Answer:
distributive property is your answer
kjs is a right triangle formed by the placement of 3 squares. what is the area of the shaded square?
area of small square = 87 in
side of big square = 18 in
The area of the square having the same length of the base of the triangle is 7245 square inches.
What is Pythagoras's theorem?In a right-angled triangle, the sum of the squares of the smaller two sides of a right-angle triangle is equal to the square of the largest side.
From the given figure as the base of the triangle is an equal length of the side of a square we can obtain the area of the square by first applying Pythagoras on the right angle triangle having a height of 87 inches and a hypotenuse of 18 inches.
So,
Base = {√(87² - 18²)}.
Base = √(7245) inches.
Base = 85.11 inches.
Now, We also know that the area of a square is (side)².
Therefore it is (87.11)² which is the same as 7245 sq inches.
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The Students' Union needs to order some pens and notebooks. How much does it cost to order 1000 pens and 2000 notebooks?
$
Pen
Quantity 100 250 500 1000 2500 5000
Price per pen (cents) 80c 72c 66c 60c 52c 45c
Notebook
Quantity 100 250 500 1000 2500 5000
Price per notebook (cents) 99c 86c 80c 76c 72c 70c
The cost to order 1, 000 pens and 2, 000 notebooks, by the Student Union, can be found to be
How to find the cost of ordering the pens and notebooks ?The cost of ordering 1, 000 pens is shown to be 60 cents per pen so the total cost would be :
= Number of pens x Cost per pen
= 1, 000 x 60 cents
= $ 600
The cost of ordering 2, 000 notebooks is 76 cents per notebook which comes to a total of :
= 2, 000 x 76 cents
= $ 1, 520
The total cost of ordering the pens and notebooks is:
= 600 + 1, 520
= $ 2, 120
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S= pi^2(b^2-a^2)
b=8
a=10
work out the value of S and give the answer to 3 significant figure
Answer:
S = pi^2 * (8^2 - 10^2)
= pi^2 * (-4)
= -12.57 pi^2
The value of S is approximately -12.57 * pi^2. To express this value to three significant figures, we would round it to -13 * pi^2, which is the same as -12.6 * pi^2. So the final answer is -12.6 * pi^2.
A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
Answer:
The three statements that are always true regarding this diagram are:
m∠3 + m∠4 + m∠5 = 180°
m∠2 + m∠3 + m∠5 = 180°
m∠2 + m∠3 = m∠6
Here's why:
The sum of the measures of the interior angles of a triangle is always 180°. Therefore, m∠2 + m∠3 + m∠5 = 180°.
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles. Therefore, m∠4 = m∠2 + m∠5, and m∠3 + m∠4 + m∠5 = 180°.
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles. Therefore, m∠6 = m∠2 + m∠3.
The other two statements are not always true. For example, if m∠5 = 100° and m∠3 = 80°, then m∠5 + m∠3 = 180°, but m∠4 ≠ 0°. Similarly, if m∠5 = 100° and m∠6 = 80°, then m∠5 + m∠6 ≠ 180°.
Step-by-step explanation:
Directions: Determine whether each relation is a function. Explain your answer.
X
12)
10)
#IN
13)
x
14)
15)
10
Answer:
10. Yes
11. No
12. Yes
13. Yes
14. No
15. No
Step-by-step explanation:
Use the vertical line test to determine whether or not a relation is a function. The vertical line test is when you draw a line through a relation and if that line intersects the relation more than ONCE, the relation is not a function.
10. Is a function, the vertical line only intersects the relation once.
11. Isn't a function, intersects the relation more than once.
12. Is a function, intersects the relation only once.
13. Is a function, only intersects the relation once.
14. Isn't the function, intersects the relation more than once.
15. Isn't a function, the relation intersects the function more than once.
Hope this helps.
helo i need help with my math please thanky uo i need help with question 3
On one tank of gas Charlie will drive 612 km
At a cost of 149.9, Charlie will fill the tank with the sum of 8994
Annual cost of filling the tank 467688
How to find how far Charlie can drive on one tank of gasInformation from the problem have it that the efficiency if the Volkswagen golf is 10.2 km/L
Hence, on one liter rides 10.2 km and on a tank which is 60 L Charlie will ride
= 60 * 10.2
= 612 km
Cost of filling the tank
The cost per liter is 149.9 for 60 L we have
= 149.9 * 60
= 8994
Filling the tank once week, the cost for filling in one year is
1 year is 52 weeks
= 8994 * 52
= 467688
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5x -2y = 1, ax -6y = b
whet are the values of a and b such that the equations have no solutions?
The system of equations will have no solutions if the two lines are parallel, then one example can be:
5x - 2y = 1
15x - 6y = 0
For which values of a and b the system has no solutions?Here we have the following system of equations:
5x - 2y = 1
a*x - 6y = b
The system will have no solutions only if the two equations are parallel. You can see that the coefficient of y on the second equation is 3 times the coefficient on the first equation.
Then a should also be 3 times the coefficient of x on the first equation:
a = 3*5
a = 15
And b should be any number but 3 times the constant on the other equation:
b ≠ 3*1
So we can take b = 0, for example.
So the system with no solutions will be:
5x - 2y = 1
15x - 6y = 0
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Shelby mixes a 25% bleach solution with 5 cups of a 10% bleach solution, resulting in a 20% bleach solution. The table shows the amount of each solution used.
Answer: 5%
Step-by-step explanation:
Answer:
answer is 10
Step-by-step explanation:
Hafiz has $25. His sister has 1/5 as much as Hafiz. His father has 40% as much as Hafiz. Calculate how much money Hafiz, his sister and his father have in total.
please answer it
Answer:
Step-by-step explanation:
According to question, we know that
His Sister has "1/5*$25 which is equal to $5, and his father has "40%*$25 which is equal to 0.4 * $25 = $10". So, the money Hafiz, his sister and his father have in total
= $25+$5+$10 = $40
Hafiz = $25
Sister = [tex]\frac{1}{5}[/tex]
Father = 40%
FindTotal money of Hafiz, Sister, and Father altogether.
SolutionSister[tex]\frac{1}{5} X[/tex] $25
= $5
Father40% (0.4) x $25
= $ 10
Add all$ 25 + $ 5 + $ 10
Answer$ 40You decide to take a hot air balloon ride and remember to take binoculars to look around while you are airborne. As the balloon rises, you use a GPS to determine your height in meters, h, and the distance in kilometers, d, to the farthest object that you can see. The table below shows the two measurements.
Height in meters 15 30 45 60 75 90 105
Distance in kilometers 13.833 19.562 23.959 27.665 30.931 33.833 36.598
1. Determine a function that could be used to model the data in the table.
Make sure to use h for height and d for distance.
2. If the balloon is 800 meters high, what is the farthest distance that you would be able to see? Round answer to the nearest whole number
3. What type of function best models the data in the table?
4. A building is 16km away. What height does the balloon have to rise for the building to be visible. Round the answer to nearest whole number.
Therefore , the solution of the given problem of solution of trigonometry d = 33.977 m is the distance from the balloon's base to its apex..
Explain trigonometry.Trigonometry is a discipline of mathematics that examines relationships between triangles' degrees and sides. Trigonometry is used frequently in geometry because every straight-sided form may be broken down into a group of triangles. Trigonometry and other areas of mathematics, particularly calculus, real or complex, infinite series, logarithms, and infinite series, have a staggering amount of interrelationships.
Here,
Angle of elevation to the balloon's peak: = 28°
When the balloon is erect, a right triangle is formed by the horizontal distance to the balloon, l, the height of the balloon, h, and the distance to the top of the balloon, d.
Aside from the hypotenuse
l = The leg next to the provided reference angle
,h = The leg perpendicular to the specified angle,
Trigonometric ratios give us;
Cosx is equal to the product of the hypotenuse and adjacent lengths.
where we obtain;
Cos x equals l/d
=>Cos 28 = 30 m /d
=> d = 30m/Cos 28 ≈ 33.977
Therefore , the solution of the given problem of solution of trigonometry d = 33.977 m is the distance from the balloon's base to its apex.
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Kiara invested some money into a savings account that earns 2.7% annual simple interest. At the end of 5 years, she earned $6.62 in interest. How much money did she put into the account initially? Round to the nearest dollar.
The initial amount that was invested in the account was $49.
What is the principal?We know that we can be able to obtain the principal by the use of the formula for the simple interest and by that formula we would now have that;
I = PRT/100
I = interest
P = principal
R = rate
T = time
Then we are going to have that;
R = 2.7
P = ?
