Answer:
a = 1, b = 7
Step-by-step explanation:
Given the 2 equations
3a + 6b = 45 → (1)
2a - 2b = - 12 → (2)
Multiply (2) by 3 and add to (1) to eliminate the term in b
6a - 6b = - 36 → (3)
Add (1) and (3) term by term
(3a + 6a) + (6b - 6b) = (45 - 36)
9a = 9 ( divide both sides by 9 )
a = 1
Substitute a = 1 in either (1) or (2) and solve for b
(1) → 3 + 6b = 45 ( subtract 3 from both sides )
6b = 42 ( divide both sides by 6 )
b = 7
What is the length of segment BC. ( ) units
Answer:
BC = 144 units
Step-by-step explanation:
It is given a line segment BC.
D is the point on the line segment.
To find the length of BC
BC = 8x
CD = 3x + 8 and BD = 4x + 10
BC = CD + BD
8x = 3x + 8 + 4x + 10
8x = 7x + 18
x = 18
BC = 8x = 8 * 18 = 144 units
Therefore the length of segment BC = 144 units
Segment BC is 144 units
What is the approximate circumference of a circle with a radius of 60 inches use pi 3.14
Answer: 376.99 is the answer
ANSWER
The approximate circumference is 377 inches
EXPLANATION
The circumference of a circle is calculated using the formula
[tex]C=2 \pi \: r[/tex]
Where r=60 inches is the radius of the circle.
We substitute π=3.4 and the radius into the formula to obtain:
[tex]C=2 (3.14)(60) \: inch[/tex]
[tex]C = 376.8inches[/tex]
The approximate circumference of the circle is 377 inches.
A book costs $12.50 plus sales tax. After tax it costs $13.25. What is the sales tax rate?
Answer:
The rate of sales tax is 6%.
Step-by-step explanation:
First you must subtract 12.50 from 13.25
This brings you to .75
Then, divide .75/12.50 to get 0.06 which is equivalent to 6 percent.
Lily is going to give away all the pieces of candy in a bag. She can give an equal number of pieces of candy to 5, 3, or 2 people. Which number of pieces of candy could be in Lily’s bag?
A. 12
B. 20
C. 30
D. 45
Answer:C 30
Step-by-step explanation: They all divide evenly when divided by 30.
The distance of a pathway around a park is 4 1/5 miles. The park manager wants to place lampposts every 3/10 mile. How many lampposts in all will be places in the pathway A - 12 B- 14 C- 24 D- 28
Answer:
14
Step-by-step explanation:
Distance of the pathway around a park = 4 1/5 miles
Distances between lamppost = 3/20 miles
Numbers of 3/10 intervals
= 4 1/5 ÷ 3/10
= 21/5 x 10/3
= 14
Number of lamp posts = 14
28 because the number of spots in the pathway where the lampposts will be placed is 1/5 divided by 3/10=14. since each spot will have 2 lampposts, there will be 14*2=28 lampposts in all.
hope this helped!!!!!!!!!!!!!!!!!!!!!!!!
1.The two legs of a right triangle measures 3 feet and 2 feet. What is the length of the hypotenuse?
Answer:
5; you add the two legs for the hypotenuse
Step-by-step explanation:
The length of the hypotenuse is 5 feet.
How to know the length of the hypotenuse of this right triangle:
The hypotenuse is the opposite side of the right angle in the triangle. It’s also the longest side of the triangle.
The Pythagorean Theorem helps us calculate the hypotenuse of a right triangle if we know the sides of the triangle.
Here, a = 3 feet.
b = 2 feet.
Then hypotenuse will be = (√3 + √2) feet
= 5 feet.
The answer is 5 feet.
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please answer will give points
Answer:
step 2
Step-by-step explanation:
Given step 1
324π = π × 12² h
Then second step should read
324π = π × 144h ← 144 not 24 is the error
Please help me I don’t understand!!
Answer:
A.) 30
Step-by-step explanation:
The entire figure consists of two angles supplementary to each other, which means that ∠YWZ + ∠ZWX = 180°. Since ∠ZWX is 20°, we know that ∠YWZ is 160°.
So now we have an equation to solve:
5x + 10 = 160
- 10 - 10
5x = 150
÷ 5 ÷ 5
x = 30
A pair of pants costs twice as much as a shirt. The total cost of 1 pair of pants and 1 shirt is $18. If s represents the cost of 1 shirt, which equation could you use to find the cost of 1 shirt?
The total cost of 1 pair of pants and 1 shirt is $18 . If s represents the cost of 1 shirt, which equation could you use to find .
For this case we propose a system of equations:
p: Variable representing the cost of a pair of pants
s: Variable representing the cost of a shirt
A pair of pants costs twice as much as a shirt, means:
[tex]p = 2s[/tex]
The total cost of 1 pair of pants and 1 shirt is $ 18:
[tex]p + s = 18[/tex]
We substitute the first equation in the second:
[tex]2s + s = 18\\3s = 18\\s = \frac {18} {3}\\s = 6[/tex]
Answer:
The following equation can be used:
[tex]2s + s = 18[/tex]
What is the area of the obtuse triangle below
Solution:
Given :
Base of triangle = 19 Height of triangle = 11So, We have to find the area of Triangle .
Area of triangle = 1/2*b×h, Where represents
B represent Base H represent HeightStep : Substitute those value in Formula;
Area of triangle = 1/2 × b × h
Area of triangle = 1/2 × 19 × 11
Area of triangle = 104.5 units Square
Therefore, Option B is correct Answer.
Area of triangle is 104.5 units Square.
What is area of a triangle?One of the most fundamental geometric shapes is the triangle. The simplest and most widely used formula is area = 0.5 * b * h, where b is the triangle's base length and h is the triangle's height or altitude. Almost everyone knows this formula from school.
Given :
Base of triangle = 19
Height of triangle = 11
So, We have to find the area of Triangle .
Area of triangle = 1/2*b×h, Where represents
B represent Base
H represent Height
Step : Substitute those value in Formula;
Area of triangle = 1/2 × b × h
Area of triangle = 1/2 × 19 × 11
Area of triangle = 104.5 units Square
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Given: KLIJ is inscribed in circle k(O)
m∠K = (9x+1)°,
m (arc) LI = (10x−1)°
m (arc) IJ = 59°,
m (arc) KJ =97°
Find: All angles of KLIJ
Check the picture below.
let's notice that the angle at K is an inscribed angle with an intercepted arc
[tex]\bf \stackrel{\textit{using the inscribed angle theorem}}{K=\cfrac{\widehat{LI}+\widehat{IJ}}{2}}\implies 9x+1=\cfrac{(10x-1)+59}{2} \\\\\\ 9x+1=\cfrac{10x+58}{2}\implies 18x+2=10x+58\implies 8x+2=58 \\\\\\ 8x=56\implies x=\cfrac{56}{8}\implies x=7 \\\\[-0.35em] ~\dotfill\\\\ K=9x+1\implies K=9(7)+1\implies \boxed{K=64}[/tex]
now, let's notice something again, the angle at L is also an inscribed angle, intercepting and arc of 97 + 59 = 156, so then, by the inscribed angle theorem,
∡L is half that, or 78°.
now, let's take a look at the picture down below, to the inscribed quadrilateral conjecture, since ∡J and ∡I are both supplementary angles, then
∡I = 180 - 64 = 116°.
∡J = 180 - 78 = 102°.
The measure of all the angle of KLIJ which is inscribed in circle k(O) are, 64, 78, 116, 102 degrees.
What is inscribed angle theorem?Inscribed angle theorem is the theorem, which state that the angle inscribed in a circle will be half of the angle which delimits the same arc on the circle.
