Mathematics High School

No. Of roots in eq 8sec^x-6secx+1=0

Answers

Answer 1
Ok, let's assume it's "sec^2 x"

[tex] 8\sec^2x-6\sec x+1=0\\ 8\sec^2x-2\sec x-4\sec x+1=0\\ 2\sec x(4\sec x-1)-1(4\sec x-1)=0\\ (2\sec x-1)(4\sec x-1)=0\\ 2\sec x-1=0\\ 2\sec x=1\\ \sec x=\dfrac{1}{2}\\ x\in\emptyset\\\\ 4\sec -1=0\\ 4\sec =1\\ \sec x =\dfrac{1}{4}\\ x\in\emptyset [/tex]

So, the number of solutions (real ones) is 0.

Related Questions

Two cards are drawn at random from a standard deck of cards without replacement. What is the probability that both cards will be from the clubs suit?

Answers

Answer:

The answer is 1/17.

Step-by-step explanation:

You will draw one club which will be 13/52. You will NOT replace it so you will draw a second card 12/51.

You will need to multiply them to find the probability.

First simplify your two fractions.

13/52 = 1/4   AND  12/51= 4/17

Multiply the two together and you will get 4/68 = 1/17

Hope this helps :)

. If ON = 4x – 6, LM = 3x + 5, NM = x – 4, and OL = 4y – 3, find the values of x and y for which LMNO must be a parallelogram.

Answers

In a parallelogram, opposite sides are congruent.

This means that
LM = ON
NM = OL

Using the equations, find x and y:
4x - 6 = 3x + 5
4x = 3x + 11
1x = 11
x = 11

x - 4 = 4y - 3
x - 1 = 4y
-1 = 3y
-1/3 = y

The values are:
x = 11
y = -1/3

The original value of the car is $18,000 and it depreciates by 50% each year what is the value of the car after three years

Answers

value = 18000*(1-0.50)^3 = 2250

value after 3 years = $2250

The formula is
A=p (1-r)^t
A the value of the car after 3 years?
P current value 18000
R rate of depreciation 0.5
T time 3years
A=18,000×(1−0.5)^(3)
A=2,250

A line with a slope of 3 passes through the point (2,5) what is the equation of this line?

Answers

y=3x-4 because the form of a line's equation is y=mx+b where m is the slope or three in this case and b is the value of y in the y intercept and in this case it is -4 so you get y=3x+(-4) or y=3x-4.
Slope of the line equals 3 at the points (2,5) so m=0
The equation is a horizontal line, therefore the slope is 0.

Can someone help me plz!!!

Answers

It is B. Identity always includes 0
you basically just say if it does equal to a+c and then say if its right or wrong

What is the taxi distance between A(2, 5) and B(7, 9)?

Answers

If by "taxi distance" you mean travelling along the sides of the right triangle created by the two points.

t=|x2-x1|+|y2-y1|

t=5+4

t=9 units

If you mean the actual distance between the two points then:

d^2=(x2-x1)^2+(y2-y1)^2

d^2=(7-2)^2+(9-5)^2

d^2=25+16

d^2=41

d=√41 units

d≈6.4 units (to nearest tenth of a unit)

The janitor found that it was leaking at a rate of 13 fl oz per minute How fast was the pipe leaking in gallons per hour​?

Answers

8oz=1cup
16cup=1gal
so

16*8=128oz per gallon


13oz/min

alrighty
13oz=13/128gal
1min=1/60hr

(13/128gal)/(1/60hr)=(13/128gal)(60hr/1)=78hr/128gal
128gal/78hr=64gal/39hr≈6.09375
about 6 gallons per hour
the answer is 6 gallons per hour

Gabriella said a triangle with an angle of 98 degrees was an obtuse angle. Cynthia said a triangle with an angle of 98 degrees was an acute triangle. Who is right and why?

Answers

an obtuse triangle has an angle that is greater than 90 degrees

so if we see gabby's statement, ,98>90 so tecnically, she is correct

cynthya's statement is false because 98>90 so it is an obtuse angle

Help me with this please!!!

Answers

do a ratio

11/2=X/24

24*11 = 264

264/2 = 132

X= 132

 so 132 students

ROUND 43.0810194943 TO THE NEAREST TEN-THOUSANDTH HELP!

Answers

43.0810
Since the hundred thousandths is a 1 which is less than a 5, you have to round down.
43.0810 is the answer. The ten thousandths is always four numbers after the decimal.

([solve by writing an equation])
A pair of jeans costs 75% as much as a pair of corduroy pants. what is the cost of each if the total cost for the jeans and cords is $42?
I know the answer is Jeans: $18 and Cords: $24 but how do I write that in an equation to solve??
thank you!!!

Answers

Let the pair of jeans cost x dollars and the pair of corduroy cost y dollars.

"A pair of jeans costs 75% as much as a pair of corduroy pants."

this means [tex] x=\frac{75}{100}*y [/tex], simplifying by 25:

[tex]x= \frac{3}{4} y[/tex]           (equation 1)


"the total cost for the jeans and cords is $42?"

x+y=42    (equation 2)

substitute x form equation 1, in equation 2

x+y=42 

[tex] \frac{3}{4} y+y=42[/tex]

[tex] \frac{3}{4} y+ \frac{4}{4} y=42[/tex]

[tex]7y=4*42 [/tex]

y=4*6=24

substitute y=24 in either of equations 1 or 2:

x+y=42    (equation 2)
x+24=42
x=42-24=18

Answer: Jeans cost 18$, Cords cost 24$ 

Determine the number of possible triangles, abc, that can be formed given c = 85°, a = 10, and c = 13.

Answers

To get the possible triangle that be formed with a triangle whose dimensions are C=85, a=10 and c=13, we need to calculate for the values of the angles. Using sine rule:
a/sin A=c/sin C=d/sin D
thus the value of angle A will be:
10/sin A=13/sin 85
10/sin A=13.05
sin A=10/13.05
sin A=0.7663
A=arcsin 0.7663
A=50
thus the n=value of angle B will be:
B=180-(85+50)
=45
The triangle formed will be an acute triangle
General rule is a<bsinA means no triangle is possible, a=bsinA means 1 triangle is possible and a>bsinA means 2 possible triangles

5x - 10y = 15 if 3x + 7y = 31

Answers

5x - 10y = 15...reduces to x - 2y = 3
3x + 7y = 31

x - 2y = 3....multiply by -3
3x + 7y = 31
---------------
-3x + 6y = -9 (result of multiplying by -3)
3x + 7y = 31
---------------add
13y = 22
y = 22/13

x - 2y = 3
x - 2(22/13) = 3
x - 44/13 = 3
x = 3 + 44/13
x = 39/13 + 44/13
x = 83/13

solution is (83/13, 22/13) <=
3(5x-10y=15)-5(3x+7y=31)

15x-30y-15x-35y=45-155

-65y=-110

y=22/13, making 3x+7y=31 become

3x+154/13=31

39x+154=403

39x=249

x=83/13

So the solution to the system of equation is the point (83/13, 22/13)


PLZ I NEED HELP ASAP

Annie has a compost pile that produces 12 pounds of compost a day from yard waste. Which function expresses the amount of compost (c) as a function of the number of days (d)? The function representing the relationship between the amount of compost and the number of days is__, with the input as__.

Answers

If it produces 12 pounds each day, for any number of days, we can just multiply by 12, correct?? So that means c=12d. Remember your input will be the days since you have to put that in the equation to calculate how much compost you have. 

Answer: number of days: c=f(d) =12d

Imput:12

Step-by-step explanation:

The pressure P exerted by a force varies inversely as the area A on which the force is applied. If 16 N/ft2 of pressure is exerted by a force on an area of 3 ft2 , what is the pressure exerted by the same force on an area of 6 ft2?
A) 8 N/ft2
B) 16 N/ft2
C) 4 N/ft2
D) 32 N/ft2

Answers

The first piece of information tells you that
16 = C / 3
Solve for C
C=16×3=48
Now find P if A = 6. and C=48
P = C/6
P = 48/6
P = 8 N/ft2

Answer:

A) 8 N/ft2

Step-by-step explanation:

Pressure is the normal force per unit area, that is, it is equivalent to the force acting on the surface unit, and is given by:

[tex]P=\frac{F}{A}[/tex]

Where:

[tex]P=Pressure\\F=Normal\hspace{3}force\\A=Area\hspace{3} where \hspace{3}force\hspace{3} is \hspace{3}applied.[/tex]

In the first case:

[tex]P=16N/ft^2\\A=3ft^2[/tex]

Using the previous equation and solving for [tex]F[/tex] :

[tex]F=P*A=16*3=48N[/tex]

Now, for the second case, since the force is the same applied in the first case, then:

[tex]P=\frac{F}{A} =\frac{48}{6} =8N/ft^2[/tex]

Therefore the answer is:

A) 8 N/ft2

What is the length of a square

Answers

That would depend on how big or small the square is. 

Which property is demonstrated by this equation? 3 + 2x = 2x + 3

Answers

Commutative Property is  moving the numbers around

answer Commutative Property
Hey Buddy!

The commutative property is demonstrated in your equation. 

An example of this property could be: a+b = b+a or 23+15 = 15+23.
It is the result of changing the order of the operands without changing the result. (whether sum, difference, product, or quotient)

Hope this helps! (Don't forget Brainliest!) :)

Find the product of (2x + 5y)2.

Answers

4x +10y is the product of (2x+5y)2
Distribute 2 to 2x and 5y using PEMDAS to get 4x+10y

Find the measure of each exterior angle of a regular polygon with 24 sides

Answers

the measure of each interior angle would be 165 degrees

The formula for finding the measure of each exterior angle of a regular polygon is similar to the formula for finding the measure of each interior angle. We take the sum of the measures of the exterior angles which is always 360 degrees and we divide this by the number of sides in the polygon which is n. So the formula for finding the measure of each exterior angle of a regular polygon is simply 360 over n. In this problem since the polygon has 24 sides, we simply plug a 24 in for n and we have 360 over 15. 360 divided by 24 is 15. Therefore, the measure of each exterior angle of a regular polygon that has 24 sides is 15 degrees.

Draw a model to represent the problem 6/12 divided by 1/4

Answers

The expression 6/12 divided by 1/4 is 2 and the model is attached

Drawing a model to represent the problem

From the question, we have the following parameters that can be used in our computation:

6/12 divided by 1/4

This can be expressed as

6/12 multiplied by 4

So, we have

0.5 multiplied by 4

When the product is evaluated, we have

2

Hence. 6/12 divided by 1/4 is 2 and the model is attached

Choose the correct description of the graph of the compound inequality

2x + 5 > 9 and 5x less than or equal to 30.

A) A number line with an open circle on 2, shading to the left, and a closed circle on 6, shading to the right
B) A number line with an open circle on 2, a closed circle on 6, and shading in between
C) A number line with a closed circle on 2, shading to the left, and an open circle on 6, shading to the right
D) A number line with a closed circle on 2, an open circle on 6, and shading in between

Answers

To do this, you first have to solve the first inequality for x: 2x+5>9, 2x>4 and x>2.  Now solve the next one for x as well: 5x <=30, x<=6.  Now work on putting them onto a number line together.  Since there is not an "equal to" with that greater than, the circle is open above the 2.  The next one has an "equal to" with it so that's a closed circle above the 6.  This is a conjunction, meaning the solution will show what is shared between the 2 inequalities, so you have an open circle above the 2 and shading to the right til you get to the closed circle above the 6 (which is technically shaded to the left down to the open circle at 2). So your choice is B.

Answer:

B) A number line with an open circle on 2, a closed circle on 6, and shading in between

Step-by-step explanation:

easy answer

HELP!!!!
Use the following data set and a separate piece of paper to make a line plot that will help you to answer questions 2-7.
(6, 4, 4, 5, 1, 8, 10, 7, 8, 6, 6, 7, 5, 4, 6)
Add a box and whisker plot to the graph. Clearly mark the ends of box by drawing vertical lines and labeling their values on the horizontal axis. What are the ends of the box and whisker plot?

A. 1 and 6

B. 4 and 7

C. 4 and 8

D. 5 and 7

Answers

1,4,4,4,5,5,6,6,6,6,7,7,8,8,10

minimum = 1
Q1 = 4
Q2 (median) = 6
Q3 = 7
maximum = 10

The beginning and end of the " box " are Q1 and Q3.....4 and 7

The hypotenuse of a right triangle is 3 times as long as the shorter leg. find the measure of the angle between the shorter leg and the hypotenuse

Answers

Let α be the angle between the shorter leg and the hypotenuse
shorter leg = x
hypotenuse = 3x

[tex]cos \alpha = \cfrac{x}{3x} = \cfrac{1}{3} \ \ \to \alpha \approx70.5^o[/tex]

The measure of the angle between the shorter leg and the hypotenuse,    [tex]\theta[/tex] = 70.53 °

What is Trigonometry?

Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangles.

Given that:

Let us consider the shorter leg be 'x'.

and, the Hypotenuse be '3x '.

Using trigonometric functions,

[tex]cos \theta= \frac{Base}{Hypotenuse}[/tex]

cos [tex]\theta[/tex] = x /3x

cos [tex]\theta[/tex] = 1/3

 [tex]\theta[/tex] = [tex]cos^{-1}[/tex] (1/3)

  [tex]\theta[/tex] = 70.53 °

Hence,  the measure of the angle between the shorter leg and the hypotenuse  70.53 °

Learn more about Trigonometric function here:

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Joseph pays $20 for his base phone in addition to the $0.10 per text. Micki pays $10 for her phone plan plus the $0.15 per text. Write a function for Joesph's phone plan and for Micki's phone plan.

Provide the number of text messages in which the plans are the same plan.

Answers

j=20+0.1t

m=10+0.15t

They wil cost the same when m=j so we can say:

10+0.15t=20+0.1t, subtract 0.1t from both sides

10+0.05t=20  subtract 10 from both sides
 
0.05t=10  divide both sides by 0.05

t=200

So when one texts 200 times, both plans cost the same amount.
Final answer:

By using the equations Cj = 20 + 0.10x for Joseph's phone cost and Cm = 10 + 0.15x for Micki's phone cost, we find their costs would both be the same if 200 text messages were sent.

Explanation:

The question is asking us to create an equation for both Joseph's and Micki's texting plans. In mathematical terms, the cost for each plan would be represented by the equation Cost = base rate + (cost per letter)x, where x represents the number of texts.

So for Joseph, the equation would be Cj = 20 + 0.10x and for Micki the equation would be Cm = 10 + 0.15x.

To find out when both plans cost the same, we set the two equations equal to each other and solve for x.

20 + 0.10x = 10 + 0.15x  

By subtracting 0.10x from both sides and then subtracting 10 from both sides we get:  

x = 200.

This means that both plans would cost the same if both parties sent 200 texts.

Learn more about mathematical equation here:

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express 3/4, 7/16,and 5/8 with the LCD

Answers

The LCD (lowest common denominator) is the lowest common denominator of two or more fractions.

4 = 2²
16 = 2⁴
8 = 2³

Take common and non-common factors with highest exponent.

So LCD = 16

The new dneominator of all fractions is 16. Divide this number for the original denominators and multiply for numerator...

16/4 = 4
4*3 = 12

3/4 = 12/16

16/16 = 1
1*7 = 7

7/16 = 7/16

16/8 = 2
2*5 = 10

5/8 = 10/16

A solution of phosphoric acid has a boiling point of 158 degrees Celsius. What is the boiling point of the solution in degrees Fahrenheit?

Answers

Final answer:

The boiling point of a phosphoric acid solution that is 158 degrees Celsius is 316.4 degrees Fahrenheit. This is found by using the formula F = C * 9/5 + 32.

Explanation:

To convert the boiling point of a solution from degrees Celsius to Fahrenheit, we use the formula F = C * 9/5 + 32, where F represents the temperature in Fahrenheit and C represents the temperature in Celsius.

In this case, the temperature in Celsius that you want to convert is 158 degrees. So you can substitute this value in the formula as follows:

F = 158 * 9/5 + 32

When you perform the calculation, you find that the boiling point of the phosphoric acid solution is 316.4 degrees Fahrenheit.

Learn more about Temperature Conversion here:

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write the ordered pair that represents yz. then find the magnitude of yz. Y(-5,7), Z(-1,2)

Answers

The order pair that represents yz can be found as follows:
yz = z - y = (-1 , 2) - (-5,7) = (4 , -5)

The magnitude of yz can be calculated as follows:
magnitude yz = sqrt [(4)^2 + (-5)^2]
                      = sqrt (41)
                      = 6.403

Answer: the answer is D on edge

Step-by-step explanation:

There are 50 jelly beans. if 7 of them are red, and 23 are black, what percentage of the jelly beans are not reed

Answers

86% bc 50 is easy to work with, you know 43 arent red, and since 43x2=86 its 86, multiply by 2 bc 50 is half of 100

Use 1% or 10% to estimate 8% of 310

Answers

We can obtain 8% of a value by finding the 10% of the value and subtract 2% of the value

10% of 310 = 310÷10 = 31
1% of 310 = 310÷100 = 3.1
2% of 310 = 2×3.1 = 6.2

8% of 310 = 31 - 6.2 = 24.8

what is f^-1(1)? inverse function

Answers

f(x) = y = x
f⁻¹(x) = x = y
If x = 1 → f(1) = y =1
if x = 1 → f⁻¹(1) = x = 1



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