If you complete the square in the quadratic equation , you get the quadratic formula for the solutions x _______.
Answers
Answer:
[tex]D. \ \ x=\frac{-b\pm \sqrt{b^{2}-4ac} }{2a}[/tex]
Step-by-step explanation:
ax² + bx + c = 0
[tex]a\left( x^{2}+\frac{b}{a} x+\frac{c}{a} \right) =0[/tex]
[tex]a\left( \left( x+\frac{b}{2a} \right)^{2} -\frac{b^{2}}{4a^2}+\frac{c}{a} \right) =0[/tex]
[tex]a\left( \left( x+\frac{b}{2a} \right)^{2} -\frac{b^{2}-4ac}{4a^2}\right) =0[/tex]
[tex]a\left( x+\frac{b}{2a} \right)^{2} -\frac{b^{2}-4ac}{4a}=0[/tex]
[tex]a\left( x+\frac{b}{2a} \right)^{2} =\frac{b^{2}-4ac}{4a}[/tex]
[tex]\left( x+\frac{b}{2a} \right)^{2} =\frac{b^{2}-4ac}{4a^2}[/tex]
[tex]x+\frac{b}{2a} =\frac{\pm \sqrt{b^{2}-4ac} }{2a}[/tex]
[tex]x=\frac{-b\pm \sqrt{b^{2}-4ac} }{2a}[/tex]
Related Questions
What would the graph of f(x)=2arcsin (x-4)+1, look like?
Answers
The graph of the given function f(x)=2arcsin (x-4)+1, looks like the curve.
We have given that the function
f(x)=2 arcsin (x-4)+1,
We have to determine the graph of f(x)
Therefore we gave
Graph
Graph the trigonometric function using the amplitude, period, phase shift, and vertical shift.
What are the coordinates of the graph?
An ordered pair (x, y) represents a position of a point on a coordinate graph, where x is the number on the x-axis that the point lines up with and y is the number on the y-axis that the point lines up with.
The numbers x and y in the ordered pair (x, y) are called coordinates.
We find the coordinate of the given graphs and draw a graph of the given function.
x f(x)
3 −π−1
7/2 −π/3−1
4 −1
9 2π/3−1
5 π−1
Therefore the graph of the given function is
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Which one of these is not a step used when constructing an inscribed equilateral triangle using technology?
A. Create a circle using the center with given point tool.
B. Connect the point with a line through the center of the circle.
C. Create another circle with the same radius as the original.
D. Connect the two circles together using the compass tool.
Answers
explanation
Answer:
The answer is D
Step-by-step explanation:
Draw the point at which your circle will be centered.
Use a compass to draw a perfect circle centered at point O.
Use a ruler to draw a vertical line straight through point O.
Draw the points at which the line intersects the circle.
Draw a second circle. This circle will be centered at Point W and the radius will extend to Point O.
Mark both places where the two circles intersect. Label the point on the left "Point Y" and the point on the right "Point Z".
Connect points X, Y, and Z using a ruler or straight edge.
Helpppp
Which choices are equivalent to the expression below (see the picture please)
Answers
Answer:
A or B ( if it is multiple choice as B is the answer to A)
Answer:
C and E
Step-by-step explanation:
C and E are both equal to (2^3)^4
Find the sine of ZD.
F
2√15
D
2-√15
E
Answers
Answer:
[tex]{ \underline{ \underline{ \mathfrak{ \: answer : \: \: { \tt{ \sin(D) = \frac{ \sqrt{2} }{2} \: \: }} }}}}[/tex]
Step-by-step explanation:
[tex]{ \rm{ \sin( \theta) = \frac{opposite}{hypotenuse} }} \\ [/tex]
Theta is Dopposite is 2sqrt(15)hypotenuse is h[tex]{ \tt{h = \sqrt{ {(opposite)}^{2} + {(adjacent)}^{2} } }} \\ { \tt{h = \sqrt{ 2{(2 \sqrt{15}) }^{2} } }} \\ { \tt{h = \sqrt{2(4 \times 15)} }} \\ { \tt{h = \sqrt{120} }}[/tex]
Therefore:
[tex]{ \tt{ \sin(D) = \frac{2 \sqrt{15} }{ \sqrt{120} } }} \\ \\ { \tt{ \sin(D) = \frac{2 \sqrt{15} }{2 \sqrt{15 \times 2} } }} \\ \\ { \tt{ \sin(D) = \frac{1}{ \sqrt{2} } }} \\ \\ { \boxed{ \tt{ \sin(D) = \frac{ \sqrt{2} }{2} }}}[/tex]
look at the image and please tell me if I was correct
Answers
Answer:
yes
Step-by-step explanation:
you seem to be correct
When the net is folded up, which sides will touch?
