Answer:
a = [tex]\frac{4}{3}[/tex]
Step-by-step explanation:
[tex]\frac{a}{4}[/tex] - [tex]\frac{5}{6}[/tex] = - [tex]\frac{1}{2}[/tex]
multiply through by 12 ( the LCM of 4, 6 and 2 ) to clear the fractions
3a - 10 = - 6 ( add 10 to both sides )
3a = 4 ( divide both sides by 3 )
a = [tex]\frac{4}{3}[/tex]
Answer:
[tex]a=\frac{4}{3}[/tex]
Step-by-step explanation:
Move all terms not containing [tex]a[/tex] to the right side of the equation.
Add [tex]\frac{5}{6}[/tex] to both sides of the equation.
[tex]\frac{a}{4}=-\frac{1}{2} +\frac{5}{6}[/tex]
To write [tex]-\frac{1}{2}[/tex] as a fraction with a common denominator, multiply by [tex]\frac{3}{3}[/tex].
[tex]\frac{a}{4}=-\frac{1}{2}*\frac{3}{3} +\frac{5}{6}[/tex]
Write each expression with a common denominator of 6, by multiplying each by an appropriate factor of 1.
[tex]\frac{a}{4}=-\frac{3}{2*3} +\frac{5}{6}[/tex]
[tex]\frac{a}{4}=-\frac{3}{6} +\frac{5}{6}[/tex]
Combine the numerators over the common denominator.
[tex]\frac{a}{4}=\frac{-3+5}{6}[/tex]
Add [tex]-3[/tex] and [tex]5[/tex] .
[tex]\frac{a}{4}=\frac{2}{6}[/tex]
Cancel the common factor of [tex]2[/tex] and [tex]6[/tex].
Factor [tex]2[/tex] out of [tex]2[/tex].
[tex]\frac{a}{4}=\frac{2(1)}{6}[/tex]
[tex]\frac{a}{4}=\frac{2*1}{2*3}[/tex]
Cancel the common factor.
[tex]\frac{a}{4}=\frac{1}{3}[/tex]
Multiply both sides of the equation by [tex]4[/tex].
[tex]4\frac{a}{4} =4(\frac{1}{3})[/tex]
Simplify both sides of the equation.
Simplify the left side.
Cancel the common factor of [tex]4[/tex].
[tex]a=4(\frac{1}{3})[/tex]
Simplify the right side.
Combine [tex]4[/tex] and [tex]\frac{1}{3}[/tex]
[tex]a=\frac{4}{3}[/tex]
Compare the two functions described below.
Function 1: Originally there were 60 people living in Schondel City. The city’s population is growing and the amount of people living in the city is double what it was from the day before!
Function 2:
x y
0 32
1 25.6
2 20.48
3 16.384
4 13.1072
Answer:zh 0 89 1 87.6
Step-by-step explanation: 0 89 1 87.6
A chocolatier makes chocolate bon-bons in the shape of a sphere with a radius of 1.7 cm. The chocolate used in the bon-bons has a density of 1.32 g/cm^3 3 . If the chocolate used costs $0.03 per gram, how much would the chocolate for 190 bon-bons cost, to the nearest cent?
The cost of 190 bon-bons is $154.8
According to the question ,
The shape of chocolate bon-bons is Sphere
Radius of sphere = 1.7cm
Density = 1.32g/cm³
[tex]Volume \ of\ sphere = \frac{4}{3}\pi r^{3}\\[/tex]
[tex]Volume of chocolate bon-bons = \frac{4}{3}\pi (1.7)^{3}[/tex]
[tex]= \frac{4}{3}\pi (4.913)\\= 20.5795cm^{3}[/tex]
Weight of bon-bons = volume × density
weight = 20.5795 × 1.32
= 27.1649g
Given , the cost of chocolate = $0.03
then cost of bon-bons = 0.03 × 27.1649
= $0.81494
We have to find cost of 190 bon-bons.
Cost of 190 bon-bons = 190 × 0.81494
= $ 154.8
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A linear function f has values f(-9)=-2 and f(-3)=-6 . The y-intercept of a linear function g is six greater than the y-intercept of f , and the x-intercept of g is the same as the x- intercept of f . Write equations that represent f and g.
The equations for the functions are f(x) = (-2/3)x - 8 and g(x) = (-2/3)x - 2
What is a function rule?The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value.
A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Given data ,
Let the function be represented as A
y - y1 = m(x - x1)
where m is the slope of the line, and (x1, y1) is a point on the line.
Using the two given points for f, we can find the slope:
m = (y2 - y1) / (x2 - x1)
m = (-6 - (-2)) / (-3 - (-9))
m = -4 / 6
m = -2/3
Let's use the point (-9, -2):
y - (-2) = (-2/3)(x - (-9))
y + 2 = (-2/3)(x + 9)
Multiplying both sides by 3 to get rid of the fraction:
3y + 6 = -2x - 18
3y = -2x - 24
y = (-2/3)x - 8
So the equation for f is:
f(x) = (-2/3)x - 8
To find the equation for g, we can use the fact that the y-intercept is 6 greater than the y-intercept of f. So if the y-intercept of f is b, then the y-intercept of g is b + 6.
f(x) = (-2/3)x - 8
0 = (-2/3)x - 8
2/3 x = -8
x = -12
The x-intercept of both f and g is -12.
Now we can use the y-intercept and x-intercept to write the equation for g. The slope of g is the same as the slope of f, which is -2/3.
y - (b + 6) = (-2/3)(x - (-12))
y - b - 6 = (-2/3)(x + 12)
Multiplying both sides by 3 to get rid of the fraction:
3y - 3b - 18 = -2x - 24
3y = -2x + 3b - 6
y = (-2/3)x + (3/3)b - 2
y = (-2/3)x + b - 2
So the equation for g is:
g(x) = (-2/3)x + b - 2
We know that the x-intercept of g is -12, so we can plug that in and solve for b:
0 = (-2/3)(-12) + b - 2
0 = 8 + b - 2
b = -6
So the y-intercept of g is -6 + 6 = 0.
Therefore, the equation for g is:
g(x) = (-2/3)x - 2
Hence , the equations for f and g are: f(x) = (-2/3)x - 8 and g(x) = (-2/3)x - 2
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What is the amount of M
42 is value of ∠JNM because ∠JNM & ∠KNL are vertically opposite angles.
What is vertically opposite angles?
Angles that are opposite one another at a certain vertex and are produced by two straight lines intersecting are known as vertically opposite angles. Angles that are vertically opposed are equal to one another. These are also known as vertical angles.∠JNM = ∠KNL
4x + 6 = 7x - 21
7x - 4x = 21 + 6
3x = 27
x = 27/3
x = 9
∠JNM = 4 * 9 + 6 = 36 + 6
∠JNM = 42
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Mr. Jones' age is 4 years more than 5 times Maggie's age. If the sum of their ages is no more than 70, how old is Maggie? Write and solve an inequality to find Maggie's age. Use the 3-4 steps. Use m as your variable
Maggie's age is less than or equal to 11, m ≤ 11
What is an inequality?An inequality can simply be described as a relation that makes an unequal comparison between two objects, numbers, elements or mathematical expressions.
