Answers
Answer:
3.97%
Step-by-step explanation:
You want to know the annual interest rate, compounded daily, that will result in $43,000 growing to $75,000 in 14 years.
FormulaThe formula for the account value is ...
A = P(1 +r/n)^(nt)
where P is the principal invested at annual rate r compounded n times per year for t years.
ApplicationFilling in the given values, we can solve for r.
75000 = 43000(1 +r/365)^(365·14)
75/43 = (1 +r/365)^5110 . . . . . divide by 43000 and reduce the fraction
Taking the 1/5110 power gives ...
(75/43)^(1/5110) = 1 +r/365 ≈ 1.00010886855
r/365 = 0.0010886855 . . . . subtract 1
r = 0.001086855·365 . . . . . multiply by 365
r ≈ 0.039737 = 3.9737%
The required interest rate is about 3.97%.
Related Questions
Write a linear equation to represent the given problem and then solve the problem.
The perimeter of a college basketball court is 96 meters and the length is 14 meters more than the width. What are the dimensions?
Perimeter = 2 x Length + 2 x Width
Answers
Answer:
Step-by-step explanation:
Let L be the length and W the width
Perimeter of a rectangle is P = 2L + 2W
We are told that L = W + 14 (m) [the length is 14 meters more than the width]
Area of a rectangle is A = L*W
We learn that A = 96 m^2
L*W = 96
Since L = W + 14, we can substitute:
L*W = 96
(W + 14)*W = 96 m^2
W^2 + 14W = 96
W^2 + 14W - 96 = 0
The solution to W in the above equation is 5.04 m
This means L = 5.04 m + 14 m
L = 19.04 meters
Perimeter = 2W + 2L
Perimeter = 2(5.04) + 2(19.04) = 96 m^2
Berti is the Shape Factory's top employee. She has received awards every month for having the top sales
figures so far for the year. If she stays on top, she will receive a $5000 bonus for excellence. She currently has
sold 16, 250 shapes and continues to sell 340 per month.
EMPL
Since there are eight months left in the sales year, Sarita is working hard to catch up. While she has only sold
8,830 shapes, she is working overtime and on weekends so that she can sell 1, 082 per month. Will Sarita
catch up with Berti before the end of the sales year? If so, when?
Answers
No, Sarita will not be able to catch up with Berti before the end of the sales year.
Berti currently has sold 16, 250 shapes
She continues to sell 340 per month.
In eight months she will be able to sell
16250 + 8 x 340
= 16250 + 2720
= 18970
Sharita has only sold 8,830 shapes
Working overtime and on weekends so that she can sell 1, 082 per month
In eight months she will be able to sell
8830 + 8 x 1082
8830 + 8656
17486
No, Sarita will not be able to catch up with Berti before the end of the sales year.
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Please help me with 24For the following exercises, write the equation for the hyperbola in standard form if it is not already, and identify the vertices and foci, and write equations of asymptotes.
Answers
Given the equation,
[tex]-9x^2+72x+16y^2+16y+4=0[/tex]Complete squares as shown below,
[tex]\begin{gathered} -9x^2+72x-a^2=-(9x^2-72x+a^2)=-9(x^2-8x+b^2) \\ \end{gathered}[/tex]Thus,
[tex]\begin{gathered} \Rightarrow-9x^2+72x-a^2=-9(x^{}-4)^2 \\ \Rightarrow a^2=16\cdot9=144\Rightarrow a=12 \\ \Rightarrow-9x^2+72x-144=-9(x^{}-4)^2 \end{gathered}[/tex]Similarly,
[tex]\begin{gathered} 16y^2+16y=16(y^2+y) \\ \Rightarrow16(y+\frac{1}{2})^2=16(y^2+y+\frac{1}{4}) \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} -9x^2+72x+16y^2+16y+4=0 \\ \Rightarrow-9(x-4)^2+16(y+\frac{1}{2})^2+4=-144+4 \\ \Rightarrow-9(x-4)^2+16(y+\frac{1}{2})^2=-144 \end{gathered}[/tex]Finally, the standard form is.
