Julio initially started with the number 20, because cubing the number and then taking the cube root returns the original number.
If Julio cubes a number and then takes the cube root of the result, and ends up with 20, then the number he started with is also 20. This is because the cube of a number n is n
to the power of 3 (n³), and the cube root of a number is the inverse operation, which will return the original number. In symbolic form, if n is cubed to get n³, then taking the cube root of n³ will return n. Since Julio ends up with 20, the number he started with must have been 20.
Which statement below is not a valid part of this proof?
Evaluate f(-2) if f(x)=-3x^2-1
2 points
11
-13
13
-11
f(x)=-3x^2-1
f(-2)= -3(-2)²-1=-3·4-1= - 13
The results of a poll indicate that between 33% and 37% of the population of a town visit the library at least once a year.
What is the poll’s margin of error?
Enter your answer in the box.
±___%
Final answer:
The margin of error for the poll, given a range of 33-37%, is ±2%. This means the actual percentage of the town's population that visits the library at least once a year could reasonably be expected to fall within 2% of the poll's reported value, which is 35%.
Explanation:
The margin of error in a poll is a statistic that reflects the degree of accuracy of the poll's results. It indicates how much the actual percentage could differ from the reported percentage in either direction. In this case, the poll indicates a visitation range between 33% and 37%. To calculate the margin of error, you find the difference between the highest value and the mean or the difference between the mean and the lowest value of the range.
In this instance, (37% + 33%) / 2 = 35%, which is the mean. The margin of error is then calculated as either 37% - 35% or 35% - 33%, both resulting in a 2%. Therefore, the poll's margin of error is ±2%.
First question. The midpoint of SR is...
The formula of a midpoint SR:
[tex]M\left(\dfrac{x_S+x_R}{2},\ \dfrac{y_S+y_R}{2}\right)[/tex]
We have
S(4, 1) and M(7, -5)
Substitute:
[tex]\dfrac{4+x_R}{2}=7\qquad|\cdot2\\\\4+x_R=14\qquad|-4\\\\x_R=10\\\\\dfrac{1+y_R}{2}=-5\qquad|\cdot2\\\\1+y_R=-10\qquad|-1\\\\y_R=-11[/tex]
Answer: R(10, -11)A car is purchased for $29500. After each year, the resale value decreases by %35. What will the resale value be after 4 years
Using the exponential decay formula, the resale value of a car initially purchased at $29,500 and depreciating at 35% per year will be approximately $5,266.08 after 4 years.
To calculate the resale value of a car after depreciation, we can use the formula for exponential decay, which is [tex]V = P (1 - r)^t[/tex], where V is the future value of the car, P is the initial purchase price, r is the rate of depreciation, and t is the time in years. In this case, P = $29,500, r = 35% or 0.35, and t = 4 years.
Following the formula, the resale value after 4 years would be:
V = $29,500 (1 - 0.35)⁴
V = $29,500 (0.65)⁴
V = $29,500 (0.17850625)
V = $5,266.08 approximately
Therefore, the resale value of the car after 4 years will be around $5,266.08.
A student has scores of 70 and 80 on two tests. What must the student score on the last test to ensure that her average is greater than 80?
What is the length of the hypotenuse of the triangle of 7ft and 4ft
To find the length of the hypotenuse in a right-angled triangle with sides measuring 7ft and 4ft, use the Pythagorean Theorem: 7² + 4²= c², which gives us the hypotenuse length of approximately 8.06 feet.
The question is asking for the length of the hypotenuse of a right-angled triangle when the lengths of the other two sides are known (7ft and 4ft).
To find the hypotenuse, we use the Pythagorean Theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). The formula is expressed as a² + b² = c².
By applying the Pythagorean Theorem:
72 + 42 = c²
49 + 16 = c²
65 = c²
c = √65 ≈ 8.06 ft
Therefore, the length of the hypotenuse is approximately 8.06 feet.
If you have 2 squares with the same side lengths are they still considerd scaled copies of each other?
Graph y=−4/7x+1 . Please help.
Go to a website called desmos graphing calculator and it will help you out but I put a image of the graphed equation as well.
Answer:
The required graph is shown below.
Step-by-step explanation:
Consider the provided function.
[tex]y=-\frac{4}{7}x+1[/tex]
The above function is a linear function.
We can draw the graph of the function with the help of 2 points.
Substitute x = 0 in the above function.
[tex]y=-\frac{4}{7}(0)+1[/tex]
[tex]y=1[/tex]
Substitute y = 0 in the above function.
[tex]0=-\frac{4}{7}x+1[/tex]
[tex]\frac{4}{7}x=1[/tex]
[tex]x=\frac{7}{4}[/tex]
Now plot the points.
Draw a straight line passing through (0,1) and (7/4,0)
The required graph is shown below.
How do you divide 2\3 divided by 7\8 using kcf answer
Answer: [tex]\frac{16}{21}[/tex]
Step-by-Step Explanation:
KCFmeans: Keep, Change, Flip
Keep: the first fractionChange: the sign from division to multiplicationFlip: the second fraction[tex]\frac{2}{3}[/tex] ÷ [tex]\frac{7}{8}[/tex]
= [tex]\frac{2}{3} * \frac{8}{7}[/tex] KCF is applied here!
= [tex]\frac{2(8)}{3(7)}[/tex]
= [tex]\frac{16}{21}[/tex]
Divide. Write the answer in simplest form. 7 1/5 divided by 1/8
First we have to change 7 1/5 into an improper fraction. 7 1/5 converted to an improper fraction is 36/5. Now, to divide this by 1/8, we need to multiply it by 8 (multiplying by the reciprocal). 36/5 * 8/1 = 288/5. In simplest form, this is 57 3/5.
The division problem 7 1/5 divided by 1/8 is solved by converting the mixed number to an improper fraction, converting the division problem to a multiplication problem by multiplying by the reciprocal, and then simplifying the resulting fraction. The final answer is 57.6.
To solve the problem 7 1/5 divided by 1/8, we first need to convert the mixed number 7 1/5 into an improper fraction. We do this by multiplying the whole number 7 by the denominator of the fraction 5 and then adding the numerator 1. So, 7 * 5 + 1 = 36.
So, 7 1/5 becomes 36/5. Now, we have 36/5 divided by 1/8.
When we are dividing by a fraction, we need to multiply by its reciprocal. The reciprocal of 1/8 is 8/1. So the problem becomes 36/5 multiplied by 8/1.
When multiplying fractions, we simply multiply the numerators and the denominators together. So, 36 * 8 = 288 and
5 * 1 = 5. Therefore, our answer is 288/5. Lastly, when we simplify this, it becomes 57.6.
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Please help will get brainiest!!
1.
Part A
Which theorems or postulates allow you to find the value of y?
a) vertical angles theorem and triangle angle-sum theorem
b) triangle exterior angles theorem and vertical angles theorem
c) triangles angle-sum theorem and angles addition postulate
d) angles addition postulate and triangles exterior angles theorem
Part B
Find the value of each variable
a) x=80, y=100
b) x=80, y=80
c) x=100, y=80
d) x=100, y=100
2. Find m<1
a) 57
b) 63
c) 117
d) 123
3. Which theorems or postulates could you use to find the measure of angle 1 in the previous question? (2 points) (2 answers)
Same-Side Interior Angles Theorem
Vertical Angles Theorem
Triangle Angle-Sum Theorem
Triangle Exterior Angle Theorem
Alternate Exterior Angles Theorem
4. Find the value of x
a) x=5
b) x=13
c) x=37
d) x=73
1. Part A
C
Part B
A
2a
4c
srry all i can do
Answers:
1.
Part A. Option a) vertical angles theorem and triangle angle-sum theorem
Part B. Option b) x=80, y=80
2. Option d) 123
3. Options 3 and 4:
Triangle Angle-Sum Theorem
Triangle Exterior Angle Theorem
4. Option c) x=37
Solution:
1. Part A
First, you can find x using the triangle angle-sum theorem: The sum of the interior angles of any triangle must be equal to 180°.
Second, you can apply the vertical angles theorem to find y: the angles opposite by the vertex must be congruent.
Then, the answer is option a) vertical angles theorem and triangle angle-sum theorem.
1. Part B.
First: Triangle angle-sum theorem
The sum of the interior angles of any triangle must be equal to 180°. The interior angles of the triangle in the figure are x°, 30°, and 70°, then:
x°+30°+70°=180°
(x+30+70)°=180°
(x+100)°=180°
x+100=180
Solving for x: Subtracting 100 both sides of the equation:
x+100-100=180-100
x=80
Second: Vertical angles theorem: The angles opposite by the vertex must be congruent:
In the figure, the angles x° and y° are opposite by the vertex, then they must be congruent:
y°=x°
y=x
and x=80, then:
y=80
Answer: Option b) x=80, y=80
2. The <1 is an exterior angle of the triangle in the figure, and according with the Triangle Exterior Angle Theorem, an exterior angle of a triangle must be equal to the sum of the interior angles no adjacents to it:
<1=60°+63°
<1=123°
Answer: Option d) 123
3.
