The equation of the line parallel to 3x + y = 7 and passing through (-3,3) is y = -3x + 12 (Option A) because parallel lines have identical slopes and using the point-slope formula provides us with the y-intercept.
To find the equation of a line parallel to 3x + y = 7 and passing through the point (-3,3), we need two pieces of information:
The slope of the parallel line
The coordinates of a point it passes through
First, let's rewrite the given equation in slope-intercept form to find the slope. Slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
y = -3x + 7
So, the slope m is -3. Because parallel lines have the same slope, our new line will also have a slope of -3.
Using the slope (-3) and the given point (-3,3), we apply the point-slope formula:
y - y1 = m(x - x1)
y - 3 = -3(x - (-3))
y - 3 = -3x - 9
y = -3x + 12
Thus, the equation in slope-intercept form for the line that passes through (-3,3) and is parallel to 3x + y= 7 is y = -3x + 12 which corresponds to Option A.
Please help ASAP first right answer gets brainliest
Answer:
1. 31/99 2. 215/999 3. 6704/9999
Answer:
31/100, 215/100, 419/1250
Convert the complex number z = -12 + 5i from rectangular form to polar form.
Answer:
[tex]z=13(\cos 157\degree +i\sin157\degree)[/tex]
Step-by-step explanation:
The given complex number is
[tex]z=-12+5i[/tex]
The polar form of this complex number is;
[tex]z=r(\cos \theta +i\sin \theta)[/tex], where
[tex]r=\sqrt{(-12)^2+5^2}[/tex]
[tex]r=\sqrt{144+25}=\sqrt{169}=13[/tex]
and
[tex]\theta =\tan^{-1}(\frac{5}{-12})[/tex]
This implies that;
[tex]\theta=157\degree[/tex] to the nearest degree.
Hence the polar form is
[tex]z=13(\cos 157\degree +i\sin157\degree)[/tex]
Help please. Question is in picture.
Hi, hope you’re having a good day!
Could you please add the picture?
Thanks, have a good day! ❤️❤️
The picture is not shown, if you could add it, I would be happy and try and answer as best I can! Have a good day! :)
Miss Balcon works 7 1/2 hours each day, 5 days a week as a secretary at a Christian school. How many hours would she work in 4 weeks?
Answer:
150
Step-by-step explanation:
Final answer:
Miss Balcon would work 150 hours in 4 weeks as a secretary at a Christian school.
Explanation:
In order to find out how many hours Miss Balcon would work in 4 weeks, we need to first calculate the number of hours she works in a week. She works 7 1/2 hours each day, and since there are 5 days in a week, she works a total of 7 1/2 x 5 = 37 1/2 hours in a week.
Now, to find out how many hours she would work in 4 weeks, we can multiply the number of hours she works in a week by 4. So, 37 1/2 x 4 = 150 hours.
Therefore, Miss Balcon would work 150 hours in 4 weeks.
What number is equivalent to |-16|
-1/16
1/16
-16
16
HelPppppp
16
absolute value is always positive
i want to say 16 or 1/16. i’m sure it’s not a negative though.
Compute the standard deviation for the set of data 2, 5, 6, 8, 14
Answer:
4.4721
Step-by-step explanation:
wich of these terms does not described polygon ABC
the answer is d i think
k-k+k-3 what is this answer?
Answer:
k-3
Step-by-step explanation:
Eliminate the opposites
K-k+k3
= k-3
The given algebraic expression simplifies to k - 3. This means, for any value of 'k', the result would be 'k' minus 3.
Explanation:The problem provided is k-k+k-3. In this case, 'k' is a variable, which is essentially an unknown number. When you subtract a variable (k) from itself, you get zero. Therefore, k - k equals zero. Adding k back again, we return to k itself. Hence, k - k + k - 3 simplifies to k - 3. That is, whatever value 'k' is, you have to subtract 3 from it to solve this equation.
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What is P(A or B)...?
the answer is A.) 3/10
Option: B is the correct answer.
[tex]B.\ \ \dfrac{7}{10}[/tex]
Step-by-step explanation:We know that P(A or B) i.e. P(A∪B) is calculated by using the formula:
[tex]P(A\bigcup B)=P(A)+P(B)-P(A\bigcap B)[/tex]
Now based on the pie chart we see that the total number of students who were surveyed are: 10The number of students who love to play basketball are: 4( The students are: Fran, Juan , Ian and Ella )
Number of student who love to play soccer are: 5( The students are: Mickey, Mai, Marcus , Ian and Ella)
The number of student who love to play both basketball and soccer i.e. n(A∩B)= 2( since those students are: Ian and Ella)
Hence, we have:
[tex]P(A)=\dfrac{4}{10}\\\\\\P(B)=\dfrac{5}{10}\\\\\\P(A\bigcap B)=\dfrac{2}{10}[/tex]
Hence, we have:
[tex]P(A\bigcup B)=\dfrac{4}{10}+\dfrac{5}{10}-\dfrac{2}{10}\\\\\\i.e.\\\\\\P(A\bigcup B)=\dfrac{4+5-2}{10}\\\\\\i.e.\\\\\\P(A\bigcup B)=\dfrac{7}{10}[/tex]
A cube-shaped gift is 11 centimeters long. What is the least amount of wrapping paper you need to wrap the gift?
You will need 721 centimeters of paper. This is because you take 11 and multiply it by 11 because a cube is equal in the length and the height. To find the total area of wrapping paper for one side you have to find the area. 11x11=121. Then you have 6 sides of the cube so you multiply 121x6=721 inches of wrapping paper to wrap the cube
Least amount of wrapping paper you need to wrap the gift = 726 cm²
What is total surface area of a cube?The total surface area of a cube is equal to six times the area of one side of the cube.
Given,
Side length of the cube = 11 cm
Area of one side of the cube = side²
Therefore, area of one side of the cube = 11² cm²
= 121 cm²
Total surface area of a cube = 6 × side²
= 6 × 121 cm²
= 726 cm²
Hence, least amount of wrapping paper you need to wrap the gift is 729 cm².
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2. A circular clock face has a diameter of 31 cm. What is the area of the
clock face?
A. 754.4 cm2
B.
3017.5 cm2
48.7 cm2
D.
961 cm2
Answer:
The answer is 754.4 cm²
Step-by-step explanation:
a = r²π
a = (31/2)²π
a ≈ 754.4
The area of the clock face is 754.4 cm²
What is an area?
The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the circle in a two-dimensional plane is called the area of the circle.
The area of the clock will be calculated as:-
a = r²π
a = (31/2)²π
a ≈ 754.4
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Write the expression in terms of cosine. Please help.
I would assume that they want a cosine value that would give the same answer. sin(30°) is equal to 1/2
Therefore cos(×) = 1/2
x = arccos(1/2)
x=60
cos(60°)
Answer:
cos60°
Step-by-step explanation:
Using the cofunction identity
sinx° = cos(90 - x)°
sin30° = cos(90 - 30)° = cos60°
Taylor school, a student must have an average of at least 75% to get a “C”in a course. Taylorhas scores of 71%, 82%, and 76% on your algebra tests. What minimum score must she have on her fourth test to guarantee a “C” in the course?
Answer:she would have at least gotten a 75 to pass.
Step-by-step explanation:76+82+71+75=304
304÷4= a solid 76%
ASAP PLEASE ANSWER quadrilateral ABCD is dilated at center (0,0) with scale factor 1/2 to form quadrilateral A'B'C'D'. wha is the length of A'B'?
a. sqrt5
b.2
c.10
d.2sqrt5
Answer:
[tex]|A'B'|=\sqrt{5}[/tex]
Step-by-step explanation:
The points A and B have coordinates at (0,4) and (4,2) respectively.
The distance formula can be used to find the length of AB.
[tex]|AB|=\sqrt{(4-0)^2+(2-4)^2}[/tex]
[tex]|AB|=\sqrt{(4)^2+(-2)^2}[/tex]
[tex]|AB|=\sqrt{16+4}[/tex]
[tex]|AB|=\sqrt{20}[/tex]
[tex]|AB|=2\sqrt{5}[/tex]
Since quadrilateral ABCD was enlarged with a scale factor of [tex]\frac{1}{2}[/tex].
The length of A'B' is
[tex]\frac{1}{2}|AB|[/tex]
[tex]=\frac{1}{2}\times2\sqrt{5}[/tex]
[tex]\therefore |A'B'|=\sqrt{5}[/tex]
The quadrilateral ABCD is dilated at the center (0,0) with a scale factor of 1/2. So, after the dilation the length of A'B' is [tex]\sqrt{5}[/tex] and this can be determined by using the formula of length between two points.
Given :
Quadrilateral ABCD is dilated at the center (0,0) with a scale factor of 1/2 to form quadrilateral A'B'C'D'.Points - A(0,4), B(4,2), C(4,-4), and D(-2,-2).Given that the quadrilateral ABCD is dilated at the center (0,0) with a scale factor of 1/2. So the points of the quadrilateral ABCD becomes:
[tex]\rm A(0,4) \to A'(0\times \dfrac{1}{2},4\times \dfrac{1}{2}) = A'(0,2)[/tex]
[tex]\rm B(4,2) \to B'(4\times \dfrac{1}{2},2\times \dfrac{1}{2}) = B'(2,1)[/tex]
[tex]\rm C(4,-4) \to C'(4\times \dfrac{1}{2},-4\times \dfrac{1}{2}) = C'(2,-2)[/tex]
[tex]\rm D(-2,-2) \to D'(-2\times \dfrac{1}{2},-2\times \dfrac{1}{2}) = D'(-1,-1)[/tex]
Now, the length of A'B' is given by:
[tex]\rm AB=\sqrt{(4-0)^2+(2-4)^2}[/tex]
[tex]\rm AB=\sqrt{4^2+(-2)^2}[/tex]
[tex]\rm AB=\sqrt{20}[/tex]
[tex]\rm AB = 2\sqrt{5}[/tex]
[tex]\rm A'B' = \dfrac{1}{2}AB[/tex]
[tex]\rm A'B' = \sqrt{5}[/tex]
Therefore, the correct option is a).
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If two ratio are equal they form a ___. I need help IMMEDIATELY. I am going to my grandmas and I need to finish quickly.
two ratios are equal and form a proportion.
Answer:
they form a proportion.
Rico is offered a permanent position that pays $45,000 a year. The same week, Rico is offered a full-time (8 hour days, 5 days a week) job that pays $20.50 an hour. Based on the monthly income of each job, which would you recommend to Rico and why?
Answer:
I recommend the work that pays $45,000 a year because the monthly income is greater than the other job
Step-by-step explanation:
we know that
The first work pays $45,000 a year
so
The monthly income is equal to
$45,000/12=$3,750 per month
The second work pays $20.50 an hour
Remember that
1 year= 52 weeks
so
In one year pays -----> (8)*(5)*(52)($20.50)=$42,640 a year
The monthly income is equal to
$42,640/12=$3,553.33 per month
I recommend the work that pays $45,000 a year because the monthly income is greater than the other job
Four times a number, decreased by eight equals twelve. What is the number?
Let the number be x.
4x - 8 =12
4x =12 +8 ( you bring the eight over to the 12, it becomes positive )
4x = 20
x = 20÷4
x = 5
The problem is a basic algebra equation. It translates to 4x - 8 = 12, which can be solved by adding 8 to both sides and then dividing by 4 to get x=5. The answer is 5.
Explanation:The subject of this question is Mathematics, specifically algebra. To solve this equation, start by translating the problem into a mathematical expression. This can be done as follows: 4 times a number is represented as 4x, then decreased by eight is -8 and the equation equals twelve (12).
Therefore, the equation is 4x - 8 = 12. To solve for x, you can start by adding 8 to both sides of the equation obtaining 4x = 20. Lastly, divide both sides by 4 to find x, which gives x = 5.
Therefore, the number that meets the condition '4 times a number, decreased by 8 equals 12' is 5.
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estimation of 9.2 * 6.8
Step-by-step explanation:
62.56
9.2 * 6.8 = about 63
Since you are estimating, first round the numbers.
Change 9.2 to 9 and change 6.8 to 7. This leaves you with 9 * 7, which is 63, and since you are estimating, your answer doesn’t need to be exact.
20 points!!!! Please answer this! This is Surface Area! I’ve been working on this. I know what to do but I’m just confused at the same time. When you answer this question please show me the work or how you got the answer. It will make my life more easier!
Answer:
SA: 62in
Step-by-step explanation:
make it into a net and find the area of each piece
What is the volume of the cone, rounded to the nearest cubic inch?
Answer: If you take 6 in and multiply by 12 You would get 72 inches
*Step By Step explanation* 6 Multiplied by 12 equals 72
Rounding would not be necessary.
Answer:
The correct option is B. 226 inches³
Step-by-step explanation:
The diameter of the cone is given to be 12 inches
So, The radius of the cone will be 6 inches
Also, The height of the cone is given to be 6 inches'
Now, we need to find the volume of the cone.
So, Volume of the cone is given by the formula :
[tex]Volume=\frac{1}{3}\pi\times radius^2\times height[/tex]
[tex]Volume=\frac{1}{3}\times 3.14\times 36\times 6[/tex]
[tex]Volume=226.08[/tex]
[tex]Volume\approx 226.08\:inches^3[/tex]
Therefore, the correct option is B. 226 inches³
simplify 35 • 34 i want the answer for this one somebody
Answer:
1190
Step-by-step explanation:
35× 34 = 1190...._ hope it help ....have a nice day
Answer:
1190
Step-by-step explanation:
Since the dot means "X" or multiply, we multiply 35 by 34.
So 35*34 = 1190.
A way to quickly multiply 35 snd 34, is to split 34 into 2*17 and multiply the 2 by 35 first to get 70*17. Since 17*7=119, we get 70*17 to be 1190.
which expressions are equivalent to the log8 1 * log3 27. check all that apply.
a - 3 * 8
b - 3 * log8 8
c - 1
d - 0
Answer:
It's d. 0.
Step-by-step explanation:
The log (to any base) of 1 = 0, so log8 1 = 0, and the whole expression is equal to 0:
0 * log3 27 = 0.
The expression log8 1 * log3 27 evaluates to 0, so the equivalent expression from the options is d - 0.
Explanation:The expressions we need to evaluate are log8 1 * log3 27. The log of 1, no matter what the base, is always 0. This is because any number raised to the power of 0 is 1. So, log8 1 is equal to 0. Now, evaluate log3 27. The log base 3 of 27 is 3 because 3 cubed (or 3 to the power of 3) is 27. So, log3 27 equals 3. Thus, log8 1 * log3 27 = 0 * 3 = 0. Comparing with the given options, we find that the only equivalent expression is option d - 0.
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Martina is 3 inches less than twice as tall as her little brother . Write an expression for Martina’s height . How tall is Martina if her little brother is 28 inches tall?
Answer:
Expression: 2x-3
Martina's height if her little brother is 28 inches: 53 inches
Step-by-step explanation:
To write the expression, first read the problem. Martina is twice as tall as her little brother, minus 3. If x represents Martina's little brother's height, the equation will be 2x-3, since she's 3 inches shorter than twice the height of her little brother.
The question says that her little brother is 28 inches tall. Since x represents Martina's little brother's height, simply plug x into our expression.
2x-3
2(28)-3
56-3
53
Therefore, if Martina's little brother was 28 inches tall, Martina would be 53 inches tall. i hope this helps! :)
This answer involves the creation of a mathematical expression based on the given information and substituting the known value to find the unknown variable. The mathematical expression is 'Martina's Height = 2 * (Brother's height) - 3 inches.' When the brother's height is 28 inches, we get Martina's height as 53 inches.
Explanation:The question relates to writing and solving expressions in Mathematics. To find how tall Martina is, we need to first write down an expression depicting the statement. According to the given statement, we can write:
Martina's Height = 2 * (Brother's height) - 3 inches
If her little brother is 28 inches tall, we substitute 28 into the expression:
Martina's Height = 2 * (28) - 3 inches
This implies:
Martina's Height = 56 - 3 inches = 53 inches
Therefore, Martina is 53 inches tall if her little brother is 28 inches tall.
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find the explicit formula for the geometric sequence
2,6,18,54
Answer:
the explicit formula for the geometric sequence 2,6,18,54 is [tex]a_{n}=a_{1}.r^{n-1}[/tex]
2,6,18,54
Step-by-step explanation:
In the sequence given: 2,6,18,54
The common ration is 3 because
a₁ = 2
a₂= 2*3 =6
a₃ = (2*3)*3 = 2*3^2 = 18
a₄= (2*3*3)*3 =2*3^3 = 54
Here we see for a₂ 3 has power 1, for a₃ 3 has power 2 and so on.
So, the formula will be
[tex]a_{n}=a_{1}.r^{n-1}[/tex]
Here aₙ is the no of term.
a₁ is the first term of the sequence
and r is the common ratio among the sequence.
Answer:
b(n)=2⋅3 ^n−1
Factor out the greatest common factor
19. 2x^2+x
20. 12x^5-36x
21. 15x-5y^2
Step-by-step explanation:
[tex]19.\\2x^2=(2)\bold{(x)}(x)\\x=(1)\bold{(x)}\\2x^2+x=\bold{x}(2x+1)\\\\20.\\12x^5=\bold{(3)(4)(x)}(x)(x)(x)(x)\\36x=\bold{(3)(4)}(3)\bold{(x)}\\12x^5-36x=\bold{(3)(4)(x)}(x^4-3)=\bold{12x}(x^2-3)\\\\21.\\15x=(3)\bold{(5)}(x)\\5y^2=\bold{(5)}(y)(y)\\15x-5y^2=\bold{5}(3x-y^2)[/tex]
sine rule and area of any triangle
find area of this triangle to 1 decimal place please
I got 61.1 as the answer but it's wrong apparently
thanks
Answer:
94.1 m²
Step-by-step explanation:
Use the sine rule to find BC
[tex]\frac{BC}{sin82}[/tex] = [tex]\frac{12}{sin40}[/tex] ( cross- multiply )
BC × sin40° = 12 × sin82° ( divide both sides by sin40° )
BC = [tex]\frac{12sin82}{sin40}[/tex] ≈ 18.487
Area = [tex]\frac{1}{2}[/tex] × 12 × 18.487 × sin58° ≈ 94.1
Find sin<c.
a. 12/13
b. 1
c. 13/12
d. 13/5
Answer:
a. 12/13
Step-by-step explanation:
For a right triangle, sin theta = opposite side/ hypotenuse
sin C = 24/26
Sin C = 12/13
5 - ___________ a0 = 14
Answer:
Final answer is [tex]a_0=-9[/tex]
Step-by-step explanation:
Given equation is [tex]5-a_0=14[/tex]
Now we need to solve the given equation 5-a_0=14 for the unknown variable [tex]a_0[/tex] .
We can do that by isolating [tex]a_0[/tex]
To isolate a_0, let's subtract 5 from both sides
[tex]5-a_0-5=14-5[/tex]
[tex]-a_0=9[/tex]
multiply both sides by -1
[tex]-a_0(-1)=9(-1)[/tex]
[tex]a_0=-9[/tex]
Hence final answer is [tex]a_0=-9[/tex]
If r=12 and t=20, find S.
Answer:
d. 53.1°
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you ...
Cos = Adjacent/Hypotenuse
You are given the lengths of t (hypotenuse) and r (adjacent to S), so you can find the angle from ...
cos(S) = r/t = 12/20
S = arccos(12/20) ≈ 53.1° . . . . . use the inverse cosine function
Answer:
d. 53.1
Step-by-step explanation:
this is the correct answer on ed-genuity, hope this helps! :)
the ratio of Males to females in the crowd at a rock concert is 5:4
there are 360 males in the crowd how many females are there
Answer:
The number of females is 288.
Step-by-step explanation:
Let the number of females be x.
5:4 = 360:x
We can write the equal ratios as a proportion.
5/4 = 360/x
Cross multiply:
5x = 360 * 4
5x = 1440
x = 288
Answer: The number of females is 288.
Answer:
288 females
Step-by-step explanation:
We can write a proportion to solve, putting males over females
males 5 360
------------ = ------------ = -------------
females 4 x
Using cross products
5x = 360*4
5x =1440
Divide by 5
5x/5 = 1440/5
x = 288
There are 288 females