Find the slope and initial value of the graph below. Then write the equation of the line. Write the equation of the line.
Answers
Answer:
y= x + 2
Hope this helps.
Related Questions
what is the coefficient of (3y^2 + 9)5
Answers
The coefficient of (3y² + 9)5 is 15.
A polynomial is of the form a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² + ... + aₙ₋₁x + aₙ.
Here, x is the variable, aₙ is the constant term, and a₀, a₁, a₂, ..., and aₙ₋₁, are the coefficients.
a₀ is the leading coefficient.
In the question, we are asked to identify the coefficient of (3y² + 9)5.
First, we expand the given expression:
(3y² + 9)5
= 15y² + 45.
Comparing this to the standard form of a polynomial, a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² + ... + aₙ₋₁x + aₙ, we can say that y is the variable, 15 is the coefficient, and 45 is the constant term.
Thus, the coefficient of (3y² + 9)5 is 15.
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An integrated transcriptomic and epigenomic analysis identifies CD44 gene as a potential biomarker for weight loss within an energy-restricted program
Answers
An integrated transcriptomic and epigenomic analysis identifies the CD44 gene as a potential biomarker for weight loss within an energy-restricted program: TRUE
What is an integrated transcriptomic and epigenomic analysis?Because of the interindividual variability in response to weight-loss treatments, new predictive biomarkers are needed to improve the efficacy of weight-loss programs. The goal of this work is to find new genes that distinguish individual responses to a weight-loss dietary regimen by combining mRNA expression and DNA methylation arrays.Different expression and DNA methylation profiles were found in LR versus HR. The integrative analysis of the array data found four genes that were differentially methylated and expressed between groups: CD44, ITPR1, MTSS1, and FBXW5. In LR, CD44 expression was higher and DNA methylation levels were lower than in HR.Therefore, the statement "an integrated transcriptomic and epigenomic analysis identifies the CD44 gene as a potential biomarker for weight loss within an energy-restricted program" is TRUE.
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Complete question:
An integrated transcriptomic and epigenomic analysis identifies the CD44 gene as a potential biomarker for weight loss within an energy-restricted program. TRUE or FALSE
plss help!!
1. Abigail is 8 years older than Cynthia. Twenty years ago Abigail was three times as old as Cynthia. How old is each now?
2. Three years ago Tom was twice as old as Jean. And in two years the sum of their ages will be 28 years. Find their present ages.
3. Bill is 5 years older than Sue is, and the sum of their ages is 67 years. How old is Bill and Sue?
4. The sum of the digits of a three-digit number is 6. The hundreds digit is twice the units digits, and the tens digit equals to the sum of the other two. Find the number.
5. The units digit is twice the tens digit. If the number is doubled, it will be 12 more than the reversed number. Find the number.
Answers
Answer:
1. a = 32, c = 24
Step-by-step explanation:
a = c+8
a-20 = 3(c-20)
(c+8)-20 = 3c-60
c = 24
a = 24+8
a = 32
2. t = 15, j = 9
t-3 = 2(j-3)
t-3 = 2j-6
t = 2j-3
t + 2 + j + 2 = 28
(2j-3)+ 2 + j + 2 = 28
3j + 1 = 28
3j = 27
j = 9
t-3 = 2(9-3)
t-3 = 2(6)
t-3=12
t = 15
3. b=36, s=31
b = s + 5
b+s = 67
(s+5)+s = 67
2s+5 = 67
2s = 62
s = 31
b = 31+5
b = 36
4. 231
h + t + u = 6
(with h=hundreds digit, t=tens digit, u=units digit)
h = 2u
t = h+u
t = (2u) + u
(2u) + (2u +u) + u = 6
6u = 6
u = 1
h = 2
t = 3
the number is 231
5. 48
u = 2t
the 2-digit number is 10t+u
2(10t+u) = 10u+t+12
2(10t + 2t) = 10(2t) + t + 12
20t + 4t = 20t + t + 12
24t = 21t + 12
3t = 12
t = 4
u = 2*4
u = 8
the number is 48
A table showing gallons of solution, acid concentration, and amount of acid. the first row shows 10 percent acid, and has the entries, 0.5, 0.10, and 0.10 times 0.5. the second row shows 35 percent, and has the entries, g, 0.35, and 0.35 g. the third row shows. mixture, and has the entries, g plus 0.5, 0.15, and 0.15 left parenthesis g plus 0.5 right parenthesis. eli wants to combine 0.5 gallon of a 10% acid solution with some 35% acid solution to make a 15% acid solution. which equation can you use to determine how many gallons of the 35% acid solution eli should add?
Answers
The number of gallons of the 35% acid solution eli should add is; 0.125 gallons
How to Simplify Basic Algebra?From the given table, since Eli wants to combine 0.5 gallon of a 10% acid solution with some 35% acid solution to make a 15% acid solution, then we can say that;
(0.10)(0.5) + 0.35g = 0.15(g + 0.5)
where g is number of gallons
Now, for us to determine how many gallons of the 35% acid solution eli should add, we will solve the word problem earlier to get;
(0.10)(0.5) + 0.35g = 0.15(g + 0.5)
⇒ 0.05 + 0.35g = 0.15g + 0.075
⇒ 0.35g - 0.15g = 0.075 - 0.005
⇒ 0.2g = 0.025
g = 0.025/0.2
g = 0.125 g
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Consider the function shown on the graph.
45-
12
9.
6
3
-13.
999
-6-
-9
-12-
-15-
(3, 0)
23
(8, 15)
((7,0)
5 6 7 8 9
X
Which function does the graph represent?
Of(x) = (x+3)(x + 7)
Of(x)=(x-3)(x-7)
Of(x)=3(x-3)(x-7)
Of(x)= 11(x+3)(x + 7)
Answers
Answer:
(c) f(x) = 3(x -3)(x -7)
Step-by-step explanation:
The correct function can be chosen by looking at the x-intercepts and the behavior around the vertex.
X-interceptsThe graph crosses the x-axis at x=3 and x=7. Each x-intercept x=p gives rise to a factor (x -p). These two x-intercepts mean the function will have factors ...
(x -3)(x -7) . . . . . . . . eliminates choices A and D
Vertex behaviorThe vertical scale factor of the quadratic is easily found by looking at the function behavior near the vertex. Specifically, the scale factor is the change in y-value at a distance of 1 unit either side of the vertex.
Here, the y-value at the vertex (x=5) is -12. The y-value at x=4 and x=6 is -9, three units up from the value at the vertex. This means the vertical scale factor (leading coefficient) is 3. (This eliminates choice B.)
EquationPutting these observations together, we have determined the equation of the function to be ...
f(x) = 3(x -3)(x -7) . . . . . . matches choice C
PLS HELP ASAP
42. Use the graph below to answer all questions. Assume the graph is incremented by one.
Does the graph represent a function? How do you know?
What is the domain?
What is the range?
What is the maximum?
What is the minimum?
Identify the intervals where the graph is increasing. What does this mean in the context of the problem?
Identify the intervals where the graph is decreasing. What does this mean in the context of the problem?
Answers
See below for the solution to each question
Is the graph a function?Yes, the graph is a function.
This is because all x values have different y values
The domainThis is the set of input values of the graph.
From the graph, we have
x = 0 to x = 17
Hence, the domain is [0, 17]
The rangeThis is the set of output values of the graph.
From the graph, we have
y = 0 to y = 10
Hence, the range is [0, 10]
The maximumThis is the maximum point on the graph.
From the graph, we have
Maximum = (12, 10)
The minimumThis is the minimum point on the graph.
From the graph, we have
Minimum = (0, 0)
The increasing intervalsThese are the intervals where the y values increase as x increase.
From the graph, we have
Increasing intervals = (0, 5) ∪ (10, 12) ∪ (14, 15)
The decreasing intervalsThese are the intervals where the y values decrease as x increase.
From the graph, we have
Decreasing intervals = (7, 10) ∪ (12, 14) ∪ (15, 17)
The constant intervalsThese are the intervals where the y values remain unchanged as x changes.
From the graph, we have
Constant intervals = (5, 7)
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Triangles A B C and T P Q are shown. Sides A C and T Q are congruent. Angles B C A and P Q T are congruent. Which statements are true about additional information for proving that the triangles are congruent? Select two options.
Answers
If Angle A ≅ Angle T, then the triangles would be congruent by ASA
If Angle B ≅ Angle P, then the triangles would be congruent by AAS.
How to Identify congruency statements?We are told that;
Sides AC and TQ are congruent.
Angles BCA and PQT are congruent.
Thus, we can say that;
Side AC and side TQ are congruent.
Angle BCA and angle PQT are congruent too.
Since angle A and angle T are congruent, it means the congruency theorem used will be ASA(Angle - Side - Angle) Theorem.
Lastly, if angle B were to be congruent to angle P, it means the congruency theorem used will be AAS(Angle - Angle - Side) Theorem.
The missing options are;
A) If AngleA ≅ AngleT, then the triangles would be congruent by ASA.
B) If AngleB ≅ AngleP, then the triangles would be congruent by AAS.
C) If all the angles are acute, then the triangles would be congruent.
D) If AngleC and AngleQ are right angles, then triangles would be congruent.
E) If BC ≅ PQ, then the triangles would be congruent by ASA.
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a. Use the properties of right triangles and AABC to prove the Law of Sines.
b. Find the length of BC, rounded to the nearest tenth of a unit.
In your final answer for parts A and B, Include all of the necessary steps and calculations.
Answers
The Law of sines defines that in a triangle, (Sin A)/a = (Sin B)/b = (Sin C)/c and as per law of sines the length of BC is 24.
The given triangle is ΔABC, we split the given triangle into two right-angled triangle ΔABD and ΔBCD.
In the triangle ΔABD,
sin θ = opposite side/hypotenuse
sin A=BD/AB
BD=(sin A)/AB
And in the triangle ΔBCD,
sin θ = opposite side/hypotenuse
sin B=BD/BC
BD=(sin B)/BC
Hence, BD=(sin A)/AB=(sin B)/BC
Let say, (sin A)/a=(sin B)/b
As per law of sine, (sin A)/a=(sin B)/b
Then,
(sin 46°)/a=(sin 31°)/17
a=(17 × sin 46°)/(sin 31°)
a=23.74
a=24
Hence, the value of BC, rounded to the nearest tenth of a unit is 24.
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Which function has a vertex at the origin?
O f(x) = (x+4)²
Of(x) = x(x-4)
Of(x)=(x-4)(x + 4)
Of(x) = -x²
Answers
Answer:
(d) f(x) = -x²
Step-by-step explanation:
For the vertex of the quadratic function to be at the origin, both the x-term and the constant must be zero. That is, the function must be of the form ...
f(x) = a(x -h)² +k . . . . . . . . . . vertex form; vertex at (h, k)
f(x) = a(x -0)² +0 = ax² . . . . . vertex at the origin, (h, k) = (0, 0)
Of the offered answer choices, the only one with a vertex at the origin is ...
f(x) = -x² . . . . . a=-1
If the area of the rectangle avove is 180 spuare inches, then x =
Answers
Given the dimension of the length and area of the rectangle, the dimension of the breadth x is 9in.
Hence, option A is the correct answer.
This question is incomplete, the missing diagram is uploaded along this answer below.
What is the value of x?Area of a rectangle is expressed as; A = l × b
Given that;
Length of the rectangle l = 20inBreadth b = xArea A = 180in²A = l × b
180in² = 20in × x
x = 180in² / 20in
x = 9in
Given the dimension of the length and area of the rectangle, the dimension of the breadth x is 9in.
Hence, option A is the correct answer.
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A board of directors consists of fourteen men and six women. A four-member search committee is randomly chosen to recommend a new company president. What is the probability that all four members of the search committee will be women
Answers
Answer:
probability of all the four women chosen over people needed in a committee=4 over 4 =1
Does this graph represent a function? Why or why not?
A. No, because it is not a straight line.
• B. Yes, because it passes the vertical line test.
C. Yes, because it is a curved line.
• D. No, because it fails the vertical line test.
SUBMIT
Answers
Answer:
B. Yes, because it passes the vertical line test.
Step-by-step explanation:
Vertical line test - if a vertical line passes through more than one pone, the relation is not a function
Any vertical line will only pass through one point, so this relation is a function
The relation is a function because it passes the vertical line test
URGENT PLEASE ANSWER THESE QUESTIONS
Answers
a) The fire is out of the reach of helicopter 1.
b) Only helicopter 3 can be sent to stop the fire.
What helicopter does stop the fire?
We have both the location of the fire and the initial position of the three helicopters set on a Cartesian plane. The locations are listed below:
Fire - (x, y) = (- 3, - 5)Helicopter 1 - (x, y) = (1, 4)Helicopter 2 - (x, y) = (- 2, 3)Helicopter 3 - (x, y) = (4, - 2)The distance is found by the straight line distance formula, an application of Pythagorean theorem:
a) [tex]d = \sqrt{[1 - (- 3)]^{2}+[4-(-5)]^{2}}[/tex]
[tex]d = \sqrt{4^{2}+9^{2}}[/tex]
[tex]d = \sqrt{97}[/tex]
d ≈ 9.849
The fire is out of the reach of helicopter 1.
b) Helicopter 2
[tex]d = \sqrt{[- 2 - (- 3)]^{2}+[3 - (- 5)]^{2}}[/tex]
[tex]d = \sqrt{1^{2}+8^{2}}[/tex]
[tex]d = \sqrt{65}[/tex]
d ≈ 8.062
Helicopter 3
[tex]d = \sqrt{[4 - (- 3)]^{2}+ [- 2 - (-5)]^{2}}[/tex]
[tex]d = \sqrt{7^{2}+3^{2}}[/tex]
[tex]d = \sqrt{58}[/tex]
d ≈ 7.616
Only helicopter 3 can be sent to stop the fire.
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Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes
respectively: (a) 3 /2 and 5
Answers
The quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively as 3 /2 and 5 is 2x² - 3x + 10
What is a quadratic polynomial?A quadratic polynomial is a polynomial of the form ax² + bx + c
How to find the quadratic polynomial?For any given quadratic polynomial we have
x² - (sum of zeros)x + (products of zeros) = 0
Given that the sum and product of its zeroes respectively 3/2 and 5,
We have that
sum of zeroes = 3/2 and product of zeros = 5Substituting the values of the variables into the equation, we have
x² - (sum of zeros)x + (products of zeros) = 0
x² - (3/2)x + (5) = 0
x² - (3/2)x + (5) = 0
Multiplying through by 2, we have
2 × x² - 2 × (3/2)x + 2 × (5) = 0 × 2
2x² - 3x + 10 = 0
So, the quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively as 3/2 and 5 is 2x² - 3x + 10
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pls i need help on this quick pls
Answers
Answer:
Answer should be 15
Step-by-step explanation:
25 divided by 15 is 1.6666666667 so if use that multiply 9 you'll get 15.
Answer:
Step-by-step explanation:
A^2 + B^2=C^2
30^2 -25^2= 16.5
answer= 16.5
10 points + BRAINEST
Answers
Pls give brainest
[tex]\textbf{Heya !}[/tex]
basic math tips -»
"of" means multiply
[tex]\sf{\cfrac{1}{10}\cdot\cfrac{5}{1}}[/tex]
multiply the numerators and denominators times each other -»
[tex]\sf{\cfrac{5}{10}}[/tex]
reduce:-
[tex]\sf{\cfrac{1}{2}}[/tex]
`hope it was helpful to u ~
Which expression belongs
Answers
For the expression to be equal to the original one, we have;
[(x + 1) * 5(x - 1)(x + 4)]/[(x - 1) * 7x]
How to Simplify Algebraic Expressions?
We are given the algebraic expression;
(5x² + 25x + 20)/(7x)
Now, looking at the numerator, a common factor to all terms is 5. Thus, we will factorize it out to get;
5(x² + 5x + 4) = 5((x + 1)(x + 4))
Now, we see that the expression that simplifies the algebra is given as;
[(x² + 2x + 1) * ( )]/[( ) * (7x² + 7x)]
Now, the numerator and denominator can be factorized to get;
[(x + 1)(x + 1) * ( )]/[( ) * 7x(x + 1)]
Thus, x + 1 will cancel out to get;
[(x + 1) * ( )]/[( ) * 7x]
For the expression to be equal to the original one, we have;
[(x + 1) * 5(x - 1)(x + 4)]/[(x - 1) * 7x]
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The function of f(x) = 3x + 6,000 represents the amount of money a tablet is being sold for, where x is the number of tablets being manufactured. The function g(x) = 20x - 400 represents the cost of production, where x is the number of tablets being manufactured. The function g(x) = 20x - 400 represents the cost of production, where x is the number of tablets being manufactured. What is (f - g)(300)? Explain.
A. $1,300 is the cost of manufacturing 300 tablets
B. $12,500 is the cost of manufacturing 300 tablets.
C. $1,300 is the profit made from 300 tablets.
D. $12,500 is the profit made from 300 tablets.
Answers
Answer:
(f - g)(300) = $1,300 is the profit made from 300 tablets
Step-by-step explanation:
(f - g)(300) is the profit made from 300 tablets
(f - g)(x) = (3 x + 6,000) - (20 x - 400)
- Simplify it
(f - g)(x) = 3 x + 6,000 - 20 x + 400
- Add like terms
(f - g)(x) = -17 x + 6,400
Substitute x by 300
(f - g)(300) = -17(300) + 6,400
(f - g)(300) = -5,100 + 6,400
(f - g)(300) = $1,300
The profit is $1,300
choose the equation that satisfies the data in the table
Answers
Answer:
B is the answer
Step-by-step explanation:
Can someone help me please
Answers
The domain of the function will therefore be 0≤x<∞
Domain of a functionDomain of a function are the independent value for which a function exists. Given the function below;
f(x) = [tex]\sqrt[4]{x}[/tex]
Since the value in the root cannot be negative hence the domain of the function will be all positive real numbers.
The domain of the function will therefore be 0≤x<∞
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DOES ANYONE KNOW THE ANSWER
Answers
Answer:
D. none
Step-by-step explanation:
we only know about the right angle at the bottom right.
that is not enough information.
we always need 3 pieces of confirmed information of each triangle to be able to say that the 2 triangles are indeed of the same shape and size.
like the other answer options would indicate :
SAS : side - angle - side.
2 sides and the enclosed angle. if we know they are equal, then the rest of the triangles follow automatically.
SSS : all 3 sides. with 3 defined sides there is only one possible shake and size for that triangle.
HL : Hypotenuse and a leg of a right-angled triangle (also 3 pieces of information - 2 sides and the right angle).
since we have only the right angle and nothing else, we cannot prove that the triangles are congruent.
A cylindrical package to be sent by a postal service can have a maximum combined length and girth (perimeter of a cross section) of 123 inches. Find the dimensions of the package of maximum volume that can be sent. (The cross section is circular.)
Answers
The height of package is 34 inches.
According to the statement
we have given that the perimeter of cylinderical package is 123 inches.
and we have to find the volume of this package.
So,
According to the perimeter
2(Pi)r + h = 123
and then
h = 123 - 2(Pi)r
then the volume become
V = (Pi) r^2h
V= (Pi) r^2 * [ 123 - 2(Pi)r ] = 123 (Pi) r^2 - 2(Pi)r^3
then differentiate it
dV/dr = 246(Pi) r - 6(Pi)r^2
Now take
r(246(Pi) - 6(Pi)r) = 0
then neglect r=0 and then find another value of r.
r = 246(Pi) / 6(pi)
here r=41 then
h = 123 - 2(Pi)r
h = 123 - 2(3.14)41
h = 123 - 2(Pi)r
Then put the value of r then h = 34 inches.
So, The height of package is 34 inches.
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Calculate x for each of the following right angled triangles.
Give your answer as a simplified surd (or integer).
Answers
[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]
(a) x = 6.5 cm (b) x = 10 cm(c) x = 7 cm(d) x = 7.9 cmStep-by-step explanation:
To find an unknown side of a right angled triangle we use a theorum called pythagorus theorum..
Formula :(Hypotenuse)^2 = (Perpendicular)^2 + (Base)^2
(h)^2 = (p)^2 + (b)^2
therefore,(a) hypotenuse = x cm, base = √30 cm, perpendicular = √12 cm.
by formula,→ h^2 = p^2 + b^2
→ (x)^2 = (√12)^2 + (√30)^2
→ x^2 = 12 + 30
→ x^2 = 42
→ x = √42
→ x = 6.480...
→ x = 6.5 cm. (approx)
___________________________(b) hypotenuse = √300 cm, base = √200 cm,perpendicular = x cm.
by formula,→ h^2 = p^2 + b^2
→ (√300)^2 = (x)^2 + (√200)^2
→ 300 = x^2 + 200
→ x^2 = 300 – 200
→ x^2 = 100
→ x = √100
→ x= 10 cm.
___________________________(c) hypotenuse = √66 cm, base = √17 cm,perpendicular = x cm.
by formula,→ h^2 = p^2 + b^2
→ (√66)^2 = (x)^2 + (√17)^2
→ 66 = x^2 + 17
→ x^2 = 66 – 17
→ x^2 = 49
→ x = √49
→ x = 7 cm.
___________________________(d) hypotenuse = x cm, base = 5√12 cm,perpendicular = 2√3 cm.
by formula,→ h^2 = p^2 + b^2
→ (x)^2 = (2√3)^2 + (5√12)^2
→ x^2 = 12 + 50
→ x^2 = 62
→ x = √62
→ x = 7.874...
→ x = 7.9 cm. (approx)
___________________________Hope it helps you!!Solve the system of equations using substitution. 6x=−6y−30−3x−3y=15
Answers
The system of equation have an infinite solution.
How to solve system of equation?6x = -6y - 30
-3x -3y = 15
Therefore, let's rearrange the system of equations.
6x + 6y = -30
-3x - 3y = 15
multiply equation(ii) by 2
6x + 6y = -30
-6x - 6y = 30
add the equations
0 = 0
Since 0 = 0 for any value of x, the system of equations has infinite solutions.
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The sum of three numbers is 69. If the second number is equal to the first diminished by 8, and the third number is 5 times the first. What are the numbers?
If x represents the first number, then which of the following equations could be used to solve the problem?
69 = 7x - 8
x = 6x - 8
69 = 6x - 8
Answers
Answer:
[tex]69 = 6x - 8[/tex]
Step-by-step explanation:
All 3 numbers must sum to 69, so we can draw out the second option [tex]x = 6x - 8[/tex]
Let the first number be x, adding 5x to the first x would give you 6x for the sum of the first and third numbers, therefore you can remove [tex]69 = 7x - 8[/tex] from your considerations as it includes 7x not 6x.
This leaves you with the one final answer [tex]69 = 6x - 8[/tex]
Which of the following is equal to m^5/2, for all value of m?
Answers
The equivalent expression is:
[tex](m^5)^{1/2} = \sqrt{m^5}[/tex]
Which is the one in option A.
How to identify the equivalent expression?
Here we start with the expression:
[tex]m^{5/2}[/tex]
Now, remember that:
[tex]\sqrt{x} = x^{1/2}[/tex]
[tex](x^a)^b = x^{a*b}[/tex]
if we define a = 5 and b = 1/2, we get:
[tex]m^{5/2} = (m^5)^{1/2}[/tex]
Using the first property, we get:
[tex](m^5)^{1/2} = \sqrt{m^5}[/tex]
Then we conclude that the correct option is A.
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Jean estimates that her friend complete a new level of a game on the first try 20% of the time. she conducts a simulation to predict how manytimes out of 80 her friend would complete a new level on the first try. jin uses a random number generator. every digit that is eight or nine representatives complete in the level. what is the problem ability that her friend completes a new level on the first try written as a percent
Answers
The friend's probability of beating the next level on her first attempt are 22.5 percent.
Describe probability.
To forecast how likely occurrences are to occur, probability has been introduced in mathematics. This is the fundamental theory of probability, which is also applied to the probability distribution, and from which you will discover the likelihood of results for a random experiment.
This idea is used to discuss the probability or likelihood of an event happening.
The frequency of the number 8 is seven.
The frequency of the number 9 is 11.
The full list of frequencies is provided as
10 + 9 + 6+ 7 + 8 + 12 + 4 + 6 + 7 + 11 = 80
7 + 11 = 18
18/80 is the probability.
= 0.225 x 100
22.5 percent
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What is the solution to the inequality?
A. y > 32
B. y > 2
C. y < 2
D. y < 32
Answers
[tex]\textbf{Heya !}[/tex]
✏[tex]\bigstar\textsf{Given:-}[/tex]✏
An inequality [tex]\sf{-\cfrac{y}{4}+7 > -1}[/tex]✏[tex]\bigstar\textsf{To\quad find:-}[/tex]✏
y -- ?▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪
✏[tex]\bigstar\textsf{Solution\quad steps:-}[/tex]✏
First, subtract both sides by 7:-
[tex]\sf{-\cfrac{y}{4} > -1-7}}[/tex]
[tex]\sf{-\cfrac{y}{4} > -8}[/tex]
Now multiply both sides by 4:-
[tex]\sf{-y > -8*4}[/tex]
[tex]\sf{-y > -32}[/tex]
last step:-
[tex]\sf{y < 32}[/tex]
`hope it was helpful to u ~
[tex] \implies \: \sf{ - \dfrac{y}{4} \: + \: 7 \: > \: - 1} \\ \\ \implies \: \sf{ - \dfrac{y}{4} \: > \: - 7 \: - 1} \\ \\ \implies \: \sf{ - \dfrac{y}{4} \: > \: - 8} \\ \\ \implies \: \sf{ \cancel- \: \dfrac{y}{4} \: > \: \cancel- \: 8} \\ \\ \implies \: \sf{ \dfrac{y}{4} \: < \: 8} \\ \\
\implies \: \sf{ y \: < \: 8 \times 4} \\ \\ \implies \: \bf{ y \: < \: 32}[/tex]
Suppose there is a triangle with sides a, b, and c and angles A, B, and C. Using the known given information below and the law of sines, what is the measure of side c? Round your answer to the nearest whole number, if necessary.
b = 11 cm
B = 80°
C = 54°
Answers
13 cm
15 cm
17 cm
9 cm
Answers
The measure of side c is 9 cm. The correct option is the last option 9 cm
Law of SinesFrom the question, we are to determine the measure of side c
From the law of sines, we have that
[tex]\frac{c}{sinC} =\frac{b}{sinB}[/tex]
From the given information,
b = 11 cm
B = 80°
C = 54°
Putting the parameters into the equation, we get
[tex]\frac{c}{sin54^\circ} =\frac{11}{sin80^\circ}[/tex]
[tex]c =\frac{11\times sin54^\circ}{sin80^\circ}[/tex]
c = 9.03647
c ≈ 9 cm
Hence, the measure of side c is 9 cm. The correct option is the last option 9 cm
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A river flows at 2m/s . Juan's boat can travel twice as fast down the river as it can go up the river. how fast the boat go in still water?
Answers
Using proportions, it is found that the boat can go 6 m/s in still water.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, we have that:
Down the river, the speed is v + 2.Up the river, the speed is v - 2.He goes twice as fast down the river, hence:
v + 2 = 2(v - 2).
v + 2 = 2v - 4
2v - v = 2 + 4
v = 6.
The boat can go 6 m/s in still water.
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