standard form for a linear equation means
• all coefficients must be integers, no fractions
• only the constant on the right-hand-side
• all variables on the left-hand-side, sorted
• "x" must not have a negative coefficient
to get the equation of any straight line, we simply need two points off of it, let's use (-6,10), (-4,18)
[tex](\stackrel{x_1}{-6}~,~\stackrel{y_1}{10})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{18}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{18}-\stackrel{y1}{10}}}{\underset{\textit{\large run}} {\underset{x_2}{-4}-\underset{x_1}{(-6)}}} \implies \cfrac{8}{-4 +6} \implies \cfrac{ 8 }{ 2 } \implies 4[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{10}=\stackrel{m}{ 4}(x-\stackrel{x_1}{(-6)}) \implies {\large \begin{array}{llll} y -10 = 4 ( x +6) \end{array}} \\\\\\ y-10=4x+24\implies -4x+y=34\implies \stackrel{standard~form}{{\Large \begin{array}{llll} 4x-y=-34 \end{array}}}[/tex]
(i) Six horses are each given 5 ml spoons of medicine three times each day.
Calculate the number of whole days a 2 L bottle of medicine will last.
Answer:22 days
Step-by-step explanation: since 6days are each given 5ml spoons of medicine three times a day,
Therefore consumption of each day is 90 ml and we have 2000 ml(2litre=2000 ml)
so, 2000/90 = we will get number of days
therefore 22.22 days
Which emplies 22 days.
The graph of y = 7x + 56 passes
through (-5, 7a) in the standard(x, y)
coordinate plane. What is the value of a ?
Answer:
a = 3
Step-by-step explanation:
The point (- 5, 7a ) satisfies the equation
Substitute the coordinate points into the equation and solve for a
7a = 7(- 5) + 56 = - 35 + 56 = 21 ( divide both sides by 7 )
a = 3
PLEASE HELP ASAP!!!!!
Answer:
Axis of Symmetry = -4
Vertex = (-4,7)
Step-by-step explanation:
The measures of the three sides of a triangle are 21 feet, 28 feet, and 35
feet. Determine whether the triangle is a right triangle.
Answer:
yes
Step-by-step explanation:
according to pythagoras theorem = hypotenuse² = √ base²+perpendicular²
so 21² + 28² = 35²
Please give me a step by step explanation
Answer:
[tex]108\pi[/tex] or approx. [tex]339.3 m^{2}[/tex]
Step-by-step explanation:
The question asks us to find the total surface area of the given hemisphere. The question gave us the formula for total surface area of a sphere, [tex]SA_{tot} =4\pi r^2[/tex]. But we need it for a hemisphere, so multiply the equation by [tex]\frac{1}{2}[/tex].
[tex]SA} = (\frac{1}{2}) 4\pi r^2[/tex] => [tex]SA} =2\pi r^{2}[/tex]
We also need the area of the base, which is circle. [tex]A_{circle}=\pi r^{2}[/tex].
Now add these equations together to get our equation.
[tex]SA_{tot} =2\pi r^2 +\pi r^{2}[/tex] => [tex]SA_{tot} =3\pi r^2[/tex]
Now we have the proper equation for total surface area of a hemisphere, [tex]SA_{tot} =3\pi r^{2}[/tex]. Plug in the value of [tex]r[/tex] which is given in the problem, [tex]r=6m[/tex].
=> [tex]SA_{tot} =3\pi (6)^{2}[/tex] => [tex]SA_{tot} =3\pi (36)[/tex] => [tex]SA_{tot} =108\pi m^{2}[/tex] or approx. [tex]339.3 m^{2}[/tex]
PLEASE NEED HELP ASAP
Answer:
its 80ft
Step-by-step explanation:
Solve this equation
18 = n -18
n=
Answer:
n= 36
Step-by-step explanation:
18=n-18 (add 18 to both sides of the equation, 18 and -18 cancel out)
36=n
The solution for n in equation 18 = n - 18 is 36.
To solve the equation 18 = n - 18, we need to isolate the variable n. Here's how:
Start with the equation: 18 = n - 18.
Add 18 to both sides of the equation to move the constant term to the other side: 18 + 18 = n - 18 + 18.
Simplify 36 = n.
Therefore, the solution for n is 36.
By adding 18 to both sides of the equation, we eliminate the -18 on the right side, leaving n isolated on the right side. Thus, the value of n that satisfies the equation is 36.
To check the solution, we substitute n = 36 back into the original equation: 18 = 36 - 18. Simplifying this equation results in 18 = 18, which confirms that n = 36 is indeed the solution to the equation.
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Find mRT. Assume that segments that appear to be tangent are tangent.
Answer:
m(arc RT) = 148°
Step-by-step explanation:
From the picture attached,
Segment RT is a chord and segment RS is a tangent of a circle O meeting at R.
By the property of tangent chord angle,
"Angle formed by an intersecting tangent and chord measures half of the intercepted minor arc"
m(∠SRT) = [tex]\frac{1}{2}(\text{minor arc RT})[/tex]
[tex]74^0=\frac{1}{2}m(RT)[/tex]
[tex]m(\text{arc RT)}=2(74^0)[/tex]
[tex]=148^0[/tex]
Therefore, measure of minor arc RT is 148°.
IM GIVING GOOD REVIEWS! EASY MATH!
Answer:
40,000
Step-by-step explanation:
can I have branliest
Answer: 40,000
Step-by-step explanation: Well it doubles every 440 minutes. Since it is asking for the size after 880 minutes, and the starting size is 20,000 just double 20,000 because 440 times 2 equals 880.
Help please,I’ll give 20points (if I can)
On solving the provided question, we can say that - here in the given equation we got x- 1 = 0; x = 1, y = 2
What is equation?An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.
y = 2x +1
y = 3x - 1
x- 1 = 0
x = 1, y = 2
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At a coffee shop, the first 100
customers' orders were as follows.
Small
Medium
Large
Hot
5
48
22
Cold
8
12
5
What is the probability that a customer ordered a
hot drink given that he or she ordered a large?
P( Hot Large ) = [?]
Round to the nearest hundredth
Answer:
0.07
Step-by-step explanation:
lets make a chart first
small | medium | large
hot | 5 | 48 | 22
cold | 8 | 1 | 5
1. add all the hot drinks
5+48+22=75
2. find 5/75,
5/75=0.0666666
Please help me??!!!!!!!!!
Answer:
g(f(x)) means that the x of the g function is the f(x) function, if that makes sense.
so you do 8(x-10)-5
8x-80-5
8x-85
hope that answers your question
Don't hesitate to comment if you don't understand something.
Step-by-step explanation:
21
Kinza goes on holiday to South Africa.
Kinza wants to change £950 into South African rand.
She wants to get as many 200 rand notes as possible.
The exchange rate is £1 = 18.53 rand.
Work out the greatest number of 200 rand notes that Kinza can get for £950
For the function f(x)=3x^2-8 what is the average rate of change on the interval from 0 to 10?
Answer:
Average rate of change
=
26.5
Explanation:
Use the slope formula to find average rate of change:
m
=
y
2
−
y
1
x
2
−
x
1
To use the slope formula, you need 2 points on the curve - we only have to x values, so we need to find f(8) and f(10).
f
(
8
)
=
92
f
(
10
)
=
145
These means are points are
(
x
1
,
y
1
)
=
(
8
,
92
)
and
(
x
2
,
y
2
)
=
(
10
,
145
)
.
m
=
145
−
92
10
−
8
m
=
53
2
m
=
26.5
Step-by-step explanation:
The average rate of change on the interval from 0 to 10 is 30
How to determine the average rate of change?The function is given as:
f(x)=3x^2-8
The interval is given as:
0 to 10
Calculate f(0) and f(10)
f(0)=3 *(0)^2 -8
f(0) = -8
f(10)=3 *(10)^2 -8
f(10) = 292
The average rate of change is then calculated as:
Rate = (f(10) - f(0))/(10 - 0)
This gives
Rate = (292 +8 )/(10 - 0)
Evaluate
Rate = 30
Hence, the average rate of change on the interval from 0 to 10 is 30
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Tree+snowman+tree=17
Answer:
tree = 8
snowman = 1
deer = 4
snowflake = 4
Step-by-step explanation:
say t = tree, s = snowman, d = deer, f = snowflake
1. For 2d + f, since you know d is equal to f, replace the snowflake with a deer, turning the equation into 3d = 12. To find the value of d divide by 3 on both sides. This will result in 4. So, the value of deer = 4.
2. Now, find the value of the snowman using the value of the deer.
4-3 = 1. This means the value of the snowman = 1.
3. Plug in the value of the snowman into 2t + s = 17.
2t + 1 = 17
Subtract on both sides to get 2t by itself and then simplify
2t = 17 -1 --> 2t = 16
Divide by 2 on both sides to find the value of the tree
2t/2 = 16/2 --> t = 8
I Forgot How To Do This For Some Reason
Answer:
A
Step-by-step explanation:
√11²+13² is the answer due to pythagoras theorem. You imagine the line between them is the hypotenuse for the right angled triangle so it’s A as 121 plus 169 is 290
1. Is the following a function?
2. Write a function that represents the following description:
“After 8 hours, a person earned $148 in wages”
3. Let f(x)=x and g(x)=x-13
Find (f+g)(9)
4. Paige is paying off her car loan. The function that models how much she has left to pay is P(m) = 6000 -300m where m is the number of months since Paige took out the loan. What was the original amount of her loan?
a) The given relation is function.
b) The function is, $x = 18.5 y
c) The value of (f+ g)(9) is 5.
d) The he original amount of her loan is 6000.
What is Linear Function?A function with one or two variables and no exponents is referred to as a linear function. It is a function with a straight line as its graph.
Given:
a) The given relation is function because is input have have output, no two outputs have same input.
b) After 8 hours, a person earned $148 in wages.
So, the unit rate change = 148/ 8
= 18.5
So, if y represents the number of hour and $x the wages, then the function is $x = 18.5 y.
c) Let f(x)=x and g(x)=x-13
(f+ g)(9)
= (x+ x-13) (9)
= 2x -13
= 2(9)- 13
= 5
d) The modeled function. P(m) = 6000 - 300m.
so, the original amount of her loan is 6000.
