Answer:
(x-3), 4 (x - 3)^2 (x + 3) (2 x + 7)
Step-by-step explanation:
Factor all the expressions,
1st expression= 4x^2 - 36=4(x^2-9)=4(x+3)(x-3)
2nd expression=2x^2 - 12x + 18 =2(x^2-6x+9)=2 (x - 3)^2=2(x-3)(x-3)
3rd expression=2x^2 + x - 21=(x - 3) (2 x + 7)
HCF=Commo factor=(x-3)
LCF=Common factor*Remaining factor=4(x+3)(x-3)(x-3) (2 x + 7)=4 (x - 3)^2 (x + 3) (2 x + 7)
Tommy types 54 words per minute, with an average of 3 mistakes. How many mistakes would you expect Tommy to make if he typed 300 words?
Answer:
around 17 mistakes
Step-by-step explanation:
We can write a ratio to solve
54 words 300 words
------------------ = -------------------
3 mistakes x mistakes
Using cross products
54x = 3*300
54x = 900
Divide by 54
54x/54 = 900/54
x =50/3
x = 16.66666666(repeating)
around 17 mistakes
X = mistakes in 300 words
54/3 = 300/X
54X = 3 x 300
X = 900/ 54
X = about 17 words, since 16 and 2/3 rounded to the nearest tenth is 17
Use exterior angle of triangle theorem to find the missing measure of an angle in a polygon.
Answer:
[tex]\boxed{x=60}[/tex]
Step-by-step explanation:
The exterior angle theorem states that the exterior angle of a triangle is equal to the sum of the two opposite interior angles of the triangle.
[tex]130=70+x[/tex]
Subtract 70 from both sides.
[tex]130-70=70+x-70[/tex]
[tex]60=x[/tex]
Answer:
x = 60°
Step-by-step explanation:
Exterior angle is equal to the sum of opposite interior angles
x + 70 = 130
Subtract 70 from both sides
x = 130 - 70
x = 60°
Find the vertex of f(x)= x^2+ 6x + 36
Pls help soon
Answer:
vertex(-3,27)
Step-by-step explanation:
f(x)= x^2+ 6x + 36 ( a=1,b=6,c=36)
V(h,k)
h=-b/2a=-6/2=-3
k=f(-3)=3²+6(-3)+36
f(-3)=9-18+36=27
vertex(-3,27)
Please answer ASAP!
Type your response in the box. Jack and Mia are playing a game with pick-up sticks. Mia places a pile of 100 pick-up sticks on the table. Forty of the sticks are black, and the rest are brown. She randomly splits all the sticks into two piles—one on Jack’s left and one on his right. Mia tells Jack that there are 44 brown pick-up sticks in the pile on his right. Jack looks at the pile of pick-up sticks on his left and estimates that it contains 44 sticks in all. Now Mia blind folds Jack and asks him to choose a stick at random. Jack knows that if he selects a black pick-up stick, Mia will treat him to dinner at his favorite restaurant. If he picks a brown one, then he will treat Mia to dinner at her favorite restaurant. Mia gives Jack three options for selecting:
Choose randomly from the pile on the left.
Choose randomly from the pile on the right.
Push the piles back together and choose randomly from the entire pile.
Which option should Jack choose so that Mia treats him to dinner at his favorite restaurant? Explain your answer.
Answer: Choose randomly from the pile on the left.
Step-by-step explanation: The ratio of brown to black sticks on the left pile is 16:28 and on the right pile is 44:12. Therefore, jack should choose from the left side because there is a higher chance in picking a black stick.
Your car gets 15 miles per gallon and your friend's car averages 25 mpg. You decide
head off to St. George Island on vacation, 361 miles away. If gas costs $2.79/gallon and you decide to split the
gas costs, how much money will you save by driving your friend's car?
Answer:
the answer is $27.90
Step-by-step explanation:
if you do 15 times 2.79 you will get $41.85
then do 25 times 2.79 and you will get $69.75
then subtract 69.75 from 41.85 and your answer will be $27.90
i hope this helps this is the only way i could find the answer!
$29.4864 money will you save by driving your friend's car.
Given that, your car gets 15 miles per gallon and your friend's car averages 25 mpg.
You decide to go on a road trip to St. George Island, which is 361 miles away.
What are Gallons?A unit of volume for measuring liquids. 1 gallon = 4 quarts = 8 pints = 16 cups = 128 fluid ounces. 1 US gallon = 231 cubic inches = 3.785411784 liters exactly.
Gallons needed for your car =361/15=24.06 gallons
Cost of 24.06 gallons of gas=24.06×2.79=$69.774
Gallons needed for friends car =361/25=14.44 gallons
Cost of 4.44 gallons of gas=14.44×2.79=$40.2876
Hence, while driving a friend's car you will save 69.774-40.2876=$29.4864
Therefore, $29.4864 money will you save by driving your friend's car.
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Please help! Thank you
Answer:
(a) 1:12
(b) 12:1
(c) 1:100
(d) 100:1
Find the missing length indicated.
Answer:
Does the answer help you?
Can someone please help me solve this ?
answer:
-1
here's the explanation below :))
Find the product of 0.3×0.23.
Answer:
0.069
Step-by-step explanation:
0.3*0.23=0.069
35.
What is the equation of the line that is
parallel to y = 4x + 3 and passes through
the point (2,6)?
HELP! answer if you can!
Hi there! :)
Answer:
[tex]\huge\boxed{y = 4x - 2}[/tex]
Given line with an equation of y = 4x + 3
Parallel lines contain equivalent slopes, so a parallel line to the given equation would contain a slope of m = 4.
Plug in the coordinates of the point given, along with the slope into the equation y = mx + b where:
m = slope
y = y-coordinate of point
x = x-coordinate of point
Solve for the 'b' value, or y-intercept:
y = mx + b
6 = 4(2) + b
6 = 8 + b
b = -2
Rewrite the equation as slope-intercept form:
y = 4x - 2
Answer:
When you see the word "parallel", you know the new line will have the same slope.
parallel to y = 4x + 3
So, the new line will have a slope of 4
"Indicate the region where y≥ 4x + 3
Plot y= 4x + 3 by finding the points that make it true. For example, (y = 0, x = 3/4), (y = 2, x = 2) and so on.
y = 4x + b
b is the y intercept ( point y when x = 0)
Insert new coefficients:
+2 = 4(0) + b
b = +2
y = 4 + 2
[tex] \: [/tex]
Let f(x)=x2+10x+37 . What is the vertex form off(x)? What is the minimum value off(x)? Enter your answers in the boxes. Vertex form: f(x)= Minimum value of f(x):
Answer:
The vertex form is f(x) = (x + 5)² + 12
The minimum value of f(x) is point (-5, 12)
Step-by-step explanation:
1) The vertex form of a quadratic equation f(x) = x² + 10·x + 37, which is the form f(x) = a·(x - h)² + k is found as follows;
For the general form of the quadratic equation, f(x) = a·x² + b·x + c
h = -b/(2·a) and k = f(h)
Therefore, for f(x) = x² + 10·x + 37,
a = 1, b = 10
∴ h = -10/2 = -5
k = f(-5) = (-5)² + 10×(-5) + 37 = 12
The vertex form is f(x) = a·(x - h)² + k gives;
f(x) = 1·(x - (-5))² + 12 = (x + 5)² + 12
The vertex form is f(x) = (x + 5)² + 12
2) The minimum value of x is found when d(f(x))/dx = 0
d(f(x))/dx = d(x² + 10·x + 37)/dx = 2·x + 10
d(f(x))/dx = 0 = 2·x + 10
x = -10/2 = -5
We check that it is the minimum by f''(x) being positive;
f''(x) = d(2·x + 10)/dx = 2 which is positive and x = -5 is the x-coordinate of the minimum value of f(x)
The x-coordinate of the minimum value of f(x) minimum value is f(-5) = (-5)² + 10×(-5) + 37 = 12
Therefore, we have;
The minimum value of f(x) = (-5, 12)
Answer:
The vertex is (-5,f(-5)=12), The minimum value of f(x) is 12.
create a line that is perpendicular to AB and passes through C. you can use the tools available in geogebra to create perpendicular lines for this construction display the measurement of the angle of intersection between the two lines???
A linear relationship can be written as:
y = a*x + b
where a is the slope and b is the y-intercept.
If we know that the line passes through two points, (x₁, y₁) and (x₂, y₂), then we can write the slope as:
a = (y₂ - y₁)/(x₂ - x₁).
Also, for a given line:
y = m*x + s
A perpendicular line to that one must have a slope:
a = -(1/m)
And the intersection between two perpendicular lines forms four 90° angles.
So first, we need to find the slope of the line that passes through A and B.
A = (-3, 3)
B = (-1, -1)
Then the slope of the line is:
a = (-1 - 3)/(-1 - (-3)) = -4/2 = -2
a = -2
The slope of a perpendicular line should be:
slope = -(1/a) = -(1/-2) = 1/2
Then the perpendicular line will be something like:
y = (1/2)*x + b
To find the value of b, we can use the other restriction.
This line needs to pass through point C.
And we can see that point C is:
C = (1, 2)
This means that when x is equal to 1, y must be equal to 2.
Then replacing these in the above equation we get:
2 = (1/2)*1 + b
2 = 1/2 + b
2 - 1/2 = 4/2 - 1/2 = 3/2 = b
Then our equation is:
y = (1/2)*x+ 3/2
The graph of this line can be seen in the image below, the green line is the line that we found.
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Answer:
Step-by-step explanation:
3 inches is what fraction of a foot?
Answer:
1/4
Step-by-step explanation:
There are 12 inches in a foot, so 3 inches is 3/12 of a foot. As a reduced fraction, that is 1/4 of a foot.
Answer: 1/4 of a foot.
Step-by-step explanation: If you ever see this, I'm guessing you're in Elementary. But all3 of your questions have gotten me weak.
**50 points Once again and brainliest** Please hurry ;w;
Answer:
Part A:
Two types of translation are;
1) Horizontal translation left T(0, 8),
2) Vertical translation T(16, 0)
Part B:
For the horizontal translation transformation, k = 8
For the vertical translation transformation, k = 16
Part C:
For the horizontal translation transformation, the equation is f(x + 8) = g(x)
For the vertical translation transformation, the equation is f(x) + 16 = g(x)
Step-by-step explanation:
Answer:
see below
Step-by-step explanation:
Part A
We can shift f(x) up to g(x)
or we can shift f(x) to the left into g(x)
Part B
y = f(x) + k k > 0 moves it up
f(x) goes from -1 to 17 for a distance of 18 units
We are moving up 18 units
k = 18
y = f(x + k) k> 0 moves it left
We are moving to the left from 0 to -6 units for a distance of 6 units
k = 6
Part C
Up:
g(x) = f(x) +18
Left:
g(x) = f(x+6)
Solve by factoring
6x^2 +13x -28 =0
Answer:
x=-7/2, x=4/3
Step-by-step explanation:
[tex]6x^2+13x-28=0[/tex]
Multiply 6 and -28 to get -168
Find 2 numbers that multiply to 168 but add to 13
They are 21 & -8
Rewrite the equation into:
[tex]6x^2+21x-8x-28=0[/tex]
Factor
[tex]3x(2x+7)-4(2x+7)=0[/tex]
(3x-4)(2x+7)=0
3x=4
x=4/3
2x=-7
x=-7/2
HELPPPPPP please guyss
A Gallup poll asked 1200 randomly chosen adults what they think the ideal number of children for a family is. Of this sample, 53% stated that they thought 2 children is the ideal number.
A Gallup poll asked 1200 randomly chosen adults what they think the ideal number of children for a family is. Of this sample, 53% stated that they thought 2 children is the ideal number. Construct and interpret a 95% confidence interval for the proportion of all US adults that think 2 children is the ideal number.
Answer:
at 95% Confidence interval level: 0.501776 < p < 0.558224
Step-by-step explanation:
sample size n = 1200
population proportion [tex]\hat p[/tex]= 53% - 0.53
At 95% confidence interval level;
level of significance ∝ = 1 - 0.95
level of significance ∝ = 0.05
The critical value for [tex]z_{\alpha/2} = z _{0.05/2}[/tex]
the critical value [tex]z _{0.025}= 1.96[/tex] from the standard normal z tables
The standard error S.E for the population proportion can be computed as follows:
[tex]S,E = \sqrt{\dfrac{\hat p \times (1-\hat p)}{n}}[/tex]
[tex]S,E = \sqrt{\dfrac{0.53 \times (1-0.53)}{1200}}[/tex]
[tex]S,E = \sqrt{\dfrac{0.53 \times (0.47)}{1200}}[/tex]
[tex]S,E = \sqrt{\dfrac{0.2491}{1200}}[/tex]
[tex]S,E = 0.0144[/tex]
Margin of Error E= [tex]z_{\alpha/2} \times S.E[/tex]
Margin of Error E= 1.96 × 0.0144
Margin of Error E= 0.028224
Given that the confidence interval for the proportion is 95%
The lower and the upper limit for this study is as follows:
Lower limit: [tex]\hat p - E[/tex]
Lower limit: 0.53 - 0.028224
Lower limit: 0.501776
Upper limit: [tex]\hat p + E[/tex]
Upper limit: 0.53 + 0.028224
Upper limit: 0.558224
Therefore at 95% Confidence interval level: 0.501776 < p < 0.558224
Tanisha has 7 less than 4 times as many
toy cars as Fernando. If Tanisha has 9
cars, how many toy cars does Fernando
have?
a. 2 toy cars
b. 4 toy cars
c. 8 toy cars
d. 29 toy cars
help!
Answer: D is my guess.
Step-by-step explanation:
If you multiply those two number and subtract it by tanisha that probably is your answer if I'm incorrect I'm sorry hopefully this helped
1. A cone is 8cm high and has a base diameter of 12cm.its slant height is a.6cm b.8cm c.10cm d.12cm
Answer:
10
Step-by-step explanation:
it is Pythagoras theorem
6*6=36
8*8=64
64+36=100
square root of 100 is 10
3 pizzas cost $22.50,how much does 1 pizza cost?
Answer:
7.50
Step-by-step explanation:
Take the total cost and divide by the number of pizzas
22.50/ 3 pizzas
7.50 per pizza
[tex] \rm \longrightarrow \:Cost \: \: of \: \: 1 \: \: pizzas \: = \frac{Cost \: \: of \: \: 3 \: \: pizzas }{Total \: \: pizzas }[/tex]
[tex]\rm \longrightarrow \:Cost \: \: of \: \: 1 \: \: pizzas \: = \frac{22.50 }{3 } \\ [/tex]
[tex]\rm \longrightarrow \:Cost \: \: of \: \: 1 \: \: pizzas \: = \cancel\frac{22.50 }{3 } \: \: ^{7.5} \\ [/tex]
[tex]\rm \longrightarrow \:Cost \: \: of \: \: 1 \: \: pizzas \: = \: 7.5 [/tex]
Hence, the cost of 1 pizza is $7.5
what is a irrational number between 9.5 and 9.7
Step-by-step explanation:
x be an irrational number between 9.5 and 9.7.
So, we consider that x = 9.562536941412578914...
Rounding to the nearest hundredth
x = 9.56.
9.56763865854637984..... (rounded 9.57)
irrational because it has no pattern
Answer: [tex]\large \sqrt{91}[/tex]
Step-by-step explanation:
An irrational number is a square root in its simplest form.
We want an irrational number between 9.5 and 9.7
[tex]\huge 9.5<\sqrt x <9.7[/tex]
square all sides 90.25 < x < 94.09
Answer: The square root of any number between 90.25 and 94.09 will work so there are an infinite number of possible answers. [tex]\sqrt{91}, \sqrt{92}, \sqrt{93}, \sqrt{94}[/tex]
On a coordinate plane, a piecewise function has 3 lines. The first line has an open circle at (negative 9, negative 2), continues horizontally at y = negative 2, then has an open circle at (0, negative 2). The second line has an open circle at (0, 1), continues up with a positive slope, then has an open circle at (4, 9). The third line has an open circle at (4, negative 2), continues down with a negative slope, then has an open circle at (8, negative 4).
What is the domain indicated on the graph for each
Answer: D: x = (-9, 0) U (0, 4) U (4, 8)
Step-by-step explanation:
Line 1: y = -2 where -9 < x < 0
Line 2: y = 2)x + 1 where 0 < x < 4
Line 3: y = -(1/2)x + 6 where 4 < x < 8
Domain represents the x-values. Since all of them are open dots, the intervals are strictly less than (<).
-9 < x < 0 and 0 < x < 4 and 4 < x < 8 is the union of these intervals
-9 < x < 0 U 0 < x < 4 U 4 < x < 8
Interval Notation: D: x = (-9, 0) U (0, 4) U (4, 8)
Answer:
1st piece:
✔ –10 < x < 0
2nd piece:
✔ 0 < x < 4
3rd piece:
✔ 4 < x < 8
Step-by-step explanation:
Prove: The square of the sum of
two consecutive integers is odd.
[tex](2n+1)^2=4n^2+4n+1[/tex] therefore, the first blank is 1.
[tex]4n^2+4n+1=2(2n^2+2n)+1[/tex] therefore, the two other blanks are both 2.
The number in the proof ''The square of the sum of two consecutive integers is odd'' is 2 and 2.
To prove that, The square of the sum of two consecutive integers is odd.
The expression to prove is,
Let us assume that two consecutive integers are n and (n + 1).
Hence, the expression is written as,
[n + (n + 1)]² = (2n + 1)²
= (2n)² + 2 × 2n × 1 + 1²
= 4n² + 4n + 1
= 2 (2n² + 2n) + 1
= odd
Therefore, the number in the blanks are 2 and 2.
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B is the midpoint of AC. What is the value of x if AC = 52 and AB = 3x - 4
Answer:
x = 10
Step-by-step explanation:
Since B is the midpoint of AC then AB = BC = 3x - 4 and
AB + BC = AC , thus
3x - 4 + 3x - 4 = 52, that is
6x - 8 = 52 ( add 8 to both sides )
6x = 60 ( divide both sides by 6 )
x = 10
Help, i just need the answers and no need for explanations.
Answer:
The equation of the quadratic function shown is;
x^2+ 2x -3
Step-by-step explanation:
Here in this question, we need to know the quadratic equation whose graph was shown.
The key to answering this lies in knowing the roots of the equation.
The roots of the equation are the solution to the quadratic equation and can be seen from the graph at the point where the quadratic equation crosses the x-axis.
The graph crosses the x-axis at two points.
These are at the points x = -3 and x = 1
So what we have are;
x + 3 and x -1
Multiplying both will give us the quadratic equation we are looking for.
(x + 3)(x-1) = x(x -1) + 3(x-1)
= x^2 -x + 3x -3 = x^2 + 2x -3
What are the zeros of this function?
A. X= 2 and x = -6
B. x= 0 and x = -6
C. X= 0 and x = 5
D. X = 0 and x= -5
Answer:
I think its C because if I remember correctly zero of the function is just the x intercept
how many eighth rests are in a half rest?
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
Of the following points, name all that lie on the same vertical line?
(0,8) (-5,0) (-1,0) (0,7)
A. (0,8) (-5,0) (-1,0) (0,7)
B. none
C. (-5,0) (-1,0)
D. (0,8) (0,7)
Answer:
D
Step-by-step explanation:
vertical is basically the x axis, so the y axis has to be 0. using elimination, (0,8) and (0,7) are the only ones left.
Marta esta poniendo sus libros en una estantería. Le faltan 7 libros para poder poner 12 en cada estante; sin embargo, si pone 10 libros en cada estante, se quedan 5 libros sin poner. ¿Cuantos es antes tiene la estantería?
Answer:
x = 6 la cantidad de estantes
y = 65 cantidad de libros
Step-by-step explanation:
LLamemos "x" la cantidad de estantes que tiene Marta, y llamaremos "y" la cantidad de libros.
La primera condición que se debe cumplir es que cuando Marta coloca 12 libros en cada estante entonces le faltan 7, esto lo expresamos así:
y + 7 = 12*x (1)
La segunda condición establece que si Marta coloca los libros en número de 10 por estante le quedan 5 sin colocar, luego esto en lenguaje matemático se expresa así:
y - 5 = 10*x (2)
Ahora hemos obtenido un sistema de dos ecuaciones con dos incógnitas que se resuelve por cualquiera de los métodos conocidos, usaremos el método de sustitución.
Despejamos y en la primera ecuación y lo sustituimos en la segunda, de esa forma obtendremos el valor de x
y = 12*x - 7
(12*x - 7 ) - 5 = 10*x
2*x -12 = 0
2*x = 12
x = 6 la cantidad de estantes, y
y = 12*x -7
y = 72 - 7
y = 65 cantidad de libros
given the mapping f:x-7x-2, determine f(2)
Answer:
Value of F(2) = 12
Step-by-step explanation:
Given:
F(x) = 7x - 2
Find:
Value of F(2)
Computation:
F(x) = 7x - 2
putting x = 2
f(2) = 7(2) -2
f(2) = 14 - 2
f(2) = 12
So, Value of F(2) = 12