Answers
1. Solving linear equations:
(a) x = 4.
(b) r = 2/3.
2. Proportion:
(a) When x = 40, y = 100.
(b) When x = 40, y = 4.
3. System of equations:
(a) r = 8, s = 3.
(b) p = 5, q = -2.
4. Graphing lines:
(a) The slope of the line through (3, 4) and (-1, 3) is 1/4.
(b) The slope of the line 3x - 4y = 7 is 3/4.
(c) The slope-intercept form of the line through (5, -2) and (-1, 6) is y = (-4/3)x + 14/3.
5. Introductory quadratics:
(a) The solutions to the equation 4x² = 81 are -9/2, and 9/2.
(b) The solutions to the equation x² + 8x + 12 are -6, and -2.
(c) The solutions to the equation x² - 3x - 88 are -8, and 11.
6. The weight of an orange is 1 unit, the weight of an apple is 5 units, and the weight of a banana is 2 units.
7. x = 3.
1. Solving linear equations:
(a) 3x - 7 = 9 - x,
or, 3x + x = 9 + 7,
or, 4x = 16,
or, x = 16/4 = 4.
Thus, x = 4.
(b) (7 - 2r)/3 = 4r,
or, 7 - 2r = 3*4r = 12r,
or, -2r - 12r = -7,
or, -14r = -7,
or, r = -7/-14 = 1/2.
Thus, r = 1/2.
2. Proportion:
(a) x and y directly proportion, means x/y = constant.
When x = 8, y = 20.
Thus, x/y = constant, or, 8/20 = constant, or, constant = 0.4.
When x = 40,
x/y = 0.4,
or, y = x/0.4 = 40/0.4 = 100.
Thus, when x = 40, y = 100.
(b) x and y indirectly proportion, means xy = constant.
When x = 8, y = 20.
Thus, xy = constant, or, 8*20 = constant, or, constant = 160.
When x = 40,
xy = 160,
or, 40y = 160,
or, y = 160/40 = 4.
Thus, when x = 40, y = 4.
3. System of equations:
(a) r - s = 5 ...(i)
3r - 5s = 9 ... (ii)
3*(i) - (ii) gives:
3r - 3s = 15
3r - 5s = 9
(-) (+) (-)
_________
2s = 6,
or, s = 3.
Substituting in (i), we get
r - s = 5,
or, r - 3 = 5,
or, r = 8.
Thus, r = 8, s = 3.
(b) 3p + 7q = 1 ...(i).
5p = 14q + 53,
or, 5p - 14q = 53 ...(ii).
2*(i) + (ii) gives:
6p + 14q = 2
5p - 14q = 53
____________
11p = 55,
or, p = 5.
Substituting in (i), we get:
3p + 7q = 1,
or, 3*5 + 7q = 1,
or, 7q = 1 - 15 = -14,
or, q = -14/7 = -2.
Thus, p = 5, q = -2.
4. Graphing lines:
(a) Slope of the line through (3, 4) and (-1, 3) is,
m = (4 - 3)/(3 - (-1)),
or, m = 1/4.
Thus, the slope of the line through (3, 4) and (-1, 3) is 1/4.
(b) The graph given: 3x - 4y = 7.
Representing in the slope-intercept form, y = mx + b, gives:
3x - 4y = 7,
or, 4y = 3x - 7,
or, y = (3/4)x + (-7/4).
Thus, the slope of the line 3x - 4y = 7 is 3/4.
(c) Slope of the line through (5, -2) and (-1, 6) is,
m = (6 - (-2))/(-1 - 5),
or, m = 8/(-6) = -4/3.
Substituting m = -4/3 in the slope-intercept form, y = mx + b, gives:
y = (-4/3)x + b.
Substituting y = 6, and x = -1 gives:
6 = (-4/3)(-1) + b,
or, b = 6 - 4/3 = 14/3.
Thus, the slope-intercept form of the line through (5, -2) and (-1, 6) is y = (-4/3)x + 14/3.
5. Introductory quadratics:
(a) 4x² = 81,
or, 4x² - 81 = 0,
or (2x)² - 9² = 0,
or, (2x + 9)(2x - 9) = 0.
Either, 2x + 9 = 0 ⇒ x = -9/2,
or, 2x - 9 = 0 ⇒ x = 9/2.
