Answer:
AC = 6 cm
Step-by-step explanation:
First, realize that these are two identical triangles. We just have to use the pythaogrean theorem on one side to find AD or DC, then multiply that by 2 to get AC.
a^2 + b^2 = c^2
8^2 + b^2 = 10^2
64 + b^2 = 100
100 - 64 = b^2
b^2 = 36
b = 6
A ladder of length 8m rests against a wall so that the angle bsetween the ladder and wall is 45 degree .How far is the base of the ladder from the wall?
help asap!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Step-by-step explanation:
\( {x}^{2} = 2 \times {4}^{2} \\ {x}^{2} = 32 \\ x = 4 \sqrt{2} \\ diameter = 4 \sqrt{2} \\ radius = 2 \sqrt{2} \\ area \: of \: half \: of \: the \: circle = \\ \)
\(a = \frac{\pi \times {(2 \sqrt{2} )}^{2} }{2} = 4\pi \\ area \: of \: triangle \: = \\ 2 \sqrt{2} \times 2 \sqrt{2} = 8 \\ area \: of \: shaded \: region \: is \: = \\ 4\pi - 8 = 4.57 \: {cm}^{2} \)
An international company has 21,300 employees in one country. If this represents 32.4% of the company’s employees, how many employees does it have in total?Round your answer to the nearest whole number.
In order to calculate the total number of employees, we can use the following rule of three:
\(\begin{gathered} employees\rightarrow percentage \\ 21300\rightarrow32.4\% \\ x\rightarrow100\% \end{gathered}\)Now, from this rule of three, we can write the following proportion and solve it for x:
\(\begin{gathered} \frac{21300}{x}=\frac{32.4}{100}\\ \\ x\cdot32.4=21300\cdot100\\ \\ x=\frac{21300\cdot100}{32.4}\\ \\ x=65740.74 \end{gathered}\)Rounding to the nearest whole number, the total number of employees is 65741.
I WILL GIVE BRAINLEST!!!!!!!
Angela has 5 fewer quarters than twice the number of her dimes. If d represents
the number of dimes Angela has, which expression represents the total number of
Angela’s quarters and dimes?
A. 2d – 5
B. 5 – 2d
C. d + (2 – 5d)
D. d + (2d – 5)
PLSSS SHOW YOUR WORK PLSSSS
Answer:
A
Step-by-step explanation:
Answer: A
Step-by-step explanation:
Let’s say that she has 10 dimes. 2(10)-5=Q
20-5=15
15 quarters
We doubled her dimes, and subtracted 5 to find quarters.
You can fill anything for D and remind true
What is the product of (3a + 2)(4a2 – 2a + 9)?
Answer: (3a + 2) • (4a2 - 2a + 9)
(no solution)
Step-by-step explanation:
Step by Step Solution
More Icon
STEP
1
:
Equation at the end of step 1
(3a + 2) • ((22a2 - 2a) + 9)
STEP
2
:
Trying to factor by splitting the middle term
2.1 Factoring 4a2-2a+9
The first term is, 4a2 its coefficient is 4 .
The middle term is, -2a its coefficient is -2 .
The last term, "the constant", is +9
Step-1 : Multiply the coefficient of the first term by the constant 4 • 9 = 36
Step-2 : Find two factors of 36 whose sum equals the coefficient of the middle term, which is -2 .
-36 + -1 = -37
-18 + -2 = -20
-12 + -3 = -15
-9 + -4 = -13
-6 + -6 = -12
-4 + -9 = -13
For tidiness, printing of 12 lines which failed to find two such factors, was suppressed
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Final result :
(3a + 2) • (4a2 - 2a + 9)
Mia rides her bike 15 1/4 miles every day.
How many miles does Mia ride in 4 days?
Answer:
61 miles
Step-by-step explanation:
Since the distance Mia travels is constant, we can find the distance travelled over four days by multiplying 15 1/4 by 4:
(15 1/4) * 4 = 61
Thus, Mia travels 61 miles in 4 days
7. Sundeep travels by train to a meeting in Barcelona.
Barcelona is 270 km from where he lives. He catches the train at 9:45 a.m.
The train travels at an average speed of 120 km/h.
At what time will the train arrive in Barcelona?
Answer:
10:10 am.
Steps:
time = distance/speed
time= 270/120
=2 hours and 25 minutes
Change one number in the equation below to safely land the plane.
Press "Submit" to see if the plane lands safely.