The quadrilateral KLIJ is inscribed in circle k(O). In this the measure of the angle are given as,
[tex]m\angle K = (9x+1)^o[/tex]
m (arc) LI = (10x−1)°
m (arc) IJ = 59°,
m (arc) KJ =97°
All angles of the quadrilateral KLIJ has to be found out. By the inscribed angle theorem,
[tex]K=\dfrac{LI+IJ}{2}\\9x+1=\dfrac {10x-1+59}{2}\\18x+2=10x+58\\8x=56\\x=7[/tex]
Therefore, the value of the angle k is,
[tex]m\angle K = (9(7)+1)^o\\m\angle K = 64^o[/tex]
Similarly, the measure of the angle L is,
[tex]m\angle L=\dfrac{KJ+IJ}{2}\\m\angle L=\dfrac {97+59}{2}\\m\angle L=\dfrac{156}{2}\\m\angle L=78^o[/tex]
Now the angles I and J are the supplementary angles of the angle K and angle L respectively. Therefore,
[tex]m\angle I=180-m\angle K=180-64=116^o\\ m\angle J=180-m\angle L=180-78=102^o[/tex]
Hence, the measure of all the angle of KLIJ which is inscribed in circle k(O) are, 64, 78, 116, 102 degrees.
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Change 455 cm to meters
Answer:
4.55 meters
Step-by-step explanation:
Answer:
Step-by-step explanation:
your answer is 4.55 :)
If the outliers are not included, what is the mean of the data set?
76, 79, 80, 82, 50, 78, 83, 79, 81, 82
A. 77
B. 78
C. 79
D. 80
Answer:
78
Step-by-step explanation:
78 is the answer because if you count inwards then you get 78
Answer:
D
Step-by-step explanation:
add them all except 50 divide by 9 because only used 9.
on a piece of paper, graph f(x)= x if x<1
Answer:
see below
Step-by-step explanation:
The function is only defined for x < 1, and is undefined for x=1 or more. Thus the graph stops at x=1, with an open circle indicating the function is not defined there.
Answer:
The required graph is shown in figure 1.
Step-by-step explanation:
Consider the provided function f(x)=x if x<1
Here the sign of inequality is x<1.
That means the value of x can be anything less then 1.
Note the sign "<" indicates that the value x is strictly less than 1 also it is not equal to 1.
For x=1 the function is not defined.
For the inequity "<" and ">" we use an open dot or open circle which shows that the value is not included.
Now draw the table and substitute some value of x as shown.
Substitute x=0 in the provided equation.
f(x)=0
For x=0 the value of f(x) is also 0.
Substitute x=-1
f(x)=-1
For x=-1 the value of f(x) is also -1.
Substitute x=-2
f(x)=-2
For x=-2 the value of f(x) is also -2.
The required table is shown below:
x 0 -1 -2
f(x) 0 -1 -2
Now plot the above points and join them.
The required graph is shown in figure 1.
I really really need help!!!!!!
ANSWER
[tex]y = 5 \sin( \frac{6}{5} x - \pi)-4 [/tex]
EXPLANATION
The given function is
[tex]y = 5 \cos( \frac{3}{5} x - \pi) + 4[/tex]
The period of this function can be determined using the formula:
[tex]T= \frac{2\pi}{ |b| } [/tex]
.
The period is
[tex]T= \frac{2\pi}{ \frac{3}{5} } = \frac{10\pi}{3} [/tex]
Half the period of this function is:
[tex] \frac{ \frac{10\pi}{3} }{2} = \frac{5\pi}{3} [/tex]
The function which has this period is
[tex]y = 5 \sin( \frac{6}{5} x - \pi) -4[/tex]
The first choice is correct.
Once you practice evaluating logarithmic expressions, you will be prepared to work with ........ functions.
Exponential
Linear
Logarithmic
The answer is logarithmic
Answer:
Logarithmic .
Step-by-step explanation:
When we evaluate the logarithmic expression then we prepared to work
with logarithmic function
If , I want to solve the logarithmic expression then first we should know about the logarithmic theorem rules .
If ,I don't know about the logarithmic rules then we can't evaluate the logarithmic expression.
So , first we should do practice with logarithmic function and we should know how to use of logarithmic rules during evaluating the logarithmic expression .
Logarithmic rules :
[tex]Log \frac{m}{n}= log m - log n[/tex]
[tex]log m\times n= log m+ log n[/tex]
[tex]log a^b= bloga[/tex]
For example ; we have [tex]log\frac{3}{4}[/tex]
Therefore, by using logarithmic rule then we get
[tex]log\frac{3}{4} = log 3- log 4[/tex]
Therefore, if i want to evaluate the logarithmic expresssion then i will be prepared to work with logarithmic function .
The function g(x) is graphed on the coordinate grid.
Which statements are true of g(x)? Check all that apply.
Answer:
the function g(X) is a translation of [tex]f(x) = \sqrt{x}[/tex]
the range is {y|y≥-1}
the function g(x) can be translated 3 units right and 1 unit up to get the function [tex]f(x) = \sqrt{x}[/tex]
Step-by-step explanation:
Given the graph of a function g(x)
g(x) looks like a square root function
So parent function is [tex]f(x) = \sqrt{x}[/tex]
the function g(X) is a translation of [tex]f(x) = \sqrt{x}[/tex]
the domain is {x| x ≥ -3}
the range is {y|y≥-1}
The parent function [tex]f(x) = \sqrt{x}[/tex] starts at (0,0)
so g(x) is translated 3 units left and 1 unit down
the function g(x) can be translated 3 units right and 1 unit up to get the function [tex]f(x) = \sqrt{x}[/tex]
Answer:
The correct options are 1, 3 and 5.
Step-by-step explanation:
The given function is a continuous increasing curve which is increasing at decreasing rate. It means it is the graph of a radical function.
Parent radical function is
[tex]f(x)=\sqrt{x}[/tex]
It means function g(x) is the translation of function [tex]f(x)=\sqrt{x}[/tex]. Option 1 is correct.
Domain is the set of input values.
Function is defined for all x ≥ -3.
Domain = { x | x ≥ -3 }
Option 2 is incorrect.
Range is the set of output values.
The values of the function are always greater than or equal to -1.
Range = { y | y ≥ -1 }
Option 3 is correct.
The graph of parent function [tex]f(x)=\sqrt{x}[/tex] shifts 3 units left and 1 unit down to get the graph of g(x). So the function g(x) is defined as
[tex]f(x)=\sqrt{x+3}-1[/tex]
Option 4 is incorrect.
The function g(x) can be translated right 3 units and up 1 unit to create the function [tex]f(x)=\sqrt{x}[/tex].
Option 5 is correct.
Which epression is equivalent to (x^4/3 x^2/3)^1/3
Answer:
The correct answer is X²/³
Step-by-step explanation:
Points to remember
Identity
Xᵃ/Xᵇ = X⁽ ᵃ⁻ ᵇ ⁾
Xᵃ * Xᵇ = X⁽ᵃ ⁺ ᵇ⁾
(Xᵃ)ᵇ = Xᵃᵇ
To find the equivalent expression
We have, (X⁴/³ X²/³)¹/³
Using identities we can write,
(X⁴/³ X²/³)¹/³ = (X⁴/³ * X²/³)¹/³
= (X⁴/³ ⁺ ²/³)¹/³
= ( X⁽⁴⁺²⁾/³)¹/³
= (X⁶/³)¹/³
= (X²)¹/³
= X²/³
Therefore the correct answer is X²/³
Given f(x) = x3 – 2x2 – x + 2,
the roots of f(x)
f(x) = x³ – 2x² – x + 2
0 = x3 – 2x2 – x + 2
(x-2)(x-1)(x+1)=0
x1=-1
x2=1
x3=2
For this case we must follow the steps below:
We factor the polynomial, starting by factoring the maximum common denominator of each group:
[tex]x ^ 2 (x-2) - (x-2)[/tex]
We factor the maximum common denominator[tex](x-2):[/tex]
[tex](x-2) (x ^ 2-1)[/tex]
Now, by definition of perfect squares we have:
[tex]a ^ 2-b ^ 2 = (a + b) (a-b)[/tex]
Where:
[tex]a = x\\b = 1[/tex]
Now, we can rewrite the polynomial as:
[tex](x-2) (x + 1) (x-1)[/tex]
To find the roots we equate to 0:
[tex](x-2) (x + 1) (x-1) = 0[/tex]
So, the roots are:
[tex]x_ {1} = 2\\x_ {2} = - 1\\x_ {3} = 1[/tex]
Answer:
[tex]x_ {1} = 2\\x_ {2} = - 1\\x_ {3} = 1[/tex]
Can I get help with 18 and 22 please
Answer:
18. 36.36%
22. 53.71
Step-by-step explanation:
If the following figure is rotated 90° counterclockwise about the origin, what is the new location?
