We have [tex]h(p)=p^2+2p[/tex] and [tex]h(p)=3[/tex] which means we can equate:
[tex]p^2+2p=3[/tex].
Subtract 3 from both sides:
[tex]p^2+2p-3=0[/tex].
Then solve for p:
[tex]p^2+2p-3=0[/tex].
[tex](p-1)(p+3)=0[/tex].
So the product of two factors (p-1) and (p+3) is 0 which means at least one of the factors must be 0:
[tex]p-1=0\implies p_1=1[/tex].
Or
[tex]p+3=0\implies p_2=-3[/tex].
Hope this helps.
(- 6x + 7) + (2x - 6) = - 4x + 1
Answer:
Step-by-step explanation:
-4x + 1 = -4x + 1
1 = 1
infinitely many solutions
Vector a = 4i + 5j
Vector b = 3i + 6j
Find the dot product.
Step-by-step explanation:
a · b = (4)(3) + (5)(6)
a · b = 12 + 30
a · b = 42
Answer:
42
Step-by-step explanation:
a*b = 4*3 + 5*6 = 12 + 30 ( where i*i = j*j = 1)
∴ a*b = 42
Sara and Jenny can both do flips in the air. The ratio of the number of flips Sara can
do to the number of flips Jenny can do is 3:8. Jenny can do 120 more flips than Sara.
If Sara increases the number of her flips by 3 and Jenny decreases the number of her
flips by 12, what will be the new ratio of the number of flips Sara can do to the
number of flips Jenny can do?
Answer:
The ratio will be 48/109
Step-by-step explanation:
Write 5.42 as a mixed number in simplest form.
5.42 =
Answer: 5 21/50
Step-by-step explanation: 5.42 = 271/50 = 521/50 as a fraction
Find the equation of the line perpendicular to y=2x-6 that passes through the point (1,5). If possible, write the equation in slope-intercept form.
Answer:
y = - [tex]\frac{1}{2}[/tex] x + [tex]\frac{11}{2}[/tex]
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 2x - 6 ← is in slope- intercept form
with slope m = 2
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{2}[/tex] , thus
y = - [tex]\frac{1}{2}[/tex] x + c ← is the partial equation
To find c substitute (1, 5) into the partial equation
5 = - [tex]\frac{1}{2}[/tex] + c ⇒ c = 5 + [tex]\frac{1}{2}[/tex] = [tex]\frac{11}{2}[/tex]
y = - [tex]\frac{1}{2}[/tex] x + [tex]\frac{11}{2}[/tex] ← equation of perpendicular line
A book shelf is 1 m wide. Joe wants to place a set of books across the shelf. He has 20 books. Each book is 5.2 cm wide. Will he have enough space for all the books?
Answer:
Only 19 books
Step-by-step explanation:
1m=100cm
1 book attains 5.2cm
x books attain 100cm
Do cross multiplication and then u will get answer as 19.23
books can't be in decimals
So answer is 19 books
how many numbers lie between 101 the square and 102 the square
Answer:
203
Step-by-step explanation:
Square of 101 = 101^2= 10201
Square of 102 = 102 ^2=10404
No. of numbers between both of them =10404-10201=203
Answer:
203
Step-by-step explanation:
✓101 kare = 10.201
✓102 kare = 10.404
✓ 10.404- 10.201 = 203
#Başarılar
#Türkiye
(3x ^3 + 4x^2)+(3x3-4x^2-9x)=
Answer:=6x3−9c
Step-by-step explanation:
3x3+4x2+3x3−4x2−9c
=3x3+4x2+3x3+−4x2+−9c
Combine Like Terms:
=3x3+4x2+3x3+−4x2+−9c
=(3x3+3x3)+(4x2+−4x2)+(−9c)
=6x3+−9c
Find the 7th term in the
sequence
-1, -3, -9,...
Answer:
The answer is 729
Step-by-step explanation:
to get the next term, the sequence multiples the previous number by -3
1 * -3 = -3
-3 * -3 = 9
and so on.
To get the 7th term:
-27 * -3 = 81 (5th term)
81 * -3 = -243 (6th)
-243 * -3 = 729 (7th)
Answer:
The seventh term in the sequence is -729.
