The equations with same value of x as (3/5)(30x - 15) = 72 is 18x - 9 = 72, 3(6x - 3) = 72 and x = 4.5
How to solve an equation?An equation shows the relationship between two or more numbers and variables.
Given the equation:
(3/5)(30x - 15) = 72
Opening the parenthesis:
18x - 9 = 72
Factorizing the equation:
3(6x - 3) = 72
Dividing through by 3:
6x - 3 = 24
6x = 27
Dividing through by 6:
x = 4.5
The solution to the equation (3/5)(30x - 15) = 72 yields x = 4.5
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Use the figure shown. Let point D be at (-4,1) . Use the sides of triangle BDA to find the slope of the line.
The slope of the line shown in the figure having equation x + 2y = 0 is 1/2.
The point A is at ( -2 , 1 ), point B is at ( -4 , 2 ) and Point C is at ( -2 , 2 ).
Let point D be at ( -4 , 1 ).
Now the new triangle is ΔBDA and the corner points are A is at ( -2 , 1 ), point B is at ( -4 , 2 ) and point D is at ( -4 , 1 ).
The equation of line passing through two points is given by:
[tex](y-y_{1} ) = (\frac{y_{2}-y_{1} }{x_{2} - x_{1} })(x - x_{1} )[/tex]
The equation of line passing through two points A( -2 , 1 ) and B( -4 , 2 ) IS
y - 1 = ((2-1)/(-4-(-2))) (x-(-2))
y - 1 = (1/(-2)) (x+2)
2y -2 = -x -2
x + 2y = 0
The equation of straight line is x + 2y = 0
The equation in slope intercept form can be written as,
y = x/2 + 0
Slope = m = 1/2
Intercept = c = 0
So, we can conclude that 1/2 is the slope of the line .
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according to insurance records a car with a certain protection system will be recovered 91% of the time. find the probability that 5 of 6 stolen cars will be recovered.
Probability that 5 of 6 stolen cars will be recovered with insurance records a car with a certain protection system will be recovered 91% of the time is equal to P(x=5)=0.3369 (approximately).
As given,
Insurance protection system recovered of a car=91%
p=0.91
q=1-p
=1-0.91
=0.09
n=6
x=5
Using Binomial theorem ,probability of 5 of 6 stolen cars will be recovered is:
ⁿCₓ(p)ˣ(q)ⁿ⁻ˣ
=⁶C₅(0.91)⁵(0.09)⁶⁻⁵
=[6!/(6-5)!5!] × (0.91)⁵× (0.09)
=6×(0.91)⁵×0.09
=0.3369
Therefore, probability that 5 of 6 stolen cars will be recovered with insurance records a car with a certain protection system will be recovered 91% of the time is equal to P(x=5)=0.3369 (approximately).
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Ryan collected 2,650 baseball cards, football cards, and hockey cards. he has 3 times as many baseball cards as football cards. he has 150 more hockey cards than football cards. how many baseball cards does he have? ryan has baseball cards.
The calculated answer after simplification in which Ryan has number of baseball cards is: 357 cards
How to simplify statement problems?
In mathematics, the statement based problems can be solved by forming the equations. And later, simplify those equation by equating to each other. This method is very common for the complicated problems to make the calculation easy.
According to the question, Ryan collected 2650 cards. In which, he has more baseball cards compared to football cards.
Now, let us assume, baseball cards be 'B'; football cards be 'F' and hockey cards be 'H'.
As per the question, the formed equation from the statement for the simplification is:
B + F + H = 2650
3B = F and H + 150 = F
Substituting above values in the formed equation to get the simplify answer,
B + 3B + 3B - 150 = 2650 ⇒ 7B = 2500 ⇒ B = 357
Now, the value of football cards is: F = 3(357) = 1071
And, the value of hockey cards is: H = 1071 - 150 = 921
Hence, after simplification Ryan has number of baseball cards is: 357 cards
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I just need to know if the answer is B or D
Firslty, we need to find the function, whcih we can do by substituting one into the other:
[tex]f(g(x))=2(g(x))^2-1=2(\sqrt[]{x-2})^2-1=2(x-2)-1=2x-4-1=2x-5[/tex]Now, for the domain we have more complicated approach.
