Answer:
735 cm²
Step-by-step explanation:
The figure is a trapezium .The area of the triangle section can be calculated using the Heron's formula.
The other part of the figure will be a square of sides 21 cm by 21 cm
Area of the square section
Area = l²
Area = 21* 21 = 441 cm²
Area of the triangle using Heron's formula
Sides of the triangle are ;
a= 28 cm
c= 35 cm
b = 21 cm -----height of the trapezium
The Heron's formula is given as;
\(A=\sqrt{s( s-a)(s-b )(s-c )}\)
where s is half the perimeter of the triangle
Perimeter of the triangle is given as ;
P= 35 + 28 + 21 =84 cm
s= 84/2 = 42 cm
\(A=\sqrt{42*(42-21 )*(42-35 )*(42-28 )} \\\\A=\sqrt{42*(21 )*(7 )*( 14)} \\\\A=\sqrt{86436} \\\\A=294\\\\\)
Total area = 294 + 441 = 735 cm²
In the coordinate plane, which of the following functions dilates by a factor of 3
about the point (9, 6)?
A. (, ) = (3 + 9, 3 +6)
B. (, ) = (3( + 9), 3( + 6))
C. (, ) = (9+ 3( − 9), 6 + 3( −6))
D. (, ) = (9+ 3(9− ), 6+ 3(6 − ))
8. The table shows the linear relationship between the balance of a student's savings
account and the number of weeks he has been saving.
Savings Account
Week
1 3
8 13
Balance
53
88
(dollars)
123
0
6
32
39
74
Based on the table, what was the rate of change of the balance of the student's
savings account in dollars and cents per week?
Answer:
7 dollars
Step-by-step explanation:
Is 5-2y=3x a linear equation
Answer:
Yes
Step-by-step explanation:
What is the height of the trapezoid if the Area = 26 un²?
Answer:4
Step-by-step explanation:
H= 2*26/5+8
plz someone help lol....
Answer:
J
Step-by-step explanation:
x represents the number of gallons of gas and realistically you can’t have negative gallons
\( \frac{x - 9}{15} = \frac{2x - 9}{10} \)
solve the proportion. Round to the nearest hundredth if necessary.
-3(n + 5) = 12
pls help me asap
Step-by-step explanation:
-3(n + 5) = 12 [Distributive property]
-3n - 15 = 12
-3n = 27
-3n/-3 = 27/-3
n = 9
Answer : 27
Step by step explanation
Find the maximum volume of a box inscribed in the tetrahedron bounded by the coordinate planes and the plane x + 4y + z = 1. (Use symbolic notation and fractions where needed.) the maximum volume of the box:
The maximum volume of the box is 3/16 cubic units.
Let the coordinate planes be defined as follows: x = 0, y = 0, and z = 0. Furthermore, assume that the edge lengths of the box are a, b, and c. We can express the coordinates of the vertices of the tetrahedron in terms of the edge lengths as follows:(0,0,0), (a,0,0), (0,b,0), and (0,0,c).
Since the tetrahedron is inscribed in the plane x + 4y + z = 1, we can express the relationship between a, b, and c as follows:1 = a/1 + 4b/1 + c/1 ⇒ 1 = a + 4b + c.
To maximize the volume of the box, we should make it a cube. Since the surface area of the box is 2(ab + ac + bc), the surface area of the cube is 2(3a²), and a = (1 - 4b - c), we get:V = a²b = a²(1 - a/4 - c) = (1/16)(16b² - 8b + 1) = 1/16(4b - 1)² + 3/16.
The maximum volume of the box is 3/16 cubic units. Thus, the answer is: 3/16.
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Find the value of x…
The value of the variable x is 53
What is a minor arc?A minor arc is defined as an arc whose measure is less than 180
Also, a major arc is defined as an arc whose measure is greater than 180 degrees.
An arc whose measure equals 180 degrees is a semicircle
Then, we have from the the information given;
Equate the angles to 180 degrees, we get;
80 + 2x - 6 = 180
collect the like terms, we get;
2x = 180 - 80 + 6
Add the values first
2x = 180 - 74
Subtract the values
2x = 106
Divide both sides by the coefficient of x, we get;
x = 106/2
x = 53
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How to evaluate 2(3+5)+17
Answer:
first do 3+5 in the parenthesis thats 8 times 2 is 16 plus 17 is 33
Step-by-step explanation:
the candy produced by a company has a sugar level that is normally distributed with a mean of 16.8 grams and a standard deviation of 0.9 grams. the company takes readings of every 10th bar off the production line. the reading points are 17.3, 14.9, 18.3, 16.5, 16.1, 17.4, 19.4. is the process in control or out of control and why? use a control chart to answer the question. homework help: 4vc. calculating probabilities from manufacturing to determine if system is in control (links to an external site.) (4:12) group of answer choices it is in control as only one of these data points is more than 3 standard deviations from the mean it is out of control as the values jump above and below the mean it is out of control as two of these data points are more than 2 standard deviations from the mean it is in control as the data points more than 2 standard deviations from the mean are not among three consecutive data points
It is not in control because at least two of the of the data points are more than 2 standard deviations from the mean are far apart.
18.3,18.4 > 18.2 Upper Control limit
14.9, > 15.4 Lower Control Limit
Step-by-step explanation:
Find the limits using μ ± 3σ and μ ± 2σ
Using μ ± 3σ
Upper Control Limit = μ + 3σ = 16.8 + 3(0.7)= 16.8 + 2.1= 18.9
Lower Control Limit = μ - 3σ =16.8 - 3(0.7)= 16.8 - 2.1= 14.7
Using μ ± 2σ
Upper Control Limit = μ + 2σ = 16.8 + 2(0.7)= 16.8 + 1.4= 18.2
Lower Control Limit = μ - 2σ =16.8 - 2(0.7)= 16.8 - 1.4= 15.4
The data points are 17.3, 14.9, 18.3, 16.5, 16.1, 17.4, 18.4.
Rearranging these data points 14.9, 16.1, 16.5, 17.3, 17.4, 18.3,18.4.
We see from the above that it is out of control because the values jump above and below the mean.
It is not in control as two of the of the data points are more than 2 standard deviations from the mean are far apart.
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Determine what type of model best fits the given situation: A. none of these B. exponential C. linear D. quadratic
The option c is correct. Linear model suits best to this graphical representation out of the exponential and quadratic model.
According to the statement
We have given that a model in the graphical representation and we have to tell that which type of model used in this representation.
So,
According to this representation,
A linear representation is a representation on a category of vector spaces or similar.
The other meaning is that when the growth increases linearly or at the constant speed.
In this graphical representation, linear representation is used because it increases or decreases linearly not suddenly.
linear representation explain this graph perfectly.
So, Linear model suits best to this graphical representation.
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pls help
Determine if each pair of ratios is equivalent or not. 6/8 21/36
Answer:
Not
Step-by-step explanation:
6/8 In Simplest Form 3/4
21/36 In Simplest Form 7/12 May Be The Answer Will Be Not Equivalent
Hope To Help!!!
i need help again please n thank you :)
Answer:
A solid line.
Step-by-step explanation:
The line would be dashed if it was either a < or > sign, but the line is dashed when it is just a < or > sign.
Step-by-step explanation:
the answer is Dashed Line
If f(x)=4x−11, what is the value of f(5)?
Juanita begins to factor an expression as shown.
x2+3x−18=(x+)(x−)
What numbers should be placed in the boxes from left to right?
Answer:
(x+6)(x-3)
solve:
\(\sf x^2+3x-18\)
the least common multiple of 1 and 18 is 18 : 6 * 3
\(\sf x^2+6x-3x-18\)
breakdown
\(\sf x(x+6)-3(x+6)\)
build parenthesis
\(\sf (x-3)(x+6)\)
4. (25 pts) Show using the substitution method that the exact solution of T(n)=4 T(n / 4)+ n is n \lg n+n .
Let's solve the given equation `T(n) = 4T(n/4) + n`
using the substitution method.Substitution method:
To show that `T(n) = n log n + n` is a solution of `T(n) = 4T(n/4) + n`,
let us substitute `T(n) = n log n + n` into `T(n) = 4T(n/4) + n` as given below:
`4T(n/4) + n = 4(n/4 log(n/4) + n/4) + n` We can also write `T(n) = n log n + n` as `T(n) = n log n` + `n`
Now, substitute `T(n) = n log n` + `n` into the equation `T(n) = 4T(n/4) + n` to get:
`T(n) = 4[(n/4 log(n/4) + n/4)] + n`
Simplifying the above expression, we get:
`T(n) = n log n + n`
Thus, `T(n) = n log n + n` is the solution of the equation
`T(n) = 4T(n/4) + n`.
Hence, it is shown using the substitution method that the exact solution of `T(n) = 4T(n/4) + n` is `n log n + n`.
solution of T(n)=4 T(n / 4)+ n is:
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Questions in photo
Please help
Applying the tangent ratio, the measures are:
5. tan A = 12/5 = 2.4; tan B = 12/5 ≈ 0.4167
7. x ≈ 7.6
How to Find the Tangent Ratio?The tangent ratio is expressed as the ratio of the opposite side over the adjacent side of the reference angle, which is: tan ∅ = opposite side/adjacent side.
5. To find tan A, we have:
∅ = A
Opposite side = 48
Adjacent side = 20
Plug in the values:
tan A = 48/20 = 12/5
tan A = 12/5 = 2.4
To find tan B, we have:
∅ = B
Opposite side = 20
Adjacent side = 48
Plug in the values:
tan B = 20/48 = 5/12
tan B = 12/5 ≈ 0.4167 [nearest hundredth]
7. Apply the tangent ratio to find the value of x:
tan 27 = x/15
x = tan 27 * 15
x ≈ 7.6 [to the nearest tenth]
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Maria used one bag of flour to bake some bread and muffins. First, she baked two loaves of bread. Then she used the remaining flour to make muffins. If the bag contained 15 cups of flour, how many muffins did Maria make?
recipe - amount of flour needed
bread - 1 1/2 cups per loaf
muffin - 1/3 cup per muffin
rolls - 1/4 cup per roll
a
12 muffins
b
4 muffins
c
36 muffins
d
45 muffins
Answer:
c
Step-by-step explanation:
1 1/2 cups x 2 bread = 12
12 cups x 3 for 1/3 per recipe =36
Answer:
C.
