The solution of the given equation -3(x-4)=2(x+8) is at x = -4/5.
According to the given question.
We have a linear equation in one variable.
-3(x-4)=2(x+8).
As we know that,the linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.
Thereofre, the solution of the given equation is given by
-3(x - 4) = 2(x + 8)
⇒ -3x + 12 = 2x + 16
⇒ -3x - 2x = 16 - 12
⇒ -5x = 4
⇒ x = -4/5
We get the solution of the given equation is at x = -4/5.
Now, we can check that x = -4/5 is a solution of the given equation or not.
Therefore,
L.H.S
= -3(-4/5 - 4)
= 12/5 + 12
= (12 + 60)/5
= 72/5
Similarly,
R.H.S
= 2(-4/5 + 8)
= -8/5 + 16
= -8 + 80/5
= 72/5
So, L.H.S = R.H.S
Hence, the solution of the given equation -3(x-4)=2(x+8) is at x = -4/5.
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PLS HELP QUICK
I NEED HELP
Answer:
B
Step-by-step explanation:
-20+-32.5= -52.5
-52.5+ 40= -12.5
put numbers in order from least to greatest. \sqrt{9} -2.2 -30/6 2.5 13/7 3.5 -4 5/9
The numbers in order from the least to the greatest is 5, -45/7, -2.2, 13/7, 2.5, √9, 3.5.
What is the order of the numbers?When ordering a number from the least to the greatest, the negative number is smaller than the positive numbers. The farther a negative number is from 0 on the number line, the smaller the number is. The farther a positive number i from 0 on the number line, the larger the number is.
To order a number from least to greatest, convert al the numbers to decimals. A decimal is a number that is made up of integers and non-integers. The integers are separated from the non integers by a decimal point.
√9 = 3
-30/6 = - 5
13 / 7 = 1.857
- 4 5/9 = -4.56
The numbers ordered from least to greatest is:- 5, -45/7, -2.2, 13/7, 2.5, √9, 3.5
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With the information given, can you prove that this quadrilateral is a parallelogram?
Yes or No
PLEASE HELP
Answer:
yes
Step-by-step explanation:
there are two sets of parrelell line
i might have spelled it wrong
The parallelogram is ABCD with the sides AD parallel to BC
What is a Parallelogram?A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure
The four types are parallelograms, squares, rectangles, and rhombuses
Properties of Parallelogram
Opposite sides are parallel
Opposite sides are congruent
Opposite angles are congruent.
Same-Side interior angles (consecutive angles) are supplementary
Each diagonal of a parallelogram separates it into two congruent triangles
The diagonals of a parallelogram bisect each other
Given data ,
Let the figure be represented as ABCD
Now , the sides AD and BC are parallel to each other
And , from the figure , we can say that the sides AB is parallel to CD
Therefore , the figure ABCD is a parallelogram
And , opposite sides of a parallelogram are parallel
Hence , the figure ABCD is a parallelogram
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The perimeter of a pool is 150m. the rectangle at the at the right is a scale drawing of the pool. the length of each square on the grid represents 1 cm. draw another scale drawing of the pool using 25 m to 2 cm.
Answer:
Step-by-step explanation:
The length and the width of the rectangle basee on the perimeter will be 2 and 4cm.
How to calculate the value?
From the given rectangle,
Length of the rectangle = 5 cm
Width of the rectangle = 10 cm
Ratio of length : width = 1 : 2
Perimeter of the rectangle = 2(l + b)= 150 cm
l + b = 75 -----(1)
Since, l : b = 1 : 2
b = 2l ------(2)
From equations (1) and (2)
l + 2l = 75
3l = 75
l = 75/3
l = 25 m
Width 'b' = 2(25) = 50 m
Now we have to draw a rectangle with a scale = 25 : 2
Therefore, the scale factor =
l = 2 cm
Similarly,
w = 4 cm
Now we can draw a rectangle with length = 2 cm and width = 4 cm.
meaghan goes to the grocery store to buy hot dogs and hamburgers for a cookout. She buys a total of 6 packages for a total of $30.46. If a package of hot dogs costs $2.65 and a package of hamburgers costs $6.29, determine how many packs of each she bought.
The number of packs of hot dogs bought is 2 packs
The number of packs of hamburgers bought is 4 packs
How to calculate the number of each packs bought ?Let x represent the number of hot dogs bought and y represent the number of hamburgers bought
x + y= 6.........equation 1
2.65x + 6.29y= 30.46.........equation 2
From equation 1
x + y= 6
x= 6 - y
Substitute 6 - y for x in equation 2
2.65(6-y) + 6.29y = 30.46
15.9 - 2.65y + 6.29y = 30.46
3.64y = 30.46 - 15.9
3.64y= 14.56
y= 14.56/3.64
y= 4
Substitute 4 for y in equation 1
x + y= 6
x + 4= 6
x= 6 - 4
x= 2
Hence 2 packs of hot dogs and 4 packs of hamburgers were bought
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Graph the line y=-3x+b if its graph goes through the given point.
B(5,2)
The equation of the line y = -3x + 17 would have a graph that is shown in the diagram attached below.
How to Graph the Equation of a Line?Given that the line y = -3x + b goes through the point B(5, 2), it means that the slope (m) of the line would be -3, while the line would intercept the y-axis at b.
To find the value of b, substitute (x, y) = (5, 2) into y = -3x + b:
2 = -3(5) + b
2 = -15 + b
2 + 15 = b
17 = b
b = 17
Thus, the equation of the line y = -3x + 17 would have a graph that is shown in the diagram attached below.
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The equation has one solution
which when substituted into the
A value of a that makes the equation true is
equation and simplified makes the equation turn into
which when substituted into the
A value of a that makes the equation false is
equation and simplified makes the equation turn into
Answer:
x+3=3+x
x+3=x+3
Step-by-step explanation:
Order the square root of 60, negative 7.7 repeating, forty-four sixths, and negative seven and one sixth from least to greatest.
The order from least to greatest is negative 7.7 repeating, negative seven and one sixth, forty-four sixths and square root of 60
How to determine the orderTo determine the order from least to greatest is to arrange the values in an ascending order.
Given the values as;
square root of 60 negative 7.7 repeating forty-four sixths negative seven and one sixthThis is expressed as;
√60 = 7. 75
-7. 7
44/ 6 = 7. 33
-7 1/6 = -43/ 6 = -7. 17
The order from least to greatest is -7. 7, -7. 17 , 7. 33 and 7. 75
Thus, the order from least to greatest is negative 7.7 repeating, negative seven and one sixth, forty-four sixths and square root of 60
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How do you solve for x?
Answer: x=60/13
Step-by-step explanation:
The smaller triangle has the same proportions as the bigger triangle.
Hence, 13/12=5/x
13/12=5/x
13 * x/12=5
13x=5*12
13x=60
x=60/13
You can choose between two tennis courts at two university campuses to learn how to play tennis. One campus charges 25 per hour. The other campus charges 20 per hour plus a one-time registration fee of 10 .
b. Find the number of hours for which the costs are the same.
For 2 hours the cost will be same.
Firstly forming the equation as per the given information in question. Let us assume the number of hours to be t.
Cost on choosing first campus -
Cost = 25 × t
Cost on choosing second campus -
Cost = 10 + 20 × t
Now, equating both the equations to find the required time..
25t = 10 + 20t
Shifting 20t to Left Hand Side of the equation
25t - 20t = 10
Performing subtraction to find the value of t
5t = 10
Shifting 5 to Right Hand Side of the equation at denominator
t = 10÷5
Performing division to find the value of t
t = 2
Therefore, the number of hours for which the costs are the same is 2.
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The equation F = (9/5) C+32 relates temperatures on the Celsius and Fahrenheit scales. Does any temperature have the same number reading on both scales? If so, what is the number?
Both Fahrenheit and Celsius scales will have the same reading at temperature -40⁰.
The equation to convert temperature reading from Celsius to Fahrenheit degree is:
F = (9/5) C + 32
Where:
F = Fahrenheit reading
C = Celsius reading
The equation tells us that the ratio of increment in Fahrenheit to Celsius scale is 9 : 5, and there is an offset 32 degree in Fahrenheit scale.
Suppose a specific temperature has the same number reading on both scales, then:
F = C
Substitute this into the equation:
F = (9/5) C + 32
C = (9/5) C + 32
C - (9/5) C = 32
-4/5 C = 32
C = 32 . (-5/4) = -40
Hence, both Fahrenheit and Celsius scales have the same reading at temperature -40⁰.
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A punch recipe calls for 12 cups of lemonade for every 4 gallons of orange juice.
The ratio of quarts of punch to cans of frozen orange is 3/2 with maintaining the ratio to make 4 quarts of a punch we need 2 2/3 cans of frozen orange.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Given that,
2 cans of frozen oranges are used to make 3 quarts of punch.
So,
quarts of punch/cans of frozen oranges = 3/2
Now with the same ratio if we use 4 quarts of punch
Then,
3/2 = 4/ cans of frozen orange
Cans of frozen orange = 4(2/3)
⇒ 8/3 = 2 2/3.
Hence " To make 4 quarts of a punch we need 2 2/3 cans of frozen orange".
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Owen washes cars for $18 per car. One Saturday, one of his customers gave Owen a $12 tip. At the end of the day, Owen had made $120. Write and solve an equation to show the number of cars Owen washed that day.
Answer:
6
Step-by-step explanation:
Let the amount of cars washed be x
120-12
---------- = x
18
108/18 =x
x=6
Please help i am not sure how to do this
Delta Math -
What is the domain of the function shown in the graph below?
Answer Type:
Interval
All Real Numbers
All values except one
All values except two
The answer type is interval and the interval is (-∞,5).
The value of x is the domain for which the function is defined. Function in this case can use value from (-∞,5).
Graphs can be used to specify the domain and set of functions. The domain of a graph is made up of all the input values displayed on the x-axis since the term "domain" refers to the set of potential input values. The range is the collection of potential output values, as displayed on the y-axis. Remember that the domain and range of the graph may be larger than the values seen if the graph extends beyond the area that is visible.
Consider the function y = f(x), which has the independent variable x and the dependent variable y. A value for x is said to be in the domain of a function f if it successfully allows the production of a single value y using another value for x.
Hence, The type of answer is interval and the values of interval is (-∞,5).
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Multiply (4.12 × 10^−9)(8.3 × 10^15). Write the final answer in scientific notation.
34.196 × 10^−134
3.4196 × 10^7
3.4196 × 10^−135
34.196 × 10^6
The product in scientific notation of (4.12 × 10^−9)(8.3 × 10^15) is 3.4196 * 10^7
How to evaluate the product in scientific notation?The product expression is given as
(4.12 × 10^−9)(8.3 × 10^15)
Rewrite properly as
(4.12 × 10^−9)(8.3 × 10^15) = (4.12 × 10^−9) * (8.3 × 10^15)
Evaluate the product of 4.12 and 8.3 in the above expression
So, we have
(4.12 × 10^−9)(8.3 × 10^15) = 34.196 * 10^−9 × 10^15
Evaluate the product of 10^−9 and 10^15 in the above expression
So, we have
(4.12 × 10^−9)(8.3 × 10^15) = 34.196 * 10^6
Rewrite the expression as
(4.12 × 10^−9)(8.3 × 10^15) = 3.4196 * 10^7
Hence, the product in scientific notation of (4.12 × 10^−9)(8.3 × 10^15) is 3.4196 * 10^7
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Answer:
Its B. 3.4196 x 10^7
Step-by-step explanation:
This is correct answer :))
Write the function rule for each function reflected in the given axis.
f(x) = x+1 ; x - axis
Functions can be reflected on the x-axis, the y-axis, or both axes. For example, function reflection y= f(x) can be written as y= -f(x) or y= f(-x) even y= -f(-x). There are four types of function or graph transformations: reflection, rotation, translation, and dilation. In mathematics, especially geometry, mirror or mirroring means flipping, so basically, the mirroring of a function is the mirror image of a given function or graph. Hence the reflection function is commonly known as the reflection function.
The reflection of the given function should be similar in size and shape to the original function.
f(x)=x+1; x-axis
(consult the pictures attached)
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what number is not irrational, their opposite is a natural number, is not a whole number, and is greater than -13?
The required no . is 1 / q where q > 2 and q is natural no .
For instance , let's take 1 / 2 ,
1 / 2 is one possible solution to this .
1 / 2 is not irrational .
Opposite of 1 / 2 is 2 which is a natural no .
Clearly , 1 / 2 is not a whole no .
Even it is greater than - 13 .
All the conditions are satisfied , hence 1 / 2 is one possible solution to this problem .
All the nos . of the form 1 / q where q > 2 and q is natural no . will satisfy the conditions of the question .
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given aright triangle with legs a and b, hypnoses c, find the lenght of side b if =
c=9, a=7
Determine whether each function is linear or quadratic. Identify the quadratic, linear, and constant terms. g(x)=-2 x²-3(x-2)
The function g(x) is a quadratic function:
Its quadratic term is -2x²Its linear term is - 3xIts constant is 6What are functions?Functions are algebraic expressions that have at least two variables, in order to make their visual representation through a graph and evaluate their behavior.
This problem deals with linear or quadratic functions, and these differ in the degree of the exponent of the variable:
1 : linear
2 : quadratic
The function:
g(x) = -2x² - 3(x- 2).
g(x) = -2x² - 3x + 6 , we have a quadratic function.
Its quadratic term is -2x²Its linear term is - 3xIts constant is 6Learn more about functions at:
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Three consecutive even integers are such that the sum of the smallest and three times the second is 38 more than twice the third. Find the largest integer.
The largest integer of the three even consecutive integers is 24
We have been given that there are 3 even consecutive integers.
Let the first integer be = x
Let the second integer be = (x+2)
Let the third integer be = (x+4)
According to the question, the equation according to the condition given will be
x + 3(x+2) = 38 + 2(x+4)
Solving the equation, the value of x will be
x + 3x + 6 = 38 + 2x + 8
4x + 6 = 46 + 2x
2x = 40
x =20
Hence, the integers are
first term = x =20
Second term = x+2 = 20+2 = 22
Third term = x+4 = 20+4 = 24
Thus the largest integers is 24
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Is it possible to find the area of a parallelogram by just multiplying the lengths of two adjacent sides?
Answer:
Yes.
Step-by-step explanation:
Is it possible to find the area of a parallelogram by just multiplying the lengths of two adjacent sides?
It is to find the area of a parallelogram by just multiplying the lengths of two adjacent sides. Let us now find a relation, if any, between the areas of two parallelograms on the same base and between the same parallels.
Please answer questions 10-16. It would help me a whole bunch! You would be a total lifesaver! I will mark you a brainliest to anyone that answers!
Answer:
Step-by-step explanation:
10)99
16)a)4/13
b)8/13
c) 7/13
Identify the segment bisector of RS
The length of RS is
Answer:
The segment bisector of RS is KM and RS Lenght is 34CM
Step-by-step explanation:
17+17=34
If x=-3, then 4x²-7x+5=
A 2
B 14
C 20
D 42
E 62
The value of the polynomial at the point [tex]x=a[/tex], just replace [tex]x[/tex] with [tex]a[/tex] in the polynomial equation.
Verify the following equation:
[tex]=4x^{2} -7x+5[/tex]
The given solution:
[tex]x=-3[/tex]
[tex]4x^{2} -7x+5[/tex]
Find the equation:
[tex]4x^{2} -7x+5[/tex]
[tex]4(-3x)^{2} -7(-3)+5[/tex]
[tex]=4(9)+21+5[/tex]
[tex]=36+26[/tex]
[tex]=62[/tex]
Therefore,The option E [tex]62[/tex] is the correct answer
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The grid above shows the graph of the parent function f(x)= |x| and a translated functions graph. Write the equation for the translated graph.
Using translation concepts, the equation for the translated graph is given by:
g(x) = |x + 2| + 1.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s range(involving values of y) or in it’s domain(involving values of x). Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis, or rotations of a degree measure around the origin.
From the graph, we have that the parent function was:
Shifted left 2 units, hence x -> x + 2.Shifted up 1 unit, hence y -> y + 1.Hence, considering the parent function f(x) = |x|, the equation for the translated graph is given by:
g(x) = |x + 2| + 1.
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You are considering renting a car from two different rental companies. Proxy car rental company charges .32 per mile plus an 18 surcharge. YourPal rental company charges .36 per mile plus a 12 surcharge.
c. Which company offers the better deal for an 820 -mile trip?
150 is the cost of renting a car from YourPal.
What is surface area of cuboid ?
The six rectangular faces of a cuboid. Add the areas of each of the cuboid's six faces to determine its surface area.Additionally, we can label the prism's length (l), width (w), and height (h), and then calculate its surface area using the formula SA=2lw+2lh+2hw.Let y = total charge for a car rental and x = miles drivenProxy car equation: y = 0.32x + 18
YourPal equation: y = 0.36x + 12
Set equations right sides equal to each other... meaning their cost, y, are equal
0.32x + 18 = 0.36x + 12
18 = 0.04x + 12 (subtract 0.32x from both sides of the equation)
6 = 0.04x (subtract 12 from both sides of the equation)
150 = x (divide both sides of the equation by 0.04)
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Find following measure.
m GH
If m FH = (31x + 3°), m GH = (33x + 3°) and m ∠FHG = (28x − 3°) then the measure of ∠FGH is 48°.
How to find the measure of ∠FGH?Given: m FH = (31x + 3°), m GH = (33x + 3°) and m ∠FHG = (28x − 3°)
Based on the above information, we get
m FG = 2(m ∠FHG) = 2(28x - 3)°= (56x - 6)°
The arcs in the circle add up to 360 degrees, then
m FG + m FH + m GH = 360°
120x = 360°
x = 3
Substitute the value of x in m ∠FHG in we get
28(3) - 3 = 81°
The measure can be found using the triangle sum theorem (all angles in a triangle must add up to 180°).
Firstly, it is known that ∠GFH would be an inscribed angle if the chord from F to G is drawn, and the arc GH would be twice its measure.
m GH = 33(3) + 3 = 102°
Half of that would be m ∠GFH = 51°
According to the triangle sum theorem all angles of the triangle must add up to 180°:
Therefore, m ∠GFH+ m ∠FGH +m ∠FHG= 180°
m ∠FGH = 48°
Therefore, the measure of ∠FGH is 48°.
The complete question is:
Given: circle k(O), m FH = (31x + 3°) m GH = (33x + 3°)
m ∠FHG = (28x − 3°) Find: m ∠FGH
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A contractor purchases 6 dozen pairs of padded work gloves for $85.68. He incorrectly calculates the unit price as $14.28 per pair for the expense report. What is the correct unit price? What is the error?
100 POINTS!!
A 28.5-Newton force is applied at a 30-degree angle to the horizontal to accelerate a 6.5-kg box across a rough surface (coefficient of friction = 0.22). Use g = 9.8 m/s/s to find frictional force (F(frict)) , normal force (F(norm)) , gravitational force (F(grav)) , and acceleration (a). Enter each answer accurate to the first decimal place.
Answer:
Frictional force (F(frict)) = 17.1 N
Normal force (F(norm)) = 78.0 N
Gravitational force (F(grav)) = 63.7 N
Acceleration (a) = 1.2 ms⁻²
Step-by-step explanation:
Newton's second law:
[tex]\boxed{F_{net}=ma}[/tex]
where:
[tex]F_{net}[/tex] = overall resultant force.m = mass.a = acceleration.Use trigonometry to resolve the 28.5 N force into its horizontal and vertical components since it is acting on the particle at 30°:
[tex]\implies F_x=28.5 \cos 30^{\circ}[/tex]
[tex]\implies F_y=28.5 \sin 30^{\circ}[/tex]
Weight (mg)Due to the particle's mass, m, and the acceleration due to gravity, g:
[tex]\boxed{W=mg}[/tex]
Given:
m = 6.5 kgg = 9.8 ms⁻²[tex]\begin{aligned}W & = mg\\\implies W & = 6.5 \times 9.8\\W & = 63.7\;\sf N\end{aligned}[/tex]
Normal reaction (R)The particle is moving parallel to the plane (the horizontal), so acceleration perpendicular to the plane is zero.
Resolving forces vertically (taking ↑ as positive):
[tex]\begin{aligned}F & = ma\\\implies R-W-28.5 \sin 30^{\circ}&=6.5 \times 0\\R-W-28.5 \sin 30^{\circ}&=0\\R & = W+28.5 \sin 30^{\circ}\\R & = 6.5(9.8)+28.5(0.5)\\R & = 63.7+14.25\\R & = 77.95\\R & = 78.0 \;\; \sf N\; (1\:d.p.)\end{aligned}[/tex]
Frictional force (F)When a moving object is acted on by a frictional force, fiction is limiting, and the frictional force F is at its maximum value:
[tex]\boxed{F = \mu R}[/tex]
(Where μ is the coefficient of friction and R is the normal reaction).
[tex]\begin{aligned}F & = \mu R\\\implies F & = 0.22 \times 77.95\\F & = 17.149\\F & = 17.1 \;\; \sf N\;(2\:d.p.)\end{aligned}[/tex]
Acceleration (a)Friction always acts in the opposite direction to motion (or potential motion).
Resolving forces horizontally (taking → as positive):
[tex]\begin{aligned}F & = ma\\\implies 28.5 \cos 30^{\circ}-F & = 6.5a\\28.5 \left(\dfrac{\sqrt{3}}{2}\right)-17.149 & = 6.5a\\\dfrac{57\sqrt{3}}{4}-17.149 & = 6.5a\\7.532724008 & = 6.5a\\a & = 1.158880617\\a & = 1.2\; \sf ms^{-2}\;\;(1\:d.p.)\end{aligned}[/tex]
