Answer:
Amira is currently 24 years old and Pam is currently 12 years old
Step-by-step explanation:
Let Amira's age be [tex]a[/tex] and Pam's age be [tex]p[/tex]. Currently, Amira is twice as old as Pam. Therefore, we can write the equation [tex]a=2p[/tex].
We can write a second equation using the other information given in the question. Nine years ago, Amira and Pam's combined ages was 18. If Amira and Pam are currently [tex]a[/tex] and [tex]p[/tex] years old, respectively, then their respective ages 9 years ago would ben [tex]a-9[/tex] and [tex]p-9[/tex]. Since these add up to 18, we have the equation [tex](a-9)+(p-9)=18[/tex].
Therefore, we have a system of equations:
[tex]\begin{cases}a=2p,\\a-9+p-9=18\end{cases}[/tex]
Substitute the first equation into the second one:
[tex]2p-9+p-9=18[/tex]
Combine like terms:
[tex]3p-18=18[/tex]
Add 18 to both sides:
[tex]3p=36[/tex]
Divide both sides by 3:
[tex]p=\frac{36}{3}=\boxed{12}[/tex]
Now substitute this into any of the equations (I'll choose the first):
[tex]a=2p,\\a=2(12),\\a=\boxed{24}[/tex]
Therefore, Amira is currently 24 years old and Pam is currently 12 years old.
You're playing a game where you defend your village from an orc invasion. There are 3 characters (elf, hobbit, or human) and 5 defense tools (magic, sword, shield, slingshot, or umbrella) to pick from. If you randomly choose your character and tool, what is the probability that you wont be a hobbit or use an umbrella
Answer:
The probability that you won't be a hobbit=
[tex] \frac{2}{3} [/tex]
The probability that you won't choose an umbrella=
[tex] \frac{4}{5} [/tex]
Step-by-step explanation:
The characters are 3, minus the hobbit gives you 2. So the probability of that=
[tex] \frac{2}{3} [/tex]
The weapons are 5, minus the umbrella is 4. So the probability of that=
[tex] \frac{4}{5} [/tex]
When a potential difference across a resistor is 2.0 V with a current of 1.5 A. What is its resistance?
V = IR
2 = 1.5 x R
R = 2 / 1.5
R = 1 1/3 ohms
Hope this helps!
Which term of the AP. 8 , -4 , -16 , -28 ,......... is -880 ?
Answer: 75th term
Step-by-step explanation:
If you look at the first terms, you can see that we're subtracting 12 from the previous term to get the number. Knowing this, we can write an expression for the nth term. The expression would be -12n + 20. Since this specific term has value of -880, we set -880 equal to the value of -12n+20. By setting your equation like this -12n + 20 = -880 and solving, you get n = 75, which means the 75th term has a value of -880.
What is the surface area of the sphere below?
A. 324pi units^2
B. 324pi^3 units^2
C. 36pi units^2
D. Cannot be determined
Answer:
C. 36π units²
Step-by-step explanation:
Surface area of a sphere: 4πr²
[tex]4\pi r^2\\4\pi (3)^2\\4\pi (9)\\36\pi[/tex]
Please help explanation if possible
Answer:
45
Step-by-step explanation:
a44 = 2 + (43 × 1) = 2 + 43 = 45
CAN SOMEONE TELL ME WHT DID I DO WRONG ASAP THANK YOU!!!
The final step. You divided wrong.
8 = 400 / 120 = 10/3
Step-by-step explanation:
The final step. You divided wrong.
[tex] s = \frac{400}{120} = \frac{10}{3} [/tex]
see question in image
Answer:
Total outcomes with two dice is:
6*6 = 3638Outcomes with sum of 7:
1 &6, 2&5, 3&4, 4&3, 5&2, 6&1 - total of 6Probability:
P(sum of 7) = 6/36 = 1/639Outcomes with sum of 5 or 10:
1&4, 2&3, 3&2, 4&1, 4&6, 5&5, 6&4 - total of 7Probability:
P(5x) = 7/3640Outcomes with same numbers:
1&1, 2&2, 3&3, 4&4, 5&5, 6&6 - total of 6Probability:
P(same) = 6/36 = 1/6Rationalize the denominator and simplify:
a) (√3 - √2)/( √3+√2)
b) (5+2√3)/(7+4√3)
c) (1+√2)/(3 - 2√2)
Answer:
A) (√3-√2)/(√3+√2)
Step-by-step explanation:
i think so
What does the greater unit rate or slope mean in terms of the situation? What can you conclude from this?
Answer:
Bruce's tiles covered more area than Felicia's, so this means Bruce has the greater unit rate.
Step-by-step explanation:
Got it right
pls help
5 1/3 ÷ 1 7/9
Answer:
3
Step-by-step explanation:
5 1/3 ÷ 1 7/9
Change to improper fractions
5 1/3 = (3*5+1)/3 = 16/3
1 7/9 = (9*1+7)/9 = 16/9
16/3 ÷ 16/9
Copy dot flip
16/3 * 9/16
Rewriting
16/16 * 9/3
1*3
3
find the measure of the indicated angle to the nearest degree
Answer:
43
Step-by-step explanation:
First you divide the opposite side from the angle by the hypotenuse.
33/44
then you take the inverse sine of 33/44, resulting in
43.43°, which rounds to 43°
Help please me please help me
Answer: (3, 18)
Step-by-step explanation: Where the lines corss the x does not go over 10 so the only other option is a 3. If you cut the box hori in half in you mind, the top half being 15-20 and the bottom half bring 10-14, then you can see the lines cross on the top half. Meaning it’s at 18 not 12.
How do I find x and y?
Answer:
x = 20
y = 70
Step-by-step explanation:
Since B and D are parallel :
6x - 10 + 3x + 10 = 180 add/subtract like terms
9x = 180 divide both sides by 9
x = 20
angle represented by y and 6x - 10 are supplementary and their sum is 180
y + 6x - 10 = 180 replace x with 20
y + 6*20 - 10 = 180
y + 120 - 10 = 180
y + 110 = 180 subtract 110 from both sides
y = 70
What is the equation of the graph
Answer:
[tex]y = 2x^2 + 1[/tex]
Step-by-step explanation:
The graph you see there is called a parabola. The general equation for the graph is as below
[tex]y = a*x^2 + b[/tex]
To find the equation we need to find the constants a and b. The constant b is just how much we're lifting the parabola by. Notice it's lifted by 1 on the y axis.
To find a it's a little more tricky. Let's use the graph to find a value for a by plugging in values we know. We know that b is 1 from the previous step, and we know that when x=1, y=3. Let's use that!
[tex]3 = a * (1)^2 + 1\\2 = a[/tex]
Awesome, we've found both values. And we can write the result.
[tex]y = 2x^2 + 1[/tex]
I'll include a plotted graph with our equation just so you can verify it is indeed the same.
Please help will give brainliest
[tex]x {}^{2} + 17x + 30[/tex]
Factorising It[tex]x {}^{2} + 2x + 15x + 30 \\ \\ = x(x + 2) + 15(x + 2) \\ \\ = (x + 2)(x + 15)[/tex]
[tex] \therefore[/tex] A= 2 And B= 15
Hope This Helps You ❤️How do I find x ………..
Answer:
x = 94
Step-by-step explanation:
The sum of the 4 angles in a quadrilateral = 360°
Sum the 4 angles and equate to 360
x + x + 2x - 75 + x - 35 = 360
5x - 110 = 360 ( add 110 to both sides )
5x = 470 ( divide both sides by 5 )
x = 94
Given: m∠V=103°, m∠VRT=71°, RS ∥ VU Find: m∠TRS, m∠U
Answer:
m∠TRS = 6°
m∠U = 103°
Step-by-step explanation:
In the given figure,
O is the center
RS ∥ VU
m∠V = 103° &
m∠VRT = 71°
So,
m∠V + m∠R = 180° (∵ sum of co-interior angles)
⇒ m∠R = 180° - 103° (m∠V = 103° is given)
∵ m∠R = 77° ...(i)
Now,
m∠R = m∠TRS + m∠VRT
by putting the values given
⇒ m∠TRS = 77° - 71°
∵ m∠TRS = 6°
As we know that,
VURT is a cyclic quadrilateral. So,
m∠U + m∠R = 180°
⇒ m∠U + 77° = 180° (from equation (i)
∵ m∠U = 180° - 77° = 103°
what is the total amount of RS.7500 at the rate of 5.5% per annum in 42 months?find it.
Answer:
Please check out the attachments below to get the answer
The fan below has been stretched open as far as it will go to form a semi-circle.
Each of the eighteen sectors formed by the fan consists of the same amount of fabric. The length of
each wooden rod that connects the center of the fan to its edge is 12 cm. The wooden rods are
glued to the fabric forming the fan. Determine the approximate area of each sector.
Answer:
Area of each sector=[tex]12.6cm^2[/tex]
Step-by-step explanation:
We are given that
Length of each wooden od that connects the center of the fan to its edge ,r=12 cm
Total number of sectors=18
We have to find the approximate area of each sector.
Area of semi-circle=[tex]\frac{1}{2}\pi r^2[/tex]
Using the formula
Area of fan=[tex]\frac{1}{2}\pi (12)^2=72 \pi cm^2[/tex]
Area of each sector=[tex]\frac{area\;of\;fan}{Total\;number\;of\;sectors}[/tex]
Area of each sector=[tex]\frac{72\pi}{18}=\frac{72\times 3.14}{18} cm^2[/tex]
Where [tex]\pi=3.14[/tex]
Area of each sector=[tex]12.56cm^2\approx 12.6 cm^2[/tex]
Find the value of each variable.
The two congruent base angles tell us that this triangle is isosceles, meaning it has two congruent sides. Therefore, we can set the two expressions equal to each other and solve from there.
9x - 73 = 3x + 23
6x - 73 = 23
6x = 96
x = 16
Side = 3(16) + 23 = 48 + 23 = 71
Hope this helps!
Answer:
x = 16
Step-by-step explanation:
Since the base angles are the same, the side lengths are the same
9x- 73 = 3x+23
Subtract 3x from each side
9x - 3x- 73 = 3x+23 -3x
6x- 73 = 23
Add 73 to each side
6x - 73 +73 = 23+73
6x = 96
Divide by 6
6x/6 = 96/6
x =16
Find x if AC = 7x - 15 and BD = 4x + 15
Answer:
x = 10
Step-by-step explanation:
7x - 15 = 4x + 15
7x - 4x = 15 + 15
3x = 30
x = 10
Answer:
x = 10
Step-by-step explanation:
Given that AC and BD are congruent , then
7x - 15 = 4x + 15 ( subtract 4x from both sides )
3x - 15 = 15 ( add 15 to both sides )
3x = 30 ( divide both sides by 3 )
x = 10
tìm điều kiện xác định để phân thức A=(1/x-2-2x/4-x^2+1/2+x).(2/x-1)
The tens digits of a certain two-digit number is 1/3 of the units digit. When the digits are reversed, the new number exceed twice the original number by 2 more than the sum of the digits. Find the original number.
Answer:
The orginal number is 26.
Step-by-step explanation:
So the units digit can be 3 6 or 9
The tens digit can be 1 2 or 3
So the original number can be 13
31 = 2*13+ (1+3) + 2
31 =? 26 + 4 + 2
This doesn't work. The right side is 32
26
62 = 2*26 + 8 + 2
62 = 52 + 8 + 2
This is your answer.
3 and 9 won't work because 39 is odd and so is 93. The result has to be even.
Complete the table, and then use the drawing tools to create the graph representing the relationship between the amount of plant food remaining, f(x), and the number of days that have passed, x.
The complete table of the function is:
[tex]\begin{array}{cccccccc}x & {0} & {1} & {2} & {3} & {4}& {5} & {6} \ \\ f(x) & {72} & {60} & {48} & {36} & {24}& {12} & {0} \ \end{array}[/tex]
The equation missing from the question is:
[tex]y = 72 - 12x[/tex]
To complete the table, we simply calculate the y value for each x value;
When [tex]x = 0[/tex], [tex]y = 72 - 12 * 0 = 72[/tex]
When [tex]x = 1[/tex], [tex]y = 72 - 12 * 1 = 60[/tex]
When [tex]x = 2[/tex], [tex]y = 72 - 12 * 2 = 48[/tex]
When [tex]x = 3[/tex], [tex]y = 72 - 12 * 3 = 36[/tex]
When [tex]x = 4[/tex], [tex]y = 72 - 12 * 4 = 24[/tex]
When [tex]x = 5[/tex], [tex]y = 72 - 12 * 5 = 12[/tex]
When [tex]x = 6[/tex], [tex]y = 72 - 12 * 6 = 0[/tex]
So, the complete table is:
[tex]\begin{array}{cccccccc}x & {0} & {1} & {2} & {3} & {4}& {5} & {6} \ \\ f(x) & {72} & {60} & {48} & {36} & {24}& {12} & {0} \ \end{array}[/tex]
To create a graph of f(x), we simply type [tex]y = 72 - 12x[/tex] on a drawing tool and the graph will be generated.
See attachment for graph
Learn more about graphs at:
https://brainly.com/question/20106471
Answer:
Step-by-step explanation:
Solve for 2. Round to the nearest tenth, if necessary.
L
58
M
Answer: 2=
Submit Answer
attempt 1 out of 2
PLS HELP
Answer:
x = 46.9
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp / hyp
sin 54 = x / 58
58 sin 54 =x
x=46.92298
To the nearest tenth
x = 46.9
Instructions: Find the value of the trigonometric ratio. Make sure to simplify the fraction if
needed
Answer:
cosC = [tex]\frac{7}{25}[/tex]
Step-by-step explanation:
cosC = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{BC}{AB}[/tex] = [tex]\frac{7}{25}[/tex]
Please write down your work on the loose leaf, take a CLEAR picture, and upload here. Thank you.
Answer:
m(∠C) = 18°
Step-by-step explanation:
From the picture attached,
m(arc BD) = 20°
m(arc DE) = 104°
Measure of the angle between secant and the tangent drawn from a point outside the circle is half the difference of the measures of intercepted arcs.
m(∠C) = [tex]\frac{1}{2}[\text{arc(EA)}-\text{arc(BD)}][/tex]
Since, AB is a diameter,
m(arc BD) + m(arc DE) + m(arc EA) = 180°
20° + 104° + m(arc EA) = 180°
124° + m(arc EA) = 180°
m(arc EA) = 56°
Therefore, m(∠C) = [tex]\frac{1}{2}(56^{\circ}-20^{\circ})[/tex]
m(∠C) = 18°
The domain for f(x) and g(x) is all real numbers.
Let f(x) = x2 + 1 and g(x) = x4 − 1.
Find f · g.
A.
x6 + x4 − x2 − 1
B.
x4 + x2 − 1
C.
x8 + x4 − x2 + 1
D.
x6 − x2 − 1The domain for f(x) and g(x) is all real numbers.
Answer:
A
Step-by-step explanation:
(f*g)(x) = f(x) * g(x)
=(x2+1)(x4-1)=x6-x2+x4-1
Find the distance across the lake. Assume the triangles are similar.\
A. 300 m
B. 425 m
C. 210 m
D. 283 m
Answer: A. 300 m
Work Shown:
L/100 = 15/5
5L = 100*15
5L = 1500
L = 1500/5
L = 300
Three consecutive integers have a sum of -42. Write and solve an equation to find the three integers.
x + ( x + 1 ) + ( x + 2 ) = -42
Opening the brackets and simplifying :
x + x + 1 + x + 2 = -42
3x + 3 = -42
Now , solving equation :
[tex]\bf \rightarrow \: \:3x \: + \: 3 \: = \: -42[/tex]
[tex]\bf \rightarrow \: \: 3x \: = \: -42 \: - 3[/tex]
[tex]\bf \rightarrow \:3x \: = \: -45 \: [/tex]
[tex]\bf \rightarrow \:x \: = \: \frac{ - 45}{ \: 3} \\ [/tex]
[tex]\bf \rightarrow \:x \: = \: \cancel\frac{ - 45}{ \: 3} \: \: ^{ - 15} \\ [/tex]
[tex]\bf \rightarrow \:x \: = \: - 15[/tex]
[tex]{\boxed{ \Large{ \red{ \rm{ \underline{ Now \: \: substitute}}}}}}[/tex]
[tex]\bf \implies \: \:x \: = \: - 15[/tex]
[tex]\bf \implies \: \:x \: + \: 1 \: = \: - 15 \: + \: 1 \: = \: - 14[/tex]
[tex]\bf \implies \: \:x \: + \:2 \: = \: - 15 \: + \: 2 \: = \: - 13[/tex]
-15 , -14 and -13 are the three consecutive integers.
