Answer:
What is the sum equal to?
Step-by-step explanation:
-6(2x+4)+1/2(8+3x)=-20
Solve the following compound inequality. Graph the solution.
5x2-30 and 5x ≤ 15
What is the solution? Select the correct answer below and, if necessary, fill in the answer boxes within your choice.
OA. xs
OB. xs
OC. x2
OD. SXS (Type integers or decimals.)
E. The compound inequality has no solution.
OF. The solution is all real numbers.
XXXB
or x2 (Type integers or decimals.)
(Type an integer or a decimal.)
(Type an integer or a decimal.)
The solution to the inequality is x ≤ 3
How to solve the compound inequality and graph the solution?The compound inequality is given as:
5x ≤ -30 and 5x ≤ 15
Divide both sides of the individual inequality in the compound inequality by the coefficient of the variable x
So, we have
x ≤ -6 and x ≤ 3
One of the above inequalities can be true
x ≤ 3 is a proper set of x ≤ -6
So, the solution to the inequality is x ≤ 3
See attachment for the graph of the inequality
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In 1985, there were 326,030 cell phone subscribers in the United States. By 2008, the number of cell phone subscribers increased to 262,359,000. What is the geometric mean annual increase for the period?
33.7618% is the geometric mean annual increase for the period
Rate of Increase Over Time(GM)=[tex]\sqrt[n]{value end period / value start period }[/tex] -1
In 1985, there were 326,030 cell phone subscribers in the United States. By 2008, the number of cell phone subscribers increased to 262,359,000. we have to find the geometric mean annual increase for the period
from 1885 to 2008 that is (2008- 1885=23 ) in 23 years the GM become
therefore n= 23
value of start period = 326030
value of end period = 262359000
rate of increase over time GM= [tex]\sqrt[23]{262359000/326030} -1[/tex]
= 1.337618 -1
=0.337618
rate of increase is 33.7618% per year
33.7618% is the geometric mean annual increase for the period
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a angle measures 10.8 more than the measure of its complementary angle what is the measure of each angle
Please I need help !!!!
A--->A'=(-2,6)
B--->B'=(7,3)
Solve for x.
A=x+y-2
Answer:
x=1
Step-by-step explanation:
Helppp!!!
How am I able to find the 14th term of an arithmetic sequence given a4=14 and a10=16
Answer:
[tex]a_{14}=\dfrac{52}{3}[/tex]
Step-by-step explanation:
General form of an arithmetic sequence:
[tex]\boxed{a_n=a+(n-1)d}[/tex]
where:
[tex]a_n[/tex] is the nth term.a is the first term.d is the common difference between terms.Given terms of an arithmetic sequence:
[tex]a_4=14[/tex][tex]a_{10}=16[/tex]Substitute the values into the general formula to create two equations:
[tex]\sf\underline{Equation \:1}\\\begin{aligned}a_4 & = 14\\\implies a+(4-1)d & = 14\\a + 3d & = 14\end{aligned}[/tex]
[tex]\sf\underline{Equation \:2}\\\begin{aligned}a_{10} & = 16\\\implies a+(10-1)d & = 16\\a + 9d & = 16\end{aligned}[/tex]
Subtract Equation 1 from Equation 2 to eliminate a:
[tex]\begin{array}{l r l}& a+9d & = 16\\- & a+3d & = 14\\\cline{2-3}&6d & = \:\:2\end{array}[/tex]
Solve for d:
[tex]\begin{aligned}\implies 6d & = 2\\\dfrac{6d}{6} & = \dfrac{2}{6}\\d & = \dfrac{1}{3} \end{aligned}[/tex]
Substitute the found value of d into one of the equations and solve for a:
[tex]\begin{aligned}a + 3d & = 14\\ \implies a+3 \left(\dfrac{1}{3}\right)&=14\\a+1&=14\\a+1-1&=14-1\\a&=13\end{aligned}[/tex]
Substitute the found values of a and d into the general formula to create an equation for the nth term of the arithmetic sequence.
[tex]\implies a_n=13+(n-1)\dfrac{1}{3}[/tex]
[tex]\implies a_n=13+\dfrac{1}{3}(n-1)[/tex]
To find the 14th term, simply substitute n = 14 into the equation:
[tex]\begin{aligned}a_n & = 13+\dfrac{1}{3}(n-1)\\\implies a_{14}& = 13+\dfrac{1}{3}(14-1)\\&=13+\dfrac{1}{3}(13)\\ & = \dfrac{39}{3}+\dfrac{13}{3}\\&=\dfrac{52}{3}\end{aligned}[/tex]
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Question 4 of 10
Assume that AGHI ALMN. Which of the following congruence statements
are correct? Check all that apply.
Π.A. LNG ΔΗ
B. IG LM
C. ME ZH
D. LG
E. GH = LM
F. TH= NM
Answer:
C. ME ZH
B. IG LM
F. TH= NM
Step-by-step explanation:
The correct congruence statements are A, B, and C such that ∠N = ∠I, GH = LM, and ∠M= ∠H are true for similar triangles.
What are Similar Triangles?Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .
To determine which congruence statements are correct, we need to identify the corresponding sides and angles of the triangles.
The corresponding sides and angles are those that are in the same position in each triangle.
Using this information, we can check each statement:
A. ∠N = ∠I: This statement is true because ∠N and ∠I are corresponding angles in the congruent triangles.
B. GH = LM: This statement is true because GH and LM are corresponding sides in the congruent triangles.
C. ∠M= ∠H: This statement is true because ∠M and ∠H are corresponding angles in the congruent triangles.
D. IG = LM: This statement is false because IG and LM are not corresponding sides in the congruent triangles.
E. IH = NM: This statement is false because IH and NM are not corresponding sides in the congruent triangles.
F. ∠L = ∠I: This statement is false because ∠L and ∠I are not corresponding angles in the congruent triangles.
Therefore, the correct congruence statements are A, B, and C.
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Michael is grocey shopping. Before adding fruit to the bag, it weighed 5/9 pounds. Michael added 2/15 pounds of fruit to the bag. How much does it weigh now?
Answer:
31/45 lb
Step-by-step explanation:
You want to know the weight of a 5/9 lb bag after 2/15 lb of fruit are added to it.
Sum of fractionsFractions can be added when they have a common denominator. Here, the denominator will need to have factors of 3² = 9 and 3·5 = 15. It can be ...
3·3·9 = 45
Using this denominator, the fractions are ...
bag weight = 5/9 lb = 25/45 lb
fruit weight = 2/15 lb = 6/45 lb
The total weight of the fruit and the bag is ...
total weight = 25/45 lb + 6/45 lb = 31/45 lb
With the fruit, the bag weighs 31/45 pounds.
32006 in standard form
Answer:
the answer is 3.456 × 108
Can you please help with this.
Solve the inequality and express your answer in interval notation. x^2+10x+6 <0
The interval where the function is negative is:
(-5 - √19 , -5 + √19)
That is the solution set of the inequality.
How to solve the inequality?Here we have the following inequality:
x^2 + 10x + 5 < 0
So we want to find the values of x for which the quadratic function is negative.
To do so, we can solve:
x^2 + 10x + 5 = 0
The solutions are given by the quadratic formula:
x = (-10 ± √(10^2 - 4*6))/(2*1)
x = (-5 ± √19)
notice that the quadratic has positive leading coefficient, so it open upwards, then the function is below zero between the two roots, on the interval:
-5 - √19 < x < -5 + √19
Then the correct option is D.
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Find the area of the polygon with the given vertices.
K(-3, 4), L(1, 4), M(-4,-2), N(0, - 2)
Answer: 24.33 units
Step-by-step explanation: If we appropriately measure the distance between the points we can depict a parallelogram with 2 sides measuring 6.083 units and 2 others measuring 4 units. We multiply 4 x 6.083 and get the area: 24.33 units
Answer: 24
Step-by-step explanation: As the formula to solve this equation is A= 1/2 | [(x1y2) - (x2y1)] + [(x2y3) - (x3y2)] + [(x3y4) - (x4y3)] + [(x4y1) - (x1y4)]
Which would be (with the numbers)
[(-3 x 4) - 1 x 4)] + [(1 x -2) - (0 x 4)] + [(10 x 2) - (-4 x -2)] + [(-4 x 4) - (-3 x -2)]
which lowers down too
(-12 - 4) + (-2 - 0) + (0 - -8) + (-16 - 6)
Then that gets us (absolute values) of
|-16| + |-2| + |8| + |-22|
using absolute values that gets us to
16 + 2 + 8 + 22
Which is equal to 48.
Don't forget to divide by 2 because we need half of it as it says in the beginning of the formula (A = 1/2)
So that gives us the answer of 24.
Hope this helped :)
Also, this could help by labeling each coordinate as a (X, Y) Number
[-3(x1) , 4(y1)} (you could write the x and y part above it)
And then you go down the list and label each as either x1 , x2 , x3 , x4 (for the left side of comma) and then y1 , y2, y3 , y4 (for the right side of the comma)
Find the value of x in each case
Answer:
x=18
Step-by-step explanation:
m(<BCD) = 2x alternative Z
c=2x d=8x
m(<CD) =180 U
180/10x
x=18
Tanner bought 7 pieces of bubble gum for 56¢. Write
and solve an equation to find g, the cost of one piece of bubble gum
Answer: 8 = g
Step-by-step explanation:
56 divided by 7 = g
8 = g
Suppose you need 6.0m of Grade 70 bow chain, which has a diameter of 3/8" and weighs 2.16 kg/m to tow a car How would you calculate theme of this much chain
The mass of the tow chain will be equal to 12.96 kg.
