Answer: x = -2 and y = -5
We are given two system of equations
-6x - 2y = 22 ---------------- equation 1
-12x + 10y = - 26------------- equation 2
These two system of equations can be solve simultaneously using elimination method
Before we can apply elimination method, we need to make one of the variables equal in both equations
Let us eliminate x
To make the co -efficient of x equal in both equations, Multiply equation 1 by 2 and equation 2 by 1
-6x - 2y = 22 * 2
-12x + 10y = -26 * 1
This becomes
-6x * 2 - 2y* 2 = 22*2
-12x*1 + 10y *1 = -26 * 1
-12x - 4y = 44------------------- equation 3
-12x + 10y = -26 --------------- equation 4
To eliminate x, substract equation 4 from equation 3
-12x - (-12x) - 4y - (10y) = 44 - (-26)
-12x + 12x -4y -10y = 44 + 26
0 - 14y = 70
-14y = 70
Divide both sides by -14
[tex]\begin{gathered} \frac{-14y}{-14}\text{ = }\frac{70}{-14} \\ y\text{ = }\frac{70}{-14} \\ y\text{ = -5} \end{gathered}[/tex]To find x, substitute the value of y = -5 into equation 1
-6x - 2y = 22
-6x - 2(-5) = 22
-6x + 10 = 22
-6x = 22 - 10
-6x = 12
Divide both sides by -6
[tex]\begin{gathered} \frac{-6x}{-6}\text{ = }\frac{12}{-6} \\ x\text{ = }\frac{12}{-6} \\ x\text{ = -2} \end{gathered}[/tex]Hence, x = -2, and y = -5 : (-2, -5)
Evalueate: 12(x - t)if x = 7 and t = 2
12(x - t)
if x = 7 and t = 2
12(x - t) = 12(7 - 2) = 12 * 5 = 60
Answer:
60
the ratio 19 yellow beads to 4 red
Answer:
[tex] = 19 : 4[/tex]
Step-by-step explanation:
it is a fixed ratio
Annie's mother asked Annie to go buy oranges, dog food, and bug spray. Each square's side length is 1 block. How many blocks will Annie have to walk in all if she visits the fruit stand, the pet store, and the supermarket, in that order, before returning home?
Here using the length of square, it is obtained that
Annie walked 14 blocks in total.
What is a square?
Square is a two dimensional four sided figure.
Here,
Length of each side of one square = 1 block
From Annie's home to the supermarket, Annie will have to walk 1 block
From Supermarket to pet store, Annie will have to walk 1 block straight and then 2 blocks to the left
From pet store to the fruit vendor, Annie will have to walk 1 block straight and then 2 blocks to the left
Total number of blocks walked by Annie from home = 1 + 1 + 2+ 1 + 2
= 7 blocks
Total number of blocks walked by Annie while returning home
= 1 + 1 + 2+ 1 + 2
= 7 blocks
Total number of blocks walked by Annie = 7 + 7 = 14 blocks
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Complete Question
The figure has been attached
So I am trying to figure how it do this again
Okay, here we have this:
Considering the provided points, we are going to identify the corresponding ordered pairs, so we obtain the following:
Let us remember that the coordinate of a point corresponds to (x,y), so from this we have:
Point A: (4,1)
Point B: (-2,3)
Point C: (1, 0)
Point D: (3, -2)
Point E: (0, -4)
Point F: (-1 , -2)
How many natural numbers less than 200 are divisible by 4 but not divisible by 3.
The answer to the given question is 32. There are 32 natural numbers less than 200 which are divisible by 4 but not divisible by 3.
What are natural numbers?
Natural numbers are those numbers used for counting and ordering. Numbers that used for counting are called cardinal numbers, and numbers that used for ordering are called ordinal numbers. Natural numbers are positive numbers which start from one up to infinity.
