Using square root property,
Square root of 4 is 2 and -2.
Both 2 and -2 are square roots of 4 as:
2 × 2 = 4
also,
-2 × -2 =4
What is the square root property?The opposite of squaring an integer is finding its square root. The result of multiplying a number by itself yields its square value, while the square root of a number can be found by looking for a number that, when squared, yields the original value.
It follows that a × a = b if "a" is the square root of "b." Every number has two square roots, one of a positive value and one of a negative value, because the square of any number is always a positive number.
In the given question,
Square root of 4 is 2 and -2.
Both 2 and -2 are square roots of 4 as:
2 × 2 = 4
also,
-2 × -2 =4
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In each of the following statements, choose one word, parallelogram, rectangle, rhombus, trapezoid, kite, or square, so that the resulting sentence is true. If none of the words makes the sentence true, answer "none." a. A quadrilateral is a _____if, and only if, its diagonals are congruent and bisect each other. b. A quadrilateral is ______if, and only if, its diagonals are perpendicular and bisect each other. c. A quadrilateral is a _______ if, and only if, its diagonals are perpendicular bisectors of each other. d. A quadrilateral is a______ if, and only if, a pair of opposite sides are parallel and congruent.
Answer:
A. rhombus
B. square
C. rhombus
D. parallelogram
There are some sandwiches on the shelf. 1/3 of them are egg sandwiches and 1/2 of them are club sandwiches. The rest are peanut butter sandwiches. What fraction of the sandwiches are peanut butter?
Answer:
Step-by-step explanation:
Fraction that are egg and club sandwiches
[tex]\frac{1}{3} +\frac{1}{2} =\frac{2}{6} +\frac{3}{6}=\frac{5}{6}[/tex]
The rest are peanut butter:
[tex]1-\frac{5}{6} =\frac{6}{6} -\frac{5}{6} =\frac{1}{6}[/tex]
Solution: [tex]\frac{1}{6}[/tex] of the sandwiches are peanut butter.
A study at an amusement park found that, of 10,000 families at the park, 1720 had brought one child, 2090 had brought two children, 2320 had brought three children, 1450 had brought four children, 1200 had brought five children, 770 had brought six children, and 450 had not brought any children.
Find the expected number of children per family at the amusement park.
Therefore, 98.3% of households took two or more kids to the theme attraction.
What is proportion, exactly?An equation known as proportion shows that the two numbers provided are equal to one another. In other terms, the proportion declares that the two ratios or portions are identical.
The following is how the info can be displayed in a table:
Number of Children Number of Families
0 450
1 1720
2 2090
3 2320
4 1450
5 1200
6 770
Total 10000
To find the proportion of families that brought two or more children, we need to add the number of families with two or more children (2090+2320+1450+1200+770) and divide by the total number of families:
(2090+2320+1450+1200+770)/10000 = 0.983
So approximately 98.3% of families brought two or more children to the amusement park.
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find the area 15, 8, 18
the area of the triangle is approximately 71.82 square units.
HOW TO SOLVE THE PROBLEM?
Using the Pythagorean theorem, we can find the length of the base of the right triangle:
Base² = Hypotenuse²- Perpendicular²
Base²= 18²- 15²
Base² = 324 - 225
Base² = 99
Taking the square root of both sides, we get:
Base = √99
Simplifying the square root of 99, we get:
Base = √(9 x 11)
Base = 3√11
Therefore, the length of the base of the right triangle is 3√11.
to find the area of the triangle 3√11-8=1.94
then we can find three side of triangles
which are 15,18,15.12
To find the area of a triangle when the lengths of its three sides are known, we can use Heron's formula:
Area = √[s(s-a)(s-b)(s-c)]
where s is the semiperimeter of the triangle, and a, b, and c are the lengths of its sides.
The semiperimeter s is half the perimeter of the triangle:
s = (15 + 18 + 15.14) / 2 = 24.57
Using this value for s, and plugging in the lengths of the sides a = 15, b = 18, and c = 15.14, we get:
Area = √[24.57(24.57-15)(24.57-18)(24.57-15.14)]
= √[24.57(9.57)(6.57)(9.43)]
= √5153.5853
= 71.82 (approx)
Therefore, the area of the triangle is approximately 71.82 square units.
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helppp i got this and i need it rq
The decay rate is r = -1.36 or 136%. This equation represents exponential decay with a decay rate of 136%.
What is exponential function?An exponential function is a mathematical function of the form. [tex]f(x) = a^x[/tex], where "a" is a constant called the base of the function and "x" is the exponent. In other words, the base "a" is raised to the power of "x" to obtain the output value of the function. Exponential functions are characterized by their rapid increase or decrease as x increases or decreases. When the base "a" is greater than 1, the function grows rapidly as x increases, and when "a" is between 0 and 1, the function decays rapidly as x increases. The function [tex]f(x) = (2/7) ^ x[/tex] represents exponential decay because as x increases, the value of the function decreases rapidly towards zero.
This is because the base of the exponential function, 2/7, is less than 1. The function [tex]y = 4e^(1/2x)[/tex] represents exponential growth because as x increases, the value of the function increases rapidly towards infinity. This is because the base of the exponential function,[tex]e^(1/2x)[/tex], is greater than 1. Additionally, the coefficient 4 indicates that the initial value of the function is 4, and as x increases,
The function grows exponentially from that initial value. Rewrite the equation in the form. [tex]y = a * (1 + r) ^ t[/tex]or[tex]y = a * (1 - r) ^ t[/tex]. Then state the growth or decay rate. 3. [tex]y = a * (2.36) ^ t[/tex]the equation [tex]y = a * (2.36) ^ t[/tex]can be rewritten in the form of [tex]y = a * (1 + r) ^ t[/tex] by dividing both sides by a and using the fact that 2.36 = 1 + r, where r is the growth rate: [tex]y/a = (1 + r) ^ t[/tex] Here, the growth rate is r = 2.36 - 1 = 1.36 or 136%.
This equation represents exponential growth with a growth rate of 136%.Alternatively, if we want to rewrite the equation in the form of [tex]y = a * (1 - r) ^ t[/tex], we can use the fact that 2.36 = 1 - (-1.36), where -1.36 is the decay rate: [tex]y/a = (1 - (-1.36)) ^ t[/tex] Here, the decay rate is r = -1.36 or 136%. This equation represents exponential decay with a decay rate of 136%
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Find how much money needs to be deposited now into an account to obtain $6,400 (Future Value) in 5 years if the interest rate is 6.5% per year compounded daily (365 times per year).
We need to deposit $4,494.08 now into the account to obtain $6,400 in 5 years if the interest rate is 6.5% per year compounded daily.
What is compound interest?
Compound interest is a type of interest where the interest earned on an investment is added to the principal amount, and then the total amount (principal + interest) earns interest again in the subsequent period.
To find out how much money needs to be deposited now into an account to obtain $6,400 in 5 years if the interest rate is 6.5% per year compounded daily, we can use the formula for compound interest:
[tex]FV = PV * (1 + r/n)^{(n*t)[/tex]
where:
FV is the future value we want to achieve, which is $6,400 in this case.
PV is the present value, or the amount of money we need to deposit now.
r is the interest rate per year, which is 6.5%.
n is the number of times the interest is compounded per year, which is 365.
t is the time period in years, which is 5 years.
Substituting these values into the formula, we get:
$6,400 = PV x [tex](1 + 0.065/365)^{(365*5)[/tex]
Simplifying the right-hand side of the equation, we get:
$6,400 = PV x [tex](1.00017808219)^{1825[/tex]
$6,400 = PV x 1.424663962
Dividing both sides of the equation by 1.424663962, we get:
PV = $4,494.08 (rounded to two decimal places)
Therefore, we need to deposit $4,494.08 now into the account to obtain $6,400 in 5 years if the interest rate is 6.5% per year compounded daily.
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please help need to finish
The answer d because it is the only option that describes a circle with a center at (-7, 2) and a radius of 10. d (x − 7)² + (y + 2)² = 10
What is standard form?The standard form of a circle equation is (x - h)² + (y - k)² = r², where (h, k) represents the coordinates of the center of the circle and r is the radius.
From this equation we can see that the x-coordinate of the center is equal to h and the y-coordinate is equal to k.
In answer d, the x-coordinate of the center is -7, and the y-coordinate is +2. This means that the center of the circle is located at (-7, 2).
The radius of the circle is given by the value of r, which is equal to 10.
Therefore, answer d is the correct answer because it is the only option that describes a circle with a center at (-7, 2) and a radius of 10.
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On a map, 1 cm represents an actual distance of 200 m. Find the actual area, in square metres, represented by 1 cm2 on the map.
Answer:
80,000 [tex]meters^{2}[/tex]
Step-by-step explanation:
200 x 400 = 80,000
Helping in the name of Jesus.
Giving a test to a group of students, the grades and gender are summarized below
The Probability for the given event will be 55/87.
What exactly is probability?
Probability is a measure of the possibility of an event to be occurred. In mathematics, it is defined as a number between 0 and 1, where 0 means that the event is impossible and 1 means that the event is certain to occur.
For example, if you flip a fair coin, the probability of getting heads is 0.5, since there are two equally likely outcomes (heads or tails) and only one of them is heads. Similarly, the probability of rolling a 6 on a fair six-sided die is 1/6, since there are six equally likely outcomes (rolling a 1, 2, 3, 4, 5, or 6) and 6 comes only once.
Now,
Given number of
Total males = 32
Total females = 55
Total =87
then probability of selecting a female will be =55/87
Hence,
The Probability for the given event will be 55/87.
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last year joose sold a painting for$200if he 25% profit of d sales how much had he paid for the painting?
In linear equation, 1600 had he paid for the painting.
What's a linear equation in calculation?
A linear equation is an algebraic equation of the form y = mxb. involving only a constant and a first- order( linear) term, where m is the pitch and b is the y- intercept. sometimes, the below is called a" linear equation of two variables," where y and x are the variables.
Jose made 25% profit, so if he bought the painting for x, he sold it for:
x + 0.25x = 1.25x = 2000
x = 2000 ÷ 1.25
= 1600
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1) A bowl is a hemisphere with radius 6 cm Water fills two-fifths of the volume of the bowl. The water is poured into a hollow cone. The depth of the water in the cone is 12 cm.
the volume of a sphere = 4÷3πr³.
the volume of a cone = 1÷3πr²h.
Solve the radius of the surface of the water in the cone?
The volume of the hemisphere is given by:
V_hemisphere = (2/3)πr^3
The volume of water in the bowl is two-fifths of the volume of the hemisphere:
V_water = (2/5)(2/3)πr^3 = (4/15)πr^3
So the remaining volume in the bowl is:
V_bowl = V_hemisphere - V_water = (1/3)πr^3
We are told that this remaining volume is poured into a hollow cone with depth 12 cm. Let's call the radius of the surface of the water in the cone "R". We can set up an equation for the volume of the cone in terms of R and solve for R:
V_cone = (1/3)πR^2(12)
Setting V_cone equal to V_bowl, we have:
(1/3)πR^2(12) = (1/3)πr^3
Simplifying:
R^2 = (r^3)/(4312) = r^3/144
Taking the cube root of both sides:
R = (r^3/144)^(1/3) = r/3
Substituting the given radius of the hemisphere, r = 6 cm, we get:
R = (6 cm)/3 = 2 cm
Therefore, the radius of the surface of the water in the cone is 2 cm.
Can anyone solve the math problem below.
Two skaters are practicing at the same time on the same rink. A coordinate grid is superimposed on the ice. One skater follows the path y= - 4x + 63, while the other skater follows the curve y= - 3x^2+ 26x. Find all the points where they might collide if they are not careful.
In the given problem, the skaters might collide at the point (7, 35) or (3, 51). This is derived by solving a system of created equations.
How to Solve for the Points?To find the points where the two skaters might collide, we need to solve the system of equations:
y = -4x + 63
y = -3x^2 + 26x
We can substitute the first equation into the second equation to eliminate y:
-4x + 63 = -3x^2 + 26x
Rearranging and simplifying, we get:
3x^2 - 30x + 63 = 0
Dividing both sides by 3, we get:
x^2 - 10x + 21 = 0
Factoring, we get:
(x - 7)(x - 3) = 0
So the possible values of x where the skaters might collide are x = 7 and x = 3.
To find the corresponding y-values, we can substitute these values of x into either equation. Using y = -4x + 63, we get:
When x = 7, y = -4(7) + 63 = 35
When x = 3, y = -4(3) + 63 = 51
Therefore, the skaters might collide at the point (7, 35) or (3, 51).
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