Answer:
[tex] y = x + 4 [/tex]
Step-by-step explanation:
Use the two-point form of the equation of a line.
[tex] y - y_1 = \dfrac{y_2 - y_1}{x_2 - x_1}(x - x_1) [/tex]
[tex] y - 4 = \dfrac{16 - 4}{12 - 0}(x - 0) [/tex]
[tex] y - 4 = \dfrac{12}{12}x [/tex]
[tex] y - 4 = x [/tex]
[tex] y = x + 4 [/tex]
Answer:
y = x + 4
Step-by-step explanation:
An equation for a line looks like:
=> y = mx +b
=> In this equation "m" is the slope.
=> "b" is the y-intercept.
To find the slope:
=> y/x - y1/x1
=> 16/12 - 4/0
=> 16 -4 / 12 - 0
=> 12 / 12
=> 1
So, the slope is 1.
Now our equation looks like:
y = 1x + b
=> y = x + b
Let's take some the values of "x" and "y" of (0,4)
So, our now look like:
=> 4 = 1 (0) + b
=> 4 = b
So, b (y-intercept) = 4
Now, our final equation is:
=> y = x + 4
inscribed angles. help asap!
Answer:
20°
Step-by-step explanation:
The measure of the inscribed angle is equal to the half of the arc it sees
Since AC is the diameter the measure of arc ABC is 180°
and since A sees arc BC and C sees the arc AB
A< + C< = 90° so angle C = 20°
Hey there please help me with this question
Answer:
see explanation
Step-by-step explanation:
sum the parts of the ratio, 2 + 1 = 3 parts , thus
81 cm² ÷ 3 = 27 cm² ← value of 1 part of the ratio
2 parts = 2 × 27 = 54 cm²
Area of A = 54 cm² and area of B = 27 cm²
The side of the original square = [tex]\sqrt{81}[/tex] = 9 cm
The width of both rectangles is 9 cm ( width remains unchanged after cut )
Thus
Rectangle A
9 × length = 54 ( divide both sides by 9 )
length = 6 cm
Rectangle B
9 × length = 27 ( divide both sides by 9 )
length = 3 cm
Rectangle A → length = 6 cm, width = 9 cm
Rectangle B → length = 3 cm , width = 9 cm
Answer:
Rectangle A Rectangle B
length = 9 cm length = 9 cm
width = 6 cm width = 3 cm
Step-by-step explanation:
Area of square At = 81 cm²
Square is cut into two pieces = A + B
The ration of area A to B = 2:1
Find
Rect A Rect B
length length
width width
---------------------------------
first, get the side of the square = A = s²
81 = s²,
s = √81
s = 9 cm
since the ratio is 2:1, therefore the side can be divided into 3
9 ÷ 3 = 3 cm ----- take note of this to get the Width
Rectangle A
L = 9 cm (which is the s = 9 cm)
W = 3 cm (2 ratio) = 6 cm
Rectangle B
L = 9 cm (which is the s = 9 cm)
W = 3 cm (1 ratio) = 3 cm
Proof:
At = A + B
81 = (9x6) + (9x3)
81 = 54 + 27
81 = 81 ----- OK
evaluate 15.2% of a 726 + 12.8% of 673
Answer:
196.496
Step-by-step explanation:
0.152x726+0.128x673
110.352+86.144
=196.496
Do the ratios 2/3 and 12/18 form a proportion?
yes
no
Answer:
Yes
Step-by-step explanation:
Because 12/18 = 2/3..(cancel 12 and 18 by 6)
Answer:
yes
Step-by-step explanation:
2x6=12
3x6=18
6 is the multiplying number
( the 2 equations are the same amount )
when the point ( k, 3 ) lies on each of these lines, find the value of k y= 3x+1 , y= 4x-2 , y=1/2x - 1 and 2x+3y=4
Answer:
see explanation
Step-by-step explanation:
Since (k, 3) lies on each of the lines, the point satisfies the equations.
