Answer:
The perimeter of the square is 64 units===========================
GivenA square with dimensions:
Width = 4x,Length = 36 - 5x.To findThe perimeterSolutionSquare has all sides equal:
width = length4x = 36 - 5x4x + 5x = 369x = 36x = 4Each side is:
4*4 = 16 unitsPerimeter:
P = 4*16 = 64 unitsThe perimeter of the square is found as 64 units.
What is defined as the perimeter of the square?The perimeter of such a square is indeed the total length of all of its sides. As a result, we can calculate the perimeter of the a square besides adding its four sides.A square's sides are all equal. As a result, the perimeter of such a square is determined by multiplying the side of a square by four.For the given question,
The dimension of the square are given as;
Width = 4xLength = 36 – 5xFor square, as all sides are equal.
Then,
Width = Length
Put the values.
4x = 36 – 5x
9x = 36
x = 4
Put in dimensions.
Width = 4×4 = 16 unitsLength = 36 – 5×4 = 16 units.The perimeter of square is;
Perimeter = 4 × side
Perimeter = 4 × 16
Perimeter = 64 units.
Thus, the perimeter of the square is found as 64 units.
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A one-day admission ticket to a park costs $43.85 for adults and $15.95 for children. Two families purchased nine tickets and spent $338.85 for the tickets. Fill in a chart that
summarizes the information in the problem. Do not solve the problem.
Using mathematical operations we know that total tickets of 2 children ($31.9) and 7 adults ($306.95) were purchased which cost the total amount of $338.85.
What are mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value. The operation's arity is determined by the number of operands. PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction (from left to right).So, a number of adults and children who purchased the tickets:
Let, adults are 'a and children be 'c':Now, the equation can be:
a + c = 9a = 9 - cNow, the second equation will be:
43.85a + 15.95c = 338.85
Now, substitute a = 9 - c in equation (2) as follows:
43.85a + 15.95c = 338.8543.85(9 - c) + 15.95c = 338.85394.65 - 43.85c + 15.95c = 338.85- 27.9c = 338.85 - 394.65- 27.9c = - 55.8c = - 55.8/ - 27.9c = 55.8/27.9c = 2Hence:
a = 9 - ca = 9 - 2a = 7Then:
c = 2 ⇒ 15.95 × 2 = $31.9a = 7 ⇒ 43.85 × 7 = $306.95Sum = $338.85Therefore, using mathematical operations we know that total tickets of 2 children ($31.9) and 7 adults ($306.95) were purchased which cost the total amount of $338.85.
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help me pleaseeeeeeeee
The value of the car after 5 years is $13,500 and the value of the car after 9 years is $10,500.
According to the question,
We have the following information:
The value of the car is given by V(x) where x is the number of years.
V(x) = -1500x + 21,000
(a) Now, to find the value of car after 5 years, we will put 5 in place of x in the given expression:
V(5) = -1500*5+21000
V(5) = -7500+21000
V(5) = $13,500
(b) Now, to find the value of car after 9 years, we will put 9 in place of x in the given expression:
V(9) = -1500*9+21000
V(9) = -10500+21000
V(9) = $10,500
(c) When V(12) = 3000 then it means that the value of the car after 12 years is $3000.
Hence, the value of car after 5 years and 9 years is $13,500 and $10,500 respectively.
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Annette Michaelson will need $11,000 in 8 years to help pay for her education. Determine the lump sum, deposited today at 4.5% compounded monthly, will produce the necessary amount.
Annette Michaelson will need $11,000 in 8 years to help pay for her education. Determine the lump sum, deposited today at 4.5% compounded monthly, will produce the necessary amount.
