The x and y intercepts of a line are when [tex]y=0[/tex] and [tex]x=0[/tex] respectively.
c and d are the x and y intercepts because they represent C/A and B/A in the standard linear equationThe x and the y intercepts are related to c and d because they represent the values of the equation when y and x equals 0 respectively.The given equation is:
[tex]\frac xc + \frac yd = 1[/tex]
(1) Why c and d are the intercepts
We have:
[tex]\frac xc + \frac yd = 1[/tex]
Multiply through by cd
[tex]cd \times \frac xc + cd \times \frac yd = cd \times1[/tex]
[tex]dx + cy = cd[/tex]
A linear equation is represented as:
[tex]Ax + By = C[/tex]
Where:
[tex]\frac CA \to[/tex] x intercept
[tex]\frac BA \to[/tex] y intercept
So, by comparing [tex]Ax + By = C[/tex] to [tex]dx + cy = cd[/tex]
[tex]\frac CA \to d \to[/tex] The x-intercept
[tex]\frac CB \to c \to[/tex] The y-intercept
(b) How the intercepts are related to c and d?
In (a) above, we have:
[tex]\frac CA \to d \to[/tex] The x-intercept
[tex]\frac CB \to c \to[/tex] The y-intercept
When [tex]x = 0[/tex]
We have:
[tex]dx + cy = cd[/tex]
[tex]d \times 0 + cy = cd[/tex]
[tex]cy = cd[/tex]
Divide by c
[tex]y = d[/tex] ---- the y-intercept
When [tex]y = 0[/tex]
We have:
[tex]dx + cy = cd[/tex]
[tex]dx + c \times 0 = cd[/tex]
[tex]dx = cd[/tex]
Divide by d
[tex]x =d[/tex] ---- the x-intercept
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48-15÷{3×(-2-4+11)}+12
Answer:
35
Step-by-step explanation:
48-15÷(3×5)+12
48-15÷15+12
48-1+12
59
calculate the area of the given quadrilaterals.
Answer:
dissect the trapezium into a square and triangle. since the triangle is a right angled one the base is 17-7=10cm
the height is found using Pythagorean theorem to be 24cm i.e 26²=x²+10²,x=√(676-100),x=√576,x=24cn
area of trapezium is (1/2)(a+b)h
a is the shorter side and b the longer side
(1/2)*(7+17)24
=288cm²
A rectangular field 50m wide and xm long, requires 260m of fencing. find x.
Answer:
80
Step-by-step explanation:
use formula for perimeter of rectangle but put X in place of length 50 m as breadth. so,
2(50+X)= 260
solve this and you will get X= 80
Answer:
80
Step-by-step explanation:
Perimeter area = 2(l × w)
Plug in:
2(x + 50) = 260
2x + 100 = 260
-100 -100
---------------------
2x = 160
---- -----
2 2
x = 80
So, x will be 80
What are the amplitude, period, phase shift, and midline of f(x) = 7 cos(2x + π) − 3? (6 points) Amplitude = −3; period: π; phase shift: x = negative pi over 2 ; midline: y = 3 Amplitude: 7; period: π; phase shift: x = negative pi over 2 ; midline: y = −3 Amplitude: 7; period: 2π; phase shift: x = pi over 2 ; midline: y = 3 Amplitude: −3; period: 2π; phase shift: x = pi over 2 ; midline: y = −3
Answer:
So the amplitude is 7
The period is pi
The phase shift is negative pi/2
The midline is -3
Step-by-step explanation:
A trigonometric function is the same as
[tex]f(x) = a \cos(b(x + c)) - d[/tex]
Where a is the amplitude, 2 pi/ absolute value of b is the period, c is the phase shift, and d is the vertical shift or midline.
Given the function
[tex]7 \cos(2x + \pi) - 3[/tex]
The amplitude is 7, and the midline is -3. The period is
[tex] \frac{2\pi}{2} = \pi[/tex]
The phase shift is
[tex]2x + \pi = 0[/tex]
[tex]2x = - \pi[/tex]
[tex]x = - \frac{\pi}{2} [/tex]
So the amplitude is 7
The period is pi
The phase shift is negative pi/2
The midline is -3.
question 8b , thanks
Answer:
Step-by-step explanation:
[tex]a = \frac{2b+1}{3b-1}[/tex]
b = 2/3
[tex]2b + 1 = 2*\frac{2}{3}+1\\\\=\frac{4}{3}+1\\\\=\frac{4}{3}+\frac{3}{3}\\\\=\frac{7}{3}\\\\3b-1 = 3*\frac{2}{3}-1\\\\=2- 1 = 1\\\\\\[/tex]
[tex]a = \frac{2b+1}{3b-1}\\\\a=\frac{\frac{7}{3}}{1}\\\\=\frac{7}{3}\\\\[/tex]
a = 7/3
b)
[tex]\frac{2b+1}{3b-1}=a\\\\[/tex]
Cross multiply,
2b + 1 = a*(3b - 1)
2b + 1 = a*3b - 3*a
2b + 1 = 3ab- 3a
2b = 3ab - 3a - 1
2b - 3ab = -3a - 1
b(2 - 3a) = -3a - 1
[tex]b =\frac{-3a - 1}{2 - 3a}[/tex]
Chris is trimming trees. He can trim 2/3 of a tree in 30 minutes. What is Chris’s rate for trimming trees in trees per hour?
[tex]\\ \rm\Rrightarrow \dfrac{2}{3}\times 2[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{2(2)}{3}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{4}{3}[/tex]
Answer:
1/1/3 of a tree
Step-by-step explanation:
30 minutes = 2/3 of a tree
Since 1 hour = 60 minutes,
60 minutes = 2/3 × 2
= 4/3
= 1/1/3 of a tree
PLS HELP WILL MAKE FIRST RIGHT ANSWER GETS BRAINLIEST
28. The choose E . y=-3/2x29. The choose D. 4
A=(–2,–4) , B=(0,4)
m=(y2-y1)/(x2-x1)= (4-(-4)) / (0-(-2))=8/2=4
30. The choose E(x+2)(x+4)=x²+4x+2x+8=x²+6x+8
I hope I helped you^_^
Answer:
E, D and E
Step-by-step explanation:
(28)
The equation of a line passing through the origin is
y = mx ( m is the slope )
Calculate the slope using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = A (- 2, 3) and (x₂, y₂ ) = B (2, - 3) ← 2 points on the line
m = [tex]\frac{-3-3}{2-(-2)}[/tex] = [tex]\frac{-6}{2+2}[/tex] = [tex]\frac{-6}{4}[/tex] = - [tex]\frac{3}{2}[/tex]
y = - [tex]\frac{3}{2}[/tex] x → E
(29)
Using the slope formula
with (x₁, y₁ ) = A (- 2, -4) and (x₂, y₂ ) = B (0, 4) ← 2 points on the line
m = [tex]\frac{4-(-4)}{0-(-2)}[/tex] = [tex]\frac{4+4}{0+2}[/tex] = [tex]\frac{8}{2}[/tex] = 4 → D
(30)
(x + 2)(x + 4)
Each term in the second factor is multiplied by each term in the first factor, that is
x(x + 4) + 2(x + 4) ← distribute both parenthesis
= x² + 4x + 2x + 8 ← collect like terms
= x² + 6x + 8 → E
FOR BRAINLIEST!!!!ASAP
19) One number is 9 more than another. Their product is 11 more than five times their sum.
Find the numbers.
Answer:
-7 and 2 or 8 and 17
Step-by-step explanation:
If we let the numbers be [tex]x[/tex] and [tex]x+9[/tex], the equation to solve this problem will be as follows:
[tex]x(x+9)=5(x+x+9)+11[/tex]
Solving the equation for [tex]x[/tex], we get:
[tex]x(x+9)=5(x+x+9)+11[/tex]
[tex]x(x+9)=5(2x+9)+11[/tex] (Combine like terms)
[tex]x^{2} +9x=10x+45+11[/tex] (Use the Distributive Property of Multiplication to multiply expressions)
[tex]x^{2} +9x=10x+56[/tex] (Combine like terms)
[tex]x^{2} -x-56=0[/tex] (Subtract [tex]10x[/tex] and [tex]56[/tex] from both sides of the equation)
[tex]x^{2} -8x+7x-56[/tex] (Split [tex]-x[/tex])
[tex]x(x-8)+7(x-8)=0[/tex] (Factor by taking a common term out)
[tex](x-8)(x+7)=0[/tex] (Factor by taking a common term out)
[tex]x-8=0[/tex] or [tex]x+7=0[/tex] (Use the Zero Product Property)
[tex]x=8[/tex] or [tex]x=-7[/tex]
Therefore, the first number could be either -7 or 8, and the second number could be -7 + 9 = 2 or 8 + 9 = 17, respectively. Hope this helps!
The scale on a map of Virginia shows that 1 centimeter represents 30 miles. The actual distance from Richmond, VA to Washington, DC is 110 miles. On the map, how many centimeters are between the two cities?
Find the value of x
HELPP PLEASEE
GIVING 20 points!!!
Answer:
A 6.09
Step-by-step explanation:
A school wants to buy a chalkboard that measures 1 meter by 2 meters. The chalkboard costs $27.00 per square meter. How much will the chalkboard cost?
Answer:
$54
Step-by-step explanation:
you just multiply 1 by 2 and get the answer 2 then multiply 27 dollars by 2 and get 54 dollars
“Write an equation in standard form of the horizontal line that goes through (-7, 10)”
Answer:
Step-by-step explanation:
A horizontal line is only concerned with the y value. The equation is y = 10 because that is the point that the line must go through.
The x value does not matter as long as the y value is given as 10. The domain is any real value. The range is 10
what is meant by derivative
Answer:
its basically just rate of change or slope. with derivatoves you can find the slope of a tangent line which is a line that touches the curve at a point.
Find the measure of the missing angle.
156°
a =
Answer:
Below!
Step-by-step explanation:
A straight line = 180 degrees, so all you need to do to find angle a is to subtract 156 from 180!
180 - 156 = 24 degrees
Hope this helped!
Five children share 24m of ribbon equally.
How much ribbon will each child get?
Write your answer as a mixed number.
Answer: 4 8/10m
Explanation:
Total Ribbon = 24m
Total children = 5
Ribbon each student gets = 24÷5
= 4.8
Now 4.8 = 48/10
4 8/10m is the mixed fraction
So each child will get 4 8/10m ribbon
Must click thanks and mark brainliest
If five children share 24m of ribbon equally then each children gets [tex]4\frac{4}{5}[/tex] of ribbon.
What is Division?A division is a process of splitting a specific amount into equal parts.
Given that five children share 24m of ribbon equally.
We have to find the amount of ribbon each children gets.
To find this we have to divide the length of the ribbon with the number of children.
Twenty four divided by five.
24 is the dividend and five will be the divisor
24/5
Now we have to write this in mixed fraction
[tex]4\frac{4}{5}[/tex]
Hence, if five children share 24m of ribbon equally then each children gets [tex]4\frac{4}{5}[/tex] of ribbon.
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The focus of a parabola is located at (0,–2). The directrix of the parabola is represented by y = 2. Which equation represents the parabola? y2 = –2x x2 = –2y y2 = –8x x2 = –8y
Answer:
[tex]\boxed{x^2=-8y}[/tex]
Step-by-step explanation:
[tex](a,b)\ is \ the\ focus\\y=k\ is \ the\ directrice\\\\Formula\ to\ use:\ y=\dfrac{(x-a)^2}{2(b-k)} +\dfrac{b+k}{2} \\\\Here: \ a=0,\ b=-2, \ k=2\\\\y=\dfrac{(x-0)^2}{2(-2-2)} +\dfrac{-2+2}{2} \\\\so\ y=-\dfrac{x^2}{8} \\\\or\ x^2=-8y[/tex]
The equation which represents the parabola is x^2 = 8y, the correct option is C.
What is vertex form of a quadratic equation?
If a quadratic equation is written in the form
y=a(x-h)^2 + k
then it is called to be in vertex form. It is called so because when you plot this equation's graph, you will see vertex point(peak point) is on (h,k)
First of all, i used this vertex formula thing since it is visible that there are quadratic functions. Otherwise, you had to use calculus to get critical points, then second derivative of functions to find the character of critical points as minima or maxima or saddle etc to get the location of vertex point.
This point (h,k) is called the vertex of the parabola that quadratic equation represents.
We are given that;
Focus of parabola= (0,–2)
Now,
The vertex is halfway between the focus and the directrix on a line perpendicular to them. Since the focus is at (0,-2) and the directrix is y = 2, we can find that:
The vertex is at (0,0), because it has an x-coordinate of 0 (same as the focus) and a y-coordinate of 0 (the average of -2 and 2).
p is equal to 2, because it is half of the distance between -2 and 2.
Now we can plug in these values into the formula:
(x - 0)^2 = 4(2)(y - 0)
Simplifying, we get:
x^2 = 8y
Therefore, the equation of the parabola will be x^2 = 8y.
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Max spent $53 and now he has no money left.How much did max have before his purchase? Why?
For the function, f(x) = -2x 2, find f(-3).
