Answer:
1. multiply (2) by -2 and add to (1)
-2x-2y=-1320
add to (1) we get
4y-2y=1440-1320
2y=120
y= $60 cost of silver ring.
2. Multiplying (distributive property, we get the equivalent equation
x+72=3x-216
Adding 216 to both sides of the equal sign, we get
x+72+216=3x-216+216 --> x+288=3x
Subtracting x from both sides, we get
x+288-x=3x-x --> 288=2x
Logan and Izzy had initially had 188 stickers between the two of them.
3.
a = d before Anna gives away 50 marbles.
5 (a-50) = a +50 after Anna gives away 50 marbles.
5a - 250 = a + 50
4a = 300
a = 75
Anna has 75 marbles at the beginning and so did David.
Together they have 150 marbles.
Jamin wants to paint a wall in his bedroom. Not only does he need to buy paint, but he also needs to buy tape to tape off all sides of the wall and the window. How many feet of painter's tape will Jamin need to buy (assume no overlap)? [Note: The wall and window are both rectangular.]
17.5 ft
35 ft
28 ft
21 ft
The perimeter of the walls is 6 + 6 + 8 + 8 = 28 feet.
The perimeter of the window is 2 + 2 + 1.5 + 1.5 = 7 feet.
Total = 28 + 7 = 35 feet of tape.
I would say B.35 is the answer.
Given the functions, F (x)=√(2x-5) and g(x) = 3x 2 + 2, perform the indicated operation. f(g(x))
Answer:
[tex]f(g(x)) =\sqrt{6x^2-1}[/tex]
Step-by-step explanation:
Given
f(x) = √2x-5
and
g(x) = 3x^2+2
We have to find the composition of both function
f(g(x)) means that we have to put function g in place of x in function f.
[tex]f(g(x))= \sqrt{2*g(x)-5}\\ =\sqrt{2(3x^2+2)-5}\\=\sqrt{6x^2+4-5}\\=\sqrt{6x^2-1}[/tex]
..
The composite function f(g(x)) is given by f(g(x)) = √(6x^2 - 1).
To find the composite function f(g(x)), you need to substitute the expression for g(x) into the function f(x). Here's how you can do it step by step:
Start with the function g(x):
g(x) = 3x^2 + 2
Now, substitute this expression into the function f(x):
f(g(x)) = √(2(3x^2 + 2) - 5)
Simplify the expression inside the square root:
f(g(x)) = √(6x^2 + 4 - 5)
Further simplify the expression inside the square root:
f(g(x)) = √(6x^2 - 1)
So, the composite function f(g(x)) is given by:
f(g(x)) = √(6x^2 - 1)
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janis jogs around a rectangular park that is 3/4 mi long and 1/4 mi wide. how far is it around the park?
Answer:
[tex]2\ miles[/tex]
Step-by-step explanation:
we know that
The distance around the park is equal to the perimeter of the rectangular park
The perimeter is equal to
[tex]P=2(L+W)[/tex]
we have
[tex]L=\frac{3}{4}\ mi[/tex]
[tex]W=\frac{1}{4}\ mi[/tex]
substitute the values
[tex]P=2(\frac{3}{4}+\frac{1}{4})[/tex]
[tex]P=2(\frac{4}{4})[/tex]
[tex]P=2\ mi[/tex]
Answer:
3 219⁄1000 km. [2 mi.]
Step-by-step explanation:
P = 2l + 2w
P = 2[¾] + 2[¼]
P = 1½ + ½
P = 2
I am joyous to assist you anytime.
If f(x) = -x + 8 and g(x) = x^4, what is (gºf)(2)?
