Water boils at 100LaTeX: ^\circ∘ Celsius or 212LaTeX: ^\circ∘ Fahrenheit. Water freezes at 0LaTeX: ^\circ∘ Celsius or 32LaTeX: ^\circ∘ Fahrenheit. If the weather forecaster says it will be 30LaTeX: ^\circ∘ Celsius today, write and solve a linear equation to find what Fahrenheit temperature this is.
Answer:
[tex]F = 1.8C +32[/tex]
[tex]F = 86^{\circ}F[/tex]
Step-by-step explanation:
Represent Celsius with C and Fahrenheit with F.
So, we have:
[tex](C_1,F_1) = (100,212)[/tex]
[tex](C_2,F_2) = (0,32)[/tex]
Solving (a): Represent as a linear equation
First, we calculate the slope:
[tex]m = \frac{F_2 - F_1}{C_2 - C_1}[/tex]
This gives:
[tex]m = \frac{32 - 212}{0 - 100}[/tex]
[tex]m = \frac{-180}{- 100}[/tex]
[tex]m = 1.8[/tex]
The linear equation is then calculated using:
[tex]F - F_1 = m(C -C_1)[/tex]
Where
[tex](C_1,F_1) = (100,212)[/tex]
[tex]m = 1.8[/tex]
[tex]F - 212 = 1.8(C -100)[/tex]
[tex]F - 212 = 1.8C -180[/tex]
Make F the subject
[tex]F = 1.8C -180+212[/tex]
[tex]F = 1.8C +32[/tex]
Solving (b): The value of F when C = 30
Substitute 30 for C in [tex]F = 1.8C +32[/tex]
[tex]F = 1.8 * 30 + 32[/tex]
[tex]F = 54 + 32[/tex]
[tex]F = 86[/tex]
Answer:
person above me is wrong
Is this congruent, or not congruent? And is it
SSS
SAS
SSA
AAS
ASA
HL
Answer:
Step-by-step explanation:
The two triangles are congruent. The diagonal is equal to itself in both triangles.
Triangle XYW = Triangle XYZ by SSS
[tex] \underline{ \underline{ \text{Question}}} : [/tex]
In the adjoining figure , ABC is an isosceles triangle. BO and CO are the bisectors of [tex] \angle[/tex] ABC and [tex] \angle[/tex] ACB respectively. Prove that BOC is an isosceles triangle.
~Thanks in advance !
Here it's given that ∆ABC is a isosceles triangle. We know that in a isosceles triangle opposite angles are equal. And the angles opposite to equal sides are also equal.
Hence here ,
AB = AC ∠ ABC = ∠ACB .Figure :-
[tex] \setlength{\unitlength}{1 cm}\begin{picture}(12,12)\put(0,0){\line(1,0){4}}\put(4,0){\line(-1,2){2}}\put(0,0.001){\line(1,2){2}}\put(0,0.01){\line(1,1){2}}\put(3.99,0){\line(-1,1){2}}\put(0,-0.3){$\bf B $}\put(4,-0.3){$\bf C$}\put(2,4.2){$\bf A$}
\put(1.8,2.2){$\bf o$}\end{picture}[/tex]
If LaTeX doesn't work on app kindly see the attachment .
Here we will use a theorem which is ,
[tex]\large\underline{\underline{\textsf{\textbf{\red{\blue{$\leadsto$} Theorem :- }}}}}[/tex]
Sides opposite to equal angles are equal.Hence here,
[tex]\tt:\implies \angle ABC =\angle ACB \\\\\tt:\implies \dfrac{1}{2}\times \angle ABC = \dfrac{1}{2}\times \angle ACB \\\\\tt:\implies \boxed{\bf \blue{\angle OBC = \angle OCB} }[/tex]
Now in ∆OBC , we can see that ∠OBC = ∠OCB. (just proved ) . Hence we can say that sides OB and OC are equal. Since the sides opposite to equal angles are equal. Therefore in ∆OBC , two sides are equal.
Therefore ∆ OBC is an isosceles triangle.
Hence Proved !Answer:
See Below.
Step-by-step explanation:
We are given the isosceles triangle ΔABC. By the definition of isosceles triangles, this means that ∠ABC = ∠ACB.
Segments BO and CO bisects ∠ABC and ∠ACB.
And we want to prove that ΔBOC is an isosceles triangle.
Since BO and CO are the angle bisectors of ∠ABC and ∠ACB, respectively, it means that ∠ABO = ∠CBO and ∠ACO = ∠BCO.
And since ∠ABC = ∠ACB, this implies that:
∠ABO = ∠CBO =∠ACO = ∠BCO.
This is shown in the figure as each angle having only one tick mark, meaning that they are congruent.
So, we know that:
[tex]\angle ABC=\angle ACB[/tex]
∠ABC is the sum of the angles ∠ABO and ∠CBO. Likewise, ∠ACB is the sum of the angles ∠ACO and ∠BCO. Hence:
[tex]\angle ABO+\angle CBO =\angle ACO+\angle BCO[/tex]
Since ∠ABO =∠ACO, by substitution:
[tex]\angle ABO+\angle CBO =\angle ABO+\angle BCO[/tex]
Subtracting ∠ABO from both sides produces:
[tex]\angle CBO=\angle BCO[/tex]
So, we've proven that the two angles are congruent, thereby proving that ΔBOC is indeed an isosceles triangle.
2x² + 3 × (-x²) + 6x + 2
Answer:
1x²+5 x 6x
Step-by-step explanation:
Work out the following and give your answer in it's simplest form:
[tex]\frac{9}{10}[/tex] ÷ [tex]\frac{3}{5}[/tex]
Plz help!!
Answer:
[tex]\frac{9}{10}[/tex] ÷ [tex]\frac{3}{5}[/tex]
=3/5
=1.5
Determine the slope of the line perpendicular to that of the function graphed below.
I AM IN DYING NEED OF HELP
Answer:
y=4/5x -5
Step-by-step explanation:
the slope is x and x is on the point -5. and d
to find the y-intercept you do rise/run
Find the volume of a cylinder with a radius of 3 inches and a height of 2
Answer:
56.55m³
Step-by-step explanation:
use a calculator, not brainly
Jorge Claims that the distance between his house and the library is 13 miles. His city is placed on a coordinate plane. Jorge's House is at the coordinates (5, 1), the mall is at coordinates (2, 11) and hte Library is at cordinates (10, 13). What equation verifies his claim?
Answer:
House coordinate = (5, 1)
Library coordinate = (10, 13)
Step-by-step explanation:
Given :
House coordinate = (5, 1)
Library coordinate = (10, 13)
Distance between house snd library :
Distance = sqrt[(x2 - x1)² + (y2 - y1)]
x1 = 5, x2 = 10, y1 = 1, y2 = 13
Distance = sqrt[(10 - 5)² + (13 - 1)²]
Distance = sqrt[(5² + 12²)]
Distance = sqrt(25 +144)
Distance = sqrt(169)
Distance = 13
Graph the line.
Y+4=1/5(x-1)
Answer:
graph the point (0, -5) and from that point go up 1 unit and to the right 5 units (5, -4) and plot that point; connect the two points
Step-by-step explanation:
8. GradPoint question
Determine whether the given lengths can be sides of a right triangle. Which of the following are true statements?
A. The lengths 14, 24 and 26 cannot be sides of a right triangle. The lengths 30, 72, and 78 cannot be sides of a right triangle.
B. The lengths 14, 24 and 26 can be sides of a right triangle. The lengths 30, 72, and 78 can be sides of a right triangle.
C. The lengths 14, 24 and 26 can be sides of a right triangle. The lengths 30, 72, and 78 cannot be sides of a right triangle.
D. The lengths 14, 24 and 26 cannot be sides of a right triangle. The lengths 30, 72, and 78 can be sides of a right triangle.
Answer:
I'm sorry but I have no clue. Actually I think it's C.
Step-by-step explanation:
Suppose you invest $2000 at a rate of 3.25% continuously, determine the worth of the investment after 10 years.
Answer:
$2650
Step-by-step explanation:
= 2000 × 0.0325 × 10 = 650
= $ 650.00
Jennifer makes 13 apple pies using 338 apples. Mateo used 9 apple pies using 216 apples. If they each have 105 apples, will Mateo And Jennifer make the same amount of apple pies ?
Answer: Yes. They'll both make 4 apple pies.
Step-by-step explanation:
Jennifer makes 13 apple pies using 338 apples. The fraction of apple pies made based on the number of apples will be:
= 13 / 338
= 0.03485
Mateo used 9 apple pies using 216 apples. The fraction of apple pies made based on the number of apples will be:
= 9 / 216
= 0.0417
When they each have 105 apples, the number of apple pies that Mateo will make will be:
= 0.03485 × 105
= 3.65925
= 4 apple pie approximately
Jennifer will make:
= 0.0417 × 105
= 4.3785
= 4 apple pie approximately
3(2x+5)-x=__x+__
put 2 numbers in the blanks to make no solutions
Answer:
5x + 15
Step-by-step explanation:
3(2x + 5)-x
6x + 15 - x
5x + 15
Hope this Helps!!!
need help with this thanks
Answer:
15.51
Step-by-step explanation:
Answer:
15.51
Step-by-step explanation:
The calculator is $49.50.
The radio is $114.99.
First, we add them together.
49.50+114.99 = 164.49
that is the total cost of both the radio and calculator.
Next, we subrtact 180.00-164.49= 15.51.
A store advertises 15% off an item that regularly sells for $300
what is the price of the item?
For this problem, we're finding the percent of 300. To do that we:
1. Multiply 300 by 15.
300 x 15 = 4500
2. Divide 4500 by 100. (% = 100)
4500 / 100 = 45
Therefore, the unit price is 45. But we're not done. We need to subtract 45 by 300.
300 - 45 = 255
Now, our answer is 255 and the unit price is 45.
Let me know of any questions!
A relation is given below.
{(0, 0), (2, 0.5), (4, 1), (3, 1,5), (4, 2), (5, 1.5), (6, 8)}
Which ordered pair can be removed to make this relation a function?
Why would removing this ordered pair make the relation a function?
solve each system by substitution
Answer:
x=2,y=5
Step-by-step explanation:
y=8x-11 ----(1)
y=-7x+19----(2)
Replace (1) in (2)
8x-11 =-7x+19
8x+7x=19+11
15x =30
x =30÷2
x =2
If x=2,then replace x=2 in (1)
y=8(2)-11
y=16-11
y=5
2x+3y=6 and 2x+y=-2 solved by elimination
28,46,25,76,18,25,47,83,44 what's the median,first quartile,third quartile, and interquartile range
Answer:
median: 44
first quartile: 25
third quartile: 61.5
interquartile range: 36.5
Step-by-step explanation:
For the given data set median is 44, first quartile is 25, third quartile is 61.5 and interquartile range is 36.5.
What is the interquartile range?The Interquartile Range (IQR) formula is a measure of the middle 50% of a data set. The smallest of all the measures of dispersion in statistics is called the Interquartile Range. The difference between the upper and lower quartile is known as the interquartile range.
Formula to find the interquartile range is Interquartile range = Upper Quartile - Lower Quartile =Q2=Q3-Q1
The given date set is 28,46,25,76,18,25,47,83,44.
The data in order 18,25,25,28,44,46,47,76,83.
Here,
Median =44
First quartile=Q₁=25
Third quartile=Q₃= (47+76)/2
= 61.5
Now, interquartile range (IQR)
= Q₃-Q₁
= 61.5-25
= 36.5
Therefore, for the given data set median is 44, first quartile is 25, third quartile is 61.5 and interquartile range is 36.5.
Learn more about the interquartile range here:
https://brainly.com/question/4135956.
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pls help!!
what would the answer be when rounded to one significant figure.
Find the slope of the line graphed below.
-
Step-by-step explanation:
1st point=(-2,2)x1=-2,y1=2
2nd point=(3,-2)x2=3,y2=-2
slope=y2-y1/x2-x1
According to the question,
slope=-2-2/3-(-2)=-4/5
A 29-meter ladder is sliding down a vertical wall so the distance between the top of the ladder and the ground is decreasing at 7 meters per minute. At a certain instant, the bottom of the ladder is 21 meters from the wall.
Complete question
A 29-meter ladder is sliding down a vertical wall so the distance between the top of the ladder and the ground is decreasing at 7 meters per minute. At a certain instant, the bottom of the ladder is 21 meters from the wall.
What is the rate of change of the distance between the bottom of the ladder and the wall at that instant(in meters per minute)
Answer:
[tex]\frac{dx}{dt}=11.94m/min[/tex]
Step-by-step explanation:
From the question we are told that
Slant height [tex]z=29m[/tex]
Change in Vertical height [tex]\triangle y=7m/s[/tex]
Horizontal length [tex]x=21[/tex]
Generally in finding the distance form the top to the bottom of the wall it is mathematically given by
[tex]x^2+y^2=z^2[/tex]
[tex]21^2+y^2=29^2[/tex]
[tex]y^2=29^2+21^2[/tex]
[tex]y=35.81[/tex]
Generally solving for the differential equation is mathematically represented as
[tex]x^2+y^2=29^2[/tex]
[tex]2x*\frac{dx}{dt} +2y*\frac{dy}{dt} =0[/tex]
[tex]x*\frac{dx}{dt} +y*\frac{dy}{dt} =0[/tex]
[tex](21)*\frac{dx}{dt} +(35.81)*(-7) =0[/tex]
[tex](21)*\frac{dx}{dt} -250.64 =0[/tex]
[tex]\frac{dx}{dt}=\frac{250.64}{21}[/tex]
[tex]\frac{dx}{dt}=11.94m/min[/tex]
The rate of change of the distance between the bottom of the ladder and the wall at that instant is 6.67 meter per minute.
