If angle 1 and angle 2 supplementary, angle 2 and angle 3 are supplementary, The measure of ∠2 = 47° and ∠3 = 133°.
What are supplementary angles?Angles that add up to 180 degrees are referred to as supplementary angles. For instance, angle 130° and angle 50° are supplementary angles as the total of these two angles is 180°. The sum of complimentary angles is 90 degrees.
Given,
the measure of angle 1 = 133°
As, ∠1 + ∠2 are supplementary angles,
⇒ ∠1 + ∠2 = 180° ......(1)
∠2 + ∠3 are supplementary angles,
⇒ ∠2 + ∠3 = 180° .......(2)
From (1),
⇒ 133° + ∠2 = 180°
⇒ ∠2 = 47°
From (2),
47° + ∠3 = 180°
∠3 = 133°
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Given the matrices A and B shown below, find -2A + 2B.
A = [0 -6] B = [-8 -1]
Answer:
The and is –6
Step-by-step explanation:
–2A= –2[0 , –6]
2B= 2[–8 , –1]
–2A= –2 [0 , +12]
2B= 2[–16 , –2]
–2A + 2B=[0 ,12] + [–16 ,–2]
=[0+(–16) + 12+(–2)]
=[0–16+12–2]
= –16+10
= –6.
Hope it was helpful
Angle DEF is an inscribed angle on a circle, and m
O 48°
O 96°
O 132°
O 24°
∠24°
What is an inscribed angle in a circle?
Inscribed angles are angles whose vertices are on a circle and that intersect an arc on the circle. The measure of an inscribed angle is half of the measure of the intercepted arc and half the measure of the central angle intersecting the same arc.
given that intercepted arc = ∠48°
The intercepted arc is the arc that is inside the inscribed angle and whose endpoints are on the angle.
If the intercepted arc is twice the size of the inscribed angle, then the inscribed angle is half the size of the intercepted arc. So if the intercepted arc is 48 degrees, the inscribed angle is 48 / 2 = 24 degrees.
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Compare the functions shown below: f(x) = (x + 3)2 − 2 g(x) linear graph with y intercept of negative 3 over 2 and x intercept of 3 h(x) x y −3 2 −2 7 −1 14 0 23 1 34 2 47 3 62 What is the correct order of the functions from least to greatest according to the average rate of change on the interval from x = −1 to x = 3?
Answer:
For f (x):
f (x) = (x + 3) ^ 2 - 2
For x = -1
f (-1) = (-1 + 3) ^ 2 - 2
f (-1) = (2) ^ 2 - 2
f (-1) = 4 - 2
f (-1) = 2
For x = 3
f (3) = (3 + 3) ^ 2 - 2
f (3) = (6) ^ 2 - 2
f (3) = 36 - 2
f (3) = 34
AVR = ((34) - (2)) / ((3) - (- 1))
AVR = 8
For g (x):
linear graph with and intercept of negative 3 over 2 and x intercept of 3
y = mx + b
b = -3/2
For me we have:
0 = m (3) - 3/2
3m = 3/2
m = 1/2
The function g (x) is:
g (x) = (1/2) x - 3/2
For x = -1
g (-1) = (1/2) (- 1) - 3/2
g (-1) = -1/2 - 3/2
g (-1) = -4/2
g (-1) = -2
For x = 3
g (3) = (1/2) (3) - 3/2
g (3) = 3/2 - 3/2
g (3) = 0
AVR = ((0) - (- 2)) / ((3) - (- 1))
AVR = 1/2
For h (x):
Using the table we have:
AVR = ((62) - (14)) / ((3) - (- 1))
AVR = 12
Step-by-step explanation:
Answer:
from least to greatest:
1) g (x)
2) f (x)
3) h (x)
Step-by-step explanation:
I WILL MARK BRAINLIEST.
Find the product of 3.2 x 1012 and 4.25 x 109. Write the final answer in scientific notation.
1.36 x 1021
13.6 x 1021
1.36 x 1022
13.6 x 1022
The product in scientific notation is 1.36 x 10^22
How to find the product of 3.2 x 1012 and 4.25 x 109?The product expression is given as:
3.2 x 1012 and 4.25 x 109
Express the product, properly
3.2 x 10^12 x 4.25 x 10^9
Regroup the factors
3.2 x 4.25 x 10^12 x 10^9
Evaluate the product
13.6 x 10^21
Rewrite as:
1.36 x 10^22
Hence, the product in scientific notation is 1.36 x 10^22
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Answer:
c 1.36 x 1012
explanation:
You are helping a friend with her flower garden. She decides to add some clematis
vines, rose bushes, and peony plants to her garden. The price of a clematis vine is $3
more than twice a peony plant. The price of a rose bush is $5 more than a clematis
vine. She decides to buy 3 clematis plants, 4 rose bushes and 2 peony plants for a total
of $233.
Write a system of three linear equations in three variables to represent this situation.
The price of a clematis vine, rose bush, and peony plant is given by a set of three linear equations with three variables: 29, 14, 13.
What do mathematical linear equations mean?A linear equation is one that has a degree of 1 as its maximum value .In a linear equation, no variable has an exponent bigger than 1, thus.. A linear equation's graph will always be a straight line.
An algebraic equation known as a linear equation has an exponent of 1 for each term, and when it is graphed, it always yields a straight line.
According to given data;
let c is price of clematis vine
let r is price of rose
P is price of peony plants.
bush
c=2p+3
r=c+5+
=3c + 4r+ 2p = 233
b) putting(1) in 2
a 2p+ 3 + 5 2 p +8 -9 putting(1) and (4)in 3
3(2p+3)+4(2p+8) + 2 p² 233
2
6p+9+8p+16+2p = 233
16p=25=233
16 p= 233-25
16p = 208
p=208÷13
p= 13
putting value of p in (1)and(4)
c= 2 p +3
=2X13+3
C = 29
r= 2p+8
=2×13+8
=34
price of clematis vines =29
rose bush = 34.
peony plants = 13.
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Which graph shows the solution of the inequality −|x − 2| + 9 > 6?
answer is -1 < x < 5
-|x - 2|+ 9 > 6
Rearrange the terms
-|x - 2| > 6 - 9
-|x - 2| > - 3
then divide both sides of the inequality by the co- efficient of variable
|x - 2| < 3
convert the absolute inequality to standard inequality
-3 <x - 2 < 3
separate compound inequalities into system of inequality
{x - 2}> -3
{x - 2 < 3}
Rearrange variable to the left side of the equation
x > -3 + 2
calculate the sum or difference
x > -1
x -2 < 3
Rearrange variable to the left side of the equation
x < 3 + 2
calculate the sum or difference
x < 5
x > -1 and x < 5
Find intersection
-1 < x < 5
Equations and inequalities are both mathematical sentences formed by relating two expressions to each other. In an equation, the two expressions are deemed equal which is shown by the symbol =. Where as in an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
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if an expression is x+4=10 could x=6
Answer:
Yep,
Step-by-step explanation:
First the expression is in this way:
x+4=10
Now shift the 4 ro RHS, then it will become as follows:
x=10-4
Now 10-4 is 6
Therefore, x=6
please help g(x) = f(x + 4) - 10 = 9^(x + 4) - 10
The expression for g(x) is 9x + 26
What is a function?A function can be defined as an expression, law or rule explaining the relationship between an independent and dependent variable.
Given the function;
g(x) = f(x + 4) - 10
Where f = 9
Substitute into the function;
g(x) = 9( x + 4) -10
expand the bracket
g(x) = 9x + 36 - 10
collect like terms
g(x) = 9x + 26
Thus, the expression for g(x) is 9x + 26
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Are 12,16,20 pythagorean triplets. Explain why.
Answer:
The numbers that make up today's date—12, 16, and 20—form a Pythagorean triple. That is, 12² + 16² = 20².
Step-by-step explanation:
Answer:Yes, these are pythagorean triplets because they are multiples of 4. 4 times 3 is twelve.4 times 4 is 4.And 4 times 5 is 20.
Please help me for scale factors
Answer:
91/7=13
so x=11×13
x=143
what is the slope of the line that passes through the points (-9,0) and (-17,4)? write your answer in simplest form
Answer: -1/2
Step-by-step explanation:
A three-centimeter cube has been painted red on all sides. it is cut into one centimeter cubes. how many cubes will be there with only one side painted red?
There will be only 6 cubes with only one side painted red.
Cube : A cube is a 3D shape having 6 equal square sides. it has 6 faces , 8 vertices and 12 edges.
According to the question
A 3 cm cube is divided into one centimeter cube.
Every face will have 9 cube each and from that 9 cube there will be only one 1 cube that will have one side painted red.
Since there are 6 faces,
cubes painted one side red = 6x1=6.
Therefore , There will be only 6 cubes with only one side painted red.
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2/5d+4/9e=-2d+7/18e-1
solve for e
Answer:
[tex]e=\frac{-5e-90}{216}[/tex]
Step-by-step explanation:
[tex]\frac{2}{5}d+\frac{4}{9}e=-2d+\frac{7}{18}e-1[/tex]
[tex]\frac{2}{5}d+\frac{4e}{9}=-2d+\frac{7}{18}e-1 < - Muiltiply[/tex]
[tex]\frac{2}{5}d+\frac{4e}{9}=-2d+\frac{7e}{18}- < - Muiltiply Again\\[/tex]
[tex]\frac{2}{5}d+\frac{4e}{9}-\frac{4e}{9}=-2d+\frac{7e}{18}-1-\frac{4e}{9} < - Subtract BothSides[/tex]
[tex]\frac{2}{5}d=-2d-\frac{e}{18}-1 < - Simplify[/tex]
[tex]\frac{2}{5}d+2d=-2d-\frac{e}{18}-1+2d < - AddToBothSides[/tex]
[tex]\frac{12}{5}d=-\frac{e}{18}-1 < - Simplify[/tex][tex]\frac{12d}{12}=-\frac{\frac{5e}{18}}{12}-\frac{5}{12} < - DivideBothSides[/tex]
[tex]e=\frac{-5e-90}{216}[/tex]
-7ab^2 + 9a^3b
factor it please
Step-by-step explanation:
= -7ab² + 9a³b
= -7b × ab + 9a² × ab
= ab × (-7b + 9a²)
Solve for the value of e.
see picture below!!
Answer:
11
Step-by-step explanation:
90=55+3e+2
33=3e
e=11
Classify this polynomial. –8r4 + 2r2 + 3r hurry pls
Answer: -r(8r^3-2r-3)
Step-by-step explanation:
Jasmine is 20 years old. Her brother Zac is 6 years more than half her age. Which of the following is the correct expression for Zac's age?
(20 ÷ 2) + 6
(20 ÷ 2) − 6
10 x 2 + 4
10 − (2 x 4)
The cost per unit of an item is called the
Answer:
breakeven point,
Step-by-step explanation:
after finishing the prep work, gilberta and maría start removing wallpaper at the same time. gilberta removes the paper at a constant rate of 4.3\,\text{m}^24.3m 2 4, point, 3, start text, m, end text, squared per hour, while maría removes 3.4\,\text{m}^23.4m 2 3, point, 4, start text, m, end text, squared of paper per hour. gilberta's room starts with 35\,\text{m}^235m 2 35, start text, m, end text, squared of paper, and maría's room starts with 30.5\,\text{m}^230.5m 2 30, point, 5, start text, m, end text, squared of paper.
The inequality that depicts when Gilberta has much more wallpaper left throughout her room than Mara does in hers using linear functions is:
t< 5.
A linear function is :A linear function has a straight line as its graph. The following is the form of a linear function. a + bx = y = f(x). One independent variable but one dependent variable make up a linear function. X and Y are the independent and dependent variables, respectively.
According to the given information:Following t hours, the quantities Gilberta and Maria have remaining are determined by:
G(t) = 35 - 4.3t.
M(t) = 30.5 - 3.4t.
Gilberta has more papers when:
G(t) > M(t).
So,
35 - 4.3t > 30.5 - 3.4t
-0.9t < -4.5
Multiplying by -1:
0.9t < 4.5
t < 4.5/0.9
t < 5.
The inequality is:
t < 5.
The inequality that depicts when Gilberta has much more wallpaper left throughout her room than Mara does in hers using linear functions is:
t< 5.
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BD bisects
Find m
ABC= 25x+34
CBD = 11x+23
The measure of angles are
i) Angle ABD = 67°
ii) Angle CBD = 67°
iii) Angle ABC = 134°
We have been given that ray BD bisects angle ABC and also
Angle ABC = (25x+34)°
Angle CBD = (11x + 23)°
Note that angle ABC = angle ABD + angle CBD (1)
And angle ABD = angle CBD = (11x + 23)° as it is bisected into two equal half.
