Answers
Answer:
[tex]\large\boxed{\tt x = 23^{\circ}}[/tex]
Step-by-step explanation:
[tex]\textsf{We are given 2 \underline{Linear Pairs}. We are asked to form an equation, and to solve for x.}[/tex]
[tex]\large\underline{\textsf{What are Linear Pairs?}}[/tex]
[tex]\textsf{Linear Pairs are 2 Adjacent Angles that form a 180}^{\circ} \ \textsf{angle, or add up to 180}^{\circ}.[/tex]
[tex]\textsf{For our problem, these 2 angles given to us are Linear Pairs, which equal 180}^{\circ}[/tex]
[tex]\textsf{when added together. Let's create an equation to find x.}[/tex]
[tex]\large\boxed{\tt 180^{\circ}=93^{\circ} + (3x+18)^{\circ}}[/tex]
[tex]\textsf{Now, let's solve for x by using the \underline{Properties of Equality}.}[/tex]
[tex]\large\underline{\textsf{What are the Properties of Equality?}}[/tex]
[tex]\textsf{The Properties of Equality are Properties that allow us to manipulate equations.}[/tex]
[tex]\textsf{There are 9 properties of equality that we can use, each allowing us to simplify}[/tex]
[tex]\textsf{one side of an equation. These properties are mainly used to find missing variables.}[/tex]
[tex]\textsf{Let's solve for x by using the Properties of Equality.}[/tex]
[tex]\large\underline{\textsf{Solving for x;}}[/tex]
[tex]\tt 180^{\circ} = 93^{\circ} + 3x^{\circ}+18^{\circ}.[/tex]
[tex]\textsf{Let's first Combine Like Terms.}[/tex]
[tex]\tt 180^{\circ} = \boxed{\tt 93^{\circ}} + 3x^{\circ}+\boxed{\tt 18^{\circ}}[/tex]
[tex]\tt 180^{\circ} = 111^{\circ} + 3x^{\circ}[/tex]
[tex]\textsf{Now, let's use the Subtraction Property of Equality which states that if 2 same}[/tex]
[tex]\textsf{numbers are subtracted from both sides of the equation, then both expressions}[/tex]
[tex]\textsf{still equal each other. Let's subtract 111 from both sides of the equation.}[/tex]
[tex]\tt 180^{\circ} - 111^{\circ} = 111^{\circ} - 111^{\circ} + 3x^{\circ}[/tex]
[tex]\tt 69^{\circ} = 3x^{\circ}[/tex]
[tex]\textsf{Let's use the Division Property of Equality, which is similar to subtraction but it's}[/tex]
[tex]\textsf{for division. Divide each side of the equation by 3.}[/tex]
[tex]\tt \frac{69^{\circ}}{3} = \frac{3x^{\circ}}{3}[/tex]
[tex]\large\boxed{\tt x = 23^{\circ}}[/tex]
Related Questions
1. In one brand of frozen dinner, there are 22 grams of fat. Each gram of fat is 9 calories. Each frozen dinner has 945calories. What percent of these calories is from fat?
Answers
There are 22 grams of fat and each gram of fat is 9 calories, then
[tex]22\text{ grams }\cdot9\frac{calories}{gram}=198\text{ calories from fat}[/tex]945 calories represents 100%, then 198 represents:
[tex]\begin{gathered} \frac{945\text{ calories}}{198\text{ calories}}=\frac{100\text{ \%}}{x\text{ \%}} \\ 945\cdot x=100\cdot198 \\ x=\frac{19800}{945} \\ x=21\text{ \%} \end{gathered}[/tex]21% of the calories are from g
While visiting Salem Connor can pay a flat rate of $10 for parking or $5 per hour. For the length of time that Connor wants to park in Salem, the two options are actually equivalent in terms of cost. How much will Connor pay
Answers
let
x = length of time Connor will spend
8=6+a/4 how do I solve this
Answers
6 is adding on the right, then it will subtract on the left
[tex]\begin{gathered} 8-6=\frac{a}{4} \\ 2=\frac{a}{4} \end{gathered}[/tex]4 is dividing on the right, then it will multiply on the left
[tex]\begin{gathered} 2\cdot4=a \\ 8=a \end{gathered}[/tex]simplify.
rewreit the expression in the form [tex]5^{n}[/tex].
