Answer:
x = 1/2, y = 1
Step-by-step explanation:
Let's change the equation,
→ 6x - y = 2
→ y = 6x - 2
Then the value of x will be,
→ -4x + 3y = 1
→ -4x + 3(6x - 2) = 1
→ -4x + 18x - 6 = 1
→ 14x = 1 + 6
→ x = 7/14
→ [ x = 1/2 ]
Hence, the value of x is 1/2 (or) 0.5.
Now the value of y will be,
→ y = 6x - 2
→ y = 6(1/2) - 2
→ y = 3 - 2
→ [ y = 1 ]
Hence, the value of y is 1.
Answer:
x = ¹/₂
y = 1
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}-4x+3y=1\\\:\:\:\:\:\:6x-y=2 \end{cases}[/tex]
Multiply the second equation by 3:
[tex]\implies 3 \cdot 6x-3 \cdot y = 3 \cdot 2[/tex]
[tex]\implies 18x-3y=6[/tex]
Add this to the first equation to eliminate the term in y:
[tex]\begin{array}{lrr}&-4x+3y & = 1\\+ & 18x-3y& = 6\\\cline{2-3} & 14x \phantom{-3x)} & = 7\end{array}[/tex]
Solve for x:
[tex]\begin{aligned}\implies 14x & = 7\\\\\dfrac{14x}{14} & = \dfrac{7}{14}\\\\\implies x & = \dfrac{1}{2}\end{aligned}[/tex]
Substitute the found value of x into the first equation and solve for y:
[tex]\begin{aligned}-4x+3y & =1\\x=\dfrac{1}{2}\implies -4\left(\dfrac{1}{2}\right)+3y & =1\\-\dfrac{4}{2}+3y & =1\\-2+3y & =1\\-2+3y+2 & =1+2\\ 3y & =3\\\dfrac{3y}{3} & =\dfrac{3}{3}\\\implies y & =1\end{aligned}[/tex]
Therefore, the solution to the given system of equations is:
x = ¹/₂ and y = 1
Learn more about systems of equations here:
https://brainly.com/question/28281431
https://brainly.com/question/27357423
The length of a rectangle is 3 cm longer than its width.
If the perimeter of the rectangle is 58 cm, find its length and width.
The length and width of the given rectangle is 16cm and 13cm.
What is a rectangle?A rectangle is a quadrilateral with four right angles in Euclidean plane geometry. It can also be defined as an equiangular quadrilateral because all of its angles are equal; or a parallelogram with a right angle. A square is a rectangle with four equal-length sides.Formula of perimeter of a rectangle: 2(l+b)
Let, width be 'x' then length will automatically be 'x+3'.
Now, put the values in the formula:
P = 2(l+b)58 = 2(x+3+x)58 = 2(2x + 3)58 = 4x + 64x = 58 - 64x = 52x = 52/4x = 13So, width is 13cm then length is (13+3) that is 16cm.
Therefore, the length and width of the given rectangle is 16cm and 13cm.
Know more about rectangles here:
https://brainly.com/question/25292087
#SPJ9
Please find me the value of x
Answer:
x = 60°
Step-by-step explanation:
See picture below. When two parallel lines are cut by a transversal there are some special relationships.
Answer:
x = 60°
Step-by-step explanation:
∠ ABO and ∠ CBO are a linear pair and sum to 180° , that is
∠ ABO + ∠ CBO = 180°
150° + ∠ CBO = 180° ( subtract 150° from both sides )
∠ CBO = 30°
∠ XYO and ∠ CBO are alternate angles and are congruent , so
∠ XYO = 30°
∠ XOY and ∠ COY are a linear pair and sum to 180° , then
∠ XOY + ∠ COY = 180°
∠ XOY + 90° = 180° ( subtract 90° from both sides )
∠ XOY = 90°
the sum of the 3 angles in Δ XOY = 180° , that is
x + 90° + 30° = 180°
x + 120° = 180° ( subtract 120° from both sides )
x = 60°
Is the expression (5x5)^3 equivalent to 5x5^3
Answer:
No.
Step-by-step explanation:
The order of operations in both problems are different, giving two very different results. Therefore, they are unequal.
