Answer:
[tex]\sec \theta = \frac{\sqrt{22}}{4}[/tex]
Step-by-step explanation:
Given
[tex]\tan^2 \theta = \frac{3}{8}[/tex]
Required
[tex]\sec\ \theta[/tex]
We have:
[tex]\sec^2\theta = 1 + \tan^2 \theta[/tex]
This gives:
[tex]\sec^2\theta = 1 + \frac{3}{8}[/tex]
Take lcm and solve
[tex]\sec^2\theta = \frac{9+3}{8}[/tex]
[tex]\sec^2\theta = \frac{11}{8}[/tex]
Take square roots
[tex]\sec \theta = \frac{\sqrt{11}}{\sqrt 8}[/tex]
[tex]\sec \theta = \frac{\sqrt{11}}{2\sqrt 2}[/tex]
Rationalize
[tex]\sec \theta = \frac{\sqrt{11}}{2\sqrt 2} * \frac{\sqrt 2}{\sqrt 2}[/tex]
[tex]\sec \theta = \frac{\sqrt{22}}{4}[/tex]
Answer:
answer is B
Step-by-step explanation:
i got it right on edg
What are the roots of the polynomial x2 - 4x + 1 ?
Work out your answer on our whiteboard. Then, click the buttons below to
see the step-by-step solution.
Answer:
x = (2 + √3) , (2 - √3)
Step-by-step explanation:
GIVEN :-
A quadratic polynomial x² - 4x + 1TO FIND :-
Roots of the quadratic polynomialGENERAL FORMULAE TO BE USED IN THIS QUESTION :-
Quadratic formulae -
For a polynomial ax² + bx + c , its roots are :-
[tex]x = \frac{-b + \sqrt{b^2 - 4ac} }{2a} \; ; \frac{-b - \sqrt{b^2 - 4ac} }{2a}[/tex]
SOLUTION :-
Use the quadratic formulae to find the roots of the polynomial.
[tex]=> x = \frac{-(-4) + \sqrt{(-4)^2 - 4 \times 1 \times 1c} }{2 \times 1} \; ; \frac{-(-4) - \sqrt{(-4)^2 - 4 \times 1 \times 1} }{2 \times 1}[/tex]
[tex]= \frac{4 + \sqrt{16 - 4} }{2} \; ; \frac{4- \sqrt{16 - 4}}{2}[/tex]
[tex]= \frac{4 + \sqrt{12} }{2} \; ; \frac{4- \sqrt{12}}{2}[/tex]
[tex]= \frac{4 + 2\sqrt{3} }{2} \; ; \frac{4- 2\sqrt{3}}{2}[/tex]
[tex]= \frac{2(2 + \sqrt{3})}{2} \; ; \frac{2(2- \sqrt{3})}{2}[/tex]
[tex]= (2 + \sqrt{3} ) \; ; (2 - \sqrt{3} )[/tex]
33. What does equal in the solution of the system of equations below? 33 – 4y - z= 14 2r + 3y - 32 = 17 x + 2y + x = 20 10 04 -10 O-4
9514 1404 393
Answer:
(a) 10
Step-by-step explanation:
Attached is a graphical solution using "substitution." An expression was written for z using the first equation, and it was substituted into the remaining two equations. This gave two equations in x and y, easily solved graphically.
We found x = 10, y = 3, so ...
z = 3(10) -4(3) -14 = 30 -12 -14 = 4
The whole solution is (x, y, z) = (10, 3, 4).
Suppose a normal distribution has a mean or 70 and a standard deviation of 7. What is P(x>=94)? O A. 0.075 O 8. 0.025 c. 0.84 OD 0,16
Answer:
0.025
Step-by-step explanation:
Mean = 79 ; Standard deviation = 7
P(x ≥ 93)
We obtain the ZSCORE :
Zscore = (x - mean) / standard deviation
x = 93
Zscore = (93 - 79) / 7 = 2
P(Z ≥ 2) = 0.02275
Help me!! Which statement is correct?
Answer:
D option is correct
( At Q3 the market is wasting society's .. )
20.
168
Which equation matches the graph? Click on the picture
enlarge.
126
84
42
0
0
6 12
18
24
b) y = 42x
a) y = 7x
D c) y= 6x
d) y = 2x
What is a reasonable estimate for the area of a circle with radius 4cm?
Answer:
Option D
Explanation:
The real answer would be a bit higher if you use the formula:
Area=π×r^2
Rick used 4 2/3 yards of fabric to sew 3 1/2 shirts. What is the unit rate of cloth he used in terms of yards per shirt?
The graph shows a 6-sided polygon on the coordinate plane. The polygon has k = 1.5. In the spaces below, enter the coordinates of B’ and C’.