Let us consider that distance between the top of the ladder and the ground is x meter and distance between the bottom of the ladder and the wall is y meter.
So, A right angle triangle is formed.
Since, the bottom of the ladder is 21 meters from the wall.
So, [tex]y=21[/tex]
Applying Pythagoras theorem,
[tex]x^{2} +y^{2}=(29)^{2} \\\\x^{2} +(21)^{2}=(29)^{2} \\\\\\x^{2} =841-441=400\\\\x=\sqrt{400} =20[/tex]
Given that, the distance between the top of the ladder and the ground is decreasing at 7 meters per minute.
[tex]\frac{dx}{dt}=-7meter/min[/tex]
Differentiate below equation with respect to time.
[tex]x^{2} +y^{2}=(29)^{2} \\\\2x\frac{dx}{dt}+2y\frac{dy}{dt}=0 \\\\2(20)(-7)+2(21)\frac{dy}{dt}=0\\\\\frac{dy}{dt}=\frac{280}{42}=6.67meter/min.[/tex]
Thus, the rate of change of the distance between the bottom of the ladder and the wall at that instant is 6.67 meter per minute.
Learn more about Differentiation here:
https://brainly.com/question/14023950
A sequence is recursively defined as a(n)=2a(n-2) for values of n>2. Find the seventh term of the sequence if a(1)=0 and a(2)=1
Answer:
a(7) = 21
Step-by-step explanation:
Using the recursive formula and a(1) = 0, a(2) = 1 , then
a(3) = a(2) + 2a(1) = 1 + 2(0) = 1 + 0 = 1
a(4) = a(3) + 2a(2) = 1 + 2(1) = 1 + 2 = 3
a(5) = a(4) + 2a(3) = 3 + 2(1) = 3 + 2 = 5
a(6) = a(5) + 2a(4) = 5 + 2(3) = 5 + 6 = 11
a(7) = a(6) + 2a(5) = 11 + 2(5) = 11 + 10 = 21
Help a girl out this is 9th grade math is really appreciate it
Answer:
Yes (2,7) Is A solution of the system
Step-by-step explanation:
Complete the steps to solve the equation 3x + 11 = 29.
Answer:
6
Step-by-step explanation:
3x+11 = 29
3x = 29 - 11 = 18
x = 18/3 = 6
25
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Expand and simplify 4(2x - 1) + 3(2x + 5)
F
AB
Type here to search
Step-by-step explanation:
4(2x-1)+3(2x+5)
8x-4+6x+15
8x+6x-4+15
14x+11
Answer:
14x +11
Step-by-step explanation:
4(2x-1)+3(2x+5)=8x-4+6x+15
=14x+11
Find the missing side length
Which spinner could not be used to simulate a baby being born male or female. a spinner 2 equal section. A spinner with 3 equal sections. a spinner with 6 equal sections. A spinner with 10 equal sections
Answer:
C spinner with 7 equal sides
Step-by-step explanation:
solve the following equation when x = 8
15x - 2 =
Answer:
118
Step-by-step explanation:
15(8)-2
120-2
118
Brainly plss?
Answer:
118
Step-by-step explanation:
you do 15 x 8 then subtract 2 from the product
Tank B, which initially contained 80 liters of water, is being drained at a rate of 2.5 liters per minute. How many liters of water remain in the tank after 30 seconds?
Answer:
78.75 ?
Step-by-step explanation:
calculator..
The volume of water remain in the tank after 30 seconds is 78.75 liters.
The given parameters;
initial volume of water in Tank B, V₀ = 80 litersrate at which water is being drained, R = 2.5 liters per minute.time of water drain, t = 30 secondsThe amount of water drained after 30 seconds is calculated as follows;
[tex]V_1 =2.5 \ \frac{liters}{\min} \times \frac{1 \min}{60 \ s} \times 30 \ s\\\\V_1 = 1.25 \ liters[/tex]
The volume of water remain in the tank after 30 seconds is calculated as follows;
V₂ = V₀ - V₁
V₂ = 80 liters - 1.25 liters
V₂ = 78.75 liters
Thus, the volume of water remain in the tank after 30 seconds is 78.75 liters.
Learn more here: https://brainly.com/question/13559135
