Answer:
Step-by-step explanation:
There are two ways to do this. You could use your calculator to find out the decimal numbers that are equivalent to the two given fractions. Then check which one of the givens falls between these two numbers. I wouldn't do it that way -- not when you are told that the answer has 56 as the denominator. So ...
The best way to do it is to change the two givens so that they have a denominator of 56
3/7 = 3*8/7*8 = 24 / 56
7*7 / 7*8 = 49 / 46
So you need a number that is between 49 and 24
There is only one 27 / 56
Q3).
0.4x + 0.3y = 1.7
0.7x - 0.2y = 0.8
Solve it by using substitution method.
Step-by-step explanation:
[tex] \green{\large\underline{\sf{Solution-}}}[/tex]
Given pair of linear equations are
[tex]\rm :\longmapsto\:0.4x + 0.3y = 1.7 \\ \\ \rm :\longmapsto\:0.7x - 0.2y = 0.8[/tex]
can be rewritten as on multiply by 10,
[tex]\rm :\longmapsto\:4x + 3y = 17 - - - - (1)\\ \\ \rm :\longmapsto\:7x - 2y = 8 - - - - - (2)[/tex]
From equation (2)[tex]\rm :\longmapsto\:2y = 7x - 8[/tex]
[tex]\rm\implies \:\boxed{\tt{ y = \frac{7x - 8}{2}}} - - - - (3) [/tex]
On substituting the value of y in equation (1), we get
[tex]\rm :\longmapsto\:4x + 3\bigg( \dfrac{7x - 8}{2} \bigg) = 17[/tex]
[tex]\rm :\longmapsto\:\dfrac{8x + 21x - 24}{2} = 17[/tex]
[tex]\rm :\longmapsto\:29x - 24 = 34[/tex]
[tex]\rm :\longmapsto\:29x = 34 + 24[/tex]
[tex]\rm :\longmapsto\:29x = 58[/tex]
[tex]\bf\implies \:x = 2 - - - - (4)[/tex]
On substituting x = 2 in equation (3), we get
[tex]\rm :\longmapsto\:y = \dfrac{7 \times 2 - 8}{2} [/tex]
[tex]\rm :\longmapsto\:y = \dfrac{14 - 8}{2} [/tex]
[tex]\rm :\longmapsto\:y = \dfrac{6}{2} [/tex]
[tex]\bf\implies \:y = 3[/tex]
So, we get
[tex]\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\:\begin{cases} &\bf{x = 2} \\ \\ &\bf{y = 3} \end{cases}\end{gathered}\end{gathered}[/tex]
VerificationFrom equation (1),
[tex]\rm :\longmapsto\:0.4x + 0.3y = 1.7[/tex]
On substituting the value of x and y, we get
[tex]\rm :\longmapsto\:0.4(2) + 0.3(3) = 1.7[/tex]
[tex]\rm :\longmapsto\:0.8 + 0.9 = 1.7[/tex]
[tex]\rm :\longmapsto\:1.7 = 1.7[/tex]
Hence, Verified▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬
Basic Concept :-To solve systems using Method of Substitution, follow this procedure:
1. Select one equation and solve it for one of its variables.
2. In the other equation, substitute the value of one variable evaluated in step 1 to reduced the equation to one variable.
3. Solve the equation to get the value of this variable
4. Substitute the value found in to first equation involving both variables and solve for the other variable.
A triangle has angle measures
x+15, 3x-35, and 4x.
What type of triangle is it? Be as specific as possible. Justify your answer.
Solve please....................................
Answer:
angle (3x-15)°=angle (2x+10)° (by vertically opposite angles)
3x-15=2x+10
3x-2x=10+15
x=25
by putting the value of x.
3x-15=3×25-15 = 60°
38°+ 60°+ <ebf= 180° (by sum of all sides is 180° )
98°+<ebf = 180°
<ebf = 180° - 98°
<ebf = 82°
Write the equation of a line, in slope-intercept form, that has a slope of m=9 and passes through the point (4, 31)
Answer:
9x-y = 5
Step-by-step explanation:
Equation of line in slope intercept form:
y-y1 = m*(x-x1), m=9, (x1,y1)=(4,31)
y-31 = 9*(x-4)
y-31 = 9x-36
9x-y = 36-31
9x-y = 5
20,612,439 in scientific notation
Find the area of the kite
A) 660 mm2
B) 744.5 mm2
C) 630 mm2
D) 106 mm2
F) 1260 mm2
Answer:
C) 630 mm²
Step-by-step explanation:
area of kite = pq
2
= 28x45
2
= 630 mm²
y>-4 help PLZ......!?!?!?!?!?
Answer:
0
Step-by-step explanation:
Which number represents the ratio comparing the average age in groupB to group A if the average age of A=50 years old and B=65 years old?
A line passed through the points (1, 2) and (3,-4).
Determine the equation of that line in slope intercept
form.
The slope of the line is m = -3
The y-intercept is (0,5)
The equation of the line in the slope-intercept form is y = 5-3x
4. In the figure, points A, B, and Clie in plane Z. Which of the following postulates can be used to show that A and B are collinear?
O Through any two points, there is exactly one line.
O Through any three points not on the same line, there is exactly one plane.
O If two lines intersect, then their intersection is exactly one point.
o If two planes intersect, then their intersection is a line.
Collinear points are points that lie on the same line.
The postulate to prove that A and B are collinear is: (a) Through any two points, there is exactly one line.
From the question, we understand that:
A, B and C are in plane ZA and B are collinearFor A and B to be collinear, then:
A line must pass through A and B, in such a way that points A and B lie on that line
Because only one line can pass through any two points, the appropriate postulate to use is: (a) Through any two points, there is exactly one line.
Read more about collinear points at:
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A park district is building an outdoor tennis court based on a scale drawing that measures 30 cm long by 13.75 cm and uses the scale 1 cm:0.8 m. What is the area of the actual tennis court in square meters?
The actual area of the tennis court is 264 m²
First use the scale to find the actual dimensions of the court:
1 cm : 0.8m
30 cm in the drawing would be:
= 0.8 x 30
= 24 m outside
13.75cm in the drawing would be:
= 0.8 x 13.75
= 11 m outside
Area of a rectangle (which is what the dimensions resemble):
= Length x width
= 24 x 11
= 264 m²
In conclusion, the area of the tennis court is 264 m²
Please help!! BRAINLIEST to correct answer!!
Answer:
Here is your equation (x+2)^2+(y+10)^2=100
, Hope this helps :)
Have a great day!!
Answer:
(x+2)²+ (y+10)²=100
Step-by-step explanation:
y=6x+2 P(-2,0)
x=-2
y=6 × (-2) + 2
y= -12+2
y= -10
M(-2,-10) r= 0 - ( - 10 ) = 10
(x+2)²+ (y+10)²=100
Hope this helps!! Can I get brainliest?? Anyways have a great day!! :3
5. Which of the following is a sign that you have a budget deficit?
Your savings account balance grows every month.
. You overdraw your checking account on a consistent basis (with a $25 cost per overdraft).
Your checking account balance grows every month.
1) soe soe had 15kg of flour. She used 4/5 of it to make some cookies. How many kilograms of flour had she left?
2) U Kyaw mixed red paint and blue paint in the ratio 5:3 for painting a wall. If he made 24 liters of paint for the painting job, how many litres of blue paint did he use?
Answer:
1) 3 liters left
2) 9 liters of blue paint
Step-by-step explanation:
1) 1/5 * 15 = 3
2) 3 liters of blue paint for each 8 liters.
24/8 * 3 = 9
Fractions and Comparisons
Level : JHS1.
The amount of flour used is :
= 4/5 × 15 kg
= 12 kg
The amount of flour left is :
= 15 kg - 12 kg
= 3 kg
2.
5 : 3 = Red : Blue
The amound of blue paint :
= 3 : (3 + 5) × 24 liters
= 3 : 8 × 24 liters
= 9 liters
So, the litres of blue paint did he use is 9 liters
#LearnWithEXO
Consuelo is buying flavored coffee and plain coffee. The total amount of money she spends on coffee is T = 5.50p + 7f, where "p" represents the cost of a package of plain coffee and "f" represents the cost of a package of flavored coffee.
a. If Consuelo has $40 to spend on coffee, describe the constraints on the formula.
b. Solve for f.
c. If Consuelo needs to buy 3 packages of plain coffee, what is the maximum number of packages of flavored coffee she can buy?
A linear equation can have one or more variables.
The constraints on the formula are the costs of plain coffee and cost of flavored coffeeThe equation of f is: [tex]\mathbf{f = \frac{40 -5.50p}7 }[/tex].The maximum number of packages of flavored coffee she can buy is 3The function is given as:
[tex]\mathbf{T = 5.50p + 7f}[/tex]
(a) The constraints when T = 40
Substitute 40 for T in [tex]\mathbf{T = 5.50p + 7f}[/tex]
[tex]\mathbf{5.50p + 7f = 40}[/tex]
The variables in the above equation are p and f
Hence, the constraints are the cost of a package of plain coffee and the cost of a package of flavored coffee
(b) Solve for f
In (a), we have:
[tex]\mathbf{5.50p + 7f = 40}[/tex]
Subtract both sides by 5.50p
[tex]\mathbf{7f = 40 -5.50p }[/tex]
Divide both sides by 7
[tex]\mathbf{f = \frac{40 -5.50p}7 }[/tex]
Hence, the equation of f is:
[tex]\mathbf{f = \frac{40 -5.50p}7 }[/tex]
(c) The maximum number of flavored coffee when she buys 3 packages of plain coffee
In (b), we have:
[tex]\mathbf{f = \frac{40 -5.50p}7 }[/tex]
Substitute 3 for p
[tex]\mathbf{f = \frac{40 -5.50 \times 3}7 }[/tex]
[tex]\mathbf{f = \frac{40 -16.50}7 }[/tex]
[tex]\mathbf{f = \frac{23.5}7 }[/tex]
Divide
[tex]\mathbf{f = 3.36 }[/tex]
Remove the decimal part (do not approximate)
[tex]\mathbf{f = 3 }[/tex]
Hence, the maximum number of packages of flavored coffee she can buy is 3
Read more about linear equations at:
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HELP MEEEE !! I’m stuck
Answer:
10
Step-by-step explanation:
because it is what it is i just did the math
I WILL MARK BRAINLIST PLS HELP
Answer:
a is parallel b
then
10x-23=27
10x=23+27=50
x=50÷10=5
Help would be appreciated!
Please explain how you got the answer c:
Answer:
-25
Step-by-step explanation:
Reading the expression:We're given the sigma notation of a series.
[tex] \mathsf{ \sum _{k = 1} ^{5}(2k - 11) }[/tex]
The variable k is the "index of notation"
The expression can be read as the sum of (2k- 11) as k goes from 1 to 5.
"To generate the terms of a series given in sigma notation, successively replace the index of summation with consecutive integers from the first value to the last value of the index" ~internet
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Generating the terms of the series:To generate the terms of the series given on sigma notation above, replace k by 1, 2, 3, 4, and 5 and add the terms, to get the answer to the given notation.
[tex]\mathsf{ \sum _{k = 1} ^{5}(2k - 11) } \\ = \mathsf{ \overline{2(1) - 11} + \overline{2(2) - 11} + \overline{2(3) - 11} } \\ \mathsf{ + \overline{2(4) - 11} + \overline{2(5) - 11}}[/tex]
[tex] = \mathsf{\overline{2 - 11} +\overline{4 - 11} + \overline{6 - 11} } \\ \mathsf{\overline{8 - 11} + \overline{10- 11}}[/tex]
[tex] = \mathsf{ - 9- 7 - 5 - 3 - 1}[/tex]
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Final Answer:[tex] \mathsf{ \underline{- 25}}[/tex]
______________________
[tex] \mathfrak{ \overline{There \: You \: Are!}}[/tex]
Let's see
[tex]\\ \rm\Rrightarrow {\displaystyle{\sum^2_{k=1}}}(2k-11)[/tex]
k=1,2,3,4,5[tex]\\ \rm\Rrightarrow 2(1)-11+2(2)-11+2(3)-11+2(4)-11+2(5)-11[/tex]
[tex]\\ \rm\Rrightarrow 2-11+4-11+6-11+8-11+10-11[/tex]
[tex]\\ \rm\Rrightarrow 30-55[/tex]
[tex]\\ \rm\Rrightarrow -25[/tex]
please help thank you
Answer:
[tex]x - 2 = 0 \\ x = 2 \\ p(2) = 0 \\ {2}^{4} - d {2}^{3} + 8 \times {2}^{2} - 14 \times 2 + 16 = 0 \\ 16 - 8d + 32 - 28 + 16 =0 \\ 8d = 36 \\ d = 36 \div 8 = 4.5[/tex]
enjoy it
Q and R are complementary. The measure of Q is 26 less than the measure of R. Find the measure of each angle
Step-by-step explanation:
Since Q and R are complementary,
⇒ Q + R = 90°
Since Q is 26° less than the measure of R
⇒ R - 26° = Q
We can therefore say that ( R - 26°) + R = 90°
⇒ 2 R = 90° + 26°
R = 58 °
Also, since R - 26° = Q
58° - 26° = Q
32 ° = Q
∴ Q = 32 ° and R = 58°Factorize mn-nq+mo-oq
mn-nq+mo-oq
n(m-q) + o(m-q)
final ans:(n+o) (m-q)
Volume Of This Cylinder
Answer:
2827.4 cm
Step-by-step explanation:
Volume of cylinder
V= π*r^2*h
H= height and r= radius
H= 9cm and r = diameter ÷ 2
r= 20cm ÷2 = 10cm
V= 22/7* 10^2* 9cm
V= 2829cm^3
heyy everyone
equivalent fraction of 3/6 with denominator 72 is
can i pls know the answer
3/6
Take a lot at the denominator 6, 6 multiplied by 12 gives 72, therefore multiply the numerator 3 by 12 to give 36.
