Factor the expression using the GCF 24y+88x

Two triangles are congruent if their corresponding sides are equal in length, and their corresponding angles are equal in measure.

What is congruent?

Congruent refers to things that are exactly the same size and shape. Even if we flip, turn, or rotate the forms, the shape and size should remain the same.

Here,

we have to prove when can we say that the two triangles are congruent.

SSS, SAS, ASA, AAS, and HL.

These tests describe combinations of congruent sides and/or angles that are used to determine if two triangles are congruent.

Hence, two triangles are congruent if their corresponding sides are equal in length, and their corresponding angles are equal in measure.

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Answer:

Step-by-step explanation:

1) 4 1/4 + 5 1/2

= 9 3/4

2) 10 4/5 - 6 1/5

= 4 3/5

3) 3 1/4 - 1 3/4

= 1 1/2

4) 3 2/5 + 7 7/10

= 11 1/10

5 ) 10 3/13 + 2 10/13

= 13

Answer:

1

Step-by-step explanation:

Its for sure 1

There are 125 of the smallest cubes that will fill the largest cube using the size of their respective volume

The volume of cube is calculated by using a × a × a = a³ where "a" is the edge.

The volume of the smallest cube = 1.5inches × 1.5inches × 1.5inches

The volume of the smallest cube = 3.375inches³

The volume of the largest cube = 7.5inches × 7.5inches × 7.5inches

The volume of the largest cube = 421.875inches³

Thus, the number of the smallest cubes it would take to fill the largest cube is derived by

421.875inches³/3.375inches³ = 125.

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Answer:

3

Step-by-step explanation:

Hope this helps..

The points of concurrency of perpendicular bisectors of triangle is circumcenter.

A point of concurrency shared by three or more lines is referred to as a single point of concurrency. Constructed lines in triangle interiors are excellent places to look for points of convergence.

When you construct a triangle's medians, perpendicular bisectors, angle bisectors, or altitudes, you create a point of concurrency for each of them.

Because the triangle can have four distinct types of line segments, it can have four distinct points of convergence. Each point of concurrency represents the intersection of a particular type of line segment: centroid, circumcenter, incenter, and orthocenter.

Thus, the points of concurrency of perpendicular bisectors of triangle is circumcenter.

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Answer: [tex](-\infty, \infty)[/tex]

Step-by-step explanation:

Absolute value is always non-negative.

The straight line has the equation, y = 5x - 4.

A straight line is made up of an infinite number of points that are joined on both sides of the point.

Any straight line's slope 'm' is given by:

m = y2 - y1 / x2 - x1

In slope-intercept form, a linear equation has the formula y = mx + b. The variables in the equation are X and Y. The values m and b represent the slope (m) of the line and the value of y when x = 0.

The obtained points from the graph are (0,-4) and (1,1)

The slope is ,

m = 1-(-4) / 1-0

   = 5/1

   = 5

Because it intersects the y-axis at the point where the intercept C = -4,

The line's equation will be:

⇒ y = mx + c

⇒ y = 5x + (-4)

⇒ y = 5x - 4

As a result, the equation for the straight line shown below is y = 5x - 4.

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The rate of change in the given interval would be 1.25 ft/s.

What is the rate of change?

The slope of a graphed function is determined using the average rate of change formula. Divide the change in y-values by the change in x-values to find the average rate of change.

By observation, we can take the points from the graph in between the given interval.

The points would be (3, 2.5) and (5, 4)

Then the rate of change = y2 - y1/ x2 - x1

                                         = 4 - 2.5/5 - 3

                                         = 2.5/2

                                         = 1.25 ft/s.

Hence, the rate of change in the given interval would be 1.25 ft/s.

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B: 1000 + 25 + Water deposit (50) + Phone connection (40) + Elect. connection (60)

1000 + 25 + 200 = 1225

The length of the line segment will be 4 units. Then the correct option is A.

The line joining the two points is known as a line segment. Let one point be (x, y) and another point be (h, k).

Then the distance between the points will be

D² = (x - h)² + (y - k)²

From the graph, the two points are (2, -2) and (2, 2). Then the distance between the points is calculated as,

D² = (2 - 2)² + (2 + 2)²

Simplify the equation, then we have

D² = (2 - 2)² + (2 + 2)²

D² = (4)²

D = 4 units

The length of the line segment will be 4 units. Then the correct option is A.

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The missing diagram is attached below.

Answer: 12 inches

Step-by-step explanation:

Answer: 15 cm

Step-by-step explanation:

There will be 35 chocolate bar cut out from the 13-meter chocolate bar.

Division is breaking a number up into an equal number of parts.

Given that, Willy Wonka makes a 13-metre chocolate and the chocolate bar is then cut into 4/11 of a metre.

Number of bars made = 13/4/11 = 35.75 ≈ 35

Hence, There will be 35 chocolate bar cut out from the 13-meter chocolate bar.

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Answer:

Step-by-step explanation:

i just need the points bro

The value of the variables x and y are,

11) x = 13,  y = 18.4

12) x = 6.9,  y = 8.

What is right angle triangle?

A right triangle is a triangle with one angle at a right angle, meaning that two of its sides are perpendicular. It is also known as a right-angled triangle, an orthogonal triangle, or more commonly as a rectangled triangle. Trigonometry's foundation is the right triangle's relationship between its sides and other angles.

11)Let the given triangle is a right angle triangle.

So we can use trigonometric ratio,

[tex]tan(45) = \frac{x}{13} \\x = 13(tan(45))\\x = 13[/tex]

Using this to find the value of y.

[tex]sin(45) = \frac{x}{y} \\sin(45) = \frac{13}{y} \\y = \frac{13}{sin(45)} \\y = 18.4[/tex]

So, the values of x and y are x = 13 and y = 18.4.

12) The given triangle is a right angle triangle.

So we can use trigonometric ratio,

[tex]tan(30) = \frac{4}{y}\\ y = \frac{4}{tan(30)} \\y = 6.9[/tex]

Now to find the value of x.

[tex]sin(30) = \frac{4}{x} \\x = \frac{4}{sin(30)} \\x = 8[/tex]

Hence, the values of x and y are, x = 6.9 and y = 8.

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A. Congruence means the same.

B. Angle addition postulate states that two angles side by side sum the measure of the two angles.

C. Linear pair theorem states that linear pair angles add up to 180 degrees.

D. Vertical angles theorem states that vertical angles are congruent.

Congruence in angles simply means the same or equals to.  Two angles are congruent when they are the same.

The angle addition postulate states that the measure of an angle formed by two angles side by side is the sum of the measures of the two angles.

The Linear Pair Theorem states that two angles that form a linear pair are supplementary. They add up to 180 degrees.

The Vertical Angle Theorem says the opposing angles of two intersecting lines must be congruent, or identical in value

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An isosceles triangle therefore has both two equal sides and two equal angles.

What is traiangle?

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

What is isosceles triangle?

An isosceles triangle in geometry is a triangle with two equal-length sides. It can be stated as having exactly two equal-length sides or at least two equal-length sides, with the latter definition containing the equilateral triangle as an exception.

Any triangle with (at least) two equal sides is said to be isosceles. The remaining side in the previous illustration has length in addition to the two equal sides. This characteristic equates to the triangle's two angles being equal. Therefore, an isosceles triangle has two equal sides as well as two equal angles. The Greek words iso (same) and skelos are the source of the name (leg).

An equilateral triangle is one in which all of its sides are equal, whereas a scalene triangle is one in which none of its sides are equal. Therefore, an equilateral triangle is a specific example of an isosceles triangle that has equal sides and angles on all three of its faces. The isosceles right triangle is yet another unique instance of an isosceles triangle.

The Pythagorean theorem can be used to determine the height of the isosceles triangle shown in figure:

[tex]h = \sqrt{b^2-\frac{1}{4}a^2 }[/tex]

Consequently, the region is given by:

A=1/2ah

A = [tex]\frac{1}{2}a\sqrt{b^2-\frac{1}{4}a^2 }[/tex]

[tex]A = \frac{1}{2}a^2\sqrt{\frac{b^2}{a^2}-\frac{1}{4} }[/tex]

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Applying the exterior angles and triangle sum theorems, the statements that are true are:

C. m∠5 + m∠6 = 180°

D. ∠2 + m∠3 = m∠6

E. m∠2 + m∠3 + m∠5 = 180°

All three interior angles of a triangle is equal to a sum of 180 degrees, based on the triangle sum theorem, while the exterior angle theorem states that the exterior angle of a triangle is equal to the two remote interior angles of the triangle.

Given the image showing the triangles and its exterior angles, the following can be deduced:

m∠2 + m∠3 + m∠5 = 180° [based on the triangle sum theorem]

m∠2 + m∠3 = m∠6 [based on the exterior angles theorem]

m∠5 + m∠6 = 180° [based on the triangle sum theorem]

Therefore, the true statements are:

C. m∠5 + m∠6 = 180°

D. ∠2 + m∠3 = m∠6

E. m∠2 + m∠3 + m∠5 = 180°

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Answer:

B) x + 1

Step-by-step explanation:

Consecutive integers mean continuous integers ( 1, 2 , 3 ,....). We will get the next number by adding 1 to the previous number.

Eg: 5 , 6 , 7 ,.....

6 = 5 + 1

7 = 6 + 1

So, if first number is x, then the next number will be x + 1

Answer:

Step-by-step explanation:

2/3 = 1/2x

2/3 / 1/3 = x

x = 4/3

Answer: The answer is 4/3

Step-by-step explanation: I have my ways ;>

1521=1521 therefore a triangle has sides with lengths of 15 inches, 36 inches, and 39 inches  form a right triangle.

What is Right traingle?

A right triangle is one that has an interior angle of 90 degrees. The hypotenuse, which is also the side of the right triangle that faces the right angle, is its longest side. The height and base make up the two arms of the right angle.

When we enter the values of the triangle's legs (15 and 36) and hypotenuse (39),

assuming it is a right triangle, into the Pythagoras theorem, the values of each side of the equation will be equal;

The Pythagoras Theorem is:

[tex]a^2+b^2=c^2[/tex]

Making substitutions and applying the math results in:

[tex]15^2 + 36^2= 39^2[/tex]

225 + 1296 = 1521

1521 = 1521

Therefore, it is a right traingle.

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The range and the domain of the function f(x) =  1 - x^2 is less than or equal to 1 and all values of x are a real number (R).

Domain: x ∈ R

Range: f ( x ) ≤ 1, ∈ R

f ( x ) = 1 − x^2 is defined for all Real values of x, and therefore the domain is all real values ( R ).

x^2 has a minimum value of 0 (for x ∈ R ) and therefore − x^2 has a maximum value of 0 and − x^2 + 1 = 1 − x^2 has a maximum value of 1.

Therefore f (x) has a maximum value of 1 and the range of f ( x ) is ≤ 1.

So, the range of f(x)≤ 1, and the domain is all real values ( R ).

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From the graph it can be calculated that Function rule for g(x) g(x) = |x - 7|

What is graph of a function?

The collection of ordered pairs with the (x,y)(x,y) sign is known as the graph of the a function in mathematics, where f(x)=y. x and f seem to be Cartesian coordinates of pts in two-dimensional space, and in the typical case where they are real numbers, they form a subset of the this plane.

Instead of the pairs "((x,y),z)" and "((x,y),z)" as in the definition above, the graph for functions of two variables, i.e. functions for whom the domain consists of pairs "(x,y)," "(x,y)," is typically the set of ordered triples "(x,y,z)" and "(x,y,z)" where "A surface for a constant real-valued function of the two real variables, this set is indeed a sub - set of three-dimensional space.

Graph of a function f(x) is the collection of points of the form (x, f(x))The given graph is a translation of |x| only,
So value of a is 1
Now since the tip of the graph lies on x- axis, k = 0So the value of g(x) is
g(x) = |x - h|g(7) = 0|7 - h| = 07 - h = 0h = 7
Function rule for g(x) g(x) = = |x - 7|

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The destroyed angle is a rectangle specifically a parallelogram also having all the angles equal and equal to 90 degree.

Given, a destroyed angle

A destroyed angle is called a figure in Geometry also known as Rectangle.

A rectangle is a quadrilateral which is specifically a parallelogram also having all the angles equal and equal to 90 degree.

So, A destroyed angle is the quadrilateral which is specifically a parallelogram also having all the angles equal and equal to 90 degree.

Therefore, the destroyed angle is a rectangle.

Hence, The destroyed angle is a rectangle specifically a parallelogram also having all the angles equal and equal to 90 degree.

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Answer: 96

Step-by-step explanation:

Isosceles triangle problem can be solved by given steps

what is isosceles triangle ?

An isosceles triangle in geometry is a triangle with two sides that are the same length. Sometimes it is stated as having exactly two sides that are the same length, and other times it is specified as having at least two sides that are the same length, the latter form containing the equilateral triangle as a particular case.

explanation:

In isosceles triangle

1. Two sides of the triangle are congruent

2. The angle opposite those sides are congruent

x + 72 +72 = 180

             x  = 180 -144

             x = 36

Hence the isosceles triangle problem can be solved by above steps and explanation

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Y = 1x – 2 is the equation for linear regression.

A linear regression line is represented by the equation Y = a + bX, where X is the explanatory variable and Y is the dependent variable. The slope of a line, b, is equal to the intercept of that line, which is the value of y when x = 0.

Based on the value of another variable, linear regression analysis can be used to predict the value of a variable. You want to be able to predict the dependent variable. You create a forecast about the value of the other variable using the independent variable.

A positive linear relationship exists if the slope of the line is positive, meaning that when one rises, the other rises as well.

Y = -2 -1 x

Y= -2 -1x

Y = 1x - 2

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The incenter of any given triangle s the point of congurrency of the angle bisectors of the triangle

we know that

The incenter is the point where the angle bisectors intersect. The incenter is also the center of the triangle's incircle.

therefore

Is the point of concurrency of the angle bisectors of the triangle

Part 2)

we know that

A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side

therefore

Is a segment drawn  from a vertex to the midpoint of the opposite side

Therefore, the incenter of any given triangle s the point of congurrency of the angle bisectors of the triangle

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The exponential decay formula can take one of three forms:

f (x) = abˣ , f (x) = a (1 – r)ˣ , P = P₀[tex]e^{-kt}[/tex]

Where,

a (or) P₀ = Initial amount ,b = decay factor, e = Euler’s constant, r = Rate of decay (for exponential decay), k = constant of proportionality

What is Exponential Decay ?

Exponential decay occurs in mathematical functions when the pace by which changes are occurring are decreasing and must thus reach a limitation, which is the horizontal asymptote of an exponential function.

The amount drops gradually, followed by a quick reduction in the speed of change and increases over time. The exponential decay formula is used to determine the decrease in growth. The exponential decay formula can take one of three forms:

f (x) = abx

f (x) = a (1 – r)x

P = P0 e-k t

Where,

a (or) P0 = Initial amount

b = decay factor

e = Euler’s constant

r = Rate of decay (for exponential decay)

k = constant of proportionality

x (or) t = time intervals (time can be in years, days, (or) months, whatever you are using should be consistent throughout the problem).

In exponential decay, the quantity decreases very rapidly at first, and then more slowly. The rate of change decreases over time. The rate of decay becomes slower as time passes. Hence, the exponential decay graph is denoted as

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First, 108/9=12

This means that are 12 groups of people.

If there are 8 students in each group, 12 x 8 = 96.

96 should be your answer.

By using the law of exponents, it has been proved that

[tex]a^{-n} = \frac{1}{a^n}[/tex]

What are exponent?

Exponent tells us how many times a number is multiplied by itself.

For example : In [tex]2^4 = 2 \times 2 \times .... \times 2[/tex]

Here, 2 is multiplied by itself 4 times.

If [tex]a^m = a \times a \times a \times ..... \times a[/tex] (m times),

a is the base and m is the index.

The laws of exponents are

[tex]a^m \times a^n = a^{m+n}\\\\a^ m \div a^n = a^{m - n}\\\\a^ 0 =1\\\\a^{-m} = \frac{1}{a^m}\\\\(ab)^m = a^m \times b^m\\\\(\frac{a}{b})^m = \frac{a^m}{b^m}\\\\(a^m)^n = a^{mn}[/tex]

We know this law

[tex]a^p \times a^q = a^{p + q}[/tex]

Putting  p = n and q = -n

[tex]a^n \times a^{-n} = a^{n + (-n)} = a^{n - n} = a^0 = 1[/tex]

So,

[tex]a^n \times a^{-n} = 1\\a^{-n} = \frac{1}{a^n}\\a^{-n} = \frac{1^n}{a^n}\\a^{-n} = (\frac{1}{a})^n[/tex]

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