Answers
Answer:
D. 13Step-by-step explanation:
Remember that in a isosceles trapezoid, its angles on the base are always congruent.
Also, we know by definition that the sum of interior angles of a trapezoid is equal to 360°, so
[tex]2(2x)+2(10x+24)=360\\4x+20x+48=360\\24x=360-48\\x=\frac{312}{24}\\ x=13[/tex]
Therefore, the right answer is D.
Answer: 13
a p e x confirmed
Related Questions
Find to slope of the line passing through the points 0,4 -8,-1
A,-8/5
B,-5/8
C, 5/8
D, 8/5
Answers
First, find the slope.
m=(y₂-y₁)/(x₂-x₁)
m=(-1-4)/(-8-0)
m=(-5)/(-8)
m=5/8 <--- this is positive because a negative divided by a negative is positive)
The correct solution is B.
Hope I helped :)
Gerry is a restaurant manager and plans to advertise her restaurant. The advertising budget is $5000, and she plans to run television and online ads. She would like to run at least 5 television ads and 10 online ads. A television ad costs $500 and an online ad costs $150. Let x represent the number of television ads and y represent the number of online ads. Two of the constraints for this situation are x≥5 and y≥10 . What is the other constraint for this situation?
Answers
We are given the two constraints:
x ≥ 5 and y ≥ 10
Now the other constraint must of course be based on the sum of the two. It was given that the budget is $5000 so the sum must be greater than that, that is:
500 x + 150 y ≤ 5000
What is the factored form of the expression? 4x2 – 81y2
Answers
4x^2-81y^2
(2x)^2-(9y)^2
(2x-9y)(2x+9y).
5u - 5u =u -u help please
Answers
Answer:
it would cancel eachother out so infinite
Step-by-step explanation:
An airplane on autopilot took 9 hours to travel 6,561 kilometers. What is the unit rate for kilometers per hour
Answers
divide total km by time
6561 / 9 = 729 km per hour
Leo drank 8 servings of iced tea and espresso beverages containing a total of 482 mg of caffeine. How many servings of espresso did he drink?
Answers
Answer:
Hope it helps
Step-by-step explanation:
Between what two consecutive positive integers is the square root of 85
Answers
A number system is defined as a system of writing to express numbers. between 9 and 10 positive integers is the square root of 85 is there.
What is Number system?A number system is defined as a system of writing to express numbers.
We need to find the two consecutive positive integers which have square root of 85 in between.
Firstly we need to know meaning of consecutive numbers.
Numbers which follow each other continuously in the order from smallest to largest are consecutive numbers.
Let us take some perfect square numbers
1,4,16,25,36,49,64,81,100
We know that square root of 81 is 9
square root of 100 is 10
square root of 85 is in between 9 and 10
Hence between 9 and 10 positive integers is the square root of 85 is there.
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The product of two consecutive odd integers is 143. find all such pairs of integers.
Answers
x^2+2x-143=0
(x+13)(x-11)=0
x=-13
x=11 solution
x+2=13 solution
proof
11*13=143
143=143
l=w+4
thus (w+4)w=117
w^2+4w-117=0
(w+13)(w-9)=0
w-9=0
w=8 for the width
l=9+4=13 for the length.
proof
9*13=117
117=117
A radio station is having a promotion in which every 12th caller receives a free concert ticket and every 15th caller receives a limo ride. Which caller will be first one to win both?
Answers
common multiples of 12 : 12,24,36,48,60
common multiples of 15 : 15,30,45,60
LCM = 60
the caller that will be the first to win both is the 60th caller
Answer: Every 60th caller would win both.
Step-by-step explanation:
Since we have given that
every 12th caller receives a free concert ticket.
And
every 15th caller receives a limo ride.
We need to find the first caller who would win.
So, for this we would find L.C.M. of 12 and 15.
And we know the least common multiple of 12 and 15 is 60.
Hence , every 60 th caller would win both.
a function is represented by the set of ordered pairs shown below.
{(-4,3), (-1,3), (0,3), (1,5), (3,7)}
what is the range of this function
Answers
---------------------------------------
---------------------------------------
The range is the set of outputs of a relation or function. In other words, it's the set of possible y values. Recall that ordered pairs are of the form (x,y) so the y coordinate is listed after the x. The output is listed after the input. The output values are y = 3, y = 3, y = 3, y = 5, y = 7. So we simply list these outputs without the "y=" portion. Toss out any duplicates. Only write the unique output values.
The curly braces surrounding the list of values tells us that we have a set.
Final answer:
The range of the given function is {3, 5, 7}.
Explanation:
The range of a function refers to the set of all possible output values (y-values) it can produce. Given the function represented by the set of ordered pairs {(-4,3), (-1,3), (0,3), (1,5), (3,7)}, to determine its range, we look at the second elements in each ordered pair since they correspond to the y-values produced by the function.
The y-values in the given set are 3, 3, 3, 5, and 7. Even though the value 3 is repeated, it is only counted once in the range. Thus, the range of this function is the set {3, 5, 7}.
Remember, the range includes all unique y-values that the function outputs. This set contains the different y-values that the function produces according to the given ordered pairs, which means these are the possible values that we can get as outputs from this function.
In the deli, meat and cheese are sold by the pound. There is usually a unit price in each variety in the refrigerator case. If honey ham costs $5.99 per lb, how much would 1.5 lbs cost? Enter your answer as a decimal rounded to the nearest cent.
Answers
How many square feet of carpeting are needed to carpet a 12-foot by 12-foot room
Answers
Area of a rectangle = length × width
Length = 12 ft
Width = 12 ft
A = l×w
= 12 ft × 12 ft
= 144 sq. ft
Thus, you would need 144 square feet of carpeting.
When writing a two column proof you should always start with ________ Information.
Answers
I hope its right
And i hope it helps
Find the area of a trapezoid with bases of 8 and 16 and a height of 10. A)1,280 sq. Units B) 240 sq. units C)120 sq. units
Answers
=[(8+10)/2]10
= 120
Answer: The answer is (C) 120 sq. units.
Step-by-step explanation: We are given to find the area of a trapezoid with bases of lengths 8 units and 16 units and height of 10 units.
We know that the area of the trapezoid with 'a' and 'b' as lengths of the bases and height 'h' is given by
[tex]A=\dfrac{1}{2}(a+b)h.[/tex]
Here, a = 8 units, B = 16 units and h = 10 units.
Therefore, the area of the given trapezoid will be
[tex]a\\\\=\dfrac{1}{2}(a+b)h\\\\=\dfrac{1}{2}\times(8+16)\times 10\\\\=24\times 5\\\\=120~\textup{sq. units.}[/tex]
Thus, the correct option is (C).