Answers
Explanation:
We can think of the square in the middle of the four others as the floor
The surrounding four squares are the walls that fold upward.
The square at the very right side will then form the ceiling.
Side E and side L join at the top left edge.
See the diagram below.
A machine produces 225 bolts in 24 minutes. At the same rate, how many bolts would be produced in 40 minutes?
Answers
Answer: 375 bolts
Step-by-step explanation:
Just do 225*(40/24)
Given ,
225 bolts in 24 minutes
So in a minute it can produce = 225/24 = 9.3 = 9 bolts
In 40 minutes it can produce = 9 x 40 = 360 bolts
Need help with problem
Answers
Answer:
17Step-by-step explanation:
SINCE THE LINES ARE PARALLEL THEN ANGLE A AND ANGLE B ARE COREESPONDING TO EACH OTHER.A = 7x + 24 B= 3x+ 92A=B7x + 24 = 3x + 927x - 3x = 92 - 24
4x = 68
x = 68 / 4
x =17
Answer:
143
Step-by-step explanation:
These are corresponding angles meaning they are congruent. So we just have to set them equal to each other and solve for x. Then plug in x.
7x + 24 = 3x + 92
subtract 3x from both sides
4x + 24 = 92
subtract 24 from both sides
4x = 68
divide both sides by 4
x = 17
Now plug in x to angle A, which is 7(17) + 24
119 + 24
then add
you get:
143
A surveyor needs to determine the distance between two points that lie on opposite banks of a river. Two points, A and C, along one bank are 250 yards apart. The point B is on the opposite bank. Angle A is 64º and angle C is 51°. Find the distance between A and B to the nearest tenth of a yard. • Write your answer as a number only. • Round answer to one decimal place.
Answers
Answer:
does anyone know
Step-by-step explanation:
That is hard
WILL GIVE BRAINLIEST 50 POINTS
Answers
These same things are present
∆PQR=∆TUVSo
PQ=TU=12<R=<V=75<Q=180-(45+75)=60°=<UUV=QR=10TV=PR=7m<T=m<P=45Answer:
[tex]\sf \overline{PQ}=12[/tex]
[tex]\sf \overline{UV}=10[/tex]
[tex]\sf \overline{TV}=7[/tex]
[tex]\sf m \angle T=45^{\circ}[/tex]
[tex]\sf m \angle R=75^{\circ}[/tex]
[tex]\sf m \angle Q=60^{\circ}[/tex]
[tex]\sf m \angle U=60^{\circ}[/tex]
Step-by-step explanation:
≅ sign means that the triangles are congruent, which means they both have the same shape and the same size.
When comparing congruent shapes, inspect the order in which the vertices are given in the statement.
Therefore, if ΔPQR ≅ ΔTUV then:
[tex]\sf \overline{PQ} \cong \overline{TU}[/tex][tex]\sf \overline{QR} \cong \overline{UV}[/tex][tex]\sf \overline{PR} \cong \overline{TV}[/tex]Similarly:
[tex]\sf m \angle P \cong m \angle T[/tex][tex]\sf m \angle Q \cong m \angle U[/tex][tex]\sf m \angle R \cong m \angle V[/tex]Therefore, from inspection of the triangles:
[tex]\sf \overline{PQ} \cong \overline{TU}=12[/tex]
[tex]\sf \overline{UV} \cong \overline{QR}=10[/tex]
[tex]\sf \overline{TV} \cong \overline{PR}=7[/tex]
[tex]\sf m \angle T \cong m \angle P=45^{\circ}[/tex]
[tex]\sf m \angle R \cong m \angle V = 75^{\circ}[/tex]
The sum of the interior angles of a triangle is 180°, therefore:
[tex]\sf m \angle Q \cong m \angle U=180^{\circ}-45^{\circ}-75^{\circ}=60^{\circ}[/tex]
6. The three sides of a triangle are in the ratio 2 : 3 : 4 and the perimeter
225 m. Find its area.
