The missing reason in Step 8 is substitution
When a triangle is not a right triangle and when either the lengths of two sides and the measurement of the included angle are known (SAS) or the lengths of the three sides are known (SSS), the Law of Cosines is used to discover the remaining pieces of the triangle.
According to the law of cosine, if a, b, and c are any triangle's three sides, then a² = b² + c² - 2bcosa
The x in statement 5 of the preceding proof is changed to c cos A from statement 6 in statement 8 of the proof.
Option C, from the list of alternatives, is the one that best explains statement 8.
Hence missing reason in Step 8 is substitution
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Answer: OPTION C
Step-by-step explanation:
EDGE22
Study each of the growing geometrical patterns. Then do the following for each pattern. (I) Give a verbal description of how the pattern is growing. (ii)Set up a table of values.(III) Write down a numerical description for each pattern (you must relate the number of the frame to the number of figures in the frame). (IV) For each pattern, write down a formula that can be used to calculate the number of building blocks in any term. (v) Write down the value of the 10th frame. Use your formula to determine how many building blocks there are in the 100th frame of each growing pattern. M M Δ Δ Δ 2 (6) (6) (8) [40]
A description of how the pattern is growing is that the pattern is growing by the addition of two blocks every time.
How to illustrate the pattern?A numerical description of the pattern is:
1 - 2 blocks.
2 - 4 blocks.
3 - 6 blocks
4 - 8 blocks.
The formula that can be used to calculate the number if building blocks in any term will be 2n. For example, the number of blocks for the 5th term will be:
= 2n = 2 × 5 = 10
The value for the 10th frame will be:
= 2n
= 2 × 10 = 20
The value for the 100th frame will be:
= 2n
= 2 × 100 = 200
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Given the data set (4,85),(7,92),(14,110), which of the following equation best represents a line of best fit
Solve the inequality graphically. 3^-8 > 6^-8
a. x < 1
b. x > 1
c. x > 0
d. x < 0
THE ANSWER IS -> b. x > 1
hope it helps
thanks
Answer: c. x>0
Step-by-step explanation:
A school bus is moving 26.8 m/s on flat ground when it begins to accelerate at 4.73 m/s^2. How much time does it take to travel 95.1 m?
The school bus will take 5.34 seconds to travel 95.1 m if the bus is moving 26.8 m/s on flat ground when it begins to accelerate at 4.73 m/s².
What is a quadratic equation?Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
As we know, the formula for the roots of the quadratic equation is given by:
[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]
We have:
A school bus is moving 26.8 m/s on flat ground when it begins to accelerate at 4.73 m/s².
From the second equation of motion:
[tex]\rm s = u + \dfrac{1}{2}at^2[/tex]
We have given:
s = 95.1 m
u = 26.8 m/s
a = 4.73 m/s²
[tex]\rm 95.1 = 26.8 + \dfrac{1}{2}(4.73)t^2[/tex]
The above equation is a quadratic equation:
After simplification:
[tex]\rm \dfrac{4.73}{2}t^2=68.3[/tex]
[tex]\rm t^2=28.879[/tex]
t = 5.373 seconds ≈ 5.34 seconds
Thus, the school bus will take 5.34 seconds to travel 95.1 m if the bus is moving 26.8 m/s on flat ground when it begins to accelerate at 4.73 m/s².
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f(a)=3a^2+2a+7 find the value of f(a)
Answer:
Step-by-step explanation:
If a = 0, f(a) = f(0) = 0 + 0 + 7 = 7;
If a = 1, f(1) = 3(1^2) + 2(1) + 7 = 12;
and so on. Normally an 'a' value would be given as part of this problem.
Actually, the value of f(a) is given and is f(a) = 3a^2+2a+7 for input value a.
If y = 2x-3, then which of the following ordered pairs lies on the graph?
O (-3,0)
O (1,-1)
O (5,4)
Plug in the points and see if they satisfy the equation.
y = 2x - 3
(1, -1)
-1 = 2(1) - 3
-1 = 2 - 3
-1 = -1
So (1, -1) satisfies the equation.