Substitute x = k, y = 3 into each and solve for k
y = 3x + 1
3 = 3k + 1 ( subtract 1 from both sides )
2 = 3k ( divide both sides by 3 )
k = [tex]\frac{2}{3}[/tex]
-------------------------------------------------------
y = 4x - 2
3 = 4k - 2 ( add 2 to both sides )
5 = 4k ( divide both sides by 4 )
k = [tex]\frac{5}{4}[/tex]
--------------------------------------------------------
y = [tex]\frac{1}{2}[/tex] x
3 = [tex]\frac{1}{2}[/tex] k ( multiply both sides by 2 to clear the fraction )
k = 6
---------------------------------------------------------
2x + 3y = 4
2k + 3(3) = 4
2k + 9 = 4 ( subtract 9 from both sides )
2k = - 5 ( divide both sides by 2 )
k = - [tex]\frac{5}{2}[/tex]
Find the value of x. A. 53–√ m B. 241−−√ m C. 6 m D. 6+35–√ m
Answer:
x = 2√41 mStep-by-step explanation:
Since the triangle is a right angled triangle we can use Pythagoras theorem to find the missing side x
Using Pythagoras theorem we have
a² = b² + c²
where a is the hypotenuse
From the question x is the hypotenuse
So we have
[tex] {x}^{2} = {8}^{2} + {10}^{2} [/tex][tex] {x}^{2} = 64 + 100[/tex][tex] {x}^{2} = 164[/tex]Find the square root of both sides
We have the final answer as
x = 2√41 mHope this helps you
Answer:
2 sqrt(41) =c
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2 + b^2 = c^2
8^2 + 10^2 = c^2
64+ 100 = c^2
164 = c^2
take the square root of each side
sqrt(164) = sqrt(c^2)
sqrt(4*41) = c
2 sqrt(41) =c
if a man works 400km in 6 minutes.How long will he work in 9 minutes
Answer:
600 kmStep-by-step explanation:
400 km = x
6 min 9 min
cross multiply:
6x = 400 ( 9)
x = 3600 / 6
x = 600 km
someone please expain how to do this, i’m really confused.
Answer:
13
Step-by-step explanation:
Basically, we have to plug in 4 for r into g(r). Doing so gives us g(4) = 25 - 3 * 4 = 25 - 12 = 13.
Some more examples:
g(6) = 25 - 3 * 6 = 25 - 18 = 7
g(1) = 25 - 3 * 1 = 25 - 3 = 22
Answer:g(4)=13
Step-by-step explanation:
g(4)=25-3r
25-3(4)
25-12
g(4)=13
[tex] \frac{ {9x}^{2} - {(x}^{2} - 4) {}^{2} }{4 + 3x - {x}^{2} } [/tex]
pls help me need help asap
Answer:
[tex] { x^2+3x-4} [/tex]
Step-by-step explanation:
Factor top and bottom.
The numerator is a difference of two squares, and the denominator is a quadratic.
