Algebra Piecewise functions!!!
Can someone help with number 1? I got some of it but I don’t know what to do next!
Answers
Answer:
f(7) = 16
Step-by-step explanation:
f(7)
Let x = 7
We use the first part of the function since 7 > 4
3(7) -5
21 -5
16
f(7) = 16
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do you want me to explain?
Related Questions
10. A rectangle whose length is twice its width has a diagonal equal to one side of a given square. The ratio of the area of the rectangle to the area of the square is
Answers
Answer:
2/5
Step-by-step explanation:
First, we can draw the rectangle out, as shown. The length is twice the width, and the diagonal, y, cuts across the rectangle. This forms a right triangle, and using the Pythagorean Theorem, we can say that
y² = x² + (2x)²
y² = x² + 4x²
y² = 5x²
square root both sides
y=√(5x²)
The diagonal, or y, is equal to √(5x²). This is equal to one side of the square
The area for the rectangle, which we need to find for the ratio, is length * width = x * 2x = 2x²
The area for the square, which we also need to find for the ratio, is (side length)² = √(5x²) = 5x²
The ratio for the area of the rectangle to the area of the square is therefore 2x²/5x² = 2/5 (crossing out the x² in both the numerator and the denominator). We know to put the rectangle on top because of the specific wording of "the ratio of the area of the rectangle to..."
what is the area of the triangle formed from (-2,2), (1,2) and (0,-6)
Answers
Answer:
I think it's 12
Step-by-step explanation:
Hope it helps!
What is Index Law 1?
please give a definition
Answers
Answer:
LAW 2: The second law of indices tells us that when dividing a number with an exponent by the same number with an exponent, we have to subtract the powers. In algebraic form, this rule is as follows . ... Example: In this example, the powers were multiplied together to give the answer which is 3 to the power of 6.
If (3x+2) is a factor of 6x³+px²+x-2, Find the remaining factors of the polynomial p(x).
Answers
let:
3x+2=0
then solve it
then put the velue of x in p(x)
Help help help help help help help help help help help help help help
Answers
Answer:
[tex]118 cm^2[/tex]
Step-by-step explanation:
[tex]===========================================[/tex]
Formulas:
Area of a rectangle/square:
[tex]A=lw[/tex]
Area of a triangle:
[tex]A=bh\frac{1}{2}[/tex]
[tex]===========================================[/tex]
Side rectangles(2):
7*5=35
Multiply by 2
35*2= 70 cm
Middle rectangle:
4*7= 28 cm
Triangles(2):
[tex]4*5*\frac{1}{2} =10 cm[/tex]
Multiply by 2
10*2= 20 cm
Total:
Add.
70+28+20= 118 cm2
If a real estate agent receives 17 percent of the selling price of each house he sells, then what would the agent make if the house sells for $180,000?
Answers
Answer:
$30600
Step-by-step explanation:
The selling price is $180,000
The commission rate is 17% of this
(17/100) * 180000 = 30600
The difference between the square of two numbers is 11. Twice the square of the first number increased by the square of the second number is 97 find the numbers
Answers
Answer:
Below in bold.
Step-by-step explanation:
x^2 - y^2 = 11
2x^2 + y^2 = 97
From the first equation:
y^2 = x^2 - 11
Substituting in the second equation:
2x^2 + x^2 - 11 = 97
3x^2 = 108
x^2 = 36
x = 6, -6.
Substituting for x in the first equation:
(6)^2 - y^2 = 11
y^2 = 36 - 11 = 25
y = 5, -5.
