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Related Questions
I am majorly stuck lol
The area of a rectangle is given by the expression 8x3 + 26x2 + 31x + 15. If the width of the rectangle is 2x + 3, what is the expression that represents the length of the rectangle?
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Is this quadratic? If so what form is it?
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Answer:
Yes. Factored form.
Step-by-step explanation:
Answer:
yes, and it's in intercept form
Step-by-step explanation:
Hi there!
We are given the function f(x)=-2(x-4)(x+3)
A quadratic function is a function that has a degree of 2 (the highest exponent in the function is to the 2nd power)
There are 3 forms to write a quadratic function:
standard form, which is f(x)=ax²+bx+c, where a, b, and c are free coefficients (numbers)
vertex form, which is f(x)=a(x-h)²+k, where a is a free coefficient and (h,k) is the vertex
intercept form, which is f(x)=a(x-[tex]x_{1}[/tex])(x-[tex]x_{2}[/tex]), where a is a free coefficient and [tex]x_{1}[/tex] and [tex]x_{2}[/tex] are the x intercepts
You may notice that f(x)=-2(x-4)(x+3) is actually in intercept form; a is -2 and [tex]x_{1}[/tex] and [tex]x_{2}[/tex] are 4 and -3 respectively (remember: the formula for intercept form has -[tex]x_{1}[/tex] and -[tex]x_{2}[/tex], but the x intercepts are [tex]x_{1}[/tex] and [tex]x_{2}[/tex]. Therefore, the x intercepts should be the opposites of -[tex]x_{1}[/tex] and -[tex]x_{2}[/tex]).
If the formula is in intercept form, it should be quadratic.
However, if you want to be sure it's quadratic, you can expand the function.
f(x)=-2(x-4)(x+3)
first, multiply the binomials together using FOIL
(x-4)(x+3)
x²-x-12
now multiply x²-x-12 by -2
-2(x²-x-12)
do the distributive property
-2x²+2x+24
It's a quadratic function! The value of the highest exponent is 2 :)
Hope this helps!
Jane was baking cookies. She needed 1/3 cup sugar and 1 2/4 cups flour. How much more flour does she need than sugar?
(Common core)
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Answer:
1 and 1/6 cups more
Step-by-step explanation:
1/3 cup sugar
*1 2/4 cups flour = 6/4 cups flour
*assuming it’s 1 and 2/4 and not 12/4 =3
6/4 - 1/3 = (18-4)/ 12 = 14/ 12 = 1 and 1/6
A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 423 gram setting. Is there sufficient evidence at the 0.05 level that the bags are underfilled or overfilled
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NASA launches a rocket at t = 0 seconds. Its height, in meters above sea-level, as a function of time is given by h ( t ) = − 4.9 t 2 + 229 t + 346 . Assuming that the rocket will splash down into the ocean, at what time does splashdown occur?
How high above sea-level does the rocket get at its peak?
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Answer:
[tex] \displaystyle 1)48.2 \: \: \text{sec}[/tex]
[tex] \rm \displaystyle 2)3021.6 \: m[/tex]
Step-by-step explanation:
Question-1:so when flash down occurs the rocket will be in the ground in other words the elevation(height) from ground level will be 0 therefore,
to figure out the time of flash down we can set h(t) to 0 by doing so we obtain:
[tex] \displaystyle - 4.9 {t}^{2} + 229t + 346 = 0[/tex]
to solve the equation can consider the quadratic formula given by
[tex] \displaystyle x = \frac{ - b \pm \sqrt{ {b}^{2} - 4 ac} }{2a} [/tex]
so let our a,b and c be -4.9,229 and 346 Thus substitute:
[tex] \rm\displaystyle t = \frac{ - (229) \pm \sqrt{ {229}^{2} - 4.( - 4.9)(346)} }{2.( - 4.9)} [/tex]
remove parentheses:
[tex] \rm\displaystyle t = \frac{ - 229 \pm \sqrt{ {229}^{2} - 4.( - 4.9)(346)} }{2.( - 4.9)} [/tex]
simplify square:
[tex] \rm\displaystyle t = \frac{ - 229 \pm \sqrt{ 52441- 4( - 4.9)(346)} }{2.( - 4.9)} [/tex]
simplify multiplication:
[tex] \rm\displaystyle t = \frac{ - 229 \pm \sqrt{ 52441- 6781.6} }{ - 9.8} [/tex]
simplify Substraction:
[tex] \rm\displaystyle t = \frac{ - 229 \pm \sqrt{ 45659.4} }{ - 9.8} [/tex]
by simplifying we acquire:
[tex] \displaystyle t = 48.2 \: \: \: \text{and} \quad - 1.5[/tex]
since time can't be negative
[tex] \displaystyle t = 48.2 [/tex]
hence,
at 48.2 seconds splashdown occurs
Question-2:to figure out the maximum height we have to figure out the maximum Time first in that case the following formula can be considered
[tex] \displaystyle x _{ \text{max}} = \frac{ - b}{2a} [/tex]
let a and b be -4.9 and 229 respectively thus substitute:
[tex] \displaystyle t _{ \text{max}} = \frac{ - 229}{2( - 4.9)} [/tex]
simplify which yields:
[tex] \displaystyle t _{ \text{max}} = 23.4[/tex]
now plug in the maximum t to the function:
[tex] \rm \displaystyle h(23.4)- 4.9 {(23.4)}^{2} + 229(23.4)+ 346 [/tex]
simplify:
[tex] \rm \displaystyle h(23.4) = 3021.6[/tex]
hence,
about 3021.6 meters high above sea-level the rocket gets at its peak?
