Answer:
a. $195
b. $4,195
Step-by-step explanation:
Use the equation A = P(1 + rt)convert rate into decimal (0.0975)convert time into years to make things easier (0.5 years)Solve: A = 4000(1 + (0.0975 × 0.5)) = 4195A = $4,195.00Interest: $4,195 - $4,000 = $195
The values of x and y vary directly
and one pair of values are given.
Write an equation that relates x
and y.
x = 2, y = 5
[?]
y =
X
The equation that relates x and y is given as y = 2.5x
What is direct variation in mathematics?The relationship between two variables in which one is a constant multiple of the other is referred to as direct variation. For instance, two variables are said to be in proportion when one affects the other. b = ka is the equation if b is directly proportional to a.
The formula for direct variation is in the form of
y = kx
where we have the value of y = 5, the value of x = 2
we have to put this in the formula above
5 = 2k
to get the value of k we would have to divide through by 2
k = 5 / 2
k = 2.5
Hence we would have y = 2.5x
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REMEMBER 4. What is the difference in length? Carrot 14 cm Show the difference in length two ways. Write an equation for each. The difference in length is Pea pod 5 cm cm.
The difference in lengths is 9 cm and the length of the carrot is 9 cm longer than the pea pod.
What is the Subtraction operation?Subtraction is a mathematical operation that deducts the right-hand operand from the left-hand operand.
for example 4 -2 = 2
We have to determine the difference in lengths
The length of the carrot = 14 cm
The length of the pea pod = 5 cm
The difference in lengths = maximum length - minimum length
The difference in lengths = 14 cm - 5 cm
Apply the subtraction operation, and we get
The difference in lengths = 9 cm
We conclude that the length of the carrot is 9 cm longer than the pea pod.
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Can somebody please help me find a answer key for these
Answer:
Step-by-step explanation:
Write an exponential function in the form y = ab^x that goes through points (0, 14)
and (4,8750).
The exponential function will be written as y = 14⁰.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given exponential function is [tex]y = ab^x[/tex]. The equation of the exponential function passing through the point is,
[tex]y = ab^x \\[/tex]
14 = ab⁰
a = 14
The equation will be written as,
y = 14b⁰
y = 14⁰
Therefore, the exponential function will be written as y = 14⁰.
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1. Identify the proportional relationship.
7x-2=y
y=2x+4
y=5x
y+1=3x
By using the concept of proportionality, it can be concluded that
y = 5x is the proportional relation
Third option is correct
What is proportionality?
Suppose there are two quantities. Proportionality indicates that if there's a change in the value of one quantity, the value of other quantity also changes but maintaining a constant ratio
Proportionality are often direct or inverse
Direct proportion
Two quantities are said to be in direct proportion if on increasing the value of one quantity, the value of other quantity also increases and vice versa.
For example cost of an article and quantity of an article are in direct proportion
Inverse proportion
Two quantities are said to be in inverse proportion if on increasing the value of one quantity, the value of other quantity decreases and vice versa.
For example Number of men and number of days taken by those men to complete a work are in inverse proportion
For the first option
7x - 2 = y
y = 7x - 2
Here a non zero constant (-2) is added after the term with variable x
So this relation is not proportional
For the second option
y = 2x + 4
Here a non zero constant (4) is added after the term with variable x
So this relation is not proportional
For the third option
y = 5x
Here, no non zero constant is added after the term with variable x
So this relation is proportional.
For the fourth option
y + 1 = 3x
y = 3x - 1
Here a non zero constant (-1) is added after the term with variable x
So this relation is not proportional
So the correct option is the third option
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The box plot shows the times for sprinters on a track team.
A horizontal number line starting at 40 with tick marks every one unit up to 59. The values of 41, 43, 49.5, 56, and 58 are all marked by the box plot. The graph is titled Sprinters' Run Times, and the line is labeled Time in Seconds.
Which of the following is the five-number summary for this data?
The five number summary from the given box plot is presented as follows:
Minimum value: 41.First quartile: 43.Median: 49.5.Third quartile: 56.Maximum value: 58.What does a box-and-whisker plot shows?A box and whisker plot shows five things of a distribution, listed as follows:
The minimum value of the data-set.The first quartile, which is the median of the bottom 50% of measures in the data-set, hence it is the value that 75% of the measures are greater than.The median, which is the middle-value of the data-set, meaning that 50% of the data-set is less than the median and 50% is greater.The thid quartile, which is the median of the upper 50% of the measures in the data-set, hence it is the value that 75% of the measures are lesser than.The maximum value of the data-set.These values are the values marked from left to right on the box plot, from the minimum value to the maximum value, passing through the first quartile, the median and the third quartile, and form the five number summary.
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Identify the solution set 3c-5-c=7+4c
Find the focus and the directrix of the parabola with the equation y = - 1/12 (x - 4) 2. (A) Focus = (4, -1), directrix is y = -5 (B) Focus = (4,2), directrix is y = 5 (C) Focus = (4,1), directrix is y = -5 (D) Focus = (4, -1), directrix is y = 5
The focus of parabola is (4 , -1) and directrix is 5
The general equation of a parabola is: y = a(x-h)²+ k or x = a(y-k)² +h, where (h ,k) denotes the vertex. The standard equation of a regular parabola is y² = 4ax.
Focus: The point (a, 0) is the focus of the parabola
Directrix: The line drawn parallel to the y-axis and passing through the point (-a, 0) is the directrix of the parabola. The directrix is perpendicular to the axis of the parabola.
Given equation of parabola is :
y = - 1/12 (x - 4) - 2
Comparing it with standard equation,
h = 4
k = 2
a = -1/12
using Focus: (h, k+ (1/4a)) and Directrix: y = k - 1/4a)
=> focus = (4 , 2+(12/4×-1))
=> focus = (4 , 2-3)
=> focus = (4 , -1)
and directrix is : y = 2-(1/4×-1/12)
y = 2 + 12/4
y=2 + 3 => 5
So, the focus is (4,-1) and directrix is 5
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There are 4 green apples and 7 red apples in a basket.
(a) What is the ratio of all apples in the basket to red apples?
0
(b) What is the ratio of green apples to all apples in the basket?
0
Answer:
1) 7:4
2) 11: 7
Step-by-step explanation:
14.4.3 Quiz: Stretching and Compressing Functions
Question 2 of 10
Suppose f(x) = x². What is the graph of g(x)=f(x)?
If f(x) = x², the graph of g(x) = f(x) is x².
What is a Graph of a function?
The graph of a function f is the set of all points in the plane of the form (x, f(x)).
How to find the graph of a function:
You must choose x-values and insert them into the equation in order to graph a function. You will obtain a y-value if you enter those values into the equation. Your coordinates for a single point are made up of your x-values and your y-values.
We are given the function; f(x) = x²
Also, we want to find the graph of g(x) = f(x)
From the above, it means that we put x in place of x for function f(x) to get the function g(x).
so, g(x) = f(x)
g(x) = (x)²
Hence the graph of g(x) = f(x) is x².
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Two triangles are shown below. 3 5 15 9 6 18 Which statement best describes the relationship between the two triangles ? The triangles are not similar all corresponding angles are not equal . The triangles are not similar ; all corresponding sides are not proportional . The triangles are similar ; the similarity ratio is 1: 3. The triangles are similar ; the similarity ratio is 2 :3.
The statement that best describes the relationship between the two triangles is the option;
The triangles are not similar; all the corresponding sides are not proportionalWhat are the conditions for the similarity of two triangles?Two triangles are similar if they satisfy the following conditions.
Two angles of one triangle are congruent to two angles in the other triangle (AA, Angle-Angle similarity postulate)Two sides of one triangle are proportional to two sides of the other triangle and the included angle of the two sides in each triangle are congruent (SAS, Side-Angle-Side similarity postulate)The three sides of one triangle are proportional to the three sides of the other triangle (SSS, Side-Side-Side, similarity postulate)The length of the sides of the triangles are;
First triangle, a₁ = 3, b₁ = 5. c₁ = 15
Second triangle. a₂ = 9, b₂ = 6, c₂ = 18
The ratio of the corresponding sides is therefore;
[tex]\dfrac{a_1}{a_2} = \dfrac{3}{9} =\dfrac{1}{3}[/tex]
[tex]\dfrac{b_1}{b_2} = \dfrac{5}{6}[/tex]
[tex]\dfrac{c_1}{c_2} = \dfrac{15}{18} =\dfrac{5}{6}[/tex]
The ratio of the three corresponding sides of the triangles are not the same such that the corresponding sides of the triangles are not constantly proportional.
Therefore the two triangles are not similar because all the corresponding sides are not proportional.
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Find the area and circumference of a circle with a diameter of 15 cm.
the answer to that question is 34cm² of the circumference
x^2-25 , (x+5) quotient and remainder
The quotient when ([tex]x^{2} -25[/tex]) is divided by (x+5) is (x-5) and the remainder is 0.
According to the question,
We have the following information:
([tex]x^{2} -25[/tex]) is divided by (x+5)
Now, we can solve this using two ways. First method is to use the long division method and second is to solve the expression using an identity.
We know that the following identity can used to expand the dividend:
[tex]a^{2} -b^{2} = (a+b)(a-b)\\[/tex]
In this case, we have a = x and b = 5.
[tex]x^{2} -(5)^{2} = (x-5) (x+5)[/tex]
Now, we have the following expression:
(x+5)(x-5)/(x+5)
(x-5)
Now, the remainder is 0.
Hence, the quotient when ([tex]x^{2} -25[/tex]) is divided by (x+5) is (x-5) and the remainder is 0.
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Write the expression 3a+2y+5ay-2y-+-52-3y in simplest form. Then, answer the following questions
using complete sentences.
a. How many terms are in the simplified expression?
b. How many of the terms in the simplified expression are negative?
The simplified expression is 3a + 5ay - 3y -52 .
(a) There are 4 terms in the simplified expression
(b) there are 2 negative terms in the simplified expression .
In the question ,
the algebraic expression is given as 3a+2y+5ay-2y-52-3y
to simplify it , we first group them in like terms
the expression becomes .
= 3a [tex]+[/tex] 2y [tex]+[/tex] 5ay -2y - 52 -3y
= 3a + 5ay + 2y - 2y - 3y - 52
= 3a + 5ay - 3y -52
Part(a)
the number of terms in the simplified expression is 4 ,
Part(b)
as we can see that the terms -3y and -52 are negative
So , there are 2 negative terms in the expression.
Therefore , (a) There are 4 terms in the simplified expression
(b) there are 2 negative terms in the simplified expression .
The given question is incomplete , the complete question is
Write the expression 3a+2y+5ay-2y-52-3y in simplest form. Then, answer the following questions using complete sentences.
a. How many terms are in the simplified expression?
b. How many of the terms in the simplified expression are negative?
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In your own words, describe the y-intercept.
Answer:
The y-intercept is the point where the graph ( line or curve ) intercepts the y-axis. The y-intercept is the y value of the point, ( x, y ).
Hope this helps!
Step-by-step explanation:
n (x) = 4x + 4; n(x) = 16
X =
x = 3
Step-by-step explanation:
[tex]{ \blue{ \sf{n(x) = 4x + 4}}}[/tex]
[tex]{ \blue{ \sf{16 = 4x + 4}}}[/tex]
[tex]{ \blue{ \sf{16 - 4 = 4x}}}[/tex]
[tex]{ \blue{ \sf{12 = 4x}}}[/tex]
Divide both the sides with 4
[tex]{ \blue{ \sf{ \frac{12}{4} = \frac{4}{4}x}}}[/tex]
[tex]{ \green{ \boxed{ \red{ \sf{x = 3}}}}}[/tex]
AB=18cm
BC=18cm
AC=16cm
What is the corresponding angles and sides?
The angle measurements are 5.38°, 87.31° and 87.31°.
What is triangle?
A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -
∠x + ∠y + ∠z = 180°
The sum of two sides of a triangle is greater then the third side. Mathematically -
a + b > c
There are different types of triangles such as -
equilateral triangle , scalene triangle , isosceles triangle etc.
Given are the sides of triangle as AB = 18cm, BC = 18cm, AC = 16cm.
The given triangle is a isosceles triangle with two sides equivalent. Angles opposite to these sides will be equal. So, we can write -
2∠x + ∠y = 180°
from the figure, it can be seen that angle B is 5.38 degrees.
2∠x + 5.38 = 180
2∠x = 174.62
∠x = 87.31°
Therefore, the angle measurements are 5.38°, 87.31° and 87.31°.
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A paper bag has six colored marbles. The marbles are red, green, blue, purple, yellow, and orange. List the sample space when choosing one marble.
S = {1, 2, 3, 4, 5, 6}
S = {red, blue, green, orange, yellow}
S = {g, r, b, y, o}
S = {green, blue, yellow, orange, purple, red}
Option D. The sample space when one marble is to be chosen is given as S = {green, blue, yellow, orange, purple, red}
What is sample space in probability?A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset of possible experiment results. Depending on the experiment, a sample area could contain a variety of results. Discrete or finite sample spaces are those that have a finite number of outcomes.
The sample space here have been listed based on the colors of the marbles that was presented in the question that we have here.
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Answer:
OPTION D is not correct I took the test and its B
Step-by-step explanation:
also here is a picture
If 3/5 of a number is 150, what is the number
let the number be = x
step by step explanation:[tex] = > \frac{3x}{5} = 150[/tex]
Cross multiply:[tex] = > 3x = 150 \times 5[/tex]
[tex] = > 3x = 750[/tex]
Divide both side by 3[tex] = > \frac{3x}{3} = \frac{750}{3} [/tex]
[tex] = > x = 250[/tex]
The number can be found by multiplying 150 by 5 and then dividing the result by 3. Therefore, the number is 250 by solving equations.
To find the number, we can set up the equation: (3/5) * x = 150. To isolate x, we multiply both sides of the equation by 5/3, resulting in x = 250. This means that the number is 250.
Start with the equation: (3/5) * x = 150.
To isolate x, multiply both sides of the equation by the reciprocal of (3/5), which is 5/3. This yields (5/3) * (3/5) * x = (5/3) * 150.
Simplify the left side of the equation: x = (5/3) * 150.
Multiply 5 by 150 and divide the result by 3: x = (750/3).
Simplify the fraction by dividing the numerator (750) by the denominator (3): x = 250.
Therefore, the number is 250.
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A house on the market was valued at $365,000. After several years, the value increased by 8%. By how much did the house's value increase in dollars? What is
the current value of the house?
Answer:
394,200
Step-by-step explanation:
You have to multiply the house value by 1.08 or 108%
365,000*1.08=394,200
x/2=8/5
what is x???
Answer:
x = 3.2
Step-by-step explanation:
[tex] \sf \frac{x}{2} = \frac{8}{5} \\ [/tex]
Use cross multiplication.
[tex] \sf5x = 8 \times 2 \\ \sf 5x = 16[/tex]
Divide both sides by 5.
[tex] \sf \: x = 3.2[/tex]
equation for the perpendicular bisector of the line segment whose endpoints
are (-9, 3) and (-3, -1).
Equation for the perpendicular bisector of the line segment is
2y = 3x +20.
A line segment that bisects another line segment at a 90° angle is known as a perpendicular bisector.
What is perpendicular bisector?A line segment that bisects another line segment at a 90° angle is known as a perpendicular bisector. In other terms, a perpendicular bisector separates a line segment into two equal halves by intersecting it at a 90° angle.
Given coordinates of the endpoints of a line segment (-9, 3) and (-3,-1).
In order to find the equation of perpendicular line, we need to find the slope between given coordinates.
Slope between (-9, 3) and (-3, -1). :
slope = [tex]\frac{-1-3}{-3+9} =\frac{-2}{3}[/tex]
Slope of the perpendicular line is reciprocal and opposite in sign.
Therefore, slope of the perpendicular line = 3/2
Now, we need to find the midpoint of the given coordinates.
[tex]Mid points : \\x= \frac{ -9-3}{2} =-6\\ y= \frac{3-1}{2} = 1\\ pint = (-6,1)[/tex]
Let us apply point-slope form of the linear equation:
y-y1 = m(x-x1)
y - 1 = 3/2 (x + 6)
2y = 3x +20
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Could you have step by step instructions? Thank you
Answer:
B (5,9)
Step-by-step explanation:
when working with fractions as slopes we use rise over run (broken down)
3 (numerator)--rise-how unit to go up or down
--
4 (denominator)--run--how many units to the left or right
since our slope is positive we will be going up 3 and 4 to the right.
if the slope is negative we go down and to the left.
hope this explanation helps for future questions
Assignment Sowe for x and y
3x² - 4y =-1 2x -4=1
plss help me with it
Answer: x=25/4 or 6.25, y=79/16 or 4.9375
Step-by-step explanation:
Normally, we would have to set up a system of linear equations, but in this case we can solve for x and plug in from there. x=5/2 or 2.5 when solving for the variable. Now we go to the second equation, plug for x, and solve for y. 5/2 times 5/2 is 25/4, multiplied by 3 is 75/4. Subtract 75/4 from -1, and divide both sides by -4.
please help 25points, please show how you did it
Answer:
Angle 1: 27
2: 153
3: 58
4: 138
Step-by-step explanation:
1. 180-(116+37)=27
2. 180-27=153
3. 180-(48+74)=58
4. 122+16=138
180-138=42
180-42=138
7. In one week, Sabrina received 18 letters and
8 bills. What was the ratio of bills to letters?
A particle moves with velocity dx/dt in the x-direction
and dy/dt in the y-direction at time t in seconds, where
dx/dt = 3t² and dy/dt = 12t.
Find the distance traveled by the particle from time
t=0 to t= 3.
Distance travelled by the particle from time t = 0 to t = 3 in x-direction and y-direction is 27 units and 54 units respectively.
How to get distance/displacement using velocity?
Velocity is defined as the rate of change of position or the rate of displacement.Velocity = dx/dt that is change in position x with respect to time t.Integration is anti derivative for any quantity. Hence to get displacement using velocity, integrate to with respect to 't' and substitute values of t accordingly.According to given data:
A particle moves with velocity (dx)/(dt) = 3t² in x- direction
and (dy)/(dt) = 12t in y-direction
Integrating both sides of these derivatives with respect to t
x= ∫3t² dt = (3t³)/3 + A = t³ + A
where A is integration constant
y= ∫12t d t = (12t²)/2 + B = 6t² + B
where B is integration constant
At t = 0 we get x = A and at t = 3 we get x = 3³ + A = 27 + A.
Therefore, the difference in position of a from t = 0 t = 3 is
27 + A - (0 + A) = 27 units.
Similarly,
At t = 0 , we get y = B and at t = 3 we get
y = 6 * 3² + B = 54 + B
Therefore, the difference in position of y from t = 0 tot t = 3 is
54 + B - (0 + B) = 54 units.
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What is the solution of the following system?
Use the substitution method.
y+7=3x
6x - 2y = 12
O The only solution is (14, 12).
O The only solution is (12, 14).
O There is no solution.
O There are an infinite number of solutions.
The solution of the system equation is C) There is no solution
What is system equation?
A set of one or more equations comprising numerous variables is referred to as a system of equations. The variable mappings that satisfy all of the component equations in a system of equations, or the points where the components of this system of equations intersect, are the solutions to that system. A system of equations in algebra is made up of two or more equations that are solved together. the process of eliminating, substituting, and graphing solutions to a system of equations or inequalities in two variables
Here the given equations are ,
=> y+7=3x-------> 1
=> y = 3x-7 ------> 2
and 6x-2y =12------> 3
Now put value of 2 into 3 then,
=> 6x-2(3x-7)=12
=> 6x-6x+14=12
=>14=12
The statement is false for any real number.
Therefore the correct option for the given system equation is C) There is no solution.
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Consider the equation and the following ordered pairs: (−3,y) and (x,2).
y=−3x−1
Step 1 of 2 : Compute the missing x and y values so that each ordered pair will satisfy the given equation.
x y
row 1−3 Answer
row 2 Answer
2
Answer:
Step-by-step explanation:
step 1 of 2:
We got pairs: (-3, y) and (x, 2), to compute the missing x and y values, we plugin the number into the equation.
(-3, y)
y = -3x - 1
y = -3(-3) - 1
y = 9 - 1
y = 8
So we solve this pair as (-3, 8).
(x, 2)
y = -3x - 1
2 = -3x - 1
3 = -3x
x = -1
So we solve this pair as (-1, 2).
Sorry that I cannot see the following questions.
Lets sets A and B be defined as follows:
A= {25, 26, 27, 28, 29}
B is the set of integers greater than or equal to -6 and less than or equal to 1.
(picture attached below)
a) The value sets of n(A) = 5, n(B) = 8
b) 33 ∈ A is false, -4 ∈ B is true, 25 ∈ A is true, 5 ∉ B is true.
What is set?Sets, in mathematics, are an organized collection of objects and can be represented in set-builder form or roster form. Usually, sets are represented in curly braces {}, for example, A = {1,2,3,4} is a set.
A = { 25, 26, 27, 28, 29}
B ( is greater or equal to -6 and equal to 1) = { -6, -5, -4, -3, -2, -1, 0, 1}
n(A) = number of elements in A which is 5 and n(B) = 8
33 ∈ A The symbol ∈ means element of. so 33 is not an element of A.
-4 is an element of B so it is true, -4 ∈ B is true
25 ∈ A is true because 25 is an element of A
5 ∉ B is true because 5 is not an element of B
In conclusion, n(A) = 5, n(B) = 8
-4 is an element of B so it is true, -4 ∈ B is true
25 ∈ A is true because 25 is an element of A
5 ∉ B is true because 5 is not an element of B
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