Answers
The expression in the form of 5ⁿ is 5⁻¹³
What is the expression?An expression is a set of numbers or variables combined using the operations + , – , × or ÷ . Arithmetic expression that contains only numbers and mathematical operators and algebraic expression that contains variables, numbers and mathematical operators.
Given:
F(x) = 5⁻⁵/5⁸
F(x) = 5⁻⁵⁻⁸
F(x) = 5⁻¹³
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Hello! Need some help on parts a,b, &c. The question and rubric is linked below. Thank you!
Answers
Part A: -5/9, 6/10, -7/11, 8/12
Part B:
[tex]f(n)=(-1)^{n}(\frac{n}{n+4})[/tex]Part C: Positive
Explanation:The given sequence is:
[tex]-\frac{1}{5},\frac{2}{6},-\frac{3}{7},\frac{4}{8},....[/tex]As seen above the sequence is an alternating sequence because it changes in sign
Also, neglecting the sign chnages, we will observe, a common diffference of 1 in the numerator and denominator
a) Therefore, if the pattern continues, the next 4 terms in the sequence are:
-5/9, 6/10, -7/11, 8/12
b)
Without the sign, the explicit equation representing the numerator is calculated below:
1, 2, 3, 4......
The first term, a = 1
The common difference, d = 1
This is an arithmetic sequence
N(n) = a + (n - 1)d
N(n) = 1 + (n - 1)(1)
N(n) = 1 + n - 1
N(n) = n
The explicit equation representing the denominator is calculated below
5, 6, 7, 8........
The first term, a = 5
The common difference, d = 1
D(n) = a + (n - 1)d
D(n) = 5 + (n - 1)(1)
D(n) = 5 + n - 1
D(n) = n + 4
The alternating sequence will include the term below:
[tex](-1)^n[/tex]Therefore, the explicit equation for f(n) representing the sequence is:
[tex]f(n)=(-1)^n(\frac{n}{n+4})[/tex]Part C) The sign of f(56) will be:
(-1)^56 = 1
Since this gives us a positive value, the sign of f(56) is positive
Every month, Michael pays $5 plus $0.10
per text message for phone service.
Which equation represents the amount
Michael pays for phone service each
month, y, if he sends and receives x text
messages?
A. y = 0.1x + 5.
B. y = 0.2x + 10
C. y = 0.1x
D.
y = 5x
Answers
Answer:
y = 0.1x + 5
Step-by-step explanation:
0.1x = the amount he pays for all his texts and 5 is a fixed amount so add them up to get y
estion 5 (1 point)Given the two images below. What is the scale used to transform GHI to G'HI?Scale Factor -->GHIGHBlank 1:SubmitSaved at
Answers
We can see the upper vertix of the triangle in the first figure is at the point (0,6) and after the shrink is at (0,2). So what's the number I can divide 6 to get a 2? It's 3. So the scale factor is 1/3
Determine the number of solutions to the given system remember to use the format(x,y) to type in your points and do not use spaces if there is only one type the point and one space and none in the other if there’s none type none in both of the boxes
Answers
Remember that
when solving a system by graphing, the solution is the intersection point both graphs
Looking at the graph
The intersection point is (5,6)
therefore
The solution is the point (5,6)evaluate
x3+x0 for x=2
Answers
Answer:
6
Step-by-step explanation:
You replace the x’s with 2 and then solve the problem like you would do with any other problem.
2(3)+2(0)
2(3)=6
2(0)=0
6+0=6
Please correct me if i’m wrong. I just finished this lesson!
The correct answer is: " 9 " .
_______
Step-by-step explanation:
Given: " x³ + x⁰ " ; Evaluate for "x = 2 ".
Plug in 2 for the x values; and solve:
" 2³ + 2⁰ " ;
Note: " 2³ = 2 * 2 * 2 = 8 " ;
" 2⁰ = 1 " .
Note: Any 'non-zero' value, raised to the 'zeroth' [0°]' exponential power, is equal to 'one' [ 1 ].
