Answer:
[tex](2 \ sin 60)(3\ cos 60) +3\ tan 30\ =\ \frac{5\sqrt3}{2}[/tex]
Step-by-step explanation:
[tex](2 \ sin 60)(3 \ cos 60) + 3\ tan 30\\\\= (2 \times \frac {\sqrt3}{2}) (3 \times \frac{1}{2})+ (3 \times \frac{1}{\sqrt3})\\\\=(\sqrt{3}\ \times \frac{3}{2})+ \frac{3}{\sqrt3}\\\\=\frac{3\sqrt3}{2}+\frac{3}{\sqrt3}\\\\=(\frac{3\sqrt3}{2} \times \frac{\sqrt3}{\sqrt3})+(\frac{3}{\sqrt3} \times \frac{2}{2})\\\\=\frac{3\times (\sqrt3)^2}{2\sqrt3}\ + \ \frac{6}{2 \sqrt3}\\\\=\frac{3 \times 3}{2 \sqrt3} +\frac{6}{2 \sqrt3}\\\\=\frac{9+6}{2\sqrt3}\\\\=\frac{15}{2\sqrt3} \times \frac{\sqrt3}{\sqrt3}\\\\[/tex]
[tex]=\frac{15 \sqrt3}{2 \times (\sqrt{3})^2}\\\\=\frac{15 \sqrt 3}{2 \times 3}\\\\=\frac{5\sqrt3}{2}[/tex]
Can someone help me with this question
Answer:
Kenji is wrong
Step-by-step explanation:
3⁵ · 4⁵ = (3 · 4)⁵ = 12⁵
but 12¹⁰ ≠ 12⁵
so , kenji is wrong
What does the point (1994, 400) on the graph represent?
Answer: There are 400 tadpoles in the year 1994.
This is because any point is of the form (x,y) where in this case
x = year number
y = tadpole population number
So (x,y) = (1994, 400) means x = 1994 and y = 400 pair up together.
In short, the year x = 1994 corresponds to the population of y = 400 tadpoles.
From the years 1990 to 1992, the population is increasing since the curve goes upward when moving from left to right. Then from 1992 to 1993, the population decreases hitting its lowest point in that specific region. From 1993 to 1997, the population increases before it decreases again from 1997 to 1999.
According to class 8 please solve
YOUR is a parallelogram
RUO=120°
RUO=RYO. {opposite angles in parallelogram are equal}
therefore...RYO=120°
RYS + RYO =180°. {linear pairs}
120°+RYO= 180°
therefore..RYO=60°
in ∆RSY
√SRY+RYS+YSR=180°. {sum of angles in triangle add up to 180°}
50°+60°+YSR=180°
110°+YSR=180°
:YSR=70°
Answer:
THEREFORE YSR = 70°
Step-by-step explanation:
RUO = 120°
Therefore,
RYO = 120°
(opposite angles of a parallelogram are equal)
Now,
RYO + RYS = 180° (linear pair of angles)
120° + RYS = 180°
RYS = 180° - 120°
RYS = 60°
Now,
By Angle sum property of a Triangle,
SRY + RYS + YSR = 180°
50° + 60° + YSR = 180°
110° + YSR = 180°
YSR = 180° - 110°
YSR = 70°
Devaughn is 7 years older than Sydney. The sum of their ages is 95. What is Sydney's age?
Answer:
44
Step-by-step explanation:
Let's say that Devaughn's age is D, and Sydney's age is S.
We know that D is 7 greater than S, so D = 7 + S.
We know that the sum of their ages, or D + S, is equal to 95, so D+S = 95
We have
D = 7 + S
D + S = 95
What we can do is plug D= 7 + S into the second equation to get
D + S = 95
= (7+ S) + S
= 7 + 2 * S
7+2 * S - 95
subtract 7 from both sides to isolate the coefficient and the variable
2 * S = 88
divide both sides by 2 to isolate the variable
S = 44
Sydney is therefore 44 years old
An article in Human Factors (June 1989) presented data on visual accommodation (a function of eye movement) when recognizing a speckle pattern on a high-resolution CRT screen. The data are as follows: 36.45, 67.90, 38.77, 42.18, 26.72, 50.77, 38.9, and 50.06. Calculate the sample mean and sample standard deviation.
Answer:
Mean = 43.969
Standard deviation = 12.341
Step-by-step explanation:
Given the data :
36.45, 67.90, 38.77, 42.18, 26.72, 50.77, 38.9, 50.06
The sample mean :
Σx / n = 351.75 / 8 = 43.969
Sample standard deviation :
√Σ(x - mean)²/n-1
√[(36.45-43.969)² + (67.90-43.969)² + (38.77-43.969)² + (42.18-43.969)² + (26.72-43.969)² + (50.77-43.969)² + (38.9-43.969)² + (50.06-43.969)² ] / ((8 - 1)
Standard deviation = 12.341
SOMEONE PLEASE ANSWER THIS PLZZZ
Answer:
.14
Step-by-step explanation:
A|B (or A given B)= A and B/B
So
Walk to school | senior= (walk to school and senior)/Senior
walk to school and senior= 5
senior= 25+5+5= 35
5/35= .14
What is the product of 3/5 and 25. Is the product more or less than 14? Explain your answer in complete sentences.
(3/5 is a fraction Not Disvison )
Answer:
15, The answer is greater than 14 because when you multiply the 2 fractions you get a number that is greater than 15
Step 1: Set up equation
[tex]\frac{25}{1}*\frac{3}{5}[/tex]
Step 2: Cross reduce
you can cross reduce 25 and 5 because they are both share a common divisor
[tex]\frac{5}{1} *\frac{3}{1}[/tex]
Step 3: Multiply numerator and denominator together
[tex]\frac{15}{1}[/tex]
Final Answer:
15
The answer is greater than 14 because when you multiply the 2 fractions you get a number that is greater than 15
Can someone help me with this math homework please!
Answer:
option 3. (4, -2)
Step-by-step explanation:
For a relation to be a function there should be exactly one output value for a given input.
In the given relation :-
4 has 2 outputs, -2 and 2, so if we remove the pair (4, -2) 4 will have only one output value ,i. e., 2. And hence the relation will be a function.
So the answer is option 3. (4, -2)
(x+4y)^(6)
Can Someone please me how to do this PLEASE!
Helppppp and explain pls and thankyou
[tex]\displaystyle\ (\sqrt{25x-16} )^2=\ (i)^2 \\\\ 25x-16=-1 \\\\25x=15\\\\\boxed{x=\frac{3}{5}}[/tex]
Find the value of m..............................................(this is the whole question btw)
Answer:
7
Step-by-step explanation:
6m = 3m + 21
6m - 3m = 21
3m = 21
m = 21 / 3
m = 7
Help please I’m so lost on this. I really need help. I can’t get any of the questions ):
Answer:
35 miles
Step-by-step explanation:
You add all of the miles on the chart up to get a final answer of 35 miles. Have a great day!
Find the value of x.
A. About 57.6
B. About 42.6
C. About 12.6
D. About 27.6
Answer:
about 27.6
Step-by-step explanation:
The sum of interior angles for this rectangle is 1080
119+140+124+6x+132+132+102 = 1080 add like terms
749 + 12x = 1080 subtract 749 from both sides
12x = 331 divide both sides by 12
x = 27.6 approximately
X2+y2-6x+2y-39=0 what is the radius and the center
Answer:
(centre = (3, - 1 ) and radius = 7
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
Given
x² + y² - 6x + 2y - 39 = 0 ( collect x/ y terms and add 39 to both sides )
x² - 6x + y² + 2y = 39
Using the method of completing the square
add ( half the coefficient of the x/ y terms )² to both sides
x² + 2(- 3)x + 9 + y² + 2(1)y + 1 = 39 + 9 + 1
(x - 3)² + (y + 1)² = 49 ← in standard form
with centre (3, - 1 ) and r = [tex]\sqrt{49}[/tex] = 7
HELP PLEASE
how do i put this into a piecewise function?
Answer:
Step-by-step explanation:
2 functions start by making a domain
Function 1: -3≤x<1
Function 2: -1≤x≤1
Now come up with equations
Function 1= x+3
Function 2= 5
Now put it all together
f(x)= x+3 for -3≤x<1 and 5 for -1≤x≤1
plss answer someone the bottom question qracias
0.6(180) is the same as asking the question - What is 60% of 180?
To find that answer, we can multiply 0.6 by 180. We use the decimal 0.6 because that is the decimal form of 60%.
0.6 x 180 = 108
Another way we can find this answer is to find 1/10 of 180 and multiply this answer by 6 because 60/100 is the same thing as 6/10.
1/10 of 180 = 18
18 x 6 = 108
Hope this helps!
The sum of two numbers is 3000. If 8% of one number is equal to 12% of the other, find the numbers.
one is 1800 and another is 1200
Step-by-step explanation:
let no's be A and B
so, A+B =3000
given, 8% = 8/100 = 2/25
12%= 12/100 = 3/25
As per question 8% of A is = 12% of B
so, (2/25)*A = (3/25)*B
now, multiply cross wise
then we get, (A/B) = 3:2
thus two numbers are in the ratio of 3:2
so, let A =3x, B=2x
cause sum of these is 3000 so, A+B =3000
3x+2x =3000
5x = 3000
x= 3000/5
.: x = 600
so, first no is 3x =3*600=1800
2nd no is 2x= 2*600= 1200
Hope this helps you
In ΔEFG, the measure of ∠G=90°, GF = 33, FE = 65, and EG = 56. What ratio represents the sine of ∠F?
Work Shown:
sin(angle) = opposite/hypotenuse
sin(F) = EG/FE
sin(F) = 56/65
Refer to the diagram below.
If a jelly bean machine contains 16 pink jelly beans, 34 blue jelly beans, 24
black jelly beans, and 26 purple jelly beans, what is the probability that a jelly
bean chosen at random will be pink?
Answer:
There are 16 pink jelly beans.
There are 16+34+24+26=100 jelly beans in total.
The probability is 4/25, or 16%.
Step-by-step explanation: hope this helps and gl :)
Answer:
The answer is 4/25
Step-by-step explanation:
Hope this helps
Find the measure of the indicated side
ANSWER:
10 units
EXPLAINATION:
The measure of the indicated side would be 10 units because the triangle shown here is a equilateral triangle this can be seen by the picture in which all the angles of the triangle are equal.
BRAINLIEST FOR EXPLANATION AND STEP BY STEP. (One question)
1) In a right triangle, the side adjacent to the 25 degree angle is 15cm long. What is the length of the side opposite the 25 degree angle to the nearest centimeter?
MY QUESTIONS:
what is the question asking for? And where is the 25 degree in a right triangle??
PLS HELP! :))
Answer:
Step-by-step explanation:
Draw a right triangle with the following conditions.
Make one of the acute angles come out to your right.
The adjacent side should be one of the sides that makes up the acute angle you just drew.
The adjacent side is also horizontal.
The other side is vertical at the left end point of the 15 cm side
The right angle is made by the two sides you have already.
Join the vertical end point to the horizontal endpoint not part of the right triangle.
Label the left side of the horizontal line as 25 degrees.
You are looking for the vertical line length.
The vertical line divided by the horizontal line length = tan(25)
vertical / 15 = tan(25) Multiply both sides by 15
vertical = 15 * tan(25)
vertical = 15 * 0.4663
vertical = 6.995
Answer:
7 cm approximately
Step-by-step explanation:
A right triangle means one of the angles is 90 degrees. It tells one of the other angles is 25 degrees. It doesn't matter which one you call 25 degrees, just don't call the right angle 25 degrees:p.
We are given the adjacent side to 25 degrees. This is the side helping to create the angle whose measurement is 25 degrees. The other side helping to create the angle is the hypotenuse.
We are asked to find the opposite side to the 25 degree angle.
Since we are given the 25 degree angle, the adjacent side measurement=15 cm, and we are asked to find the opposite side measurement=x, we should use tangent ratio.
I like to refer to the acronym to help me remember which trig ratio to use: Soh Cah Toa.
So we need to solve tan(25)=x/15.
We can do this by multiplying both sides by 15 giving us 15tan(25)=x.
Now we punch it into our calculator giving us 6.995 cm approximately.
4a+b+16a^2-b^2 how to factorize this
hope it helps
stay safe healthy and happy...Answer:
4a + b)( 1 + 4a - b )
Step-by-step explanation:
4a + b + 16a² - b²
Step 1 :- Use a² - b² = ( a - b ) ( a + b ) to factor the expression.
4a + b + ( 4a - b ) ( 4a + b ).
Step 2 :- Factor out 4a + b from the expression.
(4a + b)( 1 + 4a - b )
The gradient of the line passing through A (2,3), B (k,7) is
23
23
. Find the value of k. help pls
Given:
The gradient of the line passing through A(2,3), B(k,7) is [tex]\dfrac{2}{3}[/tex].
To find:
The value of k.
Solution:
The gradient or slope of a line is:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
The gradient of the line passing through A(2,3), B(k,7) is [tex]\dfrac{2}{3}[/tex]. So,
[tex]\dfrac{2}{3}=\dfrac{7-3}{k-2}[/tex]
[tex]\dfrac{2}{3}=\dfrac{4}{k-2}[/tex]
On cross multiplication, we get
[tex]2(k-2)=4(3)[/tex]
[tex]2k-4=12[/tex]
[tex]2k=12+4[/tex]
[tex]2k=16[/tex]
Divide both sides by 2.
[tex]k=\dfrac{16}{2}[/tex]
[tex]k=8[/tex]
Therefore, the value of k is 8.
Write an equation for a quadratic function in vertex form with
Vertex (-1, 6) that passes through the point (-3,4).
Answer:
[tex]\displaystyle f(x)=-\frac{1}{2}(x+1)^2+6[/tex]
Step-by-step explanation:
We want to write the equation for a quadratic function in vertex form with vertex at (-1, 6) that passes through the point (-3, 4).
Vertex form is given by:
[tex]\displaystyle f(x)=a(x-h)^2+k[/tex]
Where (h, k) is the vertex and a is the leading coefficient.
Since our vertex is at (-1, 6), h = -1 and k = 6. Substitute:
[tex]f(x)=a(x-(-1))^2+(6)[/tex]
Simplify:
[tex]f(x)=a(x+1)^2+6[/tex]
Next, since the quadratic passes through the point (-3, 4), f(x) = 4 when x = -3. Substitute:
[tex](4)=a(-3+1)^2+6[/tex]
Solve for a. Simplify:
[tex]-2=a(-2)^2[/tex]
Hence:
[tex]\displaystyle -2=4a\Rightarrow a=-\frac{1}{2}[/tex]
Therefore, our function in vertex form is:
[tex]\displaystyle f(x)=-\frac{1}{2}(x+1)^2+6[/tex]
знайка и незнайка розв'язували задачі з математики,знайка розв'язав 15\19 усіх задач.Скільки всього задач розв'язали Знайка і Незнайка,якщо Знайка розв'язав на 44 задачі більше,ніж Незнайка?
Whoever finishes this gets "brainliest".
just for fun
35a^7--11a^7
Answer:
a=0
Step-by-step explanation:
Factor:
a^7 (35-11)
Set it equal to zero and solve:
a^7=0
a=0
We can use SOH-CAH-TOA for
A. Any triangle ever
B. Non-right triangle only
C. right triangle only
D. Never
Answer:
C. right triangle only
Step-by-step explanation:
Other triangles use other laws such as law of cosines or sines to solve them. Right triangles exclusively use SOH-CAH-TOA because side opposite to 90 degree is always hypotenuse.
Step 1: –10 + 8x < 6x – 4
Step 2: –10 < –2x – 4
Step 3: –6 < –2x
Step 4: ________
What is the final step in solving the inequality –2(5 – 4x) < 6x – 4?
x < –3
x > –3
x < 3
x > 3Step 1: –10 + 8x < 6x – 4
Step 2: –10 < –2x – 4
Step 3: –6 < –2x
Step 4: ________
What is the final step in solving the inequality –2(5 – 4x) < 6x – 4?
x < –3
x > –3
x < 3
x > 3
PLEEEEEAAASE ASAP!
a) Describe how the line of best fit and the correlation coefficient can be used to determine the correlation between the two variables on your graph.
b) Describe the type of correlation between the two variables on your graph. How do you know?
c) Does the correlation between the variables imply causation? Explain.
d) How do you calculate the residuals for a scatterplot?
e) Calculate the residuals for your scatterplot in step 2d.
f) Create a residual plot for your data.
g) Does your residual plot show that the linear model from the regression calculator is a good model? Explain your reasoning.
Graph&data are attached
Answer:
Kindly check explanation
Step-by-step explanation:
Given the data showing the relationship between GPA and hours of study :
From the regression model given :
Regression equation is:
y = 0.141x + 1.096
Also, the regression Coefficient, R = 0.957
a) Describe how the line of best fit and the correlation coefficient can be used to determine the correlation between the two variables on your graph.
From the regression equation, we can infer if the relationship or correlation between the two variables is positive or negative from the value of the slope, a positive slope Value means a positive relationship while a negative slope value means a negative relationship.
The Correlation Coefficient, R also gives the strength of relationship, with values close to - 1 or 1 depicting a strong relationship while positive and negative R values also depictava positive or negative relationship.
Here there is a strong positive relationship between GPA and Hours.
Correlation does not imply causation. Correlation only shows the type of relationship between variables and it does not mean that high GPA values are causes by long hours of study and vice versa.
According to class 8 please solve
Answer:
i) 2 + 2x
ii) 154 = 2(2 + 2x + x)
iii) Length = 52m
Breadth = 25m
Step-by-step explanation:
Perimeter of swimming pool = 154m
Breadth = x
Length = 2 + 2x
Formula for finding perimeter = P = 2(l + b)
Therefore,
154 = 2 ( 2 + 2x + x)
154 = 4 + 4x + 2x
154 = 4 + 6x
154 - 4 = 6x
150 = 6x
150/6 = x
25 = x
With the value of x,
we can fInd the length and the breadth
Breadth = x
= 25
Length = 2 + 2x
= 2 + 2(25)
= 2 + 50
= 52