex]y =k(x - x_1)(x - x_2)[/tex]
Substitute [tex]x_1 = -2[/tex] and [tex]x_2 = 3[/tex]
[tex]y =k(x - -2)(x - 3)[/tex]
[tex]y =k(x +2)(x - 3)[/tex]
To solve for k, we substitute [tex](x,y) = (-1,2)[/tex]
[tex]2 = k(-1+2)(-1-3)[/tex]
[tex]2 = k(1)(-4)[/tex]
[tex]2 = -4k[/tex]
Divide by -4
[tex]k=\frac{2}{-4}[/tex]
[tex]k=-\frac{1}{2}[/tex]
So, the equation is:
[tex]y =k(x +2)(x - 3)[/tex]
[tex]y =-\frac{1}{2}(x +2)(x - 3)[/tex]
Answer: c
Step-by-step explanation:
What is the product?
(x − 3)(2x2 − 5x + 1)
Answer:
5x2+20x−15
Step-by-step explanation:
Write the log equation as an exponential equation. You do not need to solve for x. \log_9\left(2\right)=2x-1 log 9 (2)=2x−1
Answer:
[tex]9^{2x-1} = 2\\[/tex]
Step-by-step explanation:
According to the law of logarithm;
[tex]If \ log_ab = x\\a^x = b[/tex]
Given
[tex]\log_9\left(2\right)=2x-1[/tex]
Comparing with the original expression;
a = 9, b = 2 and c = 2x - 1
Substitute into the result indicinal expression;
[tex]9^{2x-1} = 2\\[/tex]
This gives the required exponential equation
HELP PLEASE! for 20 points
$5 out of every $100 a worker earns goes for clothes. On $4,000 a year wages, how much does he spend on clothes?
If $5 out of every $100 a worker earns goes for clothes, the worker spends $200 on clothes from a $4,000 annual wage.
To determine how much a worker spends on clothes from a $4,000 annual wage, we need to calculate 5% of that amount.
The worker spends $5 out of every $100 earned on clothes. This means the worker spends 5% of their earnings on clothes.
To find 5% of $4,000, we can multiply $4,000 by 0.05:
$4,000 * 0.05 = $200
This calculation is based on the assumption that the worker consistently spends 5% of their income on clothes throughout the year.
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Please help thanks this is due today!
D. [tex] ({ - 8})^{2} - 9 + ( - 7)[/tex] ✅
Step-by-step explanation:
[tex] {( - 32 \div4 })^{2} - 9 + ( - 7) \\ \\ = ({ - 8})^{2} - 9 +(- 7 )\\ \\=64-9-7\\\\ = 64 - 16 \\ \\ = 48[/tex]
Note:-
[tex]\sf\red{PEMDAS\: rule.}[/tex]
P = Parentheses
E = Exponents
M = Multiplication
D = Division
A = Addition
S = Subtraction
[tex]\sf\red{(+\:x\:-)\:=\:-}[/tex]
[tex]\sf\red{(-\:x\:-)\:=\:+}[/tex]
[tex]\bold{ \green{ \star{ \orange{Mystique35}}}}⋆[/tex]
You are on a ship at sea. You see a lighthouse in the distance. You know the lighthouse is 175 feet tall. You measure the angle of elevation to the top of the lighthouse at 5 degrees. How far are you from the bottom of the lighthouse
Answer: 2000.25 ft
Step-by-step explanation:
Given
Height of lighthouse [tex]h=175\ ft[/tex]
Angle of elevation [tex]\theta=5^{\circ}[/tex]
Suppose, you are x feet away from lighthouse
From the figure, we can write
[tex]\Rightarrow \tan 5^{\circ}=\dfrac{175}{x}\\\\\Rightarrow x=\dfrac{175}{\tan 5^{\circ}}\\\\\Rightarrow x=2000.26\ ft[/tex]
Thus, the ship is 2000.25 ft away from the light-house
HELPPPPP!!!! ASAPPPPP!!!!!
Answer:
24
Step-by-step explanation:
XW=WY=12
If the opposite angle is 30, the hypotenuse is double the small side.
XZ=XW=2·12=24
Pls I need this before midnight (USA)
Answer:
I can’t post an image, but I’ll explain below
Step-by-step explanation:
Start at a point where the line crosses through a coordinate exactly, like (0,1), and find a second one. Draw a line from the first to the right until it’s over the second point, then go down to the second point. It should look like half of a rectangle. Just follow the lines of the graph :)
What is the probability of an event that is certain?
Answer:
Nvm my answer is wrong
An event that is certain to happen has a probability of 1. An event that cannot possibly happen has a probability of zero. If there is a chance that an event will happen, then its probability is between zero and 1.
Jordan is baking brownies and will choose to use either a round or a rectangular pan. The dimensions of the bottom of each pan are shown below.
A full waterbed mattress is 6 ft by 2 ft by 1 ft. The mattress is to be filled with water that weighs 62.4 lb /ft3. Find the weight of the water in the mattress to the nearest pound.
Answer:
749 lbs
Step-by-step explanation:
weight of the water in the mattress = volume of the mattress x weight of water
volume of the mattress = volume of a cuboid = length x width x height
6 x 2 x 1 = 12 ft³
weight of the water in the mattress = 12 x 62.4 = 748.8 lbs
749 lbs to the nearest pound
A line that includes the point (2, 9) has a slope of 8. What is its equation in slope-intercept
form?
Answer:
y-8x+7=0
Step-by-step explanation:
slope(m)=8
using slope intercept form of equation of staright line we get
y=mx+b
y=8*x+b
y-8x=b ................ eq(i)
since the line include the point (2,9) it satisfies the euation,
here x=2 and y=9
equation: y-8x=b
9-8*2=b
9-16=-b
-7=b
substituting the value of b in eq(i) we get
y-8x=-7
y-8x+7=0 is a required equation of the line.
plzz helppp it's due today
Answer:
8
Step-by-step explanation:
use trig functions
2 sides and 1 angle given
Sides given
hypotenuse -> xopposite side to 30˚ -> 4Angle
30˚trig function associated with hyp and opp is sin
sin(x) = opp/hyp
substitute
sin 30˚ = 4/x
solve for x
0.5 = 4/x
0.5x = 4
x = 8
Answer:
Step-by-step explanation:
sin 30° = [tex]\frac{4}{x}[/tex]
x = [tex]\frac{4}{sin 30}[/tex]
x = [tex]\frac{4}{0.5}[/tex]
x = 8
Discover the rate of change (slope) of these two points. (-4, 5) and (5,-4).
Answer:-1
Step-by-step explanation:
slope = y2-y1/x2-x1
Plug in all the values
-4-5/5+4
-9/9
= -1
Lucas took an express train into the city last weekend without any stops. He boarded the train at 9:30 am, and arrived in the city at 11:15 a.m. The
train's average speed was 60 miles per hour. How far did Lucas travel by train?
75 miles
105 miles
135 miles
165 miles
The distance travelled by the Lucas will be equal to 105 miles.
What is an average speed?Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance. Speed is the ratio of the distance travelled by time. The unit of speed in miles per hour.
The average speed is defined as the total distance travelled by train in total time.
Given that Lucas took an express train into the city last weekend without any stops. He boarded the train at 9:30 am and arrived in the city at 11:15 a.m. The train's average speed was 60 miles per hour.
Time = 105 minutes = 105 / 60 = 1.75 hours
The distance travelled by train will be calculated as,
Distance = Speed x Time
Distance = 60 x 1.75
Therefore, the distance travelled by Lucas will be equal to 105 miles.
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What are the coordinates of the point 1/6 of the way from a to b?
Answer:
B. (2, 6)
Step-by-step explanation:
Xp = 1 + (1/6 × (7-1)) = 1 + (1/6×6) = 1+1 = 2
Yp = 8 + (1/6 × (-4-8)) = 8+(1/6×(-12))
= 8+(-2) = 6
the coordinate => (2, 6)
Fifty-five petcent of people in a survey said that they do exercise on a fairly regular basis. If 12,000 people were sureveyed, how many of them exercised on a fairly regular basis? A. 5,000 B. 5,500 C. 6000 D. 6,600
Help! What is the answer?
Answer:
c ......................
Which data set could be represented by the box plot shown below?
Answer:
The answer is C
Step-by-step explanation:
the lowest point of the box plot is at 1 and the highest is at 19, so by that it can't be A.
The box plot shows 12 being the median so that automatically leaves C but just to make sure the first half would be 6 and half of the last part would be 16 if that makes sense.
The ratios a: B and B :c are equivalent to one another
Select all the statements that must be true
Answer:
Options (2) and (5)
Step-by-step explanation:
Given ratio is a : b and b : c
[tex]\frac{a}{b}=\frac{b}{c}[/tex]
[tex]\frac{b}{a}= \frac{c}{b}[/tex] [Option 2]
[tex]\frac{a}{b}=\frac{b}{c}[/tex]
b × b = a × c
b² = ac
If a = b,
b² = bc
b = c [Option 5]
Therefore, Options (2) and (5) are the correct options.
There is a special baking tray for skinny cakes whose length is 13 more than 2 times its width, and the area is 115 square inches. What are the dimensions of the baking tray?
Answer:
5 inches by 25 inches
Step-by-step explanation:
From the question,
Let the width of the baking tray be(w) = x inches,
Then the lenght of the baking tray(l) = (2x+13) inches
If the area of the baking tray = 115 square inches
Applying,
A = lw................. Equation 1
Therefore,
x(2x+13) = 115
2x²+13x = 115
2x²+13x-115 = 0
Using factorization method to solve the quadratic equation
2x²-10x+23x-115 = 0
(2x²-10x)+(23x-115) = 0
2x(x-5)+23(x-5) = 0
(2x+23)(x-5) = 0
Either
2x+23 = 0
x = -23/2
or
x-5 = 0
x = 5.
dimensions of the tray is
w = 5 inches
l = (2×5)+15 = 10+15 = 25 inches
Hence the dimensions of the baking tray = 5 inches by 25 inches
Match them BRAINLIEST IF CORRECT
Answer:
1/2 for the red card
1/52 for queen of hearts
1/4 for clubs
3/13
Step-by-step explanation:
the red card is 1/2 because the only other color is black
there is only one queen of hearts
it is one of four possible symbols
because that is the only one left
Please help thank you!
Answer:
24.
(-24 ÷
[tex] {6}^{2} [/tex]
16+8= 24
how long will they take to make 504 muffins if they will be using 4 ovens?
Answer:
,♀️♀️♀️☺️️️️️️⚖️⚖️❤️❤️❤️❤️️️☘️️️☃️⭐njdjdnfjfnfnfnf
I NEED HELP WITH C , help i dont understand
Answer:
SAS
Step-by-step explanation:
SAS (Side-Angle-Side) is a proof of congruence for two triangles. Since C stipulates that [tex]\angle ENM=\angle ZNM[/tex], the two triangles would share two sides and the angle between them, thus being congruent from SAS.
Which sentence explains why polygon ABCDEFGH is congruent to polygon MNOPQRST?
A.
A sequence of translations will map MNOPQRST onto ABCDEFGH.
B.
A sequence of rigid transformations will map MNOPQRST onto ABCDEFGH.
C.
A sequence of rotations will map MNOPQRST onto ABCDEFGH.
D.
A sequence of reflections will map MNOPQRST onto ABCDEFGH.
Answer:
correct option if Option D
Answer:
The answer is B.
Step-by-step explanation:
It can't be A, C, or, D because if the polygons were in a certain position, those transformations wouldn't work.
The definition of a rigid transformation is either a translation, rotation, or reflection. Therefore it must be B.
Sorry about how vague this is. It's hard to explain this without diagrams.
se cumple que: A^2 + B = 486 y el M.C.D. de A y B es 9. ¿Cuál es el valor de B
Answer:
i dont know spanish
Step-by-step explanation:
Runner A runs at 10 km/h due north. Runner B leaves the same spot and runs at 12 km/h due east. Find the distance and bearing of runner B from runner A after 30 minutes
Answer: [tex]7.81\ km[/tex]
Step-by-step explanation:
Given
Runner A runs towards North at speed of 10 km/h
Runner B runs towards East at speed of 12 km/h
After half hour, they covered a distance of
[tex]\Rightarrow d_a=10\times 0.5\\\Rightarrow d_a=5\ km[/tex]
[tex]\Rightarrow d_b=12\times 0.5\\\Rightarrow d_b=6\ km[/tex]
They are running in perpendicular direction to each other
So, the distance between them is given by
[tex]\Rightarrow d=\sqrt{d_a^2+d_b^2}\\\Rightarrow d=\sqrt{5^2+6^2}\\\Rightarrow d=\sqrt{61}\\\Rightarrow d=7.81\ km[/tex]
Tell whether the triangle with the given side lengths is a right triangle. Y/N question
Answer: need a picture of the traingle but if it's at a 90 degree angle on any sides then yes
Step-by-step explanation:
у=-3x+3
y = -9x + 15
Answer:
(2, - 3 )
Step-by-step explanation:
Given the 2 equations
y = - 3x + 3 → (2)
y = - 9x + 15 → (2)
Substitute y = - 3x + 3 into (2)
- 3x + 3 = - 9x + 15 ( add 9x to both sides )
6x + 3 = 15 ( subtract 3 from both sides )
6x = 12 ( divide both sides by 6 )
x = 2
Substitute x = 2 into either of the 2 equations and solve for y
Substituting into (1)
y = - 3(2) + 3 = - 6 + 3 = - 3
solution is (2, - 3 )