The measure of one of the small angles of a right triangle is 6 more than 3 times the measure of the other small angle. Find the measure of both angles.
Input your answers into the following boxes.
The measures of the two angles in the order from the smallest to the greatest are
degrees and
degrees.
Answers
The measures of two angles in the order from the smallest to the greatest are 21° and 69°.
What is a right triangle?
A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangle triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.
Given the acute angle of a right triangle is 6 more than 3 times the measure of the other small angle.
Assume that the measurement of smaller angle is x.
Then the mathematical expression of 6 more than 3 times of x is 6 + 3x.
The measure of third angle is 90° since it a right triangle.
The sum of all interior angles of a right triangle is 180°.
The equation is
x + (6 + 3x) + 90 =180
x + 6 + 3x + 90 =180
Combine like terms:
(x + 3x) + (6 + 90) = 180
4x + 96 = 180
Subtract 96 from both sides:
4x = 180 - 96
4x = 84
Divide both sides by 4
x = 21
Putting x = 21 in the expression (6 + 3x) :
6 + 3x = 6 + 63 = 69.
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Related Questions
What expression is equivalent to 5(x+3)
Answers
Answer:
5x + 15
Step-by-step explanation:
5(x + 3) ← multiply each term in the parenthesis by 5
= 5x + 15
"5x+15" is an expression equivalent to "5(x+3)".
Step-by-step explanation:If we expand this factorization, the resulting expression is equivalent to the original expression. This is how you expand it:
1. Write the expression.[tex]5(x+3)[/tex]
2. Apply the distributive property of multiplication.Check the attached image.
[tex](5)(x)+(5)(3)=\\ \\5x+15[/tex]
3. Conclude.
5x+15 is an expression equivalent to 5(x+3).
A rectangular prism has a volume of 960 cubic units. The area of the base is 80 square units.
What is the height of the prism?
Answers
Answer:
12 units
Step-by-step explanation:
V = (area of base) × height
height = V/(area of base)
height = 960 units³ / 80 units²
height = 12 units
Use a graphing calculator to find an equation of the line of best fit for the data. Round the slope to the nearest tenth and the y -intercept to the nearest integer.
A table listing pairs of x and y values.
X values: 0, 1, 2, 3, 4, 5, 6, 7.
Y values: -8, -5, -2, -1, -1, 2, 5, 8.
Answers
The equation of the line in slope-intercept form is y = 3x - 11.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
We know slope(m) = (y₂ - y₁)/(x₂ - x₁).
∴ Slope(m) = (- 5 + 8)/(1 - 0) = 3.
So, y = mx + b can be written as - 5 = 3(2) + b ⇒ b = - 11.
So, The required line is y = 3x - 11.
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View in which one or more faces of the object are not perpendicular to the rest of the faces, so their projection planes are not parallel but inclined.
Answers
We can say that the view in which one or more faces of the object are not perpendicular to the rest of the faces, but are inclined projections, are the auxiliary views.
¿What are auxiliary views?Initially, we must know that the views of an object or body are orthogonal projections associated with it.
In this sense, auxiliary views are a type of view that are characterized by arising from a change in projection plane, they are usually used when highly complex parts or objects must be represented.
¡Hope this helped!
The actual weights of 10 sample “1 lb packages” of meat are found to be:
sample 1 2 3 4 5 6 7 8 9 10
weight 1.01 1.03 0.98 0.99 1.01 1.02 0.98 1.05 0.97 0.98
What is the mean of the actual weights?
1.002
1.003
1.01
1.0
Answers
The solution is Option A.
The mean of the actual weights of the samples is 1.002
What is Mean?
The mean value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values.
Mean = Sum of Values / Number of Values
Given data ,
Let the mean of the observations be represented as M
Now , the value of mean M is calculated as
The number of samples be = 10
The weight of the samples can be given from set A
The value of set A is
Set A = { 1.01 , 1.03 , 0.98 , 0.99 , 1.01 , 1.02 , 0.98 , 1.05 , 0.97 , 0.98 }
The sum of the values of weights of set A is S
Sum S = 1.01 + 1.03 + 0.98 + 0.99 + 1.01 + 1.02 + 0.98 + 1.05 + 0.97 + 0.98
Sum of weights S = 10.02
Now , the mean of the weights is given by
Mean = Sum of Values / Number of Values
Mean = Sum of weights / Number of samples
Substituting the values in the equation , we get
Mean = 10.02 / 10
Mean M = 1.002
Therefore , the value of M is 1.002
Hence , The mean of the actual weights of the samples is 1.002
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which expression is equivalent to 9^-4?
A. -9^4
B. 9^4
C. 1/9^-4
D. 1/9^4
Answers
Answer:
D
Step-by-step explanation:
as a negative exponent always means 1/..., D is the correct answer.
9^-4 = 1/(9^4)
that is the precise definition of a negative exponent.
Michael just retired, and has $740,000 to invest. A very safe Certificate of Deposit (CD) account pays 1.5%, while a riskier bond fund pays 8.5% in interest. Michael figures he needs $22,000 a year in interest to live on. How much should he invest in each account to make enough interest while minimizing his risk?
$ __ at 1.5%
$ __ at 8.5% (Round answers to the nearest dollar.)
Answers
The amount invested in the account that pays 1.5% interest is $584,285.71.
The amount invested in the account that pays 8.5% interest is $155,714.29.
How much was invested in each account?The system of equations that represent the information in the question is:
x + y = 740,000 equation 1
0.015x + 0.085y = 22,000 equation 2
Where:
x = amount invested in the certificate of deposity = amount invested in the bondIn order to determine the values, the elimination method would be used.
Multiply equation 1 by 0.015
0.015x + 0.015y = 11,100 equation 3
Subtract equation 3 from equation 2
0.070y = 10,900
Divide both sides of the equation by 0.070
y = 10,900 / 0.07
y = 155,714.29
Subtract 155,714.29 from $740,000
x = 740,000 - 155,714.29
x = 584,285.71
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Suppose you purchased an annuity for $12,083 offering annual income of $1,193 based on a 6.1% interest rate. For how many years would the annuity provide you with payments? Your answer should be expressed in years rounded to the 2nd place to the right of the decimal point
Answers
For 10.75 years I'll receive an amount of $1,193 for an annuity of $12,083.
What is simple interest?Simple interest is often a predetermined percentage of the principle amount borrowed or lent paid or received over a specific time period.
We know simple interest (SI) is given by SI = (p×r×t)/100, where
p = principle, r = rate in percentage, and t = time in years.
A principle of $12,083 with 6.1% interest rate becomes $(12,083×1.061)
= $12,820.063.
∴ The no. of years the annuity provides you with payments of $1,193 is
= (12,820.063/1193).
= 10.75 years Or 10 years 9 months.
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geometry! please help gracias!
Answers
The equation of the conic represents a circle with an area of 36π square units.
What kind of conic does a quadratic equation represent?
In this problem we find the equation of the conic in general form, on which we need to determine what kind of conic it represents. This can be done by finding the standard form of the equation by means of algebra properties, using a strategy known as completing the square. The quadratic equation in general form is described by the quadratic equations of the form:
A · x² + B · y² + C · x + D · y + E · x · y + F = 0
Now we proceed to find the standard form of the equation. First, write the equation in standard form:
x² + y² - 3 · x + 6 · y = 7 · x + 2
x² + y² - 10 · x + 6 · y - 2 = 0
Second, complete the square:
(x² - 10 · x + 25) + (y² + 6 · y + 9) = 2 + 25 + 9
(x - 5)² + (y + 3)² = 36
The standard form of the quadratic equation indicates the equation of a circle with a diameter of 12 units and a center at (h, k) = (5, - 3). The area of the circle is calculated below:
A = 0.25π · D²
Where D is the diameter of the circle, in units.
