Answer:
[tex]y \: = \: \frac{2}{13} x \: + \: \frac{9}{13} [/tex]
Step-by-step explanation:
we need to write it in the form y = mx + c where m is the slope(gradient) and y is the y intercept
1) add 9 to both sides
2x = 13y - 9
2x + 9 = 13y
2)divide 13 on both sides
2x + 9 = 13y
2/13x + 9/13 = y
final equation is
[tex]y \: = \: \frac{2}{13} x \: + \: \frac{9}{13} [/tex]
Determine which postulate or theorem can be used to prove that ASEA = A PEN E O A. ASA OB. SSS O C. AAS O D. SAS
Answer:
asa is the correct answer
The postulate or theorem can be used to prove that triangles are congruent is ASA rule.
What are congruent triangles?Two triangles are said to be congruent when they have congruent corresponding parts.
Given is a figure having two triangles, we need to find the rule, that can prove that both the triangles are congruent,
∠ S ≅ ∠ P [given]
∠ SEA ≅ ∠ PEN [vertically opposite angles]
SE ≅ EP [given]
∴ Δ SEA ≅ Δ PEN by ASA rule
ASA rule :-
If any two angles and the side included between the angles of one triangle are equivalent to the corresponding two angles and side included between the angles of the second triangle, then the two triangles are said to be congruent by ASA rule.
Hence, the postulate or theorem can be used to prove that triangles are congruent is ASA rule.
Learn more about congruent triangles click;
https://brainly.com/question/22062407
#SPJ7
What is the slope of a line that contains the point
(3,7) and has a y-intercept of 1?
Write the equation of a line that goes through the points (-5,6) and (10,-6). The final answer should be in Slope Intercept Form.
Answer:
y=-4/5x+2
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-6-6)/(10-(-5))
m=-12/(10+5)
m=-12/15
simplify
m=-4/5
y-y1=m(x-x1)
y-6=-4/5(x-(-5))
y-6=-4/5(x+5)
y=-4/5x-20/5+6
y=-4/5x-4+6
y=-4/5x+2
The Royal Fruit Company produces two types of fruit drinks. The first type is 80% pure fruit juice, and the second type is 100% pure fruit juice. The company is attempting to produce a fruit drink that contains 95% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 220 pints of a mixture that is 95% pure fruit juice?
Answer:
55 from un-pure and 165 from pure
Step-by-step explanation:
to get 220 pints with 95% purity you need a mixture of 209 parts to 11 parts (220 *0.95 and 220 * 0.05)
we call the un-pure mixture a and the pure mixture b
all un-pure parts come from a and b in the following ratios
11 = 0.2a + 0b (each pint of mixture a adds 0.2 pints of unpure stuff and each pint of b adds no unpure stuff)
which we can then solve as:
a = 55
all pure parts come from a and b in the following rations
209 = 0.8a + 1b (each pint of mixture a adds 0.8 pints of pure stuff and each pint of b adds a full pint of the pure stuff)
now we can replace a with 55 (from above)
209 = 44 + b, and solve to
b = 165
now to double check
55 * (0.8x + 0.2y) + 165x would give you
44x + 11y + 165x, which is
11x + 209y and if you then check the ratio
209 / (209+11) = 0.95 again
There will be 55 pints and of un-pure and 165 pints of pure fruit drinks.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
To get 220 pints with 95% purity you need a mixture of 209 parts to 11 parts (220 *0.95 and 220 * 0.05)
We call the un-pure mixture a and the pure mixture b
All un-pure parts come from a and b in the following ratios
11 = 0.2a + 0b (each pint of mixture a adds 0.2 pints of unpure stuff and each pint of b adds no unpure stuff)
which we can then solve as:
a = 55
All pure parts come from a and b in the following rations.
209 = 0.8a + 1b (each pint of mixture a adds 0.8 pints of pure stuff and each pint of b adds a full pint of the pure stuff)
Now we can replace a with 55 (from above)
209 = 44 + b, and solve to
b = 165
Now to double check
55 x (0.8x + 0.2y) + 165x would give you
44x + 11y + 165x, which is
11x + 209y and if you then check the ratio
209 / (209+11) = 0.95
Therefore, there will be 55 pints of unpure and 165 pints of pure fruit drinks.
