Answer:
x= 1; y= 0; z= -2 and w= 3.
Step-by-step explanation:
Given that,
1) x + 2y - z = 3
2) 2x - y + z - w = -3
3) y + 2z - w = -7
4) x + 3y + 2z + 2w = 3
now, from 1) z = x + 2y -3 →→(5)
from 2) w = 2x -y + z +3
⇒w = 2x -y + x + 2y -3 +3 (from (5))
w = 3x + y →→(6)
Now substitute (5) and (6) in 3), we get
y +2(x + 2y -3) - (3x + y) = -7
⇒ 4y - x = -1 →→→(7)
Now substitute (5) and (6) in 4), we get
x + 3y + 2(x + 2y -3) + 2(3x + y) = 3
⇒ 9x +9y = 9
⇒ x + y =1 →→→(8)
⇒ x= 1-y , substituting this in (7) gives 5y -1 = -1
⇒ y = 0 and x = 1
substituting these values in
(5) and (6) gives, z = -2 and w = 3
⇒ x= 1; y= 0; z= -2 and w= 3.
the ratio of pennies to quarters in a piggy bank is 14:3. if there are 51 quarters in the bank, how many pennies are there
The number of pennies in bank is 42
Solution:
Given that ratio of pennies to quarters in a piggy bank is 14 : 3
Let 14x be the number of pennies in piggy bank
Let 3x be the number of quarters in piggy bank
To find: number of pennies
Given that there are 51 quarters
number of pennies in piggy bank + number of quarters in piggy bank = 51
14x + 3x = 51
17x = 51
x = 3
number of pennies = 14x = 14(3) = 42
Thus the number of pennies in bank is 42
To find the number of pennies in the piggy bank, set up a proportion using the given ratio and the number of quarters. Cross-multiply and solve for x to find the number of pennies. There are 238 pennies in the piggy bank.
Explanation:To find the number of pennies in the piggy bank, we need to use the given ratio and information. The ratio of pennies to quarters is 14:3. This means that for every 14 pennies, there are 3 quarters. We are given that there are 51 quarters in the bank. We can set up a proportion to find the number of pennies:
So, there are (14 * 51) / 3 = 238 pennies in the piggy bank.
f(x) = -2x - 2 + k. What is value of k
Answer:
k=f(x)+2x+2
Step-by-step explanation:
f(x)=-2x-2+k
-2x-2=f(x)-k
f(x)-(-2x-2)=k
f(x)+2x+2=k
A tablet takes 120 mins to charge. The fully charged tablet gives 180 mins of game time. If the battery is completely discharged but the power cord is plugged in, how long will it take to fully charge the battery, whilst playing a game?
Answer:
Full charge will be done in 360 minutes.
Step-by-step explanation:
A tablet takes 120 mins to charge.
So, in one minute the tablet is charged by [tex]\frac{1}{120} = 0.00833[/tex] parts.
Again, the fully charged tablet gives 180 mins of game time.
So, the tablet discharges fully in 180 mins gaming.
Then, in 1 minute of game playing the tablet is discharged by [tex]\frac{1}{180} = 0.00556[/tex] parts. (Appx.)
If charging and discharging by playing games both continue from the zero charge in the tablet, then in one minute it will be charged by (0.00833 - 0.00556) = 0.00277 parts. (Appx.)
Then full charge will be done in [tex]\frac{1}{0.00277} = 360[/tex] minutes. (Answer)
What is 0.66666666666 rounded
The number 0.66666666666 rounded to the nearest whole number is 1, and rounded to the nearest tenth is 0.7, following standard rounding rules.
Explanation:The number 0.66666666666, when rounded, will depend on what decimal place you are rounding to. For example:
If you're rounding to the nearest whole number, you would round up to 1 since the digit after the decimal is greater than 5.If you're rounding to the nearest tenth, the number rounds up to 0.7, as the number after the 6 is another 6, which is greater than 5.These rounding rules apply consistently across various operations including multiplication and division, similar to those in addition and subtraction. Let's consider a few examples where these rules are used:
18.3384 rounds "down" to 18.3 because the digit after the decimal to be rounded (3) is less than 5.6.8752 rounds "up" to 6.88 because the digit after the decimal to be rounded (5) is followed by a nonzero digit.These examples demonstrate the standard rules of rounding numbers with precision.
Final answer:
To round 0.66666666666 to the nearest tenth, it rounds up to 0.7 because the digit after the tenths place is greater than 5.
Explanation:
When rounding the number 0.66666666666, we must first decide the decimal place to which we want to round.
If we round to the nearest tenth, the number would round up to 0.7 because the digit following the tenth's place is a 6, which is greater than 5.
These same rules apply for other numbers: for example, 0.028675 rounds up to 0.0287 as the dropped digit, a 7, is greater than 5.
It's important to consider the digit immediately following the place value you're rounding to, as it will determine whether you round up or down.
What is the mean 3, 3, 4, 5, 6, 6, 7, 7, 7, 8, 8
Answer:
Step-by-step explanation:
3+3+4+5+6+6+7+7+7+8+8=64
64÷11=5.81818181818
simplify to......5.82
Answer: 5.81818181818
Step-by-step explanation: The mean of a data set is equal to the sum of the set of numbers divided by how many numbers are in the set.
So to find the mean of the data set shown here, let's begin by adding the numbers.
So we have [tex]\frac{3 +3+4+5+6+6+7+7+7+8+8}{11}[/tex] and notice that I put an 11 on the bottom since there are 11 numbers.
Adding the numbers, we get 64. This will be divide by how many numbers are in the set or 11.
[tex]\frac{64}{11} = 5.81818181818[/tex]
Therefore, the mean of the data set is 5.81818181818.
Shen is going to rent a truck For one day. There are two companies he can choose from, and they have the following prices.
Company a charges $110 and allows unlimited mileage.
Company B has an initial fee of $65 in charges an additional $0.90 for every mile driven.
For what mileages Will company a charge less than Company B
Answer:
The mileages for which company A charge less than company B when , y [tex]>[/tex] 50 .
Step-by-step explanation:
Given as :
The two truck companies have following prices
Company A
The initial fee = i = $110
And unlimited mileage
Company B
The initial fee = I = $65
Additional charge = $0.90 per mile driven
Let it driven x mile
Let The mileages for which company A charge less than company B = y
Now, According to question
Charges of company A = charges of company B
i.e i = I + 0.90 × x
Or, $110 = $65 + 0.90 × x
Or, $110 - $65 = 0.90 × x
Or, $45 = 0.90 × x
∴ x = [tex]\dfrac{45}{0.90}[/tex]
i.e x = 50
i.e Company B driven x = 50 miles
So, The mileages for which company A charge less than company B = y
And y [tex]>[/tex] x
i.e y [tex]>[/tex] 50
Hence, The mileages for which company A charge less than company B when , y [tex]>[/tex] 50 . Answer
what kind of solution is 2(7x-5)=14x- 10?
~ Simplifying
-2(7x + -5) = -14x + 10
~ Reorder the terms:
-2(-5 + 7x) = -14x + 10
(-5 * -2 + 7x * -2) = -14x + 10
(10 + -14x) = -14x + 10
~ Reorder the terms:
10 + -14x = 10 + -14x
~ Add '-10' to each side of the equation.
10 + -10 + -14x = 10 + -10 + -14x
~ Combine like terms: 10 + -10 = 0
0 + -14x = 10 + -10 + -14x
-14x = 10 + -10 + -14x
~ Combine like terms: 10 + -10 = 0
-14x = 0 + -14x
-14x = -14x
~ Add '14x' to each side of the equation.
-14x + 14x = -14x + 14x
~ Combine like terms: -14x + 14x = 0
0 = -14x + 14x
~ Combine like terms: -14x + 14x = 0
0 = 0
~ Solving
0 = 0
~ This equation is an identity, all real numbers are solutions.
Match the statements with their values. *see photo for reference*
Answer:
See the attached figure.
Step by step solution:
Part (1):
When ΔABC is an isosceles triangle with AB = AC
The summing of the three of the triangle = 180°
∴ m∠ABC + m∠BAC + m∠ACB = 180°
================================================
Part (2):
When ΔABC is an isosceles triangle with AB = AC
So, m∠ABC = m∠ACB = x
if m∠BAC = 70
∵ m∠ABC + m∠ACB + m∠BAC= 180°
∴ x + x + 70 = 180 ⇒ x = 55°
∴ m∠ABC = 55°
===================================================
Part (3):
When m∠QRP = 30°, and ΔPQR is an isosceles triangle with PQ = QR
So, m∠QPR = m∠QRP = 30°
====================================================
Part (4):
When m∠BAC = 45° and points D and E are the midpoints of AB and BC in ΔABC
∵ Points D and E are the midpoints of AB and BC in ΔABC
∴ DE // AC
∴ m∠BDE = m∠BAC ⇒ the corresponding angles are congruent
∴ m∠BDE = 45°
Question 2 and 3 in picture
Write the point slope form of the equation of the line through the given points.
EXPLAIN AND SHOW WORK! Please and thanks.
through: (5, -3) and (0, 3)
Answer:
[tex]\displaystyle y - 3 = -1\frac{1}{5}x\:OR\:y + 3 = -1\frac{1}{5}x - 5[/tex]
Step-by-step explanation:
First, find the rate of change [slope]:
[tex]\displaystyle \frac{-y_1 + y_2}{-x_1 + x_2} = m \\ \frac{3 + 3}{-5 ± 0} = -\frac{6}{5} = -\frac{1}{5}[/tex]
Then plug these coordinates into the Point-Slope Formula Remember, in this formula, all the negative symbols give the OPPOSITE terms of what they really, so be EXTREMELY CAREFUL inserting the coordinates into the formula with their CORRECT SIGNS. It does not matter which ordered pair you choose:
[tex]\displaystyle y - y_1 = m[x - x_1] \\ \\ y - 3 = -1\frac{1}{5}x\:OR\:y + 3 = -1\frac{1}{5}x - 5[/tex]
I am joyous to assist you anytime.
Help me on this please
Answer:
1. (x, y) → (x + 3, y - 2)
Vertices of the image
a) (-2, - 3)
b) (-2, 3)
c) (2, 2)
2. (x, y) → (x - 3, y + 5)
Vertices of the image
a) (-3, 2)
b) (0, 2)
c) (0, 4)
d) (2, 4)
3. (x, y) → (x + 4, y)
Vertices of the image
a) (-1, -2)
b) (1, -2)
c) (3, -2)
4. (x, y) → (x + 6, y + 1)
Vertices of the image
a) (1, -1)
b) (1, -2)
c) (2, -2)
d) (2, -4)
e) (3, -1)
f) (3, -3)
g) (4, -3)
h) (1, -4)
5. (x, y) → (x, y - 4)
Vertices of the image
a) (0, -2)
b) (0, -3)
c) (2, -2)
d) (2, -4)
6. (x, y) → (x - 1, y + 4)
Vertices of the image
a) (-5, 3)
b) (-5, -1)
c) (-3, 0)
d) (-3, -1)
Explanation:
To identify each IMAGE you should perform the following steps:
List the vertex points of the preimage (the original figure) as ordered pairs.Apply the transformation rule to every point of the preimageList the image of each vertex after applying each transformation, also as ordered pairs.1. (x, y) → (x + 3, y - 2)
The rule means that every point of the preimage is translated three units to the right and 2 units down.
Vertices of the preimage Vertices of the image
a) (-5,2) (-5 + 3, -1 - 2) = (-2, - 3)
b) (-5, 5) (-5 + 3, 5 - 2) = (-2, 3)
c) (-1, 4) (-1 + 3, 4 - 2) = (2, 2)
2. (x,y) → (x - 3, y + 5)
The rule means that every point of the preimage is translated three units to the left and five units down.
Vertices of the preimage Vertices of the image
a) (0, -3) (0 - 3, -3 + 5) = (-3, 2)
b) (3, -3) (3 - 3, -3 + 5) = (0, 2)
c) (3, -1) (3 - 3, -1 + 5) = (0, 4)
d) (5, -1) (5 - 3, -1 + 5) = (2, 4)
3. (x, y) → (x + 4, y)
The rule represents a translation 4 units to the right.
