Step-by-step explanation:
2x + 28° + 90° = 180° ( The sum of all angle of triangle is 180° )
Now you may add 28° and 90° and subtract it from 180° ...
2x = 62° ..
Now...divide 62 by 2 ...
x = 31°
hence the value of x is 31°....
What is the future value of a 5-year annuity due with annual payments of $ 2,535 , evaluated at a 14.18 percent interest rate? Enter your answer to the nearest $.01. Do not use $ or , signs in your answer. Enter your answer as a positive number.
Answer:
$19,201.09
Step-by-step explanation:
The future value of the annuity due can be found using any of a number of apps, calculators, or spreadsheets. It can also be found using the formula ...
A = P(1 +r)((1 +r)^n -1)/r
where P is the annual payment, r is the annual interest rate, and compounding is yearly for n years.
A = 2535(1.1418)(1.1418^5 -1)/0.1418 ≈ 19,201.09
The value will be $19,201.09.
Write two numbers that multiply to the value on top and add to the value on bottom.
-84
17
Two numbers multiply the value on top (-84) and add to the value on the bottom (17) is 21 and -4.
What is multiplication?Multiplication is one of the four basic arithmetic operations, alongside addition, subtraction, and division. Multiplication essentially means the repeated addition.
The two given numbers are -84 and 17.
We need to write two numbers that multiply to the value on top (-84) and add to the value on the bottom (17).
If we multiply 21 and -4, we get the product as -84.
That is, 21×(-4)=-84
If we add 21 and -4, we get the sum as -17.
That is, 21+(-4)=21-4=17
Therefore, two numbers multiply the value on top (-84) and add to the value on the bottom (17) is 21 and -4.
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Determine whether each triangle with sides of given length is a right triangle. justify your answer
7 yd, 5 yd, 9 yd
10 ft, 24ft, 26 ft
The triangles with the side lengths 10 ft, 24ft, 26 ft, is a right triangle while a triangle with side lengths of 7 yd, 5 yd, 9 yd is NOT based on the Pythagorean theorem.
What is a Right Triangle?A triangle is said to be a triangle based on the Pythagorean theorem, if the square of the longest side equals the sum of the squares of the other smaller sides of the triangle.
9² = 7² + 5²
81 = 74 (NOT TRUE), therefore, the triangle with the side lengths 7 yd, 5 yd, 9 yd, is not a right triangle.
26² = 10² + 24²
676 = 676 (TRUE), therefore, the triangle with the side lengths 10 ft, 24ft, 26 ft, is a right triangle.
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( - 37 + 37 ) ÷ - 15 = What is the answerr
Answer:
0
Step-by-step explanation:
[tex]~~~(-37+37 )\div(-15)\\\\=0\div (-15)\\\\=0[/tex]
Answer:
0
Step-by-step explanation:
Following PEMDAS -37+37 is 0 and 0/-15 is also 0
find the sum. 1-2+3-4+5-6+7-8...99-100
Answer:
-50
Step-by-step explanation:
1 - 2 + 3 - 4 + 5 - 6 + 7 - 8...99 - 100
just means,
1 - 2 = -1
3 - 4 = -1
5 - 6 = - 1
7 - 8 = - 1
99 - 100 = -1
basically, -1 + -1 + -1 + -1 + ....+ -1 or -1 - 1 - 1 - 1 - ... - 1
[tex](-1)^{n}[/tex]
Treating Grandi's series as a divergent geometric series we may use the same algebraic methods that evaluate convergent geometric series to obtain a third value:
S = 1 − 1 − 1 + ..., so
1 − S = 1 − (1 − 1 − 1 ...) = 1 − 1 − 1 ... = S
1 - S = S
1 = 2*S
resulting in S = 1/2. The same conclusion results from calculating −S, subtracting the result from S, and solving 2S = 1
1/2 of the last term is 100 x 1/2 = 50
This because you are using 2 numbers per -1
example: 1 - 2 = -1 or 3 - 4 = -1 resulting in 50 of the -1 being subtracted
If we changed the 3 to a 0 in the equation, what would happen to the graph?
A function assigns the values. The function will move down by 3 units.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The graph of the function is given below. Now if 3 is replaced by a 0, then the y-intercept of the function will become zero while keeping the slope the same. Therefore, the function will move down by 3 units.
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F. In what order should items weighing
51 pounds, 40 pounds, 48 pounds,
and 44 pounds be stacked if you want
them in order from heaviest to lightest?
Answer:
51 pounds, 48 pounds, 44 pounds and 40 pounds in that chronological order.
Deion has 62 m of fencing to build a four-sided fence around a rectangular plot of
land. The area of the land is 228 square meters. Solve for the dimensions (length and
width) of the field?
The dimensions of the the plot of land is a length of 19 meters and width of 12 meters.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the length of the field and y represent the width of the field, hence:
Deion has 62 m of fencing:
2(x + y) = 62
x + y = 31
y = 31 - x (1)
The area of the land is 228 square meters. hence:
xy = 228
x(31 - x) = 228
x² - 31x + 228 = 0
x = 12 or x = 19
when x = 12; y = 31 - 12 = 19
when x = 19; y = 31 - 19 = 12
The dimensions of the the plot of land is a length of 19 meters and width of 12 meters.
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If a sample proportion is 0.65, which range of possible values best describes
an estimate for the population parameter?
O A. (0.5, 0.89)
• B. (0.5, 0.8)
• C. (0.65, 0.7)
• D. (0.6, 0.69)
The range of possible values that best describes an estimate for the population parameter is; (0.5, 0.8)
How to estimate proportion?The range of possible values that best describes an estimate for the population parameter is; (0.5, 0.8).
When we are talking about population parameters, we also have to look at the way of estimating the population, we have to add two extremes and divide by 2.
Thus, the correct one is;
(0.5 + 0.8)/2 = 0.65
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Help for college scholarships! Must be a paragraph.
How has your family background affected the way you see the world?
Family background refers to the culture and tradition of the family into which a person is born.
What is family background?Family background refers to the culture and tradition of the family into which a person is born. it is worthy of note that most of this family traditions are unspoken yet are firmly entrenched in the psyche of individual as he/she grows.
My family is strictly conservative having had a Southern Baptist orientation. My dad believes deeply in religion and a moralist and perfectionist.
As a result of this, I find myself always grappling with the unfortunate disorder in the world; always trying to bring order to my world as much as I can.
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What is true of the function g(x) = -2x² + 5?
O g(x) is the multiplication of g and x.
O-212 +5 is the input of the function.
The variable x represents the independent variable.
The variable g represents the input of the function.
Answer:
C.) The variable x represents the independent variable
Step-by-step explanation:
The variable "x" is the independent variable because that is the value that we can manipulate. We cannot manipulate the dependent variable because it is determined by the independent variable. In that case, "y" would be the dependent variable because its value is dependent on what "x" is.
A.) is incorrect because g(x) symbolizes the input of the variable "x" into the g function.
B.) is incorrect because "x" is the input.
D.) is incorrect because "x" is the input.
solve for x in the following equations
Answer:
2.
[tex]x = \frac{11}{4} = 2 \frac{3}{4} = 2.75[/tex]
3.
[tex]x = \frac{5}{2} = 2 \frac{1}{2} = 2.5[/tex]
4.
[tex]x = \frac{3}{7} ≈0.428571429[/tex]
Select the correct answer. Which expression is equivalent to the complex number 10 + 3i?
The expression that is equivalent to the complex number 10 + 3i is (4+7i)-2i(2+3i)
Complex numbersComplex numbers are square root of negative numbers. They are expressed as a + bi
Using the expression
(4+7i)-2i(2+3i)
Expand
4 + 7i - 4i -2i(3i)
4 + 3i - 2(-3)
4 + 6 + 3i
10 + 3i
Hence the expression that is equivalent to the complex number 10 + 3i is (4+7i)-2i(2+3i)
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what is the area of the figure?
Answer:
area = 62ft
Step-by-step explanation
so you section the polygon into a big rectangle and 2 small rectangles
the area of the small rectangle will be 2ft x 3ft which will be 6 ft, and as there are 2 of them the area of it will be 12ft
the area of the big rectangle will be 10ft x 5ft, as 8ft - 3ft is 5ft so 5x10=50ft
now add the areas you got, 50+12 which is 62ft
hope this helps:)
4. Evaluate e^-2 to one decimal place
A) 0.7
B) -1.4
C) 0.1
D) 1.4
suppose y varies inversely as x and y=12 when x=6 find y if x=8
Answer:
y = 9
Step-by-step explanation:
given that y varies inversely as x then the equation relating them is
y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation
to find k use the condition y = 12 when x = 6
12 = [tex]\frac{k}{6}[/tex] ← multiply both sides by 6 to clear the fraction
72 = k
y = [tex]\frac{72}{x}[/tex] ← equation of variation
when x = 8 , then
y = [tex]\frac{72}{8}[/tex] = 9
Admission to a baseball game is $3.00 for general admission and $5.50 for reserved seats. The receipts were $3277.50 for 845 paid admissions. How many of each ticket were sold?
Answer:
548, 297
Step-by-step explanation:
We can set this up as a system of equations. The first equation is for how many tickets were sold, which is x+y=845. The second equation is for the cost of the tickets, which is 3x+5.5y=3277.50. The best method for this problem (other than graphing) is elimination. First, we need to multiply one equation to get the opposite of one of the variables. The easiest one to do for this problem is x. The opposite of 3 is -3, so we have to multiply ALL of the first equation by -3. If you do this, then you get -3x-3y=-2535. Now, combine the equations:
3x + 5.5y = 3277.50
-3x -3y = -2535
________________
0x+2.5y=742.5
Now, isolate y by dividing both sides by 2.5. If you do this, you get y=297. Now, plug this in for the y in the first equation. Isolate x.
x+297=845
-297 -297
__________
0 548
x=548
Hope this helps!
Two adjacent rooms are rectangles, both of length 13 feet by 10 feet. Jerry wants to change the carpets in both rooms. How many square feet should he order?
Answer:
260 square feet
Step-by-step explanation:
The area of a rectangle is given by the formula ...
A = LW
The area of two same-size rectangular rooms will be double the area of one of them.
__
room areaEach room has an area of ...
A = LW = (13 ft)(10 ft) = 130 ft²
carpet orderThe order for carpet must be for 2 times the area of one room:
carpet order = 2 × 130 ft² = 260 ft²
Jerry should order 260 square feet of carpet.
Please show how you solved
Answer:
x = 7 degrees
Step-by-step explanation:
The unlabelled angle at M PLUS 12x + 24 = 180
then the unlabelled interior angle is 180 - (12x+24)
The sum of the interior angles then = 180
80 + 4x + 180-(12x+24) = 180
236 -8x = 180
x = 7
Given that 24w = 14ten .Find the unknown base
Answer:
w = 5
Step-by-step explanation:
24w = (14)10
2w + 4 = 10 + 4
2w = 10
w = 5
What is the length of the hypotenuse of the right triangle shown below? bottom is 4 right side 3
Type your answer as an integer.
Answer:
5
Step-by-step explanation:
This is a 3,4,5 triangle
and to prove that;
3^2 + 4^2 = 5^2
25 = 25 is a correct statement
Review the graph of complex number z.
On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. Point z is at (negative 3, 1).
What is the modulus of z?
2
2StartRoot 2 EndRoot
3
StartRoot 10 EndRoot
Answer:
√10Step-by-step explanation:
[tex]\text {modulus of z } = =\sqrt{\left( -3\right)^{2} +\left( 1\right)^{2} } =\sqrt{9+1} =\sqrt{10}[/tex]
Answer:
square root of 10
Step-by-step explanation:
write a Pythagorean triplet whose smallest member is 6
Answer:
6, 8, 10
Step-by-step explanation:
Where:
a = 6
b = 8
c = 10
Pythagorean theorem: [tex]a^2 + b^2 = c^2[/tex]
[tex]6^2 + 8^2 = c^2[/tex]
[tex]36 + 64 = c^2[/tex]
[tex]100 = c^2[/tex]
c = [tex]\sqrt{100}[/tex]
c = 10
Please solve with explanation (high points)
Answer:
see the attachment photo!
What is true about AngleQRT? Select two options.
Measure of angleQRT = 90°
Measure of angleQRT = Measure of angleSRT
AngleQRT Is-congruent-to AngleSTQ
Measure of angleQRT = 2*Measure of angleRTQ
AngleQRT Is-congruent-to AngleRTQ
The complete question is
"Triangle QST is isosceles, and Line segment R T bisects AngleT. Triangle Q S T is cut by bisector R T. The lengths of sides S T and Q T are congruent. Line segments S R and R Q are congruent. Angles S T R and R T Q are congruent. What is true about AngleQRT?
Select two options. Measure of angleQRT = 90° Measure of angleQRT = Measure of angleSRT AngleQRT Is-congruent-to AngleSTQ Measure of angleQRT = 2*Measure of angleRTQ AngleQRT Is-congruent-to AngleRTQ"
The true about AngleQRT options are A abd B; ∠QRT = 90 and ∠QRT = ∠SRT
What is the congruent triangle?Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.
Given information;
The triangle QST is isosceles with QT ≅ ST.
The ∠STR and ∠RTQ are congruent.
Now, consider two triangles ∠QTR and ∠STR
In the following triangle
TR ≅ TR
QTR ≅ STR
QT ≅ ST
Now, according to SAS rule, two congruent triangles have congruent corresponding to their sides,
1. QR ≅ SR
2. QRT ≅ SRT
Since the above two angles are congruent so, they will have the same measure
That will be 90 degree.
Hence, The correct options are; ∠QRT = 90 and ∠QRT = ∠SRT
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Amalia and Alec are studying the growth of a plant over time. They measure the height of the plant at the end of each week for several weeks and display the data in a scatter plot. They then find the equation for the best-fit line to be y=2.5+ 1.25x
X=the number of weeks that have passed
Y = the height of the plant
How tall will with plant be after 7 weeks?
After 7 weeks the plant will 11.25 units tall if the equation for the best-fit line to be y = 2.5 + 1.25x.
What is the line of best fit?A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.
[tex]\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2} \\\\\rm c = \dfrac{\sum y -m \sum x}{n}[/tex]
We have a line of best fit:
y = 2.5 + 1.25x
Plug x = 7 weeks
y = 2.5 + 1.25(7)
y = 11.25 units
Thus, after 7 weeks the plant will 11.25 units tall if the equation for the best-fit line to be y = 2.5 + 1.25x.
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can someone help me with this worksheet please!!!!
(1) The missing term in the sequence, a₁₂ = 0.8.
(2) The missing term in the sequence, a₈ = 102.5.
(3) The missing term in the sequence, a₈ = 111.
(4) The missing term in the sequence, a₁₂ = -19.
(5) The missing term in the sequence, a₁₂ = 94.
(6) The missing term in the sequence, a₆ = 40.
(7) The missing term in the sequence, a₃₆ = -52.
(8) The missing term in the sequence, a₂₁ = -58.
Missing term of the sequenceThe missing term in the sequence is determined as follows;
Tₙ = a + (n - 1)d
1.0 a₄ = 18.4 and a₅ = 16.2, a₁₂ = ?T₄ = a + 3d
18.4 = a + 3d ---(1)
T₅ = a + 4d
16.2 = a + 4d ---(2)
subtract (1) from (2)
-2.2 = d
18.4 = a + 3(-2.2)
a = 25
a₁₂ = a + 11d
a₁₂ = 25 + 11(-2.2)
a₁₂ = 0.8
2.0 a₂ = 57.5 and a₅ = 80, a₈ = ?a₂ = a + d
57.5 = a + d -- (1)
a₅ = a + 4d
80 = a + 4d --- (2)
solve (1) and (2)
d = 7.5
a = 50
a₈ = a + 7d
a₈ = 50 + 7(7.5)
a₈ = 102.5
3.0 a₁₀ = 141 and a₁₃ = 186, a₈ = ?a₁₀ = a + 9d
141 = a + 9d --- (1)
a₁₃ = a + 12d
186 = a + 12d --- (2)
Subtract (1) from (2)
d = 15
a = 6
a₈ = a + 7d
a₈ = 6 + 7(15)
a₈ = 111
4.0 a₂₂ = -49 and a₂₅ = -58, a₁₂ = ?a₂₂ = a + 21d
-49 = a + 21d ---- (1)
a₂₅ = a + 24d
-58 = a + 24d --- (2)
subtract (1) from (2)
d = -3
a = 14
a₁₂ = a + 11d
a₁₂ = 14 + 11(-3)
a₁₂ = -19
5.0 a₄ = -2 and a₈ = 46, a₁₂ = ?a₄ = a + 3d
-2 = a + 3d --- (1)
a₈ = a + 7d
46 = a + 7d ---- (2)
Subtract (1) from (2)
d = 12
a = -38
a₁₂ = a + 11d
a₁₂ = -38 + 11(12)
a₁₂ = 94
6.0 a₉ = 64 and a₁₂ = 88, a₆ = ?a₉ = a + 8d
64 = a + 8d --- (1)
a₁₂ = a + 11d
88 = a + 11d --- (2)
Subtract (1) from (2)
d = 8
a = 0
a₆ = a + 5d
a₆ = 0 + 5(8)
a₆ = 40
7.0 a₂₀ = -4 and a₂₃ = -13, a₃₆ = ?a₂₀ = a + 19d
-4 = a + 19d ---- (1)
a₂₃ = a + 22d
-13 = a + 22d --- (2)
Subtract (1) from (2)
d = -3
a = 53
a₃₆ = a + 35d
a₃₆ = 53 + 35(-3)
a₃₆ = -52
8.0 a₂₈ = 5 and a₃₃ = 50, a₂₁ = ?a₂₈ = a + 27d
5 = a + 27d ---- (1)
a₃₃ = a + 32d
50 = a + 32d --- (2)
Subtract (1) from (2)
d = 9
a = -238
a₂₁ = a + 20d
a₂₁ = -238 + 20(9)
a₂₁ = -58
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The number line shows four points, which point represents the approximate location of √92?
A) Point A
B) Point B
C) Point C
D) Point D
Answer: Point D
Step-by-step explanation:
92 is in between 81 and 100, so [tex]9 < \sqrt{92} < 10[/tex]
Gravano Engineering co has the following items appearing in its statement of financial position at the year end:
What is the total for:
1. Non-current assets?
2. Current assets?
Trade payables 39000
2) Cash at bank 14,000
3). Motor vans 25000 4)Inventories 7000
5) Bank overdraft 13,000 6)Property 96,000
7)Trade receivables 43,000
8)Plant and equipment 26,000
9)Trademarks 28,000 10. Fixtures and fittings 17,000 11. Mortgage on property 45,000
Based on the items appearing in Gravano Engineering's Statement of Financial Position at the year-end, the totals for the following are:
1. Non-current Assets = $192,000
2. Current Assets = $64,000
What is a Statement of Financial Position?A Statement of Financial Position is a financial statement that shows an entity's assets, liabilities, and equity.
Assets are items owned by an individual or entity that generate current, future, or potential economic benefits.
Liabilities are financial obligations that an individual or entity owes creditors.
Equity is the difference between assets and liabilities, which refers to the financial benefits accruing to the stockholders.
Data and Calculations:1. Trade payables $39,000
2. Cash at bank 14,000
3. Motor vans 25,000
4. Inventories 7,000
5. Bank overdraft 13,000
6. Property 96,000
7. Trade receivables 43,000
8. Plant and equipment 26,000
9. Trademarks 28,000
10. Fixtures and fittings 17,000
11. Mortgage on property 45,000
Current Assets:2. Cash at bank 14,000
4. Inventories 7,000
7. Trade receivables 43,000
Total current assets = $64,000
Non-Current Assets:3. Motor vans 25,000
6. Property 96,000
8. Plant and equipment 26,000
9. Trademarks 28,000
10. Fixtures and fittings 17,000
Total non-current assets = $192,000
Thus, the total non-current assets are $192,000 and the current assets total $64,000.
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Hoang has worked as a nurse at Springfield General Hospital for 5 years longer than her friend Bill Two years ago she has been at the hospital for twice as long How long has each been at r=the hospital
Answer:
Hoang has been at the hospital for 12 years while Bill has worked for 7 years.
Step-by-step explanation:
Let the years Hoang has worked as a nurse equal h and let the years Bill has worked as a nurse equal b.
Since Hoang has worked 5 years longer, h is five more than b:
h = b + 5
Now we move onto the situation 2 years ago. 2 years ago, Hoang had worked at the hospital two less than h or h-2 years while Bill has worked for b-2 which is two years less than b. We are also told that at the time, Hoang worked twice as longs, so
h - 2 = 2(b - 2)
This can be simplified:
h - 2 = 2b - 4
h = 2b - 2
We can use substitution. Since h = b + 5 and h = 2b - 2,
b + 5 = 2b - 2
b = 7
Therefore, since Hoang has worked five more years, h = 12. So, Hoang has been at the hospital for 12 years while Bill has worked for 7 years.