Rate of interest for
A = $5000
THEN apply formula
A-P= P•R•T/100
T = 3 years
Then
6050 - 5000= 1050 =
1050= P•R•T/100
Now find R
R= (1050•100)/(P•T) = (105000)/(5000•3) = 7
Then ANSWER IS
ANUAL RATE(%) = 7%
Which of the following graphs represent the system of equations f(x) = x2 + 2x + 2 and g(x) = –x2 + 2x + 4?
The Solution:
Given:
[tex]\begin{gathered} f(x)=x^2+2x+2 \\ \\ g(x)=-x^2+2x+4 \end{gathered}[/tex]We are required to determine the graphs of the given functions.
Below is the graph of the function:
Thus, the correct answer is:
Determine whether a tangent line is shown in this figure
Given:
Required:
To determine whether a tangent line is shown in the given figure.
Explanation:
By the definition of tangent line, we know that tangent line is a straight line that touches the circle at one point.
Now consider the given figure, there is a tangent line in the given figure.
Final Answer:
Yes.
Find the distance between the points (4,1) and (2,4) using distance formula
Given:-
[tex](4,1)(2,4)[/tex]To find the distance.
So the distance formula is,
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Substituting we get,
[tex]\begin{gathered} d=\sqrt{(2-4)^2+(4-1)^2} \\ d=\sqrt{-2^2+3^2} \\ d=\sqrt{4+9} \\ d=\sqrt{13} \end{gathered}[/tex]So the required distance is root 13.
The length of a rectangle is 2 inches more than its width.If P represents the perimeter of the rectangle, then its width is:oAB.O4Ос. РOD.P-2 별O E, PA
Given:
a.) The length of a rectangle is 2 inches more than its width.
Since the length of a rectangle is 2 inches more than its width, we can say that,
Width = W
Length = L = W + 2
Determine the width with respect to its Perimeter, we get:
[tex]\text{ Perimeter = P}[/tex][tex]\text{ P = 2W + 2L}[/tex][tex]\text{ P = 2W + 2(W + 2)}[/tex][tex]\text{ P = 2W + 2W + }4[/tex][tex]\text{ P = 4W + }4[/tex][tex]\text{ P - 4 = 4W}[/tex][tex]\text{ }\frac{\text{P - 4}}{4}\text{ = }\frac{\text{4W}}{4}[/tex][tex]\text{ }\frac{\text{P - 4}}{4}\text{ = W}[/tex]Therefore, the answer is D.
To the function attached,Is f(x) continuous at x=1? Please explain
Recall that a function is continuous at a point if the limit as the variable approaches a value is the same as the value of the function at that point.
Now, notice that, using the definition of the function:
[tex]\begin{gathered} \lim_{x\to1^+}f(x)=\sqrt{1}+2=3, \\ \lim_{x\to1^-}f(x)=3, \end{gathered}[/tex]therefore:
[tex]\lim_{x\to1}f(x)=3.[/tex]Given that the limit and the value of the function at x=1 are equal, the function is continuous at x=1.
Answer: It is continuous at x=1.
what is the better buy 4GB flash drive for $8 2 GB for $6 or 8 GB for $13
In order to find out which of the options would be better to buy we would have to calculate the better unit price that eacho of the following options offer.
So, unit price for the offers would be:
For 4GB flash drive for $8, unit price=$8/4
unit price=$2
For 2 GB for $6, unit price=$6/2=$3
For 8 GB for $13, unit prince=$13/8=$1.625
Therefore, as the unit price of 8 GB for $13 is the lower one, then the better choice to buy would be 8 GB for $13
1 pts
4. If line segment AB has coordinates A(-2,4) and B(2,0) and line segment
CD has coordinates C(3,4)and D(-3,-2), how would you describe these two
line segments?
