The interval notation for all real numbers between -3 and 8 is:
[-3, 8].
How to list all real numbers between a and b?There are an infinite number of real numbers between a and b, hence we list all them in interval notation, as follows:
[a,b]: including a and b.(a,b): excluding a and b.In this problem, we include -3 and 8, hence the notation is:
[-3, 8].
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Identify a horizontal or vertical stretch or compression of the function f(x) = x by observing the equation of the function g(x) = 5x.
The vertical stretch of f(x) to g(x) is a factor of 5
How to determine the dilation?The functions are given as:
f(x) = x
g(x) = 5x
Substitute f(x) = x in g(x) = 5x
g(x) = 5f(x)
In th above equation, the factor is 5.
5 is greater than 1 (this means vertical stretch)
Hence, the vertical stretch of f(x) to g(x) is a factor of 5
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Given functions f and g, find f-g.
f(x) = 3x -8, g(x) = 8x - 3
OA. 5x+5
OB. 11x-11
O C. -5x -5
D.-5x-11
Answer:
[tex]-5x-5[/tex]
Step-by-step explanation:
original functions:
[tex]f(x)=3x-8\\g(x)=8x-3[/tex]
Subtract the polynomials:
[tex]f(x)-g(x) = (3x-8) - (8x-3)[/tex]
Distribute the negative sign:
[tex]3x-8-8x+3[/tex]
Combine like terms:
[tex](3x-8x)+(-8+3)[/tex]
Add like terms:
[tex]-5x-5[/tex]
What is the determinant of K =
[6 8
0 3]
Solve for x. Round to the nearest tenth, if necessary.
X
H
In this problem we are given an angle and two sides. Therefore, we should use a trigonometric function to solve for x.
Trigonometric Functions: SOH-CAH-TOA
Looking from the 23 degree angle, we have the adjacent side and the opposite side. Therefore, we should use the tangent function.
tan(23) = x / 2
x = tan(23) * 2
x = 0.8489
x = 0.8
Hope this helps!
Step-by-step explanation:
ATTACHED IS THE SOLUTION!What is the factored form of 8x² + 12x?
O 4(4x² + 8x).
O 4x(2x + 3)
O8x(x + 4)
O 8x(x² + 4)
Answer:
Step-by-step explanation:
Solution
The factored form is going to be the HCF (highest common factor)
The fest way to do this is to turn this into primes.
8x^2 + 12x
8x^2 = 2*2*2*x*x
12x = 2 * 2 * x
Now bold the HCF.
8x^2 = 2*2*2*x*x
12x = 2 * 2 * x
The HCF = 2*2*x
Divide that into the original question to determine the second factor.
8x^2 / 4x = 2x
12x / 4x = 3 Notice how the x-s cancel
Answer
4x (2x + 3)
If the sum of all other interior angles is 620∘, what is the angle measure of x. do not include x= or the degree sign in your answer.
The measure of angle x from the diagram is 100 degrees
Sum of interior angle of an hexagonThe formula for calculating the sum of interior angle of a polygon is given as:
s = (n-2)180
Since hexagon has 6 interior angles, the sum of the interior will be 720 degrees. Hence
x + 620 = 720
x = 720 - 620
x= 100
Hence the measure of angle x from the diagram is 100 degrees
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The tile edging for a bathroom is in the shape of a triangle. The area of a triangle with base b and height h is A=1/2 bh. Find the area of the tile if the base measures 3.5 cm and the height measures 8 cm.
Final answer:
Area of tile is 14 cm².
Step-by-step explanation:
Area of triangle is:
[tex]\frac{1}{2} base.height[/tex]
Putting [tex]b=3.5[/tex] and [tex]h=8[/tex] in [tex]\frac{1}{2} base.height[/tex]
[tex]\frac{1}{2}bxh=\frac{1}{2}3.5x8[/tex]
[tex]=3.5x4[/tex]
[tex]=14[/tex]
In your own words, explain why every natural number is also a rational number but not every rational number is a natural number.
Answer:
Every natural number is also a rational number but not every rational number is a natural number because the set of natural numbers is a subset of the set of rational numbers.
Explanation:
Since all natural numbers, n can be written as n/1. Thus all natural numbers are rational. Since 3/4 is a rational number but not natural thus all rational numbers are not natural.
Hint:
Natural numbers : All positive numbers except zero.
Rational numbers: All numbers in the form of p/q, where q ≠ 0 (p,q are integers)
The following subjects reference the same area on a polynomial graph: zeros,
solutions, roots, x-intercepts, and factors.
True or false?
Zeros, solutions, roots, x-intercepts, and factors are subjects that reference the same area on a polynomial graph.
What is a polynomial graph?A polynomial graph can be defined as a type of graph that can be used to represent only positive (non-negative) integer exponents of a variable in an equation.
This ultimately implies that, a polynomial graph touches the x-axis at zeros, solutions, roots, x-intercepts, and factors with even multiplicities.
In conclusion, we can logically deduce that zeros, solutions, roots, x-intercepts, and factors are subjects that reference the same area on a polynomial graph.
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Question Each answer choice below represents a relation by a set of ordered pairs. In which of the answer choices is the relation a function? Select all correct answers. Select all that apply: {(-3, 10), (-2, 13), (3, 13), (8, 12)} {(-2, 13), (-5, 9), (-5,-5), (-3,-1)} □ {(4,-4), (4,2), (-3, 4), (-2,-5)} □ {(-4,11), (5, 10), (-3, 3), (-1, 10)} □ {(1,7), (1,-5), (0, 13), (2, 1)}
The ordered pairs that represent functions are:
{(-3, 10), (-2, 13), (3, 13), (8, 12)} {(-4,11), (5, 10), (-3, 3), (-1, 10)}How to determine the ordered pairs?For a set of ordered pairs to represent a function, the following must be true:
The x value must point to only one y value
In {(-3, 10), (-2, 13), (3, 13), (8, 12)} and {(-4,11), (5, 10), (-3, 3), (-1, 10)}, the x value point to only one y value
Hence, {(-3, 10), (-2, 13), (3, 13), (8, 12)} and {(-4,11), (5, 10), (-3, 3), (-1, 10)} are functions
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The weights in ounces of a sample of running shoes for men and women are shown. Test the claim that the means are different. Use the P-value method with α = 0.05.
Men
9.6 12.6 11.2 15.0 11.6 13.3 12.5 12.6 12.7 13.6
Women
10.2 9.2 9.5 9.9 8.8 10.4 10.5 10.6 10.4 9.9
8.9 9.8 9.9 10.1 12.0
Group of answer choices
Since the P-value is greater than α = 0.05, do not reject the null hypothesis. There is not enough evidence to support the claim that there is a difference in the weights of running shoes.
Since the P-value is less than α = 0.05, reject the null hypothesis. There is enough evidence to support the claim that there is a difference in the weights of running shoes.
Since the P-value is less than α = 0.05, do not reject the null hypothesis. There is not enough evidence to support the claim that there is a difference in the weights of running shoes.
Since the P-value is greater than α = 0.05, reject the null hypothesis. There is enough evidence to support the claim that there is a difference in the weights of running shoes.
The conclusion will be; Since the P-value is less than α = 0.05, reject the null hypothesis. There is enough evidence to support the claim that there is a difference in the weights of running shoes. Option B.
What is the conclusion?Parameters
Group 1
n1=10
x=18.47
[tex]s^2_1[/tex]=2.12
Group 1
n2=15
x2=10.01
[tex]s^2_2[/tex]=0.62
Generally, the equation for the hypothesis is mathematically given as
[tex]H_0=\mu_1 =\mu=2 \\\\H_a= \mu_1 \neq \mu=2[/tex]
Therefore
[tex]t=\frac{12.47-10.01}{\sqrt{\frac{2.12}{10}+\frac{0.61}{15}}}[/tex]
t=4.8966
In conclusion, The pvalue from table is
p-value (4.8966, [tex]\alpha[/tex] =0.06)
[tex]p-value < \alpha=0.05[/tex]
since [tex]p-value < \alpha=0.05[/tex] we reject the null hypothesis and state that there is no difference b/w the two means.
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-3x+4y=2 & -6x+6y=-3 solve by elimination
Answer:(4,7/2)
Step-by-step explanation:
Find the sum of the first 5,000 odd numbers
Step-by-step explanation:
this is an arithmetic sequence :
a1 = 1
an = an-1 + 2 = a1 + (n-1)×2
the sum of n terms of an arithmetic sequence is
S = n×(a1 + an)/2
n = 5000
an = a1 + 4999×2 = 9999
S = 5000×(1 + 9999)/2 = 5000×5000 = 25,000,000
a company promises to release model every month. each model's battery life will be 6% longer than the previous model's. if the current model's battery is 671.0 minutes, in how many months will the latest model's battery life reach 1,008.9 minutes?
The number of months that it will take the latest model's battery life to reach 1,008.9 minutes is; 8 months
How to solve geometric progression?
Each month, there is an increase by a factor of 0.06 of the previous months model.
From geometric sequence formula of aₙ = ar^(n - 1),
where;
a is first term
r is common ratio
aₙ is nth term
we have;
1,008.9 = 671 * 1.06^(n - 1)
1008.9/671 = 1.06^(n - 1)
In 1.504 = (n - 1) In 1.06
0.408 = (n - 1) * 0.058
n - 1 = 0.408/0.058
n = 7.03 + 1
n ≈ 8 months
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Simplify √3. √21
√24
√63
O 3√7
09√7
Answer:
•3✓7
✓3.✓21
=✓3×✓3✓7
=3✓7
Answer:
3rd answer is correct
Step-by-step explanation:
√3 × √21
√3 × √(7 × 3)
√( 3 × 3 × 7 )
√ ( 3 × 3 ) × √7
3√7
Choose what the expressions below best represent within the context of the word problem.
The tens digit of a number is twice the ones digit. The sum of the digits in the number is 12. What is the number?
x represents
the ones
digit
2x represents
the tens
digit
The number which represent tens digit of a number is twice the ones digit is;
x represents the ones digit2x represents the tens digitWord problemComplete question:
The tens digit of a number is twice the ones digit. The sum of the digits in the number is
12. What is the number?
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QUESTION 1 -
If f(x)=3x²-5x+4, then f(-2)=
a.) - 18
b.) 26
c.) 2
d.) 6
Question 2 -
For an ordered pair (x, y) in a relation, the y element represents the _____
a.) input
b.) range
c.) domain
d.) function
Need help urgently! Will give brainliest.
Given: f(x) = 3x² -5x + 4
To find f(-2), simply substitute x = -2 in function f(x).
f(-2) = 3(-2)² -5(-2) + 4
f(-2) = 12 + 10 + 4
f(-2) = 26
Answer: 26
#2For an ordered pair (x, y) in a relation, the y element represents the range.
Answer: range
What is 42% of 17?
round up
Hello
42. ?
100 17
We use cross product.
[tex] \frac{42 \times 17}{100} = 7.14[/tex]
42% of 17 => 7.14
Have a nice day ;)
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Question reads....}[/tex]
[tex]\large\textbf{What is 42\% of 17?}[/tex]
[tex]\huge\textbf{Answering your question}[/tex]
[tex]\mathbf{42\% \ of \ 17}[/tex]
[tex]\huge\textbf{Translating it to easier to terms}[/tex]
[tex]\mathbf{42\% \ of \ 17}[/tex]
[tex]\mathbf{= 42\%\times 17}\\[/tex]
[tex]\mathbf{= \dfrac{42}{100}\times 17}[/tex]
[tex]\mathbf{= \dfrac{42\div2}{100\div2}\times17}[/tex]
[tex]\mathbf{= \dfrac{21}{50}\times17}[/tex]
[tex]\mathbf{= \dfrac{21}{50} \times \dfrac{17}{1}}[/tex]
[tex]\mathbf{= \dfrac{21\times17}{50\times1}}[/tex]
[tex]\mathbf{= \dfrac{357}{50}}[/tex]
[tex]\mathbf{= 357 \div 17}[/tex]
[tex]\mathbf{= 7.14}[/tex]
[tex]\huge\textbf{Answer }\bf \huge\boxed{\downarrow}[/tex]
[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{7.14}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
The endpoints of are A(2, 2) and B(3, 8). is dilated by a scale factor of 3.5 with the origin as the center of dilation to give image . What are the slope (m) and length of ? Use the distance formula to help you decide: .
A.
B.
C.
D.
The slope is m=6 and length of line is 3.5√37.
What is slope?The slope of a line is a measure of its steepness.
Given:
endpoints of are A(2, 2) and B(3, 8). is dilated by a scale factor of 3.5
slope= 8-2/3-2= 6
Now, using distance formula,
d= √(3-2)² + (8-2)²
d= √1+ 36
d= √37
As, Line AB is dilated by a scale factor of 3.5.
So, new d= √37*3.5
new d= 3.5√37
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4. Identify a transformation of the function f(x) = x by observing the equation of the function g(x)
= x - 90.
The base graph has been shifted left 90 units.
The base graph has been shifted up 90 units.
The base graph has been shifted down 90 units.
The base graph has been shifted right 90 units.
Answer: The base graph has been shifted down 90 units.
Step-by-step explanation:
See attached image.
Find the error in the calculations below:
Line (1): -3(2x + 5) <21
Line (2): -6x
15 < 21
Line (3): -6x < 36
Line (4): x <- 6
Line (5):
-
O The error occurred from line (1) to line (2).
O The error occurred from line (4) to line (5).
O The error occurred from line (3) to line (4).
O The error occurred from line (2) to line (3).
Answer: Line 3 to line 4
Step-by-step explanation:
When dividing by a negative, you need to flip the inequality sign.
Given that
10 - V18 = a + bV2 , where a and b are integers.
V2
Find the values of a and b.
The values of a and b if they are integers are -10 and 3
Equations and surdSurd functions are square root of prime numbers. Given the following equation;
10 - √18 = a +b√2
Equate the real and surd part to form the equation
b√2 = √18
2b² = 18
b² = 9
b = 3
Similarly
a = -10
Hence the values of a and b if they are integers are -10 and 3
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The bisection method is being used to calculate the zero of the following function between x = 0 and x = 1.
The bisection method will converge to the solution after three iterations.
How to illustrate the information?It should be noted that after one iteration, x1 will be:
= (1 + 9)/2
= 10/2
= 5
Since f(x¹) > 0, x² will then replace x1. Now x0 = 1 and x1 = 5.
After the second iteration, x2 will be:
= (1 + 5)/2
= 3
Also, this is greater than 0. The third iteration will be:
m= (1 + 3)/2
= 2.
Now, f(2) = 2⁴ -2³ - 2² - 4
= 0
Therefore, the method converges exactly to the root in 3 iterations.
Complete question:
The bisection method is applied to compute the zero to a function f(x) = x⁴ - x³ - x² - 4 in the interval (1, 9). The method converges y a solution after .............. iterations.
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Which figure shows a line of reflectional symmetry for the letter T?
A letter T is folded at the horizontal line.
A letter T is folded diagonally.
A letter T is folded vertically through the middle.
A letter T is folded diagonally through its center.
Mark this and return
The figure that will depict a line of reflectional symmetry of letter T is: Option C: A letter T folded vertically through the middle.
What is a Line of Reflectional Symmetry?A line of reflectional symmetry is defined as an imaginary line that divides a figure into two halves in such a way that each of the halves are a mirror image of the other.
When a line divides letter T vertically, it means that two mirror images will be created.
Therefore, the figure that will depict a line of reflectional symmetry of letter T would be: A letter T folded vertically through the middle.
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find the lowest common multiple ( L.C.M. ) of the (a² - 4), (a³ - 8), ( a + 2 ) ²
Answer: according to my work i got
LCM - Lowest Common Factor
HCF - Highest common factor
Step-by-step explanation:
please mark brainlest!!
yw! =^.^=
(07.01 MC)
The picture shows a triangular island:
Island
Z
O x sin 50°
O
Which expression shows the value of z? (1 point)
cos 50°
O x cos 50°
O
sin 50°
y
50
Answer:
Option (2)
Step-by-step explanation:
cos 50° = y/z
z = y/cos 50°
Dominick borrowed $6,000 from a credit union at 9% simple interest for 30 months. What is the total amount of interest Dominick will pay throughout the life of the loan?
The total amount of interest Dominick will pay throughout the life of the loan is $1350
What is Simple Interest ?Simple Interest is the interest applied only on the Principal amount invested or borrowed .
It is calculated by the formula
I = ( P * R * T ) /100
P is the Principal
R is the Rate of Interest
T is the Time Period
Here
P = $ 6000
R= 9 %
T = 30 months = 30/12 year = 2.5 years
I = ( 6000 * 9 * 2.5 ) / 100
Interest = $1350
Therefore , the total amount of interest Dominick will pay throughout the life of the loan is $1350
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A square room is 14m long. Find the area of its floor
Answer: 196m squared
Step-by-step explanation: A square has equal sides, so if one side were to be equal to 14m, the other would too. 14 x 14 = 196.
When you start your career, you decide to set aside $250 every month to deposit into an investment account. The investment firm claims that historically their accounts have earned an annual interest rate of 9.0% compounded monthly. Assuming this to be true, how much money will your account be worth after 20 years of depositing and investing? Round your answer to the nearest cent. Do not include labels or units. Just enter the numerical value.
After 20 years of depositing and investing there will be 168474.01 dollars in your account.
What is compound interest?It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.
We can calculate the compound interest using the below formula:
[tex]\rm A = P(1+\dfrac{r}{n})^{nt}[/tex]
Where A = Final amount
P = Principal amount
r = annual rate of interest
n = how many times interest is compounded per year
t = How long the money is deposited or borrowed (in years)
The formula for calculating how much money will your account be worth after 20 years of depositing and investing is:
P = $250, r = 9% = 0.09, t = 20 years, n = 12 and PMD = $250(per month deposit)
[tex]\rm A = P(1+\dfrac{r}{n})^{nt}+\dfrac{PMD((1+\dfrac{r}{n})^{nt}-1)}{\dfrac{r}{n}}[/tex]
[tex]\rm A = 250(1+\dfrac{0.09}{12})^{12\times20}+\dfrac{250((1+\dfrac{0.09}{12})^{12\times12}-1)}{\dfrac{0.09}{12}}[/tex]
A = 1502.287 + 166971.717
A = $168474.01
Thus, after 20 years of depositing and investing there will be 168474.01 dollars in your account.
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For a population with μ = 60 , z-score =3.15, and σ = 10. Find random variable / data value X . Round your answer to the nearest hundredths place. Round your answer to 2 decimal places.
Answer:
X = 91.50
Step-by-step explanation:
The relation that defines a Z value can be used to find an X value when the appropriate parameters are given.
Z-scoreThe equation for finding the Z-score associated with an X-value is ...
Z = (X -μ)/σ
Solving this for X using the values given, we have ...
3.15 = (X -60)/10
31.5 = X -60 . . . . . . . multiply by 10
91.5 = X . . . . . . . . add 60
The random variable value is ...
X = 91.50