Final answer:
To simplify the expression 6a - 2(a - 1), distribute the -2 across the terms inside the parentheses, and then combine like terms to get the simplest form, which is 4a + 2.
Explanation:
To simplify the expression 6a - 2(a - 1), you need to distribute the -2 across the terms inside the parentheses and then combine like terms. Here's the process step by step:
Distribute the -2 to both a and -1 inside the parentheses: -2 x a gives us -2a, and -2 x -1 gives us +2.Write out the new expression without parentheses: 6a - 2a + 2.Combine like terms by subtracting -2a from 6a, which results in 4a.Add the constant term 2 to get the final simplified expression: 4a + 2.The simplest form of the expression is 4a + 2.
Mario made 6 batches of cookies. His friends asked him to make an extra batch. He used 15 3/4 cups of sugar and needs another 5/8 cup for the extra Batch. How many cups of sugar will Mario use altogether? Show work.
Answer:
57
Step-by-step explanation:
6x?=5/8x15 3/4
Jeramy took 6 hours to read 222 pages of his book. What is Jeramy’s reading speed
Answer:
37 pages/hour
Step-by-step explanation:
This is a unit rate problem.
You are trying to find the number of pages per hour.
Divide the number of pages by the number of hours.
222 pages in 6 hours
(222 pages) / (6 hours) = 37 pages/hour
Answer:
37 pages/hour
Step-by-step explanation:
To find the reading speed, we take the pages read and divide by the time it took.
222 pages/ 6 hours
37 pages/hour
can someone please answer this or explain it?
The x in the formula is the depth.
You are given two different depths, replace x with the depths, solve for T, then subtract the to find the difference:
At 1200 meters the temperature is:
T = 4500/1200 = 3.75 degrees
At 3750 meters the temperature is:
T = 4500 / 3750 = 1.20 degrees.
The difference in temperature between the two depths is:
3.75 - 1.20 = 2.55 degrees C.
Am I right?
I want to know if I am right
Answer:
B $13
Step-by-step explanation:
Julie has 16.73 That is approximately 17 dollars
She buys a purse that is 4.12. That is approximately 4 dollars
17 -4 = 13
She will have approximately 13 dollars left
Solve the inequality graphically. 4^x > 2^x
A. x > 0
B. x < 0
C. x > 1
D. x < 1
Answer:
A. x > 0
Step-by-step explanation:
As long as the number (x) is a number greater than 0, the inequality would be correct. Take for example, 1 (a number greater than 0)
4^1 = 4; 2^1 = 2; 4 > 2
Another example is 2
4^2 = 16; 2^2 = 4; 16 > 4
etc.
~
Answer:
A. x > 0
Step-by-step explanation:
see graph
4^x > 2^x
Replace 4 with 2^2
2^2^x > 2^x
a^b^x = a^(b*c) so
2^ 2x > 2^x
If the bases are the same, the exponents must keep the same ratio
2x>x
This is true if x>0
What is sin 60 degree
Answer: if talking square root, it is sqrt3/2. if talking decimals, it is about 0.87.
Answer:
Sine 60°= √3/2
=1.732/2
0.8660
Step-by-step explanation:
In mathematics, the sine is a trigonometric function of an angle. The sine of an acute angle is defined in the context of a right triangle: for the specified angle, it is the ratio of the length of the side that is opposite that angle to the length of the longest side of the triangle (the hypotenuse).
From the triangle shown in the attachment
The sine of an angle =
Opposite/hypotenuse
Sine 60°= √3/2
=1.732/2
0.8660
Use slope formula to find the missing coordinate.
(r, 1) and (5, -7) Slope = 8/3
Answer:
r=8
Step-by-step explanation:
The formula for slope is
m = (y2-y1)/ (x2-x1)
Substitute in what we know.
8/3 = (-7-1)/(5-r)
Simplify
8/3 = -8/(5-r)
We can use cross products to help us solve.
8 * (5-r) = 3 * (-8)
divide each side by 8
8/8 * (5-r) = 3 * (-8)/8
5-r = -3
Subtract 5 from each side
5-r-5 = -3-5
-r = -8
Multiply by -1
r = 8
Salar's Drama class is performing a play. He wants to buy as many tickets as he can afford. If tickets cost $3.50 each and he has $15.25 to spend, how many tickets can he buy?
Answer: 4 tickets
Step-by-step explanation: If $15.25 is Salar’s total and each ticket costs $3.50, we need to use division to figure out how many tickets Salar can purchase. When we divide 15.25/3.50, we get 4.35 (approximately). Salar can’t have .35 of a ticket, so we round down to 4 whole tickets.
