Answer:
a = 2, b = 0 , x = [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Given that x = 0 and x = 2 are zeros of p(x) , then
p(0) = 0 and p(2) = 0
p(0) = 2(0)³ - 5(0)² + a(0) + b = 0 , that is
0 - 0+ 0 + b = 0, then b = 0
p(2) = 2(2)³ - 5(2)² + 2a + b = 0 , that is
16 - 20 + 2a + 0 = 0
- 4 + 2a = 0 ( add 4 to both sides )
2a = 4 ( divide both sides by 2 )
a = 2
Then
p(x) = 2x³ - 5x² + 2x ← factor out x from each term
= x(2x² - 5x + 2)
= x(2x - 1)(x - 2)
To find zeros equate p(x) to zero
x(2x - 1)(x - 2) = 0
Equate each factor to zero and solve for x
x = 0
x - 2 = 0 ⇒ x = 2
These are the 2 zeros already known (given)
2x - 1 = 0 ⇒ 2x = 1 ⇒ x = [tex]\frac{1}{2}[/tex] ← third zero of p(x)
Given the function h(x) = x^2 + 10x + 32, determine the average rate of change
of the function over the interval 3 < x < 11.
================================================
Explanation:
Plug in x = 3 to get
h(x) = x^2 + 10x + 32
h(3) = 3^2 + 10*3 + 32
h(3) = 71
Repeat for x = 11
h(x) = x^2 + 10x + 32
h(11) = 11^2 + 10*11 + 32
h(11) = 263
Now use the average rate of change formula
m = average rate of change
m = ( h(b) - h(a) )/(b - a)
m = ( h(11) - h(3) )/(11 - 3)
m = (263 - 71)/(11 - 3)
m = 192/8
m = 24
In ΔRST, m∠R = 92° and m∠S = 71°. Which list has the sides of ΔRST in order from shortest to longest?
Answer:
RS, RT, ST
Step-by-step explanation:
We require the third angle in the triangle
∠ T = 180° - (92 + 71)° = 180° - 163° = 17°
The shortest side is opposite the smallest angle
∠ T = 17° → opposite side RS
The longest side is opposite the largest angle
∠ R = 92° → opposite side ST
Then sides from shortest to longest is
RS, RT, ST
4. Given the diagram below what is the length of RS or the distance across a body of water?
Answer:
62 ft
i know its a late answer but i just did the test
If the length of ST is 62 feet the length of RS or the distance across a body of water will also be 62 feet.
What is the congruent triangle?Congruent triangles are those that are exactly the same size and shape. Congruent is represented by the symbol ≅. When the three sides and three angles of one triangle match the dimensions of the three sides and three angles of another triangle, they are said to be congruent.
It is given that the length of s ST is 62 feet and PS = PQ.
The measurements of the sides and angles of two or more triangles determine their congruence. A triangle's size is determined by its three sides, and its shape is determined by its three angles. If the pairs of corresponding sides and angles of two triangles are equal, they are said to be congruent.
Since the one angle in both triangles is 90° and the two sides are equal the two triangles are equal.
The ratio of the sides is equal if the triangle is congruent. As a result,
PS / PQ = RS / ST
1 = RS / ST
RS = ST
RS = 62 feet
Thus, if the length of ST is 62 feet the length of RS or the distance across a body of water will also be 62 feet.
Learn more about the congruent triangle here:
brainly.com/question/12413243
#SPJ5
Please help!! 20 points
(-78) + 69 =
Answer:
-9
Step-by-step explanation:
Since the signs are different, subtract the two numbers and take the sign of the larger number
78 - 69
9
Since 78 is the larger number and it was negative
-9
Answer:
-9
Step-by-step explanation:
-78+69
=-9
happy to help
Someone help pleasee
Answer:
-80
Step-by-step explanation:
We can write the quadratic as
ax^2 + bx+c
4x^2 +8x+9
a=4 b = 8 c=9
The discriminant is
b^2 -4ac
8^2 - 4(4)(9)
64 - 144
-80
Answer:
-80
Step-by-step explanation:
The discriminant is the value under the radical in the quadratic formula. The part of the quadratic formula that is under the radical is [tex]\sqrt{b^2-4ac}[/tex]. So, plug in the needed values and solve for what is under the radical. The b-value is 8; this squared is 64. Then, plug in a and c, 4 and 9. Then multiply these by 4, 4*4*9=144. Finally subtract, 64-144=-80.
calculate w reasons the size of the unknown angles
Answer:
a= 75°
β= 30°
Step-by-step explanation:
α = 75° This is because triangle PQR isosceles. Thus two of its angles are equal and these two are angle α and the one labelled 75.
β = 30° This is because angles in a triangle sum up to 180°. We already know two of these angles. To find β you say 180 - ( 75 × 2)
The answer becomes 30°.
HOPE THIS HELPED
If each side of a cube is doubled, its volume?
If you double each side the volume is 8 times
Must click thanks and mark brainliest
Two consecutive even whole numbers have a product of 360. What is the smaller of the
two number?
Answer:
18
Step-by-step explanation:
To find this answer you would need to use the formula x(x+2) = 360 where x is an even number. This is the formula because any number plus 2 equals the next consecutive, even whole number. If we look at the factors of 360 we see the factors-
360: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, and 360.
If we look through all of the factors 18 and 20 are the only ones with a 2 number difference.
Next, if we plug 18 into the equation:
x(x+2) =360
18(18+2) = 360
324+36 = 360
360 = 360
Since the equation works, x = 18.
Write (25x^2 + 30x + 12) in the form (ax + b)^2 + c.
Answer:
25 x^2 + 30 x + 12
Parcelas
Plots
Parcelas
Figura geométrica
parabola
Formas alternativas
x (25 x + 30) + 12
(5 x + 3)^2 + 3
5 x (5 x + 6) + 12
Raíces complejas
x = -1/5 i (sqrt(3) + -3 i)
x = 1/5 i (sqrt(3) + 3 i)
Step-by-step explanation:
Best answer gets brainliest and 5 star
Answer:
d no.
Step-by-step explanation:
because in my my personal opinion the function shown on the graph has a smaller rate of change, but a higher starting point
Given the function g(x) = x^2 + 5x + 14, determine the average rate of change
of the function over the interval 1 < x < 7.
Answer:
13
Step-by-step explanation:
The average rate of change is
f(7) - f(1)
---------------
7-1
f(7) = 7^2 + 5*7 +14 = 49 +35 +14=98
f(1) = 1^2 +5(1)+14 = 1+5+14=20
98-20
--------
7-1
78/6
13
How much money will be in a bank account after 3 years if $9 is deposited at an interest rate of 5% compounded annually? Round to the nearest tenth.
Answer:
Step-by-step explanation:
$13.1
1. What property could you use to show that triangles ACT and ODG are congruent?
Answer:
SSS
Step-by-step explanation:
We do not know any of the angles, and we also do not know if the triangles are right triangles. Thus, SSS is the only option left. We know that all three sides are congruent anyway.
Answer:
SSS
Step-by-step explanation:
AC = OD
AT = OG
CT = DG
You have three congruent sides making ΔACT & ΔODG congruent by SSS.
2*cosx*(2x+30°) + √3=0
Answer: x ≈ 1.59688927, −1.60312387, −4.67045686, 4.69039614, 7.872914, −7.91513776, −10.89002194
Step-by-step explanation:
Solve for x by simplifying both sides of the equation, then isolating the variable.
Simplify 2*cosx*(2x+30°) + √3=0
Simplify each term.
Apply the distributive property.
2 cos ( x ) ( 2 x ) + 2 cos ( x ) * 30 ° + √ 3 = 0 Multiply 2 by 2 4 cos ( x ) x + 2 cos ( x ) *30 ° + √ 3 = 0 Multiply 30 °by 2 4 cos ( x ) x + 60 cos ( x ) + √ 3 = 0Reorder factors in 4 cos ( x ) x + 60 cos ( x ) + √34xcos(x)+60cos(x)+√3=0Graph each side of the equation. The solution is the x-value of the point of intersection. x ≈ 1.59688927 , − 1.60312387 , − 4.67045686 , 4.69039614 , 7.872914 , − 7.91513776 , − 10.89002194
Answer:
Step-by-step explanation:
please click thanks and mark brainliest if you like :)
Simplify.
4-3i/6-4i
A. 18-i/26
B. 15-3i/26
C. -4+3i
D. 3+2i/13
Answer:
A
Step-by-step explanation:
To simplify the expression multiply the numerator and denominator by the conjugate of the denominator.
Note that i² = - 1
The conjugate of 6 - 4i is 6 + 4i , then
= [tex]\frac{(4-3i)(6+4i)}{(6-4i)(6+4i)}[/tex] ← expand numerator./ denominator using FOIL
= [tex]\frac{24+16i-18i-12i^2}{36+24i-24i-16i^2}[/tex]
= [tex]\frac{24-2i+12}{36+16}[/tex]
= [tex]\frac{36-2i}{52}[/tex]
= [tex]\frac{2(18-i)}{52}[/tex]
= [tex]\frac{18-i}{26}[/tex] → A
find the surface area. Leave your answer in terms of pi
Answer:
210*pi
Step-by-step explanation:
Surface area=2*pi*r*(r+h)
=2*pi*5*(21)=210*pi
What’s the value of each variable?
Answer:
Step-by-step explanation:
(A). y = 110 , z = 63
If p(x) = 3x³-7x-4 and g(n)-4x^3-7x^2- 2x are polynomials then find the degree of p(x)+q (x)
Answer:
3.
Step-by-step explanation:
p(x) + q(x)
= -x^3 - 7x^2 - 9x - 4
- whose degree is 3 ( the highest index is 3)
Which equation is the inverse of 5y+4= (x+37 + 2?
O y=z28++
O y = 32, 5x + 7 /
054-4--4x+3)2-1
O y=-32, 5x + 1 / 3
ASAP please!!!
Answer:
It's option D. -3 ± √5x+7/2
See the images below for step by step explanation. I also included a graph for better understanding of the inverse.
Please help with this question!
9514 1404 393
Answer:
about 0.31°
Step-by-step explanation:
First of all, solve for sin(2θ):
3000 = (1/32)(3000^2)sin(2θ)
32(3000)/3000^2 = sin(2θ)
4/375 = sin(2θ) . . . . . . . simplify
Now, we find the corresponding angle:
2θ = arcsin(4/375) ≈ 0.61117°
θ ≈ 0.30558° ≈ 0.31°
The angle of elevation must be about 0.31°.
what is the decimal expansion of -11/15
Answer:
−0.73333333333333
Step-by-step explanation:
This is the decimal form of -11/15
LCM of two even number is 220, find their sum
Answer:
Two consecutive even terms and LCM = 180
Let’s assume the two terms:
1st term : 2x
2nd term : 2x + 2
There is a rule which states that
If ‘a’ and ‘b’ are two numbers, then their product is equal to the product of their LCM and HCF.
i.e,
a∗b=HCF∗LCM - (i)
We can logically say that the HCF of any two consecutive even numbers is always equal to ‘2’ provided that the smallest no. is at least ‘2’.
i.e.,
HCF of ‘2x’ and ‘2x + 2’ is ‘2’ - (ii)
Therefore,
from (i) and (ii),
2x∗(2x+2)= HCF * LCM
2x∗(2x+2)=2∗180
x∗(2x+2)=180
2x2+2x−180=0
Solving the quadratic equation we get,
x=9,−10 (we discard -10 since it is negative)
Therefore, the numbers are
2∗9=18 (1st no.)
2∗9+2=18+2=20 (2nd no.)
Answer : 18,20
Step-by-step explanation:
What must be added to each term of the ratio 2:5 so that it maay be equal to 5:6
Please give explanation
9514 1404 393
Answer:
13
Step-by-step explanation:
Let n represent that number.
(2 +n)/(5 +n) = 5/6 . . . . . . . . n is added to numerator and denominator
6(2 +n) = 5(5 +n) . . . . . . . . . multiply by 5(5+n)
12 +6n = 25 +5n . . . . . . . . . eliminate parentheses
n = 13 . . . . . . . . . . . subtract 5n+12
Adding 13 to each term will give 5/6.
__
Check
(2 +13)/(5 +13) = 15/18 = (3·5)/(3·6) = 5/6
_____
Alternate solution
The difference of denominator and numerator in 2/5 is 5-2 = 3. The difference of denominator and numerator in 5/6 is 6-5 = 1. In order to make the latter difference 3, we must have (3/3)(5/6) = 15/18. We can get 15/18 from 2/5 by adding 13 to numerator and denominator.
answer for brainiest
Answer:
Hello
answer :B and C
Step-by-step explanation:
√25=5 is an integer
b) is not an integer
c) is not an integer=0.75
d) is an integer
Find the length of the third side. If necessary, round to the nearest tenth.
15
20
Submit Answer
Answer:
attempt 1 out of 2
PLS HELP ASAP
Answer:
It's 13.2
Step-by-step explanation:
From pythogras theorem:
[tex]{ \bf{ {a}^{2} = {b}^{2} + {c}^{2} }}[/tex]
[tex] = \sqrt{ {20}^{2} - {15}^{2} } \\ = \sqrt{175} \\ = 13.2[/tex]
Is this a function or no ?
32% of 300 is what number?
Answer: 96
Step-by-step explanation:
This equation helps
X / 100 = is / of
32/100 = X / 300 (cross multiplication)
32 times 300, divided by 100
= 96
Answer:
96
Step-by-step explanation:
every percent is out of hundred so (32 * 300)/100 = 96
If you flip three fair coins, what is the probability that you'll get a tail on the first flip, a head on the second flip, and another tail on the third flip?
Please explain,... I'll give you Brainliest if you Explain,... thanks
Answer:
1/8 of a chance to flip 3 coins and get that exact combination in that order
Explanation:
a coin has 2 sides, heads and tails, with an equal chance to land on each of them. 1/2 chance to get tails on the first flip x 1/2 chance to get heads on the second flip x 1/2 chance to get tails on the third flip. 1/2 x 1/2 x 1/2 = 1/8.
A geometric series has a common ratio of (-2) and the first term is 3.
Show that the sum of the first eight positive terms of the series is 65 535.
Answer:
see explanation
Step-by-step explanation:
The sum to n terms of a geometric series is
[tex]S_{n}[/tex] = [tex]\frac{a_{1}(r^{n}-1) }{r-1}[/tex]
where a₁ is the first term and r the common ratio
Given a₁ = 3 and r = - 2 , then
3 × - 2 = - 6
- 6 × -2 = 12
12 × - 2 = - 24
- 24 × - 2 = 48
48 × - 2 = - 96
- 96 × - 2 = 192
The positive terms are in a geometric progression
3, 12, 48, 192, ....
with a₁ = 3 and r = 12 ÷ 3 = 48 ÷ 12 = 4 , then
S₈ = [tex]\frac{3(4^{8}-1) }{4-1}[/tex] = [tex]\frac{3(65536-1)}{3}[/tex] = 65536 - 1 = 65535
help me please!!!!!!!!
Answer:
BC = 29.4
Step-by-step explanation:
30² = 20² + BC² -2•20•BC•cos(108)
900 = 400 +BC² -12.4•BC
900 -400 = BC² -12.4•BC
BC² -12.4•BC -500 = 0
Solve the equation using Bhaskara and you'll find two possible values for BC, which are:
BC = -17 and BC = 29.4
A negative number doesn't make sense because it is a side of a triangle, so we choose BC = 29.4