I = 6.62
T = 5
Then;
6.62 = P * 2.7 * 5/100
6.62 * 100 = P * 2.7 * 5
P = 6.62 * 100/2.7 * 5
P = 662/13.5
P = 49
Thus we have but in at the beginning about $49
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Graph the solution to this inequality on the number line.
The
Using a straight line and either an open circle or a closed circle to indicate the end points, we can depict inequalities on a number line by displaying the range of integers.
How do you identify inequalities?By drawing a straight line and designating the end points with either an open circle or a closed circle, we can depict inequalities on a number line by illustrating the range of integers. An open circle indicates that it excludes the value. A closed circle indicates that it does contain the value.
Both equations and inequalities are mathematical phrases created by connecting two expressions. The equal sign (=) in an equation denotes that the two expressions are regarded as equal. In contrast, an inequality indicates that the two phrases are not always equal by using the symbols >,,, or.
With regard to the inequality expression
-3m + 5 > 14
5 from each side is subtracted.
-3m + 5 - 5 > 14 - 5
-3m > 9
Subtract -3 from both sides.
-3m/-3 < 9/-3
m < -3
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Find two consecutive odd numbers such that the difference between their reciprocals is 2/99.
note (the answer key said 9 and 11 and after testing it, it was correct, but I don't know how to get that answer)
Note (the chapter name is fractional equations, so they want us to make an equation and solve it)
The two consecutive odd numbers such that the difference between their reciprocals is of 2/99 are given as follows:
9 and 11.
How to obtain the numbers?The two numbers are odd numbers and consecutive, hence they are symbolized as follows:
n and n + 2. (as n + 1 is even).
Their reciprocals are given as follows:
1/n.1/(n + 2).The difference of their reciprocals is obtained as follows:
1/n - 1/(n + 2) = 2/99.
The least common factor of n and n + 2 is of n x (n + 2), hence:
(n + 2 - n)/[n(n + 2)] = 2/99
2/[n(n + 2)] = 2/99.
As the numerators are equal, we take the denominators to solve for n as follows:
n(n + 2) = 99.
n² + 2n - 99 = 0.
(n - 9)(n + 11) = 0.
Applying the Factor Theorem, the solutions are given as follows:
n - 9 = 0 -> n = 9.n + 11 = 0 -> n = -11.We want the positive numbers, hence the numbers are:
n = 9 and n + 2 = 9 + 2 = 11.
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Suppose we have a bag with 10 slips of paper in it. Eight slips have a 3 on them and the other two have a 5 on them.
(a) What is the expected value of the number shown when we draw a single slip of paper?
(b) What is the expected value of the number shown if we add one additional 3 to the bag?
(c) What is the expected value of the number shown if we add two additional 3's (instead of just one) to the bag?
The expected values for each experiment are:
A) 3.4
B) 3.36
C) 3.33
How to get the expected values?If we have an experiment with the outcomes:
{x₁, x₂, ..., xₙ}
Each one with the correspondent probability:
{p₁, p₂, ..., pₙ}
Then the expected value of that experiment will be:
EV = x₁*p₁ + x₂*p₂ + ... + xₙ*pₙ
A) in this case we have 10 slips of paper, 8 of them with the number 3, and 2 of them with the number 5.
So the outcomes are:
{3, 5}
The probabilities are:
{8/10, 2/10}
Then the expected value is:
EV = 3*(8/10) + 5*(2/10) = 3.4
B) If we add another slip of paper with a number 3 on it, the new probabilities are:
{9/11, 2/11}
Then the new expected value is:
EV = 3*(9/11) + 5*(2/11) = 3.36
C) Finally, if we add 2 slips of paper with the number 3, now we will have a total of 12 slips of paper, then the new probabilities are:
{10/12, 2/12}
So the new expected value is:
EV = 3*(10/12) + 5*(2/12) = 3.33
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Melissa opened a savings account and deposited $700.00 as principal. The account earns 15% interest, compounded annually. What is the balance after 8 years?
Use the formula A=P1+
r
n
nt, where A is the balance (final amount), P is the principal (starting amount), r is the interest rate expressed as a decimal, n is the number of times per year that the interest is compounded, and t is the time in years.