4. If 2 Cos A-1 = 0, then the value acute value A is
Answers
Answer:
[tex]A=60^{\circ}[/tex]
Step-by-step explanation:
Given [tex]2\cos A-1=0[/tex],
Add 1 to both sides:
[tex]2\cos A=1[/tex]
Divide both sides by 2:
[tex]\cos A=\frac{1}{2}[/tex]
Take the inverse cosine of each side (note that the question stipulates that A is acute):
[tex]\arccos(\cos A)=\arccos(\frac{1}{2})[/tex]
[tex]A=\arccos(\frac{1}{2}), A\in (0^{\circ}, 90^{\circ}),\\A=\boxed{60^{\circ}}[/tex]
YOU’RE WELCOME:))
(x^2 + 5x + 2) – (5x^2 – x – 2) =
Answers
Answer:
[tex]{ \tt{( {x}^{2} + 5x + 2) - (5 {x}^{2} - x - 2) }} \\ = { \tt{(1 - 5) {x}^{2} + (5 + 1)x + (2 + 2)}} \\ = { \tt{ - 4 {x}^{2} + 6x + 4 }} \\ = { \tt{ - 2(2 {x}^{2} - 3x - 2) }}[/tex]
6. The right triangles ABC and DEF
are similar. The hypotenuse of ABC
measures 12 cm and the hypotenuse
of DEF measures 24 cm. If one of
the legs of ABC measures 9 cm,
what does the corresponding leg
of DEF measure?
A 4.5 cm
B 18 cm
Answers
Answer:
B. 18 cm
Step-by-step explanation:
24 / 12 = 2.
9 x 2 = 18 cm.
Hope this helps!
Use the cross product property to determine witch of the following equalities are proportions:
6.6/1.1 = 0.3/0.05
Answers
Answer:
proportion
Step-by-step explanation:
6.6/1.1 = 0.3/0.05
Using cross products
6.6 * .05 = 1.1 * .3
.33 = .33
Since this is a true statement, the statement is a proportion
The function f(x) = x2 has been translated 9 units up and 4 units to the right to form the function g(x). Which represents g(x)?
g(x) = (x + 9)2 + 4
g(x) = (x + 9)2 − 4
g(x) = (x − 4)2 + 9
g(x) = (x + 4)2 + 9
Answers
[\tex]
We apply the following transformations
Vertical translations :
Suppose that k > 0
To graph y=f(x)+k, move the graph of k units upwards
For k=9
We have
[tex]h(x)=x^2+9
[\tex]
Horizontal translation
Suppose that h>0
To graph y=f(x-h) , move the graph of h units to the right
For h=4 we have :
[tex ] g (x) =(x-4) ^ 2+9
[\tex]
Answer :
The function g(x) is given by
G(x) =(x-4)2 +9
g(x)=(x-4)^2+9
if p is the smallest prime factor of 511, then
a. 18 ≤ p ≤ 23
b. 10 ≤ p ≤ 17
c. 3 ≤ p ≤ 9
d. none of these
Answers
Answer:
C. [tex]3 \le p \le 9[/tex]
Step-by-step explanation:
The prime factor decomposition of 511 is [tex]7\times 73[/tex], where 7 is the smallest prime factor. Hence, the correct answer is C.
What is the value of the expression below when 4x=4? 2
x
2
+
x
−
5
2x
2
+x−5
Plzzz help!!
Answers
Answer:
I dont understand the problem because of the way its written out but I believe that the value of x itself is 1.
x=1
Step-by-step explanation:
1 x 4 = 4
(hope it helps a bit)
The sequence 3,9,15,21,27 is an arithmetic sequence. What is the common difference d of this sequence
Answers
Answer:
6
Step-by-step explanation:
We can find the common difference by subtracting one number in the sequence from the one ahead of it.
27-21=6
21-15=6
15-9=6
9-3=6
The differences between each number is 6.
Because the difference is the same between each number in the sequence, that makes 6 the common difference.
[tex]\fbox{Hii\:student!}[/tex]
__________________________________________________________
[tex]\multimap\parallel\boldsymbol{Answer.}\parallel\gets[/tex]
[tex]\textsl{the common difference is 6!}[/tex]
__________________________________________________________
[tex]\multimap\parallel\boldsymbol{Explanation.}\parallel\gets[/tex]
[tex]\textsl{here's how we find the common difference in the sequence:}[/tex]
[tex]\sf 27-21=6 \\ 21-15=6 \\ 15-9=6 \\ 9-3=6 \\the\;result\;is\;the\;common\;difference}[/tex]
[tex]\maltese\boldsymbol{\therefore,\:6\:is\;the\;common\;dif\!ference}[/tex]
Hope that this helped! Best wishes.