Which system of inequalities is shown? A.y2 B.yx y<2 D.y>x y>2
Answer: y > x, y > 2
The horizontal line goes through 2 on the y axis. This boundary line is represented by the equation y = 2, since every point on this line has a y coord of 2. The shading above it means that the inequality is y > 2. Every point in the shaded region of y > 2 has a y coord that is larger than 2.
The other inequality is y > x because we shade above the dashed boundary line y = x, which is that slanted dashed line.
Combining the two regions of y > 2 and y > x leads to what is shown.
Final answer:
The question regarding systems of inequalities is incomplete, but linear inequalities like y < x or y > 2 can be graphically represented. The same is true for linear equations, with options A, B, and C all depicting linear forms.
Explanation:
The question which system of inequalities is shown seems to be missing some context or parts, but in general, inequalities can be represented on a graph and used to describe the relationship between variables. When dealing with linear inequalities, such as y < x or y > 2, these can be shown graphically with a line dividing the plane into two regions: one where the inequality is true and the other where it is false. For instance, y < x would be represented by a line that slopes upward to the right, and the region below this line (where y is less than x) is shaded. Similarly, for y > 2, a horizontal line is drawn at y=2, and the area above this line is shaded, indicating where y is greater than 2.
When looking at linear equations, all the options A. y = -3x, B. y = 0.2 + 0.74x, and C. y = -9.4 - 2x are indeed linear, as they can all be written in the form y = mx + b, where m and b are real numbers and represent the slope and y-intercept of the line, respectively.
Solve for a in the equation a-17=42
Answer:
a = 59
Step-by-step explanation:
Note the equal sign, what you do to one side, you do to the other. Isolate the variable (a). Add 17 to both sides
a - 17 = 42
a - 17 (+17) = 42 (+17)
a = 42 + 17
Simplify. Combine like terms
a = 42 + 17
a = 59
59 is your answer
~
Solve for a (this means they want you to get "a" by itself in the equation)
So:
a - 17 = 42 Add 17 on both sides to get "a" by itself
a - 17 + 17 = 42 + 17
a = 59
Please help with this last question
I need help with this question quickly please! Show steps!
Answer:
A y = -x+2
Step-by-step explanation:
To find the slope of the line m we use the formula
slope = (y2-y1)/(x2-x1)
= (-9--7)/(4-2)
= (-9+7)/(4-2)
= -2/2
= -1
When lines are parallel, the slopes are the same. We need to find a line with slope of -1
y = -1x+2 is written in the form y =mx+b where m is the slope
m=-1 so the slope is -1
This line has the same slope so it is parallel to the line above.
Answer:
would be A
Step-by-step explanation:
SLOPE HAS TO BE -1
What does this symbol “ mean in math
I think, it's the symbol of the inches.
3" = 3 inches
or it's the second derivative of the function
[tex]\dfrac{d^2y}{dx^2}=f''(x)[/tex]
if x - 4 , x + 2 and 3x + 6 form a geometric sequence, find x.
Answer:
x =7
Step-by-step explanation:
Remark
A geometric sequence always has terms that are separated by a common ratio. For example 3 9 27 81 243 .... Each term is multiplied by a common number and the term before it. In this case the common term is 3. To get the next term after 9, you multiply 9 by 3.To get the common ratio divide the second term by the first and then the third term by the secondEquation
(x + 2)/(x - 4) = (3x + 6)/ (x + 2)
Solution
I would begin this problem by taking out the common factor on the top right term. You'll see why in a second.
(x + 2)/(x - 4) = 3(x + 2)/ (x + 2) Notice the two binomials on the right cancel.
(x + 2)/(x - 4) = 3/1 Cross multiply(x + 2)*1 = 3*(x - 4) Remove the brackets on the right.x + 2 = 3x - 12 Add 12 on both sides.x + 2 + 12 = 3x - 12 + 12 Simplifyx + 14 = 3x Subtract x from both sides14 = 3x - x2x = 14 Divide by 2x = 14/2x = 7Someone help me on my question.
Answer:
C < A < B
Step-by-step explanation:
Answer:
Step-by-step explanation:The answer is C<A<B and the reason is is because angle A and C are the same and angle B is the largest.
HURRY 30 POINTS! The diameter of mercury is approximately 4.9x10^3 kilometers. The diameter of Saturn is 1.2x10^5 kilometers. About how many times greater is the diameter of Saturn than the diameter of Mercury?
2.4
24
240
2400
Answer:
The answer is 2.4
Step-by-step explanation:
Divide 1.2x10^5 by 4.9x10^3 and you should get the answer of 2.44.
Hope this helps
Which of these sets of numbers contain all rational numbers?
A. π, 1/2, -13
B. -3.0541...,√99, 0.14363
C. -6, -√225, 4 7/8
D. √21, 0.75, 0
The answer is C, -6, -√225, 4 7/8.
