Answers
Related Questions
An isosceles trapezoid has bases of 4 and 10. If the base angle is 45°, find the area.
A: 42 sq. units
B: 21√2 sq. units
C: 21 sq. units
Answers
DC, the larger one (=10)
From A & B draw the altitude AA' & BB'. You notice that ABA'B' is a rectangle and A'B' = 4,. You conclude that DA' = B'C = 3 .
Now let's calculate the altitude AA'.
The right triangle ADA' is also an isosceles right triangle:
( angle DA'A=90, angle ADA' = 45 and angle DAA' =45) , then
DA' = AA' (altitude) = 3 units. Now we can calculate the area of the trapezoid:
Area = (B+b).H/2
Area = (4+10)x3/2 = 14x3/2 = 42/2 = 21 sq.unit
Answer:
21 sq. units
Step-by-step explanation:
The area of a certain rectangle is 288 yd2. the perimeter is 68 yd. what are the dimensions of the rectangle?
Answers
P = 68
68 = 2(L + W)
68/2 = L + W
34 = L + W
34 - L = W
A = L * W
A = 288
W = 34 - L
288 = L(34 - L)
288 = 34L - L^2
L^2 - 34L + 288 = 0
(L - 16)(L - 18)
L - 16 = 0
L = 16
L - 18 = 0
L = 18
not exactly sure which (length or width) , but one is 16 yds and one is 18 yds
The dimensions of the rectangle are a length of 16 yds and a width of 18 yds.
What is the area of the rectangle?The area of a rectangle is defined as the product of the length and width.
The area of a rectangle = L × W
Where W is the width of the rectangle and L is the length of the rectangle
Given that the perimeter is 68 yd
We know that the perimeter of a rectangle is:
P = 2(L + W)
∴ P = 68
68 = 2(L + W)
68/2 = L + W
34 = L + W
34 - L = W ....(i)
The area of a rectangle is:
A = L × W ....(ii)
∴ A = 288
Substitute the value W = 34 - L in equation (ii), and solve for L
288 = L(34 - L)
288 = 34L - L²
L² - 34L + 288 = 0
(L - 16)(L - 18)
L - 16 = 0 and L - 18 = 0
L = 16 and L = 18
Take L = 16 and substitute the value in the equation (i)
So, W = 34 - 16 = 18
Therefore, the rectangle's length is 16 yds and its width is 18 yds.
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Generally, how would one work out the surface area of a frustum?
Answers
see the formula in the picture
R is larger diameter, r is smaller diameter
It doesn't matter which of the two points on a line you choose to call (x1, y1) and which you choose to call (x2, y2) to calculate the slope of the line.
A. True
B. False
Answers
A. True
EXPLANATION
Let
[tex](x_1,y_1) = (1,2)[/tex]
and
[tex](x_2,y_2) = (2,3)[/tex]
be two points on the straight line.
Then the slope is given by
[tex]m = \frac{y_2-y_1}{x_2-x_1} [/tex]
This implies that,
[tex]m = \frac{3 - 2}{2 - 1} = \frac{1}{1} = 1[/tex]
Let us now choose it the other way round,
[tex](x_1,y_1) = (2,3)[/tex]
[tex](x_2,y_2) = (1,2)[/tex]
Then the slope is,
[tex]m = \frac{2 - 3}{1 - 2} = \frac{ - 1}{ - 1} = 1[/tex]
We still had they same result. Hence it doesn't matter which one you choose to call
[tex](x_1,y_1)[/tex]
and which to call
[tex](x_2,y_2) [/tex]
Answer:
the answer is true
Step-by-step explanation:
it's what I got
Which is the best approximation for the value of √102?
A.10
B.11
C.50
D.51
Answers
which would be round to 10 because after the decimal the number is 0 below 5 so 10 stays as 10
so √102 is approximately 10
How can x2 = x2 + 2x + 9 be set up as a system of equations?
Answers
Final answer:
To set up x^2 = x^2 + 2x + 9 as a system of equations, we would have x^2 = x^2 + 2x + 9 and x = -4.5.
Explanation:
To set up x2 = x2 + 2x + 9 as a system of equations, we can separate it into two separate equations:
Equation 1: x2 = x2 + 2x + 9
Equation 2: 0 = 2x + 9
By rearranging Equation 2, we can rewrite it as:
x = -4.5
Therefore, the system of equations for x2 = x2 + 2x + 9 is: x2 = x2 + 2x + 9 and x = -4.5.
What is the value of
x/3y, when x = 18 and y = 3?
Answers
x=18 and y=3
[tex]\frac{18}{(3)(3)}=\frac{18}{9}=2[/tex]
this has been asked at least 3 times so far today
18/3*3 = 18/9 = 2
answer is 2
a gas-filled balloon rises 40 feet in the 1st minute, 60 feet in the 2nd minute, and 80 feet in the 3rd minute, how many feet will the balloon rise during the 15th minute?