Answer: Last option.
Step-by-step explanation:
We need to apply the Rule for 90° counterclockwise rotation about the origin. Given a point [tex]P(x,y)[/tex]:
[tex]P(x,y)[/tex] → [tex]P'(-y,x)[/tex]
We can observe in the figure that the coordinates of the points E, F, G and H are:
[tex]E (2,6)[/tex]
[tex]F(7,-4)[/tex]
[tex]G(-2,-7)[/tex]
[tex]H (-5,1)[/tex]
Then, applying the rule, we get the coordinates of the new location of the figure EFGH:
[tex]E (2,6)[/tex] → [tex]E'(- 6,2)[/tex]
[tex]F(7,-4)[/tex] → [tex]F'(4,7)[/tex]
[tex]G(-2,-7)[/tex] → [tex]G'(7,-2)[/tex]
[tex]H (-5,1)[/tex] → [tex]H'(-1,-5)[/tex]
PLEASE HELP 13 POINTS
The formula for finding the circumference of the circle is 2 pi r or pi d. R stand for radius and D stand for diameter. The problem gave you the length of the diameter so can either put it in form of pi as in 30pi or multiply it by pi (3.14) which will give you the result of 94.2
Answer:
- 30pi
- 94.2
what is the period of the function y = 2 sinx
Answer:
The period is 360° ( in radians, the period is 2π)
Step-by-step explanation:
For a sine/cosine (sinusoidal) function in the form
y = ASin(Bx-C) + D, we can say
A is the amplitude
360/B is the period
C is the phase shift
D is the vertical translation
The function given is y = 2Sinx
To find the period, we need 360/B. Since "B" is just "1", the period is
360/1 = 360
Answer:
The period of the function [tex]y = 2sinx[/tex] is [tex]2\pi[/tex]
Step-by-step explanation:
The sinosuidal functions have the following form
[tex]y = Asin (bx) +k[/tex]
Where A is the amplitude of the function
k is the vertical displacement
[tex]\frac{2\pi}{b}[/tex] is the period.
In this case we have the function
[tex]y = 2sinx[/tex]
Therefore the amplitude A = 2
The vertical displacement is k = 0
The period is [tex]\frac{2\pi}{1} = 2\pi[/tex] because b=1
Therefore the function completes a cycle every [tex]2\pi[/tex]
Find the volume in ft cubed
Answer:
7x6x2= 84 ft cubed
Step-by-step explanation:
multiply length by width by height
WILL GIVE BRAINEST IF CORRECT!!!!!
The area of a triangle is 24 square inches. What is the height of the triangle if the base length is 8 inches?
Answer:
6 inches
Step-by-step explanation:
area of triangle = 1/2 b* h
24 = 1/2 * 8* h
4h = 24
divide both sides by 4
h = 6 inches
Area is 1/2 x base x height.
24 = 1/2 x 8 x H
Multiply both sides by 2:
48 = 8 x Height
Divide both sides by 8:
Height = 48 / 8
Height = 6 inches.
Solve 5x + 8 < 3(x + 2)
Answer:
x < - 1
Step-by-step explanation:
Given
5x + 8 < 3(x + 2) ← distribute
5x + 8 < 3x + 6 ( subtract 3x from both sides )
2x + 8 < 6 ( subtract 8 from both sides )
2x < - 2 ( divide both sides by 2 )
x < - 1
The inequality 5x + 8 < 3(x + 2) simplifies to x < -1.
To solve the inequality 5x + 8 < 3(x + 2), we must simplify and isolate the variable x. We start by distributing the 3 on the right side:
5x + 8 < 3x + 6
Next, we'll subtract 3x from both sides to get:
2x + 8 < 6
Now subtract 8 from both sides to isolate the term with x:
2x < -2
Finally, we divide both sides by 2:
x < -1
The solution to the inequality is all x-values that are less than -1.
An Olympic swimmer competes in the same events during each long course swim season. A swimmer currently competing on the United States Women’s Olympic Swim Team, will swim her best events each year with the hope of continuous improvement. The following table is a record of the swimmer’s best times for the 100 meter freestyle event, measured in long course meters.
Long Course
Season Recorded
Best Time
2005 2:33.42
2006 2:24.81
2007 2:10.93
2008 2:03.45
2009 1:58.67
2010 1:59.17
2011 1:55.06
2012 1:55.82
2013 1:54.81
2014 2:00.03
Create a scatter plot representing the data displayed in the table.
Use the scatter plot to determine whether there is positive, negative or no correlation between the data values.
Write a conclusion statement regarding the data and the rate of change present in the line of best fit. Do not actually calculate the slope or write the equation for the line of best fit.
I don't know if you still need this but here you go
Answer: Equation for the line of best fit is given by
f(x)=-4.28402x+0.0875
Step-by-step explanation:
Long Course Season Recorded Best time
2005 2:33.42
2006 2:24.81
2007 2:10.93
2008 2:03.45
2009 1:58.67
2010 1:59.17
2011 1:55.06
2012 1:55.82
2013 1:54.81
2014 2:00.03
Since we can see from the scatter plot that it has negative correlation.
Equation for the line of best fit is given by
f(x)=-4.28402x+0.0875
HELP PLEASE A cylinder and its dimensions are shown. Which equation can be used to find V, the volume of the cylinder in cubic centimeters?
A)
V = π(4.5h)2
B)
V = π(9h)2
C)
V = π(4.5)2h
D)
V = π(9)2h
Answer:
WRONG THE ANSWER IS ACUALLY C
Step-by-step explanation:
I know this because i decided to take th4e test use his answer and it was wrong telling me the right answer it's (c).
The equation that can be used to find the volume of the cylinder is V = π(4.5)²h (option C).
Explanation:The equation that can be used to find the volume of the cylinder is V = π(4.5)²h (option C). To find the volume of a cylinder, you need to use the formula V = πr²h, where r is the radius of the base and h is the height of the cylinder. In this case, the radius is 4.5 cm and the height is not given, so it is represented as h. By substituting the values into the formula, you get V = π(4.5)²h.
please helppppppppppp due tomarrow very easyyyyy
Answer: 6
Step-by-step explanation: -8 x -8 = 64
64 - -58 = 6
Answer:
The answer is 6.
Step-by-step explanation:
Since negative × negative = positive, therefore -8(-8)=64 and 64-58=6.
The points (4, 1) and (x, -6) lie on the same line. If the slope of the line is 1 what is the value of x?
Answer:
The value of x is -3
Step-by-step explanation:
* Lets explain how to solve the problem
- The slope of a line that passes through points (x1 , y1) and (x2 , y2) is
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
* Lets solve the problem
∵ The points (4 , 1) and (x , -6) lie on the same line
∵ The slope of the line is 1
- Let the point (4 , 1) is (x1 , y1) and the point (x , -6) ix (x2 , y2)
∵ x1 = 4 , x2 = x and y1 = 1 , y2 = -6
∴ [tex]m=\frac{x-4}{-6-1}[/tex]
∴ [tex]m=\frac{x-4}{-7}[/tex]
∵ The slope of the line is m = 1
∴ [tex]\frac{x-4}{-7}=1[/tex]
- By using cross multiplication
∴ x - 4 = -7 ⇒ add 4 to both sides
∴ x = -3
* The value of x is -3
the value of x for the point on the line is -3.
The student is asking how to find the value of x for a point on a line with a given slope. Since the slope of the line is 1, we can use the slope formula, which is (y2 - y1) / (x2 - x1) = slope, to find the value of x. Here, we have two points, (4, 1) and (x, -6), and a slope of 1.
Using the formula, we get (-6 - 1) / (x - 4) = 1. Simplifying, we get -7 / (x - 4) = 1. To find the value of x, we solve the equation -7 = x - 4, which gives us x = -3. So, the value of x for the point on the line is -3.