Answers
Add up all the parts in the ratio:
2 + 3 + 4 = 9
Second step:
Do 225 divided by 9, this helps you get the value of each part:
225 divided by 9 = 25
Third step:
Find the value of each ratio sector, this is done by doing:
2 times 25 = 50
3 time 25 = 75
4 times 25 = 100
Last step:
Area:
75 times 50 = 3750
Final answer is 3750.
Hope this helps!
Please give Brainliest!
Find the area of the figure.
Answers
Answer:
Area = 38 ft^2
Step-by-step explanation:
Divide two parts of a rectangle.
Big Rect: A = 10 ft * 3 ft = 30 ft^2
Small Rect: A = 2 ft * 4 ft =8 ft^2
Total Area = 30 + 8 = 38 ft^2
Find the area of the figure. Round to the nearest hundredth where necessary.
22 ft
30 ft
Answers
[tex]\bold{ANSWER:}[/tex]
215.20 ft^2
[tex]\bold{SOLUTION:}[/tex]
Which expression product is modeled by the tiles(2x+1)(x+1)
Answers
[tex](2x + 1)(x + 1)[/tex]
•Distribute
[tex](2x + 1)(x + )[/tex]
[tex]2x(x + 1) + 1( x + 1)[/tex]
•Distribute
[tex]2x(x + 1) + 1(x + 1)[/tex]
[tex]2x² + 2x1(x + 1)[/tex]
•Multiply
[tex]2x² + 2x + 1(x + 1)[/tex]
[tex]2x² + 2x + x + 1[/tex]
•Combine like terms
[tex]2x² + x + x + 1[/tex]
[tex]2x²+ 3x + 1[/tex]
Solution:
[tex]2x² + 3x + 1[/tex]
Explanation:
see the graph
Brainly for the one who help me
Answers
Answer:
prior to
Step-by-step explanation:
PLS HELP ME ANSWER THIS! 25 POINTS! How much does Janet make in 16 hours?
Answers
Answer: 120
Step-by-step explanation:
Janet makes 60 in 8 hours
60 x 2
8 x 2
so the answer is 120
Draw lines to match equivalent time intervals.
day
5 days
6 days
120 hours
13 weeks
144 hours
-12
10 days
720 minutes
91 days
240 hours
Answers
Answer:
120h = 5 days
240h = 10 days
144h = 6 days
720m = 1/2 (half a day)
13w = 91 days
please make this brainliest
PLS URGENT! WILL GIVE BRAINLIEST!!!!
A certain company's main source of income is a mobile app. The function h models the company's annual profit (in millions of dollars) as a function of the price they charge for the app (in dollars).
Which of these statements are true?
(A) Greater app price always relates to greater profit.
(B) Greater app price relates to greater profit as long as the app's price is more than about 7 dollars.
(C) The largest possible profit the company can make is 7 million dollars.
(D) The largest possible profit the company can make is about 40 million dollars.
Thank you! God Bless!
Answers
Answer:
(C) The largest possible profit the company can make is 7 million dollars
Step-by-step explanation:
Proverbs 3:5-6
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Trust in the Lord with all your heart
and lean not on your own understanding;
in all your ways submit to him,
and he will make your paths straight.
_________________________________________________________
Have a blessed day!!
:)
Which set of transtormations results in two polygons that are similar but not congruent?
Answers
Reason; Dilation changes the figure size to bigger or smaller so it is not congruent.
Translation, rotation and reflection transformations are congruent
What is a good estimate and the actual measurement for this angle measurement?
