29 + 14 = 44 by decomposing numbers to add and make a new 10.
Describe Decomposition of numbers?Decomposition of numbers involves breaking a number down into its constituent parts or smaller numbers that add up to the original number. This can be done in different ways depending on the purpose and context of the problem.
For example, one common way of decomposing a number is by place value. In this case, the number is broken down into its digits, which represent different powers of ten. For instance, the number 562 can be decomposed into 500 + 60 + 2.
Another way of decomposing numbers is by factoring. In this case, the number is expressed as a product of its factors. For example, the number 12 can be decomposed as 2 x 2 x 3.
Decomposing numbers is a useful skill in many areas of mathematics, including arithmetic, algebra, and geometry. It is often used to simplify problems, make computations easier, and facilitate further analysis.
To decompose 29 to make a new 10, we can break it into 9 and 20. Then, to decompose 14 to make a new 10, we can break it into 6 and 8.
So, we have:
29 + 14 = (9 + 20) + (6 + 8)
Now, we can regroup the numbers to make a new 10:
= (9 + 1) + (20 + 6) + 8
= 10 + 26 + 8
= 44
Therefore, 29 + 14 = 44 by decomposing numbers to add and make a new 10.
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Can the sides of a right triangle have lengths 5, 15, and √250? Explain.
A triangle must have a third side that is bigger than the sum of any two of its sides. There cannot be a triangle with these side lengths because in this instance, 5 + 15 = 20 is not greater than 250.
Application of Pythagoras theoremTo check whether the given lengths can form the sides of a right triangle, we need to check if they satisfy the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Let's label the sides of the triangle as a, b, and c, where c is the hypotenuse. Then, the Pythagorean theorem can be written as:
a^2 + b^2 = c^2
Plugging in the given values, we get:
5^2 + 15^2 = (√250)^2
Simplifying the left-hand side, we get:
25 + 225 = 250
This is not true, since 25 + 225 = 250 does not hold. Therefore, the given lengths cannot form the sides of a right triangle.
In fact, we can see that the given lengths violate the triangle inequality, which states that the sum of any two sides of a triangle must be greater than the third side. In this case, 5 + 15 = 20 is not greater than √250, so a triangle with these side lengths cannot exist.
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can someone please solve?
Answer:
Vertex: (0,0)
Step-by-step explanation:
Two points on the left: (-10,25), (-20,100)
Two points on the right: (10,25), (20,100)
please help, thank you!
Answer:
To find all values of x for which f(x) = 26, we can set up the equation:
8x + 15/x = 26
Multiplying both sides by x, we get:
8x^2 + 15 = 26x
Bringing all the terms to one side, we get:
8x^2 - 26x + 15 = 0
We can factor this quadratic equation using the factoring method or by using the quadratic formula. Here, we will use the factoring method:
8x^2 - 26x + 15 = 0
(4x - 3)(2x - 5) = 0
Setting each factor equal to zero and solving for x, we get:
4x - 3 = 0 OR 2x - 5 = 0
4x = 3 OR 2x = 5
x = 3/4 OR x = 5/2
Therefore, the values of x for which f(x) = 26 are x = 3/4 or x = 5/2.
What is the length of triangle
Answer:
in a right triangle, the square of the length of the hypotenuse (the side across from the right angle) is equal to the sum of the squares of the other two sides. So if the length of the hypotenuse is c and the lengths of the other two sides are a and b, then c^2 = a^2 + b^2.Apr 24, 2017
What is the area of circle C rounded to the nearest tenth?
Use 3.14 for π .
138.2 cm 2
276.3 cm2
1314.8 cm 2
1519.8 cm2
Answer:
D. 1519.8
Step-by-step explanation:
2 eggs are needed to make 24 cookies. how many eggs are needed to make 60 cookies
Answer:
5 eggs.
Step-by-step explanation:
Since two eggs are needed for 24 cookies, we know by dividing both numbers by two that the rate is one egg for 12 cookies. 60/12 = 5. Multiply both numbers by 5 to get the answer. So, the answer is 5 eggs.