(-3, 0)
0 = 2(-3) - 3
0 = -6 - 3
0 = -9
So (-3, 0) does not satisfy the equation.
(5, 4)
4 = 2(5) - 3
4 = 10 - 3
4 = 7
So (5, 4) does not satisfy the equation.
Therefore your answer is (1, -1).
Answer:
the answer is 5,4
Rick bought some tetra fish and goldfish for his fish tank. He bought twice as many goldfish as he did tetras. Each goldfish costs $1.50, and each tetra fish costs $2.00. He spent $20 on the fish. Which system can be used to represent x, the number of tetra fish, and y, the number of goldfish, he purchased?
x = 2 y. 2 x + 1.5 y = 20
2 x = y. 2 x + 1.5 y = 20
x = y. 2 x + 1.5 y = 20
x + y = 20. 2 x + 1.5 y
Answer:
B. 2x = y; 2x +1.5y = 20
Step-by-step explanation:
The two given relations can be written as two equations, one for the numbers of fish, and one for their cost.
__
number of fishThe number of goldfish (y) is twice the number of tetras (x), so one equation can be ...
2x = y
cost of fishThe tetras (x) are $2 each, and the goldfish (y) are $1.50 each. Their total cost is the sum of products of the number of fish and the cost of each. That total is given as $20, so the other equation could be ...
2x +1.5y = 20
Then the appropriate system of equations is ...
2x = y2x +1.5y = 20_____
Additional comment
The solution can be found by substituting for 2x to get ...
y +1.5y = 20 . . . . . . substitute for 2x
y = 20/2.5 = 8 . . . . divide by the coefficient of y
x = y/2 = 4 . . . . . . . find the number of tetras
Rick bought 4 tetras and 8 goldfish.
__
The wording "twice as many goldfish as tetras" easily causes confusion. It is helpful to reword it as "goldfish were twice the number of tetras."
You buy a CD for $9000 that earns $172.92 in interest every 2 months. What is the
annual yield on your investment?
Answer:
$4,000.343
Step-by-step explanation:
Divided the months of the year and caculate the intrest.
Emma bought 1305 bags of carrot for 16910 dollars. Find the unit rate in terms of bags per dollar.
Answer: $12.96
Given:
1305 bags of carrots purchased
Total cost = $16,910
Step-by-step explanation:
To find the unit cost, divide 16910 by 1305 to find the cost of one bag of carrots:
[tex]\frac{16910}{1305} = 12.96[/tex] (rounded to nearest hundredth)
David throws a ball up in the air. The graph below shows the height of the ball hh in feet after tt seconds. What is the ball’s greatest height?
HELP ASAP!
The greatest height is 9 feet.
What is projectile?
A projectile is any object thrown into space upon which the only acting force is gravity.
As, from the graph we can see that
The highest point the ball reaches shown by the coordinates (0.75, 9)
As, the maximum height is shown by y- axis(vertical axis).
Hence, the greatest height is 9 feet.
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Consider the following hypothesis test: 0 : 12 a : 12 HH A sample of 25 provided a sample mean x = 14 and a sample standard deviation s = 4.32. a. Compute the value of the test statistic. b. Use the t distribution table to compute a range for the p-value. c. At a = 0.05, what is your conclusion? d. What is the rejection rule using the critical value? What is your conclusion?
a) The test statistic is given as t = [tex]\dfrac {14-12}{\dfrac{4.32}{\sqrt25}}}[/tex]= 2.315
b) The pa value will be P = P( t₂₄ > 2.315 ) = 0.015
c) If we compare the p-value and the significance level is given we see that so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is higher than 12 at 1% of significance
What is a null hypothesis?In null hypotheses, there is no relationship between the two phenomena under the assumption that it is not associated with the group. And in alternative hypotheses, there is a relationship between the two chosen unknowns.
