The solution for the given linear equation is z = 6
How to solve the linear equation?
Here we have the following linear equation:
10 = z/2 + 7
To solve it, we need to isolate the variable in one of the sides of the equation.
First, we can subtract 7 in both sides:
10 - 7 = z/2 + 7 - 7
3 = z/2
Now we can multiply both sides by 2 to get:
2*3 = 2*(z/2)
6 = z
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graph a line that is perpendicular to the given line. determine the slope of the given line and the one you graphed in simplest form. click and drag on the graph to draw a line. click and drag to plot a perpendicular line. the line will change colors when a parallel or perpendicular line is drawn accurately.
The line given passes through two points. These are (-6,0) and (0,-8).
Remember that two lines are perpendicular if the product of their slopes is -1. So, the first thing we're going to do is to find the slope of the line given.
The slope between two points (x1,y1) and (x2,y2) can be found using the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]If we replace our values:
[tex]m=\frac{-8-0}{0-(-6)}=\frac{-8}{6}=-\frac{4}{3}[/tex]To find other perpendicular line to this one, we have to find a number which multiplication with -4/3 is -1.
This number is clearly 3/4. Because
[tex]\begin{gathered} m_1\cdot m_2=-1 \\ -\frac{4}{3}\cdot m_2=-1 \\ \\ m_2=\frac{3}{4} \\ \\ -\frac{4}{3}\cdot\frac{3}{4}=-1 \end{gathered}[/tex]Therefore, the slope of the perpendicular line must be 3/4, and the original slope is -4/3.
If we graph this:
Which expression is equivalent to 7^ -2
Please finish the question provided with a screen shot.
Answer:
Angle VSR + Angle SRU = 180° (corresponding angles, sum of angles on a straight line = 180°)
(5x + 4) + (44 + x) = 180
6x + 48 = 180
6x = 132
x = 22
thanks in advance for the help
a. The decrease road line verified by given function while increase in the highway The function representing the railroad miles has a negative slope, indicating a decrease. The function representing the highway miles has a positive slope, indicating an increase.
b. It is estimated that the number of railroad miles and the number of highway miles were the same during the year 1986.
Given
The function y =-1518x + 144.068 represents the railroad miles.
While the function y =-360.5x + 155.18models the number of highway miles.
For each function, x is the number of years after 1995.
The year in which it is estimated that the number of the country's railroad miles and the number of the country's highway miles were the same.
Therefore,
-1518x + 144.068= -360.5x + 155.18
-1518x+360.5x = 155.18-144.068
1157.5x = 11.112
x = 9
Then,
1995 - 9 = 1986
It is estimated that the number of railroad miles and the number of highway miles were the same during the year 1986.
What are miles?A mile, sometimes an international mile or base mile to distinguish it from other miles, is an imperial unit in the United Kingdom and a standard unit of distance in the United States. both are based on the older English unit of length, which is 5280 English feet or 1760 yards. The legal mile was standardized by an international agreement between the Commonwealth of Great Britain and the United States in 1959, when it was officially redefined in SI units to exactly 1609.3 meters.
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The first term of a pattern is 12. The pattern follows the rule "multiply by 4." What are the next three terms?
The next three terms for the pattern will be 12, 48, 192 and 768.
What is a pattern?It is important to note that a pattern is used to show the sequence of events.
In this case, the first term of a pattern is 12 and the pattern follows the rule "multiply by 4."
This will be:
First term = 12
Second term = 12 × 4 = 48
Third term = 48 × 4 = 192
Fourth term = 768
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Any tricks for finding the nth term?
Step-by-step explanation:
An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 5, 7, 9, 11, 13, 15.. . is an arithmetic progression with a common difference of 2.
Arithmetic progression is S = 1/2n[2a+(n-1)d]
----------------------------------------
In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
Geometric progression is Uₙ = arⁿ ⁻ ¹
PLEASE HELPPPPPPP I NEED THIS DONE
50 POINTS
Answer:
y to the power of -8
:) hope this help
Answer: y^8
Step-by-step explanation:
You see that the equation has two negative numbers, so it will become positive.
(y^-2)^-6 = y^8
The base of it will cancel each other out and left with y^8
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Michael thinks of a number she multiplies the number by 100÷8 then add six. 50 the answer is 1206.5 what was the starting number
The starting number of Michael's thought is 96
How to determine the starting number?From the question, the given parameters are:
Multiplies a number by 100÷8Add 6.50 The answer is 1206.5The above sequence of statements can be represented as
x * (100÷8) + 6.50 = 1206.5
Where x represents the number
So, we have
x * (100÷8) + 6.50 = 1206.5
Evaluate the quotient
x * 12.5 + 6.50 = 1206.5
Subtract 6.50 from both sides
x * 12.5 = 1200
Divide both sides by 12.5
x = 96
Hence, the initial number is 96
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Please only answer if you know the correct answer thank you.
Answer:
y = 1/2x - 5
Step-by-step explanation:
The y intercept is negative 5. The line slowly goes one point up and two points to the right, staying positive. This makes it 1/2.
Solve the inequality
r/-3.2>7.6 for r
Answer:
> -24.32 I hope that help so it is a on your screen
how can I covert this 0.688= to a fraction
You have to convert the following number into a fraction:
[tex]0.6\bar{8}\bar{8}[/tex]This is a periodic decimal number, which explicitely is 0.68888888....
In order to convert this number to a fraction you proceed as follow:
[tex]0.6\bar{8}=\frac{68-0}{99}=\frac{68}{99}[/tex]You put 0.68 and not 0.688 because to do the convertion you need only the first periodic number (that is, only the first 8). The key is to put in the numerator the complete number as whole number, that is, 68. To this number you subtract the whole part of the decimal number, this whole part is 0 because of the 0.688. Then, in the numerator you have 68 - 0. In the denominator you write a number composed only by 9's. The number of 9 numbers is determined by the number of digits of the first number in the numerator. That is two 9 numbers
How many solutions does the following system of equations have?
2x - Y=3
-4x + 2y=5
Answer:
no solutions
Step-by-step explanation:
2x - y = 3 → (1)
- 4x + 2y = 5 → (2)
multiply (1) by 2 and add to (2)
4x - 2y = 6 → (3)
add (2) and (3) term by term
0 + 0 = 11
0 = 11 ← not possible
this indicates the system has no solution
In 3 hours, 5 people can paint a hall with the area of 750 ft 2. How long would it take for 2 people to paint the hall with the same rate of speed?
ANSWER:
STEP-BY-STEP EXPLANATION:
In this case, we can make a proportion, since we know the time when there are 5 people, we need to know the time when there are two people
[tex]\frac{5}{3}=\frac{2}{x}[/tex]solving for x:
[tex]undefined[/tex]if i get a 60% on a math test then what would my final grade be overall
its an 80% rn
Answer:
A D
Step-by-step explanation:
An A is 90% to 100% A B is 80% to 89% A C is 70% to 79% A D is 60% to 69%
can anyone help on this
-3+(-17)
A line passes through the points (5, 1) and (7, 11). Which equation represents the line?
The equation of line is y = -x + 6
What is Equation of line ?
A straight line's general equation is y = mx + b, where m denotes the gradient and y = b denotes the point at which the line crosses the y-axis. On the y-axis, this value b is referred to as the intercept.
The given point are (5, 1) and (7, 11)
We know, the equation of line is,
y = mx + b
where, m = slope
b = y-intercept
First, find slope i.e m
we know the formula of slope (m) = (y2 - y1) / (x2 - x1)
The points, (x1, x2) = (5, 1) and,
(y1, y2) = (7, 11)
put these values in slope formula,
m = (11 -7) / (1 - 5)
= 4 / -4
m = -1
we get the slope is -1
Next, find y-intercept i.e 'b'
for that, take any one point I'm taking (5, 1) and put these in equation ,
y = mx + b
1 = -1 * 5 + b
1 = -5 + b
b = 6
Now, put slope (m) and y-intercept (b) value in ,
y = mx + b
we get,
y = -x + 6
Hence, the equation of line is y = -x + 6
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when measuring for average, where should 17.3167 be rounded from?
It depends on the number of decimal points of the values from which we get the average.
Normally it must be rounded to the nearest tenth, 17.3
What values of x and y make △QRS≅△FDE?
PLEASE ANSWER QUICK IT IS THE LAST PROBLEM ON HERE AND IT IS DUE TODAY!!!
Answer should be inequality!
Ray had scores of 75, 82, 94, and 77 on his first four algebra tests. What must he score on the next test to have an average of at least 85?
Please show work as well if possible.
Answer:
x ≥ 97
Step-by-step explanation:
Average = Sum of values divided by the amount of numbers in a data set
Data Set: {75, 82, 94, 77, ?}
75 + 82 + 94 + 77 + ? = ? ÷ 5 = 85
85 x 5 = 425
75 + 82 + 94 + 77 + ? = 425 ÷ 5 = 85
75 + 82 + 94 + 77 = 328
425 - 328 = 97
Ray must score greater than or equal to 97, or x ≥ 97 in order to have an average of at least 85.
find the remainder when 2 to the 100th power is divided by 5. explain your work
When 2 to the power of hundred is divided by 5 it show s remainder of 1
How to calculate the value of 2 to the 100th power divided by 52 to the 100th power is solved as follows
2 ^ 100 = 1.2676506 * 10^30
This is solved using a calculator and the solution means that
2 * 2 * 2 * 2 * 2 * 2 * 2 * 2...............2 (2 multiplying itself till the number of 2's are up to 100)
This gives the value = 1.2676506 * 10^30
Division of the 2^100, by 5
2^100 / 5
2^1 / 5 remainder =2
2^2 / 5 remainder = 4
2^3 / 5 remainder = 3
2^4 / 5 remainder = 1
2^5 / 5 remainder = 2
2^6 / 5 remainder = 4
2^7 / 5 remainder = 3
2^8 / 5 remainder = 1
2^9 / 5 remainder = 2
2^10 / 5 remainder = 4
2^11 / 5 remainder = 3
It can be seen that it generates a pattern which is
1243The pattern counts in 4's. If we follow the pattern and count to 2^30
= 100 / 4
= 25 ⇒ this is a multiple of 4 and multiples of 4 goes with remainder 1
This is to say
2^97 / 5 remainder = 2
2^98 / 5 remainder = 4
2^99 / 5 remainder = 3
2^100 / 5 remainder = 1
Hence 2^100 divided by 5 will give a remainder of 1
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pls help me with this
the data shows the price over time for selling Gidgets. Use the data to make a scatter plot in Desmos and find the LINEAR REGRESSION equation. Round to the nearest hundredth. What is the equation? Do not use spaces.
a) The linear regression equation is y = 1.360x + 6.540
b) The linear regression equation is y = -0.8909x + 37.59
Given,
a) The data;
Time in years, x ; 1, 1.5, 3, 5, 6, 7, 8.5, 10
Price, y ; 8, 9.75, 10.25, 11.80, 13.90, 17, 18, 20.75
We have to find the linear regression equation to the above given data.
We can use regression calculator ;
There are 8 xy pairs.
The linear regression equation is;
y = 1.360x + 6.540
b) The data
Time in years, x ; 1, 1.5, 3, 5, 6, 7, 8.5, 10
Price, y ; 32.5, 35, 37.3, 36.4, 35.7, 32.4, 29, 25
We have to find the linear regression equation to the above given data.
We can use regression calculator ;
There are 8 xy pairs.
The linear regression equation is;
y = -0.8909x + 37.59
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Sylas loves cookies! If he bought 5 cookies for $6.65, how many cookies
could he buy with $20?
Answer:
15
Step-by-step explanation:
6.65:5=1.33
1.33х15=19.95$
we need to around the 19.95 and we get a 20$
have a nice day
The Tasty Cookies Factory has a new robotic oven that produces 3,258 cookies each day. They sell the cookies in boxes of 12 cookies each. Managers Fatima and Jorge need to figure out how many boxes they can ship out of the factory each day.
As per the concept of division, they sold 271 cookies boxes per day and there are 6 cookies are remained.
Division:
Division means splitting of a large group into smaller groups such that every group will have an equal number of items.
There are four parts of the division, which are dividend, divisor, quotient, and remainder.
Given,
The Tasty Cookies Factory has a new robotic oven that produces 3,258 cookies each day. They sell the cookies in boxes of 12 cookies each.
Here we need to find the number of boxes sold per day.
Through the given question we know that,
Number of cookies per day = 3,258
Number of cookies in one box = 12
So, the dividend is 3,258 and the divisor is 12.
So, the number of boxes per day is illustrated using the following diagram.
Based on these, there are 271 boxes are sold per day with 6 remaining cookies.
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5x-13+7y+26x how do I do this?
The expression to simplify is
[tex]5x-13+7y+26x[/tex]We will simplify by combining like terms.
• There are FIVE x's and TWENTY-SIX more x's. We add.
5x + 26x = 31 x
• There is 1 constant, NEGATIVE THIRTEEN. No combining required so leave it as is.
,•
,• There is 1 term with y, which is SEVEN y. No combining required, so we leave it as is.
The final expression is
[tex]\begin{gathered} 5x-13+7y+26x \\ =31x+7y-13 \end{gathered}[/tex]3. For the following function, evaluate 2f(-2), *
f(x) = -2x²-x+3
Answer: 26
Step-by-step explanation:
[tex]f(-2)=-2(-2)^2 -(-2)+3=13\\\\2f(-2)=2(13)=26[/tex]
Marsha is filing her federal income tax return with the Single filing status. She had an adjusted gross income of $56,800 last year and is trying to decide whether to take the standard deduction of $5700 or to itemize deductions. Last year she had $4900 in medical expenses, $3100 in state and local income taxes paid, $1940 in mortgage interest paid, $530 in charitable contributions, and $1200 in non-reimbursed work expenses
Marsha must claim for itemized deductions.
Given,
Last year's gross income is $56,800.
Medical expenses = $4900
State and local income taxes paid = $3100
The mortgage interest paid = $1940
Charitable contributions = $530
Non-reimbursed work expenses = $1200
Standard deduction = $5700
The sum of all the expenses of last year = $4900 + $3100 + $1940 + $530 + $1200 = $11,670
And the Standard deduction is $5700.
Which is, $11,670 - $5700 = $5970 lesser.
Therefore, Marsha must claim for itemize deductions rather than the standard deductions.
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Find the Factor Pairs (LOTS OF POINTS!)
The factor pairs which matches the number of tents to sleep exactly 40 boys with each tent having an equal number of boys are;
1 tent ===> 40 boys.2 tents ===> 20 boys each.3 tents ===> No match.4 tents ===> 10 boys each.5 tents ===> 8 boys each.6 tents ===> No match.7 tents ===> No match.What are the correct matches of factors such that each tent contains an equal number of students as the others?Since 40 students are to be equally distributed in each of the number of tents arrangement.
It follows that first, one must list the integer pairs whose products yield 40 as follows;
Hence, we have;
1 × 40.2 × 20.4 × 10.5 × 8.Hence, the factor pairs for each scenario of number of tents are as listed in the answer section above.
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Assume that blood pressure readings are normally distributed with a mean of 125 and a standard deviation of 8 if 100 people are randomly selected find the probability that their mean blood pressure will be less than 127
According to the normal distribution table, the probability that their mean blood pressure will be less than 127 is 99.38%.
Given :
Blood pressure readings are normally distributed with a mean of 125 and a standard deviation of 8.
The formula of z-score is used to determine the probability that their mean blood pressure will be less than 127. The formula of z score is given by:
[tex]z = \frac{\frac{x - m}{\alpha } }{\sqrt{n} }[/tex]
Now, substitute the values of known terms in the above equation.
[tex]z = \frac{\frac{127 - 125}{8} }{\sqrt{100} }[/tex]
[tex]z = \frac{\frac{2}{8} }{10} }[/tex]
Further, simplify the above expression.
z = 2.5
P(z < 2.5) = 0.9938
So, the probability is 99.38%.
Therefore, according to the normal distribution table, the probability that their mean blood pressure will be less than 127 is 99.38%.
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Find A (please help)
Answer: Solve 5x=(2x+3)
Step-by-step explanation:
Using the Elimination method Solve the system:x+y-z=143x+2y+4z=17-x+5y+z=8
Given the system of equations:
x + y - z = 4 eq.(1)
3x + 2y + 4z = 17 eq.(2)
-x + 5y + z = 8 eq.(3)
Add the equations 1 and 3
so,
x + y - z + ( -x + 5y + z ) = 4 + 8
x + y - z - x + 5y + z = 12
6y = 12
y = 12/6 = 2
Substitute with y at eq. (1)
So,
x + 2 - z = 4
x - z = 4 - 2
x - z = 2 eq. (4)
Substitute with y at eq.(2)
3x + 2 * 2 + 4z = 17
3x + 4 + 4z = 17
3x + 4z = 17 - 4
3x + 4z = 13 eq.(5)
solve the equations (4) and (5) together
x - z = 2
3x + 4z = 13
Multiply [ x - z = 2 ] by 4
4x - 4z = 8
3x + 4z = 13
Add the last two equations
4x - 4z + 3x + 4z = 8 + 13
7x = 21
Divide both sides by 7
x = 21/7 = 3
So, x = 3 and y = 2
Substitute with the values of x and y at the equation [ -x + 5y + z = 8 ]
So,
-3 + 5 * 2 + z = 8
solve for z
-3 + 10 + z = 8
z = 8 + 3 - 10
z = 11 - 10 = 1
So,
x = 3 , y = 2 and z = 1