Answer:
3(6g - 5)
Step-by-step explanation:
1. First, find the GCF of 15 and 18.
Factors of 15:
1, 3, 5, 15
Factors of 18:
1, 2, 3, 6, 9, 18
The GCF of 15 and 18 is 3.
2. Factorize
3(6g - 5)
3. Check you answer:
3(6g) + 3(-5)
18g - 15
Hope this helps!
Which of the following is an equation of a line perpendicular to the equation
y =3x + 1?
O A. y = 3x + 5
O B. y=x+5
X
3
O C. y = -3x+5
OD. y - 3x+5
O 5
3
ТУ
Which quadratic function is represented by the graph?
6
5
4
O FUX) = - (x + 1)(x – 5)
O f(x) = - (x – 11x + 5)
3
2-
14
O f(x) = -5(x + 1)(x - 5)
2 3 4 5 x
3 -5 -5 -4 -3 -2 -21
-2
O f(x) = -5(x - 1)(x + 5)
+
-3
4
6
Answer:
the first one
Step-by-step explanation:
because I know the answer
The quadratic function represented in the graph is f(x) = -5 (x - 1) (x + 5).
What are Quadratic Functions?Quadratic functions are polynomial functions consisting of variables and exponents and the degree of the variable is 2.
The general form of a quadratic function is f(x) = ax² + b x + c.
Given a graph of a quadratic function.
The graph is directed downwards. So the leading coefficient is negative.
The function touches the X axis at two points, x = -5 and x = 1.
So -5 and 1 are the zeroes of the function.
So the function can be factored as,
f(x) = (x + 5)(x - 1)
So the quadratic equation is,
f(x) = -5 (x - 1) (x + 5)
Hence the equation of the given quadratic equation is f(x) = -5 (x - 1) (x + 5).
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What is the value of y in the solution to this system of equations?
3x + 2y = -12
2x + y = 4
A.
B.
C.
D.
-36
-12
4
20
Answer:
x= 20,y= −36
Step-by-step explanation:
3x+2y=−12
2x+y=4
Subtract 2x
from both sides of the equation.
y=4−2x
3x+2y=−12
Replace all occurrences of y
with 4−2x
in each equation.
Tap for more steps...
−x+8=−12
y=4−2x
Solve for x
in −x+8=−12
.
Tap for more steps...
x=20
y=4−2x
Replace all occurrences of x
with 20
in each equation.
Tap for more steps...
y=−36
x=20
The solution to the system is the complete set of ordered pairs that are valid solutions.
(20,−36)
The result can be shown in multiple forms.
Point Form:
(20,−36)
Equation Form:
x=20,y=−36
Multiply 2 with (1) and 3 with (2)
6x+4y=-24--(1)6x+3y=12--(4)Subtract
y=-24-12y=-36A watering can hold 12 1/2 litres.it’s filled 11 times from a tank containing 400 litres.how much water is left in the tank
Answer:
262 1/2 liters
Step-by-step explanation:
Remaining water in tank :
Volume (tank) - 11 x Volume (watering can)400 - 11 x 12 1/2400 - 137 1/2262 1/2 litersAnswer:
262.5 litres
Step-by-step explanation:
Water taken from the tank
⇒ 11 × 12.5 litres = 137.5 litres
Water left in tank
⇒ 400 - 137.5 = 262.5 litres
If k (x) = x^2 and p (x) = k (x) + n, what is the value of n?
The equation k(x) = x^2 is quadratic equation, and the value of n in p (x) = k (x) + n is -6
How to determine the value of n?The equations are given as:
k(x) = x^2
p (x) = k (x) + n
From the graph, we can see that the graph of k(x) is shifted down by 6 units.
This means that the equation of p(x) is
p (x) = k (x) - 6
By comparison;
n = -6
Hence, the value of n in p (x) = k (x) + n is -6
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(1) a) Why is 8x²y + 5x³y² - 2 considered as an expression and not an equation?
Answer & step-by-step explanation:
An expression is a number, a variable, or a combination of numbers and variables and operation symbols. An equation is made up of two expressions connected by an equal sign. As you can clearly see here, there is no equal sign connecting anything here, thus, it is an expression.
Because for it to be called an equation you need to have the equal symbol (=) comparing two epressions.
Example of expression:
2x - 4y + 14
Example of equation:
-3y - 2 = -2x - 8
⇔ -3y = -2x + 6
⇔ -y = -[tex]\frac{2}{3}[/tex]x + 2
⇔ y = [tex]\frac{2}{3}[/tex]x - 2
(3 squared)to the power of 6
Answer:
531,441
Step-by-step explanation:
3^2=9
9^6=531,441
Answer:
[tex] \sqrt{ {2}^{6 } } = 27 if thats what you meant here is another answer{ {2}^{6} = 64[/tex]
In triangle abc, points d and e are the midpoints of and respectively. what are the slope and length of , if the slope and length of are 0.5 and 3.2 units, respectively? a. slope = -2, length = 3.2 units b. slope = 0.25, length = 3.2 units c. slope = 0.5, length = 1.6 units d. slope = -2, length = 1.6 units e. slope = 0.25, length = 1.6 units
The slope and length of segment DE in the given triangle are: 0.5, and 1.6 units respectively.
