Answer:
7A-42
Step-by-step explanation:
A grain of salt is an example of which geometric figure?
Answer: point
Step-by-step explanation:
If y varies directly as x and y = 42 when x = 6, find the equation that gives the relationship between x and y.
Question 5 options:
A)
y = 7∕x
B)
y = 7x
C)
x = 7y
D)
y = x∕x
Answer:
B
Step-by-step explanation:
since K is constant ( the same for every point) we can find k when given any point by dividing the y-coordinate by the x-coordinate.
The solution is Option B.
The equation for the relationship between x and y is y = 7x
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
The value of y varies directly with x
So , y = kx and k is the constant of proportionality
Now , when x = 6
y = 42
Substituting the value of y and x in the equation , we get
y = kx
42 = 6k
6k = 42
Divide by 6 on both sides of the equation , we get
k = 7
Therefore , the equation becomes y = 7x
Hence , the equation for the relationship between x and y is y = 7x
To learn more about equation click :
https://brainly.com/question/10413253
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Find the number of five-digit numbers which are not divisible by 5?
Answer:
72000
Step-by-step explanation:
First five digit number is 10000
And the last five digit number is 99999.
There are 99999-10000+1 five digits in all.
That simplifies to 89999+1=90000.
Any number whose units digit is 5 or 0 is divisble by 5.
10000 is the first five digit number that is divisble by 5.
10000+5k where k is a positive integer can be used to find any after.
The last five digit number divisible by 5 is 99995. What is k then?
10000+5k=99995
5k=89995
k=89995/5
k=17999
How many 5 digit numbers are divisble by 5?
So the first one happens at k=0 and the last one happens at k=17999.
How many numbers is that? 17999+1=18000.
So the number of 5 digit numbers that aren't divisble by 5 is 90000-18000=72000
Show that an exponential model fits the data. Then write a recrusive rule that models the data.
n = 0, 1, 2, 3, 4, 5,
f(n) = 0.75, 1.5, 3, 6, 12, 24.
(this is a rectangular graph ^)
Answer:
Exponential function:
f(x) = abˣUse the given data to determine the function.
f(0) = ab⁰ = a*1 = a ⇒ a = 0.75b = 2 as each of the f(n) is twice the previous one in series.The model is:
f(n) = 0.75*2ⁿRecursive rule to reflect this is:
f(0) = 0.75f(n) = 2*f(n-1)Find the measure of a.
Answer:
C
Step-by-step explanation:
The angle at the centre is twice the angle on the circle subtended on the same arc, then
a = 2 × 25° = 50° → C
Trigonometric ratios
class 9
please answer my questions
Step-by-step explanation:
Hi there!
Please see the answer in the picture.
Hope it helps!
1. Approach
One is given a trigonometric equation with and one is asked to prove that it is true. Using the attached image, combined with the knowledge of trigonometry, one can evaluate each trigonometric function. Then one can simplify each ratio to solve. To yield the most accurate result, one has to each of the ratios in a fractional form, rather than simplifying it into a decimal form. Remember the right angle trigonometric ratios, these ratios describe the relationship between the sides and angles in a right triangle. Such ratios are as follows,
[tex]sin(\theta)=\frac{opposite}{hypotenuse}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}\\\\tan(\theta)=\frac{opposite}{adjacent}\\\\csc(\theta)=\frac{hypotenuse}{opposite}\\\\sec(\theta)=\frac{hypotenuse}{adjacent}\\\\cot(\theta)=\frac{adjacent}{opposite}[/tex]
Please note that the terms (opposite) and (adjacent) are relative to the angle uses in the ratio, however the term (hypotenuse) refers to the side opposite the right angle, this side never changes its name. Use these ratios to evaluate the trigonometric functions. Then simplify to prove the identity.
2. Problem (9)
[tex]\frac{sin(60)+cos(30)}{1+sin(30)+cos(60)}=sin(60)[/tex]
As per the attached image, the following statements regarding the value of each ratio can be made:
[tex]sin(60)=\frac{\sqrt{3}}{2}\\\\cos(30)=\frac{\sqrt{3}}{2}\\\\sin(30)=\frac{1}{2}\\\\cos(60)=\frac{1}{2}[/tex]
Substitute,
[tex]\frac{sin(60)+cos(30)}{1+sin(30)+cos(60)}=sin(60)[/tex]
[tex]\frac{\frac{\sqrt{3}}{2}+\frac{\sqrt{3}}{2}}{1+\frac{1}{2}+\frac{1}{2}}=\frac{\sqrt{3}}{2}[/tex]
Simplify,
[tex]\frac{\frac{\sqrt{3}}{2}+\frac{\sqrt{3}}{2}}{1+\frac{1}{2}+\frac{1}{2}}=\frac{\sqrt{3}}{2}[/tex]
[tex]\frac{\frac{2\sqrt{3}}{2}}{1+\frac{1}{2}+\frac{1}{2}}=\frac{\sqrt{3}}{2}[/tex]
[tex]\frac{\frac{2\sqrt{3}}{2}}{1+1}=\frac{\sqrt{3}}{2}[/tex]
[tex]\frac{\sqrt{3}}{1+1}=\frac{\sqrt{3}}{2}[/tex]
[tex]\frac{\sqrt{3}}{2}=\frac{\sqrt{3}}{2}[/tex]
Thus, this equation is true.
2. Problem (10)
Use a similar strategy to evaluate this equation,
[tex]\frac{1-cos(30)}{sin(30)}=\frac{1-cot(60)}{1+cot(60)}[/tex]
Use the attached image to evaluate the ratios.
[tex]cos(30)=\frac{\sqrt{3}}{2}\\\\sin(30)=\frac{1}{2}\\\\cot(60)=\frac{1}{\sqrt{3}}[/tex]
Substitute,
[tex]\frac{1-cos(30)}{sin(30)}=\frac{1-cot(60)}{1+cot(60)}[/tex]
[tex]\frac{1-\frac{\sqrt{3}}{2}}{\frac{1}{2}}=\frac{1-\frac{1}{\sqrt{3}}}{1+\frac{1}{\sqrt{3}}}[/tex]
Simplify,
[tex]\frac{1-\frac{\sqrt{3}}{2}}{\frac{1}{2}}=\frac{1-\frac{1}{\sqrt{3}}}{1+\frac{1}{\sqrt{3}}}[/tex]
[tex]\frac{\frac{2-\sqrt{3}}{2}}{\frac{1}{2}}=\frac{1-\frac{1}{\sqrt{3}}}{1+\frac{1}{\sqrt{3}}}[/tex]
[tex]\frac{\frac{2-\sqrt{3}}{2}}{\frac{1}{2}}=\frac{\frac{\sqrt{3}-1}{\sqrt{3}}}{1+\frac{1}{\sqrt{3}}}[/tex]
[tex]\frac{\frac{2-\sqrt{3}}{2}}{\frac{1}{2}}=\frac{\frac{\sqrt{3}-1}{\sqrt{3}}}{\frac{\sqrt{3}+1}{\sqrt{3}}}[/tex]
[tex]2-\sqrt{3}=\frac{\frac{\sqrt{3}-1}{\sqrt{3}}}{\frac{\sqrt{3}+1}{\sqrt{3}}}[/tex]
[tex]2-\sqrt{3}=\frac{\sqrt{3}-1}{\sqrt{3}}*\frac{\sqrt{3}}{\sqrt{3}+1}}[/tex]
[tex]2-\sqrt{3}=\frac{\sqrt{3}-1}{\sqrt{3}+1}[/tex]
Rationalize the denominator,
[tex]2-\sqrt{3}=\frac{\sqrt{3}-1}{\sqrt{3}+1}[/tex]
[tex]2-\sqrt{3}=\frac{\sqrt{3}-1}{\sqrt{3}+1}*\frac{\sqrt{3}-1}{\sqrt{3}-1}[/tex]
[tex]2-\sqrt{3}=\frac{(\sqrt{3}-1)^2}{3-1}[/tex]
[tex]2-\sqrt{3}=\frac{3-2\sqrt{3}+1}{2}[/tex]
[tex]2-\sqrt{3}=\frac{4-2\sqrt{3}}{2}[/tex]
[tex]2-\sqrt{3}=2-\sqrt{3}[/tex]
Therefore, this equation is also true.
Algebra 1
Simplify 9) y(x + 4) - 6(x + 4)
Answer:
[tex]xy+4y-6x-24[/tex]
Step-by-step explanation:
[tex]y(x+4) = xy+4y[/tex]
[tex]6(x+4) = 6x+24[/tex]
[tex]xy+4y - (6x+24) =xy+4y-6x-24[/tex]
What is the value of x + y(3 − x) when x = −5 and y = 3?
Answer:
19
Step-by-step explanation:
x + y(3 − x)
Let x = -5 and y = 3
-5 +3(3 - -5)
Subtracting a negative is like adding
-5 +3(3+5)
Parentheses first
-5 +3(8)
Multiply
-5+24
Subtract
19
Correct answer gets 5 stars and brainliest
Answer:
a=3
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2+b^2 = c^2 where a and b are the legs and c is the hypotenuse
a^2+4^2 = 5^2
a^2 +16 = 25
a^2 =25-16
a^2 = 9
Taking the square root of each side
sqrt(a^2) = sqrt(9)
a =3
Find the equation of the line that
is parallel to y = 4x + 1 and
contains the point (1, 1).
y = [? ]X + [ ]
Answer:
y = 4x - 3
Step-by-step explanation:
A parallel line will have the same slope so the slope will remain 4. To fine the new y-intercept, we can substitite the point we are given.
1 = 4(1) + b
1 = 4 + b
-3 = b
Now, we can create the new equation with the information we found.
y = 4x - 3
Best of Luck!
Answer: y = 4x - 3
Step-by-step explanation:
y-y=m(x-x)
y-1=4(x-1)
y-1=4x-4
y=4x-3
which answer is right?
Answer:
i think A
Step-by-step explanation:
there are 10 boys and 6 girls. How many ways are there to choose 8 people to get at most 5 girls
Answer:
Hello,
Step-by-step explanation:
0 girls and 8 boys :
[tex]\left(\begin{array}{c}10\\ 8\end{array}\right)=10*9*8*7*6*5*4*3/8!=45\\\\[/tex]
1 girl and 7 boys:
[tex]\left(\begin{array}{c}6\\ 1\end{array}\right)*\left(\begin{array}{c}10\\7\end{array}\right)=6*10*9*...*4/7!=6*120=720\\\\[/tex]
2 girl and 6 boys:
[tex]\left(\begin{array}{c}6\\ 2\end{array}\right)*\left(\begin{array}{c}10\\6\end{array}\right)=60*210=1260\\[/tex]
3 girl and 5 boys:
[tex]\left(\begin{array}{c}6\\ 3\end{array}\right)*\left(\begin{array}{c}10\\5\end{array}\right)\\[/tex]
4 girls and 4 boys:
[tex]\left(\begin{array}{c}6\\ 4\end{array}\right)*\left(\begin{array}{c}10\\4\end{array}\right)[/tex]
5 girls and 3 bys:
[tex]\left(\begin{array}{c}6\\ 5\end{array}\right)*\left(\begin{array}{c}10\\3\end{array}\right)[/tex]
I let you to calculate and make the sum.
help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!1
Answer:
x= – 7
Step-by-step explanation:
-3x + 2 = 2x + 37
2x+3x = 2-37
5x= -35
x= –35 / 5= – 7
I hope I helped you^_^
Answer:
x = -7
Step-by-step explanation:
-3x + 2 = 2x +37
transpose everything
-3x -2x = 37-2
-5x = 35
x = 35/-5
x = -7
A. 110
B. 90
C. 135
D. 45
Answer:
answer is
D. 45. hhhisukwk
math help
please. thank you.
Answer:
AC=EG AND BC = FG I THINK IT IS ONLY THIS
Answer:
BC=FG
Step-by-step explanation:
Because BC and FG is congruent side of angle A
hope you understand
If a+b+c = 0 then a3 + b3 + c3 is equal to
a.abc
b.0
c.3abc
d.9abc
Why 1975 can't be the sum of two squares. Or prove that the equality x ^ 2 + y ^ 2 = 1975 has no solutions in integers
Answer:
Step-by-step explanation:
If a number can be expressed by sum of two square, only if the number can be represented by 4k + 1 form
1975 = 4*493 + 3
So, 1975 can't be a sum of two squares
How much would $500 invested at 9% interest compounded annually be
worth after 4 years? Round your answer to the nearest cent.
Answer:
I think 705.79 if I did it right
Step-by-step explanation:
500(1+.09/1)^4 = 705.79
Find the probability that a randomly selected point within the circle falls in the white area. Please, and thank you.
Answer:
About 68.2%.
Step-by-step explanation:
We want to find the probability that a randomly selected point lands in the white area.
To do so, we can find the probability that the point does not land in the white area (i.e. the red area) and then subtract it from 100%.
The circle has a radius of 4 cm. Note that the base of the triangle is the diamater, so the base measures 8 cm. The height of the triangle is the radius, so it measures 4 cm. Thus, the area of the triangle is:
[tex]\displaystyle \begin{aligned} A &= \frac{1}{2}bh \\ &= \frac{1}{2}(8)(4) \\ &= 16\text{ cm}^2\end{aligned}[/tex]
Likewise, the area of the entire circle will be:
[tex]\displaystyle \begin{aligned} A &= \pi r^2 \\ &= \pi(4)^2 \\ &=16\pi \text{ cm}^2\end{aligned}[/tex]
Then the probability that a randomly seleted point lands in the red area is:
[tex]\displaystyle P\left(\text{Red}\right) = \frac{\text{Red}}{\text{Total}} =\frac{16}{16\pi} = \frac{1}{\pi}[/tex]
The probability that the point lands in the red area or the non-red area (i.e. white area) must total 100%. In other words:
[tex]\displaystyle P\left(\text{Red}\right) + P\left(\text{White}\right) = 1[/tex]
Thus:
[tex]\displaystyle P\left(\text{White}\right) = 1 - P\left(\text{Red}\right)[/tex]
Substitute:
[tex]\displaystyle P\left(\text{White}\right) = 1 - \left(\frac{1}{\pi}\right)[/tex]
Use a calculator. Hence:
[tex]\displaystyle P\left(\text{White}\right) \approx 0.6817 = 68.2\%[/tex]
The probability that a randomly selected point lands in the white area is about 68.2%.
Correct answer gets 5 star
Answer:
Step-by-step explanation:
A
hhhhelppp pleaseeeeee
Answer:
The Answer is 3 3/8
Step-by-step explanation:
If she needs 2 1/4 cups for 2 cups of orange juice then she would need 3 3/8 cups for 3 cups of orange juice.
b. 14 divided by 5/6
Answer:
16.8 or 16 whole 4/5
Step-by-step explanation:
14 divided by 5/6
take reciprocal
14 x 6/5
84/5
16.8
find a number such that when 3/4 of it is added to 3.5 the sum is the same as when 2/3 of it is subtracted from 6.5
Answer:
2.1
Step-by-step explanation:
let unknown number be x
3/4x + 3.5= 6.5 - 2/3x
collect like terms
3/4x+2/3x=6.5 - 3.5
17/12x = 3
cross multiply
12 * 3=17x
36=17x
x=36/17
x=2.1
Simplify:
5x+2(3−2x)+7
x + 13
12x
9x + 13
Answer:
x+13
Step-by-step explanation:
The answer would be 1 or uh.. x+13
1. t — 19 = 2
2. 1 + s = 3
3. 24 = 4c
4. v/5 = 9
(show work)
Answer:
1. t = 21
2. s = 2
3. c = 6
4. v = 45
Step-by-step explanation:
1. t - 19 = 2
*Add 19 to both sides.
t = 21
2. 1 + s = 3
*Subtract 1 from both sides.
s = 2
3. 24 = 4c
*Divide each side by 4.
6 = c
4. v/5 = 9
*Multiply each side by 5.
v = 45
please help ! pick two answers
Answer:
B and C
Step-by-step explanation:
25% of 60 = 15
B. 25/100*60 = 15
C. 0.25*60 = 15
Using the order of operations, what should be done first to evaluate 12+(-6)(3)+(-2)?
O Divide 12 by 5.
O Multiply -6 and 3.
O Divide 12 by -6.
Add 3 and -2.
Answer:
hello there...
you know BODMAS for sure
First brackets then of then divi then multi then add and then subtract
going by BODMAS
we need to first of all multiply of -6 and 3
hence ans is multiplying -6 and 3
( option 1 Is wrong by the equation u sent if the equation is correct then ans is which given bur by options I think equation is wrong becoz I don't see divide symbol)
ABCD is a rectangle. AB = 3x+5, AC = 7x-9, BC = 2y+5, BD = 2x+62. Solve for x. (Round your answer to one decimal place, if necessary.)
Answer:
x=14.2
Step-by-step explanation:
AC = BD
The diagonals of a rectangle are equal
7x-9 = 2x+62
Subtract 2x from each side
7x-9-2x = 2x+62-2x
5x-9 = 62
Add 9 to each side
5x-9+9 = 62+9
5x= 71
Divide by 5
5x/5 = 71/5
x=14.2
i really need your help
Help with a,b and c i will rate
Answer:
I could only see the full choices for letter A, so I'll help with that. But if you send the full image of the page I'll help you out :)
a. The answer is B
Step-by-step explanation:
The square root of 73 is about 8.5440037... which is in between 6 and 9
The square root of 55 is about 7.416198... which is also in between 6 and 9
The square root of 39 is about 6.24499799... which is also in between 6 and 9
The other letters will not work because they are either larger or smaller than 6 and 9, or they are rational.
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Have a great summer :)