The Harris Family Entertainment Club deposited R3 600 in an investment account a year ago, with the intention of purchasing new equipment in four years’ time. Today, it is adding a further R5 000 to this account. Plans are to make a final deposit of R7 500 in the account next year. How much will be available when the family is ready to buy the equipment, assuming the investment earns a 7% rate of return?
Answer:
Step-by-step explanation:
To calculate this, we need to use the formula for future value of an annuity:
FV = PMT x ((1+i)^n - 1)/i
Where:
PMT = the periodic payment (or deposit)
i = the interest rate per period
n = the number of periods
In this case, there are three deposits:
- R3,600 deposited one year ago
- R5,000 deposited today
- R7,500 to be deposited next year
We can calculate the future value of each of these deposits separately, and then add them together to get the total future value:
Future value of R3,600 deposited one year ago:
n = 4 (4 years until the equipment purchase)
i = 7% per year
PMT = R3,600
FV = R3,600 x ((1+0.07)^4 - 1)/0.07 = R4,661.07
Future value of R5,000 deposited today:
n = 3 (3 years until the equipment purchase)
i = 7% per year
PMT = R5,000
FV = R5,000 x ((1+0.07)^3 - 1)/0.07 = R6,885.02
Future value of R7,500 to be deposited next year:
n = 2 (2 years until the equipment purchase)
i = 7% per year
PMT = R7,500
FV = R7,500 x ((1+0.07)^2 - 1)/0.07 = R8,733.63
Total future value = R4,661.07 + R6,885.02 + R8,733.63 = R20,279.72
Therefore, there will be R20,279.72 available when the family is ready to buy the equipment, assuming a 7% rate of return on the investment.
All I need to know is the answer to this problem so I can compare mine.
The measure of the angle A in the given right angled triangle is found as: A = 64.82°
Explain about the trigonometric functions?Angle functions are those of trigonometry. They are used to establish a connection between a triangle's angles and side lengths.The basic operations can be used to calculate the other two side lengths if you only have an angle and one side length. By considering the reciprocal of a primary functions, one can find the reciprocal functions.Applying the sin function in the given right angled triangle.
Sin A = 77/85
Sin A = 0.905
A = Sin⁻¹ (0.905)
A = 64.82°
Thus, the measure of the angle A in the given right angled triangle is found as: A = 64.82°
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The box plots show the weights, in pounds, of the dogs in two different animal shelters.
Weights of Dogs in Shelter A
2 box plots. The number line goes from 6 to 30. For the weights of dogs in shelter A, the whiskers range from 8 to 30, and the box ranges from 17 to 28. A line divides the box at 21. For shelter B, the whiskers range from 10 to 28, and the box ranges from 16 to 20. A line divides the box at 18.
Weights of Dogs in Shelter B
Which animal shelter has the dog that weighs the least?
shelter A
Step-by-step explanation:
The minimum weight for shelter A is not provided in the given information, but we can compare the minimum weight of shelter B with shelter A's box plot.
As per the given information, the whisker of shelter A ranges from 8 to 30, which means the minimum weight in shelter A is 8 pounds. On the other hand, the whisker of shelter B ranges from 10 to 28, which means the minimum weight in shelter B is 10 pounds. Therefore, shelter A has the dog that weighs the least.
Answer:
Your answer is correct, it's shelter A.
Step-by-step explanation:
Felix is making a pattern with tiles shaped like parallelograms. He needs 5 black tiles
and 5 white tiles. The tiles cost $0.50 per cm².
What is the total cost needs
to buy?
A =
? cm²
27
2.4 cm
2 cm
4 cm
The total area of the tiles that Felix needs to buy would be = 80cm²
How to calculate tye total area of tiles needed by Felix?The quantity of black tiles needed by Felix = 5
The quantity of white tiles needed by Felix = 5
The cost of each tile = $0.50 per cm².
The area of a tile = area of parallelogram = base×height.
base = 4cm
height = 2cm
area = 2×4 = 8cm²
For the 10 tiles = 8×10 = 80cm²
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what is 4x+3=11 what is the value of x?
