To solve this plug in 9 for b and solve for a like so...
3a + 9 = 54
9 must be combined with 54. To do this you must subtract 9 from both sides. This will cancel out 9 from the left and bring it over to the right
3a + (9 - 9) = 54 - 9
3a + 0 = 45
3a = 45
Now we must isolate the a. To do this you have to divide 3 to both sides. This will make 3 on the left side 1 and bring 3 over to the other side
3a/3 = 45/3
1a = 15
a = 15
Hope this helped!
~Just a girl in love with Shawn Mendes
What is the factorization of the polynomial below?
9x^2-16
The factorized form of the given polynomial is (3x + 4)(3x - 4). Using one of the factorization methods of polynomial, the result is obtained.
What is the factorization of a polynomial?Writing a polynomial as the product of its factors (monomial, binomial or and so on) is called the factorization of the polynomial.
There are different methods of factorization. Some of them are the grouping method, GCF method, the difference of squares method, etc.
Factorizing the given polynomial:The given polynomial is [tex]9x^2-16[/tex]
Using the difference of squares method we can write the given polynomial as
[tex]9x^2-16 = (3x)^2-(4)^2[/tex]
We know that difference between any two squares is
[tex]a^2-b^2=(a+b)(a-b)[/tex]
So,
[tex]9x^2-16[/tex] = (3x + 4) (3x - 4)
Therefore, the factors of the given polynomial are (3x + 4) and (3x - 4).
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I need to know how many approximate miles you drive in a week for a statistics project. I dont have any social media, and I need to ask at least 50 people to compete my project. Ask your friends and family, and then give me your answer for easy points!
Answer:
My mom drives about 120 miles, grandpa: 160, and dad: 200
Step-by-step explanation:
Answer:
My dad drives about 80
Step-by-step explanation:
He only goes shopping and takes me to school.
31. ABCD has area equal to 28 sq. unit. BC is parallel to AD and BA perpendicular to AD. If BC = 6 and AD = 8,
then value of CD =
B.213
A. 2 12
C.4
D. 275
Answer:
The value of CD is 2√5
Step-by-step explanation:
* Lets describe the figure to know its name
- ABCD is a quadrilateral
∵ BC parallel to AD
∵ BC = 6 units and AD = 8 units
- The quadrilateral which has two parallel sides not equal in length is a
trapezoid
∴ ABCD is a trapezoid, where BC and AD are its bases
∵ BA perpendicular to AD
∴ BA is the height of the trapezoid
- The area of the trapezoid = 1/2 (base 1 + base 2) × its height
∵ The bases of the trapezoid are BC and AD
∵ BC = 6 and AD = 8
∵ Its area = 28 units²
∴ 1/2 (6 + 8) × height = 28
∴ 1/2 (14) × height = 28
∴ 7 × height = 28 ⇒ divide both sides by 7
∴ height = 4
∵ The height is BA
∴ BA = 4 unit
- To find the length of CD draw a perpendicular line from C to AD and
meet it at E
∵ BA and CE are perpendicular to AD
∴ BA // CE
∵ BC // AD
- Perpendicular lines between parallel lines are equal in lengths
∴ BA = CE and BC = AE
∵ BA = 4 and BC = 6
∴ CE = 4 and AE = 6
∵ AD = 8 units
∵ AD = AE + ED
∴ 8 = 6 + ED ⇒ subtract 6 from both sides
∴ ED = 2 units
- In ΔCED
∵ m∠CED = 90°
∴ CD = √[(CE)² + (ED)²] ⇒ Pythagoras theorem
∵ CE = 4 and ED = 2
∴ CD = √[(4)² + (2)²] = √[16 + 4] = √20 = 2√5
* The value of CD is 2√5
Final answer:
The value of the unknown side CD in quadrilateral ABCD can be found using the area of a trapezoid formula and the Pythagorean theorem. Given the area, and the lengths of BC and AD, we calculated that CD equals 8 units.
Explanation:
The student has asked to find the value of CD in a quadrilateral ABCD, where BC is parallel to AD, BA is perpendicular to AD, the area of quadrilateral ABCD is 28 square units, BC is 6 units, and AD is 8 units.