[tex] \frac{ {9x}^{2} - {(x}^{2} - 4)^{2} }{4 + 3x - {x}^{2} } [/tex]
= [tex]\frac{ (3x+x^2-4)(3x-x^2+4) }{(1+x)(4-x)}[/tex]
= [tex] \frac{ (x-1)(x+4) (1+x)(4-x) }{(1+x)(4-x)} [/tex]
If x does not equal -1 and does not equal 4, we can cancel the common factors in italics to give
= [tex] { (x-1)(x+4)} [/tex]
= [tex] { x^2+3x-4} [/tex]
Answer:
The answer is
x² + 3x - 4Step-by-step explanation:
[tex] \frac{9 {x}^{2} - ( { {x}^{2} - 4})^{2} }{4 + 3x - {x}^{2} } [/tex]
To solve the expression first factorize both the numerator and the denominator
For the numerator
9x² - ( x² - 4)²
Expand the terms in the bracket using the formula
( a - b)² = a² - 2ab + b²
(x² - 4) = x⁴ - 8x² + 16
So we have
9x² - (x⁴ - 8x² + 16)
9x² - x⁴ + 8x² - 16
- x⁴ + 17x² - 16
Factorize
that's
(x² - 16)(-x² + 1)
Using the formula
a² - b² = ( a + b)(a - b)
We have
(x² - 16)(-x² + 1) = (x + 4)(x - 4)( 1 - x)(1 + x)
For the denominator
- x² + 3x + 4
Write 3x as a difference
- x² + 4x - x + 4
Factorize
That's
- ( x - 4)(x + 1)
So we now have
[tex] \frac{(x + 4)(x - 4)( 1 - x)(1 + x)}{ - (x - 4)(x + 1)} [/tex]
Simplify
[tex] \frac{ - (x + 4)(1 - x)(1 + x)}{x + 1} [/tex]
Reduce the expression by x + 1
That's
-( x + 4)( 1 - x)
Multiply the terms
We have the final answer as
x² + 3x - 4Hope this helps you
Desmond is 2 inches taller than Niki. If we let w represent Nikis height in inches, write an algebraic expression for Desmonds height. Enter your answer as an expression. Example: 3x^2+1
Answer:
w + 2
Step-by-step explanation:
Niki's height = w in
Desmond height = w + 2
Answer:
w+2
Step-by-step explanation:
Since Desmonds is 2 inches taller than Niki, w+2 would make the most sense.
Sarah has $20 saved. She gets $10 per week for her allowance, and she saves her allowance for the next 3 weeks. At the end of the week, she gets $150 in birthday money. How much money will she have after the 3 weeks? Which of the following sets of equations represents this problem?
Answer:
$200
Step-by-step explanation:
We know that she already has $20. And we know that every week, for three weeks she gets $10.
20+3(10)+150=m
We add all of this up, and we find that at the end of 3 weeks Sarah has $200 saved.
The heights of two similar parallelograms are 16 inches and 20 inches. Their
respective areas are (3x+5) square inches and 9x square inches. Find the value of
X?
Answer: [tex]x=\dfrac{25}{21}[/tex]
Step-by-step explanation:
Area of parallelogram = Base x height
If two parallelograms are similar, then their corresponding sides are proportional.
That means, [tex]\dfrac{\text{Area of first parallleogram}}{\text{Area of second parallleogram}}=\dfrac{\text{height of first parallelogram}}{\text{height of second parallelogram}}[/tex]
[tex]\Rightarrow \dfrac{3x+5}{9x}=\dfrac{16}{20}\Rightarrow \dfrac{3x+5}{9x}=\dfrac{4}{5}\\\\\Rightarrow 5(3x+5)=4(9x)\\\\\Rightarrow\ 15x+25 = 36x\\\\\Rightarrow\ 36x-15x=25\\\\\Rightarrow\ 21x = 25\\\\\Rightarrow\ x=\dfrac{25}{21}[/tex]
Hence, [tex]x=\dfrac{25}{21}[/tex]
a broker gets rs 20000 as commission from sale of a piece of land which costs rs 8000000. Find the rate of commission.
Answer:
0.25%
Step-by-step explanation:
Rate of commission
= (commission*100)/cost of land
=( 20000*100)/8000000
= 2000000/8000000
=2/8
= 0.25%
ux=x+y/k, solve for x
Answer:
x = y/( ku-1)
Step-by-step explanation:
Here in this question, we are asked to solve for x.
we have;
Ux = x+ u/ k
cross multiply;
k * Ux = x + y
kUx = x + y
kUx- x = y
x(KU-1) = y
x = y/( ku-1)
in the equation z=x^2-3y, find the value of z when x=-3 and y=4
Answer:
z=-3
Step-by-step explanation:
z=(-3)^2 - 3(4)
z=9 - 12
z=-3
really urgent...i need the working also ...pls help me
Answer:
See below.
Step-by-step explanation:
In each case, you are looking for time. We know speed is distance divided by time. Lets start with the speed formula.
speed = distance/time
Now we solve it for time. Multiply both sides by time and divide both sides by speed.
speed * time = distance
time = distance/speed
Time is distance divided by speed. In each problem, you have a speed and a distance. Divide the distance by the speed to to find the time.
