When x = 1:
1³ + 1 - 3 = -1
When x = 2:
2³ + 2 - 3 = 7
Since f(x) = x³ + x - 3 is continuous, it follows from the intermediate value theorem that for some c in the interval (1, 2), we have f(c) = 0, since f(1) < 0 < f(2).
find the sum of n first natural numbers is 496 ,find the number of terms
Answer:
Number of terms = 31.
Step-by-step explanation:
Sum of n terms of an A S with first term 1 and common difference 1:-
496 = (n/2)(2(1) + 1(n - 1))
496 = (n/2)(n + 1)
n^2/2 + n/2 = 496 Multiply through by 2:-
n^2 + n = 992
n^2 + n - 992 = 0
(n - 31)(n + 32) = 0
n = 31 (we ignore the negative).
Pre-calc/trig
Suppose that θ=arcsin(1/7) in the first quadrant. What is cos(θ/2)? (round to 4 decimals)
Answer:
0.9974
Step-by-step explanation:
[tex]arcsin( \frac{1}{7} ) = 0.1433 \\ cos( \frac{0.1433}{2} ) = 0.9974[/tex]
Consider a game in which you draw playing cards from a standard 52-card deck, one at a time. If a player draws a face card (a jack, a queen, or a king), the player is awarded 10 points. Any other card drawn costs the player 3 points. What is the expected value of drawing a card in this game? A. 0 points B. 3 points C. 6.5 points D. 10 points
Answer: B
Step-by-step explanation: There are many less face cards in the deck than other cards, you would think youre getting 3 points each time rather than thinking 10 points each time
A concession stand owner bought some bottles of water for $0.75 each and began selling them for $1.25 each. When he made back all the money he spent, he still had 20 bottles left to sell. What equation can be written to determine the amount of money the owner spent?
the second choice is "reverse" and "do not reverse"
Answer:
Divide by -8reverseStep-by-step explanation:
Multiplying or dividing an inequality by a negative number requires that the inequality symbol be reversed.
__
To solve this inequality, we can divide by the coefficient of x, which is -8. Dividing by -8 means we need to reverse the inequality symbol.
_____
Additional comment
Actually, applying any function that has a negative slope means the ordering is reversed. That is the more general case.
Here, we're specifically concerned with division by a negative number. You can see the effect on the ordering relation by considering ...
-2 < 12 > -1 . . . . divide both sides by -1-9v -6(8-7v)
Explain please
Answer:
33v - 48
Step-by-step explanation:
- 9v - 6(8 - 7v) ← multiply each term in the parenthesis by - 6
= - 9v - 48 + 42v ← collect like terms
= 33v - 48
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Let's solve ~
[tex]\qquad \sf \dashrightarrow \: - 9v - 6(8 - 7v)[/tex]
[tex]\qquad \sf \dashrightarrow \: - 9v - [(6 \times 8) - (6 \times 7v)][/tex]
[tex]\qquad \sf \dashrightarrow \: - 9v - (48 - 42v)[/tex]
[tex]\qquad \sf \dashrightarrow \: - 9v - 48 + 42v[/tex]
[tex]\qquad \sf \dashrightarrow \:33v - 48[/tex]
Hope it helps ~
BOOM Creations has offered to sell its balloon
bouquets for a fixed down payment of $65 and an
additional charge of $2.75 per bouquet.
Answer:
y intercept: 65
rate of change: $2.75
Step-by-step explanation:
Really quite simple lad. Your equation is y=2.75x+65. 65 is your y-intercept, and you have a rate of change of 2.75 per bouquet.
The length of AB is 9 centimeters. A dilation with a scale factor of 2 is applied to AB. What is the length of the image AB after the dilation is applied?
Answer:
18cm
Step-by-step explanation:
Given:
- The length of AB is 9 centimeters
- A dilation with a scale factor of 2
The length of the image AB after the dilation is applied:
9 x 2 = 18
dilation is used to make an image or in this case AB, with a scale factor of 2 means that its doubling in size. If the scale factor was 1/2 that it would be decreasing in size since it will be half of the original size
Use the table below to find each probability. 5. P(the recipient is male) 6. p(the degree is a bachelors) 7. p(the recipient is female, given that the degree is advanced) 8. p( the degree is not an associates, given that the recipient is male)
Degree Male Female
Associate 245 433
Bachelors 598 858
Advanced 293 376
P(the recipient is male)= 40.5%
p(the degree is a bachelors) = 52%
p(the recipient is female, given that the degree is advanced) = 56.2%
p( the degree is not an associates, given that the recipient is male) = 78.4%
What are the probabilities?Probability determines the chances that a random event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
P(the recipient is male) = total number of males / total number of recipients
1136/2803 = 40.5%
p(the degree is a bachelors) = total number of bachelors degree / total number of degree
= 1456 / 2803 = 52%
p(the recipient is female, given that the degree is advanced) = total number of females with advanced degree / total number of advanced dgree
376 / 669 = 56.2%
p( the degree is not an associates, given that the recipient is male) = number of males that that have degrees other than associates / total number of males
891 / 1136 = 78.4%
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Find:
Number X. if
3
of x is 12.
Answer:
x=4
or
x=36
Step-by-step explanation:
I am wondering if you mean 3x=12 or x/3=12
if 3x=12, then x=4
if x/3=12, then x=36
Rearrange the formula below to make x the subject. α y+1=2x - 10/x+1
Answer:
cross multiplication
x
Help me please I need this done quick
Solve the problem.
A recipe calls for 6 ounces of unsweetened chocolate for 20 brownies. How much of unsweetened chocolate is needed to make 30 brownies?
The diameter of the circle above is 14 cm. What is the circumference of the circle? Use a = 3.14.
Circumference 2пт
A. 153.86 cm
B. 21.98 cm
C. 43.96 cm
D. 307.72 cm
Answer:
43.96 or C
Step-by-step explanation:
c=(pi)(d)
pi --> 3.14
d --> diameter (in your case 14.)
c=3.14*14
c= 43.96
Both formulas work, 2(pi)r and (pi)(d)
But, if they give you the diameter then use (pi)(d).
If they give you the radius then use 2(pi)r
3
6
2
•
3
12
O y=2x+:
O y = 3x
O y =3x+3
O y=x+3
Which equation represents the relationship shown in the table? •
Answer:
y = 3x + 3
Step-by-step explanation:
when you check, only that equation delivers the correct x and y pairs.
x = 0, => y = 3×0 + 3 = 3
x = 1, y = 3×1 + 3 = 3+3 = 6
x = 2, y = 3×2 + 3 = 6 + 3 = 9
x = 3, y = 3×3 + 3 = 9 + 3 = 12
it all fits.
Find an equation of a line through (2, 1) and perpendicular to - 2x + 4y = 8.
y = -2x - 1
y = -2x + 5
О.
y = -2x - 3
O
y = -2x + 3
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]-2x+4y=8\implies 4y=2x+8\implies y=\cfrac{2x+8}{4} \\\\\\ y=\cfrac{2x}{4}+\cfrac{8}{4}\implies y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{1}{2}}x+2\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
since we know that's its slope, then
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{1}{2}} ~\hfill \stackrel{reciprocal}{\cfrac{2}{1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{2}{1}\implies -2}}[/tex]
so then we're really looking for the equation of a line whose slope is -2 and passes through (2 , 1)
[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{1})\qquad \qquad \stackrel{slope}{m}\implies -2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{-2}(x-\stackrel{x_1}{2}) \\\\\\ y-1=-2x-4\implies y=-2x-3[/tex]
Soo i need yall help rlly bad w it pls
The total number of inches yards that she have is 6.95 yards
Sum of fractionsGiven the following parameters
Amount of red yards = 4.2 inches
Amount of blue yards = 2.75inches
In order to determine the total yards, the sum of the yards is expressed as:
Total yards = 4.2 + 2.75
Total yards = 6.95 yards
Hence the total number of inches yards that she have is 6.95 yards
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Someone show me step for step please!
[tex]\csc \theta \tan \theta - \tan \theta \sin \theta \\\\\\=\dfrac 1{\sin \theta} \cdot \dfrac{\sin \theta }{\cos \theta }- \dfrac{\sin \theta }{\cos \theta} \cdot \sin \theta\\\\\\=\dfrac{1}{\cos \theta}-\dfrac{\sin^2 \theta}{\cos \theta}\\\\\\=\dfrac{1- \sin^2 \theta}{\cos \theta}\\\\\\=\dfrac{\cos^2 \theta}{\cos \theta}~~~~~~~~~~~~~~;[\sin^2 \theta + \cos^2 \theta =1 ]\\\\\\=\cos \theta[/tex]
Let's write out some trigonometric identities that we can use:
[tex]tan(x)=\frac{sin(x)}{cos(x)} \\[/tex][tex]csc(x)=\frac{1}{sin(x)}[/tex][tex]sin^2(x)+cos^2(x)=1[/tex] ⇒ [tex]cos^2(x)=1-sin^2(x)[/tex]Now let's try solving them out:
[tex]csc(x)tan(x)-tan(x)sin(x)=\frac{1}{sin(x)}tan(x)-sin(x)tan(x)\\\\ csc(x)tan(x)-tan(x)sin(x)=tan(x)(\frac{1}{sin(x)}-sin(x))\\\\ csc(x)tan(x)-tan(x)sin(x)=tan(x)(\frac{1}{sin(x)} -\frac{sin^2(x)}{sin(x)} )\\\\csc(x)tan(x)-tan(x)sin(x)=tan(x)*(\frac{1-sin^2(x)}{sin(x)} )\\\\csc(x)tan(x)-tan(x)sin(x)=\frac{sin(x)}{cos(x)}*\frac{cos^2(x)}{sin(x)} \\\\csc(x)tan(x)-tan(x)sin(x)=\frac{sin(x)}{sin(x)}*\frac{cos^2(x)}{cos(x)}\\\\csc(x)tan(x)-tan(x)sin(x)=1 * cos(x)\\\\ csc(x)tan(x)-tan(x)sin(x)=cos(x)[/tex]
*I used a different variable, but that doesn't change the answer
Answer: cos(x)
Hope that helps!
A large tank is 120 meters long, 65 meters wide, and 48
meters high. Express the volume of the tank in cubic
meters using scientific notation.
Step-by-step explanation:
the volume of a rectangular block or tank is
length × width × height
so, it is like all regular 3D objects
base area × height.
so, we get
120 × 75 × 48 = 374,400 m³ = 3.744 × 10⁵ m³
why ?
374,400 = 374400 × 10⁰ = 37440 × 10¹ =
= 3744 × 10² = 374.4 × 10³ = 37.44 × 10⁴ =
= 3.744 × 10⁵
Cácule o limite de:
lim [tex]3^{2n} + 1[/tex]
_____________________
n-∞[tex]4^{n+2} - 3[/tex]
R:∞
The limit of the expressions [tex]3^{2n} + 1[/tex] and [tex]4^{n + 2} - 3[/tex] for n to infinity is infinity
How to calculate the limits?The expressions are given as:
[tex]3^{2n} + 1[/tex]
[tex]4^{n + 2} - 3[/tex]
The limits of the expressions as they approach infinity are represented as:
[tex]\lim_{n \to \infty} 3^{2n} + 1[/tex] and [tex]\lim_{n \to \infty} 4^{n + 2} - 3[/tex]
Substitute [tex]\infty[/tex] for n in both expressions
[tex]\lim_{n \to \infty} 3^{2 * \infty} + 1[/tex] and [tex]\lim_{n \to \infty} 4^{\infty + 2} - 3[/tex]
Solve both expressions independently;
[tex]\lim_{n \to \infty} 3^{2n} + 1 = 3^{2 * \infty} + 1[/tex]
Evaluate the product
[tex]\lim_{n \to \infty} 3^{2n} + 1 = 3^{\infty} + 1[/tex]
Evaluate the exponent
[tex]\lim_{n \to \infty} 3^{2n} + 1 = \infty + 1[/tex]
Evaluate the sum
[tex]\lim_{n \to \infty} 3^{2n} + 1 = \infty[/tex]
Also, we have:
[tex]\lim_{n \to \infty} 4^{n + 2} - 3 = 4^{\infty + 2} - 3[/tex]
Evaluate the sum
[tex]\lim_{n \to \infty} 4^{n + 2} - 3 = 4^{\infty} - 3[/tex]
Evaluate the exponent
[tex]\lim_{n \to \infty} 4^{n + 2} - 3 =\infty - 3[/tex]
Evaluate the difference
[tex]\lim_{n \to \infty} 4^{n + 2} - 3 =\infty[/tex]
Hence, the limit of the expressions for n to infinity is infinity
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I need a the answer please!!
-4√x + 5 + 5
I’m not sure how to solve. Radical quadratic function.
Answer:
si es funcion radical al final se pondra con raiz y las raizes son como potenciacion pero al revez es como multiplicacion y su opuesto en divicion haci que 5 mas 5 es 10 mas 4 es 14 pero sigue al raiz haci que se tiene que buscar una raiz a 14 seria 3,7288 y haci pero si no tenemos entonces una divicion 7 por 2 14 pero no se puede haci que 4 entre 7 la respuesta la pondrias como 4 (imagen de raiz encima del 7) 7
Step-by-step explanation:
espero ayudarte utilice un 64/1 de mi cabeza
A(5, 10) and B(13,-2) are two points on the line AB.
The perpendicular bisector of the line AB has gradient
Find the equation of the perpendicular bisector of AB
Answer:
hope you understand......
Solve the equation 14x + 7y= 28 for x.
O A. x-y-2
OB. x = 28-7y
O C. x = 2-y
O D. x = 4-y
The equation that represents the solution of x is x = 2 - y/2
How to solve the equation?The equation is given as:
14x + 7y = 28
Divide through by 7
2x + y = 4
Subtract y from both sides
2x = 4 - y
Divide both sides by 2
x = 2 - y/2
Hence, the equation that represents the solution of x is x = 2 - y/2
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Find the vertex, axis of symmetry, and y-intercept of the quadratic function.
Answer:
See below ~
Step-by-step explanation:
Details of Graph
Maximum = 2Domain : all real numbersRange : y ≤ 2There is 1 2 of a pizza left for 4 friends to share. What fraction of a pizza will each friend get to eat? please help.
Answer:
1/3
Step-by-step explanation:
Number of pizza=12
Number of students=4
Therefore,4/12=4/4
=1/3
Give the value of x .
A. 60 degrees
B. 180 degrees
C. 120 degrees
D. 45 degrees
Answer:
x=120°
Step-by-step explanation:
sum of all angles in a triangle is equal to 180
let the unknown angle be
[tex] \alpha [/tex]
[tex]60 + 60 + \alpha = 180 \\ \alpha = 180 - 60 - 60 \\ \alpha = 60 \\ [/tex]
[tex] \alpha + x = 180 \\ x = 180 - \alpha \\ x = 180 - 60 \\ x = 120[/tex]
A right angled triangle has sides 12m and 5 m.what is the length of the hypotenuses of this triangle?
Answer:
13 m
Step-by-step explanation:
Given: sides of the right triangle are 12 m and 5 mTo find: Length of hypotenuseBy Pythagoras Theorem:[tex]l(hypotenuse)=\sqrt{12^2+5^2}[/tex][tex]\implies l(hypotenuse)=\sqrt{144+25}[/tex][tex]\implies l(hypotenuse)=\sqrt{169}[/tex][tex]\implies l(hypotenuse)=13\: m[/tex]How do I solve 15=3p/6 ?
solve 4(x-7)+10=-10 A=X-2 B=X=4 C=X=1 D=X=3
Answer:
A. -2
Step-by-step explanation:
