The equivalent expression is: B. y = ((z + 4x)) / 7
To find an equation equivalent to 4x + 7y = z, we want to isolate one of the variables (either x or y on one side of the equation.
Let's isolate x in terms of y and z:
Starting with 4x + 7y = z, subtract 7y from both sides:
4x = z - 7y
Now, divide both sides by 4 to solve for x:
[tex]\[x = \frac{z - 7y}{4}\][/tex]
Therefore, the correct choice is option B: [tex]\(x = \frac{z - 7y}{4}\)[/tex].
Complete question:
Which of the following is equivalent to the equation 4x+7y=z ?
A. x=4z-28y
B. x= ((z-7y))/4
C. y=7z+28x
D. y= ((z+4x))/7
A mosquito starts his flight in the air at 10 feet below sea level in a canyon. He then ascends to 18 feet above sea level. What was the change in the height if his flight
ascended 28 ft!
10 - (-18) = 28
Unit 4 HomeWUIR
The following table shows the times for
athletes running a 100-meter race.
100-Meter Race
Time
Runner
(seconds)
Mary
0.34
Rhea
0.394
Lindsay
0.402
Mei
0.334
Brooke
0.35
If the first three places receive ribbons, which
runners received ribbons for the race?
1st Place Ribbon:
2nd Place Ribbon:
3rd Place Ribbon:
Answer:
1st Place: Mei
2nd Place: Mary
3rd Place: Brooke
A bacterium cell splits into 2 cells every hour. Write and evaluate an exponential expression to find how many cells there will be in 6 hours. Then use your answer to help you find the number of hours it will take for there to be 1,024 cells.
Answer:
2^x
64 bacterium
10 hours
Step-by-step explanation:
doubles every hour
if x = hours
2^x
2^x --> 2⁶ = 64
2^x = 1024
1024 = 2^10 ---> x=10
What is the slope of the line represented by the equation y = –y equals negative StartFraction one-half EndFraction x plus StartFraction one-fourth EndFraction.x + StartFraction one-fourth EndFraction.?
Answer:
Slope:
[tex]m = -\displaystyle\frac{1}{2}[/tex]
Step-by-step explanation:
We are given the equation:
[tex]y = -\displaystyle\frac{1}{2}x + \displaystyle\frac{1}{4}[/tex]
Comparing this equation to the slope-intercept form:
[tex]y = mx + c[/tex]
where m is the slope of line and c is the y-intercept that is the value of y when x is zero.
on comparing, we get:
[tex]m = -\displaystyle\frac{1}{2}\\c = \displaystyle\frac{1}{4}[/tex]
The slope of the given line is
[tex]m = -\displaystyle\frac{1}{2}[/tex]
The slope of the given line is -1/2
How to find the slope of an equationThe standard equation of a line is expressed as y = mx +b
where
m is the slope
b is the y-intercept
Given the equation y = -1/2x + 1/4
Compare the equations
mx = -1/2 x
m = -1/2
Hence the slope of the given line is -1/2
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Which function has an axis of symmetry of x = −2?
Answer:
Step-by-step explanation:
f(x) = a(x+2)² +k
Answer:
f(x) = (x + 2)2 − 1
Step-by-step explanation:
HEY LUVS
a printer that sells for $190 is on sale for 20% off what is the sale price of the printer to work please
Hey!
---------------------------------------------------
Solution:
20% = 0.2 (percentage as decimal)
190 x 0.2 = 38 (discount)
190 - 38 = 152 (sale price)
---------------------------------------------------
Answer:
The sale price of the printer is $152.
---------------------------------------------------
Hope This Helped! Good Luck!
For a math project you need to complete 4 math worksheets in 5 days each worksheet contains 15 problems evaluate the expression 4 times 5+15 divide by 5 to find how many problems you need to complete each day
What is a whole number
Answer:
Whole numbers are positive numbers (this includes 0) that do not have decimals or fractions to them.
Example:
1, 2, 3, 4, 5,etc are all whole numbers, because they are positive and do not have decimals or fractions
1.25 would not be a whole number, because although it is positive, it has a decimal.
