Answer:
The value of x is 14
The length of each diagonal is 24 units
Step-by-step explanation:
Let us revise the properties of the rectangle
Each two opposite sides are parallel and equalIts four vertices are right anglesIts diagonals equal each other and bisect each otherIn rectangle TUVW
∵ TV and UW are its diagonals
∴ TV = UW
∵ TV = 2x - 4
∵ UW = x + 10
- Equate them to find x
∴ 2x - 4 = x + 10
- Subtract x from both sides
∴ x - 4 = 10
- Add 4 to both sides
∴ x = 14
The value of x is 14
Substitute the value of x in the expression of TV OR UW to find the length of each diagonal
∵ TV = 2(14) - 4
∴ TV = 28 - 4
∴ TV = 24 units
The length of each diagonal is 24 units
Final answer:
To solve for x, we equate the lengths of TV and UW, since they are opposite sides of a rectangle. Solving the equation yields x = 14. We then find the lengths of TV and UW (both 24 units), and use the Pythagorean theorem to calculate the length of the diagonal, which is approximately 33.94 units.
Explanation:
We are given that TUVW is a rectangle with sides TV and UW. We are also given that the lengths of these sides can be expressed as TV = 2x - 4 and UW = x + 10. Since TUVW is a rectangle, opposite sides are equal in length, so TV equals UW.
Setting the expressions for TV and UW equal to each other gives us:
2x - 4 = x + 10Solving for x:
2x - x = 10 + 4x = 14Now we can find the lengths of TV and UW:
TV = 2(14) - 4 = 24UW = 14 + 10 = 24Therefore, each diagonal of the rectangle is of the same length because diagonals of a rectangle are congruent. We can use the Pythagorean theorem to find the length of the diagonal:
Let d be the length of the diagonal:
d² = TV² + UW²d² = 24² + 24²d² = 576 + 576d² = 1152d = √1152d ≈ 33.94The length of each diagonal of the rectangle is approximately 33.94 units.
Simplify. 10/27 divided by 5/9
Answer:
2/3 or 0.6
Step-by-step explanation:
Answer:
2/3
Step-by-step explanation:
According to the question,10/27÷5/9
So we will have to be careful when solving this kind of question
So let's solve
10/27÷5/9
To solve we will have to convert the division to multiplication and during this process the 5/9 will actually change to 9/5
10/27×9/5
If you calculate it well,you will get
2/3
Which means that the final answer is 2/3 since it cannot be solved further
So 10/27÷5/9 gives 2/3
what is 1 and 1/8 plus 1 and 1/4
Answer:2.375
Step-by-step explanation:
1 and 1/8 =(1×8+1)/8=9/8
1 and 1/4 =(1×4+1)/4=5/4
9/8+5/4=9/8+10/8=19/8=2.375
Answer: 2.375
The Highly Improbable Foods Company makes vegetarian versions of burgers, hot dogs, and chicken wings, and they offer two platters. Platter A consists of one burger, three hot dogs, and $5$ chicken wings, which costs $\$16.$ Platter B consists of two burgers, one hot dog, and $8$ chicken wings, which costs $\$20.$
A picnic organizer requires $80$ hamburgers, $95$ hot dogs, and $380$ chicken wings. (There can be leftovers, but these are the minimum requirements.) What is the minimum cost (in dollars)?
Answer:
$1020
Step-by-step explanation:
Let x and y represent the numbers of Platter A and Platter B the organizer needs to purchase, respectively. The given conditions can be summarized as ...
x + 2y ≥ 80 . . . . . . 80 or more hamburgers are required
3x + y ≥ 95 . . . . . . 95 or more hot dogs are required
5x +8y ≥ 380 . . . . 380 or more chicken wings are required
16x +20y = c . . . . . c must be minimized
__
It is useful to graph these inequalities, and look for the vertex of the feasible region that is closest to the origin. That vertex is (x, y) = (20, 35). The other vertex that is close to the origin is (60, 10). The cost of that order would be $1310.
The value of an order of 20 Platter A and 35 Platter B is ...