Thus, the solutions to the equation 4x² = 81 are -9/2, and 9/2.
(b) x² + 8x + 12 = 0,
or, x² + 2x + 6x + 12 = 0,
or, x(x + 2) + 6(x + 2) = 0,
or, (x + 6)(x + 2) = 0.
Either, x + 6 = 0 ⇒ x = -6,
or, x + 2 = 0 ⇒ x = -2.
Thus, the solutions to the equation x² + 8x + 12 are -6, and -2.
(c) x² - 3x - 88 = 0,
or, x² - 11x + 8x - 88 = 0,
or, x(x - 11) + 8(x - 11) = 0,
or, (x + 8)(x - 11) = 0.
Either, x + 8 = 0 ⇒ x = -8,
or, x - 11 = 0 ⇒ x = 11.
Thus, the solutions to the equation x² - 3x - 88 are -8, and 11.
6. We assume the weight of one orange, one apple, and one banana to be x, y, and z units respectively.
Thus, we have:
3x + 2y + z = 15 ... (i)
5x + 7y + 2z = 44 ... (ii)
x + 3y + 5z = 26 ... (iii)
2(i) - (ii) gives:
6x + 4y + 2z = 30
5x + 7y + 2z = 44
(-) (-) (-) (-)
______________
x - 3y = -14 ... (iv)
5(i) - (iii) gives:
15x + 10y + 5z = 75
x + 3y + 5z = 26
(-) (-) (-) (-)
________________
14x + 7y = 49 ... (v)
14(iv) - (v) gives:
14x - 42y = -196
14x + 7y = 49
(-) (-) (-)
_____________
-49y = -245,
or, y = 5.
Substituting in (v), we get:
14x + 7y = 49,
or, 14x + 35 = 49,
or, x = 14/14 = 1.
Substituting x = 1 and y = 5 in (i), we get:
3x + 2y + z = 15,
or, 3 + 10 + z = 15,
or, z = 2.
Thus, the weight of an orange is 1 unit, the weight of an apple is 5 units, and the weight of a banana is 2 units.
7. 3/(1 - (2/x)) = 3x,
or, 3/((x - 2)/x) = 3x,
or, 3x/(x - 2) = 3x,
or, 3x = 3x(x - 2),
or, 3x = 3x² - 6x,
or, 3x² - 9x = 0,
or, 3x(x - 3) = 0.
Either, 3x = 0 ⇒ x = 0,
or, x - 3 = 0 ⇒ x = 3.
Since we had a term 2/x, x cannot be 0.
Thus, x = 3.
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Related Questions
SOLVE THE FOLLOWING PROBLEMS.
A) IN HOW MANY WAYS CAN THE LETTERS OF THE WORD “TRACK” BE ARRANGED?
B) A STUDENT MUST SELECT AND ANSWER SIX OUT OF TEN QUESTIONS ON AN EXAM. IN HOW MANY WAYS CAN THIS BE DONE?
C) A TEACHER DECIDES TO GIVE SIX IDENTICAL PRIZES TO 6 OF THE 20 STUDENTS IN HIS CLASS. IN HOW MANY WAYS CAN THIS BE DONE
Answers
The answers to the question are:
12021038760How to solve for permutations and combinations1. The letters of the word track can be arranged in 5! ways
These are 5 x 4 x 3 x 2 x1
= 120
2. The way that the student would be able to select 6 out of 10 questions would be by 10C6
= 210 ways
C)This teacher would be able to make the decision of the prices to the students using =20C6= n!(n-r!r!)
= 38760
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question:
|x-2|, if x > 5
simplify without the absolute value sign
Answers
Answer:
x - 2, if x > 5
Step-by-step explanation:
The vertical lines either side of the expression mean absolute value.
The absolute value of a number is its positive numerical value.
if x > 5 then as 5 > 2, the values inside the vertical lines will always be positive. Therefore, we can disregard the absolute value.
Therefore:
x - 2, if x > 5
To find the range (output values) of the expression, substitute x = 5 into the expression:
⇒ 5 - 2 = 3
Therefore, |x - 2| > 3, if x > 5
HELP ASAP 20 POINTS CAUSE IM DESPERATE ToT
Write each expression in the standard form for the complex number a + bi.
