Answer:
set mary is x years old, and helen is y years old.
first sentence:x=2y
second one:4(y-8)=x+4
bring x=2y in 4(y-8)=x+4
=>4y-32=2y+4
=>2y=36
=>y=18
=>x=36
mary:36
helen:18
We want to write and solve a system of equations that models given situation. We will see that Helen is 18 years old, and Mary is 36 years old.
Let's define the variables we will be using.
m = Mary's age.h = Helen's age.We know that "Mary is twice as old as Helen’s age"
Then:
m = 2*h
"If 8 is subtracted from Helen’s Age and 4 is added to Mary Age, Mary will be 4 times as old as Helen."
(m + 4) = 4*(h - 8)
Then the system of equations is:
m = 2*h
(m + 4) = 4*(h - 8)
To solve it, we can replace m by 2*h in the second equation, so we get:
(2h + 4) = 4*(h - 8)
2*h + 4 = 4*h - 32
4 + 32 = 4*h - 2*h
36/2 = h = 18
And we know that:
m = 2*h = 2*18 = 36
So Helen is 18 years old, and Mary is 36 years old.
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Use the zero product property to find the solutions to the equation x2 + x – 30 = 12.
Answer:
x= 6, -7
Step-by-step explanation:
Which graph shows the line y = - 3x + 1
Answer:
i need a picture
Step-by-step explanation:
Suppose tan(b) = –2, and the terminal side of b is located in quadrant II. What is cot(b)?
Answer:
- 1/2
Step-by-step explanation:
Just took the test
The value of cot (b) using trigonometry is -1/2 when tan b = -2.
Since we are given that tan(b) = -2 and the terminal side of angle b is in quadrant II, determine the value of cot(b).
In quadrant II, the sine and cosine values are positive, while the tangent and cotangent values are negative.
Given:
tan(b) = -2
The cotangent (cot) of an angle is the reciprocal of the tangent:
cot(b) = 1 / tan(b)
Now, substituting the given value of tan(b):
cot(b) = 1 / (-2)
cot(b) = -1/2
So, the value of cot(b) is -1/2.
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A jar that contains quarters and dimes is worth $7.15. If there are a total of 40 coins,
how many of each type of coin is there?
Answer:
21 quarters and 19 dimes
Step-by-step explanation:
Create a system of equations where q is the number of quarters and d is the number of dimes.
0.25q + 0.1d = 7.15
q + d = 40
Solve by elimination by multiplying the bottom equation by -0.25
0.25q + 0.1d = 7.15
-0.25q - 0.25d = -10
Add them together and solve for d:
-0.15d = -2.85
d = 19
Then, plug in 19 as d into the second equation to solve for q:
q + d = 40
q + 19 = 40
q = 21
So, there are 21 quarters and 19 dimes
Answer:
21 Quarters, 19 Dimes.
Step-by-step explanation:
21 x .25 = 5.25
19 x .10 = 1.90
5.25 + 1.90 = 7.15
Kyle is drawing a rectangle on the coordinate plane. Which coordinate pair could be Point M, the missing vertex of the rectangle?
Answer:
Step-by-step explanation:
5,2
Please help me guys!!!
Why is near impossible to draw a rhombus on Geoboard and easy to draw a square?
Thank you in advance :)
Answer: Think about diagonal sides and horizontal bases.
Step-by-step explanation: "Think outside of the box." as they say.
See the screenshot attached.
Which of the following is the value or PQ
Answer:
B. 61
Step-by-step explanation:
Given:
∆PQR ≅ ∆PQS
PQ = 2x + 41
QS = 7x - 24
QR = 3x + 16
Required:
Numerical value of PQ
SOLUTION:
First, create an equation to find the value of x as follows:
Since both triangles are congruent, therefore:
QS = QR
7x - 24 = 3x + 16 (Substitution)
Collect like terms
7x - 3x = 24 + 16
4x = 40
Divide both sides by 4
4x/4 = 40/4
x = 10
Find PQ by plugging x = 10 into PQ = 2x + 41
PQ = 2(10) + 41
PQ = 20 + 41
PQ = 61
PLZ HELP WILL GIVE BRAINLIST
A. A number less than 2
B. A number greater than 1
C. An odd number
D. A multiple of 2
Answer:
Option A
Step-by-step explanation:
The answer is option A "A number less than 2." That is because we check off each of the following given options. It won't be option C because they're 4 odd numbers a equal amount of multiplies of two (option D) which means they both have a equal (4 out of 8) chance. It won't be option B because they're 7 out of 8 numbers that are greater then on which means you have a greater chance of getting a number greater then one but the question is asking for the most unlikely.....therefore the answer is option A because you have a 1 out of 8 chance of getting a number less then two.