How do I graph
(4+9i),(-3+7i),(-8-9i),(4+3i),(-5-6i)
Answer:
Step-by-step explanation:
To graph a set of complex numbers in the form of a + bi on the complex plane, you can use the following steps:
Plot the real part of the complex number along the x-axis and the imaginary part along the y-axis.
For each complex number, locate the point on the plane that corresponds to its real and imaginary parts.
Connect the dots to form the graph.
For example, to graph (4+9i), the point would be located at x = 4, y = 9 on the complex plane, and then connect the dots for all the complex numbers you have.
It is also possible to use software such as graphing calculators, spreadsheet programs or specialized software to graph complex numbers in the complex plane.
Is 4x - 3x + 2 and x+2 equivalent?
Answer:yes
Step-by-step explanation:4x minus 3x is 1x, or x, and then it's just x+2
Answer:
Yes
Step-by-step explanation:
Both of these equations have the same X and Y intercepts. The X intercepts being -2,0 and the Y intercepts being 0,2
the question is below please answer fast i need help
Answer:
n = 4
Step-by-step explanation:
\(\sqrt{64} \cdot \sqrt[3]{8} = \sqrt{8 \times 8} \cdot \sqrt[3]{2 \times \ 2 \times 2 }\)
\(= 8 \cdot 2\\=2^3 \cdot 2\\=2^4\\\)
Answer:
Step-by-step explanation:
\(\sqrt{64}\) .\(\sqrt[3]{8}\)
8.\(8^{1/3}\)
\(8^{1+1/3}\)
\(8^{4/3}\)
\(2^{2*4/3}\)
\(2^{8/3}\)
therefore n=8/3
Perform the indicated operation. PLEASEE HELPP HURRYY!! (3 + i) + (5 + 7i) = A) -2 + 6i B) 2 + i C) 8 + 6i D) 8 + 8i
Answer:
\( \boxed{ \bold{ \huge{ \boxed{ \sf{8 + 8i}}}}}\)
Option D is the correct option.
Step-by-step explanation:
\( \sf{(3 + i) + (5 + 7i)}\)
When there is a ( + ) in front of an expression in parentheses , there is no need to change the sign.
That means, the expression remains the same.
Just remove the unnecessary parentheses
⇒\( \sf{3 + i + 5 + 7i}\)
Collect like terms and simplify
⇒\( \sf{3 + 5 + i + 7i}\)
⇒\( \sf{8 + 8i}\)
Hope I helped!
Best regards!!
Please help me solve
Answer:
I could but can you please put down the problem.
Step-by-step explanation:
I NEED HELP NOWwwwwwww
Answer:
523 cm^3
Step-by-step explanation:
The volume of a sphere is
V = 4/3 pi r^3
V = 4/3 (3.14) (5)^3
V = 523.33333
Rounding to the nearest whole number
V = 523
what is the largest odd number using all four numbers,4536
Answer:It is 6543.
Step-by-step explanation:
A company is developing its weekly production plan. The company produces two products, A and B, which are processed in two departments. Setting up each batch of A requires $60 of labor while setting up a batch of B costs $80. Each unit of A generates a profit of $17 while a unit of B earns a profit of $21. The company can sell all the units it produces. The data for the problem are summarized below.
The decision variables are defined as Xi = the amount of product i produced
Yi = 1 if Xi > 0 and 0 if Xi = 0
Using the approach discussed in the text, what is the appropriate value for M1 in the linking constraint for product A?
The appropriate value for M1 in the linking constraint for product A is $17.
In the given scenario, the decision variable Yi is defined as 1 if the amount of product i produced (Xi) is greater than 0, and 0 if Xi equals 0. This implies that Yi represents whether or not product i is produced. In this case, we are dealing with product A.
The linking constraint is used to ensure that if product A is produced (Yi = 1), then the amount produced (Xi) must be greater than 0. This can be expressed as Xi ≥ Yi * M1, where M1 is a sufficiently large value that ensures the constraint holds.
Since the profit per unit of A is $17, setting M1 equal to this value guarantees that if Yi is 1 (product A is produced), then Xi must be greater than 0 (at least one unit of A is produced). This ensures that the linking constraint is satisfied and reflects the condition that the company can sell all the units it produces.
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On the first day of measles outbreak at a school, 8 students were identified to have
the measles. Each day for the following two weeks. the number of new cases
doubled from those identified with the disease the day prior.
How many students are identified to have measles in all at the end of day (10 )of the
outbreak?
The sum a geometric sequence is:
\(S_n=\dfrac{a_1(1-r^n)}{1-r} \ \text{where} \ a_1 \ \text{is the first term and r is the ratio}\)
In the given problem, \(a_1=10\) and \(r = 2\)
\(S_{10}=\dfrac{8(1-2^{10})}{1-2}\)
\(. \ \ \ \ =\dfrac{8(1-1024)}{-1}\)
\(. \ \ \ \ =-8(-1023)\)
\(. \ \ \ \ \bold{=8184}\)
f(x) = -2x + 10
f(-1.5)
a 13
b -13
c 20
d -20
Answer:
f( -1.5) = 13
Step-by-step explanation:
F(-1.5)= -2(-1.5)+10
-2 times -1.5 = 3
3+10
f( -1.5) = 13
Can I get help please
The amount of money that I will have at the end of 20 years would be =$4,480. That is option D
What is compound interest?Compound interest is defined as the interest that is being earned on an account which is based on the rate and the time the investment was made.
The total amount invested (p)= $2,000
The rate of investment (r) = 5%
The time of investment(t)= 12 year
The compound interest warm from that account;
= P×T×R/100.
= 2,000×12×5/100
= 120000/100
= $1200
For the next 8 years with the rate of 8% ;
= 2,000×8×8/100
= 128000/100
= $1280
The total compound interest = $1200+$1280= $2,480
Therefore, the amount of money that I will have at the end of 10 years would be = 2000+2480 = $4,480
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Identify which of the following sequences is a geometric sequence. Check all that apply.
A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a constant called the common ratio.
To identify which of the given sequences is a geometric sequence, we need to check if each term is obtained by multiplying the previous term by a constant ratio.
1. {1, 4, 16, 64, 256} - This sequence is a geometric sequence because each term is obtained by multiplying the previous term by 4, which is the common ratio.
2. {2, 4, 8, 16, 32} - This sequence is also a geometric sequence because each term is obtained by multiplying the previous term by 2, which is the common ratio.
3. {3, 7, 11, 15, 19} - This sequence is not a geometric sequence because the difference between consecutive terms is not constant.
Therefore, the main answer is that sequences 1 and 2 are geometric sequences, while sequence 3 is not.
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Which of the following accurately defines all possible values?
Answer:
C
Step-by-step explanation:
it is C
Which of the following does not have a value that is greater than 0?
a) (-14)^
b) (1/4)^2
c) 0.05^2
d) -4^2
Therefore , the solution of the given problem of expression comes out to be option d -4² is the right response.
Explain expression.The mathematical processes of multiplying, dividing, variables adding, and deleting are crucial. They would result in the following phrase if combined: An equation, some statistics, and a mathematical formula Values, variables, and operations like deletions, additions, multiplications, and divisions make up a statement of truth. Words and phrases can be compared and evaluated.
Here,
The option that does not have a value greater than 0 is (d) -4^2.
(d) -42 is the option that lacks a value higher than 0.
(a) The value of (-14)² = 196 is larger than zero.
(b) (1/4)² Equals 1/16, which is more than 0 (decimal).
(c) The number 0.05² = 0.0025 is larger than zero.
(d) The number -4² = -(4)² = -16 is less than zero.
Therefore, (d) -4² is the right response.
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q log a -3 log b
Condense logarithm
Answer:
Step-by-step explanation:
q log a is equivalent to log a^q. Note: This assumes that the base of your logarithmic system is 10.
-3 log b is equivalent to log b^(-3)
and so q log a -3 log b in condensed logarithm form is
log {a^q*b^(-3)}
a^q
or log -----------------
b^3
Consider the expression: 7+4(n 3)
1) Which math word would NOT be used to describe the given
expression?
A)
divisor
B)
difference
subtract
D) product
If you buy 3 shirts, you get 10% discount. If you paid $189 for 6 shirts what is the original price of a T-shirt?
items that are purchased together at a certain discount store are priced at $3 for the first item purchased and $1 for each additional item purchased. what is the maximum number of items that could be purchased together for a total price that is less than
The maximum number of items that could be purchased together for a total price that is less than the given amount T would be the integer part of (T - $3).
Let's analyze the pricing structure to determine the maximum number of items that can be purchased together for a total price that is less than a given amount.
The first item is priced at $3, and each additional item is priced at $1. This implies that the price increases by $1 for each additional item.
To find the maximum number of items, we need to consider the total price and the number of additional items beyond the first item. Let's denote the total price as P and the number of additional items as n.
The total price can be expressed as follows:
P = $3 + $1 * n
To determine the maximum number of items, we need to find the highest value of n that satisfies the condition P < T, where T is the given amount that the total price should be less than.