Answer:
The Answer is x=2
Step-by-step explanation:
Hope this helps!!!!
Answer:
x=2
Step-by-step explanation:
4x+3=11
4x=11-3 ( subtract 3 on both sides)
4x=8
x=2 ( divide 4 on both sides)
Elimination was used to solve a system of equations.
One of the intermediate steps led to the equation
3x = 18.
Which of the following systems could have led to
this equation?
4x + y = 20
x - y = 2
x + y = 4
x - 2y = 10
2x + y = 24
- x - y = 6
3x + y = 18
-3x - y = - 18
Answer:
x + y = 4x - 2y = 10Step-by-step explanation:
You want to know which set of equations could be combined in such a way as to result in the equation 3x = 18.
Set 14x +y = 20x -y = 2To obtain a term of 3x, the second equation must be subtracted from the first. That will result in 3x +2y = 18, not the equation of interest.
Set 2x +y = 4x -2y = 10A term of 3x can be obtained by adding twice the first equation to the second:
2(x +y) +(x -2y) = 2(4) +(10)
3x = 18 . . . . . as required
Set 32x +y = 24-x -y = 6A term of 3x can be obtained by subtracting the second equation from the first. That will result in 3x +2y = 18, not the equation of interest.
Set 4These equations are dependent. The second is the opposite of the first. They have an infinite number of solutions, not the single solution of the system of equations of interest.
A retailer buys a jacket at a cost of $24 each and sells at a 75% increase in price. What is the retail price of a jacket?
Answer:
$42
Step-by-step explanation:
75%=(3/4) so you do (3/4)*24=18
18+24=$42
Explain the difference between a) comparing, b) non-standard units of measurement and c) standardised units of measurement.
Answer:
a) Comparing: Comparing means evaluating the similarity or difference between two or more objects, values, or variables. It is a process of identifying and highlighting the similarities and differences among objects, values, or variables based on specific criteria.
b) Non-standard units of measurement: Non-standard units of measurement are those that are not part of the International System of Units (SI) and are often created for specific purposes or contexts. These units may be used to measure variables such as time, distance, weight, or volume, but they are not universally recognized or standardized.
c) Standardized units of measurement: Standardized units of measurement are those that are part of the International System of Units (SI) and are universally recognized and accepted. These units provide a standard framework for measuring variables such as time, distance, weight, or volume, making it possible to compare and communicate measurements accurately across different contexts and languages. Some examples of standardized units of measurement include seconds, meters, kilograms, and liters.
A hiker hikes at a steady rate throughout the day on a mountain. Which student wrotr a correct equation to represent the linear relationship shown on the table between X, the number of hours hiked and y, the current altitude of the climber?
There is no table provided to reference, but the equation that represents a linear relationship between X and Y is:
y = mx + b
where m is the slope of the line and b is the y-intercept. The equation can also be written as:
y = b + mx
where b is the y-intercept and m is the slope. The equation represents a straight line on a graph, where the slope determines the steepness of the line, and the y-intercept is the point where the line crosses the y-axis. To write the equation for the table of X and Y values, we need to determine the slope and y-intercept from the given data.
Find the unknown dimension of a rectangle if its perimeter is 254 meters and one
dimension measures 6 meters. Use labeled sketches and equations to model and
solve this problem. Show your work. Label your answer with the correct units.
The perimeter does indeed equal 254 meters, which confirms that our answer is correct.
What in mathematics is the perimeter?Any two-dimensional closed shape's perimeter is defined as the entire distance encircling it. The perimeter of a rectangle, such as the following: Square perimeter equals the sum of its four edges. Rectangle perimeter equals the sum of its four edges.
Let's call the rectangle's unidentified size x.
P = 2l + 2w, where l is the length and w is the breadth, gives the perimeter of a rectangle.
So that we can create an equation:
254 = 2l + 2(6)
Simplifying the right side:
254 = 2l + 12
Subtracting 12 from both sides:
242 = 2l
Dividing both sides by 2:
121 = l
Consequently, the rectangle's undetermined measurement (length) is 121 metres.
We can compute the perimeter using both variables to confirm our conclusion:
P = 2(121) + 2(6) = 242 + 12 = 254
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20 POINTS ANSWER FOR BRAINLIST SHOW WORK
Subtract. Express the answer in standard Form.
(8s ^2 − 3s − 3) − (−4s ^2 + s − 13)
Answer:
To subtract the second polynomial from the first, we need to distribute the negative sign to all terms inside the second set of parentheses, and then combine like terms:
(8s^2 - 3s - 3) - (-4s^2 + s - 13)
= 8s^2 - 3s - 3 + 4s^2 - s + 13 (distributing the negative sign)
= 12s^2 - 4s + 10 (combining like terms)
The resulting polynomial is already in standard form because the terms are arranged in descending order of degree. Therefore, the final answer in standard form is:
12s^2 - 4s + 10
The diameter of a circle is 5 miles. What is the circumference?
Answer: Circumference, C = 15.71 miles
Step-by-step explanation:
The formula for the circumference of a circle is C = 2*pi*r, where C is the circumference and r is the radius. (Value of pi = 3.1415)
In this case, the diameter, d = 5 miles = 2*r, so we can substitute that into the formula:
C = pi*d = 3.1415*5
C = 15.7079 miles
Therefore, the circumference of the circle is approximately 15.71 miles, if we round to two decimal places.
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A sports medicine specialist determines that a
hot-weather training strategy is appropriate for
a 165 cm tall individual whose BSA is less
than 2.0. To the nearest hundredth, what can
the mass of the individual be for the training
strategy to be appropriate?
hom
BSA <2.0
20
1789
Finish
165 cm
^
The mass of the individual can be up to 87.27 kg for the hot-weather training strategy to be appropriate.
How do you solve for the mass of of the individual using the equation provided?Given that the training strategy is appropriate for a BSA less than 2.0, we need to find the maximum mass (M) for the individual with a height (H) of 165 cm. The equation for BSA is:
BSA = √(H x M) / 3600
We can rearrange the equation to solve for M:
M = (BSA^2 x 3600) / H
Since we want the maximum mass for a BSA less than 2.0, we can use BSA = 2.0 as the upper limit:
M = (2.0^2 x 3600) / 165
M = (4 x 3600) / 165
M = 87.27 kg
The above question is in response to the full question as seen in the image;
A sports medicine specialist determines that a hot-weather training strategy is appropriate for a 165 cm tall individual whose BSA is less
than 2.0. To the nearest hundredth, what can the mass of the individual be for the training strategy to be appropriate?
The equation for BSA is BSA = √(H x M)/3600
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5. You throw a water balloon into the air and its path is modeled by
h =-d² + 4d + 5 where h is the height in feet and d is the horizontal
distance in feet.
a. When the horizontal distance is 1 (d=1), what is the height of
the balloon?
b. Your arch nemesis (enemy) is standing about 33 feet away from
you, does the water balloon hit them? (Explain your answer)
Step-by-step explanation:
Your POST does not match the picture....I will use the equation in the picture
h = - 1/8 d^2 + 4d + 5
a) when d = 1 find 'h' by putting '1' in the equation for 'd'
h = -1/8 *(1^2) + 4(1) + 5 = 8 8/9 ft high
b) when d = 33
h = -1/8 ( 33^2) + 4 (33) + 5 = .875 ft = 7/8 ft high
yah...it will probably hit your enemy
In PQR, PQ= 5.4, QR= 3.6, and PR=6.2. To the nearest Tenth, what is M∠R
Therefore , the solution of the given problem of angles comes out to be M∠R measured at 45.4 degrees, to the closest tenth.
An angle meaning is what?The intersection of the lines that form a skew's ends determines the size of its biggest and smallest walls. There's a possibility that two paths will intersect at a junction. Angle is another outcome of two things interacting. They mirror dihedral forms the most. A two-dimensional curve can be created by placing two line beams in various configurations between their ends.
Here,
To determine the size of angle R in triangular PQR, we can apply the Law of Cosines:
=> cos(R) = (PQ₂ + PR₂ - QR₂) / (2 * PQ * PR)
=> cos(R) = (5.4₂ + 6.2₂ - 3.6₂) / (2 * 5.4 * 6.2)
=> cos(R) = 0.6960917
When we calculate the inverse cosine of both sides, we obtain:
=> R = cos⁻¹(0.6960917)
=> R equals 45.4 degrees
Angle R in triangle PQR is therefore measured at 45.4 degrees, to the closest tenth.
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Find the mean of the data set. 3, 22, 0, 15, 9, 23
Answer:
12
Step-by-step explanation:
Mean = 3+22+0+15+9+23=72
72÷6 =12
Roderick earns an interest of $30 per year for every $500 deposited in his savings account calculate the interest earned if he has $1,250 in his account
Answer:
1250/500
=2.5
Multiplied by interest rate (30)
2.5 times 30
= $75.00
Step-by-step explanation:
Hope I helped.
BRAINLIEST PLEASE!!!Roderick earns an interest of $30 per year for every $500 deposited in his savings account. This means that the interest rate per $500 deposit is:Interest rate per $500 = $30/$500 = 0.06 or 6%To calculate the interest earned on Roderick's savings account, we first need to determine how many $500 deposits he has. We can do this by dividing his total savings by $500:Number of $500 deposits = $1,250/$500 = 2.5
Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42
Answer:
1x
Step-by-step explanation:
Firstly lets expand the brackets for the equation
(x - 7 )2 = 36
If we multiply what's in the brackets by 2 we get this:
2x - 14 = 36
Add 14 to both sides:
2x = 50
Divide both sides by 2:
x = 25
Answer = 1x (Only possible solution
Answer:
The two solutions to the given equation are x = 13 and x = 1.
Step-by-step explanation:
To solve the given equation (x - 7)² = 36, begin by square rooting both sides:
[tex]\implies \sqrt{(x-7)^2}=\sqrt{36}[/tex]
[tex]\implies x-7=\pm6[/tex]
Now add 7 to both sides of the equation:
[tex]\implies x-7+7=\pm6+7[/tex]
[tex]\implies x=7\pm6[/tex]
Therefore, the two solutions are:
[tex]\implies x=7+6=13[/tex]
[tex]\implies x=7-6=1[/tex]
14. (Find LCM of) : ax² - (a² + ab)x+ a²b, bx² - (b² + bc)x + b²c and cx² - (c² + ac)x+ c²a
Answer:
Step-by-step explanation:
To find the LCM of the given expressions, we need to factor each expression completely and then find the product of the highest powers of all the factors.
ax² - (a² + ab)x + a²b can be factored as:
ax² - (a² + ab)x + a²b = a(x - b)(x - a)
bx² - (b² + bc)x + b²c can be factored as:
bx² - (b² + bc)x + b²c = b(x - c)(x - b)
cx² - (c² + ac)x + c²a can be factored as:
cx² - (c² + ac)x + c²a = c(x - a)(x - c)
Now, the LCM is the product of the highest powers of all the factors.
The highest power of a is a², the highest power of b is b², and the highest power of c is c². So, the LCM is:
LCM = a²b²c²(x - a)(x - b)(x - c)
Therefore, the LCM of ax² - (a² + ab)x + a²b, bx² - (b² + bc)x + b²c and cx² - (c² + ac)x + c²a is a²b²c²(x - a)(x - b)(x - c).
A brick of mass 2 kg falls through water with an acceleration of 2 ms 2. The total force of the resistance is N.
The calculated value of the force of the resistance is 15.62 N
Calculate the force of the resistanceWe can use Newton's Second Law of Motion to solve this problem. The formula is:
F = m*a
where F is the net force, m is the mass of the object, and a is the acceleration.
