The solution of the system of linear equations are,
1) (2.2, -1.4).
2) (1.33, 1)
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.
Here, We have to given that;
Two lines, with their corresponding equations are given and we have to find the solution to the system of equations.
The given lines are:
Equation of Line 1 is,
⇒ y = - 7/4x + 5/2
And, This line passes through the points (0, 2.5) and (2.2, -1.4).
Equation of Line 2 is,
⇒ y = 3/4x - 3
And, This line passes through the points (0, -3) , (2.2, -1.4)
By looking at the graph/given data we have to find the solution of these linear equations as;
Remember that the solution of linear equations is an ordered pair, through which both the lines pass i.e. the point at which both the given lines intersect is the solution of the linear equations.
So, From the given data we can see that both the lines pass through one common point, (2.2, -1.4).
Since, both lines pass through this point, this means this is the point of intersection of the lines and hence there solution.
So, The answer to this questions is (2.2, -1.4)
For the second question;
The given equations are:
⇒ y = 1.5x - 1 .. (i)
⇒ y = 1 .. (ii)
Now, We can solve these equations by method of substitution.
So, Substituting the value of y from Equation 2, in Equation 1, we get:
1 = 1.5x - 1
1 + 1 = 1.5x
2 = 1.5x
x = 2/1.5
x = 1.33
And, y = 1
Thus, The solution of the given linear equations is, (1.33, 1)
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When the dimensions of a particular rectangle are expressed in feet, the ratio of the numerical value of the perimeter to the numerical value of the area is $\frac{3}{4}$. What is this ratio if the dimensions are expressed in inches instead of feet
The ratio if the dimensions are expressed in inches instead of feet is 1/16.
Ratio is defined as the relationship between two quantities. It can be expressed as a to b, a : b, or a / b.
Meanwhile, proportion is defined as the equality between two ratios.
a / b = c / d
If the ratio of the numerical value of the perimeter to the numerical value of the area, expressed in feet, is 3/4, then converting each component to inches will give its ratio, expressed in inches.
perimeter / area
= 3 feet / 4 feet²
= 3 feet(12 inches / 1 foot) / 4 feet²(12 inches / 1 foot)(12 inches / 1 foot)
= 36 inches / 576 inches²
Simplifying the ratio by dividing both by 36.
36 / 576 = 1 / 16
Hence, the ratio will become 1/16.
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The graph shows the relationship between the number of cubic yards of mulch ordered and the total cost of the mulch delivered. a. What is the constant rate of change? What does it represent? b. What is the initial value? What might that represent? The constant rate of change is (Type a whole number.) Cost in Dollars (y) 500 400 300 200 Ay 100 X 10 20 30 40 50 Cubic Yards (x)
The equation for the graph is y = 20x + 50, where the rate of change is 20 and the initial value is 50.
What is a linear equation?When an algebraic equation is graphed, it always results in a straight line since each term in a linear equation has an exponent of 1. For this reason, it is referred to as a "linear equation."
There are both one-variable and two-variable linear equations.
Given graph shows the relationship between the number of cubic yards of mulch ordered and the total cost of the mulch delivered,
x-axis shows the cubic yards and y-axis shows cost,
A. to find the constant rate of change,
from graph, we find that x₁ = 0 and x₂ = 5
y₁ = 50 and y₂ = 150
constant rate of change = (y₂ - y₁)/(x₂ - x₁)
rate of change = (150 - 50)/(5 - 0)
rate of change = 100/5 = 20
the constant rate represents the slope of the line,
for equation of line y = mx + c
here m = slope of the line or constant rate of change.
2. to find the initial value,
the initial value represents the y-intercept or the value of constant for equation y = mx + c,
where c is the initial value
we have m = 20 x = 0 and y = 50
50 = 20(0) + c
c = 50
the equation for the graph is y = 20x + 50
Hence the rate of change is 20 and the initial value is 50.
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you deposit $4000 in an account earning 4% interest compounded quarterly. How much will you have in the account in 10 years
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$4000\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &10 \end{cases} \\\\\\ A = 4000\left(1+\frac{0.04}{4}\right)^{4\cdot 10}\implies A=4000(1.01)^{40} \implies A \approx 5955.45[/tex]
Answer:
$5955.45
Step-by-step explanation:
We can use the formula to find the sum of the money, when we calculate the amount of money according to compound interest.
