Answer:
\(\textsf{1.} \quad x=-6, \quad x=6\)
\(\textsf{2.} \quad x=-5, \quad x=2\)
\(\textsf{3.} \quad x=-3, \quad x=7\)
\(\textsf{4.} \quad x=\dfrac{-5 +\sqrt{57} }{4}, \quad x=\dfrac{-5 -\sqrt{57} }{4}\)
\(\textsf{5.} \quad x=\dfrac{7+ \sqrt{309} }{10}, \quad x=\dfrac{7-\sqrt{309} }{10}\)
Step-by-step explanation:
Question 1Method: Extracting the Square Root
\(\begin{aligned}& \textsf{Given}: & x^2 & = 36\\& \textsf{Square root both sides}: & \sqrt{x^2} & = \sqrt{36}\\& \textsf{Simplify}: & x & = \pm 6\\&\textsf{Solution}:&x& = -6, 6\end{aligned}\)
Question 2Method: Factoring
\(\begin{aligned}& \textsf{Given}: & x^2+3x-10 & = 0\\& \textsf{Split the middle term}: & x^2+5x-2x-10 & = 0\\& \textsf{Factor the first two and the last two terms}: & x(x+5)-2(x+5)&=0\\& \textsf{Factor out the common term $(x+5)$}: & (x-2)(x+5)&=0\\& \textsf{Apply the zero-product property}: & (x-2)=0 \implies x&=2\\ &&(x+5)=0 \implies x&=-5\\ & \textsf{Solution}: & x&=-5,2\end{aligned}\)
Question 3Method: Factoring
\(\begin{aligned}& \textsf{Given}: & x^2-4x-21 & = 0\\& \textsf{Split the middle term}: & x^2-7x+3x-21 & = 0\\& \textsf{Factor the first two and the last two terms}: & x(x-7)+3(x-7)&=0\\& \textsf{Factor out the common term $(x-7)$}: & (x+3)(x-7)&=0\\& \textsf{Apply the zero-product property}: & (x+3)=0 \implies x&=-3\\&&(x-7)=0 \implies x&=7\\& \textsf{Solution}: & x & = -3, 7\end{aligned}\)
Question 4Method: Quadratic Formula
\(\boxed{\begin{minipage}{4 cm}\begin{center}\underline{Quadratic Formula}\end{center}\\\\\begin{center}$x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$\end{center}\\\\\\\begin{center}when $ax^2+bx+c=0$\end{center}\end{minipage}}\)
Given:
\(5x-4=-2x^2\)
Rearrange into standard form by adding 2x² to both sides:
\(\implies 2x^2+5x-4=0\)
Therefore:
\(a=2, \quad b=5, \quad c=-4\)
Substitute the values into the quadratic formula and solve for x:
\(\implies x=\dfrac{-5 \pm \sqrt{5^2-4(2)(-4)} }{2(2)}\)
\(\implies x=\dfrac{-5 \pm \sqrt{25+32} }{4}\)
\(\implies x=\dfrac{-5 \pm \sqrt{57} }{4}\)
Therefore, the solutions are:
\(x=\dfrac{-5 +\sqrt{57} }{4}, \quad x=\dfrac{-5 -\sqrt{57} }{4}\)
Question 5Method: Quadratic Formula
\(\boxed{\begin{minipage}{4 cm}\begin{center}\underline{Quadratic Formula}\end{center}\\\\\begin{center}$x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$\end{center}\\\\\\\begin{center}when $ax^2+bx+c=0$\end{center}\end{minipage}}\)
Given:
\(5x^2-7x-13=0\)
Therefore:
\(a=5, \quad b=-7, \quad c=-13\)
Substitute the values into the quadratic formula and solve for x:
\(\implies x=\dfrac{-(-7) \pm \sqrt{(-7)^2-4(5)(-13)} }{2(5)}\)
\(\implies x=\dfrac{7 \pm \sqrt{49+260} }{10}\)
\(\implies x=\dfrac{7 \pm \sqrt{309} }{10}\)
Therefore, the solutions are:
\(x=\dfrac{7+ \sqrt{309} }{10}, \quad x=\dfrac{7-\sqrt{309} }{10}\)
The midpoint of AB is M(1,-4). If the coordinates of A are (-3, -6), what are
the coordinates of B?
\(~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{-3}~,~\stackrel{y_1}{-6})\qquad B(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x -3}{2}~~~ ,~~~ \cfrac{ y -6}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE M}}{(1~~,~~-4)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x -3}{2}=1\implies x-3=2\implies \boxed{x=5} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y -6}{2}=-4\implies y-6=-8\implies \boxed{y=-2}\)
ASAPPPPPPPPPPPPPPPPPPPPPP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
The sum will be close to 1/4
Step-by-step explanation:
1/8+1/6 is 7/24, and 1/4th of that is 6/24, so it is very close.
Answer: The sum will be close to 1/4
Step-by-step explanation:
You can start by making the fractions have the same denominator, (8*6) which gets you 48
You then want to use the butterfly method, so 1/8 becomes 6/48 and 1/6 becomes 8/48. You then add these up to 14/48.
12/48 is 1/4, and 14/48 is close to 12/48, thus making the answer the first option.
if 5(2x-1)=35, then x=
Answer:
x=4
Step-by-step explanation:
Answer:
x = 4
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityStep-by-step explanation:
Step 1: Define
5(2x - 1) = 35
Step 2: Solve for x
[Division Property of Equality] Divide 5 on both sides: 2x - 1 = 7[Addition Property of Equality] Add 1 on both sides: 2x = 8[Division Property of Equality] Divide 2 on both sides: x = 4What is the distance between the two points plotted?
101y
8
(-6,4)
10-8
1 unit
|
-6 -4
0-1 unit
11 units
-11 units
6
4
2
-20
-2
-4
-6
-8
-10
2
(5,4)
4
6
8
X
10
The distance between the points (-6, 4) and (5, 4) is 11 units.
To find the distance between two points in a Cartesian coordinate system, we can use the distance formula:
Distance = √[(x2 - x1)² + (y2 - y1)²]
Given the two points (-6, 4) and (5, 4), we can plug in the coordinates into the distance formula:
Distance = √[(5 - (-6))² + (4 - 4)²]
= √[(5 + 6)² + 0²]
= √[11² + 0]
= √[121]
= 11
Therefore, the distance between the points (-6, 4) and (5, 4) is 11 units.
In this case, since the y-coordinates of both points are the same (4), the distance between them only considers the difference in their x-coordinates. As the x-coordinate of the second point is 11 units greater than the x-coordinate of the first point, the distance between them is simply the absolute value of the difference, which is 11.
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Find the value of x please help ASAP picture below
Answer:
7
Step-by-step explanation:
Because these two triangles share an angle and their corresponding sides are parallel, they are similar.
So, we can set up a proportion relating corresponding sides:
10 / (10 + 8) = (3x - 6) / (3x - 6 + 12)
10/18 = (3x - 6) / (3x + 6)
Cross-multiply:
18 * (3x - 6) = 10 * (3x + 6)
54x - 108 = 30x + 60
24x = 168
x = 168/24 = 7
The answer is 7.
~ an aesthetics lover
Use the average daily balance method to compute the finance charge on the credit card account
for the month of August (31 days). The starting balance from the previous month is $270. The
transactions on the account for the month are given in the table to the right. Assume an annual
interest rate of 19% on the account and that the billing date is August 1st.
aug 7th. payment of $70
aug. 10 purchase of $135
aug. 15 purchase of $20
aug. 29 purchase of $25
what is the finance charge for the month of August?
The finance charge for the month of August is $4.93.
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. Moreover, it is indicated by the symbol "%."
Given:
The starting balance from the previous month is $270.
The transactions on the account for the month are given in the table to the right.
Assume an annual interest rate of 19% on the account and that the billing date is August 1st.
After finding the balance outstanding each day, we sum it up.
And get the average as $305.4839
Now we find the average balance by dividing it by 31 days of the August month.
Average balance = $305.4839
Finance charge = $305.4839 x19 x 31/365 days
Finance charge = $4.929589
Finance charge = $4.93
Therefore, the Finance charge = $4.93.
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if the point ( -2 2 ) is reflected across the y-axis what is the new coordinates
The new coordinates of the reflected point will be (2, 2).
Reflection:
In mathematics, reflection is a transformation that "flips" an object over a line or plane. Reflection is a type of symmetry, where an object appears exactly the same after being reflected as it did before.