A = 0.25π · 12²
A = 36π
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Question 6
Drew works for a retail store marking items for sale. The selling price he lists includes the store's cost for the item and which of the following?
Answers
Answer:
I'm not sure exactly me myself
8.) write in standard form a line
perpendicular to
y=-1/3x +2
Passes through (9,-12)
Answers
Answer:
-3x + y = -39
Step-by-step explanation:
If it is perpendicular to y=-1/3x+2, then the slope is positive 3. If it passes through (9, -12), then we can set up our equation:
y+12 / x-9 = 3. Simplifying, we have:
y=3x-39, which in standard form is:
-3x+y= -39
Hope this helps!
It the triangies below are sımılar. It so, state the reason and write the sımılarity statement.
Note: For scale factor, go from top to bottom.
Δ Q R S_____
Similar due to SSS and a scale factor of 3.5. Triangle QRS is similar to triangle TUV.
Similar to due SAS and a scale factor of 0.29. Triangle QRS is similar to triangle TUV.
Similar due to AA. Triangle QRS is similar to triangle VUT.
Similar due to SSS and a scale factor of $0.29$. Triangle QRS is similar to triangle VUT.
Answers
The option 1 "Similar due to SSS and a scale factor of 3.5. Triangle QRS is similar to triangle VUT." is correct.
In the given question, the triangles below are similar.
So, we have to state the reason and write the similarity statement.
ΔQRS≈
(a) Similar due to SSS and a scale factor of 3.5. Triangle QRS is similar to triangle VUT.
(b) Similar to due SAS and a scale factor of 0.29. Triangle QRS is similar to triangle TUV.
(c) Similar due to AA. Triangle QRS is similar to triangle VUT.
(d) Similar due to SSS and a scale factor of $0.29$. Triangle QRS is similar to triangle VUT.
As we know that, the ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor.
Since the both triangle area similar so using the SSS theorem;
Triangle QRS congruence to triangle VUT.
QR/VU = RS/UT = SQ/TV
So QR/VU = 56/16; RS/UT = 70/20; SQ/TV = 98/28
QR/VU = RS/UT = SQ/TV = 3.5
Hence, ΔQRS≈ΔVUT using the SSS theorem with the scale factor of 3.5. So the option 1 "Similar due to SSS and a scale factor of 3.5. Triangle QRS is similar to triangle VUT." is correct.
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Write an equation in slope-intercept form for the linear function that meets these conditions. Don't use decimals in your equation.
Goes through the points (3. -1) and (5, -4).
Answers
The slope intercept form is y= ( -3/2 ) x + 7/2
What is slope ?
A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).
(x1,y1)= (3. -1) and (x2,y2)= (5, -4)
slope intercept form:
y=mx+b , m=slope, b = constant
m= (y2-y1) /( x2-x1) = (-4-(-1)) / ( 5-3) = -3/2
line equation:
y-y1=m(x-x1)
Substitute the values
y-(-1)=( -3/2 ) (x-3)
y+1=( -3/2 ) x + 9/2
y= ( -3/2 ) x + 9/2 - 1
y= ( -3/2 ) x + 7/2
Thus, the slope intercept form is y= ( -3/2 ) x + 7/2
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A right triangle has a leg of 5 feet and a hypotenuse of 8 feet. What is the length of the other leg? Round answer to the nearest tenth place. Question 12 options: 2.6 6.2 4.5 5.4
Answers
Answer:
6.2 ft
Step-by-step explanation:
a² + b² = c²
a² + 5² = 8²
a² = 64 - 25
a² = 39
a = √39
a = 6.2
Answer: 6.2 ft
If y varies directly as xand z, and y=4 when x=6 and z=1, find y when x=7 and z=4
Answers
If y varies directly as x and z, and y=4 when x=6 and z=1, then value of y will be 56/3 when x=7 and z=4.
Define direct proportionality.One kind of proportionality relationship is the direct proportion. When two values are in direct proportion, one value rises when the other rises and vice versa when one value falls. A proportionate relationship is represented by the symbol. When one of the variables is a multiple of the other, there is a direct proportion between the two. For instance, 1 cm equals 10 mm. The multiplier for converting cm to mm is always 10. Petrol prices and foreign exchange rates are determined using a direct proportion.
Given,
We know that y fluctuates in direct proportion to x and z.
We are aware that the form of the equation y = kx for two quantities that are directly proportional is, where k is the proportionality constant.
Because y directly varies as x and z, our equation would be y = kxz
Additionally, it is stated that and y = 4, x = 6 and z = 1. Let's define the proportionality constant as follows:
4 = k × 6 × 1
4 = k ×6
k = 2/3
y = 2/3 × x ×z
Substituting value of x by k = 2/3 , x = 7 and z = 4
y = 2/3 × 7 × 4
y = 56/3
If y varies directly as x and z, and y=4 when x=6 and z=1, then value of y will be 56/3 when x=7 and z=4.
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Find the value of each variable.
Answers
Answer:
Step-by-step explanation:
The sum of exterior angles in a quadrilateral is always 360 degrees.
So, 2x+x+4x+3x=10x=360
Soling for x, we get x=36 degrees.
look at circle m
what is the value of x
Answers
The answer to this Question based on circles is 9
What is circle?
A circle is a two-dimensional geometric shape defined by a set of points equidistant from its center. It is the set of all points in a plane that are the same distance from a given point, called the center. A circle is a special type of ellipse, and all circles are similar. It is one of the most fundamental shapes in geometry, and is used in art, architecture, engineering, and many other disciplines. The circumference of a circle is the length of its perimeter, which is determined by its radius. A circle's area is the space enclosed by its circumference, and is equal to the value of pi multiplied by the square of the radius.
In the given Circle
Lets us denotes the 2 chords by AB and CD and let their intersecting point be E
Then from property of intersecting chords in circle we can write
(AE)(BE) = (CE)(DE)
4x = 36
x = 9
Hence proved
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what number must be added to complete the square in the expression x^2+1.8x
Answers
The number that must be added to complete the square in the expression is 0.9².
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
x² + 1.8x
The complete square is given as,
(a + b)² = a² + 2ab + b²
Now,
x² + 2 x 0.9(x) + 0.9²
(x + 0.9)²
Thus,
0.9² completes the square in the expression.
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what is the best name for this shape? use the drop-down menus to explain your answer
Answers
We can say that the given Quadrilateral is Parallelogram
What is Parallelogram?
A parallelogram is a quadrilateral with two parallel sides (and therefore opposite angles equal). A rhombus is a quadrilateral with equal sides, while a rectangle is a parallelogram with all right angles.
Solution:
Since, the given Quadrilateral has all the opposite angles equal
and we do not know weather the opposite sides are equal or not it is closest to assume that the given Quadrilateral is Parallelogram
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How many x-intercepts does the graph of the function y= 3x^2 - 6x + 5 have?
Answers
(-6)^2-4(3)(5)
=36-60
=-24
Therefore there are 0 X-intercepts
(-3x - 7) + (4x + 7) =
Answers
Answer: x
Step-by-step explanation:
-3x-7+4x+7
than because the 7's cancel each other out it would become
-3x+4x which would be equal to x
Find the value of x in the triangle.
Answers
Answer:
Step-by-step explanation:
180 = x + 50 +50
180 = x + 100
x + 100 = 180
x = 80
80 is the value of x.
PLEASE HELP!!! I will mark BRAINLIST!!!!!!!
Answers
Answer:69.69
Step-by-step explanation:
FIrst add the sides then subtract the top and then mutilpy it by 2
Find the inequality represented by the graph.
Answers
Inequality:
y > 1/3x - 3
Find the volumes of the solids generated by revolving the regions bounded by the graphs of the equations about the given lines. y = x y = 0 x = 6 (a) X-axis (b) y-axis (c) x = 6 (d) x = 9 Find the volumes of the solids generated by revolving the regions bounded by the graphs of the equations about the given lines. y = 3x2 y = 0 x = 3 (a) y-axis (b) x-axis (c) y = 27 (d) X = 3 Find the volumes of the solids generated by revolving the regions bounded by the graphs of the equations about the given lines. y = x2 y = 6x - x2 (a) x-axis (b) y = 10
Answers
Using rule of volume integral , The answer of y=x, y-=0 and x=6 is [tex]216 \pi[/tex].
What do you mean by integration?The process of combining smaller parts into a single, cohesive whole is known as integration.
What do you mean by volume integral?A volume integral is a specific instance of multiple integrals and is used to denote an integral across a 3-dimensional domain in mathematics, notably multivariable calculus. In physics, volume integrals are crucial for many applications, such as calculating flux densities.
area covered by y=x y=0 and x=6 is [tex]\frac {1}{2} * 6 * 6[/tex]
=18 [tex]unit^{2}[/tex]
Perimeter covered by revolving the area about x-axis, y-axis , x=6 and x=9 is [tex]2*\pi *6[/tex]
=[tex]12 \pi[/tex]
Volume = [tex]18 * 12 \pi[/tex]
=[tex]216 \pi unit ^{3}[/tex]
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2. What is the measure of one interior angle of a regular Decagon?
O144
O 180
O216
O 160
Answers
Answer:
the correct answer is 144
Step-by-step explanation:
Hence, the measure of each interior angle is 144∘.
hope this helps
Answer:
Step-by-step explanation:
each exterior angle=360/n=360/10=36°
each interior angle=180-36=144°
Write the equation of the line described below in slope-intercept form.
Find the equation of the line that is perpendicular to the line y=2 x and passes through the point (10,2).
Answers
Equation of the line passes through (10,2) and is perpendicular to the line y = 2x is given by y = -x / 2 + 7.
As given in the question,
Given equation of the line :
y = 2x
Line passes through the point (x₁ , y₁ ) = (10, 2)
Standard form of slope intercept form
y = mx + c
'm' is the slope
slope of the given line 'm₁' = 2
let 'm₂' be the slope of the required line
Multiplication of the Slope of two perpendicular lines is given by :
m₁ × m₂ = -1
⇒2 × m₂ = -1
⇒m₂ = -1/2
Equation of the line perpendicular to the given line and passes through
(x₁ , y₁ ) = (10, 2)
y - y₁ = m₂ ( x - x₁ )
⇒ y - 2 = (-1/2) ( x - 10 )
⇒ y = -x / 2 + 7
Therefore, the required equation of the line in slope intercept form is given by y = -x / 2 + 7 .
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y = ab
a = 5 x 108, b = 9 × 107
Work out the value of y
Give your answer in standard form
Answers
If a right angle is bisected, the resulting angles will always be acute angles.
True
False
Answers
Answer: True.
Step-by-step explanation:
First, a right angle will always be equal to 90 degrees.
Next, bisecting an angle means cutting it into two parts.
Since the resulting two angles will always be less than 90 degrees, they will always be acute angles. The answer to this question is true.
The red strip will be cut into
pieces that are 1/2 foot long. How many pieces will there be?
Answers
15 pieces will there be.
How many pieces will there be?.5 is the same as 1/2, while 7.5 is the same as 7 1/2. To determine how many strips may be cut, use the following expression:
.5x = 7.5
This is due to the fact that the ribbon length that has to be cut is .5 feet, and we are attempting to determine how many pieces of that length might be cut from a roll of ribbon that is 7.5 feet long.
Divide both sides by 2.5 to separate the variable, and that's all there is to it.
7.5/.5 is 15.
x = 15.
Eli is able to slice a ribbon into three pieces that are each .5 feet long.
The complete question is: The red strips that are 1/2 feet long. The roll of ribbon is 7 1/2 feet long. Which expression could be one of the steps in determining how many strips can be cut?
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