Answer:
A: 10x^2 +53x +63 B: degree 2; quadratic trinomial C: the result of the multiplication of polynomials is a polynomial
Step-by-step explanation:
Part A:
The area is the product of length and width. The distributive property is useful for simplifying the expression.
A = LW
A = (2x +7)(5x +9) = 2x(5x +9) +7(5x +9)
A = (10x^2 +18x) +(35x +63)
A = 10x^2 +53x +63 . . . . area expression
Part B:
The highest power of x is 2. There are 3 terms. A degree-2 polynomial is called a "quadratic." A 3-term polynomial is called a "trinomial."
degree 2
quadratic trinomial
Part C:
In part A we multiplied two polynomials and came up with a result that is a polynomial. This suggests polynomials are closed with respect to multiplication.
I hope this helps!!
Three times the sum of a number and 7 is 4.
Rachel currently has $836 in a savings account that has earned 4. 5% annual compound interest for the past year. What was Rachel’s beginning balance one year ago if she has made no other deposits during the year?
Rachel's beginning balance one year ago was $800.
What is compound interest?Compound interest is applicable when there will be a change in the principle amount after the given time period.
For example, if you give anyone $500 at the rate of 10% annually then $500 is your principle amount. After 1 year the interest will be $50 and hence principle amount will become $550 now for the next year the interest will be $550, not $500.
Given that,
The current balance is $836 which is the result of compound interest of 4.5 % annually.
The original amount was a priciple amount P on which interest was applied and the final amount $836 made.
Compound interest formula;
A = P[ 1 + RT/100]^T
Where A is the final amount and T is the time period.
Here,
A = 836 , R = 4.5% and T = 1 year.
So,
836 = P[1 + 4.5/100]^1
P = 836/1.045 = $800
Hence "Rachel's beginning balance one year ago was $800".
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Determine the number of real solutions each quadratic equation has. y = 12x2 - 9x 4 real solution(s) 10x y = -x2 2 real solution(s) 4y - 7 = 5x2 - x 2 3y real solution(s) y = (-x 4)2 real solution(s)
All the given equations have 2 real solutions except for equation 4 which has only one real root.
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
The given quadratic equation
[tex]y = 12x^2 - 9x+ 4[/tex]
where, a = 12, b = -9 and c = 4
x = [tex]-b + \sqrt{b^2 - 4ac} /2a[/tex]
x = [tex]-(-9)+ \sqrt{(-9)^2 - 4(12)(4)} /2(12)[/tex]
x = 1.063 or -0.313
Second Equation
[tex]10x +y = -x^2 +2 \\y = x^{2} +10x - 2[/tex]
where, a = 1, b = 10, c = -2
substitute the values into the equation
x = [tex]-b + \sqrt{b^2 - 4ac} /2a[/tex]
[tex]-10 + \sqrt{10^2 - 4(1)(-2)} /2(1)[/tex]
x = 0.195 or -10.195
Third Equation
[tex]4y - 7 = 5x^2 - x +2 +3y[/tex]
[tex]y = 5x^{2} -x -5[/tex]
where, a = 5, b = -1, c = - 5
x = [tex]-b + \sqrt{b^2 - 4ac} /2a[/tex]
[tex]-(-1) + \sqrt{(-1)^2 - 4(5)(-5)} /2(5)[/tex]
x = 0.905 or -0.55
Fourth Equation
[tex]y = (-x +4)^2 \\y = x^{2} -8x +16[/tex]
where, a = 1, b = -8, c = 16
x = [tex]-b + \sqrt{b^2 - 4ac} /2a[/tex]
x = [tex]-(-8) + \sqrt{(-8)^2 - 4(1)(16)} /2(1)[/tex]
x = 4
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Answer:
y = 12x2 - 9x + 4
✔ no
real solution(s)
4y - 7 = 5x2 - x + 2 + 3y
✔ no
real solution(s)
10x + y = -x2 + 2
✔ two
real solution(s)
y = (-x + 4)2
✔ one
real solution(s)
Step-by-step explanation:
hope this helps:)
please help asap tysm <33
The depth of two lakes is measured at multiple spots. For the first lake, the mean depth is about 45 feet with a mean absolute deviation of 8 feet. For the second lake, the mean depth is about 60 feet with a mean absolute deviation of 27 feet.
