Answer:
The slope of the line through the points is -5/7
Step-by-step explanation:
Here, we want to calculate the value of the slope through the lines
Mathematically;
m = y2-y1/(x2-x1)
Where (x1,y1) = (-4,2)
and (x2,y2) = (3,-3)
Substituting these values, we have;
m = (-3-2)/(3-(-4)) = -5/7 = -5/7
Answer:
2 units to the LEFT
Step-by-step explanation:
i used khan
To factor the quadratic expression x^2−8x−10 by completing the square, what value would be added? A. 64 B. 8 C. 16 D.-16
Answer:
C
Step-by-step explanation:
When completing the square, we essentially want to create a perfect square trinomial by adding a constant.
If we have the following expression:
[tex]x^2+bx[/tex]
And we want to complete the square, we will need to divide the b-coefficient by half and then square it.
Thus, the added term should be:
[tex](b/2)^2[/tex]
In the given equation, we have:
[tex](x^2-8x)-10[/tex]
The b term here is 8. Therefore:
[tex](8/2)^2\\=(4)^2\\=16[/tex]
The value we would add would be 16.
The answer is C.
Further notes:
To complete the square, add 16 like mentioned earlier. However, we also need to subtract 16 to balance things out:
[tex](x^2-8x)-10\\=(x^2-8x+16)-10-16\\[/tex]
The expression inside the parentheses is now a perfect square trinomial. Factor it:
[tex]=((x)^2-2(4)(x)+(4)^2)-26\\=(x-4)^2-26[/tex]
And we are done!
A quadratic function equation is as follows:
[tex]ax^{2} + bx + c[/tex]
To complete the square, move the constant (c) to the other side of the equation and take half of the b value, square it, and add and subtract the same number.
In this problem, you will add 16.
[tex] \frac{ - 8}{2} = - 4[/tex]
[tex] - 4^{2} = 16[/tex]
A cruise ship charges $125 per night for a room there are 250 rooms on the ship if every room on the ship is booked how much money does the cruise ship make in a single night
Answer:
125
×
250
_____
000
6250
25000
answer 31250
125
⋅
250
is
31250
Answer:$31250
Step-by-step explanation: 125x250=000+6250+25000=$31250
Solve 3x+2y−z=2 2y+z=7 −2x−4z=−2 Enter your answer, in the form (x,y,z), in the boxes in simplest terms. x= y= z=
Answer:
(-1, 3, 1)
x=-1, y=3, z=1.
Step-by-step explanation:
So we have the three equations:
[tex]3x+2y-z=2\\2y+z=7\\-2x-4z=-2[/tex]
And we want to find the value of each variable.
To do so, look at the equations and try to think about what we can do to isolate one of the variables by itself.
We can see that both the second and equation has a variable and then the variable z.
In other words, we can solve for y in the second equation and x in the third equation and then substitute them in the first equation to isolate the variable z and then solve for z. With that, we can then easily arrive at our solution.
Therefore, solve for y in the second equation:
[tex]2y+z=7[/tex]
Subtract z from both sides. The zs on the left side cancels:
[tex](2y+z)-z=(7)-z\\2y=7-z[/tex]
Now, divide both sides by 2. The 2s on the left cancel and we've isolated the y variable:
[tex]\frac{(2y)}{2} = \frac{(7-z)}{2}\\y=\frac{(7-z)}{2}[/tex]
Now, do the same for the third equation. Isolate the x variable:
[tex]-2x-4z=-2[/tex]
First, divide everything by -2 to make things simpler:
[tex]\frac{(-2x-4z)}{-2}=\frac{(-2)}{-2}\\ x+2z=1[/tex]
Now, subtract 2z from both sides to isolate the x variable:
[tex](x+2z)-2z=1-2z\\x=1-2z[/tex]
We have isolated the x and y variables. They are:
[tex]y=\frac{(7-z)}{2}\\x=1-2z[/tex]
Now, we can substitute them back into the first equation. Therefore:
[tex]3x+2y-z=2\\3(1-2z)+2(\frac{7-z}{2})-z=2[/tex]
Distribute the first and second terms. The second term cancels out:
[tex]3(1)-3(2z)+(7-z)-z=2\\3-6z+7-z-z=2[/tex]
Combine like terms:
[tex]-6z-z-z+3+7=2\\-8z+10=2\\[/tex]
Subtract 10 from both sides:
[tex](-8z+10)-10=2-10\\-8z=-8[/tex]
Divide both sides by -8:
[tex]z=1[/tex]
Now that we've determined that z=1, plug it back into the isolated second and third equations:
Second equation:
[tex]y=\frac{(7-z)}{2}\\y=(7-1)/2\\y=(6)/2=3[/tex]
Third equation:
[tex]x=1-2z\\x=1-2(1)\\x=1-2=-1[/tex]
Therefore, our answer is (-1, 3, 1)
Answer:
(x, y, z) = (-1, 3, 1)
Step-by-step explanation:
Any of a number of web sites will solve systems of equations for you. Your graphing calculator will, too.
The solution is the right-most column in reduced row echelon form. Top to bottom, the variables are in order x, y, z.
(x, y, z) = (-1, 3, 1)
_____
If you like, you can use substitution to do this by hand.
z = 3x +2y -2 . . . . from the first equation
2y +(3x +2y -2) = 7 . . . . substituting into the second equation
3x +4y = 9 . . . . . in standard form
-2x -4(3x +2y -2) = -2 . . . . substituting for z into the third equation
14x +8y = 10 . . . . . in standard form
Subtract half the second equation from the first:
(3x +4y) -(7x +4y) = (9) -(5)
-4x = 4 . . . simplify
x = -1 . . . . . divide by 4
y = (9 -3x)/4 = (9 -3(-1))/4 = 12/4 = 3
z = 3(-1) +2(3) -2 = 1
The solution is (x, y, z) = (-1, 3, 1).
ZWXY is a right angle. If Z
is in the interior of ZWXY,
mZWXZ = 7x+8, and
m_ZXY = 5x-2, find the
value of x.
Answer:
The value of x = 7
Step-by-step explanation:
To solve this, we will have to fist of all know that the sum of all the angles in a right-angled triangle is 180 degrees.
In addition to that, since the triangle is a right-angled triangle, automatically, one of the angles is = 90 degrees
The next thing to do is to add all the angles together and equate them to 180 degrees.
Angle WXZ + Angle ZXY + 90 = 180 degrees
7x+8 + 5x-2 + 90 = 180
12x + 96 = 180
12x = 84
x = 7
can you guys please help me solve these
Answer:
See explanation below
Step-by-step explanation:
In all cases you need to isolate x on one side of the inequality symbol using inverse operations.
1.-
[tex]15+x\leq -45\\15-15+x\leq -45-15\\x\leq -60[/tex]
where we subtracted from both side 15 in order to leave x by itself on the left.
2.-
[tex]x-14>12\\x-14+14>12+14\\x>26[/tex]
where we added 14 in order to isolate x on the left
3.-
In this case we need to divide both sides by -5 in order to isolate the x which is being multiplied by the factor -5, but he have to recall that multiplying or dividing by a negative number changes the direction of the inequality symbol (in our case from < into > )
[tex]-5x<35\\\frac{-5\,x}{-5} >\frac{35}{-5} \\x>-7[/tex]
4.-
[tex]2x>-42\\\frac{2\,x}{2} >\frac{-42}{2} \\x>-21[/tex]
In this case we simply divide both sides by two, and there is no change in the direction of the inequality because the number we are using to divide is a positive number (2)
Jeff wants to go to a university where the tuition is $9,000 per year he has a scholarship that pays for 70% of his tuition yesterday his $3,000 toward the first Year's tuition does he have enough to pay for the first year tuition?
Scholarship will pay=
After the scholarship, Jeff will pay=
Answer:
Step-by-step explanation:
Amount of Jeff tuition per year = $9,000
If Jeff has a scholarship that pays 70% of his tuition, the amount the scholarship will pat Jeff = 70% of his yearly tuition fee.
Scholarship amount = 70/100 * $9,000
Scholarship amount = 70*90
Scholarship amount = $6,300
Hence the scholarship will pay Jeff $6,300
If the amount saved by Jeff is $3,000
Total amount that Jeff has = Scholarship amount + Amount saved
Total amount that Jeff has = $6,300 + $3000 = $9300
Since the total amount that Jeff has is more than the yearly tuition fee, this shows that he has enough to pay for the first year's tuition
2x - 2y = 2(x - y)
Name the property that justifies the given statement.
Answer:
Distributive property (Reversed)
Step-by-step explanation:
With the distributive property, it is possible to simplify expressions that consist of an expression term such as (a + b) being multiplied by one singular term such as c given as follows
c ×(a + b) = c·a + c·b
Factoring, which is the reverse use of the distributive property enables the difference or the sum of two products, each having a common factor to be the presented as the difference or the sum of two numbers multiplied by the common factor as follows;
2·x - 2·y = 2·(x - y).
Please solve (a^3 - 2a^2) - (3a^2 - 4a^3).
Hi there! Hopefully this helps!
-------------------------------------------------------------------------------------------------------
Answer: [tex]5a^{3} - 5a^{2}[/tex]. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~|[tex](a^{3} - 2a^{2}) - (3a^{2} - 4a^{3} )[/tex]
|
| To find the opposite of [tex]3a^{2} -4a^{3}[/tex], find the opposite of each term.
\/
[tex]a^{3} - 2a^{2} - 3a^{2} + 4a^{3}[/tex]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
|Combine [tex]-2a^{2}[/tex] and [tex]-3a^{2}[/tex] to get [tex]-5a^{2}[/tex].
\/
[tex]a^{3} - 5a^{2} + 4a^{3}[/tex]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
|Combine [tex]a^{3}[/tex] and [tex]4a^{3}[/tex] to get [tex]5a^{3}[/tex].
\/
Answer: [tex]5a^{3} - 5a^{2}[/tex]7b-b+1+3b
I’m trying to combine like terms plz help
Answer:
9b+1
Step-by-step explanation:
combine like terms
7b-1b+3b=9b
Answer:
9b+1
Step-by-step explanation:
7b-b+1+3b
(7b-b+3b) +1
(7-1+3)b +1
9b+1
What is the simplest form of (4x3 + 6x – 7) + (3x3 – 5x2 – 5x + 9)
Answer:
The simplest form of the given expression is 7x³ + 5x² + x + 2
Step-by-step explanation:
(4x³ + 6x - 7) + (3x³ - 5x² - 5x + 9)
Group like terms together.
(4x³ + 3x³) + 5x² + (6x - 5x) + (-7 + 9)
Combine like terms.
7x³ + 5x² + x + 2
So, this will be your simplest form of the given equation.
Answer:
7x³ + 5x² + x + 2
Step-by-step explanation:
What is the value of x?
Answer:
14
Step-by-step explanation:
You have the values for the hypotenuse (50) and one of the sides (48). You now have to find the second side using the Pythagorean Theorem.
a² + b² = c²
(48)² + b² = (50)²
2304 + b² = 2500
b² = 196
b = √196
b = 14
name the property illustrated by each statement
A dilation maps (6, 10) to (3,5). What are the coordinates of the image of (12, 4) under the same dilation?
Answer:
(6,2)
Step-by-step explanation:
Below are two parallel lines with a third line intersecting them.
2°
50°
The two angles are corresponding angles. Corresponding angles are congruent when we have parallel lines like this. The double arrow markers on the two lines show the lines are parallel.
Corresponding angles are angles that are on the same side of the parallel line, and also on the same side of the transversal line. Both 50 and x are in the upper right corner of each X four corner region.
O preço à vista de uma mercadoria é R$ 130,00. O comprador pode pagar 20% no ato da compra e o restante em uma única parcela vencível em 3 meses. Admitindo-se que nesta parcela será acrescido um valor correspondente a 10% sobre o saldo devedor (saldo devedor é o que falta pagar do valor da mercadoria), quanto custará essa parcela? a) R$ 114,40 b) R$ 117,00 c) R$ 110,20 d) R$ 112,23 e) R$ 128,96
Resposta: a) R $ 114,40
Explicação passo a passo:
Dado o seguinte:
Preço à vista da mercadoria = R $ 130
Pagamento inicial = 20% na compra
O saldo pode ser parcelado, o que adicionará 10% ao saldo devedor.
Portanto ; Pagamento inicial :
20% * 130
0,2 * 130 = R $ 26
Saldo devedor = R $ (130 - 26) = R $ 104
Parcela total devida:
Saldo de débito + 10% do saldo de débito
10% do saldo devedor:
0,1 * 104 = R $ 10,40
Parcela total:
R $ (104,00 + 10,40) = R $ 114,40
Which graph shows a system with an infinite number of solutions?
solve for brainliest
Answer:
7) 9.135x10^10
8) 3.428x10^-2
9) 2.5x10^-7
10) 4x10^10
Step-by-step explanation:
You’re only supposed to have one number to the left of the decimal point in scientific notation.
7) 9.135x10^10
8) 3.428x10^-2
9) 2.5x10^-7
10) 4x10^10
please help!! Thank you
Answer:
2. 3^2
Step-by-step explanation:
Use PEMDAS. First parenthesis, exponents (3^2), multiplication, division, addition, and subtraction.
The answer is 2 because you do the exponents in the parenthesis first.
NEED HELP ASAP ALGEBRA 2
Answer:
3√6
Step-by-step explanation:
[tex] {a}^{2} = {b}^{2} + {c}^{2} [/tex]
[tex] = {1}^{2} + {( \sqrt{53} )}^{2} [/tex]
[tex] = 1 + 53[/tex]
[tex] {a}^{2} = 54[/tex]
[tex]a = \sqrt{54} = 3 \sqrt{6} [/tex]
8x - 2 = -9 + 7x what does x equal
Answer:
x = - 7
Step-by-step explanation:
8x - 2 = -9 + 7x (add 2 to both sides)
8x - 2 + 2 = -9 + 7x + 2
8x = 7x - 7 (subtract 7x from both sides)
8x - 7x = 7x - 7 - 7x
x = - 7
Answer:x=-7
Step-by-step explanation:
Regroup terms.
8x-2=7x-98x−2=7x−9
2 Subtract 7x7x from both sides.
8x-2-7x=-98x−2−7x=−9
3 Simplify 8x-2-7x8x−2−7x to x-2x−2.
x-2=-9x−2=−9
4 Add 22 to both sides.
x=-9+2x=−9+2
5 Simplify -9+2−9+2 to -7−7.
x=-7x=−7
Solve the following equation for x to find the total number of sale items stocked on the shelves of a toy store for a certain week: x = 0.7x + 24 How many total items were stocked for that week?
Answer: 80 items
Step-by-step explanation:
The equation x=0.7x + 24 can be rewritten as 1x = 0.7x + 24 because the is a number on in front of any variable.
1x = 0.7x + 24 subtract 0.7 from both sides
-0.7 -0.7
0.3x = 24
x = 80
Write two inequalities to compare 25 and 23
Answer:
[tex]\huge \boxed{25>23} \\ \\ \huge \boxed{25 \geq 23}[/tex]
Step-by-step explanation:
25 is greater than 23.
greater than ⇒ [tex]>[/tex]
25 is greater than or equal to 23.
greater than or equal to ⇒ [tex]\geq[/tex]
Answer:
1) [tex]25 > 23[/tex]
2) [tex]25 \geq 23[/tex]
Step-by-step explanation:
25 is greater than 23
=> [tex]25 > 23[/tex]
25 is also almost equal to 23
=> [tex]25 \geq 23[/tex]
10(4-3i)= whats the answer
Answer: Hi!
To solve this equation, we first distribute to the terms inside of the parentheses.
