If VX is the bisector of V, find the perimeter of VUW.
A 35
B. 46
C. 58
D. 70
Answers
Answer:
D. 70
Step-by-step explanation:
If VX is the bisector of V, then UX=WX.
This implies that:
[tex]3z-4=z+6[/tex]
Group similar terms:
[tex]3z-z=4+6[/tex]
[tex]2z=10[/tex]
z=5
WU=2(z+6)
WU=2(5+6)
WU=2(11)=22 units
VW=VU=5z-1
Put z=5 to get;
VW=VU=5(5)-1
VW=VU=25-1
VW=VU=24
The perimeter of VWU=24+24+22=70 units
Answer:
Perimeter of triangle VUW = 70.
Step-by-step explanation:
Since VX is angle bisector and VX is perpendicular to UW then triangle UVX is congruent to triangle WVX using ASA property.
then UV=WV...(i) {corresponding sides of congruent triangle are equal.}
and UX=WX ...(ii) {corresponding sides of congruent triangle are equal.}
then 3z-4=z+6
3z-z=6+4
2z=10
z=5
then UW=(3z-4)+(z+6)=3(5)-4+(5)+6=22
WV=5z-1=5(5)-1=24
UV=WV=24
Then perimeter of triangle VUW is
UV+WV+UW=24+24+22=70
Hence final answer is:
Perimeter of triangle VUW = 70.
Related Questions
Stay the amplitude and maximum output for the function!!! Help needed!!
Answers
ANSWER
The amplitude is 2 and the maximum value is 2.
EXPLANATION
The given function is
[tex]f(t) = 2 \sin(t) [/tex]
This function is of the form:
[tex]f(t) = a\sin(bt) [/tex]
The amplitude of this function is
[tex] |a| [/tex]
Hence the amplitude is
[tex] |2| = 2[/tex]
Since the amplitude is 2, and there is no vertical shift, it means the function is bounded by
y=-2 and y=2.
The maximum value is :
2
Wei has $150.00 to make a garland using 60-cent balloons. He wants to purchase 100 blue balloons and some number of white balloons. He learns that the white balloons are on sale for half price. He writes and solves an equation to find the number of white balloons he can purchase.
Answers
Answer:
Step-by-step explanation
i believe the answer is 300
100 times 60 cents would be 60.00$
the question states that the white balloons are half off making it 30 cents
300 times 30 is 90.00
90.00 plus 60.00 would be 150.00$
300 white balloons is what he may purchase
He can purchase 300 white balloons.
Wei can purchase 100 blue balloons for $60.00 (100 * $0.60). He has $150.00 - $60.00 = $90.00 left to spend on white balloons. Since the white balloons are on sale for half price, each white balloon costs $0.60 / 2 = $0.30. Therefore, Wei can purchase $90.00 / $0.30 = 300 white balloons. In total, he can purchase 100 blue balloons and 300 white balloons for the garland.
To calculate the number of white balloons Wei can purchase, we first find the total cost of the blue balloons, which is 100 * $0.60 = $60.00. Then, we subtract this from Wei's budget of $150.00 to find the remaining amount for white balloons: $150.00 - $60.00 = $90.00.
Since the white balloons are on sale for half price, each white balloon costs $0.60 / 2 = $0.30. We divide Wei's remaining budget by the cost per white balloon to find how many he can purchase: $90.00 / $0.30 = 300 white balloons.
So, Wei can purchase 100 blue balloons and 300 white balloons for the garland.
Complete question:
Wei has $150.00 to make a garland using 60-cent balloons. He wants to purchase 100 blue balloons and some number of white balloons. He learns that the white balloons are on sale for half price. He writes and solves an equation to find the number of white balloons he can purchase.
Surface area of a cylinder with a radius and height of 1.5 m
Answers
Answer:
28.27
Step-by-step explanation:
Answer:
The surface area of cylinder = 28.26 m²
Step-by-step explanation:
Points to remember
Surface area of cylinder = 2πr(r + h)
Where r - Radius of cylinder and
h - Height of cylinder
To find the surface area of given cylinder
Here r = 1.5 m and h = 1.5 m
Surface area = 2πr(r + h)
= 2 * 3.14 * 1.5(1.5 + 1.5)
= 2 * 3.14 * 1.5 * 3
= 28.26 m²
Therefore the surface area of cylinder = 28.26 m²
Allison, Brianna, and Celeste went on a hike. Allison brought 9 homemade
cookies and Brianna brought 15 cookies she had made. Celeste forgot to bring
treats, but she had $2.16. Allison and Brianna agreed that if the three were to
share the cookies equally, then the two of them should divide Celeste's money
equitably. Celeste agreed. What was the fair way to divide the money?
I don't get this at all PLEASE HELP!
Answers
Answer:
Allison = $0.27
Brianna = $1.89
Step-by-step explanation:
The total cookies that the three girls have are:
Allison's cookies + Brianna's Cookies
= 9+15
=24
There is a total of 24 cookies which has to be divided between the 3.
So
Each girl gets 24/3 = 8 cookies.
Since Celeste had no cookies she will have to pay for the 8 cookies.
Allison had 9, she will give one to Celeste
Brianna had 15 out of which she will use 8 for her self and 7 will be given to Celeste.
Celeste is paying 2.16 for 8 cookies.
Price of one cookie = 2.16/8
=$0.27
So, amount that will be given to Allison = 0.27 * 1 = $0.27
Amount that will be given to Brianna = 0.27 * 7 = $1.89
Each person gets 8 cookies. Allison and Brianna each receive $1.08 of Celeste's $2.16.
To find the fair way to divide Celeste's money, we first need to determine how many cookies each person gets when the total number of cookies is divided equally among them.
Total number of cookies = Allison's cookies + Brianna's cookies
Total number of cookies = 9 cookies + 15 cookies
Total number of cookies = 24 cookies
Now, we'll divide the total number of cookies by the number of people (3) to find out how many cookies each person gets:
Number of cookies per person = Total number of cookies / Number of people
Number of cookies per person = 24 cookies / 3
Number of cookies per person = 8 cookies
So each person will get 8 cookies.
Now, since Celeste forgot to bring treats, Allison and Brianna agreed to divide Celeste's money equally between them. To do this fairly, they'll each receive half of Celeste's money.
Celeste's money = $2.16
Now, we'll find out how much each person gets from Celeste's money:
Amount per person = Celeste's money / Number of people
Amount per person = $2.16 / 2
Amount per person = $1.08
So each person will receive $1.08 from Celeste's money.
In summary:
- Each person will get 8 cookies.
- Each person will receive $1.08 from Celeste's money.
cody wants to attend the fall festival at school. the price of admission to the festival is $5.50 and each game costs an additional 75 cents . if cody has 15 dollars to spend at the festival, which inequality can be used to solve for g, the number of games that he can play, and what is the maximum number of games he can play?
Answers
Cody can play 12 games.
PLEASE HELP ME!!!!
The figure shows the location of 3 points around a lake. The length of the lake, BC, is also shown.
Which of the following options is closest to the distance (in miles) between points A and B?
2.24 miles
2.65 miles
3.74 miles
5.29 miles
Answers
Answer:
AB² = VAC²-BC²
= V8²-6²
= V64-36 = V28
AB = V7×4 = 2V7 = 5.29
Factor 3k^2+13k-56.
Answers
Answer:
(k + 7)(3k - 8)
Step-by-step explanation:
To factor the quadratic
Consider the factors of the product of the k² term and the constant term which sum to give the coefficient of the k- term
product = 3 × - 56 = - 168 and sum = + 13
The factors are + 21 and - 8
Use these factors to split the k- term
3k² + 21k - 8k - 56 ( factor the first/second and third/fourth terms )
= 3k(k + 7) - 8(k + 7) ← factor out (k + 7)
= (k + 7)(3k - 8)
Need help with financial algebra
Answers
Answer: [tex]c(x) =\left \{ {{18\qquad 0<x\leq 3} \atop {6.5x+18\quad x>3}} \right.[/tex]
Step-by-step explanation:
The first equation is c(x) = 18 when x is between 0 and 3 (including 3).
The second equation is c(x) = 6.5x + 18 when x is greater than 3
The results of joes survey show that baseball is the favorite sport for 18 out of 25 people. What percent do not like sports?
Answers
well if 18 out of 25 like it, then the remaining 7 doesn't like it, namely 7 out of 25.
if we take 25 to be the 100%, what is 7 off of if in percentage?
[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 25&100\\ 7&x \end{array}\implies \cfrac{25}{7}=\cfrac{100}{x}\implies 25x=700\implies x=\cfrac{700}{25}\implies x=28[/tex]
A company makes plastic beach balls with a radius of 2 inches. How many square inches of plastic does the company need to make 10 beach balls? Use 3.14 for mc017-1.jpg and round to the nearest tenth.
Recall the formula mc017-2.jpg.
mc017-3.jpg
mc017-4.jpg
mc017-5.jpg
mc017-6.jpg
Answers
Answer:
125.6 square inches of plastic is needed
Step-by-step explanation:
To make 10 plastic beach balls each with a radius of 2 inches, the company would need approximately 502.4 square inches of plastic.
To determine the amount of plastic needed to make 10 beach balls, we first calculate the surface area of one beach ball. The formula for the surface area of a sphere is 4πr². Given the radius of 2 inches, we plug this into the formula:
A = 4πr² = 4 × 3.14 × (2 inches)² = 4 × 3.14 × 4 square inches = 50.24 square inches.
Since this is for one beach ball, we need to multiply this amount by 10, to account for the total plastic needed for 10 beach balls:
Total surface area for 10 beach balls = 50.24 square inches × 10 = 502.4 square inches.
Therefore, the company would need approximately 502.4 square inches of plastic to make 10 beach balls, rounding to the nearest tenth.
Let f(x)=x^2+x−42 . Enter the x-intercepts of the quadratic function in the boxes. x = and x =
Answers
We simply have to solve a quadratic equation [tex]ax^2+bx+c=0[/tex] using the quadratic formula
[tex]x_{1,2} = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
In your case, [tex]a=b=1,\ c=-42[/tex]. So, the formula becomes
[tex]x_{1,2} = \dfrac{-1\pm\sqrt{1+168}}{2} = \dfrac{-1\pm 13}{2}[/tex]
So, if we choose the two signs, we have
[tex]x_1 = \dfrac{-1-13}{2}=-7,\quad x_2 = \dfrac{-1+13}{2}=6[/tex]
Answer:
x = -7, x = 6
Step-by-step explanation:
f(x) = x² + x − 42
You can use the quadratic formula to find the roots (x-intercepts), or, if it's "factorable", you can use the AC method.
Here, a = 1, b = 1, and c = -42.
The product a times c is -42.
Factors of ac that add up to b are +7 and -6.
So the quadratic factors to:
f(x) = (x + 7) (x − 6)
To find the x-intercepts, we set this equal to 0:
0 = (x + 7) (x − 6)
x + 7 = 0, x − 6 = 0
x = -7, x = 6
What is the y intercept of the parabola y = x2 + 8x + 6
Answers
6
The formula for a quadratic equation (parabola) is y = ax^2 + bx + c, and c is the y-intercept. Following this, the y-intercept of this parabola is 6.
In the year 2000 the population of Mexico was about 100 million, and it was growing by 1.53% per year. At this growth rate, the function f(x) = 100(1.0153)^x gives the population, in millions, x years after 2000. Using this model, in what year would the population reach 118 million? Round your answer to the nearest year.
Answers
Answer:
11 years
Step-by-step explanation:
Set the function f(x) = 100(1.0153)^x = to 118 and solve for x:
100(1.0153)^x = 118
Taking the natural logarithm of both sides, we get:
ln 100 + x ln 1.0153 = ln 118
Then x ln 1.0153 = ln 118 - ln 100, or
= 4.7707 - 4.6052
... which leads to:
4.7707 - 4.6052
x = --------------------------- = 11 years (rounded up from 10.888 )
0.0152
Answer:
11 years
Step-by-step explanation:
Someone plz help with this
Answers
Answer:
the answer is: [tex]5y^6 \sqrt{2}[/tex]
Step-by-step explanation:
We need to solve the equation:
[tex]\sqrt{50y^{12}}[/tex]
We know 50 = 2*5*5
2*5*5 can be written as: 2* 5^2
and √ = 1/2
Solving:
[tex]=\sqrt{2*5*5*y^{12}}\\= \sqrt{2*5^2*y^{12}}\\=(2)^{1/2}*(5^2)^{1/2}*y^{12}^{1/2}\\=(2)^{1/2}*5*y^6\\=5y^6 \sqrt{2}[/tex]
So, the answer is: [tex]5y^6 \sqrt{2}[/tex]
A fountain is located between two trees. Each tree has a height of 60 feet. The angles of elevation from the
base of the fountain to the top of each tree are 64° and 48° as shown below.
What is the horizontal distance between the two trees (rounded to the nearest foot)
A 40
B 837
C 147
D 190 ft
Answers
The answer is:
The correct option is:
B) 83 feet
Why?To solve the problem, we need to use the following trigonometric identity:
[tex]Tan(\alpha)=\frac{Opposite}{Adjacent}[/tex]
Which, translated to our problem, will be:
[tex]Tan(\alpha)=\frac{Height}{Base}[/tex]
We are given two triangles, and we know their height and their angles between their hypothenuse and their bases.
So,
For the first triangle, we have:
[tex]height=60ft\\\alpha=64\°[/tex]
So, using the trigometric identity of the tangent, we have:
[tex]Tan(\alpha)=\frac{Height}{Base}\\\\Tan(64\°)=\frac{60ft}{Base}\\\\Base=\frac{60ft}{Tan(64\°)}=\frac{60ft}{2.05}=29.27ft[/tex]
Therefore, we have that the base of the first triangle is equal to 29.27 feet.
For the second triangle, we have:
[tex]height=60ft\\\alpha=48\°[/tex]
So, using the trigometric identity of the tangent, we have:
[tex]Tan(\alpha)=\frac{Height}{Base}\\\\Tan(48\°)=\frac{60ft}{Base}\\\\Base=\frac{60ft}{Tan(48\°)}=\frac{60ft}{1.11}=54.05ft[/tex]
Therefore, we have that the base of the second triangle is equal to 54.05 feet.
Now, to calculate the horizontal distance between the two trees (x), we need to use the following formula with the obtained values of both triangles:
[tex]HorizontalDistance=FirstTriangleBase+SecondTriangleBase\\\\HorizontalDistance=29.27ft+54.05=83.29ft[/tex]
Hence, we have that the distance between the two trees rounded to the nearest foot is 83 feet.
Have a nice day!
Greatest common factor of 12a and 9a^2
Answers
Answer:
3aStep-by-step explanation:
[tex]12a=\bold{(3)}(4)\bold{(a)}\\\\9a^2=\bold{(3)}(3)\bold{(a)}(a)\\\\GCF(12a,\ 9a^2)=\bold{(3)(a)}=3a[/tex]
Which polynomial is in standard form.
Answers
Answer:
4- [tex]7x^{7} y^{2} + 5x^{11} y^{5} - 3xy^{2} + 2[/tex]
Step-by-step explanation:
In a standard polynomial degree drops from left to right
so , option 4 is correct.
[tex]7x^{7} y^{2} + 5x^{11} y^{5} - 3xy^{2} + 2[/tex]
Two people share £350 in the ratio 1 : 6.
Calculate each share.
Answers
Answer:
£50 and £300
Step-by-step explanation:
Sum the parts of the ratio 1 + 6 = 7 parts
Divide the amount by 7 to find the value of one part of the ratio
£350 ÷ 7 = £50 ← value of 1 part of ratio
Hence
1 person receives £50
the other person receives 6 × £50 = £300
To find the two shares in the given ratio, divide the total amount by the sum of the ratio. The first share is 1/7 of the total, while the second share is 6/7 of the total.
Explanation:To find the two shares, we need to divide £350 into two parts using the ratio 1:6. To do this, we must first understand that the ratio sum is 1+6=7. The first share is 1/7 of the total amount, calculated as (1/7)*£350 = £50. The second share is 6/7 of the total amount, calculated as (6/7)*£350 = £300.
Learn more about Calculating Shares here:https://brainly.com/question/32553819
#SPJ1
A sales representative from a local radio station is trying to convince the owner of a small fitness club to advertise on her station. The representative says that if the owner begins advertising on the station today, the club's total number of members will grow exponentially each month. She uses the given expression to model the number of club members, in hundreds, after advertising for t months. 1.8(1.02)^12t What does the value 1.8 represent?
Answers
Answer:
The value 1.8 represent the club's total number of members today or the present number of members
Step-by-step explanation:
Given an exponential function;
[tex]y=ab^{x}[/tex]
b is the base or the growth factor
a is the initial value, that is the value of y when x = 0
We have been given the exponential function;
[tex]y=1.8(1.02)^{12t}[/tex]
The value 1.8 simply represents the initial value of y. Plug in t = 0 in the equation;
[tex]y=1.8(1.02)^{12(0)}=1.8[/tex]
Therefore, the value 1.8 represent the club's total number of members today or the present number of members
what is the solution to the system of equations represented by these two lines ?!!
Answers
The solution is the point where the two lines intersect, so it is (3,1)
I need help! Can anyone help me?! Thanks
Answers
Answer:
not sure what you need help on but im guessing:
7 > H, 3r-8
Choose the compound inequality that can be used to solve the original inequality |3x – 5| > 10
Answers
Answer: C. would be your option
Step-by-step explanation:
Answer:
3x – 5 < –10 or 3x – 5 > 10
Answer choice C on Edge
1. Which expression represents the following calculation?"Add 4 and 6, then multiply 5,then add 10.
2.Write an algebraic expression for: 9 times the sum of 9b and 2.
3.What is the coefficient in the expression 40a-61=17?
4. Write the algebraic expression into words.
4/5(9+r)+8w.
5.What is the quotient in the expression c=45/d?
Answers
Answer:
1. 5(4 + 6) + 1-0
2. 9(9b + 2)
3. 40
4. Nine plus r multiplied by four over five and then added to eight w.
5. The quotient is [tex]\frac{45}{d}[/tex]
Step-by-step explanation:
The pine scrub rail trial is 72 miles long. if the willy-nilly bike club rides 18 miles per day, how many days will it take them to ride from one end of the trail to the other?
Answers
It would take the willy-nilly bike club 4 days to ride from one end of the trail to the other
By dividing the total distance of the trail (72 miles) by the distance the bike club covers each day (18 miles), we find it would take 4 days for the Willy-Nilly Bike Club to ride from one end of the Pine Scrub Rail Trial to the other.
Explanation:To find out how many days it will take the Willy-Nilly Bike Club to ride the entire Pine Scrub Rail Trial, we will use division. This kind of mathematical problem is a practical application of division in real-life scenarios.”
The total length of the trail is 72 miles. If they cover 18 miles each day, we can divide the total miles by the miles they ride each day.
So, 72 ÷ 18 = 4 days.
Therefore, it will take the Willy-Nilly Bike Club 4 days to ride from one end of the trail to the other, assuming they ride 18 miles every day without taking any breaks.
Learn more about Division here:https://brainly.com/question/2273245
#SPJ12
16.72911 liters rounded to the nearest whole is liters.
Answers
Answer:
17 liters
Step-by-step explanation:
0.5 and above will make 1, 0.4 and below makes it the same
What is the equation of a circle with center (3, 8) and radius 2?
Answers
Answer:
(x - 3)² + (y - 8)² = 4
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
here (h, k) = (3, 8) and r = 2
(x - 3)² + (y - 8)² = 4 ← equation of circle
The equation of a circle with center (3, 8) and radius 2 will be given as
[tex]( x -3 )^2 + ( y -8 )^2 = 4[/tex].
Equation of circle is given as,
[tex]( x -a )^2 + ( y -b )^2 = r^2[/tex]
where,
(a,b) are the coordinates of the center of the circle in form (x, y),
r is the radius of the circle.
Now, the equation of a circle with center (3, 8) and radius 2.
Given to us,
a = 3,
b = 8,
r = 2.
substituting the values,
[tex]( x -a )^2 + ( y -b )^2 = r^2[/tex]
[tex]( x -3 )^2 + ( y -8 )^2 = 2^2[/tex]
[tex]( x -3 )^2 + ( y -8 )^2 = 4[/tex]
Hence, the equation of a circle with center (3, 8) and radius 2 will be given as [tex]( x -3 )^2 + ( y -8 )^2 = 4[/tex].
Learn more about circles:
https://brainly.com/question/10165274
what is the value of x
Answers
The value of x is 114 degrees.
X is a vertical angle with the given angle of 114.
This means X is also 114 degrees.
The exact value of cos(17pi/8) is
Answers
[tex]\frac{\sqrt{2 + \sqrt2}}{2}[/tex]
Answer:
Step-by-step explanation:
Note that 17pi/8 can be rewritten as 16pi/8 + 1pi/8. 16pi/8 represents 2 full rotations around the center and can be ignored if we just want the cosine of the angle 17pi/8. We are left then with 1pi/8.
We need to find the cosine of this angle. Note that 1pi/8 is 1/2 of 1pi/4, so this situation calls for use of the half angle formula
1 + cos Ф
cos Ф/2 = √(---------------). Here Ф = π/4, and half that is ω = π/8, and the
2 cosine of π/4 is 1/√2.
1 + 1/√2 √2 + 1 2 + √2
So we get cos pi/8 = √( -------------- ) = √ ------------- = √ ---------------
2 2√2 4
one cook can make enough food for 350 people a night. how many cooks are needed to feed 2,944 a night?
Answers
Answer:
9
Step-by-step explanation:
the answer is 8.4 so it might not be rounded up but I figure what about the other people?
9 chefs are needed. you have to divide 2,944 by 350
Given f(x) = 3x - 1 and 9(x) = 2x-3, for which value of x does g(x)=f(2)?
Answers
Answer:
g(x) = f(2) at x = 4
Step-by-step explanation:
Assuming that you meant g(x) = 2x - 3:
Set f(2) = g(x) and solve the resulting equation for x:
f(2) = 3(2) - 1 = g(x) = 2x - 3.
Thus, 6 - 1 = 2x - 3.
Adding 3 to both sides and simplifying the result, we get:
8 = 2x, or x = 4.
g(x) = f(2) at x = 4.