CAN SOMEONE HELP ME PLS
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How many feet are in 18 yards?
6 feet
30 feet
54 feet
216 feet
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Answer:
54 is the answer
have a great dayyyy
Answer:
there are 64 feet in18 yards
Step-by-step explanation:
1 yard equals 3 feet
Ricardo has a wooden board that measures 5 feet in length. How many 1/4 foot long pieces can Ricardo cut from the board
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Answer:
20 pieces of wood
Step-by-step explanation:
5 divided by 1/4: 20
another way to look at it is if there are 4 of these pieces in a foot, and there are 5 feet, 4 times 5 is also 20.
solve the literal equation for C. -3x+2c=-3
Answers
Step-by-step explanation:
I'm sorry I can't answer that but I know something so you can answer that. search Chrome quickmath all your problems, equations and more can be solved
Answer:
c = 3/2x + −3/2
Step-by-step explanation:
Let's solve for c
-3x+2c=-3
Step 1: Add 3x to both sides.
2c −3x + 3x = −3 + 3x
2c = 3x −3
Step 2: Divide both sides by 2.
2c = 3x−3
2 2
c = 3/2x + −3/2
Answer:
c = 3/2x + −3/2
Help me wit this rq…………..
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A Canadian study examined the pregnancy weight gain of underweight mothers, women who had been underweight before becoming pregnant. A Normal distribution with mean 36.6 lb and standard deviation 11.9 lb is a reasonable model for the distribution of pregnancy weight gains in this population.
a) Perform the appropriate computation and fill in the blank to complete this sentence in context: In this population, the first quartile of pregnancy weight gains is_____.
b) For underweight mothers, health organizations recommend a pregnancy weight gain between 27.5 lb and 39.5 lb. What is the probability that a randomly selected underweight mother in Canada would have a pregnancy weight gain in the recommended range?
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Answer:
The correct answer is:
(a) 44.6 lb
(b) 0.371
Step-by-step explanation:
Given values are:
Mean,
[tex]\mu=36.6[/tex]
Standard deviation,
[tex]\sigma=11.9[/tex]
(a)
The z distance third quartile will be:
⇒ [tex]P(Z<0.674)=0.75[/tex]
[tex]z =0.674[/tex]
By using the z-score formula, we get
⇒ [tex]x=z\times \sigma+ \mu[/tex]
[tex]=0.674\times 11.9+36.6[/tex]
[tex]=44.62[/tex]
(b)
⇒ [tex]P(27.5<x<39.5) = P[{\frac{(27.5-36.6)}{11.9} <\frac{(x-\mu)}{\sigma} <\frac{(39.5-36.6)}{11.9} }][/tex]
[tex]=P(-0.76<z<0.24)[/tex]
[tex]=P(z<0.24)-P(z<-0.76)[/tex]
By using the z table, we get
[tex]=0.5948-0.2236[/tex]
[tex]=0.371[/tex]
Necesito ayuda con este ejercicio hay que determinar el valor de la a: [tex]a^{20} : a^{2x} = a^{12}[/tex]
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Answer:
x = 10 + log(1/a^12)/(2 log(a)) + (i π n)/log(a) for n element Z
Step-by-step explanation:
Solve for x:
a^(20 - 2 x) = a^12
Take reciprocals of both sides:
a^(2 x - 20) = 1/a^12
Take the logarithm base a of both sides:
2 x - 20 = log(1/a^12)/log(a) + (2 i π n)/log(a) for n element Z
Add 20 to both sides:
2 x = 20 + log(1/a^12)/log(a) + (2 i π n)/log(a) for n element Z
Divide both sides by 2:
Answer: x = 10 + log(1/a^12)/(2 log(a)) + (i π n)/log(a) for n element Z
Can someone please help me? I'm stuck.
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Answer:
Sure i can help you
Step-by-step explanation:
Answer:
Sure! What’s the question?
Step-by-step explanation:
Write 5/9
as an equivalent fraction with a denominator of 18
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Answer:
10/18
Step-by-step explanation:
Multiply both the numerator and denominator by 2
To get an equivalent fraction with a denominator of 18. Means we need to move the denominator of 9 to get to 18.
In order to do so we multiply the bottom by 2. 9x2=18. However because we want an equal fraction, the top needs to be multiples by 2
when does two plus two equal five
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guys please help me :(((((((((( crying
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Answer:
18
Step-by-step explanation:
2/6
4/12
6/18
Answer:
x = 18
Step-by-step explanation:
We can write ratios
2 2+4
---- = -----
6 x
Using cross products
2x = 6(2+4)
2x = 6(6)
2x = 36
Divide by 2
2x/2 = 36/2
x = 18
Factor completely
9 – 25x^2
Pls help i will mark the brainliest!
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Answer:
more
Step-by-step explanation:
The answer is (5x+3)(-5x+3)
[tex]2 + y = 1[/tex]
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Answer: y= -1
Step-by-step explanation:
2+y=1
y=1-2
y=-1
Step-by-step 2+y=1
-2 -2
Y= -1
Please help it’s summer school and i need serious help
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Answer:
B
Step-by-step explanation:
Find the missing terms.
3, _____, _____, 21 (arithmetic)
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Answer:
Hello There!!
Step-by-step explanation:
The answer is 3,9,15,21.
hope this helps,have a great day!!
~Pinky~
Answer:
the common difference is 6. So, the missing two terms are 9 and 15 using
3 + (n-1)(6)
Let W be part of the solid sphere of radius 4, centered at the origin, that lies above the plane z = 2. Set up an integral in cylindrical coordinates to find the volume of the region. Do NOT actually integrate.
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Answer:
V = ∫∫∫rdrdθdz integrating from z = 2 to z = 4, r = 0 to √(16 - z²) and θ = 0 to 2π
Step-by-step explanation:
Since we have the radius of the sphere R = 4, we have R² = r² + z² where r = radius of cylinder in z-plane and z = height² of cylinder.
So, r = √(R² - z²)
r = √(4² - z²)
r = √(16 - z²)
Since the region is above the plane z = 2, we integrate z from z = 2 to z = R = 4
Our volume integral in cylindrical coordinates is thus
V = ∫∫∫rdrdθdz integrating from z = 2 to z = 4, r = 0 to √(16 - z²) and θ = 0 to 2π
Answer:
[tex]\displaystyle V = \int\limits^{2 \pi}_{0} \int\limits^{2\sqrt{3}}_{0} \int\limits^{\sqrt{16 - r^2}}_2 {r} \, dz \, dr \, d\theta[/tex]
General Formulas and Concepts:
Multivariable Calculus
Cylindrical Coordinate Conversions:
[tex]\displaystyle x = r \cos \theta[/tex][tex]\displaystyle y = r \sin \theta[/tex][tex]\displaystyle z = z[/tex][tex]\displaystyle r^2 = x^2 + y^2[/tex][tex]\displaystyle \tan \theta = \frac{y}{x}[/tex]Volume Formula [Cylindrical Coordinates]:
[tex]\displaystyle V = \iiint_T \, dV \rightarrow V = \iiint_T {r} \, dz \, dr \, d\theta[/tex]
Step-by-step explanation:
Step 1: Define
Identify given.
Solid sphere w/ radius 4 centered at (0, 0, 0) → x² + y² + z² = 4²
Plane z = 2
Step 2: Find Volume Pt. 1
Find bounds of z.
[Sphere] Substitute in plane z:[tex]\displaystyle x^2 + y^2 + 2^2 = 4^2[/tex]Substitute in cylindrical conversions:
[tex]\displaystyle (r \cos \theta)^2 + (r \sin \theta)^2 + 2^2 = 4^2[/tex]Simplify:
[tex]\displaystyle r^2 + 4 = 16[/tex]Solve for r:
[tex]\displaystyle r = 2\sqrt{3}[/tex]
∴ 0 ≤ r ≤ 2√3
Step 2: Find Volume Pt. 2
[Sphere] Substitute in plane z:[tex]\displaystyle x^2 + y^2 + 4 = 16[/tex]Isolate variables:
[tex]\displaystyle x^2 + y^2 = 12[/tex][Unit Circle] Graph [See 2nd Attachment]
∴ 0 ≤ θ ≤ 2π
Step 3: Find Volume Pt. 3
[Sphere] Substitute in cylindrical conversions:[tex]\displaystyle (r \cos \theta)^2 + (r \sin \theta)^2 + z^2 = 4^2[/tex]Simplify:
[tex]\displaystyle r^2 + z^2 = 4^2[/tex]Solve for z:
[tex]\displaystyle z = \sqrt{16 - r^2}[/tex]
∴ 2 ≤ z ≤ √(16 - r²)
Step 4: Find Volume Pt. 4
Substitute in variables [Volume Formula - Cylindrical Coordinates]:[tex]\displaystyle V = \int\limits^{2 \pi}_{0} \int\limits^{2\sqrt{3}}_{0} \int\limits^{\sqrt{16 - r^2}}_2 {r} \, dz \, dr \, d\theta[/tex]
∴ the volume of the region is found with the integral above.
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Learn more about multivariable calculus: https://brainly.com/question/17203772
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Topic: Multivariable Calculus
Unit: Triple Integral Applications
y-4=7(x-6)y−4=7(x−6)
Answers
Answer:
I believe the question was written twice on accident
y=7x-38
Step-by-step explanation:
y-4=7(x-6)
y-4=7x-42
y=7x-38
Find the area of the triangle.
24 in.
32 in.
Answers
Answer:
A = 384 inches^2
Step-by-step explanation:
The area of a triangle is given by
A = 1/2 bh where b is the length of the base and h is the height
A = 1/2 ( 32) *(24)
A = 384 inches^2
Answer:
The area of triangle is 384 inches².
Step-by-step explanation:
Given : -Base of triangle = 24 inchesHeight of triangle = 32 inches To Find :-Area of triangleFormula Used :-Area of triangle = 1/2 × base × height
Solution :-Using Formula
Area of triangle = 1/2 × base × height
substitute the values into the formula
Area of triangle = 1/2 × 32 inches × 24 inches.
multiply,
Area of triangle = 1/2 × 768 inches ²
Divide, we get
Area of triangle = 384 inches ²
Therefore, The area of triangle is 384 inches².
What is the solution to flog4(x+8) - 427
Answers
Answer:
4270
Step-by-step explanation:
Following the car in front of you at a closer distance _____.
A. Gets you to your location faster
B. Doesn’t get you to your location faster
C. Is a safer way to drive
D.saves you some gas
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Step-by-step explanation:
the answer is b, it doesnt get you to your location faster
Answer: Option A will be the correct answer
Step By Step Explanation: Because Main thing is its matching to the sentence
Which graph represents an increasing function? (1 point) Four graphs of y against x are shown. The title for the first graph is Graph A, the title for the second graph is Graph B, the title for the third graph is Graph C, and the title for the fourth graph is Graph D. Graph A is a straight line joining the ordered pairs 0, 6 and 3, 0. Graph B is a straight line joining the points 3, 0 and 3, 5. Graph C is a straight line joining the points 0, 3 and 3, 3. Graph D is a straight line joining the points 0, 0 and 3,3.
Graph A
Graph B
Graph C
Graph D
Answers
Answer:
a
Step-by-step explanation:
aàaaaaaaaaaqaaaarsgbfyjvdujcgujhgkud parlo
Answer:
d
Step-by-step explanation:
Solve for x in the equation x squared + 2 x + 1 = 17.
Answers
Step-by-step explanation:
quadratic formula
-b+-√b^2
2a
-2+-√2^2-4×1×-16
2×1
-2+-√68
2
either
x= 3.125
or
x= -5.125
Write the expression in exponential form nd then evaluate 2.1x2.1
Answers
Answer:
exponential form = 2.1^2
evaluation = 4.41
Step-by-step explanation:
it is times-ing 2.1 two times, therefore its 2.1^2
2.1 times 2.1 = 4.41
6
Find the slope of the line that passes through
(-4, 7) and (-6,-4)
b) -2/11
a) 2/11
d) -11/2
c) 11/2
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Answer:
c) 11/2
Step-by-step explanation:
(-4, 7) and (-6, -4)
To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)
Plug in these values:
(-4 - 7) / (-6 - (-4))
Simplify the parentheses.
= (-11) / (-6 + 4)
= (-11) / (-2)
Simplify the fraction.
-11/-2
= 11/2
This is your slope.
Hope this helps!
Let g(x) be the indicated transformation of f(x). Write the rule for g(x) f(x)=3x + 1: translation 2 units right
Answers
Answer:
3x +3
Step-by-step explanation:
3x + 1 + 2units(on the x axis)= 3x +3