10*4 = 40
10*-3i = -30i
Our equation now looks like this:
40 - 30i
There is nothing left to simplify, so you're done!
Hope this helps!
Jim completed half the floor in 9 hours Pete completed the other half of the floor in 5 hours of Pete can lay 35 more tiles per hour than Jim. What equation would you use to find the rate that Jim can lay tiles. Let x represent Jim's rate
Answer:
[tex]\bold{ 9x = (x+35)\times 5 }[/tex]
Step-by-step explanation:
Jim completed half of the floor in 9 hours.
Let the rate of Jim = [tex]x[/tex] tiles/hr
So, number of tiles that Jim lays in 9 hours = Rate of Jim multiplied by number of hours i.e. [tex]9 \times x[/tex] ..... (1)
Let [tex]y[/tex] tiles/hr be the rate at which Pete lays the tiles.
As per the given question, Pete can lay 35 more tiles per hour than Jim.
i.e. [tex]\bold{ y =x+35}[/tex]
It is given that half of the floor is done by Jim and other half by Pete.
So, we can say that number of tiles for both of them are equal.
Number of tiles by Pete = Rate of Pete [tex]\times[/tex] Number of hours = [tex](x+35) \times 5[/tex]...(2)
Now, we can equate the equations (1) and (2) because the number of tiles are same.
i.e.
The equation that we can use is:
[tex]\bold{ 9x = (x+35)\times 5 }[/tex]
Factor each of the following polynomial
lows.
1. 2x2 - 8x
Answer:
2x (x - 4)
Step-by-step explanation:
The linear function is represented by the equation y = Negative three-fifthsx – 2. What can be determined of this equation written in slope-intercept form? Check all that apply.
The y-intercept is Negative three-fifths
The y-intercept is 2.
The y-intercept is –2.
The slope is Negative three-fifths
The slope is 2.
The slope is –2.
Answer:
The y-intercept is –2.
The slope is Negative three-fifths
Step-by-step explanation:
A linear function is a function whose graph is a straight line. A linear function can be represented as:
f(x) = y = a + bx
where y is the dependent variable and x is the independent variable. The equation of a linear function in slope intercept form is given as:
y = mx + c
Where m is the slope and c is the y intercept.
Given that:
[tex]y=-\frac{3}{5}x-2[/tex], and comparing with y = mx + c:
The slope (m) = [tex]-\frac{3}{5}[/tex]
The y intercept (c) = -2
Answer:
The y-intercept is –2.
The slope is Negative three-fifths
Step-by-step explanation:
determine whether the square of the following numbers are odd or even. i) 2826 ii)7779 iii)30018 iv)8204
Answer:
Step-by-step explanation:
The square of an even number is an even .
The square of an odd number is an odd.
2826-even
7779-odd
30018-even
8204-even
Find the missing probability.
P(A)=720,P(A∩B)=49400,P(B)=?
P
(
A
)
=
7
20
,
P
(
A
∩
B
)
=
49
400
,
P
(
B
)
=
?
==========================================
Work Shown:
Given info
P(A) = 7/20
P(A∩B)=49/400
P(B) = unknown
--------------------
P(A∩B) = P(A)*P(B), assuming A and B are independent events
49/400 = (7/20)*P(B)
(7/20)*P(B) = 49/400
P(B) = (20/7)(49/400)
P(B) = (20*49)/(7*400)
P(B) = (20*7*7)/(7*20*20)
P(B) = 7/20
---------------------
Note how
P(A∩B) = P(A)*P(B)
P(A∩B) = (7/20)*(7/20)
P(A∩B) = (7*7)/(20*20)
P(A∩B) = 49/400
which helps to confirm the answer.
EXERCISE - 2.1
1. Find the degree of each of the polynomials given below
x power 5 - x power 4 + 3
Answer:
5
Step-by-step explanation:
the degree is 5
As degree means the largest exponent of a term
SOMEONE PLZ HELP ME!!!!!
Answer:
5 m/s
Step-by-step explanation:
cos 60 = 300/x
x = 300/cos 60 = 600
600m / 120sec
5 m/s