Step-by-step explanation:
Notice that the sequence is not increasing linearly. Therefore, this is a geometric sequence.
Recall that the explicit formula for a geometric sequence is given by:
[tex]x_n=a(r)^{n-1}[/tex]
Where a is the first term, r is the common ratio, and n denotes the nth term.
From the sequence, we can see that our first term a is -1.
Because each term is thrice the previous, our common ratio r is 3.
By substitution:
[tex]x_n=-(3)^{n-1}[/tex]
Hence, the seventh term is:
[tex]\displaystyle \begin{aligned} x_7 & = -(3)^{(7)-1} \\ \\ & = -(3)^{6} \\ \\ & = -729\end{aligned}[/tex]
In conclusion, the seventh term is -729.
A collection of nickels,dimes,and quarters consist of 9 coins with a total of $1.20. If the number of dimes is equal to the number of nickels, find the number of each type of coins.
Answer:
129
Step-by-step explanation:
120 +9 =129
because it is total and total means add
12. Write the first five terms of two different sequences that have 10 as the
second term. Describe the pattern in each of your sequences.
Answer:
a) The arithmetic sequence with common difference 2 that has 8 as the first term.
b) The arithmetic sequence of common difference -5 and first term 15.
Step-by-step explanation:
Let's use for example the arithmetic sequence with common difference 2 that has 8 as the first term. Then the first two terms of this sequence are:
8, and (8+2) = 10 Therefore the second term is 10.
Another arithmetic sequence of common difference -5 and first term 15. The firs two terms of this sequence are:
15, and (15 - 5) = 10. Therefore again a 10 as second term.
Consider a simple clock.
A. Find the measure of the angle swept by the hour hand between noon and 9:55 pm
B. Find the exact angle between the minute and hour hands at 1:25 pm
Answer:
A. 280degree
B. 137degree
When solving this problem, what is the first step you would need to do? 3 (4x - 5) = 10 Add 5 Divide by 4 Distribute the 3 Subtract 4x - 5
Answer:
Distribute the 3
Step-by-step explanation:
order of operations mate
Find the missing variable and indicated angle measure. pls help lol
Answer:
see below (I hope this helps!)
Step-by-step explanation:
∠VZY and ∠VXW form a linear pair and are supplementary, and since m∠VZY = 90°, m∠VXW = 180 - 90 = 90°. Since m∠WXU + m∠UXV = ∠VXW, we can write the following equation:
44 + 5x - 4 = 90
5x + 40 = 90
5x = 50
x = 10°
Therefore, m∠UXV = 5 * 10 - 4 = 46°
Answer:
x = 10 m(UXV)=46°
Step-by-step explanation:
m(UXV) + m(UXW) = 90° because m(VXY)= 90°
m(UXW) = 44°
m(UXV) + 44° = 90°
m(UXV) = 46°
5x - 4 = 46°
5x = 50
5x/5 = 50/5
x = 10
Hope this helps ^-^
solve
10a -7 = 21 - ба
Answer:
A=1.75
Step-by-step explanation:
[tex]10a + 6a = 21 + 7 \\ 16a = 28 \\ divide \: both \: sides \: by \: 16 \\ a = 1.75 \: or 1 \ \frac{3}{4} [/tex]
Answer:
a = 7/4
Step-by-step explanation:
10a -7 = 21 - 6а
Add 6a to each side
10a+6a -7 = 21 - 6а+6a
16a -7 = 21
Add 7 to each side
16a+7-7=21+7
16a = 28
Divide each side by 16
16a/16 = 28/16
a = 7/4
20x4=10
30x13=12
10x12=3
40x11=
Answer:
440
Step-by-step explanation:
I’d rather draw a map than give someone Verbal directions true or false
Answer:
True because there would be more understanding
Step-by-step explanation:
Answer:
FALSE
Step-by-step explanation:
Drawing map takes a while but verbal directions are quite simple and easy to understand
Hope it helps!
PLEASE HELP ME SOLVE THIS QUESTION(PLS CHECK IMAGE)
Type the correct answer in each box. Round your answers to two decimal places. Find the average rate of change of f(x) = log2(3x − 6) on [3, 4], [4, 5], and [5, 6].
Answer:
on [3, 4] = 0.30
on [4, 5] = 0.18
on [5, 6] = 0.12
Step-by-step explanation:
The average rate of change f, of a function f(x) on an interval [a, b] is given by;
[tex]f = \frac{f(b) - f(a)}{b - a}[/tex] -------------(i)
In our case,
f(x) = log 2(3x - 6)
Now let's get the average rate of change of f(x) on;
(i) [3, 4]
Here, a = 3 and b = 4
f(a) = f(3) [This is f(x) at x = 3]
=> f(3) = log[2(3(3) - 6)]
=> f(3) = log[2(9 - 6)]
=> f(3) = log[2(3)]
=> f(3) = log[6]
Also,
f(b) = f(4) [This is f(x) at x = 4]
=> f(4) = log[2(3(4) - 6)]
=> f(4) = log[2(12 - 6)]
=> f(4) = log[2(6)]
=> f(4) = log[12]
Now substitute the values of a, b, f(a) and f(b) into equation (i) as follows;
[tex]f = \frac{log 12 - log 6}{4 - 3}[/tex] [Remember that log m - log n = log (m / n)]
[tex]f = \frac{log (12 / 6)}{4 - 3}[/tex]
[tex]f = \frac{log (2)}{1}[/tex]
f = log 2 = 0.3010
f = 0.30 [to two decimal places]
∴ The average rate of change on [3, 4] = 0.30
(ii) [4, 5]
Here, a = 4 and b = 5
f(a) = f(4) [This is f(x) at x = 4]
=> f(4) = log[2(3(4) - 6)]
=> f(4) = log[2(12 - 6)]
=> f(4) = log[2(6)]
=> f(4) = log[12]
Also,
f(b) = f(5) [This is f(x) at x = 5]
=> f(5) = log[2(3(5) - 6)]
=> f(5) = log[2(15 - 6)]
=> f(5) = log[2(9)]
=> f(5) = log[18]
Now substitute the values of a, b, f(a) and f(b) into equation (i) as follows;
[tex]f = \frac{log 18 - log 12}{5 - 4}[/tex] [Remember that log m - log n = log (m / n)]
[tex]f = \frac{log (18 / 12)}{5 - 4}[/tex]
[tex]f = \frac{log (1.5)}{1}[/tex]
f = log 1.5 = 0.176
f = 0.18 [to two decimal places]
∴ The average rate of change on [4, 5] = 0.18
(iii) [5, 6]
Here, a = 5 and b = 6
f(a) = f(5) [This is f(x) at x = 5]
=> f(5) = log[2(3(5) - 6)]
=> f(5) = log[2(15 - 6)]
=> f(5) = log[2(9)]
=> f(5) = log[18]
Also,
f(b) = f(6) [This is f(x) at x = 6]
=> f(6) = log[2(3(6) - 6)]
=> f(6) = log[2(18 - 6)]
=> f(6) = log[2(12)]
=> f(6) = log[24]
Now substitute the values of a, b, f(a) and f(b) into equation (i) as follows;
[tex]f = \frac{log 24 - log 18}{6 - 5}[/tex] [Remember that log m - log n = log (m / n)]
[tex]f = \frac{log (24 / 18)}{6 - 5}[/tex]
[tex]f = \frac{log (1.33)}{1}[/tex]
f = log 1.33 = 0.124
f = 0.12 [to two decimal places]
∴ The average rate of change on [5, 6] = 0.12
Answer:CORRECT ANSWER ON PLATO
[3,4]= 1
[4,5]=0.59
[5,6]= 0.41
Defining Terms
Warm-Up
Active
Reviewing Undefinable Terms
The intersection of plane R and plane P is
R
H
Point is not on plane P.
E and 8 intersect at point
P
Intro
Answers: line DB
H
D
HELP ASAP,,,,,,,,,,,,,,,
Answer:
3. it should be positive 3.5
4. (-2,4); (4,2); (6,-9)
Step-by-step explanation:
A school has 1500 students. Given that 3% of them were late for school on a particular day, find the no of students who were punctual for school
Answer:
1455
Step-by-step explanation:
0.03% x 1500 = 45
therefore, 45 students were late
1500 - 45 = 1455 punctual
my hw write find an equation of the line passing through (-2,3) and (4,-5) I have to write the equation in slope-intercept form I need help
Answer:
The line passing through the given points is:
[tex]y=-\frac{4}{3}x+\frac{1}{3}[/tex]
in its slope-intercept form
Step-by-step explanation:
Start by finding the slope of the segment that joins the two given points using the slope formula:
[tex]slope=\frac{y_2-y_1}{x_2-x_1}[/tex]
which for our case renders:
[tex]slope=\frac{3-(-5)}{-2-4}=\frac{8}{-6} =-\frac{4}{3}[/tex]
Now we can find the y-intercept by using any one of the given points in the general slope-intercept form of a line with this slope:
[tex]y=-\frac{4}{3} x+b\\3=-\frac{4}{3} (-2)+b\\3=\frac{8}{3}+b\\b=3-\frac{8}{3} \\b=\frac{9-8}{3} \\b=\frac{1}{3}[/tex]
Therefore, the equation of the line becomes:
[tex]y=-\frac{4}{3}x+\frac{1}{3}[/tex]
Mrs. Kleim bought 5 boxes of 15 pencils to give to her students. If she has 26 students in her class, how many pencils can she give each student? How many pencils will she have left over?
Answer:2
Step-by-step explanation: 15x5=75
75/26=2.886
miranda made some cupcakes for the school bake sale. Of the cupcakes 1/2 are choclate and 1/2 are strawberry. Of the strawberry cupcakes, 1/3 are frosted with vanilla frosting, and the rest are frosted with choclate frosting. What portion of the cupcakes are strawberry with chocalate frosting?
Answer:
2/3
Step-by-step explanation:
3/3 = 1 whole
3/3 - 1/3 = 2/3
What is the area of the parallelogram?
Answer:
A = 60 cm^2
Step-by-step explanation:
The area of a parallelogram is
A = bh
A = 14*5
A = 60 cm^2
[tex] area \: of \: parallelogram \: = \: base \times height[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: a \: \: \: \: \: \: \: \: \: \: \: \: = \: \: \: \: \: \: \: \: \: \: \: 14cm \times 5cm[/tex]
[tex]a \: \: \: \: \: \: \: \: \: \: \: \: \: = \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 70 {cm}^{2} [/tex]
Solve the following equations
(a) tydt + (t + 1)dy = 0,
(b) y dy dt + t = 1,
(c) ty0 + y = y 2 , with the initial condition, y(1) = 1 2
Answer:
A) In y = - [ x-In (x+1) ] + c
B) [tex]\frac{y^2}{2} = t - \frac{t^2}{2} + c[/tex]
Step-by-step explanation:
A) tydt + ( t + 1 ) dy = 0
dy/y = - ( [tex]\frac{tdt}{t+1}[/tex] ) we have to integrate both sides of the equation
In y = - [ x- In (x +1) ] + c
B) y dy/dt + t = 1
we can express the equation as :
y dy = ( 1 - t ) dt
when we integrate the equation we have
[tex]\frac{y^2}{2} = t - \frac{t^2}{2} + c[/tex]
What’s the measure of x for the for each figure?
Answer:
a)73
b)27
c)58
d)70
How to calculate the value of i=?
Answer:
0.200
Step-by-step explanation:
∑ₓ₌₁⁴⁰ (1 + i)⁻ˣ = 5
∑ₓ₌₁⁴⁰ ((1 + i)⁻¹)ˣ = 5
This is a geometric series. The sum of the first n terms of a geometric series is:
S = a₁ (1 − rⁿ) / (1 − r)
where a₁ is the first term and r is the common ratio.
Here, a₁ = (1 + i)⁻¹, r = (1 + i)⁻¹, and n = 40. For simplicity, let's write both a₁ and r in terms of r. So a₁ = r and r = r.
5 = r (1 − r⁴⁰) / (1 − r)
5 (1 − r) = r (1 − r⁴⁰)
5 − 5r = r − r⁴¹
r⁴¹ − 6r + 5 = 0
Solving with a calculator, r ≈ 0.8334.
Therefore:
(1 + i)⁻¹ = 0.8334
1 + i = 1.200
i = 0.200
State the domain and the range of each relation. Then determine whether the relation is a function. Write yes or no. {(2,7), (3,10), (1,6)}