1) speed = 44.1 km/h; distance = 150 km
time = distance/speed = 150 km/(44.1 km/h) =
= 3.401 hours = 3 hours + 0.401 hour * 60 min/hour = 3 hours 24 minutes
2) speed = 120 km/h; distance = 90 km
time = distance/speed = 90 km/(120 km/h) =
= 0.75 hours = 0.75 hour * 60 min/hour = 45 minutes
3) speed = 125 m/s; distance = 500 m
time = distance/speed = 500 m/(125 m/s) =
= 4 seconds
Pregunta N° 1: ¿Cuántas fracciones propias e irreductibles con denominador 24 existen? 1 punto A) 2 B) 4 C) 6 D) 8 E) 10 Pregunta N° 2: ¿Cuántas fracciones impropias e irreductibles con numerador 25 existen? 1 punto A) 19 B) 21 C) 25 D) 29 E) 33 Pregunta N° 3: La edad de Miguel es 4/5 de la edad de su novia. Si las edades de los dos suman 63 años, calcule la edad de la novia de Miguel. 1 punto A) 20 años B) 26 años C) 32 años D) 35 años E) 40 años Pregunta N° 4: Si son las 8 a. m., ¿qué fracción del día ha transcurrido? 1 punto A) 1 B) 2 C) 1/2 D) 1/3 E) 1/5
ayuden porfavor
Answer:
Pregunta 1: Opcion D. 8
Pregunta 2: Opción A. 19 (aunque lo correcto es decir que son 20)
Pregunta 3: 28 años (no está como opción)
Pregunta 4: Opción D. 1/3
Step-by-step explanation:
Las fracciones irreductibles son aquellas que después de dividirlas por un común divisor, una vez que no se pueden dividir más se dice que son irreducibles, por lo tanto no existe ningún número que sea divisor común del numerador y del denominador más que 1.
Fracciones irreductibles con común denominador 24.
Como máximo divisor tenemos el 24 y como mínimo el 1
entre 1/24 y 1 estarán nuestras fracciones o sea:
1/24 < x/24 < 1. Ahora convertimos el 1 en fracción de 24, lo que sería 24/24 para igualar el numerador en ambos lados de la ecuación, para poder determinar x
1/24 < x/24 < 24/24
Como vemos que x tiene que estar entre 1 y 24, las respuestas serán:
2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22 y 23
Eliminamos los números divisores de 24, aquellos pares, y nos focalizamos en los que no podriamos dividir por nada con 24, o sea los números primos
5, 7, 11, 13, 17, 19, 23. Como nos falta el 1, obtenemos un total de 8 fracciones: 1/24, 5/24, 7/24, 11/24, 13/24, 17/24, 19/24, 23/24
Mismo procedimiento para el 25:
1/25 es una de las fracciones irreductibles. Pensamos en los valores de x
1/25 < x/25 < 25/25
2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25
Los números divisibles por 25, son los multiplos de 5, asi que esas respuestas no irían. Las fracciones irreductibles son:
1/25, 2/25, 3/25, 4/25, 6/25, 7/25, 8/25, 9/25, 11/25, 12/25, 13/25, 14/25, 16/25, 17/25, 18/25, 19/25, 21/25, 22/25, 23/25 y 24/25 haciendo un total de
20. Por alguna razón está mal formulada la pregunta, son 20 pero no está como opción y como te piden fraccion impropia (numerador > denominador), contamos a partir de 26. FIjate que hasta el proximo entero que sería 50/25, también son 20 fracciones (irreductibles e impropias)
26/25, 27/25, 28/25, 29/25, 31/25, 32/25, 33/25, 34/25, 36/25, 37/25, 38/25, 39/25, 41/25, 42/25, 43/25, 44/25, 46/25, 47/25, 48/25, 49/25
Próxima pregunta:
Miguel tiene 4/5 de la edad de la novia, y ambas edades suman 63.