We first have to find the domain for both f(x) and g(x).
The domain of f(x) is all real number, because it is a quadratic polynomial.
The domain of g(x) is all the real numbers except the x values that makes the square root interior negative, so all real numbers so that:
[tex]\begin{gathered} x-2\ge0 \\ x\ge2 \end{gathered}[/tex]Now, the domain of the composite function f(g(x)) is the set of all the values of x in the domain of g(x) such that the corresponding g(x) is in the domain of f(x).
Since the domain of f(x) is all real numbers and g(x) is a real number function, all the values of g(x) will be in the domain of f(x), so we just need to check the values of x that are in the domain of g(x).
The domain of g(x), as we saw, is:
[tex]D=\mleft\lbrace x\mright|x\ge2\}[/tex]And any value of x will give a g(x) that will be in the domain of f(x) so, the domain of f(g(x)) is:
[tex]D=\mleft\lbrace x\mright|x\ge2\}[/tex]So, the correct alternative is:
[tex]\begin{gathered} f(g(x))=2x-5 \\ D\colon\mleft\lbrace x\mright|x\ge2\} \end{gathered}[/tex]Question 10 (1 point)
What are the coordinates of the midpoint of segment whose endpoints are A(-2,7) and B(4,-2)?
Make sure to use decimals, if necessary, and write with no spaces in the format (x,y) with you solving for x and y
A/
The midpoint of the line segment given is (1, 4.5)
Midpoint of a LineIn geometry, the midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints. It bisects the segment equally into two halves.
The formula of midpoint of a line is given as
[tex]M_x_y = \frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}[/tex]
A = (-2, 7)B = (4, -2)Substituting the given values;
[tex]M_x_y = \frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\\M_x_y = \frac{-2+4}{2}, \frac{7+2}{2} \\M_x_y = 1, \frac{9}{2} \\M_x_y = 1, 4.5[/tex]
The midpoint of the line AB is equal to (1, 4.5)
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Please only answer if you know the answer thank you.
Answer:
the slope is 0 and the equation is y = -2
Step-by-step explanation:
A triangle has an angle that measures 111°. The other two angles are in a ratio of 6:17. What are the measures of those two angles?
Answer:
18 and 51
Step-by-step explanation:
the sum of the two other angles would be 69 degrees because there has to be 180 degrees in a triangle
given that we can create the equation 6x + 17x = 69 and solve for x
x = 3
so now we can plug in each part of that equation and find out the two angles
√15/√3 pls answer this for me so i can chill
Answer:
[tex]\sqrt{5}[/tex]
Step-by-step explanation:
to simplify use the rule of radicals
[tex]\frac{\sqrt{x} }{\sqrt{y} }[/tex] ⇔ [tex]\sqrt{\frac{x}{y} }[/tex] , then
[tex]\frac{\sqrt{15} }{\sqrt{3} }[/tex] = [tex]\sqrt{\frac{15}{3} }[/tex] = [tex]\sqrt{5}[/tex]
What numbers are equivalent to 4/8?
Answer:numbers that are equal to 4/8 would be 2/4 and 1/2 and are you multiplying up?
Step-by-step explanation:
Write "less" or "greater" in the blank 179 is_than 31
Answer: Greater
Step-by-step explanation:
Answer:
179 is greater than 31
i need help pls and thank you...
Answer:
AB = 32
Step-by-step explanation:
Since line l bisects AB at point M, we have AM = MB.
[tex]4x = 5x - 4[/tex]
[tex]4x + 4 = 5x[/tex]
[tex]x = 4[/tex]
AM = 4(4) = 16, MB = 5(4) - 4 = 16.
