We can say that if the measure of angle 1 = (7x-19), and the measure of angle 2 = (x+5), then the measure of angle 2 is 18°.
Define supplementary angle.
Supplementary angles are those two angles whose sum is always equal to 180 degrees.
Mathematically, a supplementary angle is calculated as follows:
Q + R = 180
Since the angles on this line segment are supplementary angles, we have:
Angle (1) + Angle (2) = 180° - Angle 3
Substituting the given values into the formula, we get;
7x - 19 + x + 5 = 180 - 90
8x - 14 = 90
8x = 90 + 14
8x = 104
x = 104/8
x = 13
Now, we can calculate the length of angle 2 by putting the 'x' value:
Angle 2 = x + 5
Angle 2 = 13 + 5
Angle 2 = 18°
If you need to learn more about angle click here;
https://brainly.com/question/25716982
#SPJ4
Points!!!!!!!!!!!!!!!!
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
d. Find the geometric mean of the term from part (c) and the first term of your sequence. What term of the sequence have you just found?
The geometric mean can be determined by multiplying the terms from part c and the first term of the sequence from part a and taking their square root.
The first term of the sequence from part a is 2 and the term from part c is 512.
Geometric mean of a sequence is the average value of a set of numbers, determined by multiplying the terms together and taking their root.
In general form, the geometric mean for a n number of terms is n√x1*x2*x3*…*xn
Since there are two terms 2 and 512, we will take the square root of the product.
Geometric mean=√2*512=√1024=32
For the geometric sequence as it is the mean, the term will be the 2nd term of the sequence
Hence, the geometric mean of the two chosen positive number 2 and 512 is 32 which is the 2nd term.
Learn more about geometric mean:
https://brainly.com/question/2292573
#SPJ4
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.
Find out more on equation at: https://brainly.com/question/13763238
#SPJ1
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
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.
To learn more about functions, refer to;
https://brainly.com/question/11624077
#SPJ4
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.
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.
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!
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.
If you want to learn more about linear equations:
https://brainly.com/question/1884491
#SPJ1
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
Learn more about sum of a series here:
https://brainly.com/question/12753365
#SPJ4
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.
To know more about an expression follow;
brainly.com/question/19876186
#SPJ2
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.
Learn more bout Distance formula here https://brainly.com/question/14348586
#SPJ4
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}
The sum of an infinite geometric series is twice its first term.
a. A student says the common ratio of the series is 3/2 . What is the student's error?
The student's error is that the common ratio would not be equal to 3/2.
What is Common Ratio:
The general form of representing a geometric progression is a1, (a1r), (a1r2), (a1r3), (a1r4) ,... where a1 is the first term of GP, a1r is the second term of GP, and r is the common ratio.
Common Ratio Formula:
Common ratio,
r =a n / a n−1
where,
an is the nth term of the geometric progression.
an−1 is the (n - 1)t h term of the geometric progression.
Now,
[tex]S_{infinity} = 2a_{1} \\\\= a_{1} / 1-r\\\\2a_{1} = a_{1} / 1-r\\\\= 1-r = 1/ 2\\\\r = 1/2 - 1\\\\r = 1/2[/tex]
To know more about "Common Ratio"
Refer this link:
https://brainly.com/question/1509142
#SPJ4
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
To learn more about equation visit , https://brainly.com/question/10413253
#SPJ9
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!
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 + 6.5
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.
Know more about a Quadrilateral here:
https://brainly.com/question/16691874
#SPJ4
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
to learn more about equations visit:
https://brainly.com/question/23752439
#SPJ1
how to show - 2by3 and 1by2 on the number line
Answer: Hope it help
Step-by-step explanation:
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.
To learn more about infinite geometric series, refer to:
brainly.com/question/27350852
#SPJ4
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:
https://brainly.com/question/12088221
#SPJ4
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 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.
Know more about expressions here:
https://brainly.com/question/723406
#SPJ1
The complete question is given below:
If h = -7, the expression has a value of _.
39(2) + 3h = x
In 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.
Learn more about the equation of a line having 2 points:
brainly.com/question/12851029
brainly.com/question/19496333
#SPJ1
Why is a simulation better the more times you perform it?
Answer:
Step-by-step explanation:
so you get a better perspective of it
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?
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]
