1) Let's solve this Linear System, using the method of Elimination/Addition
-x+y=-7 Multi
4x+4y = 20
2 Sue is x years old. She is over 2.
Ben is twice as old as Sue.
Ceri is 4 years older than Sue.
The total of their three ages is less than 28.
a Write this information as an inequality.
b What age could Sue be?
c What are the corresponding ages of Ben and Ceri?
a. x < 2
b. Sue's age = 4
c. Ben's age = 8 and Ceri's age = 16
How to solve Ages problems ?
- If the present age is y, then n times the present age = ny.
- If the present age is x, then age n years later/hence = x + n.
According question,
Sue = x
She is over 2, so Sue = x+2
Ben age is twice as old as Sue,
so, Ben = 2(x+2)
Ceri is 4 years older than Sue.
so, Ceri = 4(x + 2)
The eq. will form as,
(x+2) + 2(x+2) +4(x+2) < 28
=> x + 2 + 2x+ 4 + 4x + 8 < 28
=> 7x < 28 - 14
=> 7x < 14
=> x < 2
Sue age = x + 2 = 2 + 2 = 4
Ben's age = 2( x + 2) = 2(2 + 2) = 8
Ceri's age = 4(x + 2) = 4(2 + 2) = 16
Therefore, the answer of a. x < 2
b. Sue's age = 4
c. Ben's age = 8 and Ceri's age = 16
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A company rents storage sheds shaped like rectangular prisms. Each shed is 12 feet long, 8 feet wide, and 10 feet tall. The rental cost is $3 per cubic foot. How much does it cost to rent one shed?
Answer:
$2880
Step-by-step explanation:
Volume of rectangular prism:First find the volume of the prism.
l = 12 ft
w = 8 ft
h =10 ft
[tex]\sf \boxed {\bf Volume \ of \ rectangular \ prism = l*w*h}[/tex]
= 12 *8 * 10
= 960 cubic feet
To find the rental cost, multiply the volume of the prism by the rental cost per cubic foot.
Rental cost = 960 * 3
= $ 2880
2) The midpoint M of line segment AB has coordinates (-3, 4). If A is the origin (0.0),
what are the coordinates of point B? (The use of the accompanying grid is optional)
Step-by-step explanation:
the coordinates of the midpoint between points A and B are
((xa + xb)/2, (ya + yb)/2)
in our case that is (-3, 4).
xa = 0
ya = 0
so we get
-3 = (0 + xb)/2
-6 = 0 + xb = xb
4 = (0 + yb)/2
8 = 0 + yb = yb
B = (-6, 8)
C is the point (1;-2) .The point D lies in the second quadrant and has coordinates (x;5) . If the Length of CD is the square root of 53 units , determine the value of x
The value of x would be -1 and the point D lies in the second quadrant and has coordinates (-1, 5).
What is the distance between two points?The distance between two points is defined as the length of the line segment between two places represents their distance. Most significantly, segments that have the same length are referred to as congruent segments and the distance between two places is always positive.
The formula of distance between two points is P(x₁, y₁) and Q(x₂, y₂) is given by: d (P, Q) = √ (x₂ – x₁)² + (y₂ – y₁) ².
We have been given as C is the point (1, -2)
The point D lies in the second quadrant and has coordinates (x, 5)
The Length of CD is the square root of 53 units.
Length of CD = √ (x – 1)² + (5 – (-2)) ²
√(53) = √ (x – 1)² + (5 – (-2))²
53 = (x – 1)² + (5 + 2)²
53 = x² - 2x + 1 + 49
x² - 2x -3 = 0
x = 3, -1
Since D lies in the second quadrant, so x-coordinate will be negative.
Therefore, the value of x would be -1.
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What is the equation of the line, in point-slope form, that passes through the given point and has the given slope?
Point: (4, -6) Slope: m = -3
A:y-6=-3(x+4)
B:y-x=-3(-6-4)
C:y-4=-3(x+6)
D:y+6=-3(x+4)
(-9√2) (4√6) in simplified form?
-72√3 is the simplified form .
What is the most basic form example?The term "reduced form" refers to the fraction's simplest form. As an illustration, the simplest form of a fraction with a common component of 1 is 34 However, while 2/4 can be further condensed and expressed as 12, it is not the most basic form.
What is the most basic radical form?Simply put, simplifying a radical eliminates the need to find any more square roots, cube roots, fourth roots, etc. when expressing it in its simplest radical form. Furthermore, it entails eliminating any radicals from the denominator of a fraction.
=> (-9√2)(4√6)
= −9√2*4√6
= -9*4√2*6
= -9*4√12
= -9*4*2√3
= -72√3
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1,000,000,000×40,000
1,000,000,000 x 40,000
This can be made easy if the numbers are expressed in standard form
[tex]\begin{gathered} 1,000,000,000=1X10^9 \\ \end{gathered}[/tex][tex]40,000=4X10^4[/tex]=>
[tex]1,000,000,000X40,000=1X10^9X4X10^4[/tex]=>
[tex]\begin{gathered} 4X10^{9\text{ + 4}} \\ \\ 4X10^{13} \\ \\ 4X10^{13}\text{ = 40, 000, 000, 000, 000} \\ \end{gathered}[/tex]Which of the following does NOT represent the distance a car travels when going 75 miles per hour
PLS HELP I WILL MARK BRAINLIEST
The answer is D which does not represent the distance a car travels when going 75 miles per hour. 1 Hour and 15mins a car travels 93 3/4 miles
How to calculate distance?Use the formula d = st, or distance equals speed times time, to find the distance. Since both represent a certain amount of distance per unit of time, such as miles per hour or kilometers per hour, rate and speed are comparable. If speed s and rate r are equal, then r = s = d/t.Speed is calculated as Distance x Time.Time is determined using the formula Time = DistancexSpeed.Distance is calculated as Distance = Speed x Time.Distance divided by time equals speed. Simply explained, it would look like this after traveling 60 kilometers in one hour: Distance (60 kilometers) divided by time (1 hour) equals 60 km/h.To learn more about Distance refer to:
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Mrs. Anderson bought $17.01 worth of ribs (r) and chicken (c). Ribs cost $1.89 per pound and chicken costs $0.90 per pound.
Write the equation that would represent this situation.
Pls hurry‼️‼️
Answer:
Step-by-step explanation:
17.01 = 1.89(r) + 0.90(c)
Giorgio fills up his car which is 60 liters.
After a certain distance, 340 deciliters remained in the tank.
How many liters did it consume?
How much did you spend if 1 liter costs € 1.45? How many liters of petrol can you buy for € 58?
My book has the answer but not step by step explanation
[ 26 liters; €37,70; 40 liters ]
The most appropriate choice for unitary method will be given by-
Volume of petrol consumed = 26 liters
Cost of 60 liters petrol = € 37.70
€ 58 is the cost of 40 liters of petrol
What is unitary method?
Unitary method is the method in which the value of single unit can be calculated from the value of multiple unit and value of multiple unit is calculated from the value of single unit.
Here,
Total volume of petrol filled by Giorgio in his car = 60 liters
Volume of petrol left = 340 deciliters
= [tex]\frac{340}{10}[/tex] liters
= [tex]34[/tex] liters
Volume of petrol consumed = (60 - 34) liters
= 26 liters
Cost of 1 liter petrol = € 1.45
Cost of 60 liters petrol = € 1.45 [tex]\times[/tex] 26
= € 37.70
€ 1.45 is the cost of one liter of petrol
€ 1 is the cost of [tex]\frac{1}{1.45}[/tex] liters of petrol
€ 58 is the cost of [tex]\frac{1}{1.45} \times 58[/tex] liters of petrol
€ 58 is the cost of 40 liters of petrol
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A nursery owner buys 9 panes of glass to fix some damage to her greenhouse. The 9 panes cost $.23.85 Unfortunately, she breaks 2 more panes while repairing the damage. What is the cost of another 2 panes of glass?
After doing some mathematical operations, we know that the cost of 2 panes is $5.3.
What exactly are mathematical operations?An operation, in mathematics, is a mathematical function that transforms zero or more input values into a precisely defined output value.The arity of the operation is influenced by the number of operands.The rules that specify the order in which we should carry out the operations required to solve an expression are referred to as the order of operations.PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction (from left to right).So, the cost of 2 panes:
The cost of 9 panes is $23.85.
Then, the cost of 1 pane will be:
23.85/9 = $2.65Now, the cost of 2 panes will be:
$2.65 × 2 = $5.3Therefore, after doing some mathematical operations, we know that the cost of 2 panes is $5.3.
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Pls help I’ll give BRAINLIEST!! :)
After doing some mathematical operations, we know that (A) Almond barks cost $0.25 more per ounce than peanut brittle.
What do we mean when we say mathematical operations?Any mathematical operation that converts zero or more discrete input values into discrete output values is known as a discrete operation.The number of operands affects how complicated the operation is.Functions that convert numerical inputs into numerical outputs are the four mathematical operations (i.e., another number).These are addition, subtraction, multiplication, and division.So, the cost of the candy per piece costs more:
Peanut brittle: weight 20 ounces and costs $20.Almond Bark: weight 16 ounces and costs $20.It is clear that Almond Bark costs more than Peanut brittle.
Now, the cost of 1 ounce:
Peanut brittle: 2/2 = $1Almond Bark: 5/4 = $1.25Difference: $1.25 - $1 = $0.25
Therefore, after doing some mathematical operations, we know that (A) Almond barks cost $0.25 more per ounce than peanut brittle.
