The total weight of 100 trucks in pounds is 300000 pounds.
According to the question,
We have the following information:
A truck weighs approximately 3000 pounds.
We have to find the weight of 100 such trucks.
We know that in order to find the total weight of 100 trucks we will multiply the weight of one truck by 100.
(More to know: we multiply a number when we have to find the weight or cost of more than one product.)
So, we have the following expression:
Weight of 100 trucks = 3,000*100 pounds
Weight of 100 trucks = 3,00,000 pounds
Hence, the total weight of 100 trucks in pounds is 3,00,000 pounds.
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Ella is working two summer jobs, making $22 per hour tutoring and making
$10 per hour clearing tables. In a given week, she can work a maximum of 9
total hours and must earn at least $130. If x represents the number of hours
tutoring and y represents the number of hours clearing tables, write and solve
a system of inequalities graphically and determine one possible solution.
The system of inequalities and a possible solution is by working 2 hours removing wires and 6 hours tutoring.
What is Inequalities?
An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The most frequent application is to size-compare two numbers on a number line.
Here are the variables defined:
x is the quantity of tutoring hours worked.
Y = quantity of h
clearing cables is our job.
Since we know she can only work a maximum of 9 hours per week:
x + y ≤ 9
She also wants to earn at least $130 each week, so:
x*$22 + y*$10 ≥ $130
As a result, we have the inequality system listed below:
x + y ≤ 9
x*$22 + y*$10 ≥ $130
The graph of this system can be shown in the graphic below, where the intersection of the two shaded regions shows where the system's solutions are.
There are some solutions there, including:
y = 0, x = 8
y = 2, x = 6.
As a result, her situation might be resolved by working 2 hours removing wires and 6 hours tutoring.
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I, III, and IV
I, II, and III
I and IV
All four quadrants
The location of the solutions of the inequality are quadrant in I, III, and IV
What is an inequality?An inequality is a non-equal comparison between quantities, variables or mathematical expressions.
The specified inequality is; [tex]y \leq\dfrac{2}{3} \cdot x-4[/tex]
The line of the inequality is a straight line that has a positive slope.
The y-intercept is at (0, -4)
The x-intercept is found as follows;
[tex]y=\dfrac{2}{3} \cdot x-4[/tex]
[tex]0 =\dfrac{2}{3} \cdot x-4[/tex]
[tex]4 =\dfrac{2}{3} \cdot x[/tex]
x = 6
The x-intercept = (0, 6)
The graph therefore from quadrant III enters quadrant IV at (0, -4), then enters into quadrant I at the x-intercept (0, 6)
The solution of the inequality, found by the coordinates of the intercepts and the path through of the line of the inequality are in I, III, and IV
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Ann took a taxi home from the airport. The taxi fare was $2.10 per mile, and she gave the driver a tip of $5 Ann paid a total of $49.10.
Write an equation to determine the distance in miles (x)(x)left parenthesis, x, right parenthesis between the airport and Ann's home.
Your plan for your t-shirt business calls for you to be able to produce 60,000 screen printed shirts in a month. If each screen press can handle 500 shirts per day, about how many presses do you need?.
Answer:
120 presses
Step-by-step explanation:
hope this helps :)
Answer:120 presses
Step-by-step explanation:
please help with this qn asap!! tyy!!
Answer:
i) AC = 6 - √3 cmii) BC² = 37 - 12√3 cm²----------------------
Given triangle withArea of 1/4(12 + 9√3),Side AB = √3 + 2,Angle BAC is 60°.Part iFind the side AC.
Use area formula:
A = ab sin∠C / 2, where a, b are adjacent sides and C is angle between a and b.Substitute and solve for AC:
1/4(12 + 9√3) = (√3 + 2) AC sin(60°) / 21/4(12 + 9√3) = AC (√3 + 2) (√3/2) / 2(12 + 9√3)/4 = AC √3(√3 + 2)/412 + 9√3 = AC√3(√3 + 2)AC = (12 + 9√3) /√3(√3 + 2)AC = (4√3 + 9) / (√3 + 2)AC = (4√3 + 9)(√3 - 2) / (√3 + 2)(√3 - 2)AC = (4√3√3 + 9√3 - 8√3 - 18) / (3 - 4) AC = (4*3 + √3 - 18) / ( - 1)AC = - (√3 - 6)AC = 6 - √3Part iiUse the law of cosines
BC² = AB² + AC² - 2 × AB × AC × cos ∠ABC² = (√3 + 2)² + (6 - √3)² - 2(√3 + 2)(6 - √3) cos 60°BC² = 3 + 4 + 4√3 + 36 + 3 - 12√3 - 2(6√3 - 3 + 12 - 2√3) / 2 BC² = 46 - 8√3 - (4√3 + 9)BC² = 46 - 8√3 - 4√3 - 9BC² = 37 - 12√3Answer:
[tex]\textsf{(i)} \quad \left(6-\sqrt{3} \right)\; \sf cm[/tex]
[tex]\textsf{(ii)} \quad \left(37-12\sqrt{3}\right)\; \sf cm^2[/tex]
Step-by-step explanation:
Part (i)[tex]\boxed{\begin{minipage}{7.6 cm}\underline{Area of a triangle} \\\\$A=\dfrac{1}{2}ab \sin C$\\\\where:\\ \phantom{ww}$\bullet$ $C$ is the angle. \\ \phantom{ww}$\bullet$ $a$ and $b$ are the sides enclosing the angle. \\\end{minipage}}[/tex]
Given:
[tex]\textsf{Area}=\dfrac{1}{4}(12+9\sqrt{3})[/tex][tex]a=(\sqrt{3}+2)[/tex][tex]C=60^{\circ}[/tex]Substitute the given values into the formula to find AC (side b).
[tex]\begin{aligned}\textsf{Area}&=\dfrac{1}{2}ab \sin C\\\\\implies \dfrac{1}{4}(12+9\sqrt{3})&=\dfrac{1}{2}(\sqrt{3}+2)b \sin 60^{\circ}\\\\\dfrac{1}{4}(12+9\sqrt{3})&=\dfrac{1}{2}(\sqrt{3}+2) \dfrac{\sqrt{3}}{2}b\\\\\dfrac{1}{4}(12+9\sqrt{3})&=\dfrac{\sqrt{3}}{4}(\sqrt{3}+2)b\\\\12+9\sqrt{3}&=\sqrt{3}(\sqrt{3}+2)b\\\\12+9\sqrt{3}&=(3+2\sqrt{3})b\\\\b&=\dfrac{12+9\sqrt{3}}{3+2\sqrt{3}}\\\\b&=\dfrac{12+9\sqrt{3}}{3+2\sqrt{3}}\cdot \dfrac{3-2\sqrt{3}}{3-2\sqrt{3}}\end{aligned}[/tex]
[tex]\begin{aligned}b&=\dfrac{36-24\sqrt{3}+27\sqrt{3}-54}{9-6\sqrt{3}+6\sqrt{3}-12}\\\\b&=\dfrac{-18+3\sqrt{3}}{-3}\\\\b&=6-\sqrt{3}\end{aligned}[/tex]
Therefore, the length of AC is (6 - √3) cm.
Part (ii)[tex]\boxed{\begin{minipage}{6 cm}\underline{Cosine Rule} \\\\$c^2=a^2+b^2-2ab \cos C$\\\\where:\\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides.\\ \phantom{ww}$\bullet$ $C$ is the angle opposite side $c$. \\\end{minipage}}[/tex]
Given:
[tex]c = BC[/tex][tex]a = AB=(\sqrt{3}+2)[/tex][tex]b = AC=(6-\sqrt{3})[/tex][tex]C = \angle BAC=60^{\circ}[/tex]Substitute the given values into the formula to find BC²:
[tex]\begin{aligned}c^2&=a^2+b^2-2ab \cos C\\\\\implies BC^2&=AB^2+AC^2-2(AB)(AC) \cos C\\\\BC^2&=(\sqrt{3}+2)^2+(6-\sqrt{3})^2-2(\sqrt{3}+2)(6-\sqrt{3}) \cos 60^{\circ}\\\\BC^2&=7+4\sqrt{3}+39-12\sqrt{3}-2(9+4\sqrt{3}) \cdot \dfrac{1}{2}\\\\BC^2&=7+4\sqrt{3}+39-12\sqrt{3}-9-4\sqrt{3} \\\\BC^2&=37-12\sqrt{3}\end{aligned}[/tex]
Therefore, BC² is (37 - 12√3) cm².
50 points need asap pleasee!!!
No
The first number is x and the second number is y. And there's no -11 on the x side of the table or 10 on the y side of the table.
a pic to help u is below
(1) The slope of the function is 11.99.
(2) The y-intercept of the function is 7.
(3) The slope indicates the per-month subscription fee.
(4) The y-intercept indicates the one-time subscription fee.
What is the slope-intercept form of a line?The slope-intercept form of a line is y = mx +c where m is the slope of the line and c is the y-intercept.
The given equation is c(m) = 11.99m+7.
Note that the equation is written in slope-intercept form.
The slope of the function is 11.99.
The y-intercept of the function is 7.
The slope indicates the value of the change in c(m) when there is a unit change in m.
Therefore, the slope of 11.99 indicates the per-month subscription fee.
The y-intercept indicates the value of c(m) when m is zero, therefore, the y-intercept to 7 represents that the one-time subscription is 7.
Hence,
(1) The slope of the function is 11.99.
(2) The y-intercept of the function is 7.
(3) The slope indicates the per-month subscription fee.
(4) The y-intercept indicates the one-time subscription fee.
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[Will give Brainliest!]
Answer Needed ASAP!!
Write the Polynomial expression for the area of the shaded region of the figure
Answer:
4x^2+6x-49
Step-by-step explanation:
(3x-8)(2x+13)-(X+11)(2x-5)
(6x^2+39x-16x-104)-(2x^2-5x+22x-55)
(6x^2+23x-104)-2x^2-17x+55
4x^2+6x-49
Hopes this helps please mark brainliest
If you were given $1000.00 what would you do with it and why?
help me please!!!!!! im in rushhh
Answer: Help my parents pay
bills and buy myself some shoes
Robert cuts a string that's 4 feet long into pieces that are each 2/6 foot long
Answer:
12 pieces
Step-by-step explanation:
Number of pieces Robert cuts
= 4 feet ÷ [tex]\frac{2}{6}[/tex] feet
= 12 pieces
Which of the following are common multiples of 60 and 1120?
Select all of the correct answers.
2³×3×7
2²×3×5
27×3×5²×7
2²x5
25×3×5×7
2³×3×5²x7
25×3×5×7²
25x5x7
The common multiple of 60 and 1120 is 2³×3×7.
What is the least common multiple?
The least common multiple, lowest common multiple, or smallest common multiple of two integers a and b, denoted by lcm in arithmetic and number theory, is the smallest positive integer that is divisible by both a and b.
The least common multiple of 60 and 1120 is 3360.
2³×3×7 = 168
2²×3×5 = 60 -----(This is the common multiple)
27×3×5²×7 = 14175
2²x5 = 20
25×3×5×7 = 2625
2³×3×5²x7 = 4200
25×3×5×7² = 18375
25x5x7 = 875
Hence, the common multiple of 60 and 1120 is 2³×3×7.
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help meeeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeeeeeeeeee!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!help meeeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeeeeeeeeee!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
(a) in 2001: 150.4 thousand
(b) in 2018: 467.5 thousand
Step-by-step explanation:
You want the value of the expression modeling the number of students abroad for different values of x. That expression is 123.1(1.069^x).
(a) 2001The value of x is the difference between the year (2001) and the reference year (1998). In the attachment, we let the calculator find that difference. It tells us, for x = 2001 -1998 = 3, the number of students is about ...
y = 123.1(1.069^3) ≈ 150.4 . . . . thousand
(b) 2018In 2018, the value of x is 2008 -1998 = 10, and the number of students studying abroad is ...
y = 123.1(1.069^10) ≈ 467.4 . . . . thousand
can anyone help with this?
Answer: can’t be simplified
Step-by-step explanation:
What is the equation of the straight line that passes through (3,10) and (7,28)
Give your answer in the form y=mx+c
Answer:
[tex]y = \frac{9}{2} x - \frac{7}{2} [/tex]
Step-by-step explanation:
[tex]m = \frac{28 - 10}{7 - 3} = \frac{18}{4} = \frac{9}{2} [/tex]
[tex]10 = \frac{9}{2} (3) + b[/tex]
[tex] \frac{20}{2} = \frac{27}{2} + b[/tex]
[tex]b = - \frac{7}{2} [/tex]
[tex]y = \frac{9}{2} x - \frac{7}{2} [/tex]
Find the coordinates of triangle PQR with vertices P(-3, -2), Q(-1, 4), and R(2, -2) under the translation
(x,y) → (x+2y-4)
a. P'(-1, 2), Q'(1,8), R(4, 2)
b. P'(-5, -6), Q'(-3, 0), R(-4, -6)
c. P'(-1, -6), Q'(1, 0), R(4, -6)
d. P'(-5, 2), Q'(-3, 8), R(-4, 2)
The coordinates of triangle PQR under the translation (x,y) → (x+2,y-4) are P'(-1,-6), Q'(1,0), R'(4,-6).
Translation of coordinates is done by adding the horizontal translation at each vertex of the triangle. It is the process of shifting the location of the figure without changing the size and dimensions of the figure.
The coordinates of the triangle PQR are given as P(-3,-2), Q(-1,4), R(2,-2). The property under translation is given as (x,y) → (x+2,y-4). Now, let us apply this for all vertices.