Therefore putting the required values of angle in equation (1) we get
(25x+34)° = 2(11x+23)°
25x+34 = 22x+46
25x – 22x = 46 – 34
3x = 12
x = 4
Hence, angle ABD = (11*4 + 23) ° = 44+23 = 67°
Angle CBD = (11*4 + 23) ° = 44+23 = 67°
angle ABC = (25*4 + 34)° = 100+34 = 134°
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What is the gradient of the graph shown?
Give your answer in its simplest form.
Answer:
1/3
Step-by-step explanation:
Gradient or slope can be found using the point-slope formula:
[tex]y-y_{1} =m(x-x_{1} )[/tex]
We can rearrange the equation to find slope (m) like so:
[tex]m=\frac{y-y_{1} }{x-x_{1} }[/tex]
To use this formula we need to find two well-defined points and use their coordinates.
Let's use (0,2) and (3,3) because they are clear points on the graph.
(0,2) will represent [tex]x[/tex] and [tex]y[/tex] in the equation respectively, and (3,3) our other point will represent [tex]x_{1}[/tex] and [tex]y_{1}[/tex].
Now we just need to plug the numbers into the equation:
[tex]m=\frac{2-3}{0-3} \\\\m=\frac{-1}{-3} \\m=\frac{1}{3}[/tex]
The gradient of the graph is 1/3.
Hope this helped!
need help with #9, & #10 please
Step-by-step explanation:
the line equation is in the slope-intercept form.
that looks like
y = ax + b
"a" is the slope (always the factor of x). "b" is the y-intercept (the y value when x = 0).
so, when it says "the same slope", we know we have to use the same factor of x.
and yes, the coordinates of a point are (x, y). so, you really need to use it in the places of x and y to get "b".
9.
y = -4x + b
2 = -4×0 + b = b
so, yes, the equation is
y = -4x + 2
but as you can see : b is NOT y in general.
10.
y = 2/3 x + b
-1 = 2/3 × 4 + b = 8/3 + b
now, let's multiply both sides by 3 to get rid of the fraction :
-3 = 8 + 3b
-11 = 3b
b = -11/3
so, the equation is
y = 2/3 x - 11/3
or
y = 1/3 × (2x - 11)
What is the simplified value of the expression, below, when x = 4 and y = 6? Leave your an
simplified fraction
Show all steps for full credit. Circle your final answer. (4 points).
3x - y/
2y + x please help
Answer:
2
-
2 - 4 ^ 5
Step-by-step explanation:
Mr.chong has some money to buy tins of paint. if he buys 18 tins of paint. he will need another $80. if he buys 10 tins of paint, he will have $32 left.
Amount of one tin of paint is $14 and the total amount Mr. Chong have is $172.
Let amount of one tin of paint = x
Let the total amount Mr. Chong having = y
On buying 18 tins of paint, he will need another $80. This can we mathematically represented as,
18x = y + 80
On rearranging this equation can be written as,
18x - y = 80 equation 1
On buying 10 tins of paint, he will will have $32 left. This can we mathematically represented as,
10x = y - 32
On rearranging this equation can be written as,
-10x + y = 32 equation 2
On adding equation 1 and equation 2, we get
18x - y -10x + y = 80 + 32
8x = 112
x = (112/8) = 14
On substituting x = 14 in equation 2 , we get
-140 + y = 32
y = 172
So, amount of one tin of paint is $14 and the total amount Mr. Chong have is $172.
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Tyler has two cube-shaped storage spaces in his apartment, one large and one big. the small on is 12 with a exponent of 3. what is the volume for both?
Answer: 19
Step-by-step explanation:
2+1+1+12+3=19
What is the slope of the line in the graph?
a)-4/3
b)-3/4
c)3/4 or
d)4/3
i will mark brainliest
100pts
Answer:
B
Step-by-step explanation:
The slope of a line is written as a fraction of the vertical distance to the horizontal distance. The line drops down from (0,1) to (4,-2). This is a vertical distance of -3 and a horizontal distance of 4. The slope if the fraction -3/4.
Answer:
[tex] \sf \: b) \: \frac{ - 3 \: }{ 4} [/tex]
Step-by-step explanation:
The coordinates are,
→ x1 = 4, y1 = -2
→ x2 = -4, y2 = 4
Formula we use,
→ Slope(m) = (y2 - y1)/(x2 - x1)
Now the required slope will be,
→ m = (y2 - y1)/(x2 - x1)
→ m = (4 -(-2))/(-4 - 4)
→ m = (4 + 2)/-8
→ m = 6/-8
→ [ m = -3/4 ]
Hence, the option (b) is correct.
It is important to understand how probability works in statistics because ______.
Probability are important information when applying descriptive statistics. Probability is the branch of mathematics concerning numerical descriptions. the correct option is (B).
What is probability?Descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty. The higher the probability of an event, the more likely it is that the event will occur.
here, we have,
A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%).
The probability formula defines the likelihood of the happening of an event. It is the ratio of favorable outcomes to the total favorable outcomes. The probability formula can be expressed as,
Probability formula:
P(A) = Probability(Event) = Favorable Outcomes/Total Outcomes
P(A) = x/n
where,
P(B) is the probability of an event 'B'.
n(B) is the number of favorable outcomes of an event 'B'.
n(S) is the total number of events occurring in a sample space
Descriptive statistics are brief informational coefficients that summarize a given data set, which can be either a representation of the entire population or a sample of a population. Descriptive statistics are broken down into measures of central tendency and measures of variability (spread). Measures of central tendency include the mean, median, and mode, while measures of variability include standard deviation, variance, minimum and maximum variables, kurtosis, and skewness.
The main purpose of descriptive statistics is to provide information about a data set. In the example above, there are hundreds of baseballs players that engage in thousands of games. Descriptive statistics summarizes the large amount of data into several useful bits of information.
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If cot 0=7/8 evaluate : (i) (1 + sin 8)(1-sin 8) (1 + cos 0) (1 - cos8) (ii) cot¹0
Answer: The value of (1 + sin 8)(1-sin 8) (1 + cos 0) (1 - cos8) =0.2086
and [tex]cot^{1}[/tex]θ=7/8
Step-by-step explanation:
Let base and height of a triangle be 7k and 8k
By applying Pythagoras theorem in Δ ABC, we get
[tex]AC^{2} = AB^{2} +BC^{2}[/tex]
= (7k)2 + (8k)2
= 49k2 + 64k2
= 113k2
AC = √113k2
= √113k
so hypotenuse =[tex]\sqrt{133}k[/tex];
now ;
=(1 + sin θ) (1 - sin θ)(1 + cos θ) (1 - cos θ)[since : (a + b)(a - b) = (a2 - b2)]
=(1 - [tex]sin^{2}[/tex]θ)(1 - [tex]cos^{2}[/tex]θ)
=[1 - (8/√113)2] [1 - (7/√113)2]
= (1 - 64/113) (1 - 49/113)
= (49/113) (64/113)
= 0.2086
hence;
The value of (1 + sin 8)(1-sin 8) (1 + cos 0) (1 - cos8) =0.2086
and [tex]cot^{1}[/tex]θ=7/8
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Answer:
Step-by-step explanation:We will use the basic concepts of trigonometric ratios to solve the problem.
Consider ΔABC as shown below where angle B is a right angle.
If cot θ = 7/8, evaluate: (i) (1 + sin θ)(1 - sin θ) / (1 + cos θ)(1- cos θ), (ii) cot²θ
cot θ = side adjacent to θ / side opposite to θ = AB/BC = 7/8
Let AB = 7k and BC = 8k, where k is a positive integer.
By applying Pythagoras theorem in Δ ABC, we get
AC2 = AB2 + BC2
= (7k)2 + (8k)2
= 49k2 + 64k2
= 113k2
AC = √113k2
= √113k
Therefore, sin θ = side opposite to θ / hypotenuse = BC/AC = 8k/√113k = 8/√113
cos θ = side adjacent to θ / hypotenuse = AB/AC = 7k/√113k = 7/√113
(i) (1 + sin θ) (1 - sin θ) / (1 + cos θ) (1 - cos θ) = 1 - sin2θ / 1 - cos2θ [Since, (a + b)(a - b) = (a2 - b2)]
= [1 - (8/√113)2] / [1 - (7/√113)2]
= (1 - 64/113) / (1 - 49/113)
= (49/113) / (64/113)
(ii) cotФ≈
= 49/64
You reflect the triangle below over the x-axis.
Answer:
(-5,3)
Step-by-step explanation:
That's the coordinates of it being reflected over X axis for point P.
I HAVE 2 MINS TO ANSWER THIS HELP
Answer:
A.
Step-by-step explanation:
In the 2nd Quadrant, the y is POS and the x is NEG. That's what will happen if reflected from the 1st Quadrant over the Y axis.
Answer: A
Step-by-step explanation: