Answer:
For a function y = f(x), the range is the set of all the possible values of y.
In the question you wrote:
y = secx - 2
This can be interpreted as:
y = sec(x - 2)
or
y = sec(x) - 2
So let's see each case (these are kinda the same)
If the function is:
y = sec(x - 2)
Firs remember that:
sec(x) = 1/cos(x)
then we can rewrite:
y = 1/cos(x - 2)
notice that the function cos(x) has the range -1 ≤ y ≤ 1
Then for the two extremes we have:
y = 1/1 = 1
y = 1/-1 = -1
Notice that for:
y = 1/cos(x - 2)
y can never be in the range -1 < x < 1
As the denominator cant be larger, in absolute value, than 1.
Then we can conclude that the range is all reals except the interval:
-1 < y < 1
If instead the function was:
y = sec(x) - 2
y = 1/cos(x) - 2
Then with the same reasoning, the range will be the set of all real values except:
-1 - 2 < y < 1 - 2
-3 < y < -1
Can someone help me with this
Answer:
Step-by-step explanation:
The formula for this, specific to our circle, is
∠RQP = [tex]\frac{1}{2}[/tex](arc SP - arc RP) and filling in:
∠RQP = [tex]\frac{1}{2}(170-86)[/tex] and
∠RQP = [tex]\frac{1}{2}(84)[/tex] so
∠RQP = 42°
Combine these radicals.
-3/81 + 16
-23
0 0 0
-11
-3797
-3.713
Need answers please
Step-by-step explanation:
-23 is the answer
√18=9
√16=4
-3×9+4= -23
Answer:
-23 is right on edg
Step-by-step explanation:
Which of the following models the rising population of a city with 8,000 residents when the annual growth rate is 4%?
Answer:
P = 8000[tex](1 + .04)^{t}[/tex] where t is the number of years
Step-by-step explanation:
Below is a histogram representing the test scores from Mrs. Smith's 3rd period Algebra class. Which set of scores below could be represented by this histogram?
Answer:
82,83,84,80,84,86,91,96,95,99,97,92
3. PLEASE HELP ME
Solve the equation using square roots.
x2 + 10 = 9
A. 1
B. ±√1
C. no real number solutions
D. –1
Answer:
C. no real number solutions
Step-by-step explanation:
Subtract 10 from both sides.
Since the square of a number, x, equals a negative number, -1, the answer cannot be a real number because the square of a real number is always non-negative. Therefore, there is no real number solution to this equation.
Answer: B. no real number solutions
no real number solutions
f(x)=square root 2x and g(x)=square root 50x find (f/g)(x)
Answer:
1/5
Step-by-step explanation:
(f/g)(x) = f(x)/g(x) = sqrt(2x)/sqrt(50x) = 1/5
Anyone help please I need it
Answer:
[tex]-10+i\sqrt{2}[/tex]
Step-by-step explanation:
One is given the following expression:
[tex]\sqrt{4}-\sqrt{-98}-\sqrt{144}+\sqrt{-128}[/tex]
In order to simplify and solve this problem, one must keep the following points in mind: the square root function ([tex]\sqrt{}[/tex]) is a way of requesting one to find what number times itself equals the number underneath the radical sign. One must also remember the function of taking the square root of a negative number. Remember the following property: ([tex]\sqrt{-1}=i[/tex]). Simplify the given equation. Factor each of the terms and rewrite the equation. Use the square root property to simplify the radicals and perform operations between them.
[tex]\sqrt{4}-\sqrt{-98}-\sqrt{144}+\sqrt{-128}[/tex]
[tex]\sqrt{2*2}-\sqrt{-1*2*7*7}-\sqrt{12*12}+\sqrt{-1*2*8*8}[/tex]
Take factors from out of under the radical:
[tex]\sqrt{2*2}-\sqrt{-1*2*7*7}-\sqrt{12*12}+\sqrt{-1*2*8*8}[/tex]
[tex]2-7i\sqrt{2}-12+8i\sqrt{2}[/tex]
Simplify,
[tex]-10+i\sqrt{2}[/tex]
Blanca runs 8 laps around the track each day to train for an endurance race. She times each lap to practice her pacing for the race. The table shows the lap times, in seconds, for three days of practice.
