Answer:
x = 84
Hope this helped! If you need to know the steps, just let me know and I'll add it :)
Answer:
Step 1: Simplify both sides of the equation.
x/4−10=11
1/4x+−10=11
1/4x−10=11
Step 2: Add 10 to both sides.
1/4x−10+10=11+10
1/4x=21
Step 3: Multiply both sides by 4.
4*(1/4x)=(4)*(21)
x=84
Answer:
x=84
Jane solved an equation, but when she checked her answer she saw her solution was incorrect. She knows she made a mistake, but she can’t find it. Where is Jane’s mistake and what is the solution to the equation?
-3(4x - 5) = 6(x + 3) + 10
-12x + 15 = 6x + 18 + 10
-12x + 15 = 6x + 18
15 = -6x + 18
-3 = -6x
1/2 = x
Jane made a mistake in her third step. The solution of the equation is x = - 13 / 18
How to solve equations correctly?An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.
The solve the equation to detect where Jane made the mistake in her solution.
-3(4x - 5) = 6(x + 3) + 10
open the brackets on both sides of the equation
-3(4x - 5) = 6(x + 3) + 10
- 12x + 15 = 6x + 18 + 10
- 12x + 15 = 6x + 28
subtract 6x from both sides of the equation
- 12x + 15 = 6x + 28
- 12x - 6x + 15 = 6x - 6x + 28
-18x + 15 = 28
subtract 15 from both sides of the equation
-18x + 15 = 28
-18x + 15 - 15 = 28 - 15
-18x = 13
divide both sides by - 18
x = 13 / -18
x = - 13 / 18
Therefore, jane made a mistake in her third step. She didn't add 18 and 10 together on the right side of the equation.
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if x=-7 and y=3, calculate the values of (x+y/x-y)²
If x = -7 and y = 3, the value of the expression (x+y/x-y)² is 4/25 .
In the question ,
it is given that ,
the algebraic expression is given as (x+y/x-y)² ,
we need to find the value of the given expression when the value of x = -7 and y = 3 .
Substituting the values of x = -7 and y = 3 in the expression ,
we get
= (x+y/x-y)²
= ((-7+3)/(-7-3))²
= (-4/(-10))²
= 16/100
cancelling out the common factor 4 , from the numerator and denominator .
= 4/25
Therefore , the value of the given expression at x = -7 and y = 3 is 4/25 .
The given question is incomplete , the complete question is
Calculate the value of the expression (x+y/x-y)² at x = -7 and y = 3 ?
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Olivia helps paint a square mural in her classroom. Then she helps paint a mural in the hallway whose length is 5 feet longer and whose width is 2 feet shorter. Let x represent the side length of the mural in Olivia's classroom write an expression that represents the two binomials you would multiply to find the area of the hallway mural. Use that expression to find the area of the hallway mural if each side of the classroom mural is 7 feet long.
Step-by-step explanation:
The square mural in Olivia's classroom has dimensions x by x.
Then she paints a mural of dimensions: x+5 (the length) by x-2 (the width).
Thus the second mural (the hallway mural) has the shape of a rectangle with dimensions (x+5) by (x-2), so the area of the second mural is
(x+5)(x-2).
each side of the classroom mural is 7 feet means that x = 7 ft,
thus the area of the hallway mural is :
(x+5)(x-2)=(7+5)(7-2)=12*5=60 (square feet)
So the answer is 60 square feet.
Find the sum of the interior angles of the polygon
Answer:
Step-by-step explanation:We can find the sum of interior angles of any polygon using the following formula: where nis the number of sides of the polygon. For example, we use $latex n = 5$ for a pentagon. This formula works regardless of whether the polygon is regular or irregular.
write down the temperature which is 5°c below -2°c
Step-by-step explanation:
below -2°
that means
-2 - 5 = -7° C
Answer:
-7 degrees
Step-by-step explanation:
true or false stratified random sampling is a sampling method that may allow for more accurate inferences to be made about a population.