Now, to answer the question, firstly we need to find out all the natural numbers which are less than 200 and divisible by 4. We need to find out all those numbers that can be divided by 4, start from 4 up to 200. Those numbers are:
4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 54, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 94, 96, 100, 104, 108, 112, 116, 120, 124, 128, 132, 136, 140, 144, 148, 152, 154, 156, 160, 164, 168, 172, 176, 180, 184, 188, 192, 194, 196, 200
So, there are 50 natural numbers that are less than 200 and divisible by 4.
Now, we need to find out the numbers that are divisible by 3 among these numbers. We need to find out all those numbers that are divisible by 3, start from 4 up to 200. Because 4 is the first number among the numbers that we found out earlier which are divisible by 4. And the numbers are:
12, 24, 36, 48, 54, 60, 72, 84, 96, 108, 120, 124, 132, 144, 156, 168, 180, 192
There are 18 natural numbers in total.
Hence, natural numbers less than 200 which are divisible by 4 but not divisible by 3 is 50 – 18 = 32.
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Solve the equations.a) 4t^2 - 5t = 0d) (y + 6)(y - 6) = - (y + 6)^2h) h) (u - 4)(u + 4) = (u + 2)(u - 2).
The equations are given
a) 4t^2 - 5t = 0
d) (y + 6)(y - 6) = - (y + 6)^2
h) (u - 4)(u + 4) = (u + 2)(u - 2).
Explanationa. 4t^2 - 5t = 0
[tex]\begin{gathered} t(4t-5)=0 \\ t=0,4t-5=0 \\ t=0,t=\frac{5}{4}=1.25 \end{gathered}[/tex]d. (y + 6)(y - 6) = - (y + 6)^2
[tex]\begin{gathered} y^2-6y+6y-36=-(y^2+36+12y) \\ y^2-36=-y^2-36-12y \\ y^2+y^2+36-36+12y=0 \\ 2y^2+12y=0 \\ 2y(y+6)=0 \\ y=0,y=-6 \end{gathered}[/tex]h. (u - 4)(u + 4) = (u + 2)(u - 2).
[tex]\begin{gathered} u^2+4u-4u-16=u^2-2u+2u-4 \\ u^2-16=u^2-4 \\ u^2-16-u^2+4=0 \\ -12\ne0 \end{gathered}[/tex]Answer
Hence the solution to the equations are
[tex]\begin{gathered} a.t=0,1.25 \\ d.\text{ y=0,-6} \\ h.\text{ no solution} \end{gathered}[/tex]Which of the following equation has one solution?
Responses
4x + 2x = 6x - 4
3 (2x + 4) = 2 (2x - 4)
5(x - 3) = 5x - 3
2x = 2x + 4
a) 4x + 2x = 6x - 4
= 6x = 6x - 4
cannot be solved further.
b) 3(2x + 4) = 2(2x - 4)
= 6x + 12 = 4x - 4
(bring the numbers and variables on one side)
= 6x + 4x = 12 - 4
10x = 8
x = 8/10 = 4/5
can be solved.
c) 5(x - 3) = 5x - 3
= 5x - 15 = 5x - 3
= (bring the variables and numbers on one side)
5x + 5x = -15 - 3
= 10x = -18
x = -18/10 = 9/5
can be solved
d) 2x = 2x + 4
= 2x + 2x = 4
= 4x = 4
x = 4/4 OR 1.
THUS, (B, (C AND (D CAN BE SOLVED WITH ONE SOLUTION.……………………………………………………..
?
Please type what you are trying to solve or any questions that you would like answers for.
Which of the following is equivalent to (5a + 2b) + 3c?
Answer:
Option C 5a+(2b + 3c)
Solve -\frac{1}{3}\left(9x+42\right)-5x=-70 please
The value of x after solving the fraction [tex]-\frac{1}{3}\left(9x+42\right)-5x=-70[/tex] is 7.
Given fraction:
⇒ [tex]-\frac{1}{3}\left(9x+42\right)-5x=-70[/tex]
⇒ -9x/3 - 42/3 - 5x = -70
⇒ -3x - 14 - 5x = -70
⇒ -8x -14 = -70
⇒ -8x = -70 + 14
⇒ -8x = -56
⇒ 8x = 56
divide by 8 on both sides
8x/8 = 56/8
x = 56/8
x = 7.
