The angles m∠ABC = (3·x - 2)° and m∠ABD formed by the ray [tex]\overrightarrow{BA}[/tex], which is an angle bisector of angle m∠CBD = (5·x + 18)°, indicates that m∠ABD is 64°
What is an angle bisector?An angle bisector is a line, segment or ray that divides an angle into two congruent angles.
The information in the question are;
The ray that bisects ∠CBD = [tex]\overrightarrow{BA}[/tex]
The measure of angle, m∠CBD = (5·x + 18)°
The measure of angle, m∠ABC = (3·x - 2)°
Therefore;
(5·x + 18)° = 2 × (3·x - 2)° (definition of angle formed by an angle bisector)
(5·x + 18)° = (6·x - 4)°
(6·x - 5·x)° = (18 + 4)°
x = 22°
m∠CBD = m∠ABD + m∠ABC (angle addition postulate)
m∠ABD = m∠ABC (angles formed by angle bisector [tex]\overrightarrow{BA}[/tex])
m∠ABC = (3·x - 2)°
Therefore; m∠ABC = (3 × 22 - 2)° = 64°
m∠ABD = m∠ABC = 64°
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HELP ME QUICK PLEASE!!!!!
Which inequality is a true statement?
Select each correct answer.
-3>-1
-3 ≥ -1
-3=-1
-3≤-1
-3 <-1
Answer:
-3 <-1
-3 is less than -1.
Please help asap!!!!!!
−8×(−10+(−7))
Evaluate the following expression.
Answer:
136
Step-by-step explanation:
solve the inside of the parentheses and you get -17, then multiply by -8
find the slope of the line that passes through (2,4) , (9,10)
The slope of the line that passes through (2,4) , (9,10) is 6/7
How to calculate the slope of the line?From the question, the points are given as
(2,4) , (9,10)
Rewrite the above points properly
So, we have the following ordered pairs
(x, y) = (2,4) and (9,10)
The slope of the line is then calculated using the following slope equation
Slope = (y₂ - y₁)/(x₂ - x₁)
Where
(x, y) = (2,4) and (9,10)
Substitute the known values in the above equation
So, we have the following equation
Slope = (10 - 4)/(9 - 2)
Evaluate
Slope = 6/7
Hence, the slope of the line is 6/7
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Are the triangles congruent Why or why not triangle congruence ASA and AAS?
ΔABC and ΔRQM are congruent triangles. They are congruent by either ASA or AAS.
Two triangles are said to be congruent if their all corresponding sides are equal and all corresponding angles are equal in measure.
For the given question,
We know that the sum of all angles of a triangle is 180°.
For ΔABC,
∠A + ∠B + ∠C = 180°
42° + 53° + ∠C = 180°
95° + ∠C = 180
∠C = 85°
For ΔABC and ΔRQM,
∠A = ∠R
∠C = ∠Q
AB = RM
So, by the AAS postulate, ΔABC and ΔRQM are congruent triangles.
For ΔRQM,
∠R + ∠Q + ∠M = 180°
42° + 85° + ∠M = 180°
∠M = 53°
For ΔABC and ΔRQM,
∠A = ∠R
∠B = ∠M
AB = RM
So, by the ASA postulate, ΔABC and ΔRQM are congruent triangles.
Therefore, ΔABC and ΔRQM are congruent triangles. They are congruent by either ASA or AAS.
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The complete question is -
Are the triangles congruent Why or why not triangle congruence ASA and AAS?
what is the solution a b to this system of linear equations 3a6b45 2a 2b 12
Solution of the system of linear equation 3a + 6b = 45 , 2a -2b = -12 is equal to a = 1 and b =7.
As given in the question,
System of linear equation are:
3a + 6b = 45 __( 1 )
2a - 2b = -12 __(2 )
Solution of the linear equation by elimination method is given by:
Multiply ( 2 ) by 3 and add it to (1) we get,
3a + 6b = 45
6a - 6b = -36
9a = 9
⇒ a = 1
Substitute the value of a = 1 in (1) we get,
3( 1 ) + 6b = 45
⇒ 6b = 42
⇒ b = 7
Therefore, the solution of the system of linear equation is a = 1 and
b =7.
The complete question is :
What is the solution (a, b) to this system of linear equations?
3a+6b = 45 , 2a-2b = -12
a. (-27, 6)
b. (-1, 7)
c. (1, 7)
d. (27, -6)
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A certain shade of light blue paint is made by mixing 1(1/2) quarts of blue paint with 5 quarts of white paint. How much white paint would you need to mix with 4 quarts of blue paint?
a) Set up the table with headings (names of the variables and the units).
b) Show how to use the table to solve the problem.
c) Record your final answer below.
By using Unitary method it can be calculated that
4 quarts of white paint is mixed with [tex]1\frac{1}{5}[/tex] quarts of blue paint
1 quart of blue paint is mixed with [tex]3\frac{1}{3}[/tex] quarts of white paint
What is unitary method?
Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity
Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.
a) Here, Unitary method will be used
Blue Paint White Paint
(Quart) (Quart)
[tex]1\frac{1}{2}[/tex] 5
[tex]1\frac{1}{5}[/tex] 4
1 [tex]3\frac{1}{3}[/tex]
5 quarts of white paint is mixed with [tex]\frac{3}{2}[/tex] quarts of blue paint
1 quart of white paint is mixed with [tex]\frac{3}{2} \times \frac{1}{5}[/tex] quarts of blue paint
4 quarts of white paint is mixed with [tex]\frac{3}{2} \times \frac{1}{5} \times 4[/tex] quarts of blue paint
4 quarts of white paint is mixed with [tex]\frac{6}{5}[/tex] quarts of blue paint
4 quarts of white paint is mixed with [tex]1\frac{1}{5}[/tex] quarts of blue paint
Again
[tex]\frac{3}{2}[/tex] quarts of blue paint is mixed with 5 quarts of white paint
1 quart of blue paint is mixed with [tex]5 \div \frac{3}{2}[/tex] quarts of white paint
1 quart of blue paint is mixed with [tex]\frac{10}{3}[/tex] quarts of white paint
1 quart of blue paint is mixed with [tex]3\frac{1}{3}[/tex] quarts of white paint
c) Finally
4 quarts of white paint is mixed with [tex]1\frac{1}{5}[/tex] quarts of blue paint
1 quart of blue paint is mixed with [tex]3\frac{1}{3}[/tex] quarts of white paint
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A mathematical statement that ________ two quantities using <, >, =
Answer:
compares
Step-by-step explanation:
How do you isolate the variable by dividing each side by factors that don't contain the variable?
We isolate the variable in an equation by dividing both sides of the equation in which one side does not contain any variable.
According to the question,
We have the following information:
Isolating a variable by dividing each side of the equation in which one side does not contain any variable.
Now, in this case, it is clearly stated that the first step to isolate the variable from the equation is to perform division.
Now, this can be done as follows in the given equation:
2x = 14
Now, the variable x can be isolated by dividing both sides of the equation by 2:
x = 14/2
x = 7
Hence, we isolate the variable in an equation by dividing both sides of the equation in which one side does not contain any variable.
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HURRY PLS!!
Kevin took $45 with him to spend on snack for himself and his friends at the movie theater. The price for each bucket of popcorn was $4. The price of each drink was half the price of a bucket of popcorn.
A. Sketch the graph that represents the situation and label the intercepts. Use one axis to represent the number of buckets of popcorn and the other axis to represent the number of drinks.
Explain your graph.
B. Graph the absolute value function.
C. (a) Graph a linear function of your choice. On the same graph, graph a linear function transformed 2 units up and 3 units down.
(b) What was the equation of your linear function in slope-intercept form?
(c) What was the equation of the transformed function in slope-intercept form?
The equation of Kevin's scenario is 4x + 2y = 45
The absolute equation is y = 2|x - 3| + 5The equation of the linear function in slope-intercept form is y = 2x + 3The equation of the transformed function in slope-intercept form is y = 2x - 1How to determine Kevin's equationFrom the question, we have the following parameters
Amount = $45Bucket of popcorn = $4Bucket of each drink= Half the bucket of popcorn = $2Represent the buckets of popcorn with x and the number of drinks with y
So, we have the following equation
4x + 2y = total amount
This gives
4x + 2y = 45
See attachment for the graph
The graph of an absolute functionAn absolute function is represented as
y = a|x - h| + k
Where the vertex is (h, k)
So, we make use of the following function
y = 2|x - 3| + 5
See attachment 2 for the graph
The graph of a linear functionHere, we are to make use of any equation
A linear equation is represented as
y = mx + b
Where
slope = m
y-intercept = b
So, we make use of
m = 2 and b = 3
This gives
y = 2x + 3
When transformed 2 units up and 3 units down, the resulting equation is
y = 2x + 2 - 3
Evaluate
y = 2x - 1
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A baseball player has 746 plate appearances in his first year, 727 plate appearances
in his second year, and 512 plate appearances in his third year. How many plate
has the player had in three years?
appearances
O 2,075
O 1,975
O 1,885
O 1,985
The player has a total plate of 1985 plate appearances (optionD)
What is addition?Addition is a way of combining things and counting them together as one large group. Addition is a process of combining two or more numbers. Addends are the numbers added, and the result or the final answer we get after the process is called the sum. For example if there a 5oranges, 6 bananas and 9 pineapple Ina basket. The total fruit in the basket is 5+6+9= 20 fruits
The baseball player has 746 plate appearances in his first year and 727 plate appearances in the second year and 512 in his third year.
The total plate appearances = 746+727+512=1985 plate appearances
Therefore the plate appearance the player had in three years is 1985 plate appearances.
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The braking distance y in feet that it takes a car to stop on wet, level pavement can be estimated by y=1/25x^2 , where x is the speed of the car in miles per hour. Find the speed associated with the braking distance of 196 feet.
in essence, find "x" when y = 196
[tex]y = \cfrac{1}{25}x^2\qquad \stackrel{\textit{when y = 196}}{196=\cfrac{1}{25}x^2}\implies (196)(25)=x^2 \\\\\\ \sqrt{(196)(25)}=x\implies {\Large \begin{array}{llll} \stackrel{\frac{m}{h}}{70}=x \end{array}}[/tex]
What is an equation of the line that passes through the points (-6,6) and (-3,1)?
Answer:
y=-[tex]\frac{5}{3}[/tex]x-4
Step-by-step explanation:
find the slope m = [tex]\frac{y2-y1}{x2-x1}[/tex]
m=[tex]\frac{1-6}{-3+6}[/tex]
m=-[tex]\frac{5}{3}[/tex]
Use the slope and one of the points to solve for the y-intercept
y1=mx1+b
6=-[tex]\frac{5}{3}[/tex](-6)+b
6=10+b
b=6-10
b=-4
plug the values for m and b into y=mx+b
y=-[tex]\frac{5}{3}[/tex]x-4
Answer:
y= -1.6x+12Step-by-step explanation:First find the slope.
m=y2-y1 / x2-x1
m= 1-6
-3-(-6)
m=-5
-3+6
m=-5
3
m= -1.6
y-y1=m(x-x1)
y-6= -1.6(x-(-6))
y-6= -1.6x+6
y=-1.6x+12help!! i’ve been stuck on this problem!
Answer:
x less than or equal to -2
Step-by-step explanation:
I believe that's the answer
Answer:
x < -2
Step-by-step explanation:
You want the domain of a function graphed as a curve with an open circle at x=-2, which is the right end of the curve.
DomainThe domain is the horizontal extent of the graph. It is the set of values for which the relation is defined.
ApplicationThe open circle at (x, y) = (-2, 0) means that point is not part of the graph. All x-values to the left of that point have corresponding y-values, so the extent of the graph can be said to be ...
x < -2
The domain of the relation is x < -2.
The monthly rents (in dollars) paid by 10 people are given below. (Note that these are already ordered from least to greatest.) 735, 935, 960, 995, 1005, 1050, 1065, 1075, 1100, 1120 Suppose that one of the people moves. His rent changes from $735 to $535. Answer the following.
The mean will decrease when the rent decrease.
The median will stay the same.
