3x + 4 is the expression that gives the same value as (3x-2x) + 2(2x-x) + 4
The Given Expression is : (3x-2x) + 2(2x-x) + 4
⇒ 1(x) + 2(x) + 4
⇒ x + 2x + 4
⇒ 3x + 4
Hence, the equivalent expression for the given expression is 3x + 4.
An Expression is composed only of variables, operators (or) symbols, and numbers. There will be no equality(=) sign in an expression.
If there is an equality(=) sign, then it is called an equation.
The value of given expression at x = 2 is :
(3(2) - 2(2)) + 2(2(2) - 2) + 4
= (6 - 4) + 2(4 - 2) + 4
= 2 + 2(2) + 4
= 2 + 4 + 4
= 10
The value of the equivalent expression is :
3(2) + 4
= 6 + 4
= 10
Both the expressions gave the same value.
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4. Mr. Smith makes lemonade. His recipe calls for 1½ cups of water for every cup of concentrate. If Mr. Smith 2 pours all 5 cups of concentrate into a pitcher to serve at a party, how much water should he add?
He should add 7.5 or 7 1/2 cups of water.
Cup of concentrate = 1
Cup of water = 1 1/2
= 3/2
= 1.5
Cups of concentrate = 5
Cups of water = 5 * 1.5
= 7.5
= 15/2
= 7 1/2
Hence, He should add 7.5 or 7 1/2 cups of water.
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What are the coordinates of the point on the directed line segment from
(
−
10
,
2
)
(−10,2) to
(
−
3
,
−
5
)
(−3,−5) that partitions the segment into a ratio of 4 to 3?
The coordinate of the point on the directed line segment from (- 10, 2) to (-3,-5) will be;
⇒ (x , y) = (- 6, - 2)
What is Coordinates?
A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.
Given that;
The two points are;
(- 10, 2) and (- 3, 5)
And, The partitions the segment into a ratio of 4 to 3.
Now,
Since, We know that;
The The coordinate of the point on the directed line segment from
(x₁, y₁) to (x₂, y₂) that partitions the segment into a ratio of m₁ to m₂ will be;
⇒ x = (m₁ x₂ + m₂ x₁) / (m₁ + m₂)
⇒ y = (m₁ y₂ + m₂ y₁) / (m₁ + m₂)
Hence, The coordinate of the point on the directed line segment from
(- 10, 2) to (-3,-5) will be;
x = (4×-3 + 3×-10) / (4 + 3)
x = (-12 - 30) / 7
x = - 42/7
x = - 6
And,
y = (4×-5 + 3×2) / (4 + 3)
y = (-20 + 6) / 7
y = - 14/7
y = - 2
Thus, The coordinate of the point on the directed line segment from
(- 10, 2) to (-3,-5) will be;
⇒ (x , y) = (- 6, - 2)
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Wally is 12 yrs old
Billy's cousin Molly is twice as
old as Wally. How old is Molly?
The age of Molly is 24 years.
We have two persons. The names of the two persons are Wally and Molly. The age of Wally is 12 years. Billy has a cousin named Molly. The age of Molly is twice the age of Wally. It means that to find the age of Molly, we will multiply the age of Wally by two. Let the age of Molly be represented by the variable "x". A constant's value remains constant across time. A variable, on the other hand, changes its value depending on the equation. Variables are often written in alphabets or symbols. Constants are frequently written in numbers.
x = 2*12 = 24
Hence, Molly is 24 years old.
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Find a recursive rule for the sequence 3, 6, 12, 24, ...
Answer:
?
Step-by-step explanation:
c.r.=6/3=12/6=2
[tex]c.r=\frac{a_{n}}{a_{n-1}} \\\frac{a_{n}}{a_{n-1}} =2\\a_{n}=2a_{n-1}[/tex]
Question 7 of 10
A construction worker needs to put a rectangular window in the side of a
building. He knows from measuring that the top and bottom of the window
have a width of 8 feet and the sides have a length of 15 feet. He also
measured one diagonal to be 17 feet. What is the length of the other
diagonal?
A. 8 feet
OB. 17 feet
O C. 15 feet
OD. 23 feet
The length of the other diagonal is 17 feet.
What is diagonal?
When two polygonal or polyhedral vertices are not on the same edge, a diagonal is a line segment connecting them.
