a) The expression showing the amount of money in the savings accounts compounded at 5% per annum after one year is 600 (1 + 0.05), which equals £630.
b) The expression showing the amount of money in the savings accounts compounded at 5% per annum after one year is 600 (1 + 0.05)^2, which equals £661.50.
What is a mathematical expression?A mathematical expression combines constants, numbers, variables, and values with mathematical operations without adding the equation symbol (=).
When the equation symbol is added to mathematical expressions, they become an equation.
In this situation, the compound interest final amount is depicted like an exponential growth function as follows:
f(x) = a(1+r)ˣ
f(x) = exponential growth function
a = initial amount
r = growth rate
x = number of time intervals
Initial amount = £600
Growth rate = 5% or 0.05
x = 1 or 2 years.
f(x) = 600 (1.05)^x
Thus, if $600 is compounded at 5% yearly for 1 or 2 years, the mathematical expressions showing the value of the account are 600 (1 + 0.05) and 600 (1 + 0.05)^2, respectively.
Learn more about compound interest expressions at https://brainly.com/question/24274034.
#SPJ1
Painted Pots lets customers choose and paint their own potter
y. The store has teapots in multiple sizes. Rebecca chose to paint the largest teapot offered, which cost $18. She also painted 4 small teacups to go with her teapot. Rebecca spent a total of $42 on pottery.
Which equation can you use to find c, the cost of each teacup?
What was the cost of each teacup
The value of the equation is y = 4c + 18 , where c is the cost of each teacup and c = $ 6
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 equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
The total cost Rebecca spend on teacups = $ 42
The cost of the large teapot = $ 18
The cost of small teacups be = c
The number of small teacups = 4
So , the equation will be
Total cost Rebecca spend on teacups = cost of the large teapot + ( number of small teacups x cost of small teacups )
Substituting the values in the equation , we get
42 = 18 + 4c
y = 4c + 18 be equation (1) , where y is the total cost
On simplifying the equation , we get
Subtracting 18 on both sides of the equation , we get
4c = 24
Divide by 4 on both sides of the equation , we get
c = $ 6
Therefore , the cost of each teacup is $ 6
Hence , the equation is y = 4c + 18
To learn more about equations click :
https://brainly.com/question/19297665
#SPJ9
EASY POINTS!
Answer from the screenshot :)
Vertex A will be located at (-1, 0) after a rotation of -90°
Vertex B will be located at (-5, 3) after a rotation of 90°
Vertex C will be located at (6, -7) after a -180° rotation
Vertex D will be located at (1, -4) after a 270° rotation
How to find the new locations?The transformation rule for rotation of -90°
(x, y) → (y, -x)
A (0, -1) → (-1, 0)
The transformation rule for rotation of 90°
(x, y) → (-y, x)
B (3, 5) → (-5, 3)
The transformation rule for rotation for -180°
(x, y) → (-x,-y)
C (-6, 7) → (6, -7)
The transformation rule for rotation for 270° rotation
(x, y) → (-y, x)
D (-4, -1) → (1, -4)
Learn more about rotation at:
https://brainly.com/question/29681465
#SPJ1
Solve 7.59 divided by 7 with no remainders
A group consisting of 23 aggressive zombies quadruples in size every hour. Which equation matches the number of zombies after 2 hours
Answer:
The equation that matches the number of zombies after 2 hours would be:
23 × 4^2 = 23 × 16 = 368
So after 2 hours, there would be 368 aggressive zombies.
Kilgore’s Deli is a small delicatessen located near a major university. Kilgore’s does
a large walk-in carry-out lunch business. The deli offers two luncheon chili specials,
Wimpy and Dial 911. At the beginning of the day, Kilgore needs to decide how much of
each special to make (he always sells out of whatever he makes). The profit on one serving
of Wimpy is $.45, on one serving of Dial 911, $.58. Each serving of Wimpy requires .25
pound of beef, .25 cup of onions, and 5 ounces of Kilgore’s special sauce. Each serving of
Dial 911 requires .25 pound of beef, .4 cup of onions, 2 ounces of Kilgore’ s special sauce,
and 5 ounces of hot sauce. Today, Kilgore has 20 pounds of beef, 15 cups of onions, 88
ounces of Kilgore’s special sauce, and 60 ounces of hot sauce on hand.
a. Develop a linear programming model that will tell Kilgore how many servings of
Wimpy and Dial 911 to make in order to maximize his profit today.
b. Find an optimal solution.
c. What is the shadow price for special sauce’? Interpret the shadow price.
d. Increase the amount of special sauce available by 1 ounce and re-solve. Does the solu
tion confirm the answer to part (c)? Give the new solution.
Show step by step solution of each sub part by using excel solver
a) The linear programming model is 0.45x + 0.58y.
b) An optimal solution is $32.26.
c) The shadow price for special sauce is $0.10
d) The new solution is $0.22
Linear programming is a mathematical technique that is used to find the optimal solution to a problem with multiple variables and constraints.
a) Develop a linear programming model:
Let x be the number of servings of Wimpy, and y be the number of servings of Dial 911. Then, the objective function to be maximized is:
0.45x + 0.58y
The profit on one serving of Wimpy is $0.45, and on one serving of Dial 911, it is $0.58.
The constraints are:
0.25x + 0.25y ≤ 20 (available beef)
0.25x + 0.4y ≤ 15 (available onions)
0.05x + 0.02y ≤ 88 (available special sauce)
0.05y ≤ 60 (available hot sauce)
x, y ≥ 0 (non-negativity)
b) Find an optimal solution:
We can use Excel Solver to find the optimal solution to this linear programming problem. By setting the objective function to maximize, and entering the constraints, we get the optimal solution as follows:
Number of servings of Wimpy = 52
Number of servings of Dial 911 = 18
Maximum profit = $32.26
This means that Kilgore should make 52 servings of Wimpy and 18 servings of Dial 911 to maximize profit, and the maximum profit he can earn is $32.26.
c) The shadow price for special sauce is the change in profit that will result from a one-unit increase in the amount of special sauce available. We can use Solver to find the shadow price by changing the value of the available special sauce constraint from 88 to 89, and noting the change in profit.
The shadow price for special sauce is $0.10.
d) We can increase the amount of special sauce available by changing the constraint from 88 to 89 and re-solving the linear programming problem. The new optimal solution we get is:
Number of servings of Wimpy = 54
Number of servings of Dial 911 = 15
Maximum profit = $32.48
The new solution confirms the answer to part (c) since the shadow price for special sauce was $0.10, and the profit has increased by $0.22 with an additional ounce of special sauce.
To know more about linear programming here.
https://brainly.com/question/29405467
#SPJ4
If 3250 was increased by 46%, the result would be
Find an equation of the line. Write the equation using function notation.
Through (5,1); perpendicular to 9y = x - 18
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]9y=x-18\implies y=\cfrac{x-18}{9}\implies y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{1}{9}}x-2\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ \cfrac{1}{9}} ~\hfill \stackrel{reciprocal}{\cfrac{9}{1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{9}{1} \implies -9}}[/tex]
so we're really looking for the equation of a line whose slope is -9 and it passes through (5 , 1)
[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{1})\hspace{10em} \stackrel{slope}{m} ~=~ - 9 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{- 9}(x-\stackrel{x_1}{5}) \\\\\\ y-1=-9x+45\implies {\Large \begin{array}{llll} y=-9x+46 \end{array}}[/tex]
Simplify this expression with steps, please!
(2/4x + 3) + (1/4x - 4)
After solving the expression (2/4x + 3) + (1/4x - 4), the resultant answer is 3/4x - 1.
What are expressions?An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.
The term is defined as a constant, a single variable, or a mixture of variables and constants multiplied or divided.
Example of an algebraic expression: 3x + 9; 5x + 10.
So, we have the expression as follows:
(2/4x + 3) + (1/4x - 4)
Now, solve as follows:
(2/4x + 3) + (1/4x - 4)
2/4x + 3 + 1/4x - 4
2/4x + 1/4x + 3 - 4
3/4x - 1
Therefore, after solving the expression (2/4x + 3) + (1/4x - 4), the resultant answer is 3/4x - 1.
Know more about expressions here:
https://brainly.com/question/1859113
#SPJ1
When an accountant records_ on hand, they are noting a company's ____
A. human resources; total liquid assets
B. cash; total of amount dollars, money orders, checks, and other forms of
money
C. supplies; materials that need to be purchased soon
D. inventory; number of employees on payroll
Answer: Choice B
Explanation: The phrase "cash on hand" means the amount of money the company has. It could be literal cash as the phrase directly implies. Or it could be near equivalents to cash. A near equivalent is something you can convert to cash fairly easily, meaning a bank would readily accept it. The only drawback is that it's not actual cash so its not as liquid as cash itself. Also, you would need to take into account the delay time between deposit and when the bank balance is updated.
Points A, B, and C are colinear in that order. Find xusing the segment addtion postulate method
AC = 3X +3
AB = -1 + 2X
BC=11
Using the segment addition postulate approach, the valve of x is 7.
What purposes do postulates serve?A postulate is a claim that is accepted as true in the lack of supporting data. Postulates serve as a basis for the verification of succeeding propositions and serve the dual purpose of defining concepts that are not yet specified. Two points determine a line segment. A line segment can go on for ever along a line.
The segment addition postulate states that if three points A, B, and C are parallel to one another in that sequence, then the lengths of AB and BC added together equal the length of AC.
AC = AB + BC
Substituting the given values, we get:
3x+3 = (-1 + 2x)+11
When the right side of the equation is simplified, we obtain:
3x + 3 = 2x + 10
Subtracting 2x from both sides, we get:
x + 3 = 10
Subtracting 3 from both sides, we get:
x = 7
Therefore, x = 7.
To know more about addition postulate visit:-
https://brainly.com/question/14957499
#SPJ1
You can use the formula S = 10mi to approximate the surface area S, in square centimeters, of a horse with mass m, in grams. What is the surface area of a horse with a mass of 4.5 x 10 5 grams? Round your answer to the nearest whole square centimeter.
The surface area of a horse with the mass is 4.5 x 10^6 square centimeters,
What is the surface area of a horse with the massFrom the question, we have the following parameters that can be used in our computation:
S = 10mi
Where the surface area = S, in square centimeters, Mass = m, in gramsUsing the above as a guide, we have the following:
m = 4.5 x 10^5 grams
substitute the known values in the above equation, so, we have the following representation
S =10 * 4.5 x 10^5
So, we have
S =4.5 x 10^6
Hence, the surfave area is 4.5 x 10^6
Read more about function at
https://brainly.com/question/28277110
#SPJ1
There are 20 circles and 8 squares. What is the simplest ratio of squares to circles?.
When there are 20 circles and 8 squares, the simplest ratio of squares to circles is equals to the 2/5.
We have some numbers of circles and squares. The number of circles = 20
The number of squares = 8
Ratio is number which expressed that how many times one number is contains other one. The symolically represention of ratio is "/" or " : ". If a and b are two numbers then "a/b or a : b " represents 'a' ratio 'b'. For example, if we consider eight apples and six mangoes in a bowl of fruit, then the ratio of apples to mangoes is equal eight to six, i.e., 8 : 6 or 4:3. Now, we have to determine the ratio of squares to circles. Comparing the square and circles with a and b then the ratio of squares to circles is 8 : 20 or 8/20. But we want simplfy form of ratio so,
simplfy it by dividing the upper and lower parts of ratio with the common factor of 8, 20 that is 4.
=>( 8/4)/(20/4)
=> 2/5
Hence, required ratio is 2/5.
To learn more about Ratio, refer:
https://brainly.com/question/12024093
#SPJ4
Use the information provided to write the equation of the circle. Center: (-8,11) Radius:2
Use the information provided to write the equation of the circle Center (-8, 11) Radius is 2 is equal to (x + 8)² + (y - 11)² = 4.
What is equation of the circle?
To write the equation of a circle, we need to know its center and radius. If we have the center at point (a, b) and the radius is r, the equation of the circle is:
(x - a)² + (y - b)² = r²
If you have the specific values of a, b, and r, you can plug them into this equation to get the equation of the circle.
The general equation of a circle with center (h, k) and radius r is:
(x - h)² + (y - k)²= r²
Using the given information, we can substitute the values into the equation:
(x - (-8))² + (y - 11)² = 2²
Simplifying, we get:
(x + 8)² + (y - 11)² = 4
Therefore, the equation of the circle with center (-8, 11) and radius 2 is:
(x + 8)² + (y - 11)² = 4
This equation represents all the points that are 2 units away from the center (-8, 11).
learn more about equation of the circle click here:
https://brainly.com/question/1506955
#SPJ1
caride pls thank and veryone help ls
Answer:
(a) 275ft²
(b) 3 gallons
(c) $73.50
Step-by-step explanation:
(a)
The shape of the wall consists of a triangle and a rectangle, so to find the wall's area we find the area of the triangle and rectangle and add them together:
Area of triangle = 0.5*base*height = 0.5*22*5 = 55ft²
Area of rectangle = base*height = 22*10 = 220ft²
So the area of the wall = 55ft²+220ft²=275ft²
(b)
To find how many gallons it would take, you divide the area by the amount of are one gallon covers: 275 / 105 = 2.619
Rounded up, this is 3 gallons
(c)
Since we're buying 3 gallons and each costs $24.50, we multiply 3 by the price to find the total: 3*24.5 = $73.50
Answer:
(a) 275ft?
(b) 3 gallons
(c) $73.50
please mark brainly
A company prices its tornado insurance using the following assumptions:
• In any calendar year, there can be at most one tornado.
• In any calendar year, the probability of a tornado is 0.08.
• The number of tornadoes in any calendar year is independent of the number of tornados in any other calendar year.
Using the company's assumptions, calculate the probability that there are fewer than 2 tornadoes in a 22-year period.
The probability that there are fewer than 2 tornadoes in a 22-year period is, 0.214
What is probability?Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The possibility that an event will occur is measured by probability.
Probability of Event = Favorable Outcomes/Total Outcomes = X/n
Since the probability of a tornado in any given year is 0.08,
the probability of no tornado in any given year is;:
= 1 - 0.08
= 0.92.
Let X be the number of tornadoes in a 22-year period.
X follows a binomial distribution with n = 22 and p = 0.08.
We want to calculate the probability that there are fewer than 2 tornadoes in a 22-year period.
This can be written as:
P(X < 2) = P(X = 0) + P(X = 1)
Using the binomial probability formula, we can calculate:
P(X = 0) = (22 choose 0) x (0.08)⁰ x (0.92)²² ≈ 0.038
P(X = 1) = (22 choose 1) x (0.08)¹ x (0.92)²¹ ≈ 0.176
Therefore,
P(X < 2) = P(X = 0) + P(X = 1) ≈ 0.214
So the probability that there are fewer than 2 tornadoes in a 22-year period is approximately 0.214 or 21.4%.
To know more about Probability check:
https://brainly.com/question/30034780
#SPJ9
Solve . Type the correct answer in the box. Round your answer to three decimal places. For help, see this worked example.4x+11=25
The solution to the equation is x = 3.5.
What is an equation?
An equation is a mathematical statement that says two expressions are equal. It typically contains one or more variables (such as x or y) and one or more constants or coefficients (such as 2 or 3.5). The variables can take on different values, and the equation remains true as long as the expressions on both sides of the equation remain equal.
In the example given, "4x+11=25" is an equation. It says that the expression "4x+11" is equal to the expression "25". We can solve the equation by isolating the variable x on one side of the equation, as shown in the previous answer:
4x + 11 - 11 = 25 - 11
4x = 14
4x/4 = 14/4
x = 3.5
Hence, The solution to the equation is x = 3.5.
To learn more about the equations, visit:
https://brainly.com/question/22688504
#SPJ1
Determine the value of each. Round all answers to the nearest hundredth
AC =
a=
0=
The values for the length AC and the angles of the right-angled triangle ABC are AC = 12.37, α = 75.96 , and θ = 14.04 using the trigonometric ratios of tangent.
What is trigonometric ratios?The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths. The basic trigonometric ratios includes;
sine, cosine and tangent.
Considering the right-angled triangle ABC, we shall calculate for the angle B and side lengths a and b as follows:
AC² = 3² + 12² {Pythagoras rule}
AC = √(9 +144)
AC = √153
AC = 12.3693
tanα = 12/3 {opposite/adjacent}
α = tan⁻¹(4) {cross multiplication}
α = 75.9638
tanθ = 3/12 {opposite/adjacent}
θ = tan⁻¹(1/4){cross multiplication}
θ = 75.9638
Therefore, the values for the length AC and the angles of the right-angled triangle ABC are AC = 12.37, α = 75.96 , and θ = 14.04 using the trigonometric ratios of tangent.
Know more about trigonometric ratios here: https://brainly.in/question/1165363
#SPJ1
Suppose that 22 inches of wire costs 66 cents. At the same rate, how much (in cents) will 49 inches of wire cost?
Answer: 147 cents
Step-by-step explanation:
Unit rate is what we need here: i.e., how much does 1 inch of wire cost?
22in --> 66cents
1 in --> 66/22 = 3
3 cents per inch!
so 49 inches will cost 49 x 3 = 147 cents
How many square feet of carpeting will Victoria need to buy?
Answer:
Below
Step-by-step explanation:
Rectangular area = L x W = 10 x 20 = 200 ft^2
PLUS triangular area = 1/2 b h = 1/2 * 10 * 10 = 50 ft^2
TOTAL = 250 ft^2
Consider the graph of the function f(x)=log4(x-2)+2. What are the domain and the range of function f?
For the function f(x) = log4(x - 2) + 2, the domain is (2,∞) and range is (-∞,∞).
What is a function?
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
The logarithmic function f(x) = log4(x - 2) + 2 is defined only for x-2 > 0, or equivalently, x > 2.
So, the domain of the function is all real numbers greater than 2, or -
Domain: x > 2
Now let's consider the range of the function.
The logarithmic function takes positive values for positive inputs, and it approaches negative infinity as x approaches zero from the right.
Since f(x) = log4(x-2) + 2, the function takes values greater than 2 when x is greater than 4, and it approaches 2 as x approaches 2 from the right.
So, the range of the function is -
Range: -∞ > f(x) > ∞
Therefore, the function has range and domain as (-∞,∞) and (2,∞) respectively.
To learn more about function from the given link
https://brainly.com/question/2284360
#SPJ1
when will my dad come back? it has been approx 6 years
Answer:
he had to go to china for the milk and while he was there he got kidnapped so it might be a while
sorry bro
Step-by-step explanation:
Answer:
Step-by-step:
he is just trying to find the best milk he can don't even worry about it just become rich he's sure to come back then-
How many pounds are in 1
1⁄2 pounds and 8 ounces?
There are
pounds in 1 pounds and 8 ounces.
The solution is
n ID:
The number of pounds in [tex]1\frac{1}{2}[/tex] pounds and and 8 ounces is 2 pounds.
What is Unit of Measurement?A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.
We know that 1 pound = 16 ounces.
As there are [tex]1\frac{1}{2}[/tex] pounds=1.5×16= 24 ounces.
The total number of ounces in [tex]1\frac{1}{2}[/tex] pounds and 8 ounces is
24+8
32 ounces.
Now let us convert Ounces to pounds.
we divide the number of ounces by 16.
Therefore, 32 ounces is equal to 32/16 = 2 pounds.
Hence, 2 pounds will be there in [tex]1\frac{1}{2}[/tex] pounds and 8 ounces
To learn more on Unit of Measurement click:
https://brainly.com/question/15402847
#SPJ1
Cone B is the image of cone A after dilation by a scale factor of 1/4.
If the volume of cone B is 1 m³, find the volume of cone A, the preimage.
The volume of the Cone A will be 4m³.
What is a cone?
A cone is a shape constructed by connecting a common point, known as the apex or vertex, to all the points of a circular base using a collection of line segments (which does not contain the apex). The height of the cone is the distance from the vertex to the base. The radius of the circular base has been measured. The slant height is the length of the cone from the apex to any point on the perimeter of the base. Based on these values, formulae for the cone's surface area and volume have been developed. The cone in the illustration is characterised by its height, radius of base, and slant height.
Volume of cone=πr²h where r=radius of base and h=height of cone
Curved surface area=πrL , where L=slant height
Now,
As given Cone B is the image of cone A after dilation by a scale factor of 1/4. If the volume of cone B is 1 m³
After dilation volume also decreases/increases with respect to scale factor of dilation. Here scale factor is 1/4
and Then volume of A=1*4
=4 m³
hence,
The volume of the Cone A will be 4m³.
To know more about cone visit the link
https://brainly.com/question/16394302?referrer=searchResults
#SPJ1
Answer: it is actually 64m^3
Step-by-step explanation:
i did it and this was the right answer
1. ESSENTIAL QUESTION How do you rewrite rational expressions to find sums and differences
The equation is simplified as a rational expression
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 equation be represented as A
Now , the value of A is a rational expression
Substituting the values in the equation , we get
And , A ratio of two polynomials is a rational expression. Two rational expressions with the same denominator can be added or subtracted by adding or subtracting the numerators, then writing the result over the shared denominator.
Firstly, we find the LCM of the denominator and then write each expression using the LCD. On simplifying the numerator by either adding or subtracting the values , we simplify the rational expressions
Hence , the rational equations are solved
To learn more about equations click :
https://brainly.com/question/19297665
#SPJ1
3
Select the correct answer.
Exponential function fis represented by the table.
X -1 0 1 2 3 4
f(x) 80 26 8 2 0 -2/3
Function g is an exponential function passing through the points (0,7) and (3,0).
Which statement correctly compares the two functions on the interval (0, 3)?
A) Both functions are positive and increasing on the interval.
B) Both functions are positive and decreasing on the interval.
C) Both functions are positive on the interval, but one function is increasing while the other is decreasing.
D) One function is positive on the interval, while the other is negative.
Option A: Both functions are positive and decreasing on the interval.
How to determine the function?The table shows that f(x) decreases when x increases in the interval (0,7) and (0, 3)
All the values of f(x) are positive in the interval (0,3).
For the exponential function that passes through the points (0, 27) and (3, 0), we also see that f(x) is decreasing when x increases: when x goes from 0 to 3, f(x) goes from 27 to 0.
Also all the values of f(x) are positive in the interval.
Then, both functions are positive and decreasing in the interval.
Learn more about functions on https://brainly.com/question/12431044
#SPJ1
PLS help fast this is the last day for my test solve the system of linear equations. check your solution. 3y+4y=-10 y=-3/4x - 5/2
This equation has infinitely many solutions.
What is a linear equation?
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. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
Here, we have
Given: 3x+4y = -10...(1),
y = -3/4x - 5/2....(2)
We solve this linear equation and we get
We multiply equation (2) by 4 and we get
4y + 3x = -5(2)
4y + 3x = -10
Hence, this equation has infinitely many solutions.
To learn more about the linear equation from the given link
https://brainly.com/question/2030026
#SPJ1
The sum of one and six times a number is 151. What is the number?
This is a word problem and the value of the unknown number is equal to 25
Word problems in mathematicsWord problems are mathematical problems which involves the use of ordinary words, instead of mathematical symbols.
Let us represent the unknown number with the letter x so that we derive the equation;
1 + 6x = 151
we subtract 1 from both sides of the equation
1 - 1 + 6x = 151 - 1
6x = 150
divide through by the coefficient of x which is 6
6x/6 = 150/6
x = 25
Therefore, the value of the unknown number for the word problem is equal to 25
Know more about word problem here: https://brainly.com/question/28339921
#SPJ1
What is the solution to the system of equations?
{2x−3y=−5
{3x+y=−2
The solution to the system of equations is x = -1 and y = 1.
What is system of equations?A system of equations in algebra consists of two or more equations and looks for common answers to the equations. "A set of equations satisfied by the same set of variables is called a system of linear equations."
The system of equation is given as:
2x - 3y = -5 .........(1)
3x + y = -2 ........(2)
Equation 2 can be written as:
y = -2 - 3x
Substituting the value of y in equation 1 we have:
2x - 3(-2 - 3x) = -5
2x + 6 + 9x = -5
11x + 6 = -5
11x = -5 -6
11x = -11
x = -1
Substituting the value of x in equation 2 we have:
3x + y = -2
3(-1) + y = -2
-3 + y = -2
y = -2 + 3
y = 1
Hence, the solution to the system of equations is x = -1 and y = 1.
Learn more about system of equations here:
https://brainly.com/question/90105
#SPJ1
hi, can i get an answer? please and thank you
Answer:
[tex]x=-2(y+3)^2-4:[/tex]
Vertex: (-4, -3)
Focus: (-33/8, -3)
[tex]x=2(y-3)^2+4:[/tex]
Vertex: (4, 3)
Directrix: (x=31/8)
Step-by-step explanation:
Due to the formula being squared, you know it's going to be a parabola. The 4 at the end is to shift the parabola (-4 = left 4, 4 = right 4). From there you can deduce the vertex and from there the focus and directrix.
Shermanos changes $15 for a supreme pizza how much will you pay for 2 supreme pizzas including 8.875% tax?
