Answer:
15x^3+26x^2-3x+42
Step-by-step explanation:
(3x+7)(5x^2-3x+6)
15x^3-9x^2+18x+35x^2-21x+42
15x^3-9x^2+35x^2+18x-21x+42
15x^3+26x^2-3x+42
Answer:
15x³ + 26x² - 3x + 42
Step-by-step explanation:
Hi there!
We are given the polynomials 3x+7 and 5x²-3x+6
We want to multiply them together
(3x+7)(5x²-3x+6)
To that, we need to distribute each term of the binomials to each other, and then add them together.
What this means is that we need to multiply 3x by 5x², -3x, and 6, then add them together. Then, multiply 7 by 5x², -3x, and 6. Add those together, and then add everything together.
So, let's first start by multiplying 3x by everything:
3x * 5x² = 15x³
3x * -3x = -9x²
3x * 6 = 18x
Add them together: 15x³ + -9x² + 18x
Now with 7:
7 * 5x² = 35x²
7 * -3x = -21x
7 * 6 = 42
Add them together: 35x² + -21x + 42
Now add 15x³ + -9x² + 18x and 35x² + -21x + 42 together:
15x³ + -9x² + 18x + 35x² + -21x + 42
Combine like terms:
15x³ + 26x² - 3x + 42
Hope this helps!
Find the area of the figure.
A: 24.5 ft²
B: 44 ft²
C: 49 ft²
D: 14.8 ft²
Answer:
49ft²
Step-by-step explanation:
A=bh
A=bh=9.8·5=49
Only 16 tho!!!!!please
Answer:
(5*2) + (1/2)(2+2+2)*4)
Step-by-step explanation:
Area of Triangle = (1/2)(2 + 2 + 2 )* 4)
Area of Rectangle = 5 * 2
Total Area = (5*2) + (1/2)(2+2+2)*4)
What’s the slope of the line that passes through (10,2) and (5,9)
Answer:
y = -1.4x + 16
Step-by-step explanation:
the slope is -1.4x
Use the slope formula:-
[tex]\displaystyle\frac{y2-y1}{x2-x1}[/tex]
Plug in the values:-
[tex]\displaystyle\frac{9-2}{5-10}[/tex]
Simplify:-
[tex]\displaystyle\frac{7}{-5}= -\frac{7}{5}[/tex]
[tex].~~~~~~~\uparrow\sf{Slope}[/tex]
note:-Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I'll comment and/or edit my answer :)
divide 5/8 ÷ 3/4 please please please please please
Answer:
this answer is 0.83
Step-by-step explanation:
5/8 is 0.625, 3/4 is 0.75 and 0.625 divided by 0.75 is 0.83
Answer: 5/6
All you have to do is combine the two equations, like so [tex]\frac{5*4}{8*3}[/tex]
Multiply [tex]\frac{20}{24}[/tex]
Then simplify [tex]\frac{5}{6}[/tex]
What is the solution to 9|x – 8| < 36?
Answer:
4 < x < 12
Step-by-step explanation:
Given:
[tex]\displaystyle \large{9|x-8| < 36}[/tex]
Divide both sides by 9:
[tex]\displaystyle \large{|x-8| < 4}[/tex]
Theorem:
For [tex]\displaystyle \large{|x-a| < b}[/tex], since absolute is less than a constant, the interval or solution is:
[tex]\displaystyle \large{-b < x-a < b}\\\displaystyle \large{-b+a < x < b+a}[/tex]
Therefore:
[tex]\displaystyle \large{|x-8| < 4 \to -4 < x-8 < 4}\\\displaystyle \large{-4+8 < x < 4+8}\\\displaystyle \large{4 < x < 12}[/tex]
Therefore, the solution is 4 < x < 12
Answer:
4 < x < 12
Step-by-step explanation:
9|x - 8| < 36
Divide both sides by 9:
|x - 8| < 4
Solution 1
(x - 8) < 4
Add 8 to both sides:
x < 12
Solution 2
-(x - 8) < 4
-x + 8 < 4
Subtract 8 from both sides:
-x < -4
Divide both sides by -1 (remembering to change the direction of the sign):
x > 4
Therefore, the solution to the inequality is 4 < x < 12
find the second derivative of the parametric equation x(t)=sin t and y(t)=cos t
Presumably you mean the second derivative of y with respect to x, d²y/dx².