Answers
so
[tex]g_1=40[/tex] ft , means that in the 1st minute, the balloon rose 40 feet
[tex]g_2=60[/tex] ft, means : in the 2nd minute the balloon rose 60 feet
[tex]g_3=80[/tex]
we notice that each minute, the balloon rises a multiple of 20, feet:
[tex]g_1=40=2*20[/tex]
[tex]g_2=60=3*20[/tex]
[tex]g_3=80=4*20[/tex]
so it is clear that [tex]g_n=(n+1)*20[/tex]
during the 15th minute the balloon rises [tex]g_1_5=16*20=320[/tex](feet)
Answer: 320
you invest 2,600 in an account that pays an interest rate of 8.5% compounded continuously. Calculate the balance of your account after 5 years
Answers
A=p e^rt
A future value?
P present value 2600
R interest rate 0.085
T time 5years
E constant
A=2,600×e^(0.085×5)
A=3,976.94
The cost of painting a circular traffic sign is $3.50 per square foot. How much, to the nearest dollar, will it cost to paint the sign if its diameter measures 36 INCHES.
Answers
area of a circle = pi x r^2
using 3.14 for pi
radius = 36/2 =18
area = 3.14 x 18^2 = 1017.36 square inches
1 sq ft = 144"
1017.36/144 = 7.065 sq ft
7.065*3.50 = $24.73 to the nearest dollar = $25
What is the slope of the line shown below?
Answers
Answer:
correct option is B) 2
Step-by-step explanation:
Slope of line is calculated by formula :-
Suppose two points on line are [tex](x_1, y_1) and (x_2 ,y_2)[/tex] then slope 'm' is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex].
We can see two points on line of graph are :- (-1, -4) and (2,2)
then slope will be calculated as,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
since [tex]x_1 = -1, x_2 =2, y_1=-4\;and\; y_2=2[/tex]
now, put in formula
[tex]m=\frac{2-(-4)}{2-(-1)}[/tex]
[tex]m=\frac{2+4}{2+1}[/tex]
[tex]m=\frac{6}{3}[/tex]
[tex]m=2[/tex]
Hence, slope is 2 of the provided graph.
Therefore, correct option is B) 2
There are 26.2 in a marathon .Write the number of miles using a fraction.
Answers
26.2 = 20+6+0.2
The decimal value 0.2 is read two tenth = 2/10
Writing 26.2 as mixed numbers
[tex]26.2=26 \frac{2}{10} [/tex]
If we want to write this as an improper fraction, multiply 26 by 10 then add the 2 to get the numerator
[tex]26.2 = 26 \frac{2}{10}= \frac{262}{10}= \frac{131}{5} [/tex]
A number is chosen at random from the integers between 11 and 99, inclusive. what is the probability that the number contains the digit 2?
Answers
The standard form of the equation of a parabola is x=y^2+6y+1. What is the vertex form of the equation?
A. X=(y+3)^2-8
B. X=(y+3)^2-5
C. X=(y+6)^2-35
Answers
What you want to do is get the quadratic (y^2+6y+1) into it's root factor form, in other words, the quantity of (y+what) squared will equal y^2+6y+1. Well it's not a perfect square so we'll have to play around with it a little.
In the format ay^2 + by + c, completing the square first requires finding out what value would do that: c = (b/2)^2 = (6/2)^2 = 3^2 = 9
So we need y^2+6y+1 to have the last number (c) to equal 9 to have (y+b/2)^2, or (y+3)^2
How do we get 9 down to the 1 that we have for c?? 9-1=8, so just subtract 8.
That means that y^2+6y+1 is the same as (y^2+6y+9)-8, and y^2+6y+9 = (y+3)^2, so now we have: y^2+6y+1 = (y+3)^2-8, which is answer [A]
Express the sum of 8.79 m and 6.0 m using the correct number of significant digits.
Answers
8.8 in this cas, so
8.79 + 6.0 = 8.8 + 6.0 = 14.8
14.8 is the answer
Answer:
The sum of the numbers is [tex]8.79+6.0=14.79[/tex]
Step-by-step explanation:
To find : Express the sum of 8.79 m and 6.0 m using the correct number of significant digits.
Solution :
Writing the sum of the numbers according to significant digits by writing in their place value,
8 . 7 9
+6 . 0 0
----------
14 . 7 9
Therefore, The sum of the numbers is [tex]8.79+6.0=14.79[/tex]
PLEASE HELP!!!! Solve the equation. Check for extraneous solutions. Type your answers in the blanks. Show your work.
x = _____ or _____
Answers
16x^2+24x+9=81+36x+4x^2 subtract the right side from both sides
12x^2-12x-72=0 now we can factor
12(x^2-x-6)=0
12(x^2+2x-3x-6)=0
12(x(x+2)-3(x+2)=0
12(x-3)(x+2)
So:
x= -2 or 3
Answer:
-3
Step-by-step explanation:
if two triangles share a common side what else must be true for the SAS triangle congruence theorem to apply
Answers
The conditions to be added are:
The two triangles have congruent angles between the sides that are not the common side.
