The solution is x = 11
Step-by-step explanation:
The original equation is
[tex]7(x+2)=91[/tex]
Lin uses the distributive property, which states that
[tex]a(x+y)=ax+ay[/tex]
By applying the property to this case,
[tex]7(x+2)=91\\7x+14=91[/tex]
Then we subtract 14 on both sides:
[tex]7x+14-14=91-14\\7x=77[/tex]
Finally, we divide by 7 on both sides:
[tex]\frac{7x}{7}=\frac{77}{7}\\x=11[/tex]
Noah starts by dividing each side by 7, so he gets
[tex]\frac{7(x+2)}{7}=\frac{91}{7}\\x+2=13[/tex]
Then he can subtract +2 from both sides:
[tex]x+2-2=13-2\\x=11[/tex]
So, they get the same result. The similarity between the two methods is that they both divide by 7, while the difference is that Lin has to subtract 14, while Noah has to subtract 2.
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Lin's solution method: 7x+14=91, 7x=77, x=11
Noah's solution method: x+2=13, x=11
Both methods involve dividing by 7, but Noah does the division first, while Lin does the division last. Also, Lin's method involves subtracting 14, while Noah's method involves subtracting 2. Both solutions are correct and valid. Noah's solution could be considered more efficient for this example, because it takes fewer steps and has equally complicated arithmetic work.
which function has a simplified base of 4^3√4?
Answer:
The function is [tex]f(x) = 4(\sqrt[3]{16} )^{2x}[/tex].
Step-by-step explanation:
We have to choose from options the exponential function which has a simplified base of 4∛4 i.e. ∛(256).
Now, the exponential function in the option III will be the answer.
The function is [tex]f(x) = 4(\sqrt[3]{16} )^{2x}[/tex].
So, the base is [tex](\sqrt[3]{16} )^{2}[/tex] = [tex]\sqrt[3]{16^{2}} = \sqrt[3]{256} = 4\sqrt[3]{4}[/tex]. (Answer)
The general formula of an exponential function is [tex]f(x) = a(b)^{x}[/tex] , where b is called the base of the function.
The function that has a simplified base of (4∛4) is;
Option C; 4(∛16)^(2x)
From the general formula of an exponential function, we know that;
f(x) = a(b)^(x)
Now, we have;
f(x) = (4∛4)^(x)
Thus, looking at the options, option C is correct because;
In 4(∛16)^(2x), the base is (∛16)² and when we simplify it, we will get 4³(√4) because;
(∛16)² = √(16^(⅔))
>> 256^(⅓)
>> 4∛4
This is the same as our initial value.
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Which expression is equivalent to (x2 +9x – 1)(-4x + 3)?
-4x3- 33x2+31x – 3
4x3 +39x2-23x + 3
4x3+33x2-31x + 3
-4x3 -39x2+23x – 3
Answer:
- 4x³ - 33x² + 31x - 3------------------------------------------------------------------------------------------
Lines a and b are parallel. What is the measure of angle 3 if angle 6 measures 84
Answer:
angle 3 is 84 degree
Step-by-step explanation:
because angle 3 and angle 6 are equal
Explain how you can use a table or graph to find the slope. What does the slope
represent in the problem?
Glenda lives in Ohio, which has a sales tax of 5.5%. She just bought a grill whose full price was $220, but she got 40% off, because the store was having a sale. What was the total amount that Glenda paid?
A. $139.26
B. $92.84
c. $88.00
D. $132.00
Answer:A ($139.26)
Step-by-step explanation:
Plot the points (–4, –3), (–3, –5), (0, –4), (0, 3), and (–2, 3) and connect them to form a polygon. What is the length of the vertical side? 2 units 3 units 6 units 7 units
Answer:
7 units
Step-by-step explanation:
I plotted your points to form the polygon in the diagram below.
The vertical side joins the points (0 ,3) and (0, -4).
The vertical distance between them is
3 - (-4) = 3 + 4 = 7
The length of the vertical side is 7 units.
Answer:
7 units
Step-by-step explanation:
A website charges $3 for each movie you
download. They also charge a one-time sign-up
fee of $14.99
What is the input variable?
DONE
Answer: A. M, the number of movies.
Step-by-step explanation: I put A, and it was the right answer.
The leas been $31 on a movie ticket for two adults and three children the Smiths Station $26 on a movie ticket for two adults and two children what are the prices for an adult and child movie ticket
Answer:
Adults: $8
Children: $5
Step-by-step explanation:
First Step:
Let's represent The leas by: 2A + 3C = 31
Let's represent The Smiths Station by: 2A+2C=26
Second step:
Solve The leas expression for A → 2A + 3C = 31
[tex]A =\frac{31-3C}{2}[/tex]
Third step:
Replace A on The Smiths Station and solve for C:
2([tex]\frac{31-3c}{2}[/tex]) + 2C = 26
31-3C+2C = 26
31-C=26
31-26 = C
C= 5
Fourth step:
Replace C=5 in expression [tex]A =\frac{31-3C}{2}[/tex]
A = [tex]\frac{31-3*5}{2}[/tex] →→ A=[tex]\frac{31-15}{2}[/tex] →→ A=[tex]\frac{16}{2}[/tex] →→ A= 8
Find the area of the triangle below. Show as much work as possible. Label your answer appropriately
Answer:
[tex]\frac{5x^{2} }{6}[/tex]
Step-by-step explanation:
Given: Base of triangle= [tex]\frac{5x}{3}[/tex]
Height of triangle= x
Now, finding the area of triangle.
We know area of triangle= [tex]\frac{1}{2} \times base\times height[/tex]
Subtituting the value of base and height in the formula.
⇒[tex]Area\ of\ triangle= \frac{1}{2} \times \frac{5x}{3} \times x[/tex]
Solving it to find area of triangle
∴ [tex]Area\ of\ triangle= \frac{5x^{2} }{6}[/tex]
Hence, area of triangle is [tex]\frac{5x^{2} }{6}[/tex]
Answer:
A=5x^2/6
Step-by-step explanation:
An algebraic equation is an equation that includes:
a no variables
b. only one variable
С.
one or more variables
just numbers
Please select the best answer from the choices provided
Answer:
ç
Step-by-step explanation:
fufujphgfhjunkksbkbbdkdbkdldbdjdbdkdjjdkdmdljdbdivdjbdkd
You open a bank account with $100 and deposit 15 every week. Create an equation to model the total amount of money,y, in dollars, you will need to save after x months. How many weeks will it take to have $250?
Answer:
[tex]Y = 15x+ 100[/tex]
x = 10 months
Step-by-step explanation:
Given:
Initial deposit = $100
Weakly deposit = $15
Solution:
We need to create an equation where total amount is y is equal to initial deposit plus multiplication of weakly deposit and month x, so the equation is written as.
[tex]Y = 15x+ 100[/tex] ---------(1)
Where:
Y = Total amount
x = Number of months.
Second thing we need to find the month for y = $250
Now, we substitute y = 250 in equation 1.
[tex]250 = 15x+ 100[/tex]
[tex]15x=250-100[/tex]
[tex]15x =150[/tex]
[tex]x=\frac{150}{15}[/tex]
x = 10 months
Therefore, we need to required 10 months for $250.
what is the solution to this problem
x+5y=4
3x-7y=-10
To solve the given system of linear equations, we use the elimination method to find the solution, which is (x, y) = (-1, 1).
The student is asking how to find the solution to a system of linear equations:
x + 5y = 4
3x - 7y = -10
To solve this system, one can use the method of elimination.
Multiply the first equation by 3 and the second equation by 1 to align the coefficients of x.
The resulting equations are:
3x + 15y = 12
3x - 7y = -10
Subtract the second equation from the first to eliminate x:
22y = 22
Divide by 22 to find y:
y = 1
Substitute y = 1 into the original first equation:
x + 5(1) = 4
Solve for x:
x = -1
The solution to the system is (x, y) = (-1, 1).
Here’s another one I don’t understand, please give me the answer and explain how you got it
Answer:
39 degrees
Step-by-step explanation:
The angle of a straight line is 180 degrees. This is constant and will never change. You will add 57 and 84 to get 141 degrees for <LMP. Take 180-141 to get 39 degrees for <PMN
A polynomial function has a root of 0 with multiplicity 1, and a root of 2 with multiplicity 4. If the function
has a negative leading coefficient, and is of odd degree, which of the following are true?
The function is positive on (-0, 0).
The function is negative on (0, 2).
The function is negative on (2,).
The function is positive on (0,0).