Before we getting ready to solve the sum, we have to keep these points in our mind.
Interest will calculate quarterly. So, we have to divide the interest by 4.I year has 4 quarters. So, number of years should me multiply by 4.Formula to find the sum of money after compound interest is:
[tex]\sf S = X ( 1 + r )^n[/tex]
Here,
S = Sum of money
X = Amount of money deposited
r = Interest rate
n = Time ( in years )
Let us solve it now.
[tex]\sf S = X ( 1 + r )^n\\\\\sf S = 4000 ( 1 + \frac{4}{100}*\frac{1}{4} )^4^0\\\\\sf S = 4000 ( 1 + \frac{4}{400} )^4^0\\\\\sf S = 4000 ( 1 + 0.01 )^4^0\\\\\sf S = 4000 ( 1.01 )^4^0\\\\\sf S = 5955.45[/tex]
Violet was given a box of assorted chocolates for her birthday. Each night, Violet treated herself to some chocolates. Violet ate 4 chocolates each night and there were originally 24 chocolates in the box. Write an equation for C,C, in terms of t,t, representing the number of chocolates remaining in the box tt days after Violet's birthday.
The equation for C, in terms of t, representing the number of chocolates remaining in the box t days after Violet's birthday is C = 24 - 4t
How to write an equation?Number of chocolate violet eats each night = 4
Number of chocolate originally in the box = 24
Number of chocolate remaining = C
Number of days after violet birthday = t
Number of chocolate remaining = Number of chocolate originally in the box - (Number of chocolate violet eats each night × Number of days after violet birthday)
C = 24 - (4 × t)
C = 24 - 4t
In conclusion, the equation which represents violet's remaining chocolate after her birthday is C = 24 - 4t
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0.0319 as a fraction
Please I need it asap
Answer:
lol.
Step-by-step explanation:
Refer to the image attached. Please rate, and let me know if you have any questions. Thanks!
Work this travel problem based on the data provided in the table. Choose the correct answers. Average costs per day country high category medium category argentina $22. 55 $10. 80 austria $17. 08 $10. 17 belgium $20. 16 $12. 96 brazil $18. 33 $12. 25 england $22. 94 $15. 88 france $29. 04 $19. 54 greece $16. 55 $9. 48 italy $21. 84 $14. 69 netherlands $20. 80 $14. 37 spain $14. 51 $8. 79 sweden $23. 51 $15. 73 switzerland $21. 57 $13. 82 united states $34. 48 $22. 46 west germany $22. 53 $14. 33 yugoslavia $10. 96 $7. 38 by what percentages are spain's high category and medium category less than the united states' categories (to the nearest tenth of a percent)? high category = % medium category = %.
The high category cost in Spain is 57.8% lower than the high category cost in the United States, while the medium category cost in Spain is 61.0% lower than the medium category cost in the United States.
We can use the following calculations to determine the percentage by which Spain's high category and medium category costs are less than those of the United States' categories:
(High in the US - High in Spain)/High in the US * 100%
Spanish medium/US medium * 100% for the medium division.
The first formula determines the percentage difference between the high category costs in the United States and Spain. The second calculation determines the percentage difference between the medium category costs in the United States and Spain.
Calculate, for instance, the percentage difference between the high category costs in Spain and the United States. The values can be entered into the formula in the following way:
High category: (19.97)/(34.48 - 14.51)/(34.48 * 100%) = 57.8%
This indicates that the high category cost in Spain is 57.8% cheaper than the high category cost in the United States.
The similar method can be used to determine how much less Spain's medium category cost is than America's medium category cost:
(22.46 - 8.79)/22.46 * 100% = (13.67)/22.46 * 100% = 61.0% for the medium group.
As a result, the medium category cost in Spain is 61.0% cheaper than the medium category cost in the United States.
.
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Answer:
High category = 58%
Medium category = 61%
Step-by-step explanation:
Corrected what he said. Brainliest?