You can apply the Triangle Angle-Sum Theorem, to find the third interior angle of the triangle. With this angle you can find the exterior <1.
You can apply the Triangle Exterior Angle Theorem to find the exterior <1.
Answer: Options 3 and 4:
Triangle Angle-Sum Theorem
Triangle Exterior Angle Theorem
4. Using the Triangle angle-sum theorem:
The sum of the interior angles of any triangle must be equal to 180°. The interior angles of the triangle in the figure are (2x-9)°, x°, and (2x+4)°, then:
(2x-9)°+x°+(2x+4)°=180°
(2x-9+x+2x+4)°=180°
Adding similar terms:
(5x-5)°=180°
5x-5=180
Solving for x: Adding 5 both sides of the equation:
5x-5+5=180+5
Adding:
5x=185
Dividing both sides of the equation by 5:
(5x)/5=185/5
x=37
Answer: Option c) x=37
What is the equivalent expression of 3p+12m+8
Answer:
3 × ( p + 4m ) + 8 and 3p + 4 × ( 3m + 2 ) are the equivalent expressions.
Step-by-step explanation:
Given: Expression = 3p + 12m + 8
To find: Equivalent Expression.
Equivalent Expression means the expression which repesent original expression .i.e., on simplifying we get back original expression.
Consider,
3p + 12m + 8
Ist Equivalent expression we get by taking 3 common from first two terms,
⇒ 3 × ( p + 4m ) + 8
Another Equivalent Expression we get by taking 4 common from last two terms.
⇒ 3p + 4 × ( 3m + 2 )
The equivalent expression of 3p+12m+8 are 3(p+4)+8 and 3p+4(3m+2).
Expression in mathematics consist of terms separated by operations like + and -.
Given expression is 3p+12m+8,
To find the equivalent expression of the given expression:
3p+12m+8
Taking 3 common from first and second term as follows:
3(p+4)+8
one more possible equivalent expression of the given expression:
Taking 3 common from first and second term as follows:
3p+4(3m+2)
Thus, 3(p+4)+8 and 3p+4(3m+2) are the equivalent expression of 3p+12m+8.
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Which of the following are measures of complementary angles? A. 50° and 41° B. 100° and 80° C. 77° and 13° D. 35° and 10°
Complimentary angles equal 90 degrees. So the answer would be C because 77+13= 90.
Answer: Two angles are complementary when they add up to 90°
then, doing all the options:
A) 50° + 41° = 91°, so this angles are non complementary.
B) 100° + 80° = 180°, so this aren't complementary, but they are Supplementary (because their addition is 180°) angles.
C) 77° + 13° = 90°, si this angles are complementary
D) 35° + 10° = 45°, this pair is not complementary.
So the only correct answer is C.
Please help!
Factor.
9x^4−64y^2
To factor 9x^4 - 64y^2, use the difference of squares formula. The factored form is (3x^2 + 8y)(3x^2 - 8y).
To factor 9x^4 - 64y^2, we can use the difference of squares formula: a^2 - b^2 = (a + b)(a - b). Applying this, we get: 9x^4 - 64y^2 = (3x^2 + 8y)(3x^2 - 8y)
Therefore, the factored form of 9x^4 - 64y^2 is (3x^2 + 8y)(3x^2 - 8y).
What should be the next number in the following series? 3 6 4 7 5 8
The next number would be 6.
The pattern is add 3, then subtract two.
The next number in the series 3 6 4 7 5 8 is 6.
Explanation:The next number in the series 3 6 4 7 5 8 is 6.
This is an alternating pattern where the first number increases by 1, the second number stays the same, and the third number increases by 1. So, starting with 3, the next number after 8 should be 9. However, since 9 is not given in the options, we can look for the closest number that follows the pattern, which is 6.
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the length of a rectangle is 4 units shorter than on-fourth of the width, x. Write an expression that represents the perimeter of the rectangle (Use one variable and a fraction) (MUST SHOW WORK PLEASE)
ASNSWER
[tex]Perimeter=\frac{5x-16}{2}[/tex]
EXPLANATION
Let [tex]w=x[/tex] represent the width of the rectangle.
One-fourth of the width will be,
[tex]\frac{1}{4}x[/tex]
Let [tex]l[/tex] represent the length of the rectangle.