1. [ 4 ( cos (7pi/9) + i sin (7pi/9))]^3
2. The complex fifth roots of 5 - 5 sqrt(3)i
Answers
1. By de Moivre's theorem,
[tex]\left(4\left(\cos\left(\dfrac{7\pi}9\right) + i \sin\left(\dfrac{7\pi}9\right)\right)\right)^3 = 4^3 \left(\cos\left(\dfrac{21\pi}9\right) + i \sin\left(\dfrac{21\pi}9\right)\right) \\\\ ~~~~~~~~ = 64 \left(\cos\left(\dfrac{7\pi}3\right) + i \sin\left(\dfrac{7\pi}3\right)\right) \\\\ ~~~~~~~~ = 64 \left(\cos\left(\dfrac\pi3\right) + i \sin\left(\dfrac\pi3\right)\right) \\\\ ~~~~~~~~ = 64 \left(\dfrac12 + i\dfrac{\sqrt3}2\right) \\\\ ~~~~~~~~ = \boxed{32 + 32\sqrt3\,i}[/tex]
2. First write the given number in exponential/trigonometric form.
[tex]z = 5-5\sqrt3\,i[/tex]
has modulus
[tex]|z| = \sqrt{5^2 + \left(-5\sqrt3\right)^2} = \sqrt{100} = 10[/tex]
and since it lies in the second quadrant of the complex plane, its argument is
[tex]\arg(z) = \pi + \tan^{-1}\left(-\dfrac{5\sqrt3}5\right) = \pi + \tan^{-1}\left(-\sqrt3\right) = \pi - \dfrac\pi3 = \dfrac{2\pi}3[/tex]
So, we have
[tex]z = 5 - 5\sqrt3\,i = 10 e^{i2\pi/3} = 10 \left(\cos\left(\dfrac{2\pi}3\right) + i \sin\left(\dfrac{2\pi}3\right)\right)[/tex]
Now we apply de Moivre's theorem again, and make sure to account for the multivalued-ness of the exponential function. For [tex]k\in\{0,1,2,3,4\}[/tex], the fifth roots of [tex]z[/tex] are
[tex]z^{1/5} = 10^{1/5} e^{i(2\pi/3 + 2\pi k)/5}[/tex]
[tex]k=0 \implies z^{1/5} = 10^{1/5} e^{i2\pi/15} = \boxed{10^{1/5} \left(\cos\left(\dfrac{2\pi}{15}\right) + i \sin\left(\dfrac{2\pi}{15}\right)\right)}[/tex]
[tex]k=1 \implies z^{1/5} = 10^{1/5} e^{i8\pi/15} = \boxed{10^{1/5} \left(\cos\left(\dfrac{8\pi}{15}\right) + i \sin\left(\dfrac{8\pi}{15}\right)\right)}[/tex]
[tex]k=2 \implies z^{1/5} = 10^{1/5} e^{i14\pi/15} = \boxed{10^{1/5} \left(\cos\left(\dfrac{14\pi}{15}\right) + i \sin\left(\dfrac{14\pi}{15}\right)\right)}[/tex]
[tex]k=3 \implies z^{1/5} = 10^{1/5} e^{i20\pi/15} = \boxed{10^{1/5} \left(\cos\left(\dfrac{4\pi}3\right) + i \sin\left(\dfrac{4\pi}3\right)\right)}[/tex] [tex]k=4 \implies z^{1/5} = 10^{1/5} e^{i26\pi/15} = \boxed{10^{1/5} \left(\cos\left(\dfrac{26\pi}{15}\right) + i \sin\left(\dfrac{26\pi}{15}\right)\right)}[/tex]
What is the ratio of my lawn if it is 4 meters by 4.5 meters
Answers
Answer:
The 1:n ratio is= 1 : 1.125
The n:1 ratio is= 8/9 : 1
Just the simple ratio is= 4 : 4.5
Question
Which of the following equations is equivalent to 8x - 6y = 12?
y = ³x - 1²/2 3
y=x-2
y = 2x - 12
y = 8x - 6
Answers
The equation that is equivalent to 8x - 6y = 12 is: B. y = 4x/3 - 2.
What are Equivalent Equations?Equations that are equivalent to each other have the same value when evaluated or simplified.
Given the equation, 8x - 6y = 12, to determine which of the given equations in the options is equivalent to, rewrite the equation in slope-intercept form, as y = mx + b.
8x - 6y = 12
Subtract 8x from both sides of the equation
8x - 8x - 6y = -8x + 12
-6y = -8x + 12
Divide both sides of the equation by -6
-6y/-6 = -8x/-6 + 12/-6
y = 4x/3 + (-2)
y = 4x/3 - 2
Therefore, the equation that is equivalent to 8x - 6y = 12 is: B. y = 4x/3 - 2.
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A COUPLE PLAN TO HAVE THREE CHILDREN.
A) LIST ALL THE POSSIBILITIES FOR THE SAMPLE SPACE.
B) WHAT IS THE PROBABILITY THAT THEY HAVE AT MOST TWO BOYS?
C) WHAT IS THE PROBABILITY THAT THEY HAVE AT LEAST TWO GIRLS?
D) WHAT IS THE PROBABILITY THAT THEY ARE ALL OF THE SAME SEX?
Answers
BBB
GBB, BGB, BBG
BGG, GBG, GGB
GGG
B) 0, 1, or 2 boys not 3
7/8
C) 2 or 3 girls
4/8=1/2
D) same sex
2/8=1/4
Astrid is looking for a job at a call center. Call center A offers her $15 per hour and call-center B offers her $.25 per minute.
Which place offers a higher wage?
Answers
Answer: They are the same
Step-by-step explanation: We convert both to $ per hour. Call center A is $15 per hour. Call center B is $.25 per minute. .25 per minute means $1.00 every 4 minutes. There are 15 4 minutes in an hour so they both offer the same wage.
The coefficient of 8 • 2N is
Answers
Answer:
16
Step-by-step explanation:
when we multiply we have 16n so thats is d coefficient
Find the area of the sector formed by the 60 degree central angle.
503π in2503π in2
103π in2103π in2
100π in2100π in2
None of the Above
Answers
The area of the sector of the circle is: A. 50/3π in.².
What is the Area of a Sector of a Circle?The area of a sector that is bounded by two radii of a circle is calculated using the formula, ∅/360 × πr², where we have the following parameters:
r = radius of the circle∅ = central angle formed by the sector.Thus, we are given the following regarding the sector of the circle:
Central angle (∅) = 60 degrees
Radius (r) = 10 inches.
Plug in the values into ∅/360 × πr²:
Area of sector = 60/360 × π(10²)
Area of sector = 1/6 × π(100)
Area of sector = 100/6 × π
Area of sector = 50/3 × π
Area of sector = 50/3π in.²
Thus, the area of the sector of the circle is: A. 50/3π in.².
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Application
I
3. Ray has a stride of about 1.4 m. He runs 9 km daily to train for a marathon. Approximately
how many strides does he need to run 9 km?
Answers
He needs to run with approximately 6429 for a distance of 9 km
How to determine the number of strides?The given parameters are:
Length of stride = 1.4 m
Distance for marathon = 9 km
The number of strides needed is then calculated as:
Number of stride = Distance for marathon/Length of stride
Substitute the known values in the above equation
Number of stride = 9km/1.4m
Convert km to m
Number of stride = 9000m/1.4m
Evaluate the quotient
Number of stride = 6428.57143
Approximate the estimate
Number of stride = 6429
Hence, he needs to run with approximately 6429 for a distance of 9 km
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30% of what number is
165
Answers
Answer:
550
Step-by-step explanation:
165 x 100= 16500/30=550
Find an nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using
a graphing utility, use it to graph the function and verify the real zeros and the given function value.
n=3;
-2 and 7+5 i are zeros;
f(2)=200
f(x) =
(Type an expression using x as the variable. Simplify your answer.)
possible
4
Answers
Answer:
f(x) = x³ -12x² +46x +148
Step-by-step explanation:
When p is a root of polynomial function f(x), (x -p) is a factor. When the coefficients are real, any complex roots come in conjugate pairs.
Factored formGiven the two roots of f(x), we know the third root is the conjugate of the given complex root. The factored form will be ...
f(x) = (x -(-2))(x -(7 +5i))(x -(7 -5i))
Rearranging a bit, this is ...
f(x) = (x +2)((x -7) -5i)((x -7) +5i)
The latter two factors are recognizable as the factors of the difference of squares, so this is ...
f(x) = (x +2)((x -7)² -(5i)²) = (x +2)((x -7)² +25)
Standard formMultiplying the factors, we have ...
f(x) = (x +2)(x² -14x +49 +25) = (x +2)(x² -14x +74)
f(x) = x³ -14x² +74x +2x² -28x +148 . . . . . use the distributive property
f(x) = x³ -12x² +46x +148 . . . . . . . . . . collect terms
A 12-yard-long pipe is cut into three equal sections. Two of the resulting sections are cut in half, and one of the halves is cut into thirds. If two pipe sections are chosen and combined end to end, what is the difference between the longest possible and shortest possible combinations? (Note: 1 yard = 3 feet)
Answers
Answer:
14ft
Step-by-step explanation:
12 yard pipe equals 36ft. Divided equally 3 times gives 3 pipes at 12ft per pipe. 2 of those are divided in half, making 4 6ft pipes. 1 of the 6ft pipes is cut into 3 2ft pipes. you now have 3 pipes at 2ft, 3 pipes at 6ft and 1 pipe at 12ft. the longest 2 pieces are 12ft and 6ft making 18ft. 2 shoetest pieces equal 4ft. 18ft minus 4ft equals 14ft.
Will mark brainliest
Answers
The plot of [tex]\sqrt{25-x^2}[/tex] is that of the top half of a circle with radius 5. The interval [-5, 0] captures the left half of this semicircle.
Adding 5 to this shifts the plot up by 5 units. The area under this curve is then the combined area of a square with side length 5 and the area of a quarter circle with radius 5.
So we have
[tex]\displaystyle \int_{-5}^0 5 + \sqrt{25-x^2} \, dx = 5^2 + \frac\pi4\cdot5^2 = \boxed{25 + \frac{25\pi}4}[/tex]
I hope you could get this answer
Answers
Answer: -12
Step-by-step explanation: x is -4 so -(-4) is positive 4. d = 3 so -3 = -3. -3x4 = -12.
A college class is made up of f freshman and s sophomores. If 5 freshmen drop this class would be 3 times the number of freshman. Which of the following equations represents a in terms of f ?
Answers
Answer:
The answer is G.
f-5 drop the class while s class is 3(f-5)
therefore, s=3(f-5)
One number is six more than three times another. If their sum is decreased by four, the result is twenty-two. Find
the numbers.
The smaller of the numbers is
Due Wed 08/10/
and the larger is
Answers
Answer: 5 is the smaller number and 21 is the larger number
Step-by-step explanation: let’s have the smaller of the numbers equal x and the larger one equal y. Y = 3x + 6 their sum is 3x + 6 + x or 4x + 6. This sum minus 4 is 22 so the sum is 26. 26-6 = 4x so 4x = 20 and x = 5 so r = 15+ 6 which is 21.
A board, 74 cm long is cut into three pieces such as the second board is twice as long as first board and the third is 4 cm longer than second. Find length of shorter piece
Answers
Answer:
The shortest piece is the first piece and it is 14 cm long.
Step-by-step explanation:
We have three unknowns so we need 3 equations.
Let x = the length of the first piece
Let y = the length of the second piece
Let z = the length of the third piece.
x + y + z = 74 y = 2x z = y + 4
There are a number of ways to solve this. I am going to plug in 2x for y into the first and the third equation to get:
x + y + z = 74
x + 2x + z = 74 Combine the x terms
3x + z = 74
Next, I am going to substitute 2x in for y in the third equation above.
z = y + 4
z = 2x + 4 I am going to put both variable on the left side of the equation
z - 2x = 4
I can know take the two bold equations that I have above and solve for the either x or z. I am going to solve for z. I need one of the equation to have a z and the other equation to have -z so that they will cancel one another out. I am going to multiple z - 2x = 4 all the way through by -1 to get:
z - 2x = 4
-1(z - 2x) = 4(-1)
-z +2x = -4
I am going to rearrange 3x + z = 74 so that the z term is first and add it to -z + 2x = -4
z + 3x = 74
-z + 2x = -4
5x = 70 divide both sides by 5
x = 14 This is the length of the first piece.
y = 2x
y = 2(14) = 28
y = 28 This is the length of the second piece.
z = y+4
z = 28 + 4 = 32
or
x + y + z = 74
14 + 28 + z = 74
42 + z = 74 Subtract 42 from both sides.
z = 32
Relate ratios in right triangles
Consider right triangle ADEF below. Which Expressions are equivalent to cos(E)?
