Answer: 2
Step-by-step explanation:
List the factors(numbers that multiply to make that number for each number
6: 1, 2, 3, 6
34: 1, 2, 16, 34
2: 1, 2
Whichever is the factor that is the greatest that they all have in common is your greatest common factor.
2
Carter is going to invest in an account paying an interest rate of 4.3% compounded daily. How much would Carter need to invest, to the nearest ten dollars, for the value of the account to reach $174,000 in 19 years?
Carter would need to invest approximately $76,869.06 to reach a value of $174,000 in 19 years with a 4.3% annual interest rate compounded daily.
What is the principal that needs to be invested?The formula accrued amount in a compounded interest is expressed as;
[tex]A = P( 1 + \frac{r}{n})^{(nt)}[/tex]
Where A is accrued amount, P is principal, r is interest rate and t is time.
Given that:
Accrued amount A = $174,000
Compounded daily n = 365
Time t = 19 years
Interest rate r = 4.3%
Principal P = ?
First, convert R as a percent to r as a decimal
r = R/100
r = 4.3/100
r = 0.043
Plug these values into the above formula and solve for principal P.
[tex]A = P( 1 + \frac{r}{n})^{(nt)}\\\\A = 174,000( 1 + \frac{0.043}{365})^{(365\ *\ 19)}\\\\A = \$ 76,869.06[/tex]
Therefore, the principal that needs to invested is $76,869.06.
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Suppose theta is an angle in the third quadrant and cos theta = 5/7. What is the value of sin(theta)
3√8
√24
24
2√12
The value of sinθ is √24/7 meanwhile the correct answer is not in the option provided or perhaps option (b) is meant to be √24/7 instead.
Understanding Quadrant in TrigonometryIn the third quadrant, both the x-coordinate (cosine) and the y-coordinate (sine) of the angle are negative.
Given that
cosθ = 5/7
we can determine the value of sinθ using the Pythagorean identity:
sin²θ + cos²θ = 1
sin²θ + (5/7)² = 1
sin²θ + 25/49 = 1
Now, let's solve for sinθ:
sin²θ = 1 - 25/49
sin²θ = 49/49 - 25/49
sin²θ = 24/49
Taking the square root of both sides, we find:
sinθ = √(24/49)
Simplifying further:
sinθ = √24 / √49
sinθ = √24 / 7
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1.2 Mr John is to deposit R 5,000 in his bank account. Deposits are calculated as follows: Cash deposit : At ATM: R4,80 +1,20% of the above value. At the Branch R8,00 + 1,50% of the above value. John claims that the difference of depositing R5 000 at ATM and at the Branch is R18, 20 Verify the stament (5) [23
The calculated difference is -R18.20, which means the deposit at the branch is higher than the deposit at the ATM by R18.20
What is simple interest?The simple interest formula is J = C ∙ i ∙ t, where J is interest, C is principal, i is interest rate, and t is time. To calculate the simple interest, just substitute the values in the formula and perform the calculation.
Calculate the deposit:
[tex]D=R4.80 + 1.20% of R5,000\\=R4.80 + (1.20/100) * R5,000\\= R4.80 + R60\\= R64.80[/tex]
Now, the deposit amount for the branch:
[tex]DB=R8.00 + 1.50% of R5,000\\= R8.00 + (1.50/100) * R5,000\\= R8.00 + R75\\= R83.00[/tex]
The difference will be:
[tex]Difference = R64.80 - R83.00\\Difference = -R18.20[/tex]
The calculated difference is -R18.20, which means the deposit at the branch is higher than the deposit at the ATM by R18.20. Therefore, John's statement is incorrect.
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What is the surface area of a cone with radius 8 in. and slant height 9 in.?
The total surface area of the cone is 427.04 square inches.
What is the surface area of the cone?For a cone of radius R and slant height L, the total surface area is given by the formula:
S = π*R*L + π*R²
Where π = 3.14
In this case, we know that the radius of the cone is 8 inches, and the slant height of the cone is 9 inches.
Then the total surface area of the cone is:
S = 3.14*8in*9in + 3.14*(8in)²
S = 427.04 in²
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The cost of packing a box of chocolates is given by 1/4 x^2, where x is the number of chocolates (a box can never have fewer than 3 chocolates). If the weight of a box of
chocolates is given by x + 2, what is the cost of packaging per weight unit
The cost of packaging per weight unit is given by (1/4) (x / (x + 2)) x.
We have,
To find the cost of packaging per weight unit, we need to calculate the cost of packaging (C) and divide it by the weight of the chocolates (W).
Given:
Cost of packaging (C) = 1/4 x²
Weight of chocolates (W) = x + 2
To find the cost of packaging per weight unit, we can express it as C/W.
Substituting the given expressions:
C/W = (1/4 x²) / (x + 2)
To simplify the expression, we can first simplify the numerator:
C/W = (1/4 x²) / (x + 2)
= (1/4) x (x² / (x + 2))
= (1/4) x (x(x) / (x + 2))
= (1/4) x (x / (x + 2)) * x
Now, we can rewrite the expression as:
C/W = (1/4) x (x / (x + 2)) x
Therefore,
The cost of packaging per weight unit is given by (1/4) (x / (x + 2)) x.
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Solve 2(2x-5)=3x+x-2x
Answer:
5=x
Step-by-step explanation:
Q=2(2x-5)=3x+x-2x
SOLUTION:
4x-10=4x-2x
-10=2x-4x
-10= -2x
(-+-=+ so 10 and 2 are positive now)
10/2=x
5=x
need help with two part edulastic question
Complete the equations. 95 × 1 0^3 =? 95 × 1 0^4=? 95×10^5 =?
Answer:
95 × 10^3 = 95000
95 × 10^4 = 950000
95 × 10^5 = 9500000
Find the surface area and volume of the for fire. Round to the nearest tenth
The surface area and the volume of the cone is 150.8 in², 116. 1in³. option A
How to determine the valuesThe formula for calculating the surface area of a cone is expressed as;
SA = πr² + πrl
Such that the parameters are;
r is the radius l is the lengthSubstitute the values, we have;
Surface area= 3.14 × 16 = 3.14 × 4 × 8
Multiply the values
Surface area = 50.24 + 100.48
Add the values
Surface area = 150.8 in²
Volume of the cone is;
Volume = 3.14 × 4² × 6.9/3
Volume = 3.14 × 16 × 6.9/3
Volume =116. 1in³
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Explain why you cannot use the product of powers property to simplify (3z + y)^3. Be specific.
Any badd answer will be reported
The product of powers of exponents cannot be used to simplify the binomial expansion
Given data ,
Let the binomial expansion be represented as A
A = ( 3z + y )³
According to the property of products of powers, exponents can be multiplied when a power is increased to a higher power.
The product of powers characteristic cannot be applied to the equation (3z + y)³. This is due to the fact that (3z + y)³ is a binomial raised to the power of 3, not just a power of a single word.
These terms cannot be simplified further using the product of powers property because they involve different variables or variable combinations.
In this case, it is more appropriate to expand the expression using the binomial expansion
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evaluate 3x+5y when x=11 and y=4.
(a)23
(b)67
(c)53
(d)13
Answer:
(c):53
Step-by-step explanation:
Let's start with the equation:
3x+5y
Since we already have the values of x and y, we can just solve the equation.
3(11)+5(4)
33+20=53
The answer is (c)53
Raj purchases a new home for $150,000. The value of the home increases by 9% every 3 years.
Determine the value of the home after 5 years.
The value of the home after 5 years would be $194,415.
How to calculate the value of the home after 5 years
First, let's calculate the increase in value for each 3-year period:
After the first 3 years:
Increase = 9% of $150,000 = 0.09 * $150,000 = $13,500
After the second 3 years:
Increase = 9% of ($150,000 + $13,500) = 0.09 * ($150,000 + $13,500) = $14,850
After the third 3 years:
Increase = 9% of ($150,000 + $13,500 + $14,850) = 0.09 * ($150,000 + $13,500 + $14,850) = $16,065
Now, let's add these increases to the initial value of the home to find the value after 5 years:
Value after 5 years = $150,000 + $13,500 + $14,850 + $16,065 = $194,415
Therefore, the value of the home after 5 years would be $194,415.
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Given that ΔA′B′C′ is a dilation of ΔABC, how are the angles and side lengths of the preimage and image related?
A. The angles are congruent and the side lengths are congruent.
B. The angles are congruent and the side lengths are proportional.
C. The angles are proportional and the side lengths are congruent.
D. The angles are proportional, and the side lengths are proportional.
When a dilation is performed on a triangle, the angles and side lengths of the preimage and image are related in a specific way. The correct answer is B. The angles are congruent, and the side lengths are proportional.
In a dilation, each corresponding angle of the preimage and image triangles is congruent. This means that if an angle in the preimage triangle measures 60 degrees, the corresponding angle in the image triangle will also measure 60 degrees.
However, the side lengths of the preimage and image triangles are not necessarily congruent. Instead, they are proportional. This means that the ratio of corresponding side lengths remains constant throughout the dilation. For example, if one side of the preimage triangle is twice as long as another side, the corresponding side in the image triangle will also be twice as long as its corresponding side.
It's important to note that the center of dilation and the scale factor determine the specific proportions between the side lengths. The scale factor represents the ratio of corresponding side lengths in the preimage and image triangles.
Therefore, in a dilation, the angles are congruent, and the side lengths are proportional.
The right answer is B. The angles are congruent and the side lengths are proportional.
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What is the end behavior of this radical function? f(x) = -2½ + 7
Answer:
Step-by-step explanation:
The function you provided, f(x) = -2.5 + 7, represents a linear function rather than a radical function. A linear function has a constant slope and a constant y-intercept.
The end behavior of a linear function is determined by its slope. In this case, the slope of the function is 0 since there is no term involving x. When the slope is 0, it means the function is a horizontal line.
The function f(x) = -2.5 + 7 represents a horizontal line at y = 4.5. As x approaches positive infinity (∞) or negative infinity (-∞), the value of y remains constant at 4.5. Therefore, the end behavior of this linear function is that y approaches 4.5 as x approaches both positive and negative infinity.
In conclusion, the end behavior of the function f(x) = -2.5 + 7 is that y approaches 4.5 as x approaches positive and negative infinity.
Write an expression to represent: 6 times the difference of 5 and x
Answer:
6 * (5 - x)
Step-by-step explanation:
This expression calculates the difference between 5 and x, and then multiplies it by 6. The difference is obtained by subtracting x from 5, and then the entire result is multiplied by 6.
From a point x, the bearing of a hill is 200⁰ and from another point Y 170km due east of x ,the bearing of the hill is 255⁰. Calculate the distance between the hill and Y
Answer:
Step-by-step explanation:
Byron worked fewer than 20 days last month. Write an inequality for d, the number of days Byron worked last month.
Answer:
[tex]d < 20[/tex]
Step-by-step explanation:
The key words in this question are fewer than, which signifies the less than sign. So, the number of days that Byron worked is less than 20.
1.1.4 Express 25/75 as a percentage.
Answer:
Hi
Please mark brainliest ❣️
Step-by-step explanation:
25/75 × 100/1
= 33.3%
here is a rhombus.A strait line joining the midpoints of two of its sides are work out the size of angle a
The size of angle can be expressed as 130 degrees
How can the side of the angle be worked out?Two angles are said to be supplementary angles because they combine to generate a linear angle when their sum is 180 degrees.
Considering the given figure, if we look at the right top triangle we can deduced that it is an isosceles, then the supplementary angle of angle α can be calculated as
(180 - 80)/2
= 50 degrees.
Hence, α = 180 - 50
= 130 degrees.
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Write the polynomial as a product of linear factors.
x^(4)-x^(3)-5^(2)-x-6
The factored form of the polynomial [tex]x^4 - x^3 - 5x^2 - x - 6[/tex] is:
[tex](x - 2)(x^3 + x^2 - 3x - 7)[/tex]
We have,
To factor the polynomial [tex]x^4 - x^3 - 5x^2 - x - 6,[/tex]
we can look for its roots and express it as a product of linear factors.
First, let's check if there are any rational roots using the rational root theorem.
The possible rational roots can be found by taking the factors of the constant term (-6) and dividing them by the factors of the leading coefficient (1).
The factors of -6 are: ±1, ±2, ±3, ±6
The factors of 1 are: ±1
The possible rational roots are: ±1, ±2, ±3, ±6
By testing these values, we find that x = 2 is a root of the polynomial.
Using synthetic division, we can divide the polynomial by (x - 2) to find the quotient.
The quotient is [tex]x^3 + x^2 - 3x - 7.[/tex]
Now, we can continue factoring the quotient.
The polynomial x³ + x² - 3x - 7 does not have any rational roots.
We can try factoring it by grouping or using other factoring methods, but in this case, it does not factor nicely into linear factors.
Therefore,
The factored form of the polynomial [tex]x^4 - x^3 - 5x^2 - x - 6[/tex] is:
[tex](x - 2)(x^3 + x^2 - 3x - 7)[/tex]
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If ΔABC is dilated from point A by a scale factor of one half, which of the following equations is true about segment D prime E prime?
segment D prime E prime = one half segment DE
segment D prime E prime = two segment DE
segment D prime E prime = segment DE
segment D prime E prime = three segment DE
An equation that is true about segment D prime E prime include the following: A. segment D prime E prime = one half segment DE
What is a dilation?In Geometry, a dilation is a type of transformation which typically changes the side lengths of a geometric object, but not its shape.
In this scenario and exercise, we would dilate the coordinates of the vertices of triangle ABC (ΔABC) by applying a scale factor of 1/2 that is centered at point A as follows:
D'E' = 1/2 × DE
In conclusion, line segment D'E' is equal to one half line segment DE.
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Identify one example of each angle pair in the diagram to the right.
Alternate exterior angles are ∠9 and (∠1 + ∠2)
Consecutive interior angles are ∠7 and ∠4
Consecutive exterior angles are ∠9 and ∠∠3
Vertical angles are ∠2 and ∠5
Linear pairs are ∠7 and ∠8
We have,
Alternate exterior angles: Pairs of angles on opposite sides of a transversal line, formed by two parallel lines, and located outside the intersected lines.
Consecutive interior angles: Pairs of angles on the same side of a transversal line, formed by two parallel lines, and located between the intersected lines.
Consecutive exterior angles: Pairs of angles on the same side of a transversal line, formed by two parallel lines, and located outside the intersected lines.
Vertical angles: Pairs of non-adjacent angles formed by the intersection of two lines, sharing the same vertex and having equal measures.
Linear pair: A pair of adjacent angles formed by the intersection of two lines, sharing a common side, and whose measures add up to 180 degrees.
So,
Alternate exterior angles
= ∠9 and (∠1 + ∠2)
Consecutive interior angles
= ∠7 and ∠4
Consecutive exterior angles
= ∠9 and ∠∠3
Vertical angles
= ∠2 and ∠5
Linear pair
= ∠7 and ∠∠8
Thus,
Alternate exterior angles are ∠9 and (∠1 + ∠2)
Consecutive interior angles are ∠7 and ∠4
Consecutive exterior angles are ∠9 and ∠∠3
Vertical angles are ∠2 and ∠5
Linear pairs are ∠7 and ∠8
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19
Evaluate the following:
25 (23 +8÷4) +5
16
B) 20
27
D) 28
List all numbers from the given set that are a. natural numbers, b. whole numbers, c. integers, d. rational numbers, e. irrational numbers, and f. real numbers.
a. Natural numbers: 0, 4.2, √9
b. Whole numbers: -8, 0, 4.2, √9
c. Integers: -8, 0, 4.2, √9
d. Rational numbers: -8, 5/6, 0, 4.2, √9
e. Irrational numbers: √2, π
f. Real numbers: -8, 5/6, 0, 0.1, √2, π, 4.2, √9
We have,
a. Natural numbers:
5/6, 0, 4.2, √9 (The natural numbers are positive integers excluding zero)
b. Whole numbers:
-8, 0, 4.2, √9 (Whole numbers include zero and all positive integers)
c. Integers:
-8, 0, 4.2, √9 (Integers include positive and negative whole numbers, including zero)
d. Rational numbers:
-8, 5/6, 0, 4.2, √9 (Rational numbers can be expressed as a fraction of two integers)
e. Irrational numbers:
√2, π (Irrational numbers cannot be expressed as a fraction and have non-repeating, non-terminating decimal expansions)
f. Real numbers:
-8, 5/6, 0, 0.1, √2, π, 4.2, √9 (Real numbers include all rational and irrational numbers)
Thus,
a. Natural numbers: 0, 4.2, √9
b. Whole numbers: -8, 0, 4.2, √9
c. Integers: -8, 0, 4.2, √9
d. Rational numbers: -8, 5/6, 0, 4.2, √9
e. Irrational numbers: √2, π
f. Real numbers: -8, 5/6, 0, 0.1, √2, π, 4.2, √9
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The complete question.
-8, 5/6, 0, 0.1, √2, π, 4.2, √9
List all numbers from the given set that are a. natural numbers, b. whole numbers, c. integers, d. rational numbers, e. irrational numbers, and f. real numbers.
Select all expressions that are squared of linear expressions
a) 9x*2 - 36
b) p*2 - 6p + q
c) (1/2x + 4)*2
d) (2d + 8)(2d-8)
e) x*2 + bx + 36
f) x*2 + 36
Part B
Select all the equations that are equivalent to x*2 + 6x = 16
a) (x+3)*2 = 16
b) (x + 3) *2 =0
c) x*2 + 6x + 9 = 0
d) (x+3*2) = 15
e) x*2 + bx + 9 = 25
f) x*2 + 6x + 9 = 16
A. The expressions that are squared of linear expressions are: c) (1/2x + 4)²; f) x² + 36. B. The equivalent expressions are: a) (x+3)² = 16; f) x² + 6x + 9 = 16.
How to Find Equivalent Equations and Expressions that are Squared of Linear Expressions?Part A: For the expressions that are squared of linear expressions:
a) 9x² - 36: This expression is not a squared linear expression because it contains a constant term (-36).
b) p² - 6p + q: This expression is not a squared linear expression because it contains a quadratic term (-6p) and a constant term (q).
c) (1/2x + 4)²: This expression is a squared linear expression because it represents the square of a linear expression, (1/2x + 4).
d) (2d + 8)(2d-8): This expression is not a squared linear expression because it represents the product of two linear expressions, (2d + 8) and (2d - 8).
e) x² + bx + 36: This expression is not a squared linear expression because it contains a quadratic term (x²) and a constant term (36).
f) x² + 36: This expression is a squared linear expression because it represents the square of the linear expression (x) and a constant term (36).
Part B: For the equations that are equivalent to x² + 6x = 16:
a) (x+3)² = 16: This equation is equivalent because it represents the square of the linear expression (x+3) equal to 16.
b) (x + 3)² = 0: This equation is not equivalent because it represents the square of the linear expression (x+3) equal to zero, not 16.
c) x² + 6x + 9 = 0: This equation is not equivalent because it represents a quadratic equation with a constant term (9), not x² + 6x = 16.
d) (x+3²) = 15: This equation is not equivalent because it represents the square of the linear expression (x+3²) equal to 15, not 16.
e) x² + bx + 9 = 25: This equation is not equivalent because it represents a quadratic equation with a constant term (9) and a different right-hand side (25), not x² + 6x = 16.
f) x² + 6x + 9 = 16: This equation is equivalent because it represents the square of the linear expression (x+3) equal to 16.
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Solve and graph. |3x+6/9|>=2
The solution to the inequality expression is -8/9 ≤ x ≥ 4/9
How to solve and graph the inequality expressionFrom the question, we have the following parameters that can be used in our computation:
|3x + 6/9| ≥ 2
Expand the inequality expression
So, we have
-2 ≤ 3x + 6/9 ≥ 2
Subtract 6/9 from both sides
So, we have
-24/9 ≤ 3x ≥ 12/9
Divide through the equation by 3
-8/9 ≤ x ≥ 4/9
Hence, the solution to the inequality expression is -8/9 ≤ x ≥ 4/9
The graph is attached
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A dentist was making note of her upcoming appointments with different aged patients and
the reasons for their visits.
Patients under 18
Patients 19-60
Patients over 60
Regular cleaning Broken tooth
Submit
5
3
3
2
6
2
What is the probability that a randomly selected appointment is not with a patient 19-60 or is
not for a broken tooth?
Simplify any fractions.
Probability that a randomly selected appointment is with patients over 60 years old and is for a regular cleaning = (5/21)
The probability of an event is calculated as the number of elements in that event divided by the total number of elements in the sample space.
For this question, we are told to find the probability that a randomly selected appointment is with patients over 60 years old and is for a regular cleaning.
Number of patients that are over 60 years and are for regular cleaning = 10
Total number of patients = 2 + 8 + 6 + 4 + 10 + 12 = 42
Probability that a randomly selected appointment is with patients over 60 years old and is for a regular cleaning = (10/42)
= (5/21)
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a triangle is shown below, find the m
The value of angle L is 61°
What is exterior angle theorem?Exterior angle theorem states that the measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles.
If angle A and B are interior angles and angle C is the exterior angle, what this theorem is saying is that;
A+B = C
Similarly,
angle L and angle E are the interior angles and 113 is the exterior angle, therefore;
113 = L + 52
L = 113 -52
L = 61°
Therefore angle L is 61°
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Solve the simultaneous equations using elimination method= x+2y-3z=0 3x+3y-z = 5 x-2y = 2z=1
Answer:
[1;1;1]
Step-by-step explanation:
try this option; all the details are in the attachment.
If the equation is an identity
The equation is an identity is discussed below.
An identity is a mathematical equation that holds true for all values of the variables involved.
In other words, it is true regardless of the specific values of the variables. When an equation is an identity, it means that both sides of the equation are equivalent and represent the same mathematical relationship.
For example, the equation 2x + 3 = 2(x + 1) is an identity because it holds true for all values of x.
When an equation is an identity, it provides a general statement or rule that is universally applicable and does not depend on specific values or conditions. Identifying an equation as an identity is important because it allows us to make general conclusions and deductions that apply in all cases.
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