Answer:
3/20
Step-by-step explanation:
By question it's given that ,
[tex]\implies \dfrac{a}{b}=\dfrac{2}{5}[/tex]
[tex]\implies \dfrac{b}{c}=\dfrac{3}{8}[/tex]
And we need to find out the value of a/c .For that Multiply both of them , we have ;
[tex]\implies \dfrac{a}{b} \times\dfrac{b}{c}=\dfrac{2}{5}\times \dfrac{3}{8} \\\\\implies \dfrac{a}{c}= \dfrac{3}{20}[/tex]
Hence the required answer is 3/20 .
Solve for x. Round to the nearest tenth of a degree, if necessary.
Step-by-step explanation:
[tex] \tan(x \degree) = \frac{54}{32} \\ = \frac{3}{4} \\ x \degree = { \tan}^{ - 1} ( \frac{3}{2} ) \\ = 56.3 \degree[/tex]
Joe wants to add cucumbers to his garden and knows the rectangular area is represented by x^2 - 4x - 21 square units. What expressions would represent the length and width of the cucumber field?
Given:
The area of rectangular garden is [tex]x^2-4x-21[/tex] square units.
To find:
The length and width of the cucumber field.
Solution:
The area of a rectangle is:
[tex]A=l\times w[/tex]
Where l is length and w is width of the rectangle.
The area of rectangular garden is [tex]x^2-4x-21[/tex] square units.
We need to find the factors of [tex]x^2-4x-21[/tex] to get the length and width.
[tex]A=x^2-4x-21[/tex]
Splitting the middle term, we get
[tex]A=x^2-7x+3x-21[/tex]
[tex]A=x(x-7)+3(x-7)[/tex]
[tex]A=(x-7)(x+3)[/tex]
Area of a rectangle is the product of length and width.
Therefore, the length and width of the rectangle are [tex](x-7)[/tex] units and [tex](x+3)[/tex] units.
What is the value of this expression?
Answer:
-3
Step-by-step explanation:
Step 1: Solve (-2+(-1))^2/3 3
1. -2+(-1) = -3
2. (-3)^2 = 9
3. 9/3 = 3
Step 2: Solve (-4)^2-17 -1
1. 3/-1
Step 3: Simplify 3/-1 = -3. I hope this helped and please don't hesitate to reach out with more questions!
could use some help on this please
Answer:
x = 15, y = 4
Step-by-step explanation:
To solve this, we have to define the triangles first. Since the triangles are congruent by HL, it means that the hypotenuse and the leg of the triangle are defined to be equal. By flipping one of the triangles upsidedown, we can visualize the hypotenuse of the triangles and the leg of the triangles (which are equal).
The two equations are the following:
[tex]x + 1 = 4y[/tex]
[tex]x = y + 11[/tex]
If I add 1 to both sides of the second equation, I get the following equation:
[tex]x + 1 = y + 11 + 1 = y + 12[/tex]
By comparing this new equation with the first one, we will get:
[tex]x + 1 = 4y = y + 12[/tex]
We can ignore x+1 for now since y can not be solved.
[tex]4y = y + 12[/tex]
By subtracting both sides of this equation by y, we will get.
[tex]3y = 12[/tex]
This solves for y, where
[tex]y = 4[/tex]
Now, we can re-use one of the equations, which is
[tex]x = y + 11[/tex]
Now that we know y is 4, we can plug it into this equation.
[tex]x = 4 + 11 = 15[/tex]
(1 + sin x)(1 – sin x) = cos^2x
Answer:
(1 + sin x)(1 – sin x) = cos^2x
1 - sin^2x = cos^2x
cos^2x = cos^2x
Step-by-step explanation:
Simplify the left hand side:
(1 + sin x)(1 – sin x) = cos^2x
1 - sin^2x = cos^2x
Using the Pythagorean Identity, we can see that the two sides are equivalent if you subtract sin^2x from both sides:
sin^2x + cos^2x = 1
cos^2x = 1 - sin^2x
Lastly, write it out:
(1 + sin x)(1 – sin x) = cos^2x
1 - sin^2x = cos^2x
cos^2x = cos^2x
-24w^2+(-4w^2)
Helppp
Answer:
-28[tex]w^{2}[/tex]
Step-by-step explanation:
-24[tex]w^{2}[/tex] + (-4[tex]w^{2}[/tex]) =
a negative plus a negative is a negative.
if you owe me 24 dollars and then I loan you another 4 dollars then you are in the negative 28 dollars to me.
Both 'w' have same exponent, making them like terms
What is the center of the circle: .22 + y2 = 4
Use the Law of Cosines to find the missing angle.
Step-by-step explanation:
180-68=112
112÷293=3.8620
68÷3.87
18
Maths assignment
a^4-16
Answer:
[tex]a^4-16[/tex]
[tex]\left(a^2\right)^2-4^2[/tex]
[tex]\left(a^2+4\right)\left(a^2-4\right)[/tex]
[tex]=\left(a^2+4\right)\left(a+2\right)\left(a-2\right)[/tex]
------------------------
Hope it helps...
Have a great day!!
Step-by-step explanation:
The difference of squares: a² - b² factors to (a - b) (a + b)
Let x⁴ = (x²)²
Let 16 = 4²
Now by difference of squares x⁴ - 16 factors as (x² - 4)(x² + 4)
The front factor, (x² - 4), can factor by difference of squares again as (x - 2)(x + 2)
Write the ratio 5/36 as a fraction in simplest form.
Use the slash key (/) to indicate a fraction.
9514 1404 393
Answer:
5/36
Step-by-step explanation:
5 and 36 have no common factors, so the fraction 5/36 is already in simplest form.
Answer:
[tex] \frac{5}{36} [/tex]Step-by-step explanation:
#CARRYONLEARNINGConsider the function f(x) = -2x2 +3x-8. Determine f(k+4). Fully simplify your answer.
Answer:
f(k + 4) = -2k² - 13k - 28
General Formulas and Concepts:
Pre-Algebra
Distributive PropertyAlgebra I
Terms/CoefficientsExpand by FOILFunctionsFunction NotationStep-by-step explanation:
Step 1: Define
Identify
f(x) = -2x² + 3x - 8
Step 2: Evaluate
Substitute in x [Function f(x)]: f(k + 4) = -2(k + 4)² + 3(k + 4) - 8Expand [FOIL]: f(k + 4) = -2(k² + 8k + 16) + 3(k + 4) - 8[Distributive Property] Distribute: f(k + 4) = -2k² - 16k - 32 + 3k + 12 - 8Combine like terms: f(k + 4) = -2k² - 13k - 28como se lee el número decimal 0.3
−3x−6+(−1)
need answer pls
Step-by-step explanation:
−3x−6+(−1)
-3x-7
Hope it helps youAnswer:
−3 −7
Step-by-step explanation:
-3x-6-1
-3x-7
Part 1- Make sure to show all work. Write both the (i) recursive formula and the (ii) explicit formula for the sequences
A) {-23,-15,-7,1,...}.
B) {5, 5.25, 5.50, 5.75,...}
Part 2- Calculate the 15th term in each of the above sequences, Use the Recursive method for one sequence and the Explicit formula for the other sequence. (make sure to label your work & show each step).
Answer:
A) The sequence is {-23, -15, -7, 1,...}
The common difference of the sequence above, d = 8
The first term, a = -23
The number of terms, n = 15
The recursive formula is, aₙ = aₙ₋₁ + d
Using the recursive method gives;
a₅ = a₍₅₋₁₎ + d
Where;
a₍₅₋₁₎ = 1
Therefore, a₅ = 1 + 8 = 9, a₆ = 9 + 8 = 17, a₇ = 17 + 8 = 25, a₈ = 25 + 8 = 33, a₉ = 33 + 8 = 41, a₁₀ = 41 + 8 = 49, a₁₁ = 49 + 8 = 57, a₁₂ = 57 + 8 = 65 a₁₃ = 65 + 8 = 73, a₁₄ = 73 + 8 = 81, a₁₅ = 81 + 8 = 89
The 15th term of the sequence, {-23, -15, -7, 1,...}, a₁₅ = 89
We check by using explicit formula to get, aₙ = a + (n - 1)·d
Therefore
a₁₅ = -23 + (15 - 1)×8 = 89
B) The given sequence is B) {5 5.25, 5.50, 5.75,...}
The common difference, d = 0.25
The first term, a = 5
The required number of terms, n = 15
Using the recursive method gives;
a₅ = a₍₅₋₁₎ + d
Where;
a₍₅₋₁₎ = a₄ = 5.75
Therefore, a₅ = 5.75 + 0.25 = 6
a₆ = 6 + 0.25 = 6.25, a₇ = 6.25 + 0.25 = 6.5, a₈ = 6.5 + 0.25 = 6.75, a₉ = 6.75 + 0.25 = 7, a₁₀ = 7 + 0.25 = 7.25, a₁₁ = 7.25 + 0.25 = 7.5, a₁₂ = 7.5 + 0.25 = 7.75, a₁₃ = 7.75 + 0.25 = 8, a₁₄ = 8 + 0.25 = 8.25, a₁₅ = 8.25 + 0.25 = 8.5
The 15th term, of the sequence, {5 5.25, 5.50, 5.75,...}, a₁₅ = 8.5
We check by explicit formula to get, aₙ = a + (n - 1)·d
Therefore
a₁₅ = 5 + (15 - 1)×0.25 = 8.5
Step-by-step explanation:
What's the answer for m⁶ - 25
Step-by-step explanation:
[tex] {m}^{6} - 25 \\ { {m}^{3} }^{2} - {5}^{2} \\ x = {m}^{3} b = 5 \\ ( {m}^{3} - 5)( {m}^{3} + 5)[/tex]
Find the sum of the series -11 - 3 + 5 + 13 + ... + 125 using the series formula.
Answer:
1026
Step-by-step explanation:
Common difference = d = 2nd term - first term
d = -3 - (-11) = -3 +11 = 8
First term = a = -11
First we need to find the number of terms in this series
[tex]a_{n} = 125\\\\a + (n- 1)d = a_{n}\\\\[/tex]
-11 + (n- 1) * 8 = 125
(n-1)*8 = 125 + 11
(n-1) * 8 = 136
n -1 = 136/8
n -1 = 17
n = 17+1
n = 18
[tex]S_{n} =\frac{n}{2}(a+a_{n})\\\\S_{18} =\frac{18}{2}(-11+125)\\\\[/tex]
= 9 * 114
= 1026
Let f(x) = 4x - 5 and g(x) = 3x + 7. Find f(x) + g(x) and state its domain.
7x - 12; all real numbers
7x + 2; all real numbers
x + 2; all real numbers
X - 12; all real numbers
Answer:
2nd option
Step-by-step explanation:
f(x) + g(x)
= 4x - 5 + 3x + 7 ← collect like terms
= 7x + 2
domain is all real numbers
Over what interval is the parabola below decreasing?
n a certain exam of grade ten, 75% students got high score in mathematics, 65%students got high score in English. If 6% of them did not get high score in both mathematics and English, then calculate: i. the percent of students who got high score in both the subjects. ii. the total number of students who got high score either in mathematics or in English if 300 students had attended the exam.
Answer:
thank you for the points
Step-by-step explanation:
Suppose that a department contains 10 men and 12 women. How many ways are there to form a committee with six members if it must have the same number of men and women
Answer:
The number of ways is 26,400 ways
Step-by-step explanation:
Given;
total number of men, M = 10
total number of women, W = 12
number of committees to be formed = 6
If there must be equal gender, then it must consist of 3 men and 3 women.
[tex]The \ number \ of \ ways = 10C_3 \times 12C_3\\\\The \ number \ of \ ways =\frac{10!}{3!7!} \times \frac{12!}{3!9!} \\\\T he \ number \ of \ ways = 120 \times 220 = 26,400 \ ways[/tex]
Therefore, the number of ways is 26,400 ways
The metric system has several advantages that include all of the following except _____.
only need to move the decimal point for conversions
prefixes are the same throughout
based on the numeral ten
only 10 base units to learn
Answer:
Only 10 base units to learn
Step-by-step explanation:
The metric system is a decimal based system developed to be universally acceptable by making use of base units from obtained from nature and the use of prefixes for multiples and submultiples of the base units, decimal ratios, which allows easy representation of quantities, as well as having a coherent structure of base and derived units which are obtained from the base units
During conversion in the metric system, which is decimal based, it is only required to move the decimal point
The prefixes which are used to specify multiples and submultiples are the same through out
The decimal system is based on the powers of ten
The number of base units to learn are 7 including; 1. Meter (m), 2. Kilogram (kg), 3. Second (s), 4. Ampere (A), 5. Kelvin (k), 6. Candela (cd), and 7. mole (mol)
Therefore the metric system has several advantages that include all of the following except; Only 10 base units to learn
ages of Raju and Ravi are in the ratio 3:4 .Four years from now the ratio of their ages will be 4:5 . Find their present ages
Answer:
Their present ages are 12 years and 16 years.
Step-by-step explanation:
Given that,
Ages of Raju and Ravi are in the ratio 3:4 .Four years from now the ratio of their ages will be 4:5.
Let their present age is 3x and 4x.
Ages after four years from now will be:
[tex]\dfrac{3x+4}{4x+4}=\dfrac{4}{5}\\\\5(3x+4)=4(4x+4)\\\\15x+20=16x+16\\\\20-16=16x-15x\\\\x=4[/tex]
So,
Raju's present age is 3(4) = 12 years
Ravi's present age is 4(4) = 16 years
given that cos θ = 8/17 and sin θ = -15/17 what is the value of tan θ
Answer:
- 1.875
Step-by-step explanation:
tan = sin ÷ cos
tan = 8/17 ÷ - 15/17
tan= - 1.875
Answer:
-8/15
Step-by-step explanation:
see image
pls pls pls answer and pls dont use this post just for extra points i actually rly need help
:( please don't
Answer:
1/2
Step-by-step explanation:
Probability is equal to the amount of desirable outcomes divided by the total amount of outcomes. Each coin has two sides, and there are three of them. This accounts for a total of 2^3 or 8 outcomes. Now, we need to find the amount of outcomes where two or more coins land on heads. We can start by listing those possibilities: THH, HTH, HHT, and HHH. Notice that the first three are just three ways of rearranging the same result. We can see that there are four desirable outcomes. This means the probability is 1/2.
the principal argument of z = —4+i4√3 is
Answer:
Let z=−4+0i. Then, ∣z∣=
(−4)
2
+0
=4
Clearly, the point (−4,0) representing z=−4+0i lies on the negative side of real axis. Therefore, principal argument of z is π.
which choice is equivalent to the expression below when x less than or equal to 0
Answer:
b
Step-by-step explanation:
What is the domain of the following function ?
Answer:
{-6, 1, 5, 8}
Step-by-step explanation:
The domain is the set of x-coordinates or inputs.
{-6, 1, 5, 8}
When 7 times a number is decreased by 8, the answer is the same as when 3 times the number is increased by 4. Find the number.
Answer:
x=3
Step-by-step explanation:
Equation: 7x-8=3x+4
4x=12
x=3
find all two digit numbers with the following property:the difference between the number and the number with the same digits in reverse order is 54
answer
71-17=54
82-28=54
93-39=54
60-06=54
Step-by-step explanation:
If a semi circle has a diameter of 5 m what is the area?
Answer:
Exact answer = 10.41666666666666666666666666666pi
Estimated answer = 32.70938
Step-by-step explanation:
Semi circle formula: 1/2 * 4/3 * pi * r^3
r = 2.5
1/2 * 4/3 * pi * 2.5^3
2/3 * pi * 2.5^3
2/3 * pi * 15.625
10.416..... * pi
Exact answer = 10.417pi
We can estimate pi as 3.14
So, 10.417 * 3.14 = 32.70938
Exact answer = 10.41666666666666666666666666666pi
Estimated answer = 32.70938
