The measure of each angles a,b and c are 32°, 74° and 74° respectively.
What is triangle?
Three edges and three vertices define a triangle as a polygon. One of geometry's fundamental shapes is this one. The symbol for an ΔABC triangle is A, B, and C.
Any three points determine a distinct triangle and a distinct plane in Euclidean geometry when they are non-collinear (i.e. a two-dimensional Euclidean space). To put it another way, each triangle is contained in a plane, and there is only one plane that includes that particular triangle. All triangles are contained in one plane if and only if all geometry is the Euclidean plane, however this is no longer true in higher-dimensional Euclidean spaces. Except as otherwise specified, the subject of this article is triangles in Euclidean geometry, more specifically, the Euclidean plane.
Let angle b be x
Therefore angle c will also be x [as given b and c are equal] and angle a will be x - 42°.
Now as we know that the sum of the measures of the angles of a triangle is 180° therefore,
x + x + x - 42° = 180°
=> 3x = 222°
=> x = 74° which is angle b and c
and angle a is (74 - 42)° =32°
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10. Physical Science Ski resorts require large amounts of water in order to make snow. Snowman Ski Area in Colorado plans to pump at least 1120 gallons of water per minute for at least 12 hours a day from Snowman Creek between mid-October and Late December. Environmentalists are concerned about the effects on the ecosystem. Find the minimum amount of water pumped in 30 days. Let y be the total number of gallons pumped x days after pumping begins.
Minimum number of gallons pumped after 30 days = 24,192,000 gallons
Explanations:The minimum amount of water pumped in 1 minute = 1120 gallons
The minimum number of hours used for pumping per day = 12 hours
Number of minutes in 1 hour = 60 minutes
Number of minutes in 12 hours = 12 x 60 = 720 minutes
The minimum amount of water pumped per day = 1120 x 720
The minimum amount of water pumped per day = 806400 gallons
Let the number of days used for pumping be x
Let the total number of gallons pumped x days after pumping begins = y
Since 806400 gallons is pumped per day:
y = 806400x
Minimum number of gallons pumped after 30 days, that is, x = 30
y = 806400 (30)
y = 24,192,000 gallons
Minimum number of gallons pumped after 30 days = 24,192,000 gallons
Hallie collects beanbag animals. She
started her collection eight weeks ago
with six animals. Each week since then,
she has been given two more animals.
How many beanbag animals does she
have now? Please help meeee
Answer:
can i see a ss of the question?
Step-by-step explanation:
HELP!! This is due soon!
From the given quadratic equation, we have that:
The maximum height is of 600 feet.The ball hits the ground after 8.9 seconds.What is the vertex of a quadratic equation?A quadratic equation is modeled by the following rule:
y = ax^2 + bx + c
The vertex has these following coordinates.
[tex](x_v, y_v)[/tex]
In which:
[tex]x_v = -\frac{b}{2a}[/tex][tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]Considering the coefficient a, we have that the vertex can represent either a maximum or a minimum point, as follows::
If a < 0, the vertex is a maximum point.If a > 0, the vertex is a minimum point.For this problem, the function is:
h(t) = -16t² + 160t + 200.
Then the coefficients are:
a = -16, b = 160, c = 200.
And the maximum height, in feet, will be of:
[tex]y_v = -\frac{160^2 - 4(-16)(200)}{4(-16)} = 600[/tex]
When does the ball hits the ground?The ball hits the ground for the positive root when h(t) = 0, hence after 8.9 seconds.
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Please
50 POINTS! BRAINLIEST!
The graphs of the conics intersect at two points.
x² + y² = 4
x^2/4 - y^2/9 =1
What are the coordinates of these points of intersection?
Enter your answer by filling in the boxes.
and
( , ) and ( , )
In linear equation, The co - ordinates of these points of intersection are ( -2,0) ( 2, 0) .
What are a definition and an example of a linear equation?
