Answers:
The +1 in f(x) is the y intercept
The +1 in g(x) is the y coordinate of the vertex
====================================================
Explanation:
For f(x), plugging in x = 0 leads to
f(x) = 2x^2+5x+1
f(0) = 2(0)^2+5(0)+1
f(0) = 1
Showing that (0,1) is the y intercept of f(x).
The same is not true for g(x)
g(x) = 2(x+5)^2+1
g(0) = 2(0+5)^2+1
g(0) = 51
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The +1 for g(x) represents the y coordinate of the vertex. Recall that vertex form in general is
y = a(x-h)^2+k
with (h,k) being the vertex. This means we can quickly spot the vertex for g(x) without having to graph. The same cannot be said for f(x) as we need to complete the square to get f(x) into vertex form. Currently, f(x) is in standard form.
Choice #1: Marie made an error when solving the equation below.
Part A: Identify Marie’s error and explain why it resulted in an incorrect solution.
Part B: Correctly solve 4x - 8 = 36 for x. Show your work.
Answer:
Marie´s error was not to consider the number 8:
4x - 8 = 36
it´s equal to:
(4x-8)/4 = 36/4
4x/4 - 8/4 = 36/4
x - 2 = 9
x = 9+2
x = 11
probe:
4*11 - 8 = 36
44 - 8 = 36
Marie did not add 8 on the right-hand side so by considering it the solution of the given equation will be 11.
What is the equation?There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
In another word, the equation must be constrained with some constraints.
As per the given equation,
4x - 8 = 36
Marie add +8 on the left-hand side but forgot to add it to the right-hand side.
Thus, add +8 on the left as well as the right-hand side.
4x - 8 + 8 = 36 + 8
4x = 44
x = 11
Hence "Marie did not add 8 on the right-hand side so by considering it the solution of the given equation will be 11".
For more about the equation,
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type the correct answer in the box. use numerals instead of words. what value of x makes this equation true? x/6 - 7 = -4
[tex]\dfrac{x}{6}-7=-4\\\dfrac{x}{6}=3\\x=18[/tex]
Answer:
x = 18
Step-by-step explanation:
x/6 - 7 = -4
Add 7 to each side
x/6 - 7+7 = -4+7
x/6 = 3
Multiply each side by 6
x/6 *6 = 3*6
x = 18
Line m and point P are shown below. Part A: Using a compass and straightedge, construct line n parallel to line m and passing through point P. Leave all construction marks. Part B: Explain the process that you used to construct line n.
Answer:
see the attached
Step-by-step explanation:
In the attachment, we will refer to the circles, bottom-to-top, as circles 1, 2 and 3. The black points of intersection, bottom-to-top, will be referred to by the letters A, B, C, D. The transversal line through the white point (W) and pink point (P) will be line q.
Step 1. Draw line q through point P so it intersects line m at some convenient point. Label that point W.
Step 2. Choose an arbitrary radius for your compass. Here, we have chosen it to be the length WB. It happens to be less than half the length of WP, but that is not a requirement.
Step 3. Draw an arc of the chosen radius centered at W and intersecting line q and line m. Label the intersection points A (on line m) and B (on line q). These intersection points are on circle 1.
Step 4. Draw an arc of the same radius centered at P. It should be a long enough arc that it would intersect the proposed line parallel to m. Label the intersection point on line q with label C. This intersection point is on circle 3.
Step 5. Adjust the compass width (radius) to the distance from A to B. This is the radius of circle 2.
Step 6. Draw an arc centered at C so that it intersects the arc of Step 4. This is circle 2, and you want it to intersect circle 3. Label that point of intersection D.
Step 7. Draw line PD parallel to m.
_____
The point of the construction is to create congruent alternate interior angles AWB and CPD, so that lines AW and PD are parallel.
10. In 2005 there were 9 million bicycles in Beijing, correct to the
nearest million.
The average distance travelled by each bicycle in one day was
6.5 km correct to one decimal place.
Work out the upper bound for the total distance travelled by all the
bicycles in one day,
Answer:
Total distance = 6,540,000 km
Step-by-step explanation:
Given
Number of bicycles = 9,000,000
Average Distance = 6.5 km (to 1 d.p)
Required
Calculate the upper bound of all bicycle distance
First, we need to determine the range of the distance traveled by each bicycle;
Since, the average distance is approximated, then the Range is:
[tex]Range = (6.45km\ to\ 6.54km)[/tex]
All number in this range approximate to 6.5km
Note that the upper bound of the range is 6.54km;
Hence, total distance is calculated as thus;
[tex]Total\ distance = Number\ of\ bicycle * upper\ bound[/tex]
[tex]Total\ distance = 1,000,000 * 6.54km[/tex]
[tex]Total distance = 6,540,000km[/tex]
Three-fourths of the voters supported the bond measure. If there were
8000 voters, how many supported the bond measure?
Answer:
6000
Step-by-step explanation:
Divide top and bottom by the common factor.
[tex]\dfrac{3 }{4} \times 8000 = 3 \times 2000[/tex]
Simplify
3 × 2000 = 6000
The perimeter of a rectangle is 62 cm. The diagonal and width of the rectangle are 25 cm and x cm respectively.
Form a quadratic equation in terms of x based on the situation.
Step 1:
62cm - (25*2)=12cm
62-25=37cm
Length for both sides 25
Width=37cm=x
The sum of 2 numbers is 250. One of them is greater than 150. Which of these is definitely true about the other number? a) It is equal to 100. b) It has to be less than 100. c) It has to be greater than 100. d) It has to be a number between 150 and 250. Please answer fast and do explain how you got the answer...
Answer:
b
Step-by-step explanation:
Answer:
d) it has to be greater than 150 and 250
Step-by-step explanation:
It says in the question it is greater than 150. So the number will be between 150 and 250.
Mark it as Brainliest pls
Hope it helps!!!
Given that ΔABC is a right triangle with the right angle at C, which of the following is true?
1. tan A = 1/(tan B)
2. tan A = sin B
3. cos A = 1/(cos B)
4. sin B = 1/(sin A)
Answer:
1. tan A = 1/(tan B)
Step-by-step explanation:
By definition,
tangent A = opposite / adjacent = a / b
and
tangent B = opposite / adjacent = b / a
Therefore tangent A = a/b = 1/tan(B)
Answer: Tan a=tan b
I belive
Step-by-step explanation:
Jack is building a square garden. Each side length measures 777 meters. Jack multiplies 7\times77×77, times, 7 to find the amount of space in his garden is equal to 494949 square meters. Which measurement does 494949 square meters represent?
Answer:
49 square meters represent area of the square garden
Step-by-step explanation:
Each side length=7 meters
He multiplied 7 × 7 times to find the amount of space
=49 square meters
Jack is trying to measure the area of his square garden
Area of the square garden = length^2
=Length × length
Recall,
Length=7 meters
Area of the square garden= 7 meters × 7 meters
=49 square meters
Convert the radian measure to degree measure. Use the value of π found on a calculator, and round answers to two decimal places. nine pi divided by twelve
Answer:
135°
Step-by-step explanation:
π in radian = 180°
∴ 9π in radians = 9 X 180° = 1620°
Then 9π/12 = 1620°/12 = 135°
The perpendicular distance of the point from x axis is 2 units and the perpendicular distance from y axis is 3 units.Write the co-ordinates of the if it lies in
Answer:
Step-by-step explanation:
Given that :
the perpendicular distance of the point from x axis = 2 units
the perpendicular distance from y axis is 3 units
The objective is to the write the coordinates of the points if it lies in
(i) | Quadrant (ii) || Quadrant (iii) ||| Quadrant (iv) |v Quadrant
The position of a point in a plane is conveniently specified by the distances fro two perpendicular lines.The lines are called the x-axis and y-axis and their [point of intersection is called the origin.
The perpendicular distance from the y-axis is called the x- coordinate or abscissa and the perpendicular distance from x-axis is called the y-coordinate or ordinate,The coordinate form an ordered pair with the abscissa written as first.
With that be said, So In the given question,
the perpendicular distance of the point from x axis = 2 units
y coordinate = ±2
the perpendicular distance from y axis is 3 units
x coordinate = ±3
The ordered pair of the coordinates = ( ±3, ±2)
Therefore;
in | quadrant ; we have (3,2) where x and y are both on the positive axis
in || quadrant ; we have (-3,2) x is on the negative axis and y is on the positive axis
In ||| quadrant ; we have (-3. -2) both x and y are on the negative axis
In |v quadrant ; we have ( 3, -2) x is on the positive axis and y is on the negative axis.
i need help with this question
Answer:
1000ml
Step-by-step explanation:
4 days she drank ½ of the bottle
so she drank ⅛ l of juice everyday
so
1000ml is the answer
3-2y-1+5x^2-7y+7+4x^2
Answer: Hi!
The only thing we can do to simplify the equation is combine like terms.
5x^2 + 4x^2 = 9x^2
-2y - 7y = -9y
3 - 1 + 7 = 9
Our equation now looks like this:
9x^2 - 9y + 9
We have nothing left to simplify, so we're done!
Hope this helps!
how many are 7 raised to 2 ???
Answer:
[tex]\huge \boxed{49}[/tex]
Step-by-step explanation:
7 raised to 2 means the base 7 is to the power of 2.
[tex]7^2[/tex]
7 is squared or multiplied by itself.
[tex]7^2 =7 \times 7=49[/tex]
Find the derivative of f(x) = -2x2 + 11x at x = 9.
Answer:
The value of the derivative at x = 9 is -25
Step-by-step explanation:
Here in this question, we are told to find the derivative of the given equation at the point where x = 9
What we need to do here is simply, differentiate f(x), then substitute that value x = 9 into the differentiated equation
In notation form, what we are to find is f’(9)
So;
f(x) = -2x^2 + 11x
f’(x) = -4x + 11
So therefore;
f’(9) = -4(9) + 11
f’(9) = -36 + 11
f’(9) = 11-36
f’(9) = -25
Ifx= 15t2 and y= 10t2, find dy by
dx
Answer:
2/3
Step-by-step explanation:
dy/dx equals derivative of y by x
dy/dx=20t/30t=2/3
Given [tex]f(x)=-x^{2} +6x-11[/tex], find [tex]f(x-3)[/tex]
Answer:
See below.
Step-by-step explanation:
[tex]f(x)=-x^2+6x-11\\f(x-3)=-(x-3)^2+6(x-3)-11\\f(x-3)=-(x^2-6x+9)+6x-18-11\\f(x-3)=-x^2+6x-9+6x-29\\f(x-3)=-x^2+12x-38[/tex]
Hello, a quick question which number is least to greatest 0.359, 0.35, 1
Answer:
0.35, 0.359, 1
Step-by-step explanation:
0.359 = 359 thousandths
0.35 = 0.350 = 350 thousandths
1 = 1.000 = 1000 thousandths
Since 350 < 359 < 1000, then from least to greatest you get
0.35, 0.359, 1
Please give me the correct answer
Answer:
Area= 452.23 ft²
Step-by-step explanation:
Angle at U = 180-48-20
Angle at U = 112°
UT/sin 112=46/sin 48
UT= 0.9272*46/0.7431
UT=57.4 ft
UV= sin 20*46/sin48
UV= 0.3420*46/0.7431
UV= 21.2 ft
S=( 21.2+57.4+46)/2
S=124.6/2
S= 62.3
Area= √((62.3)(62.3-21.2)(62.3-57.4)(62.3-46))
Area= √((62.3)(41.1)(4.9)(16.3))
Area= √204509.5311
Area= 452.23 ft²
PLEASE HELP!! Find the coordinates.
Answer:
Option (D)
Step-by-step explanation:
Coordinates of the points J, E and V are,
J → (-4, -5)
E → (-4, -3)
V → (-1, -1)
This triangle is translated by the rule [tex]T_{<2,4>}[/tex] given in the question.
Coordinates of the image will follow the rule,
(x, y) → [(x + 2), (y + 4)]
following this rule coordinates of the image triangle will be,
J(-4, 5) → J'(-2, -1)
E(-4, -3) → E'(-2, 1)
V(-1, -1) → V'(1, 3)
Therefore, points given in the option (D) will be the answer.
Graph the image of H(-8,5) after a reflection over the x-axis.
Answer ?
Answer: plot a point at (-8, -5)
The y coordinate flips from positive to negative, or vice versa, when we reflect over the horizontal x axis. The x coordinate stays the same.
The rule can be written as [tex](x,y) \to (x,-y)[/tex]
Rami goes running in Central Park every Sunday. He runs at a constant speed. He can run 6 3/5 miles in 1 2/3 hours.what is his speed In miles?
Answer:
3 24/25 MPH
Step-by-step explanation:
We know Rami runs 6 3/5 miles in 1 2/3 hrs --> Convert into an improper fraction
--> 6 3/5 = 33/5
--> 1 2/3 = 5/3
Speed = Distance divided by Time
Distance = 33/5
Time = 5/3
33/5 / 5/3 = 33/5 x 3/5
33/5 x 3/5 = 99/25
1/25 less than 4 = 3 24/25
Thus, our answer is 3 24/25 MPH
Hope this helps!
a zookeeper has both flamingos and alligators in his zoo there are 78 feet and 27 heads how many flamingos and aligators are there
Answer:
15 flamingos and 12 alligators
Step-by-step explanation:
Because there are 27 heads, that means there is a total of 27 flamingos and alligators. Flamingos have 2 feet and alligators have 4 feet.
1. Set up a system of equations
(x = number of flamingos, y = number of alligators)
1x + 1y = 27 heads
2x + 4y = 78 feet
2. Multiply to get the same coefficient
2(1x + 1y = 27) → 2x + 2y = 54
3. Subtract
2x + 2y = 54
- 2x + 4y = 78
0x + -2y = -24
4. Solve for y
-2y = -24
y = 12
5. Plug in y to solve for x
1x + 1(12) = 27
x + 12 = 27
x = 15
u and v are position vectors with terminal points at (-1, 5) and (2, 7), respectively. Find the terminal point of -2u + v.
==================================================
Work Shown
We'll be using these vector properties
Rule 1: (a,b) + (c,d) = (a+c, b+d)Rule 2: k*(a,b) = (k*a, k*b)To get the following
-2u + v = -2*(-1, 5) + (2,7)
-2u + v = (-2*(-1), -2*5) + (2,7) .... apply rule 2
-2u + v = (2, -10) + (2, 7)
-2u + v = (2+2, -10+7) .... use rule 1
-2u + v = (4, -3)
3. A doctor treated 2,000 patients over a period of time. If he worked for
5 hours a day and spent 15 minutes pach patient, how many days
did the doctor spend to treat all the patients?
Answer:
100 days
Step-by-step explanation:
the doctor works 5 hrs per day, which means 20 patients per day, in 100 days he will be able to treat 2000 patients
Given: -1/2x > 6. Choose the solution set. A {x | x R, x > -12} B{x | x R, x > -3} C{x | x R, x < -3}D {x | x R, x < -12}
Answer:
D
Step-by-step explanation:
-1/2x > 6 (you have to flip the sign when you multiply or divide by negative
x < -12
If it takes 2 whole cups of chocolate chips to make 100 cookies, how many cups of chocolate chips do you need to make 25 cookies?
Answer:
1/2 cup
Step-by-step explanation:
We can use ratios to solve
2 cups x cups
--------------- = ----------------
100 cookies 25 cookies
Using cross products
2 *25 = 100x
50 = 100x
Divide by 100
50/100 = x
1/2 = x
p^2/2+2/q^2)(p^2-2/q^2)
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Hi my lil bunny!
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[tex]( \frac{p^{2} }{2} + \frac{2}{2_{q} }) ( p^{2} - \frac{2}{2_{q}})[/tex]
[tex]= \frac{\frac{1}{2}p^{4}q^{4} + p^{2} q^{2} - 4 }{q^{4}}[/tex]
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Have a great day/night!
❀*May*❀
Answer:
ree
Step-by-step explanation:
For each of the following paralellogram calculate the unknown angles marked. x, y and z
Answer:
x = 50°, y = z = 40°
Step-by-step explanation:
x = 50° ( Alternate angle )
z = 180° - (110 + 30)° = 180° - 140° = 40° ( sum of angles in Δ )
y = z = 40° ( Alternate angles )
can u help me. where do u plot it. what is x and what is y
Answer:
Step-by-step explanation:
for the first equation x= -2 and y=-7
the second equation x=3 and y is 3 now just plot x and y from the same equation on the same line
Answer:
[tex]\huge\boxed{x = -4; y = 7}[/tex]
Step-by-step explanation:
By plotting the points, we see that both of the lines intersect at (-4, 7)
Which means (X,y) = (-4,7)
So,
x = -4
y = 7
See the attached file so that you can know how would it be graphed.