Therefore The value of x after solving the fraction [tex]-\frac{1}{3}\left(9x+42\right)-5x=-70[/tex] is 7.
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System word problems 1. The cost of 3 boxes of envelopes and 4 boxes of paper is $13.25. 2 boxes of envelopes and 6 boxes of paper cost $17. What is the cost of each?Define Variables:System of Equations:Answer as a sentence:
ANSWER
The cost of a box of envelopes is $1.15
The cost of a box of paper is $2.45
EXPLANATION
Define Variables:
Let 'e' represent a box of envelopes
Let 'p' represent a box of papers.
System of Equations:
3e + 4p = 13.25 ...........................(equ 1)
2e + 6p = 17 ...........................(equ 2)
[tex]\begin{gathered} (\text{equ 1) }\times-2\Rightarrow-6e\text{ -8p = -26.5 }\ldots\ldots..(equ\text{ 3)} \\ (\text{equ 2) }\times3\text{ }\Rightarrow\text{ 6e + 18p = 51 }\ldots\ldots\ldots\ldots..(equ\text{ 4)} \\ \text{ -----------} \\ \text{ 0 e + 10p = 24.5} \\ p\text{ = 2.45} \end{gathered}[/tex][tex]\begin{gathered} \text{Substitute the value of 'p' into (equ 1)} \\ 3e\text{ + 4p = 13.25} \\ 3e\text{ + 4(2.45) = 13.25} \\ 3e\text{ + 9.8 = 13.25} \\ 3e\text{ = 13.25 - 9.8} \\ 3e\text{ = 3.45} \\ e\text{ = }\frac{3.45}{3} \\ e\text{ = 1.15} \end{gathered}[/tex]Answer as a sentence
Hence, the cost of a box of envelopes is $1.15 and the cost of a box of paper is $2.45.
A parabola has x-intercepts of (-2, 0) and (4, 0) and a = 2. What is the equation of the parabola?
y=2x²-4x-16 will be the required equation of parabola as the x-intercepts of parabola is (-2, 0) and (4, 0) and a = 2.
What is parabola?A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. A parabola can be described using a point and a line. Drawing a parabola for the quadratic function f(x) = ax² + bx + c results in a U-shaped curve. When an is less than zero, the parabola's graph is downward (or opens downward). Three different parabolas exist. Vertex form, standard form, and intercept form are the three forms. You can access a unique key feature for the graph on each form.
Here,
y = a(x − p)(x − q)
p=-2
q=4
a=2
y=2(x--2)(x-4)
y=2(x+2)(x-4)
y=2(x²-4x+2x-8)
y=2x²-4x-16
The necessary parabola equation will be y=2x²-4x-16 since its x-intercepts are (-2, 0) and (4, 0) and its value of a is 2.
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I have this thing I have to do for homework but in unsure of how to do it.
To check if those segments are parallel, we can compare the slope of the lines that contain them. To find the slope using two points, we can use the following formula
[tex]m=\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]Using this formula for the segment AB, we have
[tex]m_1=\frac{((-2)-3)}{((-12)-(-8))_{}}=\frac{-5}{-12+8}=\frac{5}{4}[/tex]Now, using this formula for CD
[tex]m_2_{}=\frac{((-7)-(-3))}{((-2)-(-7))_{}}=\frac{-7+3}{-2+7}=-\frac{4}{5}[/tex]When the slopes are equal, the lines are parallel, if one slope is minus the inverse of the other, they are perpendicular, otherwise they are neither.
Since
[tex]\frac{5}{4}=-(-\frac{4}{5})^{-1}\Rightarrow m_1=-\frac{1}{m_2}[/tex]They are perpendicular.
6. Chester paid a $30 membership fee to a toddler gym and $8 for each of 6 tumbling
classes for his son. The expression 30 + 8 x 6 can be used to evaluate the total cost
of the program. Is the cost $228 or $78? Explain.
Answer:
$78
Step-by-step explanation:
pemdas says we multiply then add
8x6+30
48+30
78
It is $78 and not $228 because we do not add first when doing order of operations and when we multiply first we get 78 also it’s each tumbling is 8 dollars and there were 6 of them so we just multiply the cost by each tumbling and add the membership fee after.
Hopes this helps please mark brainliest
What is the solution to 4x+63 18?
What is the solution to;
[tex]\begin{gathered} 4x+6\leq18 \\ \text{Subtract 6 from bothy sides} \\ 4x+6-6\leq18-6 \\ 4x\leq12 \\ \text{Divide both sides by 4} \\ \frac{4x}{4}\leq\frac{12}{4} \\ x\leq3 \end{gathered}[/tex]The first option is the correct answer
Find the value of x and the value of y.
Answer: y=18, x=30
Step-by-step explanation:
$57Mr. Harris attaches a full tank of propane to his grill. Then he turns on the grill and cooks food for a barbecue.Which graph shows the relationship between the amount of propane in the tank and time?OAOB.РРtTime (min.)PropanePropane
As he cooks on the barbecue, the weight of the tank goes down because some of the propane is getting used up.
Given that is happening, the graph showing that has to start with a lot in it and slowly decrease.
That being said, the graph representing the decrease in propane as time passes is C.
Answer: C.
The equation for line g can be written as y–8=– 2(x–4). Line h is parallel to line g and passes through (– 5,1). What is the equation of line h?
The equation of line h is y = -2x - 9
When are two lines said to be parallel?We say that two lines (on the same plane) are parallel to each other
if they never intersect each other, regardless of how far they are extended on either side.
In such lines, their gradient or slope are always equal.
if y - 8 = -2(x -4) is line g it can be written in slope intercept form as
y = 8 - 2(x - 4)
multiply out the bracket,
y = 8 -2x +8
y = -2x + 16
if equation of straight line is y = mx + c
comparing the two equations
slope(m) = -2
This slope is same for line h since they are parallel
for line h, m = -2, x = -5, y = 1
if y = mx + c
Then,
1 = -2(-5) + c
1 = 10 + c
c = 1 - 10
c = -9
equation of line h is y = -2x - 9
In conclusion the new equal of line h passing through point (-5, 1) is y = -2x - 9
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Find the vaule of U.
Write the equation of the line that is parallel to y=5 and passes through point (4,2)
Answer:bro need more classification
Step-by-step explanation:
The area of an 19-cm-wide rectangle is 456 cm2. What is its length? The length is .......cm.
The area of a rectangle is given by:
[tex]\begin{gathered} A=w\times l \\ \text{where:} \\ A=\text{Area}=456 \\ w=\text{width}=19 \\ l=\text{length} \\ 456=19\times l \\ l=\frac{456}{19} \\ l=24\operatorname{cm} \end{gathered}[/tex]three runners start running simultaneously from the same point on a 500500-meter circular track. they each run clockwise around the course maintaining constant speeds of 4.4, 4.8,~\text{and}~5.04.4,4.8, and 5.0 meters per second. the runners stop once they are all together again somewhere on the circular course. how many seconds do the runners run?
the runners stop once they are all together again somewhere on the circular course. then the runners run (C) 2500$ seconds
first consider the first two runners . the faster runner will lap the slower runner exactly once or run 500 meters farther. let x be the time these runners run in seconds
4.8x - 4.4 x =500
x = 1250
because 4.4(1250) = 5500 is a multiple of 500 it turns out they just meet back at the start line
Now we must find a time that is a multiple of $1250$ and results in the 5.0 m/s runner to end up on the start line. Every $1250$ seconds, that fastest runner goes $5.0(1250)=6250$ meters. In $2(1250)=2500$ seconds, he goes $5.0(2500)=12500$ meters. Therefore the runners run (C) 2,500$ seconds.
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t 1.4.3 Test (CST): Describing Data GraphicallyQuestion 19 of 25Which of these frequency counts would be represented by the tallest bar on ahistogram?OA. 15B. 17OC. 18OD. 16SUBMIT
The tallest bar on a a histogram represents the greatest frequency.
From the options, the greatest frequency is 18.
Answer: C. 18.
Y=(5x+2) (5x-2)
Write in standard form
Show work
Answer:
y= 25x^2 -4
Step-by-step explanation:
y=(5x+2)(5x-2)
y= 5x(5x-2)+2(5x-2)
y= 25x^2- 10x + 10x -4
here we cancel +10 and -10
y= 25x^2 -4 . Answer
I need help on the last two finding the function notation
For the second before last f(f), you have to replace x with the function f(x).
For the last one you have to replace x with the function g(x)
[tex]g(x)=2x^2+1[/tex][tex]\begin{gathered} f(g)=3(2x^2+1)+5 \\ f(g)=(3\cdot2x^2)+(3\cdot1)+5 \\ f(g)=6x^2+3+1 \\ f(g)=6x^2+4 \end{gathered}[/tex]i need help with a couple more im really confused. i'll post all of them.
The all three given problem are equivalent to each other.
64(2⁻ˣ)64/2ˣ64(1/2)ˣWhat is referred as the index/ indices?An index can be assigned to a number or a variable. A variable's index (or constant) is a value raised to a power of a variable. Indexes are also referred to as powers and exponents. It indicates how many times a provided number must be multiplied.If a constant or parameter has an index of '0,' the outcome will be one, regardless of the base value.If the index is negative, it can be represented by the reciprocal of a positive score raised to the identical variable.For the given three problems;
Problem 1: 64(2⁻ˣ)
Taking reciprocal of the (2⁻ˣ),
64/(2ˣ) ....1
Problem 2: 64/2ˣ ....2
Problem 3: 64(1/2)ˣ
Taking (1)ˣ = 1.
64/(2)ˣ ....3
Thus, three equation 1, 2 and 3 are in the same form so are equivalent.
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Classify the four angles of the quadrilateral. A B 70° 140° 60° 90° с D ZA LB ZC ZD √ Right Acute Obtuse O X S ?
Solution:
Given the shape;
Acute angles measure less than 90 degrees.
Right angles measure 90 degrees.
Obtuse angles measure more than 90 degrees.
ANSWER:
1
Drag the tiles to the correct boxes to complete the pairs.
Determine whether each pair of lines is perpendicular, parallel, or neither.
4y= 2x - 4
y = -2x +9
y = 2x + 4
2y = 4x - 7
Neither
2y = 4x + 4
y=-2x - 2
Perpendicular
Parallel
For lines to be parallel, the slope has to be the same.
For lines to be perpendicular, the slope has to be the negative reciprocal.
what are perpendicular lines?These lines always intersect at right angles.If two lines are perpendicular to the same line, they are parallel to each other and will never intersect. The sides of the right-angled triangle enclosing the right angle are perpendicular to each other.Two distinct lines intersecting each other at 90°, or a right angle, are called perpendicular lines.Learn more about perpendicular lines clcick here:
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A fishing boat determines a pod of fish located in the ocean at an angle of depression of 25° from the current boat location. The fishing boat determines the distance through the ocean to the fish is 150 yards. What distance does the boat need to travel on the surface of the ocean to be located directly above the fish? Round to the nearest unit.
Let's draw the situation and see what is the information that we have:
So we have to find the distance x which is the distance that the boat has to travel in order to be located directly above the fish. For this let's use Cosine which is cosine=Adjancent/Hypotenuse
The boat has to travel 136 yards on the surface of the ocean to be located directly above the fish.
write 10x10x10x10x10 with an exponet explain how you decided what exponet to write
Answer:
10^5
Step-by-step explanation:
10 was being multiplied with itself 5 times
Answer: 10^5
Step-by-step explanation:
10^5 is the same as saying 10x10x10x10x10