Plantiemos la siguiente ecuacion donde x es la edad de la novia
4/5x + x = 63
9/5x = 63
x = 63 . 5/9 (como 9/5 pasa al otro lado de la igualdad dividiendo, damos vuelta la fraccion multiplicandola)
x = 35
Si la novia tiene 35 años y la edad de Miguel es 4/5 de esa edad
4/5 .35 = (35 .4) /5 = 28
Es raro porque no está la respuesta como tal.
Próxima pregunta:
Al ser las 8 am, quiere decir que han pasado 8 horas de que empezó el día
y el día tiene 24 horas.
8 horas transcurridas / 24 horas totales = 1/3
a rectangular garden is fenced on all sides with 128 feet of fencing. The garden is 4 feet longer than it is wide. Find the length and width of the garden
Answer:
Length = 34 feet
Breadth = 30 feet
Step-by-step explanation:
Perimeter= 128 ft
Let the breadth be = [tex]x[/tex]
Let the length be = [tex]x+4[/tex]
∴by the problem ,
2(length+breadth)= perimeter
[tex]2(x+4+x)=128\\2(2x+4)=128\\4x+8=128\\4x=128-8\\4x=120\\x=120/4\\x=30[/tex]
Therefore, length of the garden = 30+4= 34 feet
breadth of the garden = 30 feet
write each number in scientific notation.
1,050,200
The number between 1 and 10:
The power of 10:
The number in scientific notation:
34,600
The number between 1 and 10:
The power of 10:
The number in scientific notation:
Michael is using a number line to evaluate the expression –8 – 3. A number line going from negative 12 to positive 12. A point is at negative 8. After locating –8 on the number line, which step could Michael complete to evaluate the expression?
Answer:
move to the left 3 more spaces
Step-by-step explanation:
you are at -8 already. Therefore, you (-3) more spaces, so you go to the left three more spaces. Use the saying keep change change to help with this.
Keep the first number sign, change the next sign, and the next sign.
Answer:
d
Step-by-step explanation:
Mildred’s salary has increased from £24,600 to £25,338. By what percentage has her salary increase?
Answer:
The answer is 3%Step-by-step explanation:
To find the percentage increase we use the formula
[tex]Percentage \: change = \frac{ change}{original \: quantity} \times 100[/tex]
To find the change subtract the smaller quantity from the bigger one
From the question
original price = $24,600
Current price = $ 25,338
Change = $25,338 - $ 24,600
Change = $ 738
So the percentage increase is
[tex] \frac{738}{24600} \times 100[/tex]
[tex] = \frac{3}{100} \times 100[/tex]
We have the final answer as
Percentage increase = 3%Hope this helps you
Two shaded identical rectangular decorative tiles are first placed (one each) at the top and at the base of a door frame for a hobbit's house, as shown in Figure 1. The distance from W to H is 45 inches. Then the same two tiles are rearranged at the top and at the base of the door frame, as shown in Figure 2. The distance from Y to Z is 37 inches. What is the height of the door frame, in inches?
Answer:
41 inches
Step-by-step explanation:
Let the point at the top of the door on the left be x
Wx + xH = 45
Let the point at the top of the door on the right be c
Yc + cZ = 37
We know the door is
xH + plus the width of the tile
The width of the tile is Yc
xH + Yc
On the right door
cZ + the height of the tile
cZ + Wx
Add the two doors together
xH + Yc + cZ + Wx = 2 times the height of the door
Rewriting
xH + Wx + Yc + cZ = 2 times the height of the door
45+ 37 = 2 times the door height
82 = 2 times the door height
Divide by 2
41 = door height
What is the rule for the transformation below?
=================================================
Explanation:
The translation notation T(-5, 3) looks like an ordered pair point, but it is not. Instead, it is a rule to tell you how to shift any point left/right and up/down. The first number is the left/right shifting as its done along the x axis. The negative value means we shift left, so we shift 5 units to the left. The positive 3 in the y coordinate place means we shift 3 units up.
We see this shifting happen when we go from
A = (-1, -1) to A ' = (-6, 2) B = (2, 3) to B ' = (-3, 6)C = (5, -3) to C ' = (0, 0)The translation notation T(-5, 3) is the same as writing [tex](x,y) \to (x-5, y+3)[/tex] which may be a more descriptive notation to use, and it would avoid confusion with ordered pair point notation.
Please help I did the first 2
Answer:
x = 1.5
Step-by-step explanation:
6 - 2x = 3
→ Minus 6 from both sides to isolate -2x
-2x = -3
→ Divide -2 from both sides to isolate x
x = 1.5
Determine if the ordered pair (6, 4) is a solution to the inequality
Answer:
[tex]\Large \boxed{\mathrm{Option \ D}}[/tex]
Step-by-step explanation:
(6, 4)
x = 6 and y = 4
y > -1/2x + 7
Plug in the values to check if it is true.
4 > -1/2(6) + 7
4 > -3 + 7
4 > 4
This statement is false.
(6, 4) lies on the line.
4. The rental for a television set changed from $80 per year to $8 per month
What is the percentage increase in the yearly rental?
Answer:
16%
Step-by-step explanation:
rental charge per year = $80
rental charge at the rate $8 per year = 8 * 12 = 96
the increased amount = 96 - 80 = 16
% = 16 / 100 = 16%
solve the following: - 3 raised to 1 by 5 the whole raised to 4 (3^1/5)^4
Answer:
8.30256
Step-by-step explanation:
Step 1: Write out expression
[tex]((-3)^{\frac{1}{5} })^{4(3^{\frac{1}{5} })^4[/tex]
Step 2: Use BPEMDAS to evaluate
[tex](-1.24573)^{4(3^{\frac{1}{5} })^4[/tex]
[tex](-1.24573)^{4(1.24573)^4[/tex]
[tex](-1.24573)^{4(2.40822)[/tex]
[tex](-1.24573)^{9.6329}[/tex]
= 8.30256
And we have our answer!
To get from home to work, Felix can either take a bike path through the rectangular park or ride his bike along two sides of the park. How much farther would Felix travel by riding along two sides of the park than he would by taking the path through the park?
Answer:
c=5.9/6(G)
Step-by-step explanation:
first find the 2 distances.
a^2+b^2=c^2 c=2.4+.7
7^2+2.4^2=c^2 c=3.1
.49+5.85=c^2
c^2=6.34
c=√6.34
c=2.51.
next subtract the two distances to find the difference.
c=2.51-3.1
c=.59
so the distance would be .59 which can be rounded up to .60/G
explanation on how I knew the answer.
Im reviewing for the math 8th grade staar.
Peter has one of each of the following coins in his pocket: a penny, a nickel, a dime, a quarter, and a half-dollar. Four of these coins are taken out of the pocket and the sum of their values is calculated. How many different sums are possible?
Answer:
10
Step-by-step explanation:
This is a combinations problem, involving factorials.
5!/3!*2!=5*4/2=20/2=10
The different sum of the 4 coins from the list of 5 coins is an illustration of combination or selection. There are 5 different possible sums.
Given
[tex]n = 5[/tex] --- number of coins
[tex]r = 4[/tex] --- coins to be selected to calculate sum
For the sum of the coin value to be calculated, the 4 coins must be selected. This means combination.
So, we make use of:
[tex]^nC_r = \frac{n!}{(n - r)!r!}[/tex]
This gives
[tex]^5C_4 = \frac{5!}{(5 - 4)!4!}[/tex]
[tex]^5C_4 = \frac{5!}{1!4!}[/tex]
Expand
[tex]^5C_4 = \frac{5*4!}{1*4!}[/tex]
[tex]^5C_4 = \frac{5}{1}[/tex]
[tex]^5C_4 = 5[/tex]
Hence, there are 5 different possible sums.
Read more about combinations at:
https://brainly.com/question/15401733
Need to find the Domain and Range
Answer:
D: {x∈R | -2 ≤ x ≤ 2 }
R: {y∈R | 0 ≤ y ≤ 4 }
Step-by-step explanation:
The domain ranges between -2 and 2
The range ranges between 0 and 4