20×$16 +35×$20 = $320 +700 = $1020
The minimum cost of the picnic food is $1020.
Which statement is true regarding the functions on the
graph?
Of(-3) = g(4)
Of(-4) = 9(-3)
f(-3) = g(-3)
Of 4) = g(4)
Answer:
f(-3) = g(-3)
Step-by-step explanation:
Remember points on the graph get their location from the x-axis (horizontal) and y-axis (vertical).
In function notation, "f(x)" means when "x" is the value in the brackets, what the value of "y" will be.
First option for example: f(-3) = g(4)
Value of "y" for f(x) when x = -3:
On the blue line, when x = -3, y = -4.
Value of "y" for g(x) when x = 4:
On the red line, when x = 4, y = -3.
Therefore:
f(-3) = g(4)
-4 = -3 <= This is false.
In the third option: f(-3) = g(-3)
On f(x) blue, when x = -3: y = -4
On g(x) red, when x = -3: y = -4
Therefore:
f(-3) = g(-3)
-4 = -4 <= This is true.
Answer:C
Step-by-step explanation:
plz help me i need work plz
For the given figure;
Perimeter = 41 cm and
Area = 49.5 cm².
Step-by-step explanation:
Step 1; The given figure consists of a rectangle and a triangle. The rectangle's length is 6 cm and the rectangle's width is 7 cm. The triangle's base is 6 cm long while its height is 2.5 cm and the third side measures 6.5 cm.
Step 2; The figure's area = The rectangle's area + The triangle's area.
The rectangle's area is given by multiplying the rectangle's length with the rectangle's width. The area of the rectangle = 7 × 6 = 42 cm².
The area of a triangle is given by multiplying [tex]\frac{1}{2}[/tex] with the product of the triangle's base and height. The area of the rectangle = [tex]\frac{1}{2}[/tex] × 6 × 2.5 = 7.5 cm².
The figure's area = 42 + 7.5 = 49.5 cm².
Step 3; The figure's perimeter = The perimeter of the rectangle + the perimeter of the triangle.
The rectangle's perimeter is 2 times the sum of the length and width. The perimeter of the rectangle = 2 × (6 + 7) = 2 × 13 = 26 cm.
The perimeter of a triangle is the sum of all the three side lengths.
The area of the triangle = 6 + 2.5 + 6.5 = 15 cm.
The perimeter of the figure = 26 + 15 = 41 cm.
Find the missing sides
Answer:
90-30=60
Step-by-step explanation:
Was
Answer:
hypotenuse is 6 square root of 3 and short leg is 3 square root of 3
Step-by-step explanation:
Tickets for the school play cost $4 for students and $7 for adults. For one performance, 146 tickets were sold for $779. How many tickets were for adults and how many were for students?
a 65 students and 81 adults
b 80 students and 66 adults
c 70 students and 77 adults
d 81 students and 65 adults
Answer: D
Step-by-step explanation:
Total tickets sold is $779
Calculate the options to get the right answer.
Option D is correct at
81 students at $4 = 324
65 adults at $7= 455
Total is $ 779
what is the equation for this line
The equation of the line is [tex]y=\frac{-1}{5} x-\frac{21}{5}[/tex].
Solution:
The points on the line are (–6, –3) and (4, –5).
[tex]x_{1}=-6, y_{1}=-3, x_{2}=4, y_{2}=-5[/tex]
Slope of the line:
[tex]$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]$m=\frac{-5-(-3)}{4-(-6)}[/tex]
[tex]$m=\frac{-5+3}{4+6}[/tex]
[tex]$m=\frac{-2}{10}[/tex]
[tex]$m=\frac{-1}{5}[/tex]
Point-slope formula:
[tex]y-y_{1}=m\left(x-x_{1}\right)[/tex]
[tex]$y-(-3)=\frac{-1}{5}(x-(-6))[/tex]
[tex]$y+3=\frac{-1}{5}(x+6)[/tex]
[tex]$y+3=\frac{-1}{5} x-\frac{6}{5}[/tex]
Subtract 3 from both sides of the equation.
[tex]$y=\frac{-1}{5} x-\frac{21}{5}[/tex]
The equation of the line is [tex]y=\frac{-1}{5} x-\frac{21}{5}[/tex].
Six is one hundred times ???????????
Answer:
0.06
Step-by-step explanation:
6 is 6.0 and 0.06 times 100 is 6.
Answer:
0.06
Step-by-step explanation:
if you times 0.06 by 10 it is 0.6
if you times it by 100 it is 6
4. What is the measure of each interior angle of a regular 28-gon?
Step-by-step explanation:
Measure of each interior angle of 28 sided polygon
[tex] \frac{(28 - 2) \times 180 \degree}{28} \\ \\ = \frac{26 \times 180 \degree }{28} \\ \\ = \frac{4680 \degree }{28} \\ \\ = 167.14\degree \\ [/tex]
The measure of each interior angle of a regular 28-gon is 167.14 degrees.
The measure of each interior angle of a regular 28-gon can be calculated using the formula:
Interior Angle = (n-2) * 180 / n
Substitute n = 28 into the formula:
Interior Angle = (28 - 2) * 180 / 28 = 24 * 180 / 28 = 167.14 degrees
5d2-50d+125 =
Fully factor each expression
Help, give me the answers for 1 through 14... (100 points)
Answer:
can you reupload the photo? so I can help.
Step-by-step explanation:
Answer:
Note that for graph, Y = mx + c, where m = slope of graph and c = y-intersect
1) equation of line: y = [tex]-\frac{3}{4} x[/tex] + 4 ∴ m = -3/4 , c = 4
2) equation of line: y = [tex]\frac{3}{2} x[/tex] + 3 m = 3/2 , c = 3
3) equation of line: y = [tex]-\frac{2}{5} x[/tex] - 2 m = -2/5 , c = -2
4) equation of line: y = [tex]\frac{1}{2} x[/tex] + 3 m = 1/2 , c = 3
5) equation of line: y = -x + 2 m = -1 , c = 2
6) equation of line: y = [tex]-\frac{5}{2} x[/tex] - 1 m = -5/2 , c = -1
Step-by-step explanation:
For each of the line equations, "m" is the slope which is also dy/dx. Also the intersect "c" is on the y axis(Vertical line).
For each equation, assume a number for 'x' then solve for y.... you will be able to get coordinates (x,y) for each graph.
Using 1) as example:
1) equation of line: y = [tex]-\frac{3}{4} x[/tex] + 4 ∴ m = -3/4 , c = 4
at intersection 'c', y = 4, when x = 0
∴ y = -3/4 (1) + 4 = [tex]3\frac{1}{4}[/tex]
repeat for x = 2, 3, 4, 5, 6
Do same for equation line 2, 3, 4, 5, 6 to get coordinates to plot each graph
42
97
-----
[tex]42 \times 97[/tex]
Answer:
4074
Step-by-step explanation:
Please answer quickly I am running out of time
The value of [tex]g(-4)=\frac{-4}{3}, \ g(-2)=3 \ \text{and} \ g(2)=\frac{8}{3}[/tex] .
Solution:
Given function:
[tex]g(x)=\left\{\begin{array}{ll}-\frac{1}{3} x^{2}+4 & \text { if } x \neq-2 \\3 & \text { if } x=-2\end{array}\right.[/tex]
Substitute x = –4 in g(x), we get
[tex]$g(-4) =- \frac{1}{3}(-4)^2+4[/tex]
[tex]$=- \frac{16}{3}+4[/tex]
To make the denominator same, multiply and divide the 2nd term by 3.
[tex]$=- \frac{16}{3}+\frac{12}{3}[/tex]
[tex]$g(-4)=- \frac{4}{3}[/tex]
It is given that, if x = –2, then g(x) = 3
Therefore g(–2) = 3
Substitute x = 2 in g(x), we get
[tex]$g(2) =- \frac{1}{3}(2)^2+4[/tex]
[tex]$=- \frac{4}{3}+4[/tex]
To make the denominator same, multiply and divide the 2nd term by 3.
[tex]$=- \frac{4}{3}+\frac{12}{3}[/tex]
[tex]$g(-2)= \frac{8}{3}[/tex]
The value of [tex]g(-4)=\frac{-4}{3}, \ g(-2)=3 \ \text{and} \ g(2)=\frac{8}{3}[/tex] .
Quadrilateral ERGF is inscribed in a circle Find the measure of angle E (Remember to show formulas equations and numbers in those formulasequations receive creditAlso, make sure to include units on your answer ) R - 2 + 6x G EK 7x - 13
The measure of angle E is 75°.
Solution:
Given data:
∠E = 5x, ∠F = 7x – 13 and ∠R = –2 + 6x
A quadrilateral inscribed in a circle is called cyclic quadrilateral.
∠R and ∠G are opposite angles in a cyclic quadrilateral.
In cyclic quadrilateral, opposite angles are supplementary.
⇒ m∠R + m∠F = 180
⇒ –2 + 6x + 7x – 13 = 180
⇒ 13x – 15 = 180
Add 15 from both sides of the equation, we get
⇒ 13x = 195
Divide by 13 from both sides of the equation, we get
⇒ x = 15
To find the measure of angle E:
m∠E = 5x
m∠E = 5(15)
m∠E = 75
The measure of angle E is 75°.
Select the correct answer. Amelia lost her credit card one day while on vacation. She reported the loss to the credit card company the next day. However, someone had used her card to make purchases worth $1,600 at different shopping outlets. What is the maximum amount that Amelia may have to pay back for the fraudulent charges of $1,600 made on her card? A. $0 B. $50 C. $800 D. $1,600
Answer:a
Step-by-step explanation:
The maximum amount that Amelia may have to pay back for the fraudulent charges of $1,600 made on her card is $50.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
According to the Fair Credit Billing Act (FCBA) in the United States, a consumer's liability for unauthorized charges on a credit card is limited to $50.
Amelia will be responsible for paying the first $50 of the fraudulent charges, but she will not be held responsible for any charges above that amount.
However, most credit card companies have a zero liability policy, which means that the consumer will not be responsible for any unauthorized charges made on their credit card.
Hence, the maximum amount that Amelia may have to pay back for the fraudulent charges of $1,600 made on her card is $50.
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URGENT!!!!!!!!
I need the answer to both parts in this screenshot.
Answer:
a) $10
b) 0.1 hours
Step-by-step explanation:
The total amount earned by Cary,E after working h hours is calculated using:
[tex]E=10h[/tex]
The dollars Cary earns per hour is the unit rate, which is $10
If Cary earns $10 per hour, then she earns
$1 in
[tex] \frac{1}{10} hours = 6mins[/tex]
Carry has to work for 0.1 hours to earn $1
The temperature at 6:00 a.m. was ‐3.5°C. From 6:00 to 7:00, the temperature increased 2.5°C. From 7:00 to 8:00, it decreased by 0.25°C, and from 8:00 to 11:00, the temperature dropped 3.25°C. Which expression shows the temperature in °C at 11:00 a.m.?
The expression that shows the temperature in °C is [tex]-3.5+2.5+(-0.25)+(-3.25)[/tex].
Step-by-step explanation:
Step 1:
The initial temperature at 6.00 am was [tex]-3.5[/tex] °C.
Step 2:
From 6.00 to 7.00 am, the temperature increased by another 2.5°C, so the temperature at 7.00 am was [tex](-3.5 + 2.5)[/tex] °C.
Step 3:
From 7.00 to 8.00 a.m, the temperature decreased by another 0.25°C, so the temperature at 8.00 am was [tex](-3.5+2.5+(-0.25))[/tex] °C.
Step 4:
From 8.00 to 11.00 a.m, the temperature dropped by another 3.25 °C, so the temperature at 11.00 am was [tex](-3.5+2.5+(-0.25)+-(3.25))[/tex] °C which is represented by the fourth option.
Answer:
A i did did question on think through math think it is the answer
Step-by-step explanation:
Part B: Set up an equation and solve for x. In your answer, include the equation, your calculations and the value of x.
Part C: Use your equation from Part A and the value of x from Part B to prove your equation to be true for the adjacent angles in the diagram.
The adjacent angles in the diagram are 112° and 68°.
Step-by-step explanation:
The measure of angle in a straight line is 180°.
Therefore, the sum of the two angles is equal to 180°.
⇒ 2x + 68 = 180
The equation formed to solve for x value is 2x+68 = 180
⇒ 2x = 180 - 68
⇒ 2x = 112
⇒ x = 112/2
⇒ x = 56
∴ The adjacent angles in the diagram are 2x=2(56)= 112° and 68°
What is the area of the figure?
Enter your answer in the box.
❏in²
Answer:32
Step-by-step explanation:
add 10 + 10 + 6 + 6 = 32
Norma has 9 pies to divide among 4 friends. How many pies will each friend receive if all of the pies must be used and can be divided into smaller parts? A. 2/9 pie B. 4/9 pie C. 1 1/4 pies D. 2 1/4 pies
Answer:
D. 2 1/2
Step-by-step explanation:
9/4 = 2.50 = 2 1/2
Answer:
D. 2¼
Step-by-step explanation:
9/4
(8+1)/4
8/4 + 1/4
2¼
Solve the system of linear equations by graphing. Y=-5/2x-7 X+2y=4
Answer:
They intersect at (-4.5, 4.25)
Assuming you can graph them, just put the equations in your calculator or graphing software and find the intersection, next time.
PAGE 11
3) Solve for x: 1/2(4x+6)=-5x+24.7
A x=3.1
B x=3
C x=7
D x=-7.23
Answer:
A x=3.1
Step-by-step explanation:
1/2(4x+6)=-5x+24.7
Multiply each side by 2 to get rid of the fraction
2*1/2(4x+6)=2(-5x+24.7)
4x+6 = -10x +49.4
Add 10x to each side
4x+6+10x=-10x+10x+49.4
14x +6 = 49.4
Subtract 6 from each side
14x+6-6 = 49.4-6
14x = 43.4
Divide each side by 14
14x/14 = 43.4/14
x = 3.1
A coin is flipped 3 times If you get tails once you get $5, tails twice you get $15, and tails on all three flips you get $40. What is the expected amount of money you will get?
Answer:
12.50
Step-by-step explanation:
The expected amount is $12.50.
What is the probability?The Probability in mathematics is possibility of an event in time. In simple words how many times that incident is happening in any given time interval.
There are 8 possibilities, if coin is flipped three times.
HHH, HHT, HTH, TTH, HTT, THT and TTH,
where H is possibility of head and T is tail.
Now the probabilities,
0 tails: 1 way out of 8 total: P(0) = 1/8
1 tails: 3 ways out of 8 total: P(1) = 3/8
2 tails: 3 ways out of 8 total: P(2) = 3/8
3 tails: 1 way out of 8 total: P(3) = 1/8
The expected amount;
(1/8)X 0 + (3/8)X 5 +(3/8)X15 +(1/8)X40
= 15/8 + 45/8 + 40/8
= 100/8
= 12.50
Therefore, the expected amount is $12.50.
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(4, 1) and (6,7)what is the slope
Answer:
3
Step-by-step explanation:
[tex]m = \frac{y}{x} = \frac{7 - 1}{6 - 4} = \frac{6}{2} = 3[/tex]
What is the value of x in the equation 3x-47=65, when y=4?
0
x=134
0
x=21
0
x=23
0
x=27
Which image shows a reflection of triangle ABC over the x-axis?
CLEAR CHECK
Math item response image
Math item response image
Math item response image
Answer:
Please add images.
Step-by-step explanation:
Doris is going to take a 3-hour-6-minute flight from New York, New York, to
Houston, Texas, that leaves at 10:05 a.m. New York time. If New York is in the
eastern time zone and Houston is in the central time zone, what will be the
local time in Houston when the flight arrives?
Use the following to help you answer the question.
12:00 p.m. eastern time = 11:00 a.m. central time = 10:00 a.m. mountain
time = 9:00 a.m. Pacific time.
O
A. 1:11 p.m.
OB. 2:11 p.m.
O C. 11:11 a.m.
O
D. 12:11 p.m
Answer:
D. 12:11pm
(10:05am + 3hrs 6mins = 1:11pm - 1hr = 12:11pm)
Final answer:
After accounting for the flight duration of 3 hours and 6 minutes and the one-hour time difference due to the Central Standard Time Zone, Doris will arrive in Houston at 12:11 p.m. local time.
Explanation:
Doris is taking a flight from New York to Houston, and we need to calculate the local time of her arrival in Houston after a 3-hour-6-minute flight. To find the answer, we must account for the time zone difference and the duration of her flight. New York is in the Eastern Standard Time Zone, while Houston is in the Central Standard Time Zone, which is one hour behind New York.
Starting from a departure time of 10:05 a.m. in New York, we first add the flight duration which is 3 hours and 6 minutes. This gets us to 1:11 p.m. New York time. Since Houston is one hour behind New York, we subtract one hour from this time to get the local time in Houston, which will be 12:11 p.m.
The correct answer is D. 12:11 p.m. This is the time Doris will arrive in Houston, local time.
Big Ben a famous clock tower London , England . The diameter of the clock face 23 feet . Find the circumference of the clock face . Round to the nearest tenth .
Answer:
23pi, or approx. 72.27
Step-by-step explanation:
circumference = 2(pi)r, or 2d
pi = approx. 3.14, r = radius, and d = diameter
You are given diameter, so all you have to do is multiply 23 feet by pi.
The circumference of the clock face of is 72.1 feet or 23π.
Given that the diameter of the clock face is 23 feet.
To calculate the circumference of the clock face, use the the following formula:
The value of π is approximately 3.14159.
Circumference = 2πr
In the formula r is the radius.
Since, the diameter is 23 and the radius is half of the diameter.
Thus, the radius r is 11.5.
Further, calculate the circumference:
Circumference = 2 × 3.14159 × 11.5
Circumference ≈ 72.08357
Circumference ≈ 72.1 feet
Therefore, the circumference of the clock face is 72.1 feet.
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This graph shows the temperature in Diego's house between noon and midnight one day.
temperature (degrees F)
R
3
TO
1
2
3 4 5 6 7 8 9
time (hours after noon)
10
11
12
Which of the statements below are true statements? Correct the statements that are false to make them
true.
Example:
The highest temperature happened at 9:00. This statement is false. The correct statement is: The
highest temperature happened at 4:00.
A. Time is a function of temperature.
B. The lowest temperature occurred between 4:00 and 5:00.
C. The temperature was increasing between 9:00 and 10:00
D. The temperature was 74 degrees twice, during the 12-hour period.
E. There was a four-hour period during which the temperature did not change.
REMEMBER TO CORRECT WRONG STATEMENTS. YOU GET 1 POINT FOR EACH LETTER, 1 FOR
CORRECT, 1 FOR CORRECTING FALSE STATEMENTS.
The first three statements are false because they are opposite from the data shown in the graph, while the two last statements are true.
To determine whether a statement is true or false, you need to:
Carefully analyze the information of the graph.Read and understand the statement.Compare the information of the statement to the one of the graph.Now, let's analyze each statement:Time is a function of temperature:This statement is false, this is because time does not change with temperature, and therefore time is an independent variable. The corrected statement would be Temperature is a function of time.
The lowest temperature occurred between 4:00 and 5:00:In the graph, you can see the lowest temperature was 67° and this occurred between 11 and 12 p.m. Therefore, the lowest temperature occurred between 11:00 and 12:00.
The temperature was increasing between 9:00 and 10:00:Based on the graph from 9 to 10 p-m the temperature went from 70° to almost 65°. Therefore the temperature was decreasing between 9:00 and 10:00.
The temperature was 74 degrees twice, during the 12-hour period:This statement is true, this temperature occurred at 3:00 and 4:00.
There was a four-hour period during which the temperature did not change:This statement is true, the temperature is the same between 5:00 and 9:00.
Note: This question is incomplete because the graph is missing, here is the graph.
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