X= represents the sample mean
s = represent the sample standard deviation
n = 25 sample size
[tex]\mu_o[/tex] = 12 represent the value that we want to test
[tex]\alpha[/tex] = 0.05 represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p-value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the mean is higher than 12, the system of hypothesis would be:
Null hypothesis: ≤ 12
Alternative hypothesis: > 12
If we analyze the size for the sample is > 30 but we don't know the population deviation so is better to apply a t-test to compare the actual mean to the reference value, and the statistic is given by:
[tex]t=\dfrac{X-\mu_o}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to a specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
[tex]\dfrac {14-12}{\dfrac{4.32}{\sqrt25}}}[/tex]= 2.315
P-value:-
The first step is calculate the degrees of freedom, on this case:
df = n - 1 =25 - 1 = 2
Since is a one side right tailed test the p value would be:
[tex]p_v[/tex] = P( t₂₄ > 2.315 ) = 0.015
Conclusion
If we compare the p-value and the significance level is given [tex]\alpha[/tex]= 0.05 we see that [tex]p_v < \alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is higher than 12 at 1% of significance.
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find the measure of angle ACB
Answer:
angle ACB=45º
Step-by-step explanation:
angle 135º lies on a straight line
a straight line = 180º
thus, angle ACB= 180-135=45º
Help is needed with this math problem!
Answer:
expression for (g + h)([tex]x\\[/tex]) = [tex]2x[/tex] + [tex]3x^2\\[/tex] and for (g - h)([tex]x[/tex]) = [tex]2x[/tex] - [tex]3x^2[/tex]
value of (g .h)(2) = 24
Step-by-step explanation:
function operations: Functions with overlapping domains can be added, subtracted, multiplied and divided. If f(x) and g(x) are two functions, then for all x in the domain of both functions we can find the sum, difference, product and quotient
given :
g([tex]x[/tex]) = [tex]2x[/tex]
h([tex]x[/tex]) = [tex]3x^2[/tex]
we know that ;
(g + h)([tex]x[/tex]) = g([tex]x[/tex]) + h([tex]x[/tex])
= [tex]2x[/tex] + [tex]3x^2[/tex]
similarly;
(g - h)([tex]x[/tex]) = g([tex]x[/tex]) - h([tex]x[/tex])
= [tex]2x[/tex] - [tex]3x^2[/tex]
now,
(g . h)([tex]x[/tex]) = 2([tex]3x^2\\[/tex])
= 6[tex]x^2\\[/tex]
for (g .h)(2) = 6([tex]2^2[/tex])
= 6 × 4
= 24
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Briana monitors the number of E. coli infections reported in a certain
neighborhood in a given week. The recent numbers are shown in
this table:
According to her reports, the reported infections are growing at a
rate of 50%.
If the number of infections continues to grow exponentially,what
will the number of infections be in week 6?
An equation is formed of two equal expressions. The number of infections in 6 weeks is 456.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The general equation of an exponential function is written as,
y = A(B)ˣ
Since the infection is increasing at a rate of 50%, therefore, the rate of growth will be,
B = 1.50
Substitute any value then we will get,
40 = A(1.50)⁰
A = 40
Thus, the exponential equation of the growth will be,
y = 40(1.50)ˣ
Now, the number of infections in 6 weeks will be,
y = 40(1.50)⁶
y = 455.625 ≈ 456
Hence, the number of infections in 6 weeks is 456.
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What is the value of the expression
(12+x) +
4+x
when X= 4 and y=-8?
OA) 4
OB)
OC)
OD 10
Step-by-step explanation:
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The value of the expression x
4
−8x
3
+18x
2
−8x+2, when x=2+
3
, is:
Medium
Solution
verified
Verified by Toppr
Correct option is B)
Let f(x)=x
4
−8x
3
+18x
2
−8x+2
Substituting x=2+
3
, we get
f(2+
3
)=(2+
3
)
4
−8(2+
3
)
3
+18(2+
3
)
2
−8(2+
3
)+2
=(2+
3
)
2
((2+
3
)
2
+18)−8(2+
3
)((2+
3
)
2
+1)+2
=(7+4
3
)(4
3
+25)−8(2+
3
)(8+4
3
)+2
=175+48−128−96+2
=1
Hence, option B is correct.