Noah says the second lake is generally deeper than the first lake. Do you agree with Noah?
No, I do not agree with Noah because the second lake has greater variability with a higher MAD so even though the mean depth is deeper the data is very spread out away from that mean.
No, I do not agree with Noah. The MAD tells us how deep it is and the 1st MAD is more.
Yes, I agree with Noah. The MAD tells us how deep it is and the second MAD is more.
Yes, I agree with Noah because the first lake has a smaller mean and MAD than the second.
Answer:
Yes, I agree with Noah because the first lake has a smaller mean and MAD than the second
Step-by-step explanation:
If the slope of a line is -6, does the line rise (from left to right), fall (from left to right), horizontal or vertical?
Answer:
it falls left to right horizontal
pls give brainlyist
Step-by-step explanation:
Answer:
The line will fall (from left to right).
Step-by-step explanation:
If the slope of any line is negative then that line will go downwards or fall (from left to right). While if the slope were to be positive, that would mean the line will rise (from left to right).
Here is a picture to justify my answer ⤴⤴⤴
Hope this helps you :)
Brainliest + thanks!!
Explanation needed :3
Answer:
To create a "mini-triangle", we could use any number pairs (coordinates matter). We can use the side lengths of 4, 6, and 7 as they are the smallest pairs. It's a pretty easy concept which I'm sure you'll be able to grasp (I know you're smart! :) ). Ask your teacher if you have more questions. <3
Good luck!,
daintysword; date :: 1899Answer:
Side Lengths of 4,6, & 7
Side Lengths of 8,9, &4
Step-by-step explanation:
According to the image given.
We must know that in order to be a triangle the following below must be include:
All 3 vector have different directionSum of sizes of 2 vector must be greater than 3rd oneNote:
< ⇒ less than
> ⇒ greater than
= ⇒ equal
Solving all the given :
-------------------------------------------------------------------------------------------------------------
Side Lengths of 4,6, & 7
4 + 7 > 7
10 > 7
True
-------------------------------------------------------------------------------------------------------------
Side Lengths of 2,10,&3
2 + 3 > 10
5 <10
False
-------------------------------------------------------------------------------------------------------------
Side Lengths of 15, 7 , &8
7+8=15
15 = 15
False
-------------------------------------------------------------------------------------------------------------
Side Lengths of 1,4,&3
1+3>4
4=4
False
-------------------------------------------------------------------------------------------------------------
Side Lengths of 8,9,&4
8+4>9
12>9
True
-------------------------------------------------------------------------------------------------------------
Side Lengths of 6,7,&1
1+6=7
7=7
False
-------------------------------------------------------------------------------------------------------------
Kavinsky
Write the expression in radical form. (1pt)
x 2/7
Write the expression in exponential form.
∛2y
Please show steps I'm so lost
[tex]\\ \rm\dashrightarrow x^{\frac{2}{7}}[/tex]
[tex]\\ \rm\dashrightarrow x^{2(1/7)}[/tex]
[tex]\\ \rm\dashrightarrow \sqrt[7]{x^2}[/tex]
And
[tex]\\ \rm\dashrightarrow \sqrt[3]{2y}[/tex]
[tex]\\ \rm\dashrightarrow 2y^{\frac{1}{3}}[/tex]
Answer:
see below
Step-by-step explanation:
Problem-1:
[tex] {x}^{ \frac{2}{7} } [/tex]
remember that,
[tex]\displaystyle {x}^{ \frac{a}{b} } = \sqrt[b]{ {x}^{a} } [/tex]
here,
a=2b=7hence,
[tex] {x}^{ \frac{2}{7} } = \boxed{\sqrt[7]{ {x}^{2} } }[/tex]
Problem-2:
recall that,
[tex] \sqrt[n]{x} = {x}^{ \frac{1}{n} } [/tex]
therefore,
[tex] \sqrt[3]{2y} = (2y {)}^{ \frac{1}{3} } \implies \boxed{{2 }^{ \frac{1}{3} } {y}^{ \frac{1}{3} } }[/tex]
A copper wire is submerged in a clear liquid in container A. After a while, the contents of the container changed to look like what is in container B, with a white crystal coating on the copper wire and the liquid turning light blue. Which are indicators that a chemical reaction has occurred? Check all that apply.
formation of a flame
formation of a precipitate
formation of a gas
change in odor
change in color
Answer:
B) formation of a precipitate
E) change in color
Step-by-step explanation:
just did the assignment on e.d.g.e
Answer:
B and E is correct
Step-by-step explanation:
Part A
Construct a circle of any radius, and draw a chord on it. Then construct the radius of the circle that bisects the chord. Measure the angle between the chord and the radius. What can you conclude about the intersection of a chord and the radius that bisects it? Take a screenshot of your construction, save it, and insert the image below your answer.
Part B
Write a paragraph proof of your conclusion in part A. To begin your proof, draw radii OA and OC.
Part C
In this part of the activity, you will investigate the converse of the theorem stated in part A. To get started, reopen GeoGebra.
Draw a circle of any radius, and draw a chord on it. Construct the radius of the circle that is perpendicular to the chord. Measure the line segments into which the radius divides the chords. How are the line segments related? What can you conclude about the intersection of a chord and a radius that is perpendicular to it? Take a screenshot of your construction, save it, and insert the image below your answer.
Part D
Write a paragraph proof of your conclusion in part C. To begin your proof, draw radii OA and OC.
Answer:
All answers are bold and links are real photos
BTW THE PHOTOS ARE IN ORDER OF THE ANSWERS
Brainlyist??
Step-by-step explanation:
Task 1
Part A
Tangent Line
Part B
PHOTO WITH LARGE CIRCLE AND LINE OUT SIDE BUT CONNECTED
Part C
2034.7
PHOTO WITH EQUATION
We calculate the point from the center of the earth to the satellite and because we have the radius we can subtract it getting the distance from the satellite to the earth.
Task 2
Gears
Part A
Approximately 10.47 inches
Part B
300°
Part C
Approximately 125.66 inches
Part D
The distance traveled increases by approximately 62.83 inches
Task 3
Circle Theorems
Part A
PHOTO WITH LINE THROUGH CIRCLE AND ONE 90 DEGREE ANGLE
Part B
Prove OC is perpendicular to AB
We know that ΔAEC≅AED by SSS criteria (SSS criteria is when all three sides of a triangle is equal making them congruent)
To prove this that they apply to the SSS criteria: m∠ADO=m∠BDO m∠ADO=90°=m∠BDO
Part C
A radius is perpendicular to a chord when the chord is equally divided in half by the radius.
PHOTO OF LINE THROUGH CIRCLE AND LINE DISTANCES
Part D
Prove OC is perpendicular to AB
AO=BO because AO and BO are both radii
OD≅OD by reflexive theorem
ΔADO≅ΔBDO because they are both right triangle with the hypotenuse and a side
AB≅BC means that OC is perpendicular to AB
Disclaimer: The images to part A and part C is the same.
Two theorems we are proving are:
Line drawn from the center of the circle to bisect a chord is perpendicular to it.Perpendicular drawn from the center of the circle to a chord, bisects it.How do we solve the given question?Part A: The image is attached
Part B:
Let there be a circle with the center at O. Let AC be a chord. Let OE be a radius of the chord such that OE bisects AC at B, that is, AB = BC.
To prove: A line drawn from the center of the circle to bisect a chord is perpendicular to it.
Construction: We join OA and OB.
Proof:
In ΔOAB and ΔOCB,
OA = OC (Radius of the same circle)
AB = BC (Given, at B, the chord is bisected)
OB = OB (common side)
∴ ΔOAB ≅ ΔOCB [SSS axiom]
∴ ∠OBA = ∠OBC [Common parts of Congruent triangles]
Let ∠OBA = ∠OBC = x.
Since AC is a straight line,
∠OBA + ∠OBC = 180° [Linear pair]
or, x + x = 180°
or, 2x = 180°
or, x = 90°.
∴ ∠OBA = ∠OBC = 90°.
So, we can say that OB ⊥ AC, hence the theorem is proved.
Part C: The image is attached
Part D:
Let there be a circle with the center at O. Let AC be a chord. Let OE be a radius of the chord such that OE is perpendicular to AC at B, that is, AB ⊥ BC.
To prove: A line drawn from the center of the circle perpendicular to the chord bisects it.
Construction: We join OA and OB.
