ANSWER
The correct answer is B.
EXPLANATION
If the point B(x,y) partitions
[tex]A(x_1,y_1)[/tex]
and
[tex]C(x_2,y_2)[/tex]
in the ratio m:n then, then we have
[tex]x = \frac{mx_2+nx_1}{m + n} [/tex]
and
[tex]y= \frac{my_2+ny_1}{m + n} [/tex]
We want to find the coordinates of the point B(x,y) that lies along the directed line segment from A(-5, 2) to C(11, 0) and partitions the segment in the ratio of 5:3.
This implies that:
[tex]x = \frac{5 \times 11+3 \times - 5}{5 + 3} [/tex]
[tex] \implies \: x = \frac{55 - 15}{8} [/tex]
[tex] \implies \: x = \frac{40}{8} = 5[/tex]
[tex]y = \frac{5 \times 0 + 3 \times 2}{5 + 3} [/tex]
[tex]y = \frac{0 + 6}{8} [/tex]
[tex]y = \frac{6}{8} = \frac{3}{4} [/tex]
Therefore the coordinates of B are
[tex](5, \frac{3}{4} )[/tex]
Answer:
B. (5,3/4)
Step-by-step explanation:
Since, when a segment having end points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is divided by or partitioned by a point, that lies on the segment, in the ratio of m : n,
Then the coordinates of that points are,
[tex](\frac{mx_2+nx_1}{m+n}, \frac{my_2+my_1}{m+n})[/tex]
Here, point B that lies along the directed line segment from A(-5, 2) to C(11, 0) and partitions the segment in the ratio of 5:3,
Thus, the coordinates of B are,
[tex](\frac{5\times 11+3\times -5}{5+3}, \frac{5\times 0+3\times 2}{5+3})[/tex]
[tex](\frac{55-15}{8}, \frac{0+6}{8})[/tex]
[tex](\frac{40}{8}, \frac{6}{8})[/tex]
[tex](5, \frac{3}{4})[/tex]
Option 'B' is correct.
Drag the tiles to the correct boxes to complete the pairs.
Match each inequality to the number line that represents its solution.
x – 99 ≤ -104
x – 51 ≤ -43
150 + x ≤ 144
75 < 69 – x
Answer:
1. Number line 2
2. Number line 1
3. Number line 4
4. Number line 3
Step-by-step explanation:
1. x – 99 ≤ -104
Solving by adding +99 on both sides
x - 99 +99 ≤ -104 +99
x ≤ -5
Number line 2 represent x ≤ -5
2. x – 51 ≤ -43
Adding +51 on both sides
x -51 +51 ≤ -43 +51
x ≤ 8
Number line 1 represent x ≤ 8
3. 150 + x ≤ 144
Adding -150 on both sides
150 + x -150 ≤ 144 -150
x ≤ -6
Number line 4 represent x ≤ -6
4. 75 < 69 – x
Adding +x on both sides
75 + x < 69 -x +x
x < 69 -75
x < -6
Number line 3 represent x < -6
The correct matches are:
[tex]\(x - 99 \leq -104\)[/tex] with the number line showing [tex]\(x \leq -5\)[/tex].
[tex]\(x - 51 \leq -43\)[/tex] with the number line showing [tex]\(x \leq 8\)[/tex].
[tex]\(150 + x \leq 14475\)[/tex] with the number line showing [tex]\(x \leq 14325\)[/tex].
[tex]\(69 - x < 14475\)[/tex] with the number line showing [tex]\(x > -14406\)[/tex].
To solve the given inequalities and match them to their corresponding number lines, we will first solve each inequality algebraically and then represent the solution on a number line.
1. For the inequality [tex]\(x - 99 \leq -104\)[/tex], we add 99 to both sides to isolate \[tex](x\)[/tex]:
[tex]\[x \leq -104 + 99\][/tex]
[tex]\[x \leq -5\][/tex]
This means that all values of [tex]\(x\)[/tex] less than or equal to -5 satisfy the inequality.
2. For the inequality[tex]\(x - 51 \leq -43\)[/tex], we add 51 to both sides:
[tex]\[x \leq -43 + 51\][/tex]
[tex]\[x \leq 8\][/tex]
This means that all values of [tex]\(x\)[/tex] less than or equal to 8 satisfy the inequality.
3. For the inequality [tex]\(150 + x \leq 14475\)[/tex], we subtract 150 from both sides:
[tex]\[x \leq 14475 - 150\][/tex]
[tex]\[x \leq 14325\][/tex]
This means that all values of [tex]\(x\)[/tex] less than or equal to 14325 satisfy the inequality.
4. For the inequality [tex]\(69 - x < 14475\)[/tex], we subtract 69 from both sides and reverse the inequality sign because we are dividing by a negative number (-1):
[tex]\[-x < 14406\][/tex]
[tex]\[x > -14406\][/tex]
This means that all values of [tex]\(x\)[/tex] greater than -14406 satisfy the inequality.
Now, let's represent these solutions on number lines:
- For [tex]\(x \leq -5\)[/tex], the number line will have a closed circle at -5 and shading to the left of -5.
- For [tex]\(x \leq 8\)[/tex], the number line will have a closed circle at 8 and shading to the left of 8.
- For[tex]\(x \leq 14325\)[/tex], the number line will have a closed circle at 14325 and shading to the left of 14325.
- For [tex]\(x > -14406\)[/tex], the number line will have an open circle at -14406 and shading to the right of -14406.
Matching the inequalities to the number lines:
- The inequality [tex]\(x - 99 \leq -104\)[/tex] corresponds to the number line with a closed circle at -5 and shading to the left.
- The inequality [tex]\(x - 51 \leq -43\)[/tex] corresponds to the number line with a closed circle at 8 and shading to the left.
- The inequality [tex]\(150 + x \leq 14475\)[/tex] corresponds to the number line with a closed circle at 14325 and shading to the left.
- The inequality [tex]\(69 - x < 14475\)[/tex] corresponds to the number line with an open circle at -14406 and shading to the right.
Therefore, the correct matches are:
[tex]\(x - 99 \leq -104\)[/tex] with the number line showing [tex]\(x \leq -5\)[/tex].
[tex]\(x - 51 \leq -43\)[/tex] with the number line showing [tex]\(x \leq 8\)[/tex].
[tex]\(150 + x \leq 14475\)[/tex] with the number line showing [tex]\(x \leq 14325\)[/tex].
[tex]\(69 - x < 14475\)[/tex] with the number line showing [tex]\(x > -14406\)[/tex].
Find the coordinates of the point which divides the join of (-1,7) and (4,-3) in the ratio 2:3
Answer:
The coordinates of the point in question is (1, 3).
Step-by-step explanation:
Point (-1, 7) is above and to the left of the point (4, -3). The point in question is to the right and below the point (-1, 7).
What will be the horizontal distance between the point (-1, 7) and the point in question?
The horizontal distance between the point (-1, 7) and (4, -3) is 5. Let the horizontal distance between the point (-1, 7) and the point in question be [tex]a[/tex]. Let the horizontal distance between the point in question and point (4, -3) be [tex]b[/tex].
[tex]\displaystyle \frac{a}{b} = \frac{2}{3}[/tex].
[tex]\displaystyle a = \frac{2}{3} \; b[/tex].
[tex]\displaystyle b = \frac{3}{2}\; a[/tex].
However,
[tex]a + b = 5[/tex].
[tex]\displaystyle a + \frac{3}{2}\; a = 5[/tex].
[tex]\displaystyle \frac{5}{2}\; x= 5[/tex].
[tex]a = 2[/tex].
In other words, the point in question is 2 units to the right of the point (-1, 7). The x-coordinate of this point shall be [tex]-1 + 2 = 1[/tex].
The vertical distance between the point (-1, 7) and the point (4, -3) is 10. Similarly, the point in question is [tex](2/5) \times 10 = 4[/tex] units below the point (-1, 7). The y-coordinate of this point will be [tex]7 - 4 = 3[/tex].
Thus, the point in question is (1, 3).
Answer:
To solve our given problem we will use section formula :]
Section Formula states that, when a point divides a line segment internally in the ratio m:n, So the coordinates are :]
[tex]\tiny: \implies (x,y) = \bigg \lgroup x = \frac{m. {x}_{2} +n. {x}_{1} }{m + n} ,y= \frac{m. {y}_{2} +n. {y}_{1} }{m + n} \bigg \rgroup \\ \\ \\ [/tex]
Let
(-1 , 7) = (x₁ , y₁)
(4 , -3) = (x₂ , y₂)
m = 2
n = 3
Upon Substituting coordinates of our given points in section Formula we get :][tex]\tiny: \implies (x,y) = \bigg \lgroup x = \frac{2 \times 4 +3 \times - 1 }{2 + 3} ,y= \frac{2 \times - 3 +3 \times 7}{2 + 3} \bigg \rgroup \\ \\ \\ [/tex]
[tex]\tiny: \implies (x,y) = \bigg \lgroup x = \frac{8 - 3 }{2 + 3} ,y= \frac{ - 6 +21}{2 + 3} \bigg \rgroup \\ \\ \\ [/tex]
[tex]\tiny: \implies (x,y) = \bigg \lgroup x = \frac{5 }{5} ,y= \frac{15}{5} \bigg \rgroup \\ \\ \\ [/tex]
[tex]\tiny: \implies (x,y) = \bigg \lgroup x = 1,y= 3 \bigg \rgroup \\ \\ [/tex]
Which method would you use to prove that the two triangles are congruent?
Answer:
AAS
Step-by-step explanation:
Given one pair of congruent angles and one pair of congruent sides.
When two lines intersect they form a pair of congruent angles (vertical angles are equal)
So the two triangles are congruent by AAS.
Answer: AAS
Step-by-step explanation:
By the figure we can say that the have one side equal. Now for the angles we have that in the part of the triangles are touching we have an oposite angles then these two angles have to be equals. Finally the two triangles have two equal angles and ones equal side. we can conclude that the correct method is AAS.
If f(x) = 7 + 4x and 9(x) = 2x, what is the value of (465)
Answer:
Step-by-step explanation:89
Which is a correct classification for the triangle?
Step-by-step explanation:
All three sides are equal, so this is an equilateral triangle.
Answer:
This is an equilateral triangle
Step-by-step explanation:
All three sides are equal, making it equilateral
given: g(a)=4a+1 and h(a)=a2-2a
find: g(h(-3+z))
Answer:
the answer should be 1
Step-by-step explanation:
4[(-3+z)2-2(-3+z)]+1
4(-6+2z+6-2z)+1
-24+8z+24-8z+1
the 24's and 8's cancel out leaving 1
To find g(h(-3+z)), we first find h(-3+z) by substituting -3+z into h(a), it becomes z^2-8z+15. Then, substitute this into g(a) to get g(h(-3+z)), which results in 4z^2-32z+61.
Explanation:In the field of Mathematics, to solve the problem g(h(-3+z)), we need to substitute h into g. It means that every 'a' in g(a) will be replaced by what h(-3+z) is equal to. To find h(-3+z), we substitute -3+z into h(a) in place of a. Therefore, h(-3+z) equals to (-3+z)^2-2(-3+z). After simplifying, it becomes z^2-6z+9+6-2z=z^2-8z+15. Next, we substitute this into g(a) to get g(h(-3+z))=4[z^2-8z+15]+1=4z^2-32z+61. Hence, the solution to the problem g(h(-3+z)) is 4z^2-32z+61.
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Evaluate a + b2 for a = 2 and b = 3.
Answer:
11
Step-by-step explanation:
In this problem we have the following expression
[tex]a + b^2[/tex]
Note that it depends on two variables a and b
Evaluating the expression for a = 2 and b = 3 means that you must replace the variable "a" with the number 2, and you must replace the variable "b" with the number 3
So we have that:
[tex]a + b^2 = 2 + 3^2[/tex]
[tex]a + b^2 = 2 +9[/tex]
[tex]a + b^2 = 11[/tex]
Finally the answer is 11
The area of a circle with radius r is given by A = π r2. Find the area of a circle with radius 7 centimeters. Use 3.14 for π.
Answer:
The area is 0.015m²
Step-by-step explanation:
Step one
Given that the expression for area of the circle is A = π r²
Step two
Now our raduis r= 7cm - - - meter =7/100= 0.07
And Pi = 3.142
Step three
Substituting r in the formula for area we have
A= 3.142*(0.07)²
A=3.142*0.0049
A= 0.015m²
Which parabola will have a minimum value vertex?