Nine increased by the product of a number and 8 is greater than -24
Answer:
x>-33/8
Step-by-step explanation:
9+8x>-24
1) Subtract 9 from both sides:
8x>-33
2) Divide both sides by 8:
x>-33/8
The algebraic representation of the problem is 9 + 8x > -24. After isolating 'x', the solution to the inequality is x > -4.125, which means any number greater than -4.125 satisfies the equation.
Explanation:The problem presented is a linear inequality, a topic of mathematics. The sentence 'Nine increased by the product of a number and 8 is greater than -24' can be represented algebraically as 9+8x > -24, where 'x' is the number in question.
To solve it, as we aim to find the value for 'x', you first isolate 'x' on one side of the inequality. Start by subtracting 9 from both sides to get 8x > -24 - 9, which results in 8x > -33. Then, you divide both sides by 8 to solve for 'x'. As a result, x > -33/8, or x > -4.125.
This means that any number greater than -4.125 will satisfy the equation 'Nine increased by the product of a number and 8 is greater than -24'. So, the solution to this inequality is x > -4.125.
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PLEASE SOMEONE HELP ASAP!!
8. The art department at a school sold 323 tickets
to an art show, for a total of $790. Students paid
$2 for tickets, and non-students paid $3.50. The
principal asked how many non-students
attended the art show.
a) Write a system of two linear equations
for this situation.
b) Solve the problem by graphing the system.
Answer:
Step-by-step explanation:
students = x
non-students=y
x+y=410
y=410-x
3x+7y=1650
3x+7(410-x)=1650
3x+2870-7x=1650
-4x=-1220 (divide both sides by -4)
x=305 y=410-305=105
Hence, 305 students attended and 105 non-students attended
The problem can be represented by two linear equations, s + n = 323 and 2s + 3.5n = 790. After putting these equations into the format y = mx + b, they can be graphed to find the solution at the point where the two lines intersect.
Explanation:First, let's define two variables, s for the number of students and n for the number of non-students. From the information we have:
Students and non-students combined bought a total of 323 tickets, so our first equation is: s + n = 323.Students paid $2 and non-students paid $3.50, making a total of $790. This gives our second equation: 2s + 3.5n = 790.To solve the problem by graphing, we need to convert these equations into y = mx + b format. Our first equation then becomes s = -n + 323 and the second becomes s = (790 - 3.5n) / 2. Plotting these equations on a graph and finding the point where the lines intersect will give us the value of s and n. The x-values corresponds to n (non-students) and y-values to s (students).
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Evaluate A 2-B 2 for A = 4 and B = -5.
Answer:
- 9
Step-by-step explanation:
Given
A² - B² ← substitute A = 4 and B = - 5 into the expression
= 4² - (- 5)²
= 16 - 25
= - 9
how do you simplify a algebraic equasion
Final answer:
To simplify an algebraic equation, combine like terms, reduce fractions, and cancel factors; multiply or divide both sides by the same number if needed, and check your work by substituting values back into the original equation.
Explanation:
Simplifying Algebraic Equations
To simplify an algebraic equation, you need to eliminate terms wherever possible. This process may involve combining like terms, reducing fractions, and canceling out factors. Multiplication or division by the same number on both sides of the equation does not change the equation's equality, so apply these operations carefully to all terms. Often, you'll want to collect constants inside the parentheses to consolidate them into a single value, making the equation simpler. After simplifying, it's important to check your answer to ensure that it is reasonable, which may involve plugging the solution back into the original equation or assessing the steps you've taken to make sure no errors were made.
Let's consider an example:
Simplify the equation by dividing both sides by a common factor, if applicable.
Collect like terms together and simplify further.
Check the simplified equation by substituting numbers to see if both sides remain equal or by ensuring logical algebraic steps were taken.
Remember, solving for an unknown variable requires doing the same operation on both sides of the equation, thereby maintaining balance. Systematic simplification and attentive checking are your keys to mastering algebraic equations.
How many times larger is 80 than 8
Answer:
10 times larger
Step-by-step explanation:
To solve this you need to divide 80 amd 8.
80/8
if 10* 8 = 80 then 80/8 = 10
Therefore 10 times larger is the answer
80 is 10 times larger than 8. This is determined by dividing the larger number (80) by the smaller number (8). The result of this division gives us the times one number is larger than the other.
Explanation:The comparison of two numbers can be done by looking at the ratio, or division result of those two numbers. In this case, we are comparing 80 and 8. We can do this by dividing 80 by 8, which equals 10. Therefore, 80 is 10 times larger than 8.
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What's this equation in vertex form? Please help!
I really need help. Thank you. [20 points]
y=8(x^2 + 4x + 4) +17 + -32
Simplify:
y = 8(x^2 + 4x + 4) + 15
Use distributive property:
y = 8x^2 + 32x +32 - 15
Simplify:
y = 8x^2 + 32x +17
Complete the square using form ax^2+bx+c:
a = 8, b = 32, c = 17
vertex form = a(x+d)^2+e
d = b/2a and e = c-b^2/4a
d = 32/2*8 = 32/16 = 2
e = 17 - 32^2/4*8 = 17-1024/32 = 17-32 = -15
Vertex form = y = 8(x+2)^2 + -15
What is 198 in simplest form
Answer:
This quantity is already simplified.
Perhaps there was a typographical error?
Answer: This quantity is already simplified.
Perhaps there was a typographical error?
Step-by-step explanation:
13. In engineering notation, the number
0.000452 is expressed as
Answer:
I think it is 4.52 × 10^-4
- Varun drove to work this morning. It took
him 15 minutes. He stopped at a traffic
light for 3 minutes after driving for
5 minutes. Sketch a graph to represent
the distance from Varun's house during
his drive to work.
Answer:
See attached graph
Step-by-step explanation:
The graph of distance from home as a function of time starts at the origin of coordinates (0,0) since at time zero minutes Varun is at home.
Then we represent his driving at constant speed (although it has not been specified in the problem) as a line with positive slope equal to his speed, that goes on for the first five minutes. After that, he reaches the traffic light that keeps him at the same distance from home for three minutes (notice the line representing the distance covered is flat from minute 5 to minute 8, while he is not moving).
Then he starts moving again (we assume at the same speed as before - so the line representing his position is again a line with positive slope and with the SAME inclination as that which represents the first 5 minutes of his trip.
The line ends at minute 15 which is the time it took him to get to work.
Which of the following expressions is equivalent to 4,325,000,000
For this case we must find an expression equivalent to:
[tex]4,325,000,000[/tex]
To express in scientific notation we must take into account that the power will be positive, that is, the decimal is run to the right.
We test each option.
Option A:
[tex]4,325 * 10^{-9}[/tex]
If we run the decimal 9 spaces to the left we have:
[tex]0.000000004325[/tex]
Option B:
We discard it because the exponent is negative.
Option C:
[tex]4,325 * 10 ^ 6[/tex]
We run the decimal 6 spaces to the right
[tex]4,325,000[/tex]
Option D:
[tex]4,325 * 10 ^ 9[/tex]
We run the decimal 9 spaces to the right
[tex]4,325,000,000[/tex]
Answer:
Option D
Final answer:
The expression that is equivalent to 4,325,000,000 is 4.325 × 10^9.
Explanation:
The expression that is equivalent to 4,325,000,000 is 4.325 × 109.
When we write a number in scientific notation, we express it as a product of a coefficient and a power of 10. In this case, the coefficient is 4.325 and the power of 10 is 9. This means that we move the decimal point 9 places to the right, resulting in a value of 4,325,000,000.
So the correct expression is 4.325 × 109.
find the perimeter and area of each figure.
Answer:
Perimeter = 89mm
area= 528 or 220
Step-by-step explanation:
hope this is useful
Answer:
Perimeter is 99 because 22+44+15+18=99
Area is 396 because 22+44=66÷2=33x12=396
The formula for the calculating the are of trapezium is a+b÷2xheight I hope this helped I gave you the formula to calculate the area of trapezium as well just to give extra help! Your welcome!
Marco Has a peice of wood that measures 9x1/10 + 6x1/100 + 4 x 1/1000 meter. How can this measurement be written as a decimal
32,467 rounded to the nearest ten
Answer:
32,470
Step-by-step explanation:
since there is a 7 in the ones place it will chnage the 6 to a 7 to make it 32,470
In order to find the answer to this question you must find the tenth place value and look to the right of the tenth place value and if the value next to the tenths higher then five you round up.
[tex]32,467[/tex]
[tex]Tenths=67[/tex]
[tex]7>5[/tex]
[tex]32470[/tex]
[tex]=32,470[/tex]
Therefore the answer is "32,470."
Hope this helps.
Colby must spend less than 275 minutes playing video games in one day. He plays different games for 25 minutes each, and Colby has already played 100 minutes today.
25x + 100 < 275
How many more games can Colby play today?
A.
x < 100
B.
x < 25
C.
x < 175
D.
x < 7
Answer:
A
Step-by-step explanation:
Answer: D. X<7
Step-by-step explanation:
In the given inequality, x represents the number of games Colby can finish. Use opposite operations to isolate x.
Therefore, the solution set for how many more games Colby can finish this week is x < 7.
Hi i just need help on this quick question, ty :)
A deck is being built around a rectangular swimming pool. The swimming pool is 35 ft x 20 ft and the deck has a uniform width of 7 ft. What is the area of the deck only?
A. 700 ft^2
B. 877 ft^2
C. 966 ft^2
D. 1134 ft^2
Answer: C. 966
Step-by-step explanation: First find the ft. of the entire area, the deck, and pool. Then get the area of the pool
Entire area: (35+7+7) * (20+7+7)= 1666
Pool: 35*20=700
Then subtract the ft. of the entire area by the pool
1666-700= 966
What is 1,000,000 written as a power of ten?
10–6
10–7
107
106
Answer:
10^6 aka D
Step-by-step explanation:
We know this because we start off with 1. we take the decimal and swipe it 6 places to the right filling the gaps with zero. As shown in the problem itself.
Answer:
10^6
Step-by-step explanation:
10^6 is 10 × 10 × 10 × 10 × 10 × 10, and that is 1,000,000.
The line parallel to y=-7x-2 through (-4,6)
The required line parallel to y = - 7x - 2 through (- 4, 6) is y = -7x - 22.
What is slope?The slope is the rate of change of the y-axis with respect to the x-axis.
The equation of a line in slope-intercept form is y = mx + b, where
slope = m and y-intercept = b.
We know the greater the absolute value of a slope is the more steeper is it's graph or rate of change is large.
We know parallel lines have the same slope.
Given line is y = - 7x - 2, hence the required line will also have a slope of - 7
which is passing through the point (-4, 6).
∴ 6 = (-7)(-4) + b.
6 = 28 + b.
b = - 22.
Hence the required line is y = -7x - 22.
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Will mark the brainliest! Which system of linear inequalities is graphed?
{x≤−3y≤−x−3
{x<−2y≤−x−1
{x<−3y≤−x−1
{x<−3y≤−x+1
Hey!
-------------------------------------------------
Steps To Solve:
~Coordinates of the line
(0, -1) and (-1, 0)
~Find slope
[tex]m = \frac{0 - (-1)}{-1 - 0} = \frac{1}{-1} = -1[/tex]
~Find the equation of the line
y = mx + b
m = slope
b = y-intercept
m = -1 or -x
b = -1
y = -x - 1
~Check using zero rule (substitute x and y for (0, 0))
y = 0 - 1
y = -1 (Correct)
0 = -x - 1
-x = 1 - 0
-x = 1 (Incorrect)
~Check
{x<−3y≤−x−1
0 < -3(0) ≤ 0 - 1
0 < 0 ≤ -1
*Note* Since the line isn't near the origin, the points (0, 0) don't satisfy the equation.
-------------------------------------------------
Answer:
{x<−3y≤−x−1
-------------------------------------------------
Hope This Helped! Good Luck!
Ed saved $50 one week. For the next 6 weeks he saved $25 more than he saved the week before. How much did he save in all? One student solved this problem using the expression $50 + 6($25) =$200. What error was made? What is the correct answer?
Answer:$825. 00
Add $25.+50. For week 1 then add $25.each additional week for 6weeks.
Step-by-step explanation:
9x + 2y = 30
6x + 4y = 12
1. Simplifying
9x + 2y = 30
Solving
9x + 2y = 30
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-2y' to each side of the equation.
9x + 2y + -2y = 30 + -2y
Combine like terms: 2y + -2y = 0
9x + 0 = 30 + -2y
9x = 30 + -2y
Divide each side by '9'.
x = 3.333333333 + -0.2222222222y
Simplifying
x = 3.333333333 + -0.2222222222y
-------------------------------------------------------------------------------------------
2. Simplifying
6x + 4y = 12
Solving
6x + 4y = 12
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-4y' to each side of the equation.
6x + 4y + -4y = 12 + -4y
Combine like terms: 4y + -4y = 0
6x + 0 = 12 + -4y
6x = 12 + -4y
Divide each side by '6'.
x = 2 + -0.6666666667y
Simplifying
x = 2 + -0.6666666667y
Answer:
For graphing, your answer is...(4,-3)
Step-by-step explanation:
1.Subtract 9x on both sides...
2y=30-9x
6x+4y=12
2. Divide each term by 2, then simplify...
-Divide... 2y=30-9x by 2.
2y/2=30/2+-9x/2
6x+4y=12
3. Reduce expression by...cancelling your common factors...
Cancel...2 from 2y/2
6x+4y=12
Divide y by 1...
y=30/2+-9x/2
6x+4y=12
4.Simplify each term...
-Divide thirty by two.
y=15+-9x/2
6x+4y=12
-Move your negative in the front of your fraction.
y=15 - 9x/2
6x+4y=12
5. Subtract 6x from both sides of your equation...
y=15 - 9x/2
4y=12-6x
6. Divide each term by four...divide terms in 4y=12-6x by four...
y=15 - 9x/2
4y/4=12/4+-6x/4
-Reduce expression by cancelling common factors in 4y/4...
Divide y by one...
y=15 - 9x/2
y=12/4+-6x/2
7. Simplify each term...Divide twelve by four...
y=15 - 9x/2
y=3+-6x/4
-Reduce expression by cancelling all common factors...
Your factor is 2 our of -6x...
y=15 - 9x/2
y=3+2(-3x)/4
-Cancel the common factors.. two out of four...
y=15 - 9x/2
y=3+2(-3x)/2(2)
-Cancel common factors again...
y=15 - 9x/2
y=3+-3x/2
8. Move your negative over to the front of your fraction...
y= 15 - 9x/2
y=3 - 3x/2
You get... (4,-3)
I hope this helps you and I also do hope that this is what you are looking for! If not, then my bad! Good luck, mate!
3.7 ft
7.2 ft
8.1 ft
what is the answer?
Answer:
if this question was a volume question, then the answer would be 215.784ft^3
why: length times width times height
if this is not what you needed ignore it. I am basing this off of the given number.s
Step-by-step explanation:
The formula
h
=
v
t
−
16
t
2
gives the height
h
, in feet, of an object projected into the air with an initial vertical velocity
v
, in feet per second, after
t
seconds.
If an object is projected upward with an initial velocity of
80
feet per second, at what times will it reach a height of
96
feet above the ground?
It'll be at
96
feet above the ground at
and
seconds
Answer:
t=6
Step-by-step explanation:
We are solving for [tex]t[/tex]. To do this, let's fill in the known variables.
[tex]h=vt-16t^2[/tex]
[tex]v=80\\h=96[/tex]
[tex]96=80t-16t^2[/tex]
[tex]16t^2-80t+96=0\\16(t^2-5t+6)=0[/tex]
Since the product must equal 0, that means that the factor in the parentheses hasto be equal to 0. Therefore,
[tex]t^2-5t+6=0\\(t+1)(t-6)=0\\\\t+1=0 OR t-6=0\\t=-1 OR t=6[/tex]
However, since the time cannot be negative, [tex]t=-1[/tex] cannot be a valid answer.
Therefore, the only valid time is t=6.
I hope this helps.
Let's start with the projectile motion formula which is h = vt - 16t².
In this formula, h is the height of the object,
v is the initial velocity, and t is the time.
We know that the initial velocity is 80 feet per second
so we can plug an 80 in for v in our formula.
We also know that the object reaches a height of 96 feet above the
ground which means we can plug an 96 in for h in our formula.
So we have 96 = 88t - 16t².
To solve this equation, we set it equal to 0 by subtracting
88t and adding 16t² to get 16t² - 88t + 96 = 0².
Now we can divide both sides by 8 to get 2t² - 11t + 12 = 0.
Now we can factor the left side to get (2t - 3)(t - 4) = 0.
So this means that 2t - 3 = 0 or t - 4 = 0.
So t = 3/2 or t = 4.
Now, the reason there are two answer is because the object will be
96 feet off the ground on its way up and on its way down.