A. 110 and 109
B. 95 and 96
C. 90 and 91
D. 70 and 71
Answers
Reason
Using theory that all angles combined will equal 360
Using theory of alternate interior angles, using 110 means alternate interior will be 110. To complete the angle the other side is 70 for the 180 degree angle.
Doing the same thing on the other side using 109 and 71 = 180
The picture might help
Jerry boards a Ferris wheel from the bottom of the wheel (the 6 o'clock position) and the Ferris wheel rotates counterclockwise. The center of the wheel is 30 feet from the ground and the radius if the wheel is 25 feet.
Using a sine function, describe a function g that represents the height above the ground (in feet) in terms of the time since the Ferris wheel began rotating if the Ferris wheel rotates at a speed of 2 radians per second.
O9(0)-25 cos(+)+30
Og(t)- 25 sin(2t - )+30
Og(t)- 25 sin(+)+30
Og(t)- 25 cos (2+)+30
Answers
function g that represents the height above the ground (in feet) in terms of the time since the Ferris wheel began rotating if the Ferris wheel rotates at a speed of 2 radians per second is g(t) = 25cos(2t) feet+30
What is angle?An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.
The height g(t) above the center after t minutes is given by
g(t) = 25cos(r(t))
g(t) = 25cos(2t) feet+30
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for a Saturday matinee, adult tickets cost $5.50 and kids under 12 pay only $4.00. If 70 tickets are sold for a total of $355, how many of the tickets were adult tickets and how many were sold to kids under 12?
Answers
Y be tickets for kids under 12, then
5.5x + 4 y = 355 ,
x+y = 70=>(y = 70-x)
5.5x + 280-4x=355
1.5x=75
X=50
Y=20
NO LINKS!!! For each below, tell whether the table represents a linear, exponential, inverse or no relationship. Write an equation for each table (if possible).
Answers
[tex]\large \boxed{\sf y = (x - 2)^2 - 4}[/tex]
[tex]\large \boxed{\sf Quadratic \ Function}[/tex]
Explanation:A linear function shall increase linearly. Here due to mass differences between points, it is visible that it is not a linear function.
There is a better way to understand what type of equation it is after plotting the coordinates on the graph.
Look at the attachment!After looking so, we can determine this as quadratic function.
** Not a exponential, inverse, linear function **
To find equation:Quadratic function: y = a(x - h)² + k
Locate (h, k) = (2, -4)
Take any other suitable point for example = (0, 0)
Insert values to find (a),
a(0 - 2)² - 4 = 0
4a = 4
a = 1
Now Join together: y = 1(x - 2)² - 4 --- Quadratic Equation
Exponential
It should be a parabola
The best shortcut trick is the fact about the parabola is that parabola is symmetric and axis of symmetry goes through vertex
So on both sides of vertex i e same distance on x from vertex the two x values have same y value .
Observe the table and find similar y values
(0,0) and (4,0)(1,-3) and (3,-3)FIND midpoint of x which is axis of symmetry
0+4/2=21+3/2=2We have been sured axis of symmetry is at x=2
Vertex (2,-4)Form equation
y=a(x-h)²+ky=a(x-2)²-4Put (5,5)
5=a(5-2)²-45=a(3²)-49a-4=59a=9a=9Final equation
y=(x-2)²-4find the lateral area of the cone. radius 32 height 25
Answers
Answer:
200201+1918191=9191919289+Step-by-step explanation:
tnksa=-2(negative 2) b=3 and c=5 what is 3ac-a+2b.With explanation
Answers
Step-by-step explanation:
a = -2
b = 3
c = 5
Question:[tex]3ac - a + 2b[/tex]
= Solution,
= 3 ( - 2 ) × 5 - ( - 2 ) + 2 × 3
here ... ( + ) × ( - ) = ( - )
= - 6 × 5 - ( - 2 ) + 2 × 3
here .... ( - ) × ( - ) = ( + )
= - 6 × 5 + 2 + 2 × 3
= - 30 + 2 + 6
= - 30 + 8
here the ( - ) have greater variable so...
= - 22
hence - 22 is the answer . ....