PLEASE HELP
Natalie invests $6,680 in a savings account with an interest rate of 2% compounded continuously.
How long will it take for the account balance to reach $8,838.51?
The time it will take the money to reach $8,838.51 is 14years
Compound interestThe formula for calculating compound interest is expressed as:
A = P(1+r)^t
where
P = $6,680
A = $8,838.51?
r = 2% = 0.02
Substitute and calculate the time 't"
8,838.51 = 6680(1+0.02)^t
1.3231 = 1.02^t
t = ln1.3231/ln1.02
t = 14years
Hence the time it will take the money to reach $8,838.51 is 14years
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whats the answer? :(
Answer:
D) 8[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
5[tex]\frac{2}{3}[/tex] ÷ [tex]\frac{2}{3}[/tex] = 8[tex]\frac{1}{2}[/tex]
400g is what percent of 80kg?
A rental car agency charges $230 per week plus $0.25 per mile to rent a car. How many miles can you travel in one week for $415?
The number of miles you can travel in one week for $415 is
Answer:
740 miles
Step-by-step explanation:
$415-$230=$185
$185÷0.25 per miles =740 miles
Find the prime factorization of the composite number 10692
When decomposing into prime factors, it is when a number is taken out of its half, third, fifth and seventh, and it is also possible for the same number number.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \left.\begin{matrix} \blue{10692 }\\ \ 5346\\ \ 2673\\ \ \ \ 891\\ \ \ \ 297\\ \ \ \ \ 99\\ \ \ \ \ 33\\ \ \ \ \ 11\\ \ \ \ \ 1 \end{matrix}\right|\begin{matrix} 2\\ 2\\ 3\\ 3\\ 3\\ 3\\ 3\\ 11\\ \: \end{matrix} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf 10692=2\cdot2\cdot3\cdot3\cdot3\cdot3\cdot3\cdot11=\bf{2^{2}\cdot3^{5}\cdot11 } \end{gathered}$}[/tex][tex]\huge \red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]
dollars per pint
pints per dollar.
▼
Find the unit rates. If necessary, round your answers to the nearest hundredth.
$6.79 for 16 pints
Answer:
0.42 dollar per pint
2.36 pints per dollar
what is the fraction 2500 of 3600
Answer:
25/36
Step-by-step explanation:
put 2500 over 3600 and you get 2500/3600 but you can simplify to get 25/36 but removing the 0's
Write each of the following numerals in base 10. For base twelve, T and E represent the face values ten and eleven, respectively.
a. 421 five
b. 11101 two
c. 13Ttwelve
(a)
421₅ = 4×5² + 2×5¹ + 1×5⁰
… = 100 + 10 + 1
… = 111
(b)
11101₂ = 1×2⁴ + 1×2³ + 1×2² + 0×2¹ + 1×2⁰
… = 16 + 8 + 4 + 0 + 1
… = 29
(c)
13T₁₂ = 1×12² + 3×12¹ + 10×12⁰
… = 144 + 36 + 10
… = 190
Consider a triangle ABC like the one below. Suppose that B=129°, a=7, and c=42. (The figure is not drawn to scale.) Solve the triangle.
Carry your intermediate computations to at least four decimal places, and round your answers to the nearest tenth.
If there is more than one solution, use the button labeled "or".
4-C-b-0
DOD
X
No
solution
5
?
The angles are: A =24.7° ; B = 40.6° ; C =114.7°.
What is Cosine law?
The law of cosine helps in establishing a relationship between the lengths of sides of a triangle and the cosine of its angles. The cosine law in trigonometry generalizes the Pythagoras theorem, which applies to a right triangle.