Substituting the expression for P, we have:
$3 + $1 * n < T
Simplifying the inequality:
$1 * n < T - $3
n < T - $3
Since the number of items must be a whole number, the maximum value of n would be the largest integer that satisfies the inequality n < T - $3.
Therefore, the maximum number of items that could be purchased together for a total price that is less than the given amount T would be the integer part of (T - $3).
For example, if T is $10, the maximum number of items would be the integer part of (10 - 3) = 7.
It's important to note that the maximum number of items calculated using this pricing structure assumes that customers can purchase fractional amounts of items. In practice, stores may have policies that limit the number of items to whole numbers or impose other restrictions.
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= 3. Find the absolute maximum and absolute minimum values of f(x) x3-12x +1 on the interval [1 , 3] (8 pts) 3 2
The absolute maximum value of \(f(x) = x^3 - 12x + 1\) on the interval [1, 3] is 1, and the absolute minimum value is -15.
To find the absolute maximum and minimum values of the function \(f(x)=x^3 - 12x + 1\) on the interval [1, 3], we need to evaluate the function at the critical points and the endpoints of the interval.
Step 1: Finding the critical points by taking the derivative of f(x) and setting it to zero:
\(f'(x) = 3x^2 - 12\)
Setting f'(x) = 0 and solving for x:
\(3x^2 - 12 = 0\\3(x^2 - 4) = 0\\x^2 - 4 = 0\)
(x - 2)(x + 2) = 0
x = 2 or x = -2
Step 2: Evaluating f(x) at the endpoints and the critical points (if any) within the interval [1, 3]:
\(f(1) = (1)^3 - 12(1) + 1 = -10\\f(2) = (2)^3 - 12(2) + 1 = -15\\f(3) = (3)^3 - 12(3) + 1 = -8\)
Step 3: After comparing the values obtained in Step 2 to find the absolute maximum and minimum:
The absolute maximum value is 1, which occurs at x = 1.
The absolute minimum value is -15, which occurs at x = 2.
Therefore, the absolute maximum value of \(f(x) = x^3 - 12x + 1\) on the interval [1, 3] is 1, and the absolute minimum value is -15.
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find the number.round to the nearest tenth if possible.95%of40
Answer:
40
Step-by-step explanation:
95 percent of 40 is 38
round to the nethest tenth and you got 40
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Karen is making a frame for a square picture with an area of 169 square inches. How many inches of framing are needed?
Answer: 13
Step-by-step explanation:
Consider the sugar-water phase diagram of Figure 9.1. (a) How much sugar will dissolve in 1000 g of water at 80°C (176°F)? (b) If the saturated liquid solution in part (a) is cooled to 20°C (68°F), some of the sugar precipi- tates as a solid. What will be the composition of the saturated liquid solution (in wt% sugar) at 20°C? (c) How much of the solid sugar will come out of solution upon cooling to 20°C?
The difference between these two values will give us the mass of solid sugar that came out of solution upon cooling to 20°C.
(a) To determine how much sugar will dissolve in 1000 g of water at 80°C, we need to find the point on the sugar-water phase diagram that corresponds to these conditions. At this point, the curve separating the liquid and solid phases (called the solubility curve) indicates the maximum amount of sugar that can be dissolved in the water at that temperature.
Once we have identified this point, we can read off the corresponding sugar concentration in the liquid phase. This will give us the maximum amount of sugar that can be dissolved in 1000 g of water at 80°C.
(b) When the saturated liquid solution in part (a) is cooled to 20°C, some of the sugar will precipitate as a solid. This means that the composition of the remaining liquid phase will be different from its composition at 80°C.
To determine the new composition, we need to find the point on the phase diagram that corresponds to 20°C and the sugar concentration we found in part (a). This point will lie on the solubility curve, which separates the liquid and solid phases at 20°C.
Once we have identified this point, we can read off the corresponding sugar concentration in the liquid phase. This will give us the composition of the saturated liquid solution at 20°C.
(c) The amount of solid sugar that comes out of solution upon cooling to 20°C can be calculated using the mass balance equation:
mass of solid sugar + mass of dissolved sugar = total mass of sugar
At 80°C, we found the maximum amount of sugar that can be dissolved in 1000 g of water. We can use this value to calculate the mass of dissolved sugar at 80°C. Then, at 20°C, we can use the composition we found in part (b) to calculate the mass of dissolved sugar in the saturated liquid solution.
The difference between these two values will give us the mass of solid sugar that came out of solution upon cooling to 20°C.
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