Answer:
[tex]\large\boxed{(g\circ f)(2)=1296}[/tex]
Step-by-step explanation:
[tex](g\circ f)(x)=g\bigg(f(x)\bigg)\\\\f(x)=-x+8,\ g(x)=x^4\\\\(g\circ f)(x)=\g\bigg(f(x)\bigg)=(-x+8)^4\\\\(g\circ f)(2)\to\text{put x = 2 to the equation}\ (g\circ f)(x):\\\\(g\circ f)(2)=(-2+8)^4=(6)^4=1296[/tex]
[tex]\bf \begin{cases} f(x)=&-x+8\\ g(x)=&x^4\\ (g\circ f)(x) =& g(~~f(x)~~) \end{cases} \\\\[-0.35em] ~\dotfill\\\\ f(2)=-(2)+8\implies f(2)=\boxed{6} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{(g\circ f)(2)}{g(~~f(2)~~)}\implies g\left( \boxed{6} \right) = (6)^4\implies \stackrel{(g\circ f)(2)}{g(6)} = 1296[/tex]
Joseph claims that a scatterplot in which the y-values increase as the x-values increase must have a linear association. Amy claims that the scatterplot could have a nonlinear association. Which statement about their claims is true?
Joseph is correct because only a line will increase along the whole data set. The scatterplot will have a positive, linear association.
Joseph is correct because only a line will decrease along the whole data set. The scatterplot will have a negative, linear association.
Amy is correct because a nonlinear association could increase along the whole data set, while being steeper in some parts than others. The scatterplot could be linear or nonlinear.
Amy is correct because only a nonlinear association could increase along the whole data set. A line has the same slope at any point, but a curve can get steeper at different points.
Answer:
The answer is C
Step-by-step explanation:
Answer:
Amy is correct because a nonlinear association could increase along the whole data set, while being steeper in some parts than others. The scatterplot could be linear or nonlinear.
Step-by-step explanation:
Both linear and nonlinear associations could increase along the whole data set. That's why Joseph and the fourth option are incorrect.
Using the given points and line, determine the slope of the line.
(1, 2) and (2, 1)
Answer:
-1
Step-by-step explanation:
To find the slope of a line given two points, you can use [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are points on the line.
Or you could just line up the points vertically and subtract them vertically, then put 2nd difference over first.
Like so:
( 2 , 1 )
-( 1 , 2 )
--------------------
1 -1
So the slope is -1/1 or just -1.
Jeri is 3 years younger than Laura, whose age is x. How old is Jeri? x - 3 yrs old x + 3 yrs old 3x yrs old
Answer:
3x yrs old
Step-by-step explanation:
What is the equation of the line that is parallel to the given line and passes through the point (-3, 2)?
4x + 3y = -6
Step-by-step explanation:
what is the domain of this function?
Answer:
x ≥ 0
Step-by-step explanation:
The domain of the function is the inputs, or in this case, the x values.
The inputs are x greater than or equal to zero all the way to infinity.
Answer:
Step-by-step explanation:
The domain includes 0 and all real numbers greater than 0: x ≥ 0
what is the approximate area of the circle shown below? 16 cm
Answer:
201.143 (approx.) cm²
area of circle = (pi)x(radius)^2
= 22/7 x (8)^2
=22/7 x 64
= 1408/7
= 201.142857143
= 201.143 cm^2 (approx.)
Answer:
the approximate area of circle is 201 cm²
D is the correct option.
Step-by-step explanation:
From, the given figure, the diameter of the circle is 16 cm.
The radius is half of the diameter.
Hence, the radius of circle is 16/2 = 8 cm
The area of a circle is given by
[tex]A=\pi r^2[/tex]
Substituting the value of r and π
[tex]A=3.14(8)^2\\\\A=200.96\\\\A\approx201[/tex]
Therefore, the approximate area of circle is 201 cm²
D is the correct option.
If X || Y and Y || Z then___
Answer:
X is parallel to Z
X || Z
Step-by-step explanation:
This is called the transitive property.
It says something like:
If f is related to g and g is related to h, then f is related to h.
The parallel relationship is transitive.
That is,
if X is parallel to Y and Y is parallel to Z, then X is parallel to Z.
- The whole batch cost $28,000 and contained 140 items. Write the two rates (ratios) implied
by this statement. What would be the price for 200 items?
Please show work
Answer:
The answer would be 14
Step-by-step explanation:
you just divide 28,00 by 200 and that gives you 14
what is the coefficient of x^3 in the expansion of (2x-3)^5?
A) -5
B) 10
C) -120
D) -360
E) 720
Answer:
309
Step-by-step explanation:
(2x-)^5
step 1
1 5 10 10 5 1
step 2
1(2x¹-3^0) 5(2x²-3^5) 10(2x³-3^4)
10(2x^4-3³) 5(2x^5-3²)
1(2x^0-3¹)
step 3
(2x) (10x²-243) (20x³-81) (20x^4-27)
(10x^5-9) (2-3)
step 4
2 -243-61-7 +1 -1=309
The coefficient of [tex]x^3[/tex] in the expansion of [tex](2x-3)^5[/tex] is 720
The correct answer is an option (E)
What is coefficient?"It refers to a number or quantity placed with a variable."
What is variable?"The alphabetic character that expresses a numerical value."
What is an expression?"It is a mathematical expression which consists of numbers, variables and mathematical operations."
Formula for [tex](a-b)^3[/tex]" [tex](a-b)^3=a^3-3a^2b+3ab^2- b^3[/tex] "
Formula for [tex](a-b)^2[/tex]" [tex](a-b)^2=a^2-2ab+b^2[/tex] "
For given question,
We have been given an expression [tex](2x-3)^5[/tex]
We need to expand given expression.
[tex](2x-3)^5\\\\= (2x-3)^3\times (2x-3)^2\\\\=[(2x)^3-3(2x)^23+3(2x)(3)^2- 3^3]\times ((2x)^2-2(2x)(3)+3^2)\\\\=[8x^3-36x^2+54x-27]\times [4x^2-12x+9]\\\\=-243+810x-1080x^2 +720x^3-240x^4+32x^5\\\\=32x^5-240x^4+720x^3-1080x^2+810x-243[/tex]
Therefore, the coefficient of [tex]x^3[/tex] in the expansion of [tex](2x-3)^5[/tex] is 720
The correct answer is an option (E)
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What is the solution to the system?
X+y+z=2
2x+y-z=-1
X=5-2z
Answer:
x = 1, y = -1, z = 2 → (1, -1, 2)Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}x+y+z=2&(1)\\2x+y-z=-1&(2)\\x=5-2z&(3)\end{array}\right\\\\\text{Substitute (3) to (1) and (2):}\\\\\left\{\begin{array}{ccc}(5-2z)+y+z=2\\2(5-2z)+y-z=-1&\text{use the distributive property}\end{array}\right\\\left\{\begin{array}{ccc}5-2z+y+z=2\\10-4z+y-z=-1\end{array}\right\qquad\text{combine like terms}\\\left\{\begin{array}{ccc}5+y-z=2&\text{subtract 5 from both sides}\\10+y-5z=-1&\text{subtract 10 from both sides}\end{array}\right[/tex]
[tex]\left\{\begin{array}{ccc}y-z=-3\\y-5z=-11&\text{change the signs}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}y-z=-3\\-y+5z=11\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad4z=8\qquad\text{divide both sides by 4}\\.\qquad\qquad \boxed{z=2}\\\\\text{Put it to the first equation:}\\\\y-2=-3\qquad\text{add 2 to both sides}\\\boxed{y=-1}\\\\\text{Put the values of}\ z\\text{to (3):}\\\\x=5-2(2)\\x=5-4\\\boxed{x=1}[/tex]
NEED HELP ASAP PLEASE
Find the ratio of the known sides and calculate X.
1. The smaller triangle is half the size of the lager one:
6/12 = 1/2
10/12 = 1/2
This means x is half the length of 16
x = 16/2 = 8
2. 18/30 = 3/5
9/15 = 3/5
This means x is 3/5 of 25
x = 25 * 3/5 = 15
3. 32/24 = 1 1/3
16 /12 = 1 1/3
X is 1 1/3 times the length of 21
x = 21 x 1 1/3
x = 28
4. 12/15 = 4/5
20/25 = 4/5
x is 4/5 the length of 40
x = 40 * 4/5
x = 32
True or false? An angle whose vertex is at the center of the circle is a central angle of that circle.
This statement would be true: if the vertex of an angle is at the center of the circle, then it would be the central angle.
Arnold has x amount of money in
his checking account. He spends
$12.36 for breakfast but has at least
$31.24 left in his account. How much
money did he have originally?
Answer:
43.60
Step-by-step explanation:
12.36+31.24
Why is the x intercept wrong?
A light bulb company produces a constant number of new light bulbs in their factory each week, and stores them in a warehouse where old light bulbs from the previous year are also stored. After 3 weeks, they have 15,000 bulbs in the warehouse. After 7 weeks, they have 65,000 bulbs.
What is the equation in point-slope formula?
Answer:
y - 15000 = 12500(x-3)
(3a-2b)(3a+3b) so this is foil but i always get messed up on it does anyone now how to do it
Answer:
9a^2 + 3ab - 6b^2
Step-by-step explanation:
(3a-2b)(3a+3b)
First term of each grouping is 3a and 3a.
Multiply those you get 9a^2.
Outer term of each grouping is 3a and 3b.
Multiply those you get 9ab.
Inner term of each grouping is -2b and 3a.
Multiply those you get -6ab.
Last term of each grouping is -2b and 3b.
Multiply those you get -6b^2.
Add up all your products from above.
9a^2+9ab+-6ab+-6b^2
There are like terms here. The 9ab+-6ab which is 3ab.
So you can write your expression now as:
9a^2 + 3ab +-6b^2
9a^2 + 3ab - 6b^2
Step-by-step explanation:
[tex]\text{Use FOIL}\ (a+b)(c+d)=ac+ad+bc+bd:\\\\(3a-2b)(3a+3b)\\\\=(3a)(3a)+(3a)(3b)+(-2b)(3a)+(-2b)(3b)\\\\=9a^2+9ab-6ab-6b^2\qquad\text{combine like terms}\\\\=9a^2+3ab-6b^2[/tex]
In the table, the parts of strawberry concentrate and the parts of water to prepare a strawberry drink are given. There is a proportional relationship between these two quantities. Find the value of x.
Parts of Water 3 9 36
Parts of Concentrate 1 3 x
Answer:
12
Step-by-step explanation:
[tex]\frac{Parts of Water}{Parts of Concentrate} =3[/tex]
3/1=3
9/3=3
36/12=3
Which equation is used to help form the combined gas law?
Need help ASAP !
If pressure is constant
then PV= nRT
is equivalent to V= ( nR/P) T
V= kT ( where k is constant nR/P)
As V is directly proportional to T
So V1/T1 = V2/T2
Answer:
The correct answer
Step-by-step explanation:
evaluate 3^-3 please explain
Answer:
D) 1/27
Step-by-step explanation:
The question is: 3^(-3).
Note that there is a negative sign in the number at the power place. This means that you must flip the number, and in this case, put it over 1. The rest is solved as usual:
3^-3 = 1/(3^3) = 1/(3 * 3 * 3) = 1/27
1/27, or D) is your answer.
~
What is the volume of the regular pyramid bellow?
Answer:
128 units^3
Step-by-step explanation:
[tex]v = \frac{b \times b \times h}{3} = \\ = \frac{8 \times 8 \times 6}{3} = \\ = 128 \: {units}^{3} [/tex]
Step-by-step explanation:
base areas x height / 3
a^2 . h / 3
8^2 . 6 / 3
= 128 units^3
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Which of these is a trinomial?
A. 2x-7
B. 2x2 - 7/3 + 14
c. 2y2 + 7y
D. 5xy
Answer:
the answer is D
Step-by-step explanation:
a is not it has a negative
a b is not it has an equation in it
so that leaves it to see and d c does not work
because it has to have two variables per one number
You have $60. The jacket you want costs $25.50 and 7% tax. what is the top tag price (excludes sales tax) left to also buy a pair of shorts?
the assumption being, that there's a 7% sales tax on any item in the store.
so if you buy the jacket, you pay 25.5 plust 7% of 25.5.
and if you buy the shoes for price say "s", then you pay "s" plus 7% of "s".
whatever those two amounts are, they must be $60, because that's all you have in your pocket anyway.
