The value of x that makes both expressions equal is 6.5.
What are expressions?An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.As an illustration, the phrase x + y is one where x and y are terms with an addition operator in between. There are two sorts of expressions in mathematics: numerical expressions, which only contain numbers, and algebraic expressions, which also include variables.So, the value of x that makes both the expression equal.
So, we can write the expression as:
5x - 8 = 3x + 5
Now, solve for x as follows:
5x - 8 = 3x + 5
5x - 3x = 5 + 8
2x = 13
x = 13/2
x = 6.5
Therefore, the value of x that makes both expressions equal is 6.5.
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2. An account is opened with $28000 earning12% interest compounded yearly. What is thebalance in the account after 4 years?
The principal is $28000 with rate 12% compounded yearly .
To determine the balance after 4 years,
[tex]SI=\frac{P\times R\times T}{100}[/tex][tex]SI=\frac{28000\times12\times4}{100}[/tex][tex]SI=13440[/tex]The balance in the account after 4 years is the sum of principal and simple interest.
[tex]A=\text{ 28000}+13440[/tex][tex]A=41440[/tex]Thus, the balance in the account after 4 years is 41440 dollar.
Gavin has a points card for a movie theater. He receives 20 rewards points just for signing up. He earns 9.5 points for each visit to the movie theater. He needs 77 points for a free movie ticket. Which equation could be used to determine vv, the number of visits Gavin must make to earn a free movie ticket?
I need help solving this I thought it was 7 but I’m not too sure now
We are given a triangle such that two line segments are drawn as medians:
[tex]MX\text{ and YL are median lines}[/tex]A meadian line has three points that are off importance as follows:
[tex]\begin{gathered} \text{Strats from one of the vertex of a triangle} \\ \text{Passes through the centroid of the triangle} \\ Bi\sec ts\text{ the opposite side of the triangle} \end{gathered}[/tex]Hence, using the above information we can extract that:
[tex]\begin{gathered} Y\text{ is the mid-point of MK} \\ X\text{ is the mid-point of KL} \\ \text{\textcolor{#FF7968}{AND}} \\ A\text{ is the centroid of the entire triangle} \end{gathered}[/tex]We can also use the properties of median length that states:
[tex]\begin{gathered} \text{Length from vertex to centroid : Centroid to bisection point of opposite side} \\ \end{gathered}[/tex]The ratio of the above two lengths for any median line of a triangle remains true for:
[tex]2\text{ : 1}[/tex]This means that the line segment from centroid to bisection ( mid ) point of the opposite side is shorter than the preceeding length; hence, the ratio is ( 2 : 1 ).
We are given the length of the line segment MA the larger part of the median line:
[tex]MA\text{ = 14 units}[/tex]We can use the property of ratio of lengths for the median lines and determine the length of the smaller part of the median line as follows:
[tex]\begin{gathered} \text{ 2 : 1} \\ MA\text{ : AX} \\ ======== \\ AX\text{ = }\frac{MA}{2} \\ \\ AX\text{ = }\frac{14}{2}\text{ = 7 units} \end{gathered}[/tex]From the above property we determined the length of the shorter line segment. Now we have lengths for the both constituent line segments of median line ( MX ). We can simply sum the individual lengths as follows:
[tex]\begin{gathered} MX\text{ = AX + MA} \\ MX\text{ = 7 + 14} \\ \textcolor{#FF7968}{MX}\text{\textcolor{#FF7968}{ = 21 units}} \end{gathered}[/tex]Hence, the answer is:
[tex]\textcolor{#FF7968}{MX}\text{\textcolor{#FF7968}{ = 21 }}\textcolor{#FF7968}{\ldots}\text{\textcolor{#FF7968}{ Option C}}[/tex]Identify all pairs of congruent corresponding parts.Then write another congruence statement for the polygons.AABC ~ADEF
1) Congruent parts possess the same length, or measure (if angles).
2) As we can see, by the marks on the angles notation within each triangle we can state the following:
[tex]\begin{gathered} AB\cong ED \\ AC\cong DF \\ BC\cong EF \end{gathered}[/tex]Note that was possible since we could base ourselves on the measure of those angles.
3) Thus, we can state that these triangles as we can see, fall under the case of:
SSS - Side Side Side Congruence
Given that those three sides are congruent to each other.
Solve the equation 7x = 91 for x.
−98
84
−13
13
Your answer will be D 13
Samuel has 10 coins that add up to $3.80. Some are 50 cent and the rest are 20 cent coins. How many 50 cent coins does he have?
Answer:
6 coins of 50cent
Step-by-step explanation:
Information we have:
1. x number of 50cent and y number of 20cent added up to 380cent.
2. x and y is 10coins
eq1 : 50x + 20y = 380
eq2: x + y = 10
write eq2 to y in term of x
y = 10 - x -> eq3
replace eq3 into eq1
50x + 20(10 - x) = 380
50x + 200 - 20x = 380
50x -20x = 380 -200
30x = 180
x = 180/30 = 6
The graph of a linear relationship passes through (0, 2), (1,5), and (3, 11) but not through (2,7). Which of the following is the equation for this linear relationship?A.O y = 2x + 3 B.O y = 3x + 2C. O y = 5xD. O y= 4x-1
There is a point that doesnt go in the curve.
So the procedure is to replace x by 2 ,and y by 7 in every option to see which doesnt belongs
So we see
Which of the following expressions are equivalent to…I will send a screenshot of the expression I need help with.
Explanation
We have an expression given as
[tex]-\frac{2}{-13}[/tex]To find the equivalent value, we will make use of the fact that when two negative signs divide or multiply each other, the resulting value is always positive
Thus
The simplified answer is
[tex]\frac{2}{13}[/tex]In our case, we will have a positive outcome
Therefore, the correct answers will be options A and B
Identify the correlation you would expect to see between the weight and the age of a child. Explain.
The correlation between the weight and the age of the child is negative.
Correlation
There are 4 types of correlation they are positive correlation, negative correlation, perfect correlation, and no correlation.
Given,
Here we need to find the correlation you would expect to see between the weight and the age of a child.
According to the type of correlation,
We know that, when the two variables are not related to each other then there is no relationship between the variables.
It is always based on the direction of the variable we decide the types of correlation.
Here the type of the correlation is negative correlation because the weight of a child decreases with age.
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What is the slope of the line passing through the points (1, -5) and (4, 1)?
Answer: 2
Step-by-step explanation: i used my brain
please help! where it says “select” the options are 1997-2006
We can find the average rate of change of change using the following expression:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]for the period betwen 1999 and 2002, we have the following:
[tex]\begin{gathered} m=\frac{1483-1336}{2002-1999}=\frac{147}{3}=49 \\ \Rightarrow m=49 \end{gathered}[/tex]therefore, the average rate of change of population between 1999 and 2000 is 49.
Next, we do the same for the period between 2001 to 2005:
[tex]\begin{gathered} m=\frac{801-1591}{2005-2001}=-\frac{790}{4}=-197.5 \\ \Rightarrow m=-197.5 \end{gathered}[/tex]thus, the average rate of change of population between 2001 and 2005 is 197.5
Finally, notice that the population increased from 1997 to 2001, while it decreased from 2002, to 2006
What is the solution of the system of equations?
13x-6y=2
3x-4y=-10
(Write as ordered pair)
Step-by-step explanation:
let's multiply the first equation by 2 and the second equation by -3, and then we add them together :
26x - 12y = 4
-9x +12y = 30
-------------------------
17x 0 = 34
x = 2
and now we use one of the original equations to solve for y :
3×2 - 4y = -10
6 - 4y = -10
-4y = -16
y = 4
the solution is (2, 4).
PLS HELP ASAP THIS IS DUE TODAY!!!!
line AD is parallel to line HE. Identify one pair of alternate interior angles.
The alternate interior angles : ∠4 and ∠5
∠3 and ∠6
In this question, we have been given line AD is parallel to line HE.
We need to identify one pair of alternate interior angles.
We know that the alternate interior angles are formed when a transversal intersects two lines which are coplanar. These angles, lie on the inner side of the parallel lines but on the opposite sides of the transversal.
For given figure alternate interior angles are:
∠4 and ∠5
∠3 and ∠6
Therefore, the alternate interior angles : ∠4 and ∠5
∠3 and ∠6
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What is 3 to the 9th power times 3 to the 5th power
Answer:
3^14
Step-by-step explanation:
Multiplication of two values with same base and different exponent:
When we are multiplicating two values with the same base and different exponents, we keep the base and add the exponents. For example:
[tex]x^a\ast x^b=x^{a+b}[/tex]In this question:
[tex]3^9\ast3^5=3^{9+5}=3^{14}[/tex]At any time t (in hours), there are 216(t +18) of Type A bacteria in a sample and 362t + 8 of Type B bacteria in a sample. After how many hours will the number of type A bacteria be less than the type B bacteria?
1. The given situation can be described in the following inequality:
[tex]216^{(t+18)}<36^{(2t+8)}[/tex]2. To solve the prevous inequality, proceedas follow:
write 216 as 6^3 and 36 as 6^2, then, apply log_6 both sides:
[tex]\begin{gathered} 6^{3(t+18)}<6^{2(2t+8)} \\ \log _66^{3(t+18)}<\log _66^{2(2t+8)} \\ 3(t+18)<2(2t+8) \end{gathered}[/tex]then, solve for t, as follow:
[tex]\begin{gathered} 3t+54<4t+16 \\ 3t-4t<16-54 \\ -t<-38 \\ t>38 \end{gathered}[/tex]Hence, from t = 38 hours the number of type A bacteria will be less than the type B bacteria
3. In a number line, you obtain:
9. Charlie has 6 more quarters than dimes in a jar and a total of $9.20. Which system of
equations can be used to determine the number of each type of coin Charlie has if
q= the number of quarters and d = the number of dimes?
A. [q=d+6
10d + 25q = 920
B. [d=q+6
10d + 25q = 920
C. [d+q=6
10d + 25q = 920
D. q=d+920
10d + 25q = 6
In linear equation the number of dimes 10d + 25q = 920 .
What are examples of linear equations?
An equation with only one variable is referred to as a linear equation in one variable. It has the mathematical formula Ax + B = 0, where A and B can be any two real numbers, and x is an unknowable variable with just one possible value. One such linear equation in one variable is 9x + 78 = 18. A linear equation is a first-order (linear) term and a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.if
q= the number of quarters and d = the number of dimes
d = q + 6
10d + 25q = 920
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Assume that each circle shown below represents one unit. Express the shaded
amount as a single fraction and as a mixed number.
Answer: what shown below?
Step-by-step explanation:
Find the equation of a line perpendicular to y = -3x + 5 that passes through the point (6,7)
789
Answer:
Step-by-step explanation:
a random sample of 2 measurements is taken from the following population of values: 1, 2, 4, 5, 8. what is the probability that the range of the sample is 7?
The probability of the sample required where the range is 7 is 0.1 .
The range of a sample is the difference of the maximum and minimum values.
The range of the sample to be 7, the maximum and minimum values should be 8 and 1.
The outcomes required are (8,1).
The total probability of the sample for 2 measured values:
P=[tex]C_{5,2}[/tex]
P=5!/(2!(5-2)!)
P=5!/(2![tex]\times[/tex]3!)
P=20/2
P=10
The probability of the outcome desired,
=(required outcomes)/(total outcomes)
=1/10
=0.1
The probability of the outcome required is 0.1 .
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10 less than 7 times a number is the same as 3 times the number plus 18
Answer:
yes, it is the same
Step-by-step explanation:
7x - 10 = 3x + 18
7x-10+10 = 3x + 18 + 10
7x = 3x + 28
7x - 3x = 3x - 3x + 28
4x = 28
4x ÷ 4 = 28 ÷ 4
x=7
Plug x back in and check the answer.
7x-10 = 3x+18
7(7)-10 = 3(7)+18
49-10 = 21+18
39 = 39
So, YES they are the same.
Learning Diagnostic Analytics Math Skill plans Recommendations Fifth grade > Z.11 Parts of a circle Q7N The radius of a circle is 12 feet. What is the circle's diameter? feet Submit
Given:
The radius of the circle = 12 feet
The circle diameter = two times of the radius
so, the diameter = 2 * 12 = 24 feet
So, the answer is 24 feet
What transformations map the figure onto itself? Select all that apply.
A.
Reflection over line y
B.
Reflection over point P
С.
Rotation 180 degrees
D.
Reflection over line m
E.
Rotation 270 degrees
Answer:
Step-by-step explanation:
C because its right
Simplify each expression. (–5x2y)(3x4)a. 15x6yb. –15x2yc. –15x6yd. –15x8y
The given expression is
[tex](-5x^2y)(3x^4)[/tex]We will multiply at first -5 by 3
[tex]-5\times3=-15[/tex]Then we will multiply x^2 by x^4 by adding their powers
[tex]x^2\times x^4=x^{2+4}=x^6^{}[/tex]And multiply y by 1 as there is no y in the second bracket, then
[tex](-5x^2y)(3x^4)=-15x^6y[/tex]The answer is C
Julia ran 1,000 meters in 9 minutes. How many meters/minute did she run?
Answer:
111.11111111111111111
Step-by-step explanation:
Write the equation of the line in fully simplified slope-intercept form.
plss help
Answer: y=2x-5
Step-by-step explanation:
ZA and B are vertical angles. If m_A = (3x + 13) and mZB = (5x + 9), then find the measure of ZA.
EXPLANATION:
The first thing to do is graph the given points of the equation to find the position of the angles.
A=(3X+13)
B=(5X+9)
Both equations to find the angle z should give me a total of 180 degrees
By adding and joining both equations, we have the following:
[tex]\begin{gathered} (3x+13)+(5x+9)=180 \\ 3x+13+5x+9=180 \\ 3x+5x=180-13-9 \\ 8x=180-22 \\ 8x=158 \\ x=\frac{158}{8} \\ x=19.75 \end{gathered}[/tex]Now plugging the value of x into the first equation to find the angle A gives us:
[tex]\begin{gathered} A=3(19.75)+13 \\ A=59.25+13 \\ \textcolor{#FF7968}{A=72.25}\text{\textcolor{#FF7968}{ DEGREES}} \\ The\text{ measure }of\text{ the angle A is: 72.25} \\ \end{gathered}[/tex]To check if the measure of angle A is correct, we must also replace x in the second equation to find the value of angle B, which has to give us exactly what is missing to complete the 180 degrees.
[tex]\begin{gathered} B=5(19.75)+9 \\ B=98.75+9 \\ B=107.75 \\ \text{Now adding the angles A y B should give us 180 }degrees. \\ \textcolor{#FF7968}{A=72.25} \\ B=107.75 \\ AB=\textcolor{#FF7968}{72.25}+107.75=\textcolor{#FF7968}{180}\text{\textcolor{#FF7968}{ degrees.}} \end{gathered}[/tex]Questions-PartA what is the perimeter of this hexagon if the side is 15 cm?Part BWhat is the apothem of this hexagon each side is 15 cm round to the nearest whole number?Part CWhat is the area of the hexagon?(I just need a brief explanation with the answer)
Step 1:
The formula for the area of a hexagon can also be given in terms of the apothem as,
Area of hexagon
[tex]=\text{ }\frac{1}{2}\text{ }a\text{ }\times\text{ P}[/tex]where 'a' is the length of the apothem and 'P' is the perimeter of the hexagon.
Step 2:
Length of the sides = 15 cm
[tex]\begin{gathered} \text{perimeter = 6 }\times\text{ 15} \\ P\text{ = 90} \end{gathered}[/tex]Step 3:
Find the Apothem ' a '
Find each angle
[tex]\text{Each interior angle = }\frac{360}{6}\text{ = 60}[/tex]Next
[tex]undefined[/tex]The population P of Phoenix, Arizona (in thousands) from 1970 through 2000 can be modeled by the equation P = 590e ^ (0.027t) where r represents the year, with t = 0 corresponding to 1970. According to this model, when will the population reach 1.5 million.
The population of Phoenix , Arizona will reach 1.5 million in the year 2005 .
In the question ,
it is given that ,
the equation , modelling the the population P of Phoenix, Arizona (in thousands) from 1970 through 2000 is
P = 590[tex]e^{0.027\times t}[/tex]
where t represents the year corresponding to 1970 .
we need to find the time required for the population to reach 1.5 million.
since population is represented in thousands , so ,
1.5 million = 1500000 will be taken as 1500 .
Substituting P = 1500 in the equation ,
we get ,
1500 = 590[tex]e^{0.027\times t}[/tex]
1500/590 = [tex]e^{0.027\times t}[/tex]
2.5423 = [tex]e^{0.027\times t}[/tex]
taking ㏑ both the sides , we get
㏑(2.5423) = (0.027t)×㏑(e)
0.93306 = 0.027×t
t = 0.93306/0.027
t = 34.55 years
t ≈ 35 years
the year will be 1970 + 35 = 2005 .
Therefore , The population of Phoenix , Arizona will reach 1.5 million in the year 2005 .
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Use the information to answer the question.Point P is located at 16 on the number line, Point Q is located at -9 on the number line.What is the distance between Point P and Point on the number line? Enter the answer in the box.units
Answer:
25units
Explanation:
Given the following points on the number line
Point P at 16
Point Q at -9
Distance between the points = Point P - Point Q
Distance between the points = 16 - (-9)
Distance between the points = 16 + 9
Distance between the points = 25
Hence the distance between Point P and Point Q on the number line is 25units
After Batman brought the Joker to justice, the crime rate in Arkham City decreased by 12\%12%12, percent. Previously, the crime rate was ccc incidents per 100010001000 people.
0.88 is the new crime rate in Arkham City.
What is crime rate?The number of offenses reported to law enforcement authorities per 100,000 people in a population is referred to as the crime rate. By dividing the total number of reported offenses by the population, the crime rate is determined.
Given,
The crime rate in Arkham City decreased by 12% when Batman managed to capture the Joker.
In the past, there were c occurrences of crime per 1000 persons.
How can one create an expression that models the issue?
A drop in the percent of crime is subtracted from the prior crime rate, which was defined as incidences per 1000 persons.
c the number of recent crimes per 1,000 individuals;
New crime rate = previous crime rate - decrease in crime %.
New crime rate = c - 12%c
New crime rate = c - 0.12c
New crime rate = 0.88c
Hence, the new crime rate is 0.88c.
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The complete question is:
"After batman brought the joker to justice , the crime rate in arkham city decreased by 12%. Previously the crime rate was c incidents per 1000 people. Which of the following expressions could represent the crime rate in Arkham City after Batman brought the Joker to justice?
a. 22/25 c
b. 0.12c
c. -0.12
d. 0.88c
e. c/1.12"