So AB = AM + MB = 16 + 16 = 32.
Question 2 of 10
Which of the following is most likely to be a relative maximum for this graph?
8-
(-1.0) (20)
-8 -84
6
Answer:it’s (-1,8)
Step-by-step explanation:
The volume, V, of a container is directly proportional to the cube of its height, h. When its height
is 4 cm, its volume is 48 cm3.
1.What is the volume if the height is 3 cm?
2.If the height is doubled to 6 cm, how many times bigger will the volume be?
Answer:
see explanation
Step-by-step explanation:
given that V is directly proportional to h³ , then the equation relating them is
V = kh³ ← k is the constant of proportion
to find k use the condition V = 48 when h = 4 , then
48 = k × 4³ = 64k ( divide both sides by 64 )
[tex]\frac{48}{64}[/tex] = k , then k = 0.75
V = 0.75h³ ← equation of proportion
1
when h = 3 , then
V = 0.75 × 3³ = 0.75 × 27 = 20.25 cm³
2
when h = 6 , then
V = 0.75 × 6³ = 0.75 × 216 = 162 cm³
then
162 ÷ 20.25 = 8
the volume will be 8 times bigger
The Sales Manager for Chicken Shack restaurants is studying the sales figures for two new varieties of chicken sandwiches recently introduced at eight of its restaurants. For four weeks, three restaurants have been selling lemon-roasted chicken sandwiches. The other five restaurants have been selling barbecued chicken sandwiches for three weeks. During the testing period, 6,000 lemon-roasted chicken sandwiches were sold, and 7,200 barbecued chicken sandwiches were sold. Which of the two new chicken sandwiches should the sales manager report as having the better sales?
Using the average sales per restaurant, the sales manager should report the Lemon-roasted chicken sandwiches as recording better sales performance than the Barbecued chicken sandwiches.
What is the average?The averages represent the total sales generated at the lemon-roasted and barbecued restaurants, respectively, divided by the number in each group.
The average is the same as the mean of a data set. It is computed by the mathematical operations of addition and division.
Lemon-roasted Barbecued
The number of restaurants 3 5
Total sales during the testing period 6,000 7,200
Average sales per restaurant 2,000 1,440
Based on the average sales, the sales manager should report that the lemon-roasted chicken sandwiches are outperforming the barbecued restaurants.
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Which segments are skewed
Answer:
AB, DC, ED, GA
Step-by-step explanation:
You want to identify the segments that are skew to edge FH of cuboid ABCDEFGH.
Skew linesTwo lines are skew when no plane exists that can contain them both. That is, skew lines are not parallel and do not intersect.
Cuboid ABCDEFGH has 12 edges. Of those, 3 are parallel to FH, and 4 intersect FH. The remaining edges are skew to FH:
AB, DC, ED, GA . . . . . segments skew to FH
If g(x) = x² + 2, find g(3).
Answer:
11
Step-by-step explanation:
[tex]3^{2}[/tex] + 2
9 + 2
11
Find the maximum length of a rod that can be kept in a cuboidal box offside 30cm, 24cm and 18 cm.
Answer:
30√2 cm
Step-by-step explanation:
Maximum length of the rod = Length of the diagonal of the cuboid
Length of diagonal of cuboid = [tex]\sqrt{l^2+w^2 + h^}[/tex]
where l = length, w =width and h = height
For this particular cuboid,
Diagonal length = [tex]\sqrt{30^2+24^2 + 18^2}[/tex]
[tex]\sqrt{800 + 576 + 324} \\\\\\= \sqrt{1500}\\\\= 30\sqrt{2} \text{ cm}[/tex]
Find a point-slope form for the line with slope 1/2
and passing through the point (-3,-8).
The point slope form for the line with slope 1/2 and passing through the point (-3,-8) is y + 8 = m(x + 3)
How to find point slope equation?A linear equation can be represented in point slope form as follows:
y - y₁ = m(x - x₁)
where
m = slopex₁ and y₁ are the coordinatesTherefore, the point slope form is represented as follows;
m = 1 / 2
It passes through the points (-3,-8).
Hence,
y + 8 = m(x + 3)
Therefore, the point slope form of the line is y + 8 = m(x + 3)
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Write an equation for the intervals of a parabola with x-intercepts at (3,0) and (9,0) that passes through the point (10,-7).
Help is always greatly appreciated.
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: y= - {x}^{2} +12x - 27[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
The values of x where a parabola cuts the x - axis (y = 0) are the roots of the quadratic equation.
I.e 3 and 9 for the given problem.
and the equation can be represented as :
[tex]\qquad\displaystyle \tt \rightarrow \: y = a(x - x1)(x- x2)[/tex]
where, x1 and x2 are the roots of the quadratic equation, a is a constant value (depicting strech in curve)
Now, plug in the values :
[tex]\qquad\displaystyle \tt \rightarrow \: y= a(x- 3)(x - 9)[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: y = a( {x}^{2} -9x - 3x +27)[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: y= a( {x}^{2} -12 +27)[/tex]
Now, we need to find the value of a, for that let's use the coordinates of a point lying on the curve (10 , -7)
[tex]\qquad\displaystyle \tt \rightarrow \: - 7= a( {10}^{2} -12(10) +27)[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: - 7= a(100- 120+27)[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: - 7= a( 7)[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: a = ( - 7) \div ( 7)[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: a = -1[/tex]
Now, we got all required values. let's plug the value of a in equation, and we will get the required equation of parabola.
[tex]\qquad\displaystyle \tt \rightarrow \: y= -( {x}^{2} -12x +27)[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: y= - {x}^{2} +12x - 27[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Answer:
[tex]y=-x^2+12x-27[/tex]
Step-by-step explanation:
Intercept form of a quadratic equation
[tex]\boxed{y=a(x-p)(x-q)}[/tex]
where:
p and q are the x-intercepts.a is some constant.Given x-intercepts:
(3, 0)(9, 0)Substitute the given x-intercepts into the formula:
[tex]\implies y=a(x-3)(x-9)[/tex]
To find a, substitute the given point (10, -7) into the equation and solve for a:
[tex]\implies a(10-3)(10-9)=-7[/tex]
[tex]\implies a(7)(1)=-7[/tex]
[tex]\implies 7a=-7[/tex]
[tex]\implies a=-1[/tex]
Therefore, the equation of the function in factored form is:
[tex]\implies y=-(x-3)(x-9)[/tex]
Expand the brackets:
[tex]\implies y=-(x^2-9x-3x+27)[/tex]
[tex]\implies y=-(x^2-12x+27)[/tex]
[tex]\implies y=-x^2+12x-27[/tex]
Therefore, the equation of the function in standard form is:
[tex]\boxed{y=-x^2+12x-27}[/tex]
While sorting some change into piggy banks, Kyle put 4 coins in the first piggy bank, 6 coins in the second piggy bank, 9 coins in the third piggy bank, 13 coins in the fourth piggy bank, and 18 coins in the fifth piggy bank. If this pattern continues, how many coins will Kyle put in the sixth piggy bank?
Answer:24
Step-by-step explanation:4+2=6,6+3=9,9+4=13,13+5=18,18+6=24
Answer:
24
Step-by-step explanation:
because in first piggy bank has 4 coins and second has 6 . difference=6-4=2
second has 6 coins and third has 9 . difference= 9 - 6 = 3 third has 9 coins and fourth has 13 . difference=13-9=4
fourth has 13 and fifth has 18 coins difference is 18 -13 =5
then,sixth has 24 because all have 2 3 4 5 difference then six has 6
Derek says the dilation was a reductionDelilah says the dilation was an enlargement who is correct and why
Delilah is correct; it is
Here, we want to check who was right
Mathematically, we can dilate a figure by reduction or enlargement by the use of a specific scale factor
When the scale factor is less than 1, it is a reduction
However, if the scale factor is greater than 1, it is an enlargement
The original point is (x,y)
From the image coordinates given, we see that the scale factor is 6/5 which is greater than 1
Thus, the dilation is an enlargement and Delilah was right
Two angles are complementary. If one angle is (x²-16x) and the other is (3x), thenwhat is the measures of the angles?
The smaller angle =
The larger angle =
Answer:
Complementary angles have a sum of 90°.
(x²-16x)+(3x) = 90
x² -13x - 90 = 0
(x-18)(x+5) = 0
x - 18 = 0 or x + 5 = 0
x = 18 or x = -5 (reject)
Substitute x into the angles.
18²-16(18) = 36
Smaller angle = 36°
3(18) = 54
Larger angle = 54°
132 = -w + 236 solve for w
Please help me with this.
least common mutiple of...
6 and 8: 24
8 and 12: 24
12 and 9: 36
6 and 9: 18
Evaluate the expression when a = -6.9 and b = -1.9,-66+2a
Evaluating Algebraic Expressions
We are given the expression:
-6b + 2a
And it's required to find the value of the expression for a=-6.9 and b=1.9
Substituting the values:
-6(-1.9) + 2(-6.9)
= 11.4 - 13.8
Operating:
=-2.4
The value is -2.4
Convert into a mixed number.
19/01
7
Answer: 2 3/7
Step-by-step explanation:
Find the value of x in the triangle below:
X =
55°
Blank 1:
X
please hurry
Answer:
35
Step-by-step explanation:
90-55= 35 degress
The pages of Jack's book are numbered from 1.
ann
The page numbers have a total of 555 digits.
How many pages has the book?
How many of the digits are a 5?
Answer:
he has 556 pages in his book
The coordinates of the vertices of quadrilateral JKLM are J(-4,
1), K(2, 3), L(5,
3), and M(0,
5)
Drag and drop the choices into each box to correctly complete the sentences.
Answer:
Slope:
JK = (1/3)
LK = (-2)
ML = (2/5)
MJ = (-3/2)
Quadrilateral JKLM is not a parallelogram because the slopes don't match.
Step-by-step explanation:
Slope = m
JK = (-4, 1), (2, 3)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ 3 - 1 2 2 1
m = ------------ = ------------- = ---------- = --------- = -------
x₂ - x₁ 2 - (-4) 2 + 4 6 3
----------------------------------------------------------------------------------------------------------
LK = (5, -3), (2, 3)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ 3 - (-3) 3 + 3 6
m = ------------ = ------------- = ---------- = --------- = -2
x₂ - x₁ 2 - 5 -3 -3
----------------------------------------------------------------------------------------------------------
ML = (0, -5), (5, -3)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ -3 - (-5) -3 + 5 2
m = ------------ = ------------- = ---------- = ---------
x₂ - x₁ 5 - 0 5 5
----------------------------------------------------------------------------------------------------------
MJ = (0, -5), (-4, 1)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ 1 - (-5) 1 + 5 6 -3
m = ------------ = ------------- = ---------- = --------- = -------
x₂ - x₁ -4 - 0 -4 -4 2
----------------------------------------------------------------------------------------------------------
I hope this helps!
suppose 48 out of every 120 people like baseball/softball. of the people who like baseball/softball, 3 out of 5 play the game. if you ask 500 people, how many would you expect play baseball/softball?
out of 500 people 200 like baseball and 120 people like to play game baseball/softball
suppose 48 out of every 120 people like baseball/softball.
of the people who like baseball/softball, 3 out of 5 play the game.
if you ask 500 people,
how many would you expect play baseball/softball
it means 40% like baseball and 60% like to play game
if there are 500 people
then 500 *(40/100)=200
thus 200 people like baseball
and 200*(60/100)=120
Hence 120 people to play game
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