What is the Slope of Parallel Lines?The slope of lines that are parallel to each other are always the same.
Segment DE is parallel to segment BC in triangle ABC.
Since slope of BC is 0.5, slope of DE would also be: 0.5.
Since E and D are the the midpoints of AC and AB respectively, it means that:
Length of DE = 1/2(length of BC)
Length of DE = 1/2(3.2)
Length of DE = 1.6 units
Therefore, slope of DE is: 0.5
Length of DE is: 1.5 units.
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Answer:
C. Slope = 0.5, length = 1.6 units.
Hope this helps!
Step-by-step explanation:
Solve: x/2-3x/4+x/6=(-2)/3
original equation
[tex]\frac{x}{2}-\frac{3x}{4}+\frac{x}{6}=-\frac{2}{3}[/tex]
multiply by lcd
[tex]12(\frac{x}{2})-12(\frac{3x}{4})+12(\frac{x}{6}) =-12(\frac{2}{3})\\\\6x-9x+2x=-8[/tex]
isolate for x
[tex]-1x=-8\\\\x=8[/tex]
verify
[tex]\frac{8}{2}-\frac{3(8)}{4}+\frac{8}{6}=-\frac{2}{3}\\\\4-6+\frac{4}{3}=-\frac{2}{3}\\\\4-2+\frac{4}{3}=-\frac{2}{3}\\\\-\frac{2}{3}=-\frac{2}{3}\\\\LS=RS[/tex]
HELPPPPPPPPPPPPPPPPpppp
What is 15 1/3 in radical form?
2/15
15
Answer:
∛15.
Step-by-step explanation:
15^1/3
= ∛15.
Mrs Tilley Keeps a variety of poultry. This pie chart shows the numbers of What each kind:
27 Geese, 72 Hens, 45 Turkeys and 36 Ducks.
32. What percentage of the poultry are hens?
33. What percentage of the poultry are geese?
34. What fraction of the poultry are ducks?
35. What fraction of the poultry are turkeys?
Answer:
32. 40%
33. 15%
34. 1/5
35. 1/4
Step-by-step explanation:
Question 32
% Hens = No. of hens / Total poultry% Hens = 72 / 27 + 72 + 45 + 36% Hens = 72 / 180 = 2/5% Hens = 40%Question 33
% Geese = No. of geese / Total% Geese = 27/180 % Geese = 3/20% Geese = 15%Question 34
% Ducks = No. of ducks / Total% Ducks = 36/180% Ducks = 1/5Question 35
% Turkeys = No. of turkeys / Total% Turkeys = 45/180% Turkeys = 1/4Answer:
32. 40%
33. 15%
34. 1/5
35. 1/4
Step-by-step explanation:
Given:
27 Geese72 Hens45 Turkeys36 Ducks⇒ Total poultry = 27 + 72 + 45 + 36 = 180
[tex]\sf Percentage = \dfrac{Part}{Whole}\times 100[/tex]
[tex]\implies \sf Hens = \dfrac{72}{180}\times 100=40 \%[/tex]
[tex]\implies \sf Geese= \dfrac{27}{180}\times 100=15 \%[/tex]
[tex]\sf Fraction= \dfrac{Part}{Whole}[/tex]
[tex]\implies \sf Ducks=\dfrac{36}{180}=\dfrac{36 \div 36}{180 \div 36}=\dfrac{1}{5}[/tex]
[tex]\implies \sf Turkeys=\dfrac{45}{180}=\dfrac{45 \div 45}{180 \div 45}=\dfrac{1}{4}[/tex]
The square to solve the quadratic equation x^2-15x+2=0
The roots of the equation [tex]x^{2}[/tex]-15x +2 =0 are 14.865 and 0.135
What is completing the square method?Completing the square method is one of the methods to find the roots of the given quadratic equation.
Given equation is:
[tex]x^{2}[/tex]-15x +2 =0
Using Completing the Square method we have
[tex]x^{2}[/tex]-15x +2 + [tex](\frac{15}{2})^{2}[/tex] - [tex](\frac{15}{2})^{2}[/tex] =0
Now,
[tex]x^{2}[/tex]-15x + [tex](\frac{15}{2})^{2}[/tex] - [tex](\frac{15}{2})^{2}[/tex] +2=0
or, [tex][x-(\frac{15}{2})]^{2}[/tex] - 225/4 +2 =0
or, [tex][x-(\frac{15}{2})]^{2}[/tex] -217*4 =0
or, [tex][x-(\frac{15}{2})]^{2}[/tex] = 217/4
or, [tex]x[/tex] = [tex]\pm \frac{14.73}{2} + \frac{15}{2}[/tex]
or, [tex]x_1[/tex]= 14.865, [tex]x_2[/tex]= 0.135
Thus, the roots of the quadratic equation are: 14.865 and 0.135
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A board 18 inches long is cut into two pieces in the ratio 1:2. Find the length of each piece.