Step-by-step explanation:
2 loaves of bread: 1 1/2 (flour per one loaf) * 2 (amt of loaves) = 3 (total flour used)
15 (total amt of flour) - 3 (flour used to bake bread) = 12 (remaining flour)
12 (remaining flour) / 1/3 (flour per muffin) = 36 (muffins able to be made)
A chemist puts 0.5 liters of liquid in each of 15 beakers. How much liquid is there in total?
Answer:
Step-by-step explanation:
The answer is 7.5 liters.
You get this answer by simply multiplying 0.5 by 15(0.5 x 15= = 7.5). Or you could add 0.5 to 0.5, 15 times(0.5 + 0.5 + 0.5 + 0.5 + 0.5 + 0.5 + 0.5 + 0.5 + 0.5 + 0.5 + 0.5 + 0.5 + 0.5 + 0.5 +0.5 = 7.5)
prove that the points (2,-2),(-2,1) and (5,2) are the vertices of a right angled triangle. also find the area of this triangle
Answer:
1st use distance formula for each side of the triangle
then use PT for checking if they are equal then u will get it as equal
then use area of triangle formula u will get the ans explanation:
8.1 geometry big ideas
Answer:
24
Step-by-step explanation:
16/12 is 1.333333333
20/15 is 1.333333333
18x1.333333333 is 24
A theater has three eight four seats each row has 16 seats how many rows of seats are there
Answer:
24 rows
Step-by-step explanation:
348 divided by 16 is 24. Hope this helps!
Answer:
24
Step-by-step explanation:
You divide 384 seats and 16 rows. (348/16=24)
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What number is 4/7 of 210
Answer:
4 / 7 of 210 is 120.
(4 / 7) * 210 = 120
Answer:
4/7 x 210
=4x 30=120
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What is a sum of 24 and a quotient of 3
Answer:
32
Step-by-step explanation:
Assuming this interpretation is correct:
24 and a quotient of 3 will lead to 8
And the sum of 24 and 8 is 32.
Cheers.
There are many answers to this question.
For example:12+2=24 and 12/4=3.
A researcher obtains z = 1.80 for a one-sample z test. What is the decision for this test at a .05 level of significance?
Group of answer choices
a. to reject the null hypothesis
b. to retain the null hypothesis
c. It depends on whether the test is one-tailed or two-tailed.
d. There is not enough information to make a decision.
The decision for this test at a .05 level of significance is not enough information to make a decision the correct answer is (d).
To make a decision for a hypothesis test, we compare the obtained test statistic (in this case, z = 1.80) with the critical value(s) based on the chosen level of significance (in this case, α = 0.05).
For a one-sample z test, if the obtained test statistic falls in the rejection region (i.e., beyond the critical value(s)), we reject the null hypothesis. Otherwise, if the obtained test statistic does not fall in the rejection region, we fail to reject the null hypothesis.
Without knowing the critical value(s) corresponding to a significance level of 0.05 and the directionality of the test (one-tailed or two-tailed), we cannot determine the decision for this test. Therefore, the correct answer is (d) There is not enough information to make a decision.
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A company estimates that it will need $97,000 in 13 years to replace a computer. If it establishes a sinking fund by making fixed monthly payments into an account paying 3.2% compounded monthly, how much should each payment be? (Round your answer to the nearest cent. Do not include any symbols. Example: 56789.12)
Thus, the company must consider fixed monthly payments of amount $497.92 into the account to reach $97,000 in 13 years.
To find the monthly payment needed to reach $97,000 in 13 years, we can use the sinking fund formula:
FV = PMT * [(1 + i)^n - 1] / i
where:
FV = future value ($97,000)
PMT = monthly payment (unknown)
i = monthly interest rate (3.2% compounded monthly, which is 0.032 / 12 = 0.002667)
n = number of months (13 years * 12 months/year = 156 months)
Rearrange the formula to solve for PMT:
PMT = FV * i / [(1 + i)^n - 1]
PMT = 97,000 * 0.002667 / [(1 + 0.002667)^156 - 1]
PMT ≈ 497.92
So, the company should make fixed monthly payments of approximately $497.92 into the account to reach $97,000 in 13 years.
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3. Determine the slope of the line that has the following coordinates: (-3, 6) (4,-2)
-8/7
8/7
-7/8
12/7
Answer:
-8/7
Step-by-step explanation:
(-3, 6) & (4,-2)
To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)
Plug in these values:
(-2 - 6) / (4 - (-3))
Simplify the parentheses.
= (-2 - 6) / (4 + 3)
= -8 / 7
Simplify the fraction.
= -8/7
This is your slope.
Hope this helps!
Kathy measured her finger using a ruler with centimeters.Then she measured the same finger with a ruler using millimeters. can Kathy compare the two measuresments ?
Answer:
no
Step-by-step explanation:
For comparison one must express quantities in the same units
find the length x of JK . hurrryyyy