Answer:
(z+7)*(z+4)
Step-by-step explanation:
The first term is, z2 its coefficient is 1 .
The middle term is, +11z its coefficient is 11 .
The last term, "the constant", is +28
Step-1 : Multiply the coefficient of the first term by the constant 1 • 28 = 28
Step-2 : Find two factors of 28 whose sum equals the coefficient of the middle term, which is 11 .
-28 + -1 = -29
-14 + -2 = -16
-7 + -4 = -11
-4 + -7 = -11
-2 + -14 = -16
-1 + -28 = -29
1 + 28 = 29
2 + 14 = 16
4 + 7 = 11 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 4 and 7
z2 + 4z + 7z + 28
Step-4 : Add up the first 2 terms, pulling out like factors :
z • (z+4)
Add up the last 2 terms, pulling out common factors :
7 • (z+4)
Step-5 : Add up the four terms of step 4 :
(z+7) • (z+4)
Which is the desired factorization
Find the value of x
34) Find the inverse of y = 5x
You purchased a new car for $32,000. The value
of the car decreases by 12% each year. Which
function could be used to model the value of the
car V after years?
a. V(t)=32,000(1+0.12)'
b. V()=32,000(1 -0.12)'
c. V(t)=32,000(0.12)'
d. V(t)=32,000 - 0.12r
The function that could be used to model the value of the car V after years is V(t) = 32000(1 - 0.12)^t
How to determine the function?The given parameters are:
Initial value, a = 32000
Rate, r = 12% --- depreciation rate
Since the value of the function decreases with time, the equation of the exponential function would be:
V(t) = a(1 - r)^t
So, we have:
V(t) = 32000(1 - 12%)^t
Express as decimal
V(t) = 32000(1 - 0.12)^t
Hence, the function that could be used to model the value of the car V after years is V(t) = 32000(1 - 0.12)^t
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Review the steps of the proof of the identity
At which step was an error made?
sin (A-3) - COSA.
= A.
step 1
step 2
3п
sin
step 3
step 4
Step 1: = sinAcos
3 п
2
-
COSAsin
n ()
Step 2: = (sinA)(0) + COSA( - 1)
Step 3: = (sinA)(0) + (1) (COSA)
Step 4: = 0 + COSA
Step 5: Cos A
Answer:
step 2
and then also in step 3 compensating the error in step 2
Step-by-step explanation:
I think I just answered this for another post.
sin(a - b) = sin(a)cos(b) - cos(a)sin(b)
so, step 1 is correct :
sin(A - 3pi/2) = sin(A)cos(3pi/2) - cos(A)sin(3pi/2)
but step 2 suddenly and incorrectly switched that central "-" to a "+".
yes, sin(3pi/2) = -1, but that is still an explicit factor in step 2. so it was not used to flip the central operation from subtraction to addition, and therefore this change was a mistake.
then, in step 3, another error was made by just ignoring the "-" sign of "-1" and still keeping the central "+" operation. this error compensated for the error in step 2 bringing us back by pure chance to the right result.
Which of the following is equal to the rational expression below when x≠2 or
9?
4(x-2)
(x-2)(x-9)
The expression equivalent to the given expression is [tex]\frac{4}{x-9}[/tex]
Rational expressionsThis are expressions written as a ratio of two expressions. Given the rational expression
[tex]f(x) = \frac{4(x-2)}{(x-2)(x-9)}[/tex]
Since (x-2) is common in both numerator and denominator, they wil cancel out to have the function below;
[tex]f(x) = \frac{4(x-2)}{(x-2)(x-9)}=\frac{4}{x-9}[/tex]
Hence the expression equivalent to the given expression is [tex]\frac{4}{x-9}[/tex]
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Erin wants to invest $3,600.00 in a savings account that pays 4.42% simple interest. How long will it take for this investment to reach a value of $6,700.00?
Round your answer to the nearest tenth of a year.
It will take
years for the investment to reach a value of $6,700.00.
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$6700\\ P=\textit{original amount deposited}\dotfill & \$3600\\ r=rate\to 4.42\%\to \frac{4.42}{100}\dotfill &0.0442\\ t=years \end{cases} \\\\\\ 6700=3600[1+(0.0442)(t)]\implies \cfrac{6700}{3600}=1+0.0442t\implies \cfrac{67}{36}=1+0.0442t \\\\\\ \cfrac{67}{36}-1=0.0442t\implies \cfrac{31}{36}=0.0442t\implies \cfrac{\frac{31}{36}}{0.0442}=t\implies 19.5\approx t[/tex]
the ratio of boys:girls in a class is 4:5
A: what is the fraction of boys in the class
B: what is the fraction of girls in the class
Answer:
Answer: 4/9 of the class are boys and 5/9 of the class are girls.
Step-by-step explanation:
There are 9 nine students in total in the class since 4 + 5 = 9.
Input the amount of boys and girls there are in the class in the numerator and have 9 as the denominator. 4/9 of the class are boys and 5/9 of the class are girls.
--~Hope this helped~--
16. Hamster Heaven charges an annual fee of $20 plus $2.50 for each day of hamster
activities you attend. Hamster Fun World charges an annual fee of $35 plus $1 for each day
of hamster activities you attend. Write and solve a linear system using a method of your
choosing and explain which company you would use for your hamster and why. A graph is
included below if you would like to graph it. Make sure you identify your variables, check
your solution and write a sentence.
Answer:
hamster heaven
y=20+2.5x
hamster fun world
y=35+x
Step-by-step explanation:
by solving we get
x=10
y=45
by comparing the graph hamster fun world 8s cheaper on the long run
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Hurry and answer this please. Find the volume of the sphere use 3.14 for pi
Answer:
44.6cm³
Step-by-step explanation:
V=3/4×3.14×2.2³=44.6cm³
Answer:
Option 2) 44.6 cm³ os the correct answer.
Step-by-step explanation:
SOLUTION :
Here we have given that the radius of the sphere is 2.2 cm. We have to find the volume of sphere.
Finding the volume of sphere by substituting all the given values in the formula :
[tex]\quad{\longrightarrow{\sf{V_{(Sphere)} = \dfrac{4}{3}\pi{r}^{3}}}}[/tex]
V = volume π = 3.14 r = radius[tex]\quad{\longrightarrow{\sf{V_{(Sphere)} = \dfrac{4}{3}\pi{r}^{3}}}}[/tex]
[tex]\quad{\longrightarrow{\sf{V_{(Sphere)} = \dfrac{4}{3} \times 3.14 \times {(2.2)}^{3}}}}[/tex]
[tex]\quad{\longrightarrow{\sf{V_{(Sphere)} = \dfrac{4}{3} \times 3.14 \times 10.65}}}[/tex]
[tex]\quad{\longrightarrow{\sf{V_{(Sphere)} = \dfrac{4}{\cancel{3}} \times 3.14 \times \cancel{10.65}}}}[/tex]
[tex]\quad{\longrightarrow{\sf{V_{(Sphere)} = 4 \times 3.14 \times 3.55}}}[/tex]
[tex]\quad{\longrightarrow{\sf{V_{(Sphere)} = 12.56 \times 3.55}}}[/tex]
[tex]\quad{\longrightarrow{\sf{V_{(Sphere)} = 44.58 \: {cm}^{3}}}}[/tex]
[tex]\quad{\longrightarrow{\sf{\underline{\underline{\pink{V_{(Sphere)} \approx 44.6 \: {cm}^{3}}}}}}}[/tex]
Hence, the volume of sphere is 44.6 cm³.
————————————————simplify the expression
4(5+ -3x) +10
Answer:
30 - 12x or 6(5 - 2x)
Step-by-step explanation:
Given expression:
4[5 + (-3x)] + 10First, let us simplify the expression inside the parentheses;
⇒ 4[5 + (-3x)] + 10⇒ 4[5 - 3x] + 10Then, let us open the parentheses by simplifying the distributive property;
⇒ 4[5 - 3x] + 10⇒ 20 - 12x + 10Finally, let us simplify the expression by adding 10 to 20.
⇒ 20 - 12x + 10⇒ 30 - 12x[Optional] Factor the expression by putting the expression in parentheses.
⇒ 30 - 12x⇒ (30 - 12x)Since 6 is divisible to all the terms in the expression, we can divide 6 to all the terms in the expression and take "6" outside the parentheses.
⇒ 6(30/6 - 12x/6)⇒ 6(5 - 2x)Therefore, the simplified expression is 30 - 12x or 6(5 - 2x).
Which type of function is shown in the table
below?
Answer:
Not a function
Step-by-step explanation:
Since 2 different points have the same x-coordinte, the relation is not a function.
Suppose a rocket is launched from a platform. The function h(t) - 4.96 + 200€ + 25gives the rocket's
height, h, in meters, in terms of time, t, in seconds. The function h(t) is equivalent to -4.9(t- 20. 41) + 2,065.82
Answer:
See below
Step-by-step explanation:
Opens Downward ( due to the - coefficient of t^2 )
when t = 0 the height is = 25 meters
initial velocity = 200 m/s
Vertex = 20.41, 2065.82
Which expressions represent the volume of the composite figure (the shaded figure)? check all that apply. (7)(12)(10) – π(32)(10) one-third(7)(12)(10) – one-thirdπ(32)(10) one-third(7)(12)(10) one-thirdπ(32)(10) 280 – 30π 280 30π 840 – 90π
Answer:
esf
Step-by-step explanation:
Answer: b and d
Step-by-step explanation: right on edge
1. Suppose a circle is divided into congruent slices. Match each number of slices with
the resulting central angle measure of each slice.
A. 2.
1.45°
B.3
2. 60°
C.4
3. 72°
D.5
4. 120°
E. 6
5. 90°
F.8
6. 180°
Answer:
Step-by-step explanation:
congruent slices means all slices with same shape and angle
a circle has 360 (angle)
For 2, 180
For 3, 120
For 4, 90
For 5, 72
For 6, 60
For 8, 45
What is the area, in square centimeters, of the trapezoid below?
8.5 cm
7.5 cm
15.7 cm
Answer:
90.75 cm^2
Step-by-step explanation:
The area of a trapezoid is given by
A = 1/2 ( b1+b2) *h
where b1 and b2 are the lengths of the bases and h is the height
A = 1/2(8.5+ 15.7) * 7.5
1/2 (24.2) 7.5
90.75 cm^2
Express 160° in radian measure
Find the inverse of the function
PLEASE PLEASE HELP QUICKLY
Complete the ratio table to convert the units of time from hours to weeks or weeks to hours.
Hours
Weeks
168
1
1,008
5
The correct answers are 1008 hours are 6 weeks and 5 weeks are 840 hours.
What is the ratio?The ratio indicates how many times one number is to the other number.For example, if you have 4 chocolates and 2 cakes the ratio of the chocolates and the cake will be 2:1 which means that chocolate is 2 times then the cake.
It is given that 168 hours is equal to 1 week. we need to find 1008 hours has how many weeks and 5 weeks has how many hours.
1.) 1008 hours has how many weeks
168 hours = 1 week
1 hour = 1 / 168 weeks
1008 hours = 1008 / 168 = 6 weeks
So 1008 hours has 6 weeks
2.) 5 weeks has how many hours.
1 week = 168 hours
5 weeks = 5 x 168 hours
5 weeks = 840 hours
So 5 weeks will have 840 hours.
Therefore correct answers are 1008 hours are 6 weeks and 5 weeks are 840 hours.
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Answer:
hours weeks
168 1
1008 6
840 5
Step-by-step explanation:
can someone tell me how do I solve this. how is the result 2.40
we still have not learned log in school
Step-by-step explanation:
Properties used
logₐ a = 1log aᵇ = b log alog ab = log a + log bSee the steps below
- log (4*10⁻³) = - (log 4 + log 10⁻³) = (log 4 ≈ 0.6 rounded)- (0.6 - 3*log 10) = - (0.6 - 3*1) = - (0.6 - 3) = - (- 2.4) = 2.4Can someone check this screen shot out and help me pls?
Answer:
A
Step-by-step explanation:
positive, the longer she run, the longer she jump
You know that 3 pencils and 7 pens cost $24 with 3 pencils and 3 pens cost $12 how many dollars are 4 pencils and 5 pens worth?
Find the length of the arc of the circle.
Answer:
25.12 in
Step-by-step explanation:
In the given circle
radius (r) = 12 incentral angle [tex](\theta) = 120\degree[/tex]Formula for length of arc is given as: [tex] l=\frac{\theta}{360\degree}\times 2\pi r[/tex]Plugging the values of r and [tex]\theta[/tex] in the above equation, we find:[tex] l=\frac{120\degree}{360\degree}\times 2(3.14) (12)[/tex][tex]\implies l=\frac{1}{3}\times 2(3.14) (12)[/tex][tex]\implies\huge\red{ l=25.12\:in}[/tex]Solve the following equation for
G:2 (g-h) = b+4
If the equation 2(g - h) = b + 4 is solved for g. Then the value of g will be b/2 + h + 2.
What is the solution of the equation?A combination of equations solution is a collection of values x, y, z, etc. that enable all of the calculations to true at the same time.
The equation is given below.
2(g - h) = b + 4
Then solve the equation for the value of g. Then we have
2(g - h) = b + 4
g - h = b/2 + 2
g = h + b/2 + 2
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Are these ratios equivalent?
12 cards to 72 animals, 11 marbles to 66 marbles
HELP ASPA PLEASE I will give brainliest
A state uses a combination of three letters (A – Z) followed by three digits (0 – 9) for
their standard vehicle license plates. How many different standard license plates are
possible using a combination of three letters followed by three digits.
Answer:
2340
Step-by-step explanation:
fundamental counting principle
Select the fraction that is equivalent to one fifth. (2 points)
a
1/10
b
2/1
c
2/5
d
3/5
Answer:
none
Step-by-step explanation:
[tex]one \: fifth = \frac{1}{5} \\ from \: the \: options \: no \: fraction \: is \: equivalent \: to \: one \: fifth \: and \: non \: of \: the \: fracrions \: can \: be \: reduced \: to \: give \: one \: fifth \\ so \: the \: answer \: is \: none[/tex]
A radioactive compound with mass 470 grams decays at a rate of 3% per hour. Which
equation represents how many grams of the compound will remain after 6 hours?
Submit Answer
O C = 470(0.03)
O C = 470(0.7)
O C = 470(1 + 0.03)
C = 470(1 – 0.03)
After 6 hours the radioactive compound with mass 470 grams becomes 391.49 grams and the equation will be C is equal to 470(1-0.03)^6.
What is exponential decay?During exponential decay, a quantity falls slowly at first before rapidly decreasing. The exponential decay formula is used to calculate population decline and can also be used to calculate half-life.
We know the decay can be as:
[tex]\rm C = a(1-r)^t[/tex]
We have:
a = 470 grams
r = 3% = 0.03
t = 6 hours
[tex]\rm C = 470(1-0.03)^6[/tex]
C = 391.49 grams
Thus, after 6 hours the radioactive compound with mass 470 grams becomes 391.49 grams and the equation will be C is equal to 470(1-0.03)^6.
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Gloria says the two expressions;
1/3 (9x + 48) - 12x and -4(2x +4) are ecuivalent. Is she correct?
Explain how you know.
Answer:
She is incorrect
Step-by-step explanation:
[tex]\begin{aligned}\dfrac{1}{3}(9x+48)-12x & =\dfrac{9}{3}x+\dfrac{48}{3}-12x\\ & = 3x+16-12x\\& = 16-9x\end{aligned}[/tex]
[tex]\begin{aligned}-4(2x+4) & =(-4)2x+(-4)4\\& = -8x-16\end{aligned}[/tex]
As [tex]16-9x\neq -8x-16[/tex] then she is incorrect.
She is incorrect
a cylinder has a diameter or 4 ft and height of 7 ft use 3.14 for pi
Answer:
87.92ft^3
Step-by-step explanation:
Formula:
V= π*r^2 *h
V=π*2^2*7V=π*4*7V=12.56 *7V=87.92ft^3A cylinder, cone, and sphere are show below. The three figures have the same radius. If the radius is 3, what is each volume?
Answer:
cylinder = 27π
cone = 9π
sphere = 36π
Step-by-step explanation:
volume of a cylinder = πr²h where r = radius and h = height
height of cylinder (h) = 3 and radius (r) = 3
so volume = π(3)²3
==> simplify exponent
volume = π9(3)
==> multiply 9 and 3
volume of cylinder = 27π
Volume of a cone = πr²(h/3) where r = radius and h = height
height of cone (h) = 3 and radius (r) = 3
so volume = π(3)²(3/3)
==> simplify exponent
volume = π9(3/3)
==> divide 3 by 3
volume = π9(1)
==> multiply 9 and 1
volume of cone = 9π
volume of a sphere = 4/3πr³ where r = radius
radius = 3
so volume = 4/3π(3)³
==> simplify exponent
volume = 4/3π27
==> multiply 4/3 and 27
volume of sphere = 36π
