An expression is defined as a set of numbers, variables, and mathematical operations. The simplified product of (2x+3)(x²+x-2) is (2x³+5x²-x-6).
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The simplified product of the binomial (2x+3) and the trinomial (x²+x-2) can be written as,
[tex](2x+3)(x^2+x-2)\\\\= (2x \times x^2)+(2x \times x) + (2x\times -2) + (3\times x^2)+(3\times x)+(3\times -2)\\\\= 2x^3 + 2x^2-4x+3x^2+3x-6\\\\= 2x^3+5x^2-x-6[/tex]
Thus, the simplified product of (2x+3)(x²+x-2) is (2x³+5x²-x-6).
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The circumference of a circle is 6π cm. What is the area, in square centimeters?
Answer:
9Pi square units
Step-by-step explanation:
Area = Pi x Radius^2
Diameter = Circumference / Pi
= 6Pi / Pi
= 6
Radius = Diameter / 2
= 6 / 2
= 3
Area = Pi x 3^2
Hope this helps!!
Find the surface area of the prism formed by each net.
Answer:
378 in^2
Step-by-step explanation:
This is the sum of the area of the 6 rectangles
That is:
8*15 + 3*15 + 3*8 + 8*15 + 3*8 + 3*15
= 378 in^2
Need help with this question please and thank you
Answer:
The answer is C. [tex]y = \frac{1}{12}(x+2)^{2}+2[/tex]
7th Grade Math) 6. A student usually saves $20 a month. He would like to reach a goal of saving $350 in 12 months. The student writes the equation 350 = 12(x + 20) to represent this situation. Solve the equation for x. Show your work or explain your answer. Write your answer as a sentence that describes what the variable x represents. Enter your answers and your work or explanation in the box provided.
Answer:
x=9.167
Step-by-step explanation:
12x+240=350
350-240 because you are getting rid of 240 to get 12x by itself so you must do it on the other side.
12x=110, then you do 12x/12 and 110/12
x=9.167
Answer: Approimately $9.16
Step-by-step explanation:
In this problem, you have to solve for x variable.
1. Distribute the 12 to the x + 20 which is 12x + 240
2. Subtract 240 from both sides so 350 - 240 is 110.
3. Now your equation is 110 = 12x
4. Divide 12 on both sides. But 12 doesn't go into 110 perfectly.
5. 110 divided by 12 is approximately 9.16.
The x represent how much the student has earn extra to get $350 in 12 months. The student has to earn 9.16 dollars every month on top of the 20 dollars.
The radius of a circle is 19m. Find its area to the nearest whole number.
1134.11m²
______----------________
Answer:
1134.11
Step-by-step explanation:
The problem with this equation is pi is an angle in radians. It has a never ending number of digits.
The area of a circle is basically a square r x r rotated through 180 degrees around the squares centre.
So the area can be written as 180 x 19 x 19 = 64980 degrees meters square.
This is a finite number. The area of a circle does not change. Pi r squared has an ever increasing result.
pi is a conversion factor between the finite areas of circles and the area in square units which can never have a result that is finite as squares cannot fill a circle, no matter how small.
To convert the round finite area to m squared you divide the area by 180/pi = 57.295779513 degrees per radian.
Area in degrees meters Squared 64980/ 57.295779513.
= 1134.1149479 radian meters squared.
If mBE=119 and mBKE=93, find mUH.
Answer:
arc UH = 67°
Step-by-step explanation:
the measure of a chord- chord angle is half the sum of the measures of the arcs intercepted by the angle and its vertical angle , then
[tex]\frac{1}{2}[/tex] ( BE + UH ) = ∠ BKE , that is
[tex]\frac{1}{2}[/tex] (119 + UH ) = 93° ( multiply both sides by 2 to clear the fraction )
119° + UH = 186° ( subtract 119° from both sides )
UH = 67°
Answer:
Step-by-step explanation:
∠HKU = ∠BKE {Vertically opposite angles}
∠HKU = 93°
Angles fromed by insecting chords equals half the sum of intercepting arcs.
[tex]\sf \angle HKU =\dfrac{1}{2}(arc \ HU + arc \ BE) \\\\ 93^ \circ = \dfrac{1}{2}(arc \ HU + 119)[/tex]
93 *2 = arc HU + 119
186 = arc HU + 119
186 - 119 = arc HU
arc HU = 67°
Given: Line segment A B is parallel to line segment D C and Measure of angle 2 equals measure of angle 4
Prove: Line segment A D is parallel to line segment B C
A parallelogram has points A B C D. Angle D A B is angle 1, Angle A B C is angle 2, Angle B C D is angle 3, and angle C D A is angle 4.
A 2-column table with 7 rows. Column 1 is labeled statements and has entries line segment A B is parallel to line segment D C, measure of angle 2 = measure of angle 4, angle 1 and angle 4 are supplements, question mark, measure of angle 1 + measure of angle 2 = 180 degrees, angle 1 and angle 2 are supplements, line segment A D is parallel to line segment B C. Column 2 is labeled reasons with entries given, given, same side interior angles theorem, definition of supplementary angles, substitution, definition of supplementary angles, converse same side interior angles theorem.
m∠1 = m∠4
m∠2 = m∠3
m∠1 + m∠4 = 180°
m∠2 + m∠3 = 180°
Answer: (3)
Step-by-step explanation:
Angles 1 and 4 are supplementary, and their measures thus add to 180 degrees.
Answer:
Step-by-step explanation:
m∠2 + m∠3 = 180°
What is 21/5 divided by 7/4
How does the volume of a cylinder with a radius of 3 units and a height of 12 units compare to the volume of a rectangular prism with dimensions 16 units x 16 units x 9 units?
a. The volume of the cylinder is greater than the the volume of the prism
b. The volume of the cylinder is smaller than the volume of the prism.
C. The volume of the cylinder is the same as the volume of the prism
d.You cannot compare the volumes of different shapes
Answer:
The volume of the cylinder is greater than the volume of the prism.
Step-by-step explanation:
The Volume of a cylinder is given as:
= πr²h
Therefore, the volume of a cylinder with a radius of 3 units and a height of 12 units will be:
= πr²h
=3.14 × 3² × 12
=339.12
The volume of a rectangular prism with dimensions 3 units x 3 units x 12 units will be:
= Length × Width × Height
Based on the calculation, the volume of the cylinder is greater than the volume of the prism.
Answer:
B: The volume of the cylinder is smaller than the volume of the prism.
Step-by-step explanation:
In order to find the volume of the cylinder, we would use to formula [tex]\pi r^{2} h[/tex]. Substitute the given measures of the cylinder to get [tex]\pi[/tex]·3²·12. The simplified and calculated form would be 108 units cubed.
Now, we find the volume of the rectangular prism, which is [tex]l[/tex]·[tex]w[/tex]·[tex]h[/tex], or 16*16*9. This means the volume is 2304 units cubed.
Therefore, since 2304 un³>108 un³, answer choice b would be correct.
Brahmagupta’s solution to a quadratic equation of the form ax2 bx = c involved only one solution. which solution would he have found for the equation 3x2 4x = 6?
The value of the quadratic equation x has a value of 0.8968 and a negative value of 2.23.
What is a factorization, and how does it work?It is a method for dividing a polynomial into parts, each of which will be multiplied. At this time, the polynomial's value will be zero.
The equation for the expression is given below.
3x² + 4x = 6
3x² + 4x - 6 = 0
we know that the formula
[tex]\rm x = \dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Then we have
[tex]x = \dfrac{-4 \pm \sqrt{4^2-4*4*(-6)}}{2*3}\\\\x = \dfrac{-4 \pm \sqrt{112}}{6}\\\\x = 0.8968, \ -2.23[/tex]
More about the factorization link is given below.
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This table gives the value of an investment for the first 14 years after the initial investment was made. The data can be modeled using an exponential function.
Years 2 4 6 8 10 12 14
Investment value $692 $952 $1,304 $1,813 $2,316 $3,256 $4,718
Based on the data, which amount is closest to the value of the investment 18 years after the initial investment? PLS HURRY I NEED THIS ANSWERED NOW, WILL GIVE 95 POINTS
Answer:
General form of an exponential equation: [tex]y=ab^x[/tex]
where:
a is the initial valueb is the growth factorx is the independent variabley is the dependent variableLet x = years
Let y = investment value
Use (2, 692) and (4, 952) to find a and b of the exponential equation:
[tex]ab^2=692[/tex]
[tex]ab^4=952[/tex]
[tex]\implies \dfrac{ab^4}{ab^2}=\dfrac{952}{692}[/tex]
[tex]\implies b^2=\dfrac{238}{173}[/tex]
[tex]\implies b=\sqrt{\dfrac{238}{173}}=1.17\:\textsf{(nearest hundredth)}[/tex]
[tex]\implies ab^2=a\left(\dfrac{238}{173}\right)=692[/tex]
[tex]\implies a=\left(\dfrac{59858}{119}\right)=503.01\:\textsf{(nearest hundredth)}[/tex]
Therefore, the exponential equation is:
[tex]y=503.01(1.17)^x[/tex]
18 years after the initial investment is when [tex]x=18[/tex]:
[tex]\implies 503.01(1.17)^{18}=8490[/tex]
Therefore, the amount closest to the value of the investment 18 years after the initial investment is $8490
(If you use the exact values for a and b rather than the rounded values, the amount is $8879)
Tamara's backyard pool needs a cover for the winter. The pool is
rectangular with a length of 12 feet and an area of 196.8 square feet.
What is the width of the pool cover Tamara's pool will need?
Answer:
16.4 feet
Step-by-step explanation:
Area of a rectangle: length * width = area
12*w=196.8
w=196.8/12
w=16.4 feet
someone help..... pls
Answer:
Go right 4 blocks. Then go down 3 blocks.
Step-by-step explanation:
From Brianna's house at (1,6), move 4 blocks to the right and you will be at (5,6). Next, move 3 blocks down and you will be at Jordan's house at (5,3).
Solve the system of equations.
5x – y = 5
5x2 – y = 5
Answers:
(0, 5) and (0, –5)
(1, 0) and (0, –5)
(2, 5) and (1, 0)
(3, 10) and (2, 15)
Answer:
Option 2: (1, 0) and (0, -5)
Step-by-step explanation:
Let's solve this system of equations using the elimination method.
Start by labelling the two equations.
5x -y= 5 -----(1)
5x² -y= 5 -----(2)
(2) -(1):
5x² -y -(5x -y)= 5 -5
Expand:
5x² -y -5x +y= 0
5x² -5x= 0
Factorise:
5x(x -1)= 0
5x= 0 or x -1= 0
x= 0 or x= 1
Now that we have found the x values, we can substitute them into either equations to solve for y.
Substitute into (1):
5(0) -y= 5 or 5(1) -y= 5
0 -y= 5 or -y= 5 -5
y= -5 or -y= 0
y= 0
Thus, the solutions are (0, -5) and (1, 0).
7. Given secθ = V10 and tanθ= 3, determine
the following
csc(90° -θ)
[tex]\csc(90^{\circ}-\theta)\\\\=\sec \theta \\\\=\sqrt{10}[/tex]
what's the answer for 2/3+x=4
Step-by-step explanation:
what is the problem for you ?
to solve an equation ?
or to deal with fractions and how to relate them to whole numbers (e.g. how to convert whole numbers into fractions) ?
if you need any additional information, please let me know.
I am just solving the equation now :
2/3 + x = 4
x = 4 - 2/3 = 12/3 - 2/3 = 10/3 = 3 1/3
Answer:
Step-by-step explanation:
x = 4 - 2/3
x = 3 3/3 - 2/3
x = 3 1/3
Please help I am very confused!