Main Body:
Given:
A construction worker needs to put a rectangular window on the side of a building.
He knows from measuring that the top and bottom of the window have a width of 8 feet and the sides have a length of 15 feet.
He also measured one diagonal to be 17 feet.
Solution:
As we know that the rectangle is a particular type of parallelogram.
So, the rectangle has diagonals that have equal lengths.
Therefore, one diagonal length is given as 17 feet.
Hence, the other diagonal length will be equal to the given diagonal length.
So, the length of the other diagonal is 17 feet.
Hence, Option B is the correct answer.
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Which equation represents a linear function?
A. y = -x² - 4
B.-3x² + 1 = y
C.y=x²
D.x+2=y
Answer: D. x + 2 = y
Step-by-step explanation:
The only answer option that represents a linear function is option D. The other three, A, B and C, all represent quadradic functions. You can tell they're quadradic functions because the highest degree is a 2, or a square. This gives a parabola and is not linear.
With this information in mind, the answer is;
"D.x+2=y"
The Rogers family and the Walker family each used their sprinklers last summer. The water output rate for the Rogers family's sprinkler was 30 L per hour. The
water output rate for the Walker family's sprinkler was 20 L per hour. The families used their sprinklers for a combined total of 45 hours, resulting in a total
water output of 1150 L. How long was each sprinkler used?
Rogers family's sprinkler:
hours
Walker family's sprinkler: hours
The Rogers family's sprinkler worked for 25 hours and Walker family's sprinkler worked for 20 hours
The water output rate of Roger's family's sprinkler = 30 liter per hour
The water output rate of Walker family's sprinkler = 20liter per hour
Total number of hours combined = 45 hours
Consider the number of hours that Rogers family's sprinkler work = x
The number of hours that Rogers family's sprinkler work = y
Then the equation will be
x + y = 45
x = 45 -y
Total water output = 1150 liters
30x + 20y = 1150
Here we have to use substitution method
30(45-y) + 20y = 1150
1350 - 30y + 20y = 1150
1350 - 10y = 1150
10y = 1350 - 1150
10y = 200
y = 200/10
y = 20 hours
Then,
x = 45 - y
x = 45 - 20
x = 25 hours
Hence, the Rogers family's sprinkler worked for 25 hours and Walker family's sprinkler worked for 20 hours
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The following data were collected from a random sample of people, who identified their favorite type of juice. The results are shown in the following two-way table.
What proportion of the children identified orange as their favorite type of juice?
A 4001,0004001,000
B 400700400700
C 4002,0004002,000
D 6001,3006001,300
E 1,0002,000
The proportion of the children identified orange as their favorite type of juice is 400 / 1000.
What is proportion?In general, the term "proportion" refers to a part, share, or amount that is compared to a total.
According to the concept of proportion, two ratios are in proportion when they are equal.
A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.
Given:
From the table
Adults who like oranges= 600
and, Children who like oranges = 400
So, proportion of the children identified orange as their favorite type of juice
= 400/ 1000
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Three of the following statements are true. Which one is NOT true?
|-12| > 1
13. What is the slope of the line represented
by 15x + 3y = 45?
A sports utility vehicle ( SUV ) was purchased for $ 23,000 . According to the automobile sales association , the buyer can expect the SUV to lose about 11 % of its value annually In 10 years , approximately for how much could an owner expect to sell the SUV ?
The amount that the owner can expect to sell the SUV in 10 years, given the loss in value annually is $7, 171 .80
How to find the selling price of the car?Assuming the selling price of the SUV will be the value of the SUV in 10 years, then the selling price can be found by the formula:
= Purchase price of SUV x ( 1 - percentage loss in value) ^ number of years
Purchase price of SUV = $23, 000
Percentage loss in value = 11%
Number of years = 10 years
The selling price of the SUV is therefore:
= 23, 000 x ( 1 - 11%) ¹⁰
= $7, 171 .80
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Fill in the table.
X(input) Y(output)
1 0
3 4
4 6
7
20
Answer:
Step-by-step explanation:
8 10
Which sequence shows the numbers in order from least to greatest?
A.
B.
C.
D.
Answer: B
Step-by-step explanation:
Because 7 and 2/3 is almost the same as III -7.82 III and [tex]\sqrt65[/tex] is 8.0622577483 so first is 7 2/3 then III -7.82 III and then the root of [tex]\sqrt65[/tex]
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At Hamburgers Plus, a hamburger regularly costs $6.00, and each additional topping costs $ 0.50.
On Mondays, the cost of the hamburger only is half off.
Create an equation to model the total cost, c, in dollars, of a hamburger with t additional toppings on Mondays.
The equation to model the total cost, c, in dollars, of a hamburger with t additional toppings on Mondays is c = 3 + 0.50t.
What is an equation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
Let the additional topping = t
Therefore, the cost will be expressed as:
c = 1/2(6) + (0.50 × t)
c = 1/2(6) + 0.50t
c = 3 + 0.50t
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← CO
Question 5 of 7
Question 1-5
Submit Test
22-23 Algebra 1 Unit 2 EUA
A hairstylist charges $15 for an adult haircut and $9 for a child haircut. She wants to earn at least $360 dollars and cut a maximum of 30
haircuts this week. The graphs represent the hairstylist's constraints.
List two points that could represent the numbers of adult and child haircuts that meet the hairstylist's goals. Enter your response in the
space provided. You may also use the drawing tool to help explain or support your answer.
The point that could represent the numbers of adults and child haircuts that meet the stylist goals exists 25, 0.
What is meant by mathematical operation?A function that converts zero or more input values into a clearly defined output value is referred to in mathematics as an operation. The operation's complexity is measured by the number of operands.
A value is computed using operands and a math operator as part of the mathematical "operation." In order to be applied to the provided operands or numbers, the math operator's symbol has predetermined rules.
Since the hairstylist change $15 for an adult haircut and $9 for a child haircut, then utilizing 25, 0 will be:
= 15(25) + 9(0)
= 375 + 0
= $375
She has earned at least 360 dollars and cut about 25 haircuts this week.
Therefore, the correct answer is option A. 25, 0.
The complete question is:
A hairstylist change $15 for an adult haircut and $9 for a child haircut. She wants to earn at least 360 dollars and cut a maximum of 30 haircuts this week. The graphs represent the hairstylist constants.
Which point could represent the numbers of adults and child haircuts the meet the stylist goals.
A. 25, 0
B. 15, 20
C. 10,15
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A __________________________ can arise when the tax return and the income statement report a revenue or expense in different years.
A deferred tax liability can arise when the tax return and the income statement report a revenue or expense in different years
What is a deferred tax liability?A deferred tax liability is a balance-sheet entry that records taxes that are owed but are not due to be paid until a later date. The liability is postponed due to a timing difference between when the tax was accrued and when it is due to be paid.
On the balance sheet, deferred income tax appears as a liability. The most common cause of deferred income tax is a discrepancy between the IRS and GAAP depreciation methods. Income tax deferral can be classified as either a current or long-term liability.
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Find the remainder when f(x) is divided by x-k
f(x)=2x^4+x^3-4x^2-4x+4
k=-2
The remainder when the given function is divided by x +2 is 36
The given function is
f(x) = 2x⁴+x³-4x²-4x+4
Remainder theorem states that if any polynomial is divided by another factor in the form of x-a , then the remainder will be given by f(a)
Hence remainder = f(-2)
f(-2) = 2(-2)⁴ + (-2)³ - 4(- 2)²- 4 (-2) + 4 = 32 - 8 + 8 + 4 = 36
The Remainder Theorem can be used to tackle polynomial division according to Euclidean geometry. The Remainder Theorem is also known as Bezout's Theorem regarding Approaching Polynomials of Euclidian's Division.
The remainder theorem says that when a polynomial f(x) is divided by the factor (x - a), even though the factor isn't always an element of the polynomial, a smaller polynomial and a remnant are created. Because the result is actually the value of the polynomial f(x), where x = a, this can only occur if f(a) = 0. The remainder theorem can be used to factor polynomials quickly.
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help please real answers *10 points*!!!!!
Answer: B SSS
Step-by-step explanation:
Activity No. 16
Find the roots of the following radical expressions.
1. √64
2. ⁴√ -1
3. ³√1000
Write each expression in radical form or with a rational exponent, and simplify.
1. (⁴√ 1)⁷
2. ³ √-64
3. (2⁹)¹/³
4. (11²)¹/²
The required roots of the given radical expressions are √64 = 8, ⁴√ -1 = 4i, and ³√1000 = 10. The required expressions for the given radical are ³√-64 = 12i, (2⁹)¹/³ = 8, and (11²)¹/²=11.
What are the radical expressions?Any expression that contains a radical symbol is considered a radical expression. To find the square roots, cubic roots, and higher, radical symbols are used. For example, √7, √6, and √11 are in the radial form.
The radical expressions are given in the question
As per the given question, the required solution would be as:
√64 = √(2 × 2 × 2 × 2 × 2 × 2)
√64 = 2 × 2 × 2 = 8
⁴√ -1 = 4i (apply the imaginary number rule)
³√1000 = ³√(10 × 10 × 10)
³√1000 = 10
(⁴√ 1)⁷ = (1)⁷ = 1
³√-64 = (³√2 × 2 × 2 × 2 × 2 × 2 × -1 )
³√-64 = 2 × 2(³√-1)
³√-64 = 4(3i) = 12i (apply the imaginary number rule)
(2⁹)¹/³ = [tex]2^{9/3} = 2^3 = 8[/tex]
(11²)¹/² = [tex]11^{2/2} = 11[/tex]
Thus, the required roots of the given radical expressions are √64 = 8, ⁴√ -1 = 4i, and ³√1000 = 10. The required expressions for the given radical are ³√-64 = 12i, (2⁹)¹/³ = 8, and (11²)¹/²=11.
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If x=44 degrees, find the measures of angled 1 and 2
M<1=
The measurement of ∠1 = 136° and ∠2 = x = 44°, using Vertically opposed angles.
What is Vertically opposed angles?
Two lines intersecting at a point create vertical angles. Every time they are on an equal footing. Alternatively stated, four angles are created anytime two lines cross or intersect. Two opposed angles are equal and are referred to as vertical angles, as we can see. Due to their position opposite one another, they are also known as "Vertically opposed angles."
Angles that are vertically opposed to one another at a certain vertex are formed by two straight lines intersecting. The equality of the vertically opposed angles has been established.
∠x = 44
∠2 = x = 44
∠1 + ∠2 = 180
∠1 = 180 - 44 = 136°
Hence, The measurement of ∠1 = 136° and ∠2 = x = 44°.
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Which is the graph of f(x) = 100(0.7)x?
On a coordinate plane, a curve approaches y = 0 in quadrant 1 and curves up into quadrant 2. It goes through (2, 49) and (0, 100).
On a coordinate plane, a curve approaches y = 0 in quadrant 1 and curves up into quadrant 2. It goes through (2, 9) and (0, 100).
On a coordinate plane, a curve approaches y = 0 in quadrant 1 and curves up into quadrant 2. It goes through (2, 70) and (0, 100).
On a coordinate plane, a curve approaches y = 0 in quadrant 1 and curves up into quadrant 2. It goes through (2, 30) and (0, 100).
The graph of f(x) = 100(0.7)^x is represented by On a coordinate plane, a curve approaches y = 0 in quadrant 1 and curves up into quadrant 2. It goes through (2, 49) and (0, 100)
How to find the pointsUsing the exponential function f(x) = 100(0.7)^x the graph is plotted and attached
Other information that can be abstracted from the equation directly
f(x) = 100(0.7)^x
at x = 2
f(x) = 100(0.7)^2
f(x) = 100(0.49)
f(x) = 49
hence the ordered pair is written as (2, 49)
f(x) = 100(0.7)^x
at x = 0
f(x) = 100(0.7)^0
f(x) = 100(1)
f(x) = 100
hence the ordered pair is written as (0, 100)
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The answer is A. its correct on EDGE 2022
please help me with this.
Answer:
The first one
Step-by-step explanation:
PLS HELP ME RIGHT NOW WILL GIVE BRAINLEST
The required equation of the line is y = -(0.5)x + 225 expressed in slope-intercept form.
Let x represent the number of months Jason's gift card has been inactive after 1 year and let y represent Jason's card balance.
We take the two points (0, 225) and (1, 224.5) in the given table.
The required equation of the line is
⇒ y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]
x₁ = 0, y₁ = 225
x₂ = 1, y₂ = 224.5
Substitute values in the equation, we get
y - 225 = (224.5-225 /1-0)(x - 0)
y - 225 = -(0.5)x
y = -(0.5)x + 225
Therefore, the required equation of the line is y = -(0.5)x + 225.
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IXL Please Help Fast !
Answer:
x=9
Step-by-step explanation:
9x-7=5x+29
9x=5x+36
4x=36
x=9
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PLEASE HELP find the measure of each marked angle
Through the use of a protractor, angles are measured in degrees (°). In order to calculate or draw angles in terms of degrees, a protractor is a measuring tool that is utilized.
Does a linear pair have a 180 degree angle?
Two lines converge at a single point to generate a pair of linear angles. If, following the junction of the two lines, the angles are next to one another, they are said to be linear. A linear pair always has an angle total of 180 degrees.Angles next to each other that add up to two right angles, or 180 degrees, are said to be in a linear pair. This indicates that the non-shared sides of them are aligned in a straight line.When the total of two angles equals 180 degrees, the angles are said to be supplementary. It is referred to as a linear pair if the two additional angles are close to one another.How to find the measure of the angle?
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need the answer. ............................
Answer:
The value of cos 0 is 1.Here, we will discuss the value for cos 0 degrees and how the values are derived using the quadrants of a unit circle. The trigonometric functions are also known as an angle function that relates the angles of a triangle to the length of the triangle sides.
Trigonometric functions are one of the most important topics which are used in the study of periodic phenomena like sound and light waves, the study of harmonic oscillators and finding the average temperature variations.
The three basic trigonometric ratios are sine function, cosine function, and tangent function. It is commonly defined for the angles less than a right angle, trigonometric functions are stated as the ratio of two sides of a right triangle containing the angle in which the values can be found in the length of various line segments around a unit circle. The angles of a triangle are calculated with respect to sin, cos and tan functions. Usually, the degrees are represented as 0°, 30°, 45°, 60°, 90°, 180°, 270° and 360°.Cos 0 Degree ValueTo define the cosine function of an acute angle, start with the right-angled triangle ABC with the angle of interest and the sides of a triangle. The three sides of the triangle are defined as follows:The opposite side is defined as the side opposite the angle of interest.The hypotenuse side is the side opposite the right angle and it is the longest side of a right triangleThe adjacent side is the remaining side where it forms a side of both the angle of interest and the right angleThe cosine function of an angle is equal to the length of the adjacent side divided by the length of the hypotenuse side and the formula is given by:Cos θ = Adjacent Side / Hypotenuse SideValue of Cos 0 Using Unit CircleAssume a unit circle with the center at the origin of the coordinate axes. Consider that P (a, b) be any point on the circle which forms an angle AOP = x radian. This means that the length of the arc AP is equal to x. So we define that cos x = a and sin x = b
Step-by-step explanation:
lots to read but answer is 1
Use the tree diagram to see if the customer buys at least 1 of the 2 customers buys a banana icecream give your answer in a simple form
The probability that at least one of the two customers buy a banana ice cream is of:
55/64.
How to calculate the probability?The probabilities are calculated from the tree diagram given by the image at the end of the answer.
The nodes that end up with none customers buying a banana ice cream are given as follows:
Cookie dough -> Cookie dough.
The probability of each node is given by:
3/8.
Hence the probability that none of the two customers buy a banana ice cream is of:
3/8 x 3/8 = 9/64.
None and at least one customer buying a banana ice cream are complementary events, hence the probability is obtained as follows:
1 - 9/64 = 64/64 - 9/64 = 55/64.
Missing InformationThe tree diagram that models the situation is given by the image presented at the end of teh answer.
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The perimeter of the triangle is 10x^2-6x+1 and the side lengths are 5x+7 and 8x^2-4x.What is the length of the missing side?
Answer:
2x^2-7x-6
Step-by-step explanation:
P=A+B+C=10x^2-6x+1
A=5x+7
B=8x^2-4x
C=?
C=P-(A+B)= 10x^2-6x+1-(5x+7+8x^2-4x)
=10x^2-6x+1-(8x^2-6x+7)
=2x^2-7x-6
3 5/9 times 1 1/2 equals?
Answer:
[tex]5\frac{1}{3}[/tex]
Step-by-step explanation:
3 5/9 x 1 1/2
32/9 x 3/2
96/18
16/3
5 1/3
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Which expression is equivalent to