300000 + 3524142532 =
Answer:
3524442532 or 3.524442532 * 10 ^9
Step-by-step explanation:
Question 10
Divide £64 in the ratio 3:5
Answer:
24:40
Step-by-step explanation:
3:5
This means there are 8 divisions altogether - 8 parts to be split (3+5=8)
64 / 8 = 8
8x3 = 24
8x5 = 40
£24:£40
Hope this makes sense!
Hey i needed help with this scale factor
Solve the equation t − 3 = 17 for t.
Answer:
t = 20
Step-by-step explanation:
add 3 to both sides to isolate t:
t = 17 + 3
t = 20
Answer: t= 20
Step-by-step explanation:
A business has a budget of $480 to spend on their marketing campaign. Each month, x, the business spends $30 on different advertisements. The amount of money remaining in the budget for marketing can be modeled by the function M(x) = −30x + 480. Based on the graph of the linear function M(x) and the context of the problem, what is the domain?
[0, ∞)
[0, 16)
[0, 480]
ℝ
This shows that a reasonable domain for this function is [0, 16)
Domain of a functionThe domain of a function is a value of the independent variable of the function for which it exists.
Given the equation below:
M(x) = −30x + 480
Since the function represents the The amount of money remaining in the budget for marketing then the function f(x) must be greater than zero;
−30x + 480 > 0
-30x> -480
x < 480/30
x < 16
This shows that a reasonable domain for this function is [0, 16)
Learn more on domain of a function here: https://brainly.com/question/26098895
#SPJ1
Use the diagram to the right to complete the statement.
Answer:
∠ GOF = 53°
Step-by-step explanation:
∠ LON and ∠ GOF are vertically opposite angles and are congruent, then
∠ GOF = 53°
The shape below is made of two rectangles joined together.
3 cm
4 cm
6 cm
6 cm
15 cm
Find the total area of the shape.
Optional working
Answer:
+
cm²
The total area of the shape is 102 cm².
Given that, two rectangles with dimensions L1=15 cm, B1=6 cm, L2=4 cm and B2=3 cm.
What is the area of the rectangle?The area can be defined as the amount of space covered by a flat surface of a particular shape. It is measured in terms of the "number of" square units (square centimetres, square inches, square feet, etc.) The area of a rectangle is the number of unit squares that can fit into a rectangle.
We know that, the area of a rectangle = Length × Breadth.
So, the area of rectangle1 = 15 × 6 = 90 cm²
The area of rectangle2 = 4 × 3 = 12 cm²
Total area = 90+12 =102 cm²
Therefore, the total area of the shape is 102 cm².
To learn more about the area of a rectangle visit:
https://brainly.com/question/20693059.
SPJ1
Henry predicted whether he got answers right or wrong in his 50 question exam.
he identified the 37 questions he thought he got right.
it turns out that henry got 5 questions wrong that he thought he got correct and he only got 3 of the questions wrong he had predicted.
what is the percentage accuracy he had with predicting his scores?
The percentage accuracy he had with predicting his scores is 90%.
Here,
Given that;
Henry predicted whether he got answers right or wrong in his 50 question exam. That is,
In total, there are 50 questions.
Of the ones he got right, he identified 30 right.
Of the ones he got wrong, he identified 15 correctly.
We have to find; the percentage accuracy he had with predicting his scores.
What is Percentage?
A percentage is a number or ratio expressed as a fraction of 100.
Now,
The percentage of a relative to b is given by:
In total, there are 50 questions.
Of the ones he got right, he identified 30 right.
Of the ones he got wrong, he identified 15 correctly.
Hence, since he identified 45 out of 50 correctly:
[tex]P = \frac{x}{y} *100[/tex]
[tex]P = \frac{45}{50} *100[/tex]
[tex]P = 90[/tex]
So,
The percentage accuracy he had with predicting his scores is 90%.
Learn more about the percentage visit:
brainly.com/question/10491646
#SPJ4
7. On a recent math test, the boys averaged
81 and the girls averaged 90. If there are twice
as many boys in the class as girls, what was
the overall average for the class?
FH bisects ZEFG. Find the indicated angle measures.
m/GFH=71 °. Find m/EFH and m/EFG.
m/EFH=
m/EFG=
O
O
The measure of angle EFH, m ∠EFH is 71°
The measure of angle EFG, m ∠EFG is 142°
Calculating angles
From the question, we are to determine the measure of angle EFH and angle EFG
From the given information, we have that
FH bisects ∠EFG.
Thus, we can write that
m ∠EFH = m ∠GFH
From the given information,
m ∠GFH = 71°
∴ m ∠EFH = 71°
Also,
Since FH bisects ∠EFG
Then,
m ∠EFH + m ∠GFH = m ∠EFG
71° + 71° = m ∠EFG
142° = m ∠EFG
m ∠EFG = 142°
Hence, the measure of angle EFH, m ∠EFH is 71°
The measure of angle EFG, m ∠EFG is 142°
Learn more on Calculating angles here: https://brainly.com/question/6823909
#SPJ1
Write 7 1/2 as a decimal number.
Answer:
First, We convert it to an improper fraction
which in this case, is 15/2
Found by Multiplying the whole number (7) with the denominator (2) and adding it with the numerator (1)
After that Use the same denominator to get 15/2
and then we divide the new numerator (15) by the denominator (2_ to get our answer.
which is, 7.5.
All Done!
Answer:
7.5
Step-by-step explanation:
Turn into an improper fraction.
2/2 + 2/2 + 2/2 + 2/2 + 2/2 + 2/2 + 2/2 + 1/2 = 15/2
Divide 15 by two.
7.5
Parallelogram WXYZ is shown on the coordinate plane.
Parallelogram W’X’Y’Z’ (not shown) is the reflection of parallelogram WXYZ across the y-axis. Which statement is true?
W'X' is parallel to W'Z'
W'X' is parallel to Z'Y'
W'X' is perpendicular to W'Z'
W'X' is perpendicular to Z'Y'
The reflection transformation of the given diagram means that; W' X' is parallel to Z' Y'
How to Interpret Transformation Reflection?
Reflection over y-axis is a reflection or flip over the y-axis where the y-axis is the line of reflection used. The formula for this is: (x,y) →(−x,y) ( x , y ) → ( − x , y ) .
To reflect an equation over the y-axis, simply multiply the input variable by -1: y=f(x)→y=f(−x) y = f ( x ) → y = f ( − x )
Thus, looking at the given image and applying the transformation rule above, we can say that the reflection of parallelogram WXYZ across the y-axis would mean that W' X' is parallel to Z' Y'
Read more about Transformation Reflection at; https://brainly.com/question/1908648
#SPJ1
luna wants to sell a Tshirt
In her shop making a profit of
25%
if the cost of the Tshirt
is 100$, in the same time
the customer will have a discut
of 30%, what shall she put
on a Sale Tag
Answer:
Price: $178.57
30% off: -$53.57
Sale Price: $125.00
Step-by-step explanation:
She buys each shirt for $100.
She wants to make a profit of 25%.
25% of $100 = 0.25 × $100 = $125
She must sell the shirt at $125.
She wants to mark the shirt at a higher price than $125, so that after the 30% discount, she will still sell it for $125.
Call the higher price x.
x - 30% of x = 125
x - 0.3x = 125
0.7x = 125
x = 125/0.7
x = 178.57
The sale tag can read:
Price: $178.57
30% off: -$53.57
Sale Price: $125.00
6. The formula for the perimeter of a
rectangle is P = 2L + 2W.
a. Solve the equation for W.
b. Using your equation in a, find the width of a
rectangle that has a perimeter of 244 inches
and a length of 59 inches.
Step-by-step explanation:
work is shown and pictured
what is r-0.2r when r equals the regular price of a cd player, which is equalivent to this expression.
(please answer step by step)
0.1r
0.8r
0.9r
1.2r
please
help
Answer:
0.8r
Step-by-step explanation:
r - 0.2r = 1r - 0.2r = (1 - 0.2)r = 0.8r
Answer:
0.8r
Step-by-step ex
took test
If angle 1 and angle 2 form a linear pair and angle 1 is x and angle 2 is 5x - 18, find the measure of angle 1
Apply the definition of linear pair, the measure of angle 1 is calculated as: 33°.
What are Linear Pair Angles?If two angles are a linear pair, then, the sum of their angle measures equal 180 degrees.
We are given that angle 1 and angle 2 are a linear pair. This means that:
Measure of angle 1 + measure of angle 2 = 180
Measure of angle 1 = x
Measure of angle 2 = 5x - 18
Substitute
x + 5x - 18 = 180
6x - 18 = 180
6x = 180 + 18
6x = 198
6x/6 = 198/6
x = 33
Measure of angle 1 = x = 33°.
Learn more about the linear pair on:
https://brainly.com/question/13218054
#SPJ1
Prime Factorization
36=
48=
Answer:
36=3×2×2×3
48=2×2×2×2×3
Explanation:
Step 1: Divide the given number by the smallest prime number.
36/3=12. (1)
48/2=24. (2)
Step 2: Again, divide the quotient by the smallest prime number.
12/2=6. (1)
24/2=12. (2)
Step 3: Repeat the process, until the quotient becomes 1.
6/2= 3. (1)
12/2=6 (2)
3/3=1 (1)
6/2=3 (2)
3/3=1. (2)
Step 4: Finally, multiply all the prime factors.
36=3×2×2×3
48=2×2×2×2×3
Answer:
36 = 2 × 2× 3 ×3
48 = 2 × 2× 2 × 2 ×3
Step-by-step explanation:
What does heuristic mean?
1) a randomly generated number
2) a function in excel
3) rule of thumb
4) an equation
Answer:
3.) rule of thumb
Step-by-step explanation:
Find x and y pleaseee
Answer:
x = 23 y = 42
Step-by-step explanation:
y + 54 + 4x - 8 = 180
y + 4x = 180 - 46
y + 4x = 134
180 - (5x - 19) = 4x - 8
180 - 5x + 19 = 4x - 8
180 + 19 + 8 = 4x + 5x
207 = 9x
207/9 = x
x = 23
y + 4(23) = 134
y = 134 - 92
y = 42
Which ordered pairs make the open sentence true?
4x+y>9
Answer:
Step-by-step explanation:
let x = 5, y = 0
so the equation is 4x+y>9
and put the value of x and y in the equation
4 (5) + 0 > 9
20 + 0 > 9
20 > 9, therefore the order pair ( 5,0) satisfies the condition. true
a 65g book is 15cm x 5cm x 3c. Find the density
PLEASE HELP
Answer:
Density=13g/45cm cubed
Step-by-step explanation:
D=M/V
D=65g/225cmcubed
D=13g/45cm cubed
How many solutions does this equation have?
3b + 4 = 10 + 3b
Answer:
None
Step-by-step explanation:
[tex]3b+4-3b=10+3b-3b\\4=10\\\sf Sides\:unbalanced.[/tex]
A new yo-yo factory is operating at 80 percent
of capacity and produces 4,000 yo-yos daily.
when the factory reaches 100 percent of
capacity, how many yo-yos should be
produced each day?
a.
800
b. 3,200
c. 4,800
d. 5,000
e. 7,200
HELPPPPPPPP PLEASEE
Answer:
35 x 30 X 27 x 30 is equal to your answer
order these following rational numbers from least to greatest:
3.4 -0.01 1/4 12% -26.1
Answer:
3.4, 1/4, 12%, -0.01, -26.1
Step-by-step explanation:
The simplest way to do these type of problems is to convert all of the numbers into either a fraction, decimal, or a percentage. In my opinion, it is easier to use a percentage here.
12% is already a percentage
-0.01 = -1%
1/4 = 25%
3.4 = 340%
-26.1 = -2610%
Now that the rational numbers are all in the same unit, it is easier to sort them. In the end, we get this list (from greatest to least):
3.4, 1/4, 12%, -0.01, -26.1
FINAL ANSWER: 3.4, 1/4, 12%, -0.01, -26.1
In the student council election, 217 students vote. Uma receives 4 votes for every 3 that Paloma Receives. How many more votes does Uma receive than Paloma?
In probability 31, more votes does Uma receive than Paloma .
In statistics, what does a probability mean?
The likelihood that an event will occur in a Random Experiment is measured by probability. A number between 0 and 1 is used to quantify probability, where, broadly speaking, 0 denotes impossibility and 1 denotes certainty. The likelihood that an event will occur increases with its probability.let uma u and paloma p votes
Uma = 4/7 = u/217
4 × 217 / 7 = u
u = 124
paloma = 3/7 = p/217
3 × 217 /7 = p
p = 93
Learn more about probability
brainly.com/question/11234923
#SPJ9
The midpoint of KL is (7,3). One endpoint is K (4,1), what is the coordinate for the
other endpoint L?
