Answer:
x=24
Step-by-step explanation:
Hi there!
We are given the following proportion:
[tex]\frac{2}{10}=\frac{3}{x-9}[/tex]
And we want to solve for x.
First, let's reduce [tex]\frac{2}{10}[/tex], as reducing fractions typically makes the process easier
[tex]\frac{2}{10}[/tex] is the same as [tex]\frac{1}{5}[/tex]
So:
[tex]\frac{1}{5}=\frac{3}{x-9}[/tex]
We can't do anything to [tex]\frac{3}{x-9}[/tex], but that's okay.
Now we can cross multiply, as this is a proportion
Multiply x-9 by 1 and 3 by 5
1(x-9)=3(5)
Multiply
x-9=15
Now this is an equation
Our goal is to isolate x on one side
So let's add 9 to both sides to remove it from the left side
x-9=15
+9 +9
_________
x=24
Hope this helps!
Answer:
24
Step-by-step explanation:
Cross multiply:
2(x - 9) = 2x - 18
3(10) = 30
2x-18 = 30
+18 +18
-----------------
2x = 48
----- -----
2 2
x = 24
Hope this helped.
if a number is added to 3, the result is 10 find the number
Answer:
7
Step-by-step explanation:
10 minus 3 will give you the number
Answer:
7
Step-by-step explanation:
let the number added to 3 be 'x'
we know;
X+3=10
X=10-3
X=7
A can do a piece of work in 15 days. B can do the same work in 12 days and C can
finish the same piece of work in 20 days. They started the work together for 2 days
and then B and C leaves. In how many days will A finish the remaining work?
Answer:
[tex]9\ days[/tex]
Step-by-step explanation:
[tex]We\ are\ given:\\No.\ of\ days\ A\ takes\ to\ complete\ some\ amount\ of\ work=15\ days\\No.\ of\ days\ B\ takes\ to\ complete\ the\ same\ amount\ of\ work=12\ days\\No.\ of\ days\ C\ takes\ to\ complete\ the\ same\ amount\ of\ work\ as\ A\ and\ B\ =20\ days\\[/tex]
[tex]Now,\\We\ can\ say\ that\ an\ object\ has\ to\ complete\ \frac{1}{n}th\ of\ the\\ work\ daily,\ to\ complete\ the\ work\ in\ n\ number\ of\ days.\ This\ is\ however\\ only\ true\ if\ the\ object\ covers\ equal\ amounts\ of\ work\ each\ day.[/tex]
[tex]Here,\\In\ 1\ day,\\A\ would\ cover\ \frac{1}{15}th\ of\ the\ work.\\B\ would\ cover\ \frac{1}{12}th\ of\ the\ work.\\C\ would\ cover\ \frac{1}{20}th\ of\ the\ work.[/tex]
[tex]Now,\\We\ are\ also\ given\ that:\\They\ work\ together\ for\ 2\ days\ on\ the\ same\ work.\\Hence,\\Total\ work\ done\ in\ 1\ day\ by\ A,B\ and\ C=\frac{1}{15}+\frac{1}{12}+\frac{1}{20}=\frac{4+5+3}{60}=\frac{12}{60}=\frac{1}{5}\\Hence, Total\ work\ done\ in\ 2\ days\ by\ A,B\ and\ C=2*\frac{1}{5}=\frac{2}{5}[/tex]
[tex]Hence,\\The\ portion\ of\ the\ total\ work\ left=1-\frac{2}{5}=\frac{5-2}{5}=\frac{3}{5}\\So,\\Since\ A\ has\ to\ complete\ \frac{3}{5}th\ of\ the\ work,\ lets\ compute\ the\ no.\ of\ days\ it\ takes\ to\ do\ so.\\Hence,\\No.\ of\ days\ A\ takes\ to\ complete\ the\ entire\ work=15\ days\\Hence,\\No.\ of\ days\ A\ takes\ to\ complete\ \frac{3}{5}th\ of\ the\ entire\ work=15*\frac{3}{5}=9\ days[/tex]
Answer:
9 days
Step-by-step explanation:
A does in 15days, so A in 1day does 1/15part
B does in 12days, so B in 1day does 1/12part
C does in 20days, so C in 1day does 1/20part
So. A+B+C in 1 day-- 1/15+1/12+1/20=(4+5+3)/60= 12/60=1/5 and in 2days 2/5 part..hence remaining work=1/1–2/5=(5–2) =3/5part.
Now A in 1/15 part takes 1day
So, in 3/5 part 15×3/5 = 9 days.
Help please! Need this answered quick!
Answer:
3.6
Step-by-step explanation:
the ratio of AB to AD is 3/5 so the ratio of BC to DE is also 3/5, therefore BC=3/5 DE= (3/5)6= 3.6
pls help G, H, I, J pls explain
Part G
The two angles ABD and DBC form a straight line, so the angles add to 180 degrees.
Let's solve for x.
angle ABD + angle DBC = 180
(0.5x+20) + (2x-10) = 180
2.5x+10 = 180
2.5x = 180-10
2.5x = 170
x = 170/2.5
x = 68
Then we'll use this to find angle ABD
angle ABD = 0.5*x + 20
angle ABD = 0.5*68 + 20
angle ABD = 34 + 20
angle ABD = 54
Answer: 54 degrees============================================================
Part H
Use the value of x we found back in part G to find the measure of angle DBC
angle DBC = 2x - 10
angle DBC = 2(68) - 10
angle DBC = 136 - 10
angle DBC = 126
An alternative is to subtract the measure of angle ABD from 180
angle ABD + angle DBC = 180
angle DBC = 180 - (angle ABD)
angle DBC = 180 - 54
angle DBC = 126
Answer: 126 degrees============================================================
Part I
This time, the two angles add to 90 degrees as shown by the square corner marker.
(angle XYW) + (angle WYZ) = 90
(1.25x - 10) + (0.75x + 20) = 90
2x + 10 = 90
2x = 90-10
2x = 80
x = 80/2
x = 40
which then leads to,
angle XYW = 1.25*x - 10
angle XYW = 1.25*40 - 10
angle XYW = 50 - 10
angle XYW = 40
Answer: 40 degrees============================================================
Part J
We can subtract the result of part I from 90 degrees to get the answer
angle WYZ = 90 - (angle XYW)
angle WYZ = 90 - 40
angle WYZ = 50
Or we could plug the x value x = 40 into the expression for angle WYZ
angle WYZ = 0.75*x + 20
angle WYZ = 0.75*40 + 20
angle WYZ = 30 + 20
angle WYZ = 50
Answer: 50 degrees============================================================
Summary:
The answers we found were
G. 54 degreesH. 126 degreesI. 40 degreesJ. 50 degreesAnswer:
G. m∠ABD = 54°
H. m∠DBC = 126°
I. m∠XYW = 40°
J. m∠WYZ = 50°
Step-by-step explanation:
∠ABD and ∠DBC are supplementary angles. This means their angles have a sum of 180°.
[tex]\frac{1}{2}x+20+2x-10=180\\\frac{5}{2}x+10=180\\\frac{5}{2}x=170\\x=68[/tex]
m∠ABD = 1/2(68) + 20 = 34 + 20 = 54
m∠DBC = 2(68) - 10 = 136 - 10 = 126
Same concept for ∠XYW and ∠WYZ only this time they are complementary angles. This means their angles have a sum of 90°.
[tex]1\frac{1}{4}x-10+\frac{3}{4}x+20=90\\2x+10=90\\2x=80\\x=40[/tex]
m∠XYW = 1 1/4(40) - 10 = 50 - 10 = 40
m∠WYZ = 3/4(40) + 20 = 30 + 20 = 50
(2x2 + 1) + 3/2x2=1=4
Answer:
3(2×2+1)+3×(2×2)/3=1×3=4×3
36+3+4=3=12
36+3+4-3-12
43-15
28
What is the value of the expression below when y = 5? Show your work and write your answer in a complete sentence.
Y exponent 2-3y+6
Answer:
y=1
Step-by-step explanation:
5=2-3y+6
3y=2-5+6
3y= -3+6
3y= 3
3y÷3=3÷3
y=1
Answer:
16
Step-by-step explanation:
Substitute y = 5 into the expression
y² - 3y + 6
= 5² - 3(5) + 6
= 25 - 15 + 6
= 16
what type of variation is this relationship
=========================================================
Explanation:
We don't have a direct variation because the initial cost isn't $0
The equation for this situation is y = 25x+375, where x is the number of yearbooks purchased and y is the total cost.
Notice how this line doesn't go through the origin. All direct variation graphs are straight lines through the origin.
So that's why we have partial variation instead.
The initial cost is simply the set up cost, aka the cost when x = 0. That initial cost is $375. The initial cost is located at the y intercept.
From that initial cost, we then add on multiples of $25 depending on how many yearbooks are purchased.
-----------------
In short, because the initial cost is $375, which is some nonzero value, this means we don't have direct variation. Instead, we have partial variation.
[tex]3-\sqrt{x} 1-16x^{2}[/tex]
Answer:
Step-by-step explanation:
This equation turns out to be a quartic. I'm not sure what should be done with. I can't believe you were asked to find its roots which are unbelievably complex. Here is a graph with the only 2 points that are easily found. If I am not solving what you need, please leave a note.
question 3&4 help me please
Answer:
3. (1-7/9)÷2 = 2/9÷2 = 1/9
reciprocal of 1/9 is 9
4. x+2/x=3
if you solve it, you get x = 1 and x = 2, so last option, 1 and 2, is the answer
Answered by GAUTHMATH
If f(x) = x2 - 4x and f(-3), then the result is:
o -3.
O 21.
0 -21.
Answer:
answer is 6
Step-by-step explanation:
f(x) = x2 - 4x
f(-3)= -3*2-4*-3
=-6-(-12)
=6
Find the value of x. Round to the nearest tenth.
Answer:
x=400 m is the correct answer
Need help nsjsisjejskskkdof
Answer:
8×4=32 and 8 groups of 4 equals 32.
Giving brainliest! View image!
Answer:
58%
Step-by-step explanation:
10*5=50
7*3=21
21/50 chance to choose inside small rectangle
21/50*2 = 42/100 chance to choose inside small rectangle
100-42=58%
The graph of which functions has an axis of symmetry at x = -1/4?
Answer:
2x^2 + x - 1
If I did anything you didn't understand let me know so I can explain.
Step-by-step explanation:
All of them are quadratics so let's use that.
The first one is 2x^2 + x - 1. To find the axis of symmetry the strategy is usually to find the two zeroes of a quadratic and pick the number between them. Something to notice though is that 2x^2 + x - 1 is just 2x^2 + x sshifted down 1, so they both have the same axis of symmetry. So I am going to ignore the constant, because then finding the zeroes is much much simpler. I am going to do this with all opions.
So 2x^2 + x - 1 I am just going to use 2x^2 + x. If you factor out an x you get x(2x + 1) So now we have it in factored form and we know the zeroes are 0 and -1/2. The number directly in between these is -1/4, so the axis of symmetry is x = -1/4. I don't know if there is only one with that axis of symmetry so i am going to check the rest.
2x^2 - x + 1 means we are only going to look at 2x^2 - x. factoring we get x(2x - 1) so the zeroes are 0 and 1/2, so the axis of symmetry is at 1/4.
x^2 + 2x - 1 we only use x^2 + 2x. Factored form is x(x+2) so zeroes are 0 and -2 whichh means axis of symmetry is -1
x^2 - 2x + 1 has the same axis of symmetry as x^2 - 2x, which has zeros at 0 and 2 so the axis of symmetry is at 1.
So yep, it was just the first one.
9514 1404 393
Answer:
(a) f(x) = 2x^2 +x -1
Step-by-step explanation:
For ax^2 +bx +c, the axis of symmetry is x = -b/(2a). For the offered answer choices, the axes of symmetry are ...
a) x = -1/(2·2) = -1/4 . . . . . . the function we're looking for
b) x = -(-1)/(2·2) = 1/4
c) x = -2/(2·1) = -1
d) x = -(-2)/(2·1) = 1
The function with axis of symmetry x = -1/4 is f(x) = 2x^2 +x -1.
"Two-thirds of a number increased by seven."
Answer:
(2/3)n + 7
Step-by-step explanation:
Represent the number by n.
Then "two thirds of (that) number" is (2/3)n.
Finally, we add 7:
"Two-thirds of a number increased by seven" is (2/3)n + 7
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
The students in Shawn's class got to choose whether to visit the zoo or the aquarium. 3 students went to the zoo and 15 students went to the aquarium. What is the ratio of the number of students who went to the zoo to the number of students who did not go to the zoo?
A. 1:3
B. 1:6
C. 1:5
D. 1:1
The ratio of the number of students who went to the zoo to the number of students who did not go to the zoo is 1: 5. Hence option C is true.
Given that;
The students in Shawn's class got to choose whether to visit the zoo or the aquarium.
Here, 3 students went to the zoo and 15 students went to the aquarium.
Hence, the ratio of the number of students who went to the zoo to the number of students who did not go to the zoo is,
Ratio = 3 : 15
Ratio = 3/15
Ratio = 1/5
Ratio = 1 : 5
Thus, option C is true.
Learn more about the ratio visit:
https://brainly.com/question/12024093
#SPJ3
HELP ME PLZZ...Complete this proof...BRAINLY TO HELPFUL ANSWER
Answer:
1. Angles 2, 3 and angles 1,3 are complementary angles(Given)
2. To prove :
Since Angles 2, 3 and angles 1,3 are complementary.
When angles are complementary, then the sum of the measures of angles is 90 degrees.
So, and (Definition of Complementary angles)
3. (Substitution)
4. (Subtraction property of equality)
Step-by-step explanation:
twice n
Algebraic expression
Answer and Step-by-step explanation:
2n is the algebraic expression for twice n.
#teamtrees #PAW (Plant And Water)
please solve this
.............
Answer:
D
Step-by-step explanation:
Note that I will be using a, b, and y instead of their Greek counterparts.
First, we know that sin(c+d) = sin(c)cos(d) + cos(d)sin(a) and sin(c-d) = sin(c)cos(d) - cos(d)sin(a). We can apply these here to get
sin(b+y) = sin(b)cos(y) + cos(b)sin(y)
sin(b-y) = sin(b)cos(y) - cos(b)sin(y)
sin(a+y) = sin(a)cos(y) + cos(a)sin(y)
sin(a-y) = sin(a)cos(y) - cos(a)sin(y)
Plugging these into our equation, we get
(sin(b)cos(y) + cos(b)sin(y) - (sin(b)cos(y) - cos(b)sin(y)))
/
(sin(a)cos(y) + cos(a)sin(y)-(sin(a)cos(y) - cos(a)sin(y)))
=
2cos(b)sin(y) / 2cos(a)sin(y)
= cos(b)sin(y)/cos(a)sin(y)
= cos(b)/cos(a)
Next, we can see that a+b = π, so we can subtract b from both sides to get a = π -b. Plugging that in for a in our equation, we get
cos(b) / cos(π-b)
After that, we know that cos(c-d) = cos(c)cos(d) - sin(c)sin(d). Plugging that in here, we get
cos(π-b) = cos(π)cos(b) - sin(π)sin(b)
= -cos(b) + 0
= -cos(b)
Plugging that back into our equation, we get
cos(b) / -cos(b) = -1
Help me with this question please‼️‼️
Explanation:
The gradient is the same as the slope
m = slope
m = rise/run
m = (change in y)/(change in x)
m = (y2-y1)/(x2-x1)
m = (6-1)/(6 - (-4))
m = (6-1)/(6+4)
m = 5/10
m = 1/2
In decimal form, this becomes 0.5
A slope of 1/2 means we move up 1 and to the right 2 units each time to generate points along the diagonal line.
A positive slope goes uphill as we move to the right (due to the positive rise value).
Answer:
One way to find the gradient is using the expression :
[tex]m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{y_{B} - y_{A}}{x_{B} - x_{A}}[/tex]
So [tex]m = \frac{6 - 1}{6- (-4)} =\frac{5}{10} =\frac{1}{2}[/tex]
Helpp mee please i need help i am stuck
Which statements are true? Check all that apply.
-2.5 = -2 1/2
-1.5 > -0.5
-0.5 < 0
-2.5 < -2
- 1/2 > 1.5
pls answer my question from the above picture
Answer:
Step-by-step explanation:
[tex]a^{m}* a^{n}=a^{m+n}\\\\\\(\frac{-1}{2})^{-19}*(\frac{-1}{2})^{8}=(\frac{-1}{2})^{-2x +1}\\\\(\frac{-1}{2})^{-19+8}=(\frac{-1}{2})^{-2x+1}\\\\\\(\frac{-1}{2})^{-11}=(\frac{-1}{2})^{-2x+1}[/tex]
As bases are equal in boht sides, we can compare the exponents.
-2x + 1 = -11
Subtract 1 form both sides
-2x = -11 - 1
-2x = -12
Divide both sides by -2
x = -12/-2
x = 6
Express (root 19 - root 7)(root 19 + root 7) in simplest form.
Answer
root 354
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
(√19 -√7)(√19 +√7)
( a +b)( a -b) = a²-b²
(√19)² -(√7)² = 19 -7 = 12
What is the quotient of (2x3 – 29x + 13) ÷ (x + 4)?
Answer:
(19-29x) over (x-4)
Step-by-step explanation:
Plz see attachment below
Answer:
Step-by-step explanation:
Table I
Given function is,
f(x) = [tex]b^x[/tex]
From the table attached,
For x = 0.827, value of function f(0.827) = 5,
f(0.827) = [tex]b^{0.827}[/tex]
Therefore, [tex]b^{0.827}=5[/tex]
[tex]\text{log}(b^{0.827})=\text{log}(5)[/tex]
0.827[log(b)] = log(5)
log(b) = 0.8452
b = [tex]10^{0.8452}[/tex]
b = 7
Therefore, function 'f' will be,
f(x) = [tex]7^x[/tex]
For f(x) = 9,
9 = [tex]7^x[/tex]
log(9) = log([tex]7^x[/tex])
log(9) = x[log(7)]
x = 1.129
Table II
Given function is g(x) = [tex]\text{log}_b(x)[/tex]
From the given table,
For x = 7, g(x) = 1
1 = [tex]\text{log}_b(7)[/tex]
[tex]b^1=7[/tex]
b = 7
Therefore, the function 'g' will be,
g(x) = [tex]\text{log}_7(x)[/tex]
For g(x) = 1.318
1.318 = [tex]\text{log}_7(x)[/tex]
[tex]x=7^{1.318}[/tex]
[tex]x=12.9968[/tex]
[tex]x=13.997[/tex]
factor x ^ 4 - 5x ^ 2 + 4
( − 2 ) ( 3+ 2 2 − − 2 )
Hope this helps, have a great day!
a map of an amusement park is shown on a coordinate plane, where each square of the grid represents 1 square meter. The water ride is at (-17,12), the roller coaster is at (26,-8), and the Ferris wheel is at (2,20). Find each distance to the nearest tenth of a meter.
* what is the distance between the water ride and the roller coaster?
*What is the midpoint between the roller coaster and the ferris wheel? what is the distance from the midpoint to the ferris wheel
Answer:
Step-by-step explanation:
Find the area of triangle ABC to the nearest tenth if AB = 11 ft, ∠BCA = 67 , and ∠CAB = 28 .
Answer:
30.7
Step-by-step explanation:
Assuming the angled are degrees and not radian.
side BC= (11÷sin67)•sin28= 5.6
angle ABC= 180-67-28=85°
A= 11•5.6•sin85÷2≈30.68
It’s urgent please help
(60 + 24) ÷ 3 = ( __ ÷ 3) + (24 ÷ 3)
Answer: 60
Step-by-step explanation:
The blank space can be filled with 60, as this is a simple problem of distributive property