Since BA is perpendicular to AD and BC is parallel to AD, we can determine that ABCD is a trapezoid with AB and CD as the non-parallel sides. The area of a trapezoid is given by the formula Area = ½ × (sum of parallel sides) × height. So we have:
½ × (AD + BC) × height = 28
½ × (8 + 6) × height = 28
½ × 14 × height = 28
7 × height = 28
height = 4 units
Since BA is perpendicular to AD, and given BA is the height of the trapezoid, this means that AB = 4 units. Now, because ABCD has right angles at A and B, triangles ABD and ABC are right triangles and we can use the Pythagorean theorem to calculate CD.
In triangle ABD:
AB² + BD² = AD²4² + BD² = 8²BD = √(8² - 4²) = √(64 - 16) = √48 = 4√3Since CD is the hypotenuse of triangle ABD:
CD² = AB² + BD²CD² = 4² + (4√3)²CD² = 16 + 48CD = √64CD = 8 unitsTherefore, the correct answer is CD = 8 units.
A rectangular prism and a cylinder have the same height. The length of each side of the prism base is equal to the diameter of the cylinder. Which shape has a greater volume?
The (blank) has the greater volume because the (blank) fits within the (blank) with extra space between the two figures.
Please fill in the blanks
Answer:
Filling in the blanks: (rectangular prism) (cylinder) (rectangular prism)
The cylinder has the greater volume because the cylinder fits within the rectangular prism with extra space between the two figures.
A prism is a three-dimensional object.
There are triangular prism and rectangular prism.
We have,
We can see this by comparing the formulas for the volumes of the two shapes.
The volume V of a rectangular prism with length L, width W, and height H is given by:
V = L x W x H
The volume V of a cylinder with radius r and height H is given by:
V = πr²H
Now,
We are told that the length of each side of the prism base is equal to the diameter of the cylinder.
Since the diameter is twice the radius, this means that the width and length of the prism base are both equal to twice the radius of the cylinder.
So we can write:
L = 2r
W = 2r
Substituting these values into the formula for the volume of the rectangular prism, we get:
V prism = L x W x H
V prism = 2r x 2r x H
V prism = 4r²H
Substituting the radius and height of the cylinder into the formula for its volume, we get:
V cylinder = πr^2H
To compare the volumes,
We can divide the volume of the cylinder by the volume of the prism:
V cylinder / V prism = (πr²H) / (4r²H)
V cylinder / V prism = π/4
π/4 is greater than 1/1,
Thus,
The cylinder has a greater volume.
The cylinder fits within the rectangular prism with extra space between the two figures because the cylinder is inscribed within the prism, meaning that it is enclosed within the prism but does not fill it completely.
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Let g(x) = 3x^3. Find g(2 + h).
Answer:
x= 1, -2/3
Step-by-step explanation:
Answer:
G(2+h)=3(2+h)^3
Step-by-step explanation:
We need to put the value of the required digit , we have to find the value of . So go on solving and you will get your answer.
Name the intersection of lines M and T
i need a picture if im going to help
The intersection of lines M and T is the point where the lines meet or cross over each other.
To find the intersection, solve the system of equations formed by the two lines. Once you have the coordinates of the intersection point, name it accordingly.
Explanation:The intersection of two lines, M and T, is the point where the two lines meet or cross over each other.
To find the intersection, we need to determine the coordinates of the point where the lines M and T intersect.
We can find the intersection by solving the system of equations formed by the equations of the two lines.
The system of equations will have two variables (x and y) and we can solve for their values.
Once we have the coordinates of the intersection point, we can name it accordingly.
For example, if the intersection point has coordinates (3, 4), we can name it as point P(3, 4).
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Divide 9x^2-6x+2 by (-1+3x)
A. 3x-1+(1/3x-1)
B. 3x-3+(1/3x-1)
C. 3x-1+(3/3x-1)
D. 3x-3-(1/3x-1)
Answer:
A. 3x - 1 + [3x - 1]⁻¹
Step-by-step explanation:
Use Polynomial Long Division to arrive at this answer.
**[3x - 1]⁻¹ = 1\[3x - 1]
When the county fair opened its gates, 68 people entered the fairgrounds. After one hour, there were 1.5 times as many people on the fairgrounds as when the gates opened. After two hours, there were 1.5 times as many people on the fairgrounds as the previous hour. If this pattern continues, write the equation representing the number of people, y, at the fair x hours after the gates open.