A Cylinder has a base diameter of 4cm and a height of 2cm. What is it’s volume in cubic cm, to the nearest tenths place
Answer: The answer is v=25.1 cm³
Step-by-step explanation:
b=4
h= 2
r= 4/2 r =2 radius is half of the diameter
V=πr²h
v= π(2)²2
v= 25.132741228718
v=25.1 cm³
The price of a notebook is 20% less than the price of a book. By
what percent is the price of the book higher than the price of the
notebook?
HELP
Answer:
125%
Step-by-step explanation:
lets just say the book is $100. 20% less would be $80
now to go back to $100, we need to add $20 to $80
20 is 25% of 80, so add the extra 25% to 100% of 80
write the equation of the line passing through the point (2,- 1) with a slope of 3
Answer:
Y= 3X-7
Step-by-step explanation:
the equation of the line has the formular
Y-Y1= M (X-X1)
here, M= slope= 3
X1=2 Y1= -1
Y--1= 3(X-2)
Y+1= 3X-6
Y= 3X-6-1
Y= 3X-7
Answer:
y=3x-7
Step-by-step explanation:
1. Use The Slope Formula
y=mx+b
m=slope
b=y-intercept
2. Fill in the given values
y=3x+b
3. Use the given points to solve for b
-1=3*2+b
-1=6+b
-7=b
4. Final equation
y=3x-7
Kara wants to buy a game that is on sale. the original price of the game is p, but it is on sale for 30% off the original price. she uses the expression p(i - 0.3) to model the price. which expressions are equivalent to kara's expression? select all correct answers and the answers are
p - 0.3
1 - 0.3p
0.7p
p - 0.3p
1.3p
The expressions equivalent to kara's expression are 0.7p and p-0.3p
How to find discount of original price?Original price = pDiscount = 30%Discount price expression = p(1 - 0.3)
= p - 0.3p
= 0.7p
Check for equivalent expression
p - 0.3
Not equivalent
1 - 0.3p
Not equivalent
0.7p
Equivalent
p - 0.3p
Equivalent
1.3p
Not equivalent
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Apples cost $1.60 at the farmers market. They cost
1.5 times as much at the grocery store.
Select all the equations that show the cost of apples at
the grocery store, g.
(Select all that apply.)
g=1.5 1.60
g=1.60 1.5
1.5g = 1.60
g=1.5 1.60
g÷1.5 1.60
Answer:
G = 1.60 x 1.5, G = 1.5 x 1.60, and G ÷ 1.5 = 1.60
Step-by-step explanation:
^ ^
Which of the following is a valid probability distribution?
Answer:
first one is the valid probability distribution
A gym charges membership dues of $25 per month. Part A
Complete the table to show how the total cost in dollars, C, and the
number of months, m, of gym membership are related. What is the cost of the blue section
you can turn this into an equation: [tex]c=25m[/tex], where c is the cost and m is number of months.
solve for blue.
[tex]c=25m\\\\c=25(14)\\\\c=350[/tex]
The blue section costs $350.
After sitting out of a refrigerator for a
while, a turkey at room temperature (
68°F) is placed into an oven. The oven
temperature is 305°F. Newton's Law of
Heating explains that the temperature of
the turkey will increase proportionally to
the difference between the temperature of
the turkey and the temperature of the
oven, as given by the formula below:
T = Ta + (To − Ta)e-kt
Ta
=
the temperature surrounding
the object
To
=
the initial temperature of the
object
t
=
the time in hours
T
=
the temperature of the object
after t hours
k = decay constant
The turkey reaches the temperature of
108°F after 3 hours. Using this
information, find the value of k, to the
nearest thousandth. Use the resulting
equation to determine the Fahrenheit
temperature of the turkey, to the nearest
degree, after 4.5 hours.
Answer:
The value of k to the nearest thousandth is -0.133
The of the turkey to the nearest degree after 4.5 hours is 186F
Step-by-step explanation:
Good evening! Can someone please answer this, ill give you brainliest and your earning 50 points. Would be very appreciated.
Answer:
1) x² + x
2) Check Below.
Explanation:
step 1 = 2 sqauresstep 2 = 6 squaresstep 3 = 12 squaresHence sequence can be created:
2, 6, 12
Find difference:
2, 6, 12
4 6
2
Find Equation:
2a = 2a = 1Then,
3a + b = 4b = 4 -3(1)b = 1Then,
a + b + c = 2c = 2 - 1 -1c = 0So Equation:
ax² + bx + c --- main formulaex² + 1x + 0 x² + x [equation]B)With Step Increasing, The step number multiplies the step number and plus the step number. That is the number of squares.
a truck tire has a diameter of 3 feet how far will the truck travel with 20 rotations of the tire?
Answer:
60 ft
Step-by-step explanation:
3 times 20 is 60 ft so there is your answer
Answer:
C
Step-by-step explanation:
Diameter is 3 feet, and the radius is half the diameter.
Radius = 3/2 = 1.5 feetCircumference
2 × π × 1.53πDistance travelled in 20 rotations
20 x 3π60π ftC-11+13+ 10x + 2x
I will give you brainliest
Answer:
12x + 2Step-by-step explanation:
-11 + 13 + 10x + 2x =
2 + 10x + 2x =
12x + 2
Answer:
2(6x+1)
Step-by-step explanation:
1. Add the number
-11 + 13 + 10x + 2x
2 + 10x +2x
2.Combine like terms
2 + 10x + 2x
2 + 12x
3.Arrange terms
2 + 12x
12x + 2
4.Common factor
-11 + 13 + 10x + 2x
2(6x+1)
NEED HELP PLEASE ANSWER ASAP! (41)
Answer:
41. (2) x² - 3x - 4 =0
Step-by-step explanation:
Question 41
Standard form of polynomial
x² - (sum of roots) + product of roots = 0(2) x² - 3x - 4 =0Answer:
(2) [tex]x^2-3x-4=0[/tex]
Step-by-step explanation:
Standard form of a quadratic equation: [tex]ax^2+bx+c=0[/tex]
When factoring a quadratic (finding the roots) we find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex], then rewrite [tex]b[/tex] as the sum of these two numbers.
So if the roots sum to 3 and multiply to -4, then the two numbers would be 4 and -1.
[tex]\implies b=1+-4=-3[/tex]
[tex]\implies ac=1 \cdot -4[/tex]
As there the leading coefficient is 1, [tex]c=-4[/tex].
Therefore, the equation would be: [tex]x^2-3x-4=0[/tex]
Proof
Factor [tex]x^2-3x-4=0[/tex]
Find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex].
The two numbers that multiply to -4 and sum to -3 are: -4 and 1.
Rewrite [tex]b[/tex] as the sum of these two numbers:
[tex]\implies x^2-4x+x-4=0[/tex]
Factorize the first two terms and the last two terms separately:
[tex]\implies x(x-4)+1(x-4)=0[/tex]
Factor out the common term [tex](x-4)[/tex]:
[tex]\implies (x+1)(x-4)=0[/tex]
Therefore, the roots are:
[tex](x+1)=0 \implies x=-1[/tex]
[tex](x-4)=0 \implies x=4[/tex]
So the sum of the roots is: -1 + 4 = 3
And the product of the roots is: -1 × 4 = -4
Thereby proving that [tex]x^2-3x-4=0[/tex] has roots whose sum is 3 and whose product is -4.
(90 POINTS) How can you find the length of RT using similarity? Explain your reasoning.
Answer:
RT = 26
Step-by-step explanation:
Based on the figure we can say :
ΔABC ~ ΔTSR (by SAS similarity)Scale factor :
AB/SR = 12/24 = 1/2Hence, as the proportions are the same :
CA/RT = 1/213/RT = 1/2RT = 13 x 2RT = 26The triangle ABC and RST will be similar triangles. Then the length of RT will be 26 units.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
If the two triangles are similar, the ratio of the corresponding sides will be constant.
The triangle ABC and RST will be similar triangles.
RT / 13 = 24 / 12
RT = 26
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Solve 6^x+2 = 10 for x using the change of base formula
Answer:
[tex]x\approx-0.7149[/tex]
Step-by-step explanation:
[tex]\displaystyle 6^{x+2}=10\\\\\log_6(6^{x+2})=\log_6(10)\\\\x+2=\frac{\log(10)}{\log(6)}\\\\x+2\approx1.2851\\\\x\approx-0.7149[/tex]
Recall that the change of base formula is [tex]\displaystyle \log_a(b)=\frac{\log(b)}{\log(a)}[/tex]
Find two integers whose sum is 3 and product is -28 ?
Answer:
-4 and 7
Step-by-step explanation:
-4 + 7 = 3
-4•7 = -28
What is the value of x?
Answer:
130° is the correct value of x.Step-by-step explanation:
In the question, there's an quadrilateral whose sum of all exterior angle is 360°.
140° + 34° + 56° + x = 360°
➝ 230° + x = 360°
➝ x = 360° - 230°
➝ x = 130°
Thus, The value of x is 130°.