The two triangles have congruent lengths for the sides adjacent to the congruent angles.
What is a triangle?A triangle is a 2-D figure with three sides and three angles.
The sum of the angles is 180 degrees.
We can have an obtuse triangle, an acute triangle, or a right triangle.
We have,
The SAS (Side-Angle-Side) triangle congruence theorem states that if two triangles have two sides and the included angle of one triangle is congruent to two sides and the included angle of the other triangle, then the two triangles are congruent.
Therefore, in addition to sharing a common side, the two triangles must have congruent angles between the sides that are not the common side. Specifically, the angle opposite the common side must be congruent in both triangles.
To summarize, for the SAS triangle congruence theorem to apply, the following conditions must be met:
The two triangles share a common side.
The two triangles have congruent angles between the sides that are not the common side.
The two triangles have congruent lengths for the sides adjacent to the congruent angles (the "included" side).
Thus,
The conditions to be added are:
The two triangles have congruent angles between the sides that are not the common side.
The two triangles have congruent lengths for the sides adjacent to the congruent angles.
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what is the vaule of 3.85+0.004+0.117 ?
Answers
Let f(x) = 16x5 − 48x4 − 8x3 and g(x) = 8x2. Find f of x over g of x.
Answers
2x^3-6x^2-x
It is given in the question that
[tex]f(x) = 16x^5 -48x^4-8x^3 \ and \ g(x) = 8x^2[/tex]
And we have to find the value of
[tex]\frac{f(x)}{g(x)}[/tex]
Substituting the values of two functions, we will get
[tex]=\frac{16x^5 -48x^4 -8x^3}{8x^2}[/tex]
8x^3 is common in the numerator, and on taking it out, we will get
[tex]= \frac{8x^3(2x^2 -6x-1)}{8x^2} = x(2x^2 -6x-1)[/tex]
And that's the required answer .
Solve the problem by writing an inequality. A club decides to sell T-shirts for $12 as a fund-raiser. It costs $20 plus $8 per T-shirt to make the T-shirts. Write and solve an equation to find how many T-shirts the club needs to make and sell in order to profit at least $100. Show your work.
Answers
Profit = Revenue - (Fixed Cost + Variable Cost)
You should note that the limit for profit is at least $100. So that means it can be more than $100 but can't be less than. Therefore, the symbol to be used is greater than or equal to, symbolized by ≥. Then the equation is
12x - (20 + 8x) ≥ 100, where x represents the minimum number of t-shirts to reach a profit of at least $100. Solving the equation,
12x - 20 - 8x ≥ 100
12x - 8x ≥ 100 + 20
4x ≥ 120
x ≥30
Therefore, the club needs to sell at least 30 shirts.
A researcher wishes to find out whether giving a student $1 million in cash will improve or ruin the student's grades in school. A high school class consists of the 8 students numbered in the following list. 0 Juanita 1 Tuan 2 Harry 3 Greta 4 William 5 Hiroshi 6 Betty 7 Jane Help the researcher by using the line from a table of random numbers (shown below) to assign 4 of these students to the treatment group. 39661 55832 02589 52612 25414 19879 60880 30641 55259 35324 Which students go in the treatment group?
Answers
Answer:
Greta, Betty, Tuan and Hiroshi
Step-by-step explanation:
Start from the beginning:
3 - Greta
Then, continue with the next numbers:
9 - skip (there is no student numbered with a 9)
6 - Betty
6 - skip (Betty is already chosen)
1 - Tuan
5 - Hiroshi
A survey asked 30 people what their favorite genre of television broadcasting was, and the results were tabulated above. Find the probability that a person chosen at random was female, given that they like comedy. Round the answer to the nearest hundredth.
Answers
The probability that a person chosen at random is female, given they like comedy, is approximately 0.53 or 53% .
First, let's find the total number of females who like comedy. In the Venn diagram, there are 8 females who like comedy. There are also 7 males who like comedy. So, there are 15 people who like comedy in total.
Next, we need to determine the total number of females. There are 16 females who like drama, and 4 females who like sports. Adding these together, we get 20 females in total.
Now, we can calculate the conditional probability that a female likes comedy given that she was chosen at random. The formula for conditional probability is P(A|B) = P(AnB) / P(B). In this case, event A is "being female" and event B is "liking comedy."