Help me please thank youuuuu ^_^
Answers
Answer:
x = 6
Step-by-step explanation:
2x - 3 = 9
so 9+3 = 12, and 12÷2 = 6
the value of x is 6
H
This diagram shows a semicircle with diameter MP
M
What is the approximate area of the shaded part?
OA. 33.8 cm²
OB. 235.3 cm²
O C. 102.7 cm²
OD. 36.3 cm²
O
Type here to search
F
12 cm
13 cm
✔
5 cm
O
<
MTWTR
^
(8
Answers
Answer:
D 36.6
Step-by-step explanation:
Here, there is a triangle inscribed inside of a semicircle where the triangle is unshaded and the remained of the semicircle is shaded and we want to find the area of that shaded untouched area of the semicircle.
To do so we must find the area of the two shapes individually and then subtract the area of the triangle from the area of the semi circle as the triangle is what is uncovering the semicircle.
Finding the area of the semicircle
Area of a semicircle = (πr²)/2 where r = radius
Here we are given the diameter of the semicircle which is 13cm. We can easily convert the diameter to radius by dividing it by 2 as the radius is equal to half the diameter
Radius = 1/2 diameter , so radius = 13 / 2 = 6.5cm
We have A = πr²/2
==> plug in radius or r = 6.5
A = π(6.5)²/2
==> simplify exponent
A = π(42.25)/2
==> multiply π and 42.25 ( note that π = 3.14 approximately
A = 132.665/2
==> divide 132.665 by 2
A = 66.366
So the area of the semicircle is 66.366cm²
Finding the area of the triangle
The area of a triangle can be calculated by dividing the product of the base length and height ( formula = bh / 2 where b = base length and h = height )
Here the base length appears to be 5cm and the height appears to be 12cm so b = 5 and h = 12
So we have A = bh/2
==> plug in b = 5 and h = 12
A = (12)(5)/2
==> multiply 12 and 5
A = 60 / 2
==> divide 60 by 2
A = 30
So the area of the triangle is 30cm²
Subtracting the area of the triangle from the area of the semicircle
Finally to find the area of the shaded region we subtract the area of the triangle from the area of the semicircle
We have area of triangle = 30cm² and area of semicircle = 66.366
So area of shaded region = 66.366 - 30 = 36.366
D , 36.6 is closest to our answer therefore the answer is D
Find the factor of each ff.
8t²-16t-4
Answers
Answer:
For me, this quadratic expression can simply be factored by 4 because all the values divide by four. so:
[tex]4( {2}t^{2} - 4t - 1)[/tex]
Step-by-step explanation:
Just factor it by 4
Answer:
4(2t^2 - 4t - 1)
Step-by-step explanation:
8t²-16t-4
= 4(2t^2 - 4t - 1)
2t^2 - 4t - 1 is prime so there are no more factors.
Suppose you have a photograph that
has a height of 8 in and a width of 5
in. If you want to enlarge the
photograph so that it has a height of
32 in, how wide will it need to be?
Answers
Answer:
20
Step-by-step explanation:
You need to times 8*4 to get 32 therefore u times 5*4 to get 20
NEED HELP WITH SLOPE
Answers
take two points
(2,4)(-3,-3)Slope
m=y2-y1/x2-x1m=-3-4/-3-2m=-7/-5m=7/5Answer:
[tex]m=\dfrac{7}{5}[/tex]
Step-by-step explanation:
To find the slope of a line, find two points on the line and define them as follows:
[tex]\textsf{let}\:(x_1,y_1)=(-3,-3)[/tex]
[tex]\textsf{let}\:(x_2,y_2)=(2,4)[/tex]
Substitute the points in the slope formula and solve for m:
[tex]\begin{aligned}\textsf{slope}\:(m) & =\dfrac{y_2-y_1}{x_2-x_1}\\\\ & =\dfrac{4-(-3)}{2-(-3)}\\\\ & = \dfrac{4+3}{2+3}\\\\ & = \dfrac{7}{5}\end{aligned}[/tex]
Therefore, the slope of the given line is [tex]\dfrac{7}{5}[/tex]