What is an expression?The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.
Given that 6.0m of Grade 70 bow chain, which has a diameter of 3/8" and weighs 2.16 kg/m.
The mass of 1 m chain = 2.16 kg
Mass of 6-meter chain = 2.16 x 6
Mass of 6-meter chain = 12.96 kg
Therefore, the mass of the tow chain will be equal to 12.96 kg.
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Write each binary number as a base-ten number. 111110
Mark is y years old. In five years' time, Jack will be twice as old as Mark and Daniel will be 2 years younger than Jack is now. Write an expression in y for the sum of their 3 ages now.
Answer:
5y + 3 is the sum of the three ages
Step-by-step explanation:
Let y=Mark, d=Daniel j=Jack, and s=The sum
Mark is y years old. In five years jack will be twice as old as Mark
j + 5 = 2(y+5)
j + 5 = 2y + 10
j = 2y + 10 - 5
j = 2y + 5
Daniel will be two years younger than jack is now
d + 5 = j - 2
d = j - 2 - 5
d = j - 7
Replace j with (2y+5)
d = (2y+5) - 7
d = 2y - 2
Expression in terms of y for the sum of the 3 ages now
s = y + j + d
replace j and d with expressions we came up with above
s = y + (2y+5) + (2y-2)
s = y + 4y + 3
s = 5y + 3 is the sum of the three ages
Calculate the distance between the points P=(1, -1) and N=(5, -8) in the coordinate plane.
Round your answer to the nearest hundredth.
PLEASE PLEASE HELP ME
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ P(\stackrel{x_1}{1}~,~\stackrel{y_1}{-1})\qquad N(\stackrel{x_2}{5}~,~\stackrel{y_2}{-8})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ PN=\sqrt{(~~5 - 1~~)^2 + (~~-8 - (-1)~~)^2} \implies PN=\sqrt{(5 -1)^2 + (-8 +1)^2} \\\\\\ PN=\sqrt{( 4 )^2 + ( -7 )^2} \implies PN=\sqrt{ 16 + 49 } \implies PN=\sqrt{ 65 }\implies PN\approx 8.06[/tex]
Solve for x.
x^2 = a
a>0
Answer:
x<0; x>0
Step-by-step explanation:
Basically, anything but zero, depending on what a is.
Answer:
x = ± [tex]\sqrt{a}[/tex]
Step-by-step explanation:
x² = a ( take square root of both sides )
x = ± [tex]\sqrt{a}[/tex]
The mean of the commute time to work for a resident of Boston is 27.1 minutes. Assume that the standard deviation of the commute time is 8.3 minutes.
a) What is the minimum percentage of commuters in Boston has a commute time within 2 standard deviation of themean?
b) What minimum percentage of commuters in Boston has a commute time within 1.6 standard deviation of the mean?
c) What are the commute times within 1.4 standard deviation?
a) The minimum 75% of commuters in Boston has a commute time within 2 standard deviation of the mean.
b) The minimum 60.93% of commuters in Boston has a commute time within 1.6 standard deviation of the mean.
c) Commute times within 1.4 standard deviation are lie between 15.48 to 38.72.
Explanation:
Given that
The mean of the commute time to work for a resident of Boston is 27.1 minutes.the standard deviation of the commute time is 8.3 minutes.To find
a) What is the minimum percentage of commuters in Boston has a commute time within 2 standard deviation of the mean?b) What minimum percentage of commuters in Boston has a commute time within 1.6 standard deviation of the mean?c) What are the commute times within 1.4 standard deviation?So, according to the question
We know that
The minimum percentage within k standard deviations of the mean,= (1- [tex]\frac{1}{k^2}[/tex] )×100
a) What is the minimum percentage of commuters in Boston has a commute time within 2 standard deviation of the mean?
The minimum percentage within 2 standard deviations of the mean,= (1- [tex]\frac{1}{2^2}[/tex] )×100
= (1- [tex]\frac{1}{4}[/tex] )×100
= ( [tex]\frac{4-1}{4}[/tex] )×100
= [tex]\frac{3}{4}[/tex] ×100
= 3 × 25
= 75%
b) What minimum percentage of commuters in Boston has a commute time within 1.6 standard deviation of the mean?
The minimum percentage within 1.6 standard deviations of the mean,= (1- [tex]\frac{1}{1.6^2}[/tex] )×100
= (1- [tex]\frac{1}{2.56}[/tex] )×100
= ( [tex]\frac{2.56-1}{2.56}[/tex] )×100
= [tex]\frac{1.56}{2.56}[/tex] ×100
= 1.56 × 39.06
= 60.93%
c) What are the commute times within 1.4 standard deviation?
Within 1.4 standard deviations,commute times = 27.1 ± (1.4×8.3)
= 27.1 ± 11.62
for + sign,
= 27.1 + 11.62
= 38.72
for - sign,
= 27.1 - 11.62
= 15.48
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How to find the slope of the line that passes through the points (−2,3) and (5,−7)
Answer:
[tex]\frac{-10}{7}[/tex]
Step-by-step explanation:
Use the formula
m= [tex]\frac{y2-y1}{x2-x1}[/tex]
another way to say this is Δy divided by Δx
Δ means "change in"
m = slope
The y2 value is -7
The y1 value is 3
The x2 value is 5
The x1 value is -2
Plug those values in the formula
m = [tex]\frac{(-7)-3}{5-(-2)}[/tex]
Simplify
m = [tex]\frac{-10}{7}[/tex]
The slope is [tex]\frac{-10}{7}[/tex]
Simplify the expression
Solution:
Substitute the value of the variable into the expression, then simplify.
Answer: -8
_________________________________________________________
Hope this helps! If so, lmk! Thanks and good luck!
Answer:
2x/y = -8
Step-by-step explanation:
The values are,
→ x = 12
→ y = -3
Given expression,
→ 2x/y
Simplifying the expression,
→ 2x/y
→ (2 × 12)/(-3)
→ (24)/(-3)
→ -(24/3) = -8
Hence, the answer is -8.
7. Ln(x)=y (log(x)) what is y? show your work.
Given the function g(x)=11x^2+28x, solve for g(x)=−12.
Answer: -2, -6/11
Step-by-step explanation:
[tex]11x^2 +28x=-12\\\\11x^2 +28x+12=0\\\\(11x+6)(x+2)=0\\\\x=-2, -6/11[/tex]
Based on the table below, evaluate f(2)
From the given table, we can see that the value of f(2) is 4
Input and output values in a tableThe input values in a function table are the dependent variables while the output values in a function table are the dependent variables.
Let the function of the table be represented as y = f(x), this shows that the variable x is independent while f(x) is dependent.
In order to determine the value of f(2), we need the output value, when the input value is 2. From the given table, we can see that the value of f(2) is 4
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For a body falling freely from rest (disregarding air resistance), the distance the body falls varies directly as the square of the time. If an object is dropped from the top of a tower 192 feet high and hits the ground in 8 seconds, how far did it fall in the first 4 seconds?
The distance covered by the falling freely body from rest will be 48 feet.
What is kinematics?The study of motion without considering the mass and the cause of the motion.
When a body falls freely from rest, the distance it travels straight changes as the square of the time (air resistance excluded). If something is dropped 192 feet from the summit of a tower, it lands on the ground in 8 seconds.
We know that the acceleration is due to gravity (g = 32 ft/s²).
d ∝ t²
d/t² = constant
Then the distance covered by the falling freely body from rest will be given as,
d / 4² = 192 / 8²
d / 16 = 192 / 64
d = 16 x 192 / 64
d = 48 feet
The distance covered by the falling freely body from rest will be 48 feet.
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Need ALL answers asap in four proofs
You get all of them right you get brainly!!!
Answer:
me not soluesan match huiudresst
Sand will be placed under the base of a circular pool with a diameter of 14 feet. 1 bag of sand covers about 3 square feet. How many bags of sand are needed? Use 3.14 for pi. Round bags up.
Number of bags of sand needed to cover the area of circular pool is 51 bags.
What is a circle?A circle is a round-shaped figure that has no corners or edges.
Now it is given that,
Diameter of pool, D = 14 feet
So, Area of pool = π(D/2)²
⇒ Area of pool = π(14/2)²
⇒ Area of pool = π(7)²
⇒ Area of pool = 153.86 square feet
Now given Area of 1 bag = 3 square feet
So, number of bags required = Area of pool / Area of 1 bag
⇒ number of bags required = 153.86/ 3
⇒ number of bags required = 51.28
⇒ number of bags required ≈ 51
Thus, Number of bags of sand needed to cover the area of circular pool is 51 bags.
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If 25 is 30% of a number, what is 130% of that
number?
(a) 83.3
(b) 89.3
(c) 102.3
(d) 108.3
(e) 110.3
Answer:
d
Step-by-step explanation:
Let the number be 'x'.
First find x and then find 130% of x.
30% of x = 25
[tex]\sf \dfrac{30}{100}*x = 25[/tex]
[tex]\sf x = 25*\dfrac{100}{30}\\\\ x = \dfrac{250}{3}\\\\[/tex]
Now, find 130% of x
130% of x = [tex]\sf \dfrac{130}{100}*\dfrac{250}{3}\\\\[/tex]
[tex]\sf = \dfrac{325}{3}\\\\ = 108.3[/tex]