Solving a system of equations we will see that two large trucks and one small truck can hold 2.625 tons
How much cargo can two large trucks and one small truck hold?Let's define the variables:
x = volume that a small truck holds.
y = volume that a large truck holds.
Then we can write the system of equations:
4x + 4y = 10.5 tons
y = 2x
Replacing the second equation into the first one we get.
4x + 4*(2x) = 10.5 tons
12x = 10.5 tons
x = 10.5 tons/12 = 0.875 tons
and:
y = 2x = 2*0.875 tons = 1.75 tons
Then the cargo that two large trucks and one small truck can hold is:
2* 1.75 tons + 0.875 tons = 2.625 tons
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Please help pethagriem entherum
Hey ! there
Answer:
13 is the answer .Step-by-step explanation:
In this question we are provided with right angle triangle having hypotenuse ( longest side ) = c , perpendicular = 5 and base = 12 . And we are asked to find the length of missing side i.e. hypotenuse and if necessary we have to round it off to 2 decimal places.
We can find the missing side by using Pythagorean Theorem . It states that sum of squares of perpendicular and base is equal to square in a right angle triangle that is ,
[tex] \: \qquad \: \qquad \: \underline{\boxed{ \frak{H {}^{2} = P {}^{2} + B {}^{2} }}}[/tex]
Where ,
H refers to HypotenuseP refers to PerpendicularB r refers to BaseSOLUTION : -
Substituting value of hypotenuse as c , perpendicular as 5 and base as 12 in formula :
[tex] \quad \longmapsto \qquad \: (c) {}^{2} = (5) {}^{2} + (12) {}^{2} [/tex]
Squaring 5 and 12 :
[tex] \quad \longmapsto \qquad \:(c) {}^{2} = 25 + 144[/tex]
Adding 25 and 144 :
[tex] \quad \longmapsto \qquad \:(c) {}^{2} = 169[/tex]
Applying square root to both sides :
[tex] \quad \longmapsto \qquad \: \sqrt{(c) {}^{2} } = \sqrt{169} [/tex]
On simplifying , We get :
[tex] \quad \longmapsto \qquad \orange{\underline{\boxed{\frak{c = 13}}}} \quad \bigstar[/tex]
Henceforth , ❝ 13 ❞ is the length of missing side .Verifying : -
Now we are checking our answer by putting all values in formula . So ,
( 13 )² = ( 5 )² + ( 12 )²169 = 25 + 144169 = 169L.H.S = R.H.SHence, Verified .Therefore , our answer is correct .
#Keep LearningAnswer :
13[tex] \: [/tex]
Step-by-step explanation :
Here, A right angled triangle is given with the measure of two sides and we are to find the measure of the third side.
We'll find the measure of third side with the help of the Pythagorean theorem,
[tex]\\ {\longrightarrow \pmb{\sf {\qquad (Hypotenuse {)}^{2}= (Base) {}^{2} + (Perpendicular {)}^{2} }}} \\ \\[/tex]
Here,
The Base is 12The Perpendicular is 5The Hypotenuse is c.[tex] \: [/tex]
So, substituting the values in the formula we get :
[tex]\\ {\longrightarrow \pmb{\sf {\qquad (c {)}^{2}= (12) {}^{2} + (5 {)}^{2} }}} \\ [/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad (c {)}^{2}= 144 + 25 }}} \\ [/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad (c {)}^{2}= 169 }}} \\ [/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad c = \sqrt{169} }}} \\[/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad c= 13 }}}\\ \\[/tex]
Therefore,
The measure of the third side (c) is 13Based on the data in the two-way table, what is the probability that a person consumes 1,500 to 2,000 calories in a day? A. 0.22 B. 0.28 C. 0.35 D. 0.50
Using it's concept, it is found that the probability that a person consumes 1,500 to 2,000 calories in a day is given by:
D. 0.50
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
Researching the problem on the internet, it is found that out of 500 people, 250 consume 1,500 to 2,000 calories in a day, hence the probability is given by:
p = 250/500 = 0.5.
Which means that option D is correct.
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hi can anyone solve my math problem
Answer:
The solutions to this equation are x = -8/9 and x = -16/3.
Step-by-step explanation:
We have this equation here:
[tex]\displaystyle \frac{1}{3}|x-4|=\frac{2}{3} x+2|x+\frac{6}{3} |[/tex]First, let's simplify the right sight of the equation by simplifying 6/3 to 2.
[tex]\displaystyle \frac{1}{3}|x-4|=\frac{2}{3} x+2|x+2 |[/tex]Multiply both sides of the equation by 3 in order to get rid of the fractions.
[tex]|x-4|=2x+6|x+2|[/tex]Move the terms on either side of the equation to set them equal to 0.
[tex]|x-4|-2x-6|x+2|=0[/tex]Now, we can split this equation up into 4 possible cases. In each case, we make the absolute values negative or positive.
Case #1 (first absolute value: positive; second absolute value: positive)[tex](x-4)-2x-6(x+2)=0[/tex]Simplify this equation by distributing -6 inside the parentheses.
[tex]x-4-2x-6x-12=0[/tex]Combine like terms.
[tex]-7x-16=0[/tex]Add 16 to both sides of the equation and divide by -7.
[tex]\displaystyle \boxed{x=-\frac{16}{7}}[/tex]Case #2 (first absolute value: negative; second absolute value: positive)[tex]-(x-4)-2x-6(x+2)=0[/tex]Distribute the negative sign and -6 inside of their respective parentheses.
[tex]-x+4-2x-6x-12=0[/tex]Combine like terms.
[tex]-9x-8=0[/tex]Add 8 to both sides of the equation and divide by -9.
[tex]\displaystyle \boxed{x=-\frac{8}{9}}[/tex]Case #3 (first absolute value: positive; second absolute value: negative)[tex](x-4)-2x-6[-(x+2)]=0[/tex]Distribute the negative sign inside the parentheses first.
[tex]x-4-2x-6(-x-2)=0[/tex]Now, distribute -6 inside the parentheses.
[tex]x-4-2x+6x+12=0[/tex]Combine like terms.
[tex]5x+8=0[/tex]Subtract 8 from both sides of the equation and divide by 5.
[tex]\displaystyle \boxed{ x=-\frac{8}{5}}[/tex]Case #4 (first absolute value: negative; second absolute value: negative)[tex]-(x-4)-2x-6[-(x+2)]=0[/tex]Distribute the negative signs inside the parentheses first.
[tex]-x+4-2x-6(-x-2)=0[/tex]Distribute -6 inside the parentheses.
[tex]-x+4-2x+6x+12=0[/tex]Combine like terms.
[tex]3x+16=0[/tex]Subtract 16 from both sides of the equation and divide by 3.
[tex]\displaystyle \boxed{x=-\frac{16}{3}}[/tex]Extraneous SolutionsWhenever we solve problems with absolute values, we will always need to check for extraneous solutions.
Definition: These are solutions that may come up while solving but do not actually fit in the domain of the original problem.
Checking for these is tedious, but it will help eliminate wrong answers, so let's plug every "solution" for x that we found back into the original equation.
1) x = -16/7Substitute this value back into the original equation.
[tex]\displaystyle \frac{1}{3}|(-\frac{16}{7}) -4|=\frac{2}{3} (-\frac{16}{7}) +2|(-\frac{16}{7}) +\frac{6}{3} |[/tex]If we do all the calculations correctly, we will get:
[tex]\displaystyle \frac{44}{21} =-\frac{20}{21}[/tex]Since this equation is NOT true, this means that x = -16/7 is NOT A SOLUTION.
2) x = -8/9Substitute this value back into the original equation.
[tex]\displaystyle \frac{1}{3}|(-\frac{8}{9}) -4|=\frac{2}{3} (-\frac{8}{9}) +2|(-\frac{8}{9}) +\frac{6}{3} |[/tex]If we do all the calculations correctly, we will get:
[tex]\displaystyle \frac{44}{27} =\frac{44}{27}[/tex]Since this equation IS true, this means that x = -8/9 IS A SOLUTION.
3) x = -8/5Substitute this value back into the original equation.
[tex]\displaystyle \frac{1}{3}|(-\frac{8}{5}) -4|=\frac{2}{3} (-\frac{8}{5}) +2|(-\frac{8}{5}) +\frac{6}{3} |[/tex]If we do all the calculations correctly, we will get:
[tex]\displaystyle \frac{28}{15} =-\frac{4}{15}[/tex]Since this equation is NOT true, this means that x = -8/5 is NOT A SOLUTION.
4) x = -16/3Substitute this value back into the original equation.
[tex]\displaystyle \frac{1}{3}|(-\frac{16}{3}) -4|=\frac{2}{3} (-\frac{16}{3}) +2|(-\frac{16}{3}) +\frac{6}{3} |[/tex]If we do all the calculations correctly, we will get:
[tex]\displaystyle \frac{28}{9} =\frac{28}{9}[/tex]Since this equation IS true, this means that x = -16/3 IS A SOLUTION.
Final AnswerThe two true solutions of the double absolute value equation, shown above, are:
[tex]\displaystyle \boxed{-\frac{8}{9} } \ \ \& \ \ \boxed{-\frac{16}{3}}[/tex]Answer:
x = -16/3 or -8/9
Step-by-step explanation:
The equation can be rewritten as a piecewise linear function with two breakpoints, or three domain regions. Each breakpoint is at the value of x where the argument of the absolute value function is zero: at x=4 and x=-2.
For each absolute value, we have ...
|q| = -q for q < 0
|q| = q for q ≥ 0
Then the three parts of the domain are ...
x < -2 . . . . . . . . where |x +2| has its vertex-2 ≤ x < 4 . . . . . between the vertices4 ≤ x . . . . . . . . . where |x -4| has its vertex__
Subtracting the right side, the equation becomes ...
1/3|x -4| -2/3x -2|x +2| = 0
Then the three piecewise functions are ...
x < -2Both absolute value arguments are negated.
1/3(-(x -4)) -2/3x -2(-(x +2)) = 0
x(-1/3 -2/3 +2) +4/3 +4 = 0 . . . . . collect terms
x +5 1/3 = 0 . . . . . . . simplify
x = -5 1/3 . . . . . . . . . subtract 5 1/3. This result is in the domain
__
-2 ≤ x < 4Only the argument of |x -4| is negated.
1/3(-(x -4)) -2/3x -2(x +2) = 0
x(-1/3 -2/3 -2) +4/3 -4 = 0 . . . . collect terms
-3x -8/3 = 0 . . . . . . . simplify
-3x = 8/3 . . . . . . . add 8/3
x = -8/9 . . . . . divide by -3. This result is in the domain
__
4 ≤ xNeither absolute value function argument is negated.
1/3(x -4) -2/3x -2(x +2) = 0
x(1/3 -2/3 -2) -4/3 -4 = 0 . . . . . collect terms
-7/3x -8/3 = 0 . . . . . . . . . simplify
-7/3x = 8/3 . . . . . . . . add 8/3
x = -8/7 . . . . . . . . . divide by -7/3. This result is not in the domain.
There is no solution in this region.
__
The solutions are ...
x = -5 1/3x = -8/9Solve the equation with rational exponents
(x-1)3/2=27
[tex]~~~~~~(x-1)^{\tfrac 32} =27\\\\\implies \left[(x-1)^{\tfrac 12} \right]^3 = 3^3\\\\\implies (x-1)^{\tfrac 12} = 3~~~~~~~~~;[\text{Cube root on both sides}]\\\\\implies x -1 = 9~~~~~~~~~~~~;[\text{Square both sides}]\\\\\implies x = 10[/tex]
HELPPPPPPPPP!!!!!!!!!!!!!!!!
Select the statement that describes this expression: fraction 1 over 2 x (734 − 246).
Half the sum of 734 and 246
fraction 1 over 2 the difference between 734 and 246
fraction 1 over 2 the quotient of 734 and 246
2 times the difference between 734 and 246
please help me quick!
Answer:
transition 1 would be 5 to the right
transition 2 would be 1 down
Step-by-step explanation:
Which of the following functions matches this graph?
The equation that match the graph is
b. y = 3x^2
What is vertical stretch?In mathematics, a vertical stretch is a transformation of a function that changes the distance between the function's graph and the x-axis without changing its shape.
A vertical stretch multiplies all the y-coordinates of a function's graph by a constant factor greater than 1. This causes the graph to be stretched vertically and move further away from the x-axis.
For example, if we have a function f(x) = x^2, a vertical stretch by a factor of 3 would result in the function g(x) = 3x^2.
The graph of g(x) would be the same as that of f(x), but stretched vertically by a factor of 3.
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rewrite! Write an new and equivalent equation that is easier to solve
[tex]\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]
Given - an equation in a standard formTo do - simplify the equation so as to obtain an easier oneSince the equation provided isn't in it's general form , let's first convert it ~
General form of a Linear equation -
[tex]\bold{ax + b = 0}[/tex]
The equation after getting converted will be as follows ~
[tex] - 7 + ( \frac{4x + 2}{2} ) = 8 \\ \\ \implies \: \frac{ - 14 + 4x + 2}{2} = 8 \\ \\ \implies \: - 14 + 4x + 2 = 16 \\ \\ \implies \: 4x = 16 + 14 - 2 \\ \\ \implies \: 4x = 28 \\ \\\bold{ General \: form \: \dashrightarrow \: 4x - 28 = 0}[/tex]
hope helpful ~
Help me with the 2 problems
Answer:
9) Vincent will not get the correct answer because the + 484 is unneccesary, as he already subtracted it.
10a) 310,000 + x = 465,000; so x = 155,000
10b) 930,000/310,000 = 3 times more
Step-by-step explanation:
For which values of m is the equation always true.
Answer:
m∈(-∞;-2]∪[6;+∞).
Step-by-step explanation:
1) Δ=b²-4ac, then
m²-4(m+3)≥0; ⇔m²-4m-12≥0; ⇔ (m-6)(m+2)≥0;
2) m∈(-∝;-2]∪[6;+∝).
What is the area of the pizza? Explain how you know and the formulas that you used.
Answer:
90.24 in²
Step-by-step explanation:
Area of the pizza :
⇒ Area (rectangle) + Area (semicircle)
⇒ length × width + π × (radius)²
⇒ 8 x 5 + 3.14 x 4²
⇒ 40 + 3.14 × 16
⇒ 40 + 50.24
⇒ 90.24 in²
The area of a 2D form is the amount of space within its perimeter. The area of the pizza is 65.1327 in².
What is an area?The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.
The area of the pizza = Area of semi-circle + Area of Rectangle
= (π/2)r² + (d×h)
= [(π/2)×4²] + (8×5)
= 25.1327 in² + 40 in²
= 65.1327 in²
Hence, the area of the pizza is 65.1327 in².
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how many circular tiles are needed for pattern 20
Which of the following graphs matches the equation y=−4x+3?
CLEAR CHECK
On a coordinate plane, a line goes through (0, 3) and (3, negative 3).
On a coordinate plane, a line goes through (negative 2, 5) and (0, negative 3).
On a coordinate plane, a line goes through (0, 3) and (3, negative 1).
Answer:
On a coordinate plane, a line goes through (0, 3) and (3, negative 1).
Answer: the bottom left
Step-by-step explanation:
you will find it or just look it up if im wrong
HELP!!! The box plots compare the speeds of cars traveling on a highway
Answer:
See below ~
Step-by-step explanation:
The statements which are true :
The interquartile range for the cars going South is 9The maximum speed for the cars going North is higher than the maximum speed for the cars going SouthThe interquartile range for the cars going North is higher than the interquartile range for the cars going SouthWhich is a statistical question that you can ask to learn about your classmates' pets?
How many students in my class have a dog for a pet?
How many pets are in each student's household?
O How many classmates have a reptile for a pet?
How many pets does Mrs. Bruckner have?
Answer:
Answer "A" is correct
Step-by-step explanation:
I got it right on edge test
EXTREMELY URGENT Which function, g or h, is the inverse function for function ƒ?
the function h because the graphs of ƒ and h are symmetrical about the line y = x
the function g because the graphs of ƒ and g are symmetrical about the line y = x
the function h because the graphs of ƒ and h are symmetrical about the x-axis
the function g because the graphs of ƒ and g are symmetrical about the x-axis
Answer:
The answer is The function g because the graphs of ƒ and g are symmetrical about the line y = x
Step-by-step explanation:
A function and its inverse function become symmetrical across the line y = x.
Isabel works for a company that makes toys. She is trying to figure out what types of toys kids enjoy playing with most. She started with a survey asking whether kids liked dolls or trains. She surveyed 80 kids. Of the kids who don't like dolls, 30% more kids like trains than don't like trains. Fill out the rest of his table.
The table that represents the survey conducted by Isabel is:
Like Dolls Don't like Dolls Total
Like Trains 40 15 55
Don't like Trains 17 8 25
Total 57 23 80
How can the table be filled?The total number of kids that like dolls = total number kids - total number of kids that don't like dolls
80 - 23 = 57
Number of kids that don't like Trains but like dolls = total number kids that like dolls - Number of kids that like Trains and dolls
57 - 40 = 17
Number of kids that don't like dolls and but like trains :
30% x 23 = 7
(23 - 7) /2 + 7 = 15
Number of kids that don't like dolls and trains = (23 - 7) / 2 = 8
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Every variable has a coefficient. That’s the number it is multiplied by. According to mathematical convention, coefficients always go in front of their variable. If there is no number in front of a variable in an expression, the coefficient is 1 since the product of any number and 1 is that number. In expressions, operations can be applied directly to a variable. Here are some examples: What is the coefficient of the variable in the expression ½ + v - 3?
Answer:
1
Step-by-step explanation:
Answer:
There is only 1 variable and it is v.
There is no coefficient.
That means the coefficient is 1.
The coefficient of the variable in the expression ½ + v - 3 is [tex]\frac{1}{2}[/tex]
What is the coefficientIn mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series, or any expression; it is usually a number, but may be any expression (including variables such as a, b, and c). When the coefficients are themselves variables, they may also be called parameters.
Given that,
[tex]\frac{1}{2}[/tex] is the coefficient
[tex]v[/tex] is the variable
[tex]3[/tex] is the constant
Therefore, The coefficient of the variable in the expression ½ + v - 3 is [tex]\frac{1}{2}[/tex]
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Your Assignment
210 students were asked whether they want to go to a water park or a roller skating rink for a class party.
50 students are girls who want to go to the water park.
45 students are girls who want to go skating.
60 students are boys who want to go to the water park.
Water park
Skating
Total
Boys
Girls
Total
Answer the questions to analyze the data.
1. Use the given information to fill in the two-way table.
find the volume of this figure. round your answer to the nearest hundredth. if necessary
#8
Answer:
30 miles²
Step-by-step explanation:
To solve the area of the prism we have to multiply the area of the base * the height of the prism. The base of the prism is a right triangle.
(b*h)÷2 = Area of a triangle
Base = 4
Height = 3
Now:
(4*3)/2 = 6 miles²
Now we have to multiply 6 miles² by 5 as our height.
We get 30 miles² as the volume of the figure.
Answer for x?
Helppp
Answer:
x = 7
The length of the side is 18
Step-by-step explanation:
40 / 16 = 2.5
meaning the shape is dilated by 2.5
45 / (2x + 4) = 2.5
→ multiply both side by the denominator
45 / (2x + 4) * (2x + 4) = 2.5 * (2x + 4)
→ simplify
45 = 2.5 * (2x + 4)
→ divided both side by 2.5
45 / 2.5 = 2.5 * (2x + 4) / 2.5
18 = 2x + 4
→ subtract 4 from both sides (want x alone)
18 - 4 = 2x + 4 - 4
14 = 2x
→ divid both side by 2
14 / 2 = 2x / 2
7 = x
Plug in x:
2x + 4 = 2(7) + 4
14 + 4 = 18
Evaluate the expression below for x = 2.
3x+4 x-81-14
Answer:
I think that the answer is -81
Step-by-step explanation:
We have 3x+4x-81-14 x is given as 2.So we'll have 3*2+4*2-81-14= -81 per my calculations. TRY THIS
Does this app offer tutoring for college algebra?
find the domain and range with a vertex of (1,-2)
Answer:
see explanation
Step-by-step explanation:
the domain ( values of x ) that a quadratic can have is all real numbers
domain : - ∞ < x < ∞
the range ( values of y ) are from the vertex upwards , that is
range : y ≥ - 2
Tony orders 3 copies of a book online. He pays $2 for
shipping.
Which expression represents his total cost?
Answer:
A. 3b + 2
Step-by-step explanation:
We know that Tony ordered 3 copies and the shipping costs $2, what we don't know is b.
What don't we know? The cost of the 3 copies.
So 3b (3 multiplied by the cost(?)) + (because shipping is more money so we use addition.) and we know that the shipping is $2. Therefore our expression is
3b + 2
A frame around a rectangular family portrait has a perimeter of 96 inches. The length of the frame is 6 inches less than
twice the width. Find the length and width of the frame.
Width of the frame is
inches
Length of the frame is
inches
The length is 30 inches.
How to get the length of the frame?
For a frame of length L and width W, the perimeter is:
P = 2*(L + W).
Here we know that:
P = 96 in
L = 2*W - 6in
Replacing that we get:
96in = 2*( (2*W - 6 in) + W)
Now we can solve that equation for W:
96in = 2*(3W - 6in)
96in/2 + 6in = 3W = 54in
W = (54in)/3 = 18in
The width is 18 inches, then:
L = 2*W - 6in = 2*(18 in) - 6in = 30in
The length is 30 inches.
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va rog, dau coroana + 20 de puncte (doar exercitiul 2)
Step-by-step explanation:
a) 1*7=7 (Litres);
b) 1*2*5=10 (Litres);
c) 10*0.5*1/0.5=10 (bottles)
What is the mean absolute deviation of 4,6,7,10,13
Answer:
2.8
Step-by-step explanation:
To find the mean aboslute deviation, you first need to find the mean:
(4 + 6 + 7 + 10 + 13)/5 = 8
Then, subtract the mean from each value, and take the abosulte value. Absolute value is essentially the same number, but if it is negative, make it positive.
4 - 8 = -4 = 4
6 - 8 = -2 = 2
7 - 8 = -1 = 1
10 - 8 = 2 = 2
13 - 8 = 5 = 5
Then, take the mean of all of these values:
(4 + 2 + 1 + 2 + 5)/5 = 2.8
What is the slope of the line through (-4,2) and (−4,2)
Answer:
Step-by-step explanation:
there is no slope. they have the same coordinates