Proof:
In ΔOAB and ΔOCB,
OA = OC (Radius of the same circle)
∠OBA = ∠OBC = 90° (∵ OB ⊥ AC)
OB = OB (common side)
∴ ΔOAB ≅ ΔOCB [RHS axiom]
∴ AB = AC [Common parts of Congruent triangles]
So, we can say that OE perpendicular to the chord AC bisects it, hence the theorem is proved.
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please help me please
Answer:
Step-by-step explanation: y axis is 6units up (y=+6)
X axis is 2units to the right. (×=+2)
Sam would like to use his extensive stamp collection as collateral for a secured loan. sam has documentation that says his stamp collection is worth $10,525.00. sam's bank has a policy that permits loan officers to lend no more than 82.5% of the value of the collateral. what is the maximum loan amount sam can get from his bank using his stamp collection as collateral? a. $8,683.13 b. $9,700.00 c. $10,525.00 d. $12,382.35 please select the best answer from the choices provided a b c d
Answer:
A on edge 2021
Step-by-step explanation:
I got it correct.
50/22 as a decimal rounded to the nearest hundred
Answer:
2.27
Step-by-step explanation:
What is the midpoint formula
Answer:
see image
Step-by-step explanation:
You average the x's and average the y's.
This means add x+x and divide by 2. And add y+y and divide by 2. See image.
The measure of an angle is 32 degrees . What is the measure of its complementary angle?
Answer:
an angle measuring 32 degrees has a complement that measures (2x-16) degrees. What is the value of x?
Step-by-step explanation:
let me know if its right
Determine the equation of the circle with radius 99 and center (-1,-8)(−1,−8).
Generally, you'd see the equation of a circle organized in the following format:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
[tex](h,k)[/tex] is the center[tex]r[/tex] is the radiusTo determine the equation given the center and the radius:
Plug both pieces of information into the general equationSimplifySolving the QuestionWe're given:
Radius: 99Center: (-1,-8)Plug the radius and center into the equation as r and (h,k):
[tex](x-(-1))^2+(y-(-8))^2=99^2\\(x+1)^2+(y+8)^2=9801[/tex]
Answer[tex](x+1)^2+(y+8)^2=9801[/tex]
Fill in the table using this function rule.
y=15-3x
x y
1:
3:
4:
5:
Answer:
(1,12) ; (2,9) ; (3,6) ; (4,3) ; (5,0)
Step-by-step explanation:
You need to plug the x values into the equation.
Your equation: y=15-3x
Example:
Plug in 1
y=15-3
y=12
Plug in 2:
y=15-3(2)
y=15-6
y=9
Plug in 3:
y=15-3(3)
y=15-9
y=6
Plug in 4:
y=15-3(4)
y=15-12
y=3
Plug in 5:
y= 15-3(5)
y=15-15
y=0
A cube is a regular prism with square faces. How can you write a simpler version of the surface area formula for a cube?
Answer:
A cube is a rectangular prism where all its sides are the same. The formula to find the surface area of a rectangular prism is A = 2wl + 2lh + 2hw, where w is the width, the l is the length, and the h is the height.
The surface area formula for a cube is 6l²
How to determine the surface area?A cube has the following features:
6 faces of equal areasEach face has equal side lengthThe area of a face of a cube is:
Area = l²
Where l represents the side length
The surface area formula for a cube is then calculated using:
Surface area = 6 * Area of a face
So, we have:
Surface area = 6 * l²
Surface area = 6l²
Hence, the surface area formula for a cube is 6l²
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Sarah chose 3 shells to purchase at a souvenir shop. The price tag for the first shell indicated $16, the second shell indicated $18, and the third shell indicated $12. After adding tax, the clerk at the shop said the total cost was $50. What percentage of the total cost was the tax?
F 12%
G 8%
H 4%
J 10%
What is the missing value in the table below?
Number of Books
3. $10.00
9. $30.00
18. $60.00
$80.00
Answer:
24 books
Step-by-step explanation:
Books are valued at $10/3 books. 18 books would have a value of (18books)*($10/3books) = $60, and so on.
X books would have a value of X($10/3)=$80
X = ($80)*(3/$10)
X = 24 books
Lorne subtracted 6x3 – 2x 3 from –3x3 5x2 4x – 7. use the drop-down menus to identify the steps lorne used to find the difference. 1. (–3x3 5x2 4x – 7) (–6x3 2x – 3) 2. (–3x3) 5x2 4x (–7) (–6x3) 2x (–3) 3. [(–3x3) (–6x3)] [4x 2x] [(–7) (–3)] [5x2] 4. –9x3 6x (–10) 5x2 5. –9x3 5x2 6x – 10
The difference between the polynomial is [tex]\rm 9x^3-5x^2-6x+10[/tex].
What is subtraction?The subtract means to take away from a group or a number of things.
Lorne subtracted 6x3 – 2x + 3 from –3x3 + 5x2 + 4x – 7.
The difference between the expression is;
[tex]\rm ( 6x^3 - 2x + 3 )- (-3x^3 + 5x^2 + 4x - 7)[/tex]
[tex]\rm 6x^3 - 2x + 3 +3x^3 -5x^2 -4x +7\\\\9x^3-5x^2-6x+10[/tex]
Hence, the difference between the polynomial is [tex]\rm 9x^3-5x^2-6x+10[/tex].
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what percent of numbers of the muffins sold were carrot
One angle of an isosceles triangle measures 92°. What measures are possible for the other two angles? Choose all that apply.44 24 76 47
Answer:
44
Step-by-step explanation:
First remmember that all triangles will add up to equal 180 degrees
so we will have to subtract 180 by 92
whitch is 88
Now sence an isoclies are to equal sides we will have to divide 88 by 2
whitch is 44
Making 44 your answer.
3. Look at the set of ordered pairs below. Determine if the three statements that follow are true or false.
If it is true, explain why you know that it is true.
If it is false, explain why you know that it is false and change the statement to a true statement.
{(3,6), (4,6), (5,7), (6,8), (7,10), (8,10)
Statement 1:
The relation is not a function because every y-value has more than one corresponding X-value
Statement 2:
The domain of this relation is 3=< x =< 8.
Statement 3:
The range of this relation is {6, 7, 8, 10}
Answer:
Statement 1 - false
A function is one-to-one or many-to-one.
One-to-one means each value in the range (y-values) corresponds to exactly one value in the domain (x-values)
Many-to-one means some values in the range (y-values) correspond to more than one (many) value in the domain (x-values).
Therefore, as some y-values correspond to more than one x-value, this is a many-to-one function.
The true statement should be:
The relation is a function because some y-values correspond to more than one x-value.
Statement 2- true
The domain is the set of input values (x-values). Therefore, the domain is 3 ≤ x ≤ 8 as the smallest x-value is 3 and the highest x-value is 8.
Statement 3 - true
The range is the set of output values (y-values). Therefore, the range is {6, 7, 8, 10} as these are the y-values of the ordered pairs.
what is an equation of the line that passes through the point (-2,-8) and has a slope of 3?
a) y=3x-2
b) y=3x-22
c) y=3x+2
d) y=3x+22
Answer:
y = 3x -2
Step-by-step explanation:
General equation of a line in the slope intercept form is
y = mx + b ,
where m is the slope and b is the y-intercept ( where intercepts the y-axis)
y = 3x + b ,
because is given slope is m = 3
For point (x = -2, y = -8) we have
-8 = 3 (-2) + b
-8 = -6 + b
-8 + 6 = b
-2 = b
The equation of the line that passes through the point (-2,-8) and has a slope of 3 is
y = 3x -2
Which is a larger volume, a candle with a height of 6. 3 inches and a radius of 3. 1 inches, or a candle with both a height and a radius of 3. 9 inches?
Select "Growth" or "Decay" to classify each function.
y=(3.5)^t/2
f(x)=1/4(2)^t
y=10(0.99)^t
Answer:
1. Growth
2. Growth
3. Decay
What is the slope and the y-intercept of the line? y = − 8x + 5
Answer:
The slope is -8 and the y-intercept is 5
NO LINKS PLEASE OR ILL REPORT!! 20 POINTS!!!
Write an equation to represent the verbal description.
The difference of six times a number and four times another number is 20.
Answer:
x=6*4y=20
Step-by-step explanation:
the difference = x, six times = 6*, 4 times = 4y, number is 20 = 20
On average, Shawnte drinks of a -ounce glass of water in hour. How much water
does she drink in an hour?
Answer:
a- ounce glass of water.