36
18
-18
-36
[tex]\pink{ \boxed{\boxed{\begin{array}{cc} \maltese \bf \: given \\ \\ \rm \: f(x) = - 2 {x}^{2} \\ \\ \rm \therefore \: f( - 3) = - 2 {( - 3)}^{2} \\ \rm = - 2 \times 9 \\ = - 18 \end{array}}}}[/tex]
Answer:
-18
Step-by-step explanation:
f(-3) = -2 (-3)²
= -2(9)
= -18
The sum of first three terms of an arithmetic series is 21. If the sum of the first two terms is subtracted from the third term then it would be 9. find the three terms of the series
Answer:
The terms are - 1, 7 and 15.
Step-by-step explanation:
Let the terms be a-d, a and a+d
ATQ, a-d+a+a+d=21, a=7. a+d-(a+(a-d))=9. d=8. The terms are - 1, 7 and 15.
The Line segments are translated 2 units to the left to form A’B’ and C’D’. Which statement describes A’B’ and C’D’?
Answer:
Line segments A'B' and C'D' do not intersect and are the same distance apart as AB and CD.
Step-by-step explanation:
Point A is located at (0, 4), and point C is located at (−3, 5). Find the x value for the point B that is located one-fourth the distance from point A to point C.
Answer:
x = (-2 , 4.5)
Step-by-step explanation
Hope it helps! later!
please look at the following attachment
Answer:
6 blocks have red faced
Step-by-step explanation:
54 blocks have 1 red face
0.135 written as a fraction is _____.
27/200
5/37
27/100
Answer:
27/200
Step-by-step explanation:
To write 0.135 as a fraction you have to write 0.135 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number. 0.135 = 0.135/1 = 1.35/10 = 13.5/100 = 135/1000
Answer:
27/200
Step-by-step explanation:
your teacher tried to be tricky.
0.135 is simply 135/1000.
that is how you can express any finite decimal number.
anyway, now, we need to transform that fraction into one of the provided fractions. so, which one fits ?
with experience you see it right away. otherwise by simply trying.
in any case, the first option is the right one.
proof :
27/200 = 135/1000 ?
the denominator is our driver : what factor do I need to turn 200 into 1000 ? right, 5 ! 200×5 = 1000
so, we multiply numerator and denominator by 5 (it is important to do that for both, so that the value of the fraction does not change).
27/200 × 5/5 = (27×5) / (200×5) = 135/1000
and that is the proof. 27/200 is indeed 0.135
3/5 divided by 3/15 equals
Answer:
3/25
Step-by-step explanation:
3/5 *3/15
9/75
Simplified 3/25
Answer:
3
Step-by-step explanation:
3/5 ÷ 3/15
=> 3/5 x 15/3
=> 3/5 x 5
=> 3
Someone help pleaseee
Answer:
the answer is 1/2 which loos like "D"
Step-by-step explanation:
the top ends up being x ^-8 and the denominator is x^-7
which is x^&/x^8 = 1/x = 1/2
Solve for q. –17 − 12q = –17 + 10q
Step-by-step explanation:
–17–12q=–17+10q
–17+17=10q+12q
0/22=22q/22
q=0
the total surface area of pencil is πr(L+2H+2r+r)
πr(L+2H+r)
πr(2L+r)
πrL
Answer:
2pi*r(r+h)
Step-by-step explanation:
SEE IMAGE FOR SOLUTION
HAVE A GREAT DAY
A sphere has a radius of 4 in. Which equation finds the volume of the sphere?
V=4/3 x(4)^3
V=4/3(4)^3
V=2/3(8)^3
V=2/3 x(8)^3
Answer:
Step-by-step explanation:
r = 4 in
[tex]Volume =\frac{4}{3}\pi r^{3}\\\\=\frac{4}{3}\pi (4)^{3}[/tex]
Answer:
V = 4/3 pi (4)^3
Step-by-step explanation:
The volume of a sphere is given by
V = 4/3 pi r^3
The radius is 4
V = 4/3 pi (4)^3
shopkeeper gains rs540by selling some fruit but loses rs 612 by selling some vegetables. find the profit or loss
Answer:
sorry i dont know.......
Answer:
Loss = R.s. 72
Step-by-step explanation:
You can see in picture
Request : Please mark it brainliest answer
worth 10pts!!! Can someone help?
Answer:
-4
Step-by-step explanation:
The average rate of change of the interval [a,b] is (f(b)−f(a)) / (b−a)
Replacing a=−5, b=4, f(x)=−x^2−5x+12.
(f(b)−f(a))/(b−a) =12−5x4− 4^2 − (12−5 x(−5)−(−5)^2)/ (4−(−5))= −4.