A linear equation with one variable is one that contains just one variable. It has the formula Ax + B = 0, with A and B being any two real numbers and x being an uncertain variable with only one possible value. One such linear equation in one variable is 9x + 78 = 18.x² + y² = 4 ..........1
x²/4 - y²/9 = 1
⇒ 9x² - 4y² = 36 ..........2
multiply equation (1) is multiply by 9
9 x² + 9y² = 36 ..............3
equation (3) - (2)
13y² = 0
y = 0
put y =0 in equation 1
x² + 0 = 4
x = ± 2
The co - ordinates of these points of intersection are ( -2,0) ( 2, 0) .
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I will give brainliest, like and rating if u solve this right
If ƒ(x) = x³+ 3x² + 4x + 5 and g(x) = 5, then g (ƒ (x)) =_
A) (5x² +15x + 25
B) 5x³+15x²+ 20x + 255
C) 5
D) 225
E) 1125
A pyramid is shown.
The pyramid has a base length of 5 centimeters, an altitude of 8 centimeters, and a lateral edge length of 9 centimeters.
What is the volume of the pyramid?
Select the correct answer. What is the solution to the equation? √3x+3-1=x A. -1 and 2 B. -2 and 1 C. 2 D. 1
Answer:
A
Step-by-step explanation:
[tex]\sqrt{3x+3}=x+1 \\ \\ 3x+3=x^2+2x+1 \\ \\ x^2-x-2=0 \\ \\ (x-2)(x+1)=0 \\ \\ x=-1, 2[/tex]
Upon substituting both of the values back into the original equation, we see they both work.
a table costs five times as much as a chair a trader bought six more chairs than tables and spent $18594. if a chair costs$ 1033 how many chairs and tables did he buy?
An athlete completes a marathon(42.2 km) at a pace of 3 min per km what was her speed in km/hrs? if the world record for marathon is 2 hrs 3 mins 23 sec what pace must an athlete achieve in order to break the world record
Answer:800
Step-by-step explanation:
x + 4x = 1000
5x = 1000
x = 1000/5 = 200 dollars.
Hello I need to find the answer on how to find (-8)(-7)(3)
Answer:
168
Step-by-step explanation:
Hello I need to find the answer on how to find (-8)(-7)(3):
This is asking to find: -8 × -7 × 3 = ?
Because a negative times a negative = positive we have:
56 × 3 = 168
A collection of black cats and crows has a total of 99 heads and legs between them. There
are twice as many crows as there are cats. How many of each is there?
Answer:
Crow=
50×2
100 leg.
cat=
49×4
196 leg.
What value(s) of x in the relation below would create a set of ordered pairs that is not a function? Justify your answer. {(0,5) (1,5) (2, 6) (x, 7)}
First, let's see the points on the coordinate plane:
Now, let's remember that a function has every element of it's domain related with only one element from it's image.
Therefore, x = 2 would create a set of ordered pairs that is not a function. Let's see it in the plane:
As we can see, x = 2 has two values on the image: f(2) = 6 and f(2) = 7, and this never can happen in a function.
Gwen spent $12.50 to purchase 5 bracelets. Each 4.
bracelet costs the same amount. What is the unit rate
for each bracelet?
Answer:
simply divide 12.50 by 5. Therefore each bracelet costs $2.05 : 2$ and 5 cents.
Step-by-step explanation:
The cost of each bracelet will be $2.5.
What is Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
The cost of 5 bracelets = $12.50
Now,
Since, The cost of 5 bracelets = $12.50
So, The cost of 1 bracelets = $12.50 ÷ 5
= $2.5
Thus, The cost of each bracelet will be $2.5.
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Calc Limits. Question Attatched.
The first mistake on the finding on the continuity of the function happened on Step 3, hence option B is correct.
What is the continuity concept?A function f(x) is continuous at x = a if it is defined at x = a, and the lateral limits are equal, that is, if these three conditions are respected:
[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]
To verify the continuity on this problem, the limit was first found at x = 4. Following the standard procedure, replacing each instance of x by 4, an undetermined value of 0/0 is reached. Thus the correct procedure was undertaken, factoring each polynomial in the numerator and in the denominator, then simplifying the common terms and calculating the limit.
However, to calculate the numeric value of the function at x = 4, the simplification cannot be applied, each instance of 4 needs to be replaced.
Replacing each instance of x by 4, the denominator will be of 0, meaning that the function is not defined at x = 4, hence the first mistake was in Step 3 and option B is correct.
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100 points
Identity the triangle congruence postulate (SSS,SAS,ASA,AAS, or HL) that proves the triangles are congruent
In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.
Which postulate establishes the congruence of triangles SSS AAS SAS ASA?
According to the Angle-Side-Angle Postulate (ASA), two triangles are congruent if two angles and the included side of one triangle are congruent with two angles and the included side of another triangle.
Congruence exists between one comparable pair of sides.
Detailed explanation:
If two triangles have three matching angles that are congruent,
The following postulates will be required to demonstrate the congruence of the triangles:
1) AAS ( Angle-Angle-Side ) ( Angle-Angle-Side )
2) ASA ( Angle - Side - Angle) ( Angle - Side - Angle)
Since we require at least one pair of congruent sides in both postulates.
Given that two triangles have three congruent corresponding angles, the extra information that will be utilized to prove their congruence is that "they have one pair of congruent corresponding angles."
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In a promotion for a local
Subway, every 5th customer will
get a free sandwich and every
3rd customer will get a free
drink. Which customer will be
the first person to get a free
sandwich and drink?
Answer:
15th customer
Step-by-step explanation:
to find the answer to this, you have to find the least common multiple(I think that’s what it is called). In this case, in order to find it, you can just multiply 5*3 to get 15 for the answer
HELP ASP ILL GIVE BRAINLIEST AND 50 points
Answer:
1. 12 days
2. more than 200 miles
3. 11 lawns
4. at least 9 hours (about 9.92 hours)
Step-by-step explanation:
1. 20x < 254, so x < 12.7. We need an integer here, so x = 12 days.
2.
[tex]70 + .15x < 50 + .25x[/tex]
[tex]20 < .10x[/tex]
[tex]200 < x[/tex]
[tex]x > 200[/tex]
3. 65x > 699, so x > 10.8. Since fractions of lawns are not accepted here, Mark must mow at least 11 lawns.
4. Assuming that the speed stays constant, 65x = 645, so x = 9.92 hours. The trip will take at least 9 hours, actually close to 10 hours.
Tripping the radius of a cylinder! Someone help me please I'm so confused :(
Before change
Dimensions: r= 2 ; h=7
Lateral Surface area= 2πrh= 28π sqyd
Total Surface area= 2πr(h+r)=4π(9)= 36π sqyd
After change(trippling radius)
Dimensions: r= 6 (3*2); h=7
Lateral Surface area= 2πrh= 84π sqyd
Total Surface area= 2πr(h+r)=12π(13)= 156π sqyd
What is surface area of a cylinder?
The total area that is occupied by the cylinder's curved surface, flat base surfaces, and flat surface is known as the surface area of a cylinder. Two separate components, a curved surface area and two flat surface areas make up the cylinder's overall surface area as the area that is covered by the curved surface of the cylinder and the flat surface of its bases.To learn more about surface area of cylinder, refer:
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a. 5x + 3x b. 9s - 3s + 4s
Answer:
Step-by-step explanation:
A) 5x+3x
5x+3x
= 8x
B) 9s-3s+4s
9s-3s+4s
6s+4s
=10s
Answer the following questions:
pahelp pls
1. Solution of the rational equation [tex]\frac{x}{3} -6=\frac{9}{3}[/tex] is x = 27
How is the equation solved?
[tex]\frac{x}{3} -6=\frac{9}{3}\\\\\frac{x- 18}{3} =\frac{9}{3}\\\\x= 18+9\\\\x= 27[/tex]
2.The two numbers = 2, 6
How to find the two numbers?
Let the two whole numbers = x, y
Given:
x+ y =8 --- (1)
1/x+1/y = 2/3 ---(2)
Considering (2),
[tex]\frac{1}{x} +\frac{1}{y} =\frac{2}{3}\\\\\frac{x+ y}{x y} =\frac{2}{3}\\\\\text{Applying } (1),\\\\\frac{8}{x(8-x)} =\frac{2}{3}\\\\(8x-x^{2} )2 =24\\\\(8x-x^{2} ) =12\\\\x^{2} -8x+12 =0\\\\(x-6) (x-2)= 0\\\\x= 2, 6[/tex]
Substituting x in (1)
We have,
When x = 2 ; y= 6
When x = 6 ; y = 2
So, the two numbers = 2, 6
3. The two numbers = 3, 9
How to find the two numbers?
Let the two whole numbers = x, y
Given:
x- y =6 --- (1)
1/y -1/x = 2/9 ---(2)
Considering (2),
[tex]\frac{x-y}{xy} =\frac{2}{9} \\\\\text{Applying } (1)\\\\\frac{6}{x y} =\frac{2}{9} \\\\x y = 27\\\\(6+y)y = 27\\\\y^{2} +6y-27=0\\\\(y+9) (y-3) = 0\\\\y= 3, -9[/tex]
Since x and y are whole numbers we will have y = 3
When y = 3 ; x=9 (substituting in (1))
So, the two numbers = 9,3
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(9n-4/7z)².
Use the binomial squares pattern to multiply
The multiplication of [tex](9n- \frac{4}{7} z)^{2}[/tex] [tex]=81n^{2} -\frac{72}{7} nz +\frac{16}{49} z^{2}[/tex]
How is the expression [tex](9n- \frac{4}{7} z)^{2}[/tex] solved?
[tex](9n- \frac{4}{7} z)^{2} \\\\=(9n- \frac{4}{7} z) (9n- \frac{4}{7} z)\\\\=81n^{2} -\frac{36}{7} nz -\frac{36}{7} nz +\frac{16}{49} z^{2} \\\\=81n^{2} -\frac{72}{7} nz +\frac{16}{49} z^{2}[/tex]
What is the binomial squares pattern?
The square of a binomial is made up of the first term's square, twice the product of the two terms and the last term's square.This approach is crucial for factoring since it makes factoring polynomials more simpler than with other approaches like the FOIL method, for example.For example : [tex](x+ y)^{2} =x^{2} +2xy+y^{2}[/tex]To learn more about binomial squares pattern , refer:
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Use the sequence below to complete each task. 972, 324, 108, ... a. Identify the common ratio (r). b. Write an equation to represent the sequence. C. Find the 6th term (ac)
(a),
The common ratio between the terms is
[tex]\frac{972}{324}=\frac{324}{108}=3[/tex](b).
The common ratio found in (a) tells us that every next number is found by dividing the previous number by 3; therefore, the equation for a_n the nth term will be
[tex]a_n=\frac{972}{3^n}[/tex](c).
The sixth term will be at n = 6. Putting n = 6 into the equation in (b) gets us
[tex]a_6=\frac{972}{3^6}=\frac{4}{3}[/tex]A triangle is placed in a semicircle with a radius of 4 mm, as shown below. Find the area of the shaded region. Use the value 3.14 for pie and do not round your answer. Be sure to include the correct unit in your answer.
The area of the shaded portion of the diagram is 9.12 mm²
How to find area of a figure?The triangle is inside the semi circle.
The shaded region of the semi circle is outside the triangle.
Therefore,
area of the shaded region = area of the semi circle - area of triangle
Therefore,
area of the semi circle = 1 / 2 πr²
where
r = radiusHence,
r = 4 mm
area of the semi circle = 1 / 2 × 3.14 × 4²
area of the semi circle = 50.24 / 2
area of the semi circle = 25.12 mm²
area of the triangle = 1 / 2 bh
where
b = base h = heightHence,
b = 8mm
h = 4mm
area of the triangle = 1 / 2 × 8 × 4
area of the triangle = 32 / 2
area of the triangle = 16 mm²
Therefore,
area of the shaded region = 25.12 - 16
area of the shaded region = 9.12 mm²
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a. what is the angle of shaded area in degrees b. what percent of circle is shaded.c. what fraction of the circle is shaded
a) The total central angle of a circle is 360 degrees.
Therefore, the angle of the shaded area is,
[tex]360^{\circ}-120^{\circ}=240^{\circ}[/tex]Therefore, the angle of the shaded area is 240 degrees.
b) The percent of the circle shaded is,
[tex]\begin{gathered} \frac{Number}{\text{Total}}\times100=\frac{240}{360}\times100=66.67 \\ \end{gathered}[/tex]Therefore, the percent of the circle shaded is 66.67%.
c) The fraction of the circle shaded is,
[tex]\frac{240}{360}=\frac{2}{3}[/tex]Therefore, the fraction of the circle shaded is 2/3.
Make h the subject of the formula A = 2nrh + 2nr.2
Given:
The formula is
[tex]A=2nrh+2nr^2[/tex]Required:
Make h the subject of the formula.
Explanation:
We will put formula in terms of h as:
[tex]\begin{gathered} A=2nrh+2nr^2 \\ A-2nr^2=2nrh \\ h=\frac{A-2nr^2}{2nr} \end{gathered}[/tex]Answer:
Hence, above is the answer.
Your test in math class has problems with 2 points (x) and problems worth 4 points (y). Altogether, the test has 100 points. Write an equation that represents the total points on the test, including the 2-point and 4-point problems.
____________x + _____________y = ___________(total points)
If you answer 30 2-point questions and 8 4-point questions correctly, what will your score be?
The equation that represents the total points on the test, including the 2-point and 4-point problems is 2x + 4y = 100
How to illustrate the equation?From the information, the test in math class has problems with 2 points (x) and problems worth 4 points (y) and the test has 100 points. The equation to illustrate this will be:
2x + 4y = 100
When one answers 30 2-point questions and 8 4-point questions correctly, the score will be:
= 2x + 4y
= 2(30) + 4(8)
= 60 + 32
= 92
The score is 92 points.
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Quadrilateral IJKL with vertices I( 5,2 ), J( 9,5), K( 5,-2 ), and L( 2,-3 ) : Reflect in the line x=1. What are the coordinates of J’?
The Solution:
Given that the vertices of a quadrilateral are:
[tex]I(5,2),J(9,5),K(5,-2)\text{ and L(2,-3)}[/tex]We are required to find the coordinate of J' when J(9,5) is reflected in the line x=1.
The new x-coordinate will become:
[tex]x=1-9=-8[/tex]So, the required coordinate of J' is:
[tex](-8,5)[/tex]Therefore, the correct answer is J'(-8,5)
Find a polynomial f(x) of degree 4 that has the following zeros.
1, -4, 0, 6
Leave your answer in factored form.
ƒ(x) = 0
X
A polynomial of degree 4 in factored form with zeros 1, -4, 0, and 6 is
f(x) = x(x - 1)(x + 4)(x - 6).
What are polynomials?An algebraic expression known as a polynomial requires that all of its exponents be whole numbers.Any polynomial must have variable exponents that are non-negative integers. The degree of a polynomial is the highest or biggest exponent of the variable in the polynomial.Given:
x₁ = 1
x₂ = -4
x₃ = 0
x₄ = 6
Utilize the fact that x - b is a factor of the polynomial if b is a root.
Simply take each zero, modify its sign, and add an x in front of it to obtain the four factors.
The polynomial is,
f(x) = (x - x₁)(x - x₂)(x - x₃)(x - x₄)
f(x) = (x - 1)(x - (-4))(x - 0)(x - 6)
= (x - 1)(x + 4(x)(x - 6)
Therefore,a 4 degree polynomial in factored form with zeros 1, -4, 0,and 6 is x(x - 1)(x + 4)(x - 6).
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Your sister is planning her wedding reception. She can have round tables that sit 8 people and rectangular tables that sit 10 people. She plans on having 200 people at the reception altogether. Write an equation that represents the possible tables that may be used to seat 200 people at the wedding.
What are two possible combinations of table types that your sister can use at
her wedding reception? Show your calculations to prove that your amounts are
viable answers to the question.
The equation that represents the possible tables that may be used to seat 200 people at the wedding is 8x + 10y = 200.
The combination will be 10 round tables and 12 rectangular tables; 15 round tables and 8 rectangular tables.
How to illustrate the information?Based on the information, there can be round tables that sit 8 people and rectangular tables that sit 10 people and the total number will be 200.
Therefore, the equation that represents the possible tables is 8x + 10y = 200
where x = number of round table
y = number of rectangular tables
The possible combinations of table types that your sister can use at her wedding reception will be 10 round tables and 12 rectangular tables. This will be:
8x + 10y = 8(10) + 10(12) = 200
Another combination will be 15 round tables and 8 rectangular tables
8x + 10y = 8(15) + 10(8) = 200
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A 35 foot ladder is set against the side of a house so that it reaches up 21 feet. If Elijah
grabs the ladder at its base and pulls it 4 feet farther from the house, how far up the
side of the house will the ladder reach now? (The answer is not 17 ft.) Round to the
nearest tenth
Answer:
14.2 feet
Step-by-step explanation:
Use the Pythagorean Theorem to solve both parts.
Part 1.
35 is the hypotenuse and 21 is a leg.
[tex]a^{2} +b^{2} =c^{2} \\a^{2} +21^{2} =35^2\\a^2 + 441 = 1225\\a^2 +441-441=1225-441\\a^2 =784\\\sqrt{a^2} =\sqrt{784} \\a = 28 feet[/tex]
28 feet represents how far the base of the ladder is from the house.
Part 2.
Now move the ladder 4 feet farther from the house. 28 + 4 = 32 ft.
Now you have a leg that is 32 feet and the hypotenuse is still 35 feet. Solve for the other leg.
[tex]a^{2} +b^{2} =c^{2} \\a^{2} +32^{2} =35^2\\a^2 + 1024 = 1225\\a^2 +1024-1024=1225-1024\\a^2 =201\\\sqrt{a^2} =\sqrt{201} \\a = 14.177 feet[/tex]
Round to the nearest tenth and you have 14.2 feet
What is the cost of equity using the capital asset pricing model if the risk free rate is 4.5%, the beta is 1.75 and the equity risk premium is 4.25%?
Review Later
9.00%
8.75%
11.94%
12.13%
[tex]11.9375\%[/tex] is the cost of equity using the capital asset pricing model if the risk free rate is 4.5%, the beta is 1.75 and the equity risk premium is 4.25%.
In the given question we have to find the cost of equity using the capital asset pricing model if the risk free rate is 4.5%, the beta is 1.75 and the equity risk premium is 4.25%.
Firstly we learn about terms used in this question,
The return needed by either a business or an individual to justify an investment in equity is known as the cost of equity.
The relationship between systemic risk, or the general dangers of investing, and expected return for assets, particularly equities, is described by the Capital Asset Pricing Model.
Since we have to find the cost of equity using the capital asset pricing model. So the formula is
Cost of equity = Risk free rate + Beta * Equity Risk Premium
Risk free rate = 4.5%
Beta = 1.75
Equity Risk Premium = 4.25%
Now putting the value in the formula
Cost of equity [tex]=4.5\%+1.75\times4.25\%[/tex]
Simplifying
Cost of equity [tex]=4.5\%+7.4375\%[/tex]
Cost of equity [tex]=11.9375\%[/tex]
Hence, [tex]11.9375\%[/tex] is the cost of equity using the capital asset pricing model if the risk free rate is 4.5%, the beta is 1.75 and the equity risk premium is 4.25%.
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