Answer:
30 inches
Step-by-step explanation:
We know that the total length of the board is 90 inches and we know that the shorter piece is two times smaller than the other so we have two pieces divided into three sections 90 divided by three is 30 and since we realize that 30x2=60 and 60+30=90 it means the longer board is 60 inches and smaller one is 30 I hope this helps.
GRIDDED RESPONSE Triangle A B C is congruent to ΔH I. The vertices of \triangle A B C are A(-1,2), B(0,3) and C(2,-2) . What is the measure of side HI?
The measures of HI will be 11.8 units under the Corresponding parts of the congruent triangles (CPCT) condition.
What is the definition of a triangle?A triangle is a three-sided polygon with three edges.It is a basic geometric shape.Triangle ABC is a three-vertical triangle with the letters A, B, and C.In Euclidean geometry, any three non-collinear points define a unique triangle and, by extension, a unique plane.So,
The formula sides of the triangle: √(x₂−x₁)²+(y₂−y₁)²
Filling the values in the formula, we obtain:
= √(0-(-1))²+(3−2)²= 11.8 unitsThen, the side of the triangle will be: 11.8 units
Since ΔABC is congruent to ΔHJI, then, the measure of HI will also be 11.8 units under the CPCT condition.Therefore, the measures of HI will be 11.8 units under the Corresponding parts of the congruent triangles (CPCT) condition.
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The width of a rectangle is 8 units less than the length. The area of the rectangle is 9 units. What is the length, in units, of the rectangle?
The length of the given rectangle is 9.
According to the statement
We have to find that the length of the rectangle.
So, For this purpose, we know that the
A rectangle is a type of quadrilateral, whose opposite sides are equal and parallel.
From the given information:
The width of a rectangle is 8 units less than the length. The area of the rectangle is 9 units
Then
Let the Length of the rectangle = x
Let the width of the rectangle = x-8
Area of the rectangle = L*B
Then
L*B = 9
x(x-8) = 9
x^2 -8x -9 = 0
x^2 -9x + 1x -9 = 0
x(x-9) +(x-9) = 0
(x+1) (x-9) = 0
here x = -1 and then x = 9.
Here neglect x = -1 then
Length of the rectangle is 9
Let the width of the rectangle is 1.
So, The length of the given rectangle is 9.
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If anyone could please answer the following questions!! (photo is below)
Answer:
Natural Numbers:
1 , 17 , 24.0
Whole Numbers:
0 , 1 , 17 , 24.0
Integers:
-775 , -54.3 , -12
Rational Numbers:
0.5 , 24.0 , 3/4 , 2 5/8
ASAP. Please help me with this question. ASAP Please
Answer:
y=x
z=110
d=3cm
A quadratic sequence begins
8, 11, 16, 23, 32,
What is the nth term rule for this
sequence
The nth term of the given quadratic sequence begins 8, 11, 16, 23, 32, = n² + 7.
What is quadratic sequence?Quadratic sequences are those that contain a word. They are distinguished by the fact that the first differences between terms really aren't equal, but really the second differences between terms remain equal.
What is a quadratic sequence's rule?The difference between each term inside a quadratic series is not equal, but the second difference between every term is equal.
How can you tell whether a sequence is straight or quadratic?A linear sequence is a number pattern that increases or lowers by the same amount each time. The common difference is the amount by which it increases or drops. Quadratic sequence: The difference between every term increases or decreases at a steady rate in quadratic sequence.
According to the given data:Given:
8, 11, 16, 23, 32,
The nth rule is:
n² = 1² , 2², 3², 4² , 5²
n² = 1 , 4 , 9 , 16 , 25
Subtracting the equation:
8 , 11 , 16 , 23, 32
1 , 4, 9 , 16 , 25
we get:
7, 7, 7, 7
So that the nth term of the given quadratic sequence begins
8, 11, 16, 23, 32, = n² + 7.
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Find each sum.