[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{7\% of 25.5}}{\left( \cfrac{7}{100} \right)25.5}\implies 0.07(25.5)~\hfill \stackrel{\textit{7\% of "s"}}{\left( \cfrac{7}{100} \right)s}\implies 0.07s \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \stackrel{\textit{jacket}}{25.5}+\stackrel{\textit{jacket's tax}}{0.07(25.5)}+\stackrel{\textit{shoes}}{s}+\stackrel{\textit{shoe's tax}}{0.07s}~~=~~\stackrel{\textit{in your pocket}}{60} \\\\\\ 25.5+1.785+s+0.07s=60\implies 27.285+1.07s=60 \\\\\\ 1.07s=60-27.285\implies 1.07s=32.715\implies s=\cfrac{32.715}{1.07}\implies s\approx 30.57[/tex]
Choose the equation that represents the line that passes through the point (6,-3,) and has a slope of 1/2
Answer:
[tex]y=\frac{1}{2}x-6[/tex]
Step-by-step explanation:
The general equation of a line: [tex]y = ax+b[/tex]
In our case a is given
[tex]a=\frac{1}{2}[/tex]
Now we plug in for a and we get:
[tex]y=\frac{1}{2}*x+b[/tex]
Now we plug in our coordinates into this equation and we solve for b
[tex]-3=\frac{1}{2}*6+b\\b = -6[/tex]
So the equation of the line is [tex]y=\frac{1}{2}x-6[/tex]
Answer:
[tex]y=\frac{1}{2}x-6[/tex]
Step-by-step explanation:
Since the Inclination of the line was already given to us. Let us use Inclination of line formula:
[tex]m=\frac{y-y_0}{x-x_0}[/tex]
Plugging it in those values then we have the equation of the line:
[tex]\frac{1}{2}=\frac{y+3}{x-6}[/tex]
Rewriting, multiplying both sides
2y+6=x-6
2y=x-12 Rearranging
[tex]y=\frac{1}{2}x-6[/tex]
Which of the following is an integer?
0
4
© -12.5
0 0.454545...
Answer: 4
Step-by-step explanation: 4 is the answer because an integer is any whole number, but not 0.
Find the length of RJ
Answer:
Option C 89
Step-by-step explanation:
In this problem we know that
KJ=KR+RJ
we have
KJ=95 units
KR=6 units
substitute and solve for RJ
95=6+RJ
subtract 6 both sides
RJ=95-6=89 units
Answer:
The correct option is C.
Step-by-step explanation:
We need to find the length of line segment RJ.
From the given figure it is clear that line segment KJ is the sum of line segments KR and RJ.
[tex]KJ=KR+RJ[/tex]
The length of line segment KJ is 95 units and the length of KR is 6 units.
Substitute KJ=95 and KR=6 in the above equation.
[tex]95=6+RJ[/tex]
Subtract 6 from both the sides.
[tex]95-6=6+RJ-6[/tex]
[tex]89=RJ[/tex]
The length of segment RJ is 89 units. Therefore the correct option is C.
Which of the following is equivalent to
Answer:
[tex]x^{4}[/tex]
Step-by-step explanation:
[tex]\frac{x^{5}y^{2} }{xy^{2} }[/tex]
= [tex]x^{4}[/tex]
Question 1:
For this case we have the following expression:
[tex]\frac {x ^ 5y ^ 2} {xy ^ 2}[/tex]
We eliminate similar terms in the numerator and denominator:
[tex]\frac {x ^ 5} {x}[/tex]
By definition of division of powers of the same base we have to place the same base and subtract the exponents:
[tex]\frac {x ^ 5} {x} = x ^ {5-1} = x ^ 4[/tex]
ANswer:
Option D
Question 2:
For this case we must indicate which expression is not equal to 125.
We tested option A:
[tex]5 (\frac {5 ^ 3} {\frac {2} {5}}) ^ 2 =[/tex]
Simplifying we have:
[tex]5 (\frac {5 ^ 3 * 5} {2}) ^ 2 =\\5 (\frac {5 ^ 8} {4}) =\\\frac {5 ^ 9} {4}[/tex]
The expression is not equal to 125.
Answer:
option A