Vertices of the preimage Vertices of the image
a) (-5, -2) (-5 + 4, -2) = (-1, -2)
b) (-3, -5) (-3 + 4, -2) = (1, -2)
c) (-1, -2) (-1 + 4, -2) = (3, -2)
4. (x, y) → (x + 6, y + 1)
Vertices of the preimage Vertices of the image
a) (-5, -2) (-5 + 6, -2 + 1) = (1, -1)
b) (-5, -3) (-5 + 6, -3 + 1) = (1, -2)
c) (-4, -3) (-4 + 6, -3 + 1) = (2, -2)
d) (-4, -5) (-4 + 6, -5 + 1) = (2, -4)
e) (-3, -2) (-3 + 6, -2 + 1) = (3, -1)
f) (-3, -4) (-3 + 6, -4 + 1) = (3, -3)
g) (-2, -4) (-2 + 6, -4 + 1) = (4, -3)
h) (-2, -5) (-2 + 3, -5 + 1) = (1, -4)
5. (x, y) → (x, y - 4)
This is a translation four units down
Vertices of the preimage Vertices of the image
a) (0, 2) (0, 2 - 4) = (0, -2)
b) (0,1) (0, 1 - 4) = (0, -3)
c) (2, 2) (2, 2 - 4) = (2, -2)
d) (2,0) (2, 0 - 4) = (2, -4)
6. (x, y) → (x - 1, y + 4)
This is a translation one unit to the left and four units up.
Vertices of the pre-image Vertices of the image
a) (-4, -1) (-4 - 1, -1 + 4) = (-5, 3)
b) (-4 - 5) (-4 - 1, -5 + 4) = (-5, -1)
c) (-2, -4) (- 2 - 1, -4 + 4) = (-3, 0)
d) (-2, -5) (-2 - 1, -5 + 4) = (-3, -1)
The function h(x) is defined as shown.
h(x) = StartLayout Enlarged left-brace 1st row 1st column x + 2, 2nd column x less-than 3 2nd row 1st column negative x + 8, 2nd column x greater-than-or-equal-to 3 EndLayout
What is the range of h(x)?
–∞ < h(x) < ∞
h(x) ≤ 5
h(x) ≥ 5
h(x) ≥
Answer:
h(x) ≤ 5
Step-by-step explanation:
The function is continuous and has a maximum value of 5. Its range is ...
h(x) ≤ 5
Answer:
b
Step-by-step explanation:
edge 2020
What is the equation of the line that passes through point (4, 12) and has a y- intercept of -2?
Answer:
y = (7/2)x - 2
Step-by-step explanation:
Use slope-intercept formula for linear equations y = mx + b
x and y show what points are on the line. We know (4, 12). x= 4 and y = 12
b is the y-intercept, which b = -2.
m is the slope.
To write the equation, you need the slope and y-intercept. Find the slope by putting x, y and b into the formula.
y = mx + b
12 = 4m - 2
14 = 4m
14/4 = m
m = 7/2
Put "m" into the formula with "b"
y = (7/2)x - 2
only 90 minutes after a reindeer calf is born it is able to run. How many seconds is that
Answer:
540 seconds
Step-by-step explanation:
1 minute is equal to 60 second
so 90 min is equal to 90 multiplied by 60 which is equal to 540 seconds.
Answer:5400 seconds
Step-by-step explanation:
After eating dinner at a restaurant, Sid's bill before tax is
$62.00. The sales tax rate is 8%. Sid decides to leave a
15% tip for the waiter based on the pre-tax amount. How
much money will Sid pay total, including tax and the tip?
Sid will pay $76.26 in total including ta and tip.
Step-by-step explanation:
Given,
Cost of Sid's bill = $62.00
Tax rate = 8%
Tip = 15%
Tax amount = 15% of bill
[tex]Tax\ amount=\frac{8}{100}*62.00\\Tax\ amount=0.08*62.00\\Tax\ amount=\$4.96[/tex]
As the tip will be on Pre-tax amount, therefore,
Tip amount = 15% of bill
[tex]Tip\ amount=\frac{15}{100}*62.00\\Tip\ amount=0.15*62.00\\Tip\ amount=\$9.30[/tex]
Total amount = Bill + Tax amount + Tip amount
Total amount = 62.00 + 4.96 + 9.30 = $76.26
Sid will pay $76.26 in total including ta and tip.
Keywords: addition, percent
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Answer:
76.26
Step-by-step explanation:
15. What is the sum of a number and its
opposite?
Answer:
the sum of two numbers is multplication and its opposite is a negative version of it
Step-by-step explanation:
please help me!!! I'm lost tap the attachment
Answer:
Below.
Step-by-step explanation:
I'll do number 20, 21, 22 for you.
20. It is ±1, ±2, ±4, ±8.
21. Reflected over the x-axis and down 4.
22. Common ratio = 25/5 = 5.
23. Imaginary roots occur in pairs so there is also a root -5i.
The answer is c.
19. Option (a).
This is a translation of 4 to the left ( due to the (x + 4).
20% tip on a bill of 83.61
Answer:
16.72
Step-by-step explanation:
To find the answer divide 83.61 by 100 then multiply it by 20
20% of 83.61 is = 16.72
What will you get if you reduce 14/35 to the lowest term?
Answer: 2/5
Step-by-step explanation:
14:7=2
35:7=5
14/35= 2/5
Answer:
The lowest form of [tex]\frac{14}{35}[/tex] is [tex]\frac{2}{5}[/tex].
Step-by-step explanation:
The given rational number is [tex]\frac{14}{35}[/tex].
At first, we will find the HCF of 14 and 35 and then divide the numerator and denominator by the HCF of 14 and 35 to evaluate the lowest form of [tex]\frac{14}{35}[/tex].
The prime factorisation of 14 and 35 is,
14 = 2 × 7
35 = 5 × 7
Since, prime factor '7' is common in the prime factorisation of 14 and 35, so the HCF of 14 and 35 is 7.
[tex]\frac{14}{35}=\frac{\frac{14}{7} }{\frac{35}{7}}=\frac{2}{5}[/tex]
So, the lowest form of [tex]\frac{14}{35}[/tex] is [tex]\frac{2}{5}[/tex].
Using the graphing function on your calculator, find the solution to the system
of equations shown below.
2y - 4x = 6
y-2x = 7
Answer:
The expression that comes after solving the two linear equation is independent of variables So , The system of equations has no solutions
Step-by-step explanation:
Given two linear equations as :
2 y - 4 x = 6 .......1
y - 2 x = 7
Or, y = 2 x + 7 .......2
Now, Solving these two equations
Put the value of y from eq 2 into eq1
So, 2 y - 4 x = 6
∴ 2 × (2 x + 7) - 4 x = 6
Or, 4 x + 14 - 4 x = 6
or, (4 x - 4 x) = 6 - 14
i.e 0 = - 8
∵ The expression that comes after solving the two linear equation is independent of variables So , The system of equations has no solutions Answer
-Help?-
Simplify.
[tex]8\sqrt{63x^{14} 14y^{9}[/tex]
Assume x and y are nonnegative.
A: [tex]24x^{7}y^{4}\sqrt{7y}[/tex]
B: [tex]3x^{7}y^{4}\sqrt{7y}[/tex]
C: [tex]24x^{5}y^{4}\sqrt{7x^{2}y}[/tex]
D: [tex]24x^{7}y^{3}\sqrt{7}[/tex]
Answer:
C.
Step-by-step explanation:
https://tex.z-dn.net/?f=24x%5E%7B5%7Dy%5E%7B4%7D%5Csqrt%7B7x%5E%7B2%7Dy%7D
this is correct
the simplified expression is [tex]\(24x^7 y^4 \sqrt{7y}\)[/tex], which corresponds to option A.
To simplify the expression [tex]\(8\sqrt{63x^{14}14y^9}\),[/tex] we can break down the radicand into its prime factors and then simplify:
[tex]\(8\sqrt{63x^{14}14y^9} = 8\sqrt{7 \cdot 9 \cdot 7 \cdot 2 \cdot (x^7)^2 \cdot (y^4)^2 \cdot (y^1)}\)[/tex]
Now, we can take the square root of perfect squares and pull them out of the square root:
[tex]\(8 \cdot 3 \cdot 7 \cdot x^7 \cdot y^4 \cdot \sqrt{y}\)[/tex]
Simplifying further:
[tex]\(24x^7 y^4 \sqrt{7y}\)[/tex]
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The fastest that a seahorse can travel is 2,640 feet per hour. What is its top speed in miles per hour?
Answer:
0.5 miles per hour
Step-by-step explanation:
evaluate this exponential expression. 25^5/2
Answer:
3.125
Step-by-step explanation:
ben is 12 years older than ishaan.ben and ishaan first met two years ago. three years ago,ben was 4 times as old as ishaan. how old is ben now?
Ben is 19 years old now
Solution:
Let the age of Ishaan be "x"
Given that ben is 12 years older than Ishaan
Therefore, age of ben = x + 12
Therefore, before three years,
Age of Ishaan before three years = x - 3
Age of Ben before three years = x + 12 - 3 = x + 9
From question,Three years ago, ben was 4 times as old as ishaan
Age of Ben before three years = 4(Age of Ishaan before three years)
x + 9 = 4(x - 3)
x + 9 = 4x - 12
4x - x = 9 + 12
3x = 21
x = 7
Therefore age of ben now = x + 12 = 7 + 12 = 19
Thus Ben is 19 years old now
If the team threw the shot put more than 110 feet, then the seventh graders earn 110
points. If not, then the eighth graders earn 110 points. Which grade should be awarded 110 points?
Answer:
the seventh graders
Step-by-step explanation:
Answer:
The Seventh Graders
Step-by-step explanation
f(x) = 4x+8
g(x) = x+3,
Find f(x)*g(x)
Answer:
4x^2+20x+24
Step-by-step explanation:
(4x+8)(x+3)=4x^2+8x+12x+24=4x^2+20x+24
Hellpp me guys please
Answer:
88 feet
Step-by-step explanation:
perimeter (P)=2πr
P= 2*22/7*14
P=88 feet
Answer:
2. B, 25.12 feet.
3. B, 88 feet.
P=2πr, r = radius or 1/2 diameter, replace [tex]\pi[/tex] with given value for each question and then simplify.
Is 4,7,9,12 an arithmetic sequence?
Answer:
No. The differences between two elements should be same. For example 4-7-10-13 is a arithmetic sequence.
Step-by-step explanation:
Angela wants to celebrate her birthday by eating pizza with her friends. She wants to buy one box of pepperoni pizza for $9.50 and c boxes of cheese pizza for &*.50 each. Which expression, in dollars, represents the amount Angela will spend on pizzas for her birthday celebration.
Answer:
Step-by-step explanation:
9.5+0.5c=t
Answer:
8.5C + 9.5
Step-by-step explanation:
Im pretty sure u meant to put 8.5
What are the domain and range of f(x) = 4* – 8?
domain: {x | x is a real number}; range: {yl y> -8}
domain: {x | x is a real number}; range: {yl y> 8}
domain: {x | x > 4}; range: {yly>-8}
domain: {x | x>-4}; range: {y | y>8}
O
Answer:
domain: {x | x is a real number}
range: {y l y> -8}
Step-by-step explanation:
f(x) = 4x² – 8 is a parabola, a U shape.
Since the stretch factor, 4, is positive, it opens up, there it will have a minimum value, the lowest point in the parabola.
y > -8 because the minimum is -8.
Parabolas do not have restricted "x" values. "4" does not restrict x because it is the stretch factor, which determines how wide the parabola is.
Quadratic standard form:
f(x) = ax² + bx + c
"a" represents how wide the graph is. If it's negative it opens down, if it's positive it opens up.
"b", if written, tells you it is not centred on the y-axis. It is not written, so the vertex is on the y-axis.
"c" is the y-intercept. In this case, since b = 0, it is also the minimum value.
The domain of f(x) = 4x - 8 is all real numbers, as x can take any value without restriction. The range is all values greater than or equal -8 because this is the function's minimum value (occurs when x=0).
Explanation:In mathematics, the domain and range of a function represent the set of input values (x-values) and output values (y-values) respectively. For the function f(x) = 4x - 8, the domain is all real numbers, represented as {x | x is a real number} because there's no restriction on the values that x can take. On the other hand, the range is all values greater than or equal to -8, which is represented as {y | y > -8}, since the function's minimum value occurs at y=-8 (when x=0).
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