9514 1404 393
Answer:
-3 ≤ x ≤ 19/3
Step-by-step explanation:
This inequality can be resolved to a compound inequality:
-7 ≤ (3x -5)/2 ≤ 7
Multiply all parts by 2.
-14 ≤ 3x -5 ≤ 14
Add 5 to all parts.
-9 ≤ 3x ≤ 19
Divide all parts by 3.
-3 ≤ x ≤ 19/3
_____
Additional comment
If you subtract 7 from both sides of the given inequality, it becomes ...
|(3x -5)/2| -7 ≤ 0
Then you're looking for the values of x that bound the region where the graph is below the x-axis. Those are shown in the attachment. For graphing purposes, I find this comparison to zero works well.
__
For an algebraic solution, I like the compound inequality method shown above. That only works well when the inequality is of the form ...
|f(x)| < (some number) . . . . or ≤
If the inequality symbol points away from the absolute value expression, or if the (some number) expression involves the variable, then it is probably better to write the inequality in two parts with appropriate domain specifications:
|f(x)| > g(x) ⇒ f(x) > g(x) for f(x) > 0; or -f(x) > g(x) for f(x) < 0
Any solutions to these inequalities must respect their domains.
The table below represents an exponential function of the form y = a . b^x
Complete the table and find the equation. Write all your numerical answers in
Fraction form.
What is the value of a?
What is the value of b?
Answer:
Step-by-step explanation:
If one of the data points has the form (0,a)
, then a is the initial value. Using a, substitute the second point into the equatio f(x)=a(b)x, and solve for b.If neither of the data points have the form (0,a)
, substitute both points into two equations with the form f(x)=a(b)x Solve the resulting system of two equations in two unknowns to find a and b.Using the a and b found in the steps above, write the exponential function in the form f(x)=a(b)x.
Identify the graph that represents y=(x-1)^2+2
Step-by-step explanation:
i hope this is what you need
what are two decimals equivalent to 0.02
Answer:
0.020
0.0200
Step-by-step explanation:
Because there's always an imaginary 0 at the end, so there are infiite equivalant answers to this.
Hope this helps, and stay safe!! :))))
What is the time in minutes, taken to cover 8.1
km at an average speed of 5 m/s?
Answer:
27 minutes
Step-by-step explanation:
(8.1 km)×(1000 m)/(1 km)/(5 m/s)×(1 min/(60 s) = (8.1×1000)/(5×60) min8100/300=27 minWhich number line model represents the expression-1/2+5/4
Answer:
B
Step-by-step explanation:
What is the value of this expression?
(−8)3
equation of the parabola in vertex form that passes through (4,-7) and has a vertex of (1,-6)
[tex]y = -\frac{1}{9}(x - 1)^2 - 6[/tex]
Step-by-step explanation:
The vertex form of the equation for a parabola is given by
[tex]y = a(x - h)^2 + k[/tex]
where (h, k) are the coordinates of the parabola's vertex. Since the vertex is at (1, -6), we can write the equation as
[tex]y = a(x - 1)^2 - 6[/tex]
Also, since the parabola passes through (4, -7), we can use this to find the value for a:
[tex]-7 = a(4 - 1)^2 - 6 \Rightarrow -7 = 9a - 6[/tex]
or
[tex]a = -\frac{1}{9}[/tex]
Therefore, the equation of the parabola is
[tex]y = -\frac{1}{9}(x - 1)^2 - 6[/tex]
Verify that the function [tex]g(x)=2x^3-3x+1[/tex] satisfies the three hypotheses of Rolle’s Theorem on the interval [tex][0,2][/tex].
Lets check if the three conditions hold.
1 : Continuity of g on the interval [0,2]
First, g(x) is a continuous function on R, as the sum of a cubic function wich is continuous on R, and a linear polynomial of the form ax + b which is also continuous on R. Finally g is also continuous on the interval [0,2]
2 : Differentiable on the same interval
Since the cubic function and the linear polynomial one are differentiable on R, g also is differentiable and particularly on the interval [0,2]
Also we have g'(x) = 2*3*x² - 3 = 6x² - 3
3 : Do we have g(0) = g(2) ?
Lets compute g(0) = 2*0^3 - 3*0 + 1 = 1
And g(2) = 2*2^3 - 3*2 + 1 = 2 * 8 - 6 + 1 = 16 - 6 + 1 = 11
Since g(0) ≠ g(2), Rolle's theorem is not applicable. Thus unfortunately, we can not conclude that there exist c ∈ (0,2) such that f'(c) = 0
2) A pizza and bottle of soda together cost $14. If the pizza costs 6 times the price of the bottle
of soda, what is the price of each item?
HELP!!
Answer:
$14.6
Step-by-step explanation: because adding how all they are in total.
La puntuación media de un examen final fue de 72 y la desviación típica de 9. El 10%
de los mejores alumnos recibió la calificación A. ¿Cuál es la puntuación mínima que
un estudiante debió tener para recibir un A?
Answer:
I don't know what to do sorry
which of the following statements are true for sin (-430°)
i. the basic angle, a lies in the second quadrant
Ii. sin (-430°) = +sin (430°)
III. sin (-430°) = sin (70°)
iv. a = 30°
Answer:
Step-by-step explanation:
sin(-430)=-sin(430)=-sin(360+70)=-sin 70
IF Tyler s currently 5 inches
tal, how many inches more
does he need to grow to be
feet tal?
Hey there! Your answer is:
7 inches
Explanation:
If Tyler is 5 inches tall, he needs to grow 7 inches to be a foot tall. This is because 12 inches are in 1 foot. We can do a simple subtraction problem to figure this out.
12 inches - 5 inches = 7 inches
Since Tyler is 5 inches tall, we know that if we subtract 12 inches from 5 inches we will get the number of inches he needs to grow.
I hope this answer helps you out! Let me know if you have any questions and have a wonderful day/night!
Plz help I need help
Answer:
proportional
Step-by-step explanation:
hope this helps
Let's try it! If we set these two ratios equal to each other and cross-multiply, the results should be the same if they are, in fact, proportional.
8/20 = 20/80
400 ? 640
400 and 640 are not the same number, so these ratios are not proportional.
Hope this helps!! :)
i asked a question a while ago and nobody has answered it pls help
Answer:
bet but need barinlyist
Step-by-step explanation:
Find the length of x of the side of the larger triangle. (Assume that the two triangles are similar, and use the fact that corresponding sides of similar triangles are proportional)
X=
Similar triangles may or may not be congruent
The value of x that makes both triangles similar is 4.5
The equivalent ratio of both triangles is:
[tex]\mathbf{2 : 1 = 9 : x}[/tex]
Express the above equivalent ratio as a fraction
[tex]\mathbf{\frac 12= \frac x9 }[/tex]
Multiply both sides of the fraction by 9
[tex]\mathbf{\frac 12\times 9 = \frac x9 \times 9 }[/tex]
Cancel out common factors
[tex]\mathbf{\frac 12\times 9 = x}[/tex]
Divide 12 by 9
[tex]\mathbf{4.5 = x}[/tex]
Rewrite the above expression as:
[tex]\mathbf{x = 4.5 }[/tex]
Hence, the value of x is 4.5
Read more about similar triangles at:
https://brainly.com/question/14926756
A friend asked you to borrow $250 and agrees to repay it with 4% interest how much interest will you earn after eight months
Answer:
I believe in the question it only states 4% interest without any time factor so therefore it would be $10 interest for 1 month or 8 months
Is this a trick question?
Step-by-step explanation:
The exterior angle of a triangle is 164 degree and one
of its interior opposite angle is 98 degree. Find the other
interior opposite angle.
Answer:
• Let the other interior angle be x
[tex]{ \rm{x + 98 \degree = 164\degree}} \\ \\ { \rm{x = 164\degree - 98\degree}} \\ \\ { \boxed{ \rm{x = 66\degree}}}[/tex]
Click on photo for question!
write an equivalent expression for x^4 over 4
help
please
Answer:
1/4 · x⁴
Step-by-step explanation:
describe the transformation of g(x)=(-1/2x) as it relates to the graph of f(x)=x
Answer:
c
Step-by-step explanation:
Evaluate the expression
6a - 2b when a = 5, b=7
[tex] = > 6a - 2b[/tex]
[tex] = > 6(5) - 2(7)[/tex]
[tex] = > 30 - 14[/tex]
[tex] = > 16[/tex]
15. In his piggy bank, Neil has three times as many dimes as nickels and he has four more quarters than nickels. The coins total $4.60. How
many of each coin does he have?
10 quarters 6 nickels 18 dimes
758 rounded of to the nearest hundred
Answer:
800
Step-by-step explanation:
Hope this helps
Answer:
800, if it's higher than 50 you can round it to the next hundred
write a Pythagorean triplet with the following numbers as one of the number
a,4 b,8 c,12 d,22 with the formula pls
class 8
Answer:
For any natural number m, we know that
2m, \mathrm{m}^{2}-1, \mathrm{m}^{2}+1m
2
−1,m
2
+1 is a Pythagorean triplet.
i. 2m = 6
\begin{array}{l} \Rightarrow \mathrm{m}=\frac{6}{2}=3 \\ \mathrm{m}^{2}-1=3^{2}-1=9-1=8 \\ \mathrm{m}^{2}+1=3^{2}+1=9+1=10 \end{array}
⇒m=
2
6
=3
m
2
−1=3
2
−1=9−1=8
m
2
+1=3
2
+1=9+1=10
∴ (6, 8, 10) is a Pythagorean triplet.
ii. 2m = 14
\begin{array}{l} \Rightarrow \mathrm{m}=\frac{14}{2}=7 \\ \mathrm{m}^{2}-1=7^{2}-1=49-1=48 \\ \mathrm{m}^{2}+1=7^{2}+1=49+1=50 \end{array}
⇒m=
2
14
=7
m
2
−1=7
2
−1=49−1=48
m
2
+1=7
2
+1=49+1=50
∴ (14, 48, 50) is not a Pythagorean triplet.
iii. 2m = 16
\begin{array}{l} \Rightarrow \mathrm{m}=\frac{16}{2}=8 \\ \mathrm{m}^{2}-1=8^{2}-1=64-1=63 \\ \mathrm{m}^{2}+1=8^{2}+1=64+1=65 \end{array}
⇒m=
2
16
=8
m
2
−1=8
2
−1=64−1=63
m
2
+1=8
2
+1=64+1=65
∴ (16, 63, 65) is a Pythagorean triplet.
iv. 2m = 18
\begin{array}{l} \Rightarrow \mathrm{m}=\frac{18}{2}=9 \\ \mathrm{m}^{2-1}=9^{2}-1=81-1=80 \\ \mathrm{m}^{2}+1=9^{2}+1=81+1=82 \end{array}
⇒m=
2
18
=9
m
2−1
=9
2
−1=81−1=80
m
2
+1=9
2
+1=81+1=82
∴ (18, 80, 82) is a Pythagorean triplet
Step-by-step explanation:
For any natural number greater than 1,(2m,m
2
−1,m
2
+1) is Pythagorean triplets.
So, if one number is 2m, then another two numbers will be m
2
−1 and m
2
+1.
Given, one number = 4
Then Pythagorean triplets:
2m=4 or m = 2
So,
m
2
−1=(2)
2
−1=4−1=3
m
2
+1=(2)
2
+1=4+1=5
Now, (3)
2
+(4)
2
=(5)
2
Or 9 + 16 = 25.
I hope you all like this answer.
Mark as a brainlist.
rate my answer guys ❤️
Use intercepts to graph the linear equation 5x+3y=30
30/5 is equal to 6
this is your x-intercept
30/3 is equal to 10
this is your y-intercept
I think you know what to do now :)
(0,10) and (6,0)
187²–87² without using mathematical table or calculator
27.400
Step-by-step explanation:
187X187 = 34.969
87X87=7.569
34.969 - 7569 = 27.400
Use the identity
(a + b)² = a ² + 2ab + b ²
Then rewrite 187² as
187² = (100 + 87)² = 100² + 2•100•87 + 87²
Subtract 87² eliminates the last term from above, so we're left with
(100² + 2•100•87 + 87²) - 87²
= 100² + 2•100•87
= 10000 + 2•8700
= 10000 + 17400
= 27400
Which represents the solution to the inequality 4x + 7(3x - 3) ≤ 9 - 5x in interval notation
Answer:
Isolate the variable by dividing each side by factors that don't contain the variable.
Inequality Form:
x < 1
Interval Notation:
( − ∞, 1)
- The weight of 72 identical marbles is 183.6 grams. What is the weight of each marble? Explain how you
know the decimal point of your quotient is placed reasonably.
Answer:
the weight of each marble is 2.55 grams
I need help with this
Answer:
Your answer is C. x=6 I hope this helps you! :D
If you need i can also provide steps.
Answer:
C. x=6
Step-by-step explanation:
You can work it out as follows:
6 - 0.2x = 2(6 - 0.6x) =>
6 - 0.2x = 12 - 1.2x =>
-0.2x + 1.2x = 12 - 6 =>
1.0x = 6 =>
x = 6
Write an equation in point slope form that goes through the point (3,5) and is perpendicular to the line y=1/3x-7
Answer:
[tex]y - 5 = - 3(x - 3)[/tex]
Step-by-step explanation:
our original equation
[tex]y = \frac{1}{3} x - 7[/tex]
A perpendicular slope of a line is the negative reciprocal
So our slope would be -3
point slope form is
[tex]y - y1 = m(x - x1)[/tex]
let's substitute our given point (3, 5) and our perpendicular slope, -3
[tex]y - 5 = - 3(x - 3)[/tex]