[tex]\textsl{Reach far. Aim high. Dream big.}[/tex]
[tex]\boldsymbol{-Greetings!-}[/tex]
________________________________________________________
Use the figure to find the angle m
Answers
Answer:
Measure of angle M = 41°
Step-by-step explanation:
From the figure attached,
NM ≅ NO [Given]
Therefore, ∠O ≅ ∠M [Opposite angle of the equal sides]
By triangle sum theorem,
m∠O + m∠N + m∠M = 180°
m∠O + m∠N + m∠O = 180° [Since, ∠M ≅ ∠O]
By substituting the values of the given angles,
(4y - 15)° + (7y)° + (4y - 15)° = 180°
(15y - 30) = 180
15y = 210
y = 14
Therefore, m∠M = (4y - 15)°
= 4(14) - 15
= 56 - 15
= 41°
If Q = 5+2i, E = i, and D = 5-2i, find Q.E.D
Answers
Answer:
Q.D.E=(5+2i).(5-2i).i = (25-4i²)i = 25i-4i³
Step-by-step explanation:
The rule T 5, -0.5° Ro, 1800(x, ) is applied to FGH to
produce F"G"H". what are the coordinates of vertex F" of F"G"H"?
Answers
Answer:
Step-by-step explanation:
Given rule for the multiple translations is,
[tex]T_{5,-0.5}.R_{0.180^{\circ}}(x,y)[/tex]
Apply the rule [tex]R_{0,180^{\circ}}[/tex] first.
(x, y) → (-x, -y)
This rule illustrates a rotation of the triangle FGH by 180° about the origin,
Vertices of ΔFGH are,
F → (1, 1)
G → (4, 5)
H → (5, 1)
After rotation vertices of the image triangle are,
F' → (-1, -1)
G' → (-4, -5)
H' → (-5, -1)
Further apply the rule,
[tex]T_{5,-0.5}[/tex]
(x, y) → (x + 5, y - 0.5)
By this rule of translation,
F'(-1, -1) → F"{(-1 + 5), (-1 - 0.5)}
→ F"(4, -1.5)
G'(-4, -5) → G"[(-4 + 5), (-5 - 0.5)]
→ G"(1, -5.5)
H'(-5, -1) → H"[(-5 + 5), (-1 -0.5)]
→ H"(0, -1.5)
Please hurry I will mark you brainliest
What is the slope of this?
Answers
Answer:
-1/4
Step-by-step explanation:
Pick two points on the line
(-4,3) and (4,1)
Using the slope formula
m = (y2-y1)/(x2-x1)
= ( 1-3)/(4 - -4)
= (1-3)/(4+4)
= -2/8
= -1/4
WILL GIVE BRAINLISEST!
The polygons are similar. Find the missing side length. Note, the shapes are not oriented the same way.
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If polygons are similar ratio if sides will be same
[tex]\\ \sf\longmapsto \frac{x}{50} = \frac{48}{40} \\ \\ \sf\longmapsto 40x = 48 \times 50 \\ \\ \sf\longmapsto x = \frac{48 \times 50}{40} \\ \\ \sf\longmapsto x = \frac{2400}{40} \\ \\ \sf\longmapsto x = 60[/tex]
Which parent function is represented by the table?
Answers
Answer:
C
Step-by-step explanation:
In fact the symbol |x| means absolute value that is ever a positive value (or equal to 0 if x = 0)
Answer:
Answer B
Step-by-step explanation:
It's a linear function
If somebody can give me the answer!!!
Please I need help
Answers
Answer:
Its B
Step-by-step explanation:
You're correct
Find the general term of the ap whose 7th term is -1 and 16th term is 17? (pls Hurry up I will mark you Brainliest and don't reply in a silly way or I'll report you)
Answers
Answer:
The answer is -13.
Step-by-step explanation:
The formula of the nth term of an AP(arthimetic progression) is a+(n-1)d.
So the 7th term will be a+6d= -1 ---(1)
The 16th term will a+15d=17 ---(2)
Subtract (2) and (1)
a+15d-(a+6d)=17-(-1)
=a+15d-a-6d=17+1
9d=18
d=18/9
d=2.
Substitute d in eq (1)
a+6(2)= -1
a+12=-1
a= -1-12= -13
Thus the general term of the ap is -13
10 fracciones que generen decimales exactos 10 fracciones que generen decimales inexactos puros y 10 fraccionarios que generen decimales periódicos mixtos
Answers
Answer:
Un número decimal exacto es algo de la forma:
3.27
Para reescribir este número como una fracción, podemos ver que tiene dos dígitos luego del punto.
Entonces podemos multiplicar y dividir por 100 (misma cantidad de ceros que dígitos luego del punto decimal)
así obtenemos:
3.27*(100)/(100) = 327/100
Entonces la fracción 327/100 genera un decimal exacto.
Así, encontrar 10 fracciones es trivial, 10 ejemplos son:
7/10 = 0.7
314/100 = 3.14
27/10 = 2.7
27/100 = 0.27
2/10 = 0.2
25/100 = 0.25
31/10 = 3.1
12/10 = 6/5 = 1.2
131/10 = 13.1
142/100 = 1.42
Ahora, un decimal inexacto puro es algo de la forma:
3.33...
donde el 3 se repite infinitamente.
Tratemos de reescribir este número como una fracción:
primero debemos ver la cantidad de dígitos que se repiten, en este caso es uno solo, el 3, entonces multiplicamos por 10:
3.33*10 = 33.33...
Ahora, podemos restar el numero original:
33.333... - 3.333... = 30
Entonces tenemos que:
3.33*9 = 30
3.33 = 30/9
La fracción:
30/9 nos da in decimal inexacto puro.
Ahora que sabemos construirlas, 10 ejemplos pueden ser:
30/9 = 3.33....
1/3 = 0.33...
40/9 = 4.44...
50/9 = 5.55...
60/9 = 6.66...
70/9 = 7.77...
20/9 = 2.22...
55/9 = 6.11...
544/99 = 5.5959...
10/9 = 1.11...
Finalmente, un periódico mixto es algo de la forma:
1.2343434...
Es decir, el 34 se repite infinitamente, pero también tenemos un 2 luego del punto decimal, por lo que este número no es puramente periódico.
Para construirlos, podemos tomar una fracción exacta, como
1.1 y una periódica, como 1.11...
Si las sumamos, obtenemos:
1.1 + 1.11... = 2.211...
donde el uno se repetirá infinitamente.
Así, simplemente sumando las fracciones del primer caso con las del segundo, obtendremos decimales periódicos mixtos, por ejemplo:
7/10 + 55/9 = 613/90 = 0.7 + 6.11... = 6.8111....
7/10 + 10/9 = 163/90 = 0.7 + 1.11... = 1.811....
31/10 + 10/9 = 379/90 = 3.1 + 1.11... = 4.2111...
31/10 + 20/9 = 479/90 = 3.1 + 2.22... = 5.322...
31/10 + 30/9 = 579/90 = 3.1 + 3.33... = 6.4333...
27/10 + 20/9 = 443/90 = 2.7 + 2.22... = 4.922...
37/10 + 20/9 = 533/90 = 3.7 + 2.22... = 5.922...
4/10 + 10/9 = 136/90 = 0.4 + 1.11... = 1.511....
3/100 + 10/9 = 1027/900 = 0.03 + 1.11... = 1.14111...
