When you are given two sides but no measurement of the angle, such as a = 15 and b = 15, we can create an infinite number of triangles.
For instance:
How many different triangles can be made if we have side lengths of 15 and 15 and an angle value of 0 to 360 degrees?
Using a protractor, make one of the triangles with sides of 25 metres and 21 metres, an angle of 12 degrees, and a third side that can be changed to your preferred length. You've constructed a triangle.
Similar to this, we can create a completely different triangle by varying the third side's length and angle measurement.
It's crucial to remember that you select the side lengths and angle. This implies that you might choose differently. You may create an infinite number of distinct triangles by using the same angles.
As a result, we can make an infinite number of triangles using just one angle and one side length.
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If h = -7, the expression has a value of _.
The value of the given expression will be 57 if the value of h = -7.
What are expressions?An expression in mathematics is a combination of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) Expressions and phrases are similar in structure. In language, a phrase may include an action on its own, but it does not constitute a complete sentence.So, let the value of expression be 'x'.
SUbstitute h = -7 in the expression as follows:
39(2) + 3h = x39(2) + 3(-7) = x78 + (-21) = x78 - 21 = x57 = xTherefore, the value of the given expression will be 57 if the value of h = -7.
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The complete question is given below:
If h = -7, the expression has a value of _.
39(2) + 3h = x
Please Help with problem 23 Algebra 1, in the attachment.
Answer:
Step-by-step explanation:
the correct answer would be -5/-1=|6x|
The absolute value equation for each of the graphs are |x + 3| = 2 and |x - 4| = 1 respectively.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
An inequality shows the non equal comparison of numbers and variables.
A) For the inequality shown, the midpoint is [(-1) + (-5)]/2 = -3. The distance from each of the endpoint to the midpoint is 2 units (i.e. from -1 to -3 or from -5 to -3). Hence:
Absolute inequality is:
|x - midpoint| = distance from endpoint to midpoint
This gives:
|x - (-3)| = 2
|x + 3| = 2
B) For the inequality shown, the midpoint is [3 + 5]/2 = 4. The distance from each of the endpoint to the midpoint is 1 units (i.e. from 3 to 4 or from 5 to 4). Hence:
Absolute inequality is:
|x - midpoint| = distance from endpoint to midpoint
This gives:
|x - 4| = 1
The absolute value equation for each of the graphs are |x + 3| = 2 and |x - 4| = 1 respectively.
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MARKING BRAINIEST!!!!!!
Answer: Side lengths: 7.2, 7.2[tex]\sqrt{3}[/tex], 14.4
Step-by-step explanation:
Take sin of 60 to calculate side opposite to angle 60
sin 60=[tex]\frac{\sqrt{3} }{2}[/tex]
cos 60=1/2
7.2 / 1/2=
7.2 * 2=14.4
[tex]\frac{\sqrt{3} }{2}[/tex]*14.4=
[tex]\frac{14.4\sqrt{3} }{2}[/tex]=7.2[tex]\sqrt{3}[/tex]
The hypotenuse:
[tex](\frac{\sqrt{3} }{2})^2[/tex]+(1/2)^2=
3/4 + 1/4 = 1
1 * 14.4 =14.4
Side lengths: 7.2, 7.2[tex]\sqrt{3}[/tex], 14.4
Step-by-step explanation:
The 30-60-90 triangle is one of the most important trigonometry concept you will learn throughout your secondary schooling.
Attached below is a triangle that you should memorize for easy practice. The way this triangle is formed can be proven trigonometrically and/or with the unit circle, but that's not what this question is asking for.
When comparing the numbers on the attachment and your question, we can generate that the side 7.2=x, because the side with the 60 degree angle and right angle contains the variable x.
Since we have x now, all we would have to do is to plug in the x values and solve the question.
The hypotenuse (longest side of the triangle) = 2x = 2(7.2) = 14.4
The side opposite to the 60 degree angle (left most side)= [tex]x\sqrt{3}[/tex] = [tex]7.2\sqrt{3}[/tex] = 12.6
I hope this helped!
Find the distance from the line to the given point.
y=-3,(5,2)
The distance from the line y = -3 to the point (5,2) is 5 units.
Distance from the line ax+by+c=0 from the point (m,n) is calculated by
[tex]distance=\frac{|am+bn+c|}{\sqrt{a^{2} +b^{2} } }[/tex]
In the given question
the equation of the line is [tex]y=-3[/tex] ⇒ [tex]y+3=0[/tex]
equation of line becomes 0.x+1.y+3=0
given the point (5,2)
Substituting the values in the distance formula we get
[tex]d=\frac{0*5+1*2+3}{\sqrt{0^{2} +1^{2} } }[/tex]
[tex]=\frac{2+3}{1} \\ \\ =\frac{5}{1} \\ \\ =5[/tex]
Therefore , the distance from the line y = -3 to the point (5,2) is 5 units.
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Ab and bc form a right angle at their point of intersection, b. if the coordinates of a and b are (14, -1) and (2, 1), respectively, the y-intercept of ab is is y= and the equation of bc
Answer:
Step-by-step explanation:
to find the y intercept of AB, first find the slope of AB: m=(1-(-1))/(2-14)=-1/6
the equation of line AB is y=-(1/6)x+b
use either of the given two points to find out b: 1=(-1/6)*2+b => b=4/3
BC is perpendicular to AB, so the slope of BC is the negative reciprocal of the slope of AB, therefore, the slope of BC is 6
Equation of BC is y=6x+b
find out b by using the coordinates of point B: 1=6*2+b => b=-11
the equation of BC is: y=6x-11
the x coordinate of point C: 13=6*x -11 =>x=4
Determine whether the event is independent or dependent. Then find the probability.
There are 6 green, 2 red, 2 brown, 4 navy, and 2 purple marbles in a hat. Sadie picks 2 marbles from the hat without replacement. What is the probability that the first marble is brown and the second marble is not purple?
Answer:
Dependent
18.46%
Step-by-step explanation:
All possible combinations for Sadie taking two marbles out from the hat:
[tex](6+2+2+4+2)×[(6+2+2+4+2)-1] [/tex]
[tex] = 16 \times 15[/tex]
[tex] = 240[/tex]
All the possible combinations that the first marble is brown and the second marble is not purple:
[tex]2 \times (6 + 2 + 1 + 4)[/tex]
[tex] = 2 \times 13[/tex]
[tex] = 26[/tex]
The probability:
[tex] \frac{240}{26} \times 100\%[/tex]
[tex] = \frac{240}{13} \times 50\%[/tex]
[tex] = \frac{1200}{13} \%[/tex]
[tex]≈18.46%[/tex]
Write an explicit formula for each sequence. 4,1.5,-1,-3.5, . . . . .
I think the answer is -2.5n + 6.5.
How to work it out:
Look at how much it goes down by (since it's going down, put a negative sign)Find out the "0th term". In this case, you would add 2.5 to 4 to find out the 0th term.If the "0th term" is positive, put + … and if its negative, put - …So I think the answer is -2.5n + 6.5In 2011, Tyson foods had sales of $32.266 billion, and in 2012, sales were $33.278 billion. Write a linear equation giving the sales y in terms of the year x. Then use the equation to predict the sales for 2013.
Considering the expression of a line and how to obtain it having 2 points, you obtain:
the linear equation giving the sales y in terms of the year x is y=1.012x - 2002.866the sales in 2013 will be $34.29 billion.Linear equation o lineA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Knowing two points (x1, y1) and (x2, y2) of a line, the slope m of said line can be calculated using the following expression:
m= (y2 - y1)÷ (x2 - x1)
Substituting the value of the slope m and the value of one of the points in the expression of a linear equation, y = mx + b, the value of the ordinate to the origin b can be obtained.
Linear equation in this caseIn this case, you want to obtaina linear equation giving the sales y in terms of the year x. You know:
In 2011, Tyson foods had sales of $32.266 billion.In 2012, sales were $33.278 billion.So, being (x1,y1)= (2011, 32.266) and (x2,y2)= (2012, 33.278), the slope m can be calculated as:
m= (33.278 - 32.266)÷ (2012 - 2011)
Solving:
m=1.012
Considering point 1 and the slope m, you obtain:
32.266= 1.012×2011 + b
32.266= 2035.132 + b
32.266- 2035.132= b
- 2002.866= b
Finally, the linear equation giving the sales y in terms of the year x is y=1.012x - 2002.866
You can use the equation to predict the sales for 2013 as follow:
y=1.012×2013 - 2002.866
Solving:
y=1.012×2013 - 2002.866
y= $34.29 billion
Finally, the sales in 2013 will be $34.29 billion.
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Evaluate the infinite geometric series 2/5 +4/25 + 8/125 + . . . . Enter your answer as a fraction.
An infinite geometric series is the outcome of an unlimited geometric sequence.
The infinite geometric series be 2/5 +4/25 + 8/125 + . . . . then the sum of the infinite geometric series is 2/3.
What is an infinite geometric series?
An infinite geometric series is the outcome of an unlimited geometric sequence. This series wouldn't have a finish. It is possible to calculate the sum of all finite geometric series. The terms in the sequence will grow steadily larger, but adding the larger numbers together will not provide a solution if the common ratio of an infinite geometric series is greater than one.
Given:
a(first term) = 2/5
r(common difference) = 2/5
Since, |r| < 1 the infinite series converges.
[tex]S_\infty[/tex] = a/1-r ; -1 < r < 1
[tex]S_\infty[/tex] = (2/5)/(1-2/5)
simplifying the above equation, we get
[tex]S_\infty[/tex] = (2/5)/(3/5) = 2/3
The sum of the infinite geometric series is 2/3.
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Mr. Drew wants to build a square sandbox with an area of 81 square feet. What is the total length of wood Mr. Drew needs to make the sides of the sandbox?
Answer: 36 feet of wood
Step-by-step explanation:
P=perimeter. P=total length of wood
s= side length. A=area
A=s^2
81=s^2
s^2=9^2
s=9
P=4s
P=4(9)
P=36 feet of wood
Answer:
P = 36 ft
Step-by-step explanation:
The given length is,
→ a = ?
Formula we use,
→ A = a²
Now the length of one side is,
→ A = a²
→ a² = 81
→ a = √81
→ [ a = 9 ]
The total length of wood needed is,
→ P = 4a
→ P = 4 × 9
→ [ P = 36 ]
Hence, the total length is 36 ft.
how to show - 2by3 and 1by2 on the number line
Answer: Hope it help
Step-by-step explanation:
Points!!!!!!!!!!!!!!!!
The equation of a line is ax + by = c. If the x value of some point on the line is d, what is the full co-ordinate of the point, in terms of a, b, c, d?
The equation of a line is ax + by = c.
full co-ordinate of the point, in terms of a, b, c, d is (d,(c-ad)/b)
equation of a line is ax + by = c
x=d
put x=d in the equation of line
ad + by = c
by = c-ad
y=(c-ad)/b
full co-ordinate of the point, in terms of a, b, c, d is (d,(c-ad)/b)
The phrase equation and its cognates in other languages can also have subtly extraordinary meanings; as an example, in French an équation is described as containing one or more variables, even as in English, any well-shaped components together with two expressions related with an equals sign is an equation.
fixing an equation containing variables includes figuring out which values of the variables make the equality real.
The variables for which the equation must be solved are also referred to as unknowns, and the values of the unknowns that satisfy the equality are referred to as answers of the equation.
There are two kinds of equations: identities and conditional equations. An identity is authentic for all values of the variables. A conditional equation is simplest genuine for particular values of the variables
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Write an example from daily life that uses each type of real number.
rational numbers
Write an example from daily life that uses rational numbers .
Real numbers that may be expressed as p/q, where p, q are integers, and q 0, are rational numbers. The money we have is a rational number. If we spend some sum out of it, it is subtraction of rational number.The running race involves rational numbers if you're an athlete.Rational numbers include the following:the distance runthe time needed to complete the distance,the number of competitors placing first, second, or thirdthe number of heartbeats you take per minute.We use fractions to represent taxes.If you split a pizza or any other food.When you finish a piece of your work, you indicate that you have done half, or 50%.Loan and mortgage interest rates.Savings account interest.To learn more about rational numbers, refer:
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Why is a simulation better the more times you perform it?
Answer:
Step-by-step explanation:
so you get a better perspective of it
K(6, 7) and L(4, 5) are the endpoints of a line segment. What is the midpoint M of that line
segment?
Write the coordinates as decimals or integers.
M =
Answer: M = (5, 6)
Formula for midpoint:
[tex]\sf (x_m, y_m) = \left(\dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2}\right)[/tex]
Here given:
[tex](x_1,y_1) = (6,7), \ (x_2, y_2) = (4,5)[/tex]Find midpoint M by substituting values:
[tex]\sf M = \left(\dfrac{6+4}{2}, \dfrac{7+5}{2}\right)[/tex]
[tex]\sf M = \left(\dfrac{10}{2}, \dfrac{12}{2}\right)[/tex]
[tex]\sf M = \left(5, 6\right)[/tex]
Given:-
Two points K(6,7) and L(4,5) . These points are endpoints of a line segment .To find:-
The midpoint of the line segment.Answer:-
Here we are interested in finding the midpoint of a line segment whose endpoints are given to us . Say if a line segment has endpoints [tex](x_1,y_1) [/tex] and [tex](x_2,y_2)[/tex] , then the midpoint of the line is given by ,
[tex]\implies Midpoint= \bigg(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\bigg) \\[/tex]
And here , we have;
[tex] x_1 = 6[/tex] [tex] x_2 = 4 [/tex][tex] y_1 = 7 [/tex][tex] y_2 = 5 [/tex]So on substituting the respective values, we have;
[tex]\implies (x_m , y_m ) =\bigg(\dfrac{ 6+4}{2},\dfrac{7+5}{2}\bigg) \\[/tex]
[tex]\implies (x_m , y_m ) =\bigg( \dfrac{10}{2} , \dfrac{12}{2}\bigg) \\[/tex]
[tex]\implies\underline{\underline{ (x_m , y_m ) = (5,6)}}\\[/tex]
Hence the midpoint is (5,6) .
and we are done!
A restaurant has 10 booths that will seat up to 4 people each. If 20 people are seated in booths, and NO booths are empty, what is the greatest possible number of booths that could be filled with 4 people?
Answer: 3
Step-by-step explanation:
mr. andrson is ordering pizzas for a class pizza party. pizza place has a special where he can buy 3 large pizzas for $18.75. at mario's pizzeria, he can buy 4 large pizzas for $22. if he needs to buy 12 pizzas, how much will he save if he buys the pizzas from mario's pizzeria instead of pizza place?
In the stained glass window design, all of the small arcs around the circle are congruent. Suppose the center of the circle is point O .
What is the measure of each of the small arcs?
The measure of each of the small arcs of the circled glass stained window is 45°.
Congruent in circle:
Circles having the same radii are said to be congruent of one another.
For example,
When two circles are congruent, we can also say that they have the same area and circumference. Thus they can also be said to be equal circles.
Given,
In the stained glass window design, all of the small arcs around the circle are congruent. Suppose the center of the circle is point O.
Here we need to find the measure of each of the small arcs.
We know that.
Congruent circles can be defined as circles which are having the same or equal radii.
So, based on this the circle we need to divided it as equal radius arcs.
We know that, the measurement of the full circle is 360°.
So, here we have to divide it by 8.
Then we have each arc as,
=> 360°/8
=> 45°.
Therefore, each arc has the measurement of 45°.
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Expand these brackets:
3(5 + b) =
2(3f + 5) =
Answer:
15+3b
6f+10
Step-by-step explanation:
Those are your answers
Answer:
15 + 3b
6f + 10
Step-by-step explanation:
Distributive property: a*(b +c) = (a*b) + a*c)Multiply 3 with 5 and multiply 3 with b and then add the results of the multiplication.
3*(5 + b) = (3*5) + (3*b)
= 15 + 3b
2*(3f + 5) = (2*3f) + (2*5)
= 6f + 10
Five times the sum of x and 5 is 8 less than twice x. Solve for x.
Answer: x=-11
Step-by-step explanation:
5(x+5)=2x-8
5x+25=2x-8
5x+25-25=2x-8-25
5x=2x-33
3x=-33
x=-11
The value of x in the given expression is -11.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that; Five times the sum of x and 5 is 8 less than twice x.
WE are asked to Solve for x.
Then the expression form as;
5(x+5)=2x-8
Now solve for x;
5x+25=2x-8
Subtract 25 on both sides;
5x+25-25=2x-8-25
5x=2x-33
3x=-33
x=-11
Therefore, the value of x in the given expression is -11.
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Quadrilateral PQRS was dilated to form quadrilateral WXYZ.
a. Is the dilation from P Q R S to W X Y Z an enlargement or reduction?
A reduction is a dilation from ▢PQRS to ▢WXYZ.
What do we mean by a Quadrilateral?A quadrilateral is a four-sided polygon with four edges (sides) and four corners in geometry (vertices). The word comes from the Latin words Quadri, a variant of four, and latus, which means "side." In analogy to other polygons, it is also known as a tetragon, which is derived from the Greek words "tetra" which means "four" and "gon" which means "corner" or "angle" (e.g. pentagon). Because "gon" means "angle," it is also known as a quadrangle or 4-angle. ▢ABCD denotes a quadrilateral with the vertices A, B, C, and D.According to the given figure:
▢WXYZ is smaller than ▢PQRS.Therefore, a reduction is a dilation from ▢PQRS to ▢WXYZ.
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a businessman earns a basic salary of r1000 plus r500 commission for every item he sells
5.1write a function for calculaling the salesman's salary (y) if he sells x items
The Salesman's salary is modeled by the linear equation:
y = $1000 + $500*x
How to write a function for the salesman's salary?We know that the businessman earns a basic salary of $1000 (it does not depend on how many items he sells) and $500 for each item he sells as a commission.
Then, if we define x as the number of items he sells, the amount he gets in commissions is: x*$500
Then the equation for his total salary, y, in terms of x which is defined above is:
y = $1000 + $500*x
That is the linear equation we wanted to write.
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The probabilities of four events are shown. List them in order from least to greatest.6/13,3 out of 9,41%,0.2
Answer:
0.2, 3 out of 9, 41%, 6/13
Step-by-step explanation:
6/13 = 0.46
3 out of 9 = 3/9 = 0.33
41% = 0.41 (change percent to decimal by dividing it by 100)
0.2
Now compare:
Least to greatest: 0.2, 3 out of 9, 41%, 6/13
If x is a real number, for what values of x is the equation (3 x-6)(x-2)⁻¹=3 true?
Answer:
all real x other than 2
Step-by-step explanation:
[tex]\frac{3x-6}{x-2}=3 \\ \\ 3x-6=3x-6[/tex]
Thus, the equation is true for all x in its domain, which is all real x other than 2.
x + 2y = 15
3x -15 = -6y
can you also right if it has a solution/no solution/many solution!
and show the steps pls tyy
Given equation x + 2y = 15 and 3x -15 = -6y are real numbers so the equation has a solution.
Some equations have no solutions. In these equations, there is no value for the variable that makes the equation true. You can tell that an equation has no solutions if you try to solve the equation and get a false statement.
We have been given that
x + 2y = 15 ..........(1)
3x -15 = -6y ..........(2)
Multiply equation (1) with 3.
3(2y+x)=5
6y+3x=-15
Subtract equation (1) from equation (2)
0=15
Instead of 6y+3x=-15, 3x-15=-6y becomes 6y+3x=15. So, these 2 equations are saying the same thing (this is the first equation times 3), and therefore the solution is all real numbers.
Hence, The equation has a solution since the given values of x + 2y = 15 and 3x -15 = -6y are real numbers.
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State which are relations. Give their domain and range. Then tell if the relation is also a function. NUMBER 8
Answer:
Not a function; D: {2, 9}; R: {8, 4, 7}
Glenn is shopping for school clothes. He plans to get one of each of the same shirt in five different colors and three
pairs of the same pant each in a different color. The total cost for his clothes is $190 before tax.
The equation which describes this situation in terms of the cost of each shirt (x) and the cost of each pair of pants (y)
is
The equation which describes this situation in terms of the cost of each shirt (x) and the cost of each pair of pants (y) is, 5x+3y=190
What is Equation?Equation: There are numerous ways in which one may define an equation. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an ‘equal’ sign. The most basic and simple algebraic equations consist of one or more variables in math.
Glenn is shopping for school clothes
Number of shirts Glenn want to buy= He plans to get one of each of the same shirt in five different colors which is equal to 5
x is the cost of each shirt
that means cost of 5 shirts = 5x
Number of pair of pants he want to buy= three pairs of the same pant each in a different color which is equal to 3
y is the cost of each pair of pants
that means the cost of three pair of pants = 3y
The total cost for his clothes is $190
The equation which describes this situation in terms of the cost of each shirt (x) and the cost of each pair of pants (y) is, 5x+3y=190
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A function g satisfies g(5) = 3 and g(3) = 0, and a function h satisfies h(3) = -2 and h(0) = 5. what is the value of h(g(3))?.
A function exists described as a relation between a set of inputs containing one output each. The value of h(g(3)) is 5.
What is meant by function?
A relationship between a group of inputs and one output is referred to as a function.
In plain English, a function is an association between inputs in which each input is connected to precisely one output.
A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.
Where, g(3) = 0
To get h, replace g(3) with 0 in the requested equation (0).
Since h(0) = 5 according to the question, your final response is 5.
Therefore, the value of h(g(3)) is 5.
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Each sequence has eight terms. Evaluate each related series. 5,13,21, . . . . . . , 61
The sum of the 8 terms of a series 5,13,21, . . , 61 is 264
The given series is:
5,13,21, . . . . . . , 61
Notice that this is an arithmetic series with:
first term, a(1) = 5
number of terns, n = 8
common difference, d = a(2) - a(1) = 13 - 5 = 8
last term, a(8) = 61
The sum of the first n terms in an arithmetic series is given by the formula:
S(n) = n/2 [a(1) +a(n)
Substitute n = 8, a(1) = 5, a(n) = 61:
S(8) = 8/2 (5 + 61)
= 4 . 66
= 264
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