Answer: -6.4, -3.6
Explanation: A souloution of the system of equations is, when two equations intercept (y= 3/2x +6, y=1/4x -2)
The graph of F(x) can be compressed vertically and shifted to the right to produce the graph of G(x) . If F(x) = x ^ 3 , which of the following could be the equation of G(x) ?
Given:
The function is:
[tex]F(x)=x^3[/tex]
To find:
The function G(x) if the graph of F(x) can be compressed vertically and shifted to the right to produce the graph of G(x).
Solution:
The transformation is defined as
[tex]g(x)=kf(x+a)+b[/tex] .... (i)
Where, k is stretch factor, a is horizontal shift and b is vertical shift.
If 0<k<1, then the graph compressed vertically by factor k and if k>1, then the graph stretch vertically by factor k.
If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.
If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.
It is given that F(x) can be compressed vertically and shifted to the right to produce the graph of G(x). So, the value of k must be lies between 0 and 1, and a<0.
In option A, [tex]0<k<1[/tex] and [tex]a<0[/tex]. So, this option is correct.
In option B, [tex]0<k<1[/tex] and [tex]a>0[/tex]. So, this option is incorrect.
In option C, [tex]k>1[/tex] and [tex]a>0[/tex]. So, this option is incorrect.
In option D, [tex]k>1[/tex] and [tex]a<0[/tex]. So, this option is incorrect.
Therefore, the correct option is A.
The combined mass of two children is 75lbs. The first child is four times the mass of the second child. What are the masses of the two children?
Someone please help me with this math problem?
Answer:
The length of the shortest side of the triangle is 10 units.
Step-by-step explanation:
Let a be the shortest side of the isosceles triangle and b be the two congruent sides.
The congruent sides b are each one unit longer than the shortest side. Hence:
[tex]b=a+1[/tex]
The perimeter of the isosceles triangle is given by:
[tex]\displaystyle P_{\Delta}=b+b+a=2b+a[/tex]
This is equivalent to the perimeter of a square whose side lengths are two units shorter than the shortest side of the triangle. Let the side length of the square be s. Hence:
[tex]s=a-2[/tex]
The perimeter of the square is:
[tex]\displaystyle P_{\text{square}}=4s=4(a-2)[/tex]
Since the two perimeters are equivalent:
[tex]2b+a=4(a-2)[/tex]
Substitute for b:
[tex]2(a+1)+a=4(a-2)[/tex]
Solve for a. Distribute:
[tex]2a+2+a=4a-8[/tex]
Simplify:
[tex]3a+2=4a-8[/tex]
Hence:
[tex]a=10[/tex]
The length of the shortest side of the triangle is 10 units.
which statement is correct?
Answer:
Option 3 is correct
tex]\frac{1yd}{36 in}=\frac{7yd}{252 in}[/tex]
Step-by-step explanation:
1.[tex]\frac{1 in}{2.54 cm}=\frac{7 in}{17.68 cm}[/tex]
1 in=2.54 cm
[tex]7 in=2.54\times 7=17.78 cm[/tex]
[tex]\frac{1 in}{2.54 cm}=\frac{1 in}{1 in}=1[/tex]
[tex]\frac{1 in}{2.54 cm}\neq \frac{7 in}{17.68 cm}[/tex]
Hence, it is not correct.
2.[tex]\frac{1 ft}{12 in}=\frac{7ft}{74 in}[/tex]
1 foot=1 2in
[tex] 7ft=7\times 12=84 foot[/tex]
[tex]\frac{1 ft}{12 in}=1[/tex]
[tex]\frac{7ft}{74 in}\neq 1[/tex]
[tex]\implies \frac{1 ft}{12 in}\neq \frac{7ft}{74 in}[/tex]
Hence, it is not correct.
3.[tex]\frac{1yd}{36 in}=\frac{7yd}{252 in}[/tex]
1 yd=36 in
[tex]\frac{1yd}{36 in}=\frac{36}{36}=1[/tex]
[tex]7yd=7\times 36=252 in[/tex]
[tex]\frac{7yd}{252 in}=\frac{252 in}{252 in}=1[/tex]
[tex]\implies \frac{1yd}{36 in}=\frac{7yd}{252 in}[/tex]
Hence, it is correct.
4.[tex]\frac{1 m}{3.28ft}=\frac{7m}{22.86ft}[/tex]
1 m=3.28 ft
[tex]\frac{1 m}{3.28ft}=\frac{3.28}{3.28}=1[/tex]
[tex]7m=7\times 3.28=22.96 ft[/tex]
[tex]\frac{7m}{22.86ft}\neq 1[/tex]
[tex]\frac{1 m}{3.28ft}\neq \frac{7m}{22.86ft}[/tex]
Hence, option is not correct.
