Using cosine rule, the length of side t is 31.5 unit
Cosine RuleCosine rule states that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.
The formula is given as
t² = s² + u² -3su cos(T)
let's define our variables
t = ?s = 34u = 40.5T = 49 degreessubstituting the values into the formula
t² = 34² + 40.5² -2(34)(40.5)cos49
t² = 1156 + 1640.25 - 1806.79
t² = 989.46
t = √989.46
t = 31.5
The length of t is 31.5 unit
Learn more on cosine law here;
https://brainly.com/question/4372174
#SPJ1
need help asappppppp
We are asked to determine the volume of the cylinder. To do that we will use the following formula:
[tex]V=\pi r^2h[/tex]Where "r" is the radius and "h" is the height. Replacing the values:
[tex]V=(3.14)(4cm)^2(10\operatorname{cm})[/tex]Solving the operations:
[tex]V=502.4cm^3[/tex]Therefore, the volume is 502.4 cubic centimeters.
EUREKA M
3. Give an example of a scale factor that produces an enlargement. Explain why you chose this
scale factor.
on. Explain why you chose this
scale factor.
We will take an example of a rectangle with a scale factor of enlargement by 2.
For example, consider a rectangle with dimensions of 6 cm and 3 cm.
If we increase the scale factor for the initial rectangle by 2, both sides of the rectangle will be doubled. By raising the scale factor, we mean multiplying the present rectangle measurement by the supplied scale factor. We have multiplied the original rectangle measurement by 2 here.
The rectangle's length was originally 6 cm and its width was 3 cm.
After multiplying by two, the length is 12 cm and the width is 6 cm.
Thus, we took an example of a rectangle with a scale factor of enlargement by 2. We consider this for a better understanding.
To learn more about scale factors visit:
https://brainly.com/question/22312172
#SPJ9
Given the end points of A(-8,-2) and B(6,19). The segment AB is divided into the ratio atAR:RB in a 2:5 ratio. Find the coordinates of point R.R=
The given coordinates in the question are
[tex]\begin{gathered} A=(-8,-2)\text{ = x1=-8, y1=-2} \\ B=(6,19)\text{ = x}2=6,y2=19 \end{gathered}[/tex]Let the coordinate at R be
[tex]R=(x,y)[/tex]The ratio of the line segment given is
[tex]AR\colon RB=2\colon5\text{ (m=2,n=5)}[/tex]The formula to calculate the coordinate of a line segment in a given ratio is given below as
[tex](x,y)=(\frac{mx_2+nx_1}{m+n}),(\frac{my_2+ny_1}{m+n})[/tex][tex]undefined[/tex]if gh=53 and hi=7 then gi=
In the given line, the length of the line gi is 60 units.
What is a line?A line is an indefinitely long, straight object that is drawn with a minimum width in geometry but is said to have no specific width in mathematics since it lacks depth.An angle is created when two straight lines or rays intersect at a single terminal. The vertex of an angle is the location where the two rays meet.So, the length of gi will be:
We know that,
gh = 53hi = 7Now, we can easily see that the given line is:
gi = gh + higi = 53 + 7gi = 60Therefore, in the given line, the length of the line gi is 60 units.
Know more about lines here:
https://brainly.com/question/24644930
#SPJ1
The product of eight and a number b
Write a variable expression for the word phrase
A true-false test contains 13 questions. In how many different ways can this test be completed. (Assume we don't care about our scores.
Answer:
Explanation:
There are two possible answers for a tue-false test:
True and False
It is given
estimated sales volume =47.81+0.47(Advertising Expenditures)If the company has a target sales volume of $175,000,how much should the sales manager allocate for the advertising in the budget ? round your answer to the nearest dollar
We are given an estimate equation.
Let the estimate sales volume be "s" and advertising expenditure be "a".
The given equation is:
[tex]s=47.81+0.47a[/tex]The company has a target sales of 175,000, which is a value for "s".
To get how much they need to allocate for advertising, we can solve for "a" in the equation and substitute the "s" value with 175,000:
[tex]\begin{gathered} s=47.81+0.47a \\ 47.81+0.47a=s \\ 0.47a=s-47.81 \\ a=\frac{s-47.81}{0.47} \end{gathered}[/tex]Now we substitute 175,000 into "s":
[tex]a=\frac{175,000-47.81}{0.47}=\frac{174,952.19}{0.47}=372,238.7021\ldots\approx372,239[/tex]So, by the equation estimate, the sales manager should allocate $327,239 for advertising.
How many one and one-sixths are in five and five-sixths?
Using operations of fractions, the answer obtained is
There are 5 [tex]1\frac{1}{6}[/tex] in [tex]5\frac{5}{6}[/tex]
What is fraction?
Suppose there is a collection of objects and a part of the collection has to be taken. The part which is taken is called fraction. In other words, part of a whole is called fraction.
The upper part of the fraction is the numerator and the lower part of the fraction is the denominator,
Let there are x [tex]1\frac{1}{6}[/tex] in [tex]5\frac{5}{6}[/tex]
[tex]1\frac{1}{6} x = 5\frac{5}{6}\\\frac{7}{6}x = \frac{35}{6}\\x = \frac{35}{6} \times \frac{6}{7}\\x = 5[/tex]
There are 5 [tex]1\frac{1}{6}[/tex] in [tex]5\frac{5}{6}[/tex]
To learn more about fraction, refer to the link -
https://brainly.com/question/17220365
#SPJ1
Ms. Perea wants to cover the floor withrectangular tiles that measure 1.5 feet by0.8 feet. Which equation can be used tofind t, the number of tiles she will need tocover the kitchen floor?
We need to find the area of a rectangle. The area of a rectangle is given by:
[tex]\begin{gathered} A=w\cdot l \\ where\colon \\ w=width \\ l=length \\ \end{gathered}[/tex]The rectangular tiles that measure 1.5 feet by 0.8 feet. So the area of each tile is:
[tex]At=1.2ft^2[/tex]Therefore, the number of tiles will be the total area of the floor divided by the area of each tile:
[tex]\begin{gathered} t=\frac{A}{At} \\ t=\frac{A}{1.2} \\ t=(22.5\times12.5)\div(1.5\times0.8) \end{gathered}[/tex]5 less than the square of a number
x^2 - 5 this will be the equation formed.
What is exponents?An exponent is the number of times a number is multiplied by itself. For example, 2 to the third (written as 23) means: 2 x 2 x 2 = 8. 23 is not the same as 2 x 3 = 6. Remember that a number raised to the power of one is itself.
Calculationlet the number be x
x^2 - 5 this will be the equation formed
learn more about exponents here :
brainly.com/question/5497425
#SPJ1
Only 1 and 2 pls helppp
Answer:
See the attached image for work.
1) The slope is 4.
2) The slope is 2.
Answer:
on the first one the rise is 20 and the run is 5. 5 divided by 20 is 4 so the slope is 4. I haven't answered the second one yet, sorry.
Tic, Tac and Toe are siblings. Toe is Tic and Tac's brother
but Tic is not Toe's brother. How is Tic related to Toe?
Answer: Tic is either Toe's brother or sister.
Step-by-step explanation: There's really no explanation. It's just outside the box thinking.
helppppppppppppppppppppppppppppppppppppppppp asapppppppppppppppppppppppppppppppp
Answer:
5
Step-by-step explanation:
((12*3)-(3*1/3))/((4*3-5))=
((36)-(1))/((12-5))=
(35)/(7)=5
Answer: it is going to be 35/7 = 5
Find a pair of adjacent angles:4 and 14Find a pair of vertical angles:233 and 21)
SOLUTION
By definition, adjacent angles are (of a pair of angles) formed on the same side of a straight line when intersected by another line.
Vertical Angles are the angles opposite each other when two lines cross.
Going by this above definition, a pair of adjacent angles in the figure in Q1 are:
4 and 2.
Going by this above definition, a pair of vertical angles in the figure in Q1 are:
3 and 2.
a ferris wheel casts a 42 m shadow. a man two meters tall casts a 3 m shadow. how tall is the first wheel (in meters)?
The ferris wheel cast a shadow of 42 meters Tall.
A man of height 2 meters cast a shadow of 3 meters . The height of the ferris wheel can be computed below
[tex]\begin{gathered} 2\text{ meters = 3 meters} \\ x\text{ meters=42 meters} \\ \text{cross multiply} \\ 3x=84 \\ x=\frac{84}{3} \\ x=28\text{ meters} \end{gathered}[/tex]height of the ferris wheel = 28 meters
Jerome and Tara played in a golf
tournament with four rounds. Their
scores for the rounds are given below.
If their final score is the sum of their
four rounds, which statement is true?
Round 1 Round 2 Round 3 Round 4
-4
5
-6
-2
2
-5
-4
-1
Jerome
Tara
Answer:JEROME
Step-by-step explanation:
Kaitlyn flew 630 miles in 60 minutes. How many miles per minute did she fly?
Answer:
10.5 miles per minute
Step-by-step explanation:
630/60=10.5
Find g(x), where g(x) is the translation 5 units left of f(x) =3(x+5)^2 -7
The rule for the translated function is:
g(x) = 3*(x + 10)^2 - 7
How to find the rule for g(x)?
First, we know that for a function f(x) a horizontal translation of N units is written as:
g(x) = f(x + N)
If N > 0, the translation is to the left.
if N < 0, the translation is to the right.
A translation of 5 units to the left is written as:
g(x) = f(x + 5)
Replacing f(x) we get:
g(x) = 3*(x + 5 + 5)^2 - 7
g(x) = 3*(x + 10)^2 - 7
Learn more about translations:
https://brainly.com/question/24850937
#SPJ1
A square pyramid and a square prism have the same length, width, and height. If the volume of the square prism is 900in3 , what is the volume of the square pyramid?
A square pyramid and a square prism have the same length, width, and height. If the volume of the square prism is 900in3 , what is the volume of the square pyramid?
we know that
The volume of the square prism is equal to
[tex]V=b^2\cdot h[/tex]where b is the length side of the square base and h is the height of the prism
The volume of the square pyramid is
[tex]V=\frac{1}{3}\cdot b^2\cdot h[/tex]Remember that
the volume of the square prism is 900in3
so
[tex]900=b^2\cdot h[/tex]substitute in the formula of volume of the pyramid
[tex]\begin{gathered} V=\frac{1}{3}\cdot b^2\cdot h \\ \\ V=\frac{1}{3}\cdot900 \\ V=300\text{ in\textasciicircum{}3} \end{gathered}[/tex]the volume of the pyramid is 300 cubic inchesGames at the carnival costs $7 each. The prizes awarded to the winners costs the owner $177.35. How many games must be played for the owner to make at least $75.
Use g as your variable. Round your inital answer to the nearest hundredth.
At least 36.05 games should be played for the owner to make at least $75.
Let the number of games played = g
According to question,
Cost of each game = $7
Cost of g games = 7g
Prizes awarded to the winner costs the owner = $177.35
To make at least $75, the equation is
7g - 177.35 ≥ 75
7g ≥ 75 + 177.35
7g ≥ 252.35
g ≥ 252.35 / 7
g ≥ 36.05
Hence, at least 36.05 games should be played.
Learn more about games on:
https://brainly.com/question/3863314
#SPJ1
what is the population standard deviation for the numbers 75,83,96,100,121,125
Answer: 332.6667
Step-by-step explanation: trust
I need some help with this problems please Number 10
Explanation:
We can see that this is an isosceles triangle, because there are two sides that are 4 units long and the third side is 3 units long.
For isosceles triangles we have the following congruences:
Therefore angle x is congruent to the one that's 66º.
Then we have that the measures of the interior angles of any triangle add up 180º:
[tex]\begin{gathered} yº+xº+66º=180º \\ y+66º+66º=180º \\ y+132º=180º \\ y=180º-132 \\ y=48º \end{gathered}[/tex]Answers:
• x = 66º
,• y = 48º
A graden plot 4m by 12m has one side along the fence.The area of the garden is to be doubled by digging a border of uniform width on the other three sides.What should the width of the border be?
The width of the border is 6 m after digging a border of uniform width on the other three sides.
Step 1:
Original garden plot is 4 m by 12 m. The 12 m side is against the wall.
A border of length D is along three sides of the plot (the 4th side is the wall).
Step 2
area of original garden plot is 12 x 4 = 48 [tex]m^{2}[/tex]
area of new plot = 96 [tex]m^{2}[/tex] (twice the original plot)
96 = (4 + D) (12 + 2D)
Set up equation for the area of the new area of the new plot (double the area of the old garden plot).
Step 3
96 = (4 + D) (12 + 2D)
[tex]96 = 2d^{2}+12d+4(2d+12)[/tex]
[tex]96 = 2d^{2}+12d+8d+48[/tex]
[tex]96 = 2d^{2}+20d+48[/tex]
[tex]96 -2d^2-20d-48 = 0[/tex]
[tex]48-2d^2-20d = 0[/tex]
[tex]-2(d^2+10d-24) = 0[/tex]
d = -12
Now solve for D
Step 4
D = 6 meters
Ignore negative answer because border must be a positive number. So Border is -12 [tex]m^{2}[/tex] (6 m).
Hence the answer is the width of the border is 6 m after digging a border of uniform width on the other three sides.
To learn more about area click here https://brainly.com/question/25292087
#SPJ1
Points A and C are two opposite
vertices of the ABCD square. Find the
area of this square.
A(3,2), C(7,2)
The area of the square is 8 square units.
According to the question,
We have the following information:
Points A and C are two opposite vertices of the ABCD square.
The coordinates of these points are A(3,2), C(7,2).
Now, we will use the distance formula to find AC:
d = [tex]\sqrt{(y2-y1)^{2}+ (x2-x1)^{2} }[/tex]
d = [tex]\sqrt{(2-2)^{2}+ (7-3)^{2} }[/tex]
d = [tex]\sqrt{4^{2} }[/tex]
d = 4 units
Now, when A and C are opposite vertices then AC is a diagonal.
Side of the square = diagonal/[tex]\sqrt{2}[/tex]
Side = 4/√2 units or 2√2 units
Formula to find the area of square:
Side*side
2√2*2√2
4*2
8 square units
Hence, the area of the square is 8 square units.
To know more about area of the square here
https://brainly.com/question/27776258
#SPJ1
help meeeeeeeeeeeeeeeeeeee pleaseee rnnnn rn!!!!
The width of the rectangle is equal to 3.42 meters
Let the width of the rectangle be represented by the variable x
thus from the question we can say that the length of the rectangle is 3 + x
Given is the area of the rectangle
we know that the area of the rectangle is Length × Breadth
Given area of the rectangle = 22 square meters
thus Area = Length × Breadth
On substituting the value we get
22 = ( 3 + x ) ( x )
x² + 3x = 22
x² + 3x - 22 = 0
b² - 4ac = 9 + 88 = 97
thus - b ± [tex]\sqrt{b^{2} -4ac}[/tex] / 2a
= - 3 ± 9.84 / 2
Thus the two values of x we will get are :
x= -12.84 / 2 = -6.42 which is rejected because width cant be negative
thus the value of x = 6.84 / 2 =3.42 meters
Thus we get values of x as
x = 3.42 meters
Thus the required width of the rectangle = 3.42 meters
To know more about rectangles you may visit the link which is mentioned below:
https://brainly.com/question/9387981
#SPJ1
In the equation (x + 4)^2 = 49, if x equals 3 what is another solution for x?
Please answer quickly.
How to find the GCF of 65,39,and 13
Answer:
13
Step-by-step explanation:
65 ÷ 13 = 5
39 ÷ 13 = 3
13 ÷ 13 = 1
(All can be divided by 13 so the GCF is 13)
jamila has a weather station in her backyard. She uses a rain gauge to track the total rainfall during storms. Answer the following questions to compare the storms. 1. Jamila graphs the function describing Mondays rainfall. is the graph nonlinear or linear? how do you know? 2. What is the real-world meaning of the slope of this graph? 3. Next, Jamila graphs functions describing Thursdays rainfall. Is this graph linear or nonlinear? how do you know? 4. what does the y-intercept of the graph of Mondays storm mean? Does the y-intercept of the the graph of Thursday's storm have the same meaning?
2.
slope: rise(precipitation) / run (time)
In the real world, the slope means the relationship between time and precipitation.
3. AS the time increases, the precipitation increases. Is a linear function.
4. The y-intercept (0,y) means the amount of precipitation when no time passed since tracking.
Both y-intercepts have the same meaning.
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer: 5.3
Step-by-step explanation:
[tex]-16t^2 +126t=217\\ \\ 16t^2 -126t+217=0\\\\t=\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(217)}}{2(16)}\\\\t \approx 5.3 \text{ } (t > 0)[/tex]
Horatios haunted house
The ratio of screamers to runners are 4:6 and 10:15.
Given,
the ratio of customers who screams and customers who run away is 2:3
Let
number of screamers be 'x'
number of runners be 'y'
To find number of screamers we can solve the ratio in proportion,
[tex]2:3::x:6\\\frac{2}{3}=\frac{x}{6}\\ \frac{2*6}{3}=x\\ 4=x[/tex]
Verify: [tex]4:6=2:3[/tex]
To find number of runners we can solve the ratio in proportion,
[tex]2:3::10:y\\\frac{2}{3}=\frac{10}{y}\\ {y}=\frac{3*10}{2}\\ y=15[/tex]
verify:[tex]10:15=2:3[/tex]
Hence, the ratio of screamers to runners are 4:6 and 10:15.
To learn more about ratios and proportion refer here
https://brainly.com/question/12024093
#SPJ9