Hello there! :)
To expand this expression, we have to use the Distributive Property, which states:
a(b+c)=ab+ac
7(2x+7)=14x+49
Hence, 14x+49 is the expression (Answer)
Hope it helps you!
~A lonely teen who helps others and listens to her favourite song "How Far I'll Go
-Grace ;-)
Good luck.
7 (2x + 7)
= (7 × 2x) + (7 × 7)
= 14x + 49
_____
Hope it helps ⚜
Form a third-degree polynomial function with real coefficients, with leading coefficient 1, such that 6+i and 5 are zeros.
Answer:
A third-degree polynomial can be written as:
f(x) = a*x^3 + b*x^2 + c*x + d
Where the leading coefficient is a, and all the coefficients are real.
If we know that the leading coefficient is 1, then the equation becomes:
f(x) = x^3 + b*x^2 + c*x + d
Now, we also know that:
(6 + i) and 5 are zeros.
This means that:
(6 + i)^3 + b*(6 + i)^2 + c*(6 + i) + d = 0
remember that:
i^2 = - 1
This is equal to:
(6 + i)*(36 + 2*6*i + i^2) + b*(36 + 2*6*i + i^2) + c*(6 + i) + d = 0
(6 + i)*(35 + 12i) + b*(35 + 12i) + c*(6 + i) + d =0
(210 + 35i + 72i - 12) + b*(35 + 12i) + c*(6 + i) + d = 0
198 + 107i + b*(35 + 12i) + c*(6 + i) + d = 0
sparating in real and imaginary part, we get:
(198 + b*35 + c*6 + d) + (107 + b*12 + c)*i = 0
Then each parentheses needs to be zero, this means that:
198 + b*35 + c*6 + d = 0
107 + b*12 + c = 0
Knowing that 5 is another zero, we have:
5^3 + b*5^2 + c*5 + d = 0
125 + b*25 + c*5 + d = 0
Then we have a system of 3 equations and 3 variables:
198 + b*35 + c*6 + d = 0
107 + b*12 + c = 0
125 + b*25 + c*5 + d = 0
To solve this, we first need to isolate one of the variables in one of the equations.
Let's isolate d in the last one, so we get:
d = -125 - b*25 - c*5
now we can replace this in the first equation to get:
198 + b*35 + c*6 + d = 0
198 + b*35 + c*6 + ( -125 - b*25 - c*5) = 0
70 + b*10 + c = 0
So now we have two equations:
70 + b*10 + c = 0
107 + b*12 + c = 0
Again, now we can isolate the one variable in one of the equations, this time let's isolate c in the first one.
c = -70 - b*10
now we can replace this in the other equation:
107 + b*12 + c = 0
107 + b*12 + (-70 - b*10) = 0
38 + b*2 = 0
now we can solve this for b
b*2 = -38
b = -38/2 = -19
Now, with the equation c = -70 - b*10 we can find the value of c.
c = -70 - b*10 = c = -70 - (-19)*10 = 120
And with the equation d = -125 - b*25 - c*5
we can find the value of d:
d = -125 - b*25 - c*5 = -125 - (-19)*25 - (120)*5 = -250
Then we have:
a = 1
b = -19
c = 120
d = -250
The eqation is:
f(x) = 1*x^3 - 19*x^2 + 120*x - 250
Will give brainliest need a quick answer
Answer the question written in the image.
Answer: 28
Step-by-step explanation:
The pattern is multiply the right and bottom, add the left
For example, 9*8+7=79
So, 24*3+x=100
72+x=100
x=28
From a group of three boys and six girls a boy and a girl will be selected to attend a conference and how many ways can the selection you made
Answer:
18
Girl = g
Boy = b
1g 1b 1g 2b 1g 3b
2g 1b 2g 2b 2g 3b
3g 1b 3g 2b 3g 3b
4g 1b 4g 2b 4g 3b
5g 1b 5g 2b 5g 3b
6g 1b 6g 2b 6g 3b
---------------------------------------
Another way you can do this,
6 × 3 = 18
In the end there will be 18 selections.
determine the equation of a line that is vertical and goes through (-5,6)
Answer:
x = -5
Step-by-step explanation:
A vertical line is a line that goes up and down. It is of the form x = constant
To go through (-5,6) is has to have the value of the x coordinate
x = -5
Givenl || m | n, find the value of x.
. m
44°
77
By
Answer: 0
Submit Answer
attempt 1 out of 2
Can someone pls help
Answer:
x = 136
Step-by-step explanation:
x and 44 are same- side interior angles and sum to 180° , that is
x + 44 = 180 ( subtract 44 from both sides )
x = 136
If 2^x-4 = 4^x-6 , then value of x is?
Answer: [tex]x=1[/tex]
Step-by-step explanation:
[tex]2^x-4=4^x-6[/tex] is the equation that you've given us.
Now if we plot these two equations on the graph we notice there's an intersection at (1,-2). Therefore meaning that [tex]x=1[/tex].
We can prove that by doing the following calculations to prove that both sides are equal to each other.
The left side of the equal sign:
Step 1: Write the equation down:
[tex]2^x-4[/tex]
Step 2: Substitute x for the numerical value we found.
[tex]2^1-4[/tex]
Step 3: Find the square of [tex]2^1[/tex], which is itself, 2.
[tex]2-4[/tex]
Step 4: Subtract 2 from 4. Which is a negative number, thus being -2.
[tex]-2[/tex]
The right side of the equal sign:
Step 1: Write the equation down:
[tex]4^x-6[/tex]
Step 2: Substitute x for the numerical value we found.
[tex]4^1-6[/tex]
Step 3: Find the square of [tex]4^1[/tex], which is itself, 4.
[tex]4-6[/tex]
Step 4: Subtract 4 from 6. Which is a negative number, thus being -2.
[tex]-2[/tex]
We know that [tex]x=1[/tex] because when substituting x with 1, we get -2 on both sides. Therefore making this statement true and valid.
[tex]-2=-2[/tex]
Grandfather Giovanni's hens lay 180 eggs per day, which are placed in containers of 6 each. How many containers will you need per day?
Answer:
6
Step-by-step explanation:
Hai giá sách có 450 cuốn sách .Nếu chuyển 50 quyển từ giá thứ nhất sang giá thứ hai thì số sách ở giá số hai sẽ bằng 4/5 số sách ở giá thứ nhất ?Tính số sách ở mỗi giá.
Step-by-step explanation:
hơi khó hiểu thông cảm UwU
A square has a perimeter of 4 cm. What is the length of each side?
Answer:
1 cm
Step-by-step explanation:
Since the perimeter is 4 cm and all the sides of the square have the same length, each side must be 1 cm long.
The area of that square is 1 cm x 1 cm, which is 1 cm2.
Step-by-step explanation:
since the all side is same,the side length is just 1 cm. And the area is just the side length square =1cmsquare× 1 cm
= ans is 1cm^2
Solve the system of equations using the substitution method. -x − 2y = 0 y = -8x (x, y) = ( , )
Answer:
[tex] = { \tt{(0, \: 0)}}[/tex]
Step-by-step explanation:
Let:
[tex]{ \bf{ - x - 2y = 0 - - - (a)}} \\ { \bf{y = - 8x - - - (b)}}[/tex]
Substitute for y in equation (b) to equation (a):
[tex]{ \tt{ - x - 2( - 8x) = 0}} \\ { \tt{ - x + 16x = 0 }} \\ { \tt{x = 0}}[/tex]
Also, y = 0
Which statements are true about David's work? Check all that apply. The GCF of the coefficients is correct. The GCF of the variable b should be b4 instead of b2. The variable c is not common to all terms, so a power of c should not have been factored out. The expression in step 5 is equivalent to the given polynomial. In step 6, David applied the distributive property.
Answer:
The GCF of the coefficients is correct.
The variable c is not common to all terms, so a power of c should not have been factored out.
In step 6, David applied the distributive property.
Step-by-step explanation:
Given the polynomial :
80b⁴ – 32b²c³ + 48b⁴c
The Greatest Common Factor (GCF) of the coefficients:
80, 32, 48
Factors of :
80 : 1, 2, 4, 5, 8, 10, 16, 20, 40, and 80
32 : 1, 2, 4, 8, 16, and 32
48 : 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.
GCF = 16
b⁴, b², b⁴
b⁴ = b * b * b * b
b² = b * b
b⁴ = b * b * b * b
GCF = b*b = b²
GCF of c³ and c
c³ = c * c * c
c = c
GCF = c
We can see that David's GCF of the coefficients are all correct
From the polynomial ; 80b⁴ does not contain c ; so factoring out c is incorrect
In step 6 ; the distributive property was used to obtain ; 16b²c(5b² – 2c² + 3b²)
40 POINTS- please help me
Answer:
a, c, d,
Step-by-step explanation:
I'm not sure if this is right but i think.
First you cant have exponents in a linear equation, so its not e or f. Then i just graphed the rest.
Determine the y-intercept of the quadratic equation Y = x^2 - 4x + 8
9514 1404 393
Answer:
(0, 8)
Step-by-step explanation:
The y-value of the y-intercept is the function value when x=0. That is the constant in the equation, since x=0 will make all of the x-terms be zero.
y-intercept = 8
Here are the ages (in years) of 12 professors at a college.
51, 34, 56, 48, 37, 39, 59, 53, 52, 45, 3367
What is the percentage of these professors who are younger than 50?
=__%
Answer:
50%
Step-by-step explanation:
6 professors younger than 50 years = 6/12 = 50
Answer:
%50
Step-by-step explanation:
If you count the number of proffessors that are under 50, there are six. If there are 12 proffessors then it would be 1/2. One half in percentage is %50.
Pls give Brainliest!
PLSSS HELP MEE
Equation: c = n
Is there any way for this equation to be true? How?
Step-by-step explanation:
if
c = 3 + 6 = 9
and
n = 4 + 5 = 9
then it could be true
Rotate the vector 3,-2 90 degrees clockwise about the origin.
Answer:
-2,-3
Step-by-step explanation:
Answer:
-2 -3
It worked for me on acellus
Step-by-step explanation:
State the quadrant in which the terminal side of the given angle lies.
0
=
Зл
5
SEE QUESTION IN IMAGE
Answer:
B. 48°Step-by-step explanation:
∠OST = 90° as ST ⊥ OS (tangent is perpendicular to radius at same point)
m∠OSP = 1/2(180° - m∠SOP) = 90° - 96°/2 = 42° (sum of interior angles of the triangle SOP)
m∠PST = 90° - m∠OSP = 90° - 42° = 48° (angle addition postulate)
Correct choice is B
How would two billion, nine hundred seventy-six million, twelve thousand, eight be written
Does this graph represent a function? Why or why not?
A. Yes, because it passes the vertical line test.
B. No, because it is not a straight line.
C. No, because it fails the vertical line test.
D. Yes, because it has two straight lines.
Answer:
with my own opinion the answer is b
Line segment QR is dilated to create line segment Q'R' using the dilation rule DT,1.5. Point T is the center of dilation. Line segment Q R is dilated to create line segment Q prime R prime. The length of R T is 6 and the length of R prime R is y. What is y, the distance between points R and R'?
Answer:
[tex]y= 3[/tex]
Step-by-step explanation:
Given
[tex]RT = 6[/tex]
[tex]k = 1.5[/tex] --- dilation ratio
See attachment
Required
Determine length, y
First, we calculate length R'T.
Since point T is the center of dilation, then:
[tex]R'T = k * RT[/tex]
Substitute known values
[tex]R'T = 1.5 * 6[/tex]
[tex]R'T = 9[/tex]
y is between R'T and RT;
So:
[tex]y = R'T - RT\\[/tex]
[tex]y = 9 -6[/tex]
[tex]y= 3[/tex]
Answer:
either 4 or 9
Step-by-step explanation:
What is the quotient?
(-3)
(-3)²
O-9
1
o
1
9
100
O 9
Answer:
(-3)
Step-by-step explanation:
follow me if you want
Identify the correct explanation and the similarity statement for the similar triangles.
A: By the Isosc. Δ Thm., ∠B ≅ ∠C, so by the Def. of ≅, m∠B = m∠A.
This gives m∠A = 75° by Substitution.
Then, by the Δ Subt. Thm., m∠C = 30°.
Now apply the Isosc. Δ Thm. and the Δ Subt. Thm. to ΔPQR to find that m∠P = m∠Q = 75°.
Therefore ΔABC ~ ΔPQR by SSS ~.
B: By the Isosc. Δ Thm., ∠B ≅ ∠C, so by the Def. of ≅ , m∠B = m∠C.
This gives m∠C = 75° by substitution.
Then, by the Δ Sum Thm., m∠A = 30°.
Now apply the Isosc. Δ Thm. and the Δ Sum Thm. to ΔPQR to find that m∠P = m∠Q = 75°.
Therefore ΔABC ~ ΔPQR by AA ~.
C: By the Isosc. Δ Thm., ∠B ≅ ∠C, so by the Def. of ≅, m∠B = m∠C.
This gives m∠C = 30° by Substitution.
Then, by the Δ Subt. Thm., m∠A = 75°.
Now apply the Isosc. Δ Thm. and the Δ Subt. Thm. to ΔPQR to find that m∠P = m∠Q = 75°.
Therefore ΔABC ~ ΔPQR by SSS ~.
D: By the Isosc. Δ Thm., ∠B ≅ ∠C, so by the Def. of ≅, m∠B = m∠A.
This gives m∠A = 75° by Substitution.
Then, by the Δ Sum Thm., m∠C = 30°. Now apply the Isosc. Δ Thm. and the Δ Sum Thm. to ΔPQR to find that m∠P = m∠Q = 75°.
Therefore ΔABC ~ ΔPQR by AA ~.
Answer:
Option B
Step-by-step explanation:
From the picture attached,
In ΔABC,
m∠B = m∠C = 75° [Isosceles triangles]
By applying triangle sum theorem,
m∠A + m∠B + mC = 180°
m∠A + 75° + 75° = 180°
m∠A = 180° - 150°
m∠A = 30°
In triangle PQR,
m∠P = m∠Q [Isosceles triangle]
By applying triangle sum theorem,
m∠P + m∠Q + m∠R = 180°
2(m∠P) + 30° = 180°
m∠P = 75°
m∠P = m∠Q = 75°
In ΔABC and ΔRPQ,
m∠B ≅ m∠Q [Given]
m∠C ≅ m∠R [Given]
Therefore, by AA property of similarity of two triangles, both the triangles will be similar.
ΔABC ~ ΔRPQ
Option B will be the answer.
if my mine craft house was burning leaves irl and i was watering my boat on a Wednesday on a weekend in December when its summer how many fish will become orphans late nights in the middle of june?
Can someone please help me to evaluate
Answer:
1
Step-by-step explanation:
a*log(b) = log(b^a), so (1/2)*log(196)=log(14)
So 1+log(15)-log(14)=1
write in simplest form :
36 minutes to 3/2hrs
Answer:
⅗hrs
Step-by-step explanation:
1hr =60 min
? = 36 min
cross-multiply .........
36 min × 1hr/60 min= 36min/60min × 1hr
=36/60 × 1 hr
= ⅗hrs
Given that the days are the independent variable, which dependent variable has a constant rate of change?
When (8x − 4) = 2x is solved, the result is:
Answer:
x = 1
General Formulas and Concepts:
Pre-Algebra
Distributive Property
Equality Properties
Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
Identify
1/2(8x - 4) = 2x
Step 2: Solve for x
[Distributive Property] Distribute 1/2: 4x - 2 = 2x[Subtraction Property of Equality] Subtract 2x on both sides: 2x - 2 = 0[Addition Property of Equality] Add 2 on both sides: 2x = 2[Division Property of Equality] Divide 2 on both sides: x = 1Answer:
x = 2/3
Step-by-step explanation:
(8x − 4) = 2x
8x - 4 = 2x
6x = 4
x = 2/3
Find the measures of
Answer:
Step-by-step explanation:
Measure of an inscribed angle intercepted by an arc is half of the measure of the arc.
From the picture attached,
m(∠A) = [tex]\frac{1}{2}m(\text{arc BD})[/tex]
= [tex]\frac{1}{2}[m(\text{BC})+m(\text{CD}][/tex]
= [tex]\frac{1}{2}[55^{\circ}+145^{\circ}][/tex]
= 100°
m(∠C) = [tex]\frac{1}{2}[(360^{\circ})-m(\text{arc BCD})][/tex]
= [tex]\frac{1}{2}(360^{\circ}-200^{\circ})[/tex]
= 80°
m(∠B) + m(∠D) = 180° [ABCD is cyclic quadrilateral]
115° + m(∠D) = 180°
m(∠D) = 65°
m(arc AC) = 2[m(∠D)]
m(arc AB) + m(arc BC) = 2(65°) [Since, m(arc AC) = m(arc AB) + m(arc BC)]
m(arc AB) + 55° = 130°
m(arc AB) = 75°
m(arc ADC) = 2(m∠B)
m(arc AD) + m(arc DC) = 2(115°)
m(arc AD) + 145° = 230°
m(arc AD) = 85°