P(-3,-2) → P'(-3+2,-2-4) → P'(-1,-6)
Q(-1,4) → Q'(-1+2,4-4) → Q'(1,0)
R(2,-2) → R'(2+2,-2-4) → R'(4,-6)
Thus, the vertices after translation are P'(-1,-6), Q'(1,0), R'(4,-6).
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Select the correct answer from each drop-down menu. Graph shows two triangles plotted on a coordinate plane. One triangle is at A (minus 4, 4), B (minus 8, 2), and C (minus 6, minus 6). Another triangle is at A prime (4, minus 2), B prime (2, 2), and C prime (6, 0). A sequence of transformations maps ∆ABC to ∆A′B′C′. The sequence of transformations that maps ∆ABC onto ∆A′B′C′ is a followed by a .
The sequence of transformations that maps ∆ABC onto ∆A′B′C′ is a 90º clockwise rotation about the origin followed by a translation six units down.
What are the transformations?The transformations are discovered building a relation between the vertices of the original triangle and of the transformed triangle.
The vertices of the original triangle ABC are given as follows:
A(-4,4), B(-8,2) and C(-6,-6).
The vertices of the transformed triangle A'B'C' are given as follows:
A'(4, -2), B'(2,2), and C'(-6,0).
Then the complete rule that describes the transformation is presented as follows:
(x,y) -> (y, -x-6).
The meaning of each transformation is given as follows:
(x,y) -> (y, -x) is a 90º clockwise rotation about the origin.(x,y) -> (x, y - 6) is a translation down 6 units.More can be learned about transformations at https://brainly.com/question/28792248
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A woman entering an outside glass elevator on the ground floor of a hotel glances up to the top of the building across the street and notices that the angle of elevation is 48°. She rides the elevator up three floors (60 feet) and finds that the angle of elevation to the top of the building across the street is 31°. How tall is the building across the street? (Round to the nearest foot.)
Answer:
131 ft
Step-by-step explanation:
You want the height of a building if two observations of its top separated by 60 vertical feet have angles of elevation of 48° and 31°.
SetupLet x be the distance to the building at street level, and y be the height of the building. The tangent relation is ...
Tan = Opposite/Adjacent
The first observation tells us ...
tan(48°) = y/x
The second observation tells us ...
tan(31°) = (y -60)/x
SolutionSolving each equation for x gives ...
x = y/tan(48°)
x = (y -60)/tan(31°)
The difference of these x-values is zero, so we have ...
x - x = 0
y/tan(48°) -(y -60)/tan(31°) = 0
y(1/tan(48°) -1/tan(31°)) +60/tan(31°) = 0
Subtracting the constant and dividing by the coefficient of y, we get ...
y = (60/tan(31°))/(1/tan(31°) -1/tan(48°)) = 60·tan(48°)/(tan(48°) -tan(31°))
y ≈ 130.724
The height of the building is about 131 feet.
Si un segmento de línea tiene extremosA(-2x+1,4x-3) y B(4x-1,2x+7) ¿cuáles son las coordenadas del punto medio de AB
The coordinates of the midpoint of AB is (x, 3x+2).
Given:
A line segment has endpoints A(-2x+1,4x-3) and B(4x-1,2x+7) .
Midpoint of AB = (-2x+1+4x-1 / 2 , 4x-3+2x+7 / 2)
= (2x+1-1 / 2 , 6x+7-3 / 2)
= (2x+0 / 2 , 6x+4 / 2)
= (2x/2 , 6x+4 / 2)
= (x, 3x+2).
Therefore the coordinates of the midpoint of AB is (x, 3x+2).
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Mike is a new photographer. In order for his work to get exposure, Mike has decided to have a booth at an arts festival. He is
charging $21.49 for his color prints and $29.84 for his black and white prints. Which is a reasonable amount that Mike would make if
he sold 7 color prints and 4 black and white prints?
OA. $561.00
OB. $267.00
OC. $357.00
OD. -$27.00
Answer: The reasonable amount that Mike would make if he sold 7 color prints and 4 black and white prints is OB 267 dollar
What do three-variable linear equations mean?
A linear equation in three variables is ax + by + cz = r if a, b, c, and r are real integers (and if a, b, and c are not all equal to 0).
How can a system of three linear equations be solved?
Choose two equation pairs from the system. Use the addition/subtraction method to remove the same variable from each pair. then use the Addition/Subtraction method to solve the system of the two newly discovered equations.
Assume there are "x" number of touchdowns, "y" extra-point kicks, and "z" number of field goals.
Step-by-step explanation:
Given that
For color print he charge x = 21.49 dollar
For black and white print he charge y = 29.84 dollar
Equation of his money
[tex]21.49(x)+29.84(y)=z[/tex]
Z is the money he earn
Now putting the value of x and y we get value of z
[tex]21.49(7)+29.84(4)=z\\z= 269.79[/tex]
Which is closest to 267 dollar
Hence the answer is Option B $267.00
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Solve for X
HELPPPPPPPPPPPPP
What is the angle for a ratio of 1 2?.
The acute angles in a right triangle have measures of 30 degrees and 60 degrees if the ratio of these angles is 1:2.
How is a right triangle formed?The hypotenuse, along with the two legs, make up a right triangle. The hypotenuse, the longest side of the right triangle and the side opposite the right angle, is where the two legs of a right triangle come together at a 90° angle. There are a few unique varieties of right triangles, including the 45°-45° and the 30°-60° varieties.
The ratio of the angular dimensions of the acute angles of a right triangle is 1:2.
Consider x
Sum of three angles is 180 degrees.
Now,
180=90 + x + 2x
180 - 90=3x
3x = 90
x = 30
here, x and 2x, are two angles 30 and 60 degrees.
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What is the y-intercept in the equation y = -3x + 7
Responses
7
7
-3x
-3x
x
x
-3
GUYS I NEED HELP!!!
your friend graphs the equation y = 4.
is your friend correct?
o yes
o no
Explain your reasoning.
Answer:
No
Step-by-step explanation:
1 ) Since there is no x, the line is horizontal and has a slope of 0.
2 ) Knowing this we can go to 4 on the y-axis and draw a horizontal line that runs both through the negative and positive sides.
Take a look at the attachment...
Hope this helps! :)
What is the correct word form of 9.602?
Answer: Nine and six hundred two thousandths
Step-by-step explanation:
Determine whether each pair of triangles is congruent. If yes, include the theorem that applies.
Answer:
The triangles are congruent.
Step-by-step explanation:
The pair of triangles shown on the image are congruent triangles by ASA postulate.
ASA postulate is the postulate where two triangles are congruent by two Angles and a Side length.
The two triangles are congruent by RHS congruency property.
What is congruency?We know two similar planer figures are congruent when we have sides or angles or both that are the same as the corresponding sides or angles or both.
Given are two right-angle triangles.
Also given the height of both the triangles are similar and the two angles are also congruent therefore sides opposite to the similar angles are also similar hence these two right-angled triangles are congruent
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Identify the slope and y-intercept of the line with the given equation.
*do not enter the y-intercept as an ordered pair
m =
b=
y=-3x+8
Answer:
m = -3
b = 8
Step-by-step explanation:
y = -3x + 8 is in slope-intercept form, which is:
y = mx + b
so the slope is the m, the number right there beside the x. In your equation its -3. The b is the y-intercept, so its the last number tacked on the end of the equation there on the right. For your question, its the 8.
Slope is -3 and y-intercept is 8.
my homework is due tomorrw and i its 10:30 but i cant get this question
please help
Answer: w= -18
Step-by-step explanation:
1.) 3(6t2+5t+-4)
2.) 12(-2)power of 2+15(-2)-12
3.) 24-30-12
4.) -6-12
5.) -18
Ray lends $3,500.00 to Aron at a simple interest of 15% per year. Aron returned him $3,000.00 and a watch after 2 years to clear the
account. What is the price of the watch?
O $550.00
O $650.00
O $1,550.00
O $1,650.00
Answer:
1550
Step-by-step explanation:
3500*15% = 525 This is interest for one year
interest for 2 years will be 525 * 2 = 1050
total amount to pay will be 3500 + 1050 = 4550
cash payed = 3000
4550 - 3000 = 1550 price of watch
PLEASE ANSWER QUICK!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Which expression represents "2 less than the product of 5 and a number"?
Responses
5+n−2
5 plus n minus 2
5n−2
5 over n end fraction minus 2
2−5n
2 minus 5 n
5n−2
What is the diameter of a sphere with a volume of 78006\text{ in}^3,78006 in 3 , to the nearest tenth of an inch?.
The diameter of the sphere is 53.01 inches.
What is volume of sphere?
The volume of sphere is the amount of space occupied, within the sphere. The sphere is defined as the three-dimensional round solid figure in which every point on its surface is equidistant from its centre. The fixed distance is called the radius of the sphere and the fixed point is called the centre of the sphere.
Given, volume of the sphere = 4/3πr^3
Where r is the radius of the sphere.
Therefore,
( 4/3 ) πr³ = 78006 inch³
πr³ = 78006
r³ = 18622.56 inch³
r = 26.506
We know diameter = 2r
d = 53.01 inches.
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