Answer:
A, B, and C are true
Step-by-step explanation:
Using the Factor Theorem to find the function, the correct statement is:
The function is positive on (0,∞).
What is the Factor Theorem?The Factor Theorem states that a polynomial function with roots
x1, x2,...xn is given by:
f(x) = a(x-x1)(x-x2).....(x-xn)
In which a is the leading coefficient.
here, we have,
The described roots means that:
x1 = 0, x2 = x3= x4 =x5 = 2
Hence the function is:
f(x) = x(x - 2)^4
(x - 2)^4 is always positive, hence the sign depends on the sign of x, which means that the correct statement is:
The function is positive on (0,∞).
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What is the slope of y = 4 - 2.x?
Answer:
The slope of y=4-2x is -2.
(ASAP: Will give Brainly to whoever answers first) Which expression shows how 6⋅45 can be rewritten using the distributive property?
A. 6⋅4+6⋅5
B. 20⋅6+20⋅5
C. 6⋅40+6⋅5
D. 6⋅40+6
Answer:
C)
Step-by-step explanation:
We have an upcoming test on Logorithms and my teacher forgot to go over how to solve logorithms with different bases. How would you solve them? for example,
3log[tex]_{4}[/tex] 2 +log[tex]_{5}[/tex] 512
The value of [tex]3log_{4}(2)+log_{5}(512)[/tex] is about 5.376
Step-by-step explanation:
Let us revise some rules of logarithm
[tex]log(a)^{n}=n.log(a)[/tex] [tex]log_{b}(a)=\frac{log(a)}{log(b)}[/tex]∵ The expression is [tex]3log_{4}(2)+log_{5}(512)[/tex]
- By using the 1st rule in the first term
∵ [tex]3log_{4}(2)=log_{4}(2)^{3}[/tex]
∵ 2³ = 8
∴ [tex]log_{4}(2)^{3}=log_{4}(8)[/tex]
- By using the second rule
∵ [tex]log_{4}(8)=\frac{log(8)}{log(4)}=1.5[/tex]
∵ [tex]log_{5}(512)=\frac{log(512)}{log(5)}=3.876[/tex]
- Add the two answers
∴ [tex]3log_{4}(2)+log_{5}(512)[/tex] = 1.5 + 3.876
∴ [tex]3log_{4}(2)+log_{5}(512)[/tex] = 5.376
The value of [tex]3log_{4}(2)+log_{5}(512)[/tex] is about 5.376
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Find the equation of the line.
y=__x+__
PLEASE HELP THIS IS DUE TODAY!! D:
Answer:
aaf ducks chicks h.c Khan ffc blackjack wUtah's hands perches yachts
I’m a given rectangle the shorter side is 2 units less than the longer side. If we let the longer side be represented as the variable x create an expression that represents the perimeter of the rectangle.
Answer:
4(x-1)units
Step-by-step explanation:
In a given rectangle, the length of the rectangle is the shorter side while its breadth is the longer side.
Since we have 2 lengths and 2 breadths in a rectangle, the perimeter of the rectangle will be 2L+2x where
L is the length(shorter side) and x is the breadth (longer side).
According to the question, the shorter side(L) is 2 units less than the longer side(x). Mathematically,
L = x-2
Substituting L = x-2 into the formula of perimeter of a rectangle we have,
P = 2(x-2) + 2x
P = 2x-4+2x
P = 4x-4
P = 4(x-1)
The perimeter of the rectangle will be 4(x-1)units
mass of a spherical grape is 8.4 grams and
The volume of an object is equal to the ratio of its mass to density,
its density is 2 grams per cubic centimeter.
What is the radius of the grape? Round to the nearest tenth of a centimeter.
O 1.0 cm
O 1.5 cm
O 1.9 cm
O 21 cm
The radius of grape is 1 cm
Solution:
Given that,
The volume of an object is equal to the ratio of its mass to density
[tex]Volume = \frac{mass}{density}[/tex]
From given,
Mass = 8.4 grams
Density = 2 grams per cubic centimeter
Substituting in above formula,
[tex]Volume = \frac{8.4}{2} = 4.2\ cm^3[/tex]
Given is a spherical grape
The formula for volume of sphere is given as:
[tex]Volume = \frac{4}{3} \pi r^3[/tex]
Where, "r" is the radius of sphere
[tex]4.2 = \frac{4}{3} \times 3.14 \times r^3\\\\4.2 = 4.187 \times r^3\\\\r^3 = \frac{4.2}{4.187}\\\\r^3 = 1.003\\\\\text{Take cube root on both sides}\\\\r = 1.000999 \approx 1[/tex]
Thus the radius of grape is 1 cm
Answer:
1.0 cm
Step-by-step explanation:
If RSU~VST, then the triangles are similar by:
show work for brainlist
Step-by-step explanation:
[tex] \because \triangle \: RSU \sim \: \triangle VST \\ \\ \therefore \: \frac{RS}{VS} = \frac{7}{14} = \frac{1}{2} ....(1) \\ \\ \angle RSU \cong \: \angle VST ....(2) \\ (vertically \: opposite \: angles) \\ \\ \frac{US}{TS} = \frac{4}{8} = \frac{1}{2} ....(3) \\ \\ from \: equations \: (1) \: (2) \: and \: (3) \\ it \: is \: clear \: that: \\ \triangle \: RSU \sim \: \triangle VST\\ ..(by \:SAS\:similarity\:postulate) [/tex]
Thus, given triangles are similar by SAS similarity postulate.
When the triangles RSU and VST are said to be similar, it means the corresponding sides and angles are proportional and equal respectively, which is known as the Angle-Angle criterion for similarity.
Explanation:If the triangles RSU and VST are similar (RSU ~ VST), it means the corresponding sides and angles of the two triangles are proportional, and the corresponding angles are equal. This is also known as the Angle-Angle (AA) criterion for similarity. The order of the letters signifies the corresponding parts of the triangles. R corresponds to V, S to S, and U to T. So, the angles R and V are congruent, as are the angles U and T. Because we have two pairs of congruent angles, we can say that the triangles are similar by the AA criterion.
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What is the equation of the function that is graphed as line a?
y = 2x - 1
y = -x - 1
y = -x
y = 3x
Answer:
[tex]y = - x-1[/tex]
Step-by-step explanation:
The line a passes through th points (-1,0) and (0,-1)
The equation of line which is passes through the point [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is
[tex](y-y_1)= \frac{y_2-y_1}{x_2-x_1} (x-x_1)[/tex]
Therefore the equation of line which passes through the points (-1,0) and (0,-1)
is
[tex]y-0=\frac{-1-0}{0-(-1)} [x-(-1)][/tex] [ [tex]x_1 = -1, y_1= 0[/tex] [tex]x_2 = 0[/tex] and [tex]y_2 = -1[/tex]]
[tex]\Leftrightarrow y = -1 (x+1)[/tex]
[tex]\Leftrightarrow y = - x-1[/tex]
Answer:
b
Step-by-step explanation:
hellppp 70 pointsss
what is the equation of the quadratic function shown in the graph ?
f(x)=___ (x + ___) (x-___)
y=a.(X-x1)(X-x2)
x1 and x2 are x-intercepts
x1=-3
x2=1
other points: (-1,8) and (0,5)
y=a.(x+3).(x-1)
a=-2
f(x)= -2.(x+3)(x-1)
The equation is [tex]\[f(x) = -2 \cdot (x + 3)(x - 1)\][/tex]
How to get the equationGiven the quadratic equation in the form \(y =[tex]a \cdot (X - x_1)(X - x_2)\), where \(x_1\) and \(x_2\)[/tex]represent the x-intercepts, and the given x-intercepts are[tex]\(x_1 = -3\) and \(x_2 = 1\).[/tex]
Using the given x-intercepts [tex]\(x_1 = -3\) and \(x_2 = 1\)[/tex], the equation becomes [tex]\(y = a \cdot (x + 3)(x - 1)\).[/tex]
We are also provided with two other points: (-1, 8) and (0, 5).
We can substitute the point (-1, 8) into the equation to solve for \(a\):
[tex]When \(x = -1\) and \(y = 8\):\[8 = a \cdot ((-1) + 3)((-1) - 1)\]\[8 = a \cdot (2)(-2)\]\[8 = -4a\]\[a = -2\][/tex]
Therefore, the value of \(a\) is -2.
Substituting [tex]\(a = -2\) into the equation \(y = a \cdot (x + 3)(x - 1)\), we get:\[y = -2 \cdot (x + 3)(x - 1)\][/tex]
[tex]\[f(x) = -2 \cdot (x + 3)(x - 1)\][/tex]
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How can you solve the equation 4x= 2X-2 graphically?