6+(-6)
Is 2 5/8 a rational number??
Answer:
2×5/8 which is 5/4 which is a rational number because denominator is not 0
Step-by-step explanation:
Hope it helps you
Answer:
yes it is
Step-by-step explanation:
rational numbers are numbers that can be expressed in the form of ratio. for example
[tex] \frac{85}{5} [/tex]
=
85:5
I need some help please:(
What is the y -coordinate of the y -intercept of the line?
The y-intercept of the equation of a line in general form is:(0, -c/b) or -c/b
The y-intercept is the point where the graph intersects the y-axis. To graph, any function that is of the form y = f(x) finding the intercepts is really important. There are two types of intercepts that a function can have. They are the x-intercept and the y-intercept. An intercept of a function is a point where the graph of the function cuts the axis.
The y-intercept of a function is a point where its graph would meet the y-axis. The x-coordinate of any point on the y-axis is 0 and we use this fact to derive the formula to find the y-intercept. i.e., the y-intercept of a function is of the form (0, y).
The equation of a straight line in general form is ax+by+c=0. For the y-intercept, we substitute x=0 and solve it for y.
a(0)+ by + c =0
by + c =0
y = - c/b
Thus, the y-intercept of the equation of a line in general form is:(0, -c/b) or -c/b
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A glide reflection includes both a reflection and a (rotation, translation).
Translation, rotations are not involved in a glide reflection.
How is a glide reflection created?
There is a mirror line in every reflection. A glide reflection is a mirror reflection that is followed by a parallel translation to the mirror. Every glide reflection has a translation distance and mirror line.
A glide reflection is made up of what two transformations?
A glide reflection is made up of a translation and a reflection in which the translation and the reflection are parallel to each other or the direction of the translation. A gliding reflection has opposite isometry and is -commutative.The translation of a glide reflection?
The composition of transformations is a glide reflection. In a glide reflection, the figure is first translated before being reflected over a line.
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A large western state consists of 4825 million acres of land. approximately 75% of this land is federally owned. find the number of acres that are not federally owned.
Answer:
1206.5 acres
Step-by-step explanation:
tatle acres=4825m
%of not federally owned =100%-75%=25%
[tex]( \frac{25}{100} ) \times 4825[/tex]
=1206.5 acres
Point X is chosen at random on AE-. Find the probability that X is on CE- .
Probability of any point X on line BD is 1/2 , on line BC is 3/10, on line AB is 1/2 and on line AC is 4/5.
A, B, C and D are four points on a line. Length of AB is 5, length of BC is 3, length of AC is 8, length of CD is 2 and length of AD is 10.
Probability of any point X on line BD = ( length of BD / length of AD) = (5/10) = 1/2.
Probability of any point X on line BC = ( length of BC / length of AD) = 3/10.
Probability of any point X on line AB = ( length of AB / length of AD) = 5/10 = 1/2.
Probability of any point X on line AC = ( length of AC / length of AD) = 8/10 = 4/5.
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A dog is chasing a squirrel and the dog is running 45 miles per hour, how long does it takes the dog if he catches the squirrel in 3 miles?
Answer:
4 minutes.
Step-by-step explanation:
45 miles in 60 minutes
3 miles in x minutes
3 x 60 divided by 45 = 4
To check yourself, 45 divided by 3 gives you 15 sets of 3 minute segments. 15 x 4 = 60 minutes or 1 hour.
f(x)=5-x,g(x)=13-3x^2 and h(x)=2x
a. Find f∘ ( g∘ h)
b. Find h ∘ ( g∘ f )
c. Find g∘ (f ∘ h)
Answer:
f(2x)=-2x+5
h(5-x)=-2x+10
The triangles are similar. Find the value of x.
First triangle:
Width: 3
Length: 17
Second triangle:
Width: x
Length: 102
Answer:
Step-by-step explanation:
I would say the width is 18 because the scale factor is 6
102/17= 6
3*6=18
Which of the following definitions pertaining to Solving Linear Equations are incorrect? Check all that apply.
Equivalent equations are two or more equations that have the same solution.
An algebraic expression is a mathematical sentence connecting one statement to another statement with an equal sign (=).
An algebraic equation is a mathematical sentence connecting one expression to another expression with an equal sign (=).
To solve an equation means to isolating the variable on the left hand side of the equal sign.
The solution to an equation is the value, or values, that makes the equation true.
To solve an equation means to "undo" all the operations of the equation, leaving the variable by itself on one side. This in known as isolating the variable.
The two incorrect definitions are:
"An algebraic expression is a mathematical sentence connecting one statement to another statement with an equal sign (=)."
"To solve an equation means to isolating the variable on the left hand side of the equal sign."
Which definitions are incorrect?Here we have some definitions pertaining to solving linear equations, and we need to identify which ones are incorrect.
The first incorrect definition is:
"An algebraic expression is a mathematical sentence connecting one statement to another statement with an equal sign (=)."
The sentences that have an equal sign are called equations, algebraic expression is more general than that.
The second incorrect definition is:
"To solve an equation means to isolating the variable on the left hand side of the equal sign."
It is true that you need to isolate the variable, but it does not matter in which side of the sign you do that.
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Compare √180 and 102/8 using <, >, or =.
Answer:
the answer is √180>102/8
Draw the net of the solid that best models the hay bales. Please include the correct dimensions on your net.
Determine whether each sequence is arithmetic, geometric, or neither. Then find the tenth term. -12,-5,2,9,16, . . . .
The sequence -12,-5,2,9,16, . . . .. is an arithmetic sequence and its 10th term is a(10) = 65
To determine whether a sequence is an arithmetic or geometric one, we need to check the relation between two consecutive terms.
In an arithmetic sequence, the nth term is obtained by adding the (n-1)th term with a constant, called a common difference (d).The given sequence is:
-12,-5,2,9,16, . . . .
In this sequence:
a(1) = -12
a(2) = -5
a(3) = 2
a(4) = 9
and so on.
Notice that:
a(2) - a(1) = -5 - (-12) = 7
a(3) - a(2) = 2 - (-5) = 7
a(4) - a(3) = 9 - 2 = 7
Since each consecutive terms have common difference, then, the given sequence is an arithmetic sequence. Furthermore, the common difference, d = 7.
The formula for the nth term in an arithmetic sequence is given by:
a(n) = a(1) + (n - 1) . d
Substitute n = 10, d = 7, and a(1) = -12
a(10) = -12 + (12 - 1) . 7
a(10) = -12 + 77 = 65
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e function.
f(x)= -x²
Find f(-1)
Answer:
f(-1) = -1
Step-by-step explanation:
f(x) = -x^2
Let x = -1
f(-1) = - ( -1) ^2
= -1
Determine whether the given measures define 0,1,2 , or infinitely many triangles. Justify your answers.
a=25, b=21, m
We can form an endless number of triangles when you are given two sides and no measurement of angle i.e a = 25 , b = 21
For Example -
We can chose the value of angle from 0-360 degrees with side length a = 25 and b =21, how many different triangles are possible to create?
Create one of the triangles with a protractor having the side lengths a = 25 m and b = 21 m and angle 12° and third side can be adjusted to your preferred length. You have built a triangle.
Similarly by changing the length of the third side and measure of the angle we will get an entirely new triangle.
It's important to notice that you choose the side lengths and angle. This suggests that you might make a different decision. By employing the same angles, you were able to make an infinite number of different triangles.
Therefore, with simply the measurements of one angle and a side length, we can create an endless number of triangles.
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If Zb= 85° and Ze = 115°, then Zc is
Answer:
∠ c = 30°
Step-by-step explanation:
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
∠ e is an exterior angle of the triangle , then
∠ b + ∠ c = ∠ e , that is
85° + ∠ c = 115° ( subtract 85° from both sides )
∠ c = 30°
The interior angle measure of a regular polygon is given. Identify the polygon.
108
The regular polygon with an interior angle of measure 108° is a pentagon.
A regular polygon is a polygon that has equal side lengths and equal interior angle measures.
Interior angle of a polygon is the angle inside it that is formed by two adjacent sides. The number of interior angles formed inside a polygon is the same as the number of its sides. Meanwhile, the sum of all the interior angles of any polygon is constant to that polygon and depends on the number of sides.
sum = 180(n - 2)
Using this formula,
sum = 180(n - 2)
where n = number of sides of the polygon = number of interior angles
sum = measure of interior angle x n
108n = 180(n - 2)
108n = 180n - 360
180n - 108n = 360
72n = 360
n = 5
If the polygon has 5 sides and 5 interior angles, then the regular polygon is a pentagon.
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Name the property of real numbers illustrated by the equation. 2(s-t) = 2 s-2 t
The Distributive property of real numbers is illustrated by the equation 2(s-t) = 2 s-2 t.
Distributive property of real number is denoted by x(y+z)=x*y+x*z , which means "x" will be multiplied with each term present inside the bracket.
For Example :
3(4+1) =3*4+3*1
=12+3
=15
In the given question
LHS = 2(s-t)
On applying Distributive property we get ,
=2*s-2*t
=2s-2t = RHS
Hence distributive property is applied here.
Therefore , the property of real numbers that is illustrated by the equation 2(s-t) = 2 s-2 t is Distributive property .
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Find the factor pairs for the number.
24
Answer:(1, 24), (2, 12), (3, 8), and (4, 6).
Step-by-step explanation:a pair of numbers when multipled you get 24.
draw a diagram of B complement
To draw a venn diagram for B', we have shade the region that excludes BIf B ⊆ U, where U is a universal set, then U \ B is called the compliment of B with respect to U. If underlying universal set is fixed, then we denote U \ B by B' and it is called compliment of B.
An ant carries food at a speed of 1 centimeter/second. How long will it take an ant to carry a cookie crumb a distance of 500 centimeters?
The total time taken by the ant to take cookie crumb from the kitchen table to an anthill is 83.33 minutes.
What is the linear system?
It is a system of an equation in which the highest power of the variable is always 1. A one-dimension figure that has no width. It is a combination of infinite points side by side.
Given
An ant carries food at a speed of 1 cm/s.
The kitchen table to an anthill, a distance of 50 m.
We know the relation between speed and time.
Time=distance/speed.
Speed = 1 cm per second = 0.6 m per minute
Distance = 50 m
Then total time taken will be
=50/0.6
=83.33
Thus, the total time taken by the ant to take cookie crumb from the kitchen table to an anthill is 83.33 minutes.
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Consider the given right triangle if A=20 and b =20 then
Which of the following is the correct solution to the linear inequality shown
below?
y<2/3x+1
Answer:
3x+1
Step-by-step explanation:
Write an explicit formula for each sequence. Then generate the first five terms. a₁ = 10, r=-1
The explicit formula for the nth term is a(n) = 10 . (-1)ⁿ⁻¹, while the first five terms are 10, -10, 10, -10, 10
In a geometric sequence, the next term is obtained by multiplying the previous term by a common ratio, usually denoted as r.
The general formula of the nth term of a geometric sequence is:
a(n) = a₁ . r^(n-1)
Here a₁ refers to the first term and r to the ratio.
In the problem, the given parameters are:
a₁ = 10, r = -1
Substitute these into the general formula, we get:
a(n) = 10 . (-1)ⁿ⁻¹
Notice that
(-1)ⁿ⁻¹ = -1 if n-1 is an odd number, or if n is an even number
(-1)ⁿ⁻¹ = 1 if n-1 is an even number, or if n is an odd number
Therefore, the first five terms are: 10, -10, 10, -10, 10
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