Answer: x= 1/7y + 19/7 (Standard form will be:7x−y=19)
Step-by-step explanation:
Step 1: Add -y to both sides.
−7x+y+−y=−19+−y
−7x=−y−19
Step 2: Divide both sides by -7.
−7x/−7
= −y−19/−7
x= 1/7y + 19/7
Write an equation of the line that passes through the points (-7,-3) and (8, -3)
y=
Answer:
y = - 3
Step-by-step explanation:
Call the line y = a + bx (d)
Since d go through (-7;-3) so -7 = a - 3b (1)
Since d go through (8;-3) so 8 = a - 3b (2)
From (1) and (2), we have equations: [tex]\left \{ {{a - 3b = -7} \atop {a - 3b = 8}} \right.[/tex]
Solve the equations, we have [tex]\left \{ {{a = 0} \atop {b = -3}} \right.[/tex]
Suppose you want to save $5000 to put towards remodeling your house in 18 months. You found a bank whose interest rate for savings accounts is 4.5% compounded monthly, but you are unsure of how much to invest to have $5000 saved in 18 months.
Using the compound interest formula, how much should you invest in order to have $5000 saved in 18 months?
The required money to be invested in order to save $5000 is $4677.26.
What is compound interest?The compound interest is a form of interest where the rate of interest is applied on the amount obtained after every interval of time.
The principal for each interval is the sum of interest And the principal for the previous interval.
Suppose the amount to be invested be P.
The rate of interest for monthly compounding is given as 4.5/12 = 0.375%.
Time is given as 18 months.
This implies number of time period is 18.
Plug n = 18, r = 0.375% and A = 5000 in A = P(1 + r/100)ⁿ as,
⇒ 5000 = P(1 + 0.375/100)¹⁸
⇒ P = 4677.26
Hence, the amount of money that should be invested is obtained as $4677.26.
To know more about compound interest click on,
https://brainly.com/question/14295570
#SPJ2
What is the length of the short side of one of the 30 60 90 triangles?
Remembering the ratio of 1: 3: 2 and understanding that the smallest side length is always opposite the shortest angle (30°) and the longest side length is always opposing the greatest angle (90°) can help you recall the 30-60-90 triangle principles.
According to the 30-60-90 triangle theorem, the hypotenuse is twice as long as the shorter leg. Additionally, the sides of this particular triangle have a ratio of 1:2: [tex]\sqrt{3}[/tex].
A 30-60-90 triangle can have three sides, and if you only know one, you can use shortcuts to discover the other two. The three scenarios you encounter when performing these computations are as follows:
You are aware of the short leg (the side across from the 30-degree angle). To find the hypotenuse, multiply the length by two. The long leg can be calculated by multiplying the short side by the square root of 3.You are aware of the hypotenuse. To get the short side, divide the hypotenuse by two. To determine the long leg, multiply this response by the square root of 3.You are aware of the long leg (the side across from the 60-degree angle). To determine the short side, divide this side by the square root of 3. To find the hypotenuse, multiply that amount by two.To know more about the 30 60 90 triangles on brainly : brainly.com/question/11751274
#SPJ4
if x+3=9 whats the answer:)
enjoy
Answer:
x=6
Step-by-step explanation:
then x=6 because replacing x 6+3=9
How do you find the third angle of a triangle if two angles are given?
To find the third angle of a triangle if you know the measures of the other two angles, you can use the fact that the sum of the measures of the angles in any triangle is always 180 degrees.
For example, let's say you know that angle A measures x degrees and angle B measures y degrees. To find the measure of angle C (the third angle), you can use the following equation:
x + y + C = 180°
To solve for C, you can subtract x and y from both sides of the equation:
C = 180 - x - y
So, the measure of angle C is equal to 180 degrees minus the measure of angle A and angle B.
To know more on Angle sum property of a triangle
https://brainly.com/question/8492819
#SPJ4
Simplify the following: (3 + 10i) - (-9 - 4i)
*PLEASE INCLUDE EXPLANATION
Answer:
12+14i
Step-by-step explanation:
For -(-9-4i), you need to clean up the parentheses so you would distribute. -1 times -9 and -1 times -4i.
You will get 9+4i
Now you have 3+10i+9+4i. You will now add like terms. 10i+4i= 14i. 9+3= 12.
12+14i
brainliest pls
The function w (t) = 29 + 0.0674t gives the estimated weight, in pounds, of a beaver t days
after June 1, where t < 90. Which of the following is the best interpretation of 29 in this context?
1)The estimated weight, in pounds, of the beaver 90 days after June 1
2)The estimated weight, in pounds, of the beaver on June 1
3)The estimated number of pounds by which the beaver's weight increased each day after June 1
4)The estimated number of pounds by which the beaver's weight increased in the 90 days after
June 1
Answer:
2) The estimated weight, in pounds, of the beaver on June 1.
Step-by-step explanation:
Given function:
[tex]w(t) = 29 + 0.0674t \quad t < 90[/tex]
where:
w = weight of a beaver (in pounds)t = time after June 1 (in days)When t = 0:
[tex]\begin{aligned}\implies w(0)&=29+0.0674(0)\\&=29+0\\&=29\end{aligned}[/tex]
Therefore, the constant of the equation (29) is the estimated weight of the beaver, in pounds, when t = 0.
As t = 0 is June 1:
29 is the estimated weight, in pounds, of the beaver on June 1.Examine the graph of the function. The graph of a line that contains points (negative 1, 7), (0, 5), and (2, 1). © 2017 StrongMind. Created using GeoGebra. What is the initial value of the function? Enter your answer as a number, like this: 42
The initial value of the function is equal to 5.
How to determine the initial value of the function?In order to determine the initial value of the function, we would have to find the slope from line graph and then write the required equation based on the data points contained in the table by using the slope-intercept form.
Mathematically, the slope-intercept form of a line is modeled by this mathematical equation:
y = mx + c
Where:
m represents the slope.x and y are the data points.c represents the y-intercept or initial value.Next, we would determine the slope of the data points as follows;
Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope, m = (y₂ - y₁)/(x₂ - x₁)
Slope, m = (5 - 7)/(0 + 1)
Slope, m = -2/1
Slope, m = -2.
At point (0, 5), an equation of this line can be calculated in slope-intercept form as follows:
Note: The y-intercept or initial value is equal to 5.
y = mx + c
y = -2x + 5
Read more on slope here: brainly.com/question/3493733
#SPJ1
What is the least common multiple of 51, 68 and 85?
Answer:
1020
Step-by-step explanation:
the monthly cost for 43 min is $17.96 and the monthly cost for 94 min is $24.72 what is the monthly cost for 88 min
Therefore , the solution to this problem of equation is y = 16.95 cost for 94 minutes.
Explain the equation.A mathematical equation is a formula that links two statements by indicating their equivalence with the equal sign (=). A mathematical statement that proves the equality of two mathematical expressions is known as an equation in algebra. For instance, the components 3x + 5 and 14 in the equation 3x + 5 = 14 are separated by an equal sign. The relationship between two sentences on either side of a letter is expressed mathematically. There is frequently only one variable, which doubles as the symbol. say that 2x - 4 Equals 2.
Here,
y = mx + b
(50,13.98)(78,17.06)
slope = (17.06 - 13.98) / (78 - 50) = 3.08 / 28 = 0.11
slope(m) = 0.11
use either of ur points...(50,13.98)...x = 50 and y = 13.98
now sub into the formula and find b, the y int
13.98 = 0.11(50) + b
13.98 = 5.5 + b
13.98 - 5.5 = b
8.48 = b
so our equation is : y = 0.11x + 8.48.......for 94 minutes...sub in 77 for x
y = 0.11(94) + 8.48
y = 8.47 + 8.48
y = 16.95 <=== this is the cost for 94 minutes
Therefore , the solution to this problem of equation is y = 16.95 cost for 94 minutes.
To know more about equation visit:
https://brainly.com/question/649785
#SPJ1
what is 8 1/4 divided by d=2/11
When 8[tex]\frac{1}{4}[/tex] is divided by 2/11, we get 45[tex]\frac{3}{8}[/tex].
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the statement -
"8[tex]\frac{1}{4}[/tex] divided by 2/11"
We can write it as -
x = {8[tex]\frac{1}{4}[/tex]} ÷ {2/11}
x = 33/4 x 11/2
x = 363/8
x = 45[tex]\frac{3}{8}[/tex]
Therefore, when 8[tex]\frac{1}{4}[/tex] is divided by 2/11, we get 45[tex]\frac{3}{8}[/tex].
To solve more questions on expressions, visit the link below -
brainly.com/question/1041084
#SPJ2
Need answer for b)iii)
Answer:
3.23, -1.23
Step-by-step explanation:
Draw the line y=1
See where it intersects x^2-2x-3
The x coordinates of the intersections are your answer
(i) Write 3^-2 as a fraction
(ii) Find the value of 3X^0 when X=5
ans Is here i) 1/9
ii) 3
tq brainlest?
What is the median of the following 9 numbers: 23, 15, 32, 27, 19, 11, 30, 19, 22?
The median of the following 9 numbers 23, 15, 32, 27, 19, 11, 30, 19, 22 will be 22.
What is a median?The median of the data is the middle value of the data which is also known as the central tendency of the data and is known as the median.
The median for odd data will be
Median = [(n + 1) / 2]th
The median for even data will be
Median = {[n / 2 + (n + 2)/ 2] / 2}th
The data is given below.
23, 15, 32, 27, 19, 11, 30, 19, 22
Arrange the data in ascending order. Then we have
11, 15, 19, 19, 22, 23, 27, 30, 32
Then the median of the following 9 numbers is calculated as,
Median = [(9 + 1) / 2]th
Median = (10 / 2)th
Median = 5th
Median = 22
The median of the following 9 numbers 23, 15, 32, 27, 19, 11, 30, 19, 22 will be 22.
More about the median link is given below.
https://brainly.com/question/300591
#SPJ1
Given g(x) = -x + 5, find g(-6).
Answer:
g(- 6) = 11
Step-by-step explanation:
substitute x = - 6 into g(x) , that is
g(- 6) = - (- 6) + 5 = 6 + 5 = 11
Answer:
11
Step-by-step explanation:
g(x) = -x + 5
Let x = -6
g(-6) = -(-6) + 5
=6+5
=11
The temperature in knowlton is 2.5 C colder than the terminal elmwood. Which equation shows the temperature, in C, in knowlton? 9 - 2.5 = 6.5 or 9 + 2.5 = 11.5 or -9 - 2.5 = - 11.5 or -9 + 2.5 = -6.5
The equation representing the asked situation is (9 - 2.5) = 6.5
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that, The temperature in Knowlton is 2.5 C colder than the terminal Elmwood.
We know, that, if temperature is colder in any area A than another area B then, A will have less temperature than B.
Therefore, temperature in Knowlton is less than that of in Elmwood.
Therefore, if the temperature in Elmwood is 9 the temperature in Knowlton will be 9-2.5 = 6.5
Hence, the required equation is 9-2.5 = 6.5
For more references on equation, click;
https://brainly.com/question/29657983
#SPJ1
Which expression is equivalent to (-3) × (-3)²?
Answer:
[tex] \sf \: (-3) × {( - 3)}^{2} = - 27[/tex]
Step-by-step explanation:
Given expression,
→ (-3) × (-3)²
Let's simplify the expression,
→ (-3) × (-3)²
→ (-3) × ((-3) × (-3))
→ (-3) × 9
→ (-3 × 9) = -27
Hence, the answer is -27.
Select all expressions that are equivalent to 8.5x + 0.5 +3.5x - 2x
12x - 2x 10x
10x + 0.5
12-2x
9x + 3.5 - 2x
12x - 2x + 0.5
To see if it makes more sense… I added a photo of the problem on my hw
All expressions that are equivalent to 8.5x + 0.5 +3.5x - 2x are (12x - 2x + 0.5) and (10x + 0.5).
What are Equivalent expressions:Expressions that are equivalent perform the same thing even when they have distinct appearances.
When we enter the same value for the variable, two algebraic expressions that are equivalent have the same value.
By combining like terms, we can create expressions that are equivalent to a given expression. Terms with the same variables raised to the same powers are said to be "like terms".
Here we have
8.5x + 0.5 +3.5x - 2x
The above expression can be simplified as given below
=> 8.5x + 0.5 +3.5x - 2x
Add and subtract like terms
=> 8.5x +3.5x - 2x + 0.5
=> 12x - 2x + 0.5
=> 10x + 0.5
Therefore,
All expressions that are equivalent to 8.5x + 0.5 +3.5x - 2x are (12x - 2x + 0.5) and (10x + 0.5).
Learn more about Equivalent expressions at
https://brainly.com/question/24242989
#SPJ1
7.9 , 8.37 , 7.293 , 7.785 , 7.476 greatest to least..pls help!!
Answer: 7.785,7.476,7.293,8.37.7.9
Step-by-step explanation:
The graph shows the cost of grapes at a grocery store. What is the slope of the line?
The slope of the line that passes through the graph is 3
How to calculate the slope of the line?From the graph, the points are given as
(0, 0) and (1, 3)
Rewrite the above points properly
So, we have the following ordered pairs
(x, y) = (0, 0) and (1, 3)
The slope of the line is then calculated using the following slope equation
Slope = (y₂ - y₁)/(x₂ - x₁)
Where
(x, y) = (0, 0) and (1, 3)
Substitute the known values in the above equation
So, we have the following equation
Slope = (3 - 0)/(1 - 0)
Evaluate
Slope = 3
Hence, the slope of the line is 3
Read more about slope at
brainly.com/question/3493733
#SPJ1
Can u please help.............
The rotation about the center that can map an equilateral triangle onto itself is C. 120 degrees.
What angle rotates an equilateral triangle onto itself ?There are three equal sides and angles in an equilateral triangle which is 60 degrees each. This means that an equilateral triangle can be divided into three-axis of symmetry such that there are three lines dividing the triangle.
Should this happen, then the angle to rotate the triangle and map it onto itself would be 120 degrees as each of these axes of symmetry measure 120 degrees.
Find out more on equilateral triangles at https://brainly.com/question/1827646
#SPJ1
When treated with an anabiotic, 97% of all the dolphins are cured of an ear infection. if 6 dolphins are treated find the probability that exactly 3 are cured.
The probability is _____
(Round your answer to 4 decimal places.)
Answer:
0.0005
Step-by-step explanation:
this is a binomial experiment -- they are either cured or not, and the outcome is random
probability = n choose r * p^r * q^(n-r)
here, n = number of trials, r = number of successes desired, p = probability event occurs, and q = probability event doesn't occur
probability = n choose r * p^r * q^(n-r) = 6 choose 3 * 0.97^3 * 0.03^(6-3)
= 0.00049284342 rounding to 0.0005
What property is illustrated in if ∠a ≅ ∠B ∠B ≅ ∠C then ∠a ≅ ∠CA reflexive property C transitive property B symmetric property d addition property?
The property of congruence illustrated in the statement is the transitive property.
What is transitive property?The transitive property states that if A is congruent to B and B is congruent to C, then A is congruent to C. In other words, if two things are congruent to a third thing, they are also congruent to each other.
here,
In the statement "If AB ≅ DE, EF ≅ DE then AB ≅ EF," AB is congruent to DE, and EF is congruent to DE, so AB must also be congruent to EF according to the transitive property.
The other properties you listed are not applicable in this case. The symmetric property states that if A is congruent to B, then B is congruent to A. The reflexive property states that every object is congruent to itself. And multiplication is not a property of congruence.
Learn more about the property of congruence at
brainly.com/question/2039214
#SPJ4
What is the median of the distinct positive values of all of the fractions less than or equal to 1 with positive integer denominators less than or equal to 5
The median of the distinct positive values of all of the fractions less then or equal to 1 with positive integer denominators less than or equal to 5 is 11/20.
In the statistics, the median is the value in the middle of a data set. It means that 50% of data points have a value smaller or equal to the median and 50% of data points have a value higher or equal to the median. The middle number is found by ordering all data points and picking out the one in the middle or if there are two middle numbers, taking the mean of those two numbers. We have to arrange data values from lowest to highest value. The median is the data value in the middle of the set. If there are 2 data values in the middle the median is the mean of those 2 values.
The set of numbers are,
1 /5, 1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 1
we have to take the average of middle two .
The middle of the set are 1/2 and 3/5. and the average of these two is 11/20.
To learn more about Median please visit:
https://brainly.com/question/26151333
#SPJ4
A 5 m 60 cm high vertical pole cat a hadow 3 m 20 cm long. Find at the ame time
(i) the length of the hadow cat by another pole 10 m 50 cm high,
On solving the provided question we can say that equation formed is x/y = k, x = ky => y₂ = (10.5 × 3.2) / 5.6 => y₂ = 6
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
x/y = k, x = ky
where k is a constant.
Thus, x₁ / y₁ = x₂ / y₂
5.6 / 3.2 = 10.5 / y₂
5.6 × y₂ = 10.5 × 3.2
y₂ = (10.5 × 3.2) / 5.6
y₂ = 6
To know more about equation visit:
https://brainly.com/question/649785
#SPJ4
What linear equation means?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included.
When a linear equation is graphed, it always produces a straight line since each term in the equation has an exponent of 1 or 0. A linear equation is an algebraic equation. If an equation has the formula y=mx+b, with m representing the slope and b the y-intercept, it is said to be linear.
The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.
You can learn more about linear equation at
https://brainly.com/question/2030026
#SPJ4
A "Pick 2" lottery game involves drawing 2 numbered balls from separate bins each containing balls labeled from 0 to 9. So there are 100 possible selections in total: 00, 01, 02, ..., 98, 99. Players can choose to play a "straight" bet, where the player wins if they choose both digits in the correct order. Since there are 100 possible selections, the probability a player wins a straight bet is 1/100. The lottery pays $50 on a successful $1 straight bet, so a player's net gain if they win this bet is $49. Let X represent a player's net gain on a $1 straight bet. Calculate the expected net gain E(X). Hint: The expected net gain can be negative. E(X) = dollars
Answer:
The probability of winning a straight bet is 1/100, and the payout is $50, so the expected value of a winning bet is (1/100) * $50 = $0.50.
The probability of losing a straight bet is 99/100, and the cost of the bet is $1, so the expected value of a losing bet is (99/100) * -$1 = -$0.99.
Therefore, the expected value of a straight bet is $0.50 - $0.99 = -$0.49.
The points (14, –3) and (–10, –3) fall on a particular line. What is its equation in slope-intercept form?
y = -3
Step-by-step explanation:Slope intercept form is y = mx + c.
"m" is the slope and "c" is the y-interecept.
The slope is calculated by dividing the change in y values by change in x values. However, you can see from these two points that as the value of x changes, the value of y stays the same (-3). This means the slope is zero, as it doesn't move up in the y-direction at all.
This means y = 0x + c
You can substitute 14 for y and -3 for x from the first point to get:
-3 = 0(14) + c
-3 = c
y = 0x + -3
Which is the equation of the line in slope-intercept form.
This is the same as saying y = -3, as for every x value, y will always be -3.
Identify the two x values?
When the points are (4, 2) and (6, 5), the slope is 3/2. The slope of a line determines its direction and degree of steepness.
what is slope ?A line's steepness and direction are determined by the slope of the line. The change in a line's y coordinate relative to its change in x coordinate is referred to as the line's slope. While there has been no net change in the x coordinate, there has been no net change in the y coordinate. hence, the shift in the y coordinate in relation to the shift in the x coordinate. The slope of a line is the rise to run ratio, or the rise divided by the run. It gives information about a line's slope in the coordinate plane. Any two clearly separated points on a line can be used to calculate the slope of any line.
given
slope = [tex]m = \frac{y2 - y1}{x2 - x1}[/tex]
points are ( 4, 2 ) and ( 6, 5)
[tex]\frac{5 - 2}{6 - 4} \\= \frac{3}{2}[/tex]
hence the slope is 3 / 2 .
To know more about slope visit :-
https://brainly.com/question/3605446
#SPJ1
Ron's car uses 12 L of gasoline per 100 km of highway driving. Asma's car as 5/6 as much fuel. How much fuel does Asma's car use per 100 km of highway driving?
10L fuel does Asma's car use per 100 km of highway driving
In this question, we have to use the unitary method
The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
What is a unitary in math?
a unitary state. (mathematics, of an algebra) That contains an identity element. (mathematics, linear algebra, mathematical analysis, of a matrix or operator) Whose inverse is equal to its adjoint.
So from the unitary method, we can solve it
12 L of gasoline per 100 km
so for 5/6
12 L * 5/6
= 10 L
Learn more about the unitary method here:
brainly.com/question/24587372
#SPJ4