Answer: 115.2 units²
Step-by-step explanation:
Since you know the length of two sides and the measure of the included angle, you can use the following trig formula:
[tex]Area=\dfrac{1}{2}ac \sin B[/tex]
Given: a = 19, c = 14, B = 60°
[tex]A=\dfrac{1}{2}(19)(14) \sin 60^o\\\\.\quad =133\sin 60^o\\\\.\quad =115.2[/tex]
Answer:
[tex]\huge \boxed{\mathrm{115.2 \ units^2 }}[/tex]
Step-by-step explanation:
We can solve for the area of the triangle when two sides are given and the angle in between the two sides.
[tex]\displaystyle A=\mathrm{\frac{1}{2}ac \cdot sinB }[/tex]
[tex]\displaystyle A=\mathrm{\frac{1}{2} \cdot 19 \cdot 14 \cdot sin60 }[/tex]
[tex]\displaystyle A=\mathrm{\frac{133\sqrt{3} }{2} }[/tex]
[tex]\displaystyle A=\mathrm{115.18137870...}[/tex]
The area of the triangle is 115.2 units².
Matt is tiling his house and he needs to find out what are the largest square tiles that he could use to
tile an area 105 cm by 280 cm?
Answer:
the largest square tile is 35cmx35 cm
Step-by-step explanation:
1. Factorize 105 = 5*7*3=35*3
Factorize 280=10*7*4=2*5*7*4=35*8
The common factor is 35.
So Matt can tile 3 tiles 35x35 along the side 105 and 8 tiles along the side 280.
Total 24 pieces 35x35 are necessary to tile the area 105x 280 cm
( However the question is only about the largest tile that Matt could use and not about the quantity of the tiles)
Two partners are starting a wedding planning business. The total investment is $45,000. Their investments are in the ratio 4:5. How much does each
investor contribute?
$20,000 and $25.000
$5,000 and $40.000
$15,000 and $30.000
$10,000 and $35.000
Answer:
Hey there!
Think of 45000 being split to 9 pieces.
Each piece would be 5000 dollars.
Thus, the ratio would be 20000 to 25000
Hope this helps :)
One partner will bring $20,000 and the other will bring $25,000.
The total investment is $45,000 and they will contribute by the ratio, 4:5.
First add up the ratio as this will form the denominator:
= 4 + 5
= 9
The amount that the first partner will pay is:
= Proportion / 9 x Total investment
= 4 / 9 x 45,000
= $20,000
The other partner will bring:
= 5 / 9 x 45,000
= $25,000
The partners will therefore bring $20,000 and $45,000
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Please help!!!! 40 POINTS 1. By the square root property, if k is a real number and x^2=k, then what is x equal to? (See picture) 4. Solve x^2=64. What property did you use? (See picture)
Answer:
x = ± sqrt(k)
x = ± 8 by the square root property
Step-by-step explanation:
x^2 = k
K is a real number
Take the square root of each side
sqrt(x^2) = ± sqrt(k)
x = ± sqrt(k)
Letting k = 64
x = ± sqrt(64)
x = ± 8 by the square root property
Answer:
x = ± √k
x = ± √8 by the square root property
Step-by-step explanation:
x² = k
where k is a real number
square root of each side
√x² = ± √k
x = ± √k
let k = 64
x = ± √64
therefore
x = ± 8 by the square root property
Operations on Rational and Irrational Numbers
Answer:
the second option 5 2/3
Step-by-step explanation:
since 0.3 with a line over it is equal to 2/3 and 3+2 is 5 our answer would be 5 2/3
Answer:
6
Step-by-step explanation:
The cost C, in dollars, of renting a minivan for a day is given by the linear equation C = 0.3x + 42, where x is number of miles driven.
Find the cost renting the minivan for a day and driving it 150 miles. (2 pt)
Find and interpret the slope of this equation. (2 pt)
Find and interpret the y intercept of this equation(2 pt)
Answer:
$87
The slope is .3
The y-intercept is 42
Step-by-step explanation:
150(.3)=45
45+42=87
Simplify: 5x+2(3−2x)+7
Answer:
x + 13
Step-by-step explanation:
5x + 2(3 - 2x) +7
Distribute the 2 into (3 - 2x)
5x + 6 - 4x + 7
Combine like terms
x + 13
PEMDAS is an acronym that refers to the sequence of operations to be employed when solving equations with multiple operations. The given expression 5x+2(3−2x)+7 when simplified will be equal to x+13.
What is PEMDAS?PEMDAS is an acronym that refers to the sequence of operations to be employed when solving equations with multiple operations. PEMDAS is an acronym that stands for P-Parenthesis, E-Exponents, M-Multiplication, D-Division, A-Addition, and S-Subtraction.
The given expression 5x+2(3−2x)+7 can be simplified as shown below.
5x + 2(3−2x) + 7
Open the parenthesis,
= 5x + 6 − 4x + 7
Bring the like terms together,
= 5x − 4x + 7 + 6
Add the like terms,
= x + 13
Hence, The given expression 5x+2(3−2x)+7 when simplified will be equal to x+13.
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PLEASE HELP!
2x+2y = 5
3x + 3y = 7
How many solutions does the system of equations above have?
Answer: no solution or zero solutions.
Step-by-step explanation:
Given System of equations
2x+2y = 5
3x + 3y = 7
have No solution
Given :
2x+2y = 5
3x + 3y = 7
We write the given equation in y=mx+b form and then we compare the slope 'm'
Solve each equation for y
[tex]2x+2y=5\\2y=-2x+5\\Divide \; by 2\\y=-1x+\frac{5}{2}[/tex]
Slope of first equation is -1
[tex]3x+3y=7\\3y=-3x+7\\Divide \; by \; 3\\y=-1x+\frac{7}{3}[/tex]
Slope of second equation is -1
Slope of both the equations are equal . So the lines are parallel to each other.
Hence , No solution
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(Please help fast!) ..........
Answer:
the sum would be located 2 notches to the right from 0.
Step-by-step explanation:
since the notches are already split up into 5, you just count 2 notches to the left (since its negative) and then count 4 notches to the right and then you land on your sum :) btw I like your profile picture
A bag has 13 red candies 7 pink candy 12 orange candies what is the possibility that you will choose an orange candy at random
Answer:
12/32, 3/8, or 37.5%
Step-by-step explanation:
Add the candies in the bag together
13+7+12=32
12 out of the thirty-two are orange
12/32
After dividing by 4 to simplify, you get
3/8
3÷8 will give us the decimal which we can then turn into a percentage
37.5%
12/32, 3/8, or 37.5%
Hope this helps :-)
Hi guys, can anyone help me with this, Thanks a lot:)
Answer:
k = 1/9
Step-by-step explanation:
In order for the function to be continuous at x=9, the values of the two expressions must be the same at x=9.
The first expression evaluates to ...
[tex]\dfrac{\sqrt{9}-3}{-9}=-\dfrac{3-3}{9}=0[/tex]
The second expression needs to have the same value:
[tex]1 -k(9) = 0\\\\1 = 9k\\\\\boxed{k=\dfrac{1}{9}}[/tex]
Answer:
[tex]k=1/9[/tex]
Step-by-step explanation:
A function is continuous at a point if and only if:
[tex]\lim_{x \to n} f(x)=f(n)[/tex]
So, we have the piecewise function:
[tex]f(x) = \left\{ \begin{array}{lI} \frac{\sqrt{x} -3}{-9} & \quad0< x <9 \\ 1-kx & \quad x\geq 9 \end{array} \right.$$[/tex]
And we want to find the value of k such that the function is continuous.
First, find the left hand limit of f(x):
[tex]\lim_{x\to9^-} f(x)[/tex]
Since we're coming from the left, we'll use the first equation. Thus:
[tex]=\lim_{x\to9^-} \frac{\sqrt{x}-3}{-9}[/tex]
Direct substitution:
[tex]=\frac{\sqrt{9}-3}{-9}[/tex]
Simplify:
[tex]=\frac{3-3}{-9}[/tex]
Subtract and divide:
[tex]=\frac{0}{-9}=0[/tex]
So, what this tells us is that for the function to be continuous, the right hand limit as f(x) approaches 9 from the right must also be equal to 0.
Therefore:
[tex]\lim_{n \to 9^+} 1-kx=0[/tex]
Direct substitution:
[tex]1-9k=0[/tex]
Subtract 1 from both sides:
[tex]-9k=-1[/tex]
Divide both sides by -9:
[tex]k=1/9[/tex]
Therefore, the value of k is 1/9.
So, our equation in the end is:
[tex]f(x) = \left\{ \begin{array}{lI} \frac{\sqrt{x} -3}{-9} & \quad0< x <9 \\ 1-\frac{1}{9}x & \quad x\geq 9 \end{array} \right.$$[/tex]
I need help finding the domain and range, I already know is not a function
Answer:
Domain: [-4, 4]
Range: [-3, 5]
Function? No
Step-by-step explanation:
Domain is all x-values that can be inputted in the graph that returns an output.
Range is all y-values that are outputted when x is inputted.
A function has to pass the Vertical Line Test.
Line t passes through points (10, 4) and (7, 9). Line u is parallel to line t. What is the slope of line u?
Answer: 3/5
Step-by-step explanation:
concept to know: the slope of perpendicular line is always opposite reciprocal
----------------------
Step 1. Find the slope of line t
(y2-y1)/(x2-x1)
=(4-9)/(10-7)
=-5/3
-------------------
Step 2. Apply the concept
Opposite reciprocal of (-5/3)=3/5
Hope this helps!! :)
Please let me know if you have any question
What is standard form for 400,000+60,000+5,000+100
Answer:
[tex]\boxed{\bold 4.651 \times {10}^{5}}}[/tex]
Step-by-step explanation:
[tex]400000 + 60000 + 5000 + 100 \\ = 465100[/tex]
Now write it in standard form.
[tex]465100 \\ = 4.651 \times {10}^{5} [/tex]
hope this helps you.
will give the brainliest!
follow~Hi1315~
Find all zeros of ƒ(x)=x4–22x3+121x2.Then determine the multiplicity at each zero. State whether the graph will touch or cross the x-axis at the zero.
Answer:
0, 11, both multiplicity 2touch, not cross, at each 0Step-by-step explanation:
The function factors as ...
f(x) = x^4 -22x^3 +121x^2
f(x) = x^2(x^2 -22x +121)
f(x) = x^2(x -11)^2
The zeros are x=0 and x=11, each of multiplicity 2.
Because the multiplicity is even, the graph will touch at each zero, not cross.
The table below shows the number of color pages a printer prints out over a period of time.
Printed Pages in Color
Time (min), x
2
6
8
18
Number of pages, y
3
9
12
27
What is the constant of variation?
Two-thirds
Three-halves
2
3
Answer:
The answer is three halves why proof is in the step by step explanation.
Step-by-step explanation:
Answer:
The answer is
3
_
2
Because y is over x
y
_
x
Step-by-step explanation:
The gasoline consumption of a small car is advertised as 16.3 km/L (1L=1liter). How many miles per gallon is this? One mile is 1.609 km and one gallon is 3.788 L.
Answer:
38.38 miles per gallon
Step-by-step explanation:
16.3 km/L to miles per gallon
1 mile = 1.609 km
16.3 km = 16.3/1.609 = 10.13 miles
1 gallon = 3.788 L
1 L = 1/3.788 = 0.2639 gallon
therefore,
16.3 km/L = 10.13/0.2639 = 38.38 miles per gallon
FOR THE FUNCTION F(X) =6x - 8 what is f(3)?
Replace x in the equation with 3
6(3) -8 = 18 -8 = 10
The answer is 10
Answer:
10
Step-by-step explanation:
To find f(3), substitute 3 in the function
f(3) = 6*3 - 8
= 10
If $4x=3y$, what is the value of $\frac{2x+y}{3x-2y}$?
Answer:
10
Step-by-step explanation:
Solving $4x=3y$ for $x$ gives $x = \frac{3}{4}y$. Substituting this into the desired expression gives\begin{align*}\frac{2x+y}{3x-2y} &= \frac{2\left(\frac34\right)y + y}{3\left(\frac34y\right) - 2y}\\
&=
\frac{\frac32y + y}{\frac94y - 2y} = \frac{\frac52y}{\frac{y}{4}} \\
&=\frac{5}{2}\cdot 4 = \boxed{10}.\end{align*}
Answer:
10
Step-by-step explanation:
Substitution and simplification
00:00
Hakim is making birdhouses. Each birdhouse uses
7
What is the total length of wood Hakim will need to build 5 birdhouses?
Į yard of wood.
4 3 yards
5 [ yards
1 yards
og yards
Answer:
[tex]4\frac{3}{8}[/tex] yards of wood
Step-by-step explanation:
The correct question is Hakim is making birdhouses. Each birdhouse uses 7 /8 yard of wood. What is the total length of wood Hakim will need to build 5 birdhouses?
Answer: Given that the amount of wood need to produce one bird house is 7/8 yard, for 5 birdhouse, the amount of wood needed would be 5 times the number needed for one birdhouse. It is given by:
Amount of wood needed for 5 birdhouse = 5 × amount of wood for 1 birdhouse
Amount of wood needed for 5 birdhouse = 5 × 7/8 yards = 35/8 = [tex]4\frac{3}{8}[/tex] yards of wood
How did Sam’s fixed mindset prevent him from succeeding when the material got harder?
Answer: he gave up so he wasn’t able to do it
Step-by-step explanation:
Solve for x using
cross multiplication.
In order to express the fraction 2/125 as a decimal, Meg will
first rewrite the fraction using a denominator that is a
power of 10. If she wants x to be a whole number, what is
the smallest power of 10 she can use?
Х
2
125
power of 10
A. 10
B.100
C. 1,000
D. 10,000
Answer:
B
Step-by-step explanation:
B because if it's 1000 then the number will be greater then the fraction.
When do lunar eclipses occur?
Step-by-step explanation:
Lunar eclipses can only happen when the Moon is opposite the Sun in the sky, a monthly occurrence we know as a full Moon.
Composition of the functions is
____ commutative.
Answer:
Composition of functions is sometimes commutative.
Step-by-step explanation:
Composition of the functions is sometimes commutative.
Under certain circumstances, they can be commutative. However, this is not guaranteed.
Consider, for example, the functions:
[tex]\displaystyle f(x) = x^2 \text{ and } g(x) = x^3[/tex]
Composition of the two functions yields:
[tex]f(g(x))=(x^3)^2=x^6 \\ \\ \text{ and} \\ \\ g(f(x))=(x^2)^3=x^6[/tex]
In this case, the composition is commutative.
Composition of functions is sometimes commutative.
Commutativity refers to the ability to change the order of operations without affecting the result. In terms of functions, it means that the order in which you perform the composition matters.
For example, if we have two functions, f(x) and g(x), the composition of f(g(x)) is not necessarily equal to g(f(x)). In other words, the result of applying one function followed by another is generally different from the result of applying them in the opposite order.
This lack of commutativity is due to the fact that the output of one function becomes the input of the other.
Thus, Composition of functions is sometimes commutative.
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Reese loves to drink healthy green smoothies a 16 oz serving of smoothie has 170 calories how many calories are in a 24 oz smoothie
Answer:
255
Step-by-step explanation:
170/16 = 10.625
10.625 x 24 = 255
can someone please help me with this :) i only have one more try to get it right and if not i get 0/10
Answer: [tex]\sqrt[5]{27}[/tex], fifthroot(27) [according to your picture, I think there will be no space between fifth and root]
Step-by-step explanation:
concept to know: any exponent that is performed in fraction, the numerator will be the real exponent for the base, while the denominator will be the root
-------------------------------------
[tex]27^{\frac{1}{5}[/tex]
This has 1 as the numerator and 5 as the denominator.
1 can be ignored because any number to the 1 power is equal to itself.
5 is the root for 27
[tex]\sqrt[5]{27}[/tex]
Hope this helps!! :)
Please let me know if you have any question
An investigator predicts that dog owners in the country spend more time walking their dogs than do dog owners in the city. The investigator gets a sample of 21 country owners and 23 city owners. The mean number of hours per week that city owners spend walking their dogs is 10.0. The standard deviation of hours spent walking the dog by city owners is 3.0. The mean number of hours country owners spent walking theirs dogs per week was 15.0. The standard deviation of the number of hours spent walking the dog by owners in the country was 4.0. Do dog owners in the country spend more time walking their dogs than do dog owners in the city?
Answer:
Yes dog owners in the country spend more time walking their dogs than do dog owners in the city
Step-by-step explanation:
From the question we are told that
The sample size from country is [tex]n_1 = 21[/tex]
The sample size from city is [tex]n_2 = 23[/tex]
The sample mean for country is [tex]\= x_1 = 15 [/tex]
The Sample mean for city is [tex]\= x_2 = 10[/tex]
The standard deviation for country is [tex]\sigma _1 = 4[/tex]
The standard deviation for city is [tex]\sigma _2 = 3[/tex]
Let the level of significance is [tex]\alpha = 0.05[/tex]
The null hypothesis is [tex]H_o : \mu_1 = \mu_2[/tex]
The alternative hypothesis is [tex]H_a : \mu_1 > \mu_2[/tex]
The pooled standard deviation is mathematically represented as
[tex]s = \sqrt{ \frac{s_1 ^2 * (n_1 - 1 ) + s_2 ^2 * (n_2 - 1 )}{ df} }[/tex]
Here df is the degree of freedom which is mathematically represented as
[tex]df = n_1 + n_2 - 2[/tex]
[tex]df = 21 + 23 -2 [/tex]
[tex]df = 42[/tex]
So
[tex]s = \sqrt{ \frac{4 ^2 * (15.0 - 1 ) + 3 ^2 * (10 - 1 )}{ 42} }[/tex]
[tex]s = 3.5[/tex]
Generally the test statistics is mathematically represented
[tex]t = \frac{\= x_1 - \= x_2 }{ s * \sqrt{\frac{1}{n_1} +\frac{1}{n_2} } }[/tex]
[tex]t = \frac{ 15 -10 }{ 3.5 * \sqrt{\frac{1}{ 21 } + \frac{1}{23} } }[/tex]
[tex]t = 4.733[/tex]
Generally the p-value is obtained from the student t-distribution table table , the value is
[tex]P(T > 4.733)= t_{4.733, 42 } = 0.000013 [/tex]
From the calculation we see that
[tex]p-value < \alpha[/tex]
So we reject the null hypothesis
Hence we can conclude that there is sufficient evidence to support the claim that dog owners in the country spend more time walking their dogs than do dog owners in the city
expansion of (−1−2√3)^2
(- 1 - 2√3)²
applicating (a - b)² = a² + b² - 2ab
a = - 1
b = 2√3
so:
(- 1 - 2√3)² =
(- 1)² + (2√3)² - 2(- 1)(2√3) =
1 + (2² * √3²) + 2(2√3) =
1 + (4 * 3) + 4√3
ps. √x² = x1 + 12 + 4√3 = 13 + 4√3
1. What are the coordinates of the midpoint of the line segment with endpoints (2,5) and (4. – 7)?
O (-2. - 2)
O (-1. - 6)
O (6, - 2)
O (3. - 1)
Answer:
(3,-1)
Step-by-step explanation:
(2+4)/2. (5-7)/2
6/2. - 2/2
3,-1
What are the coordinates for the origin of the coordinate plane? (0.1) (1,0) (1,1) 0 (0.0)
Step-by-step explanation:
Remember: the origin is at the very center of the graph: (0,0). Not (0,1), (1,0), or 0. The first two options are not at the center. (0,1) takes us one unit above the middle, and (1,0) takes us one unite to the right of the origin. The number 0 is not used to find a point. So, our final answer is: (0,0).