[tex]\begin{gathered} \Rightarrow-\frac{(x-4)^2}{16}+\frac{(y+\frac{1}{2})^2}{9}=-1 \\ \Rightarrow\frac{(x-4)^2}{16}-\frac{(y+\frac{1}{2})^2}{9}=1 \end{gathered}[/tex]As for the vertices, foci, and asymptotes,
[tex]\begin{gathered} c=\pm\sqrt[]{16+9}=\pm5 \\ \text{center:}(4,-\frac{1}{2}) \\ \Rightarrow\text{foci:}(4-5,-\frac{1}{2})_{},(4+5,-\frac{1}{2})_{} \\ \Rightarrow\text{foci:}(-1,-\frac{1}{2}),(9,-\frac{1}{2}) \end{gathered}[/tex]Foci: (-1,-1/2), (9,-1/2)
Vertices
[tex]\begin{gathered} \text{center:}(4,-\frac{1}{2}),\text{vertices:}(4\pm a,-\frac{1}{2}) \\ \text{vertices:}(4+4,-\frac{1}{2}),(4-4,-\frac{1}{2}) \\ \text{vertices:}(8,-\frac{1}{2}),(0,-\frac{1}{2}) \end{gathered}[/tex]Vertices: (8,-1/2), (0,-1/2)
Asymptotes:
[tex]\begin{gathered} y=\pm\frac{3}{4}(x-4)-\frac{1}{2} \\ \Rightarrow y=\frac{3}{4}x-\frac{7}{2} \\ \text{and} \\ y=-\frac{3}{4}x+\frac{5}{2} \end{gathered}[/tex]Asymptotes: y=3x/4-7/2 and y=-3x/4+5/2
how to find the inverse of f(x) = 3x - 7
Answers
To get the inverse of this function you need two steps. First, we leave the variable [tex]x[/tex] alone in the function. Finally, write [tex]f^{-1}(x)[/tex] where you see the letter [tex]x[/tex] and [tex]x[/tex] where you see the letter [tex]y[/tex].
First step:Leave the variable [tex]x[/tex] alone.
[tex]y=3x-7[/tex][tex]y+7=3x[/tex][tex]\frac{y+7}{3}=x[/tex]Last step:Make lettering according to the rule above.
[tex]\frac{x+7}{3} =f^{-1}(x)[/tex]
A farm is being divided so that each section of land has equal access
to the canal running through the property for watering crops. If the road on the
opposite side of the property runs parallel to the canal, explain how this can be
done.
Answers
The best way to divide the land having canal and road parallel, is divide land with the line perpendicular to the road and canal.
What is parallel and perpendicular?
In simple geometry, two geometric objects cross at a right angle (90 degrees or /2 radians) if they are perpendicular to one another. The perpendicular symbol,⟂, can be used to graphically depict the condition of perpendicularity. It can be defined between two planes, between two lines (or line segments), and between two lines.
In geometry, parallel lines are coplanar, straight lines that never intersect. Any parallel planes in the same three-dimensional space are those that never intersect. Parallel curves are those that have a predetermined minimum separation between them and do not touch or intersect.
We need to give equal access of canal to each section of land so, the best way to divide land is divide land perpendicularly to canal and the road.
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solve the equation, and enter the solutions from least to greatest. If there is only one solution, enter “n.a” for the second solution. (picture of equation listed below)
Answers
Answer
x = 1 or x = n.a.
Step-by-step explanation
[tex]\frac{1}{x}+\frac{1}{x-10}=\frac{x-9}{x-10}[/tex]Multiplying by (x - 10) at both sides of the equation:
[tex]\begin{gathered} (x-10)(\frac{1}{x}+\frac{1}{x-10})=\frac{x-9}{x-10}(x-10) \\ \text{ Distributing and simplifying:} \\ \frac{x-10}{x}+\frac{x-10}{x-10}=x-9 \\ \frac{x-10}{x}+1=x-9 \end{gathered}[/tex]Multiplying by x at both sides of the equation:
[tex]\begin{gathered} x(\frac{x-10}{x}+1)=x(x-9) \\ \text{ Distributing and simplifying:} \\ \frac{x(x-10)}{x}+x=x^2-9x \\ x-10+x=x^2-9x \\ 2x-10=x^2-9x \end{gathered}[/tex]Subtracting 2x and adding 10 at both sides of the equation:
[tex]\begin{gathered} 2x-10-2x+10=x^2-9x-2x+10 \\ 0=x^2-11x+10 \end{gathered}[/tex]We can solve this equation with the help of the quadratic formula with the coefficients a = 1, b = -11, and c = 10, as follows:
[tex]\begin{gathered} x_{1,2}=\frac{-b\pm{}\sqrt{b^2-4ac}}{2a} \\ x_{1,2}=\frac{11\pm\sqrt{(-11)^2-4\cdot1\operatorname{\cdot}10}}{2\operatorname{\cdot}1} \\ x_{1,2}=\frac{11\pm\sqrt{81}}{2} \\ x_1=\frac{11+9}{2}=10 \\ x_2=\frac{11-9}{2}=1 \end{gathered}[/tex]The solution x = 10 is not possible because it makes zero the denominator in 2 of the rational expressions of the original equation. In consequence, it must be discarded.
Please answer fast
The boxplot displays the arm spans for 44 students.
Which of the following is not a true statement?
There are no outliers in this distribution.
The shape of the boxplot is fairly symmetric.
The range of the distribution is around 60 cm.
The center of the distribution is around 180 cm.
Answers
The statements The range of the distribution is around 60 cm and
the center of the distribution is around 180 cm are true.
What is statistics?Statistics is the study and manipulation of data, including ways to gather, review, analyze, and draw conclusions from data.
In the given statements
There are no outliers in this distribution.
The shape of the boxplot is fairly symmetric.
The range of the distribution is around 60 cm.
The center of the distribution is around 180 cm.
The statement "The range of the distribution is around 60 cm" is true.
The range is the spread of your data from the lowest to the highest value in the distribution.
In the given graph
Range=200-140
=60
So it is true.
The center of the distribution is around 180 cm is also true.
Hence the statements The range of the distribution is around 60 cm and
the center of the distribution is around 180 cm are true.
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NOBODY IS ANSWERING!! I WILL GIVE BRAINLIEST!! PLS HELP!!
Answers
Find y please help me !
Answers
Answer:
y = 5
Step-by-step explanation:
since the triangles are congruent then corresponding sides are congruent, so
AB = CD , that is
7y = 3y + 20 ( subtract 3y from both sides )
4y = 20 ( divide both sides by 4 )
y = 5
darnel is the executive chef at a mediterranean restaurant famous for its spicy tomato sauce. every week, he takes inventory and then places an order for what he needs. since his spicy tomato sauce is so popular, darnel needs to order more tomatoes every week. there is a proportional relationship between the amount of tomatoes he orders (in pounds), x, and their cost (in dollars), y. x (pounds) y (dollars) 22 $88 23 $92 24 $96 25 $100 what is the constant of proportionality? write your answer as a whole number or decimal. dollars per pound
Answers
The constant of proportionality between the amount of tomatoes he orders (in pounds), and their cost (in dollars) is: 4 dollars per pound
To solve this problem we must perform the following algebraic operations with the given information
Information about the problem:
pounds , dollars
22, $8823, $9224, $9625, $100Calculating the proportion of the amount of tomatoes he orders and their cost we get:
Proportion dollars per pound = Dollars / pound
Proportion dollars per pound = $88/ 22 pounds = 4 $/pound
Proportion dollars per pound = $92/ 23 pounds = 4 $/pound
Proportion dollars per pound = $96/ 24 pounds = 4 $/pound
Proportion dollars per pound = $100/ 25pounds = 4 $/pound
As we could get the constant of proportionality is 4 $/pound
What are algebraic operations?They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.
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in the long-run we can expect the population mean or proportion/percentage to occur. explain what is mean by the phrase in the long run? hint: imagine if we repeatedly took samples from the population. what would the average of the sample means be equal to?
Answers
The Central Limit Theorem states that over a large number of samples, the sampling average of the sample means would be closer to the population mean.
What does the Central Limit Theorem state?The Central Limit Theorem states that for a random variable X, with mean given by [tex]\mu[/tex] and standard deviation given by [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
This means that over a large number of trials, i.e., of samples from the population, the mean of the sample means will be close to the population mean, with a small standard error, as the standard error is inversely proportional to the square root of the sample size.
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7/12 x 4x3 =? I need help
Answers
Cyphon, this is the solution:
We have to multiply the following fractions:
7/12 * 4/3
7 * 4 / 12 * 3
28/36
Simplifying, we have:
7/9 (Dividing by 4 numerator and denominator)
We have to add the following fractions:
- 1/2 + 4/9
Let's find the lowest common denominator between 2 and 9, as follows:
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22
9, 18, 27, 36
The lowest common denominator is 18
PLSS HELP I DO NOT UNDERSTAND THIS PLSSS
Answers
The rate of change is 18 units and 24 ≤ x ≤ 96 is 24 < 42, 60, 78 < 96.
What is the rate of change?The rate at which a variable alters over a predetermined amount of time. It is frequently used when discussing momentum and is typically expressed as a ratio of one variable's change to another's corresponding change. This ratio is graphically represented by a line's slope.So, the rate of change in column 'x':
24 - 6 = 18The rate of change per unit is 18.
Now, 24 ≤ x ≤ 96.
Between 24 and 96, there are three values given in the column which are:
426078So, x can be 42, 60, and 78.
Therefore, the rate of change is 18 units and 24 ≤ x ≤ 96 is 24 < 42, 60, 78 < 96.
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If Susie's age is 8 less than 3 times her brother's age, and Susie is 13. How old is her brother?
Answers
Answer:
correct me if im wrong but my answer is x=7, or in other words, 7.
Step-by-step explanation:
Answer:
7 years old
Step-by-step explanation:
You would start by going backward. If 13 is 8 less, then you would first add 8. You would have 21. Now all you have to do is divide by three. So your answer would be 7. If you would want to check you could plug it back in. 7 multiplied by 3 is 21. 21 - 8=13
The Answer, 7 years old
what is (9x10^4) (6x10^-7)
Answers
The simplified form of the expression ( 9 × 10⁴ ) × ( 6 × 10⁻⁷ ) in scientific notation form is 5.4 × 10⁻²
How to multiply numbers in scientific form?The scientific notation form is simply a method of presenting larger or smaller numbers in a more simple way.
Given the data in the question;
( 9 × 10⁴ ) × ( 6 × 10⁻⁷ )
First, multiply 9 and 6
( 9 × 10⁴ ) × ( 6 × 10⁻⁷ )
9 × 6 ( 10⁴ × 10⁻⁷ )
54( 10⁴ × 10⁻⁷ )
Next, multiply 10⁴ × 10⁻⁷ by adding the exponents.
Using power rule mᵃ × mᵇ = mᵃ ⁺ ᵇ
54( 10⁴ × 10⁻⁷ )
54( 10⁴ ⁺ ⁻⁷ )
54( 10⁴ ⁻⁷ )
Subtract 7 from 4
54 × 10⁻³
Move the decimal point in 54 to the left by place and increase the power of 10⁻³ by 1
5.4 × 10⁻³ ⁺ ¹
5.4 × 10⁻²
Therefore, the simplified form is 5.4 × 10⁻².
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Give an example of a percent problem involving the simple interest formula. Then solve your problem.
Answers
The example of the simple interest problem is: What will be the simple interest on $2500 invested at an interest rate of 6% for 2 years?
What is simple interest?
Calculating the amount of interest that will be owed on a sum of money at a certain rate and for a specific period of time is possible using simple interest. Contrary to compound interest, where we add the interest of one year's principal to the next year's principal to compute interest, the principal amount under simple interest remains constant.
Solution for the above problem is:
The formula to calculate simple interest is:
[tex]S.I. = P \times I \times T[/tex]
Here, S.I. is simple interest, P = principal amount, I = interest rate, T = time
Given in the question:
P = $2500
I = 6% = 0.06 (in decimals)
T = 2
Putting the value in the question:
S.I. = 2500(0.06)(2)
S.I. = 300
Therefore, the simple interest is $300.
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Find the value of each variable
Answers
Step by step
The two “x” variable angles are supplementary so combined they will equal 180 degrees
2(5x -5) + (3x -5) = 180
Distribute
10x -10 + 3x -5 = 180
Combine
13x -15 = 180
Add 15 to both sides to isolate variable
13x -15 + 15 = 180 + 15
Combine
13x = 195
Divide both sides by 13 to solve for x
13/13 x = 195/13
x = 15
The two “y” variable angles are supplementary so combined they will equal 180 degrees
5y + 5 + 20y = 180
Combine
25y + 5 = 180
Subtract 5 from both sides to isolate y
25y +5 -5 = 180 -5
25y = 175
Divide both sides by 25 to solve for y
25/25 y = 175/25
y = 7
Rewrite without parentheses.