Hope this helps.
9x6=9x(4+ )
=( X4)+(9x )
= +
=
idkStep-by-step explanation:
Is perpendicular to the line y = 2x + 1
and through the point (-1,5)
Answer:
-2x+3
Step-by-step explanation:
Using y=mx+b
To make the line perpendicular, you just need to make the slope (m=2) negative. To make it go through (-1, 5), you just need to adjust the b value to raise the graph to a point where it will pass through the point.
Supposed y varies directly as x and y =21 when x=3
If a 25 kg car Accelerates at a speed of 100ms what will the force of the car be
Answer:
force = 100 m/s/25 s = 4 m/s^2
multiply express your anwser in simplest form
Answer:
1/6
Step-by-step explanation:
9: 9,18,27,36,45,54,63,72,81,90
10: 10,20,30,40,50,60,70,80,90,100
Since, 90 is the LCM of 9 and 10 that turns into your denominater then your equation turns into this...
5/90 x 3/90
The denomineter stays the same so you get 90 then 5 x 3 equals 15 so you get 15 and in total that gives you 15/90. Divide the top and bottom by the greatest number that will divide both numbers exactly which gives you 1/6
HOPE THIS HELPED :D
12x ÷ 4y (if x = -8 and y = 3)
Answer:
- 8
Step-by-step explanation:
Step 1:
12x ÷ 4y Equation
Step 2:
12 ( - 8 ) ÷ 4 ( 3 ) Input x and y
Step 3:
- 96 ÷ 12 Multiply
Answer:
- 8 Divide
Hope This Helps :)
Simplify. 863x14y9−−−−−−√
Answer: 1
Step-by-step explanation: 863x14ysqrt9= 3 simplified is 1
Is this a function or not a function? (Picture)
Use the definition:
f'(x)=[tex]\lim_{h \to 0} \frac{f(x+h)-f(x)}{h}[/tex]
to find f'(x) for:
f(x)=[tex]\frac{1}{\sqrt{x}}[/tex]+x
I need the WORK, not the answer. Thanks!
Using the given definition, for [tex]f(x)=\frac1{\sqrt x}+x[/tex], we have
[tex]f'(x)=\displaystyle\lim_{h\to0}\frac{\left(\frac1{\sqrt{x+h}}+x+h\right)-\left(\frac1{\sqrt x}+x\right)}h[/tex]
Right away, we see x and -x in the numerator, so we can drop those terms.
[tex]f'(x)=\displaystyle\lim_{h\to0}\frac{\frac1{\sqrt{x+h}}+h-\frac1{\sqrt x}}h[/tex]
Remember that limits distribute over sums, i.e.
[tex]\displaystyle\lim_{x\to c}(f(x)+g(x))=\lim_{x\to c}f(x)+\lim_{x\to c}g(x)[/tex]
so we can separate the h from everything else in the numerator:
[tex]f'(x)=\displaystyle\lim_{h\to0}\frac{\frac1{\sqrt{x+h}}-\frac1{\sqrt x}}h+\lim_{h\to0}\frac hh[/tex]
Since h ≠ 0, we have [tex]\frac hh=1[/tex], so the second limit is simply 1.
[tex]f'(x)=\displaystyle\lim_{h\to0}\frac{\frac1{\sqrt{x+h}}-\frac1{\sqrt x}}h+1[/tex]
For the remaining limit, focus on the numerator for now. Combine the fractions in the numerator:
[tex]\dfrac1{\sqrt{x+h}}-\dfrac1{\sqrt x}=\dfrac{\sqrt x-\sqrt{x+h}}{\sqrt x\sqrt{x+h}}[/tex]
Recall the difference of squares identity,
[tex]a^2-b^2=(a-b)(a+b)[/tex]
Let [tex]a=\sqrt x[/tex] and [tex]b=\sqrt{x+h}[/tex]. Multiply the numerator and denominator by [tex](a+b)[/tex], so that the numerator can be condensed using the identity above.
