Answer:
6x^2 + 3x - 7.
Step-by-step explanation:
(6x^2 - 2x) + (5x - 7)
= 6x^2 - 2x + 5x - 7 Adding like terms we get:
6x^2 + 3x - 7.
Final answer:
To simplify the algebraic expressions (6x²-2x)+(5x-7), you combine like terms to get the final expression 6x² + 3x - 7.
Explanation:
The student's question involves adding and simplifying algebraic expressions. To add the expressions (6x²-2x)+(5x-7), you need to combine like terms. Like terms are those terms that contain the same variable raised to the same power. Here is the process step-by-step:
Identify like terms in both expressions.Combine like terms by adding their coefficients. For the terms, 6x² and 0x² (the second expression doesn't have an x² term, so it's 0x²), add 6 + 0 = 6. For the terms -2x and 5x, add -2 + 5 = 3.Finally, the constant terms -7 and 0 (again, no constant term in the first expression) are combined by adding -7 + 0 = -7.The resulting simplified expression is 6x² + 3x - 7.
Find the distance between -18 and 8 using the ruler postulate
[tex]\bf \underset{\textit{\Large 18 + 8 = 26 units}}{\stackrel{\textit{18 units}}{\boxed{-18}\rule[0.35em]{10em}{0.25pt}}0\stackrel{\textit{8 units}}{\rule[0.35em]{5em}{0.25pt}\boxed{8}}}[/tex]
Answer:
26Step-by-step explanation:
The ruler Postulate:
the distance between number A and number B
AB = |B - A|
We have A = -18 and B = 8. Substitute:
|8 - (-18)| = |8 + 18| = |26| = 26
what will be the circumference of a circle if the area is 64cm
Given that area of circle is 64cm we can assume we will need to first find radius and then calculate circumference.
First we know that area of a circle is [tex]A=\pi r^2[/tex] hence [tex]r=\sqrt{\dfrac{A}{\pi}}[/tex]
We can now put in our area,
[tex]r=\sqrt{\dfrac{64}{\pi}}\approx20.37[/tex]
Then we use the formula for circumference,
[tex]C=2\pi r\Longrightarrow C=2\pi\cdot20.37\approx\boxed{128\mathbf{cm}}[/tex]
Hope this helps.
r3t40
for a baseball team the ratio of wins and ties and losses is 4:3:1 if the team has won 12 games how many games have they lost
Answer: 3 losses
Step-by-step explanation: The win to loss ratio is 4:1. Their losses are 1/4 of their wins. Multiply 12, their number of wins, by 1/4.
12 x 1/4 = 3
They have lost 3 games.
Given the ratio of 4:3:1 for wins, ties, and losses, and the information that the team has won 12 games, you calculate that '1 part' of the ratio equals 3 games by dividing 12 by 4. As losses are represented by '1 part' in the ratio, the team has lost 3 games.
Explanation:In this baseball team scenario, the ratio of wins to ties to losses is 4:3:1 respectively. You know that the team has won 12 games. In a ratio, every part represents something equivalent, so we need to find what '1 part' is. Since '4 parts' represents 12 wins, you divide 12 by 4 to get '1 part', which is 3 games. Therefore, since losses represent '1 part' of your ratio, the team has lost 3 games.
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A student was given the following diagram and asked to prove that 21 4 22.
What would be the reason for the third step in the proof?
Given: Line A and line Bare parallel.
Prove: 21 22
Answer: vertical angles are congruent.
Step-by-step explanation:
Answer: Vertical angles are congruent.
Step-by-step explanation:
Given : Line A and line Bare parallel.
To prove : ∠1≅∠2
We know that when two lines crosses each other, they make vertically opposite angles.
In picture , we have ∠2 and ∠3 are vertical angles.
And it is known that the vertical angles are congruent.
Therefore, ∠2 ≅ ∠3
So the correct reason to the statement "∠2 ≅ ∠3" is "Vertical angles are congruent."
What is the slope of the line?
y+5=2(x+1)
A. 1/5
B. 2/5
C. 2
D. 1/2
Rewrite the equation in slope-intercept form:
y+5=2(x+1)
Use the distributive property:
y+5 = 2x +2
Subtract 5 from each side:
y = 2x -3
The slope is the value with the X
The slope = 2
Answer:
2.5
Step-by-step explanation:
2(x+1)=y+5
2x+1=y+5
y+5=6
in addtion y can be add
so we have now...
2x+1=6
minus 1 from 6 and get 5
2x=5
5 divide by 2 = 2/5
Hope it helps
Simplity
[tex]( \sqrt{5} )( \sqrt[3]{5} )[/tex]
A.
[tex] 5\frac{5}{6} [/tex]
B.
[tex]5 \frac{1}{6} [/tex]
C.
[tex]5 \frac{2}{3} [/tex]
D.
[tex]5 \frac{7}{6} [/tex]
Answer:
A.
5 ^ (5/6)
Step-by-step explanation:
5 ^ (1/2) * 5 ^ (1/3)
We know that a^b * a^ c = a ^ (b+c)
5 ^ (1/2 + 1/3)
5^ (3/6+2/6)
5^ (5/6)
Answer:
5^(5/6)
Step-by-step explanation:
5^(1/2)*5^(1/3)=5^(1/2+1/3)=5^(5/6)
When multiplying numbers with same base you add the exponents.
Simplify the expression and then evaluate it for the given value of the variable:
12+7x−(1−3) for x=−1.7
Answer:
25.9
Step-by-step explanation:
12+7x−(1−3) (evaluate parentheses first)
= 12+ 7x - (-2)
= 12+ 7x + 2
= 14+ 7x
When x = 1.7, equation becomes
14+ 7(1.7)
= 14 + 11.9
= 25.9
Convert the improper fraction into a mixed number. 6 1/8 divided by 1 3/4
Answer:
4 19/32
Step-by-step explanation:
convert into improper fractions
6 1/8= 49/8
1 x 3/4= 3/4
49/8 x 3/4 = 147/32
reduce into mixed number
4 19/32
To convert the mixed numbers 6 1/8 and 1 3/4 to improper fractions, resulting in 49/8 and 7/4, respectively. Then, perform the division as multiplication with the reciprocal of the second fraction, which yields 3 1/2.
Explanation:Firstly, it's essential to convert the mixed numbers into improper fractions. The given mixed numbers are 6 1/8 and 1 3/4. We can convert 6 1/8 to an improper fraction by multiplying 6 (the whole number) by 8 (the denominator) and then adding 1 (the numerator) to get 49/8. With 1 3/4, we multiply 1 (the whole number) by 4 (the denominator), then add 3 (the numerator), which gives us 7/4.
Now, the division 49/8 ÷ 7/4 can be performed. To divide fractions, we multiply the first fraction by the reciprocal of the second. Therefore, we will multiply 49/8 by 4/7. The result is 196/56. This simplifies to 3 1/2 when converted back to a mixed number.
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Subtract 15mn - 22m +2n from 14mn - 12m +7n.
Answer:
[tex]\large\boxed{-mn+10m+5n}[/tex]
Step-by-step explanation:
[tex](14mn - 12m +7n)-(15mn - 22m +2n)\\\\=14mn-12m+7n-15mn-(-22m)-2n\\\\=14mn-12m+7n-15mn+22m-2n\qquad\text{combine like terms}\\\\=(14mn-15mn)+(-12m+22m)+(7n-2n)\\\\=-mn+10m+5n[/tex]
PLEASE HUREY IXL QUESTION
Answer:
5 12/24 -> -0.5 -> -5 6/20
Step-by-step explanation:
Negatives are lasts and positive goes first! Since the order is greatest to least.
-5 6/20 is less than -0.5 because *think of a number line -5 6/20 will be all the way to the left because it large in negative value
Solve please I’m desperate
Answer:
-2
Step-by-step explanation:
[tex]\sqrt{16+9}-(\sqrt{16}+\sqrt{9})[/tex]
We are going to use PE(MD)(AS) to evaluate.
We are going to do the operations in the grouping symbol.
A grouping symbol is anything that operations grouped together in it like that first square root.
[tex]\sqrt{25}-(\sqrt{16}+\sqrt{9})[/tex]
We can also perform the operation inside the other grouping symbols ().
But it has addition and square roots. The square roots come first then the addition.
Now the square roots can be kind of though as exponents and actually you could think of something like [tex]\sqrt{9}[/tex] as [tex]9^{\frac{1}{2}}[/tex].
Anyways, this gives us:
[tex]\sqrt{25}-(4+3)[/tex]
Now the addition inside the ( ):
[tex]\sqrt{25}-(7)[/tex]
Now we have square root and subtract left. The square root part will come first and then the subtract:
[tex]5-7[/tex]
[tex]-2[/tex]
A bag has 4 yellow, 6 red, 2 green, and 8 purple marbles. What is the probability of picking a purple marble, not replacing it, and then picking another purple marble?
A.12/95
B.1/190
C.14/95
D.2/25
Answer:
Step-by-step explanation:
Add all 8/20 marbles multiply Times 5 40/100 = 40%
Answer =40%
How do you do 6 divided by 11 bus stop method, please explain the steps?
A pair of parallel lines is cut by a transversal, as shown below.
A (x=y)
By vertical angles, the angle opposite y is equal to y, and x = y because it would transform isometrically onto x (as can be seen by the parallel lines because the transversal can be treated as parallel to itself)
What is the area of the sector having ....
Answer:
D) 160π/3 units²
Step-by-step explanation:
Step 1: Write the formula for area of sector
Area of sector = 1/2 x r² x angle in radians
Step 2: Substitute values in the formula
Area of sector = 1/2 x 8² x 5π/3
Step 3: Solve to find the value of area of sector
Area of sector = 160π/3 units²
Therefore, the correct option is D
!!
A coffee distributor needs to mix a(n) Organic Free Trade coffee blend that normally sells for $8.30 per pound with a Rift Valley coffee blend that normally sells for $13.90 per pound to create 80 pounds of a coffee that can sell for $10.82 per pound. How many pounds of each kind of coffee should they mix?
Answer: They must mix
_____ pounds of the Organic Free Trade Blend
______ pounds of the Rift Valley Blend.
Round your answers to the nearest whole number of pounds.
Answer:
They must mix
_44_ pounds of the Organic Free Trade Blend
_36__ pounds of the Rift Valley Blend.
Round your answers to the nearest whole number of pounds.
Step-by-step explanation:
The formula you are using is:
Total price * total amount= Organic price * amount organic + Rift price * amount rift
First we will simplify it by calculating it for each pound of final mix.
So this is 10.82 * 1 = 8.30 * x + 13.90 * y.
Since the total amount should be 1 pound, you could say that x+y = 1, or that y = 1-x.
If you fill this in you get
10.82 * 1 = 8.30 * x + 13.90 * (1-x)
Which you can solve as follows.
10.82 * 1 = 8.30 * x + 13.90 - 13.90x
10.82 = 13.90 - 5.6x
-5.6x = -3.08
x = -3.08/-5.6 = 0.55
So you will need 0.55 of Organic coffee for each pound of the final mix.
So in total you will need 0.55 * 80 = 44 pounds of Organic coffee.
So you need 80 - 44 = 36 pounds of Rift Valley Coffee.
To produce the desired coffee blend, the coffee distributor needs to mix approximately 51 pounds of Organic Free Trade Blend with 29 pounds of Rift Valley Blend.
Explanation:This problem falls under a category of Mathematics known as Algebra. We'll start by defining two variables: x, representing the weight of the Organic Free Trade Blend, and y, representing the weight of the Rift Valley Blend.
From the total weight of the mix, we get our first equation: x + y = 80
Then, by weighing the cost of each part against the total, we get our second equation: 8.3x + 13.9y = 10.82 * 80.
Solving these two equations simultaneously, we find that approximately 51 pounds of Organic Free Trade and 29 pounds of Rift Valley blend are needed to create the desired mixture.
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3y2+5y-(4y2+5)-8y2-(-7-3y2)
Answer:
[tex]-6y^2+5y+2[/tex]
Step-by-step explanation:
I'm assuming you want to simplify:
[tex]3y^2+5y-(4y^2+5)-8y^2-(-7-3y^2)[/tex]
Distribute to get rid of the ( ):
[tex]3y^2+5y-4y^2-5-8y^2+7+3y^2[/tex]
Put like terms together:
[tex]3y^2-4y^2-8y^2+3y^2+5y-5+7[/tex]
Combine the like terms:
[tex]-6y^2+5y+2[/tex]
If p(x)=2x^2 -4 and q(x)=x-3, what is (p*q)(x)
Answer:
2x^3 - 6x^2 - 4x + 12.
Step-by-step explanation:
(p*q) (x) = (2x^2 - 4)(x - 3)
= 2x^3 - 6x^2 - 4x + 12.
For this case we have the following functions:
[tex]p (x) = 2x ^ 2-4\\q (x) = x-3[/tex]
We must find [tex](p * q) (x).[/tex] For definition, we have to:
[tex](p * q) (x) = p (x) * q (x)[/tex]
So:
[tex](p * q) (x) = (2x ^ 2-4) (x-3)[/tex]
We apply distributive property:
[tex](p * q) (x) = 2x ^ 3-6x ^ 2-4x + 12[/tex]
Answer:
[tex](p * q) (x) = 2x ^ 3-6x ^ 2-4x + 12[/tex]
Point C is reflected across the y-axis.
Point C is reflected across the y-axis.
Which point represents the reflection?
A. Point D
B. Point E
C. Point G
D. Point M
To describe a specific arith-
metic sequence, Elijah wrote
the recursive formula:
[ f(0) = 30
f(n+1)=f(n)+7
Write a linear equation that
models this sequence
Answer:
[tex]f(x) = 7x + 30[/tex]
Step-by-step explanation:
We need at least two points to write the equation of a straight line.
The recursive formula that Elijah wrote is:
[tex]f(0) = 30[/tex]
[tex]f(n + 1) = f(n) + 7[/tex]
When we substitute n=0, we get:
[tex]f(0 + 1) = f(0) + 7[/tex]
[tex]f(1) = 30 + 7[/tex]
[tex]f(1) = 37[/tex]
The points (0,30) and (1,37) lies on this line.
The equation of this line is of the form:
[tex]f(x) = mx + b[/tex]
where b =30 is the y-intercept and m=7 is the slope.
We plug in these values to get:
[tex]f(x) = 7x + 30[/tex]
Note that the slope of the line is equal to the common difference of the Arithmetic Sequence.
You could also use the two points to find the slope:
[tex]m = \frac{37 - 30}{1 - 0} = 7[/tex]
A population of 1,000 bacteria is treated with a medicine and begins to die 5% each hour. How can the bacteria population be determined after a number of hours, ℎ?
a. (ℎ)=0.95(ℎ+1,000)
b. (ℎ)=1,000·ℎ^0.95
c. (ℎ)=0.95ℎ+1,000
d. (ℎ)=1,000·0.95^ℎ
Answer:
[tex]1000(.95)^h[/tex]
Step-by-step explanation:
[tex]h(t)=A \cdot B^t[/tex] is an exponential equation where A is the beginning amount and B is the rate that the population grows or dies.
So we start with 1000 bacteria, they are giving us A.
The bacteria population is decreasing because they are dying 5% each hour.
So that is after the first hour we have 1000-.05(1000) or 1000(1)-1000(.05)=1000(1-.05)=1000(.95).
We will keep multiplying by .95 per hour. 0.95 is the repeated factor.
That is the function is [tex]1000(.95)^h[/tex].
If you let h=0 which means 0 hours has happened, you will see the bacteria is 1000 as desired. 1000(.95)^0=1000(1)=1000.
The bacteria population can be determined using the formula (ℎ)=1,000·0.95^ℎ, which represents exponential decay at a rate of 5% each hour. therefore, option D is correct
Explanation:To determine the bacteria population after a number of hours, we need to use the formula (ℎ)=1,000·0.95^ℎ. This formula represents the exponential decay of the bacteria population at a rate of 5% per hour. The initial population is 1,000, and each hour the population decreases by 5% (or 0.95).
For example, after 1 hour, the population can be calculated as (1,000)·(0.95)^1 = 950 bacteria. After 2 hours, the population would be (1,000)·(0.95)^2 = 902.5 bacteria, and so on.
Therefore, the correct answer is (d) (ℎ)=1,000·0.95^ℎ.
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HELPP MEEEEEEEE pleaasssssssseeeeee
Answer: Not sure if I’m correct but I’m pretty sure
x = 90
Step-by-step explanation:
Total figure = 360 degrees
107+72+91=270
360-270=90
Answer:
x=90 degrees
Step-by-step explanation:
The sum of the 4 angles of a quadrilateral add to 360 degrees
Add the 4 angles
72+107+x+91 = 360
Combining like terms
270 +x = 360
Subtract 270 from each side
270+x-270 = 360-270
x = 90
The unknown angle is 90
Brayden starts out riding his bike for 5 kilometers. He stops and takes a turn and rides his bike
14 more kilometers. After resting, he takes another road that will lead him back toward his starting
point. He is only on that road for 8 kilometers. Is it possible that he made it back to his starting point
Explain your answer and include a sketch to support your argument.
Part I: Sketch the route that represents Brayden's route. Label the distance traveled for each
portion of his ride.
Part ll: Is it possible that he made it back to his starting point?
Answer:
it is not possible that Brayden made it back to his starting point.
Step-by-step explanation:
Part 1: Step 1: Define the map scale
REAL:MAP
1 km : 1 cm
5 km : 5 cm
14 km : 14 cm
8 km : 8 cm
Step 2: Sketch the map according to the scale.
Shown on the map in the picture attached.
Part 2: As shown on the map, it is not possible that Brayden made it back to his starting point.
!!
Mr. Jones asks his students to generate the next two numbers in the sequence beginning –5.5, 11, ....
Taquan suggests that the sequence is geometric and the next two numbers are –22 and 44. Julia suggests that the sequence is arithmetic and the next two numbers are 27.5 and 44.
Which best explains which student is correct?
Taquan is correct. When the signs change in a sequence, the sequence is geometric. Each successive term is generated by multiplying by –22 .
Julia is correct. When the numbers alternate between decimals and whole numbers, the sequence is arithmetic. Each successive term is generated by adding 16.5.
Both students could be correct about the types of possible sequences. However, one student made a computational error because it is not possible to arrive at a fourth term of 44 in two different ways.
Both students could be correct. Because two numbers are given in the original sequence, it is possible to find a common difference and common ratio between the successive terms.
Answer:
D
Step-by-step explanation:
Both students could be correct. Because two numbers are given in the original sequence, it is possible to find a common difference and common ratio between the successive terms.
A sequence could either be arithmetic or geometric. The truth statement about the correct student is:
Both students could be correct. Because two numbers are given in the original sequence, it is possible to find a common difference and common ratio between the successive terms.
Given that:
[tex]-5.5, 11, .....[/tex]
If the sequence is arithmetic, then the common difference is
[tex]d = 11 --5.5[/tex]
[tex]d = 16.5[/tex]
So, the next two elements are:
[tex]T_3 = 11 + 16.5 =27.5[/tex]
[tex]T_4 = 27.5 + 16.5 =44[/tex]
If the sequence is geometric, then the common ratio is
[tex]r =\frac{11}{-5.5}[/tex]
[tex]r= -2[/tex]
So, the next two elements are:
[tex]T_3 = 11 \times -2 = -22[/tex]
[tex]T_4 = -22 \times -2 = 44[/tex]
Based on the above computations, both students are correct.
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What is the solution set for x-4>2?
Answer:
(6,∞)
x > 6
Step-by-step explanation:
Solve by adding 4 to both sides.
[tex]x-4>2\\x>6[/tex]
To put this in interval notation for your solution set, consider your sign.
You have a greater than sign, which means that 6 is not a solution. In interval notation, that means that you should use parentheses " ( " instead of brackets " [ ".
Your solution set goes on infinitely, and infinity also uses parentheses rather than brackets.
You can write your solution set in interval notation as follows:
(6, ∞)
The whole batch cost $28,000 and contained 140 items. Write the two rates (ratios) implied
by this statement. What would be the price for 200 items?
Please show work
The price for 200 items is $40,000.
What is problem-solving?
Calculation:-
The whole batch cost $28,000
Number of items=140
Cost of one items= $28000/140
∴cost of 200 items= 200*200
⇒$40000
Problem-solving is the act of defining a problem; figuring out the purpose of the trouble; identifying, prioritizing, and selecting alternatives for an answer; and imposing an answer.
Problem-solving starts with identifying the issue. As an example, a trainer may need to parent out a way to improve a scholar's overall performance on a writing talent test. To do that, the instructor will overview the writing exams looking for regions for improvement.
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Find the measure of C in the picture please
Answer:
Option A. The measure of angle C is 140°
Step-by-step explanation:
see the attached figure with letters to better understand the problem
we know that
The triangle OAB is an isosceles triangle
Because
OA=OB=radius
m∠BAO=m∠ABO=20°
Find the measure of angle C
Remember that the sum of the interior angles of a triangle must be equal to 180 degrees
so
m∠BAO+m∠ABO+m∠C=180°
substitute the given values
20°+20°+m∠C=180°
m∠C=180°-40°=140°
write the equation of the direct variation that includes the given point (-6,5)
[tex]\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ (\stackrel{x}{-6},\stackrel{y}{5})~~ \begin{cases} x=-6\\ y=5 \end{cases}\implies 5=k(-6)\implies \cfrac{5}{-6}=k~\hfill \boxed{y=-\cfrac{5}{6}x}[/tex]
30m = 6000 Find m
I don't have any answers to choose from, I have to figure this out myself, but i can't, evidently
Answer:
m = 200
Step-by-step explanation:
30 m = 6000 Divide both sides by 30
30 m / 30 = 6000 / 30
m = 200
What is(y^4/3 x y^2/3)^-1/2
[tex]\bf \left( y^{\frac{4}{3}}xy^{\frac{2}{3}} \right)^{-\frac{1}{2}}\implies \left( y^{\frac{4}{3}}y^{\frac{2}{3}}x \right)^{-\frac{1}{2}}\implies \left( y^{\frac{4}{3}+\frac{2}{3}}x \right)^{-\frac{1}{2}}\implies \left( y^{\frac{6}{3}}x \right)^{-\frac{1}{2}} \\\\\\ (y^2x^1)^{-\frac{1}{2}}\implies \left( y^{-\frac{1}{2}\cdot 2}x^{-\frac{1}{2}\cdot 1} \right)\implies y^{-1}x^{-\frac{1}{2}}\implies \cfrac{1}{y}\cdot \cfrac{1}{x^{\frac{1}{2}}}\implies \cfrac{1}{y\sqrt{x}}[/tex]
Step-by-step explanation:
[tex]\text{Use}\\\\a^n\cdot a^m=a^{n+m}\\\\(a^n)^m=a^{nm}\\\\a^{-1}=\dfrac{1}{a}\\============================\\\\\bigg(y^\frac{4}{3}\cdot y^\frac{2}{3}\bigg)^{-\frac{1}{2}}=\bigg(y^{\frac{4}{3}+\frac{2}{3}}\bigg)^{-\frac{1}{2}}=\bigg(y^{\frac{4+2}{3}}\bigg)^{-\frac{1}{2}}\\\\=\bigg(y^{\frac{6}{3}}\bigg)^{-\frac{1}{2}}=\bigg(y^2\bigg)^{-\frac{1}{2}}=y^{(2)\left(-\frac{1}{2}\right)}=y^{-1}=\dfrac{1}{y}[/tex]