A: neither
B: perpendicular
C: parallel
Answer:
B
Step-by-step explanation:
[tex]m_{\overline{AB}}=\frac{4-0}{-2-2}=-1 \\ \\ m_{\overline{CD}}=\frac{-2-4}{-3-3}=1 [/tex]
Since the slopes are negative reciprocals of each other, and since they intersect, they are parallel.
Mrs barker wants to tile her washroom floor. The area of the washroom floor is 6.75 square metres. She determines that she will use 300 square tiles. What are the dimensions of the tiles, in centimetres?
ANSWER
15 centimeters
EXPLANATION
First, we have to find the area of the washroom floor in square centimeters, by multiplying the area in square meters by 10,000 or, in other words, moving the decimal point 4 units to the right,
[tex]6.75m^2=6.75\times10,000cm^2=67,500cm^2[/tex]Now, we know that Mrs. Barker will use 300 square tiles, so the area of each tile must be,
[tex]A_{tile}=\frac{A_{floor}}{number\text{ }of\text{ }tiles}=\frac{67,500cm^2}{300}=225cm^2[/tex]Thus, if the tiles are squared, the side length of each tile is the square root of the area of each tile,
[tex]s=\sqrt{A_{tile}}=\sqrt{225cm^2}=15cm[/tex]Hence, the side length of each tile is 15 cm.
5. Joseph Cheyenne is earning an annual salary of $24,895. He has been offered the job in the ad. How much more would he earn per month if he is paid: a. the minimum? b. the maximum
Joseph has an annual salary of $24895 dollars and she get the new job that is between 28000-36000 dollars so:
the minimum will be:
[tex]24895+28000=52000[/tex]and the maximun will be:
[tex]24895+36000=60895[/tex]6. A line goes through these two points, (-4, -1) anti (-9,-5).A. Find an equation for this line in point slope form.B. Find the equation for this line in slope intercept form. Be sure to show your work.C. If the y-coordinate of a point on this line is 7, what is the x-coordinate of this point?
A. In order to find the equation, first we need to find the slope
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]m is the slope
(-4, -1)=(x1,y1)
(-9,-5)=(x2,y2)
we substitute the values
[tex]m=\frac{-5+1}{-9+4}=\frac{-4}{-5}=\frac{4}{5}[/tex]then we use the point-slope form
[tex]y-y_1=m(x-x_1)[/tex]we substitute the values
[tex]y+1=\frac{4}{5}(x+4)[/tex]B. in order to find the slope-intercept form we need to isolate the y
[tex]y=\frac{4}{5}x+\frac{11}{5}[/tex]C. if the y coordinate is 7
[tex]7=\frac{4}{5}(x)+\frac{11}{5}[/tex]then we isolate the x
[tex]\frac{4}{5}x=7-\frac{11}{5}[/tex][tex]\begin{gathered} \frac{4}{5}x=\frac{24}{5} \\ x=\frac{5\cdot24}{5\cdot4} \\ x=6 \end{gathered}[/tex]the value of the x-coordinate is 6 when the y-coordinate is 7
I wondered if you could teach me how to do this so I can do these problems independently.
Answer
a)
A' (-2, 6)
B' (7, 3)
C' (4, 0)
b)
D' (3, 3)
E' (-5, 0)
F' (2, 2)
c)
G' (3, 1)
H' (0, 4)
P' (-2, -3)
Explanation
For the coordinate (x, y)
A transformation to the right adds that number of units to the x-coordinate.
A transformation to the left subtracts that number of units from the x-coordinate.
A transformation up adds that number of units to the y-coordinate.
A transformation down subtracts that number of units from the y-coordinate.
For this question,
a) The coordinates are translated to the right by 4 units and upwards by 1 unit
That is,
(x, y) = (x + 4, y + 1)
A (-6, 5) = A' (-6 + 4, 5 + 1) = A' (-2, 6)
B (3, 2) = B' (3 + 4, 2 + 1) = B' (7, 3)
C (0, -1) = C' (0 + 4, -1 + 1) = C' (4, 0)
When a given point with coordinates P (x, y) is reflected over the y-axis, the y-coordinate remains the same and the x-coordinate takes up a negative in front of it. That is, P (x, y) changes after being reflected across the y-axis in this way
P (x, y) = P' (-x, y)
For this question,
b) The coordinates are reflected over the y-axis
D (-3, 3) = D' (3, 3)
E (5, 0) = E' (-5, 0)
F (-2, 2) = F' (2, 2)
In transforming a point (x, y) by rotating it 90 degrees clockwise, the new coordinates are given as (y, -x). That is, we change the coordinates and then add minus to the x, which is now the y-coordinate.
P (x, y) = P' (y, -x)
For this question,
c) The coordinates are rotated about (0, 0) 90 degrees clockwise.
G (-1, 3) = G' (3, 1)
H (-4, 0) = H' (0, 4)
I (3, -2) = P' (-2, -3)
Hope this Helps!!!
Hi, I need help on this. the sentence says Write the Numbers that represent each Expression
H = 1, P =2, R = 3 B = -1, C = -2, A = -3, Q = -5
Explanation:
For the first number line:
From the tick mark to the tick mark with 4, there are 4 tick marks
Distance from 0 to 4 = 4 - 0 = 4
Each tick mark = 4/4 tick marks
Each tick mark = 1
This means each tick mark increases by 1 to the right after 0 and decreases by one to the left before zero.
H, P and R are after 0
H = 0 + 1 = 1
P = 1 + 1 = 2
R = 2 + 1 = 3
B, C, A and Q are all before 0
B = 0 - 1 = -1
C = -1 - 1 = -2
A = -2 - 1 = -3
Q = -4 - 1 = -5
For the 2nd number line:
from 0 to 100, there 5 tick marks
Distance from 0 to 100 = 100 - 0 = 100
Each tick mark = 100/5 tick marks
Each tick mark = 20
This means each tick mark after zero increases by 20 to the right and decreases to the before 0 by 20.
A, L and M are after zero
Number before A is 20, increasing the number by 20
A = 20 + 20 = 40
L = 40 + 20 = 60
M = 60 + 20 = 80
J, P, T, V are before zero
Number before J = 0, decreasing by 20
J = 0 - 20 = -20
P = -20 - 20 = -40
T = -40 - 20 = -60
V = -60 - 20 = -80
In Mr. Peter's class, 75% of the students have a pet. There are 15 students with pets in the class. How many total students are in the class?
Answer:
20 Students
Explanation:
Let the total number of students in the class = x
Number of students that have pets = 15
Percentage of students that have pets = 75%
Therefore:
[tex]75\%\text{ of x=15}[/tex]We then solve for x.
[tex]\begin{gathered} \frac{75}{100}\times x=15 \\ 0.75x=15 \\ x=\frac{15}{0.75} \\ x=20 \end{gathered}[/tex]We have 20 students in total in the class.
Suppose that a household's monthly water bill (in dollars) is a linear function of the amount of water the household uses (in hundreds of cubic feet, HCF). When graphed, the function gives a line with a slope of 1.45. See the figure below.
If the monthly cost for 22 HCF is $45.78, what is the monthly cost for 19 HCF?
Using a linear function, it is found that the monthly cost for 19 HCF is of $41.43.
What is a linear function?A linear function, in slope-intercept format, is modeled according to the rule presented below:
y = mx + b
In which the parameters of the function are described as follows:
The coefficient m is the slope of the function, representing the rate of change of the function, that is, the change in y divided by the change in x.The coefficient b is the y-intercept of the function, which is the value of y when the function crosses the y-axis(x = 0).As stated in the problem, the slope is of 1.45, hence:
y = 1.45x + b.
The monthly cost for 22 HCF is $45.78, hence when x = 22, y = 45.78, meaning that the intercept b can be found as follows:
45.78 = 1.45(22) + b
b = 45.78 - 1.45 x 22
b = 13.88.
Then the function is:
y = 1.45x + 13.88.
And the cost for 19 HCF is given by:
y = 1.45(19) + 13.88 = $41.43.
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Find the circumference of a circle with a diameter of centimeters. Round your answer to the nearest centimeter.
Circumference = 2* pi * r
r = radius
r = diameter/2
r = 50/2
r = 25 cm
Circumference = 2*3.14 * 25
Circumference = 157 cm
Result = 157 cm
The second choice
14. A waterway contains 10.3 milligrams of an impurity per gallon of water. How many micrograms of impurity arepresent per liter of water?
1) Gathering the data
10.3 mg of impurity per gallon of water
? μg of impurity per liter?
2) Since this is a matter of units conversion, then let's work remembering
the Metrical and Customary equivalences:
1 μg = 0.001 mg
1 gallon = 3.78 liters
3) As we have a ratio, let's write it as a ratio:
[tex]undefined[/tex]Dalia works mowing lawns and babysitting. She earns $8.40 an hour for mowing and $7.90 an hour for babysitting . How much will ahe earn for 7 hours of mowing and 1 hour of babysitting?
Given that she earns $8.40 an hour for mowing then for 7 hours of mowing, the amount earned
= 7 * $8.40
=$58.80
Furthermore, given that she earns $7.90 for baby sitting for an hour
Hence for mowing for 7 hours and baby sitting for 1 hour, the total amount she will earn
= $58.80 + $7.90
= $66.70
b. Function h will begin to exceed f and g around x = [. (Round up to the nearest whole number.)
If we evaluate x = 10 on all the functions, we have:
[tex]\begin{gathered} h(10)=1.31^{10}=14.88 \\ f(10)=1.25(10)=12.5 \\ g(10)=0.1562(10)^2=15.625 \end{gathered}[/tex]and then, evaluating x = 11, we get:
[tex]\begin{gathered} h(11)=1.13^{11}=19.49 \\ f(11)=1.25(11)=13.75 \\ g(11)=0.15625(11)^2=18.9 \end{gathered}[/tex]notice that on x = 10, h(x) does not exceed g(x), but on x = 11, h(x) exceeds the other functions. Therefore, h will begin exceed f and g around 11
Use the distance formula, slopes and your knowledge of characteristics of different
types of quadrilaterals to determine the type of quadrilateral formed by the
following four points (-3, 1) , (-2, 3) , (0, 4) , (-1, 2)
This quadrilateral is square . It have same length of side.
How to Find type of quadrilaterals?In geometry, a quadrilateral is a four-sided polygon with four edges and four corners. The angles stood present at the four vertices or corners of the quadrilateral. If ABCD is a quadrilateral, the angles of the vertices are A, B, C, and D. The sides of a quadrilateral are AB, BC, CD, and DA. The four vertices of the quadrilateral ABCD are A, B, C, and D.The diagonals are formed by connecting the quadrilateral's opposite vertices.Quadrilaterals are typically four-sided shapes such as rectangles, squares, and trapezoids.In a concave quadrilateral, one interior angle is greater than 180°, and one of the two diagonals lies outside the quadrilateral.A convex quadrilateral's interior angles are all less than 180°.Therefore,
From question the coordinates of A,B,C,D are given as ,
A = (-3, 1) B = (-2, 3) C = (0, 4) D = (-1, 2)
We use distance formula :
Distance = √(x2 -x1)²+(y2 - y1)²
AB = √(-2 + 3)²+(3 - 1)² = √(5)
BC = √(0+2)²+(4–3)² = √5
CD = √(-1 –0)²+(2–4)² =√5
DA = √(-1 +3)²+(2–1)² =√5
We get the distance is √5 for all points, so the type of quadrilateral is square.
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In how many ways can the letters in the word PAYMENT be arranged using 4 letters?A. 42B. 840C. 2520D. 1260
The word PAYMENT has 7 letters. They can be arranged in groups of 4 like shown below:
PYNT, TA
You start a trip when your odometer reads 23,672 miles, and you have a full tank of gas. After
driving a few hours, you fill up your tank. If you buy 16.5 gallons and your odometer reads
23,927, how many miles to the gallon are you getting, rounded to the nearest tenth of a gallon.
I need helppp with example pliss
Answer:
15.6 MPG
Step-by-step explanation:
You start a trip when your odometer reads 23,672 miles, and you have a full tank of gas. After driving a few hours, you fill up your tank. If you buy 16.5 gallons and your odometer reads 23,927, how many miles to the gallon are you getting, rounded to the nearest tenth of a gallon.
You went 23,927 - 23,672 = 255 miles
Because you started on a full tank, you went 255 miles on 16.5 gallons
to figure MPG:
255/16.5 = 15.4545... MPG
rounded to nearest 10th of gallon:
15.6 MPG
The floor of a shed has an area of 80 square feet. The floor is in the shape of a rectangle whose length is 6 feet less than twice the width. Find the length and the width of the floor of the shed. use the formula, area= length× width The width of the floor of the shed is____ ft.
Given:
The area of the rectangular floor is, A = 8- square feet.
The length of the rectangular floor is 6 feet less than twice the width.
The objective is to find the measure of length and breadth of the floor.
Consider the width of the rectangular floor as w, then twice the width is 2w.
Since, the length is given as 6 feet less than twice the width. The length can be represented as,
[tex]l=2w-6[/tex]The general formula of area of a rectangle is,
[tex]A=l\times w[/tex]By substituting the values of length l and width w, we get,
[tex]\begin{gathered} 80=(2w-6)\times w \\ 80=2w^2-6w \\ 2w^2-6w-80=0 \end{gathered}[/tex]On factorizinng the above equation,
[tex]\begin{gathered} 2w^2-16w+10w-80=0 \\ 2w(w-8)+10(w-8)=0 \\ (2w+10)(w-8)=0 \end{gathered}[/tex]On solving the above equation,
[tex]\begin{gathered} 2w+10=0 \\ 2w=-10 \\ w=\frac{-10}{2} \\ w=-5 \end{gathered}[/tex]Similarly,
[tex]\begin{gathered} w-8=0 \\ w=8 \end{gathered}[/tex]Since, the magnitude of a side cannot be negative. So take the value of width of the rectangle as 8 feet.
Substitute the value of w in area formula to find length l.
[tex]\begin{gathered} A=l\times w \\ 80=l\times8 \\ l=\frac{80}{8} \\ l=10\text{ f}eet. \end{gathered}[/tex]Hence, the width of the floor of the shed is 8 ft.
Determine the required value of a missing probability to make the distribution a discrete probability distribution… p(4) =
The table given showed the discrete probability distribution for random variables 3 to 6 and their corresponding probability except for the probability of 4
It should be noted that for a probability distribution, the cummulative probabibility (that is the sum of all the probability) must be equal to one.
This means that
[tex]P(3)+P(4)+P(5)+P(6)=1[/tex]From the given table, it can be seen that
[tex]\begin{gathered} P(3)=0.32 \\ P(4)=\text{?} \\ P(5)=0.17 \\ P(6)=0.26 \end{gathered}[/tex]Then, p(4) is calculated below
[tex]\begin{gathered} P(3)+P(4)+P(5)+P(6)=1 \\ 0.32+P(4)+0.17+0.26=1 \\ P(4)+0.32+0.17+0.26=1_{} \\ P(4)+0.75=1 \\ P(4)=1-0.75 \\ P(4)=0.25 \end{gathered}[/tex]Hence, P(4) is 0.25
The average of 13, 15, 20 and x is 18. What is the value of x?
x will be equal to 24.
Given,
There are 4 numbers:
13, 15, 20, and x.
Average of all numbers = 18.
We know that,
Average = ( sum of all numbers) / ( total numbers)
In this case,
Average = ( 13 + 15 + 20 + x) / 4
According to the question,
18 = (48 + x) / 4
=> 72 = 48 + x
=> x = 72 - 48
=> x = 24.
So, in order to make the average equal to 18, x should be equal to 24.
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which expressions are equivalent to 9 divided by 0.3
Answer:
Step-by-step explanation:
So the answer would be 90 divided by 3 because all you have to do is multiply 0.3 times 10 and 9 times 10 simple hope this was understandable30 will be the expressions that are equivalent to 9 divided by 0.3.
What is an equivalent expression?In general, something is considered equal if two of them are the same. Similar to this, analogous expressions in maths are those that hold true even when they appear to be distinct. However, both forms provide the same outcome when the values are entered into the formula.
An expression is equivalent even when both sides are multiplied or divided with the same non-zero value.
The expression 9 divided by 0.3 can be written as 9/0.3
The expression that will be equivalent will be determined as:
= 9/0.3
= 90/3
= 30
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What is the value of x? Enter your answer in the box. x =
The value of x from the given isosceles triangle is 8 units.
The measures of sides of triangle are given AB=4x-10, AC=5x-22 and BC=3x+2.
What is an isosceles triangle?Isosceles triangles are those triangles that have at least two sides of equal measure and two base angles are equal.
Here, AC = BC
⇒ 5x-22 = 3x+2
⇒ 5x-3x = 22+2
⇒ 3x = 24
⇒ x = 8 units
Therefore, the value of x from the given isosceles triangle is 8 units.
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Matt and Amy each had summer jobs. Matt worked at a restaurant as a bus boy. He earned $10 per hour, plus tips. Amy worked as a dog-groomer. She earned $8 per hour, plus tips.A) Create an equation to represent their total earnings in each situation. Explain what each of the variables represent.
Given:-
Matt and Amy each had summer jobs. Matt worked at a restaurant as a bus boy. He earned $10 per hour, plus tips. Amy worked as a dog-groomer. She earned $8 per hour, plus tips.
To find:-
An equation to represent their total earnings in each situation.
Miguel made $17.15 profit from selling 7 custom t-shirts through a website. Miguel knows the total profit he earns is proportional to the number of shirts he sells, and he wants to create an equation which models this relationship so that he can predict the total profit from selling any number of t-shirts.
Let:
[tex]\begin{gathered} P(x)=\text{profit} \\ k=\text{price of each t-shirt} \\ x=\text{Number of t-shirts sold} \end{gathered}[/tex]Miguel made $17.15 profit from selling 7 custom t-shirts, therefore:
[tex]\begin{gathered} P(7)=17.15=k(7) \\ 17.15=7k \\ \text{Solving for k:} \\ k=\frac{17.15}{7}=2.45 \end{gathered}[/tex]Therefore, the equation that models this relationship is:
[tex]P(x)=2.45x[/tex]Transform y f(x) by translating it right 2 units. Label the new functiong(x). Compare the coordinates of the corresponding points that makeup the 2 functions. Which coordinate changes. x or y?
If we translate y = f(x) 2 units to the right, we would have to sum and get g(x) =f(x+2).
That means the x-coordinates of g(x) are going to have 2 extra units than f(x).
[tex](x,y)\rightarrow(x+2,y)[/tex]Therefore, with the given transformation (2 units rightwards) the function changes its x-coordinates.Can you explain this math to me please I’ve never seen it before and don’t understand
For a quadratic function in standard form,
[tex]\begin{gathered} \text{a = coefficient of x}^2 \\ b\text{ = coeffcient of x} \\ c=\text{ the constant term} \end{gathered}[/tex]For the polynomial f(x),
a = 2, b = -3 and c = 4
For the polynomial g(x)
a = 4, b = -6, c = 10
For the polunomial h(x),
a = 7, b = 0, c = 8
For the polynomia p(x),
a = 1, b = -10, c = 0