To know more about an expression follow
https://brainly.com/question/14022405
#SPJ2
Help me I don’t know if it -7 and -12
Answer:
I think it's-12
I am not sure
Please ask to some one else please
Need help ASAP! Directions in picture;)
please help me :)
ty ty
Answer:
The slope is steeper and the line is shifted flatter.
Step-by-step explanation:
I have provided a graph to help illustrate the relationship between these two lines, (The red line is line A which is y = 2x + 4, and the blue line is line B which is y = 4x + 9).
As you can see, the slope does determine the steepness of the lines. This means that line A's slope is going up 2 units and over to the right 1 unit, whereas line B's slope is going up 4 units and to the right 1.
Therefore, if line A is to transform into line B, then its slope will be steeper.
Hope this helps you :)
Also, P.S. I don't know if there are supposed to be more options, so I apologize if flatter does not belong in the second box.
I need help bad with this equation
don't quote me on this but I'm pretty sure it's H multiplication property of inequality
Y=-2(x+1)(x+3) convert the function into standard form
−2x^2−8x−6
Expand (−2x-2)(x+3) using the FOIL Method.−2x⋅x−2x⋅3−2x−2⋅3
please help ! 20 pts please
The given ratios expresses the number of time a value is larger or smaller
than another value.
The correct responses are;
3. (B) 12 and 244. (D) 6, 9, 215. [tex]\underline{(E) \ \displaystyle \frac{11}{2}}[/tex]6. [tex]\underline{(E) \ \displaystyle \frac{5}{14}}[/tex]7. (B) [tex]\overline{EF}[/tex] = 6, [tex]\overline{AC}[/tex] = 9·√58. (C) The values are equal9. (A) The value in column A is greaterReasons:
3. Given that the perimeter of the rectangle = 72
The ratio of the lengths of the sides = 1:2
Let a and b represent the sides, we have;
2·a + 2·b = 72
[tex]\displaystyle \frac{a}{b} = \mathbf{\frac{1}{2}}[/tex]
Which gives;
2·a = b
2·a + 2·(2·a) = 72
6·a = 72
a = 72 ÷ 6 = 12
b = 2·a = 2 × 12 = 24
The lengths of the sides are; (B) 12 and 24
4. Extended ratio = 2:3:7
The perimeter = 36
The lengths of the sides are;
[tex]\displaystyle \frac{2}{2 + 3 + 7} \times 36 = \mathbf{6}[/tex]
[tex]\displaystyle \frac{3}{2 + 3 + 7} \times 36 = \mathbf{9}[/tex]
[tex]\displaystyle \frac{7}{2 + 3 + 7} \times 36 = \mathbf{21}[/tex]
The lengths are; (D) 6, 9, 21
5. The given equation is presented as follows;
[tex]\displaystyle \frac{5}{x + 7} = \mathbf{\frac{3}{x + 2}}[/tex]
5 × (x + 2) = 3 × (x + 7)
5·x + 10 = 3·x + 21
5·x - 3·x = 21 - 10
2·x = 11
[tex]\displaystyle x = \mathbf{ \frac{11}{2}}[/tex]
The correct option is; [tex]\displaystyle \underline{(E) \ \frac{11}{2}}[/tex]
6. The width to length ratio is [tex]\displaystyle \mathbf{\frac{2.5}{7.0}}[/tex]
The simplified ratio is therefore;
[tex]\displaystyle \frac{2.5}{7.0} = \frac{2 \times 2.5}{2 \times 7.0} = \mathbf{\frac{5}{14}}[/tex]
The correct option is (E) [tex]\displaystyle \underline{(E) \ \frac{5}{14}}[/tex]
7. The given ratio of the lengths is 3:1
Therefore;
[tex]\overline{BC}[/tex]:[tex]\overline{EF}[/tex] = 3:1
Which gives;
[tex]\displaystyle \mathbf{\frac{\overline{BC}}{\overline{EF}}} = \frac{3}{1}[/tex]
[tex]\overline{BC}[/tex] = 18
Therefore;
[tex]\displaystyle \frac{18}{\overline{EF}} = \frac{3}{1}[/tex]
18 × 1 = 3 × [tex]\overline{EF}[/tex]
[tex]\displaystyle \overline{EF} = \frac{18 \times 1}{3} = 6[/tex]
[tex]\overline{EF}[/tex] = 6
By Pythagorean theorem, we have;
[tex]\overline{DF}[/tex]² = [tex]\mathbf{\overline{DE}}[/tex]² + [tex]\mathbf{\overline{EF}}[/tex]²
Which gives;
[tex]\overline{DF}[/tex]² = 3² + 6² = 45
[tex]\overline{DF}[/tex] = √(45) = 3·√5
Using the given ratio, we have;
[tex]\overline{AC}[/tex] = 3 × [tex]\mathbf{\overline{DF}}[/tex]
Which gives;
[tex]\overline{AC}[/tex] = 3 × 3·√5 = 9·√5
[tex]\overline{AC}[/tex] = 9·√5
The correct option is; (B) [tex]\overline{EF}[/tex] = 6, [tex]\overline{AC}[/tex] = 9·√5
8. EF = 1, AB = 2
CD = 2, CE = 4
Therefore;
[tex]\displaystyle \mathbf{\frac{EF}{AB}} =\frac{1}{2}[/tex]
[tex]\displaystyle \mathbf{\frac{CD}{CE}} =\frac{2}{4} = \frac{1}{2}[/tex]
Which gives;
[tex]\displaystyle \frac{EF}{AB} =\displaystyle \mathbf{\frac{CD}{CE}}[/tex]
(C) The values are equal
9. AC = 6, BE = 8
DF = 3, BD = 6
Column A
[tex]\displaystyle \frac{AC}{BE} =\displaystyle \mathbf{\frac{6}{8}} = \frac{3}{4}[/tex]
Column B
[tex]\displaystyle \frac{DF}{BD} =\displaystyle \mathbf{\frac{3}{6}} = \frac{1}{2}[/tex]
[tex]\displaystyle \frac{3}{4} > \mathbf{\frac{1}{2}}[/tex]
Therefore;
Column A is greater than column B
(A) The value in column A is greater
Learn more about ratios here:
https://brainly.com/question/2774839
what is the answer to this problem ( 1/5)² (3+2+5²)
Three boards are placed end to end to make a walkway. The first board is 2 feet 8 inches long, the second board is 6 feet 10 inches long, and the third board is 4 feet 9 inches long. How long is the walkway?
Answer:
The walkway is 14ft and 3in
Step-by-step explanation:
9/5 - (-2 7/10) and write it as a fraction and simplest form
Answer:
probably 4.5 if im not mistaking
Answer:
4 1/2
Step-by-step explanation:
(-2 7/10) = (-2.7)
9/5 = 1.8
1.8 - (-2.7)
= 1.8 + 2.7
= 4.5 or 4 1/2
Give a summary of the lesson what you have learned. about EXPONENTS!!
Please help
Is (6, 3) a solution to this system of inequalities?
x + 3y ≥ 15
10x + 3y > 3
Answer:
Graph both inequalities and see if the point lies in the overlapping shaded region.
Step-by-step explanation:
Eric has to read a 250-page novel by Friday. With four days left until Friday, he has read 110 pages of the novel. What percentage of the pages does Eric still have to read?
Answer:
56% left of the book
Answer:
56 %
Step-by-step explanation: There are two ways to arrive at the answer.
1st Way: 110/250 = 0.44
0.44 * 100 = 44%
44% is the amount he has read and we are looking for the amount that is left to read.
So we know 100% is the maximum percentage.
We then subtract 44 from 100 which is 56, So 56 is the answer.
2nd Way: 250-110 = 140
140/250=0.56
0.56*100= 56%
Hope this helps.
NEED HELP ASAP!!!!!
Jeff and Ed are climbing a small mountain. The height Jeff climbed with respect to time is given by the function H(t) = -250|x − 4| + 1,000. Ed’s height with respect to time is modeled in the graph.
Ed and Jeff both climb to the mountain’s peak and then climb back down.
The maximum height of the mountain is (blank) feet. Jeff takes (blank) hour(s) less than Ed to go up all the way and come back down.
Answer:
Step-by-step explanation:
The maximum height of the mountain is 1000 feet. Jeff takes 10 hour(s) less than Ed to go up all the way and come back down
A sandwich shop has a catering program. There is a flat fee of $30.00 plus $5 per boxed lunch (sandwich, cookie, and bottled water) ordered. If a total order is $150 , how many boxed lunches were ordered?
24?
5?
6?
or 36?
2.
In a box of 80 glasses, 3 are broken.
Work out the percentage of broken glasses in the box.
Answer: the answer is 3.7%
Step-by-step explanation:
We know there’s total 80 glasses and if 3 are broken we can represent it in a fraction which is 3/80
3/80=0.0375
to find percentage take 0.0375 and multiply it by 10 to get 3.7
therefor the answer is 3.7%
Need help l don’t understand due soon
Answer:
x = 9
Step-by-step explanation:
44 = 2(3x-5)
2(3x-5) expanded is 6x -10
44= 6x -10
+10 to both sides
=
54 =6x
54 divide by 6 = 9
x = 9
please mark as brainlesit is correct.
Answer:
First solve the paranthesis, 2*3x and 2*5, from here we will get the new equation, 44= 6x-10, now you can change sides of the known values to simplfy the question, 44+10=6x -> 54=6x, now divide each side by 6 to find x, 9=x
Step-by-step explanation:
What is the measure of ZB?
Answer:
Answer:[tex] m\angle A = 72\degree \m\angle B = 108\degree [/tex] Step-by-step explanation:ABCD is a parallelogram. Since, op
Please help. 0=25x^2 + 80x + 68
solve pls brainliest
I'm just doing this for achievement sorry bro
Step-by-step explanation:
dud
Graph y=2x+5 on the plane
Answer:
Incorrect
Step-by-step explanation:
for your slope go down two to the right one
One pentagon weighs how much
Answer:
11
Step-by-step explanation:
4.3-3 (4r-3)=0.7 (6r-10)
4.3-3(4r-3(=0.7(6r-10
We move all terms to the left:
4.3-3(4r-3(-(0.7(6r-10)=0
Evaluate 6/8×4/5 Give your answer in its simplest form.
Answer: 3/8
Step-by-step explanation:
Answer:
your answer is
its 3.5
i need help with this math question
Answer:
D. f(x) = -6x^3 -5x^2 +21x
Step-by-step explanation:
The given zeros mean the function has factors ...
(x -(-7/3))(x -3/2)(x -0)
Multiplying by 6, we can write this as ...
(3x +7)(2x -3)(x) = 6x^3 +5x^2 -21x
And multiplying by -1 gives ...
-6x^3 -5x^2 +21x . . . . . matches choice D
__
Additional comment
The product of factors will be zero when f(x) = 0. This means we can multiply or divide by any convenient factor and the product will remain zero. Effectively, we have multiplied our original factorization by -6 to make the expression match one of the given forms. When we write this final expression as the function f(x), it remains true that the given zeros are zeros (x-intercepts) of f(x).
Is this sample of the coins likely to be representative?
Answer: yes
Step-by-step explanation:
Solve for a.
a+(−1.2)=−5.5
Enter your answer in the box.
a =
Answer:
-4.3
Step-by-step explanation:
a+(-1.2)= -5.5
a-1.2=-5.5
add 1.2 to both sides
a-1.2+1.2= - 5.5+1.2
simplify
a= - 4.3
Answer:
a=-4.3
Why?:
You would have to keep the answer negative, this is because if it were to be positive it would make the negative decrease.
You could easily get a line paper and line up-
-4.3
+ -1.2
_______
-5.5
-5.5-(-1.2) would make the equation end up like -5.5+1.2, and -5.5+1.2=-4.3
Therefore,
a=-4.3