Cosine Law
a² = b²+c²-2bc cos A
b² = c²+a² -2ca cos B
Sum of three angles of a triangle is 180°.
a = 34 ; b= 53; c = 74
Substituting the given values in the cosine law, we have
34² = 53² + 74² - 2*53 *74 * cos A
7844 cos A = 2809 + 5476 - 1156 = 7129
cos A = 7129/7844 = 0.9088
A = cos⁻¹ (0.9088) = 24.6600° = 24.7°
53² = 74² + 34² - 2 (74)(34) cos B
5032 cos B = 5476 + 1156 - 2809 = 3823
cos B = 3823/5032 = 0.7597
B = cos⁻¹ (0.7597) = 40.5622° = 40.6°
Also, A + B + C = 180°
24.7 + 40.6 + C =180
C =180 - 65.3 = 114.7°
Thus, the angles are: A =24.7° ; B = 40.6° ; C =114.7°
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Olympic Enterprises has the following inventory data: Assuming average cost, what is the cost of goods sold for the June 14 sale?
Assuming average cost of $55.5, the cost of goods sold by Olympic Enterprises for the June 14 sale is equal to $444.
How to calculate cost of goods?In Financial accounting, the cost of goods sold for a business firm can be calculated by multiplying the total quantity of goods by an average cost. Mathematically, this is given by:
Cost of goods = quantity × average cost
Note: We would assume an average cost of $55.5.
Substituting the parameters into the formula, we have:
Cost of goods sold = 8 × 55.5
Cost of goods sold = $444.
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Given that (1, 0, 1) is a solution to a system of three linear equations, which of the following is true about the system?
The true option about the system of linear equation is that the system can only be independent and consistent.
How to illustrate the equation?It should be noted that the system is consistent as it can illustrate more than a solution.
Also, it can't be independent and dependent at the same time as depicted in some of the option given.
In this case, true option about the system is that the system can only be independent and consistent.
The complete question is:
Given that (1, 0, 1) is a solution to a system of three linear equations, which of the following is true about the system?
The system can be either inconsistent or consistent.
The system can be either independent or dependent.
The system can only be independent and consistent.
The system can only be dependent and inconsistent.
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Step 1: Choose the lowest common denominator.
02 03 04 05 06 08 010 012
3/4
50/80
O
Find the sum: -and
The expression written in equivalent form with a
common denominator is
The sum is
The expression written in equivalent form with a common denominator is -1/6
Adding fractionsFractions are written as ratio of two integers. For instance a/b is a fraction.
Given the sum of the fractions shown;
-3/4 and 5/8
Sum = -3/4 + 5/8
Sum = 5/8 - 3/4
Sum = 5-6/8
Sum = -1/8
Hence the sum of the given fraction -1/3 and 5/8 is -1/6
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What does the ratio 6 to 8 represent in the situation?
Answer:
its 80
Step-by-step explanation:
the ratio is 80 hope this helps!
Identifying an Error
Identify the error in the student solution shown
below. Find the correct answer.
2ln(x)= In(3x) - [In(9) - 2ln(3)]
In(x²) In(3x)-[In(9) - In(9)]
In(~2) 1/25)
The incorrect step is ln(x²) = ln(3x/0) because ln(x/y) = lnx - lny and the solutions are x = 0, 3
What is a logarithm?It is another way to represent the power of numbers, and we say that 'b' is the logarithm of 'c' with base 'a' if and only if 'a' to the power 'b' equals 'c'.
[tex]\rm a^b = c\\log_ac =b[/tex]
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have:
2ln(x) = In(3x) - [In(9) - 2ln(3)]
In(x²) = In(3x) - [In(9) - In(9)]
ln(x²) = ln(3x) - 0
ln(x²) = ln(3x/0) (incorrect step)
ln(x²) = ln(3x)
x² = 3x (correct step)
x² - 3x =0
x(x - 3) = 0
x = 0, 3
Thus, the incorrect step is ln(x²) = ln(3x/0) because ln(x/y) = lnx - lny and the solutions are x = 0, 3
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Here are the first five numbers in a sequence.
47 41
(a) Find the first negative number in the sequence.
35
29
23
Answer:
- 1
Step-by-step explanation:
note there is a common difference of 6 between consecutive terms , that is
23 - 29 = 29 - 35 = 35 - 41 = 41 - 47 = - 6
by subtracting 6 from the previous term we get
23 - 6 = 17
17 - 6 = 11
11 - 6 = 5
5 - 6 = - 1
the first negative number in the sequence is - 1
