Answers
For product=6 and sum=7, the numbers or integers are 1 and 6.
What exactly are integers?
In mathematics, integers are the collection of positive and negative numbers. Integers, like whole numbers, do not include the fractional element. Thus, integers are numbers that can be positive, negative, or zero, but not fractions. On integers, we can do all arithmetic operations such as addition, subtraction, multiplication, and division. Integers include numbers such as 1, 2, 5, 8, -9, -12, and so on. "Z" is the symbol for integers.
now,
As given product=6 and sum=7
make factors for 6 i.e 1,2,3,6
from these choose the numbers whose sum=7
and they are 1,6.
Hence,
For product=6 and sum=7, the numbers are 1 and 6.
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Related Questions
Use the Pythagorean Theorem to find the length of the missing side of the right triangle. Then find the value of each of the six trigonometric functions of .
θ
A
B
C
a = 16
b = 30
c
Question content area bottom
Part 1
The length of the missing side of the right triangle is
Answers
1) The length of the missing side of the right triangle is 34.
2) The values of the six trigonometric functions of θ are:
sin θ = sin A = 8/17
cos θ = cos A = 15/17
tan θ = tan A = 8/15
csc θ = csc A = 17/8
sec θ = sec A = 17/15
cot θ = cot A = 15/8
What is Pythagorean Theorem?
Pythagoras Theorem is a method for calculating the missing length of a right-angled triangle. The triangle has three sides: the hypotenuse (which is usually the longest), the opposite (which does not touch the hypotenuse), and the adjacent (which is always the shortest) (which is between the opposite and the hypotenuse).
Part 1
To find the length of the missing side (c) of the right triangle, we can use 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. In this case, we have:
a² + b² = c²
Substituting the given values, we get:
16² + 30² = c²
Simplifying, we get:
256 + 900 = c²
1156 = c²
Taking the square root of both sides, we get:
c = sqrt(1156) = 34
Therefore, the length of the missing side of the right triangle is 34.
Part 2
To find the values of the six trigonometric functions of θ, we need to know one of the acute angles of the triangle. Let's call the acute angle opposite side a as angle A. Using the given values, we can find the sine, cosine, tangent, cosecant, secant, and cotangent of angle A as follows:
sin A = a/c = 16/34 = 8/17
cos A = b/c = 30/34 = 15/17
tan A = a/b = 16/30 = 8/15
csc A = 1/sin A = 17/8
sec A = 1/cos A = 17/15
cot A = 1/tan A = 15/8
Therefore, the values of the six trigonometric functions of θ are:
sin θ = sin A = 8/17
cos θ = cos A = 15/17
tan θ = tan A = 8/15
csc θ = csc A = 17/8
sec θ = sec A = 17/15
cot θ = cot A = 15/8
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For the transformation to be a translation, which statements are true? Select four options
Answers
Answer:
do it yourself
Step-by-step explanation:
Answer:
A. The transformation preserves distances and angles between points.
B. The transformation preserves the orientation of the figure.
C. The transformation involves a sliding of the figure in a fixed direction.
D. The transformation results in a change of size or shape of the figure.
E. The transformation results in a reflection of the figure.
For the transformation to be a translation, statements A, B, C and E are not true, while statement D is true.
Step-by-step explanation:
A pack of gray wolves was reintroduced to a forest. The table gives the size of
this population of wolves over time.
Which model,in which t represents that time in year,best fits the data in the table
Answers
The exponential regression equation that best fits the data in the table is given as follows:
C. f(t) = 11.9(1.12)^t.
How to obtain the exponential function?The standard definition of an exponential function is given as follows:
y = a(b)^x.
In which:
a is the value of y when x = 0.b is the rate of change.For this problem, we have that the parameters are estimated as follows:
a = 11.9, as when x = 0, y = 12, and the closest option to 12 is a = 11.9.b = 1.12, as the population increases over time, hence b > 1.This means that the correct option is given by option C.
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How to transform the graph of a function using more than one transformation
Answers
The transformation used are:
(a)
This is a translation of one unit to the left and one unit up.
(b)
- There is a vertical stretch of 2 units.
- This is a translation of four units down.
What is translation?It is the movement of the shape in the left, right, up, and down directions.
The translated shape will have the same shape and shape.
There is a positive value when translated to the right and up.
There is a negative value when translated to the left and down.
We have,
The graph from y = h(x) to y = h(-x) + 1.
This is a translation of one unit to the left and one unit up.
The graph from y = g(x) to y = 2g(x) - 4.
- There is a vertical stretch of 2 units.
- This is a translation of four units down.
Now,
The graph of y = h(-x) + 1 is given below.
The graph of y = 2g(x) - 4 is given below.
Thus,
(a)
This is a translation of one unit to the left and one unit up.
(b)
- There is a vertical stretch of 2 units.
- This is a translation of four units down.
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A boat has a top speed of 26 knots and a displacement of approximately 81000 tons. (1 knot= 1 nautical mile per hour; 1 metric tonne =1000 kilograms)
Answers
On solving the provided question we can say that 2 decimal places =29.92 miles per hour
what is decimal?Integer and non-integer numbers are often expressed using the decimal numeral system. The Hindu-Arabic numeral system has been expanded to include non-integer values. Decimal notation is the name for the method used to represent numbers in the decimal system. A decimal is a number with a whole and a fractional component. Decimal numbers, which are in between integers, are used to express the numerical value of full and partially whole amounts. A decimal point separates the complete number and the fractional portion of a decimal number. The dot between the whole number and the fractions is known as the decimal point. A decimal number is, for instance, 25.5. In this instance, 25 is the entire number, while 5 is the
top speed is 26 knots,
1 knot = 1.15078 miles per hour
26 knots = 26 * 1.15078
= 29.92028 miles per hour
2 decimal places
=29.92 miles per hour
boat has a displacement of 96000 tons
1 ton = 0.907185 metric tonnes
96000 tons = 0.907185 * 96000
= 87,089.76 metric tonnes
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Find value of x. Round to the nearest tenth
Answers
Answer:
Step-by-step explanation:
x/sin90=17.3/sin53
sin90=1
x=17.3/sin53
x=13.8
One cubic foot holds 7.48 gallons of water, and 1 gallon of water weighs 8.33 pounds. How much does 4.3 cubic feet ofwater weigh in pounds? In tons?
Answers
To find the weight of 4.3 cubic feet of water, we need to first find the number of gallons of water that 4.3 cubic feet holds and then multiply that by the weight of 1 gallon of water.
1 cubic foot holds 7.48 gallons of water, so 4.3 cubic feet holds 4.3 x 7.48 = 31.964 gallons.
1 gallon of water weighs 8.33 pounds, so 31.964 gallons of water weigh 31.964 x 8.33 = 265.9012 pounds.
Therefore, 4.3 cubic feet of water weigh 265.9012 pounds.
To find the weight in tons, we need to divide the weight in pounds by 2000:
265.9012 pounds ÷ 2000 = 0.13295 tons
So 4.3 cubic feet of water weigh 0.13295 tons.
Answer:
0.13314 tons.
Step-by-step explanation:
We can start the calculation by first converting the cubic feet of water to gallons and then converting the gallons to pounds.
Conversion from cubic feet to gallons:
4.3 cubic feet = 4.3 cubic feet * 7.48 gallons/cubic foot = 32.084 gallons
Conversion from gallons to pounds:
32.084 gallons = 32.084 gallons * 8.33 pounds/gallon = 266.279 pounds
Conversion from pounds to tons:
266.279 pounds = 266.279 pounds / 2000 pounds/ton = 0.13314 tons
So, 4.3 cubic feet of water weigh 266.279 pounds or 0.13314 tons.
Which algebraic expression is equivalent to the expression below? 23x+9-5x
Answers
Answer:
18x+9
Step-by-step explanation:
Answer: 18x + 9
Step-by-step explanation:
1) Combine like terms 23x -5x to get a new equation of 18x + 9.
What is the least number and greatest number of shells he would need
Answers
Answer:
Step-by-step explanation:
What is the least number and greatest number of shells he would need
Three different accounts are described below. Order the accounts according to their values after 10 years, from greatest to least.
You deposit $950 in an account that earns 5% interest semiannually.
You deposit $800 in an account that earns 7.5% annual interest compounded quarterly.
You deposit $700 in an account that earns 7.75% annual interest compounded monthly.
Answers
Answer:
$800 at 7.5%$950 at 5%$700 at 7.75%Step-by-step explanation:
You want to order the accounts greatest to least by their value after 10 years.
$950 at 5%, compounded semiannually$800 at 7.5%, compounded quarterly$700 at 7.75%, compounded monthlyValueThe value of each account can be found using the compound interest formula:
A = P(1 +r/n)^(nt)
Principal P earning rate r compounded n times per year for t years.
For the three accounts, the corresponding values are ...
950(1 +0.05/2)^(2·10) = 1556.69800(1 +0.075/4)^(4·10) = 1681.88 . . . . . . . greatest value700(1 +0.0775/12)^(12·10) = 1515.63 . . . . . least valueComparisonThe order, greatest to least, according to the account values is ...
$800 at 7.5%$950 at 5%$700 at 7.75%__
Additional comment
The $700 account will overtake the $950 account after 11 years. It will take about 46 years for it to overtake the $800 account. Eventually, the higher interest rate with greater frequency of compounding wins out.
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Add the two expressions 3z - 4 and 2z + 5
Answers
We obtain the sum of the expressions as 5z + 1. The solution has been obtained by using arithmetic operations.
What are arithmetic operations?
Four fundamental mathematical operations which can be used to express any real number are known as arithmetic operations. The four operations are addition, subtraction, multiplication and division.
We are given two expressions as 3z - 4 and 2z + 5.
In order to add the expressions, we will add the like terms.
On adding the like terms, we get
⇒(3z - 4) + (2z + 5)
⇒3z + 2z - 4 + 5
⇒5z + 1
Hence, we get the expression as 5z + 1.
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There are two routes you can take from your house to the store.Main Street is 1/3 of a mile long. Oak Street is 1/4 of a mile long. How much longer is Main Street thank Oak Street
Answers
The Main Street is 1/12 of a mile longer than the Oak Street
How much longer is Main Street thank Oak StreetFrom the question, we have the following parameters that can be used in our computation:
Main Street is 1/3 of a mile long. Oak Street is 1/4 of a mile long.Using the above as a guide, we have the following:
Difference = Main Street - Oak Street
substitute the known values in the above equation, so, we have the following representation
Difference = 1/3 - 1/4
Evaluate the difference
Difference = 1/12
Hence, the difference is 1/12 of a mile
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Choose the ratio below that is equivalent to the greatest fraction.
A. 5:3
B8:4
C. 2:7
D 9:5
Answers
The ratio that is equivalent to the greatest fraction is B. 8:4.
What is a ratio?A ratio is a relative size or value contained in another quantity. It is computed as the quotient of the smaller and larger values.
Ratios are fractional values, which we can depict as fractions, decimals, or percentages.
Ratios are also depicted using the ratio symbol (:), describing the numerical relationship between two or more values or variables.
Ratio 5:3The sum of ratios = 8
5/8 = 0.625
Ratio 8/4The sum of ratios = 12
8/12 = 0.67
Ratio 2:7The sum of ratios = 9
2/9 = 0.22
Ratio 9:5The sum of ratios = 14
9/14 = 0.64
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If f (x) = 5x - 4 find f(2).
10
48
2
6
Answers
Answer:
6
Step-by-step explanation:
f(2) = 10-4 = 6
Answer:
[tex] \sf \: d) \: 6[/tex]
Step-by-step explanation:
Given function,
→ f(x) = 5x - 4
We have to find,
→ The required value of f(2).
Now value of f(2) will be,
→ f(x) = 5x - 4
→ f(2) = 5(2) - 4
→ f(2) = 10 - 4
→ [ f(2) = 6 ]
Therefore, the answer is 6.
Faith invests £800 for 3 years in a bank account.
The account pays simple interest at a rate of 0.4% per year
Work out the total amount of interest Faith has got at the end of the 3 years.
Answers
Faith earned £96 in interest at the end of the 3 years.
How to calculate the interest rateUsing the simple interest formula:
I = P x r x t
where
I is the interest earned,
P is the principal or initial amount invested,
r is the interest rate as a decimal, and t is the time period in years.
In this case, Faith invested £800 for 3 years at a simple interest rate of 0.4% per year, or 0.04 as a decimal. Plugging in the values:
I = £800 x 0.04 x 3
= £96
Therefore, Faith earned £96 in interest at the end of the 3 years.
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Assume that hybridization experiments are conducted with peas having the property that for offspring, there is a 0.75 probability that a pea has green pods. Assume that the offspring peas are randomly selected in groups of 16. Complete parts (a) through (c) below.
Answers
a)The standard deviation is given by σ = sqrt(np(1-p)) = sqrt(24 × 0.75 × 0.25) = 2.12 . b)Significantly low: μ - 2σ = 18 - 2 × 2.12 ≈ 13.76 ,Significantly high: μ + 2σ = 18 + 2 × 2.12 ≈ 22.24 ,c)z = (x - μ) / σ = (3 - 18) / 2.12 ≈ -7.08.
How to calculate standard deviation?A group of 24 peas with green pods has a binomial distribution with n = 24 and p = 0.75. The mean is calculated as = np = 24 0.75 = 18, and the standard deviation is calculated as = sqrt(np(1-p)) = sqrt(24 0.75 0.25) = 2.12 (rounded to two decimal places).
b) The range rule of thumb states that results that deviate from the mean by more than two standard deviations are considered significantly low or significantly high. In this case, the values separating significantly low and significantly high results are:
Significantly reduced: - 2 = 18 - 2 2.12 13.76
Significantly greater: + 2 = 18 + 2 2.12 22.24
c) To see if a result of three peas with green pods is significantly low, we must calculate its z-score, which is given by:
z = (x - μ) / σ = (3 - 18) / 2.12 ≈ -7.08
Because the z-score is much lower than -2, the cutoff for significantly low results, we can conclude that a result of 3 peas with green pods is significantly low.
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There are 3 swimmers in a race. There will be a first-place and a second-place prize awarded. In how many different ways can the 2 prizes be awarded?
Answers
Answer:
Step-by-step explanation:
6
I’ve attempted this question so many times I’m stuck please help
Answers
Answer:
Step-by-step explanation:
Range: the difference between the highest and lowest values
Heights:
130
142
142
143
144
145
147
147
149
150
151
153
154
154
158
161
162
Formula to find the range
R= H-L
R = range
H = highest value
L = lowest value
R = 160 - 130.
The range is 30.
Find the inverse of each of the given functions.
f(x)=4x-12
DONE
+
h(x)
O
O
H
2x - 4
3
h¯¹(x) = 3x - 12
2
h¯¹(x) =
h"¹(x) =
DONE
3
(2x - 4)
3x + 4
2
Answers
Answer:B
Step-by-step explanation:
Help pls Thank you mwa
Answers
Step-by-step explanation:
Same as the triangles. Find the area of the large rectangle and the small rectangle, then subtract.
A = L x W
For the large rectangle
A = 30 x 25 = 750
For the small rectangle
A = 26 x 21 = 546
Now to subtract these two
750 - 546 = 240
19. For the period 2009-2013, if T is the number (in millions) of
Comcast video subscribers, then 7 10.3 is approximately the
number (in millions) of Time Warner Cable video subscrib-
ers (Source: Comcast, Time Warner Cable). There were about
21.7 million Comcast video subscribers in 2013. Estimate the
number of Time Warner Cable video subscribers in 2013.
Answers
The estimated number of Time Warner Cable video subscribers in 2013 is approximately 14.8 million.
Estimation by ProportionsWe are given that for the period 2009-2013, 7/10.3 is approximately the number of Time Warner Cable video subscribers for every Comcast video subscriber. We are also given that there were 21.7 million Comcast video subscribers in 2013.
To estimate the number of Time Warner Cable video subscribers in 2013, we can use the following proportion:
7/10.3 = x/21.7
where x is the number of Time Warner Cable video subscribers in 2013.
Solving for x, we get:
x = (7/10.3) x 21.7
x ≈ 14.8 million
Therefore, the estimated number of Time Warner Cable video subscribers in 2013 is approximately 14.8 million.
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Show that ∶ [– 1, 1] → ℝ, given by () =
(2+)
is one-one. Find the inverse of the function
∶ [– 1, 1] → Range . (Hint: For ∈ Range , = () =
(2+)
, for some in [– 1, 1], i.e., =
(2+)
Answers
The inverse of the given function is f(x) = 2x/(1 - x)
What is a function?
A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two varying quantities.
Given function is
f(x) = x/(2+x)
Assume that y = f(x) = x/(2+x)
Solve y = x/(2+x) for x:
y = x/(2+x)
Multiply (2+x) on both sides:
y(2+x) = x
2y + xy = x
Subtract xy from both sides:
2y = x - xy
2y = x(1 - y)
x = 2y/ (1 - y)
Now replace x with y and y with x:
y = 2x/(1 - x)
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What is the solution to this inequality 6 - 5y < -34
Answers
Answer: y > 8
Step-by-step explanation:
6 - 5y < -34
-5y < -40
y > 8
[tex]6-5y < -34[/tex]
Simplify:
[tex]-5y+6 < -34[/tex]
Subtract 6 from both sides:
[tex]-5y+6-6 < -34-6[/tex]
[tex]-5y < -40[/tex]
Since we are dividing by a negative number, the sign will reverse.
Divide both sides by -5:
[tex]\dfrac{-5y}{-5} > \dfrac{-40}{-5}[/tex]
[tex]\boxed{y > 8}[/tex]
Geometry teacher doesnt teach
Answers
The area of the kite is 0.08 metres squared.
How to find the area of a kite?A kite is a quadrilateral. Therefore, the window has the shape of a kite. The square metres of glass that will be used to construct the kite can be calculated as follows:
The area of a kite is half the products of the diagonals of the kite.
Therefore,
area of the kite = 1 / 2 pq
where
p and q are the diagonals.Therefore,
p = 20 + 20 = 40 cm
q = 25 + 15 = 40 cm
Hence,
area of the kite = 1 / 2 × 40 × 40
area of the kite = 1600 /2
area of the kite = 800 cm²
area of the kite = 0.08 m²
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3 1/2x - 5 1/3x , x = 2/5
Answers
The value of the expression is -11/15
How to determine the value of the expressionIt is important to note that algebraic expressions are expressions having factors, constants, variables, coefficients and terms.
From the information given, we have that;
3 1/2x - 5 1/3x
turn into improper fractions
7x/2 - 16x/3
Now, let's determine the value by substituting the value of x as 2/5 in the expression, we have;
7(2/5)/2 - 16(2/5)/3
Multiply the values
14/5/2 - 32/5 /3
Take inverse of the denominator
14/5 ×1/2 - 32/5 × 1/3
7/5 - 32/15
21 - 32/15
-11/5
Hence, the value is -11/15
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Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
11
24
Find the value of x. Round to the nearest tenth. The diagram is not drawn to scale.
Answers
The value of x is 12. The solution has been obtained by using trigonometry.
What is trigonometry?
The primary objective of the branch of mathematics known as "trigonometry" is the study of the sides, angles, and connections of the right-angle triangle. The angles of 0, 30, 45, 60, and 90 degrees are the most typical trigonometric angles to be utilised in computations.
We are given a right - angled triangle with one angle equal to 24° and the length of the base is 11.
Using trigonometry,
We know that cos theta = adjacent side/hypotenuse
So,
⇒cos θ = 11/x
Here, θ = 24°
So,
⇒cos 24° = 11/x
⇒x = 11/cos 24°
⇒x ≈ 12.04
⇒x ≈ 12
Hence, the value of x is 12.
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If 0 = 2x +9 and W = 2(2x-6), what is the measure of p
Answers
Answer:
Angle P= Angle W=2(2x-6)
=4x-12
I need help with the picture problem below
Answers
Using the fact that the figures are similar, we will find that MN = 12.4
How to find the length of segment MN?We know that both figures are similar, then there is a scale factor that relates them.
We know the length of two correspondent sides, these are:
HI and LM
HI = 3
LM = 18.6
if k is the scale factor, then we can wite:
3*k = 18.6
k = 18.6/3 = 6.2
Now the length of MN will be 6.2 times the length of the correspondent side on the smaller figure:
MN = 6.2*2 = 12.4
That is the lenght.
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The profit a company makes decreases exponentially at a rate of 0.9% per year. In 2014, the profit was $9500. Calculate the profit in 2019.
Answers
Answer: The formula for exponential decay is given by:
P(t) = P0 * e^(-rt)
where P(t) is the profit at time t, P0 is the initial profit, r is the rate of decrease in percentage, and t is the time elapsed in years.
In this case, P0 = $9500, r = 0.9%, and t = 5 (the time elapsed from 2014 to 2019).
First, we need to convert the rate of decrease from a percentage to a decimal:
r = 0.9% / 100 = 0.009
Now, we can plug in the values into the exponential decay formula:
P(5) = $9500 * e^(-0.009 * 5) = $9500 * e^(-0.0455)
We can calculate the value of e^(-0.0455) using a calculator or mathematical software. The result is approximately 0.955.
Therefore, the profit in 2019 is:
P(5) = $9500 * 0.955 = $9027.25
So, the profit in 2019 would be $9027.25.
Step-by-step explanation:
The Robinson family ordered snacks at the State Fair. They bought the
following drinks (d), pizza (p), and ice cream cones (c).
Answers
Answer:
a. 2p + 2d + 1c + 1p + 1c + 2p + 1d
b. 5p + 3d + 2c
c. In an algebraic expression each term can only be combined with another like term. For example x terms can be combined only with x terms, y terms can be combined only with y terms etc.
This is similar to the above example in which pizza(p) can only be combined with pizza(p), drinks (d) can only be combined with drinks(d) and cone(c) can only be combined with cone(c)
Step-by-step explanation:
a.
From the cute diagram we see that the family bought
2 pizzas + 2 drinks + 1 cone + 1 pizza + 1 cone + 2 pizzas + 1 drink
Using the variables provided, this becomes
2p + 2d + 1c + 1p + 1c + 2p + 1d
b.
Combining like terms the total purchase is:
(2p + 1p + 2p) + (2d + 1d) + (1c + 1c)
Adding the coefficients of each grouped term we get
(5p) + (3d) + (2c)
Opening the brackets, this becomes
5p + 3d + 2c
c.
In an algebraic expression each term can only be combined with another like term. For example x terms can be combined only with x terms, y terms can be combined only with y terms etc.
This is similar to the above example in which pizza(p) can only be combined with pizza(p), drinks (d) can only be combined with drinks(d) and cone(c) can only be combined with cone(c)
