The solution of the equation 4y − x + 9 = 0 and y = 6 − 2x will be (11/3, −4/3). Point (2, 3) is not the solution of the system.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The linear equations are given below.
−x + 4y = −9 ...1
y = −2x + 6 ...2
From equations 1 and 2, then we have
−x + 4(−2x + 6) = −9
−x − 8x + 24 = −9
−9x + 24 = −9
9x = 24 + 9
9x = 33
x = 11 / 3
Then the value of the variable 'y' is calculated as,
y = −2(11/3) + 6
y = −22/3 + 6
y = −4/3
The arrangement of the situation 4y − x + 9 = 0 and y = 6 − 2x will be (11/3, −4/3). Point (2, 3) isn't the arrangement of the framework.
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The point (2, 3) does not satisfy either of the given equations, −x + 4y = −9 and y = −2x + 6. Therefore, it is not a solution to the system of equations.
Explanation:To determine if the point (2, 3) is a solution to the system of equations consisting of −x + 4y = −9 and y = −2x + 6, we need to check whether the point satisfies both equations.
For the first equation, substitute x with 2 and y with 3: −(2) + 4(3) = −9 to see if it results in a true statement.For the second equation, substitute x with 2: −2(2) + 6 = 3 to see if it equates to the y-value of 3.
Let's substitute the values into the first equation:
−(2) + 4(3) = −8 + 12 = 4, which does not equal −9. Therefore, the point does not satisfy the first equation.
For the second equation:
−2(2) + 6 = −4 + 6 = 2, which does not equal 3. Hence, the point does not satisfy the second equation either.
Since the point (2, 3) does not satisfy either equation, it is not a solution to the system of equations.
Which of the following statements are true of the parabola shown?
1. It has a directrix of x = -4.
2. It opens to the left.
3. It has a vertex at the origin.
4. The axis of symmetry is the y-axis.
5. It has a focus at (4, 0).
True statements are:
It has a directrix of x = - 4.It has a focus at (4, 0).Step-by-step explanation:
We have the following statements to check on whether it's right or wrong:
1. It has a directrix of x = -4:
According to figure , parabola directrix is at -4 i.e. at x = -4 , Therefore this statement is true!
2. It opens to the left:
In figure, Parabola opens to right not left , Therefore this statement is wrong!
3. It has a vertex at the origin:
Vertex of Parabola is at what points not shown in figure. Therefore this statement cannot be confirmed as true.
4. The axis of symmetry is the y-axis:
Axis of symmetry for above parabola is x-axis as it cuts parabola into two equal halves , y-axis doesn't do this ! Therefore this statement is wrong!
5. It has a focus at (4, 0):
Parabola focus is at [tex]F(4,0)[/tex] on x-axis . And so, Therefore this statement is true!
1. True it has a directrix of x = -4; 2. False it opens to the left; 3. False it has a vertex at the origin; 4. True the axis of symmetry is the y-axis; 5. True it has a focus at (4, 0).
In this parabola, the given statements can be evaluated as follows:
1. Directrix : The given directrix is x = -4. The directrix of a parabola is a vertical line that is equidistant from all points on the parabola. In this case, the directrix is to the left of the origin, so it's possible that the parabola opens to the right.
2. Direction of Opening : The parabola cannot open to the left because the given directrix is to the left of the origin. Parabolas open towards their focus or away from their directrix. Since the directrix is to the left, the parabola opens to the right.
3. Vertex : The vertex is the point where the parabola changes direction. The origin (0, 0) is not the vertex in this case, as the parabola opens to the right.
4. Axis of Symmetry: The axis of symmetry is a vertical line that passes through the vertex and divides the parabola into two equal halves. Since the parabola opens to the right, its axis of symmetry is the y-axis.
5. Focus : The focus is a point inside the parabola that is equidistant to the vertex and the directrix. The focus should indeed be to the right of the vertex, and at a distance of 4 units, based on the given directrix
x = -4.
Mathematically, the equation of a parabola that opens to the right, with its vertex at the origin, is of the form:
[tex]\[x^2 = 4py\][/tex]
Given that the directrix is x = -4, the distance from the origin to the directrix is 4 units. So, the equation becomes:
[tex]\[x^2 = 16y\][/tex]
The focus is at a distance of p units from the vertex, where [tex]\(p = 4\)[/tex], so the focus is at (4, 0).
In summary, the given parabola opens to the right, has a vertex at the origin, its axis of symmetry is the y-axis, and its focus is at (4, 0), with a directrix of x = -4.