[tex]\dfrac{\sqrt x-\sqrt{x+h}}{\sqrt x\sqrt{x+h}}\cdot\dfrac{\sqrt x+\sqrt{x+h}}{\sqrt x+\sqrt{x+h}}[/tex]
[tex]=\dfrac{(\sqrt x)^2-(\sqrt{x+h})^2}{\sqrt x\sqrt{x+h}(\sqrt x+\sqrt{x+h})}[/tex]
[tex]=\dfrac{x-(x+h)}{\sqrt x\sqrt{x+h}(\sqrt x+\sqrt{x+h})}[/tex]
[tex]=-\dfrac h{\sqrt x\sqrt{x+h}(\sqrt x+\sqrt{x+h})}[/tex]
Back to the limit: all this rewriting tells us that
[tex]f'(x)=\displaystyle\lim_{h\to0}\frac{-\frac h{\sqrt x\sqrt{x+h}(\sqrt x+\sqrt{x+h})}}h+1[/tex]
Again, the h's cancel, and we can pull out the factor of -1 from the numerator and simplify the fraction:
[tex]f'(x)=\displaystyle-\lim_{h\to0}\frac1{\sqrt x\sqrt{x+h}(\sqrt x+\sqrt{x+h})}+1[/tex]
The remaining expression is continuous at h = 0, so we can evaluate the limit by substituting directly:
[tex]f'(x)=-\dfrac1{\sqrt x\sqrt{x+0}(\sqrt x+\sqrt{x+0})}+1[/tex]
[tex]f'(x)=-\dfrac1{2x\sqrt x}+1[/tex]
or, if we write [tex]\sqrt x=x^{1/2}[/tex], we get
[tex]f'(x)=-\dfrac12x^{-3/2}+1[/tex]
What is the expanded form of (a + b)^2?
Answer:
[tex] {a}^{2} + 2ab + {b}^{2} [/tex]
Answer:
(a + b) × (a + b)
Step-by-step explanation:
(a + b)²
(a + b) × (a + b)
Please help ❤️ What percent of 24 is 15?
Answer:
62.5
Step-by-step explanation:
There ya gooo :)
Answer:
62.5%
Here You go
Step-by-step explanation:
4x + 10 + 3x = 40 - 3x
O A. x = 3
B. X=
x = 1
15
2
25
O C. X=
2
O D. x = 5
Answer:
a. 3
Step-by-step explanation:
Answer:
(A) X = 3
Step-by-step explanation:
-_-
The total sales tax in a certain city is 8.75%. The state sales tax rate is 7.25%, and the county adds an additional sales tax of 0.5%. How much in sales tax is added by the city?
a.) 0.1%
b.) 0.25%
c.) 1%
d.) 2.5%
Answer:
C.1%
Step-by-step explanation:
Finding Decimal Products Which statements are true for the product of 0.2 and 0.2? Check all that apply. The product will be smaller than both the factors. ✓ There will be a zero in the tenths place, There will be a zero in the hundredths place. The answer is 0.4. ✓ The answer is 0.04.
Answer:
0 The product will be smaller than both the factors.
0 There will be a zero in the tenths place.
0 The answer is 0.04.
some helps plssss i need help
Answer:
Yess
Step-by-step explanation:
If you multiply all the numbers together you get 39690000. And the square root of that number is 6300. So it is a perfect square. If you did 6300² = 39690000.
The area of a rectangle is x²-4x-21
Write down an expression for the width and the length of
the rectangle.
Answer:
Step-by-step explanation:
Area of rectangle= Length x Width
and the given Area is a quadratic expression
A=[tex]x^{2} -4x-21[/tex]
We use the factorization method so,
we need 2 numbers that when multiplied we get -21 and when we add/subtract we get -4 so,
A=[tex]x^{2} -7x+3x-21[/tex]
now we simplify,
A=[tex]x(x-7)+3(x-7)[/tex]
A=[tex](x-7)(x+3)[/tex]
This looks familiar doesn't it, when we write the formula for the area of rectangle its
A= Length x Width and the equation here shows that
A= [tex](x-7)(x+3)[/tex]
So the expression for the length is x-7 and
the expression for the width is x+3 i think u have missed maybe some information on the question as such that the perimeter might be missing because length could be either x-7 or even x+3 same goes for width maybe someone can correct me if im wrong
Odd number between 3 and 19
Answer:
11, there both 8 away so its right in ze middle :D
Step-by-step explanation:
Joseph and Wendy were catching tadpoles. At first Wendy caught nine times three more than Joseph caught. Joseph was upset and released half of Wendy ’s tadpoles, and then six times as many as Joseph caught swam away. After all of this, Wendy only had three tadpoles left. How many tadpoles did Joseph catch?
Answer:
7
Step-by-step explanation:
Step 1: translate the given word problem into solvable algebraic equation.
Let "t" represent the number of tadpoles Joseph caught.
"Wendy caught nine times three more than Joseph caught" can be expressed as 9(t + 3)
Number of Wendy's tadpole = [tex] 9(t + 3) [/tex]
Given that half of Wendy's tadpole and also 6 times Joseph's tadpoles swarm away leaving Wendy with only 3, the following equation can be written:
[tex] \frac{9(t + 3)}{2} - 6t = 3 [/tex]
Step 2: solve for t using the equation created.
[tex] \frac{9(t + 3)}{2} - 6t = 3 [/tex]
Add 6t to both sides
[tex] \frac{9(t + 3)}{2} - 6t + 6t = 3 + 6t [/tex]
[tex] \frac{9(t + 3)}{2} = 3 + 6t [/tex]
Multiply both sides by 2
[tex] \frac{9(t + 3)}{2}*2 = (3 + 6t)*2 [/tex]
[tex] 9(t + 3) = 2(3 + 6t) [/tex]
[tex] 9t + 27 = 6 + 12t [/tex]
Collect like terms
[tex] 9t - 12t = 6 - 27 [/tex]
[tex] -3t = -21 [/tex]
Divide both sides by -3
[tex] t = 7 [/tex]
Joseph caught 7 tadpoles
Question 9 of 10 What is the scale factor of ABC to DEF?
An expression is shown below if this expression is equivalent to 60, what must be the value of a? A.) 3 B.) 4 C.) 9 D.)16
Answer:
Option (A)
Step-by-step explanation:
Given expression is,
[tex]5\sqrt{48a}=60[/tex]
Squaring on both the sides of the equation,
[tex](5\sqrt{48a})^2=(60)^2[/tex]
25(48a) = 3600
1200a = 3600
By dividing the equation by 1200,
a = [tex]\frac{3600}{1200}[/tex]
a = 3
Therefore, Option (A) will be the answer.
What is (8p - 2)(6p + 2)
answer:
48p² + 4p - 4
solution:
8p × 6p +8p × 2 - 2 × 6p - 2 × 2
48p² + 8p x 2 - 2 ×6p - 2 × 2
48p² + 16p - 12p - 4
48p² + 4p - 4
The required algebraic product is 48[tex]p^{2}[/tex] + 4p - 4.
Given the two binomial (8p - 2)(6p + 2).
To multiply two binomials, take the first term of the first binomial and multiply with the entire second binomial and positive or negative as per given in the first binomial ,take the second term of the first binomial and multiply with the entire second binomial.
Let a, b, c and d be any four variables. Consider (a - b)(c + d) gives
a(c + d) - (c + d).
That implies, (8p - 2)(6p + 2) = 8p(6p + 2) - 2(6p + 2)
Multiply by removing the brackets gives,
(8p - 2)(6p + 2) = 48[tex]p^{2}[/tex] + 16p - 12p - 4
Combining like terms and algebraic sum gives,
(8p - 2)(6p + 2) = 48[tex]p^{2}[/tex] + 4p - 4.
Hence, the required algebraic product is 48[tex]p^{2}[/tex] + 4p - 4.
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