Rational means that the number can be expressed as a fraction and integer numerators and denominators. -6 and 4 7/8 can clearly be expressed as a fraction. -6 can be expressed as -6/1 and 4 7/8 can be expressed as 39/8.
-√225 is equivalent to -15, which is rational.
A is wrong because the number includes Pi.
B is wrong because -3.0541 never ends and √99 is irrational.
D is wrong because √21 is also irrational.
The Set C. -6, -√225, 4 7/8 is the only set that contains all rational numbers.
Explanation:The set of rational numbers consists of numbers that can be expressed as a fraction of two integers. To determine which set of numbers contains all rational numbers, we need to check if all the numbers in each set can be expressed as a fraction.
In set A, only 1/2 is a rational number.
In set B, -3.0541... and 0.14363 can be expressed as fractions, but √99 cannot.
In set C, -6, -√225, and 4 7/8 can all be expressed as fractions.
In set D, √21 is not a rational number, while 0 and 0.75 are rational numbers.
Therefore, set C is the only set that contains all rational numbers.
Learn more about Rational numbers here:https://brainly.com/question/24398433
#SPJ2
Today is my birthday! Four-fifths of my current age is greater than three-quarters of my age one year from now.
Given that my age is an integer number of years, what is the smallest my age could be?
Answer: His smallest age could be 16 years.
Step-by-step explanation:
Since we have given that
Four-fifths of his current age is greater than three-quarters of his age one year from now.
Let his present age be x
So, According to question,
[tex]\frac{4}{5}x>\frac{3}{4}(x+1)[/tex]
Take the equality,
[tex]\frac{4}{5}x=\frac{3}{4}(x+1)\\\\\frac{4}{5}x=\frac{3}{4}x+\frac{3}{4}\\\\\frac{4}{5}x-\frac{3}{4}x=\frac{3}{4}\\\\\frac{16x-15x}{20}=\frac{3}{4}\\\\\frac{x}{20}=\frac{3}{4}\\\\x=\frac{3\times 20}{4}\\\\x=15[/tex]
So, [tex]x>15[/tex]
Hence, Nearest and smallest integer greater than 15 is 16 .
Therefore, His smallest age could be 16 years.
Answer:
Answer: His smallest age could be 16 years.
Step-by-step explanation:
Since we have given that
Four-fifths of his current age is greater than three-quarters of his age one year from now.
Let his present age be x
So, According to question,
Take the equality,
So,
Hence, Nearest and smallest integer greater than 15 is 16 .
Therefore, His smallest age could be 16 years.
If p(x) is a cubic polynomial with zeros at -3,-1, and 2, and p(0)=6, find p(x).
Answer:
[tex]p(x)=-x^3-2x^2+5x+6.[/tex]
Step-by-step explanation:
If a cubic polynomial has zeros [tex]x_1,\ x_2,\ x_3,[/tex] then it has a form
[tex]p(x)=a(x-x_1)(x-x_2)(x-x_3).[/tex]
In your case, zeros are -3, -1 and 2, then the polynomial is
[tex]p(x)=a(x-(-3))(x-(-1))(x-2),\\ \\p(x)=a(x+3)(x+1)(x-2).[/tex]
If [tex]p(0)=6,[/tex] then
[tex]p(0)=a(0+3)(0+1)(0-2)=6,\\ \\-6a=6,\\ \\a=-1[/tex]
and
[tex]p(x)=-(x+3)(x+1)(x-2)=-x^3-2x^2+5x+6.[/tex]
PLZ HURRY
Which graph represents the function f(x) = 2|x|?
Answer:c
Step-by-step explanation:
Answer: Hey he got it right it's C
Step-by-step explanation:
graph the solution set. please help
Answer:
In the attachment.
Step-by-step explanation:
Rewrite [tex]x\geq-3y-6[/tex] as a [tex]y\geq -\frac{1}{3}x-2[/tex]. Then mark each set with different color and take the intersection of these.
Tom knows that his school 10 out of every 85 students are left-handed. There are 391 students in Tom's school.
How many students in toms school are left-handed?
please show work if you help and i will mark as most BRAINLY THANK YOU GUYS!! ;)
which graph represents the function f(x)=0.25x+5
Answer:
Option D.
Step-by-step explanation:
Consider the given function
[tex]f(x)=0.25^x+5[/tex]
We need to find the graph of given function.
Substitute x=0 in the given function to find the y-intercept of the function.
[tex]f(0)=0.25^(0)+5[/tex]
[tex]f(0)=1+5[/tex]
[tex]f(0)=6[/tex]
So, y-intercept of the function is 6.
[tex](0.25)^x\rightarrow \infty[/tex] as [tex]x\rightarrow -\infty[/tex]
[tex](0.25)^x\rightarrow 0[/tex] as [tex]x\rightarrow \infty[/tex]
We can concluded that
[tex]f(x)\rightarrow \infty[/tex] as [tex]x\rightarrow -\infty[/tex]
[tex]f(x)\rightarrow 5[/tex] as [tex]x\rightarrow \infty[/tex]
Therefore, the correct option is D.
Answer:
D
Step-by-step explanation:
which linear function represents a slope of 1/4
Answer: The second option represents a slope of 1/4
Step-by-step explanation:
To find slope, select two points along the line and plug them into this equation: (y2-y1)/(x2-x1)
We'll take the two points in the second graph and plug them into the equation above: (4-3)/(4-0)= 1/4
Therefore, the second option represents a slope of 1/4. Hope this helps:)
Answer:
(B) would be the best answer choice
Step-by-step explanation:
HELP I NEED THESE QUESTIONS ANSWERED BEFORE THERE DUE PLZ HELP!!!!!!!
Answer:
Please, see the answers in the attached files.
Step-by-step explanation:
Please, see the attached files.
Thanks.
How do I factor quadratics?
Ok so factoring quadratics is fairly easy once you get the hang of it
So we have a quadratic [tex]x^2+x-2[/tex]
My first question would be what 2 numbers multiply to -2 and add to +1
the answer is 2 and -1
Second question what 2 values multiply to get [tex]x^2[/tex]
the answer x and x
your factored form would be [tex](x-1)(x+2)[/tex]
This is as far as i can explain there is a whole lot about quadratics to be learned. You have to ask your teacher on more information
{EASY POINTS} Write the converse of the conditional statement.
If it is January, then there are 31 days this month.
| Not True False, Converse |
Answer:
If there are 31 days in this month, it is January
Step-by-step explanation:
The converse of a statement is when you switch the conclusion with the hypothesis. If you do this, you get:
If there are 31 days in this month, it is January.
This is false btw. December has 31 days, and it's not January
The converse of the statement 'If it is January, then there are 31 days this month' is 'If there are 31 days this month, then it is January'. This is done by reversing the order of the 'if' (antecedent) and 'then' (consequent) parts of the statement.
Explanation:The converse of the conditional statement 'If it is January, then there are 31 days this month.' is 'If there are 31 days this month, then it is January.'
In a conditional statement, the order of the 'if', known as the antecedent, and the 'then', known as the consequent, makes up the statement's direction. The converse of a conditional statement simply flips or reverses this order. It's important to note that the truth of the original statement does not guarantee the truth of its converse.
Learn more about Converse of Conditional Statement here:https://brainly.com/question/36974334
#SPJ2
You are working as an office apprentice for the bksb Newcastle Arena.
The arena is attempting to cut down on some of its running costs. Look at the table below that lists the costs for the previous five years.
Year Costs (£)
Year One 1.4 million
Year Two 1.6 million
Year Three 1.8 million
Year Four 2.5 million
Year Five 1.7 million
What is the mean amount of costs?
Answer:
Mean = £1.8 million
Step-by-step explanation:
The MEAN is the sum of all the numbers divided by the number of numbers.
There are 5 numbers in totalThe sum is [tex]1.4+1.6+1.8+2.5+1.7=9[/tex] millionHence the mean is [tex]\frac{9}{5}=1.8[/tex] million
In a supermarket bin the number of packages of red to peppers to the number of packages of green peppers is in the ratio of 8 is to 13.The peppers are sold in 2 pound packages.What is the least possible weight of red peppers in the bin?
Answer:
16 pounds
Step-by-step explanation:
The ratio of no. of packages of red pepper to no. of packages of green pepper is given 8 is to 13.
So, atleast 8 packages of red pepper are sold
Therefore, least possible weight of red peppers in the bin = 2×8 = 16 pounds.
The least possible weight of red peppers in a supermarket bin with a ratio of 8 to 13 of red to green peppers, where each package weighs 2 pounds, is 16 pounds.
To find the least possible weight, we assume the smallest number of packages that maintain the ratio. Multiplying both numbers of the ratio by 2 pounds gives us the weight of the red and green peppers, but since we want the least possible weight of red peppers, we'll only calculate for red.
Therefore, if we have 8 packages of red peppers, each weighing 2 pounds, the calculation would be:
8 packages × 2 pounds/package = 16 pounds of red peppersEvaluate - 2/5- x + (-9/10) where x = 4/5.
Answer:
- 2 1/10
Step-by-step explanation:
-2/5 -x -9/10
Let x = 4/5
-2/5 - 4/5 - 9/10
Combine like terms
-6/5 - 9/10
Get a common denominator of 10
-6/5 * 2/2 - 9/10
-12/10 - 9/10
-21/ 10
Change this to a mixed number
10 goes into 21 2 times with 1 left over
-2 1/10
Answer:
- 2 1/10
Step-by-step explanation: