Answer:
[tex]\boxed{(\frac{3}{2} ,-1)}[/tex]
Step-by-step explanation:
[tex]\left \{ {{2x-3y=6} \atop {4x+2y=4}} \right.[/tex]
It seems this system of equations would be solved easier using the elimination method (the x and y values are lined up).
Multiply everything in the first equation by -2 (we want the 4x to be able to cancel out with a -4x).
[tex]2x-3y=6 \rightarrow -4x+6y=-12[/tex]
Now line up the equations (they are already lined up - convenient) and add them from top to bottom.
[tex]\left \{ {{-4x+6y=-12} \atop {4x+2y=4}} \right.[/tex]
The -4x and 4x are opposites, so they cancel out.
Adding 6y and 2y gives you 8y, and adding -12 and 4 gives you -8.
[tex]8y=-8[/tex]
Divide both sides by 8.
[tex]y=-1[/tex]
Since you have the y-value you can substitute this in to the second (or first equation, it doesn't necessarily matter) equation.
[tex]4x +2(-1)=4[/tex]
Simplify.
[tex]4x -2=4[/tex]
Add 2 to both sides.
[tex]4x=6[/tex]
Divide both sides by 4.
[tex]x=\frac{6}{4} \rightarrow\frac{3}{2}[/tex]
The final answer is [tex]x=\frac{3}{2} ,~y=-1[/tex].
[tex](\frac{3}{2} ,-1)[/tex]
For a line that goes through points (2,-2) and (1.-6), what is the equation
of the line in point-slope form?
Answer:
y + 2 = 4(x - 2)Step-by-step explanation:
[tex]\text{The point-slope form of an equation of a line:}\\\\y-y_1=m(x-x_1)\\\\m-slope\\(x_1,\ y_1)-point\ on\ a\ line\\\\\text{The formula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\======================================[/tex]
[tex]\text{We have the points:}\ (2,\ -2)\ \text{and}\ (1,\ -6).\\\\\text{Substitute:}\\\\m=\dfrac{-6-(-2)}{1-2}=\dfrac{-4}{-1}=4\\\\y-(-2)=4(x-2)\\\\y+2=4(x-2)[/tex]
8 lbs of cashew nuts cost $32. What is the cost of one pound?
Answer:
$4 per pound
Step-by-step explanation:
To find how much one pound of cashew nuts cost you have to use money over unit.
So money/unit, in this problem the money is 32 and the unit is 8.
So 32/8, now you divide 32 by 8 to get the price for one pound.
32 divided by 8 is 4
So $4 per pound
Answer:
The total cost of one pound is $4.
Step-by-step explanation:
[tex]\Large\textnormal{First, you divide the numbers from left to right to find the answer.}[/tex]
[tex]\displaystyle 32\div8=4[/tex]
[tex]\displaystyle \frac{8}{8}=1[/tex]
[tex]32\div4=8[/tex]
[tex]\displaystyle \frac{32}{8}=4\times1=4[/tex]
[tex]\Large \boxed{4}[/tex], is the correct answer.
I hope this helps you and have a wonderful day!
LOOK AT PICTURE. GEOMETRY SOLVING FOR MISSING ANGLE
If you are given the graph of h(x)=log(6)x, how could you graph m(x)=log(6)(x+3)? Translate each point of the graph of h(x) 3 units up. Translate each point of the graph of h(x) 3 units down. Translate each point of the graph of h(x) 3 units right. Translate each point of the graph of h(x) 3 units left.
Answer:
Last option: Translate each point of the graph of h(x) 3 units left.
Step-by-step explanation:
There are some transformations for a function f(x). The following is one of these transformations:
If [tex]f(x+k)[/tex], then the function is shifted "k" units to the left.
Given the function [tex]h(x)=log_6(x)[/tex] and the function [tex]m(x)=log_6(x+3)[/tex], you can notice that the function m(x) is the function h(x) but shifted left 3 units.
Therefore, you could graph the function m(x) by translating each point of the graph of the function h(x) 3 units left.
This matches with the last option.
Answer:
Last option (D) Translate each point of the graph of h(x) 3 units left.
All of the following are equivalent except___. 7x^3,4x+3x,(4+3)x,7x
Answer:
The one that is not equivalent is 7x^3
Step-by-step explanation:
7x^3= 7 * x*x*x
4x+3x = 7x = 7*x
(4+3)x = (7)x = 7*x
7x= 7*x
Answer:
7x^3
Step-by-step explanation:
All of the following are equivalent except 7x^3.
7x^3 = 7x^3
4x+3x = 7x
(4+3)x = 7x
7x = 7x
Which expression is equivalent to 6^-3?
6^3
3^6
3sqrt6
(1/6)^3
For this case we must find an expression equivalent to[tex]6 ^ {- 3}[/tex]
By definition of power properties we have to:
[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]
So, we can rewrite the given expression as:
[tex]6 ^ {3} = \frac {1} {6 ^ 3}[/tex]
This is equivalent to:
[tex](\frac {1} {6}) ^ 3[/tex]
Answer:
Option D
Answer:
The correct answer option is D. ( 1 / 6 ) ^ 3.
Step-by-step explanation:
We are given the following expression and we are to determine whether which of the given answer options is equivalent to this:
[tex] 6 ^ { - 3 } [/tex]
Rewriting this as a fraction to get:
[tex] \frac { 1 } { 6 ^ 3 } [/tex]
Therefore, the correct answer option is D. ( 1 / 6 ) ^ 3.
What transformation maps rectangle QRST to rectangle
Q'R'S'T'?
Answer:
The shaped is being reflected.
Answer: Reflection
Step-by-step explanation:
When we look at the picture, the two rectangles QRST and Q'R'S'T' appears as the mirror images of each other , also the corresponding sides and angles are congruent.
The transformation that create a mirror image of the figure is known as reflection. It is a rigid transformation because it produces congruent shapes.
Therefore, the transformation maps rectangle QRST to rectangle Q'R'S'T' is reflection.
What is the y-value of the vertex of the function f(x)=-(x-3)(x+11)
so, this is a quadratic equation, meaning two solutions, and we have a factored form of it, meaning you can get the solutions by simply zeroing out the f(x).
[tex]\bf \stackrel{f(x)}{0}=-(x-3)(x+11)\implies 0=(x-3)(x+11)\implies x= \begin{cases} 3\\ -11 \end{cases} \\\\\\ \boxed{-11}\stackrel{\textit{\large 7 units}}{\rule[0.35em]{10em}{0.25pt}}-4\stackrel{\textit{\large 7 units}}{\rule[0.35em]{10em}{0.25pt}}\boxed{3}[/tex]
so the zeros/solutions are at x = 3 and x = -11, now, bearing in mind the vertex will be half-way between those two, checking the number line, that midpoint will be at x = -4, so the vertex is right there, well, what's f(x) when x = -4?
[tex]\bf f(-4)=-(-4-3)(-4+11)\implies f(-4)=7(7)\implies f(-4)=49 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{vertex}{(-4~~,~~49)}~\hfill[/tex]
Write the following as an expression.
I have 10 pounds of nuts worth $d per pound. What is the value of the nuts?
Answer:
$10d
Step-by-step explanation:
The unit price is $d per pound. It is a dollar amount divided by the number of pounds. If you multiply the unit price by pounds, then the units work out like this:
$/lb * lb = $
When you multiply the unit price in dollars per lb by lb, you get dollars.
In your case:
$d/lb * 10 lb = $10d
That value of the nuts is $10d.
Which expression is equivalent to (4 ^5/4 times 4^1/2 divided by 4^1/2)
Answer:
[tex] 2 ^ { \frac { 5 } { 2 } [/tex]
Step-by-step explanation:
We are given the following expression which we are to find its simplest form:
[tex] \frac { 4 ^ { \frac { 5 } { 4 } } \times 4 ^ { \frac { 1 } { 2 } } } { 4 ^ { \frac { 1 } { 2 } } }[/tex]
Cancelling the like terms to get:
[tex] 4 ^ { \frac { 5 } { 4 } } [/tex]
[tex] 2 ^ { 2 .\frac { 5 } { 4 } } = 2 ^ { \frac { 5 } { 2 } } [/tex]
[tex] 2 ^ { \frac { 5 } { 2 } [/tex]
Answer:
B
Step-by-step explanation:
Which line contains the point (2,1)
4x-y=7
2x+5y=4
7x-y=15
X+5y=21
Answer:
4x - y = 7.
Step-by-step explanation:
We substitute for x and y and see if they fit.
4x - y = 7
4(2) - 1 = 7
So it is the first line.
Answer: First option.
Step-by-step explanation:
To find which line contains the point (2,1), we can substitute the coordinates into each equation of the line provided in the options:
First option:
[tex]4x-y=7\\4(2)-1=7\\7=7[/tex]
It contains the point (2,1)
Second option:
[tex]2x+5y=4\\2(2)+5(1)=4\\9\neq 4[/tex]
It does not contain the point (2,1)
Third option:
[tex]7x-y=15\\7(2)-1=15\\13\neq15[/tex]
It does not contain the point (2,1)
Fourth option:
[tex]x+5y=21\\2+5(1)=21\\7\neq 21[/tex]
It does not contain the point (2,1)
1,547.489 which digit is in the ten place
1,547.489
4 - Bold and underline one above is in the ten place.
Answer:
1,547.489
Step-by-step explanation:
Note that there is a decimal point in between 7 & 4, and the numbers to the left are whole numbers, while the numbers to the right is part of the decimal.
From the decimal point, count to the left two place value (to find the tens place):
1,547
1,547
4 is your digit in the ten's place, & is your answer.
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Alan's dogs have a total of 24 legs (l). If each dog has 4 legs, which equation gives the number of dogs (d) that Alan has?
Answer: 24/4=D
Step-by-step explanation:
24LEGS/4LEGS=6DOGS
Answer:
4d=24
Step-by-step explanation:
4(dogs)=24 legs
so the answer is 6 dogs (in case you need it)
What are the solutions to x2 + 8x + 7 = 0?
A.x= -8 and x = -7
B.x=-7 and x = -1
C.x= 1 and x = 7
D.x= 7 and x = 8
Answer:
B
Step-by-step explanation:
x² + 8x + 7 = 0
x²+x+7x+7=0
x(x+1)+7(x+1)=0
(x+1)(x+7)=0
Either x=-1or x=-7.
2 PUNTS
This circle is centered at the origin, and the length of its radius is 2. What is
the circle's equation?
Answer:
x^2 + y^2 = 4
Step-by-step explanation:
The center-radius form (formally called the standard form) of a circle is
(x-h)^2+(y-k)^2=r^2 where (h,k) is the center and r is the radius.
So if we replace (h,k) with (0,0) since the center is the origin and r with 2 since the radius is 2 we get:
(x-0)^2+(y-0)^2=2^2
Let's simplify:
x^2 + y^2 = 4
How to solve 3,4 and 6
Answer:
[tex]\large\boxed{3.\ V\approx130.88\ m^3}\\\boxed{4.\ V\approx35.21}\\\boxed{6.\ V\approx1.06\ in^3}[/tex]
Step-by-step explanation:
3.
The formula of a volume of a sphere:
[tex]V=\dfrac{4}{3}\pi R^3[/tex]
R - radius
We have R = 3.15 m. Substitute:
[tex]V=\dfrac{4}{3}\pi(3.15)^3\approx\dfrac{4}{3}\pi(31.26)\approx\dfrac{4}{3}(3.14)(31.26)\approx130.88\ m^3[/tex]
4.
The formula of a volume of a cone:
[tex]V=\dfrac{1}{3}\pi r^2H[/tex]
r - radius
H - height
We have 2r = 11.6 → r = 5.8 and H = x. Substitute:
[tex]V=\dfrac{1}{3}\pi(5.8)^2(x)=\dfrac{1}{3}\pi(33.64)x\approx\dfrac{1}{3}(3.14)(33.64)x\approx35.21[/tex]
6.
The formula of a volume of a cube:
[tex]V=s^3[/tex]
s - edge
We have s = 1.02 in. Substitute:
[tex]V=(1.02)^3\approx1.06\ in^3[/tex]
An object is launched from a platform.
Its height (in meters), x seconds after the launch, is modeled by
h(x)=-5(x+1)(x-9)
What is the height of the object at the time of launch?
_________ meters
Please answer as soon as possible please!
Answer:
45 meters
Step-by-step explanation:
If x represents the seconds after the launch, then the time of launch is when x=0 so you just need to solve for h(0)
h(0) = -5(1)(-9)
h(0) = 45
Answer:
45 m
Step-by-step explanation:
At the time of launch, the time x = 0
Substitute x = 0 into h(x)
h(0) = - 5 (0 + 1)(0 - 9) = - 5(1)(- 9) = - 5 × - 9 = 45
x2 + 2x2 + 3x + 6
Factor
Answer:
See Below.
Step-by-step explanation:
I'm going to take the equation to be
y = x3 + 2x2 + 3x + 6
That is, the first term is a typo
make 2 groups. Put brackets around both groups.
group 1: x^3 + 2x^2 Take out the common factor of x^2
group 1: x^2(x + 2)
group 2: 3x + 6 Take out the common factor of x^2
group 2: 3(x + 2)
Now put the two groups together
Cubic = group 1 + group 2
Cubic = x^2 (x + 2) + 3(x + 2)
Now take out the common factor of x + 2
Cubic = (x + 2) (x^2 + 3)
in the first quadrant you start at (4,5) and move 2 units down
Answer:
(4,3)
Step-by-step explanation:
asoming 4 is x and 5 is y down 2 turns 5 into 3
Start at the point (4,5). Moving 2 units down decreases the y-coordinate by 2, thus bringing you to the new point (4,3). Draw a graph to visualize this better.
Explanation:In the context of a grid in Mathematics, the first quadrant is where both x and y coordinates are positive. The given point starts at (4,5). If you move 2 units down, it means you are reducing the y-coordinate by 2 units. So, starting at (4,5) and moving 2 units down would land you at a new point, which will be (4,3).
To visualize this, you may want to draw a graph on an x-y axis and plot the points (4,5) and (4,3) to see how the position change looks.
Learn more about Co-ordinates here:https://brainly.com/question/32595209
#SPJ2
The height of the parallelogram, h, can be found by dividing the area by the length of the base. If the area of the parallelogram is represented by 4x2 – 2x + 5 and the base is 2x – 6, which represents the height? 2x + 5 + 2x – 7 – 2x – 7 + 2x + 5 –
Answer:
[tex]\frac{4x^{2}-2x+5}{2x-6} =2x + 5 + \frac{35}{2x-6}[/tex]
Step-by-step explanation:
We know that the height of a parallelogram can be found by divind the area by the lenght of the base.
The area is 4x2 – 2x + 5 and the base is 2x – 6. To find the height, we need to divide both polynomials:
[tex]\frac{4x^{2}-2x+5}{2x-6} =2x + 5 + \frac{35}{2x-6}[/tex]
Answer:
[tex]2x+5+\frac{35}{2x-6}[/tex]
Step-by-step explanation:
Given,
The area of the parallelogram, A = [tex]4x^2-2x+5[/tex]
The length of its base, b = [tex]2x-6[/tex]
∵ The height of the parallelogram.
[tex]h=\frac{A}{b}[/tex]
[tex]\implies h=\frac{4x^2-2x+5}{2x-6}[/tex]
[tex]=2x+5+\frac{35}{2x-6}[/tex] ( by long division shown below )
Hence, the height of the given parallelogram is,
[tex]2x+5+\frac{35}{2x-6}[/tex]
Suppose line n has a slope of 5/7 and passes through (4,8). what is the equation for n in point-slope form?
Answer:
[tex]\large\boxed{y-8=\dfrac{5}{7}(x-4)}[/tex]
Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
We have the slope [tex]m=\dfrac{5}{7}[/tex] and the point [tex](4,\ 8)[/tex].
Substitute:
[tex]y-8=\dfrac{5}{7}(x-4)[/tex]
I need help please.
Answer:
= 9x³+ 0x²+0x -52....
Step-by-step explanation:
Descending powers means you start with highest power and then decrease.
In this expression the highest power is 3. We do not have any variable with power 2 and 1. So we will write it as:
9x³ - 52
= 9x³+ 0x²+0x -52....
find the value of x if A, B and C are collinear points and B is between A and C. AB= 6x, BC= x-5, AC= 23
Answer:
x=4
Step-by-step explanation:
AB + BC = AC
AB= 6x, BC= x-5, AC= 23
Substituting what we know
6x + x-5 = 23
Combine like terms
7x -5 = 23
Add 5 to each side
7x-5+5 =23+5
7x = 28
Divide each side by 7
7x/7 = 28/7
x=4
the first two steps in determining the solution set of the system of equations y=x^2-6x
+12 and y=2x-4. Which represents the solution(s) of this system of equations?
For this case we have the following system of equations:
[tex]y = x ^ 2-6x + 12\\y = 2x-4[/tex]
Equating the equations:
[tex]x ^ 2-6x + 12 = 2x-4\\x ^ 2-6x-2x + 12 + 4 = 0\\x ^ 2-8x + 16 = 0[/tex]
We look for two numbers that when multiplied, get 16, and when added together, get -8.
These numbers are -4 and -4.
[tex](x-4) (x-4) = 0\\(x-4) ^ 2 = 0[/tex]
So, the solution is[tex]x = 4[/tex]
We look for the value of y:
[tex]y = 2x-4\\y = 2 (4) -4\\y = 8-4\\y = 4[/tex]
Finally, the solution is:[tex](4,4)[/tex]
ANswer:
[tex](4,4)[/tex]
What is the smallest positive integer that will make x^x > 500,000? What
is the largest negative integer that will make x^(-x) >500000?
Answer:
For [tex]x^x > 500,000[/tex] [tex]x=7[/tex]
For [tex]x^{(-x)} > 500,000[/tex] [tex]x=-7[/tex]
Step-by-step explanation:
We need to find the smallest positive whole number that satisfies the inequality:
[tex]x^x > 500,000[/tex]
We tested with x = 6
[tex]6^6=46,656[/tex]
[tex]46,656 > 500,000[/tex]
Inequality is not met because [tex]46,656 < 500,000[/tex]
We test with the following integer x = 7
[tex]7^7=823,543[/tex]
[tex]823,543 > 500,000[/tex]
Then the smallest positive integer that will make [tex]x^x > 500,000[/tex] is 7
Inequality is met.
In the same way the largest negative integer that will make [tex]x^{(-x)} >500000[/tex] is [tex]x=-7[/tex] Beacuse [tex]7^{-(-7)}=823,543[/tex]
Answer:
Smallest positive integer value for [tex]x^x>5000[/tex] is,
x = 7,
Largest negative integer value for [tex] x^{-x} >500000[/tex] is,
x = -8
Step-by-step explanation:
If [tex]x^x>500000[/tex]
∵ If x is a positive integer then the possible values of x = 1, 2, 3, 4, 5, 6, 7.....
Case 1 : If x < 7,
[tex]x^x < 500000[/tex]
Case 2 : If x ≥ 7,
[tex]x^x > 500000[/tex]
Hence, smallest positive integer value of x is 7.
Now, if [tex]x^{-x}>500000[/tex]
∵ If x is negative integer then the possible value of x = -1, -2, -3, -4,.....
Case 1 : if x is odd negative integer,
[tex]x^{-x} < 50000[/tex]
eg : -1, -3, -5, -7,...
Case 2 : If x is even negative integer then there are further two cases,
(i) x is more than or equal to -6,
[tex]x^{-x} < 500000[/tex]
eg x = -6, -4, -2,
(ii) x is less than -8,
[tex]x^{-x} > 50000[/tex]
eg : x = -10, -12, -14,...
Hence, the largest negative integer value that will make [tex]x^{-x}> 500000[/tex] is x = -8.
Find the distance between the points (–9, 0) and (2, 5).
Answer:
sqrt( 146)
Step-by-step explanation:
To find the distance between two points, we use the formula
d = sqrt( ( y2-y1)^2 + (x2-x1)^2)
Where (x1,y1) and (x2,y2) are the two points.
(–9, 0) and (2, 5).
Substituting into the equation
d = sqrt( (5-0)^2 + (2- -9)^2)
d = sqrt( ( 5^2 + (2+9)^2)
sqrt( ( 5^2 + (11)^2)
= sqrt( 25+121)
= sqrt( 146)
The distance between the two points is sqrt(74)
Final answer:
The distance between the points (–9, 0) and (2, 5) in the Cartesian plane is approximately [tex]\sqrt{146}[/tex] units.
Explanation:
To find the distance between two points in the Cartesian plane, we can use the distance formula.
The distance formula is:
distance = [tex]\sqrt{((x_2 - x_1)^2 + (y_2 - y_1)^2)}[/tex]
Using the given points (–9, 0) and (2, 5), we can plug in the values:
distance = [tex]\sqrt{((2 - (-9))^2 + (5 - 0)^2)}[/tex]
distance = [tex]\sqrt{((11)^2 + (5)^2)}[/tex]
distance = [tex]\sqrt{(121 + 25)}[/tex]
distance = [tex]\sqrt{146}[/tex]
So, the distance between the points (–9, 0) and (2, 5) is approximately [tex]\sqrt{146}[/tex] units.
Which statements are true regarding the prism? Check
all that apply.
The prism has no vertices.
The prism has 9 edges.
The bases of the prism are triangles.
The bases of the prism are rectangles.
The prism has 5 faces.
O
Answer:
1. The base is a triangle.
Step-by-step explanation: This one seems like it's the only corret one, You might have to wait and see the other answers roll in.
Answer:
2,3&5
Step-by-step explanation:
got it right on edg 2020
what’s the value of y ?
hey! the value of y is 57
3 sin^{2} x +cos 2x= (5/4)
answer in radians
Answer:
I believe it's 0.540717
Step-by-step explanation:
3(sin(2))x+(cos(2))(x)=5/4
Simplify: 2.311745x=5/4
Divide: 2.311745x/2.311735=5/4/2.311745
x=0.540717
h(x) = 3x - 4
What is h(6)?
ETĀ. 14
e c. 22
SUBMIT
[tex]h(6)=3\cdot6-4=14[/tex]
Answer:
a. 14 is your answer.
Step-by-step explanation:
h(x) = 3x - 4
h(6) = ?
Plug in 6 for x: x = 6
h(6) = 3(6) - 4
Remember to follow PEMDAS. First, multiply, then subtract:
h(6) = (3 * 6) - 4
h(6) = (18) - 4
Simplify:
h(6) = 18 - 4
h(6) = 14
a. 14 is your answer.
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