Answer:
The last choice.
Step-by-step explanation:
That would be the last one, with a minimum value of -4.
Answer:
IV graph
Step-by-step explanation:
Given is a picture consisting of 4 parabolas with first 3 open up and last one open down.
We are to find the minimum value vertex
Seeing the graph we can write coordinates of vertex as where they turn their direction.
Hence vertices are
Graph Vertices y value
I (0,5) 5
II (0,0) 0
III (1,2.5) 2.5
IV (0,-4) -4
Of the 4 y values, IV graph has the minimum value vertex
What is the equation of the line that passes through (-3, -1) and has a slope of 2/5? Put your answer in slope-intercept.
[tex]\bf (\stackrel{x_1}{-3}~,~\stackrel{y_1}{-1})~\hspace{10em} slope = m\implies \cfrac{2}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-1)=\cfrac{2}{5}[x-(-3)]\implies y+1=\cfrac{2}{5}(x+3) \\\\\\ y+1=\cfrac{2}{5}x+\cfrac{6}{5}\implies y=\cfrac{2}{5}x+\cfrac{6}{5}-1\implies y=\cfrac{2}{5}x+\cfrac{1}{5}[/tex]
what is the fifth term in the geometric sequence described by this explicit formula y=40×(-2)^(n-1)
Answer:
The fifth term is 620
Step-by-step explanation:
y=40×(-2)^(n-1)
The 5th terms means n=5
y = 40 * (-2) ^ (5-1)
= 40 * (-2) ^4
= 40 * (16)
= 640
Last year amusement park received 236,758 visitors it was open every day of the year but 7 Holliday’s what was the average number of visitors to the park per day
Answer:
An average of 661 people per day.
Step-by-step explanation:
1. 365-7= 358
2. 236,758/ 358= 661.3351
3. Round to 661
find the sum of 7 E 3i - 15
i =2
answers :
9
0
-9
6
Answer:
-9
Step-by-step explanation:
find the value of i2, which is -9, find the value of i7, which is 6
Then, add them together and multiply by the number of terms in the sequence divided by 2 (6/2=3)
how do you find the equation of the axis of symmetry and the coordinates of the vertex of the graph of the function y= -2x^2+6x-1
Answer:
The vertex is: [tex](\frac{3}{2},\ \frac{7}{2})[/tex]
The axis of symmetry is:
[tex]x=\frac{3}{2}[/tex]
Step-by-step explanation:
For a quadratic equation of the form:
[tex]y=ax^2 + bx +c[/tex]
The vertex of the parabola will be the point: [tex](-\frac{b}{2a},\ f(-\frac{b}{2a}))[/tex]
In this case we have the following equation:
[tex]y= -2x^2+6x-1[/tex]
Note that:
[tex]a=-2\\b=6\\c=-1[/tex]
Then the x coordinate of the vertex is:
[tex]x=-\frac{b}{2a}[/tex]
[tex]x=-\frac{6}{2(-2)}[/tex]
[tex]x=\frac{3}{2}[/tex]
Then the y coordinate of the vertex is:
[tex]y= -2(\frac{3}{2})^2+6(\frac{3}{2})-1[/tex]
[tex]y=\frac{7}{2}[/tex]
The vertex is: [tex](\frac{3}{2},\ \frac{7}{2})[/tex]
For a quadratic function the axis of symmetry is always a vertical line that passes through the vertex of the function.
Then the axis of symmetry is:
[tex]x=\frac{3}{2}[/tex]
Which line is perpendicular to a line that has a slope of
[tex] - \frac{5}{6} [/tex]
line JK
line LM
line NO
line PQ
Answer:
Option C is correct.
Step-by-step explanation:
Slope of line JK
J (1,-6) K (0,4)
slope of JK = y₂ - y₁ / x₂ - x₁
Slope of JK = 4-1/0-(-6) = 3/6 = 1/2
so slope of JK = 1/2
Slope of line LM
L (-5,-3) and M(0,3)
slope of LM = y₂ - y₁ / x₂ - x₁
slope of LM = 3-(-5)/0-(-3) = 3+5/3 = 8/3
Slope of line NO
N(-6,-5) and 0 (0,0)
slope of NO = y₂ - y₁ / x₂ - x₁
slope of NO = 0-(-6)/0-(-5) = 6/5
So, slope of line NO = 6/5
Slope of PQ
P(-5,4) Q(0,-2)
slope of PQ = y₂ - y₁ / x₂ - x₁
slope of PQ = -2-4/0-(-5) = -2/5
so slope of line PQ = -2/5
the two lines are perpendicular if slope of one line is m then slope of other line is -1/m
The slope of given line =m= -5/6
The slope of line perpendicular to the given line = -1/m = 6/5
So, line NO is perpendicular to the given line as its slope is 6/5
Option C is correct.
How large is one side of the square garden plot
in meters?
Two garden plots are to have the same
area. One is square and one is
rectangular. The rectangular plot is 4
meters wide and 16 meters long.
Given - Length of the Rectangular Plot : 16 meters
Given - Width of the Rectangular Plot : 4 meters
We know that - Area of a Rectangle is given by : Length × Width
[tex]:\implies[/tex] Area of the Rectangular plot = (16 × 4) m²
[tex]:\implies[/tex] Area of the Rectangular plot = 64 m²
Given : Square plot and Rectangular plot have same Area
[tex]:\implies[/tex] Area of Rectangular plot = Area of Square plot
[tex]:\implies[/tex] Area of Square plot = 64 m²
We know that - Area of Square is given by : Side × Side
[tex]:\implies[/tex] Side × Side = 64 m²
[tex]:\implies[/tex] S² = 64 m²
[tex]:\implies[/tex] S² = 8² m²
[tex]:\implies[/tex] S = 8 m
Answer : One side of the Square Garden plot is 8 meter
Answer:
Side of the square plot = 8 m
Step-by-step explanation:
l = 16 m
b = 4 m
Area of the rectangular plot = l * b
= 16 * 4 = 64 m²
Area of square plot = Area of rectangular plot
side * side = 64 m²
side = √64 = 8 m
write 3 times the square root of 2 plus the 2 times the square root of 3 in simplest form
Answer: Option 'D' is correct.
Step-by-step explanation:
Since we have given that
3 times the square root of 2 +2 times the square root of 3 =3sqrt2+2sqrt3
We need to simplify the above expression.
In addition and subtraction, there is a rule of adding or subtracting of like terms is possible only.
But, here, √2 ad √3 are unlike term.
so, we cannot simplified it.
Hence, Option 'D' is correct.
Step-by-step explanation:
Please mark brainliest and have a great day!
Answer:
Step-by-step explanation:
3√2 + 2√3 is as simple an expression as you'll get for this quantity.
Anastasia uses the equation p = 0.7(rh + b) to estimate the amount of take-home pay, p, for h hours worked at a rate of r dollars per hour and any bonus received, b.
What is an equivalent equation solved for h?
Answer:h= [tex]\frac{(p/0.7-b)}{r}[/tex]
Step-by-step explanation:
1) p/0.7=rh+b
2) (p/0.7)-b=rh
3) [tex]\frac{(p/0.7-b)}{r}[/tex] =h
h= [tex]\frac{(p/0.7-b)}{r}[/tex]
The equivalent equation for isolated variable h = [tex]\frac{p-0.7b}{r}[/tex] obtained from the equation p = 0.7(rh + b).
What is meant by isolating a variable?Isolating a variable is the re-arrangement of the equation for the required variable. Even though rewriting the terms, doesn't affect the logic of the equation. It forms an equivalent equation.
Isolating the variable h from the given equation:The given equation is p = 0.7(rh + b)
Where,
p - home pay
h - working hours
r - the rate of dollars per hour
b - bonus received
Re-writing the equation for the variable h:
p = 0.7(rh + b)
⇒ p/0.7 = rh + b
⇒ p/0.7 - b = rh
⇒ h = p/0.7r -b/r
∴ h = [tex]\frac{p-0.7b}{r}[/tex]
Therefore, variable h is isolated and obtained an equivalent equation.
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two square regions have an area of 125 and 5 how many yards of fencing is needed to enclose? ( assume regions fenced separately)
Answer:
[tex]24\sqrt{5}\ yards[/tex]
Step-by-step explanation:
Let A1 be the area of one square and A2 be the area of second square
So,
A1 = s^2
where s is side of square
[tex]s^2=125\\\sqrt{s^2}=\sqrt{125}\\s=\sqrt{25*5}\\ s= \sqrt{5^2 * 5}\\ s= 5\sqrt{5}[/tex]
So side of one square is [tex]5\sqrt{5}[/tex]
To calculate the length of fence we need to find the perimeter of the square
So,
P1 = 4 * s
[tex]=4*5\sqrt{5} \\=20\sqrt{5}[/tex]
For second square:
[tex]A_2=s^2\\5=s^2\\\sqrt{s^2}=5\\{s}=\sqrt{5}[/tex]
The perimeter will be:
[tex]P_2 = 4*s\\=4 * \sqrt{5} \\=4\sqrt{5}[/tex]
So the total fence will be: P1+P2
[tex]= 20\sqrt{5}+4\sqrt{5} \\= 24\sqrt{5}\ yards[/tex]
Solve for
5(x + 1) = 4x + 8)
Answer:
x =3
Step-by-step explanation:
5(x + 1) = 4x + 8
Distribute the 5
5x+5 = 4x+8
Subtract 4x from each side
5x-4x+5 = 4x-4x+8
x+5 =8
Subtract 5 from each side
x+5-5 = 8-5
x =3
Which equation is the inverse of 2(x - 2)^3=8(7+y)
Answer:
[tex]\large\boxed{y=2\pm\sqrt{28+4x}}[/tex]
Step-by-step explanation:
[tex]2(x-2)^2=8(7+y)\\\\\text{exchange x to y, and vice versa:}\\\\2(y-2)^2=8(7+x)\\\\\text{solve for y:}\\\\2(y-2)^2=(8)(7)+(8)(x)\\\\2(y-2)^2=56+8x\qquad\text{divide both sides by 2}\\\\(y-2)^2=28+4x\iff y-2=\pm\sqrt{28+4x}\qquad\text{add 2 to both sides}\\\\y=2\pm\sqrt{28+4x}[/tex]
Answer:
y is inverse: 2 ±[tex]\sqrt{28+ 4x}[/tex] .
Step-by-step explanation:
Given: 2(x - 2)²=8(7+y).
To find: Find inverse.
Solution : We have given
2(x - 2)²=8(7+y).
Step 1: inter change the x and y.
2(y - 2)²=8(7+x).
Step 2:
Solve for y
On dividing both sides by 2
(y - 2)² = 4 (7+x).
Distributes 4 over ( 7 + x)
(y - 2)² = 28 + 4x
Taking square root both sides.
[tex]\sqrt{(y-2)^{2} } = ±\sqrt{28+ 4x}[/tex].
y - 2 = ±[tex]\sqrt{28+ 4x}[/tex].
On adding both sides by 2
y = + 2 ±[tex]\sqrt{28+ 4x}[/tex] .
Therefore, y is inverse : 2 ± [tex]\sqrt{28+ 4x}[/tex].
What is the following quotient? 2/sqrt13+sqrt11
Answer:
Answer is [tex]\sqrt{13}-\sqrt{11}[/tex]
Step-by-step explanation:
We need to divide
[tex]\frac{2}{\sqrt{13}+\sqrt{11}}[/tex]
For solving this, we need to multiply and divide the given term with the conjugate of [tex]{\sqrt{13}+\sqrt{11}[/tex]
The conjugate is: [tex]{\sqrt{13}-\sqrt{11}[/tex]
Solving
[tex]=\frac{2}{\sqrt{13}+\sqrt{11}} *\frac{\sqrt{13}-\sqrt{11}}{\sqrt{13}-\sqrt{11}} \\=\frac{2(\sqrt{13}-\sqrt{11})}{(\sqrt{13}+\sqrt{11})(\sqrt{13}-\sqrt{11})}\\We\,\, know\,\, that\,\, (a+b)(a-b) = a^2-b^2\\=\frac{2(\sqrt{13}-\sqrt{11})}{(\sqrt{13})^2-(\sqrt{11})^2}\\=\frac{2(\sqrt{13}-\sqrt{11})}{13-11}\\=\frac{2(\sqrt{13}-\sqrt{11})}{2}\\=\sqrt{13}-\sqrt{11}[/tex]
So answer is [tex]\sqrt{13}-\sqrt{11}[/tex]
Answer:
The correct Answer is D[tex]\sqrt{13} - \sqrt{11}[/tex]
Step-by-step explanation:
x(x-3)=x then the possible value of X are...
[tex]x(x-3)=x\\x^2-3x-x=0\\x^2-4x=0\\x(x-4)=0\\x=0\vee x=4[/tex]
[tex]\text{Hey there!}[/tex]
[tex]\text{In order for you can do the distributive property then work from there}[/tex]
[tex]\text{x(x - 4) = x}\\\\\text{x(x)=x}^2\\\\\text{x(-3)= -3x}[/tex]
[tex]\text{Subtract by the value of x on your sides!}[/tex]
[tex]\text{Your new equation becomes: x}^2\text{- 3x = x}[/tex]
[tex]\text{Like}\downarrow[/tex]
[tex]\text{x}^2\text{- 3x - x = x - x}[/tex]
[tex]\text{x - x = 0 }[/tex]
[tex]\text{-3x + (-1x) = -4x}[/tex]
[tex]\text{Our equation becomes: x}^2\text{- 4x = 0}[/tex]
[tex]\text{Next, we have to FACTOR on the LEFT side of your equation}[/tex]
[tex]\text{x(x - 4) = 0}[/tex]
[tex]\text{Set the numbers to FACTOR out to 0}[/tex]
[tex]\text{Like: x = 0 or x - 4 = 0}\text{ (solve that and you SHOULD have the x-values)}[/tex]
[tex]\boxed{\boxed{\bf{Answer: x = 0\ or \ x =4}}}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirt:)}[/tex]
Which of the following sequences are geometric? Check all that apply.
Answer:
A. 3,1,1/3,1/9,1/27 because you are multiplying by 1/3 every time to get new term.
C. 1,6,36,216,1296 because you are multiplying by 6 every time to get new term.
The other sequences you are not multiplying repeatedly to get new terms..
Step-by-step explanation:
The sequence is geometric sequence is 3, 1, 1/3, 1/9, and 1/27.
The sequence is a geometric sequence that is 1, 6, 36, 216, 1, 296.
What is the geometric series?A sequence is a list of elements that have been ordered in a sequential manner, such that members come either before or after.
If the common ratio between the two successive terms must be constant. Then the sequence is called a geometric sequence.
The sequences are given below;
3, 1, 1/3, 1/9, 1/27
The common ratio between the terms are;
[tex]\rm \dfrac{a_2}{a_1}=\dfrac{1}{3}\\\\\dfrac{a_3}{a_2}=\dfrac{\dfrac{1}{3}}{1}= \dfrac{1}{3} \times \dfrac{1}{1}=\dfrac{1}{3}\\\\\dfrac{a_4}{a_3}=\dfrac{\dfrac{1}{9}}{\dfrac{1}{3}}=\dfrac{3}{9}=\dfrac{1}{3}[/tex]
The sequence is a geometric sequence.
The sequences are given below;
1, 6, 36, 216, 1, 296.
The common ratio between the terms are;
[tex]\rm \dfrac{a_2}{a_1}=\dfrac{6}{1}=6\\\\\dfrac{a_3}{a_2}=\dfrac{36}{6}=6\\\\ \dfrac{a_4}{a_3}=\dfrac{216}{36}=6\\[/tex]
The sequence is a geometric sequence.
More about the sequence link is given below.
brainly.com/question/21961097
#SPJ2
How many solutions are there to the equation 12x+6=5x
Answer:
One solution; x = -[tex]\frac{6}{7}[/tex]
Step-by-step explanation:
12x + 6 = 5x
12x - 5x = -6
7x = -6
x = -[tex]\frac{6}{7}[/tex]
A company makes globes with a radius of 11 inches. The material to make the globes costs the company $0.04 per square inch. To the nearest cent, how much does the company pay for the material to create one globe? Use 3.14 for pi.
Recall the formula SA=4 pi r^2.
$11.05
$60.79
$243.16
$607.90
Answer:
One globe costs $60.79
Step-by-step explanation:
The area of the globe is
A = 4.π.r^2
Since the radius is 11 inches
A = 4*(3.14)*(11 in)^2 = 1519.76 in^2
We apply a rule of three
1 in^2 --------------------------------- $0.04
1519.76 in^2 ------------------------- x
x = (1519.76 in^2/ 1 in^2)*$0.04
x = (1519.76)*$0.04
x = $60.79
x ≈ $60.8
Answer: Second Option
$60.79
Step-by-step explanation:
To solve this problem let's suppose that the balloons are spherical
Then the surface area of a sphere is given by the formula:
[tex]SA=4\pi r^2[/tex]
Where r is the radius of the sphere
In this case we know that the radius of each globes is 11 inches, then:
[tex]SA=4(3.14) (11)^2[/tex]
[tex]SA=4(3.14)(121)[/tex]
[tex]SA=1519.76\ in^2[/tex]
If the material to make globes costs $ 0.04 per square inch then the cost of a globes is:
[tex]C=1519.76*0.04[/tex]
[tex]C=\$60.79[/tex]
What is the center point
Answer:
Center of the circle= (-9,6)
Radius = 5 units
Step-by-step explanation:
Once the equation of the circle has been written in the format
(x-h)²+(y-k)²=r² , (h,k) is the center while r is the radius of the circle.
From the given equation, -h=9 therefore h= -9.
-k = -6 therefore k = 6. r² = 25 therefore r= √25=5
Center of the circle= (-9,6) radius = 5 units
X = y +3, 0.8 x + 1.2 y = 6.4
Answer:
y=2
x=5
Step-by-step explanation:
what is the answer to this 3x8y4
The answer is [tex]\( 24xy^2 \)[/tex].
To solve the expression [tex]\( 3x \cdot 8y^4 \)[/tex], we first multiply the coefficients and the variables separately. The coefficients are 3 and 8, and when multiplied, they give us 24. For the variables, we multiply x by [tex]\( y^4 \)[/tex], keeping in mind that when multiplying exponents with the same base, we add the exponents. Therefore, [tex]\( x \cdot y^4 \)[/tex] remains [tex]\( xy^4 \)[/tex].
Combining the coefficient and the variables, we get \( 24xy^4 \). However, we can simplify this further by recognizing that any variable raised to the power of 1 is simply the variable itself. Thus, [tex]\( xy^4 \)[/tex] is equivalent to [tex]\( xy^2 \)[/tex] because [tex]\( y^1 \)[/tex] is just [tex]\( y \)[/tex].
So the final simplified expression is [tex]\( 24xy^2 \)[/tex].
HELP ASAP WILL REWARD BRAINLIEST
How many books that are 10 inches long, 6 inches wide,
and 2.5 inches high will fit into a trunk that is 40 inches
long, 24 inches wide, and 20 inches high?
a. 108
b. 128
c. 148
How many cups of tomato juice will fit into a can that is
12 inches high and has a 4-inch radius if 1 cup of tomato
juice takes up 12 cubic inches?
a. 4
b. 12.56
c. 50.24
Answer:
3. B. 128
4. B. 50.24
Step-by-step explanation:
3. The Books
The numbers of the problem make it quite easy.
We can easily figure out how many books will be stacked in each dimension of the trunk.
Length:
Books: 10 inches
Trunk: 40 iinches.
How may books can you fit lengthwise in the trunk? 40 / 10 = 4
We then to the same for the width:
Books: 6 inches
Trunk: 24 inches
How many books can you stack wide-wise in the trunk? 26/4 = 4
And then the height:
Books: 2.5 inches
Trunk: 20 inches
How many books stacked in height? 20 / 2.5 = 8
So, we can saw the trunk is 4 books long, by 4 books wide by 8 books thick... so, the number of books you can fit in that trunk is:
B = 4 * 4 * 8 = 128
4. Tomato juice
First, we have to find the volume of that big can...
Since it's a cylinder, its volume is calculated by:
V = π * r² * h and we have everything we need:
V = 3.14 * 4² * 12 = 192 * 3.14 = 602.88 cu in
We know a cup of tomato juice takes 12 cu inches...
So, how many cups of juice fit in that can?
C = 602.88 cu in / 12 cu in/cup = 50.24 cups