Answers
Answer:
B
Step-by-step explanation:
Cos is the adjacent side over the hypotenuse. The adjacent side to <E is side ED. The hypotenuse is side EF. ED/EF. They do not go right out and give you this choice, but you see that B says the same thing.
Find the last number of the following series
10 8 16 13 39 35
1)75
2)100
3)130
4)140
Answers
The answer is 4) 140.
If we closely examine the pattern of the series, we see that after a number is subtracted by a value, it is multiplied by the same value, and then it moves on to the next natural number.
10 - 2 = 88 × 2 = 1616 - 3 = 1313 × 3 = 3939 - 4 = 35The next step, according to the pattern, would be to multiply 4.
35 × 4140Armando tiene 25 chocolates en una caja y caja y cada chocolate tiene un relleno de 4 posibles fresa, mora y piña. De los 25 chocolates de la caja de armando sabes que tiene 8 tienen relleno de mora y 5 de piña si una persona torna al azar un chocolate de la caja
cuales de la posibles posibilidades se puede calcular
Answers
La probabilidad que se pueden calcular es:
c: Probabilidad de que el chocolate no tenga relleno de piña.
¿Como encontrar las probabilidades?
Sabemos que hay 25 chocolates en total en la caja, tal que:
8 son de mora.5 son de piñalos 12 restantes son de fresa o cereza.La probabilidad de obtener un tipo particular de sabor se obtiene como el cociente entre el número de chocolates de ese sabor y el total de chocolates.
La probabilidad que se pueden calcular es:
c: Probabilidad de que el chocolate no tenga relleno de piña.
Sabemos que 5 chocolates tienen relleno de piña, entonces 20 no tienen relleno de piña. es decir, la probabilidad es:
P = 20/25 = 4/5
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Ali’s ate 1/3 of a pizza for lunch. Later, she ate 2/5 of the remaining pizza as a snack. How much of the pizza did she eat altogether?
Answers
Step by step
We know she ate 1/3 of a pizza, that leaves 2/3 left over
We know she ate 2/5 of the 2/3 left overs
So
2/5 x 2/3 = 4/15 she ate as a snack
Add this to the 1/3 she ate for lunch
1/3 + 4/15 = total pizza she ate
To add these, we need the denominator the same
1/3 = x/15, we multiply the 3 x 5 to get 15 so we do the same to the numerator, 1 x 5 = 5
So 5/15 + 4/15 = 9/15
We can simplify this to 3/5
Problem solved
Como derivar cos(2x)/tan(2x)
Answers
Use the quotient and chain rules. If
[tex]y = \dfrac{\cos(2x)}{\tan(2x)}[/tex]
then the derivative is
[tex]\dfrac{dy}{dx} = \dfrac{\tan(2x) \frac d{dx}\cos(2x) - \cos(2x) \frac d{dx}\tan(2x)}{\tan^2(2x)}[/tex]
[tex]\dfrac{dy}{dx} = \dfrac{\tan(2x) (-\sin(2x)) \frac d{dx}(2x) - \cos(2x)\sec^2(2x) \frac d{dx}(2x)}{\tan^2(2x)}[/tex]
[tex]\dfrac{dy}{dx} = \dfrac{-2\sin(2x)\tan(2x) - 2 \sec(2x) }{\tan^2(2x)}[/tex]
and we can rewrite this by
• multiplying by [tex]\frac{\cos^2(2x)}{\cos^2(2x)}[/tex],
[tex]\dfrac{dy}{dx} = \dfrac{-2\sin^2(2x)\cos(2x) - 2 \cos(2x) }{\sin^2(2x)}[/tex]
• factorizing,
[tex]\dfrac{dy}{dx} = -\dfrac{2\cos(2x) \left(\sin^2(2x) + 1\right)}{\sin^2(2x)}[/tex]
etc
A 22-ft ladder leans against a building so that the angle between the ground and the ladder is 64°. How high does the ladder reach on the building?
Answers
The height of the ladder on the building is 19.77 feet
How high does the ladder reach on the building?Represent the height of the ladder on the building with h
So, the given parameters are:
Angle, x = 64 degrees
Length of ladder, l = 22 feet
The height of the ladder on the building is calculated using
sin(x) = h/l
Substitute the known values in the above equation
sin(64) = h/22
Multiply both sides by 22
h = 22 * sin(64)
Evaluate the product
h = 19.77
Hence, the height of the ladder on the building is 19.77 feet
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Landon Wallin is an auto mechanic who wishes to start his own business. He will need $4200 to purchase tools and equipment. Landon decides to finance the purchase with a 36-month fixed installment loan with an APR of 5.5% a) Determine Landon's finance charge. b) Determine Landon's monthly payment.
Answers
Landon's finance charge is $613.2
Landon's monthly payment is; $80.22
How to find the finance charge?
It is convenient to compute the monthly payment first, then figure the total amount repaid and the finance charge.
The amortization formula is:
A = Pr/(1 - (1 + r)⁻ⁿ)
where;
A is the monthly payment
P is the loan amount
r is the monthly interest rate
n is the number of months
b) Using the above formula, we can get the monthly payment as;
A = $4200(0.055/12)/(1 - (1 +0.055/12)⁻⁶⁰) = $19.708333/0.23995049
A = $80.22
The monthly payment amount is $80.22
a) 60 monthly payments add up to;
$80.22 × 60 = $4813.2
Since $4200 of that amount is principal, the finance charge is;
$4813.2 - $4200.00 = $613.2
Landon's finance charge is $613.2
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3a²+ab²-b² x a²-2ab²-3b²
/a+b
Answers
Answer:
It might be - c² or b³ *SORRY IF IM WRONG HAVE A GOOD DAY :D)
Step-by-step explanation:
I agree with the person above ^^^
In a school, all pupils play either Hockey or Football or both. 400 play Football, 150 play Hockey, and
130 play both the games. Find
(i) The number of pupils who play Football only,
(ii) The number of pupils who play Hockey only,
(iii) The total number of pupils in the school
Answers
Answer:370 play football and 20 play hockey
Step-by-step explanation: because 400 - 130 equals 370 for football
then hockey 150-130 equals 20
Then the total students are 420
150+400-130 equals 420
A shark begins 172.5 meters below sea level and then swam up 137.1 meters,. Where is the sharks location now in relation to sea level
Answers
Answer:
35.4m below sea level
Step-by-step explanation:
172.5 - 137.1 = 35.4
The shark's location is now 35.4m below sea level.
What are Arithmetic operations?Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.
+ Addition operation: Adds values on either side of the operator.
For example 4 + 2 = 6
- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.
For example 4 -2 = 2
Using the arithmetic operations of addition and subtraction, the shark's location is now in relation to sea level if the shark begins 172.5 meters below sea level and then swam up 137.1 meters.
Assume that distance below sea level is positive,
⇒ 172.5 - 137.1 = 35.4
Hence, the shark's location is now 35.4m below sea level.
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A motorist travels from town A to town B, which are 84km apart. If he has completed 7/8 of his journey, what is the distance he has travelled?
Answers
The distance that he has traveled exists 73km 500m.
What is the distance?
Distance exists described as the amount of space between two items or the condition of existing far apart. The distance of an object can be described as the complete path traveled by an object.
Given: A motorist travels from town A to town B, which exists 84km apart. He has finished 7/8 of his journey.
To estimate the distance that he has traveled
He covered 7/8 out of 84 km
So, 7/8 × 84 = 73.5 km
The distance he has traveled = 73 km 500 m
Therefore, the distance that he has traveled exists 73km 500m.
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A
a = 10
C = 15
B
b
Find the length of b using
the Pythagorean Theorem.
Hint: a² + b² = c²
Round your answer to the nearest tenth.
Answers
Applying the Pythagorean theorem, the length of b, to the nearest tenth, is: 11.2.
What is the Pythagorean Theorem?The Pythagorean theorem is the theorem that is applied when finding any length of a right triangle. Where a and b are the smaller sides of the right triangle, and c is the longest side (hypotenuse) of the right triangle, the Pythagorean theorem states that: a² + b² = c².
We are given the following regarding a right triangle:
a = 10 (one of the smallest side)
c = 15 (the longest side/hypotenuse)
Plug in the values into a² + b² = c²:
10² + b² = 15²
100 + b² = 225
Subtract 100 from both sides
100 + b² - 100 = 225 - 100
b² = 125
Square both sides
√b² = √125
b ≈ 11.2
The length of b, to the nearest tenth, is: 11.2.
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