It is used to compare numbers on the number line on the basis of their sizes
From the information given, we have that;
Mr Jones' age = 5m + 4Maggie's age = mThe sum of their ages is less than or equal to 70Let's substitute the values
5m + 4 + m ≤ 70
Now, let's collect like terms
6m ≤ 70 - 4
Subtract like terms
6m ≤ 66
Make 'x' the subject of formula by dividing both sides by its coefficient
m ≤ 66/ 6
m ≤ 11
Hence, the value is m ≤ 11
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if x varies inversly as the square root of y varies and x=1 when y=4, find;
relationship between x and y
the value of x when y =9
the value of y when x=12
Answer:
x = 2/√y or y = 4/x²x = 2/3y = 1/36Step-by-step explanation:
When x varies inversely as the square root of y, and x=1 when y=4, you want to find ...
the relationship between x and ythe value of x when y =9the value of y when x=12.Inverse variationThe given relation can be written using a constant of proportionality as ...
x = k/√y . . . . x varies as the inverse of the square root of y
The value of k can be found from the given values for x and y:
1 = k/√4 = k/2
2 = k . . . . . . . . . multiply by 2
RelationshipThe relationship between x and y can be written as ...
x = 2/√y
Solving for y, it can also be written as ...
y = 4/x²
For y = 9The value of x is ...
x = 2/√9
x = 2/3
For x=12The value of y is ...
y = 4/12² = 4/144
y = 1/36
At a grocery store, three- dozen cookies costs $9.00. What would it cost for one cookie
Why are the tops of mountains round and the soil often rough, rocky, and thin in many places in the Northeast?
The early settlers abused and overused the land.
Glaciers scoured the landscape, grinding the high places and mixing the soil with rocks.
The Indian population purposely destroyed the countryside when they discovered the white settlers would not leave.
During the past three centuries, the urban dwellers in the area have appropriated the fine soil for the cities. what is 4+2
Glaciers scoured the landscape, grinding the high places and mixing the soil with rocks.
Given,
In the question:
Why are the tops of mountains round and the soil often rough, rocky, and thin in many places in the Northeast?
Now, According to the question:
The correct answer is:
Glaciers scoured the landscape, grinding the high places and mixing the soil with rocks.
Other question is
4 + 2
By addition:
4 + 2 = 6
Hence, Glaciers scoured the landscape, grinding the high places and mixing the soil with rocks.
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Answer:
Glaciers scoured the landscape, grinding the high places and mixing the soil with rocks.Step-by-step explanation:
Let (-12, 5) be a point on the terminal side of theta.
Find the exact values of sin theta , sec theta, and tan theta.
- 13/12 is the value of trigonometric functions sec θ .
What do trigonometric functions mean?
The functions of an angle in a triangle are known as trigonometric functions, commonly referred to as circular functions. In other words, these trig functions provide the relationship between a triangle's angles and sides.r = √( -12 - 0 )² + ( 0 - 5 )²
r = √144 + 25
r = √169
r = 13
Now we can calculate the trigonometric functions
sinθ = y/r = 5/13
cosθ = x/r = -12/13
tan θ = y/x = - 5/12
cot θ = x/y = -12/5
sec θ = r/x = - 13/12
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on their 560-mi trip, the bruins basketball team spent two more hours on the interstate highway than they did on local highways. they averaged 45 mph on local high-ways and 55 mph on the interstate highways. how many hours did they spend driving on local highways?
They spent 6.5 hours driving on local highways by travellin with diffrent average speeds.
Given that,
The bruins basketball team spent two more hours on the interstate than they did on local roadways during their 560-mile journey. They traveled at an average speed of 55 mph on interstates and 45 mph on local routes.
I=interstate
L=local
using d=rt the first rows gives you d=55t
the second row gives you 560-d=45(t-2)
Since the two distances add up to 560. Add the two distance expression and set their sum equal to the given total
560=55t+45(t-2) which equals
560=55t+45t-90
650=55t+45t
650=100t
6.5=t
Hence on local roadways, they traveled at various average speeds for 6.5 hours.
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How do I know where to shade on this graph?
y≤-3x+4 has lesser than or equal to symbol so we shade the below line.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Relationship between two expressions or values that are not equal to each other is called 'inequality.
y≤-3x+4 is the given inequality.
The sign of the inequality will let you know which half-plane to shade. If the symbol ≥ or > is used, shade above the line. If the symbol ≤ or < is used shade below the line.
In the inequality we have lesser than or equal to symbol so we shade the below line.
Hence, y≤-3x+4 has lesser than or equal to symbol so we shade the below line.
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f(x)=x²-5x - 9
Find f(-9)
Answer:
117
Step-by-step explanation:
f(-9)=-9^2-5(-9)-9
f(-9)=81+45-9
f(-9)=126-9
f(-9)=117
hopes this helps please mark brainliest
Write an equation of a line that passes through the point (1, -2) and is parallel to the line y = x - 5.
Answer:
y = x - 3
Step-by-step explanation:
y - y1 = m( x - x1 )
y - (-2) = 1 (x - 1)
y + 2 = x - 1
y = x - 3
Which ordered pair is NOT a solution to the equation y = 2x? Four points plotted on a coordinate plane. Point A has coordinates 1 comma 2. Point B has coordinates 2 comma 4. Point C has coordinates 3 comma 8. Point D has coordinates 5 comma 10. point A point B point C point D
Point C (3,8) is the required ordered pair that is not the solution of the given equation. Option C is correct.
Given that,
To determine which ordered pair is NOT a solution to the equation y = 2x.
Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
Given relation y = 2x
Now substitute every value of x from the ordered pair and match the output with the corresponding value of the ordered pair.
put x = 1, 2, 3, 5
Y = 2(1)
y = 2
Similarly the outcome of the values,
x = 2, 3, 5
y = 4, 6, 10
Thus, Point C (3,8) is the required ordered pair that is not the solution of the given equation. Option C is correct.
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A box contains 3 red marbles and 4 black marbles. You simultaneously draw 3 marbles. What is the probability
that at least one marble is black?
A.4/35
B.34/35
C.19/21
D.None of the above
Answer:
Probably b or c. Not great with probabilities.
What is one possible y coordinate
Answer:
Step-by-step explanation:
Answer x = 4 or x = -4.
Explanation: you can make what is called a 3-4-5 triangle. The base in this case is 3(from -2 to -5 there is 3 units), the hypotenuse is 5(length given in the question) therefore the height (also known as the y coordinate) is 4 or -4 if you flip the triangle.
Thank you for those answering!
In this triangle, what is the value of x?
Enter your answer, rounded to the nearest tenth, in the box.
Find the measure of the angle indicated by 11x + 1.
10x+10
11x +1
The measure of angle 11x+1 is 100°.
According to the question,
We have the following information:
We have a figure where two parallel lines are divided by a line. We know that the vertically opposite angles are equal. And when two parallel lines are cut by another line then the alternate interior opposite angles are equal.
Now, we have 10x+10 as the alternate opposite interior angle to 11x+1.
So, we have the following expression:
10x+10 = 11x+1
11x-10x = 10-1
x = 9
Putting the value of x in 11x+1:
11*9+1
99+1
100°
Hence, the measure of angle 11x+1 is 100°.
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x^2-6x-3=(x-a)^2-b where a and b are constants.Find the values of a and b
Answer:
a = 3, b = 12
Step-by-step explanation:
x^2-6x-3=(x-a)^2-b
Lets expand the right side:
(x-a)^2-b = (x-a)(x-a)-b
(x-a)(x-a)-b = x^2 -2ax + a^2 - b
The left side is equal to the right, as per the original equation:
x^2-6x-3 = x^2 -2ax + (a^2 - b)
Compare each term:
1) x^2 = x^2 OK
2) -6x = -2ax; a = 3 so that -6x = -2(3)x
3) -3 = (a^2-b); a^2 = (b-3)
a = [tex]\sqrt{b-3}[/tex]
a is 3, from above
3 = [tex]\sqrt{b-3}[/tex]
9 = b-3
b = 12
yesterday, Austin burned 199 calories while exercising. Today, he burned 1008.8 calories. How many more calories did Austin burn today than yesterday?
Answer: Austin burn 809.8 more calories today than yesterday.
Order the following from least to greatest -0.2, 4.22,2.02,-3/10, 4 1/8
The correct order is -3/10, -0.2, 2.02, 4.22, 4 1/8 .
Firstly we will convert the fractions into decimal units i.e
-3/10 = -0.3
41/8 = 5.125
We know that the higher the number in negative number line lower will the value of it so the -0.3 < -0.2
Now we can easily arrange these numbers according to the number line i.e;
Negatives will be first to come on number line and the correct order will be as follow :
-0.3 , -0.2, 2.02, 4.22, 4 1/8
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PLEASE HELP FAST!!!! ILL GIVE BRAINLIEST!!!!
Which statement correctly compares the function shown on this graph with the function y = 4x - 8?
A. The function shown on the graph has a greater rate of change but
a lower y-intercept.
B. The function shown on the graph has a smaller rate of change but
a higher y-intercept.
C. The function shown on the graph has a greater rate of change and
a higher y-intercept.
D. The function shown on the graph has a smaller rate of change and
a lower y-intercept.
Marlee is making jewelry for a class craft show. She began with 115 inches of wire. She used 25.75 inches for rings. Then her teacher gave her 3014 inches of wire to make more jewelry. She then used 3812 inches for the bracelets and 60.2 inches for necklaces. How much wire does Marlee have left? Write your answer as a mixed number in simplest form.
Marlee is in short of -768.95 inches of wire for making jewelry.
Given that, Marlee is making jewelry for a class craft show. She began with 115 inches of wire.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
The numerical expression for the given situation is
115-25.75+3014-(3812+60.2)
= 89.25+3014-3872.2
= 3103.25-3872.2
= -768.95 inches
Therefore, Marlee is in short of -768.95 inches of wire for making jewelry.
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I need help me thank you
Step-by-step explanation:
s = 17b
when b =2:
s = 17b
s = 17(2)
s = 34
when b = 4
s = 17b
s = 17(4)
s = 68
What is the slope of the line below?
Answer:
1/2
Step-by-step explanation:
if you take the (2,2) and make it (6,10), you add 4 to the x and 8 to the y. putting this as rise over run (x/y) it comes out to four eighths (4/8). reducing that comes out to one half (4/8).
Decide whether each equation is true for all, one, or no values of x.
1. 3x + 9 = -4.5x + 20 ; This is true for one value of x.
2. 9(x + 3) = 9x + 12 ; This is true for no values of x.
3. 4(2x + 3) = 12 + 8x ; True for any values of x.
Given,
The equations;
1. 3x + 9 = -4.5x + 20
2. 9(x + 3) = 9x + 12
3. 4(2x + 3) = 12 + 8x
We have to find whether each equation is true for all, one or no values of x.
Here,
1. 3x + 9 = -4.5x + 20
Solve for x;
3x + 4.5x = 20 - 9
7.5x = 11
x = 11/7.5
x = 1.47
Then,
This is true for one value of x.
2. 9(x + 3) = 9x + 12
Solve using distributive property;
9x + 27 = 9x + 12
9x - 9x = 12 - 27
0 = -15
This is true for no values of x.
3. 4(2x + 3) = 12 + 8x
Use distributive property and solve;
8x + 12 = 12 + 8x
8x - 8x = 12 - 12
0 = 0
True for any values of x.
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What is the direct variation equation for the line passing through the points A(4,−2) and B(10,−5)
The direct variation equation for the line passing through the points A(4,−2) and B(10,−5) as given in the task content is; y = -2x.
What is the direct equation of the points given?It follows from the task content that the direct variation of equation of the two points given be determined.
On this note, since the relation is said to be a direct variation.
It follows that the ratio of inputs to output in both ordered pairs, k is same and can be determined as;
10/-5 = 4/-2 = k = -2.
Therefore, the required direct variation equation is written as;
y = -2x.
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a stone dropped into a still pond sends out a circular ripple whose radius increases at a constant rate of 3.3 ft/s. how rapidly is the area enclosed by the ripple increasing at the end of 6.4 seconds?
In 139.4 [tex]\pi[/tex] [tex]ft^2[/tex]sec rapidly is area of enclosed by the ripple increasing at the end of 6.4 seconds.
What is area of circle?
For measuring the area occupied by a circular field or plot, use the area of a circle formula. The area formula will allow us to determine how much fabric is required to completely cover a circular table, for example. We can determine the boundary length, or the circle's circumference, using the area formula.
Here area of circle
=> A= π[tex]r^2[/tex]--------> 1
Differentiating 1 with respect to to time then
=> [tex]\frac{dA}{dt}= 2\pi r\frac{dr}{dt}[/tex]
If the radius is increasing at a constant rate 3.3ft/sec then after 6.4 seconds, radius is
=> 6.4*3.3=21.12 ft.
We know [tex]\frac{dr}{dt}= \frac{3.3ft}{sec}[/tex] and so ,
=> [tex]\frac{dA}{dt}[/tex] = 2*[tex]\pi[/tex]*21.12*3.3=139.4 [tex]\pi[/tex] [tex]ft^2[/tex]sec.
Hence In 139.4 [tex]\pi[/tex] [tex]ft^2[/tex]sec rapidly is area of enclosed by the ripple increasing at the end of 6.4 seconds.
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is y=10.5x-5 proportional
The equation y = 10.5x - 5 is proportional
Given,
y = 10.5x - 5
We have to find this equation is proportional or not.
In mathematics, proportional relationships exist when two variables consistently change by the same multiple. The formula y = kx, where k is a constant multiplier that depicts the relationship between x and y, is used to represent proportional relationships. The line on the graph is always straight and goes through (0,0).
Here,
y = 10.5x - 5
10.5 is the constant multiplier that depicts the relationship between x and y.
So,
The equation y = 10.5x - 5 is proportional
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Calculus Ladder Sliding Down
Answer:
[tex]\left.\dfrac{\text{d}x}{\text{d}t}\right|_{h=2}\approx0.184\; \sf m/s[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]
Given variables:
a = length of the ladder.h = height of the ladder's top at time t.x = distance of the ladder from the wall at time t.Given a = 8.9, use Pythagoras Theorem to create an equation for x² in terms of h²:
[tex]\implies x^2+h^2=a^2[/tex]
[tex]\implies x^2+h^2=8.9^2[/tex]
[tex]\implies x^2+h^2=79.21[/tex]
[tex]\implies x^2=79.21-h^2[/tex]
Differentiate with respect to h:
[tex]\implies 2x\dfrac{\text{d}x}{\text{d}h}=0-2h[/tex]
[tex]\implies \dfrac{\text{d}x}{\text{d}h}=-\dfrac{2h}{2x}[/tex]
[tex]\implies \dfrac{\text{d}x}{\text{d}h}=-\dfrac{h}{x}[/tex]
Given:
[tex]\dfrac{\text{d}h}{\text{d}t}=-0.8\; \sf m/s[/tex]
Therefore:
[tex]\begin{aligned} \dfrac{\text{d}x}{\text{d}t}&=\dfrac{\text{d}x}{\text{d}h}\times \dfrac{\text{d}h}{\text{d}t}}\\\\ \implies &=-\dfrac{h}{x} \times -0.8\\\\ &=\dfrac{0.8h}{x} \end{aligned}[/tex]
Calculate x when h = 2:
[tex]\implies x^2=79.21-2^2[/tex]
[tex]\implies x^2=79.21-4[/tex]
[tex]\implies x^2=75.21[/tex]
[tex]\implies x=\sqrt{75.21}[/tex]
Substitute the values of h and x into the equation for dx/dt:
[tex]\implies \dfrac{\text{d}x}{\text{d}t}=\dfrac{0.8 \times 2}{\sqrt{75.21}}=0.1844939751[/tex]
Therefore, the rate of the ladder's distance from the wall is 0.184 m/s (3 d.p.)