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-14 + 3d = 13 what is d
how do you show a number with a decimal side repeating like 23.3333333333…
i’m slow mb guys i didn’t pay attention in 6th grade so 7th and 8th have been
Answer:
You can write 23.3 with a dot on the three after the decimal point
Ten out of every 32 people survey to play Amung us. what percent of people surveyed play amung us
The area of a circle is 1217 in². What is the
circumference, in inches? Express your answer in
terms of T.
Answer:
Your answer is [tex]T= 123.665974[/tex] inches
Margot goes to the store to buy curtains without measuring the lenght of her windows. she guesses the windows are 36 inches in length. when she gets home she measures and finds they are 40 inches in length.what is the percent error of her guess.
Answer:
The percent error is 10%
Step-by-step explanation:
The lengh of the windows are 40 inches, which is the 100% of the lengh.
What you have to do is to put 40 and 100 in a proportion with her guess, which is 36:
40 / 100 = 36 / x
so you do: (100 x 36) / 40 = 90%
This means that the percent error of her guess is 100% - 90% = 10%
Grammy Wolf has 7 coins in his pocket worth 65 cents how many quarters dimes and nickels does he have?
please help asap thank u so much
Answer: 2 quarters, 1 dime, 1 nickel
Step-by-step explanation: 2 quarters= 25+25=50, 1 dime=10, 1 nickel=5
50+10+5=60
jose va a comprar una bicicleta de tiene 28% de descuento si la bicicleta cuesta 3,600 ¿cuanto fue el descuento? ¿cuál es el nuevo precio de la bicicleta?
Answer:2,592
Step-by-step explanation:
Tienes que quitar de 3,600-28% = 2,592.
Answer:
el porcentaje es 0.28 o .28 y pagara por la bici 2402
Step-by-step explanation:
primero sacamos porcentaje 100 entre 28= 0.28
luego multiplico 3600 x .28= 998.00 (se le puede quitar los 00)
despues resto 3600-998 = 2402
y listo xdd
hi help please thanks
∠8 and ∠4 are the pair of alternate exterior angles.
What are alternate exterior angles?The pair of angles known as alternate exterior angles are those that are formed on the outer side of the parallel lines but on the transverse side. A triangle's exterior angle is the product of its two opposite interior angles. 180 degrees is the sum of the exterior angle and the interior angle. They form two pairs (four total angles) of alternate exterior angles because they are situated "outside" the two parallel lines but on opposite sides of the transversal.So, in the given image ∠8 and ∠4 are the pair of alternate exterior angles.
Therefore, ∠8 and ∠4 are the pair of alternate exterior angles.
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a line is drawn perpendicular to y=(1/2)x+6 and passes through the points (b,1) and (-3,2). what is the value of b
Answer:
[tex]{ \tt{y = \frac{1}{2} x + 6}} \\ [/tex]
- If two lines areperpendicular, their gradients have a relation below;
[tex]{ \tt{m_{1} \times m _{2} = - 1 }} \\ [/tex]
- Therefore, gradient for points (b, 1) and (-3, 2);
[tex]{ \tt{ \frac{1}{2} \times m _{2} = - 1}} \\ \\ { \tt{m = - 2}}[/tex]
- Therefore:
[tex]{ \tt{ - 2 = \frac{2 - 1}{ - 3 - b} }} \\ \\ { \tt{ - 2( - 3 - b) = 1}} \\ \\ { \tt{6 + 2b = 1}} \\ { \tt{2b = - 5}} \\ { \tt{b = - \frac{5}{2} }}[/tex]
If f(x) = 3x – 2 and g(x) = 2x + 1, find (f + g)(x).
Put your answer in standard form with no spaces.
The value of the composite function (f + g)(x) is 5x - 1
How to evaluate the function?The functions are given as
f(x) = 3x - 2
g(x) = 2x + 1
The composite function definition is given as
(f + g)(x)
This composite function is calculated using the following composite function formula
(f + g)(x) = f(x) +g(x)
Substitute the known values in the above equation
So, we have the following equation
(f + g)(x) = 3x - 2 + 2x + 1
Evaluate the like terms
(f + g)(x) = 5x - 1
Hence, the composite function is (f + g)(x) = 5x - 1
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A phone company charges a monthly fee of $13 plus 12 cents per text message. Another company charges $20 each month plus 8 cents per text message for the same plan. How many text messages will have to be sent for the cost of a phone plan from the first company to equal the cost of a phone plan from the second company?
The number of text messages that will have to be sent for the cost of a phone plan from the first company to equal the cost of a phone plan from the second company is 175.
Number of text messagesWe have to formulate and equation and then use the formulated equation to find the number of text messages.
Let c represent charges
Let t represent test messages
c = 13 + 0.12t
c = 20 = 0.08t
Hence,
13 +0.12t = 20 +0.08t
Collect like terms
7 =0.04t
Divide both side by 0.04t
t = 7 / 0.04
t= 175
Therefore 175 is the number of text messages needed.
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-3x-3y=3 y=-5x-17 its solving a question using subsitution
The required solutions are x = - 4 and y = 3 to the given linear system of equations. which are determined by the substitution method.
The linear system of equations is given in the question
-3x - 3y = 3 ....(i)
y = -5x - 17 ....(ii)
Substitute the value of equation (ii) in equation (i),
-3x - 3(-5x - 17) = 3
-3x - 3 ×-5x - 17 × -3 = 3
-3x + 15x + 54 = 3
Rearrange the terms likewise and apply the arithmetic operation,
12x + 51 = 3
12x = -48
x = -48/12
x = - 4
Substitute the value of x = - 4 in equation (ii), and solve for y
y = -5(-4) - 17
y = 20 - 17
y = 3
Thus, the required solutions are x = - 4 and y = 3 to the given linear system of equations.
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jeffrey has $1.20 more than ryan. when ryan hands jeffrey $7.50, jeffrey's money becomes 7 times as much as Ryan's. How much money did they each have at the beginning?
Ryan had $1.45 and Jeffrey had $2.65 in the beginning.
Let Ryan has $x. So, amount with Jeffrey is x + 1.20.
As per the information on exchange of money, the equation relating their possession is -
x + 1.20 + 7.50 = 7x
Evaluating the equation to find the value of x
7x - x = 7.50 + 1.20
Performing subtraction on Left Hand Side and addition on Right Hand Side
6x = 8.70
x = 8.70 ÷ 6
Performing division on Right Hand Side of the equation
x = 1.45
Amount with Jeffrey = 1.45 + 1.20
Amount with Jeffrey = $2.65
So, at the beginning Ryan had $1.45 and Jeffrey had $2.65.
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PLEASE HELPPPPP DUE IN A BIT
For the function f(x) and the given domain: {-1, 0, 1}, the range is {-8, -1, 6}
What is the range of the function?
For a function y = f(x), we define the domain as the set of the inputs (possible values of x) and the range as the set of the outputs (possible values of y).
In this case, the function is:
y = 7x - 1
And the domain is: {-1, 0, 1}
By evaluating ni the values of the domain, we will get the values of the range.
if x = -1, then:
y = 7*(-1) - 1 = -8
if x = 0, then:
y = 7*0 - 1 = -1
if x = 1, then:
y = 7*1 - 1 = 6
Then for the given domain and function, the range is:
R: {-8, -1, 6}
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Write 84000 in standard form
Answer: 8.4000
Step-by-step explanation:
Answer: Or i could be 8.4 × 104
Step-by-step explanation: You multiply this and get 840000 or 8.4000
Solve for a.
Give an exact answer.
3+0.5(4a+8)=9-2a
The value of a for which 3 + 0.5(4a + 8) = 9 - 2a is 1/2
What is a linear equation?A linear Equation is an Algebraic equation with the highest degree of the variable as 1.
Linear equations when plotted on a graph results to straight line graphs.
3 + 0.5(4a + 8) = 9 - 2a
Opening of bracket by multiplying the two terms in the bracket by 0.5
3 + 2a + 4 = 9 - 2a
collecting like terms
2a + 2a = 9 - 7
4a = 2
a = 2/4
a = 1/2
In conclusion, the value of a for the given equation is a = 1/2
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Solve for x and y
Please help I forgot what I needed to do!
Find the first four terms of the following
(1 + x)¹²
The first four terms are 1, 4096, 531441 and 16777216.
Define expansion.Expansion is a scale-increasing affine transformation, sometimes known as enlargement or dilatation. It is also frequently referred to as an enlargement and is the polar opposite of a geometric contraction. When a mathematical object is scaled by a scale factor that is bigger in absolute value than one, an expansion happens. The image grows larger than the actual mathematical entity when an expansion takes place. When scaling happens near a point, the transformation is known as a dilation, and the "point" is referred to as the center of the dilation. either the process of expanding or the condition of expanding. An expanded object, surface, or component. the amount by which anything extends; its degree, extent, or size. a growth, expansion, or development in a company's operations.
Given Data
(1+x)¹²
Putting x = 0
Expanding,
(1+0)¹²
1
Putting x = 1
(1+1)¹²
2¹²
Solving,
4096
Putting x = 2
(1+2)¹²
3¹²
531441
Putting x = 3
(1+3)¹²
4¹²
16777216
The first four terms are 1, 4096, 531441 and 16777216.
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