The system of linear equations, \(x + 2y = 4\) and \(-2x + 5y = 10\), was solved graphically. The lines intersect at (2, 1), yielding the solution \(x = 2\) and \(y = 1\).
To solve the system of linear equations graphically, we'll plot the lines corresponding to each equation and find their point of intersection, which represents the solution to the system.
Let's rearrange the equations to be in slope-intercept form (\(y = mx + b\)) for ease of graphing:
a. \(x + 2y = 4\)
\[ 2y = -x + 4 \]
\[ y = -\frac{1}{2}x + 2 \]
b. \(-2x + 5y = 10\)
\[ 5y = 2x + 10 \]
\[ y = \frac{2}{5}x + 2 \]
Now, we'll plot these lines on the graph:
The graph shows that the two lines intersect at the point \((2, 1)\). Therefore, the solution to the system of linear equations is \(x = 2\) and \(y = 1\).
Learn more about system of linear equations here:
https://brainly.com/question/14323743
#SPJ6
Dave is 8 years younger than 4 times Julia‘s age. If Dave is 16, how old is Julia?
A. 6 years
B. 24 years
C. 32 years
D. 56 years
Answer: d
Step-by-step explanation:
so 16+16=32
and to make things easier 32+32=64
64-8=56
The age of Julia is,
⇒ 6 years
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Dave is 8 years younger than 4 times Julia‘s age.
Let Julia age = x
Hence, Age of Dave is,
⇒ 4x - 8
Here, Age of Dave is, 16
Hence,
⇒ 4x - 8 = 16
⇒ 4x = 16 + 8
⇒ 4x = 24
⇒ x = 6
Thus, The age of Julia is,
⇒ 6 years
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ3
-3x - 42 >3
SOLVE THE EQUATION WITH WORK!!!!
A) x > -13
B) x < -13
C) x > -15
D) x < -15
Answer:
D) x < -15
Step-by-step explanation:
-3x - 42 >3
Add 42 to each side
-3x - 42+42 >3+42
-3x > 45
Divide each side by -3. Remember to flip the inequality since we are dividing by a negative
-3x/-3 < 45/-3
x < -15
QUICK !!! Find the equation of the linear function represented by the table below in slope-intercept form.
The answer is 1.
To find the answer you would take y/ x for the first thing in the table ( -2/1 ) then the second row of the table ( -1/2 ) then you would find out how much the points increased or decreased.
In this case y went up 1 and so did x so the slope would be 1/1 or just 1. Then check with the other points to make sure it is linear throughout then bam done. :)
closest 2 integers closest to -0.001
The closest integers to -0.001 are 0 and -1. -0.001 lies just to the left of 0 on the number line, making 0 the nearest positive integer and -1 the nearest negative integer.
The two integers that are closest to -0.001 are 0 and -1. Since -0.001 is a negative number that is very close to zero, it lies between these two integers on the number line. The integer 0 is the closest on the positive side, and -1 is the closest on the negative side.
I'm really confused, can someone please help me with this problem?
Answer: x = 6.25
5 ÷ 0.8
= 6.25
the points show different locations in joe's town. each unit represents 1 mile
Answer:
7.8 miles
Step-by-step explanation:
Please help me on number 5
The answer is 5 slices because a pie is 360 degrees and 360/72=5 making each slice 72 degrees and 5 slices in all.
y varies inversely with x. k, the constant of inverse variation, is 9.62. When y is 2.6, what is x? Round your answer to the nearest tenth, if necessary.
Answer:
3.7
Step-by-step explanation:
2.6 = 9.62/x
2.6x = 9.62 Multiplied each side by x
x = 3.7 Divided each side by 2.6.
I need help on 13 and 14
Im a randomly generated list of numbers from 0 to 6, what is the chance that each number will occur?
Answer:
1/7
Step-by-step explanation:
The list of numbers generated is; 0, 1, 2, 3, 4, 5, 6,
There are 7 possible outcomes and each outcome is equally likely. The probability or chance that each number will occur is given by;
number of times the number occurs / 7
In our case, each number occurs only once, so the chance will be;
1/7
Answer:
of it say 0 out of 3 its on the one with 3 numbers
Debits are entered on the _____ side of a T-account. FETL Unscramble
The LEFT side is the correct answer
Debits are entered on the left side of a T-account.
Debits and credits are fundamental concepts in accounting used to record financial transactions. In a T-account format, which visually splits an account into two sides, debits are always entered on the left side of the T-account. Conversely, credits are recorded on the right side.
For example, when a company purchases office supplies for cash, the office supplies account will have a debit entry (left side), while the cash account will have a credit entry (right side). This ensures that the accounting equation balances.
The answer to this wuestion
Answer:
A 942
Step-by-step explanation:
3/5ths is .6
125.6 / 2 = 62.8
62.8 * 15 = 942
Answer: Its A 942 hope this helped
Find the slope and y- intercepts of the line given by 3x+5y=45
[tex]\huge\text{Slope: $\boxed{-\frac{3}{5}}$}\\\huge\text{$y$-intercept: $\boxed{9}$}[/tex]
We need to convert this line to slope-intercept form, or [tex]y=mx+b[/tex], where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept.
[tex]\begin{aligned}3x+5y&=45&&\smash{\Big|}&&\text{Start with the original equation.}\\5y&=-3x+45&&\smash{\Big|}&&\text{Subtract $3x$ from both sides.}\\y&=\boxed{-\frac{3}{5}}x+\boxed{9}&&\smash{\Big|}&&\text{Divide everything by $5$.}\end{aligned}[/tex]
what is the measure of qrp
Check the picture below.
notice chord QR is a diameter, thus the vertex at P has a right-angle by Thales theorem.
QUICK
What is the image point of (1,4) after a translation left 5 units and down 3 units ?
Answer:
(-4,1)
Step-by-step explanation:
First, subtract 1-5. (When you move left or down you subtract. When you move right or up you add.) Left and right affect the x-axis
Second, subtract 4-3. Up and down Affect the y-axis
It would look like this:
(1,4)
=(1-5,4-3)
=(-4,1)
Answer:
here you go(image included)
Step-by-step explanation:
3,350 to the nearest ten.
Mary bought 7 dozen candles. How many candles did she buy?
Answer:
the answer is 84
Step-by-step explanation:
a dozen is 12 so you take 12 times 7 and get 84
Heyaaa
The answer is 84 Candles .
There are 12 in a dozen , and there are 7 dozen.
12 x 7 = 84
Good luck :)
2n^-4 rewrite the expression without using a negative exponent
The expression[tex]\(2n^{-4}\)[/tex] rewritten without a negative exponent is [tex]\(\frac{2}{n^4}\)[/tex]. This means the same as [tex]\(2\)[/tex] times the reciprocal of [tex]\(n\)[/tex] raised to the fourth power.
To rewrite the expression [tex]\(2n^{-4}\)[/tex] without using a negative exponent, we'll follow these steps:
1. Understand the Negative Exponent Rule: The rule states that [tex]\(a^{-b} = \frac{1}{a^b}\)[/tex]. It means that to convert a negative exponent to a positive one, you flip the base to the denominator of a fraction.
2. Apply the Rule to the Given Expression: We apply this rule to[tex]\(2n^{-4}\)[/tex].
3. Simplify the Expression: We simplify the expression to its final form without a negative exponent.
Let's apply these steps:
Step 1: Understand the Negative Exponent Rule
- The rule [tex]\(a^{-b} = \frac{1}{a^b}\)[/tex] tells us that to eliminate a negative exponent, we place the base with the positive exponent in the denominator of a fraction.
Step 2: Apply the Rule to the Given Expression
- Apply this to [tex]\(2n^{-4}\)[/tex]. It becomes [tex]\(2 \times \frac{1}{n^4}\)[/tex].
Step 3: Simplify the Expression
- Simplify [tex]\(2 \times \frac{1}{n^4}\)[/tex] to get the final expression.
Let's simplify it.
Step 3: Simplify the Expression
After applying the negative exponent rule to [tex]\(2n^{-4}\)[/tex], the expression simplifies to [tex]\(\frac{2}{n^4}\)[/tex].
Solve |x| + 7 < 4.
1. {x | x < -11 or x > -3}
2. {x | -3 < x < 3}
3. Ø
Answer:
3. ØStep-by-step explanation:
[tex]|a|=a\ \text{for}\ a\geq0\\\\|a|=-a\ \text{for}\ a<0[tex]|x|+7<4\qquad\text{subtract 7 from both sides}\\\\|x|+7-7<4-7\\\\|x|<-3\to x\in\O\ \text{because}\ |x|\geq0\ \text{for any value of }\ x.[/tex]===================[/tex]
find the mean median and interquatile for the data set below . 17 23 8 5 9 16 22 11 13 15 17 18
Answer: Interquartile: 8.25
Mean: 14.5
Median: 15.5
Step-by-step explanation:
Answer please !!! how many faces are in the polyhedron ?
Answer:
The correct answer is four
Step-by-step explanation:
From the figure we can see that, it is a triangular pyramid.
The base is a triangle.
In the lateral surface there are 3 faces. All the three faces are triangle shape.
Therefore the given figure consists of four faces.
All the the four faces are in triangular faces.
The correct answer is four
The given polyhedron have four faces where all four faces are in triangular faces.
In a polyhedron, faces refer to the flat surfaces or sides of the three-dimensional object.
These faces are typically polygonal regions and are connected by edges and vertices.
In the figure, the base is a triangle.
and, in the lateral surface there are 3 faces.
Therefore. the given figure consists of four faces.
Learn more about Faces here:
https://brainly.com/question/1657574
#SPJ6
Over the summer, Alexis read 15 books in 12 weeks. The diagram below can be used to track her progress. If Alexis read at the same rate each week, how many books had she read in 4 weeks? in 8 weeks? complete the diagram
12weeks-15 books
4 weeks-5 books
8 weeks-10 books
Answer:
4 to 5
8 to 10
Step-by-step explanation:
What is the measure of the vertex angle of an isosceles triangle if one of its base angles 54
In an isosceles triangle, the two angles at the base are the same. So, the base angles are both 54°, for a total of 108.
Since the interior angles of a triangle sum up to 180°, the remaining angle must be
[tex]180-54-54=180-108=72[/tex]
Lara is a skier. She completed a ski race in 1 minute 54 seconds. The race was 475 m in length. Lara assumes that her average speed is the same for each race.
a) Using the assumption, work out how long Lara should take to complete a 700m race. Give your answer in minutes and seconds.
b) Lara's average speed actually increases the further she goes. How does this affect your answer to part a?
Answer:
a) 2 minutes 48 seconds
b) The time would decrease as it takes less time for Lara to finish the race.
Step-by-step explanation:
Speed = Distance / Time
Speed = 475 / 114
Speed = 4.16m/s
Distance = 700m
Time = Distance/Speed
Time = 700/4.16
= 168 seconds
= 2 minutes and 48 seconds
how do you represent 12 fourths in 3
Answer:
See below for explanation
Step-by-step explanation:
Another way to think about this is to think "How many fourths are in 3". There are 4 fourths in 1, and there are 3 1's in 3, so we have
3(4) = 12 fourths in 3
Algebraically you can write it as.
1(4)x = 3 this means "one fourth time some value is 3" which is a rewording of what I explained above. Solve for x by multiplying both sides by 4...we get x = 12, so
one fourth, 12 times gives us 3
The fraction 12/4 simplifies to 3 because the numerator and denominator can both be divided by their greatest common divisor, which is 4.
Explanation:The question is related to the conversion of a fraction to a simpler form. The fraction 12/4 can be converted into a simpler form by dividing both the numerator and the denominator by their greatest common divisor. The greatest common divisor of 12 and 4 is 4. So, we can divide the numerator 12 and the denominator 4 by 4.
Here's how to do it:
12 ÷ 4 = 3 4 ÷ 4 = 1
As a result, the fraction 12/4 reduces to the whole number 3. Thus, 12 fourths is represented as 3 in its simplest form.
Learn more about Simplifying Fractions here:https://brainly.com/question/18435083
#SPJ2
find the product of
(x2 + 3x + 1)(x2 + x + 2)
Answer: [tex]x^4+4x^3+6x^2+7x+2[/tex]
Step-by-step explanation:
To solve the exercise you must apply the following proccedure:
- Apply the distributive property.
- Keep on mind that when you multiply two powers with equal base, you must add the exponents.
- Add like terms.
Therefore, you obtain the following product:
[tex]=x^{(2+2)}+x^{(2+1)}+2x^2+3x^{(1+2)}+3x^{(1+1)}}+6x+x^{2}+x+2\\=x^4+x^3+2x^2+3x^3+3x^2+6x+x^2+x+2\\=x^4+4x^3+6x^2+7x+2[/tex]
The answer is: [tex]x^{4}+4x^{3}+6x^{2}+7x+2[/tex]
Why?To find the product of the given expression, we need to apply the distributive property and then, group each like term.
The distributive property states that:
(a+b+c)(d+e+f)=a*d+a*e+a*f+b*d+b*e+b*f+c*d+c*e+c*f
Then, we have to group each like term. Like terms are the terms that have the same variable and exponent , for example:
[tex]x+x+x^{2}=2x+x^{2}[/tex]
For this case, the variable "x" has two Like terms, since both have the same exponent (1), then, we add each other in order to group term.
Also, we must remember the following power property:
Product of powers property,
[tex]a^{n}*a^{m}=a^{n+m}[/tex]
So, solving the product we have:
[tex](x^{2}+3x+1)(x^{2}+x+2)=x^{2}*x^{2}+x*x^{2}+2x^{2}+3x*x^{2}+3x*x+6x+x^{2}+x+2\\(x^{2}+3x+1)(x^{2}+x+2)=x^{2+2}+x^{1+2}+2x^{2}+3x^{2+1}+3x^{1+1}+6x+x^{2}+x+2\\(x^{2}+3x+1)(x^{2}+x+2)=x^{4}+4x^{3}+6x^{2}+7x+2[/tex]
Have a nice day!
the histogram shows the lengths of flight delays at several airports. hiw many flights were delayed?
The total number of flights delayed at several airport based on the histogram is 25.
How many flights were delayed?An histogram is a graphical display of numerical data in the form of upright bars, with the area of each bar representing frequency.
Flight delayed 0 - 1 hour = 9
Flight delayed 1 - 2 hour = 3
Flight delayed 3 - 4 hour = 7
Flight delayed 4 - 5 hour = 5
Flight delayed 6 - 7 hour = 1
Total flights delayed = 9 + 3 + 7 + 5 + 1
= 25
Therefore, 25 flights were delayed.
Read more on histogram:
https://brainly.com/question/2962546
#SPJ2
the simple interest I ( in dollars) for a savings account is jointly proportional to the product of the time t (in years) and the principal P (in dollars). After five months, the interest on a principal of $3892 is $92. a) find the constant of variation.
b) what will the interest be after 3 years
Answer:
Part a) The constant of variation is [tex]r=0.0567[/tex] or [tex]r=5.67\%[/tex]
Part b) [tex]I=\$662.03[/tex]
Step-by-step explanation:
Part a) Find the constant of variation.
we know that
The simple interest formula is equal to
[tex]I=P(rt)[/tex]
In this linear direct variation the constant r represent the constant of proportionality
where
I is the Interest Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
in this problem we have
[tex]t=5/12\ years\\ P=\$3,892\\ I=\$92\\r=?[/tex]
substitute the values and solve for r
[tex]92=3,892(r(5/12))[/tex]
[tex]r=(92*12)/(3,892*5)[/tex]
[tex]r=0.0567[/tex]
Part b) what will the interest be after 3 years
in this part we have
[tex]t=3\ years\\ P=\$3,892\\ I=?\\r=0.0567[/tex]
substitute the values
[tex]I=3,892(0.0567*3)=\$662.03[/tex]
A florist arranges 10 flowers in each vase how many vases does the florist need to arrange 49 flowers
Answer:
Five Vases
Step-by-step explanation:
In this type of questions, you can't have a reminder. You would have to round up instead.
49 flowers / 10 per case = 4 remainder 9
Because you have a remainder you need to round 4 up to 5.
You need 5 vases.
Add the polynomial below.
(-12.7z³ - 14z) + (-8.9z³ + 12z + 2)
Answer:
-21.6 z^3 - 2 z + 2
Step-by-step explanation:
(-12.7z³ - 14z) + (-8.9z³ + 12z + 2)
I like to line them up vertically
(-12.7z³ - 14z)
+ (-8.9z³ + 12z + 2)
---------------------------------
-21.6 z^3 - 2 z + 2