Two triangles are similar if and only if there corresponding angles are congruent and the ratio of there corresponding sides are equal. Triangle STU is similar to triangle XYZ than [tex]\rm \angle S \cong \angle X[/tex] , [tex]\rm \angle T \cong \angle Y[/tex] and [tex]\rm \dfrac{ST}{XY}=\dfrac{TU}{YZ}=\dfrac{SU}{XZ}[/tex].
Given :
[tex]\rm \Delta STU \sim \Delta XYZ[/tex]
Two triangles are similar if and only if there corresponding angles are congruent and the ratio of there corresponding sides are equal.
Now, it is given that triangle STU is similar to triangle XYZ. This condition is only true when:
[tex]\rm \angle S \cong \angle X[/tex][tex]\rm \angle T \cong \angle Y[/tex][tex]\rm \dfrac{ST}{XY}=\dfrac{TU}{YZ}=\dfrac{SU}{XZ}[/tex]It can be conclude that if triangle STU is similar to triangle XYZ than [tex]\rm \angle S \cong \angle X[/tex] , [tex]\rm \angle T \cong \angle Y[/tex] and [tex]\rm \dfrac{ST}{XY}=\dfrac{TU}{YZ}=\dfrac{SU}{XZ}[/tex] . Therefore, the correct option is A), C) and D).
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19/8 as a mixed number
At a sporting event the price for 3 cheeseburgers and 2 cups of lemonade is $14 and the price for 2 cheeseburgers and 4 cups of lemonade is $12. how much does it cost for 1 cheeseburger and 2 cups of lemonade
If f(x) = (1/9)(9^x) what is f(3)
Answer: The required value of f(3) is 81.
Step-by-step explanation: We are given the following function :
[tex]f(x)=\left(\dfrac{1}{9}\right)9^x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We are to find the value of f(3).
Substituting x = 3 in equation (i), we get
[tex]f(3)\\\\\\=\left(\dfrac{1}{9}\right)\times9^3\\\\=9^2\\\\=81.[/tex]
Thus, the required value of f(3) is 81.
Answer:
81
Step-by-step explanation:
APEX
The area of a rectangle is 28^2 , and the length of the rectangle is 1ft more than double the width. find the dimensions of the rectangle.
A toddler crawled 2 yards, stopped, then continued to crawl 8 more feet. How many feet did he travel in total?
The toddler crawled a total of 14 feet after converting the initial 2 yards into feet and adding the additional 8 feet crawled.
To determine the total distance the toddler traveled, we first need to convert the units so they are the same. We know that 1 yard is equivalent to 3 feet. If the toddler crawled 2 yards initially, we can calculate this distance in feet as follows:
2 yards * 3 feet/yard = 6 feet
After stopping, the toddler continued to crawl for 8 more feet. To find the total distance traveled, we simply add the two distances together:
6 feet + 8 feet = 14 feet
Therefore, the toddler traveled a total of 14 feet.
Please help, I’m so confused :/
What does it mean to say that a polynomial equation is solvable by radicals?
What is the graph of the equation 4x – 5y = 15?
A cylindrical water tank has a diameter of 6 meters and a height of 9 meters. What is the maximum volume of water the tank can hold? (to nearest whole number) A) 254 m3 B) 509 m3 C) 1018 m3 D) 2290 m3
Answer:
The answer is A) 254 m3
Solve each system using elimination.
3x+3y=27
x-3y=-11
9. 2x+4y=22
2x-2y=-8
11. 5x-y=0
3x+y=24
Please show your work!! Thank you!!
What is the surface area of the figure shown?
989.1 square centimeters
910.6 square centimeters
1,852.6 square centimeters
832.1 square centimeters
The total surface area = 910.6 square centimeters. Option B
The surface area of a cylinder with a conical top can be found by calculating the sum of the areas of the circular base, the curved surface of the cylinder, and the lateral surface of the cone.
From the image, we can find that the radius of the cylinder is 5 cm and the height of the cylinder is 13 cm. We are not given the slant height of the cone.
Let's denote the slant height of the cone as sl.
Here's how to find the surface area of each part:
Curved surface area of the cylinder:
2πrh = 2π(5 cm)(20 cm)
= 628.31 cm²
Lateral surface area of the cone
A=πrl+πr2
= π*5*13+π*5²
= 282 square centimeters
Therefore, the total surface area of the cylinder with a conical top is equal to:
Total surface area = Area of circular base + Curved surface area of cylinder + Lateral surface area of cone
Total surface area = 282 + 628.31 cm²
Total surface area = 910.6 square centimeters
Anna took a job that paid $200 the first week. She was guaranteed a raise of 5% each week.
How much money will she make in all over 8 weeks?
Round the answer to the nearest cent.
The answer is 1909.82 (rounded to the cent).
I just took this test.
Austin rented a truck for one day. there was a base fee of $15.99 , and there was an additional charge of 82 cents for each mile driven. austin had to pay $123.41 when he returned the truck. for how many miles did he drive the truck?
When a number is subtracted from x the result is 6. What is that number
What is the perimeter of triangle ABC with the vertices A(-2,9), B(7,-3),C(-2,-3) in the coordinate plan
A)21 units
B) 15 units
C)34 units
D)36 units
PLZZZZZZZZZZ HELPPPPPPP MEDALS AND FAN
Final answer:
The perimeter of triangle ABC with the given vertices can be found by calculating the distances between the points. The lengths are 15 units for AB, 9 units for BC, and 12 units for AC, and their sum is 36 units. The correct option is D.
Explanation:
To determine the perimeter of triangle ABC with the given vertices A(-2,9), B(7,-3), C(-2,-3), we first need to calculate the lengths of the sides of the triangle using the distance formula, which is d = √((x₂ - x₁)² + (y₂ - y₁)²).
Length of AB: √((7 - (-2))² + ((-3) - 9)²) = √(81 + 144) = √225 = 15 unitsLength of BC: √((-2 - 7)² + ((-3) - (-3))²) = √(81 + 0) = √81 = 9 unitsLength of AC: √((-2 - (-2))² + (9 - (-3))²) = √(0 + 144) = √144 = 12 unitsThe perimeter is the sum of the lengths of the sides, so P = AB + BC + AC = 15 + 9 + 12 = 36 units.
The correct answer is 36 units which corresponds to option D.
A gift box is 12 inches long, 8 inches wide and 2 inches high. how much wrapping paper needed to wrap the box?
A.) 272 inches
B.) 192 inches
C.) 384 inches
D.) 184 inches
Matt's Ice Cream Shoppe has 7 cups of sprinkles to use on sundaes for the rest of the day. If each sundae is served with
1/8
cup of sprinkles, how many sundaes can they serve?
Final answer:
Matt's Ice Cream Shoppe can serve 56 sundaes with 7 cups of sprinkles, assuming each sundae uses 1/8 cup of sprinkles.
Explanation:
The question asks: How many sundaes can Matt's Ice Cream Shoppe serve with 7 cups of sprinkles if each sundae is served with 1/8 cup of sprinkles?
To find the answer, we divide the total amount of sprinkles by the amount used per sundae. Here's the calculation:
Total amount of sprinkles = 7 cups.Amount of sprinkles per sundae = 1/8 cup.Number of sundaes that can be served = Total amount of sprinkles ÷ Amount of sprinkles per sundae = 7 cups ÷ 1/8 cup = 56 sundaes.Therefore, Matt's Ice Cream Shoppe can serve a total of 56 sundaes with their current stock of sprinkles.
Matt's Ice Cream Shoppe can serve 56 sundaes with the 7 cups of sprinkles they have.
To find out how many sundaes Matt's Ice Cream Shoppe can serve with 7 cups of sprinkles, we need to divide the total amount of sprinkles by the amount of sprinkles used per sundae.
Given:
- Total amount of sprinkles: 7 cups
- Amount of sprinkles per sundae: [tex]\( \frac{1}{8} \)[/tex] cup
Let ( x ) be the number of sundaes that can be served.
We can set up the equation:
[tex]\[ \text{Total amount of sprinkles} = \text{Amount of sprinkles per sundae} \times \text{Number of sundaes} \][/tex]
[tex]\[ 7 = \frac{1}{8} \times x \][/tex]
Now, to solve for ( x ), we can multiply both sides of the equation by 8:
[tex]\[ 7 \times 8 = x \][/tex]
[tex]\[ x = 56 \][/tex]
Therefore, Matt's Ice Cream Shoppe can serve 56 sundaes with the 7 cups of sprinkles they have.
Solve for x. Simplify completely.
x^2+4x+4=8
A. x=-6 or x=2 is the answer
Solve the following system of equations
x + y =-5
-3x - y =7
On level ground, a vertical rod 12 feet tall casts a shadow 4 feet long, and at the same time a nearby vertical flagpole casts a shadow 12 feet long. how many feet tall is the flagpole?
Answer:
36 feet.
Step-by-step explanation:
We have been given that on level ground, a vertical rod 12 feet tall casts a shadow 4 feet long, and at the same time a nearby vertical flagpole casts a shadow 12 feet long.
To find the length of flagpole, we will use proportions as:
[tex]\frac{\text{Actual length of flagpole}}{\text{Shadow of flagpole}}=\frac{\text{Actual length of rod}}{\text{Shadow of rod}}[/tex]
Substitute given values:
[tex]\frac{\text{Actual length of flagpole}}{12\text{ ft}}=\frac{12\text{ ft}}{4\text{ ft}}[/tex]
[tex]\frac{\text{Actual length of flagpole}}{12\text{ ft}}\times 12\text{ ft}=\frac{12\text{ ft}}{4\text{ ft}}\times 12\text{ ft}[/tex]
[tex]\text{Actual length of flagpole}=12\text{ ft}\times 3[/tex]
[tex]\text{Actual length of flagpole}=36\text{ ft}[/tex]
Therefore, the actual length of flagpole is 36 feet.
Find the average rate of change of
f(x) = -2x² - x from x=1 to x=6
Simplify your answer as much as possible
Which of the following statements best describes the graph of x + y = 4?
It is a line which intersects the x-axis at (4, 4).
It is a line which intersects the y-axis at (4, 4).
It is a line joining the points whose x- and y-coordinates add up to 8.
It is a line joining the points whose x- and y-coordinates add up to 4.
You are studying for your final exam on the semester. Up to this point, you received 3 exam scores of 99%, 80%, And 70%. To receive a grade of B in the class, you must have an average exam score between 80% and 89% for all 4 exams including the final. Find the widest range of scores that you can get on the final exam in order to receive a grade of B for the class. Use interval notation
Answer: The interval would be [71,107]
Step-by-step explanation:
Since we ave given that
Scores received in 3 exams are 99%, 80%, and 70%.
To receive a grade of B in the class, he must have an average exam score between 80% and 89% for all 4 exams for all 4 exams.
So, Minimum marks he needs for all 4 exams is given by
[tex]80\times 4=320[/tex]
Maximum marks he needs for all 4 exams is given by
[tex]89\times 4=356[/tex]
And his total marks in 3 exams is
[tex]99+80+70\\\\=249[/tex]
Minimum marks he needs in final exam is given by
[tex]320-249\\\\=71[/tex]
Maximum marks he needs in final exam is given by
[tex]356-249\\\\=107[/tex]
Hence, the interval would be [71,107]
Quadrilateral ABCD is inscribed in a circle. Find the measure of each of the angles of the quadrilateral. Show your work.
In a circle, adjacent angles of a quadrilateral sum up to 180 degrees. Thus, all angles in quadrilateral ABCD inscribed in a circle would each sum up to 180°. Consequently, sum of all the angles of the quadrilateral is 360°.
Explanation:In a circle, adjacent angles of a quadrilateral sum up to 180 degrees. Since a circle consists of 360 degrees, the quadrilateral ABCD has four angles, each angle would sum up to 180 degrees as well. This is because when two cords intersect each other in a circle, they split each other into two segments and the product of the segments of one chord is equal to the product of segments of the other chord.
Let's take an example if we have the angles as A, B, C, and D: A + B = 180° and C + D = 180°. So all the angles of the quadrilateral ABCD inscribed in a circle will sum up to 360°. Hence, A + B + C + D = 180° + 180° = 360°
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please help algebra 2!!
Which represents the solution set of 5(x+5)<85
Using the properties of equality, fill the blanks with the correct value to show the solution for y.
3(y-2)=18
3y-___=18
3y=___
name the postulate or theorem, 50 points please help!
When you use postulates and theorems, you need to make sure to only use the given information that you know. Look for the given statements, and congruence marks on the figure. Those are also considered gives
The waiter places a bowl in front of Caesar. In a counterclockwise direction, he passes the soup to jada who then passes it to Haifa. Which two rotations about the center of the table describes passing the soup?
A) First 200° and then 80°
B) First 180° and then 72°
C) First 150° and then 60°
D) First 100° and then 40°
Answer:
Step-by-step explanation:
first 150 then 60
The question is asking for the correct degree of rotations to simulate the passing of a soup bowl at a circular table. Without specific arrangement details, it's challenging to give a definitive answer, but if people are equidistant, option B 'First 180° and then 72°' would be the closest match.
Explanation:The question asks which two rotations about the center of a circular table would describe the passing of a soup bowl from Caesar to Jada and then to Haifa. Given that the rotation is counterclockwise, we must determine the correct degree of rotations that match the sequence of passing the soup. We can visualize the table as a circle and consider that a full rotation around a circle is 360°.
Depending on the actual arrangement of the people around the table, the combined angles of rotation to pass the soup from Caesar to Jada to Haifa should add up to less than 360°, as they would not have gone a full circle. If we were to look at the options provided:
First 200° and then 80° adds up to 280°,First 180° and then 72° adds up to 252°,First 150° and then 60° adds up to 210°,First 100° and then 40° adds up to 140°.The only way to determine the correct answer is to know the specific arrangement of people around the table, which the question does not provide. Without this information, we cannot definitively choose the correct rotations. However, in general terms, if each person is equidistant from the others in a regular polygon arrangement, we can then divide 360° by the number of people to find the angle corresponding to one pass. Assuming five people at the table, each angle would be 72°. In this case, the closest matching option provided would be First 180° and then 72°.
Austin left for school at 7:35
a.M.He arrived at school 15 minutes later.What time did Austin arrived at school?