What is the binomial expansion of (x + 2)4? x4 + 4x3 + 6x2 + 4x + 1 8x3 + 24x2 + 32x x4 + 8x3 + 24x2 + 32x + 16 2x4 + 8x3 + 12x2 + 8x + 2
Answers
Answer-
[tex]\boxed{\boxed{(x+2)^4=x^4+8x^3+24x^2+32x+16}}[/tex]
Solution-
Given expression is [tex](x+2)^4[/tex]
Applying Binomial Theorem
[tex]\left(a+b\right)^n=\sum _{i=0}^n\binom{n}{i}a^{\left(n-i\right)}b^i[/tex]
Here,
a = x, b = 2 and n = 4
So,
[tex]\left(x+2\right)^4=\sum _{i=0}^4\binom{4}{i}x^{\left(4-i\right)}\cdot \:2^i[/tex]
Expanding the summation
[tex]=\dfrac{4!}{0!\left(4-0\right)!}x^4\cdot \:2^0+\dfrac{4!}{1!\left(4-1\right)!}x^3\cdot \:2^1+\dfrac{4!}{2!\left(4-2\right)!}x^2\cdot \:2^2+\dfrac{4!}{3!\left(4-3\right)!}x^1\cdot \:2^3+\dfrac{4!}{4!\left(4-4\right)!}x^0\cdot \:2^4[/tex]
[tex]=\dfrac{4!}{0!\left(4\right)!}x^4\cdot \:2^0+\dfrac{4!}{1!\left(3\right)!}x^3\cdot \:2^1+\dfrac{4!}{2!\left(2\right)!}x^2\cdot \:2^2+\dfrac{4!}{3!\left(1\right)!}x^1\cdot \:2^3+\dfrac{4!}{4!\left(0\right)!}x^0\cdot \:2^4[/tex]
[tex]=1\cdot x^4\cdot \:1+4\cdot x^3\cdot \:2+6x^2\cdot \:4+4\cdot x\cdot \:8+1\cdot 1\cdot \:16[/tex]
[tex]=x^4+8x^3+24x^2+32x+16[/tex]
Answer:
The answer to this question can be viewed in the images attached.
Hope it helps. Thanks
Write a linear factorization of the function. f(x) = x4 + 4x2
Answers
Final answer:
The function f(x) =[tex]x^4 + 4x^2[/tex] is factored using the difference of squares method to achieve its linear factorization. The final factorization over complex numbers is f(x) = x * x * (x + 2i) * (x - 2i).
Explanation:
To write a linear factorization of the function f(x) = [tex]x^4 + 4x^2[/tex] to find the factors of the polynomial that are linear, meaning each factor will be of the form (x - c) where c is a constant.
First, notice that the given polynomial is a quadratic in form, where [tex]x^2[/tex] is our variable. This gives us [tex]f(x) = (x^2)2 + 4(x^2)[/tex]which resembles the sum of squares [tex]a^2 + 2ab + b2 = (a + b)^2.[/tex] However, we only have [tex]a^2 + 2ab[/tex], with b being 2, and a being [tex]x^2[/tex].
To create a perfect square, we can write it as a difference of squares by adding and subtracting 4: [tex]f(x) = (x^2 + 2)^2 - (2)^2[/tex]. This can be factored further using the difference of squares formula, giving us[tex]f(x) = (x^2 + 2 + 2)(x^2 + 2 - 2)[/tex] which simplifies to [tex]f(x) = (x^2 + 4)(x^2).[/tex]
The linear factorization can be found by recognizing that x2 is already a product of linear factors x * x. Since [tex]x^2[/tex] + 4 cannot be factored over the real numbers, we need to use complex numbers to factor it further.
Using the sum of squares, we get [tex]x^2[/tex] + 4 = (x + 2i)(x - 2i), resulting in the final linear factorization over the complex numbers: f(x) = x * x * (x + 2i) * (x - 2i).
Realize income is ____.
A .The amount of income on hand
B.Income already spent
C. Income that comes from future investment
D. The amount of income you anticipate having
Answers
Realized income refers to the amount of income you expect to have, not yet received, including anticipated earnings and future investments.
Realized income represents the income an individual or entity expects to receive but has not yet received. It encompasses anticipated earnings, future investments, and any other income sources that have not yet materialized.
This includes income from salaries, investments, rental properties, or any other sources.
Unlike earned income, which refers to income already received, realized income is a forward-looking concept, reflecting the anticipated financial gains.
It plays a crucial role in financial planning and budgeting, guiding individuals and organizations in making decisions about expenditures, savings, and investment strategies based on expected future income streams.
Juanita receives her paycheck and knows that her gross pay and federal tax are correct. Using the fact that Social Security tax is 6.2% of gross pay, Medicare tax is 1.45% of gross pay and state tax is 19% of federal tax, determine if Juanita's net pay is correct.
Earnings
Deductions
Week Ended
Regular
FED. SOC. MED STATE
WITH. WITH. CARE. WITH.
NET PAY
11/17
$1,020.00
$107.00 $63.24 $14.79 $20.33
$814.64
Choose the true statement below.
a.
The net pay is correct.
b.
The Social Security tax is not correct.
c.
The Medicare tax is not correct.
d.
The state tax is not correct.
Answers
fed tax is 107.00
social security is 6.2% of gross pay......6.2% of 1020.00 =
0.062(1020) = 63.24
medicare is 1.45% of gross pay....1.45% of 1020.00 =
0.0145(1020) = 14.79
state tax is 19% of fed tax....19% of 107.00 =
0.19(107) = 20.33
therefore, her net pay is : 1020 - (107 + 63.24 + 14.79 + 20.33) =
1020 - 205.36 = 814.64
answer : the net pay is correct <==
The answer is A. The net pay is correct.
How to find the quadratic equation when given the vertex and y intercept?
Answers
The vertex form of a quadratic equation is given by:
[tex]y=a(x-h)^2+k=ax^2-2ahx+ah^2+k[/tex]
y-intercept is the value of y when x is 0.
Thus, given a y-intercept, c, we have:
[tex]c=ah^2+k \\ \\ \Rightarrow ah^2=c-k \\ \\ \Rightarrow a= \frac{c-k}{h^2} [/tex]
Therefore, given a vertex (h, k) and y-intercept, c, the quadratic equation is given by
[tex]y=\left(\frac{c-k}{h^2}\right)x^2-2\left(\frac{c-k}{h^2}\right)hx+\left(\frac{c-k}{h^2}\right)h^2+k \\ \\ =\left(\frac{c-k}{h^2}\right)x^2-2\left(\frac{c-k}{h}\right)x+c-k+k \\ \\ =\bold{\left(\frac{c-k}{h^2}\right)x^2-2\left(\frac{c-k}{h}\right)x+c}[/tex]
Find the nth term of this sequence: 1,5,9,13,17
Answers
Just add four.
The cost of producing x soccer balls in thousands of dollars is represented by h(x) = 5x + 6. The revenue is represented by k(x) = 9x – 2. Which expression represents the profit, (k – h)(x), of producing soccer balls?
Answers
Answer:
(K-h) (x) = 4(x-2)
Step-by-step explanation:
The cost of producing x soccer balls in thousands of dollars is represented by h (x) = 5x + 6
Revenue generated is represented by K(x) = (9x-2)
Them ( K-h) (x) will represent
( K-h )x = cost of revenue - production
= profit
( K-h )x = K(x) - h(x)
= (9x-2) - (5x + 6)
= (9x - 5x) - (2+6)
= 4x - 8
Profit = (K-h) (x) = 4(x-2)
The formula for the future value V (in dollars) of an investment earning simple interest is V=p+prt, where p (in dollars) is the principal, r is the annual interest rate (in decimal form) and t is the time (in years). a. Solve the formula for p
.
p=
b. An investment earns 6% simple interest. What amount of principal is needed to have $3000 after 5 years? Round your answer to the nearest cent.
Amount of principal: $
Answers
The answer is for the equation...
V/(1+rt)
It is written as a fraction... and the V goes on top and the (1+rt) goes on the bottom. Make sure that the V is a capital.
Then the amount of principal is 2,307.69
Using the formula given, we find that:
a) The solution for p is [tex]p = \frac{V}{1 + rt}[/tex]b) The principal will be of $2,307.69.------------------
Item a:
The future value formula is given by:
[tex]V = p + prt[/tex]
Solving for p:
[tex]p + prt = V[/tex]
[tex]p(1 + rt) = V[/tex]
[tex]p = \frac{V}{1 + rt}[/tex]
------------------
Item b:
6% interest means that [tex]r = 0.06[/tex]Amount of $3000 means that [tex]V = 3000[/tex]5 years means that [tex]t = 5[/tex]The principal is:
[tex]p = \frac{V}{1 + rt} = \frac{3000}{1 + 5(0.06}} = 2307.69[/tex]
The principal will be of $2,307.69.
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A bag contains 144 ping-pong balls. more than half of the balls are painted orange and the rest are painted blue. two balls are drawn at random without replacement. the probability of drawing two balls of the same color is the same as the probability of drawing two balls of different colors. how many orange balls are in the bag?
Answers
There are approximately 72 orange balls in the bag.
We have,
Let's assume the number of orange balls in the bag is x.
Given that more than half of the balls are painted orange, we have the inequality:
x > 144/2
x > 72
Now, let's consider the probability of drawing two balls of the same color:
The probability of drawing two orange balls.
= (x/144) * ((x-1)/(144-1))
= (x(x-1))/(144*143)
The probability of drawing two blue balls.
= ((144-x)/144) * ((144-x-1)/(144-1))
= ((144-x)(143-x))/(144*143)
Given that the probability of drawing two balls of the same color is the same as the probability of drawing two balls of different colors, we can set up the equation:
(x(x-1))/(144143) = ((144-x)(143-x))/(144143)
Simplifying the equation:
x(x-1) = (144-x)(143-x)
x^2 - x = 144143 - 287x + x^2
288x = 144143
x = (144*143)/288
x ≈ 72
Therefore,
There are approximately 72 orange balls in the bag.
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The amount of radioactive element remaining, r, in a 100-mg sample after d days is represented using the equation r=100[tex]( \frac{1}{2})^ \frac{d}{5} [/tex] . What is the daily percent of decrease?
87.06%
12.94%
3.13%
10%
Answers
how much is 12.94 in percent of 100? well, since is 100, is just 12.94%.
Answer:
its 12.94%
Step-by-step explanation
the length of a rectangle is 5cm less than 3 times the width.if the perimeter of a rectangle is 54cm, find the length and the width
Answers
To solve for the length and width of the rectangle, equations were set up based on the given perimeter and the relation between length and width. The width was found to be 8 cm, and substituting this into the length formula gave a length of 19 cm.
The question concerns finding the length and width of a rectangle given that the length is 5 cm less than three times the width and the perimeter is 54 cm. To solve this, let's denote the width of the rectangle as 'w' and the length as 'l'. The relationship between the length and width can be expressed as 'l = 3w - 5 cm'. The perimeter (P) of a rectangle is given by P = 2l + 2w, and substituting our expressions in terms of 'w' into the formula gives us 2(3w - 5) + 2w = 54. Simplifying and solving for 'w' gives us the width. Subsequently, we can substitute this width into the equation for length to find 'l'.
So, let's start by setting up the equation:
2(3w - 5) + 2w = 54
6w - 10 + 2w = 54
8w - 10 = 54
8w = 64
w = 8 cm
Now we substitute w = 8 cm into the length formula:
l = 3(8) - 5
l = 24 - 5
l = 19 cm
Therefore, the width of the rectangle is 8 cm and the length is 19 cm.
please help.
A doghouse is to be built in the shape of a right trapezoid, as shown below. What is the area of the doghouse?
A.45.5 square feet
B.63 square feet
C.66.5 square feet
D.84 square feet
Answers
A = 1/2(19)(7)
A = 1/2(133)
A = 66.5
answer
C.66.5 square feet
Answer:
Option C
The area of the doghouse is [tex]66.5\ ft^{2}[/tex]
Step-by-step explanation:
we know that
The area of trapezoid is equal to
[tex]A=\frac{1}{2}(b1+b2)h[/tex]
where
b1,b2 are the parallel bases of trapezoid
h is the height of trapezoid
in this problem we have
[tex]b1=7\ ft[/tex]
[tex]b2=7+5=12\ ft[/tex]
[tex]h=7\ ft[/tex]
substitute
[tex]A=\frac{1}{2}(7+12)7=66.5\ ft^{2}[/tex]
The volume of a rectangular prism is given by the formula V = lwh, where l is the length of the prism, w is the width, and h is the height. Which expression represents the volume of the following rectangular prism?
h=2x+9
l= x+2
w= 3x
A) 2x^2+13x+18
B) 6x^3+27x^2+54x
C) 6x^3+39x^2+54x
D) 18x^4+117x^3+162x^2
Answers
Solution: As given, Volume of a rectangular prism is given by the formula V = l w h, where l is the length of the prism, w is the width, and h is the height.
also , h=2x+9
l= x+2
w= 3 x
So, volume of prism= (2 x+9)(x+2)(3 x)= (3 x)(2 x+9)(x+2)→Using associative property
=3 x[2 x(x+2)+9(x+2)]→Using (x+a)(x+b)= x(x+a)+a(x+b)=x²+(a+b)x+ab
= 3 x [ 2 x²+ 4 x+ 9 x+18]
= 3 x[ 2 x² +13 x+18]
= (3 x)(2 x²) + (3 x)×(13 x) + (3 x)×(18)→ Using distributive property
= 6 x³+ 39 x² + 54 x → [ use [tex]x^{m} \times x^{n}= x^{m+n}[/tex]
Option (C) is correct.
The expression which represents the volume of the rectangular prism is; Choice C: 6x³+39x²+54x
Volume of a rectangular prismThe volume of the rectangular prism as given is;
V = lwhwhere, h=2x+9, l= x+2, and w= 3x
Therefore, Volume;
V = (2x+9) (x+2)(3x)V = (2x² +13x +18)(3x)V = 6x³+39x²+54xRead more on volume of rectangular prism;
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Amanda exercised for 10 minutes every day in the first week, 20 minutes in the second week, 30 minutes in the third week, and 40 minutes in the fourth week.
Billy exercised for 5 minutes every day in the first week, 10 minutes in the second week, 20 minutes in the third week, and 40 minutes in the fourth week.
Which statement best describes the methods used by Amanda and Billy to increase the time they spent exercising? (1 point)
Amanda's method is linear because the number of minutes increased by an equal number every week.
Billy's method is linear because the number of minutes increased by an equal factor every week.
Both Billy's and Amanda's methods are exponential because the number of minutes increased by an equal factor every week.
Both Billy's and Amanda's methods are exponential because the number of minutes increased by an equal number every week.
Answers
Answer:
Amanda's method is linear because the number of minutes increased by an equal number every week.Step-by-step explanation:I took the test and got it right.
Amanda
Billy1st week 10 52nd week 20 10 3rd week 30 204th week 40 40A)
Amanda's method is linear because the number of minutes increased by an equal number every week.common difference is 10.1st week 0 + 10 = 102nd week 10 + 10 = 203rd week 20 + 10 = 304th week 30 + 10 = 40Billy's method is exponential:5(2)^x1st week 5(2⁰) = 5(1) = 52nd week 5(2¹) = 5(2) = 103rd week 5(2²) = 5(4) = 204th week 5(2³) = 5(8) = 40Mark
A scalene triangle has side side lengths of 12 feet, 8 feet, and 15 feet. what is the perimeter of the triangle
Answers
P= 35 ft
The answer is 35 ft
Answer:
gh
Step-by-step explanation:
Which of the quadratic functions has the widest graph? y = 0.3x2 y = –4x2
Answers
A vertical compression is the squeezing of the graph towards the x-axis.
A compression is a stretch by a factor less than 1.
For the parent function y = f(x), the vertical stretching or compression of the function is a f(x).
If | a | < 1 (a fraction between 0 and 1), then the graph is compressed vertically by a factor of a units.
If | a | > 1, then the graph is stretched vertically by a factor of a units.
For values of a that are negative, then the vertical compression or vertical stretching of the graph is followed by a reflection across the x-axis.
Thus, the equation with the widest graph is 0.3x^2.Yes, Y = 0.3x^2 is correct!!