If you invested $500 at 5% simple interest for 2 years, how much interest do you earn? Show work and answer in complete sentences to earn full credit.
If you invest $500 at 3% compounded monthly for 2 years, how much interest you do earn? Show work and answer in complete sentences to earn full credit.
Which would you rather do?
Therefore I earn $50 interest
Therefore I earn $30.88 interest.
I would do the first one.
Step-by-step explanation:
A.
Given , I invested $500 at 5% simple interest for 2 years.
P=$500, r =5% and t = 2 years
[tex]Interest (I) =\frac{P \times r \times t}{100}[/tex]
[tex]=\$\frac{500 \times 5 \times 2}{100}[/tex]
=$50
Therefore I earn $50 interest.
B.
Given , I invested $500 at 3% compounded monthly for 2 years.
P=$500, r =3% = 0.03 and t = 2 years
[tex]Amount (A) =P(1+\frac{r}{n})^{nt}[/tex]
[tex]=\$500(1+\frac{0.03}{12})^{ 2\times 12}[/tex]
=$530.88
Interest = $(530.88-530) = $30.88
I would do the first one.
What is the approximate area of a circle with a diameter of 14 inches
if A's income is 25% less than that of B, then how much percent is B's income more than that of A ?
Answer:
125%
Step-by-step explanation:
this is because the difference is 25% so b is 125% more than a
Given: Angle T S R and Angle Q R S are right angles; Angle T Is-congruent-to Angle Q
Prove: Triangle T S R Is-congruent-to Triangle Q R S
Triangles T S R and Q R S share side S R. Angles T S R and S R Q are right angles. Angles S T R and S Q R are congruent.
Step 1: We know that Angle T S R Is-congruent-to Angle Q R S because all right angles are congruent.
Step 2: We know that Angle T Is-congruent-to Angle Q because it is given.
Step 3: We know that Line segment S R is-congruent-to line segment R S because of the reflexive property.
Step 4: Triangle T S R Is-congruent-to Triangle Q R S because
of the ASA congruence theorem.
of the AAS congruence theorem.
of the third angle theorem.
all right triangles are congruent.
Answer:
B. of the AAS congruence theorem.
Step-by-step explanation:
Triangles TSR and QRS share side SR
SR=RS
Angle TSR and Angle QRS are right angles, so
∠S= ∠R
Angle T Is-congruent-to Angle Q, so
∠T= ∠Q
From these data, we have one congruent side and two congruent angles. The possible congruence theorem that we can apply will be either ASA or AAS. In the ASA theorem, the congruence side must be between the two congruent angles.
The congruence side required for the ASA theorem for this triangle is ST = RQ. It is wrong because the congruent side we have is SR=RS. The correct option is the AAS theorem.
A metalworker has a metal alloy that is 15% copper and another alloy that is 75% copper. How many kilograms of each alloy should the metalworker combine to create 120 kg of a 51% copper alloy?
48 kilograms of 15 % copper is combined with 72 kilograms of 75 % copper to create 120 kg of a 51% copper alloy
Solution:
Let "x" be the kilograms of 15 % copper
Then, (120 - x) be the kilograms of 75 % copper
Then, according to question,
"x" kilograms of 15 % copper is combined with (120 - x) kilograms of 75 % copper to create 120 kg of a 51% copper alloy
Thus we frame a equation as:
15 % of x + 75 % of (120 - x) = 51 % of 120
Solve the equation for "x"
[tex]15 \% \times x + 75 \% \times (120-x) = 51 \% \times 120\\\\\frac{15}{100} \times x + \frac{75}{100} \times (120-x) = \frac{51}{100} \times 120\\\\0.15x + 0.75(120-x) = 0.51 \times 120\\\\0.15x + 90 - 0.75x = 61.2\\\\0.6x = 90 - 61.2\\\\0.6x = 28.8\\\\Divide\ both\ sides\ by\ 0.6\\\\x = 48[/tex]
Thus 48 kilograms of 15 % copper used
Then, (120 - x) = (120 - 48) = 72
Thus, 72 kilograms of 75 % copper is used
Where do you add the parentheses in this equation?
3 + 6 × 5 + 4÷2 - 7
Answer: to get to what answer
Step-by-step explanation: