The simplified expressions are:
12x + 3 − 4x + 7 = 8x + 10
8 − 7x − 13 + 2x = −5x − 5
−3x − 18 + 5x − 2 = 2x − 20
What is an expression?A term is a single mathematical phrase. It might consist of only one variable—a letter—one number—positive or negative—or several variables multiplied but never added or subtracted. A number is placed in front of some nouns that have variables. Coefficients are numbers that come before phrases.
To simplify each expression, we combine like terms:
Expression 1:
12x + 3 − 4x + 7 = (12x − 4x) + (3 + 7)
12x + 3 − 4x + 7 = 8x + 10
Expression 2:
8 − 7x − 13 + 2x = (−7x + 2x) + (8 − 13) = −5x − 5
Expression 3:
−3x − 18 + 5x − 2 = (−3x + 5x) + (−18 − 2) = 2x − 20.
Therefore, the simplified expressions are:
12x + 3 − 4x + 7 = 8x + 10
8 − 7x − 13 + 2x = −5x − 5
−3x − 18 + 5x − 2 = 2x − 20
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which pair of triangles is congruent by AAS?
Answer:
Triangles PQT and RQT are congruent (option D)
Step-by-step explanation:
The AAS or Angle- Angle- Side Theorem says that if two angles and any side of one triangle are congruent to two angles and any side of another triangle, then the triangles are congruent.
So, triangles PQT and RQT are congruent.
Both triangles have angle Q as right angle and angle P and R are also equal. And both have side QT common.
So, these are congruent via AAS.
What are MODE,MEDIAN
EXPLAIN pls.
after examining the figure shown here, Daniel determines that FG/TU= EF/ST wich theorem or collary allowed him to draw that conclusion?
A. Side-splitting theorem
B. two- transversal proportionality corollary
C.Proportional Altitudes theorem
D. Proportional Medians Theorem
The Proportional Medians Theorem states:If two triangles are similar, then the ratio of the lengths of two corresponding medians is the same as the ratio of the lengths of two corresponding sides.
A median of a triangle is a line segment joining a vertex to the midpoint of the opposing side, bisecting it.
It is given the two triangles are similar.FG and TU are the medians of the triangle .
By Proportional Medians Theorem ratio of the lengths of two corresponding medians is the same as the ratio of the lengths of two corresponding sides.
So [tex] \frac{FG}{TU} =\frac{EF}{ST} [/tex]
Option D. Proportional Medians Theorem is the right answer.
Write the equation in slope-intercept form of the line that has a slope of -5 and a y-intercept of 2.
Then, the dot ran from −34 to −66. What distance did it cover? If this run took the dot 5 minutes, what was its average speed?
Final answer:
The dot covered a distance of 32 units when it ran from -34 to -66. Assuming the distance is measured in meters, and the dot took 5 minutes (300 seconds) to cover this distance, the average speed would be 0.1067 m/s.
Explanation:
To determine the distance the dot covered when it ran from -34 to -66, we need to calculate the absolute value of the difference between the two points. The formula for distance in this case is |final position - initial position|, so the distance covered = |-66 - (-34)| = |-66 + 34| = | -32 | = 32 units.
Now, to determine the average speed of the dot, we divide the total distance traveled by the time it took to cover that distance. Given that it took the dot 5 minutes to cover the distance, we convert minutes to seconds because speed is typically measured in meters per second (m/s) in physics. There are 60 seconds in a minute, so 5 minutes is 300 seconds. Therefore, the average speed is distance/time = 32 units / 300 seconds.
The exact units of measurement for distance have not been specified in the question, but assuming the distance is in meters (m), the average speed would be calculated as 32 m / 300 s = 0.1067 m/s.
What is the quotient (2x3 − 13x2 + 16x − 5) ÷ (x − 5)?
2x2 − 3x + 1
2x2 + 3x − 1
2x2 − 3x − 1
2x2 + 3x + 1
Answer:
Correct choice is A
Step-by-step explanation:
1 step. Multiply [tex]x-5[/tex] by [tex]2x^2[/tex] to get [tex]2x^3-10x^2[/tex] and subtract this polynomial from the polynomial [tex]2x^3-13x^2+16x-5:[/tex]
[tex]2x^3-13x^2+16x-5-(2x^3-10x^2)=2x^2-13x^2+16x-5-2x^3+10x^2=-3x^2+16x-5.[/tex]
2 step. Multiply [tex]x-5[/tex] by [tex]-3x[/tex] to get [tex]-3x^2+15x[/tex] and subtract this polynomial from the polynomial [tex]-3x^2+16x-5:[/tex]
[tex]-3x^2+16x-5-(-3x^2+15x)=-3x^2+16x-5+3x^2-15x=x-5.[/tex]
3 step. Multiply [tex]x-5[/tex] by [tex]1[/tex] to get [tex]1[/tex] and subtract this polynomial from the polynomial [tex]x-5:[/tex]
[tex]x-5-(x-5)=x-5-x+5=0.[/tex]
Then
[tex]2x^3-13x^2+16x-5=(x-5)(2x^2-3x+1).[/tex]
Answer:
Correct answer is 2x2 − 3x + 1
Step-by-step explanation:
Katie decides to sell lemonade to make some money. Katie’s mom said she will double the amount of money she makes. If Katie sells 66 cups of lemonade at $0.75 each, how much money does she make?
The answer is $99! :)
Shari plans to bake cherry pies and sell them for $9.50 each how much pies dose she have to sell to make $100 profit
Write three to five sentences explaining which levels of production provide Alonzo’s Cycling with the maximum profit.
The optimal level of production for Alonzo's Cycling is at the point where the profit reaches its peak before starting to decline with further increases in production. This is the level of production that Alonzo's Cycling should aim for to achieve the marginal profit.
To determine which levels of production provide Alonzo's Cycling with the maximum profit, one must consider both the fixed costs and the variable costs associated with production.
The profit for each level of production is calculated by subtracting the total costs (fixed costs plus variable costs) from the total revenue generated by sales. The level of production at which profit is maximized is where the difference between total revenue and total costs is the greatest.
This can be found by analyzing the marginal cost and marginal revenue of production. When marginal revenue equals marginal cost, and if the additional production leads to a decrease in profit, that is the point of maximum profit.
Beyond this point, producing more units would decrease the total profit due to the law of diminishing returns, where the cost of producing additional units exceeds the revenue they generate.
Therefore, the optimal level of production for Alonzo's Cycling is at the point where the profit reaches its peak before starting to decline with further increases in production. This is the level of production that Alonzo's Cycling should aim for to achieve the maximum profit.
For what values of x is x2 + 2x = 24 true?
–6 and –4
–4 and 6
4 and –6
6 and 4
Answer:
C. is the correct answer i took the quiz
Step-by-step explanation:
The number of animals in a population is 775, and it increases by of 51% each year.
a. Model the situation with an exponential function.
b. Find how many animals there will be in 10 years.
c. How many years will it take for the population to become 1150.
Show all work!
Answer(a):
Exponential growth formula is given by
[tex]A=P(1+r)^t[/tex]
Where preset population = P= 775
Rate of increase = r = 51% = 0.51
t= number of years
A= Future value.
Plug these values into above formula:
[tex]A=775(1+0.51)^t[/tex]
[tex]A=775(1.51)^t[/tex]
Hence required exponential function is [tex]A=775(1.51)^t[/tex]
Answer(b):
plug t=10 years
[tex]A=775(1.51)^t=775(1.51)^{10}=775(61.6267795034)=47760.7541151[/tex]
which is approx 47761.
Answer(c):
Plug A=1150
[tex]1150=775(1.51)^t[/tex]
[tex]\frac{1150}{775}=(1.51)^t[/tex]
[tex]\ln(\frac{1150}{775})=t*\ln(1.51)[/tex]
[tex]0.394654192004=t*0.412109650827[/tex]
0.957643654334=t
Which is approx 1 year.
Type 3xxyyy using exponents.
helppppppppppppppppppppppppp
What are the zeros of the quadratic function f(x) = 2x2 + 8x – 3? x = –2 – and x = –2 + x = –2 – and x = –2 + x = 2 – and x = 2 + x = 2 – and x = 2 +
Write the equation of the circle with center (0, 0) and (5, 2) a point on the circle.
In triangle QRS, QR is congruent to SR and RT bisects QS. What justification can you give for QRT congruent to SRT and give the Triangle Congruence Postulate that supports your reason.
Answers:
Midpoint Theorem, SSS
Given, SSS
Definition of a segment bisector; SSS
Definition of an isosceles triangle, SAS,
Solve the system algebraically. Check your work.
4x + 2y = 10
3x + 2y = 6
ANSWER: {(
a0)}
Answer:
x = 4 and y = -3.
Step-by-step explanation:
Given : 4x + 2y = 10 and 3x + 2y = 6.
To find : Solve the system algebraically. Check your work.
Solution : We have given that
4x + 2y = 10 ----(1)
3x + 2y = 6.------(2)
Subtracting equation 2 from 1
4x + 2y = 10
(-)3x + (-)2y =(-) 6.
_____________
x + 0 = 4
x =4
Plug x = 4 in equation 1
4 (4) + 2y = 10.
16 + 2y = 10.
2y = 10 -16.
2y = -6.
On dividing by 2 both sides
y = -3.
Check:
Plug the values x =4 , y =-3 in equation 1
4 (4) + 2 ( -3) = 10
16 -6 = 10
10 =10
Verify,
Therefore, x = 4 and y = -3.
The number 64 is a perfect
A.square and cube
B.square
C.cube
What is 1,400,000 multiplied by 3.5x10^5 expressed in scientific notation?
The answer is [tex]\( 4.9 \times 10^{11} \)[/tex].
To solve the given mathematical problem, we will multiply the two numbers and then express the result in scientific notation.
First, let's multiply 1,400,000 by 3.5x10^5 without converting them to scientific notation:
[tex]\[ 1,400,000 \times 3.5 \times 10^5 \][/tex]
[tex]\[ = 1400000 \times 3.5 \times 10^5 \][/tex]
[tex]\[ = 4900000 \times 10^5 \][/tex]
Now, we have the product 4900000. To express this in scientific notation, we must write it as a number between 1 and 10 multiplied by a power of 10. The number 4900000 can be written as 4.9 followed by 11 zeros, which in scientific notation is [tex]\( 4.9 \times 10^{11} \)[/tex].
Therefore, the final answer, expressed in scientific notation, is:
[tex]\[ \boxed{4.9 \times 10^{11}} \][/tex]
Find the first four terms of the given sequence tn = (-1)n(n).
A.
-1, -2, -3, -4
B.
-1, 2, -3, 4
C.
1, ½, 2/3, ¾
D.
1, 2, 3, 4
The distance formula is d = rt. A trip of 92 miles traveled at 65 mph will take 1.35 hours.
A. True
B. False
13 Pts
PLEASE SOMEONE HELP ME WITH THIS QUESTION
PLZ EXPLAIN
THANK U
Parallelogram DEFG has been rotated. Which statements are correct? Check all that apply.
In geometry, rotation involves turning of an object about a center. The statements that are correct are:
point F [tex]\to[/tex] point F'point D of the preimage corresponds to point D' of the imageparallelogram DEFG maps to parallelogram D'E'F'GWhen rotation is applied to a shape, the orientation of the shape will change; however the corresponding points will be unchanged.
This means that:
DEFG will be mapped to D'E'F'GPoints D, E, F and G will correspond to points D', E', F' and G'.Hence, the true statements are: (a), (c) and (e)
Read more about rotation at:
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y+15 <3 for inequality
Haruka hiked several kilometers in the morning. She only hiked 666 kilometers in the afternoon, which was 25\%25%25, percent less she had hiked in the morning.How many kilometers did Haruka hike in all?
Answer:
its 14 in all actually
Step-by-step explanation:
Which of the following forms of bonds has the least risk
Municipal bonds
Below investment grade bonds
Corporate bonds
Treasury bonds
Treasury Bonds is the correct answer.
Treasury Bonds has the least risk as these bonds are issued and backed by the United States federal government. They are credit-risk free as they have practically no default risk and thus the safest bonds to buy. These are issued by the government to finance its budget deficits.
what is 85% of 2500 meters
HELP FAST - given that ig= x-4 , ik = 9x-19 and jk = 5x+12 find ij, jk and ik
Answer:
THIS IS WRONG I TOOK THE TEST... DONT KNOW THE ANSWER STILL.
Step-by-step explanation:
What is the value of b in the equation (yb) 4= 1/y24
Answer:
The value of b is [tex]\frac{1}{y^7}[/tex].
Step-by-step explanation:
Here the given expression is,
[tex](yb)^4=\frac{1}{y^{24}}[/tex]
[tex]y^4b^4=\frac{1}{y^{24}}[/tex] ( Using [tex](ab)^m=a^mb^m[/tex] on left side )
[tex]y^4b^4y^24 = 1[/tex] ( By cross multiplication )
[tex]y^{4+24}b^4=1[/tex] ( Using [tex]a^ma^n=a^{m+n}[/tex] on left side )
[tex]y^{28}b^4=1[/tex]
[tex]b^4=\frac{1}{y^{28}}[/tex]
[tex]b=(\frac{1}{y^{28}})^{\frac{1}{4}}[/tex] ( [tex]a^m=b^n\implies a=b^\frac{n}{m}[/tex] )
[tex]b=\frac{1^{\frac{1}{4}}}{(y^{28})^\frac{1}{4}}[/tex] ( [tex](\frac{a}{b})^m=\frac{a^m}{b^m}[/tex] )
[tex]b=\frac{1}{y^{28\times \frac{1}{4}}}[/tex] ( [tex](a^m)^n=a^{m\times n}[/tex] )
[tex]b=\frac{1}{y^7}[/tex]
Answer:
It is -6
Step-by-step explanation:
Sketch the following to help answer the question. Kite QRST has a short diagonal of QS and a long diagonal of RT. The diagonals intersect at point P. Side QR = 5 m and diagonal QS = 6 m. Find the length of segment RP.
3 m
4 m
5 m
6 m
Answer:
Given: Kite QRST has a short diagonal of QS and a long diagonal of RT. The diagonals intersect at point P. Side QR = 5m and diagonal QS = 6m.
Since, diagonals of kite bisect each other, thus QP=6m
Now, in ΔPQR, we have
(QR)²= (RP)²+(QP)²
(5)²= (3)²+(RP) ²
25=9+(RP)²
25-9= (RP)²16= (RP)²
RP= 4m
Therefore, the length of segment RP is 4m.
Step-by-step explanation: