Answer:
10) 6
11) 18
12) 7.1
13) 1.3
Step-by-step explanation:
all you have to do is substitute
10 - 4 = 6
12 + 6 = 18
1.9 + 5.2 = 7.1
3.4 - 2.1 = 1.3
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
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
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
Learn more about proportionality here;
https://brainly.com/question/8598338
#SPJ1
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°.
To know more about measure of the angle here
https://brainly.com/question/14684647
#SPJ1
Solve for w.
63 =
3
Simplify your answer as much as possible.
W =
Answer:
That doesn't even make any sense you can't simplify or solve for anything if there isn't the right equation???????
Step-by-step explanation:
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.)
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
To know more about correct order https://brainly.com/question/7327329
#SPJ1
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.
Learn more about Mountains at:
https://brainly.com/question/23936814
#SPJ1
Answer:
Glaciers scoured the landscape, grinding the high places and mixing the soil with rocks.Step-by-step explanation:
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.
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.
To learn more on Graph click:
https://brainly.com/question/17267403
#SPJ1
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
To learn more about function rule click :
https://brainly.com/question/3760195
#SPJ2
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.
learn more about function here:
brainly.com/question/21145944
#SPJ1
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).
there are more than 200 pages but fewer than 800 in my book. all thre digits of my number are the same. the number is divisible by 9. how many pages sre in my book
Answer:777
Step-by-step explanation: I do not care
There are 333 pages are in my book.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
There are more than 200 pages but fewer than 800 in my book.
And, All the digits of my number are the same and the number is divisible by 9.
Now,
Let a number with three same digit = xxx
So, We get;
200 < xxx < 800
Since, the number is divisible by 9.
So, By the rule of the number divide by 9, we get;
x + x + x = 9k
3x = 9k
for k = 1;
x = 3
Thus, Number of pages = 333
Therefore,
There are 333 pages are in my book.
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ2
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.
Learn more about distance :
brainly.com/question/15172156
#SPJ4
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
Learn more about inequalities here:
https://brainly.com/question/25275758
#SPJ1
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
Learn more about vertically opposite angles
brainly.com/question/68367
#SPJ13
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
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
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
Learn more about trigonometric functions
brainly.com/question/14746686
#SPJ13
determined whether the graph on the right is that of a function by using the vertical-line test. If it is, use the graph to find the following. the domain and range Does the graph represent a function? Choose the correct answer below A No because no horizontal line can intersect the graph in more than one point No because no vertical line can intersect the graph in at most one point. OC Yes, because every vertical line can intersect the graph in more than one point OD. Yes, because every vertical line can intersect the graph in at most one point DE Yes because every horizontal line can intersect the graph in at most one point OF No. because no horntal line can intersect the graph in at most one point. OG Yes, because every horizontal line can intersect the graph in more than one point. 04. No, because no vertical time can intersect the graph in more than one point.
x - intercept is at ( 1, 0 ) graph intersect at x = 1 .
What are intercepts?
The x-intercept and y-intercept are the points at which a line crosses the x- and y-axes, respectively.An intercept is the location of the intersection of two axes in a graph. The term "x-intercept" specifically refers to this one.The x-axis and y-axis are intersected by two intercepts, P(2,0) and Q(0,3), respectively. => 3x + 2y – 6 = 0, Consequently, the line's equation is 3x + 2y - 6 = 0.Domain - values of x on x -axis taken by function
- ( 0,5 )
Range = values of y on y -axis taken by function
= (- ∞ , 2 )
= ( as, x ⇒ 0 then graph goes below
b) x - intercept is at ( 1, 0 ) graph intersect at x = 1
no y - intercept is there .
c) graph is not symmetric .
Learn more about intercepts
brainly.com/question/14180189
#SPJ13
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
To know more about Sphere here
https://brainly.com/question/16686115
#SPJ1
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.
To learn more about area of circle refer the below link
https://brainly.com/question/10645610
#SPJ4
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.
Learn more about equations here;
https://brainly.com/question/29473237
#SPJ1
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.
15. Mindy has $20. She spent $8.64 including tax to buy a new card game. She
needs to set aside $10 to buy lunch. If Lollipops cost $.28 including tax, what is
the maximum number of lollipops that Maya can buy?
Step-by-step explanation:
she can therefore only spend $10 of the $20.
$8.64 are adjust gone for the card game.
that leaves us with
10 - 8.64 = $1.36
to spend on lollipops.
1 lollipop costs $0.28
so, she can buy a many lollipops as times 0.28 fits into 1.36 :
1.36 / 0.28 = 4.857142857...
that means she can buy 4 lollipops max.
she would keep some change, but not enough to buy a 5th lollipops, because then she would have to cut into the $10 reserve she needs for lunch.
for 5 lollipops she would need $1.40 (5×0.28).
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.
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.
Read more on direct variation equation;
https://brainly.com/question/1553745
#SPJ1
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.
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.