Answer:
y=68(1.5)^(x-1)
Step-by-step explanation:
Answer:
The function is:
[tex]y = 68 (1.5) ^ x[/tex]
Step-by-step explanation:
Note that the number of people increases by a factor of 1.5 per hour, and the initial number of people is 68.
So:
After an hour the number of people is:
[tex]y = 68 (1.5)[/tex]
After two hours the number of people is:
[tex]y = 68 (1.5) (1.5) = 68 (1.5) ^ 2[/tex]
After x hours the number of people is:
[tex]y = 68 (1.5) ^ x[/tex]
Therefore, the exponential growth function that models the number of people y at the fair after x hours is:
[tex]y = 68 (1.5) ^ x[/tex]
The area of a garden is given by the trinomial g2 - 2g - 24. The garden’s length is g + 4. What is the garden’s width?
Final answer:
To find the garden's width, factor the area trinomial to match the given length of the garden. The width is represented by the other factor, which in this case is g - 6.
Explanation:
The area of a garden is given by the trinomial [tex]g^2[/tex] - 2g - 24, and the garden's length is g + 4. To find the garden's width, we need to factor the trinomial such that it is the product of two expressions, one of which must be the length (g + 4).
Factoring [tex]g^2[/tex] - 2g - 24, we look for two numbers that multiply to -24 and add up to -2. These numbers are -6 and +4. So, we can factor the area trinomial as:
(g - 6)(g + 4) = [tex]g^2[/tex] - 2g - 24.
Since the length of the garden is g + 4, the other factor, g - 6, must represent the width of the garden. Thus, the garden's width is g - 6.
or what value of x does 4x=(1/8)^x+5?
–15
–3
3
15
Answer:
x = -3Step-by-step explanation:
[tex]4^x=\left(\dfrac{1}{8}\right)^{x+5}\qquad\text{use}\ a^{-1}=\dfrac{1}{a}\\\\4^x=(8^{-1})^{x+5}\\\\(2^2)^x=\bigg((2^3)^{-1}\bigg)^{x+5}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\2^{2x}=2^{-3(x+5)}\iff2x=-3(x+5)\qquad\text{use the distributive property}\\\\2x=-3x-15\qquad\text{add}\ 3x\ \text{to both sides}\\\\5x=-15\qquad\text{divide both sides by 5}\\\\x=-3[/tex]
Answer:
B, -3
Step-by-step explanation:
Write the sentence as an equation.
b increased by 281 is d
Answer:
B + 281d
Step-by-step explanation:
I think that's the answer the "is" is throwing me off "is" is either = or (x)
Hope my answer has helped you and if not i'm sorry.
A. Find 18% more than 200
B. Find 18% less than 200
Answer:
A. 236
B. 164
Step-by-step explanation:
18% of 200= 36
200+36=236
200-36=164
Answer:
A. 236
B. 164
Step-by-step explanation:
To solve it first you need to find what 18% of 200 is. To do that take the 18% and make it a decimal % is out of 100, so 18/100 = .18. Then to find how much 18% out of 200 is, multiply .18 * 200. You should get 36. Then you can add and subtract that from 200 to get 18% more and 18% less.
Which is equivalent
Answer:
4x^4
Hope this helps
For this case we must find an expression equivalent to:
[tex](256x^{16}) ^ {\frac {1} {4}[/tex]
By definition of power properties we have to:
[tex](a ^ n) ^ m = a ^ {n * m}[/tex]
Then, rewriting the expression:
[tex](256 ^ {\frac {1} {4}} * x ^ {\frac {16} {4}}) =[/tex]
We have by definition:
[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]
So:
[tex]\sqrt [4] {256} * x ^ 4 =\\\sqrt [4] {4 ^ 4} * x ^ 4 =\\4x ^ 4[/tex]
ANswer:
Option B
Which equation is represented by table?
Answer:
The equation y = 1 - 2x is represented by this table.
The correct answer is A.
In one U.S. city, the taxi cost is $5 plus $0.90 per mile. If you are traveling from the airport, there is an additional charge of $5.00 for tolls. How far can you travel from the airport by taxi for $59.50?
The data set gives the number of bottles filled by each of the workers in a bottling plant in one day.
{36, 18, 16, 28, 68, 35, 37, 66, 38, 40, 41, 44, 72, 29}
The best measure of center for this data set is the
, and its value expressed up to one decimal place is
Answer:
Step-by-step explanation:
Before we can determine which measure of central tendency is the best we need to determined whether data set is skewed or not.
We can determine the skewness, if we know at least the median and the mean.
The array of the above data set is,
16,18,28,29,35,36,37,38,40,41,44,66,68,72
The Median of the above array is
\frac{37 + 38}{2} = \frac{75}{2} = 37.5
The mean is
\frac{16 + 18 + 28 + 29 + 35 + 36 + 37 + 38 + 40 + 41 + 44 + 66 + 68 + 72}{14} = \frac{532}{14} = 38
Since the mean and the median are not the same, the distribution is skewed.
<b>For a skewed distribution, the best measure of central tendency is the median.</b>
To one decimal place, the median is;
37.5
NB: If the distribution is not skewed then it is normal. In a normal distribution the median is equal to the mean. The mode is considered the best measure of center in this case.
Step-by-step explanation:
The median of a data set is the measure of center that is the middle value when the original data values are arranged in order of increasing (or decreasing) magnitude
Two systems of equations are shown below. The first equation in System B is the original equation in system A. The second equation in System B is the sum of that equation and a multiple of the second equation in System A.
A. x + 3y = 11 → x + 3y = 11
5x − y = 17 → 15x − 3y = 51
15x = 62
B. x + 3y = 11
15x = 62
What is the solution to both systems A and B?
Answer:
The answer is [4,3] Hope this helps.
Step-by-step explanation:
The solution to the both system of equations A and B are (3.875, 2.375) for system A and (4.133, 2.289) for system B.
What does a System of Linear Equations define?Linear equations involve one or more expressions including variables and constants and the highest exponent of the variable is 1.
System of linear equations involve two or more linear equations.
Consider system A.
x + 3y = 11
15x − 3y = 51
Adding both equations,
16x = 62
x = 3.875
3y = 7.125
y = 2.375
Consider system B.
x + 3y = 11
15x = 62 ⇒ x = 4.133
3y = 6.867
y = 2.289
Hence the solutions are (3.875, 2.375) for system A and (4.133, 2.289) for system B.
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How much money will you have if you started with $20 and put it in an account that earned 12% every year for 3 years?
Answer:
34,560
Step-by-step explanation:
Started of with 20 and earned 12% each year.
12% is just 12 as a whole number
so from that 20 12x12x12=1,728
1,728x20=
34.560
find the image of (5,7) obtained by translating 3 units to the right, followed by a reflection over the x-axis
Answer: (8, -7)
Step-by-step explanation:
Answer:
(8,-7)
Step-by-step explanation:
2. Solve the following systems of equations:
1) y=6x-2
y=6x-4
Answer:
Step-by-step explanation:
y=6x-2
y=6x-4
6x - 2 = 6x - 4
6x -6x = -4+2
0 = -2 ....false
no solutions
BRAINLIEST WILL BE AWARDED
PLEASE HELP
What is the solution to this system of equations?
x+2y=4
2x-2y=5
a. (3, -5.5)
b. (3, 0.5)
c. no solution
d. indefinitely many solutions
Answer:
b. (3, 0.5).
Step-by-step explanation:
x + 2y = 4
2x - 2y = 5
Adding the 2 equations eliminates the y:
3x = 9
x = 3
Substitute fro x in the first equation:
3 + 2y = 4
2y = 1
y = 0.5.
Option B is correct, (3, 0.5) is the solution of the system of equations.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The two equations are
x+2y=4...(1)
2x-2y=5...(2)
Add equation 1 and 2
x+2y+2x-2y=4+5
3x=9
Divide both sides by 3
x=3
3+2y=4
Subtract 3 from both sides
2y=1
y=1/2
y=0.5
Hence, option B is correct, (3, 0.5) is the solution of the system of equations.