P(A|B) = (Number of females who like comedy) / (Total number of people who like comedy)
P(A|B) = 8 / 15
To express this as a percentage, multiply by 100:
P(A|B) * 100 ≈ 0.5333
Rounded to the nearest hundredth, the probability is 0.53 or 53%.
The probability that a person chosen at random is female, given they like comedy, is approximately 0.53 or 53% .
First, let's find the total number of females who like comedy. In the Venn diagram, there are 8 females who like comedy. There are also 7 males who like comedy. So, there are 15 people who like comedy in total.
Next, we need to determine the total number of females. There are 16 females who like drama, and 4 females who like sports. Adding these together, we get 20 females in total.
Now, we can calculate the conditional probability that a female likes comedy given that she was chosen at random. The formula for conditional probability is P(A|B) = P(AnB) / P(B). In this case, event A is "being female" and event B is "liking comedy."
P(A|B) = (Number of females who like comedy) / (Total number of people who like comedy)
P(A|B) = 8 / 15
To express this as a percentage, multiply by 100:
P(A|B) * 100 ≈ 0.5333
Rounded to the nearest hundredth, the probability is 0.53 or 53%.
Branliest and 30 points to who answers first
To make one dose chispa put 2 drops of a herbal remedy into a 30 ml bottle and adds spring water he has now used 54 drops of the 120 that the full bottle contained how many more times can chispa use his herbal remedy
Answers
Find the equation of the line specified.
The slope is 3, and it passes through ( -4, -7).
a.
y = 6x + 5
c.
y = 3x - 7
b.
y = 3x + 5
d.
y = 3x - 19
Please select the best answer from the choices provided
A
B
C
D
Answers
B. y = 3x + 5
Answer:
B
Step-by-step explanation:
Edge 2021
what is the greatest integer that satisfies the inequality 3x-4≤8 ?
A.4
B.5
C.6
D.7
Answers
3x ≤ 12
x ≤ 4
answer
A.4
For example, answer choice "A.)";
3(4) -4 <_ 8
We plugged in 4 for x.
Let's see if A.) is correct.
3(4) -4 <_ 8
12 - 4 <_ 8
8 <_ 8
This is the GREATEST possible integer, as the question asks for what the highest possible number would match the inequality.
Your correct answer choice is "A.)"
I hope this helps!
Find the area of the triangle with the given measurements. round the solution to the nearest hundredth if necessary. b = 107°, a = 10 cm, c = 22 cm
Answers
Answer:
105.19 cm²
Step-by-step explanation:
The applicable area formula is ...
area = (1/2)ac·sin(B) = (1/2)(10)(22)sin(107°) ≈ 105.19 cm²
1 oz of walnuts were mixed with 4 oz of peanuts which cost $4/oz to make mixed nuts which cost $5/oz. what is the price per oz of walnuts
Answers
total cost of walnuts = 1oz * w
Total cost of peanuts = 4 oz * $4/oz = $16
Total cost of nuts = 5oz * $5 /oz = $25
=> 1oz*w + $16 = $25 => w = ($25 - $16) /1oz = $9/oz
Verfify:
1oz * $9/oz + 4oz * $4/oz = $9 + $16 = $25, which is equal to 5oz * $5/oz.
Answer: $9 per oz.
Suppose you toss a coin 100 times and get 76 heads and 24 tails. based on these results, what is the probability that the next flip results in a head?
Answers
The probability that the next flip results in a head is 50% or 0.5.
We have,
Total number of coins tossed = 100
Number of heads outcome = 76
Number of tails outcome = 24
Now,
The probability of getting heads in the tossing of coins 100 times.
= 76/100
= 0.76
= 76%
Now,
Generally for an unbiased coin.
The probability of getting a head in tossing a coin is 50%.
So,
Based on the results of the first 100 coin tosses, even if the probability of getting a head is 76% the probability that the next flip results in a head is still 50%.
Thus,
The probability that the next flip results in a head is 50% or 0.5.
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HELPPPPPP make sure your right !:)
Answers
(04.02 LC)
The graph represents function 1 and the equation represents function 2:
Function 2
y = 3x + 1
How much more is the rate of change of function 2 than the rate of change of function 1?
1
2
3
4
Answers
y=3 it has a slope of zero.
Function 2 is
y=3x+1, it is in slope-intercept form, y=mx+b where m is the slope and b is the y=intercept so in this case it has a slope of 3.
So the difference in slopes is 3-0=3
The rate of change of function 2 is 3 times greater than the rate of change of function 1.
Explanation:The rate of change of a function measures how much the output of the function changes when the input changes by 1 unit. In function 1, since the graph is a straight line, the rate of change is constant. We can find the rate of change of function 1 by finding the slope of the line, which represents the rate of change. In function 2, the equation is y = 3x + 1, so the rate of change is 3. Therefore, the rate of change of function 2 is 3 times greater than the rate of change of function 1.
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