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y=x^2-10x-2
Find the equation of the axis of symmetry
How to solve 16 * 12.5
Answer: 200
Step-by-step explanation:
First I would do it like this.
12.5
X. 16
—————-
6 times 5 is 0, carry the 3, 6 times 2 is 12 and add 3 from the other which is 15, put the 1 from the 15 to the one next to the 12. 6 times 1 is 6 plus 1 is 7 which now you have 750. 5 times 1 is 5, 2 times 1 is 2, 1 times 1 is 1. It should look like this now.
12.5
X 16
—————
750
+ 1250
——————-
Which is 8750 but wait. Where is the decimal? Well, there is only one number behind the decimal so it is 875.0 or 875.
Larry had $480 he used to thirds of it to buy an electric band he also bought tea set for 60 how much money did he have left
Answer:
Here's our equation:
480 * 1/3 - 60 = []
The 1/3 comes from 1 - 2/3 = 1/3 for note, as that's how much of her money is left after the fan's purchased. (if you're unsure, you can multiply 480 and 2/3 together, and then subtract that amount from 480, and you'll see you end up with the same answer as below)
The order of operations means we deal with the 480 * 1/3 first.
480 * 1/3 → 480/3 = 160
Next is subtraction:
160 - 60 = 100
So Mrs. Ricci has $100 left.
Step-by-step explanation:
what fraction is equivalent to 3/4
Answer:
6/8
Step-by-step explanation:
3/4 = 6/8 = 9/12 and so on
Answer:
9/12
Step-by-step e
$9.60 for 4 pounds i need help
hey bro, what do you mean by this question?
do you want to convert 9.60 dollars into pounds? if so then right now the exchange rate for dollars to pounds is 0.80. So you will do this (0.80)(9.60)=7.68
If you mean pounds like how much something weighs then all you need to do is just divide 9.60 by 4 = 2.4 which means $2.4 per pound.
Find the area of the following geometric figure
area of a triangle with
ase of 15 m and altitude of 12 m.
The area of the triangle is 90 m²
Explanation:
Given that the base of the triangle is 15 m
The altitude of the triangle is 12 m
Area of the triangle:
The area of the triangle can be determined using the formula,
[tex]Area=\frac{1}{2}bh[/tex]
where b is the base and h is the altitude
Thus, we have,
[tex]b=15[/tex] and [tex]h=12[/tex]
Substituting the values in the above formula, we get,
[tex]Area=\frac{1}{2}(15)(12)[/tex]
Multiplying the terms, we get,
[tex]Area=\frac{180}{2}[/tex]
Dividing, we get,
[tex]Area=90 \ m^2[/tex]
Therefore, the area of the triangle is 90 m²
Simplify this expression
a) 2a + 5a
Answer:
7a
Step-by-step explanation:
Rotate (-4,8) 90cc. What is the new order pair?
Answer:
(- 8, - 4 )
Step-by-step explanation:
Under a counterclockwise rotation about the origin of 90°
a point (x, y ) → (- y, x ), thus
(- 4, 8 ) → (- 8, - 4 )
Eliza bought a meal that cost $12.00. She tipped the waiter 25%of that amount . How much was the tip ?
The question is about calculating a tip which is 25% of a meal cost of $12.00. The tip is calculated by multiplying the total cost of the meal by the tip percentage, converted into decimal form. The answer is $3.00.
Percentage is a mathematical concept used to express a portion of a whole as a fraction of 100. It is a versatile tool in various fields, including finance, statistics, and everyday calculations. To calculate a percentage, you divide a part by the whole and then multiply by 100. Percentages are commonly used to represent proportions, express changes, and compare values, making them vital for analyzing data, understanding discounts, and determining growth rates. In essence, percentages simplify the representation of relative quantities and are fundamental in both practical and academic mathematics.
The subject of the question is Mathematics, specifically Percentage. The student is being asked to calculate 25% of $12.00, which is the cost of Eliza's meal. To calculate the tip, multiply the total meal cost by the percentage of the tip. Here's how we can do it:
Convert the percentage into a decimal: 25% is equal to 0.25 in decimal form.Multiply the total cost of the meal by the decimal: $12.00 * 0.25 = $3.00So the tip Eliza left for the waiter was $3.00.
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what is the unit price of a 16-ounce box of cereal that sells for $2.48?
Answer:
0.155
Step-by-step explanation:
Answer:
$0.15 per ounce
Step-by-step explanation:
2.48/16 = 0.155
2. The number of years that Elijah has been on the soccer team is 2 less than 5 times the number of years that Deaundre
has. In total, the boys have been on the soccer team for 10 years. How long has Elijah been on the soccer team?
The Elijah have been on the soccer team for 8 years.
Step-by-step explanation:
Let,
The number of years that Deaundre have been on the soccer team "x".The number of years that Elijah have been on the soccer team = 2 less than 5 times the number of years that Deaundre.The number of years that Elijah have been on the soccer team = 5x - 2.Given that,
The boys have been on the soccer team for 10 years.
Number of years of Deaundre + Number of years of Eliijah = 10 years.
x + (5x-2) = 10
Keep x terms on one side and constants on another side to solve for x value :
6x = 10+2
6x = 12
x = 12/6
x = 2
The Deaundre have been on the soccer team for 2 years.
Substitute x=2 in (5x-2) to find the number of years of Elijah,
5(2)-2 = 8 years.
Therefore, the Elijah have been on the soccer team for 8 years.
List all the multiples of 8 that are less than or equal to 100. List all the multiples of 12 that are less than or equal to 100. What are the common multiples of 8 and 12 from the two lists?
Answer:
24,48,72,96
Step-by-step explanation:
Multiples of 8
8, 16,24,32,40,48,56,64,72,80,88,96
Multiples of 12
12,24,36,48,60,72,84,96
Common multiples
24,48,72,96
Answer:
See below.
Step-by-step explanation:
"List all the multiples of 8 that are less than or equal to 100."
0, 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96
"List all the multiples of 12 that are less than or equal to 100."
0, 12, 24, 36, 48, 60, 72, 84, 96
Common multiples: 0, 24, 48, 72, 96
An electrician cut 36 feet of wire into sections that were each 8 1/2 feet long. After cutting, how many pieces of wire did the contractor have?
What is the length of line segment QP? Round to the
nearest unit.
O
O
O
o
13 units
17 units
18 units
20 units
Answer:
[tex]QP=20\ units[/tex]
Step-by-step explanation:
The picture of the question in the attached figure
Let
O ---> the center of the circle
we have that
Line segment QP is tangent to the circle
That means
OQ (radius) is perpendicular to segment QP
OQP is a right triangle
Applying Pythagorean Theorem
[tex]OP^2=OQ^2+QP^2[/tex]
we have
The radius is equal to
[tex]r=24/2=12\ units[/tex] ----> the radius is half the diameter
[tex]OP=r+NP=12+11.5=23.5\ units[/tex]
[tex]OQ=r=12\ units[/tex]
substitute
[tex]23.5^2=12^2+QP^2[/tex]
[tex]QP^2=23.5^2-12^2[/tex]
[tex]QP^2=408.25[/tex]
[tex]QP=20\ units[/tex]
Answer:20 units
Step-by-step explanation:
I need help with problem 27
Answer:
0+7-4=3
Step-by-step explanation:
They started with none, hence the 0. "Gained" typically means addition, so you add seven. "Lost" is a signal word for subtraction, so subtract zero. It comes out to 4.
a ladder 20 feet long leans against a building, forming an angle of 71° with the level ground. To the nearest foot, how high up the wall of the building does the ladder touch the building?
The wall is 18.79 feet high from the ground.
Data;
Length of ladder = 20ftangle of elevation = 71 degreeslength of the wall = ?Trigonometric RatioTo solve this problem, we need to use trigonometric ratio SOHCAHTOA in which we can find the missing side.
if we draw an illustration of this question, we would get
hypothenuse = 20ftangle = 71 degreesopposite = ?Using the sine angle ratio,
[tex]sin\theta=\frac{opposite}{hypothenuse}\\sin71=\frac{x}{20}\\ x=20sin71\\x=18.79ft[/tex]
The wall is 18.79ft high
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To calculate the height the ladder reaches on the wall, we use sine function and find it to be approximately 19 feet.
To find out how high up the wall the ladder touches the building when a 20-foot ladder forms an angle of 71° with the level ground, we can use trigonometry. Specifically, the sine function relates the opposite side to the hypotenuse in a right triangle. The ladder represents the hypotenuse, and the height reached on the wall is the opposite side.
Using the formula:
sin(angle) = opposite/hypotenuse
For this problem:
sin(71°) = height / 20 feet
Now we solve for height:
height = 20 feet × sin(71°)
We can calculate this using a calculator:
height ≈ 20 feet × 0.945
height ≈ 18.9 feet
To the nearest foot, the ladder reaches approximately 19 feet up the wall.
A triangular prism has a volume of 350 cubic meters. If the dimensions are tripled what is the volume of the new
prism?
Answer:
9450 m³
Step-by-step explanation:
(S1/S2)³ = V1/V2
3³ = V1/350
New Volume = 27 × 350
= 9450 m³
9. D is 20 + h
But help :)
Answer:
8. D 269.6
9. A 20 +10h
Step-by-step explanation:
8. The large rectangle is 4+6.4+4+6.4 = 20.8 width and 10.5 length. The area is
A = l*w = 20.8* 10.5 =218.4
The top rectangle is 6.4 width and length is 4
A = l*w =6.4*4 =25.6
The same is true for the rectangle on the bottom.
Add the three rectangles together to get the total surface area
218.4+25.6+25.6 =269.6
9. The plant is 20 inches tall
It grows 2h inches a week for 4 weeks
20 +2h*4
20 +8h
It grows h inches a week after 4 weeks
At 6 weeks, that is 2 weeks of growth
The growth is h *2
Add that to the previous total
20 +8h +2h
20 +10h
Does 9,12,15 form a right triangle
Answer:
Yes.
Step-by-step explanation:
Note that 15^2 = 122^ + 9^2 ( 225 = 144 + 81 = 225).
So by the Inverse of Pythagoras Theorem it is a right triangle.
The given values of side makes a proper right angle triangle.
To determine if the three given side lengths, 9, 12, and 15, form a right triangle, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Let's check if this holds true for the given side lengths:
[tex]9^2 + 12^2 = 81 + 144 = 225\\\\15^2 = 225[/tex]
The sum of the squares of the two shorter sides, 9 and 12, is equal to the square of the longest side, 15. This satisfies the Pythagorean theorem.
Therefore, the side lengths 9, 12, and 15 do form a right triangle.
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Help please !!!!!!!!!!!!!!!!!!!!!
Answer:
The last one
Step-by-step explanation:
volume is v= [tex]\pi r^{2} h[/tex] . this means volume is mathematical number pi, times the (radius squared), times the height. the radius is marked at the yellow line, and the height on the side. this means you would have v = [tex]\pi[/tex][tex](x+2)^{2}[/tex][tex](3x+8)[/tex]
first, lets work out [tex](x+2)^{2}[/tex]. we can rewrite this as (x+2)(x+2). we are going to use a system called FOIL. this stands for First Outside Inside Last. This means we are going to take the first number from both and multiply them together, then the outside, inside, and last. so, for first, we will multiply x and x and then we have [tex]x^{2}[/tex], for outside we multiply x and 2 and we get [tex]2x[/tex], for inside we multiply 2 and x and we get [tex]2x[/tex], and for last we multiply 2 and 2 and we get [tex]4[/tex]. then we add all these together. [tex]x^{2} + 2x + 2x + 4[/tex]. then simplify like terms to get
[tex]x^{2} + 4x + 4[/tex]. now, we can't forget about our times [tex]\pi[/tex] and (3x+8)
this means we have to multiply [tex]x^{2} + 4x + 4[/tex] by those two.
it would look like this: ([tex]x^{2} + 4x + 4[/tex])(3x+8)[tex]\pi[/tex]
so now we are going to multiply the other two sets of parentheses
we multiply each number from the first set to each number in the second set.
A family buys 6 tickets to a show. They also pay $3 parking fee. They spend $27 to see the show.
Answer:
They paid $4.00 per ticket
Step-by-step explanation:
Step 1: Convert words into an inequality
A family buys 6 tickets to a show. They also pay $3 parking fee. They spend $27 to see the show.
6t + 3 = 27
Step 2: Solve for t/tickets
6t + 3 = 27
6t + 3 - 3 = 27 - 3
6t / 6 = 24 / 6
t = 4
Answer: They paid $4.00 per ticket
Answer:
4
Step-by-step explanation:
3 - 27 = 24
24 ÷ 6 = 4
4 · 6 = 24
3 + 24 = 27
A = $27
Explain how the product 1\2 ×1\3 relates to the model
Final answer:
The product 1/2 x 1/3 equals 1/6, which can be visualized using a two-dimensional model where a rectangle is divided into halves and then thirds, resulting in 1/6 of the total area.
Explanation:
The product 1/2 times 1/3 can be understood through a two-dimensional model. If you take a rectangle and divide it into 2 equal parts, taking 1/2 of the whole, and then divide one of those halves into 3 equal parts, taking 1/3 of that half, you will have 1 out of the 6 equal parts of the original rectangle, which is 1/6, the product of 1/2 and 1/3.
To visualize this process, imagine a bar or a piece of chocolate that is first divided down the middle, and then one of those halves is divided into 3 equal pieces.
Taking one of these smaller pieces represents 1/6 of the original chocolate bar. In mathematical terms, when we multiply fractions, we multiply the numerators ( 1 times 1) to get the numerator of the product, and the denominators (2 times 3) to get the denominator of the product, yielding 1/6 as the answer. This demonstrates the first partial product principle, where in this case the third vector (1/3) is multiplied by the scalar product of 1/2.
Liam's last grocery bill was $105. This week, his bill was $85. Calculate the percent change. Round to the nearest hundredth.
Answer:
.199 or 20% (.20)
Step-by-step explanation:
Percentage change:
p=(85-105)/105=-20/105=-19.047%
Rounded value: -19.05%
The minus sign indicates a decrease in amount spent.
What is the slope of (3, 3) and (-6, -3)
Answer:
m=2/3
Step by Step Explanation:
x1,y1= 3,-6
x2,y2=3,-3
m={-3-3} (Fraction Form)
{-6-3}
Refine:
m={2}{3}
Answer:
Slope = [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
Step 1: Identify x1, x2, y1, y2
Slope Formula: [tex]\frac{y2-y1}{x2-x1}[/tex]
(x1, y1) -> (3, 3)
(x2, y2) -> (-6, -3)
Step 2: Plug into the formula
Slope = [tex]\frac{-3 - 3}{-6 - 3}[/tex]
Slope = [tex]\frac{-6}{-9}[/tex]
The top negative sign and the bottom negative sign cancel to make a positive number.
Slope = [tex]\frac{-6}{-9}[/tex]
Slope = [tex]\frac{6}{9}[/tex]
The top and bottom can be simplified by a factor of 3.
Slope = [tex]\frac{6}{9}[/tex]
Slope = [tex]\frac{6/3}{9/3}[/tex]
Slope = [tex]\frac{2}{3}[/tex]
Answer: Slope = [tex]\frac{2}{3}[/tex]
An engineer scale model shows a building that is 3 inches tall. If the scale is 1 inch = 600 feet, how tall is the actual building in feet ?
Answer:
1800ft tall
Step-by-step explanation:
What is the surface area of this triangular prism rounded to the nearest tenth? A) 48.6km2 B) 63.4 km2 C) 72.6 km2 D) 84.4 km2
Correct option B)[tex]63.4km^2[/tex] .
Step-by-step explanation:
We have the following figure attached as shown below.
Now, this triangular prism have 2 similar right angled surfaces and 3 rectangular surfaces , Let's calculate area for all of them:
2 similar right angled surfaces
We know that area of triangle = [tex]\frac{1}{2} b(h)[/tex]
⇒ [tex]area = \frac{1}{2} b(h)[/tex]
⇒ [tex]area = \frac{1}{2} (3.6)(7.7)[/tex]
⇒ [tex]area = 13.86km^{2}[/tex]
But there 2 such surfaces so , [tex]area = 2(13.86) = 27.72km^2[/tex]
3 rectangular surfaces
Area of rectangle = [tex]length(breadth)[/tex]
⇒ [tex]area_1 = 3.6(1.8)[/tex]
⇒ [tex]area_1 = 6.48km^2[/tex]
⇒ [tex]area_2= 7.7(1.8)[/tex]
⇒ [tex]area_2 = 13.86km^2[/tex]
⇒ [tex]area_3 = 8.5(1.8)[/tex]
⇒ [tex]area_2 = 15.3km^2[/tex]
Total area =[tex]6.48 + 13.86 + 15.3 = 35.64km^2[/tex]
Adding area of 2 similar right angled surfaces & 3 rectangular surfaces:
[tex]Area = 27.72+35.64 = 63.36km^2[/tex] = [tex]63.4km^2[/tex]
Correct option B)[tex]63.4km^2[/tex] .
Answer:
It is B.
Step-by-step explanation:
Trust me it's B
What is the measurement of the unknown fourth interior angle of this quadrilateral? A) 80° B) 95° C) 100° D) 115°
Answer: The Answer is 100, sorry that you got it so late.
Step-by-step explanation:
What I did
1. Find the difference between the numbers
2. Look through answer choices
3. Because the difference of 80 and 75 was 5, 105 would be 100.
Sorry if this doesn't make sense.
ted, sam, and jack can do a piece of work in 15, 12 and 20 days respectively. they started the work together, but jack left after 2 days. in how many days will the remaining work be completed by ted and sam?
Answer:
the answer was 24
Step-by-step explanation:
I'LL GIVE YOU BRAINLIEST!!
Which scatterplot suggests no relationship between x and y?
A) II only
Eliminate
B) III only
C) I and III only
D) II and III only
Answer:
B) III only, it doesn't suggests relationship between x and y.