A 3-column table with 8 rows. The first column is labeled day 1 lap times (seconds) with entries 83, 92, 91, 89, 94, 93, 88, 84. The second column is labeled day 2 lap times (seconds) with entries 87, 90, 92, 91, 92, 95, 90, 85. The third column is labeled day 3 lap times (seconds) with entries 85, 86, 91, 93, 91, 89, 88, 84.
Which histogram represents Blanca’s lap times for the three days of practice?
A graph shows lap time (seconds) labeled 82 to 98 on the horizontal axis and number of laps on the vertical axis. 1 lap was 82 to 84 seconds. 4 laps were 84 to 86 seconds. 2 laps were 86 to 88 seconds. 4 laps were 88 to 90 seconds. 6 laps were 90 to 92 seconds. 5 laps were 92 to 94 seconds. 2 laps were 94 to 96 seconds. 0 laps were 96 to 98 laps.
A graph shows lap time (seconds) labeled 82 to 98 on the horizontal axis and number of laps on the vertical axis. 1 lap was 82 to 84 seconds. 3 laps were 84 to 86 seconds. 3 laps were 86 to 88 seconds. 5 laps were 88 to 90 seconds. 5 laps were 90 to 92 seconds. 3 laps were 92 to 94 seconds. 3 laps were 94 to 96 seconds. 1 lap was 96 to 98 seconds.
A graph shows lap time (seconds) labeled 82 to 98 on the horizontal axis and number of laps on the vertical axis. 1 lap was 82 to 84 seconds. 3 laps were 84 to 86 seconds. 3 laps were 86 to 88 seconds. 4 laps were 88 to 90 seconds. 6 laps were 90 to 92 seconds. 4 laps were 92 to 94 seconds. 2 laps were 94 to 96 seconds. 1 lap was 96 to 98 laps.
A graph shows lap time (seconds) labeled 82 to 98 on the horizontal axis and number of laps on the vertical axis. 1 lap was 82 to 84 seconds. 4 laps were 84 to 86 seconds. 2 laps were 86 to 88 seconds. 4 laps were 88 to 90 seconds. 6 laps were 90 to 92 seconds. 3 laps were 92 to 94 seconds. 4 laps were 94 to 96 seconds. 0 laps were 96 to 98 laps.
Answer:
A graph shows lap time (seconds) labeled 82 to 98 on the horizontal axis and the number of laps on the vertical axis. 1 lap was 82 to 84 seconds. 4 laps were 84 to 86 seconds. 2 laps were 86 to 88 seconds. 4 laps were 88 to 90 seconds. 6 laps were 90 to 92 seconds. 5 laps were 92 to 94 seconds. 2 laps were 94 to 96 seconds. 0 laps were 96 to 98 seconds
Step-by-step explanation:
The given table is presented as follows;
[tex]\begin{array}{ccc}Day \ 1 \ lap \ times \ (seconds)&Day \ 2 \ lap \ times \ (seconds)&Day \ 3 \ lap \ times \ (seconds)\\83&87&85\\92&90&86\\91&92&91\\89&91&93\\94&92&91\\93&95&89\\88&90&88\\84&85&84\end{array}[/tex]The number of laps in the range 82 to 84 seconds = 1
The number of laps in the range 84 to 86 seconds = 4
The number of laps in the range 86 to 88 seconds = 2
The number of laps in the range 88 to 90 seconds = 4
The number of laps in the range 90 to 92 seconds = 6
The number of laps in the range 92 to 94 seconds = 5
The number of laps in the range 94 to 96 seconds = 2
The number of laps in the range 96 to 98 seconds = 0
Therefore, the histogram that represents Blanca's lap times for the three days of practice is described as follows;
A graph shows lap time (seconds) labeled 82 to 98 on the horizontal axis and the number of laps on the vertical axis. 1 lap was 82 to 84 seconds. 4 laps were 84 to 86 seconds. 2 laps were 86 to 88 seconds. 4 laps were 88 to 90 seconds. 6 laps were 90 to 92 seconds. 5 laps were 92 to 94 seconds. 2 laps were 94 to 96 seconds. 0 laps were 96 to 98 seconds
Answer: A.
Step-by-step explanation: On Edge!
Please help me. I have no idea to this question.
a) 3ax+3ay-bx-by
b) 10ay²-5by²+2a²y-aby
Answer:
a)3a(x+y)-b(x+y)
=(3a-b)(x+y)
b)5y(2ay-by)+a(2ay-by)
=(5y+a)(2ay-by)
Franklin used the polynomial expression x(x−3)(x+4) to model the volume of a rectangular prism. What is the length of the shortest side of this prism? A x B x−3 C x2−3x D x3+x2−12x
Answer:
[tex]x - 3[/tex]
Step-by-step explanation:
Given
[tex]Volume = x(x - 3)(x + 4)[/tex]
Required
The shortest side
The volume of a rectangular prism is:
[tex]Volume = Length * Width * Height[/tex]
By comparison, we have:
[tex]Length = x[/tex]
[tex]Width = x-3[/tex]
[tex]Height = x + 4[/tex]
In ascending order, the sides are:
[tex]Width = x-3[/tex]
[tex]Length = x[/tex]
[tex]Height = x + 4[/tex]
This is so because:
Irrespective of the value of x
x - 3 will be less than x
x + 4 will be more than x
Hence, the shortest length is:
[tex]Width = x-3[/tex]
Answer:
b
Step-by-step explanation:
Find the volume of a sphere with a diameter of 15 cm
Answer:
V= 562.5 pi cm^3 or approximately 1766.25 cm^3
Step-by-step explanation:
If the diameter is 15, the radius is d/2 = 15/2 = 7.5
The volume of a sphere is
V = 4/3 pi r^3
V = 4/3 ( pi ) (7.5) ^3
V= 562.5 pi
If we use the approximation of 3.14 for pi
V = 1766.25 cm^3
HELPPPPPPPP MEEEEE PLEASEEEE
Step-by-step explanation:
a rectangle has two pairs of equally long sides and each of the 4 angles between the sides is 90 degrees.
given that ABCDEF is a regular hexagon, it means that all its sides are equally long, and therefore also all internal angles are the same size.
that means for ACDF that the sides DC and FA are equally long.
DEF and ABC are congruent triangles, as the sides DE = BC, EF = AB, and the angle E is congruent to angle B.
based on the SAS criteria this confirms that DF is congruent to AC.
the angles ACB, CAB, EDF and EFD have to be all the same, and therefore also the angles FDC, DCA, CAF and DFA.
so, all 4 angles of the parallelogram ACDF are the same, and the sum of all these angles has to be 360 degrees, we have
360 = 4×angle
angle = 90 degree.
so, all angles are 90 degrees and we have two pairs of equally long sides : this process that ACDF us a rectangle
find the value of a and b if 5+√3/7+2√3=a-b√3
Answer:
Step-by-step explanation:
find the value of a and b if 5+√3/7+2√3=a-b√3
A group of students is arranging squares into layers to create a project. The first layer has 5 squares. The second layer has 10 squares. Which formula represents an arithmetic explicit formula to determine the number of squares in each layer ?
Answer: Its B i just took the test
Step-by-step explanation:
Helpppp pleaseeee !!!!!!
Answer:
149 inches squared
Step-by-step explanation:
top rectangle: 25 * 7 = 175
second rectangle: 8 * (25 - 17) = 8^2 = 64
triangle in bottom right: 1/2 * (13 - 8) * (15 - 11) = 10
175 + 64 + 10 = 149 sq in
hopefully got this right!
Solve the mean for the data set. (4,11,25,1,17,34,11,30)
A. 12
B. 14.5
C. 16.6
D. 18.9
Answer:
The mean is C. 16.6
Step-by-step explanation:
the mean is the average, to find the average add all the numbers together and divide by the amount of numbers
4+11+25+1+17+34+11+30=133
133/8 = 16.6
if U= π(r+h), find r when U =16/1/2 and h = 2/3/4
π = 3/1/7
Answer:
r = 2.5
Step-by-step explanation:
U= π(r+h)
Where,
U = 16 1/2
h = 2 3/4
π = 3 1/7
U= π(r+h)
16 1/2 = 3 1/7(r + 2 3/4)
33/2 = 22/7(r + 11/4)
33/2 = 22/7r + (22/7 * 11/4)
33/2 = 22/7r + 242/28
33/2 - 242/28 = 22/7r
(462-242) / 28 = 22/7r
220/28 = 22/7r
r = 220/28 ÷ 22/7
= 220/28 × 7/22
= (220 * 7) / (28 * 22)
= 1540/616
= 2.5
r = 2.5
work out the area of a semicircle take pi to be 3.142 11cm
Answer:
if the diameter is 11, them the answer is 47.52275cm
Which Venn Diagram is NOT correct?
Please help!![tex]2^x=\sqrt{2}[/tex]
factorize: xy-3x - 5y + 15
Answer:
Step-by-step explanation:
xy-3x-5y+15
x(y-3)-5(y-3)
(y-3)(x-5)
find x...............................
Answer:
sqrt(2) =x
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp/ hyp
sin 45 = x/2
2 sin 45 =x
2 ( sqrt(2)/2) =x
sqrt(2) =x
WHO CAN HELP ME WITH THIS QUESTION
Answer:
No
Step-by-step explanation:
These two triangles aren't similar. The left triangle angle measures are 30,60,90. The left triangle measure is 35,55,90.
The side lengths aren't proportional as well. These triangles not similar.
Answer: I'm not sure but
similar : no
similarity statement: it's not similar because the corresponding angle of the two triangle are different
scale factor : 8/4 = 2 ( so, triangle ABC is 2 times the size of triangle LMN)
Step-by-step explanation:
Find the area of the figure.
we observe that this figure could be divided into a triangle and a rectangle.
for the area of the triangle, bxh/2, we have 15 x 12/2 = 90
and for the rectangle, we have 5 x 12 = 60
so, 90 + 60 = 150
hope it helps :)
whats the area in square inches
Answer:
Area of triangle =1/2b×h
1/2×10×8.7
=44 square inches
Answer:
44
Step-by-step explanation:
The area of a triangle is given by
A = 1/2 bh
where b is the base and h is the height
A = 1/2 (10) (8.7)
A= 43.5
Rounding to the nearest whole number
A = 44
Father is four times the age of his daughter. If after 5 years, he would be 3 times of daughter's age, then further after 5 years, how many times he would be of his daughter's age?
Answer:
The father is 40 years old, and his daughter is 10 years old.
Step-by-step explanation:
Given that a father is four times the age of his daughter, and after 5 years, he would be 3 times of daughter's age, then further after 5 years, to determine how many times he would be of his daughter's age, the following calculation must be done:
F = 4D
F + 5 = 3D
F = 40
D = 10
40 + 5 = 3 x (10 + 5)
45 = 45
Therefore, the father is 40 years old, and his daughter is 10 years old.
There are 7 blue counters, 3 green counters and 1 red counter in a bag.
There are no other counters in the bag.
Hubert takes at random 2 counters from the bag.
Work out the probability that both counters are blue.
Answer:
21/55
Step-by-step explanation:
7 blue counters, 3 green counters and 1 red counter = 11 counters
1st counter
P(blue)= blue / total = 7/11
Now there are only 10 counters
6 blue counters, 3 green counters and 1 red counter = 10 counters
2nd counter
P(blue)= blue / total = 6/10 = 3/5
P(blue blue) = 7/11 * 3/5 = 21/55
In this truss bridge, AAOB ABDC. AO=5 meters, BD=10 meters, AB=5 meters. What is the length of BC? A. 5 m B. 8 m C. 10 m D. 15 m
Consider [tex]\Delta AOB\cong \Delta BDC[/tex].
Given:
[tex]\Delta AOB\cong \Delta BDC, AO=5\ m,BD=10\ m, AB=5\ m.[/tex]
To find:
The length of BC.
Solution:
We have,
[tex]\Delta AOB\cong \Delta BDC[/tex]
We know that the corresponding parts of congruent triangles are congruent (CPCTC).
[tex]AB=BC[/tex] (CPCTC)
[tex]5\ m=BC[/tex]
The length of BC is 5 m. Therefore, the correct option is A.
Which of the following have a total of 8 possible outcomes? Check all that apply.
Answer:
Probably the first three answers
Step-by-step explanation:
The rest are
4) 3×5=15 (which is not 8)
5) 6×2=12 (≠8)
So it's just the first three
Find the value of x. Round to the nearest tenth.
Answer:
x=5.9
Step-by-step explanation:
tan(26)=x/12. x=12*tan(26)=5.9