The stratified random sampling is a sampling method that may allow for more accurate inferences to be made about a population.
It is the true statement.
Given,
In the question:
Stratified random sampling is a sampling method that may allow for more accurate inferences to be made about a population.
To check the above statement is true or false.
Now, According to the question:
Let's know about
Stratified random sampling:Stratified random sampling is a method of sampling that involves the division of a population into smaller subgroups known as strata. In stratified random sampling, or stratification, the strata are formed based on members' shared attributes or characteristics, such as income or educational attainment.
In stratified random sampling, the strata are formed based on member's shared characteristics (e.g. female or male, occupation, education) or attribute (e.g. black or white).
Hence, The stratified random sampling is a sampling method that may allow for more accurate inferences to be made about a population.
It is the true statement.
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Someone pls help me. i dont understand this at all :c
The equation for the function described, using the translations, is given as follows:
f(x) = 2^(x - 4) + 5.
What are the translations to a function?There are four cases for the translation of a parent function, and they can be represented as follows:
Horizontal translation left a units: f(x + a).Horizontal translation right a units: f(x - a).Vertical translation up a units: f(x) + a.Vertical translation down a units: f(x) - a.In the context of this problem, the parent function is defined as follows:
f(x) = 2^x
The definitions for each translation are given as follows:
Horizontal shift right four units: f(x - 4).Vertical shift up five units, considering the horizontal shift right four units: f(x - 4) + 5.Hence the translated function is defined as follows:
f(x) = 2^(x - 4) + 5.
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The rate of change for of y = 2x + 6 is __________.
Answer:
2
Step-by-step explanation:
the rate of change is the coefficient of x
Given that line t is the perpendicular bisector of Jk, JG=x+12, and KG=3x-17, find KG
1. In the following figure, തതതത is the bisector of ∠BAC. GE is perpendicular to AB, GF is perpendicular to AC.
Andrea says that ∆ ≅ ∆ by the AAS congruence postulate. Do you agree or disagree? Explain
Based on the information given in the figure, you will agree with Andrew because ∆AEG ≅ ∆AFG by the AAS congruence postulate.
What is the AAS Congruence Postulate?Two triangles that have a pair of congruent included sides that is non-included and two pairs of corresponding angles are proven to be congruent to each other by the AAS congruence postulate.
In the figure shown above, the following information are ascertained:
Side AG is congruent to side AG by the reflexive property Angle AEG and angle AFG are congruent to each other because they are both right angles.Angle GAF and angle GAE are congruent to each other because they are angles formed when angle BAC is bisected line AD.Thus, the above information shows that triangle AEG has two angles and one non-included side that are congruent to two corresponding angles and one non-included side in triangle AFG.
Therefore, you will agree with Andrea for stating that ∆AEG ≅ ∆AFG by the AAS congruence postulate.
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been stuck on these last 2 questions. can anybody help? thanks in advance!
The equation that passes through the point (7, -2) and (11, 5) is y = 4/7x - 9
Equation of the line:
The standard form of the equation of the line is written as
y = mx + b
here
x and y represents the coordinates of the equation
m refers the slope of the equation
b refers the y intercept of the equation
Given,
Here we have the points (7, -2) and (11, 5).
Now we have to find the equation that passes through this points.
If you want to find the equation of the line, we have to find the slope and the intercept of the line.
The slope of the line is calculated by using the given point (7, -2) and (11, 5),
=> m = (11 - 7) / ( 5 - (-2))
=> m = 4/7
Now, we have to use the slope and the point (11, 5) to find the value of y intercept of the equation,
=> 5 = (4/7) (11) + b
=> 35 = 44 + b
=> b = -9
Therefore, the equation that passes through the points is y = 4/7x - 9
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Please help in the first 1,2 and the other page do one of them FOR 50 Points
The solutions to the rectangles located on the coordinate plane questions in the first page are;
1. Jordan ran a total distance of 6 miles
2. The fourth vertex is located at (5.5, -3.5)
3. The area of the pool is 48 square yards
What is the area occupied by a shape?The area of a figure is the region covered by the closed boundary of the shape or figure.
1. The coordinates of the points expressed as decimals are;
H(-0.75, 0.5), B(1, 0.5), L(1, -0.25), (0.5, -0.25), C(0.5, -0.75), S(-0.75, -0.75)
The distances between the points Jordan visited are;
HB = 1 - (-0.75) = 1.75
BL = |-0.25 - 0.5| = 0.75
LP = |0.5 - 1| = 0.5
PC = |-0.75 - (-0.25)| = 0.5
SC = |-0.75 - 0.5| = 1.25
SH = 0.5 - (-0.75) = 1.25
The total distance Jordan ran = 1.75 + 0.75 + 0.5 + 0.5 + 1.25 + 1.25 = 6
The total distance Jordan ran is 6 miles
2. The shape of the piece of material = A rectangle
The vertices of the rectangle are; (-1.2, -3.5), (-1.2, 4.4) and (5.5, 4.4)
The above vertices indicates that the sides of the rectangle are parallel to the x and y-axis as each two of the three points share a common coordinate
(-1.2, -3.5) and (-1.2, 4.4) represent a vertical side
(-1.2, 4.4) and (5.5, 4.4) represent a horizontal side
Therefore, based on plotting the points on the coordinate plane using MS Excel, we have;
(-1.2, -3.5) and (5.5 ,-3.5) will represent the other horizontal side
(5.5, 4.4) and (5.5, -3.5) represents the other vertical side
The coordinates of the fourth vertex is (5.5, -3.5)
3. The vertices of the pool are;
A(-5, 7), B(1, 7), C(1, -1), and D(-5, -1)
The length of the sides of the pool are;
AB = 1 - (-5) = 6
BC = 7 - (-1) = 8
CD = 1 - (-5) = 6
AD = 7 - (-1) = 8
The length of the rectangular pool = 8 yards
The width = 6 yards
The area of a rectangle = Length × Width
Area of the pool = 8 yard × 6 yards = 48 square yards
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please help me solve this.
Answer:
a) gradient
b) Line A and Line C
Step-by-step explanation:
Parallel lines are lines that have the same slope - they never intersect! Another name for slope is gradient.
Of all the lines in the image, only Line A and Line C will never intersect! They are parallel!
Peaceful Travel Agency offers vacation packages. Each vacation package includes a city, a month, and an airline. The agency has 3 cities, 1 month, and 3
airlines to choose from. How many different vacation packages do they offer?
If the agency has 3 cities, 1 month, and 3 airlines to choose from. then there are 9 different vacation packages they can offer.
What is the multiplication rule in permutation and combination?
1. Using the multiplication principle, we can count the number of ways to complete a sequence of tasks by multiplying the number of ways to complete each task together.
2. A permutation is a particular arrangement of objects.
Peaceful Travel Agency offers vacation packages.
If the agency has 3 cities, 1 month, and 3 airlines to choose from.
then by using the multiplication rule,
The number of different packages = 3 × 1 × 3
= 9 packages
Hence, If the agency has 3 cities, 1 month, and 3 airlines to choose from. then there are 9 different vacation packages they can offer.
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1. Choose the correct answer.
Which theorem, term, or corollary is represented by the picture? The bold lines in the pictures represent the hypothesis of the theorem or corollary.
Converse to the Isosceles Triangle Theorem
Corollary 1 to the Isosceles Triangle Theorem
CPCTC
Corollary 2 of the Isosceles Triangle Theorem
Isosceles Triangle Theorem
The equilateral triangle shown has three sides and three angles that are all the same. This should be the equilateral triangle theorem, however the answer selections do not cover it.
What is equilateral triangle?An equilateral triangle is a triangle with three equal-length sides in geometry. An equilateral triangle's sides are congruent, which indicates that all sides are the same length. All of the inner angles are also identical (60 degrees). An equilateral triangle is a triangle with all of its sides equal in length. Because the three sides are equal, the three angles opposing the equal sides are also equal in size. As a result, it is also known as an equiangular triangle, with each angle measuring 60 degrees.
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is the relation shown below a function? Use the graph below to justify your response.
(0, 0), (2, 0), (2, 2), and (3, 4)
9
8
7
6
S
4
3
2
y
01
OA
4 5 6 7 8 9
G
Yes; Each x-value has a unique y-value.
Yes; Each y-value has a unique x-value.
No: Two points have different y-values for the same x-value of 2.
No: Two points have different x-values for the same y-value of 2.
Helppppp pls
The relation is shown in the graph is not a function. Two points have different y-values for the same x-value of 2.
What is a relation?
A relation in mathematics describes the connection between two sets of values for ordered pairs. The set of items in the first set are referred to as domain, and they are connected to the set of elements in the second set, referred to as range.
What is a function?
A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable).
A relation becomes a function if there is an unique output for each input.
The given ordered pairs are (0, 0), (2, 0), (2, 2), and (3, 4).
First element of each ordered pair is the input and second element is output.
The inputs are 0, 2, 2,3. The outputs are 0, 0, 2, 4 .
For the input 2, there are 2 outputs 0 and 2.
The given relation is not a function.
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Find the LCM of 1 and 5 using lists of multiples.
Answer:
5
Step-by-step explanation:
Multiples of 1: 1, 2, 3, 4, 5, 6, 7, ...
Multiples of 5: 5, 10, 15, 20, 25, ...
The smallest number that appears in both lists is 5, and that is the least common multiple.
i need help, please.
1a) The number of whole servings Susan can make from 4.25 pounds of flour if one serving uses ²/₃ is 6.
1b) The quantity of flour Susan has after making 6 servings is ¹/₄ pounds.
2) Garrison can drink ⁷/₈ gallons of lemonade each of the next six days.
3) The student council sold 122 bags of chips.
4) If a container can hold 3¹/₃ ounces of peanuts, 5 containers will hold 16²/₃ ounces.
5) The number of people at the football game (400) last night who were not wearing orange and black is 240.
6) The number of long sleeves in Jordan's outfits is 45.
How are the numbers determined?The numbers and values can be determined using suitable mathematical operations.
The basic mathematical operations used include division, subtraction, and multiplication.
1) The total quantity of flour available = 4.25 pounds
The amount of flour required per serving = ²/₃ pounds
The number of servings from 4.25 pounds = 6³/₈ servings (4.25 ÷ ²/₃)
= 6 servings.
Quantity of flour left = ¹/₄ pounds [4 - 6(²/₃)]
2) The number of lemonades available = 5.5 gallons
The quantity Garrison took on Monday = ¹/₄ gallons (0.25)
The remaining number of gallons = 5.25 gallons (5.5 - 0.25)
The gallons for the remaining 6 days = ⁷/₈ gallons (5¹/₄ ÷ 6)
3) The total amount realized from sales = $73.20
The unit price per bag of chips = $0.60
The units sold = 122 ($73.20 ÷ $0.60)
4) The ounces of peanuts per container = 3¹/₃
The number of containers = 5
The ounces of peanuts for 5 containers = 16²/₃ ounces (3¹/₃ x 5)
5) The total number of people at the game = 400
The proportion of people wearing orange and black = ²/₅
The proportion of people not wearing orange and black = ³/₅ (1 - ²/₅)
The number of people not wearing orange and black = 240 (400 x ³/₅)
6) The total number of outfits in Jordan's closet = 200
The proportion of shirts = ³/₄
The proportion of long sleeve shirts = ³/₁₀
The number of long sleeve shirts = 45 (200 x ³/₄ x ³/₁₀)
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The missing quantity in the double number line
Answer: 1840 pounds
Step-by-step explanation:4x4=16
460 x 4 = 1840
58 rooms on 2 floors = ____ rooms per floor
Write the equation of the function in slope-intercept form:
A line with a slope of 2 and passes through (-8, 3)
Answer:
y = -2x-13
1) plot the coordinate you have on a graph (starting at (0,0) move to the left until you hit -8 and then up until you are at +3)
2) Since your slope is negative the line will be higher on the left and lower on the right, so starting at the point you have plotted move down 2 units and to the right one unit.
3) Do this until you intersect with the y-axis (at -13), this is your value for 'b'
4) Plug your values for 'b' and 'm' into the slope-intercept equation
#8 i
Write an equation of the line passing through the point A(3,-4) that is parallel to the line y = -x +8.
y =
1/x+1242
Answer:
y = -x -1
Step-by-step explanation:
You want an equation of the line parallel to y=-x+8 through point (3, -4).
Parallel lineThe parallel line will have the same slope as the given line. That slope is the coefficient of x: -1.
Point-slope formThe point-slope form of the equation of a line with slope m through point (h, k) is ...
y -k = m(x -h)
You have m=-1, (h, k) = (3, -4), so the desired line has equation ...
y -(-4) = -1(x -3)
y +4 = -x +3 . . . . . . point-slope form
Slope-intercept formAdd -4 to get this to slope-intercept form.
y = -x -1 . . . . . . . . . slope-intercept form
What is this expression in simplified form?
Answer:
[tex]15\sqrt{5}[/tex]
Step-by-step explanation:
simplify [tex]\sqrt{20}[/tex] and [tex]3\sqrt{50}[/tex]
[tex]\sqrt{20}[/tex] simplifies into [tex]\sqrt{5}[/tex]
so [tex]\sqrt{20}[/tex] = [tex]\sqrt{4} \sqrt{5}[/tex]
we can simplify [tex]\sqrt{4[/tex] into a whole number
[tex]\sqrt{4[/tex] =2
= 2[tex]\sqrt{5}[/tex]
[tex]\sqrt{50[/tex] simplifies into [tex]\sqrt{2[/tex]
so [tex]\sqrt{50[/tex] =3( [tex]\sqrt{25} \sqrt{2}[/tex])
we can simplify [tex]\sqrt{25}[/tex] into a whole number
[tex]\sqrt{25[/tex] = 5
= 15[tex]\sqrt{2[/tex]
then we add these simplified roots back into the question
2[tex]\sqrt{5}[/tex] + [tex]5\sqrt{2[/tex] -[tex]2\sqrt{5[/tex]
we simplify again as [tex]2\sqrt{5[/tex] cancels out
to get a final answer of:
[tex]15\sqrt{5}[/tex]
Mohammed is trying to find angle h. He finds angle g first and then he finds angle h from angle g.
a) Which angle fact does he use to find angle g
b) which angle fact does he then use to find angle h
a. The angle fact that Mohammed can use to find angle g is alternate angles
b) The angle fact that he then use to find angle h is alternate interior angles.
What is an alternate angle?When two parallel lines are cut by a transversal, the resulting alternate interior angles or alternate exterior angles are congruent, according to the alternate angle theorem. To demonstrate: If a transversal cuts two parallel lines, the alternate interior angles are equal.
When two parallel lines are intersected by a transversal, the angles formed inside them are equal to their alternate pairs. These are known as alternate interior angles.
In this case, it should be noted that the angles will be 137° based on the illustration.
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Jenny opens a "Charity Bank Account". Any interest gained goes to a local charity.
It pays 2% per annum simple interest.
She puts £1500 into the account.
She does not make any deposits or withdrawals.
How much interest will the charity have received after 3 years?
Interest will the charity have received after 3 years is £60
Jenny opens a "Charity Bank Account". Any interest gained goes to a local charity.
It pays 2% per annum simple interest.
She puts £1500 into the account.
interest will the charity have received after 3 years
Interest = PRT/100
Interest = 1500 x 2 x 3/100
Interest = 60
Therefore, interest will the charity have received after 3 years is £60
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Students were asked to schedule one from each category: chorus or band; French, Spanish, or German; art, wood shop, or physical education.
Answer:
Have you finished this question? I don't understand.
Step-by-step explanation:
Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2
The equations that are equivalent include:
2 + x = 5
x + 1 = 4
-5 + x = -2
What is an equation?It is important to note that an equation is used to illustrate the relationship between the variables that are given.
In this case, the given equation is illustrated as:
2 + x = 5
Collect like terms
x = 5 - 2
x = 3
x + 1 = 4
Collect like terms
x = 4 - 1
x = 3
-5 + x = -2
Collect like terms
x = -2 + 5
x = 3
Therefore, the three equations illustrated are equal.
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Q8.
(a)
Work out the value of
(√2)^4
[tex]=\sqrt{2} *\sqrt{2} *\sqrt{2} *\sqrt{2} \\=(\sqrt{2} *\sqrt{2})(\sqrt{2} *\sqrt{2})\\=2*2\\=4[/tex]
The answer is 4
The value of [tex](\sqrt2)^4[/tex] is 4.
The number of times a number has been multiplied by itself is referred to as its exponent. The rules of multiplying exponents are of different types. The given equation can be calculated using the Power of a Power rule.
According to this rule, when a base has an exponent, and that entire term has an exponent, the exponents are multiplied together. This is written as
[tex](a^x)^y=a^{xy}[/tex]
Here, both exponents are multiplied together.
Therefore, using the above rule the given square root with an exponent can be written as,
[tex]\begin{aligned}\left(\sqrt2\right)^4&=\left(2^{\frac{1}{2}\right)^4\\&=2^{\frac{1}{2}\times4}\\&=2^2\\&=4\end{aligned}[/tex]
The value is 4.
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Translate this sentence into an equation. 53 is the sum of 22 and Han's height. Use the variable h to represent Han's height.
Answer:
22 + h = 53
Step-by-step explanation:
I don't know if I am correct
Answer:
The answer is 31, H=31
Step-by-step explanation:
53-22=31 :)
1. The quality control manager at a light bulb factory needs to estimate the mean life of a new type of light-bulb. The population standard deviation is assumed to be 50 hours. A random sample of 30 light-bulbs shows a sample mean life of 475 hours. Construct and explain a 90% confidence interval estimate of the population mean life of the new light-bulb. 2. A survey of first-time home buyers found that the sample mean annual income was $46,000. Assume that the survey used a sample of 20 first-time home buyers and that the sample standard deviation was $1,200. Compute and explain a 95% confidence interval estimate of the population mean. 3. A telephone poll of 750 American adults asked "where would you rather go in your spare time?" One response, by 275 aduits, was "the Mall. Compute and explain a 99% confidence interval estimate of the proportion of all American adults who would respond "the Mall". 4. For problem #1 above, what size sample would be needed to achieve a margin of error of 15 hours or less? 2. A survey of first-time home buyers found that the sample mean annual income was $46,000. Assume that the survey used a sample of 20 first-time home buyers and that the sample standard deviation was $1,200. Compute and explain a 95% confidence interval estimate of the population mean cer
At 95% of confidence interval estimate of the population is
(478.332, 471.668)
Given that,
Population standard deviation is assumed to be 50 hours.
Random sample of 30 light bulb
and, sample mean of 475 hours.
Sample size n =30,
x = 475 and σ = 50
At 95% confidence interval for μ is,
x ± zₙ₎₂ σ /n -------------------- (1)
We already know that the table value of z = 1.96
At 95% confidence interval,
putting the values in equation (1),
x ± zₙ₎₂ σ /n
= 475 ± 1.96 × 50/30
Taking the positive sign, we get,
= 475 + 1.96 × 1.7
= 475 + 3.332
= 478.332
Now,
Taking the negative value, we get,
= 475 - 1.96 × 1.7
= 475 - 3.332
= 471.668
Therefore, At 95% of confidence interval estimate of the population is
(478.332, 471.668)
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