What’s the answer for this question?
Given a triangle with vertices U(6, −1), W(0, −5), and X(4, −9), and Y is the midpoint of segment UW and Z is the midpoint of segment WX comma what is the length of YZ?
Here we have to use the distance formula
Please see the image attached with the solution , for the figure
Firstly we have to find the length of line segment XU
and the triangle has a property that the length of line segment that connects the midpoint of the two sides is half the length of the third side.
It means here
Length of YZ = half the length of XU
So lets find the length of XU
[tex] \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}= \sqrt{(6-4)^2 +(-1+9)^2} =\sqrt{4+64} [/tex]
[tex] =\sqrt{68} [/tex]
[tex] =2\sqrt{17} [/tex]
Now the length of YZ = half of [tex] =2\sqrt{17} [/tex]
So length of YZ = [tex] =\sqrt{17} [/tex]
Yvonne purchased a jacket at Right Price, and the lowest price on the tag was $4. This was the sale price, which was calculated by taking 75% off of the original price. What was the original price of Yvonne's jacket?
A Ferris wheel has a circumference of 440 feet. What is the approximate diameter of the Ferris wheel? Use 3.14 for pi
Over a 12 hour period the students estimate that 2,400 bees will leave the hive. How many bees should they expect to travel west?
The sketch shows two parallel lines cut by a transversal. Which pair of angles are alternate interior angles?
Answer:
angle 5 and angle 4
Step-by-step explanation:
The picture frames shown are both squares. The area of the smaller frame is 1/4 the area of the larger frame. Find the side length of the larger frame.
The side length of the larger frame will be 12 inches.
What is an area?The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the square in a two-dimensional plane is called the area of the square.
Given that the area of the smaller frame is 36 square inches and the area of the smaller frame is 1/4 times the area of the larger frame.
The area of the larger frame will be calculated as:-
1/ 4 x Area of larger frame = Area of the smaller frame
Area of the larger frame = 36 x 4
Area of the larger frame = 144 square inches
a² = 144
a = √144
a = 12 inches
Therefore, the length of the larger frame is 12 inches.
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A rectangle is 3 times as long as it is wide. The perimeter is 40 feet. Find the dimensions.
Jackets R us is having a 35% off sale at its outlet store this month.todd is figuring the sale price of a winter jacket normally priced at $89.99.
a. Estimate the sale price. Describe how you found your estimate.
b. calculate the amount that todd will pay for the jacket.
[tex] - 30 = 2(x - 97)[/tex]
what is the slope of a line that is perpendicular to the line that passes through (1,0) and is parallel to y=3x+5
Dora is purchasing a $162,000 home with a 30-year mortgage at 5.15%. What is her monthly principal and interest payment?
A. $829.23
B. $884.56
C. $807.81
D. $876.09
Answer:
Option B is the answer.
Step-by-step explanation:
The formula for EMI is :
[tex]\frac{p\times r\times (1+r)^{n} }{(1+r)^{n} -1}[/tex]
Here p = 162000
r =[tex]5.15/12/100=0.004292[/tex]
n = [tex]30\times12=360[/tex]
Now putting the values in the formula we get,
[tex]\frac{162000\times 0.004292\times (1+0.004292)^{360} }{(1+0.004292)^{360} -1}[/tex]
[tex]\frac{162000\times 0.004292\times (1.004292)^{360} }{(1.004292)^{360} -1}[/tex]
= $884.60 close to option B.
So, option B is the answer.
Which of the numbers 4, 5, or 6 is a solution of x+7>12
Angelo rode his bike around a bike trail that was 1/4 of a mile long. He rode his bike around the trail 8 times. Angelo said he rode his bike a total of 8/4 Miles. Teresa said he was wrong and that he actually rode 2 miles. Who is correct?
identify the type for each quadrilateral
1. Quadrilateral 5: Square (4 equal sides, 4 right angles)
2. Quadrilateral 8: Parallelogram (2 sets of parallel sides, opposite sides not equal)
3. Quadrilateral 11: Trapezoid (1 set of parallel sides, opposite sides not equal, no right angles)
The image shows three quadrilaterals, each labelled with a number:
1. Quadrilateral 5: This shape has four equal sides and four right angles. Therefore, it is a square.
2. Quadrilateral 8: This shape has two sets of parallel sides, but its opposite sides are not equal in length. It also does not have four right angles. Therefore, it is a parallelogram.
3. Quadrilateral 11: This shape has only one pair of parallel sides. Its opposite sides are not equal in length, and it does not have four right angles. Therefore, it is a trapezoid.
Mark raises guppies in an aquarium. He finds out that guppies reproduce very rapidly, and the number quadruples every month. He starts out with only 2 guppies, and the function y equals 2 times 4 to the x models the number of guppies he will have after x months. Which graph represents this function?
In this exercise we have to recognize the graphics given in the images and in this way identify which functions are being represented, in this way we have to:
[tex]y = 2 * (4 ^ x)[/tex]
What is the exponential function?The exponential function represents a dependency relationship. In this type of mathematical operation there is a variable (unknown) in the exponent and the real number (greater than zero and different than one) in the base.
So we know that the graphs are of exponential functions and their form is given by:
[tex]y=a^x[/tex]
With this form we have that the function of the graph is:
[tex]y = 2 * (4 ^ x)[/tex]
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BIG Nicks Moving Company unloaded 72% of the 300 boxes they delivered in 30 minutes. How many boxes did they unload each minute?
greatest common factor of 3 in 10
The greatest common factor of 3 and 10 is 1.
Greatest common factorThe greatest common factor (GCF) of two or more numbers is the largest number that is a factor of all the numbers.
The greatest common factor (GCF) of 3 and 10 is 1. There are no common factors other than 1 that evenly divide both 3 and 10.
Because 3 and 10 do not have any common prime factors, The greatest common factor of 3 and 10 is 1.
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Simplify 8 over -3 divided by -4 over 9
Answer:
2/3
Step-by-step explanation:
you take the problem and write it down then flip the last fraction and multiply them together.
The graph shows Susan’s distance from her office, in yards, as she runs errands, over time, in minutes.
For which values of t (time) is Susan’s distance from her office decreasing from 70 yd to 0 yd?
A.
from t = 0 to t = 6
B.
from t = 10 to t = 12
C.
from t = 16 to t = 22
D.
from t = 22 to t = 26
This figure is made up of a quadrilateral and a semicircle.
What is the area of this figure?
Use 3.14 for pi. Round your answer to the nearest tenth.
A.) 22.8 units²
B.) 40.4 units²
C.) 45.5 units²
D.) 74.5 units²
Answer:
The correct option is B. The area of the figure is 40.4 units².
Step-by-step explanation:
The line AB divides the figure in two parts one is a rectangle and another is semicircle.
The distance formula is
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
The length of AB is
[tex]AB=\sqrt{(2+3)^2+(4-2)^2}=\sqrt{25+4}=\sqrt{29}[/tex]
The length of AD is
[tex]AD=\sqrt{(-1+3)^2+(-3-2)^2}=\sqrt{4+25}=\sqrt{29}[/tex]
Since AB=AD, therefore ABCD is a square. The area of the of square is
[tex]A_1=a\times a=\sqrt{29}\times \sqrt{29} =29[/tex]
The area of square is 29 units².
The area of a semicircle is
[tex]A_2=\frac{\pi}{2}r^2[/tex]
Since AB is the diameter of the semicircle, therefore the radius of the semicircle is
[tex]r=\frac{d}{2}=\frac{\sqrt{29}}{2}[/tex]
The area of the semicircle is
[tex]A_2=\frac{3.14}{2}(\frac{\sqrt{29}}{2})^2=40.3825[/tex]
The area of the figure is
[tex]A=A_1+A_2=29+11.2825=40.3825\approx 40.4[/tex]
Therefore the area of the figure is 40.4 units². Option B is correct.
A finance company offers a 36-month installment loan with an APR of 10.5%. Jerry wishes to use the loan to finance an engagement ring for $21,500. After first using Table 13-1 to find the finance charge, calculate the monthly payment.
what rational number between 9.5 and 9.7
Bill had a salary of $48,000 last year. This year his salary is $49,920. What is the percent increase of Bill's salary?
A circle has a sector with are of (17/2)pi and a central angle of (17/90)pi radians. What is the area of the circle? Either enter an exact answer in terms of pi or use 3.14 pi and enter your answer as a decimal.
Answer:
17pi/2= R* 17pi/90
R=45
A=45^2 * pi
A=90 pi or 282.6
Step-by-step explanation:
Tubas, trombones and French horns are bass instruments. Fully stretched out, the length of a tuba is 18 feet. The length of a trombone is 8 13/14, and the length of a French horn is 17 3/14. The tuba is how much longer than the French horn? And the French horn is how much longer than the trombone?
The length of the Tuba is 11/14 feet longer than the length of the French horn.
The length of the French is 8 ²/₇ feet longer than the length of a Trombone horn.
What is subtraction?It absolutely indicates subtracting something from a commodity, group, location, etc. Subtracting from an assemblage or a list of ways is known as subtraction.
Tubas, trombones, and French horns are bass devices. Fully pulled out, the measurement of a Tuba is 18 feet. The measurement of a trombone is 8¹³/₁₄ feet, and the measurement of a French horn is 17³/₁₄ feet.
The difference between the length of the Tuba and the French horn is given as,
⇒ 18 - 17 ³/₁₄
⇒ 18 - 241/14
⇒ (252 - 241) / 14
⇒ 11/14 feet
The difference between the length of the French and the Trombone horn is given as,
⇒ 17 ³/₁₄ - 8 ¹³/₁₄
⇒ 241/14 - 125/14
⇒ 116 / 14
⇒ 8 ²/₇ feet
The length of the Tuba is 11/14 feet longer than the length of the French horn.
The length of the French is 8 ²/₇ feet longer than the length of a Trombone horn.
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calculate the interquartile range of the following data set: 36, 54, 49, 39, 41, 48, 50
Answer:
14
Step-by-step explanation:
Simplify. (4x4 + 7x2 + 6x) - (x3 - 7x + 10)
A) 4x4 + 6x -10
B) 3x3 + 6x + 10
C) 3x7 +14x3 - 4x
D) 4x4 - x3 + 7x2 + 13x - 10
The ratio of girls to boys who participated in the geography bee was 5:4 there were 36 total students how many were boys
Answer:
There are 16 boys and 20 girls
y 2 + 5y Choose the constant term that completes the perfect square trinomial.
The constant term that completes the perfect square trinomial is 6.25.
Explanation:To complete the square for the given expression y² + 5y, we take half of the coefficient of the linear term (5/2) and square it to find the value to be added. Half of 5/2 is 5/4, and squaring it gives 25/16. Adding 25/16 to the expression yields a perfect square trinomial: y² + 5y + 25/16 = (y + 5/4)².
To write it in standard form, we convert 25/16 to 1.5625. Therefore, the constant term that completes the perfect square trinomial is 1.5625, or 6.25 when expressed as a decimal.