[tex]( x - 4 ) + ( 2x - 7 )[/tex]
Combine Like Terms:
[tex](x+2x)+(-4+-7)[/tex]
[tex](3x)+(-11)[/tex]
[tex]\fbox{3x - 11}[/tex]
Answer:3x-11
Step-by-step explanation:
(x-4)+( 2x-7)
x-4+2x-7
3x-11
Zachary is a waiter at a restaurant. Each day he works, Zachary will make a guaranteed wage of $40, however the additional amount that Zachary earns from tips depends on the number of tables he waits on that day. From past experience, Zachary noticed that he will get about $7 in tips for each table he waits on. How much would Zachary expect to earn in a day on which he waits on 11 tables? How much would Zachary expect to make in a day when waiting on tt tables?
Zachary expects to make $40 + $7 x tt (number of tables) in a day when waiting on tt tables
If Zachary waits on 11 tables, he can expect to make an additional $7 in tips for each table, for a total of 11 tables * $7/table = $77 in tips.
When added to his guaranteed wage, Zachary can expect to earn $40 (guaranteed wage) + $77 (tips) = $117 for that day.
To calculate how much Zachary would expect to make in a day when waiting on tt tables, we can use the equation:
Earnings = $40 (guaranteed wage) + $7 (tips/table) x tt (number of tables)
So if tt represents the number of tables Zachary waits on, then he can expect to earn:
Earnings = $40 + $7 x tt
For example, if Zachary waits on 15 tables, he can expect to earn $40 + $7 x 15 = $190.
Zachary can use this equation to calculate his expected earnings for any number of tables he waits on in a day.
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The table shows the approximate area
in square miles of the largest and smallest
states in the United States. What is the
difference between the areas in
square miles?
State
Area (mi?)
873
Alaska
Rhode Island
392
The difference between the areas is 481 square miles.
Given information:
Alaska is 873 sq miles in size, as well as Rhode Island, is 392 sq miles in total.
To determine the difference between the areas in square miles, the following calculation must be performed: subtract Alaska from Rhode Island square miles then we get:
Let X be the total difference:
873 - 392 = X
481 = X
Therefore, the difference in the areas in square miles is 481.
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Guliskhan plans to cover a certain distance by running and bicycling. She runs at a constant speed, and she bicycles at a speed of 7 meters per second (m/s)
Therefore, the inequality problem solution is even if Guliskhan runs for 60 seconds and cycles for 90 seconds, she will not be able to travel the required distance.
What is inequality?Both formulae and inequalities are mathematical phrases created by connecting two expressions. The equal sign (=) in an equation denotes that the two expressions are regarded as equal. In contrast, an inequality indicates that the two phrases are not always equal by using the symbols >,≥,≤, or.<
Here,
R should stand for Guliskhan's running seconds, and B should stand for her bicycling seconds.
Guliskhan is said to bike at a pace of 7 meters per second, hence the distance (in meters) that he covers in B seconds will be 7B.
An inequity of 3R + 7B 1000 has been handed to us.
We can observe that 7B reflects the cycling distance covered by Gulkishan in meters in B seconds.
Guliskhan covers a distance of 3R meters in the number of seconds she runs for, where R is the number of seconds she runs for.
Guliskhan moves at a steady pace of 3 meters per second because of this.
B. Since Gulkiskhan 3R plus 7B has traveled a total distance greater than or equal to 1000 meters, her minimum intended distance is 1000 meters.
C. Let's replace R=60 and B=90 in our inequality to see if Guliskhan is capable of traveling this minimum distance.
=>3*60 + 7*90 ≥ 1000
=>180 + 630 ≥ 1000
=>810 ≠> 1000
Therefore, even if Guliskhan runs for 60 seconds and cycles for 90 seconds, she will not be able to travel the required distance.
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The force,
F
(Newtons), between two objects is inversely proportional to the square of the distance,
d
(metres), between them.
The force is 0.045 Newtons when the distance between the objects is 2.4 metres.
Work out
d
(rounded to 2 DP) when
F
=
0.7
Newtons.
The value of d when F = 0.7 Newton's by solving with inverse variation is 0.61 meters to 2 D.P
How to find inverse variation?Let
F = force in Newton'sd = distance in metersF = k/ d²
Where k = constant of proportionality
If F = 0.045 Newtons and d = 2.4 metres
F = k/ d²
0.045 = k / 2.4²
cross product
k = 0.045 × 2.4²
k = 0.2592
Find d when F = 0.7 Newton's
F = k/ d²
0.7 = 0.2592 / d²
cross product
0.7 × d² = 0.2592
0.7d² = 0.2592
divide both sides by 0.7
d² = 0.2592 / 0.7
d² = 0.370285714285714
find the square root of both sides
d = √0.370285714285714
d = 0.6085110634045
d = 0.61 to 2 decimal place.
Therefore, d is equal to 0.61 meters to 2 decimal place if F is 0.7 Newton's.
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The line has a slope 5 / 4 and passes through ( − 3, 4 ). What is the equation of the line ? Select one: a. 4x + 5y + 31 = 0 b. 5x − 4y + 31 = 0 c. 4x − 5y + 31 = 0 d. 5x − 4y − 31 = 0
Answer:
b: 5x-4y+31=0
Step-by-step explanation:
Let's look for an equation of the form y=mx+b, where m is the slope and b the y-intercept (the value of y when x=0).
We are given the slope, m, as (5/4), so we can write: y = (5/4)x+b.
To find b, just enter the given point, (-3,4), into the above equation and solve for b:
y=(5/4)x + b
4=(5/4)(-3) + b for (-3,4)
4 = -(15/4)+b
4 + (15/4) = b
4 + (3 3/4) = b
b = 7 3/4
The equation becomes y = (5/4)x + 7 3/4
Also written as: y = (5/4)x + (31/4)
To match this with one of the options, let's multiply by 4 to remove the two fractions:
y = (5/4)x + (31/4)
4y = (5)x + (31)
Rearrange so that the expression is = 0:
4y-5x-31 = 0
Now multiply by -1: -4y+5x+31=0
Rearrange and this will match option b: 5x-4y+31=0
Marisol writes the equation 1. 6 : n=0. 16. Right your answer using an exponent. Explain how you know your answer is correct.
The equation 1.6: n = 0.16 can be written as: [tex]1.6 = 2.511^n[/tex]
And we know that this is correct because we can check that it is the equivalent by multiplying [tex]2.511^n[/tex] by itself n times which results in 1.6.
What is an exponent?
An exponent is a mathematical operation that represents the number of times a value is multiplied by itself. It is usually written as a small number raised to the power of a larger number, such as 2^3, which means 2 multiplied by itself 3 times, or 2 * 2 * 2 = 8.
To write the equation 1.6: n=0.16 using an exponent, we can divide both sides of the equation by 1.6 to get: n = 0.16/1.6 = 0.1
And then we can raise the base 10 to the power of n: [tex]10^n = 10^{0.1} = 2.511[/tex]
Hence, the equation 1.6: n = 0.16 can be written as: [tex]1.6 = 2.511^n[/tex]
And we know that this is correct because we can check that it is the equivalent by multiplying [tex]2.511^n[/tex] by itself n times which results in 1.6.
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The equation 1.6: n = 0.16 can be written as: 1.6 = [tex]2.511^n[/tex]
And we know that this is correct because we can check that it is the equivalent by multiplying [tex]2.511^n[/tex] by itself n times which results in 1.6.
What is an exponent?
An exponent is a mathematical operation that represents the number of times a value is multiplied by itself. It is usually written as a small number raised to the power of a larger number, such as 2^3, which means 2 multiplied by itself 3 times, or 2 * 2 * 2 = 8.
To write the equation 1.6: n=0.16 using an exponent, we can divide both sides of the equation by 1.6 to get: n = 0.16/1.6 = 0.1
And then we can raise the base 10 to the power of n: [tex]10^n=10^{0.1}=2.511[/tex]
Hence, the equation 1.6: n = 0.16 can be written as: 1.6 = [tex]2.511^n[/tex]
And we know that this is correct because we can check that it is the equivalent by multiplying [tex]2.511^n[/tex] by itself n times which results in 1.6.
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Is Avogadro's number the same for all elements?
The Avogadro's number of every element remains is the same. The number of atoms of 1 mole in every element is Avogadro's number. One mole of an element is 6.02214076×10²³ atoms.
What is an atom?
Each atom is made up of a nucleus and one or more electrons that are linked to it. One or more protons and a significant number of neutrons make up the nucleus. Only the most prevalent type of hydrogen is neutron-free. Atoms that are neutral or ionized make up every solid, liquid, gas, and form of plasma.
The proportionality factor that connects the number of constituent particles (often molecules, atoms, or ions) in a sample with the amount of material in that sample is called the Avogadro constant, also known as NA or L. It has a precise value of 6.02214076 × 10²³ reciprocal moles and serves as a SI defining constant.
The number of atoms of one mole substance is 6.02214076 × 10²³ which is Avogadro's number.
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Six times the sum of a number and 25 is at least 30
Answer:
Step-by-step explanation:
Let the number be x then:.
According to the question:
6 * (x + 25) = 30
therefore,
x + 25 = 30 / 6
x + 25 = 5
x = 5 - 25 = -20
•35 POINTS• (it’s not SAS)
1.SSS
2.ASA
3.SAA
Answer:
SAA
Step-by-step explanation:
The cross-sectional shape of the archway of a bridge (measured in feet) is modeled by the
function ƒ(x) = -0. 5x2 + 6x where ƒ(x) is the height of the arch and x is the horizontal
distance from one side of the base of the arch. How wide is the arch at its base? Will a box truck
that is 8 feet wide and 13. 5 feet tall fit under the arch? If not, what is the maximum height a
truck that is 8 feet wide and is passing under the bridge can be
The width of the arch at its base can be found by setting ƒ(x) = 0 and solving for x. This gives x=12 feet.
What is horizontal distance?Horizontal distance is the length of a straight line between two points, measured only in the horizontal direction. It is typically measured in units such as kilometres, meters, miles, or yards.
No, the box truck will not fit under the arch. The height of the arch at a horizontal distance of 8 feet is ƒ(8) = -0. 5(8)2 + 6(8) = 4 feet, which is less than the height of the truck (13. 5 feet).
The maximum height a truck that is 8 feet wide and is passing under the bridge can be is ƒ(8) = 4 feet.
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How much faster is parallel computing?
The amount of a program that can be parallelized limits the amount of time it takes to run. For example, if 90% of the program can be parallelized, the theoretical maximum speedup utilizing parallel computing would be 10 times regardless of the number of processors employed.
What is parallel computing?The amount of a program that can be parallelized limits the amount of time it takes to run. For example, if 90% of the program can be parallelized, the theoretical maximum speedup utilizing parallel computing would be 10 times regardless of the number of processors employed. Parallel computing is a sort of computation in which several computations or processes are performed at the same time. Large issues are frequently broken into smaller ones, which may then be tackled concurrently.
Here,
Parallelization can only speed up a program so much. For example, if 90% of the program can be parallelized, the theoretical maximum speedup utilizing parallel computing would be ten times regardless of the number of processors employed.
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At Central Middle School the 108 students who take the AMC 8 meet in the evening to talk about problems and eat an average of two cookies apiece. Walter and Gretel are baking Bonnie's Best Bar Cookies this year. Their recipe, which makes a pan of 15 cookies, lists these items: 1/2 cups of flour 2 eggs, 3 tablespoons butter, 3/4 cups sugar 1 package of chocolate drops They will make only full recipes, no partial recipes. They learn that a big concert is scheduled for the same night and attendance will be down 25%. How many recipes of cookies should they make for their smaller party? (Some eggs and some cookies may be left over. )
(A) 1.