Answer:
m = -1
the line goes down in a straight line from the starting point
Answer: -1
Step-by-step explanation:
Slope formula y2-y1/x2-x1. -9-(-4)/3-(-2). -5/5= -1
Nadia needs one cup of ice cream for every student in her class for their year-end party. The ice cream is only sold in pints. If there are 24 students in her class, how many pints of ice cream will she need? Describe how to solve this problem.
Using proportions, it is found that she will need 12 pints of ice cream.
What is a proportion?A proportion is a fraction of a total amount.
Each cup is equivalent to 0.5 pints. There are 24 students, and each student needs a cup, hence 24 cups are needed.
In pints, the equivalent amount is given by:
P = 24 x 0.5 = 12.
She will need 12 pints of ice cream.
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4) What is 15% of 22?
A) 3
B) 3.3
C) 30
D) 33
Answer: 3.3
Step-by-step explanation: Find the calculation in the picture
PLease help i will give brainliest
Answer:
I don't have a good knowledge of means but I know it isn't B or D.
Step-by-step explanation:
!!40 points and Brainliest if it’s correct!!ANSWER IT ONLY IF YOU KNOW THE ANSWER. IF YOU DONT KNOW DONT ANSWER IT. Make sure you explain please!
Which of the following shows the correct first step to solve x^2 - 16x = -21 by completing the square?
A)x^2 - 16x + 64 = -21
B) x^2 - 16x + 64 = -21 + 64
C) x^2 - 16x + 16 = -21 + 16
D) x^2 - 16x + 8 = -21 + 8
Answer:
I believe the answer would be B) x^2 - 16x + 64 = -21 + 64
Step-by-step explanation:
When you're completing the square you take the "middle" term (in this case it's -16) and you divide it by two, then square it. By doing that for this problem you get 64 (16/2 = 8 - 8^2 = 64; signs don't matter in this case because you multiply 2 negatives). You have to add that 64 to BOTH sides so that the equation evens out.
Ultimately, with it factored, the answer will be (x-8)^2
Need help, see photo below.
Answer:
The correct answer would be option 2; Regular Hexagon
Hope this helps!
The circumference of a circle is 71 in. Find its radius, in inches.
Answer: r = 11.3
Step-by-step explanation:
In order to find the radius given circumfrence we use the following formula
[tex]r=\frac{C}{2*\pi }[/tex]
[tex]r=\frac{71}{2*3.14 }[/tex]
r = 11.3
Is 3x^2-5x+205x^7 a perfect square?
Write 1/20 as a percent
help
Answer:
5%
Step-by-step explanation:
1/20 of 100% is 5%. So that means 5%
You went shopping and bought a total of 31 items, some of them pants and some of them shirts. The shirts cost $7 and the pants cost $22 and you spend $517 in total. How many shirts and how many pants did you buy?
Shirts________
Pants________
30 POINTS!!
LOOK AT PHOTOS!! (THERES 2!!)
Which graph displays points that correspond to the x and y values in the table?
Answer:
A
Step-by-step explanation:
A is the only one with (4,0) (1,-1) (0,0) and (-2,5)
A gift bag has width $w$ and is in the shape of a rectangular prism. The volume of the gift bag is 1152 cubic inches. The height is greater than the width. What are the dimensions of the gift bag?
A gift bag is in the shape of a rectangular prism. It has a height left-parenthesis 18 minus w right-parenthesis inches. It has a width of w inches and a length of left-parenthesis 2 times w plus 4 right-parenthesis inches.
The length is
inches, the width is
inches, and the height is
inches.
Answer:
Step-by-step explanation:
multiply the equation base times height times width and you get 12000 for height and base you get 5600 and then for the heith you get 567
Which terms complete the factorization of x2 27x 162 represented by the model? 27, 9x, 18x 9, 9x, 18x 27, 9x, 27x 9, 9x, 27x
Answer: 9, 9x, 18x
Step-by-step explanation:
Hope it helps :D
Please help and match the following. Pt2
Answer:
the first one will be B) x^2-4x+4
the sencond one will be A) x^2-16
the third one will be C) x^2+x-2
the fourth one will be D) -2x^3+4x^2+16x
Step-by-step explanation:
hope this helps now i gotta really go :)