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WHAT IS 10000-22 CAN ANYONE HELP
Answer:
9978
Step-by-step explanation:
10000 - 22 = 9978
9978 is the answer
Answer: 9978
Step-by-step explanation:
Stack the numbers up like this 10000
22
borrow from the one make the zero a ten, and then borrow from that to make the next one and make it a nine and then do it to the last one and subtract. Hope this makes sense
2) You roll one die. What is the probability that you roll a 6?
A) 1/2
B) 1/4
C) 1/6
D) 2/6
Answer: c 1/6
Step-by-step explanation
Becouse it has six numbers so that means that 1 is a factor so taking in every other number the answer should be 1/6
An underwater telephone cable is to cross a shallow lake from point A to point B. Stakes are located at
A, B, and C. Distance AC is measured as 112 m, mZCAB = 118.4° and m ZABC =19.2°. Find the
distance of AB. Round your answer to the nearest meter.
A
300 m
B
230 m
C
193 m
D
256 m
heyy! i’ll give brainliest please help
Answer:
a season your welcome: ]
Answer:
Seasons shouldn't be capitalized
What is the surface are of the triangular prism?
Answer:
114.12
Step-by-step explanation:
jake ran 2 kilometers to train for an upcoming marathon.
how many meters did jake run ?
Answer:
2000
Step-by-step explanation:
1 kilometer is = 1000 meters
give brainliest pls
PLEASE HELP ME ILL BRAINLIEST YOU
Answer:
7
Step-by-step explanation:
a^2 + b^ = c^2
x^2 + 24^2 = 26^2
x^2 = 100
x=10
Can i have brainliest please
Answer:
x = 10
Step-by-step explanation:
This is a right triangle problem
use the Pythagorean Theorem
a^2 + b^2 = c^2
x^2 + 24^2 = 26^2
x^2 + 576 = 676
Subtract 576 from both sides
x^2 = 100
Take the square root of both sides
x = 10
hi can someone explain what does consecutive angles are supplementary mean
Answer:
key note is that when the angles are added it equals 180 degrees
HELP THIS IS URGENT!!!!!!!!!!
Find the percent decrease from 133 to 120. Round your answer to the nearest tenth
PLEASE MARK BRAINLIEST
Find the percent decrease from 133 to 120. Round your answer to the nearest tenth
1. Subtract
133-120= 13
2. Find
13/133 x 100
1300/133
= 9.77443609
3. Round
9.77 rounded is 9.8
Answer: 9.8%
Answer:
9.8 is your answer
the percentage decrease from 133 to 120 is 9.7744
but rounded to the nearest tenth is 9.8
Factor the expression: 24w + 48
Answer:
24(w+2)
Step-by-step explanation:
You must look for a common denominator between the two parts of the expression. In this case, 48 is divisible by 24. 48/24 = 2. So you can now move the common denominator out to the front. Then use this common denominator and divide each term by it. 24w/24 = w and 48/24 = 2. Therefore, your expression factored is 24 (w+2)
What is the degree of [tex]9x^5y^3[/tex]
5
9x⁵=5
5y³=3
so 5>3=5
pls mark me as brainlist
PLEASE HELP ASAP
Which is the following is not an attribute of a right rectangular prism?
1 apex
12 edges
rectangular faces
square bases
Square bases is not an attribute of a right rectangular prism. Option D
What is a right rectangular prism?A right rectangular prism can be described as a three-dimensional solid shape with 6 faces, 12 edges, and 8 vertices.
It is sometimes called a cuboid.
All the faces of the right rectangular prism are rectangular in shape.
Examples of right rectangular prisms are books, bricks and aquarium.
Some properties of a right rectangular prism include;
There are 12 edges There are 8 verticesAll the faces are rectanglesAll the angles formed at the vertices are of 90 degreesThese prisms have no square base(s)
Hence, the right option is square bases.
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6 2/3 times 12 simplest form
Answer:
80
Step-by-step explanation:
[tex]6\frac{2}{3} *12[/tex]
First, write the fractions as improper fractions.
[tex]\sf\frac{20}{3} *\frac{12}{1}[/tex]
Multiply.
[tex]\sf\frac{240}{3}[/tex]
Divide.
80
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{6\dfrac{2}{3}\times 12}[/tex]
[tex]\mathsf{= \dfrac{6\times3+2}{3}\times\dfrac{12}{1}}[/tex]
[tex]\mathsf{= \dfrac{18 + 2}{3} \times\dfrac{12}{1}}[/tex]
[tex]\mathsf{= \dfrac{20}{3} \times\dfrac{12}{1}}[/tex]
[tex]\mathsf{= \dfrac{20\times12}{3\times1}}[/tex]
[tex]\mathsf{= \dfrac{240}{3}}[/tex]
[tex]\mathsf{= 240\div 3}[/tex]
[tex]\mathsf{= 80}[/tex]
[tex]\huge\text{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{80}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]