4/10 + 20/9 = 236/90 = 0.4 + 2.22... = 2.622....
El periodo de un movimiento circular uniforme es de
8 segundos. ¿Cuál es su velocidad angular?
Answers
Answer: I dont understand what your saying im sorry, I'd really like to help but I cant :(
Angles of triangle are in the ratio of 23:5. What is the Size of the smallest angle?
Answers
Answer:
ratio 2 : 3 : 5
size of smallest angle
[tex]180 \times \frac{2}{10} \\ = 36[/tex]
Answer:
The smallest angle of a triangle is 36°.
Step-by-step explanation:
Given, the ratio of angles of a triangle is 2 : 3 : 5
Let the angles of a triangle be ∠A, ∠B and ∠C.
∠A = 2x, ∠B = 3x, ∠C = 5x
∠A+∠B + ∠C= 180°
[sum of all the angles of a triangle is 180°]
2x + 3x + 5x = 180°
10x = 180°
x=180°/10 =18°
∠A=2x=2 x 18° = 36°
∠B = 3x = 3 x 18° = 54°
∠C = 5x = 5 x 18° = 90°
Hence, the smallest angle of a triangle is 36°.
HOPE IT HELPS!!!
Find the value of x that makes m||n
.
135°
m
(2x + 15)
n
Answers
Answer:
x = 60
Step-by-step explanation:
Since m is parallel to n, that means they are equal to each other.
In other words:
135 = 2x + 15
Solve for the variable:
120 = 2x
60 = x
Check your work:
135 = 2(60) + 15
135 = 120 + 15
135 = 135
Correct!
Answer:
x = 60
Step-by-step explanation:
For these two lines to be parallel, the angles m and n must be equal. Thus, 135 = 2x + 15.
Excellent. Let’s solve this equation. Subtract 15 from each side. 120 = 2x. Divide by 2, and we get 60 = x, so x = 60.
Hope this helps!
helpppp meeeee outttttt pleaseeeee ASAPPPP!!!!
Answers
Answer:
[tex]\boxed{\sf sin\ C =\frac{40}{41}}[/tex]
Step-by-step explanation:
We need to find out the value of sinC using the given triangle . Here we can see that the sides of the triangle are 40 , 41 and 9 .
We know that the ratio of sine is perpendicular to hypontenuse .
[tex]\sf\longrightarrow sin\theta =\dfrac{ perpendicular}{hypontenuse}[/tex]
Here we can see that the side opposite to angle C is 40 , therefore the perpendicular of the triangle is 40. And the side opposite to 90° angle is 41 . So it's the hypontenuse . On using the ratio of sine ,
[tex]\sf\longrightarrow sinC =\dfrac{ p}{h}\\\\\sf\longrightarrow sin\ C =\dfrac{AB}{AC}[/tex]
Substitute the respective values ,
[tex]\sf\longrightarrow \boxed{\blue{\sf sin\ C =\dfrac{40}{41}}}[/tex]
Hence the required answer is 40/41.
Find the equation of the straight line whose portion is bisected at (2, 3).
Answers
Answer:
Let P(2,3) be the point passes through the line
Let a,b be x-intersept and y-intersept of line respectively
∵ Point P(2,3) bisect the points (a,0) and (0,b)
∴ we have 2=a+02 and 3=b+02
∴a=4 and b=6
∴ by using intersept form
x4+y6=1
Step-by-step explanation:
Hope it helps you pls mark me as brain list.
Answer:
Let P(2,3) be the point passes through the line
Let a,b be x-intersept and y-intersept of line respectively
∵ Point P(2,3) bisect the points (a,0) and (0,b)
∴ we have 2=(a + 0)÷2 and 3=(b + 0)÷2
∴a=4 and b=6
∴ by using intersept form
x/4+y/6=1
Graph :
Find the length of the diagonal of a rectangular football pitch with sides 42.9 m and 78.4 m.
Give your answer rounded to 1 DP.
Answers
Answer:
triganometry is mathematics
