Step-by-step explanation:
1/(seca-tana) - 1/cosa=1/cosa -1/(seca+tana)
There are many ways to solve this, let's take a look at a simple one
1/(seca-tana) + 1/(seca+tana) =1/cosa + 1/cosa
((seca-tana)+(seca+tana))/(sec^2a-tan^2a)=2/cosa
(seca-tana+seca+tana)/1=2*1/cosa
2seca=2seca
Complete the table, and then use the drawing tools to create the graph representing the relationship between the amount of plant food remaining, f(x), and the number of days that have passed, x.
The complete table of the function is:
[tex]\begin{array}{cccccccc}x & {0} & {1} & {2} & {3} & {4}& {5} & {6} \ \\ f(x) & {72} & {60} & {48} & {36} & {24}& {12} & {0} \ \end{array}[/tex]
The equation missing from the question is:
[tex]y = 72 - 12x[/tex]
To complete the table, we simply calculate the y value for each x value;
When [tex]x = 0[/tex], [tex]y = 72 - 12 * 0 = 72[/tex]
When [tex]x = 1[/tex], [tex]y = 72 - 12 * 1 = 60[/tex]
When [tex]x = 2[/tex], [tex]y = 72 - 12 * 2 = 48[/tex]
When [tex]x = 3[/tex], [tex]y = 72 - 12 * 3 = 36[/tex]
When [tex]x = 4[/tex], [tex]y = 72 - 12 * 4 = 24[/tex]
When [tex]x = 5[/tex], [tex]y = 72 - 12 * 5 = 12[/tex]
When [tex]x = 6[/tex], [tex]y = 72 - 12 * 6 = 0[/tex]
So, the complete table is:
[tex]\begin{array}{cccccccc}x & {0} & {1} & {2} & {3} & {4}& {5} & {6} \ \\ f(x) & {72} & {60} & {48} & {36} & {24}& {12} & {0} \ \end{array}[/tex]
To create a graph of f(x), we simply type [tex]y = 72 - 12x[/tex] on a drawing tool and the graph will be generated.
See attachment for graph
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Answer:
Step-by-step explanation:
The volume of this cube is 64 cubic feet. What is the value of a?
Answer:
a = 4 feet
Step-by-step explanation:
Since it's a cube, we know that each value will be equal. Because of this, you can cube root the cube's volume to find a.
[tex]\sqrt[3]{64}=4[/tex]
Therefore, a = 4 feet.
Answer:
4
Step-by-step explanation:
To find the area of a cube, we have to multiply the width, height, and length, which, since they are all the same value, would be a side multiplied by itself 3 times(cubed). So, the area of this cube in terms of a(side) is a*a*a or a^3. The area is given to be 64, so we can write:
a^3 = 64
With the equation, we can realize 4*4*4 is 64, meaning a is 4.
Which number is a solution of the inequality?
3x - 15 ≥ 3
a.) -9/11
b.)6/11
c.)6
d.)5
Answer:
6
Step-by-step explanation:
[tex]3x - 15 \geqslant 3[/tex]
[tex]3x \geqslant 3 + 15[/tex]
[tex]x \geqslant \frac{18}{3} [/tex]
[tex]x \geqslant 6[/tex]
Does the graph represent a function? Why or why not?
Answer:
D. Yes, because it passes the vertical line test.
Step-by-step explanation:
In order to be a function, it needs to pass the vertical line test as a function can not have multiple y's for one x. However, functions can have multiple x's for one y such as in a quadratic function.
Answer:
D.
Brainliest, please!
Step-by-step explanation:
This function passes both the horizontal and vertical line tests. But when determining if it is a function or not, the vertical line test is the only one that matters. If we wanted to know if this function had an inverse or not, then B. would be right.
PLEASE HELP ASAP!!!!! The following graph shows a proportional relationship. What is the constant of proportionality between y and x in the graph?
Answer:
2/3
Step-by-step explanation:
The graph point is on (3,2)
Find the measure of the indicated angle to the nearest degree.
Answer:
Step-by-step explanation:
Adjacent to the undetermined angle is 6, and the hypotenuse has been given. We can conclude, after looking at our SOHCAHTOA, that we will be using cosine(CAH) to solve this problem.
Let the unspecified angle be [tex]\theta\\[/tex] (This sign is called theta, which is just a sign for angle)
Lets start!
cos[tex]\theta\\[/tex] = adj/hyp
cos[tex]\theta\\[/tex] = 6/13
[tex]\theta\\[/tex] = [tex]cos^{-1}[/tex](6/13)
[tex]\theta\\[/tex] = 62.5
[tex]\theta\\[/tex] = 63
Hope that helped!
Write the equation of the line that passes through the points (−7,5) and (-7,-8).
Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal line.
Answer:
x = -7
Step-by-step explanation:
First we find the slope using
m = ( y2-y1)/(x2-x1)
= ( -8 - 5)/( -7 - -7)
= (-8-5)/(-7+7)
= -13/0
This means the slope is undefined and the line is vertical
Vertical lines are in the form
x= constant and the constant is the x value of the points
x = -7
Kristina wants to buy a flute that costs 240 . She has saved 20 each week for 3 weeks . How many more weeks does Kristina need to save money if she continues to save 20 each week
If P =
1 2
then, prove that P2 - 2P - 5 = 0, 1 = 0, where I and 0 are unit
3 1
matrix and null matrix of order 2 x 2 respectively.
Answer:
thanks for free ponits you dint gave it free but I theft I'm sorry
A P E X fasted answer is getting 30 points please hurry.
suppose a normal distribution has a mean of 98 and a standard deviation of 6. what is p(x ≥ 92)
Answer:
Step-by-step explanation:
If the mean is 98 and standard deviation is 6, then 92 is one standard deviation to the left of the mean; that means that 34% + 34% + 13.5% + 2.35% + .15% of the data is included in this area. Add those up and you get, as a percentage, 84%.
Answer:
0.84
Step-by-step explanation:
yee its right
Which of the following planets has the strongest winds in the solar system?
O Jupiter
O Mars
O Neptune
O Venus
Answer: The answer is Neptune ^-^
Step-by-step explanation:
Got it correct on the test :]
according to the rational root theorem which of the following are possible roots of the polynomial function below? F(x)=6x^3-7x^2+2x+8
Answer:
Hello,
Step-by-step explanation:
all potential roots are of the form a/b where a is a divisor of 8
and b is a divisor of 6 ( in Z)
So A,D,E,F may be roots
but B and C not.
Which shapes have the greatest area?
(Select all that apply.)
Answer:
the trapiezium
Step-by-step explanation:
It has a area of 4 which is the highest
The distributive property can be applied to which expression to factor 12x3 – 9x2 + 4x – 3?
3(4x3– 1) – (9x2 + 4x)
4x(3x2 + 1) – 3(3x2 – 1)
3x(4x – 3) – (3+ 4x)
3x2(4x – 3) + 1(4x – 3)
IM ON EDGE
Answer:
12x^3-9x^2+4x-3
3(4x^3-1)-(9x^2+4x)
therefore option A is right
thank you, and mark it as brainliest if u find it useful
Which plane geometry has countless symmetry axis ? (except for circle)
Sorry if there are some grammatical mistakes in my question because English isn't my first language. Thank you very much !
Countless symmetry axis of a parabola is vertical line which divides the parabola into two congruent halves.
The axis of symmetry always passes through vertex of parabola. These will cause the plane to divide into two parts.
The geometric shape may have countless symmetry axis. This actually divides the shape into two halves and creates a mirror like effect.
The x-coordinate of vertex is equation of axis symmetry of parabola. Lets say if we take an example of quadratic equation which is ,
y = ax^2 + bx + c , here in this equation the axis of symmetry is vertical line which is x = - b^2 a
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Find m<DCV and m<VBD
Answer:
∠ DCV = ∠ VBD = 50°
Step-by-step explanation:
The inscribed angles DCV and VBD are half the measure of their intercepted arcs, that is
∠ DCV = [tex]\frac{1}{2}[/tex] DV = [tex]\frac{1}{2}[/tex] × 100° = 50°
∠ VBD = [tex]\frac{1}{2}[/tex] DV = [tex]\frac{1}{2}[/tex] × 100° = 50°
PLEASE help me!!!
Amina has two bags.
In the first bag there are 3 red balls and 7 green balls.
In the second bag there are 5 red balls and 4
green balls.
Amina takes at random a ball from the first bag.
She then takes at random a ball from the second bag.
(a) Complete the probability tree diagram.
Answer:
Step-by-step explanation:
first
3/10 & 7/10
second
5/9 & 4/9
Darryl has written 60 percent, or 12 pages, of his history report. Darryl wants to figure out how many total pages he needs to write. Darryl’s work is shown below.
Step 1: Write 60 percent as a ratio. StartFraction part Over whole EndFraction = StartFraction 60 Over 100 EndFraction
Answer:
total pages = 20
Step-by-step explanation:
60% of an unknown number is 12
Let the unknown number (total pages) be x.
60/100 of x = 12
60/100 * x = 12
3/5 x = 12
x = 12 * 5/3
x = 20
find the measure of one exterior angle for the following regular polygon
Answer:
36 degrees
Step-by-step explanation:
10 corners/sides.
the sum of all exterior angles in a polygon is always 360 degrees.
so, one exterior angle here is 360/10 = 36 degrees
PLS HELP WILL MAKE FIRST RIGHT ANSWER GETS BRAINLIEST
(x^2+1)(x-1)=0 help me pls
Answer:
x = ±i , x=1
Step-by-step explanation:
(x^2+1)(x-1)=0
Using the zero product property
x^2 +1 = 0 x-1= 0
x^2 = -1 x=1
Taking the square root of the equation on the left
sqrt(x^2) = sqrt(-1)
x = ±i where i is the imaginary number
We still have x=1 from the equation on the right
If the lengths of the legs of a right triangle are 4 and 8, what is the length of the hypotenuse?
PLEASE HELP
Answer:
[tex]4\sqrt{5}[/tex]
Step-by-step explanation:
In order to solve this problem, we can use the pythagorean theorem, which is
a^2 + b^2 = c^2, where and b are the legs of a right triangle and c is the hypotenuse. Since we are given the leg lengths, we can substitute them in. So, where a is we can put in a 4 and where b is we can put in an 8:
a^2 + b^2 = c^2
(4)^2 + (8)^2 = c^2
Now, we can simplify and solve for c:
16 + 64 = c^2
80 = c^2
c = [tex]\sqrt{80}[/tex]
Our answer is not in simplified radical form because the number under is divisible by a perfect square, 16. We can divide the inside, 80, by 16, and add a 4 on the outside, as it is the square root of 16:
c = [tex]4\sqrt{5}[/tex]
The length of the hypotenuse in the given right triangle, with legs measuring 4 and 8, is approximately 8.94.
To find the length of the hypotenuse in a right triangle, we can use the Pythagorean theorem. According to the theorem, in a right triangle, the square of the hypotenuse's length is equal to the sum of the squares of the lengths of the other two sides.
In this case, let's label the lengths of the legs as 'a' and 'b', with 'a' being 4 and 'b' being 8. The hypotenuse, which we need to find, can be represented as 'c'.
Applying the Pythagorean theorem, we have:
[tex]a^2 + b^2 = c^2[/tex]
Substituting the given values:
[tex]4^2 + 8^2 = c^2[/tex]
16 + 64 = [tex]c^2[/tex]
80 = [tex]c^2[/tex]
To find the length of the hypotenuse 'c', we need to take the square root of both sides:
√80 = √ [tex]c^2[/tex]
√80 = c
The square root of 80 is approximately 8.94.
Therefore, the length of the hypotenuse in the given right triangle, with legs measuring 4 and 8, is approximately 8.94.
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8.52 The heights of 2-year-old children are normally distributed with a mean of 32 inches and a standard deviation of 1.5 inches. Pediatricians regularly measure the heights of toddlers to determine whether there is a problem. There may be a problem when a child is in the top or bottom 5% of heights. Determine the heights of 2-year-old children that could be a problem.
Answer:
Heights of 29.5 and below could be a problem.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
The heights of 2-year-old children are normally distributed with a mean of 32 inches and a standard deviation of 1.5 inches.
This means that [tex]\mu = 32, \sigma = 1.5[/tex]
There may be a problem when a child is in the top or bottom 5% of heights. Determine the heights of 2-year-old children that could be a problem.
Heights at the 5th percentile and below. The 5th percentile is X when Z has a p-value of 0.05, so X when Z = -1.645. Thus
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.645 = \frac{X - 32}{1.5}[/tex]
[tex]X - 32 = -1.645*1.5[/tex]
[tex]X = 29.5[/tex]
Heights of 29.5 and below could be a problem.
write down amultiple of 4 and 14 which is less than 30
28
How?
Multiples of 4=8,12,16,20,24,28Multiples of 14=28,42We can see that 28 is the lowest common multiple also it is <30
Answer: 28.
Step-by-step explanation: 28 is divisible by 4: 28 / 4 = 7. 28 is divisible by 14: 28 / 14 = 2. And 28 is less than 30
please help:
give an example of an undefined term and how it relates to a circle.
Which of the following statements best describes the relationship between
any point on an ellipse and each of its two foci?
A. The quotient of the distances to each focus equals a certain
constant.
B. The difference of the distances to each focus equals a certain
constant.
C. The sum of the distances to each focus equals a certain constant.
D. The product of the distances to each focus equals a certain
constant.
Answer:
C
Step-by-step explanation:
The sum of distances from any point on the ellipse to each foci equals a certain amount, no matter what point on the ellipse it starts from. The foci are on the major radius of the ellipse (the longer length of horizontal/vertical). The foci are of equal distance from the center, with one on each side.
If you wanted to find where the foci are using the major and minor radius, we can find that, representing the distance between the center and any foci as g,
g² = major radius² - minor radius². Then, the distance between the center and the foci is equal to g
Please hurry I will mark you brainliest
What is the equation of the line parallel to y = 2x - 4 and with the same x - intercept as 3x – 4y = 12?
Answer:
y=2x-8
Step-by-step explanation:
Hi there!
We want to find an equation of the line parallel to y=2x-4 but has the same x intercept as 3x-4y=12
Parallel lines have the same slope, but different y intercepts
In y=2x-4, which is written in y=mx+b form, m is the slope and b is the y intercept
2 is in the place of where the slope would be, so the slope of that line is 2
That means the slope of the line parallel to it would also have a slope of 2
Here is the equation of the parallel line so far:
y=2x+b
We need to find b, the y intercept
Typically, we'll substitute a point into the equation to solve for b, but we don't have a point, yet
We're given that the new line has the same x intercept as 3x-4y=12
The x intercept is the point where the line passes through the x axis, and so the value of y at that point is 0
Let's substitute 0 for y in 3x-4y=12 and solve for x to find the x intercept
3x-4(0)=12
Multiply
3x=12
Divide both sides by 3
x=4
So the value of the x intercept is 4. As a point, it's (4,0)
So now substitute the values of the point (4,0) into y=2x+b to find b
0=2(4)+b
Multiply
0=8+b
Subtract 8 from both sides
-8=b
Substitute -8 as b into the equation
y=2x-8
Hope this helps!
the best way to learn math formulas
Writing down the formulas on charts and pasting it in your room,by seeing this daily it helps to memorize the formulas.
Saying the formulas louder also helps to memorize the formula.
Watching videos related to maths formulas and equations helps to remember the formulas easier.
Doing many problems regularly will helps you to remember the formulas.
lastly study to Understand The Formula not to memorize
Which is the equation of a parabola with Vertex (0,0) and focus (0, 2)?
a. ya = 8x
c. x2 = 8
b. y2 = 4x
d. x2 = 4y
Answer:
So the equation of the parabola is x2=8y i don't really know
I am not sure. Is this right?
Answer:
14.4
Step-by-step explanation:
since the longest side is 24,find the shortest side
√20^2-12^2
√400-144
√256
=16
which means the other shortest side is 24-16
which is 8
then you have to use the 12 and 8 to find the unknown side
√12^2+8^2
144+64
√208
14.4
I hope this helps