Answer:
[tex]B' = (-3,-3)[/tex]
[tex]C' = (-4.5,-7.5)[/tex]
Step-by-step explanation:
Given
[tex]k = 1.5[/tex]
[tex]B = (-2,2)[/tex]
[tex]C =(-3,-5)[/tex]
Required
B' and C'
This is calculated as;
[tex]B' = k * B[/tex]
[tex]B' = 1.5 * (-2,-2)[/tex]
[tex]B' = (-3,-3)[/tex]
and
[tex]C' =k * C[/tex]
[tex]C' = 1.5 * (-3,-5)[/tex]
[tex]C' = (-4.5,-7.5)[/tex]
Find the area of a regular
polygon with 6 sides that has a
perimeter of 42 inches and an
apothem of 5 inches,
Answer:
The area of a regular polygon is A = (1/2)ap, where a is the apothem and p is the perimeter of the polygon.
The apothem is 8 inches and the perimeter is 6(7) = 42 since there are 7 sides of 6 inches.
Then the area is
A = (1/2)(8)(42) = 336/2 = 168 in2
I hope this helped!
Step-by-step explanation:
Mark me as brainlist pleasee
you spend $40 on a meal for you and your friends. Sandwiches cost $5 and beverages cost $2 each. Write and equation in standard form where x is the number of sandwiches purchased and y is the number of beverages posted.
Which of the following logarithmic expressions have been evaluated correctly, to the nearest hundedth? Select all that apply.
A. log3 8 = 0.43
B. log3 6 = 1.63
C. log4 5 = 1.16
D. log2 32 = 1.51
Answer:
b
Step-by-step explanation:
ive done it before
The area of a garden plot is 432m2 .If the length is 24 m, what is the width?
Answer:
18m
Step-by-step explanation:
Width= 432m2 ÷ 24m
= 18m
Answer:
Step-by-step explanation:
432m^2 / 24m = 18 m is the width of the garden plot
The volume of a cylinder can be expressed as V=πr2h, where r is the radius, and h is the height of the cylinder. Which expression represents the volume of this cylinder?
h= 2x+7 r=x-3
Answer:
The answer is V= ([tex]\pi[/tex]) ([tex]x-3^{2}[/tex]) (2x+7).
Step-by-step explanation:
To find the volume of the cylinder, plug in the information given in the question into the formula for the volume of a cylinder, which is V = [tex]\pi[/tex] [tex]r^{2}[/tex] h.
800 is 1/10 of-----------?
The local pavilion is hosting an outdoor concert. There are both lawn seats and reserved seating available. Lawn seats cost
$10, while reserved seats are $25. A sponsoring business has given the school $375 to purchase seats. If the school
purchased 30 seats using all of the money, how many lawn seats and how many reserved seats did the sponsoring business
purchase?
The business purchased ____ lawn seats and _______ reserved seats
Let the lawn seats purchased by the business be : L
Let the reserved seats purchased by the business be : R
Given :
⊕ Cost of each lawn seat : $10
⊕ Cost of each reserved seat : $25
⊕ Sponsoring business has given the $375 to purchase seats
⊕ School purchased 30 seats using all of the money
⇒ L + R = 30 ---------- (1)
⇒ 10L + 25R = 375 ----------- (2)
Multiplying equation (1) with 10, we get :
⇒ 10L + 10R = 300 ------------- (3)
Subtracting equation (3) from equation (2), we get :
⇒ 10L + 25R - (10L - 10R) = 375 - 300
⇒ 25R - 10R = 75
⇒ 15R = 75
⇒ R = 5
Substituting R = 5 in equation (1), we get :
⇒ L + 5 = 30
⇒ L = 25
Answer: The Business purchased 25 lawn seats and 5 reserved seats
1 point
1. To win a prize, Jada must get a ball with an even number. Should she try
to win the prize using the tank of table tennis balls or the tank of golf balls?
A large fish tank is filled with table tennis balls with numbers written on them. Jada chooses 10
table tennis balls from the tank and writes down their numbers.
1
3
5
1
3.
2
4
1
5
3
A second tank is filled with golf balls with numbers written on them. Jada chooses 10 golf balls
from the tank and writes down their numbers.
1
4
5
2
6
2
2.
1
4
8
O Jada should use the tank of tennis balls.
O Jada should use the tank of golf balls.
1b. Explain your reasoning."
3 points
Your answer
Answer:
Jada should use the tank of golf balls
Step-by-step explanation:
Jada should choose the tank that has a higher probability of choosing a ball with even number from.
Tank of tennis balls has two even numbers out of the ten balls (2, 4)
Tank of golf balls has seven even numbers out of the ten balls.
Tank of golf balls would give Jada more chance to pick an even number to win the game
Therefore, Jada should use the tank of golf balls
what is a circumference of a circle with a dimeter of 1 inch (use 3.14)
Given diameter = 1 inch
radius= D/2 = 1/2 = 0.5 inch
Circumference of circle = 2πr = 2×3.14×0.5= 3.14 inch
Answer circumference of a circle is 3.14 inch
Given the statement “If a line is horizontal, then it has slope equal to zero,” what is its contrapositive?
Answer:
"If the line has a slope that is not 0, then the the line is not horizontal".
Step-by-step explanation:
The contrapositive of "If p then q" is "If not q then not p".
p=a line is horizontal
not p= a line that is not horizontal
q=the line has a slope equal to zero
not q=the line has a slope that is not zero
The equivalent statement in contrapositive form is therefore:
"If the line has a slope that is not 0, then the the line is not horizontal".
The lifetime of a certain brand of battery is known to have a standard deviation of 9 hours. Suppose that a random sample of 90 such batteries has a mean lifetime of 38.9 hours. Based on this sample, find a 90% confidence interval for the true mean lifetime of all batteries of this brand.
Answer:
lower limit : 36.44
upper limit : 39.56
Step-by-step explanation:
Given :
s = 9
n = 90
x = 38.9
Alpha, α = 0.10
∴ [tex]$z_{\alpha/2}=z_{0.05} = 1.645$[/tex]
The confidence interval is :
[tex]$=x \pm\left(z_{\alpha /2} \times \frac{s}{\sqrt{n}}\right)$[/tex]
[tex]$=38.9 \pm\left(1.645 \times \frac{9}{\sqrt{90}}\right)$[/tex]
[tex]$=38.9 \pm 1.56$[/tex]
[tex]$=(36.44, 39.56)$[/tex]
Therefore,
lower limit : 36.44
upper limit : 39.56
Help me ASAP plzzz……
Answer:20, 40, 40,100
Step-by-step explanation:
5x+2x+2x=180 9x=180 x=20
Complete the problems in measurements. Show answers in simplest terms.
b. Allan has 5 boxes of baseballs. Each box contains 2 dozen balls. He wants to divide the balls between 6 teams. How many balls will each team receive?
Answer:
20 balls to each team
Step-by-step explanation:
If 5 boxes contains 2 dozens
And 2 dozens= 24
Multiply boxes by dozens of balls
5×24=120
Then to share, you divide it buy the number of teams
120÷6= 20 balls
HELP ASAP PLEASE!!!
Answer:
the function g because the graphs the graphs of f and g are symmetrical about the line y=x
Step-by-step explanation:
Inverse functions are symmetrical to each other about the line y=x. This means that if you flip a function over y=x, that will be its inverse function. It makes sense because inverse functions turn the input of the original function (x) into the output of the inverse function (y), so y=x and x=y. Take the point (-6,0) on f, it becomes (0,-6) on g.
Maya read 40 pages in 60 minutes
A variable expression cannot consist of numbers or operstions. true false
Answer:
False
Step-by-step explanation:
A variable expression can contain numbers (that work alongside the variables) and operations (that describe how the numbers and variables interact)
What is the equation, written in vertex form, of a parabola with a vertex of (–2, 6) that passes through (1, –3)?
Answer:
Step-by-step explanation:
( x - 1 )2 + ( y + 3 )2 = 90
Please help me! I will give you Brainlist if you get it right!
Answer:
B
Step-by-step explanation:
Find the area of the circle with r = 36/2 Area1 = π r²
divide Area1 by two since the upper part of the figure is a semi-circle
then finally add and area of the rectangle Area2 = (18)(36)
Total area = Area 1 + Area 2
Answer:
1156.7 cm^2
Step-by-step explanation:
for finding area of semi circle
diameter=36 cm
radius=diameter/2
=36/2
=18 cm
area of semi circle=πr^2/2
=3.14*(18)^2/2
=3.14*324/2
=1017.36/2
=508.68 cm^2
area of rectangle=length*breadth
=18 cm *36 cm
=648 cm^2
area of the figure=area of semi circle + area of rectangle
=508.68 + 648
=1156.68
=1156.7 cm^2
gold that is 24 karat is 100% pure gold. gold that is 14 karat is 14 parts pure gold and 10 parts another metal, such as copper,zinc,silver, or nickel. What percent of 14 karat gold if pure gold.
help im confused
Dhani has 4 cards numbered 1 through 4. He removes 2 cards at random and adds their values.
What is the probability that the sum is less than or equal to 5?
7/12
2/3
3/5
3/4
Answer:
[tex]2/3[/tex]
Step-by-step explanation:
The total number of sums (not distinct) is [tex]4\cdot 3=12[/tex], because we're removing without replacement.
Count the sums that fit the stipulation (sum [tex]\leq[/tex] 5):
[tex]1,2,\\2,1\\1,3\\3,1\\1, 4\\4, 1\\2, 3, \\3,2[/tex]
There are 8 sums that work. Therefore, the desired answer is [tex]\frac{8}{12}=\boxed{\frac{2}{3}}[/tex]
please answer thank you
The answer is surface area of composite shape= 411.8 Cm²
Find the median of the following data 9,15,17,18,6,20,8,5,18,18,10,5,14,12,10,7
Answer:
11
Step-by-step explanation:
first, sort the numbers from lowest to highest.
5,5,6,7,8,9,10,*10,12*,14,15,17,18,18,18,20
the median is the number in the middle of the data
average if you need to (10+12 and divide by 2)
