Answers
The diagonal length will be 7 x 2 = 14yd
Area of one triangle = 1/2 x 14 x 7 = 49 yd²
Area of the polygon = 2 x triangles
Area of the polygon = 2 x 49
Area of the polygon = 98 yd²
Answer: The regular polygon is 98 yd²
Related Questions
For what values of b will F(x) = logb x be an increasing function?
A. b < 0
B. b > 0
C. b < 1
D. b > 1,
Answers
logb x = n is the equivalent of asking "you should raise the base b to what number n in order to get x?": bⁿ = x
From this follows that b must be positive, otherwise the function is not defined everywhere in R: for example, take log(-2) x = 0.5 ? This means: [tex] (-2)^{1/2} [/tex] =√(-2) which is impossible in R.
Therefore, both answers A and C are not correct because they take in consideration negative values.
If we take the base between 0 and 1 excluded, we have a fraction whose denominator is bigger than the numerator. Such a fraction, elevated to increasing exponents get smaller, for example:
(1/2)² = 1/4
(1/2)³ = 1/8
(1/2)⁴ = 1/16
Therefore the function is dereasing and answer B is incorrect.
The right answer is, therefore, D) b > 1.
Final answer:
The logarithmic function F(x) = logb x is an increasing function when the base b is greater than 1, because the value of logb x increases as x increases for b > 1.(Option D)
Explanation:
The question asks for what values of b will F(x) = logb x be an increasing function. To determine this, we need to understand the behavior of logarithmic functions based on their base value (b). A logarithmic function is increasing if the base of the logarithm is greater than 1. This is because as x increases, the value of logb x increases when b>1. Conversely, if b<1 (but b>0), the function is decreasing because the power to which b must be raised to produce x decreases as x increases. We also know that the base of a logarithm cannot be negative or zero, as this would not produce a valid logarithmic function.
Therefore, the correct answer is D. b > 1, where the logarithmic function F(x) = logb x is an increasing function.
Can anyone answer this for me?
Answers
All you need to do is count the spaces between each line of the numerator and then the same with the denominator.
19. You can see that there are 4 spaces between Point A and Point B. There are 6 spaces between point A and Point C. So if you will get ratio you will get:
[tex] \frac{4}{6} [/tex] Then you simplify the expression.
[tex] \frac{2}{3} [/tex]
20. There are 2 spaces from points B to C. There are 3 spaces from points C to D. So the ration then will be:
[tex] \frac{2}{3} [/tex]
This is already in its simplest form. You may be wondering why we did not count from 0. This is because the reference point for the two lines are given. For the first it is B and for the second is C.
21. Moving on to number 21. The distance from point B to D is 5 spaces, and the distance from point A to E is 12 spaces. So you can say that the ratio would be:
[tex] \frac{5}{12} [/tex] Again, this is already in its simplest form.
22. To get the geometric mean between two numbers you first need to multiply them and then get the square root:
STEP 1: Multiply 7 and 28
7 x 28 = 196
STEP 2: Get the square root of the product
√196 = 14
14 is the geometric mean.
23. Simplifying ratios is relatively easy. When you simplify the ratio between two values that are of different units, you first need to make both units the same.
In your case, we need to either convert 10ft to inches or convert 30 inches to feet. So we will not come up with a decimal, let us just convert 10 ft into inches.
[tex] 10 ft [/tex] x [tex] \frac{12in}{1ft} [/tex] = 120 inches
So our new ratio is:
[tex] \frac{120in}{30in} [/tex]
Now we simplify it to its simplest form:
[tex] \frac{4in}{1in} [/tex]
24. The two figures are what we call similar figures. This means that the lengths of each side are proportional to their corresponding sides.
AB is proportional to line FG.
AB = 4 and FG =8
This means that the sides of ABCDE is half the lengths of the sides of FGHJK. Thus we can say that the perimeter of ABCDE is half the perimeter of FGHJK
To get the perimeter of a polygon, all you have to do is add all the sides.
Let's get the perimeter of FGHJK
8 + 8 + 10 + 12 + 10 = 48
Half of 48 =24
So the perimeter of ABCDE is 24
If you want to double check your answer you can get the sides of polygon of ABCDE by getting half of each corresponding side.
AB = 4
BC = 4
CD = 5
DE = 6
EA = 5
If you get the sum of all sides, you can get the perimeter:
4 +4 +5 + 6 + 5 = 24
What is the value of x?
Answers
4x^2 = 100
x^2 = 25
x = 5
answer
5 units
MATH HELP PLEASE LOOK AT THE PICTURES BELOW!!!
5 QUESTIONS
Answers
The equation is in form y=mx+b
m is the slope and b is the y-intercept
Slope: -6 and y-intercept: 2
2)
The equation is in form y=mx+b
m is the slope and b is the y-intercept
Slope: 1 and y intercept: -3
3)
C = 14d + 3
4)
8x + 6y = 12
6y = -8x + 12
y = -4/3 + 2
5)
First change the equation to y=mx+b form.
4x + 6y = 12
6y = -4x + 12
y = -2/3x + 2
Slope: -2/3
Hope that helps :)
Which pair of times has the longest elapsed time between the two times?
3:05 to 9:40
8:35 a.m. to 2:35 p.m.
4:25 to 10:45
7:10 p.m. to 1:40 a.m.
What is the elapsed time between 9:30 p.m. and 2:15 a.m.?
7 hours and 45 minutes
5 hours and 15 minutes
4 hours and 45 minutes
4 hours and 15 minutes
Subtract 1 hour, 50 minutes from 4 hours, 10 minutes.
2 hours, 20 minutes
2 hours, 40 minutes
3 hours, 40 minutes
3 hours, 30 minutes
Answers
.. 14:35 -8:35 = 6:00
.. 10:45 -4:25 = 6:20
.. 13:40 -7:20 = 6:30
b) 14:15 -9:30 = 5:(-15) = 4:45 (3rd selection)
c) 4:10 -1:50 = 3:(-40) = 2:20 (1st selection)
Find the perimeter of the rectangle.
If the rectangle has vertices M(−2,4), N(1,5), O(3,−1), and P(0,−2), what is the perimeter of the rectangle?
Round each side length to the nearest tenth, if necessary.
Answers
Evaluate the function below for x = 2 F(x) = 4x3 - x2 - 5x + 7
Answers
Answer:
The value of the given function is 25 for x = 2.
Step-by-step explanation:
Given function is,
[tex]F(x) = 4x^3 - x^2 - 5x + 7[/tex]
At x = 2,
The value of the function is,
[tex]f(2)=4(2)^3-(2)^2-5(2)+7[/tex]
[tex]=4(8)-4-10+7[/tex]
[tex]=32 - 7[/tex]
[tex]=25[/tex]
Hence, the value of the given function is 25 for x = 2.
If a circle has an diameter of 14, what would the area be?
Use 3.14 for π
Answers
A = 3.14 x 7^2
A = 3.14 x 49
A = 153.86
answer
153.86
If 5x-4=26 what does the x equal
Answers
------------------------------------------------
Add 4 to both sides:
------------------------------------------------
5x - 4 + 4 = 26 + 4
5x = 30
------------------------------------------------
Divide by 5 on both sides:
------------------------------------------------
5x ÷ 5 = 30 ÷ 5
x = 6
------------------------------------------------
Answer: x = 6
------------------------------------------------
Tom caught 4 fish and his son caught 12 fish.
The number of fish that Tom caught was what percent of the number of fish that his son caught?
Answers
To solve this problem, we need to divide 4 by 12.
4 ÷ 12 = 1/3
1/3 = 33.33%
Hope this helps!
according to the tree diagram below what is the probability that someone buys a book that is paperback and fiction
Answers
see the attached figure to better understand the problem
we know that
[tex]0.65\ (65\%)[/tex] of the buyers buy paperback and [tex]0.45\ (45\%)[/tex] of them buy fiction.
Hence
The probability that they buy both fiction and paperback is equal to
[tex]0.65*0.45=0.2925[/tex]
the answer is
[tex]0.2925[/tex]
-7x^6*(-2x^8) will mark as brainiest
SIMPLIFY!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
DO NOT SOLVE FOR X
Answers
50 POINTS!!!!! HELPFor the exponential function f(x)=a^x,a>0,a≠1 what is the domain? what is the range?
Answers
There are no minus y values.
0<y< infinity y is included in the reals.
The domain is
- infinity < x < infinity.
I don't want to say that either x or y can equal - or + infinity. Some teachers allow it. You have to ask your instructor what they will accept.
The blue line is y = 4^x
The red line is y = 2^x
Jalen traded $4100 for Mexican pesos, immediately changed his mind, and then promptly traded his Mexican pesos back into dollars. Which of these amounts is he most likely to have?
A. More than $0 but less than $4100
B. $0
C. $4100
D. More than $4100
Answers
Because, when currency is exchanged for another currency, the bank or trader usually charges commission for changing it.
APEX APEX APEX APEX APEX APEX APEX APEX APEX APEX
More than $0 but less than $4100
help plsss need this for tomorrow
Answers
12 + 1x = 8 + 2x
We do this, because there are already some of each color in the bag. 1x makes one counter each and 2x is two counters for every blue counter in the bag. Let's solve it. Subtract 1x from each side. 1x - 1x cancels out. 2x - 1x is 1x or just simply x. That simplifies to 12 = 8 + x. Subtract 8 from each side to get the variable by itself. 8 - 8 cancels out. 12 - 8 is 4. That leaves 4 = x. Nothing else needs to be done. Let's plug the value in and see if it works. 1 * 4 is 4. 12 + 4 is 16. 2 * 4 is 8. 8 + 8 is 16. 16 = 16. There. x = 4. 4 blue counters and 8 green counters were added to the bag.
what is the sum of the arithmetic series 18 t=1 (3t-4)
a. 234
b. 441
c. 25.5
d. 49
Answers
The given arithmetic series is
[tex] \sum_{t=1}^{18} (3t-4) [/tex]
When t =1, we will get the first term,a, which is
[tex] 3(1)-4 =3-4=-1 [/tex]
When t =18, we will get the last term,l , which is
[tex] 3(18)-4 = 50 [/tex]
Now we use the formula of sum of n terms which is
[tex] S = \frac{t}{2} (a+l) [/tex]
Substituting the values of t,a and l, we will get
[tex] S = \frac{18}{2} (-1+50) = 9*49 =441 [/tex]
Consider the arithmetic series [tex] _{t=1}\Sigma^{t=18} (3t-4) [/tex]
Let t=1 in the given series, we get
first term = [tex] a_{1} [/tex] = 3-4 = -1.
Let t=2 in the given series, we get
second term = [tex] a_{2} [/tex] = [tex] (3 \times 2)-4 = 2 [/tex]
Let t=3 in the given series, we get
third term = [tex] a_{3} = (3 \times 3)-4=5 [/tex]
Now, let t=18 in the given series, we get
last term = l = [tex] l = (3 \times 18)-4 = 50 [/tex]
We get the series as
-1, 2, 5,..... 50
Sum = [tex] \frac{n}{2}(a+l) [/tex]
= [tex] \frac{18}{2}(-1+50) [/tex]
= [tex] = 9 \times 49 [/tex]
= 441
Therefore, the sum of the given arithmetic series is 441.
Line r passes through points (2, 11) and (10, 4). Line s is perpendicular to r. What is the slope of line s?
Answers
------------------------------------------------------
Work Shown:
Use the slope formula to find the slope of line r
m = (y2-y1)/(x2-x1)
m = (4-11)/(10-2)
m = -7/8
The slope of line r is -7/8
Now we take the negative reciprocal. In other words, we flip the fraction and flip the sign from negative to positive.
Flip the fraction: -7/8 ---> -8/7
Flip the sign: -8/7 ----> +8/7
The slope of line s is 8/7
Note how multiplying the slope of line r (-7/8) and the slope of line s (8/7) yields -1. Multiplying any two perpendicular slopes leads to a product of -1. This is excluding vertical lines as the slope is undefined.
How far does a ball that is hit from a height of 3 feet at a speed of 120 feet per second travel before it hits the ground if it is hit at an angle of 45 degrees? Round your answer to the nearest integer.
A) 376 Feet
B) 395 Feet
C) 426 Feet
D) 453 Feet
Answers
It is convenient to solve for the time of flight, then compute the distance traveled in that time. The ball is in the air about 5.338 seconds.
Select ALL the correct answers.
The square of the sum of a number and 6 plus twice the number is equal to 189.
Which equations could be used to represent this relationship?
(3x + 6)2 = 189
(x + 6)2 + 2x = 189
(x + 6)2 = 189 + 2x
x2 + 10x + 36 = 189
x2 + 14x + 36 = 189
x2 + 2x + 6 = 189
Answers
Answer:
[tex](x+6)^{2}+2x=189[/tex]
and
[tex]x^{2}+14x+36=189[/tex]
Step-by-step explanation:
Let
x -----> the number
we know that
The equation that represent the situation is
[tex](x+6)^{2}+2x=189\\ \\x^{2} +12x+36+2x=189\\ \\x^{2}+14x+36=189[/tex]
therefore
The equations that could be used are
[tex](x+6)^{2}+2x=189[/tex] and [tex]x^{2}+14x+36=189[/tex]
Answer:
(x+6)^{2}+2x=189
and
x^{2}+14x+36=189
Step-by-step explanation:
HELP ASAP WILL MARK AS BRAINILEST TO WHOEVER GETS IT RIGHT
Answers
Kevin goes fishing every Saturday. The table below shows the number of fish he caught each week for the last six weeks.
Fish Caught
Week Number of Fish
1 4
2 0
3 2
4 8
5 4
6 6
What is the mean absolute deviation of the data above?
A. 8
B. 2
C. 4
D. 1
Answers
One number is one less than five times another. if their sum is decreased by three, the result is eight. find the numbers.
Answers
One number is one less than five times another ....
Let one number be x
The other number is 5x - 1
Their sum ...
x + 5x - 1 = 6x - 1
Their sum is decreased by 3
6x - 1 - 3 = 6x - 4
The result is eight
6x - 4 = 8
6x = 8 + 4
6x = 12
x = 2
x = 2
5x - 1 = 5(2) - 1 = 9
One number is 2 and the other is 9.
What is the slope-intercept form for each equation in this system? Compare the slopes and y-intercepts to describe the graph of the system. 3x - 4y = 28 4x + 10y = 20 A) y = 3 4 x − 7; y = −2 5 x + 2; one line B) y = - 3 4 x − 7; y = −2 5 x + 2; parallel lines Eliminate C) y = 3 4 x − 7; y = 2 5 x + 2; intersecting lines D) y = 3 4 x − 7; y = −2 5 x + 2; intersecting lines
Answers
4x + 10y = 20
First we rewrite the system of equations:
Equation 1:
3x - 4y = 28
3x - 28 = 4y
(3/4) x - 7 = y
Equation 2:
4x + 10y = 20
10y = 20 - 4x
y = 2 - (2/5) x
We have then:
y = (3/4) x - 7
y = - (2/5) x + 2
One line has a positive slope and the other line has a negative slope.
Thus, both lines are connected.
Answer:
D) y = 3/4 x - 7; y = -2/5 x + 2; intersecting lines
The slope - intercept form of the equations are : [tex]y = \frac{3}{4} x - 7 [/tex] and [tex]y = - \frac{2}{5} x + 2[/tex]
Given the standard form of the equations :
3x - 4y = 28 - - - - (1)4x + 10y = 20 - - - - - (2)The General form of a slope - intercept equation :
y = bx + cFor equation (1) :
3x - 4y = 28
Make y the subject
-4y = 28 - 3x
Divide both sides by - 4 to isolate y
y = -7 + 3/4x
[tex]y = \frac{3}{4} x - 7 [/tex]
For equation (2) :
4x + 10y = 20
Make y the subject
10y = 20 - 4x
Divide through by 10 to isolate y
y = 2 - 2/5x
[tex]y =- \frac{2}{5} x + 2[/tex]
Hence, the slope - intercept equations are : [tex]y = \frac{3}{4} x - 7 [/tex] and [tex]y = - \frac{2}{5} x + 2[/tex]
Learn more :
The asymptote of the function f(x) = 3x + 1 – 2 is_________ . Its y-intercept is_____ .
Options for the first blank is
y= -2
y= -1
y= 1
y= 2
Options for the second is
(0,-2)
(0,-3)
(0,1)
(0,-1)
Answers
Answer:
In first blank : y = - 2,
In second blank : ( 0, 1 )
Step-by-step explanation:
Given function is,
[tex]f(x)=3^{x+1}-2[/tex]
The horizontal asymptote of the function f(x),
[tex]y=lim_{x\rightarrow \infty} f(x)[/tex]
[tex]y=lim_{x\rightarrow \infty} 3^{x+1}-2[/tex]
[tex]y=3^{\infty+1}-2[/tex]
[tex]y=3^\infty - 2[/tex]
[tex]y=0-2[/tex]
⇒ y = -2
First option is correct.
Also, the function has no vertical asymptote,
2. For finding the y-intercept, x = 0,
[tex]f(0)=3^{0+1}-2=3-2=1[/tex]
Hence, the y-intercept = (0,1)
Third option is correct.
Final answer:
The function f(x) = 3x + 1 – 2 is a linear function and does not have an asymptote, contrary to the options provided. The y-intercept is found by setting x to 0, which results in the point (0, – 1).
Explanation:
The function in question is f(x) = 3x + 1 – 2. To determine its asymptote and y-intercept, we analyze its structure.
Since this is a linear function and not a rational function, it does not have an asymptote like those found with rational functions, whose denominators can become zero. Instead, the original function is a modification of the function f(x) = 3x, with vertical shifts up by 1 and down by 2, effectively canceling each other out. Therefore, the asymptote is essentially the x-axis, which can be represented by the equation y = 0. However, since none of the provided options include y = 0, and the function we are analyzing is, in fact, linear without any asymptotes, there must be an error in the question regarding this part.
To find the y-intercept, we set x equal to 0 and solve for f(0):
f(0) = 3(0) + 1 – 2 = 1 – 2 = – 1.