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
A=11,000
t=8 years
n=12
r=4.5%=0.045
substitute in the formula above
[tex]\begin{gathered} 11,000=P(1+\frac{0.045}{12})^{(12\cdot8)} \\ 11,000=P(\frac{12.045}{12})^{(96)} \\ \\ P=7,679.61 \end{gathered}[/tex]therefore
the answer is
$7,679.61thereforeWhat is the equation of the line that passes through the point (7,6) and has a slope of 0
The equation of the line that passes through the point (7, 6) with slope 0 is y = 6
Given,
The points which the line passes, (x₁, y₁) = (7, 6)
Slope of the line, m = 0
We have to find the equation of the line:
We know that,
y - y₁ = m(x - x₁)
So,
y - 6 = 0(x - 7)
y - 6 = 0
y = 6
That is,
The equation of the line that passes through the point (7, 6) with slope 0 is y = 6
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NEED ASAP IF CORRECT ILL GOVE BRAINLIEST
Answer:
I believe the answer is g(x)=x+10
Step-by-step explanation:
it moves 4 units to the right making it positive, adding to the previous 6 units, making it move 10 units to the right
Hey I just need someone to check my work and see what else i might need to add on. This is algebra 2
To answer this question we will use the following property of sets:
[tex]|A\cup B|=|A|+|B|-|A\cap B|[/tex](a) Since Ash has 153 cards in his collection (without any duplicates), Brock has 207 cards in his collection (also without any duplicates) and they have 91 cards in common, then:
[tex]\begin{gathered} |AshCards\cup BrockCards|=|AshCards|+|BrockCards|-|AshCards\cap BrockCards| \\ =153+207-91. \end{gathered}[/tex]Simplifying the above result we get:
[tex]|AshCards\cup BrockCards|=269.[/tex](b) Expressing the above result using set notations:
[tex]|A\cup B|=269.[/tex]Answer:
(a) There are 269 unique cards in between them.
(b)
[tex]|A\cup B|=269.[/tex]
Solve the given equation:x = -8y + 9
We have to solve the equation.
[tex]x=-8y+9[/tex]We have 2 unknowns and one equation, so we can only express one in function of the other.
We already have x in function of y, so we will now express y in function of x:
[tex]\begin{gathered} x=-8y+9 \\ x-9=-8y+9-9 \\ \frac{x-9}{-8}=\frac{-8y}{-8} \\ \\ -\frac{x}{8}+\frac{9}{8}=y \\ \\ y=-\frac{x}{8}+\frac{9}{8} \end{gathered}[/tex]Answer:
y = -x/8 + 9/8
a wall in marcus bedroom is 8 2/5 feet high and 16 2/3 feet long. of he paints 1/2 of the wall blue, how many square feet will be blue?140128 2/157064 2/15
Answer:
[tex]70[/tex]Explanation:
What we want to answer in this question is simply, the area of the room that will be painted blue if he decides he would paint exactly have the room blue
So, we need to simply get the area of the room and divide this by half
Mathematically, the area of a rectangle is the product of its two sides
Thus, we have it that the area of the room is:
[tex]\begin{gathered} 8\frac{2}{5}\times16\frac{2}{3} \\ \frac{42}{5}\times\frac{50}{3}\text{ = 14}\times10=140ft^2 \end{gathered}[/tex]Now, to get the area painted blue, we divide this by 2 as follows or multiply by 1/2
We have this as:
[tex]140\times\frac{1}{2}=70ft^2[/tex]
Find the first three terms of this sequence Un=5n-2n3.
The first three terms of the sequence defined by the formula; Un=5n-2n³ as in the task content are; 3, -6 and -39 respectively.
What are the first three terms of the sequence given by the formula; Un=5n-2n³?It follows from the task content that the first three terms of the sequence defined by the formula be determined.
On this note, it follows that the first three terms are at; n = 1, n = 2 and n = 3 respectively.
Hence we have;
1st term; U(1) = 5(1) - 2(1)³ = 3.2nd term; U(2) = 5(2) - 2(2)³ = -6.3rd term; U(3) = 5(3) - 2(3)³ = -39.Hence, the first three terms are; 3, -6 and -39.
The first three terms of the sequence are as listed above.
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Mrs. Navarro has 36 students in her class, 16 boys and 20 girls.Select all ratios below that correctly describe the ratio of boys to girls in Mrs.Navarros's class.
First, we need to know the ratio of boys to girls in Mrs. Navarro's class. There are 16 boys and 20 girls. The ratio would be 16:20.
From this given, we can choose from the options which rations are equivalent to our given ratio.
8 to 10 is a ratio that is equivalent from our given. If we scale are ratio by 2, we can get 8:10.
5:4, 8:18, and 5 to 9, however, are NOT equivalent to 16:20.
4:5 is equivalent. We just need to scale 16:20 by 4, and we will get 4:5.
10:8 is another ratio that is NOT equivalent to 16:20.
*Scaling ratios are similar to finding the lowest terms of fractions.
In the following diagram, we know that line AB is congruent to line BC and angle 1 is congruent to angle 2. Which of the three theorems (ASA, SAS, or SSS) would be used to justify that triangle ABC congruent triangle CDA?
The theorem that justifies why triangle ABC is congruent to triangle CDA is the: SAS.
What is the SAS Theorem?The SAS theorem states that if we can show that two triangles have a pair of corresponding congruent included angles, and two pairs of corresponding sides that are also congruent to each other, then we can prove that both triangles are congruent to each other.
The triangles, ABC and CDA have:
Two pair of corresponding sides that are congruent to each other, which are AB ≅ BC, and AC ≅ CA.
A pair of corresponding included angles, which is angle 1 ≅ angle 2.
Based on the above known information, we can conclude that triangle ABC is congruent to triangle CDA by SAS theorem.
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Approximately how old would you be in the years if you lived 1,000,000 hours? round your answer to the nearest whole number.
First let's see how many hours are in a year:
[tex]\begin{gathered} 1\text{ year }\rightarrow\text{ 365 days} \\ 1\text{ day }\rightarrow\text{ 24 hours} \\ \Rightarrow1\text{ year }\rightarrow365\cdot24=8760\text{ hours} \end{gathered}[/tex]We found that 1 year has 8769 hours, then if we lived 1,000,000 hours, we have to divide it by 8760 to know the number of years lived:
[tex]\frac{1000000}{8760}=114.15[/tex]therefore, you would have lived 114.15 years
Question 2, please let me know if you have any questions regarding the materials, I'd be more than happy to help. Thanks!
Mean Value Theorem
Supposing that f(x) is a continuous function that satisfies the conditions below:
0. f(x) ,is continuous in [a,b]
,1. f(x) ,is differentiable in (a,b)
Then there exists a number c, s.t. a < c < b and
[tex]f\mleft(b\mright)-f\left(a\right)=f‘\left(c\right)b-a[/tex]However, there is a special case called Rolle's theorem which states that any real-valued differentiable function that attains equal values at two distinct points, meaning f(a) = f(b), then there exists at least one c within a < c < b such that f'(c) = 0.
As in our case there is no R(t) that repeats or is equal to other R(t), then there is no time in which R'(t) = 0 between 0 < t < 8 based on the information given.
Answer: No because of the Mean Value Theorem and Rolle's Theorem (that is not met).
The distance from the Old North Church in Boston to Charlestown is approximately 1,410 meters . Even on fast horse , that distance would take several minutes to travel . On April 18 , 1775 , lanterns were shown from the steeple of the Old North Church across the Charles River to warn American patriots that British soldiers were travelling Inland via water . The speed of light is approximately 3 x 10 to the power of 8 meters per second . How many seconds did it take for the light to be visible in Charlestown ?
We were told that the distance from the Old North Church in Boston to Charlestown is approximately 1,410 meters.
Given that the speed of light is approximately 3 x 10 to the power of 8 meters per second and
speed = distance/time
It means that the number of seconds it took for the light to be visible in Charlestown is also the time it took the light to travel through 1410 meters
Therefore,
time = distance/speed
time = 1410/3 * 10 ^8 = 0.0000047 seconds
time = 4.7 * 10^-6 seconds
I need help please!!
DISREGARD THE LAST ONE
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
A company manufactures computer memory chips as circular silicon wafers with a diameter of 10 Inches. The wafers are cut into
different sized sectors. Match each wafer's central angle to the area of that sector.
48°
20°
62°
45°
55°
Answer:
25/18 - 20
155/36 - 62
25/8 - 45
Step-by-step explanation:
in triangle ABC, point E (5, 1.5) is the circumcenter, point He (4.3, 2.3) is the incente, and point I (3.6, 2.6) is the centroid.what is the approximate length of the radius that circumscribes triangle ABC?
1) Gathering the data
E (5,1.5) Circumcenter
H (4.3,2.3) incenter
I (3.6, 2.6) is the centroid.
2) Examining the figure we can see point C and B as the vertices of the
triangle, to find the radius let's use the distance formula between point E and C
E(5, 1.5) and C(3,5)
[tex]\begin{gathered} d=\sqrt[]{(x_1-x_2)^2+(y_1-y_2)}^2 \\ \\ d=\sqrt[]{(5-3_{})^2+(1.5_{}-2.6_{})}^2 \\ d=2.28 \end{gathered}[/tex]Since the radius is a line segment from the origin to the circumference then the distance BC = radius of the circumscribed triangle
Radius = 2.28
A line has slope 3. Through which two points could this line pass? a. (24. 19), (8, 10) b. (10, 8). (16, 0) C. (28, 10). (22, 2) d. (4, 20). (0, 17) Please select the best answer from the choices provided D
Step 1: Concept
You are going to apply the slope formula to find the slope of the line through each coordinate.
Step 2: Slope formula
[tex]\text{Slope = }\frac{y_2-y_1}{x_2-x_1}[/tex]I have tried but but there is some part that i keep getting wrong
we have that
K is the center of circle
J -----> point of tangency
segment IK is a radius
segment JL is a chord
segment GI is a secant
segment JI is a diameter
segment GJ is a tangent
arc JIL is a major arc
arc JL is a minor arc
arc JLI is a half circle (180 degrees)
Part 2
we have that
arc TU=87 degrees -------> by central anglearc ST
Remember that
arc ST+87+72=180 degrees ------> by half circle
so
arc ST=180-159
arc ST=21 degreesarc WV
we have
arc WV+arc UV=180 degrees -----> by half circle
arc UV=72 degrees
so
arc WV=180-72
arc WV=108 degreesarc VUT
arc VUT=arc VU+arc UT
substitute given values
arc VUT=72+87
arc VUT=159 degreesarc WU=180 degrees -----> by half circle def(x) = 3x² - 5x+20
Find f(-8)
Answer:
Substitute x = -8 into f(x).
f(-8) = 3(-8)² - 5(-8) + 20
= 3(64) + 40 + 20
= 192 + 60
= 252
4x + 3x = 56. What is the value of x?
Given
The expression is given as
[tex]4x+3x=56[/tex]Explanation
To find x, add the expression.
[tex]\begin{gathered} 7x=56 \\ x=\frac{56}{7} \end{gathered}[/tex][tex]x=8[/tex]Answer
Hence the value of x is 8.
[tex]4x + 3x = 56\\7x = 56\\x = 56/7\\x = 8[/tex]
The answer is X=8
what is the range of the number of goals scored?
The minimum number of goals scored is 0 and maximum number of goals scored is 7. The range is equal to difference between maximum number of goals and minimum number of goals.
Determine the range for the goals scored.
[tex]\begin{gathered} R=7-0 \\ =7 \end{gathered}[/tex]So answer is 7.
Please help me my answer is correct or no
Answer:
the answer is c actully
Step-by-step explanation:
iv'e took that test b4 so you welcome
The points −−5, 11 and r, 9 lie on a line with slope 2. Find the missing coordinate r.
Solution
[tex]\begin{gathered} Let\text{ }(x_1,y_1),\text{ }(x_2,y_2) \\ Let\text{ }m=slope \\ m=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex][tex]\begin{gathered} If(-5,-11)=\text{ }(x_1,y_1),then\text{ }x_1=-5,\text{ }y_1=-11 \\ (r,9)=\text{ }(x_2,y_2),then\text{ }x_2=r,\text{ }y_1=9 \end{gathered}[/tex]Using the Slope formula written above;
[tex]\begin{gathered} 2=\frac{9-(-11)}{r-(-5)} \\ 2=\frac{20}{r+5} \\ Cross\text{ }multiply \\ 2(r+5)=20 \\ Expansion\text{ }of\text{ }bracket \\ 2r+10=20 \\ 2r=20-10 \\ 2r=10 \\ Divide\text{ }both\text{ }sides\text{ }by\text{ }2 \\ \frac{2r}{2}=\frac{10}{5} \\ r=5 \end{gathered}[/tex]Therefore, the missing co-ordinate r is 5.
Find equation of line containing the given points (4,3) and (8,0) Write equation in slope-intercept form
SOLUTION
Write out the given point
[tex]\begin{gathered} (4,3) \\ \text{and } \\ (8,0) \end{gathered}[/tex]The equation of the line passing through the point above will be obtain by following the steps
Step1: Obtain the slope of the line
[tex]\begin{gathered} \text{slope,m}=\frac{y_2-y_1}{x_2-x_1} \\ \text{Hence } \\ x_1=4,x_2=8 \\ y_1=3,y_2=0 \end{gathered}[/tex]Substituting the values we have
[tex]\begin{gathered} \text{slope,m}=\frac{0-3}{8-4}=-\frac{3}{4} \\ \text{Hence } \\ m=-\frac{3}{4} \end{gathered}[/tex]Step 2: Obtain the y- intercept
The y-intercept is the point where the graph touch the y, axis
[tex]\begin{gathered} \text{slope, m=-3/4} \\ y=6 \\ y-intercept=6 \end{gathered}[/tex]Steps 3; use the slope intercept rule
[tex]\begin{gathered} y=mx+b \\ \text{Where m=-3/4,b=y-intercept} \\ \text{Then } \\ y=-\frac{3}{4}x+6 \end{gathered}[/tex]Hence
The equation in slope intercept form is
y = - 3/4 x + 6
Solve the inequality: 3x + 4 ≤ 5
Answer in interval notation.
(-∞,1/3] will be the required option in interval notation for the given inequality 3x + 4 ≤ 5 as it's definition states "a relationship between two expressions or values that are not equal to each other".
What is inequality?A difference between two values indicates whether one is smaller, larger, or simply not equal to the other. a ≠ b says that a is not equal to b. a < b says that a is less than b. a > b says that a is greater than b. a ≤ b means that a is less than or equal to b. a ≥ b means that a is greater than or equal to b.
What is interval notation?When using interval notation, we first write the set's leftmost number, then a comma, and finally its rightmost number. Depending on whether those two numbers are a part of the set, we then enclose the pair in parentheses or square brackets (sometimes we use one parenthesis and one bracket!).
Here,
3x+4≤5
3x≤1
x≤1/3
(-∞,1/3]
As it's definition states "a relationship between two expressions or values that are not equal to each other" (-∞,1/3] will be the required option in interval notation for the given inequality 3x + 4 ≤ 5.
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Assume that when adults with smartphones are randomly selected , 52% use them in meetings or classes. If 7 adults smartphone users are randomly selected, find the probability that exactly 4 of them use their smartphones in meetings or classes.The probability is:
From the information available;
The population is 52% and the sample size is 7. The probability that exactly 4 of them use smartphones (if 7 adults are randomly selected) would be calculated by using the formula given;
[tex]\begin{gathered} p=52\text{ \%, OR 0.52} \\ n=7 \\ p(X=x) \\ We\text{ shall now apply;} \\ p(X=4)=\frac{n!}{x!(n-x)!}\times p^x\times(1-p)^{n-x} \end{gathered}[/tex]We shall insert the values as follows;
[tex]\begin{gathered} p(X=4)=\frac{7!}{4!(7-4)!}\times0.52^4\times(1-0.52)^{7-4} \\ =\frac{5040}{24(6)}\times0.07311616\times0.110592 \\ =35\times0.07311616\times0.110592 \\ =0.28301218 \end{gathered}[/tex]Rounded to four decimal places, this becomes;
[tex](\text{selecting exactly 4)}=0.2830[/tex]ANSWER:
The probability of selecting exactly 4 smartphone users is 0.2830
Use the law of detachment to determine what you can conclude from the given information
In mathematical logic, the Law of Detachment says that if the following two statements are true:
( 1 ) If p, then q.
( 2 ) p
Then we can derive a third true statement:
( 3 ) q.
In our question, we have
( 1 ) If 0º< A <90º, then A is an acute angle.
( 2 ) The measure of A is 58º.
Then, from the first statement, we can affirm
( 3 ) A is an acute angle.
A company has net sales revenue of $175000 reporting period and $148000 in the next. using horizontal analysis, it has experienced a decrease of what percentage?A. 15%B. 18%C. 8%D. 12%
ANSWER:
A. 15%
STEP-BY-STEP EXPLANATION:
We can determine the percentage using the following formula:
[tex]\begin{gathered} r=\frac{\text{ fiinal value - initial value}}{\text{ initial value}}\cdot100 \\ \\ \text{ we replacing} \\ \\ r=\frac{148000-175000}{175000}\cdot100 \\ \\ r=-15.42\%=15\% \end{gathered}[/tex]Therefore, the correct answer is A. 15%
Use Descartes Rules of signs to complete the chart with possibilities for the nature of the roots of the following equations:A) x^3 - x^2 + 4x - 6 = 0B) x^5 - x^3 + x + 1 = 0
Given:
[tex]\begin{gathered} x^3-x^2+4x-6=0 \\ x^5-x^3+x+1 \end{gathered}[/tex]Required:
To determine the possibilities for the nature of the roots of the given equation.
Explanation:
(A)