If f(x) = 2x + 1 and g(x) = x2 + 5,
what is g(f(2))?
Answer:
30 if that is an [tex]x^{2}[/tex] in g(x)
Step-by-step explanation:
f(2) = 2x + 1
= 2(2) + 1
= 4 + 1
f(2) = 5
g(5) = [tex]x^{2}[/tex] + 5
= [tex]5^{2}[/tex] + 5
= 25 + 5
g(5) = 30
Answer: 30
Step-by-step explanation:
First find f(2)
f(2) = 2(2) + 1 = 4 + 1 = 5
Therefore g(f(2)) = g(5)
Now solve for g(5)
g(5) = (5)² + 5 = 25 + 5 = 30
What are the solutions to X2 + 8X + 7 = 0?
Answer:
x = - 7, x = - 1
Step-by-step explanation:
Given
x² + 8x + 7 = 0
Consider the factors of the constant term (+ 7) which sum to give the coefficient of the x- term (+ 8)
The factors are + 7 and + 1 , since
7 × 1 = 7 and 7 + 1 = 8 , then
(x + 7)(x + 1) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 7 = 0 ⇒ x = - 7
x + 1 = 0 ⇒ x = - 1
Answer:
[tex]x=-1,-7[/tex]
Step-by-step explanation:
[tex]x^2+8x+7=0[/tex] where a [tex]\neq[/tex] 0 so a = 1 b = 8 c = 7
Quadratic Formula: [tex]x=-b\frac{\sqrt{b^2-4ac} }{2a}[/tex]
[tex]x=-8\frac{\sqrt{8^2-4(1)(7)} }{2(1)}[/tex]
[tex]x=-8\frac{\sqrt{64-28} }{2}[/tex] Evaluate the exponent and multiply 4ac
[tex]x=-8\frac{\sqrt{36} }{2}[/tex] Subtract b^2 - 4ac and multiply 2a
[tex]x=-8\frac{\sqrt{6} }{2}[/tex] Solve for the sqrt root of 35
x = - 8 ± 6/2 =
x = - 8 + 6/2 = -1
x = - 8 - 6/2 = -7
Help me please!!! Thanks
Answer:
Cylinder H has the greater volume.
Step-by-step explanation:
Recall that the volume of a cylinder is given by:
[tex]\displaystyle V=\pi r^2h[/tex]
Where r is the radius and h is the height.
Cylinder H has a radius of 4.5 meters and a height of 3 meters. Thus, its volume is:
[tex]\displaystyle \begin{aligned} V&=\pi(4.5)^2(3)\\&=60.75\pi \\&\approx190.8518\text{ m}^3\end{aligned}[/tex]
Cylinder J has a diameter of 7 meters and a height of 4.5 meters. The radius is half the diameter, so Cylinder J's radius is 3.5 meters. Thus, its volume is:
[tex]\displaystyle \begin{aligned}V&=\pi(3.5)^2(4.5)\\&=55.125\pi \\&\approx 173.1803\text{ m}^3\end{aligned}[/tex]
Thus, Cylinder H has the greater volume.
what is the value of b?
Answer: The b-value is the middle number, the number next to the X
Tomaz realized that the tip of a second hand on a clock rotates about the center of the clock. He watched the second hand rotate around the center of the clock for 15 seconds. Which describes the rotation he observed?
270 degrees clockwise rotation
90 degrees clockwise rotation
180 degrees rotation
90 degrees counterclockwise rotation
Answer:
Step-by-step explanation:
Second hand on a clock rotates at rate 360 degrees per 60 seconds.
360 degrees - 60 sec
x degrees - 15 sec
90 clockwise rotation (none hand of a clock rotates counter-clockwise :))
Answer:
90 degrees clockwise rotation
Step-by-step explanation:
does the point (-4, 2) lie inside or outside or on the circle x^2 + y^2 = 25?
Given equation of the Circle is ,
[tex]\sf\implies x^2 + y^2 = 25 [/tex]
And we need to tell that whether the point (-4,2) lies inside or outside the circle. On converting the equation into Standard form and determinimg the centre of the circle as ,
[tex]\sf\implies (x-0)^2 +( y-0)^2 = 5 ^2[/tex]
Here we can say that ,
• Radius = 5 units
• Centre = (0,0)
Finding distance between the two points :-
[tex]\sf\implies Distance = \sqrt{ (0+4)^2+(2-0)^2} \\\\\sf\implies Distance = \sqrt{ 16 + 4 } \\\\\sf\implies Distance =\sqrt{20}\\\\\sf\implies\red{ Distance = 4.47 }[/tex]
Here we can see that the distance of point from centre is less than the radius.
Hence the point lies within the circle .
What are the center and radius of the circle defined by the equation (x -2)squared + (y + 3) squared equals 16
Answer:
Center (h, k) = 2 and -3
Radius = 4
Step-by-step explanation:
Given the mathematical expression;
(x - 2)² + (y + 3)² = 16 ......equation 1.
The general equation for a circle is given by the formula;
x² + y² + 2hx + 2ky + c = 0 ......equation 2.
Where the center is C(-h, -k)
Similarly, the standard form of the equation of a circle is;
(x - h)² + (y - k)² = r² ......equation 3.
Where;
h and k represents the coordinates of the centre.r represents the radius of the circle.Comparing equation 1 and equation 3, we have;
The center of the circle, C(h, k) are 2 and -3
Radius = √16 = 4
How to Evaluate9^ 1/2
Lesson name- Algebra
Answer:
ayan po answer nasa picture
Answer:
3
Step-by-step explanation:
9½=√9=3
ie. a number to the power of ½ is the same as the square root of the number
Solve for X.
-8x - 4(x - 4) = 88
Please show work
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]\huge x=-6[/tex]
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{Solving for 'x'...}}\\\\-8x-4(x-4)=88\\-------------\\\rightarrow -8x-4x+16=88\\\\\rightarrow -12x + 16 = 88\\\\\rightarrow -12x + 16 - 16 = 88 - 16\\\\\rightarrow -12x = 72\\\\\rightarrow \frac{-12x=72}{12}\\\\\rightarrow \boxed{x=-6}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Answer: x = -6
Step-by-step explanation: Start by changing the - 4 to plus a negative 4 so that you know you're distributing a -4 through the parentheses.
So we have -8x - 4x + 16 = 88.
Simplifying the left side further gives us -12x + 16 = 88.
Now subtract 16 from both sides to get -12x = 72.
From here it should be easy to find the x = -6.
According to class 8 please solve
YOUR is a parallelogram
RUO=120°
RUO=RYO. {opposite angles in parallelogram are equal}
therefore...RYO=120°
RYS + RYO =180°. {linear pairs}
120°+RYO= 180°
therefore..RYO=60°
in ∆RSY
√SRY+RYS+YSR=180°. {sum of angles in triangle add up to 180°}
50°+60°+YSR=180°
110°+YSR=180°
:YSR=70°
Answer:
THEREFORE YSR = 70°
Step-by-step explanation:
RUO = 120°
Therefore,
RYO = 120°
(opposite angles of a parallelogram are equal)
Now,
RYO + RYS = 180° (linear pair of angles)
120° + RYS = 180°
RYS = 180° - 120°
RYS = 60°
Now,
By Angle sum property of a Triangle,
SRY + RYS + YSR = 180°
50° + 60° + YSR = 180°
110° + YSR = 180°
YSR = 180° - 110°
YSR = 70°
Evaluate the question in the photo attached please. ASAP
Cans of soda at a local store a six-pack of soda costs $2.59 and indivdual cans cost $0.80. What is the maximum of cans of soda that can be purchased for $15
Answer: 30 cans (buy them by the six-pack; so you'd buy 5 six-packs)
==============================================================
Explanation:
Let's say you buy six-packs only. Divide the amount of money you have over the cost per six-pack.
15/(2.59) = 5.7915 which rounds down to 5.
If you buy six-packs only, then you can buy a max of 5 of them. That gets you 5*6 = 30 cans of soda.
-------------
Now let's say you buy individual cans only. We'll use the same idea mentioned earlier but this time divide over 0.80
15/(0.80) = 18.75 which rounds down to 18
We round down because we can't buy that 19th can of soda (note how 19*0.80 = 15.2 which is larger than 15).
So if you buy individual cans only, then you can get a max of 18 cans.
We see that it's better to go with the six-pack option (in the first section) since we can get 30 cans compared to 18 cans.
Can someone help me with this math homework please!
Answer:i dont know
Step-by-step explanation:
Which equation is a radical equation? 4p =√-3 + p x√3 + x =^3√2x 7√11– w = –34 5 – ^3√8= v√16
Answer:
See explanation
Step-by-step explanation:
The given options are not properly formatted; so, I will give a general explanation instead
An equation is said to be radical if its variable is in a radicand sign.
For instance, the following equation is a radical;
[tex]\sqrt x + 2 = 4[/tex]
In the above equation, x is the variable, and it is in [tex]\sqrt[/tex] sign
However, the following equation is not a radical equation
[tex]x + \sqrt 4 = 2[/tex]
Because the variable is not in a radicand
Will mark brainlest help me please
Answer:
no le entiendo por qué estás en inglésGiven the roll of paper towels below how much plastic would be needed to cover the role so it can be sold given the diameter of the role is 10 inches and the height is 13 inches
Answer:
Amount of plastic need to cover paper role = 565.2 inches
Step-by-step explanation:
Given:
Diameter of paper role = 10 inch
Height of paper role = 13 inch
Find:
Amount of plastic need to cover paper role
Computation:
Radius of paper role = Diameter of paper role / 2
Radius of paper role = 10 / 2
Radius of paper role = 5 inch
Amount of plastic need to cover paper role = Total surface area of cylinder
Amount of plastic need to cover paper role = 2πr(h+r)
Amount of plastic need to cover paper role = 2(3.14)(5)(13+5)
Amount of plastic need to cover paper role = (3.14)(10)(18)
Amount of plastic need to cover paper role = 565.2 inches
A swimmer can swim 50.2 meters in 1 minute. How far can he swim in half an hour? *
Answer:
1506meters
Step-by-step explanation:
1hour-60minutes
which means half an hour is 30minutes,so it's more like they are asking you to find how far the swimmer can swim in 30minutes
50.2-1min
x -30min
x=50.2×30
x=1506meters
SOMEONE PLEASE HELP MEEEEEEE PLZZZZZZZZZZ!!!!!!!
Answer:
possibility of yellow÷ total possibilities
1÷8
1/8
Step-by-step explanation:
hope this is helpful
Aubrey tiene un nuevo estuche de arte con forma de prisma rectangular. El estuche es de 12 cm por 20 cm por 5cm. Lo único dentro del estuche es un nuevo borrador rosa con las dimensiones que se muestran a continuación.
¿Cual es el volumen del estuche que no ocupa por el borrador?
Respuesta:
720 cm³
Explicación paso a paso:
El volumen de un prisma rectangular viene dado por:
V = largo * ancho * alto
Dimensión de la caja de arte = 12 por 20 por 5
Dimensión del borrador = largo * ancho * alto
Volumen del borrador = 2 por 4 por 0,5
Dimensión del estuche de arte que no contiene borrador:
(12 por 20 por 5) - (2 por 4 por 0,5)
(10 por 16 por 4,5)
Volumen de la caja que no contiene borrador:
10 * 16 * 4,5 = 720 cm³
Please help me with this... will give brainliest
Answer:
94 cm^2
Hope it helps!
SOMEONE PLEASE HELP ME I'M STUCK
Answer:
57%
Step-by-step explanation:
200+245+125 = 570
570/1000 = .57
Answer:
57%
Step-by-step explanation:
First find the total number of families in the sample.
Total = 350 + 200 + 245 + 125 + 66 + 10 + 4
Total = 1000
Next find the number of families that have 3, 4 or 5 people.
Total(3,4 or 5) = 200 + 245 + 125
Total(3,4 or 5) = 570
Now the % = (Total 3,4 or 5) / Total ) * 100
% = 570 / 1000 * 100
% = 57%
One circle has a circumference of 12π cm. Another circle has a circumference of 32π cm. What is the ratio of the radius of the smaller circle to the radius of the larger circle?
Options:
A: 3:8
B: 8:3
C: 1:3
D: 3:1
3:8
The ratio of small circle
12:32
If we divide both of them by 4 we get 3:8
If you vertically compress the absolute value parent function, (x) = |X|, by a
factor of 4, what is the equation of the new function?
O A. g(x) = |4x|
O B. g(x) = 1/4 |x|
O C. g(x) = 4|x|
O D. g(x) = |x-4|
pls mark me as brainlist
thanks a lot
How many triangles are there in the picture?
five I think I am not sure
help pls i’m very confused
Hello,
A=(1,2) ==> A'=(1,2)+(1,1)=(2,3)
B=(6,2) ==> B'=(6,2)+(1,1)=(7,3)
C=(4,4) ==> C'=(4,4)+(1,1)=(5,5)
D=(1,4) ==> D'=(1,4)+(1,1)=(2,5)
Domain and rang of these
Answer:
Domain: {-3, -1, 1}
Range: {-1, 2, 4, 5}
Step-by-step explanation:
The domain is all the x-values, and the range is all the y-values. When listing values, repeated values are only written down once.