When a point is reflected across the y-axis, its x-coordinate changes sign while its y-coordinate remains the same.
Here we have
The point (-2, 2) is reflected across the y-axis
When a point is reflected across the y-axis, its x-coordinate changes sign while its y-coordinate remains the same.
The new coordinate of the point = (-(-2), 2) = (2, 2)
Therefore,
The new coordinates of the reflected point will be (2, 2).
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WILL GIVE BRAINLIEST FOR THE CORRECT ANSWER!!
What scale factor was applied to the first rectangle to get the resulting image?
Enter your answer as a decimal in the box.
Answer:
2.5
Step-by-step explanation:
the length has increased by 7.5/3 = 2.5.
so the scale factor is 2.5
What is Orthocentre?
The intersection of altitudes traced perpendicularly from a triangle's vertices to its opposite sides is known as an orthocenter.
Given that,
We have to find what is orthocenter.
We know that
What is Orthocenter?The intersection of altitudes traced perpendicularly from a triangle's vertices to its opposite sides is known as an orthocenter. It is the location in a triangle where the three angles of the triangle intersect. An orthocenter's three primary characteristics are as follows:
Triangle: A three-sided polygon with three edges.
A triangle's height is the line that runs between its vertices and perpendicular to the other side. A triangle can therefore have three heights, one from each vertices.
Vertex - A vertex is the intersection of two or more lines.
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A biologist estimated that the current population of ladybugs in the region was 8.3 x 106. He predicts that a swarm of
950,000 ladybugs will be arriving into the region.
According to the biologist's estimates, how many ladybugs will be in the region after the swarm arrives? math
According to the biologist's estimates, there will be 9.25 million ladybugs in the region after the swarm arrives.
How many ladybugs will be in the region after the swarm arrives?To find the total population of ladybugs in the region after the swarm arrives, we need to add the number of ladybugs in the region before the swarm arrives to the number of ladybugs in the swarm:
Total ladybugs = 8.3 x 10⁶ + 950,000
Total ladybugs = 8,300,000 + 950,000
Total ladybugs = 9,250,000
Therefore, according to the biologist's estimates, there will be 9.25 million ladybugs in the region after the swarm arrives.
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LuANN is playing a math game. She chooses 3 cards. The value of her cards is hownn below
First card: -12
Second card: 3
Third card: -5
What was the sum of the value of LuANNS three cards?
The expression factors as: (n4 + 3)(n4 + 3)
(n4 - 3)(n4 + 3)
(n4 – 3)(n4 – 3)
Answer:
(n 4)
Step-by-step explanation:
Answer:
B - the second one (on EDGE)
Step-by-step :
Rationalize the denominator.
Answer:
work is shown and pictured
Answer:
\(\frac{\sqrt[3]{18}}{3}\)
Step-by-step explanation:
Hello!
To rationalize the denominator, we have to remove of any square root or cube root (or any root) operations.
Since \(\sqrt[3]{3}\) is the same as \(3^{\frac13}\), we have to multiply the numerator and denominator by \(3^{\frac23}\) or \(\sqrt[3]{3^2}\).
Rationalize\(\frac{\sqrt[3]{2}}{\sqrt[3]{3}}\)\(\frac{\sqrt[3]{2}}{\sqrt[3]{3}} * \frac{\sqrt[3]{3^2}}{\sqrt[3]{3^2}}\)\(\frac{\sqrt[3]{2 * 3^2}}{\sqrt[3]{3^3}}\)\(\frac{\sqrt[3]{18}}{3}\)The radical in the numerator cannot be further simplified.
The answer is \(\frac{\sqrt[3]{18}}{3}\).
find the values of variables, then find the lengths of the sides of each quadrilateral
Helppppppppp plzzzzzzzzzz
what is 6 ÷ ⅓ 1/18 1/2 12 18
Answer:
18
Step-by-step explanation:
\(\frac{6}{1/3} =\frac{6*3}{1} \\=18\)
Geometry, Unit 2, Lesson 6)
Triangles ACD and BCD are isosceles. Angle DBC has a measure of 84 degrees and angle
BDA has a measure of 24 degrees. Find the measure of angle BAC.
ADAC and BDBC
A
D
+
B
C
Type the answer in the box below.
Angle BAC has a measure of
degrees
Answer:I think the answer is 18 degrees.
Step-by-step explanation:in the picture.
Need help ASAP!! Please!!
Answer:
Step-by-step explanation:
hi, Green should have smelled more tranquil, but somehow it just tasted rotten.
Doris enjoyed tapping her nails on the table to annoy everyone.
His son quipped that power bars were nothing more than adult candy bars.
Trash covered the landscape like sprinkles do a birthday cake.
PLS HELP MY GRADE DEPENDS ON IT
Image is attached below
Answer: the first one
Step-by-step explanation: head math
I need help
I don’t understand how to do it
Answer:
tan60 = \(\frac{x}{6}\)
x = 6 x tan60
= 10.4 ( cor to 3 significant figures)
cos60 = \(\frac{6}{y}\)
y = \(\frac{6}{cos60}\)
= 12
to understand the eating habits of babies at TLC daycare Lisa survey 30 mothers and baby boys
A City Park is in the Shape of a triangle where the sides have Lengths 163m, 145m, and 145m.if a fence was built around the perimeter the park, how long would the fence need to be?
The required fence to be built around the perimeter of the park should be 453 m long.
What is the triangle?The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°.
Here,
A City Park is in the Shape of a triangle where the sides have Lengths of 163 m, 145m, and 145m.
The perimeter of the triangle = sum of all sides
= 163 + 145 + 145
= 453 m
Thus, the required fence to be built around the perimeter of the park should be 453 m long.
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5. Find two equations of a circle if one of the end points of the diameter is at the origin and the
radius is 3.
Step-by-step explanation:
there are many possibilities, 4 of them really easy.
the endpoint of a diameter is simply a point on the circle arc.
the easy options are to assume that the center of the circle is on the x- or the y-axis.
let's go with the x-axis (we only need 2 circles : one with the center left, and one with the center right of the origin).
we know the radius is 3.
so, the center of either circle is 3 units away from the origin.
so, center of circle1 = (-3, 0), center of circle2 = (3, 0).
the equation for a circle is
(x - h)² + (y - k)² = r²
r is the radius, (h, k) is the center point.
equation for circle1 :
(x - -3)² + (y - 0)² = 3²
(x + 3)² + y² = 9
equation for circle2 :
(x - 3)² + (y - 0)² = 3²
(x - 3)² + y² = 9
you see ?
the other 2 easy options would be to put the centers on the y-axis : (0, -3) and (0, 3)
find x and round to the nearest tenth! will give thanks
Answer:
3.6 cm
Step-by-step explanation:
For the 20-deg angle, x is the opposite leg. 10 cm is the adjacent leg. The trig ratio that relates the opposite leg to the adjacent leg is the tangent ratio.
tan A = opp/hyp
tan 20 deg = x/10
x = 10 tan 20 deg
x = 3.6
Answer and Step-by-step explanation:
To find x, we need to use the tangent trig function.
tan(angle) = opposite/adjacent
\(tan(20) = \frac{x}{10}\)
Multiply by 10 to both sides, and solve with a calculator.
10(tan(20)) = x
x = 3.639702343
x ≈ 3.6 is the answer.
#teamtrees #WAP (Water And Plant)
Which expression is equivalent to StartRoot 8 x Superscript 7 Baseline y Superscript 8 Baseline EndRoot? Assume x greater-than-or-equal-to 0.
x y squared StartRoot 8 x cubed EndRoot
2 x cubed y cubed StartRoot x y squared EndRoot
2 x cubed y Superscript 4 Baseline StartRoot 2 x EndRoot
4 x cubed y Superscript 4 Baseline StartRoot x EndRoot
The expression that is equivalent to StartRoot \(8 x^7 y^8\) EndRoot is (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2.
To understand why this is the case, let's break down each expression and simplify them step by step:
StartRoot \(8 x^7 y^8\) EndRoot:
We can rewrite 8 as \(2^3\), and since the square root can be split over multiplication, we have StartRoot \((2^3) x^7 y^8\) EndRoot. Applying the exponent rule for square roots, we get StartRoot \(2^3\) EndRoot StartRoot \(x^7\) EndRoot StartRoot \(y^8\) EndRoot.
Simplifying further, we have 2 StartRoot \(2 x^3 y^4\) EndRoot StartRoot \(2^2\) EndRoot StartRoot \(x^2\) EndRoot StartRoot \(y^4\) EndRoot. Finally, we obtain 2 \(x^3 y^4\) StartRoot 2 x EndRoot, which is the expression in question.
(\(2 x y^2\) StartRoot 8 x^3 EndRoot)^2:
Expanding the expression inside the parentheses, we have \(2 x y^2\)StartRoot \((2^3) x^3\) EndRoot. Applying the exponent rule for square roots, we get \(2 x y^2\) StartRoot \(2^3\) EndRoot StartRoot \(x^3\) EndRoot.
Simplifying further, we have \(2 x y^2\) StartRoot 2 x EndRoot. Squaring the entire expression, we obtain (\(2 x y^2\) StartRoot 2 x EndRoot)^2.
Therefore, the expression (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2 is equivalent to StartRoot \(8 x^7 y^8\) EndRoot.
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AABC ~ AXYZ
Find the missing side length, s.
B
6
9
A
•C
8
Х-
Z
S
s = [?]
Enter
Answer:
The value of s is 12.Step-by-step explanation:
We know that:
ΔABC ≅ ΔXYZWork:
[{6 + (1/2 x 6)} + {8 + (1/2 x 8} + {BC + (1/2 x BC) = 9 + s + YZ=> s = 8 + (4)=> s = 12Hence, the value of s is 12.
Hoped this helped.
\(BrainiacUser1357\)
PLEASE HELP WORTH 25 POINTS
Model with Mathematics The outline of a park is
shown in the diagram. Each square on the grid represents
a square yard. Use shapes to model the area of the park.
Explain your reasoning and justify your calculations.
Answer:
We are trying to calculate the area of the park by modeling it with shapes. To start, the larger rectangle (green) toward the top is the easiest to calculate. Its length is 8 yards and its width is 4 yards, so the area would be 8 x 4 = 32 yards^2.
Next, the 3 rectangles at the bottom (white). The one in the middle has a length of 4 yards and a width of 3 yards, so its area is 4 x 3 = 12 yards^2. The two rectangles to either side are the same size, so together their area will be 2 x 4 x 3 = 24 yards^2.
Now that we have modeled the park with 3 shapes, we need to add the areas together to get the total area. So, we have 32 + 12 + 24 = 68 yards^2. The total area of the park is 68 yards^2.
Step-by-step explanation:
The area of the park is about :
95 + 27 = 122 yards
We have the following information available from the question is:
The outline of a park is shown in the diagram. Each square on the grid represents a square yard. Use shapes to model the area of the park.
Now, According to the question:
Each square on the grid represents a square yard, and as we can see from the figure that the complete square is about 95, the incomplete grid is about 27,
So the area of the park is about :
95 + 27 = 122 yards
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Convert 1.4394 to a percent
Answer: = 143.94%
Step-by-step explanation:
Multiply 1.4394 by 100/100. Since 100/100 = 1, we are only multiplying by 1 and not changing the value of our number.
1.43941×100100=143.94100
143.94/100 is 143.94 over 100 and means 143.94 per 100. 143.94 "per 100" means 143.94 "percent" or 143.94%
Therefore, we have shown that
1.4394 = 143.94%
Answer:
143.94%
It is a whole number so it is 100% plus the 43 so it is 143.94
Find the equation of the line in slope-intercept form.
The line has a slope of -5 and a y-intercept of 6.
∠A ≅ ∠B, ∠C is a complement of ∠A. m∠C = 25°; m∠B =
Using the fact that ∠A is congruent to ∠B and ∠C is a complement of ∠A, we determined that the measure of ∠B is 65° based on the given measure of ∠C as 25°.
If ∠A is congruent (≅) to ∠B and ∠C is a complement of ∠A, we can use the properties of complementary angles to find the measure of ∠B.
Given that m∠C = 25° and ∠C is a complement of ∠A, we know that ∠A + ∠C = 90°.
Since ∠A is congruent to ∠B, we can replace ∠A with ∠B in the equation:
∠B + ∠C = 90°.
Substituting the given value, we have:
∠B + 25° = 90°.
To isolate ∠B, we subtract 25° from both sides of the equation:
∠B = 90° - 25°.
Simplifying, we get:
∠B = 65°.
Therefore, the measure of ∠B is 65°.
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