Then, subtracting 4 units from one-fourth the width gives us the length
[tex]\Rightarrow l=\frac{1}{4}x-4[/tex]
Perimeter[tex]=2x+2l[/tex]
[tex]\Rightarrow Perimeter=2x+2(\frac{1}{4}x-4)[/tex]
We expand to obtain;
[tex]Perimeter=2x+\frac{x}{2}-8[/tex]
[tex]Perimeter=\frac{x+4x-16}{2}[/tex]
[tex]Perimeter=\frac{5x-16}{2}[/tex]
How u conver 2 1/4 into a improper fraction
what is the solution of 3x+8/x-4 >;= 0
The division between two numbers is positive if and only if they have the same sign. So, this fraction is positive if numerator and denominator are either both positive or both negative.
For this reason, you want to study the sign of numerator and denominator separately first.
As for the numerator, you have
[tex] 3x+8 \geq 0 \iff 3x \geq -8 \iff x \geq -\dfrac{8}{3} [/tex]
Similarly, for the denominator you have
[tex] x-4 > 0 \iff x > 4 [/tex]
(note that we used strict inequality for the denominator, since it can't be zero).
So, the sign of the fraction works like this:
If [tex] x \leq -\frac{8}{3} [/tex] both numerator and denominator are negative (or, at most, the numerator is zero if [tex] x = -\frac{8}{3} [/tex]), so the ratio is greater than or equal to zero.If [tex] -\frac{8}{3} \leq x < 4 [/tex] the numerator is positive and the denominator is negative (or, at most, the numerator is zero if [tex] x = -\frac{8}{3} [/tex]), so the ratio is less than or equal to zero.If [tex] x >4 [/tex] both numerator and denominator are positive, so the ratio is greater than or equal to zero.Answer:
A. x ≤ −8/3 or x>4
Step-by-step explanation:
Edge 2020 answer is A
Jordan bought 9/16 of a pound of sunflower seeds and divided them evenly into 9 snack bags for his lunch what is the weight of sunflower seeds in each snack bag?
A)1/16 of a pound
B)1/9 of a pound
C)16/81 of a pound
D)81/16 of a pound
A.1/16 of a pound. Hope i helped
Answer:
A
Step-by-step explanation:
Which of the following is a binomial?
A. b²-14
B. x²
C. s⁴-s+12
D. f³+f²-f+16
Binomial: A polynomial that is the sum of two terms, each of which are monomials. The answer here would be A. b² - 14, because it is comprised of two terms. Answer B is a monomial because it only has ONE term, C is a trinomial because it has three terms, and D. is a multinomial, or a polynomial because it has more than three terms. Hope that helps!
Represent the following sentence as an algebraic expression, where "a number" is the letter x. You do not need to simplify.
{Nine times the difference of 8 and a number.}
Nine times the difference of 8 and a number.
To represent the sentence 'Nine times the difference of 8 and a number.' as an algebraic expression, we can use the expression 9(8 - x), where x represents 'a number'.
Explanation:To represent the sentence 'Nine times the difference of 8 and a number.' as an algebraic expression, we can start by assigning the letter x to represent a number. Then, we can write the expression as 9(8 - x), where 8 - x represents the difference of 8 and the number x.
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The given sentence 'Nine times the difference of 8 and a number' can be translated into the algebraic expression 9(8 - x).
Explanation:The given sentence, 'Nine times the difference of 8 and a number' can be represented as an algebraic expression as follows: First, identify the operation for 'difference' which is subtraction. Then, identify the 'number', which is given as x. So, 'the difference of 8 and a number' would be 8 - x. 'Nine times the difference' implies multiplication, so the entire expression would be 9(8 - x). Therefore, the algebraic expression to represent the sentence in question is 9(8 - x).
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please help on this one?
The answer is (-3,0) if you plug the coordinates into the equation you will find that it satisfies it and indicates that you should shade below the line
:)
Dennis traveled at an average speed of 60 mph on his vacation trip. How far did he travel in the first 4.5 hours
Answer: 280 Miles.
Step-by-step explanation: 60 x 4 = 240 + 40 = 280 Miles.
Find S5 for a geometric series for which a1=81 and r=1/9.
ANSWER
[tex]S_5=91\frac{10}{81}[/tex]
EXPLANATION
The sum of the first [tex]n[/tex] terms of a geometric sequence is given by;
[tex]S_n=\frac{a_1(1-r^n)}{1-r} ,-1<\:r<\:1[/tex]
Where [tex]n[/tex], is the number of terms and [tex]a_1[/tex] is the first term.
When [tex]n=5[/tex], we have [tex]a_1=81[/tex], we get;
[tex]S_5=\frac{81(1-(\frac{1}{9})^5)}{1-\frac{1}{9}}[/tex]
[tex]S_5=\frac{81(1-\frac{1}{59049})}{1-\frac{1}{9}}[/tex]
[tex]S_5=\frac{81(\frac{59048}{59049})}{\frac{8}{9}}[/tex]
[tex]S_5=\frac{7381}{81}[/tex]
[tex]S_5=91\frac{10}{81}[/tex]
Write the slope-intercept form of the equation that fits the conditions.
Perpendicular to y=-1/3x+1
Passes through (5,-2)
How do I solve this??
Answer:
y = 3x - 17
Step-by-step explanation:
Here is the point-slope form of the equation of a line.
[tex] y - y_1 = m(x - x_1) [/tex]
If you are given a slope, m, and a point on the line, (x1, y1), you just plug in the values into the equation above, and you get the equation of the line.
In your problem, you are given a point on the line, (5, -2). Now you need the slope of the line. Your line is perpendicular to the given line. The slopes of perpendicular lines are negative reciprocals. If you know the slope of a line, the slope of its perpendicular is found by flipping the fraction and changing the sign.
The given line has slope -1/3.
Flip -1/3 to get -3.
Now change the sign to get 3.
The slope of the line you need is 3. The line passes through point (5, -2).
Now we use the point-slope equation and we plug in the values we have.
[tex] y - y_1 = m(x - x_1) [/tex]
[tex] y - (-2) = 3(x - 5) [/tex]
[tex] y + 2 = 3x - 15 [/tex]
[tex] y = 3x - 17 [/tex]
When simplified completely, the product of a monomial and a monomial is sometimesalwaysnever a monomial
Answer:
Always
Step-by-step explanation:
A mononomial's variable can only have exponents 0,1,2,3 etc so the product will also be a mononomial.
Answer:
the answer is -always
Step-by-step explanation:
Describe how to find the number of seats on the middle and lower levels of the stadium when solving for the variable only gives the number of seats on the upper level.
Use the value for the variable to solve for the other unknowns. Substitute the value for the variable into the expression for the number of seats on the middle level. Substitute the value for the variable into the expression for the number of seats on the lower level.
Use the value for the variable to solve for the other unknowns. Substitute the value for the variable into the expression for the number of seats on the middle level.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Use the value for the variable to solve for the other unknowns. Substitute the value for the variable into the expression for the number of seats on the middle level. Substitute the value for the variable into the expression for the number of seats on the lower level.
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Find the value of X and Y.
A. X=15, Y=12
B. X=14, Y=11
C. X=14, Y=12
D. X=15, Y=11
Yeah, I am a little stuck right now, I would love for somebody to help me out on this one.
The values of x and y have been calculated as [tex]15[/tex] and [tex]12[/tex] respectively making option A the appropriate choice.
In the given question we can see that the angles [tex]62[/tex] degrees and [tex]4x + 2[/tex] degrees are alternate interior angles because they are alternately on the interior side of two parallel lines and transversal. hence, we can calculate x as:
[tex]62 = 4x + 2\\4x = 60\\x = 60/4 = 15[/tex]
Similarly, we can find the value of y as the angles [tex]12y[/tex] degrees and [tex]144[/tex] degrees are alternate interior angles.
[tex]12y = 144\\y = 144/12\\y = 12[/tex]
The values of x and y are [tex]15[/tex] and [tex]12[/tex] respectively.
Therefore, option A is the correct answer.
What variation is f(x) = 3x
A. Direct variation
B. Indirect variation
C. Inverse variation
D. Quadric variation
E. None of the above
Direct variation
The equation is written as y=mx+b
The variation f(x) = 3x is A. Direct variation.
The function f(x) = 3x represents a type of relationship called a direct variation. In mathematics, a direct variation can be expressed in the form y = kx, where k is a constant. Here, k is 3. This means that as x increases or decreases, f(x) = 3x changes proportionally. The correct answer is therefore:
A. Direct variationTo further illustrate, consider two pairs of values for x and f(x):
if x = 2, then f(x) = 3(2) = 6,
And if x = 4, then f(x) = 3(4) = 12.
Notice that the ratio f(x)/x = 3 is constant.