Answer:
y = (1/4)x² - (5/4)x + 1
Step-by-step explanation:
The x-intercepts of the quadratic equation are simply it's roots.
Thus, we have;
(x + 1) = 0 and (x - 4) = 0
Now, formula for quadratic equation is;
y = ax² + bx + c
Where c is the y intercept.
At y-intercept: (0,1), we have;
At (-1,0), thus;
0 = a(1²) + b(1) + 1
a + b = -1 - - - (1)
At (4,0), thus;
0 = a(4²) + b(4) + 1
16a + 4b = -1
Divide both sides by 4 to get;
4a + b = -1/4 - - - (2)
From eq 1, b = -1 - a
Thus;
4a + (-1 - a) = -1/4
4a - 1 - a = -1/4
3a - 1 = -1/4
3a = 1 - 1/4
3a = 3/4
a = 1/4
b = -1 - 1/4
b = -5/4
Thus;
y = (1/4)x² - (5/4)x + 1
Help,anyone can help me do quetion,I will mark brainlest.
Answer:
c) 25 cm^2
d) 52.5 cm^2
Step-by-step explanation:
5*2 = 1
10/2 = 5
40/2 = 20
20+5 = 25
This is just scratch work^
please help asap!!!!
Answer:
Step-by-step explanation:
Given functions are,
f(x) = [tex]\sqrt{x} +3[/tex]
g(x) = 4 - [tex]\sqrt{x}[/tex]
22). (f - g)(x) = f(x) - g(x)
= [tex]\sqrt{x}+3-(4 - \sqrt{x} )[/tex]
= [tex]\sqrt{x} +3-4+\sqrt{x}[/tex]
= [tex]2\sqrt{x}-1[/tex]
Domain of the function will be [0, ∞).
23). (f . g)(x) = f(x) × g(x)
= [tex](\sqrt{x}+3)(4-\sqrt{x} )[/tex]
= [tex]4(\sqrt{x}+3)-\sqrt{x}(\sqrt{x}+3)[/tex]
= [tex]4\sqrt{x} +12-x-3\sqrt{x}[/tex]
= [tex]-x+\sqrt{x}+12[/tex]
Domain of the function will be [0, ∞).
Of the 144 animals in the pet store, 56 are cats. The rest are dogs. What fraction of the pets are dogs?
Answer:
11/18
Step-by-step explanation:
56/144 = cats.
144 - 56 = 88
88/144 are dogs.
Simplified: 11/18
Solve the inequality.
k + 4 – 2(k – 12) > 0
k > 28
k > –20
k < –20
k < 28
k<28
Step 1: Simplify both sides of the inequality.
−k+28>0
Step 2: Subtract 28 from both sides.
−k+28−28>0−28
−k>−28
Step 3: Divide both sides by -1.
−k /−1 > −28 /−1
k<28
Answer:
k < 28
Step-by-step explanation:
Given inequality :-
k + 4 - 2( k - 12 ) > 0 k + 4 - 2k + 24 > 0-k + 28 > 0 28 > k k < 28Last Option is correct .
What is the next step for this construction?
Connect points A' to C.
A. Connect points A’C
B. Draw another arc
C. Erase BC
D. Connect points C’ and B’
Can someone help me with this
Answer:
Step-by-step explanation:
-3 raised to the power 0=
Given:
The statement is "-3 raised to the power 0".
To find:
The value of the given expression.
Solution:
We know that [tex]a[/tex] raised to the power [tex]b[/tex] can be written as [tex]a^b[/tex].
Any non zero number raised to the power 0 is always 1. It means,
[tex]a^0=1[/tex], where [tex]a\neq 0[/tex].
-3 raised to the power 0 [tex]=(-3)^0[/tex]
[tex]=1[/tex]
Therefore, the value of the given statement is 1.
What is the next term in the sequence below?
24, 12, 6, 3, . . .
A. 0.5
B. 1.5
C. 1.75
D. 2.5
Answer:
1.5(B)
Step-by-step explanation:
This is a geometric sequence where each number is 1/2 times the last. So 3/2 is 1.5.
(g) (2 sin 60°)(3 kos 60°) + 3 tan 30°
Answer:
[tex](2 \ sin 60)(3\ cos 60) +3\ tan 30\ =\ \frac{5\sqrt3}{2}[/tex]
Step-by-step explanation:
[tex](2 \ sin 60)(3 \ cos 60) + 3\ tan 30\\\\= (2 \times \frac {\sqrt3}{2}) (3 \times \frac{1}{2})+ (3 \times \frac{1}{\sqrt3})\\\\=(\sqrt{3}\ \times \frac{3}{2})+ \frac{3}{\sqrt3}\\\\=\frac{3\sqrt3}{2}+\frac{3}{\sqrt3}\\\\=(\frac{3\sqrt3}{2} \times \frac{\sqrt3}{\sqrt3})+(\frac{3}{\sqrt3} \times \frac{2}{2})\\\\=\frac{3\times (\sqrt3)^2}{2\sqrt3}\ + \ \frac{6}{2 \sqrt3}\\\\=\frac{3 \times 3}{2 \sqrt3} +\frac{6}{2 \sqrt3}\\\\=\frac{9+6}{2\sqrt3}\\\\=\frac{15}{2\sqrt3} \times \frac{\sqrt3}{\sqrt3}\\\\[/tex]
[tex]=\frac{15 \sqrt3}{2 \times (\sqrt{3})^2}\\\\=\frac{15 \sqrt 3}{2 \times 3}\\\\=\frac{5\sqrt3}{2}[/tex]
What is the scale factor from ABC to DEF?
Answer:
0 so D
Step-by-step explanation:
The shape didnt change at all. All the sides are 5 for both triangles.
so I have 40 dollars and i am buying 10$ gift card so how many 10$ gifts cards can I buy?
Answer:
4 gift card
Step-by-step explanation:
40 dollar /gift card price 10
=4
Answer:
4 dollar gift card
Step-by-step explanation:
40÷10=4
4 dollar gift card
Write the equation of the line parallel to 4y - x = -20 that passes through the point (8,3).
Answer:
y= ¼x +1
Step-by-step explanation:
Rewriting the equation into the slope-intercept form (y= mx +c, where m is the gradient and c is the y- intercept):
4y -x= -20
4y= x -20 (+x on both sides)
y= ¼x -5 (÷4 throughout)
Thus, slope of given line is ¼.
Parallel lines have the same gradient.
Gradient of line= ¼
y= ¼x +c
To find the value of c, substitute a pair of coordinates into the equation.
When x= 8, y= 3,
3= ¼(8) +c
3= 2 +c
c= 3 -2
c= 1
Hence the equation of the line is y= ¼x +1.
The elevation of a city is 2633 feet above sea level.
Write a signed number to represent this elevation
Answer:
+2633 ft
Step-by-step explanation:
The city is above sea level meaning it is a positive number.
Solve the quadratic equation by factoring. Show your work and explain the steps you used to solve. 6x2 + 11x + 3 = 0
Answer:
6 x 2 = 8 + 11 = 19 x 3 = 57
Step-by-step explanation:
A girl cycled a total of 15 kilometers by making 5 trips to work. How many trips will she have to make to cover a total of 24 kilometers
Answer:
8 trips
Step-by-step explanation:
You can solve this by unitary method.
15 kilometers in 5 trips means 1 trip consist of 3 kilometers
Therefore, 24/3 = 8
So the required answer is 8 trips.
Thank you!!
Type the correct answer in the box.
The formula for the volume, V, of a cone having the radius, r, and the height, h, is shown below.
V = 3721
Write the formula to calculate the height, h.
Answer:
V=1/3(pi)*r^2*h
Step-by-step explanation:
Think about a cylinder. If you combine 3 cones, you get a cylinder. Find the volume of a cylinder
Answer:
Step-by-step explanation:
V = 1/3 r^2 * π * h
3V = r^2 *π * h
3V/π = r^2 * h
h = 3V/(r^2 * π)
What is the value of x?
Enter your answer in the box.
Answer:
solution
Step-by-step explanation:
ADC = Sum of triangle
AD+ AC = 2.25+3 =5.25
Step 2:
BCD = Sum of acute angled triangle = a+b+
c
BCD= 2.25+4+3
BCD = 9.25
The value of x =ADC+BCD
= 5.25+ 9.25
= 14.5
in need help
Relationships in Triangles
Answer: x = 17
Step-by-step explanation: Since ray SQ bisects <TSR, we know
that the m<TSQ ≅ m<QSR by the definition of an angle bisector.
So we can setup the equation (3x - 9) + (3x - 9) = 84
using the angle addition postulate.
Simplifying on the left gives us 6x - 18 = 84.
Now add 18 to both sides to get 6x = 102.
Now divide both sides by 6 so x = 17.
Which equation is a radical equation? 4p =√-3 + p x√3 + x =^3√2x 7√11– w = –34 5 – ^3√8= v√16
Answer:
See explanation
Step-by-step explanation:
The given options are not properly formatted; so, I will give a general explanation instead
An equation is said to be radical if its variable is in a radicand sign.
For instance, the following equation is a radical;
[tex]\sqrt x + 2 = 4[/tex]
In the above equation, x is the variable, and it is in [tex]\sqrt[/tex] sign
However, the following equation is not a radical equation
[tex]x + \sqrt 4 = 2[/tex]
Because the variable is not in a radicand
If trstan has a pickup truck that could carry 7/4 cord of firewood, FInd the number trips needed to cary 63 cords of wood
Answer:
36
Step-by-step explanation:
63/(7/4) 63 divided by 7/4
63* 4/7 63 multiplied by 4/7
=36 answer is 36
The function f(t) = 4t2 − 8t + 7 shows the height from the ground f(t), in meters, of a roller coaster car at different times t. Write f(t) in the vertex form a(x − h)2 + k, where a, h, and k are integers, and interpret the vertex of f(t).
Answer:
Vertex form is f(t) = 4 [tex](t-1)^{2}[/tex] +3 and vertex is (1, 3).
Step-by-step explanation:
It is given that f(t)= 4 [tex]t^{2}[/tex] -8 t+7
Let's use completing square method to rewrite it in vertex form.
Subtract both sides 7
f(t)-7 = 4 [tex]t^{2}[/tex] -8t
Factor the 4 on the right side.
f(t) -7 = 4( [tex]t^{2}[/tex] - 2 t)
Now, let's find the third term using formula [tex](\frac{b}{2} )^{2}[/tex]
Where 'b' is coefficient of 't' term here.
So, b=-2
Find third term using the formula,
[tex](\frac{-2}{2} )^{2}[/tex] which is equal to 1.
So, add 1 within the parentheses. It is same as adding 4 because we have '4' outside the ( ). So, add 4 on the left side of the equation.
So, we get
f(t) -7 +4 = 4( [tex]t^{2}[/tex] -2 t +1)
We can factor the right side as,
f(t) -3 = 4 [tex](t-1)^{2}[/tex]
Add both sides 3.
f(t) = 4[tex](t-1)^{2}[/tex] +3
This is the vertex form.
So, vertex is (1, 3)
Which equation does the graph above represent?
A. y = 2x
B. y = 1/2x
C. y = 1/2
D. y = 2 + x
Answer:
y=2x
Step-by-step explanation:
Hi there!
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when x is 0).
1) Determine the slope (m)
The slope is the rate of change, or the number of units the line moves up divided by the number of units the line moves to the right.
Looking at the graph, we can see that for every 1 space the line travels to the right, the line travels 2 spaces up. This makes the slope of the line 2. Plug this into [tex]y=mx+b[/tex]:
[tex]y=2x+b[/tex]
2) Determine the y-intercept (b)
When x=0 on the graph, y=0. Therefore, the y-intercept is 0. Plug this into [tex]y=2x+b[/tex]:
[tex]y=2x+0\\y=2x[/tex]
I hope this helps!
If a = ba and b = 2a, what is the value of a + b?
a = ba
1 = b
Since b = 1,
b = 2a
1 = 2a
a = 0.5
Therefore,
a + b = 0.5 + 1
a + b = 1.5
An acute angles measure is
A. Between 0 and 90
B. Between 90 and 180
C. Exactly 90
Answer: the correct answer is A. Between 0 and 90
If an angle is between 0 and 90 it is acute
If an angle is EXACTLY 90 it is a right angle
If an angle is between 90 and 180 it is obtuse angle
If it's 360 then it is a full circle
5 plus 6 times 8 plus 9 times 10 plus 8 plus 4 plus 2 plus 9 plus 8 plus 7 plus 5 plus 7 plus 6 times 7 times 9 times 8 times 5 times 4 times 3 times 2 times 1 times 6 times 8 times 9 times 12 times 17 times 19 times 20 times 12 times 11 times 13 times 14 times 15 times 16
i dont know
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Simplify the expression below.
50 - 2(32 + 1)
Answer:
[tex] = { \tt{50 - 2(32 + 1)}}[/tex]
Solve the bracket:
[tex] = { \tt{50 - 2(33)}}[/tex]
Open the bracket:
[tex]{ \tt{ = 50 - 66}}[/tex]
Subtract the expression:
[tex]{ \bf{ = - 16}}[/tex]
Step-by-step explanation:
Multiply 2 by 32 and 1
50-64-2
-14-2
-16 Answer
plzz help me out i really need help
A rectangular floor of area 360 m2 is going to be tiled. Each tile is rectangular, and has an area of 240 cm2. An exact number of tiles can be put into the space. How many tiles will be needed??
Answer:
1500
Step-by-step explanation:
The area of the regtangular floor is 360m². The floor is going to be retired with tiles having area of 240cm² . We need to find the number of times . Therefore ,
[tex]\implies 360m^2 = 360 \times 10^4 \ cm^2 [/tex]
And , the number of tiles required will be ,
[tex]\implies n =\dfrac{Area \ of \ floor}{Area \ of \ a \ tile }\\\\\implies n =\dfrac{ 360 \times 10^4 \ cm^2}{240 cm^2} \\\\\implies \underline{\underline{ n = 1,500 }}[/tex]
Hence the required answer is 1500 .
Answer:
[tex] \displaystyle\rm 15000[/tex]
Step-by-step explanation:
we given the area of rectangular floor and tile we want to find the number of tiles needed to tile the floor
notice that the area of the rectangular floor is in meter and the tile in cm so we need to convert cm to meter in order to figure out the number of tiles needed to tile the floor
therefore,
[tex] \rm 1m \implies 100 c m\\ \rm{1m}^{2} \implies10000 {cm}^{2} [/tex]
remember that,
[tex] \displaystyle\rm \: N _{ \rm tile} = \frac{A _{ \rm floor} }{A _{ \rm tile} } [/tex]
Thus substitute:
[tex] \displaystyle\rm \: N _{ \rm tile} = \frac{360 \times 10000 {cm}^{2} }{ {240cm}^{2} } [/tex]
simplify which yields:
[tex] \displaystyle\rm \: N _{ \rm tile} = 15000[/tex]
hence,
15000 of tiles needed to tile the floor
Is (18,-4) a solution to the equation y = -6x - -87? yes no
Replace x with 18, solve the equation. If it equals -4 it’s a solution.
Y = -6(18) - -87
Y = -108 + 87
Y = -21
-21 does not equal -4 so (18,-4) is not a solution.
PLZ help fast thank you
Answer:
Step-by-step explanation:
An isosceles triangle is one that has 2 sides that are the same length, like ours here. Because of the Isosceles Triangle Theorem, if 2 side lengths are congruent, then the angles opposite those sides are congruent, as well. That means that both base angles are 53 degrees. However, we are looking for the altitude, or height, of the triangle. That changes everything. Drawing in the height serves to cut the triangle in half, splitting both the vertex angle (the angle at the top of the triangle) and the base exactly in half. Now we have 2 right triangles which are mirror images of each other. We only need concentrate on one of these triangles. What the triangle looks like now:
One base angle is 90 degrees and the other is 53 degrees. By the Triangle Angle-Sum Theorem, the third angle has to be a degree measure which ensures that all the angles add up to 180. Therefore, the third angle measures 180 - 90 - 53 = 37. Even still, besides knowing all the angle measures, we really don't need any besides the 53 degree one.
As far as side lengths go, the base is 12 (because the height cut it in half). To find a missing side in a right triangle you either use Pythagorean's Theorem or right triangle trig, depending upon the info you're given. We only have enough to use right triangle trig.
We have the base angle of 53, which is our reference angle, the side next to, or adjacent to, the reference angle, and we are looking for the side length opposite the reference angle. This is the tan ratio where
[tex]tan\theta=\frac{opp}{adj}[/tex] where tangent of the reference angle is equal to the side opposite the reference angle over the side adjacent to the reference angle. Filling in that ratio:
[tex]tan53=\frac{opp}{12}[/tex] and multiply both sides by 12 to get
12tan53 = opp and do this on your calculator to get that
opp = 15.9 inches