3/6= 36/72
please mark Brainliest.
Answer:
What is 31/72
Step-by-step explanation:
3/6 is really 1/2 as 3 is half of 6
So half of 72 would be 31
Hope this helps you see it in a much more simpler way!
<3Miss Hawaii
Find the length of the third side. If necessary, write in simplest radical form.
Answer: [tex]3\sqrt{3[/tex]
Step-by-step explanation: use pythagorean theorem to solve this. which is a^2 + b^2 = c^2
lets say b=3 and c=6. plug this into the equation. (6)^2 - (3)^2 + = 36 - 9 which is 27 = c^2. to get c from c^2, square root the c^2 value
the square root of 27 is [tex]3\sqrt{3[/tex] in simplest radical form
Can someone help me do this
Answer:
6
Step-by-step explanation:
Find the missing angle:
180⁰ - 82⁰ = 98⁰
Find the sum of the angles given without the missing angle:
180⁰ - 98⁰ = 82⁰
The sum of both the angles is 82⁰
Write an equation:
5x + 8 + 6x + 8 = 82⁰
Collect the like terms together
11x + 16⁰ = 82⁰
Subtract 16⁰ from both sides
11x = 66⁰
Divide by 11 on both sides
x = 6⁰
(x+3)(x²-3x+9)-(54+x³)
Answer:
x² - 3x ≤ 54 m²
Step-by-step explanation:
Step-by-step explanation:
and ? what do we need to do with this ?
compress/simplify this ?
if that is true :
(x+3)(x²-3x+9)-(54+x³)
x³ - 3x² + 9x + 3x² - 9x + 27 - 54 - x³ = -27
Austin's town voted on a new speed limit. 90% of the 20 votes were in favor of the new speed limit. How many votes were in favor?
Answer:
18
Step-by-step explanation:
times 20 by 0.90
20*0.90=18
The temperatures for the week were as follows Sunday 72 Monday 72 Tuesday 85 Wednesday 69 Thursday 72 Friday 80 and Saturday 77 determine the mean rounded to the nearest tenth median mode and range of the results
Answer:
Mean- 75.3
Median- 72
Mode- 72
Range- 77
Step-by-step explanation:
A polygon is translated and then stretched vertically. Which statement is correct?
A.
Neither the translation nor the vertical stretch preserves side lengths and angles of the preimage.
B.
The translation does not preserve side lengths and angles, but the vertical stretch preserves side lengths and angles of the preimage.
C.
Both the translation and the vertical stretch preserve side lengths and angles of the preimage.
D.
The translation preserves side lengths and angles, but the vertical stretch does not preserve side lengths and angles of the preimage.
The translation preserves side lengths and angles, but the vertical stretch does not preserve side lengths and angles of the preimage is correct statement.
What is translation?A translation is a type of transformation that takes each point in a figure and slides it the same distance in the same direction.
A transformation allows something(shape) to moves, flip, or changes a shape (called the preimage) to create a new shape.
The length or angle of the image is not changed by translation but stretching will change the angle of image.
By transformation rules A,B C are false.
The translation preserves side lengths and angles, but the vertical stretch does not preserve side lengths and angles of the preimage. is correct statement.
Hence, The translation preserves side lengths and angles, but the vertical stretch does not preserve side lengths and angles of the preimage.
To learn more on translations click:
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Step-by-step explanation:
solve for r to find the missing term in geometric sequence
—
hi can someone please answer my question. thank you ❤️
Step-by-step explanation:
given :
120, 60, 30, _, _, _
find r!
solution :
r = 60/120 = ½.
=> 120,60,30, 15, 15/2 , 15/4 , ...
Step-by-step explanation:
Calcute the ratio :
r = Un/Un-1
r = 60/120
r = ½
Calculate 4th term :
Un = ar^n-1
U4 = 120 × ½^4-1
U4 = 120 × ½³
U4 = 120 × 0.125
U4 = 15
Calculate 5th term :
Un = ar^n-1
U5 = 120 × ½^5-1
U5 = 120 × ½⁴
U5 = 120 × 0.0625
U5 = 7.5
Calculate 6th term :
Un = ar^n-1
U6 = 120 × ½^6-1
U6 = 120 × ½⁵
U6 = 120 × 0.03125
U6 = 3.75