What is a mean?It's important to note that a mean simply means the average of a set of numbers that are given. The mean is the average of the given numbers and is calculated by dividing the total number of numbers by the sum of the given numbers. A data set's mean (average) is calculated by adding all of the numbers in the set and then dividing by the number of values in the set.
Mean = (sum of all observations divided by the total number of observations)
In this case, the rents are 735, 935, 960, 995, 1005, 1050, 1065, 1075, 1100, 1120 and one of the people moves, and his rent changes from $735 to $535.
In this case, changing 735 to 535 will make the average lower.
On the other hand, the median isn't affected as it's still 1057.50.
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In, a city had a population of 310,000 people. Each year since 2007, the population has grown by 4.8%.
Let t be the number of years since. Let y be the city's population.
Write an exponential function showing the relationship between t and y.
The exponential function showing the relationship between t and y is y = 310000(1.048)⁺
How to determine the exponential function?From the question, we have the following parameters that can be used in our computation:
Initial population = 310000
Rate of growth = 4.8%
These parameters can be represeted as
a = 310000 and r = 4.8%
An exponential function is represented as
y = a(1 + r)⁺
Substitute the known values in the above equation, so, we have the following representation
y = 310000 (1 + 4.8%)⁺
Evaluate
y = 310000(1.048)⁺
Hence, the function is y = 310000(1.048)⁺
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Please help will mark Brainly
Answer: Horizontal Translation
Step-by-step explanation:
How do you solve a proof question?
To solve a proof question, firstly you have to identify the question and visualize it and then try to connect the given conditions.
Mathematical proofs can be difficult, but can be conquered with the proper background knowledge of both mathematics and the format of a proof.
To solve a proof question you have to remember following steps:
Identify the question = You must first determine exactly what it is you are trying to prove. Identify the question. You must first determine exactly what it is you are trying to prove. Draw diagrams = When trying to understand the inner working of a math problem, sometimes the easiest way is to draw a diagram of what is happening. Use the information given in the problem to sketch a drawing of the proof. Label the knowns and unknowns.Study proofs of related theorems = Proofs are difficult to learn to write, but one excellent way to learn proofs is to study related theorems and how those were proveTo know more about proof here
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Graph the line for y-6=-4(x+2) on the coordinate plane.
Answer:
x
Step-by-step explanation:
x
Answer:
Step-by-step explanation:
the answer is 8
What are rational roots Class 10?
The rational root theorem, as its name suggests, is used to find the rational solutions of a polynomial equation (or zeros or roots of a polynomial function). The solutions derived at the end of any polynomial equation are known as roots or zeros of polynomials. A polynomial doesn't need to have rational zeros.
Rational root theorem, also called rational root test, in algebra, theorem that for a polynomial equation in one variable with integer coefficients to have a solution (root) that is a rational number, the leading coefficient (the coefficient of the highest power) must be divisible by the denominator of the fraction and the constant term (the one without a variable) must be divisible by the numerator.
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write -1/2x + 4 = 10 in slope intercept form
Answer: y=-1/2x+4
Step-by-step explanation:
A line is parallel to the line y = -x + 5 and passes through the point (4. - 1). Which of the following is an equation of the
line?
Answer:
y = -x + 3; could also be y + 1 = -(x - 4) or y = -(x - 4) - 1 or x + y = 3
Step-by-step explanation:
No options given, so I hope this helps.
1. Identify any of the equations that have the same slope as your given equation (-1). If there's only one, stop here.
2. Find the y-intercept by replacing (x,y)=(4,-1) in the equation y = -x + b and solve for b: -1 = -(4) + b ==> 3 = b
3. Replace b in the equation y = -x + b with 3.
By rounding each number to the nearest 10, estimate the value of 197 ÷ 10.3
Answer:
20
Step-by-step explanation:
197 rounded to the nearest 10 is 200.
10.3 rounded to the nearest 10 is 10.
So, 200 ÷ 10 = 20
Answer:
20
Step-by-step explanation:
We are rounding to the nearest 10.
197≈200
10.3≈10
After you have rounded the numbers, The equation simplifies a whole bunch.
200/10=20
Please Mark As Brainliest2. Claire is painting some windows that are all the same size. She used gallon of paint to paint 2 windows. How many gallons of paint are needed to paint 1 window?
Answer:3
Step-by-step explanation:
since 7 is a number and b is to u should just put 3 windows cause u need to add them all up i think, not sure but just do that, why not,
a rectange has the area of 60 in2. what can its dimentions be? copy and fill in the chart. length 1,2,10,30,120,3,_,5,_ width 60,_,_,_,_,_,5,_,100
PLS HELP FAST
The length and width of the rectangle can be 30 and 2 inches, 1 inches and 60 inches and 12 inches and 5 inches.
How to find the area of a rectangle?A rectangle is a quadrilateral with opposite sides equal to each other. Opposite sides of a rectangle is equal to each other.
A rectangle has the area of 60 in².
The dimension of the rectangle can be as follows:
area of a rectangle = lw
where
l = lengthw = widthTherefore,
60 = 30 × 2
60 = 1 × 60
60 = 12 × 5
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Does 15 20 25 form a right triangle?
Any triple would still represent the sides of a right triangle if we multiplied it by a constant. Therefore, the sides of a right triangle would be represented by 6, 8, 10, 15, 20, and 25, among countless other numbers.
What is right triangle?
A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and other angles of the right triangle.
Input the Pythagorean Theorem with the given numbers:
c^2 = a^2 + b^2
25^2 = 15^2 + 20^2
625 = 225 + 400
625 = 625
Yes, the numbers 15, 20 and 25 form a right triangle and the Pythagorean triple.
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Solve for w.
2w²-2w+32 = (w-5)²
[tex]2w^2-2w+32=(w-5)(w-5)[/tex]
[tex]2w^2-2w+32=w^2-10w+25[/tex]
Subtract [tex]w^2[/tex] from each side:
[tex]w^2-2w+32=-10w+25[/tex]
Add [tex]10w[/tex] to each side:
[tex]w^2+8w+32=25[/tex]
Subtract 25 from each side:
[tex]w^2+8w+7=0[/tex]
Factor:
[tex](w+1)(w+7)[/tex] =0
Both solutions work, so w=-1 and w=-7What is the double of 8 in math?
Using doubles plus one fact the sum of 8 + 8 + 1is equal to 17 it is done by simply adding 1 to the given number.
Doubles plus one fact is used to add numbers which are next to each other.
Doubles plus one fact is simply done by doubling the number and adding one to it.
The sum of 8 + 8 can be determined by using doubles plus one fact as:
Simply add 1 in 8 + 8 + 1 to get the result required.
8 + 8 + 1 = 17
Therefore by using doubles plus one fact the sum of 8 + 8 + 1 is equal to 17.
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PLEASE HELP ASAP!!! FULL ANSWER!!!
A person standing close to the edge on top of a 40-foot building throws a ball vertically upward. The quadratic function h = − 16t^2 + 72t + 40 models the ball's height above the ground, h , in feet, t seconds after it was thrown.
a) What is the maximum height of the ball? _____________ feet
b) How many seconds does it take until the ball hits the ground? _____________ seconds
Answer:
a) 121 feet ; b) 5 seconds
Step-by-step explanation:
maximum height = y coordinare of vertex
x coordinate = -72/2 * -16
-72/-32 = 9/4 = 2.25
y coordinate =
-16(2.25)^2 + 72(2.25) + 40
-81 + 162 + 40
-81 + 202 = 121 feet
The ball hits the ground when y = 0
-16t^2 + 72t + 40 = 0
-2t^2 + 9t + 5 = 0
discriminant = 81 -4 (-2 * 5) = 81 -4(-10) = 81 + 40 = 121
We are searching only positive value
t = (-9 -11)/-4 = -20/-4 = 5 seconds
Please help! Need this by tonight thanks! Question 7 Click on picture
Answer:
Oh god, I don't really know much about this, but I am going to assume that the 25 represents the mn so maybe you have to put 25mn + 6600 on the first box?
Step-by-step explanation:
I just looked up how to do this. I think the form has to be a C=mn+b format. For the third box, I think you need to solve 54100=25mn+6600. On the second box I think you just need to solve C(3600)=25(3600)+6600. idrk