Therefore, the y-intercept of the function is the point (0, – 1).
Can anyone help me!?!?!?!?! Here is my question:
Compare the functions shown below:
f(x) = 4 sin (2x − π) - 1
g(x)
x y
-1 6
0 1
1 -2
2 -3
3 -2
4 1
5 6
h(x) = (x − 2)2 + 4
Which function has the smallest minimum y-value?,
Answers
g(x) obviously has a minimum value of -3.
h(x) has a squared term that cannot be negative, so its minimum value is +4.
f(x) has the smallest minimum value.
Please help!! Which of the following could represent the scale factor of the smaller figure to the larger figure?
Smaller figures volume is 216in.^3
Larger figures volume is 343in.^3
Answers
The scale factor from the smaller figure to the larger figure is found by taking the cube root of the ratio of their volumes, which is the cube root of 216/343.
Explanation:The student asked: Which of the following could represent the scale factor of the smaller figure to the larger figure? When comparing the volumes of two geometric figures, we can determine the scale factor of their linear dimensions by understanding the relationship between volume and linear scale factor.
Given that the smaller figure's volume is 216 cubic inches and the larger figure's volume is 343 cubic inches, we are looking for the cube root of the ratio of these volumes to find the linear scale factor.
To find the scale factor from the smaller figure to the larger figure, divide the volume of the smaller figure by the volume of the larger figure and then calculate the cube root: Scale factor = ∛(216/343). This calculation will give you the scale factor of the linear dimensions from the smaller figure to the larger figure.
3. A prop for the theater club’s play is constructed as a cone topped with a half-sphere. What is the volume of the prop? Round your answer to the nearest tenth of a cubic inch. Use 3.14 to approximate pi.
Answers
[Volume of a cone]=pi*r²*h/3
and
[Volume of a half-sphere]=(4/6)*pi*r³
then
h=14 in
r=9 in
[Volume of a cone]=pi*r²*h/3-------------> pi*9²*14/3------------> 1186.92 in³
[Volume of a half-sphere]=(4/6)*pi*r³--------->(4/6)*pi*9³------> 1526.04 in³
the volume of the prop=1186.92+1526.04--------> 2712.96 -----------> 2713 in³
the answer is 2713 in³
I have the same problem but with 14 being 15 in and 9 being 7 in, can someone help?
Can someone please help? In the circle at right, AZB is a(n): (A) minor arc, (B) central angle, (C) major arc, (D) arcezoid, or (E). None of these? Thanks
Answers
In this question it has been clearly indicated that AZB is to be taken as an arc. This is because there is the arc symbol on top of AZB. Thus, we have [tex] \overarc{AZB} [/tex] and we need to answer what does the arc [tex] \overarc{AZB} [/tex] represent.
As we can see from the diagram, by visual inspection, that AZ is the chord which is lesser than the diameter and AZB is the segment on that lesser side of the circle. Therefore, the arc [tex] \overarc{AZB} [/tex] must be the minor arc.
Therefore, Option A, minor arc is the correct answer.
Solve by factoring write the steps.
x2−7x+10=0
Please help show me all the steps and the answers
Answers
Step 1: Factor left side of equation.
(x−2)(x−5)=0
Step 2: Set factors equal to 0.
x−2=0 or x−5=0
x=2 or x=5
Answer: x=2 or x=5
The middle term should be factored in such a way that the sum of two numbers is -7x and their product is 10x2. These two factors are -5x and -2x. So re-writing the equation, we get:
[tex] x^{2} - 5x - 2x +10 = 0[/tex]
Taking common, we get:
[tex]x( x - 5) -2 (x-5)=0 \\ \\ (x-5)(x-2)=0[/tex]
This means:
x - 5 = 0
⇒ x = 5
or
x - 2 = 0
⇒ x = 2
Therefore, the solution to the given equation are x = 2 and x = 5
Help Help Help!!! :)
solve the system of equations y=2x^2-3 y=3x-1
Answers
y = 2x^2 - 3 ---- equation 1
y = 3x - 1 ------equation 2
Then we get,
2x^2 - 3 = 3x - 1
Now, simplifying the equation, we get
2x^2 - 3x - 3 + 1 = 0
2x^2 - 3x - 2 = 0
After factoring the equation, we get
(2x+1)(x-2) = 0
So, this means
(2x+1) = 0 and (x-2) = 0
From this, we get
x = -1/2 and x = 2
Putting values of x = -1/2 in equation 2
y = 3(-1/2) - 1
y = -2.5
Now, putting value of x = 2 in equation 2
y = 3(2) -1
y = 5