Answer: -1 1/2 < -1/4
Explanation: Since the number is negative, -1 1/2 is further to the left on the number line, meaning it has less value.
The relationship between -1 1/2 and -1/4 can be expressed as an inequality. In this case, -1 1/2 is less than -1/4, so the inequality is -1 1/2 < -1/4.
Explanation:The relationship between -1 1/2 and -1/4 may be written as an inequality. Remember, an inequality indicates that one number is larger or smaller than another. In this case, it shows which negative number, either -1 1/2 or -1/4, is larger. On the number line, a negative number situated to the right is larger than a number situated to the left. So, in terms of value, -1/4 is larger than -1 1/2 as it's less negative. This can be written as:
-1 1/2 < -1/4
.
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Please answer right awat
Answer:
The correct answer option is 0.2.
Step-by-step explanation:
We are given that there are 3 red marbles and 3 green marbles in an opaque bag.
If two marbles are chosen one after one without replacement, we are to find the probability of getting both green marbles.
P (1st green marble) = [tex] \frac { 3 } { 6 } [/tex]
P (2nd green marble) = [tex] \frac { 2 } { 5 } [/tex]
P (both green marbles) = [tex] \frac { 3 } { 6 } \times \frac { 2 } { 5 } [/tex] = 0.2
Answer:
i think its forty
Step-by-step explanation:
im sorry if its wrong
Ieda bakes 73 cupcakes and accidentally drops 5 of them. She divides them equally into 13 containers for a bake sale for the school band. How many cupcakes does Ieda have left
Answer:
3 left
Step-by-step explanation:
If she starts out with 73 and drops 5 she is left with 68, an you cannot evenly divide 68 and 13 so you divide it as much as you can evenly which is five containers leaving 3 extra cupcakes.
For this case we have that initially there are 73 cupcakes, if Leda dropped 5 then we are left with:
[tex]73-5 = 68[/tex]
Now, you must equally divide the 68 cupcakes into 13 containers:
putting 5 cupcakes in each of the 13 containers we have;
[tex]13 * 5 = 65[/tex]
[tex]68-65=3[/tex]
So, we have 3 cupcakes left.
Answer:
3 cupcakes
What is the degree of x4 – 3x + 2?
Answer: 4
Step-by-step explanation:
The degree is the highest exponent , in which in this problem it is 4. The 3x counts as an exponent of 1 because the variable x is 1, and the 2 counts as an exponent of zero. Which means the degree is 4.
what are two division expressions that have the same value as 61.12 divided by 3.2
Answer:
Other division expression that have the same value as 61.12 divided by 3.2 are
122.24 divided by 6.4 AND
183.36 divided by 9.6
Step-by-step explanation:
61.12/3.2 = 19.1
Other division expression that have the same value as this:
122.24/6.4 = 19.1
183.36/9.6 = 19.1
What is the cosine ratio for angle F?
Check the picture below.
kieran is flying a kite. he gets tired, so he stakes the kite into the ground. the kite is on a string that is 18 feet long and makes a 30 degree angle with the ground. how high is the kite
see if u understand, note that the degree is 90
The height of the kite is 9 feet.
Trigonometric ratio is used to show the relationship between the sides of a triangle and its angles.
Let h represent the height of the kite. Hence, using trigonometric ratios:
sin(30) = h / 18
h = 9 feet
Therefore the height of the kite is 9 feet.
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What is the volume of the cylinder?
A.
600π ft3
B.
720π ft3
C.
300π ft3
D.
60π ft3
Answer:
300π ft^3
Step-by-step explanation:
let's use the volume of a cylinder formula:
π*r^2*h
π=3.14
r=5
h=12
since we need to solve in terms of pi, do not plug the value of pi into the formula
π*5^2*12= 300π
300π
What is the area of the regular hexagon? This is due tomorrow please help! :)
Check the picture below.
so then, the perimeter of that hexagon will just be the sum of all its 6 sides, or namely 3⅖ + 3⅖ + 3⅖ + 3⅖ + 3⅖ + 3⅖, or just 6( 3⅖ ).