SOMEONE PLEASEEEE HELP MEE ASAP 20 POINTTSS
Answer:
x intercept is 7.5
y intercept is -3
Step-by-step explanation:
let me know if you need more help
A solid is in the form of cone mounted on a hemisphere in such a way that the centre of the base of the cone just coincide with the centre of the base of the cone is 1 upon 2 hour where r is the radius of the hemisphere prove that the total surface area of the solid is pie upon 4 (11 r 2 l) r ?
When proved, the total surface area of the solid is π/4 r(11r - 2l)
What is the total surface area of the solid?
The Solid comprise a cone mounted on top of a hemisphere. The total surface area of the object is given as follows
Total surface area = Total surface area of cone -total surface area of the hemisphere.
This implies that TSA = 1/2πr(1/2r +l) -3πr²
πr/2(r+2l)/2 -3πr²
This implies that the expression will be (πr² +2πrl)/4 - 3πr²
⇒(πr² +2πrl - 12πr²)/4
Conclusively, the expression finally gives π/4 r (11r - 2l)
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could someone please help me with this shape I have to find the perimeter and the area of that shape But I have no clue Where to start from, so could anybody help me figure this out this is very important to me, and please do not Try to give me the wrong answer because I really need the right answer and please do it Step-by-step explanation for the answer
The perimeter of the shape is approximately 20.57 inches.
What is Perimeter?The perimeter of a shape is defined as the total distance around the shape. It is the length of the outline or boundary of any two-dimensional geometric shape. The perimeter of different figures can be equal in measure depending upon the dimensions.
The shape consists of two shapes; a square and 2 semi-circles
Perimeter of square = 4L
where L = 2 inches
Perimeter = 4(2)
Perimeter = 8 inches
Perimeter of Semi-circle = [tex]\pi r}[/tex]
where [tex]\pi = 3.142[/tex]
r = 2 inches
Perimeter of Semi-circle = 3.142 x 2
Perimeter of Semi-circle = 6.284 inches
Perimeter of shape = Perimeter of square + 2 x Perimeter of Semi-circle
Perimeter of shape = 8 inches + 2 x 6.284 inches
Perimeter of shape = 8 inches + 12.568 inches
Perimeter of shape = 20.568 inches
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On the spinner below, what is P(odd)?
A circle is divided equally into eight sections.· One of the sections is labeled with a 1.
· One of the sections is labeled with a 2.
· Two of the sections are labeled with a 3.
· One of the sections is labeled with a 4.
· Two of the sections are labeled with a 5.
· One of the sections is labeled with a 6.
· The pointer originating from the middle of the circle is pointing at one of the sections labeled with a 3.
A. start fraction 5 over 8 end fraction
B. The fraction is 5 over 3.
C. one-half
Answer:
Isha Chawla the viewer's attention to detail and the game name is the viewer's of the viewer's the viewer's of math and science and time of year for you are interested please contact me homework for the same to the viewer's attention to the seller if
Please help!!!!! Find the perimeter of the figure. Round to the nearest hundredth if needed
The perimeter of the figure is 48 meters
How to determine the perimeter of the figureFrom the question, we have the following parameters that can be used in our computation:
Shape = rectangle
length = 10 meters
width = 14 meters
The perimeter of the figure is then calculated as
Perimeter = 2 * (length + width)
Substitute the known values in the above equation, so, we have the following representation
Perimeter = 2 * (10 + 14)
Evaluate
Perimeter = 48
Hence, the perimeter is 48 meters
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Solve the equation for all values of x.
|4x +9|-6 = x
Answer: x = 4
Step-by-step explanation: (4x+9)−6.
Subtract 6 from 9 to get 3.
d/dx (4x+3)
The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^n
is nax^n-1.
4x^1-1
Subtract 1 from 1.
4x^0
For any term t, t×1=t and 1t=t.
x = 4
Find the mean of a distribution if it's median and mode are 45 and 13 respectively
The mean of the distribution is 61.
What is Mean?The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency.
Given, the median and mode of a dataset are 45 and 13 respectively
They have given that the median of the distribution is 45
They have given that the mode of distribution is 13
To find the mean of the distribution, let's consider
The relationship between the mean, mode, and the median is given by
Mode = 3 Median - 2 Mean
Mean = (3* 45 - 13)/2
Mean = 122/2
Mean = 61
Therefore, the mean of a distribution if its median and mode are 45 and 13 respectively is 61.
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Pete traveled 1,380 miles in two days. The first day, he traveled 1.5 times as far as he did the second day. How many miles did he drive on
He drove 828 miles on the first day.
An algebraic expression is the combination of numbers and variables in expressing and solving a particular mathematical question.
Let x = distance Pete traveled on the second day
If on the first day, he traveled 1.5 times as far as he did the second day, then
distance Pete traveled on the first day = 1.5x
If Pete traveled 1,380 miles in two days, the the sum of the distance he traveled in two days is equal to 1380.
x + 1.5x = 1380
Simplify the equation and solve for the value of x.
x + 1.5x = 1380
2.5x = 1380
x = 552
distance Pete traveled on the second day = 552 miles
distance Pete traveled on the first day = 1.5(552) = 828miles
Therefore, he drove 828 miles on the first day.
The problem seems incomplete. The question must be
"Pete traveled 1,380 miles in two days. The first day, he traveled 1.5 times as far as he did the second day. How many miles did he drive on the first day?"
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A conical water tank with vertex down has a radius of 12 feet at the top and is 26 feet high. If water flows into the tank at a rate of 20 ft3/minft3/min, how fast is the depth of the water increasing when the water is 17 feet deep?
The depth of the water is increasing at _____________ ft/min
The depth of the water is increasing at 0.167 ft/min.
In this problem, we are given the radius of the conical tank (12 feet), the height of the tank (26 feet) and the rate at which water is flowing into the tank (20 ft3/min). To calculate the rate of the water's increase in depth, we need to first calculate the volume of the tank.
The volume of a conical tank can be calculated using the formula V = 13r2h, where r is the radius and h is the height. Using this formula, we can calculate the volume of the tank to be 13(12)2(26) = 7584 ft3.
Next, we need to calculate the rate at which the depth of the water is increasing. This can be done by dividing the rate at which water is flowing into the tank (20 ft3/min) by the volume of the tank (7584 ft3). This gives us a rate of 0.0026 ft3/min. To get the rate at which the depth is increasing, we need to divide this number by the area of the tank's base (113 ft2). This gives us a rate of 0.167 ft.
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For j(x) = 5^x − 3, find j of the quantity x plus h end quantity minus j of x all over h period
For j(x) = 5^x − 3, find j(x+h) - j(x)/h
If j(x) = 5^(x - 3), using laws of exponents to solve the given expression [j(x + h) - j(x)]/h gives; [j(x + h) - j(x)]/h = [(5^(x - 3))(5^(h) - 1)]/h
How to utilize laws of exponents?We are given the function as;
j(x) = 5^(x - 3)
Now, we want to solve the expression;
[j(x + h) - j(x)]/h
This gives us;
j(x + h) = 5^(x - 3 + h)
Thus, our expression is now;
[j(x + h) - j(x)]/h = [5^(x - 3 + h) - 5^(x - 3)]/h
Now, according to laws of exponents, we know that;
y³ × y² = y³ ⁺ ²
Thus;
5^(x - 3 + h) = 5^(x - 3) × 5^h
Therefore;
[5^(x - 3 + h) - 5^(x - 3)]/h = [(5^(x - 3))(5^(h) - 1)]/h
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What does an HL triangle look like?
An HL triangle is a type of triangle with two sides of equal length and one side that is longer than the other two sides. The triangle has an acute angle between the two equal sides, and an obtuse angle between the longest side and one of the equal sides.
Understanding the HL TriangleAn HL triangle can be described as an isosceles triangle with one side longer than the other two. The sides that are of equal length form an acute angle, while the longest side forms an obtuse angle with one of the equal sides. The longest side of the HL triangle is typically referred to as the hypotenuse, while the two equal sides are referred to as the legs. The hypotenuse is always the longest side, and the two legs are always of equal length.
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if we set c=19!, then express 21!-20! in terms of c
[tex]\begin{array}{ll|ll} 21!\implies &21\cdot 20\cdot 19\cdot 18\cdot 17.....\\&\\ &21\cdot 20\cdot 19! \end{array} \begin{array}{llll} 20!\implies &20\cdot 19\cdot 18\cdot 17\cdot 16\cdot 15.....\\\\ & 20\cdot 19! \end{array} \\\\[-0.35em] ~\dotfill\\\\ (21\cdot 20\cdot 19!)-(20\cdot 19!)\implies (21\cdot 20\cdot c)-(20\cdot c) \\\\\\ 420c-20c\implies \text{\LARGE 400c}[/tex]
PLEASE HELP WILL GIVE BRANLIEST!!
Answer:
B. x <= -17 or x >= 15
Step-by-step explanation:
To solve this inequality, we need to split the absolute value expression into two separate cases, one for each possible sign of the expression within the absolute value bars.
For the case where the expression within the absolute value bars is positive, we can remove the absolute value bars and solve the resulting inequality as follows:
1/4(x+1) >= 4
(x+1) >= 16
x >= 15
For the case where the expression within the absolute value bars is negative, we can again remove the absolute value bars and solve the resulting inequality as follows:
-1/4(x+1) >= 4
-(x+1) >= 16
x <= -17
Combining these two cases, we get that the solution to the inequality is:
x <= -17 or x >= 15
So, the correct answer is B.
Write the equation the line through the point b) (1,3) with slope = -4
Answer:
Below
Step-by-step explanation:
Here is the point-slope form of this line to start:
y-3 = -4 ( x-1) which can be re-arranged to
y = -4x +7 which is y = mx + b form ( slope -intercept from)
or
4x + y = 7 sometimes called 'standard form'
Will mark Brainiest
How can you find the unit price for 1 can of diet soda if a case of 24 costs 5.99
I’m too lazy to solve it
Will mark brainiest
Answer:
Original: 0.24958333333... | Rounded Up: 0.25
Step-by-step explanation:
unit price = total price divided by quantity
5.99 divided by 24 = 0.24958333333...
We can round this to 0.25
someone please. i need help w this,
Answer:
y = [tex]\frac{-8}{3}[/tex] x + [tex]\frac{8}{3}[/tex]
Step-by-step explanation:
The slope is the change in y over the change in x.
[tex]\frac{0-8}{1 - -2}[/tex] = [tex]\frac{-8}{1+2}[/tex] = [tex]\frac{-8}{3}[/tex]
The slope (m) is [tex]\frac{-8}{3}[/tex]
Use the slope and one of the points to find the y intercept
I will use the point (1,0)
x = 1
y = 0
m = [tex]\frac{-8}{3}[/tex]
y = mx + b Substitute in what you know and solve for b
0 = [tex]\frac{-8}{3}[/tex](1) + b
0 = [tex]\frac{-8}{3}[/tex] + b Add [tex]\frac{8}{3}[/tex] to both sides
[tex]\frac{8}{3}[/tex] = b
The y-intercept (b) is [tex]\frac{8}{3}[/tex]
y = mx + b
y = [tex]\frac{-8}{3}[/tex] x + [tex]\frac{8}{3}[/tex]
PLEASE HELP
question 3
Determine the solution to the inequality.
The solution to the inequality expression 1/4|x + 1| ≥ 4 is (b) x ≤ -17 or x ≥ 15
How to determine the solution to the inequality.From the question, we have the following parameters that can be used in our computation:
1/4|x + 1| ≥ 4
Multiply through the inequality by 4
So, we have the following representation
|x + 1| ≥ 16
Remove the absolute bracket
-16 ≥ x + 1 ≥ 16
Subtract 1 from all sides
-17 ≥ x ≥ 15
So, we have
x ≤ -17 or x ≥ 15
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What's the principal sum?
The principal sum refers to the amount payable in one sum in the case of accidental death and, in some cases, accidental dismemberment.
The amount paid in the case of accident or medical insurance in the event that the insured person dies, loses a limb, or loses sight is known to be as principal sum. It means that the principal sum amount is the maximum amount paid to the insured person for all injuries resulting from the accident.
Thus, the principal sum is the amount insured to be paid by the company to the beneficiary in the case of the insured individual's accidental death as well as in the loss of limb or sight.
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x/3 +x/5=8 solve in equation
Answer:
x=15
Step-by-step explanation:
x/3+x/5=8
Both multipling 15: 15(x/3+x/5)=15*8
5x+3x=120
8x=120
x=15
Please help me asap, I suck at math fr fr
Answer:
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
C : is the hypotenuse
A and B are two sides
[tex] {6}^{2} + \: {x}^{2} = {15}^{2} \\ {15}^{2} - {6}^{2} = 189 \\ \sqrt{189} = 3 \sqrt{21} [/tex]
26. Which of the following is an equation for the line that is perpendicular to the line y = 2x - 9
and passes through the point (-4,5)?
A. y = 2x+7
B. y = -1/2x+3
C. y = 2x+5
D. y = -14x-9
Answer:
y = -1/2x+3
Step-by-step explanation:
We have y = 2x-9
This is in slope intercept form
y = mx+b where m is the slope
The slope is 2
We want a line that is perpendicular
Perpendicular lines have slopes that are negative reciprocals
The slope is -1/2
The equation of the new line is
y = -1/2x+b
Substituting the point into the equation
5 = -1/2(-4)+b
5 = 2+b
5 -2=b
3=b
y = -1/2x+3
Answer:
y = -1/2x + 3
Step-by-step explanation:
We know that if two lines are perpendicular to each other the multiplication of the slopes of those 2 lines equals -1.
m₁ × m₂ = -1
Given that, the slope of one line is 2 (m₁). Now, let us find the slope of the other line (m₂) using the above formula.
2 × m₂ = -1
2m₂ = -1
Divide both sides by 2.
m₂ = -1/2
And now let us find the value of the y-intercept ( c in the formula y = mx + c) using the given coordinate.
( -4 , 5 )⇒ ( x , y ).
Let us find it now.
y = mx + c
5 = -1/2x × -4 + c
5 = 2 + c
5 - 2 = c
3 = c
And now let us write the equation for the new line.
y = m x + c
y = -1/2x + 3
(please help asap T-T) Using long division, find the quotient of (6x^3 + x^2 - 2x + 15) / (2x + 3)
a. 3x^2 - 4x + 5
b. 3x^2 + 5x - 6
c. 2x^2 + 3x - 5
d. 3x^2 - 5x - 5
The polynomial 6x³ + x² - 2x + 15 divided by 2x + 3 will give a quotient of 3x² - 4x + 5 and a remainder of zero, which makes option a correct.
How to calculate for the quotient and remainderThe long division method will require us to; divide, multiply, subtract, bring down the next number and repeat the process to end at zero or arrive at a remainder
We shall divide the polynomial 6x³ + x² - 2x + 15 by 2x + 3 as follows;
x³ divided by 2x equals 3x²
2x + 3 multiplied by 3x² equals 6x³ + 9x²
subtract 6x³ + 9x² from 6x³ + x² - 2x + 15 will result to -8x² - 2x + 15
-8x² divided by 2x equals -4x
2x + 3 multiplied by -4x equals -8x² - 12x
subtract -8x² - 12x from -8x² - 2x + 15 will result to 10x + 15
10x divided by 2x equals 5
2x + 3 multiplied by 5 equals 10x + 15
subtract 10x + 15 from 10x + 15 will result to a remainder of 0
Therefore by the long division method, 6x³ + x² - 2x + 15 divided by 2x + 3 gives a quotient 3x² - 4x + 5 and a remainder of 0.
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What is the value of the expression ƒ2+ 5 if ƒ = 3?
Answer:
f2 + 5 when f = 3 is 11.
Step-by-step explanation:
So let's start by replacing f with 3:
3(2) + 5 =
When we have a variable right next to another number, we multiply. Some examples of this are 2x or 5y or 10000t, or even 0.001j.
Therefore, we multiply the 3 and 2 together, which gets us 6:
6 + 5 =
And 6 plus 5 equals 11
6 + 5 = 11, final answer.