Compute the first derivative. By the chain rule,
[tex]\dfrac{dy}{dx} = \dfrac{dy}{dt} \times \dfrac{dt}{dx} = \dfrac{\frac{dy}{dt}}{\frac{dx}{dt}}[/tex]
Differentiate the two parametric equations with respect to t :
[tex]x = \sin(t) \implies \dfrac{dx}{dt} = \cos(t)[/tex]
[tex]y = \cos(t) \implies \dfrac{dy}{dt} = -\sin(t)[/tex]
Then the first derivative is
[tex]\dfrac{dy}{dx} = \dfrac{-\sin(t)}{\cos(t)} = -\tan(t)[/tex]
Now, dy/dx is a function of t, so we can denote it by, say, dy/dx = f(t). Then by the chain rule, the second derivative will be
[tex]\dfrac{d^2y}{dx^2} = \dfrac{df}{dx} = \dfrac{df}{dt} \times \dfrac{dt}{dx} = \dfrac{\frac{df}{dt}}{\frac{dx}{dt}}[/tex]
Differentiating f(t) :
[tex]f(t) = -\tan(t) \implies \dfrac{df}{dt} = -\sec^2(t)[/tex]
Then the second derivative is
[tex]\dfrac{d^2y}{dx^2} = \dfrac{-\sec^2(t)}{\cos(t)} = \boxed{-\sec^3(t)}[/tex]
and since y = cos(t), we can go on to say
[tex]\dfrac{d^2y}{dx^2} = -\dfrac1{y^3}[/tex]
Can someone help me?
Answer:
(i) [tex]y = 2x(x-5)[/tex]
(ii) zeros: x = 0 and x = 5
axis of symmetry: x = 2.5
(iii) vertex: (2.5, -12.5)
(iv) see attached
Step-by-step explanation:
Part (i)
Factor: [tex]y=2x^2-10x[/tex]
Factor out the common term [tex]2x[/tex]:
[tex]\implies y=2x(x-5)[/tex]
Part (ii)
Zeros occur when [tex]y=0[/tex]
[tex]\implies 2x(x-5)=0[/tex]
Therefore:
[tex]\implies 2x=0 \implies x=0[/tex]
[tex]\implies (x-5)=0 \implies x=5[/tex]
So the zeros are x = 0 and x = 5
The axis of symmetry of a parabola is x = a where a is the midpoint of the zeros.
[tex]\textsf{midpoint of zeros}=\dfrac{0+5}{2}=2.5[/tex]
Therefore, the axis of symmetry is [tex]x=2.5[/tex]
Part (iii)
The axis of symmetry is the x-coordinate of the vertex. To find the y-coordinate of the vertex, substitute this into the given equation.
[tex]\implies 2(2.5)^2-10(2.5)=-12.5[/tex]
So the vertex is (2.5, -12.5)
Part (iv)
Plot the zeros and the vertex.
As the leading coefficient is positive, the parabola will open upwards, so the vertex is the minimum point.
Draw the axis of symmetry, then sketch the parabola, ensuring each side of the axis of symmetry is symmetrical.
*see attached*
For each table, determine whether the relationship shows a linear function. If
so, write the function.
X
1
y
b) 1
c)
y
y
1
9
O
3.2
1
O
4.2
2
4
5.2
3
8
6.2
4
16
7.2
5
24
2345
6303
-3
246
2
4
6
8
Step-by-step explanation:
7.2
5
24
2345
6303
-3
2467.2
5
24
2345
6303
-3
246
The linear function is given by table B and the equation y = ( 1/2 )x + 3.2
What are Linear Equations?An equation is said to be linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero.
The linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution
On a graph, a linear equation forms a straight line. On a graph, a nonlinear equation produces an S-curve, a bell curve, or another nonlinear shape.
Given data ,
Let the linear function be represented as A
Now , the value of A is
Let the x values be x = { 0 , 2 , 4 , 6 , 8 }
Let the y values be y = { 3.2 , 4.2 , 5.2 , 6.2 , 7.2 }
Now , the equation of line is y - y₁ = m ( x - x₁ )
where m is the slope
m = ( 4.2 - 3.2 ) / ( 2 - 0 )
m = 1/2
On simplifying , we get
y - 3.2 = ( 1/2 ) ( x - 0 )
Adding 3.2 on both sides , we get
y = ( 1/2 )x + 3.2
Hence , the linear function is y = ( 1/2 )x + 3.2
To learn more about linear equations click :
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use a sum or difference formula to simplify the expression Sin (x+π)
Answer:
- sin (x)
Step-by-step explanation:
A set of data is normally distributed with a mean of 327 and a standard deviation of 27.
What percentage of the data is below 357?
Enter your answer as a number rounded to the nearest tenth, like this: 42.5
Answer:
86.7%
Step-by-step explanation:
For questions regarding values related to a normal distribution, a suitable calculator is required. Numerous calculators, apps, web sites, and spreadsheets are capable of answering this question.
__
One standard deviation above the mean is 327 +27 = 354, so the value is expected to be slightly more than 50% +34% = 84%. It is no surprise, then, that a calculator tells you 86.7% of the data is below 857.
_____
Additional comment
The "empirical rule" tells you 68% of the area is within 1 standard deviation of the mean. The distribution is symmetrical, so half that, 34%, is between the mean and 1 standard deviation above the mean. Of course, 50% of the data is below the mean.
236 megabytes and 12.6% is downloaded how many megabytes have been downloaded
236 x 0.126
29.736 MB have been downloaded
Observe the sequences below. I. 3, 6, 9, 12, ... II. 3, 9, 27, 81, III. 2, 4, 8, 16, ... IV. 3, 5, 7, 9, Which of these are geometric sequences? III only O Il and me II and IV O I and IV
how to convert a improper fraction to a mixed number
Answer:
Step-by-step explanation:
Divide the numerator by the denominator.
Write down the whole number part of the quotient.
Take the remainder and write it over the original denominator.
Please help ASAP I need an answer now!
Answer:
Final answer -
Area of paperboard = [tex]565.92 \: inches {}^{2} [/tex]
hope helpful :D
Johnson has 19 bowls of ice cream he gives away d ice cream bowls write the expression that shows the number of ice cream bowls are left?
Answer:
19 -d
Step-by-step explanation:
The number Johnson has left is found by subtracting the number he gave away from the number he started with.
19 -d . . . . . . . number of ice cream bowls left
Which net represents this solid figure?
Answer: TThere is no picture
Step-by-step explanation:
Brianna has $620 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.
She buys a new bicycle for $261.04.
She buys 3 bicycle reflectors for $13.07 each and a pair of bike gloves for $13.57.
She plans to spend some or all of the money she has left to buy new biking outfits for $51.03 each.
Write and solve an inequality which can be used to determine xx, the number of outfits Brianna can purchase while staying within her budget.
Answer: 6 outfits
Step-by-step explanation:
$620 should be greater than the price of the new bicycle + 3 * bicycle reflectors + a pair of bike gloves + unknown number of biking outfits
Therefore, the inequality will be:
620 ≥ 261.04 + 3 × 13.07 + 13.57 + 51.03x
620 ≥ 313.82 + 51.03x
[tex]\text{Solving \ for \ x}[/tex]
[tex]620\ge \:313.82+51.03x[/tex]
[tex]\mathrm{Switch\:sides}[/tex]
[tex]313.82+51.03x\le \:620[/tex]
[tex]\mathrm{Multiply\:both\:sides\:by\:}100[/tex]
[tex]313.82\cdot \:100+51.03x\cdot \:100\le \:620\cdot \:100[/tex]
[tex]\mathrm{Refine}[/tex]
[tex]31382+5103x\le \:62000[/tex]
[tex]\mathrm{Subtract\:}31382\mathrm{\:from\:both\:sides}[/tex]
[tex]31382+5103x-31382\le \:62000-31382[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]5103x\le \:30618[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}5103[/tex]
[tex]\frac{5103x}{5103}\le \frac{30618}{5103}[/tex]
[tex]\text{Simplify}[/tex]
[tex]{x\le \:6}[/tex]
Therefore, Brianna can buy 6 or fewer outfits while staying within her budget
how many real numbers solutions does the equation have
Answer:
this would be 2
Step-by-step explanation:
what is the area of this circle to the nearest hundredths place
Answer:
Step-by-step explanation:
It would be about 3.14 as since it is only 1 inch pi is multiplyed by one and when rounding pi to the hundreths you get 3.14 hope this helps
Find the area of the figure.
Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).
Answer:
The only true statement is :
The graph of the function is a parabola
Step-by-step explanation:
f(x) = x² – 5x + 12
Option 1: The value of f(–10) = 82
Reason : f(-10) = (-10)² – 5(-10) + 12 = 100 + 50 + 12 = 162 ≠ 82
Option 2: The graph of the function is a parabola [tex]\huge\checkmark[/tex]
Option 3: The graph of the function opens down
Reason : the coefficient of x² is 1 ,which is a positive number then the graph opens up.
Option 4: The graph contains the point (20, –8)
Reason : f(20) = 312 ≠ -8
Option 5: The graph contains the point (0, 0)
Reason : f(0) = 12 ≠ -8
Answer:
ABC
Step-by-step explanation:
Find the measures of the interior angles that maximize the area of an isosceles trapezoid
where the length of the non-parallel sides are each 4 inches and the length the shorter of
the two bases is 6 inches.
The internal angles of 64.801° (2 in total) and 115.199° (2 in total) lead to a maximum area of 27.88 square units.
How to determine the maximum possible area of an isosceles trapezoid
Quadrilaterals are figures formed by four line segments and whose sum of internal angles equals 360°. By geometry we know that the area of a trapezoid is the average of the length of the two bases (B, b), in inches, multiplied by the height of the quadrilateral.
A = 0.5 · (B + b) · h (1)
By trigonometry the measure of the longer base and the height of the isosceles trapezoid are, respectively:
B = b + 2 · l · cos θ (2)
h = l · sin θ (3)
Where θ is an internal angle, in degrees.
By (2) and (3) in (1):
A = 0.5 · (2 · b + 2 · l · cos θ) · (l · sin θ)
A = (b + l · cos θ) · (l · sin θ)
A = b · l · sin θ + l² · sin θ · cos θ
A = b · l · sin θ + 0.5 · l² · sin 2θ (4)
If we know that b = 6 in and l = 4 in, then the area of the isosceles trapezoid is represented by the following function:
A = 24 · sin θ + 8 · sin 2θ (5)
Now we determine the angle associated to the maximum area by graphic approach.
According to this approach, the internal angles of 64.801° (2 in total) and 115.199° (2 in total) lead to a maximum area of 27.88 square units. [tex]\blacksquare[/tex]
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Please help me ASAP I’ll mark brainly
Answer: 7
Step-by-step explanation:
rewrite 4+2/3x=3/4 so it does not have fractions.
Answer:
48 + 8x = 9
Step-by-step explanation:
4 + [tex]\frac{2}{3}[/tex] x = [tex]\frac{3}{4}[/tex]
multiply through by 12 ( the LCM of 3 and 4 ) to clear the fractions
48 + 8x = 9
HELP ME OUT PLS!!!!
The radius of a sphere is 7 cm. What is the sphere's volume? Round to the nearest tenth, and use 3.14 for pi.
O 723,2 cm
O 1868.2 cm
O 1436,0 cm
O 2052,5 cm
⠀
Explanation :
⠀
We know,
[tex]{ \longrightarrow{\qquad \pmb {\sf Volume_{(Sphere)} = \dfrac{4}{3} \pi {r}^{3} }}}[/tex]
⠀
Here,
The radius of the sphere is 7 cm.We will take the value of π as 3.14⠀
Substituting the values in the formula :
⠀
[tex]{ \longrightarrow {\qquad {\sf Volume_{(Sphere)} = \dfrac{4}{3} \times3.14 \times {\bigg(7 \bigg)}^{3} }}}[/tex]
⠀
[tex]{ \longrightarrow {\qquad {\sf Volume_{(Sphere)} = \dfrac{4}{3} \times 3.14 \times 343 }}}[/tex]
⠀
[tex]{ \longrightarrow {\qquad {\sf Volume_{(Sphere)} = \dfrac{4 \times 3.14 \times 343}{3} }}}[/tex]
⠀
[tex]{ \longrightarrow {\qquad {\sf Volume_{(Sphere)} = \dfrac{4308.08}{3}}}}[/tex]
⠀
[tex]{ \longrightarrow{\qquad \pmb {\sf Volume_{(Sphere)} = 1436.02 }}}[/tex]
⠀
Therefore,
The volume of the sphere is 1436.0 cm³!!!!!!!!!!!!!!!!!!!!!
Answer:
I believe it would be 9.
Step-by-step explanation:
Finding Dialation: 16/12 = 1.3
Height: 16/1.3 = 12
Width: 12/1.3 = 9
A middle school principal wants to change the lunch menu. The principal surveys the students to determine how the students would feel about the change. What served method will produce the best repersentative sample
A)survey every 5th student who rides in a car to school
B)survey 3 randomly selected students from every homeroom
C) survey every 10 7th grade student during lunch
D) survey 5 randomly selected students
Answer:
B
Step-by-step explanation:
B is the best answer because it's a lot of students and unbiased
Blank × 0.1 = 47.2 find the missing number
Answer:
472 :)
Step-by-step explanation:
47.2/0.1 = 472
Have an amazing day!
Please rate and mark brainliest!!
100 points
See attachment below
Answer:1)x =-30
2)x=-30
Step-by-step explanation: 1: 2(3x+5)=5(x-4) ( remove the parenthesis)
then 6x+-5x=-20x-10 (collect the like trems calulate) so (-20 and -20 on each side) the x=-20-10.
2: 6x+10=5x-20 (move the like trems) so move the variable to the left hand side and change its sign like this 6x+10-5x=-20
6x-5x=-20-10
x=-20-10 which it ='s x=-30
follow my TT at yvngxmiia
Solving Stepwise:
2(3x+5) = 5(x-4) [ Given ]2(3x)+2(5) = 5(x) -5(4) ---------------6x + 10 = 5x - 20 [ Distributive property ]6x + 10 - 5x = 5x -20 -5x ---------------x + 10 = -20 [ subtraction property of equality ]x + 10 -10 = -20 -10 -------------x = -30 [ subtraction property of equality ]Additional Explanation
Distributive property:
a(b+c) = a(b) + a(c)symmetric property of equality:
both sides can be interchanged, x = y, then y = xsubtraction property of equality:
when same number subtracted from both sides, a - c = b - cclosure property:
addition, subtraction and multiplication of integers, a + b = cdivision property of equality:
when both sides divided by same number, a/c = b/cPLEASE HELP ASAP W EXPLANATION !!!
Based on the net shown below, what is the type of solid this represents and find the surface area of the solid to the nearest hundredth.
Answer:
326.6 cm²Step-by-step explanation:
The figure has 2 triangular and 3 rectangular faces.
This is a right triangular prism.
Find the area of each face and add up to get the total surface area.
Each triangle has base of 10 and height of:
[tex]h = \sqrt{10^2-5^2} =\sqrt{75} =8.66[/tex] cmTotal surface area is
[tex]A = 2(1/2*10*8.66) + 3(10*8) = 326.6[/tex]