Answer:
[tex] 10\sqrt{5} - 4 \sqrt{10} [/tex]
Step-by-step explanation:
[tex] \sqrt{5} (10 - 4 \sqrt{2} )[/tex]
Multiply
[tex] \sqrt{5} [/tex]
with each term within the bracket
[tex] = \sqrt{5} + \times 10 - \sqrt{5} \times 4 \sqrt{2} [/tex]
[tex] = 10 \sqrt{5} - 4 \sqrt{10} [/tex]
What is the midpoint of the segment below?
(2, 3)
(-3.-2)
The formula for finding the midpoint of a line segment is[tex](\frac{x1+x2}{2}, \frac{y1+y2}{2})[/tex]. Plug in and solve:
[tex](\frac{2-3}{2} , \frac{3-2}{2})[/tex]
(-1/2, 1/2)
(-0.5, 0.5)
Hope this helps!!
The midpoint of the segment is (-0.5, 0.5)
What is midpoint of the segment?The midpoint of a line segment is a point that lies halfway between 2 points. The midpoint is the same distance from each endpoint.
Given points: (2, 3) and (-3.-2).
The formula for midpoint is
(x1+x2/2, y1+y2/2)
= (2-3/2, 3-2/2)
=(-1/2, 1/2)
= (-0.5, 0.5)
Hence, the midpoints of the segment is (-0.5, 0.5).
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Which graph represents a function?
Select one:
Answer:
C
Step-by-step explanation:
Because none of the X coordinates are the same.
Shania is making a scale diagram of the badminton court at the community center. She uses a scale of 1 centimeter to 0.5 meter to draw the scale diagram. If the scale length of the badminton court is 26.8 centimeters and the scale width is 12.2 centimeters, what is the actual area of the court?
Answer: 13.4 meters by 6.1 meters
Step-by-step explanation: Applying the scale to the given measurements gives us: 13.4 meters long and 6.1 meters wide
What is the measure of 3?
Answer:
∠3 = 60°
Step-by-step explanation:
Since g and h are parallel lines then
∠1 and ∠2 are same side interior angles and are supplementary, hence
4x + 36 +3x - 3 = 180
7x + 33 = 180 ( subtract 33 from both sides )
7x = 147 ( divide both sides by 7 )
x = 21
Thus ∠2 = (3 × 21) - 3 = 63 - 3 = 60°
∠ 2 and ∠3 are alternate angles and congruent, hence
∠3 = 60°
The measure of angle 3 is 60 degrees, the correct option is B.
Given
In the diagram, g is parallel to h.
The measurement of angle 1 is (4x +36).
The measurement of angle 2 is (3x-3).
Interior angles;
The angles that lie in the area enclosed between two parallel lines that are intersected by a transversal are also called interior angles.
∠1 and ∠2 are the same side interior angles and are supplementary then the sum of both angles is equal to 180 degrees.
[tex]\rm 4x+36+3x-3=180\\\\7x+33=180\\\\7x=180-33\\\\7x=147\\\\x=\dfrac{147}{7}\\\\x=21[/tex]
The measure of the angle 2 is = 3(21)- 3= 63 - 6 = 60 degrees.
Hence, Angle 2 and ∠3 are alternate angles and congruent then the measure of angle 3 is 60 degrees.
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How do you solve this? 2/10 • 9/12
Answer:
3/20
Step-by-step explanation:
First simplify the fractions
2/10 Divide top and bottom by 2
= 1/5
9/12 Divide top and bottom by 3
= 3/4
2/10 * 9/12
1/5*3/4
Multiply the top
1*3 = 3
Multiply the bottom
5*4=20
3/20
Which of the following transformations will result in an image that maps onto
itself?
A. rotate 90 degrees counterclockwise and then reflect across the y
axis
B. reflect across the x-axis and then reflect across the y-axis
c. rotate 90 degrees counterclockwise and then translate 4 units up
D. reflect across the x-axis and then reflect again across the x-axis
I agree. It reflects A G A I N
"Reflect across the x-axis and then reflect across the y-axis" will result in an image that maps onto itself. The correct option is B.
What is transformations?Transformations in mathematics refer to the process of changing the position, size, or shape of a geometric figure in a coordinate plane.
When a figure is reflected across the x-axis, the y-coordinate of each point on the figure is multiplied by -1, while the x-coordinate remains unchanged.
Similarly, when a figure is reflected across the y-axis, the x-coordinate of each point on the figure is multiplied by -1, while the y-coordinate remains unchanged.
When we reflect a figure across the x-axis and then across the y-axis, we essentially multiply the x-coordinate of each point by -1 and then the y-coordinate by -1.
This corresponds to a 180-degree rotation around the origin. Because a 180-degree rotation maps a figure onto itself, this transformation will produce an image that also maps onto itself.
Thus, the correct option is B.
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Which is a solution to (x - 2)(x + 10) = 13?
O x = 3
Ox=8
x = 10
x = 11
The required solutions to the equation (x - 2)(x + 10) = 13 are x = -11 and x = 3.
What is simplification?Simplification involves using rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression. The goal is to obtain an expression that is easier to work with, manipulate, or solve.
We can solve the equation (x - 2)(x + 10) = 13 using the following steps:
Expand the left-hand side of the equation: x² + 10x - 2x - 20 = 13Simplify the left-hand side by combining like terms: x^2² + 8x - 20 = 13Move the constant term to the right-hand side: x² + 8x - 33 = 0Factor the quadratic expression: (x + 11)(x - 3) = 0Apply the zero product property and solve for x: x + 11 = 0 or x - 3 = 0x = -11 or x = 3Therefore, the solutions to the equation (x - 2)(x + 10) = 13 are x = -11 and x = 3.
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Write an equation of the line given the two points below (Write your equation in slope-intercept form, y=mx+b): (-4, 4) and (6, -4)
[tex]\bf (\stackrel{x_1}{-4}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{-4}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-4-4}{6-(-4)}\implies \cfrac{-8}{6+4}\implies \cfrac{-8}{10}\implies -\cfrac{4}{5}[/tex]
[tex]\bf \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-4=-\cfrac{4}{5}[x-(-4)]\implies y-4=-\cfrac{4}{5}(x+4) \\\\\\ y-4=-\cfrac{4}{5}x-\cfrac{16}{5}\implies y=-\cfrac{4}{5}x-\cfrac{16}{5}+4\implies y=-\cfrac{4}{5}x+\cfrac{4}{5}[/tex]
Matti built a greenhouse in his backyard as shown below
well, Matti's house is a triangular prism, and to get the volume of it, we simply get the area of the triangle upfront and multiply by its length of 15.
[tex]\bf \stackrel{\stackrel{\textit{area of }}{\textit{triangular front}}}{\cfrac{1}{2}(7)(7)}\times \stackrel{\textit{length}}{15}\implies \cfrac{49}{2}\cdot 15\implies 367.5~ft^3[/tex]
Answer:
Option B.
Step-by-step explanation:
Volume of a green house in the backyard which in the shape of triangular prism V = (Area of base)×(Height)
In the figure attached,
Height of the triangular base = 7 ft
Base = 7 ft
Area of the triangle = [tex]\frac{1}{2}(7)(7)[/tex]
Area = [tex]\frac{49}{2}=24.5[/tex] ft²
Therefore, volume of the prism = 24.5 × 15
= 367.5 ft²
Option B. is the correct option.
What type of triangle has side lengths 2, √12, and √19?
Answer:
Is an scalene obtuse triangle
Step-by-step explanation:
step 1
Find the type of triangle by the measure of the interior angles
we know that
If applying the Pythagoras Theorem
[tex]c^{2}=a^{2}+b^{2}[/tex] ----> we have a right triangle
[tex]c^{2} > a^{2}+b^{2}[/tex] ----> we have an obtuse triangle
[tex]c^{2}< a^{2}+b^{2}[/tex] ----> we have an acute triangle
where
c is the greater side
we have
[tex]c=\sqrt{19}\ units[/tex]
[tex]a=2\ units[/tex]
[tex]b=\sqrt{12}\ units[/tex]
substitute
[tex]c^{2}=(\sqrt{19})^{2}=19[/tex]
[tex]a^{2}+b^{2}=(2)^{2}+(\sqrt{12})^{2}=16[/tex]
so
[tex]19 > 16[/tex] -----> [tex]c^{2} > a^{2}+b^{2}[/tex]
we have an obtuse triangle
step 2
Find the type of triangle by the measure of the sides
we have that
The measure of its three sides is different
therefore
Is an scalene triangle
Marlena has 3 straws. Two straws have the lengths
shown. She does not know the length of the shortest
straw, but when she forms a triangle with all three, the
triangle is obtuse. Which are possible lengths of the
shortest straw? Check all that apply.
5 inches
6 inches
7 inches
8 inches
9 inches
Answer:
5 6 7 is the correct answer
Step-by-step explanation:
The possible lengths of the shortest straw are 5 inches, 6 inches, 7 inches and 8 inches
How to determine the possible lengths of the strawThe lengths of the two straws are given as: 9 inches and 12 inches
Represent the length of the shortest straw with x.
So, we have the following inequality
[tex]x + 9 > 12[/tex]
Subtract 9 from both sides
[tex]x > 3[/tex]
This means the length of the shortest straw is greater than 3 inches
Hence, the possible lengths are 5 inches, 6 inches, 7 inches and 8 inches
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Find (fog)(x).
1 =
x
+
2
g(x) = x² + 6
Answer:
fog(x)=[tex]x^2+8[/tex]
Step-by-step explanation:
Here we are given two functions
f(x) = x+2
g(x)=[tex]x^2+6[/tex]
We are required to find fog(x)
fog(x) is a composite function.
fog(x) = f(g(x))
g(x) = [tex]x^2+6[/tex]
f(g(x)) = f( [tex]x^2+6[/tex] )
f(x)= x+2
Hence we replace x in f(x) with [tex]x^2+6[/tex]
f(g(x))=([tex]x^2+6[/tex])+2
f(g(x))=[tex]x^2+8[/tex]
Hence
fog(x) = [tex]x^2+8[/tex])
write the equation of the graph shown below in factored form
Answer:
[tex]f(x)=(x-3)^{2}(x-2)(x-1)[/tex]
Step-by-step explanation:
we know that
The roots (or x-intercepts) of the equation are
x=1 -----> with multiplicity 1
x=2 -----> with multiplicity 1
x=3 -----> with multiplicity 2 (because is a turning point)
so
The factors are
[tex](x-1), (x-2), (x-3),(x-3)[/tex]
The equation is equal to
[tex]f(x)=(x-3)(x-3)(x-2)(x-1)\\ \\f(x)=(x-3)^{2}(x-2)(x-1)[/tex]
To write a quadratic equation in factored form, find two binomials that when multiplied together yield the original quadratic. Factoring is essential in understanding the roots and the shape of a parabolic graph. For more complex quadratics, techniques like completing the square might be required.
Explanation:When we are looking to write the equation of a graph in factored form, we are typically dealing with a polynomial function, and specifically when the graph is of a parabola, we are working with a quadratic equation. Factoring a quadratic equation involves finding two binomials that when multiplied together give us the original quadratic. For example, if we have a graph of a quadratic with its roots at x = p and x = q, the factored form would be y = a(x - p)(x - q), where a represents the leading coefficient.
If given an equation like 6x² + xy - y² - 17x - y + 12 = 0, it can be factored into two linear terms, which represents the intersection of two lines. In cases where completing the square is needed, such as x² - ( ) x = -() y, we add to each side (half the coefficient of x)² to form a perfect square on the left-hand side, leading us to an equation of the form (x − A)² = -4a(y − B).
