Answer:it’s distributive property
Step-by-step explanation:
f(x) = (x - 5) (2x - 7) (7x - 3) has zeros at x = -3.5, x = 3/7, and x = 5.
what is the sign of f on the interval 3/7 < x < 5 ?
1. f is always positive on the interval.
2. f is always negative on the interval.
3. f is sometimes positive and sometimes negative on the interval.
The function f(x) will be sometimes positive and sometimes negative on the interval so option (3) will be correct.
What is a function?
A certain kind of relationship called a function binds inputs to essentially one output.
In other terms, a function is a relationship between variables, and the type of relationship that exists between the variables defines the function, such as y = sinx and y = x +6.
Given function is
f(x) = (x - 5) (2x - 7) (7x - 3)
The term (x - 5) will be negative if x < 5.
The term (2x - 7) will be negative if x<3.5
Let's say if x = 4 then (x - 5) will be negative but (2x - 7) will be positive and hence overall value will be negative.
But if x = 3 then (x - 5) will be negative and (2x - 7) will also be negative and hence overall value will be negative
Hence the function f is sometimes positive and sometimes negative on the interval.
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Answer:
always negative the other guy was wrong because when you wrote 2x - 7 you meant 2x + 7 I know this because it’s on Khan Academy
Step-by-step explanation:
the sum of two numbers is 10, the sum of their squares is 58 determine the two numbers
Answer:
7 and 3
Step-by-step explanation:
Using the given information, one can form an equation. Let the first number be (x) and the second (y). For two equations based on the given information.
"the sum of two numbers is 10"
x + y = 10
" the sum of their squares is 58 determine"
[tex]x^2+y^2=58[/tex]
Solve for the equation for (x), then substitute the expression for (x) into the second equation. Simplify and solve to find the value of (y), and backsolve for the value of (x).
x + y =10
x = 10 -y
Substitute into the other equation:
[tex]x^2+y^2=58[/tex]
[tex](10-y)^2+y^2=58[/tex]
Simplify, remember the pattern for opening a binomial squared:
[tex](a - b)^2=a^2-2ab+b^2[/tex]
Apply this pattern here to simplify,
[tex](10-y)^2+y^2=58[/tex]
[tex]100-20y+y^2+y^2=58[/tex]
Simplify further,
[tex]100-20y+y^2+y^2=58[/tex]
[tex]2y^2-20y+100=58[/tex]
Inverse operations,
[tex]2y^2-20y+100=58[/tex]
[tex]2y^2-20y+42=0[/tex]
Factor, take out a common factor that all of the terms have. Then rewrite the quadratic trinomial as the product of two linear binomials. Remember the general pattern for factoring, add the inverse of the factors of the constant term to the variable, the sum of these factors must equal the coefficient of the linear term of the quadratic trinomial.
[tex]2y^2-20y+42=0[/tex]
[tex]2(y^2-10y+21)=0[/tex]
[tex]2(y-7)(y-3)=0[/tex]
Now use the zero product property to solve, the zero product property states that any number times zero equals zero.
[tex]2(y-7)(y-3)=0[/tex]
[tex]y = 7, y = 3[/tex]
Since the sum of (7) and (3) is (10), one has found the values of (y), it can be either (7) or (3), it doesn't matter which equals which.
Find the indicated side of the
right triangle.
45°
y
6
45°
Answer:
6
Step-by-step explanation:
tan 45 = 6 / x
1 = 6 / x
x = 6
Note :
Tan 45 value = 1
Answer:
x=6
Step-by-step explanation:
Since this is an isosceles triangle, the sides must be equal next to the base angles that are equal
x=6
Find cos A and cot B exactly if a=15 and b=11 , what will Cos A be and Cot B be?
Answer:
D. <15/√346>
Have a nice day! :)
help
1) find the value of x
2)find length of a side of the square
Answer:
x = 12 , s = 41
Step-by-step explanation:
The sides of a square are equal , so
4x - 7 = 3x + 5 ( subtract 3x from both sides )
x - 7 = 5 ( add 7 to both sides )
x = 12
Then
length of side s is
s = 4x - 7 = 4(12) - 7 = 48 - 7 = 41
Show that the line 4y = 5x-10 is perpendicular to the line 5y + 4x = 35
Step-by-step explanation:
concept :concept :When two lines are perpendicular, then the product of their slopes is equivalent to -1.concept :When two lines are perpendicular, then the product of their slopes is equivalent to -1.Equation of line in the form y = mx + c have m as slope of line and c as y-intercept.concept :When two lines are perpendicular, then the product of their slopes is equivalent to -1.Equation of line in the form y = mx + c have m as slope of line and c as y-intercept.Solution:concept :When two lines are perpendicular, then the product of their slopes is equivalent to -1.Equation of line in the form y = mx + c have m as slope of line and c as y-intercept.Solution:Given equations of lines areconcept :When two lines are perpendicular, then the product of their slopes is equivalent to -1.Equation of line in the form y = mx + c have m as slope of line and c as y-intercept.Solution:Given equations of lines are4y = 5x-10concept :When two lines are perpendicular, then the product of their slopes is equivalent to -1.Equation of line in the form y = mx + c have m as slope of line and c as y-intercept.Solution:Given equations of lines are4y = 5x-10or, y = (5/4)x(5/2). .....(1)5y + 4x = 355y + 4x = 35ory = (-4/5)x + 7. ......(2)Let m and n be the slope of equations i and ii, respectively.Let m and n be the slope of equations i and ii, respectively.Here, m = 5/4Let m and n be the slope of equations i and ii, respectively.Here, m = 5/4n= -4/5Let m and n be the slope of equations i and ii, respectively.Here, m = 5/4n= -4/5therefore, mx n = -1Let m and n be the slope of equations i and ii, respectively.Here, m = 5/4n= -4/5therefore, mx n = -1Hence, the lines are perpendicular.Verify the identity.
[tex]cot (x-\frac{\pi }{2})=-tan[/tex]
Answer:
True
Step-by-step explanation:
assuming that you meant to write
cot (x-π//2) = - tan x
the identity is TRUE because,
- you can graph cot (x-π//2) and - tan x, and see that the graphs overlap
OR
-you solve for cot (x-π/2)
useful to know is that :
cot x=1/tan x, tan x = sin x/cos x,
cos(x) =cos(-x), sin(-x) = -sin x,
cos(π/2 -x) =sin x, sin (π/2-x) =cos x
cot (x-π/2) = 1/tan (x-π/2) , yet tangent is sin x/cos x
cot (x-π/2) = cos (x-π/2) /sin (x-π/2) , factor -1
cot (x-π/2) = cos -(π/2-x) /sin -(π/2-x), use facts: cos(x) =cos(-x), sin(-x) = -sin x
cot (x-π/2) = cos (π/2-x) / -sin (π/2-x), use cos(π/2 -x) =sin x, sin (π/2-x) =cos x
cot (x-π/2) = sin x / -cos x , again sin x /cos x = tan x
cot (x-π/2) = -tan x
find the value of a) 4:12
Step-by-step explanation:
1:4 bcos u need to divide both sides by 4
Brianna's Bakery offers 3 flavors of bagels. Customers can choose from plain, cinnamon, or blueberry bagels. Yesterday, a customer ordered 144 bagels for a company meeting. The order was for twice as many blueberry bagels as plain bagels and 3 times as many cinnamon bagels as blueberry bagels.
How many cinnamon bagels did the customer order
Answer:
96 darling
Step-by-step explanation:
youre gonna take all the times this was teice as mich as that
like this:blueberrybagel twice as much 2
than plain bagels 1
cinnamonbags 3 times as much than
blueberry bagels 2×3= 6+
=9
EACH portion contains144:9=16 bagels
blueberry ones16×2=32
plain ones16×1=16
cinnamon ones 3×32=96
question 1…. help please
Answer: The number = 3 /4 or 4 / 3
Concept:
Here, we need to know the idea of a reciprocal.
Reciprocal is also called the multiplicative inverse. It is similar to turning the number upside down which is found by interchanging the numerator and denominator.
Number ⇒ Reciprocal = 1 / Number
Solve:
STEP ONE: Set up the equation
Let x = the number
Let 1 / x = the reciprocal
x + 1 / x = 25 / 12
STEP TWO: Multiply x on both sides
(x + 1 / x) · x = (25 / 12) · x
x² + 1 = 25x / 12
STEP THREE: Multiply 12 on both sides
(x² + 1) × 12 = (25x / 12) × 12
12x² + 12 = 25x
STEP FOUR: Subtract 25x on both sides
12x² + 12 - 25x = 25x - 25x
12x² - 25x + 12 = 0
STEP FIVE: Solve for the quadratic equation
(3x - 4) (4x - 3) = 0 ⇔ (Factorization of the equation)
(x - 4 / 3) (x - 3 / 4) = 0
x = 4 / 3 or x = 3 / 4
Hope this helps!! :)
Please let me know if you have any questions
Urgent ! Help me please
Answer:
B
Step-by-step explanation:
x -> x and y -> y+5
-1 -> - 1 and - 3 -> 2, so b is the correct answer.
Express -5/8 as a rational number with -24 as the denominator
Answer:
Step-by-step explanation:
Hello!
-5/8 = (-5*-3)/ (8*-3) = 15/-24
Can u please solve this
Answer:
522.5in^3
Step-by-step explanation:
4/3 ×3.14×5^3
4/3×3.14×125
1.33×3.14×125
4.18×125
522.5
Step-by-step explanation:
[tex]v = \frac{4}{3} \pi {r}^{3} \\ = \frac{4}{3} \times 3 \times {5}^{3} \\ = 4 \times 125 \\ = 500 {in}^{3} \\ thank \: you[/tex]
What is the initial value of the sequence?
1
2
3
8
Answer:
2
Step-by-step explanation:
The initial value is the y value of the first term shown ( when x=1)
y = 2 when x=1
The initial value is 2
Answer:
What is the initial value of the sequence?
1 2 <<<CORRECT 3 8
Step-by-step explanation:
Edge 2021
HELP!!!!!! so many points for this one!!!!!! x^2+y^2+4x-2y=-1
The equation of a circle in the xy-plane is shown above. What is the radius of the circle
A.2
B.3
C.4
D.9
Answer:
A. 2Step-by-step explanation:
Given circle:
x² + y² + 4x - 2y = -1Convert the equation into the standard form of (x - k)² + (y - h)² = r²:
x² + 4x + 4 + y² - 2y + 1 = -1 + 4 + 1(x + 2)² + (y - 1)² = 2²As per above:
r = 2Correct choice is A
A.2
Answer:
Solution given:
equation of a circle is:
x²+y²+4x-2y=-1
x²+y²+4x-2y+1=0
Comparing above equation with
ax²+by²+2gx+2fy+c=0
we get
a=1
b=1
g=2
f=-1
c=1
now
radius of a circle (r)=[tex]\sqrt{g²+f²-c}[/tex]
substituting value
r=[tex]\sqrt{2²+(-1)²-1}=2[/tex]
therefore radius of a circle is 2 units
Goalie is determined using the formula A = 60 a equals 60 left-parenthesis StartFraction g Over t EndFraction right-parenthesis.. In
Answer:
g = At/60
Step-by-step explanation:
A = 60(g/t)
To solve for 'g'
Open the bracket
A = 60g/t
Multiply both sides by t
At = 60g
Divide both sides by 60
At/60 = 60g/60
At/60 = g
A right triangle has a 12in base and an 8in height. What is the area of the triangle, in in??
Answer:
48
Step-by-step explanation:
using the formula 1/2 b*h
8*12=96
96/2=48
please anyone give me a answer i need it rn
Answer:
The first option is the right one.
Step-by-step explanation:
7/2. Rate is rise/run
7 is your rise
and 2 is your run
therefore, the answer is 7/2
what is the value of x
Answer: 24(option A) is the answer
exterior angle = 360/n
so, n = 15
then, 360/15 = 24
Someone Help! PLEASE!
Jesse is taking the tests needed to join the math team. His scores were 89, 92, 94. What's the lowest score he can get on the fourth test and still have a 90 average?
Answer:
The lowest score could be 85
Step-by-step explanation:
Let the lowest score = x
(x + 89 + 92 + 94)/4 = 90 Add the 3 scores you know
(x + 275)/4 = 90 Multiply both sides by 4
(x + 275) = 360 Remove the brackets.
x + 275 = 360 Subtract 275
x = 360 - 275
x = 85
First, find the length of each edge of the cube.
Then, find the volume.
since in a cube length, width and height are equal,
h = 6
w = 6
l = 6
and volume is 6³ = 216cm³
hope it helps :)
solve for x on the diagram below
Answer:
20 is the answer
Step-by-step explanation:
x+3x+10=90(right angle triangle)
4x=90-10
x=80/4
x=20°
Answer:
x = 20
Step-by-step explanation:
Based on the square indication at the corner of the angle, we can assume it's a right angle, so 90°. This means that x + 3x + 10 = 90. Solve it like any algebraic equation, isolating x. add x to 3x + 10, this would net you 4x + 10 = 90. Subtract 10 on both sides of the equation to further isolate x, meaning 4x = 80. Simplify this, dividing 4 on both sides, meaning x = 20.
I will mark as the brillianest plzzzzzzzzzzzzzzzzzzzz be helpful to me ......
c) If C.P. = Rs 750, loss percent = 8% find S.P.
Answer: SP is Rs 690
Step-by-step explanation:
CP= Rs 750
loss percent = 8%
so
loss = 8% of CP
= 8/100 * 750
= Rs 60
Loss = Rs 60
so
SP = Rs 750-60
= Rs 690
Answer:
here,
CP=750
loss%=8%
now,
SP= (100-L)×cp/100
= (100-8)×750/100
= (92×750)/100
= 69000/100
= 690
hence the SP of the article is Rs 690
any problem then comment it
hope this helped you ☺️
Find the missing side
Answer:
x = 14
[tex]h^2 = p^2 + b^2\\h^2 = 7^2 + 12^2\\x^2 = 49 + 144\\x^2 = 193\\so, x = 13.89\\so, x = 14[/tex]
An aircraft carrier can travel 450 km in the same time a container ship travels 300 km. If the aircraft carrier was travelling 5 km/h faster what was the speed of the container ship?
Answer:
10 Km/h
Step-by-step explanation:
Let the speed of the container ship be y
The speed of the aircraft = y + 5
Next, we shall determine the time taken by the aircraft to travel 450 Km. This can be obtained as follow:
Speed of aircraft (Sₐ) = y + 5
Distance travelled (dₐ) = 450 Km
Time for aircraft (tₐ) =?
Speed = distance / time
Sₐ = dₐ / tₐ
y + 5 = 450 / tₐ
Cross multiply
(y + 5) × tₐ = 450
Divide both side by (y + 5)
tₐ = 450 / (y + 5)
Finally, we shall determine the speed of the carrier. This can be obtained as follow:
Speed of container ship (S꜀) = y
Distance travelled (d꜀) = 300 Km
Time for container ship (t꜀) = Time for aircraft (tₐ)
Time for aircraft (tₐ) = 450 / (y + 5)
t꜀ = tₐ
t꜀ = 450 / (y + 5)
Speed = distance / time
S꜀ = d꜀ / t꜀
y = 300 ÷ 450 / (y + 5)
y = 300 × (y + 5) / 450
y = (300y + 1500) / 450
Cross multiply
450y = 300y + 1500
Collect like terms
450y – 300y = 1500
150y = 1500
Divide both side by 150
y = 1500 / 150
y = 10 Km/h
Thus, the speed of the container ship is 10 Km/h.
Please Help!!
To find the distance AB across a river, a distance BC of 786 m is laid off on one side of the river. It is found that B = 110.2° and C = 13.5°. Find AB. I don't understand how to do this but I know you need to use the Law of Sines, so please show work.
Answer:
~ 220.6
Step-by-step explanation:
sine rule : a/sinA =b/sinB = c/sinC
AB/sinC =BC/sinA
A = 180 - 110.2 - 13.5 = 56.3 degrees
AB/sin13.5 = 786/sin56.3
AB = 786sin13.5/sin56.3 = 220.5506
The distance across the river of AB is 220.55 m.
What is Law of Sines?Law of sines is defined as that ratio of the length of the sides of a triangle to the sine of the angle opposite to the these sides are equal.
That is, if a, b and c are sides opposite to the angles A, B and C respectively, then,
a / sin A = b / sin B = c / sin C
Given a triangle ABC.
We have,
∠B = 110.2° and ∠C = 13.5°
We know that the sum of the interior angles of a triangle is 180°.
∠A = 180 - (110.2 + 13.5) = 56.3°
Using the law of sines,
BC / Sin A = AB / Sin C
Substituting the values,
786 / sin (56.3°) = AB / sin (13.5°)
AB = (786 / sin (56.3°)) sin (13.5°)
= 220.55 m
Hence the distance is 220.55 m.
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SOMEONE HELP ME PLEASE
Daphne borrows $2500 from a financial institution that charges 6% annual interest, compounded monthly, for 2 years. The amount that Daphne will need to pay back at the end of the term is
Find the value of x.
Answer:
ᴀꜱ ᴡᴀʀᴍ ᴀꜱ ꜱᴜɴ
ᴀꜱ ꜱɪʟʟʏ ᴀꜱ ꜰᴜɴ
ᴀꜱ ᴄᴏʟᴅ ❄️ ᴀꜱ ᴀ ᴛʀᴇᴇ
ᴀꜱ ꜱᴄᴀʀʏ ᴀꜱ ꜱᴇᴀ
ᴀꜱ ʜᴏᴛ ᴀꜱ ꜰɪʀᴇ
ᴀꜱ ᴄᴏʟᴅ ᴀꜱ ɪᴄᴇ
ꜱᴡᴇᴇᴛ ᴀꜱ ꜱᴜɢᴀʀ
ᴀɴᴅ ᴇᴠᴇʀʏᴛʜɪɴɢ ɴɪᴄᴇ
ᴀꜱ ᴏʟᴅ ᴀꜱ ᴛɪᴍᴇ ⌛
ᴀꜱ ꜱᴛʀᴀɪɢʜᴛ ᴀꜱ ʟɪɴᴇ ➖
ᴀꜱ ʀᴏʏᴀʟ ᴀꜱ ᴀ ᴀɴɢᴇʟ☺️
ᴀꜱ ʙᴜᴢᴢᴇᴅ ᴀꜱ ʙᴇᴇ
ᴀꜱ ꜱᴛᴇᴀʟᴛʜ ᴀꜱ ᴛɪɢᴇʀ
ꜱᴍᴏᴏᴛʜ ᴀꜱ ɢʟɪᴅᴇʀ
ᴘᴜʀᴇ ᴀꜱ ʜᴇᴀʀᴛ ❤️
ᴘᴜʀᴇ ᴀꜱ ɪ ᴡᴀɴɴᴀ ʙᴇ
Step-by-step explanation:
hehehehehe I'm xxxxxdSaniya........ Khan ❤️the perimeter of a rectangular plot of land whose length is (2x+5)m and width (x-10)m is 80m. Find the
i)value of x
ii)area
Answer:
P.=2(2x+5)+2(x-10)=80cm
6x-10=80
x=90/6=15cm
Area= L*W= 35*5=175 squared cm= 0.0175 squared m