[tex]\bf \textit{area of a regular polygon}\\\\ A=\cfrac{1}{2}ap~~ \begin{cases} a=apothem\\ p=perimeter\\[-0.5em] \hrulefill\\ a=3\\ p=6\left(3\frac{2}{5} \right) \end{cases}\implies A=\cfrac{1}{2}(3)\left[ 6\left(3\frac{2}{5} \right) \right]\implies A=\cfrac{1}{2}(3)\left[ 6\left(\cfrac{17}{5} \right) \right] \\\\\\ A=\cfrac{1}{2}(3)\left(\cfrac{102}{5} \right)\implies A=\cfrac{1}{2}\left( \cfrac{306}{5} \right)\implies A=\cfrac{153}{5}\implies A=30\frac{3}{5}[/tex]
What is the vertical asymptote of this function?
Answer:
D
Step-by-step explanation:
If y = log x is the basic function, let's see the transformation rule(s):
Then,
1. y = log (x-a) is the original shifted a units to the right.
2. y = log x + b is the original shifted b units up
Hence, from the equation, we can say that this graph is:
** 2 units shifted right (with respect to original), and
** 10 units shifted up (with respect to original)
only, left or right shift affects vertical asymptotes.
Since, the graph of y = log x has x = 0 as the vertical asymptote and the transformed graph is shifted 2 units right (to x = 2), x = 2 is the new vertical asymptote.
Answer choice D is right.
PLEASE HELP RIGHT AWAY
Answer:
203 minutes
Step-by-step explanation:
This can be expressed as an arithmetic sequence, that is
20, 23, 26, 29,...
With first term a = 20 and common difference d = 3
The sum to n terms of an arithmetic sequence is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a + (n - 1)d ], hence
[tex]S_{7}[/tex] = [tex]\frac{7}{2}[/tex] [ (2 × 20) + (6 × 3) ]
= 3.5 ( 40 + 18) = 3.5 × 58 = 203
Solve for a!
264=π×a×(20-a)
Thank you!
Answer:
a ≈ 14 or 6
Step-by-step explanation:
264 = π × a × (20 - a)
a(20 - a) = [tex]\frac{264}{Pi}[/tex] ≈ 84 (rounded off to nearest whole number)
Opening the brackets we get;
a² - 20a + 84 = 0
Applying the quadratic formula we get:
a ≈ 14 or 6
the volume of a box is 10000 cm cube. the base is 25cm by 10 cm how tall is the box?
Answer:
40cm
Step-by-step explanation:
1. 10000cm^3/25cm= 400cm^2
2. 400cm^2/10 cm= 40cm
Final answer:
To find the height of the box, divide the volume of the box by the area of the base. In this case, the height is 40 cm.
Explanation:
To find the height of the box, we need to divide the volume of the box by the area of the base. The volume is given as 10000 cm³ and the base has dimensions 25 cm by 10 cm. So, the area of the base is 25 cm * 10 cm = 250 cm². Now, we can find the height by dividing the volume by the area: Height = Volume / Area = 10000 cm³ / 250 cm² = 40 cm.
what is the y-intercept ofa line that has a slope of -3 and passes through (0,-7)
Answer:
y = - 7
Step-by-step explanation:
The y- intercept is the point on the y- axis that the line passes through.
The line passes through the y- axis at (0, - 7), hence
the y- intercept is - 7
Slope-intercept form: y = mx + b [m is the slope, b is the y-intercept or the y value when x = 0 ---> (0 , y)]
Since you know m = -3, you can plug that into the equation
y = mx + b
y = -3x + b To find b, plug in the point they gave you into x and y, but since x = 0, your y-intercept is -7
if the dimensions of a rectangle are decreased by 50%, then the area of the rectangle is decreased by what percent?
The area of the rectangle is decreased by 75%, when the dimensions of a rectangle are decreased by 50%.
What is Area of rectangle?The area of the rectangle is the multiplication of length and width.
Area = l × b
It is given that: length and breadth is by 50%
New Length = l × (1-50/100)
= l × (1-1/2)
= l/2
New Width = b × (1-50/100)
= b × (1-1/2)
= b/2
New area = new length × new width
= (l/2) x (b/2)
= lb/4
Change percent =[tex]\frac{Final Area\;-\; Initial Area}{Initial Area} * 100[/tex]
= [tex]\frac{(lb/4)\;-\; lb}{lb} * 100[/tex]
= (- 3lb)/4× 100
= (-3)/4 × 100
= -75%
Hence, the area decreased by 75 %.
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Final answer:
Decreasing the dimensions of a rectangle by 50% results in a new area that is 25% of the original, equating to a decrease of 75% in the area.
Explanation:
When the dimensions of a rectangle are decreased by 50%, each dimension (length and width) becomes 50% of the original. To determine the effect on the area, you can use the formula for the area of a rectangle, which is Area = length tmes width.
Let's consider the original length to be L and the original width to be W. The original area is L times W. When both dimensions are decreased by 50%, the new length is 0.5L and the new width is 0.5W. Therefore, the new area is (0.5L) times (0.5W), which is 0.25 times (L times W). This means the new area is 25% of the original area, representing a 75% decrease.
The zero of F -1(x) in F(x) = x + 3 is
Answer:
-3
Step-by-step explanation:
We have
y = F(x) = x + 3
so
x = y - 3
so
F⁻¹(y) = y - 3
which we can write
F⁻¹(x) = x - 3
We solve
0 = F⁻¹(x) = x - 3
x = 3
Answer: 3
how many solutions do these equations have
Answer:
[tex]\large\boxed{\bold{one\ solution}\ (1,\ -4)\to x=1,\ y=-4}[/tex]
Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}y=2x-6\\y=-x-3\end{array}\right\\\\\text{These are linear functions. We only need two points to draw a graph.}\\\\\text{Choice two values of x, substitute to the equation,}\\\text{and calculate the values of y.}\\\\y=2x-6\\for\ x=0\to y=2(0)-6=0-6=-6\to(0,\ -6)\\for\ x=3\to y=2(3)-6=6-6=0\to(3,\ 0)\\\\y=-x-3\\for\ x=0\to y=-0-3=0-3=-3\to(0,\ -3)\\for\ x=-3\to y=-(-3)-3=3-3=0\to(-3,\ 0)\\\\\text{Look at the picture}[/tex]
[tex]\text{The intersection of the line is the solution of the system of equations:}\\\\(1,\ -4)\to x=1,\ y=-4[/tex]
One number exceeds another number by 18. Find the numbers if the result of adding their sum and their product is a minimum.
Answer:
8
Step-by-step explanation:
The number is a, another number is b.
a = b + 18 So, b=a - 18
(a+b) + ab
= a + a - 18 + a (a - 18)
= 2a - 18 + a^2 - 18a
{ ax^2 + bx + c }
= a^2 -1 6a - 18 {a = 1b = -16 }
When a = b/-2a = -16/-2*1 = 8
the a^2 - 1ba - 18 is minimum,
So the number is 8
If the diameter of a circle is 6 Inches, what is the area?
if the diameter is 6 units, then the radius is half that, or 3.
[tex]\bf \textit{area of a circle}\\\\ A=\pi r^2~~ \begin{cases} r=radius\\ \cline{1-1} r=3 \end{cases}\implies A=\pi 3^2\implies A=9\pi \implies A\approx 28.27[/tex]
Final answer:
To calculate the area of a circle with a 6-inch diameter, use the radius (3 inches) in the area formula πr² to get an approximate area of 28.274 square inches.
Explanation:
To find the area of a circle with a diameter of 6 inches, we use the formula for the area of a circle, which is πr², where r is the radius of the circle. Since the diameter is 6 inches, we divide by two to find the radius (r = diameter / 2 = 6 / 2 = 3 inches).
Substituting the radius into the formula gives us π(3²) = π(9), and using the approximation π ≈ 3.14159, we find the area to be approximately 28.274 square inches.
The city aquarium got a new tank for their dolphins. The tank is 16 feet high with a radius of 28 feet. Answer these questions about the new dolphin tank.
Approximately how much water will it take to fill the tank?
= 39,408.14 cubic feet (I know this answer just not the second one)
The aquarium needs to purchase a plastic cover for the tank. What should the approximate size of the cover be?
A) 50.27
B) 87.96
C) 804.25
D) 2,463.01
Answer:
This answer would be 2,463.01 "D"
Step-by-step explanation:
The approximate size of the cover will be 2463.01 square feet
What is a cylinder?'A cylinder is a three-dimensional solid that holds two parallel bases joined by a curved surface, at a fixed distance.'
According to the given problem,
The size of the cover of the tank = area of the circle of the tank (approximately)
r = 28 feet
Area of the circle = [tex]\pi r^{2}[/tex]
= [tex]\pi *28^{2}[/tex]
= [tex]2463.01[/tex]
Hence, we have concluded that in order to cover the tank, which is a circular area, the area of the cover has to be approximately 2463.01 square feet.
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9. What is the distance between (5, –2) and (5, 3)?
A. 5 units
B. –5 units
C. 3 units
D. 1 unit
Answer:
The correct answer is option A. 5 units
Step-by-step explanation:
Points to remember
Distance formula
Length of a line segment with end points (x1, y1) and (x2, y2) is given by,
Distance = √[(x2 - x1)² + (y2 - y1)²]
It is given that, two points are
(5, –2) and (5, 3)
To find the distance
(x1, y1) = (5, -2) and (x2, y2) = (5, 3)
Distance = √[(x2 - x1)² + (y2 - y1)²]
= √[(5 - 5)² + (3 - -2)²]
= √[(5)² = 5
Therefore the correct option is Option A 5 units
What proportion results in the equation 9m=10n
It might have come from
9/n = 10/m
Answer: Hi, in the equation 9*m = 10*n the proportion is 9 to 10, which means that 9 times the number m is equal to 10 times the number n.
So n is proportional to m in the way that n= (9/10)*m
and m is proportional to n in the way that m= (10/9)*n
This means that the proportion can be written as 9 to 10, or 9:10.
5. Two similar figures have volumes 27 in.? and 125 in.?. The surface area of the smaller figure is 63 in.. (1 point)
Find the surface area of the larger figure.
O105 in.?
О 136 in.?
О 175 in.?
О292in 2
Answer:
[tex]175\ in^{2}[/tex]
Step-by-step explanation:
step 1
Find the scale factor
we know that
If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube
Let
z----> the scale factor
x----> volume of the larger solid
y----> volume of the smaller solid
[tex]z^{3}=\frac{x}{y}[/tex]
we have
[tex]x=125\ in^{3}[/tex]
[tex]y=27\ in^{3}[/tex]
substitute
[tex]z^{3}=\frac{125}{27}[/tex]
[tex]z=\frac{5}{3}[/tex]
step 2
Find the surface area of the larger solid
we know that
If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared
Let
z----> the scale factor
x----> surface area of the larger solid
y----> surface area of the smaller solid
[tex]z^{2}=\frac{x}{y}[/tex]
we have
[tex]z=\frac{5}{3}[/tex]
[tex]y=63\ in^{2}[/tex]
substitute
[tex](\frac{5}{3})^{2}=\frac{x}{63}[/tex]
[tex]x=\frac{25}{9}*63=175\ in^{2}[/tex]
NEED HELP FAST!!!!!!!!!!
Answer:
A. [tex]h=\dfrac{2A}{b}[/tex]
Step-by-step explanation:
You are given formula
[tex]A=\dfrac{1}{2}bh[/tex]
Multiply this equation by 2 to get rid of fraction:
[tex]2A=bh[/tex]
Divide this equation by b to find h in terms of A and b:
[tex]h=\dfrac{2A}{b}[/tex]
Given: - 1/2x > 6.
Choose the solution set.
{x | x R, x > -12}
{x | x R, x < -12}
{x | x R, x > -3}
{x | x R, x < -3}
Answer:
It's option 2.
Step-by-step explanation:
- 1/2x > 6
Divide both sides by -1/2:
x < -12 (Note the inequality sign flips when we divide by a negative value).
Answer: {x |x ∈ R, x < -12}
Step-by-step explanation:
Given the following inequality:
[tex]-\frac{1}{2}x>6[/tex]
You can find the solution set by solving for the variable "x".
Then, to solve for the variable "x" you need to multiply both sides of the inequality:
[tex](-\frac{1}{2}x)(2)>(6)(2)[/tex]
[tex]-x>12[/tex]
And finally, you must multiply both sides of the inequality by (-1). Notice that the direction of the symbol of the inequality will change:
[tex](-x)(-1)>(12)(-1)[/tex]
[tex]x<-12[/tex]
Therefore, the solution set is: {x |x ∈ R, x < -12}
A sports ball has a diameter of 29 cm . Find the volume of the ball.
The volume is 12 770.05 cubic centimeters (cm3)
12 770.50 cubic centimeters
Examine the following table of points, which are all on a certain line.
x y
−2 4
0 2
1 1
3 −1
What is the slope of this line? Enter your answer as a number, like this: 42, or, if the slope is undefined, enter the lowercase letter "u".
[tex]\bf \begin{array}{|cc|ll} \cline{1-2} x&y\\ \cline{1-2} {-2}~~\ast&{4}~~\ast\\ 0&2\\ 1&1\\ {3}~~\ast&{-1}~~\ast\\ \cline{1-2} \end{array}~\hspace{10em} (\stackrel{x_1}{-2}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-1-4}{3-(-2)}\implies \cfrac{-5}{3+2}\implies \cfrac{-5}{5}\implies -1[/tex]
The slope of this line is -1.
The slope formula is useful:
m = (y2 -y1)/(x2 -x1)
where:
m is the slope of the line
y1 and y2 are the y-coordinates of two points on the line
x1 and x2 are the x-coordinates of the two points on the line
m = (2 -4)/(0 -(-2)) = -2/2 = -1
The slope of this line is -1.
The points on the line drop 1 unit for each 1 unit to the right.
m = rise/run = -1/1 = -1
Which of the following are not trigonometric identities? Check all that apply. A. tan^2x+sec^2x=1. B. sin^2x+cos^2x=1. C. sec^2x-tan^2x=1. D. sec^2x+csc^2x=1.
Answer:
a
Step-by-step explanation:
Answer:
Option (A) and (D) are not trigonometric identities.
Step-by-step explanation:
Option (A ) tan²x + sec²x = 1
Since [tex]tanx =\frac{sinx}{cosx}[/tex] and [tex]secx =\frac{1}{cosx}[/tex]
put these in left hand side of tan²x + sec²x = 1
[tex](\frac{sinx}{cosx})^{2}[/tex] + [tex](\frac{1}{cosx})^{2}[/tex]
[tex](\frac{sin^{2}x}{cos^{2}x})[/tex] + [tex](\frac{1}{cos^{2}x})[/tex]
Take L.C.M of above expression,
[tex](\frac{sin^{2}x + 1}{cos^{2}x})[/tex]
since, sin²x = 1 - cos²x
[tex](\frac{1-cos^{2}x+1}{cos^{2}x})[/tex]
[tex](\frac{2-cos^{2}x}{cos^{2}x})[/tex]
we are not getting 1
so, this is not a trigonometric identity.
Option (A) is correct option
Option (B) sin²x + cos²x = 1
This is an trigonometric identity
Option (C) sec²x - tan²x = 1
Divide the trigonometric identity sin²x + cos²x = 1 both the sides by cos²x so, we get
[tex]\frac{sin^{2}x}{cos^{2}x}+\frac{cos^{2}x}{cos^{2}x}\,=\,\frac{1}{cos^{2}x}[/tex]
[tex]tan^{2}x}+1\,=\,sec^{2}x}[/tex]
subtract both the sides by tan²x in above expression
[tex]tan^{2}x}+1\,-tan^{2}x=\,sec^{2}x-tan^{2}x[/tex]
[tex]1=\,sec^{2}x}-tan^{2}x[/tex]
Hence, this is the trigonometric identity.
Option (D) sec²x + cosec²x = 1
Since [tex]secx =\frac{1}{cosx}[/tex] and [tex]cosecx =\frac{1}{sinx}[/tex]
put these in left hand side of sec²x + cosec²x = 1
[tex](\frac{1}{cosx})^{2}+(\frac{1}{sinx})^{2}[/tex]
[tex]\frac{1}{cos^{2}x}+\frac{1}{sin^{2}x}[/tex]
we are not getting 1
so, this is not a trigonometric identity.
Option (D) is correct option.
Hence, Option (A) and (D) are not trigonometric identities.
Which ratio is equivalent to 9/36
Answer:
1/4
Step-by-step explanation:
Step 1: Find the GCF. List out the factors of the numerator and the denominator. 1, 3, 9 are the factors of 9, while 1, 2, 3, 4, 6, 9, 12, 18, and 36 are the factors of 36. 9 is a common factor of both of them, so the GCF is 9.
Step 2: Divide the numerator and denominator by 9 (the GCF). 9/9 is 1. 36/9 is 4. This means that our fraction is 1/4. The fraction is in simplest form.
Which line is the best model for the data in the scatter plot? I need this question answer really fast and who ever gets it gets a brain list plz I need it ASAP
I think it is bottom right because it goes through the most points.
the area of the rectangular park is 4 1/2 square miles. if the length is 1/2 mile, how wide is the park?
Answer: 9
Step-by-step explanation: 4.5=.5xZ. 4.5/.5=9=z