Round your answer to the nearest cent.
Balance after 8 years is $2,306.86 at an interest rate of 15 % compounded yearly.
What is compound interest?Compound interest simply refers to the fact that an investment, loan, or bank account's interest accrues exponentially over time as opposed to linearly over time. The word "compound" is crucial here.
given, Melissa opened a savings account and deposited $700.00 as principal. The account earns 15% interest
from the general formula of compound interest
A = [tex]P(1 + r/n)^{nt}[/tex]
where A is the balance (final amount), P is the principal (starting amount), r is the interest rate expressed as a decimal, n is the number of times per year that the interest is compounded, and t is the time in years.
Given, P = 700$
r = 15%
t = 8 years
A = 700(1 + 15/100)⁸
A = 2306.86$
Therefore, At a 15% annual compounded interest rate, the remaining balance after 8 years is $2,306.86.
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What is the solution for the system of linear equations shown in the graph?
Graph and answers in picture below
Answer:
(d) (-1/4, 3/4)
Step-by-step explanation:
You want the solution to the graphed system of equations.
SolutionThe solution is the point that satisfies both equations, the point where the lines intersect. That point is in the 2nd quadrant, where x-values are negative.
The only suitable answer choice is ...
(x, y) = (-1/4, 3/4)
Which statement correctly compares the centers of the distributions?
Answer:
B
Step-by-step explanation:
Center of the distributions -> mean/median (preferably mean)
The option with range is eliminated
Median might not be accurate as median is the center person, not the center result.
Based on the graphs, identify the graph with the intervals of greatest frequency.
For North Heights -> between 30 and 32 (right-skewed, some higher values)
For Southview -> between 28 and 30 (most concentrated there)
Hence, mean of Southview is lower than North Heights.
find the slope for 1-6
Answer:
1) 10/3
2) -1./3
3) -2/5
4) 1
5) undefined
6) 0
Step-by-step explanation:
Find two easy to read points. Go from one point to the other by going vertically first then horizontally. Moving up is positive and down is negative. Moving right is positive and left is negative.
slope = rise/run = (difference in y)/(difference in x)
1) slope = 10/3
2) slope = -1/3
3) slope = -2/5
4) slope = 1/1 = 1
5) slope = undefined (The slope of a vertical line is undefined.)
6) slope = 0 (The slope of a horizontal line is 0.)
find the truth value Of 3+4= 12, then 3+2=6
The truth value of "If 3 + 4 = 12, then 3 + 2 = 6", is true.
What is Truth Values?Truth value is defined as whether the given proposition is either true or false, not both.
Here the proposition is of the form if p, then q.
Here p is the statement 3 + 4 = 12 and q is the statement 3 + 2 = 6.
Here, both of the propositions are false.
The truth value of 'if p, then q' is false only when p is true and q is false. In all other cases the truth value is true.
Here, since both of the statements are false, the truth value is true.
Hence the truth value of the given proposition is true.
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Laura, Tom and Alex share £95 in the ratio 8:7:4 find how much money each of them will receive
Answer:
Laura: £40Tom: £35Alex: £20Step-by-step explanation:
You want the amount of money each receives if Laura, Tom, and Alex share £95 in the ratio 8:7:4.
Ratio unitsThe total number of ratio units is 8+7+4 = 19, corresponding to a total amount of £95. That makes each ratio unit represent £95/19 = £5.
Multiplying the ratio units by £5, we find the distribution to be ...
Laura : Tom : Alex = £40 : £35 : £20
Answer:
Money received by Laura = 8x = 8x5 = £40
Money received by Tom = 7x = 7x5 = £35
Money received by Alex = 4x = 4x5 = £20
Step-by-step explanation:
Given ,
Laura, Tom and Alex share £95 in the ratio 8:7:4To Find : How much money will each of them receive
Let us take the variable as 'x' to find the money received by them
When we convert it to a equation
8x+7x+4x = 95
19x = 95
x = [tex]\frac{95}{19}[/tex]
x = 5
Money received by Laura = 8x = 8x5 = £40
Money received by Tom = 7x = 7x5 = £35
Money received by Alex = 4x = 4x5 = £20
Hence, the money received by each of them is £40, £35 and £20
Write the number 4,207 in expanded form
Answer:
That's easy! four thousand two hundred and seven or 4,000+200+7
Step-by-step explanation:
Find tan0, where 0 is the angle shown.
Give an exact value, not a decimal approximation.
The exact value of tan θ = 15/ 8
What are trigonometric identities?Trigonometric Identities are defined as the equalities involving trigonometry functions and also one that holds true for all the values of the variables in the given equation.
The trigonometric functions are;
sinecosinetangentcotangentsecantFrom the information given, we have;
tan θ = opposite/ adjacent
To determine the adjacent sent
17² - 15² = x²
x = √64
x = 8
Substitute the value
tan θ = 15/8
Hence, the value is 15/8
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please answer this with work
Answer:
Step-by-step explanation:
-38 + -12x < -200
Answer:
-38 - 12x > -200
x = 13.5 min
Step-by-step explanation:
let x = minutes of the dive
-38 ft - 12 ft/min(x) > -200 ft
-12 ft/min(x) < -162 ft
x > -162/-12 **flip the inequality when you divide by a (-) number
x > 13.5 min
Starting at -38 ft, he has to dive longer than 13.5 minutes to go deeper than -200 ft at a rate of -12 ft/min
Which expression is equivalent to 10 ?
0 x²(√²)
Ox2.2
O
**(√)
5
Mark this and retur
Save and Exit
Next
Submit
The expression 10+(-8) is equivalent to 10 - 8.
What is expression?Different branches of mathematics exist. The branch of knowledge that deals with numbers and operations is arithmetic. We learned how to add, subtract, multiply, and divide two or more numbers through arithmetic.
Shapes and how they are created with various tools, such as a compass, ruler, and pencil, are the focus of geometry. Another fascinating area of study is algebra, which helps us communicate the numerical and alphabetic aspects of daily life (variables).
Any mathematical statement made up of numbers, variables, and an operation between them is called an expression or an algebraic expression. As an illustration, the expression 4m + 5 consists of the terms 4m and 5, as well as the variable m, all of which are separated from one another by the arithmetic sign +.
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Full question
What expression is equivalent to 10-8?
if its a linear equation in two variables
Answer:
SOLVE A SYSTEM OF LINEAR EQUATIONS BY GRAPHING.
Graph the first equation.
Graph the second equation on the same rectangular coordinate system.
Determine whether the lines intersect, are parallel, or are the same line.
Identify the solution to the system. ...
Check the solution in both equations.
Step-by-step explanation:
An equation is said to be linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero. For example, 10x+4y = 3 and -x+5y = 2 are linear equations in two variables.
A scientist uses a submarine to study ocean life.
She begins at sea level, which is an elevation of 0 feet.
She travels down 4.2 feet.
She then travels directly up 3.4 feet.
Next, she descends a second time, 10 feet.
Answer:
Below
Step-by-step explanation:
0 ft -4.2 + 3.4 - 10 = -10.8 ft or 10.8 ft below the surface
Which of the following is equivalent to 5/20 ? *
Mark only one oval.
2/10
10/30
5/10
1/4
Consider all five-digit numbers that can be created from the digits 0-9 0 - 9 where the first and last digits must be odd and no digit can repeat. What is the probability of choosing a random number that starts with 7 7 from this group? Enter a fraction or round your answer to 4 4 decimal places, if necessary.
Find the slope of the line that has an equation of 4x-2y=6
4x - 2y = 6
2y = 4x - 6
y = (4x - 6)/2
y = 2x - 3
Nevaeh has $0.80 worth of nickels and dimes. She has a total of 11 nickels and dimes altogether. Graphically solve a system of equations in order to determine the number of nickels, x,x, and the number of dimes, y,y, that Nevaeh has.
Answer: We can set up a system of equations to represent this problem. The first equation represents the total value of the nickels and dimes in terms of the number of nickels and dimes that Nevaeh has:
0.05x + 0.1y = 0.80
The second equation represents the total number of nickels and dimes that Nevaeh has in terms of the number of nickels and dimes that she has:
x + y = 11
To graphically solve this system of equations, we can use the slope-intercept form of the linear equations.
y = -2x + 22
y = -1/2 x + 8
The solution would be the point where the lines intersect , which x = 4, and y = 7 .
So she has 4 nickels, and 7 dimes.
Step-by-step explanation: