Answer:
Sally is currently 4 years old.
Step-by-step explanation:
Kaden is 18 years older than Sally now. In 5 years, Kaden will be 3 times as old as Sally. How old is Sally now?
Let Kaden's current age be [tex]k[/tex] and Sally's current age be [tex]s[/tex]. We can write the following algebraic equation using the fact that Kaden is currently 18 years older than Sally:
[tex]k=s+18[/tex]
Next, we will use the fact that in 5 years, Kaden will be 3 times as old as Sally. If Kaden and Sally's current ages are [tex]k[/tex] and [tex]s[/tex] respectively, then their ages in 5 years will be [tex]k+5[/tex] and [tex]s+5[/tex] respectively. Therefore, we have:
[tex]k+5=3(s+5)[/tex]
We have two equations with two variables. To solve for either variable, we need to create an equation with only one variable. Therefore, let's substitute the first equation into the second:
[tex](s+18)+5=3(s+5)[/tex]
Distribute and combine like terms:
[tex]s+18+5=3s+15,\\s+23=3s+15[/tex]
Subtract [tex]s[/tex] from both sides, then subtract 15 from both sides:
[tex]8=2s[/tex]
Divide both sides by 2:
[tex]s=\frac{8}{2}=\boxed{4}[/tex]
Therefore, Sally is currently 4 years old.
Answer:
Sally is 4 years old now.
Step-by-step explanation:
Let Sally's age = x
Kaden's age = x + 18
In 5 years, they are both 5 years older than now.
Sally will be x + 5
Kaden will be x + 18 + 5 = x + 23
"In 5 years, Kaden will be 3 times as old as Sally."
x + 23 = 3(x + 5)
x + 23 = 3x + 15
-2x = -8
x = 4
Answer: Sally is 4 years old now.
. f(x) = Square root of quantity x plus nine. ; g(x) = 8x - 13 Find f(g(x)). (1 point)
f(g(x)) = 2 Square root of quantity two x minus one.
f(g(x)) = 8 Square root of quantity x minus four.
f(g(x)) = 2 Square root of quantity two x plus one.
f(g(x)) = 8 Square root of quantity x plus nine - 13
Answer:
2 sqrt(2x-1)
Step-by-step explanation:
f(x) = sqrt( x+9)
g(x) = 8x-13
f(g(x))
place the function g(x) in for x in f(x)
f(g(x)) = sqrt(8x-13+9)
Combine like terms
f(g(x)) = sqrt(8x-4)
Factor out 4
f(g(x)) = sqrt(4*(2x-1)
2 sqrt(2x-1)
[tex]\\ \sf\longmapsto f(x)=\sqrt{x+7}[/tex]
[tex]\\ \sf\longmapsto g(x)=8x-11[/tex]
g(x) will be put on the place of x[tex]\\ \sf\longmapsto f(g(x))=\sqrt{8x-11+7}[/tex]
[tex]\\ \sf\longmapsto f(g(x))=\sqrt{8x-4}[/tex]
[tex]\\ \sf\longmapsto f(g(x))=\sqrt{4(2x-1)}[/tex]
[tex]\\ \sf\longmapsto f(g(x))=2\sqrt{2x-1}[/tex]
Rachel's birthday party will cost $18 if she invites 6 guests. What is the unit rate?
Answer:
3
Step-by-step explanation:
Answer:
$3 per guest
Step-by-step explanation:
18/6
= 3
Help pls :(
Solve for x.
-4 + 3x = 20
Answer:
x = 8
Step-by-step explanation:
Given
- 4 + 3x = 20 ( add 4 to both sides )
3x = 24 ( divide both sides by 3 )
x = 8
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\textsf{-4 + 3x = 20}\\\rightarrow\large\textsf{3x - 4 = 20}\\\\\large\text{ADD 4 to BOTH SIDES}\\\large\textsf{3x - 4 + 4 = 20 + 4}\\\large\text{CANCEL out: \textsf{-4 + 4} because that gives you \textsf 0}\\\large\text{KEEP: \textsf{20 + 4}} \text{ because it gives you the \textsf{x-value}}}\\\\\large\textsf{20 + 4 = \bf 24}\\\\\large\text{DIVIDE 3 to BOTH SIDES}\\\\\mathsf{\dfrac{3x}{3}= \dfrac{24}{3}}\\\large\text{CANCEL out: }\mathsf{\dfrac{3}{3}}\large\text{ because that gives you \textsf 1}[/tex]
[tex]\large\text{KEEP: }\mathsf{\dfrac{24}{3}}\large\text{ because it helps gives you the result of the \textsf{x-value}}\\\\\mathsf{x = \dfrac{24}{3}}\\\\\large\textsf{x= 24}\div \large\textsf{3}}\\\large\textsf{x = \bf 8}\\\\\boxed{\boxed{\huge\text{Therefore, your answer is: \textsf{x = 8}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Help with both plz :)
Step-by-step explanation:
Concept Required :-
BODMASBrackets , Of , Division , Multiplication , Addition , Subtraction .
Solution 9:-
We are here given ,
32 ÷ 10 - 8 ÷ 2 -3Putting brackets after and before 10 -8
32 ÷ ( 10 - 8 ) ÷ 2 - 3On simplifying,
32 ÷ 2 ÷ 2 - 3 16 ÷ 2 - 3 8 - 3 5Expression :- 32 ÷ (10 -8) ÷ 2 - 3
Solution 10 :-
We are given,
1/2 × 12 ÷ 2 - 2 + 11Putting brackets ,
1/2 × ( 12 ÷ 2 - 2 ) + 111/2 ( 6 - 2 ) + 111/2 × 4 + 112 + 1113Expression :- 1/2 × (12 ÷ 2 - 2 ) +11
Step-by-step explanation:
1. 32 ÷ 10 - 8 ÷ 2 - 3
32 ÷ 2 ÷ 2 - 3
16 ÷ 2 - 3
8 - 3
5
2.
½ × 12 + 2 - 2 + 11
6 + 2 - 2 + 11
19 - 2
17
A waitress pours 3/4 gallon of orange juice equally into 5 pitchers. what fraction of a gallon of orange juice is in each pitcher?
Answer:
15/100
Step-by-step explanation:
3/4 or a gallon is equal to 75/100
Because its 5 pitchers we divide by 5 and 75 divided by 5 is 15
name least to greatest
3780
3.78
0.378
378
0.0378
Answer:
0.0378
0.378
3.78
378
3780
Answer: 0.0378, 0.378, 3.78, 378, 3780
Step-by-step explanation:
Simplify 6 - (-2) - 3(-5).
-11
-7
19
23
Answer:
23
Step-by-step explanation:
6-(-2)-3(-5)
you first have to multiply the signs
a negative×a negative is a positive.positive times negative is negative, positive times positive is positive.
so for this question
6+2+15
23
I hope this helps
Find the solutions to x2 = 28.
A. x = 14,2
O B. x = +2./14
O C. X = +2,7
O D. x = -7/2
Answer: [tex]x = \pm2\sqrt{7}\\\\[/tex]
Work Shown:
[tex]x^2 = 28\\\\x = \pm\sqrt{28}\\\\x = \pm\sqrt{4*7}\\\\x = \pm\sqrt{4}*\sqrt{7}\\\\x = \pm2\sqrt{7}\\\\[/tex]
This can be rewritten into [tex]x = 2\sqrt{7} \ \text{ or } \ x = -2\sqrt{7}[/tex]
What is 6/10 + 9/10 in simplest form?
Answer: 3/2
Step-by-step explanation:
Given
6/10 + 9/10
Add the numerator together
= (6 + 9) / 10
Simplify by addition
= 15 / 10
Simplify to simplest form by division
= (15 ÷ 5) / (10 ÷ 5)
= 3 / 2
Hope this helps!! :)
Please let me know if you have any questions
Hello there! The answer is:
3/2 OR 1 1/2
Step-by-step explanation:
With like denominators we can add the numerators.
6 + 9 = 15.
Then that answer over the denominator which gives us 15/10. Then simplifying the answer.
That gives us: 3/2 = 1 1/2
I hope this answer helps you out. Let me know if you have any questions/concerns.
Mary has borrowed 48 books from the library. This is 22% of all of the books in the library. How many books are in the library?
Answer:
218
Step-by-step explanation:
ATQ,
22%of total books = 48
Let the total no. of books in library be x.
22/100x=48
x=4800/22
X=218(approximately)
What is the scale factor of this dilation?
A 2/3
B 1 1/2
C 3
D 5
Answer:
B. 1 1/2
Step-by-step explanation:
The post-image is clearly larger than the pre-image. The ratio of the post to the pre is 9 : 6 and 10 : 15, which are equal to 3 : 2, and equal to 1 1/2.
Geometry, please answer question ASAP
Answer:
XY = 24
Step-by-step explanation:
In similar triangles, the corresponding sides are in same ratio.
[tex]\frac{AC}{XZ}=\frac{AB}{XY}\\\\\frac{x+6}{30}=\frac{16}{2x-4}[/tex]
Cross multiply,
(x + 6 )(2x-4) = 16*30
Use FOIL method
x*2x + x*(-4) + 6*2x + 6*(-4) = 480
2x² - 4x + 12x - 24 = 480 {Combine like terms}
2x² + 8x - 24 = 480
2x² + 8x - 24 - 480 = 0
2x² + 8x - 504 = 0
Divide the entire equation by 2
x² + 4x - 252 = 0
Sum = 4
Product = -252
Factors = 18 , -14 {18 +(-14) = 4 & 18*(-14) = -254 }
x² + 4x - 252 = 0
x² + 18x - 14x - 252 = 0 {Rewrite middle term}
x(x + 18) - 14(x + 18) = 0
(x + 18)(x - 14) = 0
x - 14 = 0 {Ignore x + 18 = 0 as measurement will not come in negative}
x = 14
XY = 2x - 4
= 2*14 -4
= 28 - 4
= 24
Solve the system by substitution.
y = -3x + 17
2x + 3y = -5
Answer:
(8, -7)
Step-by-step explanation:
Hi there!
We are given this system:
y=-3x+17
2x+3y=5
And we want to solve the system
Let's solve it by substitution.
In the first equation, we are given y=-3x+17, which we can substitute -3x+17 as y into the second equation
2x+3(-3x+17)=5
Now do the distributive property
2x+-9x+51=-5
Combine like terms
-7x+51=-5
Subtract 51 from both sides
-7x=-56
Divide both sides by -7
x=8
Now substitute 8 as the value of x in y=-3x+17 to find the value of y
y=-3(8)+17
y=-24+17
y=-7
The answer is x=8, y=-7. If you need it as a point, it's (8, -7)
Hope this helps!
Choose the algebraic description that maps the image ΔABC onto ΔA′B′C′.
Question 2 options:
(x,y) → (x – 4,y)
(x,y) → (x,y + 4)
(x,y) → (x,y – 4)
(x,y) → (x + 4,y)
Answer:
(x,y+4)
Step-by-step explanation:
This shows a translation of 4 units up, so the y coordinate increases by 4. Please mark brainliest as I need 1 more to move up. It would be much appreciated.
Answer:B
Step-by-step explanation:
17. Find an equation of the straight line that is perpendicular to x - y = 5 and passes through the point (8, -1).
18. Find the equation of the line in slope-intercept form that passes through the points (12, 4) and (4, 6)
Answer:
17.y=-x+12
18.y=-1/4x+7
Step-by-step explanation:
17.a Solve for y (y=-5+x)
17. b Reciprocal (y=-1x-5)
17. c Subsitute equation into (8,-1) (-1=-13=y=x+12)
18.a Subtract y values and x values= (6-4)/(4-12)=2/-8=-1/4, this will be your slope
18. b Plug in -1/4 into either of the two ordered pairs to find y value=(12,4)=(4=-3)=y value=7.
18. c=y=-1/4x+7
Find the third angle of a triangle if two of its angles are equal to:
25 degrees and 80 degrees
and
25 degrees and 120 degrees
Answer:
60 degrees
Step-by-step explanation:
Answer:
75 degrees, 35 degrees
Step-by-step explanation:
a. Adding 25 degrees and 80 degrees yields 105 degrees. The third angle of the given triangle must therefore be 180 degrees less 105 degrees, or 75 degrees.
b. Adding 25 degrees and 120 degrees yields 145 degrees. The third angle of the given triangle must therefore be 180 degrees less 145 degrees, or 35 degrees.
Enter an inequality that represents the graph in the box.
Answer:
stop cheating
Step-by-step explanation:
get smart
Find the slope of the line that passes through the following points: (0, -3), (-6,8)
Answer:
-11/6
Step-by-step explanation:
To find the slope, we use the formula
m = ( y2-y1)/(x2-x1)
= ( 8- -3)/( -6 - 0)
= (8+3)/(-6-0)
= 11 / -6
= -11/6
Need help ASAP!!!Please explain how to solve the problem
Answer:
Step-by-step explanation:
(b) Work out the probability Jennifer hits the Bullseye at least once.
Can someone work this out for me ?
Answer:
1/2
Step-by-step explanation:
Filling out the tree diagram,
On the first throw, there is a 4/4 = 100%* chance Jennifer hits or misses. Therefore, the chance she misses is equal to the difference between
(chance she hits or misses) - (chance she hits) = 4/4 - 1/4 = 3/4
For the second throw, the chance she hits is independent of whether she hits or misses on the first throw. This means that it does not matter whether she hits or misses on the first throw; her chance to hit the second throw will always be 1/3. Therefore, 1/3 can go into the hit category on each hit line on the second throw, and in the miss category, we can put
100% - 1/3 = 1 - 1/3 = 3/3 - 1/3 = 2/3
For Jennifer to hit the bullseye at least once, she must either:
- Hit and then hit
- Hit and then miss
- Miss and then hit
From this, we can determine that if Jennifer hits the first bullseye, she will have hit it at least once, no matter what. Therefore, Jennifer must either:
- Hit the first one
- Miss and then hit
In probability, OR /either means that we add the probabilties. The probability that she hits the first one is 1/4, and the probability that she misses and then hits is
(probability she misses the 1st one) * (probability she hits the second one). We know to multiply here because both scenarios must happen, and for AND probabilities, we multiply. We thus have
(3/4) * (1/3) = 3/12 = 1/4 as the probabilty that she misses then hits, and 1/4 as the probability that she hits the first one. We add these up to get 1/4 + 1/4 = 2/4 = 1/2 as our probability that she hits the bullseye at least once
* we know 4/4 = 100% because 100% = 1, and anything divided by itself is equal to 1.
How many more unit tiles must be added to the function f(x)=x2−6x+1 in order to complete the square? 1 6 8 9
Answer:
easy
Step-by-step explanation:
8
Answer:
its 8
Step-by-step explanation:
which kind of triangle is shown?
A. Acute isosceles
B. Right scalene
C. Right isosceles
D. Acute scalene
Answer: B
Step-by-step explanation:
Acute isosceles: angle less than 90, 2 equal sides
Right scalene: right angle, different side lengths
RIght isosceles: right angle, 2 equal sides
Acute scalene: angle less than 90, different side lengths
Find the measure of the numbered angles.
Angle 1 =
Angle 2 =
Angle 3 =
Angle 4 =
Angle 5 =
Angle 6 =
Angle 7 =
Angle 8 =
Explanation in pictures.
Hope this helps!! Have a good day!
Help please anyoneee
Answer:
here's the answer to your question
\HURRY PLZ
evaluate k divided (-11) for k=33
Answer:
-3
Step-by-step explanation:
k/-11
Let k =33
33/ -11
-3
Answer:
-3
Step-by-step explanation:
33/-11 = -3
NOTE
division and multiplication = negative
addition and subtraction are a pair.
I hope this helped!
Find the area of the sector in
terms of pi.
90°
24
Area = [?]
TT
Answer:
288*pi
Step-by-step explanation:
Area=2*pi*(24)^2*(90/360)=288*pi
the angle of elevation to a nearby tree from a point of the ground is measured to be 39 degrees
Answer:
66.4
Step-by-step explanation:
tan(39)=x/82
x=tan(39)×82
x=66.4 (rounded to the nearest tenth)
Answered by GAUTHMATH
I need help with this does anybody know the answer
Answer:
X = 50; Y = 50
Answers are the same by following the correct order of operations.
Step-by-step explanation:
This problem deals with the correct order of operations. Multiplication is done before addition.
22 * 2 + 6 = X
44 + 6 = X
X = 50
6 + 22 * 2 = Y
6 + 44 = Y
Y = 50
The answers are the same despite the order in which the operations were written since by following the correct order of operations, you must do the multiplication first in each chase.
Which expression is equivalent to d - 8 - 8d?
Answer:
−7d−8
Step-by-step explanation:
Subtract 8d from d.
form a polynomial whose factors are (x+1) , (x+2) and (x-3)
Answer:
x³-7x-6
Step-by-step explanation:
Find the products of the factors
(x+1)(x+2)(x-3)
x²+3x+2(x-3)
x³+3x²+2x-3x²-9x-6
x³-7x-6