Learning about graphing polynomials provides insights into how the constants in an equation affect the shape of the curve. By adjusting coefficients and analyzing the individual terms, we can understand how these terms combine to produce the overall graph of the polynomial.
Which statement is true about f(x)=-6x+5-2
Not enough information (attach the statements).
if you run for 4 hours at 8 miles and walk 8 hours at 2 miles how far will you have gone at the end of 12 hours?
Answer:
4 times 8 is 32 then 8 times 2 is 16 then add them together
Step-by-step explanation:
Please mark brainliest and have a great day!
Answer:
48 miles
Step-by-step explanation:
4 times 8 equals 32 plus 8 times 2 equals 16 add them up equals 48
20 points: Use long division to find the quotient below.
(16x3 + 40x2 + 72)/ (2x + 6)
Answer:
8x2-4x+72. good luck.
Each side length of a triangle is 4cm what type of triangle is it
Answer:
equilateral
Step-by-step explanation:
If all 3 sides of a triangle are the same length, then it is an equilateral triangle.
scalene: no sides the same length
isosceles: 2 sides the same length
equilateral: 3 sides the same length
Suppose y varies directly with x. Write a direct variation equation that relates x and y. Then find the value of y when x=12
Y=7 when x=3
If LP = 15 and PR = 9, find LR. Explain.
Answer:
LR is 12
Step-by-step explanation:
LP is hypotenuse and PR is base so LR is perpendicular
formula to calculate perpendicular is
p^2=H^2 -b^2
p^2=15^2-9^2
p^2=225-81
p^2=144
p=12(root of 144 is 12)
Answer:
it would be 24 cuz 15 + 9 = 24
Slallau
Solve for x.
16x – 6 = 26
Answer:
Step-by-step explanation:
X=2
6. A circle has an area of 78.5 square inches.
What is the radius of the circle?
Answer:
The radius is equal to 5 inches or 12.7 cm
Step-by-step explanation:
16 is 64% of what number
Answer:
25
Step-by-step explanation:
Is means equals and of means multiply
16 = 64% * W
Change to decimal form
16 = .64 * W
Divide each side by .64
16/.64 = .64W/.64
25 = W
Answer:
25
Step-by-step explanation:
We can model this question with:
16 = 0.64x
x represents "what number."
0.64x = 16
Divide 0.64 from both sides
0.64x ÷ 0.64 = 16 ÷ 0.64
16 ÷ 0.64 = 25.
Therefore, 16 is 64% of 25.
Thank you for this a lot
Remember that the slope intercept formula is:
y = mx + b
m is the slope
b is the y-intercept
In this case:
m = -5
b = -8
so...
y = -5x - 8
Hope this helped!
Answer:
B
Step-by-step explanation:
Slope-intercept form of a line:
y = mx + b
m = slope
b = y-intercept
The question asks for a line w/ a slope of -5 and y-int of -8.
B would be the correct choice as in y = -5x - 8,
m (slope) = -5 and
b (y-int) = -8.
Maya is mailing packages. Each small package costs her $2.90 to send . Each larded package costs her $4.50. How much will it cost her to send 6 small packages and 4 large packages
Answer:$35.40
Step-by-step explanation:
1. $4.50 multiplied by 4 is $18
2. $2.90 multiplied by 6 is $17.4
3. $18+$17.4=$35.40
In triangle DEF, FE=3 and M^F =37 find DE to the nearest tenth
U ARE GOING TO MULTIPLY THEM ALL TOGETHER
drako found an emarald in a cave at a depth between negative 1\2 and negative 1 2\3 meters. Which number could represent the depth at which the emerald is located ?
Answer:
[tex](-\frac{7}{6} )[/tex]
Step-by-step explanation:
From the question the emerald was located at a depth which is between -1/2 and -1 2/3 meters
This statement can be written as
[tex](-1\frac{2}{3}) -(-\frac{1}{2} )[/tex]
To get the depth, you find the depth of the emerald location, you find difference between the two mentioned depths
[tex]-(1\frac{2}{3} )-(-\frac{1}{2} )\\\\[/tex]
Change first term to improper fraction
[tex]=-(\frac{5}{3} )-(-\frac{1}{2} )\\\\[/tex]
Find the LCM to solve the operation the involves the fractions.The Least common multiple here is 6 i.e 3*2
[tex]=(-\frac{5}{3} )-(-\frac{1}{2})\\[/tex]
[tex]=\frac{-5}{3} +\frac{1}{2} =\frac{-10+3}{6} =\frac{-7}{6}[/tex]
The number that could represent the depth at which the emerald was located is
[tex]=\frac{-7}{6}[/tex]
The circle below is centered at the point (3,1) and has a radius length of 2.What is its equation
Answer:
C. [tex](x-3)^2+(y-1)^2=2^2[/tex]
Step-by-step explanation:
The standard equation of a circle, given the radius r units and center (h,k) is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
From the question, we have the center of the circle to be (3,1) and the radius is 2 units.
We substitute the center and radius of the circle into the equation to get:
[tex](x-3)^2+(y-1)^2=2^2[/tex]
The correct answer is C
Shawn solved the system of equations below and found that x = 3. Which
ordered pair is the solution to the system?
2x+4y = 34
6x +2y = 32
A. (3,7)
B. (3,9)
C. (3,6)
D. (3,8)
Answer:
A
Step-by-step explanation:
it would equal 34 nd on the bottom would be 32 so AAAA
(3,7) ordered pair is the solution to the system.
What is a system of equations?A finite collection of equations for which we searched for common solutions is referred to in mathematics as a system of equations, sometimes known as a set of simultaneous equations or an equation system. Similar to single equations, a system of equations can be categorized.
Given
2x+4y = 34
6x +2y = 32
x = 3
[tex]2*3[/tex] + 4y = 34
[tex]6*3[/tex] + 2y = 32
18 + 2y = 32
y = 7
(3,7) ordered pair is the solution to the system.
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Write the expression in complete factored
form.
5n_(c - 3) - n(C - 3) =
Answer:
(c-3) (4n)
Step-by-step explanation:
5n(c - 3) - n(C - 3) =
Factor out (c-3) from each term
(c-3) (5n-n)
Simplify the 2nd term
(c-3) (4n)
(a) Find the differential dy.
y = cos(x)
dy =?
(b) Evaluate dy for the given values of x and dx. (Round your answer to three decimal places.)
x = π/3, dx = 0.1.
dy=?
a. Practically speaking, you compute the differential in much the same way you compute a derivative via implicit differentiation, but you omit the variable with respect to which you are differentiating.
[tex]y=\cos x\implies\boxed{\mathrm dy=-\sin x\,\mathrm dx}[/tex]
Aside: Compare this to what happens when you differentiate both sides with respect to some other independent parameter, say [tex]t[/tex]:
[tex]\dfrac{\mathrm dy}{\mathrm dt}=-\sin x\dfrac{\mathrm dx}{\mathrm dt}[/tex]
b. This is just a matter of plugging in [tex]x=\dfrac\pi3[/tex] and [tex]\mathrm dx=0.1[/tex].
[tex]\boxed{\mathrm dy\approx-0.087}[/tex]
The differential dy for y = cos(x) is evaluated by finding the derivative of y which is -sin(x), then multiplying by dx. For x = π/3 and dx = 0.1, the calculated differential dy is approximately -0.0866 when rounded to three decimal places.
Explanation:The differential dy of a function y with respect to x is given by the derivative of y with respect to x, multiplied by dx. For the function, y = cos(x), the derivative of y is -sin(x), hence dy = -sin(x)dx.
To evaluate dy for x = π/3 and dx = 0.1, we substitute x into -sin(x) and multiply by dx. This results in dy = -sin(π/3) × 0.1, which simplifies to dy = -0.1 √3/2. Rounding to three decimal places, dy ≈ -0.0866.