Answer:
5 is the answer
Step-by-step explanation:
because i said it was
Simultaneous equations can be solved by substitution, elimination, graphs and by matrices.
The values of x, y and z are:
[tex]\mathbf{x =3}[/tex].[tex]\mathbf{y = 6}[/tex].[tex]\mathbf{z = -1}[/tex]The equations are given as:
[tex]\mathbf{-x - y -z = -8}[/tex]
[tex]\mathbf{-4x + 4y +5z = 7}[/tex]
[tex]\mathbf{2x +2z = 4}[/tex]
Make z the subject in [tex]\mathbf{2x +2z = 4}[/tex]
[tex]\mathbf{2z = 4 - 2x}[/tex]
Divide by 2
[tex]\mathbf{z = 2 - x}[/tex]
Substitute [tex]\mathbf{z = 2 - x}[/tex] in [tex]\mathbf{-x - y -z = -8}[/tex]
[tex]\mathbf{-x - y -z = -8}[/tex]
[tex]\mathbf{-x - y - (2-x) = -8}[/tex]
[tex]\mathbf{-x - y - 2+x = -8}[/tex]
Cancel out common terms
[tex]\mathbf{- y - 2 = -8}[/tex]
Add 2 to both sides
[tex]\mathbf{- y = -8+2}[/tex]
[tex]\mathbf{- y = -6}[/tex]
Divide by -1
[tex]\mathbf{y = 6}[/tex]
Substitute [tex]\mathbf{z = 2 - x}\mathbf{\ and\ y = 6}[/tex] in [tex]\mathbf{-4x + 4y +5z = 7}[/tex]
[tex]\mathbf{-4x + 4 \times 6 + 5 \times (2 - x) = 7}[/tex]
[tex]\mathbf{-4x + 24 + 5 \times (2 - x) = 7}[/tex]
Open brackets
[tex]\mathbf{-4x + 24 + 10 - 5x = 7}[/tex]
Collect like terms
[tex]\mathbf{-4x - 5x =- 24 - 10 + 7}[/tex]
[tex]\mathbf{-9x =-27}[/tex]
Divide through by -9
[tex]\mathbf{x =3}[/tex]
Recall that: [tex]\mathbf{z = 2 - x}[/tex]
So, we have:
[tex]\mathbf{z = 2-3}[/tex]
[tex]\mathbf{z = -1}[/tex]
Hence, the results are:
[tex]\mathbf{x =3}[/tex]
[tex]\mathbf{y = 6}[/tex]
[tex]\mathbf{z = -1}[/tex]
Read more about simultaneous equations at:
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The points (80, 20) and (120, 30) form a proportional relationship. What is the slope of the line that
passes through these points?
1
N
4
3
ООО
10
40
4
Previous
5
Answer:
The slope is 1/4.
Step-by-step explanation:
m = y2-y1 / x2-x1
Hope this helps. Pls give brainliest.
Answer:
The slop is 1/4
Step-by-step explanation:
m = y2-y1 / x2-x1
State if the given functions are inverses. *
Answer:
i beleive its a yes
Step-by-step explanation:
Use the provided information to write the standard form equation of the parabola.
Opens up or down, and passes through (4,-5), (0,3), and (-1,10)
Answer:
f(x) = x² - 6x + 3Step-by-step explanation:
Parabola f(x) = ax² + bx + c passing through point (x₁, y₁) means if x=x₁ then f(x)=f(x₁)=y₁
(0, 3) ⇒ 3=a·0²+b·0+c ⇒ c=3
f(x) = ax² + bx + 3
(4, -5) ⇒ -5 = a·4² + b·4 + 3
-5 = 16a + 4b + 3
-4b = 16a + 8
b = - 4a - 2
(-1, 10) ⇒ 10 = a·(-1)² + b·(-1) + 3
10 = a - b + 3
b = a - 7
a - 7 = - 4a - 2
5a = 5
a = 1
b = 1 - 7 = - 6
So the equation:
f(x) = x² - 6x + 3
6 3/5 - 1 2/3 = ?
find the answer to the Mix number problem.
Answer:
4 14/15
Step-by-step explanation:
pls help i don't know what it is asking
Answer:
e=1
Step-by-step explanation:
Whats the slope of the equation 6x + 8y = 16?
Answer:
-3/4
Step-by-step explanation:
6x+8y=16
(subtract 6x from both sides)
8y=-6x+16
(divide everything by 8)
y=-6/8x+16
(simplify)
y= -3/4x+16
this is now in y=mx+b form. m=slope
what’s the slope of (6,6) and (1,9)
Answer:
-3/5
Step-by-step explanation:
always remember rise by run. subtract the second y value from the first (9 minus 6) and the same with the x values (1-6). rise is y axis and run is x axis. therefore, you get 3/-5 or -3/5. (because 9-6 is 3 for the numerator and 1-6 is -5 for the denominator)
Can someone divide these two? I forgot how to over quarantine and it’s my sisters homework
Answer:
Step-by-step explanation:
Carli can walk 40 dogs in 8 hours. How many dogs can she walk in 12 hours?
Answer:
60 dogs
Step-by-step explanation:
40/8 = 5 dogs per hour
12 x 5 = 60 dogs in 12 hours
Write the equation of the line that has the indicated slope and y-intercept.
Slope = 5; y-intercept = 9
Answer:
slope intercept form: y=5x+9
standard form: x-5/y =-9/5
Step-by-step explanation:
slope intercept form: y=mx+b, m=slope, b=y-intercept
m= 5, b=9 therefore,
y=5x+9
Which of the following represents 2 – 4i?
Answer:
Graph B
Step-by-step explanation:
edge
Solve using long division
(x^2 – 3x - 40) / (x+5)
Answer:
X-8
Step-by-step explanation:
Thats it.
1/2 +4/7 please help me
Answer:
next time dont answer my question saying dumb shi
Step-by-step explanation:
Please help me It was due a few weeks ago!
these two polygons are similar
Answer:
w=9
Step-by-step explanation:
Find the first, fifth, and tenth terms of the sequence that has the rule:
A(n)=-8+(n-1)(4)
Step-by-step explanation:
A(n)=-8+(n-1)(4)
A(1)=-8
A(5)=-8+16
=8
A(10)=-8+36
=18
Determine if the Mean Value Theorem for Integrals applies to the function f(x) = 3 - x2 on the interval the closed interval from 0 to the square root of 3 . If so, find the x-coordinates of the point(s) guaranteed by the theorem
Answer: Yes, Mean Value Theorem for Integrals applies for the function [tex]f(x)=3-x^{2}[/tex] and values of x are 1 and -1
Step-by-step explanation: Mean Value Theorem for Integrals states that if a function is continuous on a closed interval, there is a value c on the interval such that
[tex]f(c)=\frac{1}{b-a} \int\limits^b_a {f(x)} \, dx[/tex]
where a and b are the closed interval given
As the graph of [tex]f(x)=3-x^{2}[/tex] shown below, the function is continuous on the interval [0,[tex]\sqrt{3}[/tex]], so the theorem applies.
To find the x-coordinates, first determine value of f(c) at [0,[tex]\sqrt{3}[/tex]]:
[tex]f(c)=\frac{1}{\sqrt{3} -0} \int\limits {3-\sqrt{x^{2}} } \, dx[/tex]
[tex]f(c)=\frac{1}{\sqrt{3}}[3x-\frac{x^{3}}{3} ][/tex]
[tex]f(c)=\frac{1}{\sqrt{3}}[ 3\sqrt{3}-\frac{(\sqrt{3})^{3}}{3} ][/tex]
[tex]f(c)=\frac{1}{\sqrt{3} } [2\sqrt{3} ][/tex]
f(c) = 2
The x-coordinates will be:
[tex]f(x)=3-x^{2}[/tex]
[tex]2=3-x^{2}[/tex]
[tex]x^{2}=1[/tex]
[tex]x=\sqrt{1}[/tex]
x = ±1
The values for x guaranteed by the Mean Value Theorem are +1 and -1.
Is the vertex of the function y-
-1
2 x² - 4
a maximum or a minimum? How can you tell?
a. Minimum, because it is below the x-axis.
b. Minimum, because there is no bx term.
C. Maximum, because the coefficient on za is a fraction smaller than 1.
d. Maximum, because the coefficient on xo is negative.
What are the coordinates of (2,5) after a reflection of the x-axis?
Answer:
(2,-5)
Step-by-step explanation:
rule: (x,y) ---> (x,-y)
(2,5) ----> (2,-5)
(2) 6(3n-3)=9 What is n?
Answer:
its 3/2
Step-by-step explanation:
6(3n-3)=9
18n -18=9
+18 +18
18n=27
------ ------
18 18
27/18=3/2
n=3/2
Solve using elimination
3x+3y=27
x-3y= -11
Answer:
(4, 5)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASEquality PropertyAlgebra I
Solving systems of equations using substitution/eliminationStep-by-step explanation:
Step 1: Define systems
3x + 3y = 27
x - 3y = -11
Step 2: Solve for x
Eliminate y (add equations): 4x = 16Divide 4 on both sides: x = 4Step 3: Solve for y
Define original equation: x - 3y = -11Substitute in x: 4 - 3y = -11Subtract 4 on both sides: -3y = -15Divide -3 on both sides: y = 5Can you leave a radical in the denominator?
Yes
No
Answer:
no
Step-by-step explanation:
Traditionally, a radical or irrational number cannot be left in the denominator (the bottom) of a fraction. When a radical does appear in the denominator, you need to multiply the fraction by a term or set of terms that can remove that radical expression.
Consider the equation r = 5 sin(θ). Use the drop-down boxes to complete the sentences.
The solutions to the blanks are Circle, y-axis and 5 units, respectively.
What is the equation of the circle?The equation of the circle whose center is coordination at (h,k) and radius is r will be
(x -h)² +(y -k)² = r²
where (h,k) is the coordination of its center and r is the radius.
We have,
r = 5 sinΘ
So,
When the center of the circle is at origin (0,0);
Then x² + y² = r²
So,
We have, r = 5 sinΘ
So,
For 0 ≤ θ ≤ π,
The circle is developed above the x-axis and symmetrical about the y-axis (θ=π/2)
The circle has a radius of 5/2, centered at (0, 5/2), so the diameter is 5 units.
And hence the greatest distance between any two points on a graph is 5 units.
Therefore, the solutions to the blanks are Circle, y-axis, and 5 units, respectively.
Learn more about the circle here:
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Paul, Colin and Brian are waiters.
One night the restaurant earns tips totalling £77.40.
They share the tips in the ratio 2:3:4.
How much more does Brian get over Paul?
=====================================================
Explanation:
x is some positive number such that the earnings of Paul, Collin, and Brian are 2x, 3x and 4x in that order
The ratio 2x:3x:4x reduces to 2:3:4 when we divide all parts by x
The total amount of tips was 77.40 pounds
This means,
(Paul's Share)+(Collin's Share)+(Brian's Share) = Total Tips
(2x)+(3x)+(4x) = 77.40
9x = 77.40
x = 77.40/9
x = 8.6
Use that x value to find each of their share of tips
Paul's Share = 2x = 2*8.6 = 17.20 poundsCollin's Share = 3x = 3*8.6 = 25.80 poundsBrian's Share = 4x = 4*8.6 = 34.40 poundsAs a check, note how 17.20+25.80+34.40 = 77.40
The last step is to subtract the values for Brian and Paul
34.40 - 17.20 = 17.20
Brian earned £17.20 more in tips compared to Paul.
what is the answer?
Answer:
4
Step-by-step explanation:
a triangle has angles that add up to 180°
an equilateral triangle has equal angles
so each angle is 60° (because 180/3 is 60)
so 10x +20 = 60
10x = 40
x = 4
There are 2.54 centimeters in 1 inch. There are 100 centimeters in 1 meter. How many inches are there in 12 meters
Answer:
1200 centimeters
Step-by-step explanation:
if you have 100 centimeters in 1 meter and there are 12 meters you can just multiply the number of centimeters by 12 or whatever number is needed in this case 12 so when you multiply 12 x 100 you get 1200
‼️GEOMETRY‼️
What is the approximate surface area of the largest sphere that can fit inside a cube with a side length of 18 inches?
1018 square inches
1356 square inches
4069 square inches
6104 square inches
Answer:
A.) 1018 square inches
Step-by-step explanation:
The largest sphere will have a diameter equaling the length of the cube (see picture).
If the side length of the cube is 18 inches, the diameter of the sphere is also 18 inches. Use the surface area formula for a circle:
[tex]SA=4\pi r^2[/tex]
For this formula, we need the radius of the sphere. Divide the diameter by 2:
[tex]\frac{18}{2}=9[/tex]
The radius is 9 inches. Plug this into the equation:
[tex]SA=4\pi *9^2[/tex]
Simplify the equation:
[tex]SA=4\pi *81\\\\SA=324\pi \\\\SA=1017.87[/tex]
Round the result to the nearest whole number:
[tex]1017.87[/tex] → [tex]1018[/tex]
The surface area is 1,018 inches².
:Done
Picture:
In a 2D version, we can clearly see that if the circle fits snuggly inside of the square, the diameter of a sphere is the same as the length of a side of the cube.
Four dice are placed into your hand and you roll all dice onto the floor. What are the odds that all
four dice will show an even number?
Answer:
0.0625 or 6.25%
Step-by-step explanation:
You have a 50% chance of each die to roll a even. Since you are rolling 4 you need to times them together. So .5*.5*.5*.5=0.0625 or 6.25%
A collection of triangular and square tiles contain 50 pieces and 170 sides. Write and solve a system to find how many triangular and square tiles there are.
Answer:
30 triangular tiles and 20 square tiles
Step-by-step explanation:
hope this helps
What is the constant term in the polynomial expression -7x2 + 32x + 240, and what does it represent?
Answer:
The constant term is 240. A constant term represents a fixed value. In other words, a term that does not change.
Step-by-step explanation:
In the polynomial expression given, the first and second terms are dependent of x, which means whatever the value x is, the terms will change. For example, if x = 2, we have -7(4) + 32(2) + 240. As you can see the constant never changes because it does not rely on a variable; it is constant.