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which expression is equivalent to the one shown below
[tex] \sqrt{36 \times 3} [/tex]
[tex]a \: \: 36 \sqrt{3} [/tex]
[tex]b \: \:6 \sqrt{3} [/tex]
[tex]c \: \: 6 \times 3[/tex]
[tex]d \: \: 36 \times 3[/tex]
Answer:
Option b: 6√3
Step-by-step explanation:
Given expression is:
[tex]\sqrt{36*3}[/tex]
We have to factorize the radicand in order to solve the given radical
So,
[tex]= \sqrt{3*3*2*2*3}[/tex]
In order to solve the square root pairs are made:
[tex]=\sqrt{2^2 * 3^2 * 3}[/tex]
To evaluate the square root, the exponents are multiplied by 1/2
[tex]= 2^{(2*\frac{1}{2})} *3^{(2*\frac{1}{2})} * 3^{(\frac{1}{2})}\\=2*3*\sqrt{3} \\=6\sqrt{3}[/tex]
Hence, option b is correct ..
Answer: b
Step-by-step explanation: b
How many states are there
Answer:
50
Step-by-step explanation:
Hello There!
There are 50 states in the United States
Alabama
Alaska
Arizona
Arkansas
California
Colorado
Connecticut
Delaware
Florida
Georgia
Hawaii
Idaho
Illinois Indiana
Iowa
Kansas
Kentucky
Louisiana
Maine
Maryland
Massachusetts
Michigan
Minnesota
Mississippi
Missouri
Montana Nebraska
Nevada
New Hampshire
New Jersey
New Mexico
New York
North Carolina
North Dakota
Ohio
Oklahoma
Oregon
Pennsylvania Rhode Island
South Carolina
South Dakota
Tennessee
Texas
Utah
Vermont
Virginia
Washington
West Virginia
Wisconsin
Wyoming
Sara needs to take a taxi to get to the movies the taxi charges $4.00 for the first mile and then $2.75 for each mile after that if the total charge is $20.50 then how far was Sara’s taxi ride to the movie
Answer:
6 miles
Step-by-step explanation:
4+2.75m=20.50
-4 -4
2.75m=16.50/2.75
m=6
Answer:
6 miles
Step-by-step explanation:
So the total charge is $20.50, what I personally did was
Subtract $4 from $20.50
You get $16.50
Now divide $16.50 by $2.75
There's your miles
What is the equation, in point-slope form, of the line that has a slope of 6 and passes through the point (–1, –8)? a. y+8 = 6 (x+1 )
Answer:
y + 8 = 6(x + 1)
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
here m = 6 and (a, b) = (- 1, - 8), hence
y - (- 8) = 6(x - (- 1)), that is
y + 8 = 6(x + 1)
ANSWER
[tex]y + 8=6(x + 1)[/tex]
EXPLANATION
The point-slope form of an equation is given by the formula:
[tex]y-y_1=m(x-x_1)[/tex]
Where
[tex](x_1,y_1)[/tex]
is a point on this line and
[tex]m[/tex]
is the slope of the line.
From the question, the line has slope 6 and passes through (-1,-8).
This means that
[tex]x_1=-1[/tex]
[tex]y_1=-8[/tex]
and
[tex]m = 6[/tex]
We substitute these values into the point-slope formula to get:
[tex]y- - 8=6(x- - 1)[/tex]
We simplify to get:
[tex]y + 8=6(x + 1)[/tex]
If carol can read 45 pages in one hour how many pages can she read in four hours
Answer:
She can read 180 pages in 4 hours
45*4=180
Carol can read 180 pages in four hours.
Simply multiply the rate (45 pages/hour) by the time (4 hours) to get 180 pages/4 hours.
Typically, a point in a three-dimensional Cartesian coordinate system is represented by which of the following
A) (x,y,v)
B) (w,x,y)
C) x,y,z
D) (x,y,z)
Answer:
option D) (x,y,z)
Step-by-step explanation:
we know that
The three-dimensional Cartesian coordinate is defined by three axes at right angles to each other, forming a three dimensional space.
The three axes are labeled x ,y and z.
The x-axis is called abscissa
The y-axis is called ordinate
The z-axis is called applicate
therefore
A point in a three-dimensional Cartesian coordinate is represented by (x,y,z)
can someone please help me with this.
[tex](x-1)(x-3)=x^2-3x-x+3=x^2-4x+3[/tex]
20 Points!!! Jason orders a data set from least to greatest.
Complete the sentence by selecting the correct word from each drop-down menu.
The middle value of the data set is a measure of____ and is called the .____
part A:
center
B:spread
part B:
Mean
A:mean absolute deviation
B:median
C:range
Answer:
Measure of central tendency (center)
it is called median