(4x²z² − 6x³)(-8xz¹)
-
Simplify your answer as much as possible
Answers
Answer:
Step-by-step explanation:-32x³z³+48x∧4z
a. cos x b. tan x c. sec x d. cot x Simplify the expression
Answers
First, multiply by 1:
cos x * 1 + cos x tan^2 x
Factor cos x out of cos x tan^2 x
cos x * 1 + cos x (tan ^2 x)
Factor again
cos x (1+ tan^2 x)
Rearrange:
cos x (tan^2 x +1 )
Apply Pythagorean identity:
cos x * sec ^2 x
Rewrite Sec x in terms of sin and cos
cos x * (1 / cos x )^2
Apply product rule:
cos x * 1^2 / cos^2 x
cos x * (1/ cos^2 x )
Cancel common factor cos x
1 / cos x
1/cosx = sec x
Answer : sec x (option c)
The first three terms of an arithmetic sequence are as follows 33,25,17 what’s the next two terms of this sequence
Answers
The next two terms of the given given sequence are 9, 1 if the first three terms of arithmetic sequence are 33, 25, 17.
An arithmetic sequence has a constant difference (d) and is defined by
a(n) = a(1) + (n-1)d ----------- (1)
Here a(1) = 33, a(2) = 25, a(3) = 17
d = a(2) - a(1)
d = 25 - 33 = -8
Substitute the values in (1)
a(n) = 33 + (n-1)(-8)
a(n) = 33 - 8n + 8
a(n) = -8n + 41 ------------- (2)
We have to find a(4) and a(5)
Substitute n = 4 in (2), we get
a(4) = -8(4) + 41 = -32 + 41 = 9
Substitute n = 5 in (2), we get
a(5) = -8(5) + 41 = -40 + 41 = 1
Hence the next two terms are 9, 1.
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PLEASE HELP RIGHT NOW, THIS IS SUPER URGENT
The graph shows the proportional relationship between the number of gems collected and the number of levels that have been completed in a video game.
Graph with x axis labeled game levels and y axis labeled gems collected. A line begins at 0 comma 0 and goes through points 6 comma 450 and 8 comma 600.
Determine the constant of proportionality for the relationship.
p equals 2 over 150
p = 0.0133
p = 75
p = 150
Answers
The constant of proportionality for the graph will be P=75. The correct option is C.
What is a slope?Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line.
The proportionality of the constant determines the linear relation between two variables. as one increases the another also increases with the same factor.
To calculate the constant of proportionality for the given graph finds the slope of the graph with the points.
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope = ( 600 - 450 ) / ( 8 - 6 )
Slope = ( 150 / 2
Slope= 75
Therefore, the constant of proportionality for the graph will be P=75. The correct option is C.
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Parallel lines investigation
Answers
From the given figure the value of x is 6 and the measure of angle 3 is 57°.
From the given figure, m∠4=(20x+3)° and m∠6=(9x+3)°.
What are angles of parallel lines?Angles in parallel lines are angles that are created when two parallel lines are intersected by another line called a transversal.
22). From the given figure
m∠4+m∠6=180° (Coointerior angles sum is equal to 180°)
(20x+3)°+(9x+3)°=180°
⇒ 29x+6=180
⇒ 29x=174
⇒ x=6
m∠4=(20x+3)°=123°
m∠3+m∠4=180° (Adjacent angles sum is equal to 180°)
m∠3+123=180
m∠3=57°
23). From the given figure
m∠3=m∠6 (Alternate interior angles are congruent)
x+10 = 4x-20
⇒ 3x=30
⇒ x=10
Now, m∠6=4x-20
=20
m∠6+m∠8=180° (Adjacent angles sum is equal to 180°)
20+m∠8=180°
⇒ m∠8=160
Therefore, from the given figure the value of x is 6 and the measure of angle 3 is 57°.
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You invest $8,000 in 3 investment accounts. The accounts are: paper, metal and glass. Paper returns 2% income, metal returns 4% income, and glass returns 5% income. The amount invested in the glass account was double the amount invested in the metal account. The yield was a total of $280 at the end of one year. How much was invested in each account?
Answers
The following investments were done:
Metal account: $ 1,500Glass account: $ 3,000Paper account: $ 3,500How much money has a person invested in three accounts?
In this problem we must determine how much money from a $ 8,000 investment has been deposited in each account based on overall yield after a period of one year. In accordance with the statement, the person deposited the following quantities in each account:
Metal: x
Glass: 2 · x
Paper: 8,000 - 3 · x
And the yield function is equal to:
280 = x · (4 / 100) + 2 · x · (5 / 100) + (8,000 - 3 · x) · (2 / 100)
280 = 0.04 · x + 0.1 · x + 160 - 0.06 · x
120 = 0.08 · x
x = 1500
The person made an investment of $ 1,500 in the metal account, $ 3,000 in the glass account and $ 3,500 in the paper account.
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Write the equation in standard form for the hyperbola with vertices (-2,0) and (2,0) and a conjugate axis of length 14
Answers
Solution
- The equation of a hyperbola is given s:
[tex]\begin{gathered} \frac{(x-h)^2}{a}-\frac{(y-k)^2}{b}=1 \\ \\ where, \\ coordinates\text{ of the vertices}=(h\pm a,k) \\ Length\text{ of conjugate axis}=2b \end{gathered}[/tex]- Thus, we can find that:
[tex]\begin{gathered} (\pm2,0)=(h\pm a,k) \\ \\ k=0 \\ \therefore h+a=2 \\ h-a=-2 \\ \text{ Subtract both equations, we have:} \\ 2a=4 \\ a=\frac{4}{2}=2 \\ \\ h+a=2 \\ h+2=2 \\ h=2-2=0 \\ \\ \text{ Thus, we have that the center of the hyperbola is: }(h,k)=(0,0) \\ \\ 2b=14 \\ \text{ Divide both sides by 2} \\ b=\frac{14}{2}=7 \end{gathered}[/tex]Final Answer
The equation of the parabola is:
[tex]\frac{x^2}{2^2}-\frac{y^2}{7^2}=1[/tex]The sum of two consecutive integers is 97. What is the smaller integer?
Answers
Answer: 48 is the smaller integer
Step-by-step explanation: 48+49=97 48 and 49 are the two integers, 48 is smaller than 49.
yeaa pls help this is past due
Answers
Answer: When you graph part a, it has a negative slope.
Step-by-step explanation:
Find the area of thisirregular figure.9 ft8 ft15 ft26 ft
Answers
The area of the irregular figure will be equal to the sum of area of triangle and the area of the rectangle.
The required area can be determined as,
[tex]\begin{gathered} A=A_t+A_r \\ =(\frac{1}{2}\times8\text{ ft}\times9\text{ ft)+(15 ft}\times26\text{ ft)} \\ =36ft^2+390ft^2 \\ =426ft^2 \end{gathered}[/tex]Thus, the required area of the irregular figure is 426 square feet.
if square one is the largest of the three squares in the model,which statement is true?
Answers
_______________
I'm reading your question
___________________
According to the Pythagorean theorem
Hypotenuse ^2 = Side 1 ^2 + Side 2 ^2
The hypotenuse is the case (Square 1 )
area of the sqaure= side of the square^2
________________________
That means the area of 1 is = area of square 2 + area fo square3 (J is false)
_______________________________
We are not sure about the relation between square 2 and 3 just the addition is the square 1 (F and H we have no certainty)
______________________________
G is true
______________________________
Answer
G
Use slope to determine if lines AB and CD are parallel, perpendicular, or neither 10. A(3, 1), B(3,-4), C(-4,1), D (-4,5)m(AB) m(CD) Types of lines
Answers
Neither parallel nor perpendicular
Explanations:The points are:
A(3, 1), B(3,-4), C(-4,1), D (-4,5)
The slope of a line is given as:
[tex]m\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex]The slope of the line AB, m(AB), with gthe points A(3, 1), B(3,-4) is given as:
[tex]\begin{gathered} m(AB)\text{ = }\frac{-4-1}{3-3} \\ m(AB)\text{ = }\frac{-5}{0} \\ m(AB)\text{ =- }\infty \end{gathered}[/tex]The slope of the line CD, m(CD), with the points C(-4,1), D (-4,5) is given as:
[tex]\begin{gathered} m(CD)\text{ = }\frac{5-1}{-4-(-4)} \\ m(CD)\text{ = }\frac{4}{-4+4} \\ m(CD)\text{ = }\frac{4}{0} \\ m(CD)\text{ = }\infty \end{gathered}[/tex]A line that has an infinite slope is a vertical line
For the two lines to be parallel, m(AB) should be equal to m(CD)
For the two lines to be perpendicular, m(AB) = -1 / m(CD)
None of the conditions for paralleleism and perpendicularity is met, the lines AB and CD are neither parallel nor perpendicular
Maths problem in indices. Pls help
Answers
Answer:
x = 9
Step-by-step explanation:
using the rule of indices
[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex] , then
[tex]5^{x}[/tex] = [tex]\frac{5^{8} }{5^{-1} }[/tex] = [tex]5^{(8-(-1))}[/tex] = [tex]5^{(8+1)}[/tex] = [tex]5^{9}[/tex]
since bases on both sides are equal, both 5 , then equate indices
x = 9
