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# The size of an exterior angle of a triangle is the supplement of smaller of two opposite interior angles. If the greater of the opposite interior angles exceeds smaller by 30°, find the measure of the interior angles of the triangle.
please help me
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Answer:
30° and 60°
Step-by-step explanation:
Let the interior angles be ∠x₁ (smaller) and ∠x₂ (larger), and the exterior angle ∠X.
Making the statements into equations :
Size of an exterior angle of a triangle is the supplement of smaller of two opposite interior angles ⇒ ∠X + ∠x₁ + ∠x₂ = 180° [Equation 1]
Greater of the opposite interior angles exceeds smaller by 30° :
⇒ ∠x₂ = ∠x₁ + 30° [Equation 2]
By exterior angle property :
⇒ ∠x₁ + ∠x₂ = ∠X [Equation 3]
Substituting Equation 3 in Equation 1 :
⇒ ∠x₁ + ∠x₂ + ∠x₁ + ∠x₂ = 180°
⇒ 2 (∠x₁ + ∠x₂) = 180°
⇒ ∠x₁ + ∠x₂ = 90°
⇒ ∠x₂ = 90° - ∠x₁ [Equation 4]
Substituting Equation 4 in Equation 2 :
⇒ 90° - ∠x₁ = ∠x₁ + 30°
⇒ 2∠x₁ = 60°
⇒ ∠x₁ = 30°
Substituting the value of ∠x₁ in Equation 2 :
⇒ ∠x₂ = 30° + 30°
⇒ ∠x₂ = 60°
The measures of the interior angles are 30° and 60°
Pls help
80 points!
function g is a transformation of f the graph below shows f as a solid blue line and G as a red dotten line
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Vertex is same x coordinate
Means y is changed
f(x) has vertex (4,3)
g(x) has vertex (4,-3)
Total change
|3+3|=6So the transmission is f(x)-6
Answer:
[tex]\textsf{D)} \quad f(x)-6[/tex]
Step-by-step explanation:
Translations
For [tex]a > 0[/tex]
[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]
From inspection of the graph, g(x) is a translation of f(x) by 6 units down.
[tex]\implies g(x)=f(x)-6[/tex]
This rectangular prism has a length of 14 inches, a height of 8 inches, and a width of 3 inches. What is the volume
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height= 8 in
length= 14 in
width= 3 in
to find:the volume of the given rectangular prism.
solution:[tex]v = whl[/tex]
[tex]v = 8 \times 14 \times 3[/tex]
[tex]v = 336 \: {in}^{3} [/tex]
hence, the volume of the given rectangular prism is 336 cubic inches.
answer= option D
[tex]\large\boxed{Formula: V= lbh}[/tex]
All the values are given so we'll simply have to solve.
Let's solve!
Substitute the values according to the formula.
We'll have to multiply the length, breadth and the height.
[tex]V= 14 \times 3 \times 8[/tex]
[tex]\large\boxed{V= 336 \: {in}^{3}}[/tex]
We get a whole number to the final answer so we won't have to round off.
Therefore, the volume of the given rectangular prism is 336 cubic inches.
Correct option: Option D
Find an equation of the plane passing through the points (1, 5, -3), (2, 5, -3) and (3, 5,2)
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Answer:
[tex]y = 5[/tex].
Or, equivalently:
[tex]\begin{aligned}\begin{bmatrix}0 \\ -3 \\ 0\end{bmatrix} \left(\begin{bmatrix}x \\ y \\ z\end{bmatrix} - \begin{bmatrix}1 \\ 5 \\ -3\end{bmatrix}\right) = 0\end{aligned}[/tex].
Step-by-step explanation:
Every plane in [tex]\mathbb{R}^{3}[/tex] could be represented with a vector equation of the form [tex]\vec{n}\, (\vec{r} - \vec{r}_{0}) = 0[/tex], where:
[tex]\vec{n}[/tex] is a vector normal to the plane (a normal vector), and [tex]\vec{r}_{0}[/tex] is the position vector of a point in the plane.Notice that in this question, the coordinates (and hence the position vectors) of the points in this plane are already given. For example, the position vector of the point [tex](1,\, 5,\, -3)[/tex] is the vector:
[tex]\begin{aligned}\vec{r}_{0} = \begin{bmatrix}1 \\ 5 \\ -3\end{bmatrix}\end{aligned}[/tex].
Specifically in [tex]\mathbb{R}^{3}[/tex], normal vectors of a plane could be found by:
finding two distinct directions parallel to that plane, and taking the cross product between the two directions.Subtracting position vectors of points in this plane from each other would give directions that are parallel to this plane:
[tex]\begin{aligned}\begin{bmatrix}2 \\ 5 \\ -3\end{bmatrix} - \begin{bmatrix}1 \\ 5 \\ -3\end{bmatrix} = \begin{bmatrix}1 \\ 0 \\ 0\end{bmatrix}\end{aligned}[/tex].
[tex]\begin{aligned}\begin{bmatrix}3 \\ 5 \\ 2\end{bmatrix} - \begin{bmatrix}1 \\ 5 \\ -3\end{bmatrix} = \begin{bmatrix}2 \\ 0 \\ 5\end{bmatrix}\end{aligned}[/tex].
The cross product between these two vectors in [tex]\mathbb{R}^{3}[/tex] would be:
[tex]\begin{aligned} \vec{n} = \begin{bmatrix}1 \\ 0 \\ 0\end{bmatrix} \times \begin{bmatrix}2 \\ 0 \\ 5\end{bmatrix} = & \begin{bmatrix}0 \times 5 - 0 \times 0 \\ 0 \times 2 - 1 \times 5\\ 1 \times 0 - 0 \times 2\end{bmatrix} = \begin{bmatrix}0 \\ -3 \\ 0\end{bmatrix}\end{aligned}[/tex].
(Note that the cross product between other directions parallel to the plane might give other normal vectors that are parallel to the one in this example.)
Using the position vector of the point [tex](1,\, 5,\, -3)[/tex] as [tex]\vec{r}_{0}[/tex], one possible vector equation for this plane would be:
[tex]\begin{aligned}\begin{bmatrix}0 \\ -3 \\ 0\end{bmatrix} \left(\begin{bmatrix}x \\ y \\ z\end{bmatrix} - \begin{bmatrix}1 \\ 5 \\ -3\end{bmatrix}\right) = 0\end{aligned}[/tex].
Expand the dot product and simplify to obtain a scalar equation for this plane:
[tex]\begin{aligned}\begin{bmatrix}0 \\ -3 \\ 0\end{bmatrix} \begin{bmatrix}x - 1 \\ y - 5 \\ z - (-3)\end{bmatrix} = 0\end{aligned}[/tex].
[tex]0\, (x - 1) + (-3)\, (y - 5) + 0\, (z - (-3)) = 0[/tex].
[tex](-3)\, (y - 5) = 0[/tex].
[tex]y = 5[/tex].
A flag pole is 35 feet high. The sun shines a shadow of the flag pole to the ground. The shadow,
going out from the base of the flag pole is 12 feet long. What is the distance from the top of the
flag pole to the tip of the shadow?
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Use the Pythagorean theorem as it’s a right triangle. I drew a picture with work because I’m too lazy to type it:
please solve the problem
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Answer:
See below ~
Step-by-step explanation:
Section (xiii) :
m(AB) : m(AC) = m(BD) : m(DC)6 : 8 = 3 : x6/8 = 3/xx = 3/6 x 8x = 0.5 x 8x = 4Section (xiv) :
DE = 1/2(AB)3 = 1/2(x + 1)x + 1 = 6x = 5It is indicated in the diagram that CE = EB :
y - 7 = x - 1y = 5 - 1 + 7y = 12 - 1y = 11Answer: xiii: x=4 xiv: x=5 y=11
Step-by-step explanation:
Ok, for xiii, there is a ratio.
BD:DC aka 3:x You're trying to solve for x (DC)
On the other side of the equation, it's AB:AC aka 6:8 This ratio can be simplified to 3:4 (when you divide both sides by 2)
To set things up:
3:x = 3:4
Notice the similarity? Since they are equal to one another, x must be 4.
Now for xiv, you're trying to find the values of x and y.
DE=3 and AB=x+1
DE=1/2 of AB
so,
3=(x+1)/2 Solving for x, multiply both sides by 2
6=x+1 subtract both sides by 1
-1 -1
x=5
If you plug x to AB, AB = 6
Plug x to BE = 4
To find y, notice how there is a dash that marks them as congruent, so the lengths BE and EC must be equal.
so y-7=4 (adding 7 to both sides)
+7 +7
y=11
y=5x-3 input and output
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Answer:
y out put x input and 3 is input and as 5 . tell me if you get it right
Holly scored an 88, 91, 89, 84, and a 98 on the last five math tests. What is her mean test score?
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Answer:the mean is 90
Step-by-step
you find the sum of the values then divide them by the amount of numbers in the set
HELPPPPPPPPPPPPPPPPPPP!!!!!!!!!!!!!!!!
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If five quarts of paint are needed for 250 square-feet of room, 13 quarts of paint will cover how many square feet of room?
Do not put units or commas, only put the number value to the nearest whole number.
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Answer:
650
Step-by-step explanation:
let the unknown feet of room = X
5 paints = 250 square feet of room
13 paints = X
cross multiply
5*X = 250*13
X =3250÷5
X = 650 square feet of room
In a certain family, the probability of having twins in 0.08 and the probability of having a single baby is 0.92.
What is the probability of a family having two sets of twins?
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Answer: SE = √. pA(1 - pA). nA. +. pB(1 - pB). nB. = √. 0.08(0.92). 200. +. 0.344(0.656). 200. = 0.039. (b) The sample sizes of 200 are large enough
Step-by-step explanation:
In Autobiography by Abraham Lincoln Lincoln avoids embellishing on his own life and keeps his portrayal of his life very______.
A.neutral
B. negative
C. humorous
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Dan's car depreciates at a rate of 9% per year.
By what percentage has Dan's car depreciated after 4 years?
Give your answer to the nearest percent.
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Answer:
about 31%
Step-by-step explanation:
[tex]1 - {.91}^{4} = 1 - .6857 = .3143 = 31\%[/tex]
Eight trucks hold a total of 10 and 1/2 tons of cargo. Half the trucks are
large and the rest are small. Each large truck holds twice as much
cargo as a small truck. How much cargo can two large trucks and
one small truck hold? Write an equation and explain how you
found your answer.
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Solving a system of equations we will see that two large trucks and one small truck can hold 2.625 tons
How much cargo can two large trucks and one small truck hold?Let's define the variables:
x = volume that a small truck holds.
y = volume that a large truck holds.
Then we can write the system of equations:
4x + 4y = 10.5 tons
y = 2x
Replacing the second equation into the first one we get.
4x + 4*(2x) = 10.5 tons
12x = 10.5 tons
x = 10.5 tons/12 = 0.875 tons
and:
y = 2x = 2*0.875 tons = 1.75 tons
Then the cargo that two large trucks and one small truck can hold is:
2* 1.75 tons + 0.875 tons = 2.625 tons
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A board 120inches long is divide into 2 sections. If the ratio of the 2 sections. 3:5 Wht are the lengths of the section
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Answer:
45, 75
Step-by-step explanation:
3+5 = 8
120 / 8 = 15
15 x 3 = 45
15 x 5 = 75
Answer:
45,75
3+5 = 8
120 / 8 = 15
15 x 3 = 45
15 x 5 = 75
Step-by-step explanation:
have a great day!
Use z scores to compare the given values.
Based on sample data, newborn males have weights with a mean of 3217.9g and a standard deviation of 780.1g. Newborn females have weights with a mean of 3086.5g and a standard deviation of 523.8g. Who has the weight that is more extreme relative to the group from which they came: a male who weighs 1700g or a female who weighs 1700g?
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Using z-scores, it is found that a female who weighs 1700g has the more extreme value relative to the group from which they came.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.For the newborn male, we have that [tex]X = 1700, \mu = 3217.9, \sigma = 780.1[/tex], hence the z-score is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1700 - 3217.9}{780.1}[/tex]
Z = -1.946.
For the newborn female, we have that [tex]X = 1700, \mu = 3086.5, \sigma = 523.8[/tex], hence the z-score is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1700 - 3086.5}{523.8}[/tex]
Z = -2.645.
Due to the higher absolute value of the z-score, a female who weighs 1700g has the more extreme value relative to the group from which they ca,e.
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tan A = 2.053 what is the measure of angle A
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Answer:
A =64.03
Step-by-step explanation:
tan A = 2.053
A = Arctan( 2.053)
A =64.03
What’s the area of the field and I need a step by step explanation. Thanks you and have a great day
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= 50 x 100 + (50/2)^2 x 3.14 x 1/2 =5981.25
or Three baseball players are playing catch. Kenny is directly south of Ling and directly west of Sidney. Kenny and Sidney are 8 feet apart and Sidney and Ling are 10 feet apart. How far apart are Kenny and Ling?
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Answer:18 feet
Step-by-step explanation:
It would be 18 feet because if you add 8 feet from how far him and Sidney are then 10 feet from how far Sidney and Ling are.
please help me do this mathematics question..experts .
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The partial differential expression is equal to the expression 30 · x · (x³ + y⁴) + 36 · x² · y² · (y² + x²) and the total differential formula is Δz = (0.9 · x² + 0.6 · y²) · cos (x³ + y³).
How to apply partial derivatives and total differentials
In the first part of this question we must apply the concept of partial derivatives to find the form of the entire expression, whose variables are two. Partial differentiation is a generalization of the ordinary differentiation:
[tex]\frac{\partial f}{\partial x} = 6\cdot x^{5}+12\cdot x^{3}\cdot y^{4}+y^{6}[/tex] (1)
[tex]\frac{\partial^{2} f}{\partial x^{2}} = 30\cdot x^{4}+36\cdot x^{2}\cdot y^{4}[/tex] (2)
[tex]\frac{\partial^{2} f}{\partial x \,\partial y} = 48\cdot x^{3}\cdot y^{3}+6\cdot y^{5}[/tex] (3)
[tex]\frac{\partial f}{\partial y} = 12\cdot x^{4}\cdot y^{3} +6\cdot x \cdot y^{5}[/tex] (4)
[tex]\frac{\partial^{2} f}{\partial y^{2}} = 36\cdot x^{4}\cdot y^{2} + 30\cdot x\cdot y^{4}[/tex] (5)
[tex]\frac{\partial f}{\partial y \,\partial x} = 48\cdot x^{3}\cdot y^{3}+6\cdot y^{5}[/tex] (6)
Then, the entire expression is:
30 · x⁴ + 36 · x² · y⁴ + 36 · x⁴ · y² + 30 · x · y⁴
30 · (x⁴ + x · y⁴) + 36 · (x² · y⁴ + x⁴ · y²)
30 · x · (x³ + y⁴) + 36 · x² · y² · (y² + x²)
In the second part we must determine the total differential of z with respect to two variables:
[tex]\Delta z = \frac{\partial f}{\partial x}\cdot \Delta x + \frac{\partial f}{\partial y}\cdot \Delta y[/tex] (7)
If we know that z = sin (x³ + y³), Δx = 0.3 and Δy = 0.2, then the total differential of the function is:
Δz = 3 · cos (x³ + y³) · x² · (0.3) + 3 · cos (x³ + y³) · y² · (0.2)
Δz = (0.9 · x² + 0.6 · y²) · cos (x³ + y³)
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CHOOSE A MYSTERY FRACTION
THEN WRITE 3 TO 5 QLUES FOR
A CLASSMATE TO USE TO GUESS
YOUR FRACTION.
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Answer:
Step-by-step explanation:
Guess My Mystery Fraction
1. My fraction has a denominator of 4*12
2. My fraction can be simplified to 5/8
3. My fraction has a numerator of 10*3
What is the value of x in | - 6| = x? O 6 and -6 00 06 -6 HOURME
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Answer:
I believe, 6.
Step-by-step explanation:
Not sure if the rest of the question is the answer choices but the absolute of any number, is it's exact opposite. The reason for this is that an absolute number, or |?| is equal to whatever distance it is from 0. Since adding 1, and subtracting 1, both do such but in opposite directions, the absolute value of both would be 1.
if x-y=5 and xy=4,find the value of x3-y3
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[tex]\text{Given that,} ~ x-y = 5~ \text{amd}~ xy = 4\\\\\text{Now,}\\\\x^3 -y^3\\\\=(x-y)(x^2 +xy+y^2)\\\\=(x-y)[(x-y)^2 +2xy +xy]\\\\=(x-y)[(x-y)^2 +3xy]\\\\=5(5^2+3\cdot 4)\\\\=5(25+12)\\\\=5(37)\\\\=185[/tex]
Can someone answer theese questions do all of them and I will give you brainily
1 .
What does each line on the protractor stand for?
five degrees
one-half of a degree
ten degrees
one degree
2 What part of the protractor do you line up with the vertex?
zero line
degree line
center mark
top of the protractor
3.
What is the first step in constructing an angle?
Make a mark at the number of degrees you want the angle to be.
Connect the endpoint and the mark at the angle measure
Draw a horizontal ray.
Place the center of the protractor on the endpoint of the ray, and line up the ray with the zero line of the protractor.
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2. Not quite sure which answer you would align with this, but I do know the bottom edge has a point that’s always lined up with the vertex.
3. Make a mark at the number of degrees you want the angle to be.
Answer: i think is b
Step-by-step explanation: because I do read lesson so I guess I think is b that why.
−11 ≤ −5; Add 16 to both sides
The resulting inequality is:
Answers
Answer:
True, (-∞, ∞) 5 ≤ 11
Step-by-step explanation:
−11 ≤ −5 Add 16 to both sides
−11 + 16 ≤ −5 + 16
5 ≤ 11
what is the different between replacing the first card and not replacing the first card
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Replacing the first card illustrates an independent event, while not replacing the card illustrates a dependent event
How to determine the difference?In probability, when a selected card or item is replaced before another item is selected, then the event is an independent event.
This is so because, the selected card do not have effect on the probability of selecting the next card
However, if the card is not replaced, then the event is dependent
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The points L, M, N and O all lie on the same line segment, in that order, such that the ratio of LM : MN : NO is equal to 3 : 1 : 5. If LO=36, find NO.
NO = ( )
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Answer:
NO = 20
Step-by-step explanation:
If the pieces are in the ratio of 3:1:5 and the whole thing is 36, then set up an equation:
3x + 1x + 5x = 36
and solve, see image.
Which relation is a function?
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Answer:
A function means that we get one input and one output. In this example that means for every x-value that we have, we only have one y-value.
Looking at the first option, we can see that there is no x-value that has more than one y-value which means that it is a function.
The rest of the options are seen with at least two values for one x-value in one of the points. Therefore, they wouldn't be considered a function leaving us with only option A as the solution.
A ladder that is 5 meters long is leaning against a wall. The vertical height from the base of the wall to the top of the ladder is 3 meters. If ∠θ is the angle that the ladder makes with the ground, what is the approximate measure of ∠θ?
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The approximate angle that the ladder makes with the ground is 37 degrees
Angle of elevationThe given question will be solved using the SOH CAH TOA identity.
The given statement will form a right triangle with the following parameters
Hypotenuse = 5m
Height(opposite) .= 3m
Determine the approximate measure of ∠θ
sin ∠θ = opp/hyp
sin ∠θ = 3/5
sin ∠θ = 0.6
∠θ = arcsin(0.6)
∠θ = 37degrees
Hence the approximate angle that the ladder makes with the ground is 37 degrees
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a package of buttery round crackers contains 4 sleeves of crackers each package of crackers cost $2.49 A function, f(x) is written to represent the cost of purchasing x packages of crackers
What is the practical domain for the function f(x)?
.All positive integers
.All whole numbers
.All whole numbers that are multiples of 4
.All real numbers
Answers
The practical domain of function f(x) has all positive integers and all whole numbers that are multiples of 4 that is option A or D is correct
What is domain?The domain is "set of all possible inputs value for the function".
According to the question,
A package of buttery round crackers contains 4 sleeves of crackers each
package of crackers cost $2.49. A function f(x) written to represent the cost of purchasing x packages of crackers.
In order to find the practical domain for the function f(x) only if analysis the value of domain function 'x' must positive number so contain 'all positive integers' and since a package of buttery round crackers contains 4 sleeves then domain must contain 'all whole numbers that are multiples of 4'.
Hence, the practical domain of function f(x) has all positive integers and all whole numbers that are multiples of 4.
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