Answer:
Gradient of A: 2
Gradient of B: -1
Step-by-step explanation:
Gradient = change in y/change in x
✔️Gradient of A using two points on line A, (2, 5) and (0, 1):
Gradient = (1 - 5)/(0 - 2) = -4/-2
Simplify
Gradient of A = 2
✔️Gradient of B using two points on line B, (0, 5) and (5, 0):
Gradient = (0 - 5)/(5 - 0) = -5/5
Simplify
Gradient of B = -1
Find a degree 3 polynomial having zeros 1,4 and 2 leading coefficient equal to 1
The degree 3 polynomial with the zeros {1, 4, 2} and a leading coefficient equal to 1 is:
p(x) = x^3 -7x^2 + 14x - 8
We know that for a polynomial of degree n, with a leading coefficient "a" and the zeros {x₁, x₂, ..., xₙ} can be written as:
p(x) = a*(x - x₁)*(x - x₂)*...*(x - xₙ)
Knowing that here we have a polynomial of degree n = 3, with a leading coefficient a = 1, and the zeros {1, 4, 2}
Replacing these in the above form, we get:
p(x) = 1*(x - 1)*(x - 4)*(x - 2)
Now we can expand that to get:
p(x) = (x^2 - x - 4x + 4)*(x - 2) = (x^2 - 5x + 4)*(x - 2)
p(x) = x^3 - 5x^2 + 4x - 2x^2 + 10x - 8
p(x) = x^3 -7x^2 + 14x - 8
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What’s the rate of change please help
Answer:
Rate of change, is also another word for slope.
Slope --> y2 - y1 / (x2-x1)
Assuming the table is already in xy, the cords are in xy form too.
1) (8,8)
2) (11,10)
Plug points into slope eq
--> 10 - 8 = 2
----> 11 - 8 = 3
2/3 Is the slope/rate of change.
please please help thank you so much
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!!
Answer:
Option B, $2020.00
Step-by-step explanation:
Volume of the pool,
12×5×14.5+4×5×7
= 1010 ft³
each cubit foot costs $2, so 1010 ft³ will cost,
1010×$2
= $2020
3
Select the correct answer.
Which statement best describes the solution to this system of equations?
3x + y= 17
x+2y= 49
OA.
It has no solution.
B.
It has infinite solutions.
O c.
It has a single solution: x = 15, y= 17.
OD
It has a single solution: x= -3, y = 26.
Answer:
X= –3, y=26
Step-by-step explanation:
3X+Y=17====> –2(3X+Y)=–34===> –6X–2Y=–34
X+2Y=49
Aight so let's head to the sum
–5X=15===> X=–3
–3+2Y=49===> 2Y=52===> Y=26
(a The Slant height of a right circular Cone with radius 7cm s 15cm . Find its Curved Surface area
Answer:
The curved surface area of the cone is approximately 329.9 cm²
Step-by-step explanation:
The parameters of the right circular cone are;
The radius of the cone, r = 7 cm
The slant height of the one, l = 15 cm
The curved surface area of a cone, CSA = π·r·l
Therefore;
CSA = π × 7 cm × 15 cm = 105·π cm² ≈ 329.9 cm².
what is the answer to
x^{2} + 2x + 15 = 0
From my knowledge:
²−2−15=0
x=5
x=-3
5. Find the measure of x and and the angle measure.
(3x - 15)
(2x + 7)
Answer:
here's the answer to your question
Can someone please assist me...thank you
Answer:
x=10, y=24
[tex]\left(34-y\right)^2+y^2=676[/tex]
Step-by-step explanation:
Answer:
x = 10 and y = 24
Step-by-step explanation:
Perimeter of triangle = sum of the 3 sides of the triangle
:. x + y + 26 = 60
x + y = 60 - 26
x + y = 34 ---- (1)
From Pythagoras theorem,
x² + y² = 26²
x² + y² = 676 ---- (2)
From equation (1): y = 34 - x
:. x² + (34 - x)² = 676
x² + 1,156 - 68x + x² = 676
x² + x² - 68x + 1,156 - 676 = 0
2x² - 68x + 480 = 0
x² - 34x + 240 = 0
(x² - 24x) - (10x + 240) = 0
x(x - 24) -10(x - 24) = 0
(x - 24)(x - 10) = 0
x = 24 or 10
y = 34 - x
y = 34 - 10 = 24
:. x = 10 and y = 24
A water butt contains 512.6
liters of water when full. It is
80% full. Daniel is using a
small bucket to empty the
butt. The bucket holds
525ml of water. How many
small buckets can be
completely filled by the water in the butt?
Answer:
u can solve ur self but let me help you
Step-by-step explanation:
simply:subtract 525ml from 512.6 liters
Find the value of 4 tenths x hundreds.
4000
400
40
4
the value of 4 tenths x hundreds.
4000
Answer:
40
Step-by-step explanation:
4/10 x 100 = 40
-8a-5=-7a+3 help someone
Answer: a = -8
Step-by-step explanation:
Given
-8a - 5 = -7a + 3
Subtract 3 on both sides
-8a - 5 - 3 = -7a + 3 - 3
-8a - 8 = -7a
Add 8a on both sides
-8a - 8 + 8a = -7a + 8a
a = -8
Hope this helps!! :)
Please let me know if you have any questions
Answer:
a = -8
Step-by-step explanation:
-8a-5=-7a+3 Add 5 to both sides.
- 8a = - 7a + 3 + 5 Combine
-8a = - 7a + 8 Add 7a to both sides
-8a + 7a = 8 Combine
-a = 8 Multiply by - 1
a = - 8
When you get a weird number like this, you should check it.
LHS = -8(-8) - 5
LHS = 64 - 5
LHS = 59
RHS = -(7*-8) + 3
RHS = -(-56) + 3
RHS = 56 + 3
RHS = 59
So a = - 8 must be right.
What is the maximum degree of a reflex angle
Answer:
Less than 360 degree
Step-by-step explanation:
I think so
16x^2 - 49 when factored is ?
Answer:
Step-by-step explanation:
16x^2 = (4x)^2
49 = 7^2
16x^2 - 49 = (4x)^2 - (7)^2
The result of adding 14 to twice a number is the same as subtracting 8 from four times that number. Find that number.
Answer:
11
Step-by-step explanation:
Let the number be x
2x + 14 = 4x - 8 Add 8 to both sides
2x + 14 + 8 = 4x Combine
2x + 22 = 4x Subtract 2x
22 = 2x Divide by 2
11 = x
Plsss help asap plsssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss
Answer:
The answer is the last one, (X^2-2)/3!
Step-by-step explanation:
To get the inverse of a function, you switch the variables and solve for y. Doing this produces the last choice.
Find the missing value can someone help me get this
Answer:
-3
Step-by-step explanation:
-5 = -8 - (- 3)
Narasimha, Madhu and Pavan started a business by investing Rs. 120,000, Rs. 135,000 and Rs. 150,000 respectively. Find the share of Pavan, out of an annual profit of Rs. 56,700.
Answer:
1.
= Here,
Narasimha invest = 120,000
Madhu 135,000
pavan =
Write an expression for the area of the square below.
4x + 2
A. 8x2 + 16x + 4
B. 16x2 + 16x + 4
C. 8x + 4
D. 16x2 + 6x + 4
Help
Area = Side^2
Area =( 4x + 2 )^2
Area = (4x)^2 + 2(4x)(2) + (2)^2
Area = 16x^2 + 16x + 4
Thus the correct answer is option B .
The area of the shaded sector of circle H is 32.
16
H
What is the area of the unshaded sector?
967
O 2247
32871
O 34571
Answer:
B
Step-by-step explanation:
Area of shaded region + Area of unshaded region = Area of circle
Area of the unshaded sector=256*pi-32*pi=224*pi
Answer:
radius Is 16
total area becomes pi r ^ 2 = 16^2 pi = 256pi
remaining area becomes
256 pi - 32 pi = 224 pi option b
brainliest pls
What is the division? 9÷890
Answer:
98.89
Step-by-step explanation:
Answer: 9/890=0.01011235955
Step-by-step explanation:
evaluate the function
f (x) = -x + 3 when x = 5
pls help :(
Answer:
f(5) = -2
Step-by-step explanation:
f (x) = -x + 3
Let x = 5
f(5) = -5+3
f(5) = -2
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\text{f(x) = -x + 3}\\\huge\boxed{\rightarrow}\huge\text{ f(x) = -5 + 3}\\\huge\boxed{\rightarrow}\huge\text{ y = -5 + 3}\\\huge\boxed{\rightarrow}\text{ y = -2}\\\\\\\boxed{\boxed{\huge\text{Answer: \bf f(x) = -2}}}\huge\checkmark[/tex]
[tex]\huge\textsf{Good luck on your \& enjoy your day!}[/tex]
~[tex]\huge\boxed{\frak{Amphitrite1040:)}}[/tex]
Find the general solution for:-
[tex]sin\:x \:cos\: 3x+cos\:x\: sin\:3x=tan140[/tex]
~Please show your work
~Thank you!
Answer:
[tex] \rm \displaystyle x \approx \bigg \{ {59.3}^{ \circ} + \frac{n\pi}{2} , - {14.3}^{ \circ} + \frac{n\pi}{2} \bigg \}[/tex]
Step-by-step explanation:
we would like to solve the following trigonometric equation:
[tex] \rm \displaystyle \sin(x) \cos(3x) + \cos(x) \sin(3x) = \tan( {140}^{ \circ} ) [/tex]
the left hand side can be rewritten using angle sum indentity of sin which is given by:
[tex] \rm \displaystyle \sin( \alpha + \beta ) = \sin( \alpha ) \cos( \beta ) + \cos( \alpha ) \sin( \beta ) [/tex]
therefore Let
[tex] \alpha = x[/tex][tex] \beta = 3x[/tex]Thus substitute:
[tex] \rm \displaystyle \sin(x + 3x) = \tan( {140}^{ \circ} ) [/tex]
simplify addition:
[tex] \rm \displaystyle \sin(4x) = \tan( {140}^{ \circ} ) [/tex]
keep in mind that sin(t)=sin(π-t) saying that there're two equation to solve:
[tex] \begin{cases} \rm \displaystyle \sin(4x) = \tan( {140}^{ \circ} ) \\ \\ \displaystyle \sin(\pi - 4x) = \tan( {140}^{ \circ} ) \end{cases}[/tex]
take inverse trig and that yields:
[tex] \begin{cases} \rm \displaystyle 4x= { \sin}^{ - 1} ( \tan( {140}^{ \circ} ) ) \\ \\ \displaystyle \pi - 4x = { \sin}^{ - 1}( \tan( {140}^{ \circ} ) ) \end{cases}[/tex]
add π to both sides of the second equation and that yields:
[tex] \begin{cases} \rm \displaystyle 4x= { \sin}^{ - 1} ( \tan( {140}^{ \circ} ) ) \\ \\ \displaystyle - 4x = { \sin}^{ - 1}( \tan( {140}^{ \circ} ) ) + \pi\end{cases}[/tex]
sin function has a period of 2nπ thus add the period:
[tex] \begin{cases} \rm \displaystyle 4x= { \sin}^{ - 1} ( \tan( {140}^{ \circ} ) ) + 2n\pi\\ \\ \displaystyle - 4x = { \sin}^{ - 1}( \tan( {140}^{ \circ} ) ) + \pi + 2n\pi\end{cases}[/tex]
divide I equation by 4 and II by -4 which yields:
[tex] \begin{cases} \rm \displaystyle x= \frac{ { \sin}^{ - 1} ( \tan( {140}^{ \circ} ) ) }{4} + \frac{n\pi}{2} \\ \\ \displaystyle x = - \frac{{ \sin}^{ - 1}( \tan( {140}^{ \circ} ) ) + \pi}{4} - \frac{n\pi}{2} \end{cases}[/tex]
recall that,-½(nπ)=½(nπ) therefore,
[tex] \begin{cases} \rm \displaystyle x= \frac{ { \sin}^{ - 1} ( \tan( {140}^{ \circ} ) ) }{4} + \frac{n\pi}{2} \\ \\ \displaystyle x = - \frac{{ \sin}^{ - 1}( \tan( {140}^{ \circ} ) ) + \pi}{4} + \frac{n\pi}{2} \end{cases}[/tex]
by using a calculator we acquire:
[tex] \begin{cases} \rm \displaystyle x \approx - {14.3}^{ \circ} + \frac{n\pi}{2} \\ \\ \displaystyle x \approx {59.3}^{ \circ} + \frac{n\pi}{2} \end{cases}[/tex]
hence,
the general solution for: for the trig equation are
[tex] \rm \displaystyle x \approx \bigg \{ {59.3}^{ \circ} + \frac{n\pi}{2} , - {14.3}^{ \circ} + \frac{n\pi}{2} \bigg \}[/tex]
13
Simplify the following expression and evaluate for x=36
b
0.02(1.4x - 300)-0.2(2.4x+10)+0.552x
answer:
Answer:
0.028x-6-0.48x-2+0.552x
(0.028-0.48+0.552)x-6-2
0.1x-8
The simplified expression, when evaluated for x=36, is -4.4, when following expression and evaluate for x=36 b= 0.02(1.4x - 300)-0.2(2.4x+10)+0.552x
To simplify the expression and evaluate it for x=36, let's break it down step by step:
0.02(1.4x - 300) - 0.2(2.4x + 10) + 0.552x
First, let's simplify the terms within each set of parentheses:
0.02 * (1.4 * 36 - 300) - 0.2 * (2.4 * 36 + 10) + 0.552 * 36
Next, perform the multiplications and additions/subtractions within each set of parentheses:
0.02 * (50.4 - 300) - 0.2 * (86.4 + 10) + 0.552 * 36
0.02 * (-249.6) - 0.2 * (96.4) + 19.872
Now, evaluate the remaining multiplications:
-4.992 - 19.28 + 19.872
Finally, perform the additions and subtractions:
-4.992 - 19.28 + 19.872 = -4.4
Therefore, the simplified expression, when evaluated for x=36, is -4.4.
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Solve for q.
39 + 4 + 9 = -14
q= [?]
[tex]\\ \sf \longmapsto 39+4+q=-14[/tex]
Simplify left side[tex]\\ \sf \longmapsto q+43=-14[/tex]
Change side.[tex]\\ \sf \longmapsto q=-14-43[/tex]
[tex]\\ \sf \longmapsto q=-57[/tex]
Calculate the value of 3√216
by using prime
factors
Answer: 43,2
Step-by-step explanation:
[tex]\bf 3\sqrt{216 }=3\cdot 6\sqrt{6}=18\sqrt{6} \approx43.2 \\\\ \sqrt{216} =\sqrt{ 2^{3}\cdot 3^3}=\sqrt{2^2\cdot 3^2\cdot 3\cdot 2}=3\cdot 2\sqrt{3\cdot 2} =6\sqrt{6}[/tex]
Profit And Loss
1. Find the profit percent when 6 pens are sold at the cost price of 9 pens.
Answer stepwise
0.7% percent is the answer
What is the value of x?
Enter your answer in the box.
Answer:
27
Step-by-step explanation:
Triangle proportionality theorem: when you draw a line parallel to one side of a triangle, it'll intersect the other two sides of the triangle and divide them proportionally
[tex]\frac{26}{39}=\frac{18}{x}[/tex]
Cross multiply and you get 702=26x
x=27
Answer:
x=27
Step-by-step explanation:
-We can use the triangle proportionality theorem: if line parallel to a side of a triangle intersects the other two sides, then it divides those sides proportionally.
-we write the proportion and solve for x
[tex]\frac{39}{26} =\frac{x}{18}[/tex]
[tex]x= \frac{39*18}{26}[/tex]
x= 27
Guys please help me with this problem
Answer:
11. 5%
Step-by-step explanation:
1 + percent increase = 1.115
Percent increase = 1.115 - 1 = 0.115 = 11.5 /100 = 11.5 %
Answer:
Step-by-step explanation:
In the exponential form of an equation, the growth or decay rate is found inside the parenthesis. The standard form of an exponential equation is
[tex]y=a(1+r)^x[/tex] if it's growth, or
[tex]y=a(1-r)^x[/tex] if it's decay.
Looking at those equations, logically a growth equation is greater than 1, while a decay equation is less than 1. Obviously, our function is a growth.
To determine the rate of growth, we look closely at (1.115) inside the parenthesis. BECAUSE that is greater than 1, we KNOW it is growth, therefore, it follows the (1 + r) pattern. Let's break up our (1.115) so it models that pattern:
(1.115) --> (1 + .115) and since these are percentages in their decimal form, it follows that 1 is 100% and .115 is 11.5%. Our growth rate is 11.5%
what is the length of AC?
Answer:
The answer is 18 feet...
Step-by-step explanation:
C. 18ft is the answer