So: " x³ + x⁰ = 2³ + 2⁰ = 8 + 1 = 9 ."
The answer is: " 9 ".
_______
Hope this is helpful! Best wishes to you!
_______
Given that a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6, select the statement that could be true for g. A. g(-4) = -11 B. g(-13) = 20 C. g(7) = -1 D. g(0) = 2
Answers
The true statement is g(-13)= 20.
What is domain and range?In mathematics, a function is represented as a rule that produces a distinct result for each input x. Mapping or transformation is used to denote a function in math. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
Given:
domain = -20 ≤ x ≤ 5
and a range = -5 ≤ g(x) ≤ 45
and g(0) = -2 and g(-9) = 6
First, g(-13)= 20
x=-13 is in our domain and 20 is also in our range .
So this is true for g(-13)= 20.
Now, g(-4) = -11
-11 does not comes under the range.
So this statement is not true.
Again, g(0) = 2 is false because g(0) = - 2.
and, g(7) = -1 D
7 is not in our domain .
So g(7) is not possible
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Moving the decimal point to the right foot places in a number is the same as ______.1. multiplying by 10^42. multiplying by 103. multiplying by 10^-44. multiplying by 4
Answers
Whenever we multiply a decimal number by 10, we are shifting the decimal point one digit to the right. For example, if we compute
[tex]12.05\times10[/tex]the answer is
[tex]120.5[/tex]We moved the decimal point one digit to the right; therefore, we can say moving the decimal point to the right foot places in a number is the same as multiplying by 10.
Hence, the correct answer choice is 2
Lines a and b are parellel.If the slope of a line a is 1/4 , what is the slope of the line b?
Answers
Answer:
D. 1/4
Explanation:
By definition, two lines are parallel if they have the same slope.
Given that lines a and b are parallel; and the slope of line a = 1/4, then:
The slope of line b = 1/4.
The correct choice is D.
What is what is 156.4÷23
Answers
Answer:
156.4 ÷ 23 = 6.8
Step-by-step explanation:
hope this helps
A spinner with 12 equally sized slices has 5 blue slices and 7 yellow slices. The dial is spun and stops on a slice at random. What is the probability that the dial stops on a red slice
Answers
Answer:
0
There are no red slices, so the probability is 0.
what us the rule that represents the function in the graph?
Answers
EXPLANATION
The reule that represents the function is y=5cos(x) + 3
In developing her science project, Leigh learned that light travels at a constant rateand that it takes 500 seconds for light to travel the 93 million miles from the Sun toEarth. Mars is 142 million miles from the Sun. About how many seconds will it takefor light to travel from the Sun to Mars?A. 235 secondsB. 327 secondsC. 642 secondsD. 763 seconds
Answers
D. 763 seconds
Explanation:
Data:
Seconds light travels distance between Sun and Earth : 500 seconds
Distance between Sun and Earth: 93 million miles
Distance between Sun and Mars: 142 million miles
Formula: (see image below)
Solution:
From Sun to Mars the light takes (142 * 500) / 93 = 763 seconds
NB:
The tactic is to first put the data given in a table like in the image above, to first multiply diagonally then divide horizontally. (starting from the data that his paired data).
Here the paired data missing is the time it takes for the light to travel from the Sun to Mars, therefore you'll multiply the distance between the Sun to Mars (known data missing a pair) by the time it takes light to travel from the Sun to Earth (known data with its pair), then divide the result by the distance between the Sun and earth (pair of the former mentioned known data)
Please help I don't get this
Find the difference or type
"impossible"
[3 –8] + [4 - 5 -6]
? ? ?
It’s a matrice
Answers
Answer:
-12
Step-by-step explanation:
explanation in the picture bruv
What is the car’s speed in miles per minute, & how many miles will the car travel in 20 minutes?
Answers
Ok, so
We know that the car is travelling at a speed of 39miles/hour. The car's speed in miles per minute will be:
[tex]39\frac{miles}{hour}\cdot\frac{1hour}{60minutes}=0.65\frac{miles}{\min ute}[/tex]Now, we're asked to find how many miles the car will travel in 20 minutes. This is:
[tex]0.65\frac{miles}{\min ute}\cdot20\min utes=13miles[/tex]When riding his bike down a hill, Lance can maintain an average speed of 55.5 km/h. When riding uphill, his speed drops to an average of 24.25 km/h. On a recent ride, 28% of Lance's ride was uphill, 33% was downhill and the rest of the ride was on a mostly flat surface. If the distance he covers is 475 km, how long do you think he took to complete his ride? Show your work.
Answers
Answer:
10.59480821 hours
Step-by-step explanation:
First, we need to know the percent of the flat surface. so we are gonna add the uphill and down hill then take the sum and find the difference from 100% 28+33+x=10061+x=100[tex]\frac{61+x}{-61} =\frac{100}{-61}[/tex]x=392. Now we know the percent for each surface
Uphill = 28%Downhill = 33%Flat = 39%3. Now that we know the percent of each surface we need to find out how many km for each surface:
Uphill
0.28×475=133kmDownhill
0.33×475=153.75kmFlat
0.39×475=185.25km3. Now that we know all the percent and distance for each surface we need to know the km/h for each
Uphill = 24.25km/h
Downhill = x
Flat = 55.5km/h
4. Since we don't have the speed for downhill we need to know the difference between uphill and flat
55.5-24.25=31.255. Now we know the difference is 31.25 we can add that to the flat surface to get the downhill speed
55.5+31.25=86.75Downhill =86.75km6. Now we know all the speeds and now we can figure out how many hours it takes for each surface
( we are going to take the distance in 1 surface and then divide that by the km/h in that surface to ket how many hours)
Uphill
133÷24.25=5.484536082 hoursDownhill
153.75÷86.75=1.772334294 hoursFlat
185.25÷55.5=3.337837838 hours7. Now we add all the hours up
5.484536082+1.772334294+3.337837838= 10.59480821 hours() Organic sugar used to be sold at a bulk price of $3.70 per pound. The price was recently increased by 20%. What is the current price per pound?
Answers
It is given that an item used to be sold for $3.70 per pound.
It is required to find the current price per pound if the price was increased by 20%.
A 20% increase in the price, $3.70 is calculated as:
[tex]\frac{100+20}{100}\cdot3.70=\frac{120}{100}\cdot3.70=4.44[/tex]Hence, the current price of the item is $4.44 per pound.
The current price of the item is $4.44 per pound.
MATRECIES: Suppose ={u,v,w}⊆R3 is linearly independent. Determine if the set 4 ={u, v, v−w, u+v+w} is linearly independent or linearly dependent.
Answers
The set is linearly dependent.
To explicitly prove this, we need to show there is at least one choice of constants [tex]c_1,c_2,c_3,c_3\in\Bbb R[/tex] such that
[tex]c_1 u + c_2 v + c_3(v-w) + c_4(u+v+w) = 0[/tex]
or equivalently,
[tex](c_1 + c_4) u + (c_2 + c_3 + c_4) v + (-c_3 + c_4) w = 0[/tex]
which is the same as solving the system of equations
[tex]\begin{cases} c_1 + c_4 = 0 \\ c_2 + c_3 + c_4 = 0 \\ -c_3 + c_4 = 0 \end{cases}[/tex]
From the first and last equations, we have [tex]c_1=-c_4[/tex] and [tex]c_3=c_4[/tex]. Substituting these into the second equation leaves us with [tex]c_2-2c_1=0[/tex], and so the overall solution set is
[tex]c_1 = \dfrac12 c_2 = -c_3 = -c_4[/tex]
for which there are infinitely many not-all-zero solutions.
Find the length of arc RS. Use 3.14 for .Round to the nearest tenth.P6.48 inS7391500 650R[? ]inEnter
Answers
Given:
[tex]\theta=150^o[/tex]The radius of the circle is 6.48 in.
To find:
We need to find the arc length of RS.
Explanation:
Consider the formula to find the length of the arc.
[tex]undefined[/tex]the function f(x)=600-100x models the value, f(x), of a video game system x years after purchase
Answers
Complete question is:
The function f(x) = 600 - 100x models the value, f(x), of a video game system x years after purchase. Which choice represents the most appropriate domain of the function?
Answer and explanation:
The domain of a function is the values you can plug into the function, the possible values for x.
While x could take any value, there are a range of apropiate values that it can take.
For example, since x represents years after purchase, x can not be a negative number, because that would represent negative years, thus x must be greater or equal to 0.
Domain:
[tex]\lbrack0,\infty)[/tex]
Find the y-intercept of the line on the graph.
Answers
Answer:
-2
Step-by-step explanation:
This is where the line crosses the y axis. It is at point (0,-2)
You need to lay tile to create a frieze above a Forrest . The title measure 2 7/8 in by 2 7/8 if the doorway is 36 1/2 inches wide how many piece of tile you need
Answers
After solving basic fractions we have come to find that, we need 12.7 tiles to create a frieze above a Forrest.
What is fraction?When describing a portion or part of a whole in mathematics, a fraction is used. The equal components of the whole are represented by it. Both the numerator and denominator are components of a fraction.
Both the top and bottom numbers are referred to as the numerator and denominator, respectively. The denominator specifies the total number of equally sized pieces in the whole, whereas the numerator specifies the number of equal parts that were taken.
A fraction is something like 5/10.
The denominator in this case is 10, and the numerator is 5.
The measure of each tile = 2⅞
= 23/8
Measure of doorway = 36½
= 73/2
No. of tiles we need = 36½ / 2⅞
= 12.7 tiles
Thus, we need 12.7 tiles to create a frieze above a Forrest.
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Question 2 of 10 What is the slope formula? O A. A. 12-1 xz - X OB. Kz - x /2 - 4 OC. c. * + x, x2 + y OD. 1/2-X Kez - V
Answers
The slope is calculated by findidng the ratio of the vertical change (change in y) to the horizontal change (change in x) between any two distinct points.
Then the slope formula is:
[tex]m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}[/tex]Diagram LabelValueUnitsRadius of the Pool Cover9feetDiameter of the Pool Cover18feetCircumference of the Pool CoverfeetArea of the Pool Coversquare feet
Answers
Step1: Write out the given parameters
[tex]\begin{gathered} \text{Diameter}=18\text{feet} \\ \text{Radius}=\frac{diameter}{2}=\frac{18}{2}=9feet \end{gathered}[/tex]We are to find the area of the pool cover and it circumference
Step2: write out the formula
[tex]\begin{gathered} \text{Area of pool cover=}\pi r^2 \\ \text{where }\pi=3.14 \end{gathered}[/tex][tex]\text{Area of pool cover=3.14}\times9^2=254.34square\text{ f}eet[/tex]Hence the area of the pool cover is 254.34 square feet
The circumference of the pool cover is given by
[tex]\begin{gathered} 2\pi r \\ 2\times3.14\times9 \\ 56.52 \end{gathered}[/tex]Therefore the circumference of the pool cover is 56.52 feet
Help pls im horrible at math
Answers
Answer:
84
- 0
92
- 88
44
- 44
= 0
Step-by-step explanation:
can you please help me with this
Answers
The image of the point P(x, y) = (4, 2) by means of a translation formula is point P'(x, y) = (- 1, 4).
What is the image of a given point after making a translation?
In this question we find the coordinates of a point set on Cartesian plane which is modified by using a translation, a kind of rigid transformation. Rigid transformations are transformations applied on geometric loci such that Euclidean distances are conserved.
Vectorially speaking, translations are described by the following formula:
P'(x, y) = P(x, y) + T(x, y)
Where:
P(x, y) - Original pointP'(x, y) - Resulting pointT(x, y) - Translation vectorIf we know that P(x, y) = (- 9, - 3) and P'(x, y) = (- 14, - 1), then the translation vector is:
T(x, y) = P'(x, y) - P(x, y)
T(x, y) = (- 14, - 1) - (- 9, - 3)
T(x, y) = (- 5, 2)
Then, the image of the point (4, 2) is:
P'(x, y) = (4, 2) + (- 5, 2)
P'(x, y) = (- 1, 4)
The image of the point (4, 2) by using a translation formula is (- 1, 4).
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Part A What is the ratio of the number of steps to the number of minutes?
Answers
Number of step = 52
Minute = 1 minute
The ratio of the number of steps to the number of minutes is
52 : 1