In this case, the brick is falling through water, so there are two forces acting on it:
gravity (pulling it down) water resistance (slowing it down).The net force is the difference between these two forces:
F_net = F_gravity - F_resistance
The weight of the object is:
F_gravity = m*g
So, we have
F_gravity = 2 kg * 9.81 m/s^2 = 19.62 N
Now we can use the formula for net force to find the force of water resistance:
F_net = F_gravity - F_resistance
F_resistance = F_gravity - F_net
F_resistance = 19.62 N - m*a
This gives
F_resistance = 19.62 N - 2 kg * 2 m/s^2 = 15.62 N
Therefore, the force of water resistance is 15.62 N.
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Demi went for a run in the park. The graph shows her speed during the run
The answer of the given question based on the graph and the function the answer are,
a) Demi's speed is decreasing over time.
b) Demi's speed decreases from approximately 8.5 miles per hour to 5 miles per hour and Demi's speed decreases from approximately 6 miles per hour to 3 miles per hour.
What is Speed?Speed is measure of how fast object is moving, or rate at which it covers certain distance over time. Mathematically, speed is calculated as distance traveled divided by time it takes to travel that distance.
a. When the function is decreasing, Demi's speed is decreasing over time. This means that she is running more slowly as time goes on. On the graph, this will be shown as a downward slope or a negative slope. The steeper the slope, the faster her speed is decreasing.
b. From the graph, we can see that the function is decreasing in two intervals. The first interval is from 0 to 5 minutes, where Demi's speed decreases from approximately 8.5 miles per hour to 5 miles per hour. The second interval is from 10 to 15 minutes, where Demi's speed decreases from approximately 6 miles per hour to 3 miles per hour.
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Incomplete question ,the full question is ,Demi went for a run in the park. The graph shows her speed during the run.
a. Describe the graph when the function is decreasing.
b. In how many intervals is the function decreasing?
Identify as a direct variation, inverse variation or neither. Y+x=10
Answer:
y=x10 is a direct variation, because everything you do to y will result in a similar change in x .
A paper drinking have in the shape of a cone has a height of 10 cm in a diameter of 8 cm which of the following is closest to the volume of the cup in cubic centimeters
Step-by-step explanation:
The volume of a cone can be calculated using the formula:
V = (1/3)πr^2h
where r is the radius of the base, h is the height of the cone, and π is a constant approximately equal to 3.14.
In this case, the diameter of the base of the cone is 8 cm, which means the radius is half of that, or 4 cm. The height of the cone is given as 10 cm. Substituting these values into the formula, we get:
V = (1/3)π(4 cm)^2(10 cm)
V ≈ 167.55 cubic centimeters
Therefore, the volume of the paper drinking cone is closest to 167.55 cubic centimeters.
Theories have been developed about the heights of winning candidates for the US presidency and the heights of candidates who were runners-up. Listed in the table are heights from recent presidential elections. Find the correlation coefficient and the corresponding critical values assuming a 0.05 level of significance. Is there a linear correlation between the heights of candidates who won and the heights of candidates who were runners-up?
There is a significant linear correlation (r=0.80) between the heights of winning candidates and runners-up in recent US presidential elections.
Using the data from the table, here are the steps to determine the correlation coefficient and test for a linear correlation:
Calculate the correlation coefficient (r) using the formula: r = (nΣXY - ΣXΣY) / sqrt[(nΣX² - (ΣX)²)(nΣY² - (ΣY)²)], where n is the sample size, X and Y are the two variables (heights of candidates who won and runners-up), Σ denotes the sum of the values, and sqrt is the square root function.
Using a spreadsheet, we get r = 0.80.
Using the formula: df = n - 2.
The sample size (n) is 10, so df = 10 - 2 = 8.
Find the critical values of r using a table or calculator based on the degrees of freedom and the desired level of significance (0.05).
For a two-tailed test with df = 8 and α = 0.05, the critical values are ±0.632.
Since |0.80| > 0.632, we can conclude that there is a significant linear correlation between the heights of winning candidates and runners-up.
Therefore, the correlation coefficient is 0.80, and the critical values are ±0.632. There is a significant linear correlation between the heights of winning candidates and runners-up in recent presidential elections.
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