By using linear equation, it can be calculated that
New Solution #1 : (-6, 1) is a solution because when you plug it into the original equation x + 3y = -3, the equation simplifies to -3 = -3
New Solution #2: (-9, 2) is a solution because when you plug it into the original equation x + 3y = -3, the equation simplifies to -3 = -3
What is linear equation?
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Equation of line : x + 3y = -3
Putting y = 1
x + 3 \(\times\) 1 = -3
x = -3 - 3
x = -6
Putting y = 2
x + 3 \(\times\) 2 = -3
x + 6 = -3
x = -3 - 6
x = -9
New solutions (-6, 1) and (-9, 2)
New Solution #1 : (-6, 1) is a solution because when you plug it into the original equation x + 3y = -3, the equation simplifies to -3 = -3
New Solution #2: (-9, 2) is a solution because when you plug it into the original equation x + 3y = -3, the equation simplifies to -3 = -3
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Help me please in need of it
Answer:
-2
Step-by-step explanation:
Substituting the points (0,2) and (1,0) into the slope formula, \(m=\frac{2-0}{0-1}=-2\).
Complete the following equation using <, >, or =
7 _ 24/4
A. =
B. >
C. <
Answer:
7 > 24/4
Step-by-step explanation:
7 _ 24/4
Simplify 24/4
24/4 = 6
7 is greater than 6
7 > 24/4
7 is greater than the fraction 24/4 so we use the ">" symbol between them. Hence, the complete equation is 7 > 24/4.
Comparison of two numbers involves determining the relationship between them. Here are a few possible outcomes when comparing two numbers:
1: If the first number is greater than the second number, we can say that the first number is "greater than" or "larger than" the second number.
2: If the first number is less than the second number, we can say that the first number is "smaller than" or "less than" the second number.
3: If the first number is equal to the second number, we can say that the numbers are "equal" to each other.
The given numbers are:
7 and 24/4
To compare these numbers,
Convert the fraction 24/4 into the simplest form
Therefore,
\(\frac{24}{4} = 6\)
Now since 7 is greater than 6 so we use ">" between them.
Hence,
The complete equation will be 7 > 24/4.
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Solve the triangle. Round to the nearest tenth.
Find c aswell
Answer:
Set your calculator to Degree mode.
a² = 17² + 20² - 2(20)(17)cos(89°)
a² = 677.13236
a = 26.0 in.
sin(89°)/26.02177 = (sin B)/17
sin B = 17sin(89°)/26.02177
B = 40.8°
C = 50.2°
Find the slope of the line that passes through (2, 12) and (8, 5)
Answer:
-7/6
Step-by-step explanation:
You can get the slope of the line that passes between two points by taking the difference of the y values and dividing that by the difference of the x values:
\(\frac{12-5}{2-8} =\frac{7}{-6} =-\frac{7}{6}\)
PLEASE HELP!!!♡︎♡︎♡︎♡︎♡︎
Answer:
the first one hehdhdhrgdhfggd
Can u pleaseee answer all parts pleaseeeee <3333
please help meee
a. In interval notation, Increasing intervals: (12pm, 1pm) U (1pm, 2pm) U (2pm, 3pm). Decreasing intervals: (8am, 9am) U (11am, 12pm). Constant intervals: (9am, 10am) U (10am, 11am)
b. The increase in cost between 12 noon and 3 pm is $2.
c. Yellow Cab has a lower price per 1km than Swift ride at (8am, 9am) (9am, 10am) (2pm 3pm)
How do you express a data set in interval notations?Interval notation is used to represent continuous intervals of numbers or values, like ranges on a number line.
The graph shows that from 8-9am, and 11-12pm, the cost from Swift Ride decreases.
We can represent it as (8am, 9am) U (11am, 12pm).
It increases at these times (12pm, 1pm) U (1pm, 2pm) U (2pm, 3pm).
And stays constant at : (9am, 10am) U (10am, 11am)
Cost increase from 12 to 3pm,We simply deduct the 12pm's cost from 3pm's cost.
So, we have
Cost increase = $3.5 - $1.5
Evaluate the difference
Cost increase = $2
Hence, the cost increase is $2
The time interval where the cost is lowerWhen you plot the points provided for Yellow cab, you'll notice that Yellow Cab has a lower price per 1km than Swift ride at (8am, 9am) (9am, 10am) (2pm 3pm)
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The general strategy for solving an equation of the form x/a=b is to?
We have discussed the general strategy for solving an equation of the form x/a = b.
What is an equation?
An equation is a mathematical statement that shows that two expressions are equal. An equation is composed of two sides, separated by an equal sign (=), with each side containing one or more variables, numbers, and/or mathematical operations.
The general strategy for solving an equation of the form x/a = b is to:
Multiply both sides of the equation by a, in order to cancel out the fraction on the left side. This will isolate the variable x on one side of the equation.
Simplify the equation by combining like terms if necessary.
Check the solution by substituting it back into the original equation and verifying that it makes the equation true.
For example, consider the equation x/2 = 4
Multiply both sides by 2: x/2 * 2 = 4 * 2
x = 8
To check the solution, substitute it back into the original equation: x/2 = 4, 8/2 = 4. The equation is true, so x = 8 is the correct solution.
It's important to keep in mind that when solving equations, it is important to follow the order of operations, and also to be careful when dividing or multiplying by zero.
Hence, we have discussed the general strategy for solving the equation.
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The length between the bases on a baseball field is 90 ft. A scale drawing shows the distance between the bases as 2 1/2 inches. One inch on this drawing equals how many feet?
Divide total feet by total inches
90 feet / 2 1/2 inches = 36 feet per inch
1 inch = 36 feet
The table shows the balance in dollars of a bank account each month for three months. What is the average balance of the account
The average balance of the account is $1126.37.
An average is one number chosen to represent a group of numbers; it is often the sum of the numbers divided by the number of numbers in the group.
Consider the table that shows the balance (in dollars) of a bank account for three months.
Months Account Balance
1 $1285.12
2 $961.36
3 $1132.63
As we are aware, the following formula for the mean or average of any set of data:
Mean, \(\overline X=\frac{\sum X}{n}\)
where, ∑X is the sum of all the observations in the data and n is the number of observations in the data
Therefore, the average balance in the account is:
\(Average{~}balance=\frac{1285.12+961.36+1132.63}{3}\)
\(Average{~}balance=\frac{3379.11}{3}\)
Average balance = $ 1126.37
So, the account's average balance is $1126.37.
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The complete question is mentioned below:
The table shows the balance (in dollars) of a bank account each month for three months. What is the average balance of the account?
Table:
Month 1, account balance: $1285.12
Month 2, account balance: $961.36
Month 3, account balance: $1132.63
The average balance of the account is $1126.37
What is an average?Average: An average is one number chosen to represent a group of numbers; it is often the sum of the numbers divided by the number of numbers in the group.
Consider the table that shows the balance (in dollars) of a bank account for three months.
Months Account Balance
1 $1285.12
2 $961.36
3 $1132.63
As we are aware, the following formula for the mean or average of any
set of data,
Mean,
where, ∑X is the sum of all the observations in the data and n is the number of observations in the data
Therefore, the average balance in the account is,
Average balance of the account = $ 1126.37
So, the account's average balance is $1126.37
The complete question is mentioned below,
The table shows the balance (in dollars) of a bank account each month for three months.
Table:
Month 1, account balance: $1285.12
Month 2, account balance: $961.36
Month 3, account balance: $1132.63
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I need help what do I put in this blank what is the last number
The graph of a function g is shown below.
Find g(-5).
Check the picture below.
19 19. Which equation could best be used to determine the value f(3) for the functior f(x) = 2x + 4? A. f(3) = 23 +4 B. f(3) = 2(3) + 4 C. f(3) = 3(2x) + 4 D. f(3) = 3(3x + 4)
f(x) = 2(3) + 4 (option B)
Explanation:function: f(x) = 2x + 4
f(3) = ?
To get the value of f(3), we would replace x with 3 in the function
Replacing x;
f(x) = 2(3) + 4
Going through the options, the correct one is option B
73 7/10−25 5/8
Enter your answer as a mixed number in simplest form.
Answer:
48 3/40 just reanswerd for points :>
Step-by-step explanation:
NEED HELP!! I"LL GIVE YOU BRAINLIEST!! Find the value of b. a = 3 and c =12
Answer: b = 11.62
Step-by-step explanation:
We can use this formula to solve for b:
\(b^{2} =\) \(\sqrt{c^{2}-a^{2} }\)
\(b^{2} =\) \(\sqrt{12^{2}-3^2 }\)
\(b^2= \sqrt{144-9}\)
= 11.61895004
We can round that to 11.62.
Hope this helped!
The equation |2x + 1 = 9 has two solutions, a and b, where a < b. Find the two solutions.
Answer:
Write down one equation or inequality that has more than two solutions, but not infinitely many solutions
Step-by-step explanation:
What is the present value of R13 000 p.a. invested at the beginning of each year for 8years at 10%p.a. compound interest? (NB Use the compound interest tables provided or work to three decimal places only.)
Given statement solution is :- The present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.
To calculate the present value of an investment with compound interest, we can use the formula for the present value of an annuity:
PV = A *\((1 - (1 + r)^(-n)) / r\)
Where:
PV = Present value
A = Annual payment or cash flow
r = Interest rate per period
n = Number of periods
In this case, the annual payment (A) is R13,000, the interest rate (r) is 10% per year, and the investment is made for 8 years (n).
Using the formula and substituting the given values, we can calculate the present value:
PV = \(13000 * (1 - (1 + 0.10)^(-8)) / 0.10\)
Calculating this expression:
PV = \(13000 * (1 - 1.10^(-8)) / 0.10\)
= 13000 * (1 - 0.46318) / 0.10
= 13000 * 0.53682 / 0.10
= 6977.66 / 0.10
= 69776.6
Therefore, the present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.
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What is the surface area of this right triangular prism?
Enter your answer as in²
Check the picture below.
so the prism is really just two triangles and three rectangles, so
\(\stackrel{ \textit{\LARGE Areas} }{\stackrel{ two~triangles }{2\left[\cfrac{1}{2}(\underset{b}{8})(\underset{ h }{3}) \right]}~~ + ~~\stackrel{ two~rectangles }{2(4)(5)}~~ + ~~\stackrel{ rectangle }{(8)(4)}}\implies 24+40+32\implies \text{\LARGE 96}~in^2\)
Answer:25²
Step-by-step explanation: add 5+5+3+8+4
Natalie invests $2,000 into a savings account
which earns 11% per year. In 20 years, how
much will Natalie's investment be worth if
interest is compounded monthly? Round to the
nearest dollar.
Answer:
We can use the formula for compound interest to find the future value (FV) of Natalie's investment:
FV = P * (1 + r/n)^(n*t)
Where:
P is the principal amount (the initial investment), which is $2,000 in this case
r is the annual interest rate as a decimal, which is 11% or 0.11
n is the number of times the interest is compounded per year, which is 12 since interest is compounded monthly
t is the number of years, which is 20
Substituting the values into the formula, we get:
FV =
2
,
000
∗
(
1
+
0.11
/
12
)
(
12
∗
20
)
�
�
=
2,000 * (1.00917)^240
FV = $18,255.74
Therefore, after 20 years of compounded monthly interest at a rate of 11%, Natalie's investment of 2,000 will be worth approximately 18,256.
Answer:
$17,870
Step-by-step explanation:
You must use the formula for compound interest.
A = P(1 + r/n)^nt
I suggest you look it up at some point so that you can do these more easily in the future!
please help. Will mark brainliest if correct. ( links will be banned)
Answer:
-1
Step-by-step explanation:
Answer:
-2
Step-by-step explanation:
4x+2=-6
-2=-2
-8
4x=-8
4=4/-8=-2
Graph the circle (x - 3)^2 + (y + 3)^2= 36.
The circle on a graph by drawing the center point and then drawing a circle around it with a radius of 6.
To graph the circle with the equation (x - 3)² + (y + 3)² = 36, we can start by finding the center and radius of the circle.
The equation of a circle in standard form is (x - h)² + (y - k)² = r² (h, k) represents the center of the circle and r represents the radius.
Comparing the given equation with the standard form, we can see that the center of the circle is (3, -3) and the radius is √36 = 6.
Using this information, we can proceed to plot the circle on a graph:
Plot the center point: (3, -3).
From the center point, move 6 units in each direction (up, down, left, and right) to determine the points on the circle.
Up: (3, -3 + 6) = (3, 3)
Down: (3, -3 - 6) = (3, -9)
Left: (3 - 6, -3) = (-3, -3)
Right: (3 + 6, -3) = (9, -3)
Connect the plotted points to form a circle.
The resulting graph should look like this:
| • (3, 3)
|
| •
| •
__|_____________________________
|
|
|
|
| • (3, -3)
The center of the circle is denoted by a solid dot (•) in the graph and the other points lie on the circumference of the circle.
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George hit his neighbor's bike while backing his vehicle out and caused $200 worth of damage. The insurance company paid for $100 of the damage while George had to pay the remaining $100. The amount George paid was his
O A. liability
O B. collision
O C. deductible
O D. premium
Use a triple integral to find the volume of the given solid. The tetrahedron enclosed by the coordinate planes and the plane 2x + y + z = 2
Answer:
\(\mathbf{V = \dfrac{2}{3}}\)
Step-by-step explanation:
Consider the tetrahedron enclosed by the coordinate planes and the plane 2x + y + z = 2
Let A be the region obtained by projecting the volume(V) onto the xy-plane.
Similarly, the plane 2x + y + z = 2 intersects with the xy-plane in y = 2 - 2x.
Using the vertical strips, the region A is to the xy-plane can be expressed as:
\(A = \{(x,y) | 0 \le x \le 1, 0 \le y \le 2 - 2x\}\)
Thus, the volume of the solid can be calculated as follows;
\(V = \int^1_0 \int ^{2-2x}_{0} \int ^{2-2x-y}_{0} \ dz \ dy \ dx\)
\(V = \int^1_0 \int ^{2-2x}_{0} (2-2x-y) \ dy \ dx\)
\(V = \int^1_0 \bigg [2\times y -2x\times y - \dfrac{y^2}{2} \bigg]^{2-2x}_{0} \ dx \\)
\(V = \int^1_0 \bigg [2\times (2-2x) -2x\times (2-2x) - \dfrac{(2-2x)^2}{2} \bigg]\ dx\)
\(V = \int^1_0 \bigg [2x^2-4x+2 \bigg]\ dx\)
\(V = \bigg [2\dfrac{x^3}{3}-\dfrac{4x^2}{2}+2 x\bigg]^1_0\)
\(V = \bigg [2\dfrac{(1)^3}{3}-\dfrac{4(1)^2}{2}+2 (1)-0\bigg]\)
\(V = \dfrac{2}{3}- 2 + 2\)
\(\mathbf{V = \dfrac{2}{3}}\)
Given that a is rational and √2 is irrational and a is not equal to 2, show that. √2-1 is irrational
Answer:
Let us assume that √2 is a rational number.
So it can be expressed in the form p/q where p, q are co-prime integers and q≠0
√2 = p/q
Here p and q are coprime numbers and q ≠ 0
Step-by-step explanation:
√2 = p/q
On squaring both the sides we get,
=>2 = (p/q)2
=> 2q2 = p2……………………………..(1)
p2/2 = q2
So 2 divides p and p is a multiple of 2.
⇒ p = 2m
⇒ p² = 4m² ………………………………..(2)
From equations (1) and (2), we get,
2q² = 4m²
⇒ q² = 2m²
⇒ q² is a multiple of 2
⇒ q is a multiple of 2
Hence, p, q have a common factor 2. This contradicts our assumption that they are co-primes. Therefore, p/q is not a rational number
√2 is an irrational number.
Maria is ordering comic books online. The equation y=8x + 4 represents the total cost in dollars, y, including shipping, for ordering x number of comic books. If the total cost including shipping is $60, how many comic books is Maria ordering? Use the graph to help you determine the answer.
Answer:
x will be equal to 7 comic books
The number of books Maria is ordering is 7 books
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number of comic books Maria orders be = x
The cost of x books is = y
Now , the equation for the total cost be
y = 8x + 4 be equation (1)
Now , the total cost of all the books be = $ 60
So , substituting the value of y as 60 in equation (1) , we get
60 = 8x + 4
Subtracting 4 on both sides of the equation , we get
8x = 56
Divide by 8 on both sides of the equation , we get
x = 7 books
Therefore , the value of x is 7
Hence , The number of books Maria is ordering is 7 books
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Which of the following is the closest estimate to the value of n? 223÷72=n
Answer:
121
Step-by-step explanation:
Finding the angle when given the right angle and two sides. Please show explanation. Thank you.
The measure of angle A in the right triangle is 75.52°
What is the measure of angle A?The figure in the image is a right triangle.
Measure of angle A = ?
Adjacent to angle A = 2
Hypotenuse = 8
To solve for the measure of angle A, we use the trigonometric ratio.
Note: cosine = adjacent / hypotensue
Hence:
cos( A) = adjacent / hypotensue
cos( A ) = 2/8
cos( A ) = 1/4
Take the cos inverse
A = cos⁻¹( 1/4 )
A = 75.52°
Therefore, the measure of the angle is 75.52 degree.
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the set
of whole number less than 20
Answer:
maybe 3, 6, 9, 12, 15, 18?
Step-by-step explanation:
sorry if this doesn't help but I hope someone else can help you! good luck
Simplify the expression completely if possible.
x^{3}-8x^{2}}{x^2-64}
The simplified expression of \(\frac{x^{3}-8x^{2}}{x^2-64}\) is \(\frac{x^2}{x + 8}\)
How to simplify the expression?The expression is given as:
\(\frac{x^{3}-8x^{2}}{x^2-64}\)
Factor the numerator
\(\frac{x^{2}(x-8)}{x^2-64}\)
Express the denominator as a difference of two squares
\(\frac{x^{2}(x-8)}{(x-8)(x + 8)}\)
Cancel out the common factor
\(\frac{x^2}{x + 8}\)
Hence, the simplified expression of \(\frac{x^{3}-8x^{2}}{x^2-64}\) is \(\frac{x^2}{x + 8}\)
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Drag the prisms to the table in order from least volume to greatest volume.
Fourth prism, first prism, second prism and fourth prism is order from least volume to greatest.
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
The volume of first prism with sides 2, 1.5 and 3.2
Volume=2×1.5×3.2
=9.6 in³
The volume of second prism with sides 1.5, 1.5 and 6
Volume=1.5×1.5×6
=13.5 in³
The volume of third prism with sides 2, 5/2 and 7/2
Volume=2×2.5×3.5
=17.5 in³
The volume of fourth prism with sides 1/2, 1/2 and 1/2
Volume=0.5×0.5×0.5
=0.125 in³
Hence fourth prism, first prism, second prism and fourth prism is order from least volume to greatest.
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Weight of three books are 23⁄4 kg, 35⁄6 kg and 23⁄8 kg. Find the total weight of all the three books.
Answer:
12.54kg
Step-by-step explanation:
(23/4 + 35/6 + 23/8)kg
\( = \frac{(23 \times 6) + (35 \times 4) + (23 \times 3)}{24} \)
\( = \frac{92 + 140 + 69}{24} \)
= 301/24
= 12.54kg