(B) 2.
(C) 5.
(D) 7.
(E) 15
The correct option is option (E) 15
To calculate the number of cookies they will need, they first determine the number of students who will be attending the meeting. Since attendance is down by 25%, the number of students attending is 108*(1-0.25) students.
=108 students * 0.75 = 81 students.
To figure out the number of cookies they will need, they multiply the number of students by the number of cookies per student, which is 81 students * 2 cookies= 162 cookies.
Since each recipe makes 15 cookies, they need to make 162 cookies / 15 cookies/recipe = 10.8 recipes.
Since they cannot make partial recipes, they round up and make 11 recipes of cookies for their smaller party.
As 11 is not a given option, we consider the option which is greater than 11, which is 15.
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what is the answer thank ya mate
Answer: The ship is going to another planet.
Step-by-step explanation:
I hate i-ready,
Your welcome mate
6) A paint store has 240 gallons of paint to pack into boxes. Each box can hold 4 gallons of
paint. Which of the following equations can be used to find the number of boxes the paint
store can pack?
Choose ALL the correct answers.
a) 240 =
b) 4x
÷
+4
= 240
_=240 +4
= 240
= 240 x 4
Answer: 347
Step-by-step explanation:
Target offers a discount if you spend at least $50. Write an inequality to represent d, how much you must spend to receive the discount.
Answer:
d ≥ 50
Step-by-step explanation:
To receive the discount, you must spend at least $50, which can be represented by the inequality d ≥ 50. This inequality means that the amount you must spend (d) is greater than or equal to $50. If you spend more than $50, you will receive the discount. If you spend less than $50, you will not receive the discount.
Let u = PQ be the directed line segment from P(0,0) to Q(9,12), and let c be a scalar such that c < 0. Which statement best describes cu?
A) the terminal point of vector cu lies in quadrant II
B) the terminal point of vector cu lies in quadrant III
C) the terminal point of vector cu lies in quadrant I
D) the terminal point of vector cu lies in quadrant IV
The terminal point of vector cu lies in quadrant III.
Option B is the correct answer.
What are coordinates in a graph?The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
We have,
p = (0, 0) and Q = (9, 12)
u = PQ = (9 - 0, 12 - 0) = (9 , 12)
Now,
cu = (9c, 12c)
where c < 0
If c = -1
cu = (-9, -12)
The coordinates (-x, -y) lie in quadrant III.
(-9, -12) is in quadrant III.
Thus,
Vector cu lies in quadrant III.
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gong rented a truck for one day. There was a base fee of $19.95, and there was an additional charge of 71 cents for each mile driven. Hong had to pay $125.74 when he returned the truck. For how many miles did he drive the truck?
Answer:
19.95 + .71 × x = 125.74
x = 141.053
x is the answer
How do you find the ratios for sin A and cos A?
In given right triangle ACB, the ratios for sin A and cos A :
sin(A) = 48/50
cos(A) = 14/50
Consider the following diagram.
In a right triangle ACB, the angle ACB = 90 degrees.
We know that in right triangle for an angle θ, the trigonmetric ratios are:
sin(θ) = opposite side of θ/ hypotenuse
cos(θ) = adjacent side of θ / hypotenuse
Here, side AC = 14 units, side CB = 48 units and the hypotenuse AB = 50 units
We need to find the ratios for sin A and cos A
In right triangle ACB for angle A,
sin(A) = opposite side of angle A/ hypotenuse
sin(A) = CB/AB
sin(A) = 48/50
And cos(A) = adjacent side of A / hypotenuse
cos(A) = AC/AB
cos(A) = 14/50
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The average age of a group of fans at a hockey game is 34 years with a standard deviation of 8 years. What percent of fans are between 18 and 27 years old?
The percent of fans that are between 18 and 27 years old is 16.80%.
How to calculate the percentage of fans?From the information, the average age of a group of fans at a hockey game is 34 years with a standard deviation of 8 years and we want to calculate the percent of fans are between 18 and 27 years old.
It should be noted that this will be Illustrated through the normal curve.
The probability will be:
P(18 ≤ X ≤ 27)
= P(18 - 34/8) ≤ Z ≤ (27 - 34 / 8
= P(-2.0 ≤ Z ≤ -0.875)
= 0.1908 - 0.02275 (From the standard normal calculator)
= 16.80%
The percentage is 16.80%.
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ine segment SU is dilated to create S'U' using point Q as the center of dilation. The scale factor of the dilation is
The scale factor of the dilation is 2. An expansion happens when the scaling factor's absolute value exceeds one.
What does a scale factor mean when defining dilation?The scale factor is defined as the proportion of the new image's size to that of the previous image. A fixed location in the plane serves as the center of dilatation. The scale factor and the center of dilation are used to determine the dilation transformation. The image stretches if the scaling factor is greater than 1.
As per the rule of scale factor
Q'U'/QU = SF
SF= Scale factor
= (5+5)/5= Scale factor
= 10/5= 2
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What is the ratio for cos?
The ratio for cos (cosine) of angle θ is: cos(θ) = adjacent side of θ / hypotenuse
We know that in right triangle the cosine of an angle is nothing but the ratio of the side adjacent of given angle to the hypotenuse.
In right tirnagle for an angle θ, the ratio for cosine of angle θ would be:
cos(θ) = adjacent side of θ / hypotenuse
Consider following right triangle PQR with angle PQR = 90 degrees
Here, PR is the hypotenuse.
Assume that angle QPR measure α degrees and angle PRQ measures θ degrees.
By definition of cosine of angle θ,
cos(θ) = adjacent side of θ / hypotenuse
cos(θ) = QR / PR
And by definition of cosine of angle α,
cos(α) = adjacent side of α / hypotenuse
cos(α) = PQ / PR
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What scale factor was used to create the dilation below centered at point C?
Answer:
-2
Step-by-step explanation:
You want to know the dilation scale factor that gives triangle A'B'C from triangle ABC.
Scale factorWe notice that point A' is 4 units down and 2 units right of C, whereas A is 2 units up and 1 unit left of C. The ratio of these distances is the scale factor.
If up and right are positive, then ...
k = (A' -C)/(A -C) = (2, -4)/(-1, 2) = -2
The dilation scale factor is -2.
What is the product of 5/8 and 4?
We can calculate the product of 5/8 and 4 to be 5/2 using multiplication.
What is multiplication?Multiplication is one of the four basic mathematical operations, along with addition, subtraction, and division.
The result of a multiplication operation is a product.
There are four different methods for multiplying: addition, long multiplication, grid multiplication, and drawing lines.
So, we have:
5/8 and 4
5/8 is in the form p/q which represents the fraction that must be multiplied by 4.
Now, calculate the product as follows:
5/8 * 4
5/2
Therefore, we can calculate the product of 5/8 and 4 to be 5/2 using multiplication.
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hirty 8th graders signed up for running club,however nine dropped out before the firstpractice. If 2 46 3 % of the club are 8th graders, how many total students are in the running club
There are 29.8 students in the running club overall.
What is meant by quotient?The quotient is the number we get when we divide two numbers. For instance, in the case of 8 4 = 2, where the division result is 2, it is the quotient. The divisor is 4, and the dividend is 8.
The remnant is the amount that does not wholly enter the divisor, whereas the quotient is the number of times a division is completed to the fullest extent possible. By way of illustration, 42 is the quotient and 1 is the remainder when 127 is divided by 3 to provide 42 R 1.
Given,
30+9-46 (2/3) % × 30
Multiply
30 + 9 - (46 × 30) × 0.00666666666666667
Calculate quotient,
30 + 9 - 1380 × 0.00666666666666667
Simplifying quotient,
30 + 9 - 9.2
Then we get,
39 - 9.2
Then 29.8
get the result: 29.8
The complete question is:
Thirty 8 th graders signed up for running club, however nine dropped out before the first practice. If 46 (2/3) of the club are 8 th graders, how many total students are in the running club?
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There are 7 1/2 pounds of potatoes. 1/6 of the potatoes are rotten. What is the weight of good potatoes. Fraction form
Answer:
6 1/4 pounds
Step-by-step explanation:
There are 7 1/2 pounds of potatoes, which is equivalent to 7 1/2 = 7.516=120
120 ounces of potatoes.
If 1/6 of the potatoes are rotten, then 1/6*120 = 20
20 ounces of potatoes are rotten.
Thus, the weight of the good potatoes is 120-20 = 100
100 ounces.
Converting this back to pounds, we get
100/16 = 6 1/4
6 1/4 pounds.
Complete the following function table for the linear equation y=4x-1
First we can find value of x and. When x=0 then y=-1 and x=1 then y= 3
What is linear equation explain?A linear equation is an algebraic equation of the form y=mx+b involving only a constant and a first-order (linear) term where m is the slope and b is the y-intercept.So the above given equation is called a "linear equation of two variables," where y and x are the variables.
How do you find the value of Y?Finding the y value is easy if you know the slope of the line and the x coordinate. Review the equation for the slope of a line. The equation for finding the slope is: m = [y1 - y2] / [x1 - x2]. If you know x, you can solve for y to find the y value for the slope of the line.
Now we have y= 4x-1
lets x=0 then y= -1
x=1 then y=3
x=2 then y=7
To find slope
y=mx+c
y= 4x-1
so by comparing we can find m=4
Then we can evaluate given equation y=4x-1
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Uncle Drew scored 28 points in 5 5/6 minutes during a game of basketball. How many points did he average per minute during that 5 5/6 minutes?
Answer:
He scored an average of 4.8 points per minute.
Cos theta = -1/6 what is tan theta
Therefore , the solution to the given problem of trigonometry comes out to be tanθ = - √35 .
What is trigonometry?Trigonometry is the discipline of mathematics that studies correlations between angles and sides of triangles. Trigonometry is present in all of geometry because every straight-sided shape may be reduced to a set of triangles. Remarkably intricate connections exist between trigonometry and other areas of mathematics, particularly calculus, real or complicated, exponentials, logarithms, and infinite series.
Here.
Given : Cosθ = -1/6
To find : Tanθ
Since cosθ is in second quadrant
Thus,
Cosθ = B/H
According to pythagoras theorem,
H²= B²+ P²
=> 6² = 1² + P²
=> 36-1 =P²
=>P= √35
So ,
value of Tanθ comes out to be
=> tanθ = - √35 /1
=>tanθ = - √35
Therefore , the solution to the given problem of trigonometry comes out to be tanθ = - √35 .
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Help me, its geometry pls show everything.
It is assumed the given figure is a parallelogram.
Use properties of a parallelogram:
opposite sides are parallel and congruent,diagonals bisect each other.Find the missing values:
ML = NP = 12 m, opposite sides are congruent,LP = MN = 10 m, opposite sides are congruent,m∠LPM = m∠NMP = 62°, alternate interior angles are congruent, as LP║MN and MP is transversal,LN = LQ*2 = 9*2 = 18 m, as Q is the midpoint of LN,m∠MLN = m∠PNL = 32°, alternate interior angles are congruent, as ML║NP and LN is transversal,QN = QL = 9 m, as Q is the midpoint of LN.A figure made by two intersecting lines or two rays extending from the same point.
A figure made by two intersecting lines or two rays extending from the same point is called an angle.
What is an angle?
Two lines intersect at a location, creating an angle. An "angle" is the term used to describe the width of the "opening" between these two rays. Angles are used in the design of buildings, roadways, and sports venues by engineers and architects.
A figure made by two intersecting lines or two rays extending from the same point is called an angle.The character ∠ is used to represent it. Angles are frequently expressed in degrees and radians, a unit of circularity or rotation. We encounter angles frequently in life.
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