Answers
Answer:
They are congruent by SAS:
Side: AB = CB
Angle: ∠ABD = ∠CBD
Side: BD = BD
Explanation:
Two triangles are congruent if they have the same interior angles and the same length of their corresponding sides.
If two of the angles are equal, we can say that all the interior angles are equal.
So, based on the given information we get:
1. AC ⊥ BD means that AC is perpendicular to BD, therefore,
∠ADB = ∠CDB = 90°
2. It is given that ∠A = ∠C
3. Since both of their interior angles are equal, we can say that all the interior angles are equal and:
∠ABD = ∠CBD
4. The triangle ABC is isosceles because two of their interior angles are equal, therefore AB = CB
5. BD = BD because it is the same segment.
6. By SAS (Side-angle-Side) we can say that ΔABD = ΔCBD
Because the side AB is equal to side CB, the angle ABD is equal to angle CBD, and the side BD is equal to itself.
Related Questions
Which transformations do not result in mapping (-k, k) to
(k, - k) ?
A) Reflection in the line y = x
B) Reflection in the line y = -x
C) Reflection in the y -axis, followed by a reflection in the x-axis
D)Translation k units right, followed by a reflection in the y-axis
Answers
The function translation / transformation rules:
f (x − b) moves the function b units to the right.−f (x) reflects the function in the x-axis (that exists, upside-down).What are the types of transformations on a graph?Function transformations specify how a function is moved on a graph and how its shape is altered. Translation, dilatation, and reflection are the three main categories of function transformations.
The technique of altering an existing graph or graphed equation to create a different version of the following graph is known as graph transformation. In particular, the change of algebraic equations is a typical kind of algebraic problem.
The function translation / transformation rules:
f (x) + b moves the function b units upward.f (x) − b moves the function b units downward.f (x + b) moves the function b units to the left.f (x − b) moves the function b units to the right.−f (x) reflects the function in the x-axis (that exists, upside-down).To learn more about transformations refer to:
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the slop of (6,2) and (24,8)
Answers
Answer:
1/3
in decimal its 0.333333
Step-by-step explanation:
I did it before
Question 1
Write the equation of the line that is parallel to the x-axis and contains point (2, 7).
Answers
PARALLEL LINES HAVE EQUAL GRADIENTS
THE GRADIENT IN THE X-AXIS IS EQUAL TO 0 SINCE THE THE Y VALUE FOR ANY X VALUES IS 0
[tex]m = \frac{0 - 0}{x2 - x1} \\ m = 0[/tex]
This just means that the gradient for the line parallel to the given line is 0
I will use the technique of the General equation of a straight line. y=mx+c
[tex]7 = (0)(2) + c \\ c = 7[/tex]
THE EQUATION IS
[tex]y = 7[/tex]
ATTACHED IS THE SOLUTION.
What is 102 divided by 105?
Answers
Answer:
102 / 105 = 0.971428571
Step-by-step explanation:
i used a calculator c:
PLEASE HELP RIGHT NOW, THIS IS SUPER URGENT
The graph shows the proportional relationship between the number of gems collected and the number of levels that have been completed in a video game.
Graph with x axis labeled game levels and y axis labeled gems collected. A line begins at 0 comma 0 and goes through points 6 comma 450 and 8 comma 600.
Determine the constant of proportionality for the relationship.
p equals 2 over 150
p = 0.0133
p = 75
p = 150
Answers
The constant of proportionality for the graph will be P=75. The correct option is C.
What is a slope?Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line.
The proportionality of the constant determines the linear relation between two variables. as one increases the another also increases with the same factor.
To calculate the constant of proportionality for the given graph finds the slope of the graph with the points.
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope = ( 600 - 450 ) / ( 8 - 6 )
Slope = ( 150 / 2
Slope= 75
Therefore, the constant of proportionality for the graph will be P=75. The correct option is C.
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Building an A-frame dog house. Your club has decided to build and sell dog houses for a fundraising project. You found this dog house and set of plans by searching the net.
A customer has offered to pay extra if you will make one half the size called for in the plans. Take each of the 5 measurements shown in the drawing and find half of the measurement. Show your work to get full credit!
Answers
The one half of the dimensions of the frame dog house is obtained.
What is termed as the mixed fractions?A mixed fraction is a form of fraction that has both a whole number as well as a fractional part. An improper fraction could also be formed from a mixed fraction. To do so, follow the steps outlined below. Step 1: Multiply the mixed fraction's denominator by the whole number part.Step 2: Subtract the numerator from the product obtained in step 1.Step 3: In numerator/denominator form, compose the improper fraction only with sum obtained in step 2.For the given question, the dimensions of the frame dog house are given as;
Gusset plate:Height = 5 ³/₂ inchesBase = 3 ¹/₂ inchesFloor plate = 47 ¹/₄ inches Thickness = 2 inchesSlope = 45 ¹/₄ inchesConvert the following fraction in improper by the above method;
Gusset plate:Height = 13/2 inchesBase = 7/2 inchesFloor plate = 189/4 inches Thickness = 2 inchesSlope = 181/4 inchesNow, customer has offered to pay extra if you will make one half the size called for in the plans.
Multiply each dimension with 1/2.
Gusset plate:Height = 13/2 × 1/2 = 13/4 inchesBase = 7/2 × 1/2 = 7/4 inchesFloor plate = 189/4 × 1/2 = 189/4 inches Thickness = 2× 1/2 = 1 inchSlope = 181/4 × 1/2 = 181/8 inchesThus, the one half of the dimensions of the frame dog house is obtained.
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True or False: The relation {(9,1), (0,1), (9,-3), (-4,12)} is a function.
Answers
Given
relation = {(9,1), (0,1), (9,-3), (-4,12)}
Find
Is this a function?
Explanation
A relation is a function only if it relates each element in its domain to only one element in the range.
here , domain 9 has two range value 1 and -3
so it is not a function
Final Answer
Hence , it is false
Answer:
False
Step-by-step explanation:
Definition:
Function is a set of coordinate points where each coordinate points do not have same domains (x-values). If we express mathematically, we can do as [tex]\displaystyle{f=\left \{(x_0,y_0),(x_1,y_1),(x_2,y_2),...,(x_n,y_n)\}\right}[/tex] where [tex]\displaystyle{x_0\neq x_1 \neq x_2\neq \dots \neq x_n}[/tex]Function is also considered to be a relation but not all relations can be functions.
As accorded to the relation, it turns out that there are two same domains (x-values) which is 9 from (9,1) and (9,-3). Therefore, this relation doesn’t satisfy the definition of function so it’s not a function.
Please let me know if you have any questions!
x+3/5 + x-2/5
as a single fraction
Answers
Answer:
x+3/5 + x-2/5
simply add variable
x+x +3/5-2/5
2x+3/5-2/5
taking L.C.M
5*2x+3-2/5
10x+1/5
Please help! I have no idea what I’m doing and I’m super behind, I absolutely suck at math!
The function f(x) is graphed below.
(Picture below)
A) what is f(0)
B)what is f(3)
C) what is f(2)
Answers
Answer: 0, 3, 0
Step-by-step explanation:
f(a) represents the value of f(x) at x=a.
Teresa surveyed 100 students about whether they like pop music or country music. Out of the 100 students surveyed, 41 like only pop, 35 only like country, 11 like both pop and country, and 13 do not likeeither pop or country. Complete the two-way frequency table.
Answers
we have
see the attached figure to better understand the problem
please wait a moment (to fill the table)
What value of b makes this equation true?:x2 + bx – 35 = (x + 5)(x - 7) a) 12 b) 2 c)-2 d)-12
Answers
Answer:
c) -2.
Step-by-step explanation:
(x + 5)(x - 7)
= x^2 - 7x + 5x - 35
= x^2 - 2x - 35
Compare with
x^2 + bx - 35
we see that b = -2.
5x+3=53
I don’t know pls help
Answers
5x/5 = 50/5
X=10
Answer:
x10
Step-by-step explanation:
How to solve your problem
5x+3=53
Subtract 3 from both sides
5x+3=53
5x+3-3=53-3
Simplify
Subtract the numbers
5x+3-3=53-3
5x=53-3
Subtract the numbers again
5x=53-3
5x50
Divide both sides by the same factor
5x=50
5x=50\
[tex]\frac{50x}{5}[/tex][tex]\frac{50}{5}[/tex]
Simplify
Cancel terms that are in both the numerator and denominator
[tex]\frac{5x}{5}[/tex]=[tex]\frac{50}{5}[/tex]
x=[tex]\frac{50}{5}[/tex]
Divide the numbers
x=[tex]\frac{50}{5}[/tex]
x=10
answer is 10
Determine if the equation is linear,quadratic,exponential, or absolute value Y=x² -5x+6
Answers
Explanations:
Note that any expression of the form:
[tex]ax^2\text{ + bx + c}[/tex]is a quadratic polynomial.
The given equation in the question is:
[tex]Y=x^2\text{ - 5x + 6}[/tex]Comparing the given equation with the general expression I wrote above:
a = 1, b = -5 and c = 6.
Since the given equation takes the form of the general expression, it is therefore quadratic.
2000x2400 need the answer
Answers
Answer: 4,800,000
Step-by-step explanation: 2 times 24 is 48 then there is 3 zeros in 2000 and 2 zeros in 2400 so just add those on to the end of 48 and then you get your final answer of 4,800,000.
What’s the area ? 50 points
Answers
Answer:
The area of the figure is 325.17 ft²===============================
The area of the given shape can be found as a sum of three simpler shapes:
Triangle, rectangle and semi-circle.The semi-circle has the radius of 9 ft, its area is:
A = πr²/2 = 3.14*9²/2 = 127.17 ft²The rectangle has dimensions of 9 ft and 26 - 9 = 17 ft, its area:
A = lw = 9*17 = 153 ft²The triangle has bas of 9 ft and height 26 - 9 - 7 = 10 ft, its area is:
A = bh/2 = 9*10/2 = 45 ft²Area of the shape is:
A = 127.17 + 153 + 45 = 325.17 ft²what do the factoring of special products have in common?
Answers
We know that specific products multiply specific kinds of binomials, so these binomials will be the product's factors.
Example:
2 × 3 = 6Factors of 6: 2 × 3What are special products?Simply put, special products are just special cases of multiplying together specific types of binomials. We offer three unique products: (a + b)(a + b) (a - b)(a - b)So, we know that special products are multiplying special types of binomials which means that these binomials will be the factors of the product.
For example:
2 × 3 = 6Factors of 6: 2 × 3Therefore, we know that specific products multiply specific kinds of binomials, so these binomials will be the product's factors.
Example:
2 × 3 = 6Factors of 6: 2 × 3Know more about special products here:
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Tell whether x and y show direct variation. Explain your reasoning.
y - x = 0. Find the value of k
Answers
In the given equation x and y show a direct variation of the form:
y = x
Where the value of k is 1.
Is there a direct variation?
A direct variation between two variables x and y is written as:
y = k*x
Where k is called the constant of proportionality.
Here we have the equation:
y - x = 0
moving x to the right side we get:
y = x
This is a direct variation with k = 1.
y = 1*x
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5x+2y=12. Convert from standard form to slope-intercept form
Answers
Answer:
y = [tex]\frac{-5}{2}[/tex] x + 6
Step-by-step explanation:
We want the form
y = mx + b
5x + 2y =12 Subtract 5x from both side of the equation
2y = -5x + 12 Divide all the way by 2
y = [tex]\frac{-5}{2}[/tex] x + 6
Use substitution to find the solution to the linear/quadratic system. y - 2x^2 = 4x + 1 y = 14x - 7 Blank 1: (___7) Blank 2: (___49) Blank # 1:Blank # 2:
Answers
The given system is
[tex]\mleft\{\begin{aligned}y-2x^2=4x+1 \\ y=14x-7\end{aligned}\mright.[/tex]Let's replace the second equation with the first one.
[tex]14x-7-2x^2=4x+1[/tex]Now, we solve the quadratic equation.
[tex]\begin{gathered} 14x-7-2x^2-4x-1=0 \\ -2x^2+10x-8=0 \\ -2(x^2-5x+4)=0 \\ x^2-5x+4=0 \end{gathered}[/tex]Then, we have to find two numbers whose product is 4 and whose sum is 5. Those numbers are 4 and 1.
[tex]\begin{gathered} (x-4)(x-1)=0 \\ x_1=4 \\ x_2=1 \end{gathered}[/tex]We use these values to find y.
[tex]\begin{gathered} y_1=14\cdot4-7=49 \\ y_2=14\cdot1-7=7 \end{gathered}[/tex]Hence, the solutions to the given system are (4,49) and (1,7).Write an exponential expression equivalent to 8^3 that has a base of 2.
Answers
The exponential expression equivalent to 8^3 that has a base of 2 is 2^9.
What is exponential expression?
Powers can simply be expressed in concise form using exponential expressions. The exponent shows how many times the base has been multiplied.
Applying the laws of indices,
The expression 8^3 can be written as,
8 x 8 x 8 = (2^3) x (2^3) x (2^3)
= 2^(3+3+3) ...{If a^m x a^n then a^(m+n) }
8 x 8 x 8 = 2^9
Therefore, the exponential expression equivalent to 8^3 that has a base of 2 is 2^9.
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Zachary purchased a computer for
$1800 on a payment plan. He plans to
pay $150 per month on his payment
plan. What is an equation that models
the balance y after x months?
Answers
Answer:
y= 1 800- 150x
Step-by-step explanation:
y= 1 800- 150x
Use the diagram and the given angle measure to find the other three measures
Answers
If angle ∠4 = 29 degrees, then
m∠1 = 151 degreesm∠2 = 29 degreesm∠3 = 151 degreesThe m∠4 = 29 degrees
Part 1
The angles on a straight line add up to 180 degrees.
∠4 + ∠1 = 180
29 + ∠1 = 1180
∠1 = 180-29
= 151 degrees
Part 2
The angles on a straight line add up to 180 degrees.
∠1 + ∠2 = 180
151 + ∠2 = 180
∠2 = 180-151
= 29 degrees
Part 3
The angles on a straight line add up to 180 degrees.
∠2 + ∠3 = 180
29 + ∠3 = 180
∠3 = 180-29
= 151 degrees
Hence, If angle ∠4 = 29 degrees, then
m∠1 = 151 degreesm∠2 = 29 degreesm∠3 = 151 degreesLearn more about angle here
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Use the diagram and the given angle measure to find the other three measures
Answers
The measures of angles ∠1, ∠3, and ∠4 is 146°, 146°, and 34°.
What are angles?When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the term "angle" originates. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.So, ∠2 = 34°:
Now calculate other angles as follows:
(1) ∠1:
We can easily tell that ∠1 and ∠2 together make a straight angle which makes 180°. Then,
∠1 + ∠2 = 180∠1 + 34 = 180∠1 = 180 - 34∠1 = 146°(2) ∠3:
∠1 and ∠3 are a pair of vertically opposite angles and thus are equal.
∠1 = ∠3 = 146°∠3 = 146°(3) ∠4:
∠2 and ∠4 are a pair of vertically opposite angles and thus are equal.
∠2 = ∠4 = 34°∠4 = 34°Therefore, the measure of angles ∠1, ∠3, and ∠4 is 146°, 146°, and 34°.
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Write the system of equations for the matrix.
[0. 2. 3. / 4
[8 -1 -2 / 5
[2. 0. 1 /9
Answers
The three equations that will emerge from the given matrix will be:
2y + 3z = 48x - 1y - 2z = 52x + z = 9What are equations?An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values. Like 3x + 5 = 15, for example. There are many different types of equations, including linear, quadratic, cubic, and others. In a mathematical equation, the equals sign is used to express that two expressions are equal.So, the equations for the given matrix will be:
[0. 2. 3. / 4]
[8 -1 -2 / 5 |
[2. 0. 1 / 9 ]
Now, the equation will be:
2y + 3z = 48x - 1y - 2z = 52x + z = 9Therefore, the three equations that will emerge from the given matrix will be:
2y + 3z = 48x - 1y - 2z = 52x + z = 9Know more about equations here:
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Explain if the triangles below are congruent or not and explain why you think that.
Answers
In this picture, we have the triangles with two common sides and one common angle. However, they are not congruent, as they do not follow any of the congruence theorems. The congruence theorem with two sides and an angle is the SAS(Side-Angle-Side). However, the angle has to be the angle between the two sides, which does not happen in this case.
Nicholas is saving money to buy a new video game. He started with $25 and after 3 weeks of doing chores he had $70.
Answers
70-25=$45
$45/3 = $15
is 1.030030003 a whole number a natural number an integer a real number a rational number or irrational number
Answers
Real numbers are numbers that are continous on the number line. They include positive and negative numbers. They can be integers, natural numbers, rational or irrational numbers.
In this exercise the number 1.030030003 is a real number because it can be found on the real number line
It is also a rational number because it is a repeating decimal
A data set includes the following numbers: eighteen over 5, two and four fifths, 97%, and 1.74.
Part A: What is the order of the numbers from least to greatest? Write your answer using the numbers in their original form.
Part B: Did you use estimation or rewrite the numbers in equivalent forms? Please explain your answer.
Answers
18/5 = 3.6 (just divide 18 by 5)
2 4/5 = 2.8 (4/5 = 0.8, so 2 4/5 = 2.8)
97% = 0.97
1.74 is already in decimal form.
Part A:
97%, 1.74, 2 4/5, 18/5
(based on the calculations above)
Part B:
I rewrote the numbers in equivalent forms, in this case the equivalent form being decimal form, to be able to determine which number was bigger or smaller than the other.
HURRY WILL MARK BRIANLIEST Evaluate.
0.33÷0.9⋅20+6.4÷0.2
Enter your answer as a decimal in the box.
Answers
Answer:
39.3
but the 3 in the the tenths place is repeating
Step-by-step explanation:
Answer:
39.33...
Step-by-step explanation:
Using PEMDAS,
First, 0.33 / 0.9 = 0.366...
Second, 0.366... * 20 = 7.33...
Then, 6.4 / 0.2 = 32
Lastly, 7.33... + 32 = 39.33...
Write an expeession equivalent to 0.4x
A. X-0.6x
B. 1-0.6x
C. X + 0.4
D. 0.4x-x
Answers
Answer:
A. X-0.6x
Step-by-step explanation:
A. X-0.6x = 0.4x YES
B. 1-0.6x = 1 - 0.6x NO
C. X + 0.4 = 1.4x NO
D. 0.4x-x = -0.6x NO