Answer:
y = 1/16
Step-by-step explanation:
y = 4 • 2^x
Let x = -6
y = 4 • 2^(-6)
The negative exponent puts it in the denominator
y = 4 • 1/ 2^6
y = 4 * 1/64
y = 4/64
y = 1/16
Which graph shows y=3⌈x⌉+1 ?
The graph located in the upper right corner of the image attached shows the graph of y = 3[x]+1.
In order to solve this problem we have to evaluate the function y = 3[x] + 1 with a group of values.
With x = { -3, -2, -1, 0, 1, 2, 3}:
x = -3
y = 3[-3] + 1 = -9 + 1
y = -8
x = -2
y = 3[-2] + 1 = -6 + 1
y = -5
x = -1
y = 3[-1] + 1 = -3 + 1
y = -2
x = 0
y = 3[0] + 1 = 0 + 1
y = 1
x = 1
y = 3[1] + 1 = 3 + 1
y = 4
x = 2
y = 3[2] + 1 = 6 + 1
y = 7
x = 3
y = 3[3] + 1 = 9 + 1
y = 10
x y
-3 -8
-2 -5
-1 -2
0 1
1 4
2 7
3 10
The graph that shows the function y = 3[x] + 1 is the one located in the upper right corner of the image attached.
Answer:
The answer you picked was correct. I just took the test and that's it.
Step-by-step explanation:
一、225 + 4.8
I don’t understand it plz help
(And do it step by step...)
[tex]\bf -\sqrt{225}+4.8~~ \begin{cases} 225=&3\cdot 3\cdot 5\cdot 5\\ &3^2\cdot 5^2\\ &(3\cdot 5)^2\\ &15^2 \end{cases}\\\\\\ -\sqrt{15^2}+4.8\implies -15+4.8\implies -10.2[/tex]
Given h(x) = |x+3| -5
•Identify the parent function f
•Describe the sequence of transformation from f to h
Answer:
The parent function f(x) is equal to [tex]f\left(x\right)=\left|x\right|[/tex]
The translations is 3 units to the left and 5 units down
Step-by-step explanation:
we have
[tex]h\left(x\right)=\left|x+3\right|-5[/tex]
The vertex of the function h(x) is the point (-3,-5)
we know that the parent function f(x) is equal to
[tex]f\left(x\right)=\left|x\right|[/tex]
The vertex of the function f(x) is the point (0,0)
so
The rule of the transformation of f(x) to h(x) is equal to
(x,y) -----> (x-3,y-5)
That means ----> The translations is 3 units to the left and 5 units down
What is the product?
(x - 3)(2x2 – 5x + 1)
Answer:
[tex]\large\boxed{(x-3)(2x^2-5x+1)=2x^3-11x^2+16x-3}[/tex]
Step-by-step explanation:
Use the distributive property: a(b + c) = ab + ac:
[tex](x-3)(2x^2-5x+1)=(x-3)(2x^2)+(x-3)(-5x)+(x-3)(1)\\\\=(x)(2x^2)+(-3)(2x^2)+(x)(-5x)+(-3)(-5x)+x-3\\\\=2x^3-6x^2-5x^2+15x+x-3\qquad\text{combine like terms}\\\\=2x^3+(-6x^2-5x^2)+(15x+x)-3\\\\=2x^3-11x^2+16x-3[/tex]
The two angles below form a linear pair, and the expressions are measured in degrees. What is the measure of the smaller angle?
62°
74°
118°
148°
Answer:
The measure of the smaller angle is 62°
Step-by-step explanation:
we know that
If two angles form a linear pair, then their sum is equal to 180 degrees (supplementary angles)
so
(2x-30)°+(x-12)°=180°
Solve for x
3x=180°+42°
3x=222°
x=74°
The measure of the angles are
(2x-30)°=2(74)-30=118°
(x-12)°=74-12=62° -----> smaller angle
One carton of eggs contains 12 eggs.
Write an equation that can be used to find the number of eggs e in any number of cartons c.
e = 120
c= 12e
e=c+12
e=C +12
Answer:
it may be e=c+12
Step-by-step explanation:
common sense
For this case we have:
e: Variable representing the number of eggs
c: Variable representing the number of cartons of eggs.
So, if in each carton there are 12 eggs we can write the following equation:
[tex]e = 12c[/tex]
Answer:
The equation is: [tex]e = 12c[/tex]
Half of a number is three times the sum of a number ad five.
10
If you treat the number as x, then [tex]\frac{1}{2}x=x+5\to-5=\frac{1}{2}x\to-10=x[/tex].
The table below shows values for x and y. If y varies directly as x, what is the constant of variation?
x y
0 0
1 -9
2 -18
3 -27
-9
0
3
9
Answer:
k = - 9
Step-by-step explanation:
Given that y varies directly as x then the equation relating them is
y = kx ← k is the constant of variation
To find k use any ordered pair from the given table of values
Using x = 1, y = - 9, then
k = [tex]\frac{y}{x}[/tex] = [tex]\frac{-9}{1}[/tex] = - 9
Answer:
-9.
Step-by-step explanation:
y varies directly as x so y = kx where k is the constant of variation.
Inserting the values of x and y.
0 = k*0
-9 = k*1 so k = -9
-18 = 2*k so k = -9
-27 = 3 *k so k = -9.
Use the discriminant to determine what type of roots the equations will have, and categorize the equations according to their roots.
two distinct roots, One repeated root, two complex roots
x^2 − 4x + 2 = 0
5x^2 − 2x + 3 = 0
2x^2 + x − 6 = 0
13x^2 − 4 = 0
x^2 − 6x + 9 = 0
x^2 − 8x + 16 = 0
4x^2 + 11 = 0
Final answer:
The discriminant of a quadratic equation informs us about the nature of its roots. By calculating the discriminant for each given equation, we categorize them accordingly: equations with discriminant greater than zero have two distinct real roots, equal to zero have one repeated real root, and less than zero have two complex roots.
Explanation:
The discriminant of a quadratic equation ax² + bx + c = 0 is given by the expression b² - 4ac. The value of the discriminant determines the nature of the roots of the equation. To find the type of roots for each given equation:
x² − 4x + 2: The discriminant is (-4)² - 4(1)(2) = 16 - 8 = 8, which is greater than zero, so this equation has two distinct real roots.
5x² − 2x + 3: The discriminant is (-2)² - 4(5)(3) = 4 - 60 = -56, which is less than zero, indicating two complex roots.
2x² + x − 6: The discriminant is (1)² - 4(2)(-6) = 1 + 48 = 49, also greater than zero, leading to two distinct real roots.
13x² − 4 = 0 has a discriminant equivalent to that for x² − 4/13 = 0, which is 0² - 4(1)(-4/13) = 16/13, which is greater than zero, so this equation will have two distinct real roots.
x² − 6x + 9: The discriminant is (-6)² - 4(1)(9) = 36 - 36 = 0, indicating one repeated root.
x² − 8x + 16: The discriminant is (-8)² - 4(1)(16) = 64 - 64 = 0, which means this equation has one repeated root.
4x² + 11 = 0 has a discriminant equivalent to that for x² + 11/4 = 0, which is 0² - 4(1)(11/4) = -11, less than zero, thus resulting in two complex roots.
Through the method of using the discriminant, we can determine the types of roots each quadratic equation will have.
Fencing costs $3.25 per foot. A certain
yard has a width of 60 feet and length of
80 feet How much is the cost to fence?
Answer:
910$
Step-by-step explanation:
It's easiest if we just add the width and length together to start which would be 2 sides of the fence so we multiply by 2 to complete the whole perimeter.
80+60 = 140 x 2 = 280
Now you need to multiply 280 by 3.25 because that is what it will cost in the end since the 280 is all of the feet together and the 3.25 is each foot's price.
3.25 x 280 = 910
910$
In the diagram below, AB is parallel to CD. What is the value of y?
А. 50
B. 30
C. 150
D. 60
The value of y = 30°
What is the property of alternating interior angle?When two parallel lines cut by a line, then their alternating interior angles will be same.By alternating interior property, alternate angle of 150° is equal to 150°.
Straight line has angle 180°
So, y + 150° = 180°
y = 30°
Hence the value of y = 30°
Learn more about alternating angle here:
https://brainly.com/question/25716982
#SPJ2
The expression on the left side of an equation is shown below.
-4(x-2)+5x=0
If the equation has no solution, which expression can be written in the box on the other side of the equation?
1)2(x + 4) - x
2)x+8
3)4(x + 2) - 5x
4)x
Answer:
4) x
Step-by-step explanation:
The expression on the left side simplifies to:
-4(x - 2) + 5x =
= -4x + 8 + 5x
= x + 8
To have an equation with no solution, you need the same x term on the right side but a different constant term. The x term on the left side is x. You need x on the right side but with a constant term different than 8.
Answer: 4) x
Answer:
D) x
Step-by-step explanation:
When simplified, the answer will result to a=b which means that it has no solution
In an election 32 thousand people voted for Mayor Jackson. A total of 56 thousand people voted in the election. What is the ratio of the number of votes that were not for mayor Jackson to the total number of votes in simplest form?
Answer:
Ratio of the number of votes that were not for mayor Jackson to the total number of votes is 3:7
Step-by-step explanation:
Votes of Mayor Jackson = 32,000
Total Votes = 56,000
Votes not for Mayor Jackson = 56000 - 32000
Votes not for Mayor Jackson = 24000
ratio of the number of votes that were not for mayor Jackson to the total number of votes = Votes not for Mayor Jackson:Total Votes
= 24,000:56,000
=24:56 (divide numerator and denominator by 8)
=3:7
So, ratio of the number of votes that were not for mayor Jackson to the total number of votes is 3:7
Answer:
3 : 7
Step-by-step explanation:
It is given that,
In an election 32,000 people voted for Mayor Jackson
A total of 56,000 people voted in the election.
To find the ratio
Total number of people voted = 56000
Number of people voted for Mayor Jackson = 32000
Number of votes that were not for mayor Jackson = 56000 - 32000 = 24000
The ratio of the number of votes that were not for mayor Jackson to the total number of votes = 24000 : 56000
= 3 : 7
What is the value of x in x + 2 = 5?
Answer:
x = 3Step-by-step explanation:
x + 2 = 5 subtract 2 from both sides
x + 2 - 2 = 5 - 2
x = 3
Check:
3 + 2 = 5 CORRECT :)
Which of the following statements justifies why the triangle shown below is
not a right triangle?
Answer:
A) 6^2 + 11^2 is not equal to 15^2
Step-by-step explanation:
To find out if a right triangle is a right triangle you have to use the Pythagorean Theorem, like it is used in A.
6^2 + 11^2 = 15^2
36 + 121 = 225
157 does not equal 225
So this is not a right triangle
Answer:
Option A
Step-by-step explanation:
Given in the picture is a triangle ABC with three sides given as 6,11 and 15
By the picture itself we can say that the largest angle is obtuse and hence the triangle is not right angled.
Using the converse of Pythagorean theorem that in a right triangle sides square add upto square of hypotenuse let us check whether this applies to this triangle.
Small sides are 6 and 11
Squaring and adding gives
[tex]6^2+11^2 = 187[/tex]
Large side = 11 and square is
[tex]15^2 =225 > 121[/tex]
Hence this is not a right triangle but obtuse
So option A is right
A system of two equations is shown below. What will you need to multiply the top equation by in order to solve this system using the elimination method?
X+2y=11
6x+4y=34
A.6
B.2
C.-2
D.-4
For this case we have the following system equations:
[tex]x + 2y = 11\\6x + 4y = 34[/tex]
To use the elimination method we must multiply the first by -2. So:
[tex]-2x-4y = -22\\6x + 4y = 34[/tex]
In this way, if we add the equations, the variable y is eliminated.
Answer:
-2
Option C
Study the following data set.
{8,15,9,18,9,17,22,10,11,9,13}
What is the interquartile range of the data set?
Enter your answer as a number, like this: 42
Answer:
8
Step-by-step explanation:
The question is on interquartile range which is the median of the upper half of the data minus the median of the lower half of data
First arrange the data in an increasing order;
8,15,9,18,9,17,22,10,11,9,13
8,9,9,9,10,11,13,15,17,18,22
Find the median, which is the center value in the data set
8,9,9,9,10,11,13,15,17,18,22⇒the median is 11
Place brackets around the numbers above and below the median
(8,9,9,9,10)11 (13,15,17,18,22)
Find the median in the lower half of the data,Q1
(8,9,9,9,10) ⇒median is 9=Q1
Find the median in the upper half of the data,Q3
(13,15,17,18,22)⇒median is 17=Q3
Subtract Q1 from Q3 to get the interquartile range
Q3=17, and Q1=9
Q3-Q1=17-9=8
the graph of g(x), shown below in pink, has the same shape as the graph of f(x)=x^2, shown in gray. which of the following is the equation for g(x)
Answer:
B
Step-by-step explanation:
The graph of g(x) has its vertex at (1, - 3)
The equation of a parabola in vertex firm is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
here (h, k) = (1, - 3), thus
g(x) = (x - 1)² - 3 → B
Answer:
B.f(x)=(x-1)²-3
Step-by-step explanation:
apex
Point M is the midpoint of AB if the coordinates of A are (-3,6) and the coordinates of M are (-5,2) what are the coordinates of B ?
Please answer #5
Answer:
The coordinates of point B are (-7 , -2)
Step-by-step explanation:
* Lets explain how to solve the problem
- The mid-point (x , y) of the line whose endpoints are (x1 , y1) and
(x2 , y2) is [tex]x=\frac{x_{1}+x_{2}}{2},y=\frac{y_{1}+y_{2}}{2}[/tex]
∵ M is the midpoint of AB
∵ The coordinates of point A are (-3 , 6)
∵ The coordinates of point M are (-5 , 2)
- Let the coordinates of point A are (x1 , y1) , The coordinates of
point B are (x2 , y2) and The coordinates of point M are (x , y)
∴ x = -5 , x1 = -3 and y = 2 , y1 = 6
- Lets use the rule of the mid point to find x2 , y2
∵ [tex]-5=\frac{-3+x_{2}}{2}[/tex] ⇒ multiply both sides by 2
∴ [tex]-10=-3+x_{2}[/tex] ⇒ add 3 to both sides
∴ -7 = x2
∵ [tex]2=\frac{6+y_{2}}{2}[/tex] ⇒ multiply both sides by 2
∴ [tex]4=6+y_{2}[/tex] ⇒ subtract 6 from both sides
∴ -2 = y2
∵ The coordinates of point B are (x2 , y2)
∴ The coordinates of point B are (-7 , -2)
The radius of a circular park is 114 yd. To the nearest yard, what is the
circumference of the park?
Answer:
716 yards
Step-by-step explanation:
Circumference = π × Diameter
2 × Radius = Diameter
2 × 114 = 228
Circumference = π × Diameter
Circumference = π × 228 = 228π = 716.283125018
Answer:
716 yd
Step-by-step explanation:
The circumference of a circle is 2*pi*radius.
The radius is 114 yd so the circumference is 2*pi*114 yd.
Put into the calculator and you obtain 716.283 yd.
The answer to the nearest yard is 716.
which of the diagram below represents the contrapositive of the statement if it is an equilateral triangle,then it is an isosceles
The diagram that represents the contrapositive of the statement "If it is an equilateral triangle, then it is an isosceles triangle" is: B. Figure B.
In Mathematics, a conditional statement is a type of statement that can be written to have both a hypothesis and conclusion. This ultimately implies that, a conditional statement has the form "if P then Q."
P → Q
Where:
P and Q represent sentences or statements.
Generally speaking, the contrapositive of a conditional statement involves interchanging the hypothesis and conclusion, and negating both hypothesis and conclusion;
~Q → ~P
In this context, the contrapositive of the given statement "If it is an equilateral triangle, then it is an isosceles triangle" can be written as follows;
"If it is not an isosceles triangle, then it is not an equilateral triangle."
Therefore, only figure correctly represent the contrapositive of the statement.
Complete Question:
Which of the diagrams below represents the contrapositive of the statement
"If it is an equilateral triangle, then it is an isosceles triangle"?
A. Figure A
B. Figure B
The domain of the following relation: R: {(-4,8),(8,10),(5,4),(1,6),(5,-9) } is
Answer:
{-4, 8, 5, 1, 5}
Step-by-step explanation:
In a set of ordered pairs, the domain is the set of the first number in every pair.
If the set of ordered pairs is {(-4,8), (8,10), (5,4), (1,6), (5,-9)},
the domain is { -4, 8, 5, 1, 5}
On the provided graph, select the locations of the x-intercepts of the following polynomial function. x^3-7x^2-26x+72
Answer:
The x-intercepts are the points (-4,0). (2,0) and (9,0)
The location of the x-intercepts in the attached figure
Step-by-step explanation:
we know that
The x-intercepts of a function are the values of x when the value of the function is equal to zero
we have
[tex]f(x)=x^{3}-7x^{2}-26x+72[/tex]
using a graphing tool
The x-intercepts are the points (-4,0). (2,0) and (9,0)
see the attached figure
Answer:
(-4,0), (2,0), (9,0)
Step-by-step explanation:
Correct on Plato
What is the equation in point-slope form of the line passing through (4, 0) and (2, 6)? (5 points) y = 4x − 2 y = 2x − 4 y = −3(x − 4) y = 3(x + 4)
For this case we have that by definition, the point-slope equation of a line is given by:
[tex]y-y_ {0} = m (x-x_ {0})[/tex]
We have the following points:
[tex](x_ {1}, y_ {1}) :( 2,6)\\(x_ {2}, y_ {2}) :( 4,0)\\m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {0-6} {4-2} = \frac {-6} {2} = -3[/tex]
We chose a point:
[tex](x_ {0}, y_ {0}) :( 4,0)[/tex]
Substituting in the equation we have:
[tex]y-0 = -3 (x-4)\\y = -3 (x-4)[/tex]
Finally, the equation is: [tex]y = -3 (x-4)[/tex]
Answer:
OPTION C
Answer:
Third option: [tex]y=-3(x-4)[/tex]
Step-by-step explanation:
The equation of the line in Point-Slope form is:
[tex]y-y_1=m(x-x_1)[/tex]
Where "m" is the slope and [tex](x_1,y_1)[/tex] is a point on the line.
Given the points (4, 0) and (2, 6), we can find the slope with this formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Substituting values, we get:
[tex]m=\frac{0-6}{4-2}=-3[/tex]
Finally, substituting the slope and the point (4,0) into [tex]y-y_1=m(x-x_1)[/tex], we get:
[tex]y-0=-3(x-4)[/tex]
[tex]y=-3(x-4)[/tex]
what is the equation of the following line written in slope intercept form? (-5,-1)
Answer:
[tex]\large\boxed{y=-\dfrac{2}{3}x-\dfrac{13}{3}}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
From the graph we have two points (-5, -1) and (-2, -3).
Look at the picture.
Calculate the slope:
[tex]m=\dfrac{-3-(-1)}{-2-(-5)}=\dfrac{-2}{3}=-\dfrac{2}{3}[/tex]
Put it to the equation in slope-intercept form:
[tex]y=-\dfrac{2}{3}x+b[/tex]
We can't read the y-intercept from the graph. Therefore put the coordinates of the point (-5, -1) to the equation and calculate b:
[tex]-1=-\dfrac{2}{3}(-5)+b[/tex]
[tex]-1=\dfrac{10}{3}+b[/tex] subtract 10/3 from both sides
[tex]-\dfrac{3}{3}-\dfrac{10}{3}=b\to b=-\dfrac{13}{3}[/tex]
Finally:
[tex]y=-\dfrac{2}{3}x-\dfrac{13}{3}[/tex]
Which of the following is equivalent to 45x-5z.
A. 5(9x-z). B. 5x(45x-z). C. 10(9x-z). D. 5(9x^2-z) please answer thanks
Answer:
A. 5(9x-z)
Step-by-step explanation:
45x-5z
We can factor out a 5 from each term
5(9x -z)
Answer:
A.
Step-by-step explanation:
Given the expression, 45x - 5z, you have to think what can be factored out of BOTH terms.
we know 5 is a factor of both terms, so it can be taken out
=
5(9x - z), nothing else can be factored
Find the slope of the line that contains the points(6,-3) and (6, 5) or is it undefined
Answer:
Yes, it's undefined.
The slope is undefined.
Step-by-step explanation:
Slope formula:
[tex]\displaystyle \frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\displaystyle \frac{5-(-3)}{6-6}=\frac{8}{0}=0[/tex]
Therefore, the slope is undefined.
Hope this helps!
Answer:
undefined
Step-by-step explanation:
To find the slope of a line, we use the equation
m = (y2-y1)/(x2-x1)
= (5--3)/(6-6)
= (5+3)/(6-6)
=8/0
Anything divided by 0 is undefined, so the slope is undefined
Help me please I’m losted
Answer:
[tex]\frac{50}{3}[/tex]
Step-by-step explanation:
Similar shapes have corresponding sides that are proportional.
So 20 corresponds to x (big to small).
So 12 corresponds to 10 (big to small).
Your information is already lined up for you to setup your proportion:
[tex]\frac{20}{12}=\frac{x}{10}[/tex]
Cross multiply:
[tex]20(10)=12(x)[/tex]
Simplify both sides:
[tex]200=12x[/tex]
Divide both sides by 12:
[tex]\frac{200}{12}=x[/tex]
Simplify by dividing top and bottom by 4:
[tex]\frac{50}{3}=x[/tex]
You buy some living room furniture. The coffee table costs $189.99, the loveseat costs $249.95, the sofa costs $493.68, and 2 chairs cost $98.75 each. Sales tax is 7.25%. How much is your total purchase? $1,032.37 $1,213.13 $1,107.22 $1,131.12
Add the totals of each item together:
189.99 + 249.95 + 493.68 + 98.75 + 98.75 = 1,131.12
Now multiply that by the tax rate as a decimal:
1131.12 x 0.0725 = 82.01
Now add that to the total of the items:
1,131.12 + 82.01 = $1,213.13 total
For this case we have that the total of the purchase is given by:
Coffee table: $ 189.99
Loveseat: $ 249.95
Sofa: $ 493.68
2 chairs: 2 * $ 98.75 = $ 197.5
Adding up we have: $ 1131.12
Now, we must find the tax amount:
$ 1131.12 ----------> 100%
x ------------------------> 7.25%
Where "x" represents the value of the tax:
[tex]x = \frac {7.25 * 1131.12} {100}\\x = 82.0062[/tex]
Finally, the amount to be paid is:
$ 1131.12 + $ 82.0062 = $ 1213.13
Answer:
Option B
Solve for x. x2 + 7x + 10 = 0 A. -2, -5 B. -2, 5 C. 2, -5 D. 2, 5
Answer:
A. -2, -5
Step-by-step explanation:
x^2 + 7x + 10 = 0
Factor the equation
What 2 numbers multiply to 10 and add to 7
2*5 =10
2+5 = 7
(x+2) (x+5)=0
Using the zero product property
x+2 =0 x+5 =0
x=-2 x = -5