Convert -5/8x + y = -1/4 to standard form.
Step-by-step explanation:
-8(-5/8x + y = -1/4)
5x - 8y = 2 is the standard form
Lucy collects data from a random sample of seventh-graders. Out of 140 respondents, 28 attend after-school programs. Of the 400 seventh-graders attending Lucy’s school, how many would be expected to attend after school programs?
We would expect about 80 seventh-graders to attend after-school programs.
How to find the number expected to attendTo estimate the number of seventh-graders attending after-school programs, we can use the proportion of respondents who attend after-school programs from the sample:
28 out of 140 respondents attend after-school programs, which is a proportion of
= 28 / 140
= 0.2.
We can use this proportion to estimate the number of seventh-graders attending after-school programs in the entire population of 400 seventh-graders:
400 * 0.2 = 80
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The length of a rectangular vegetable garden i 4ft more than it' width. After a 2 foot boarder i placed around the garden, the area of the garden and boarder i 320ft^2. Find the original dimenion of the garden
The original dimensions of the garden are 12 ft by 16 ft.
Width: x + 4 (not 2 because the width has two ends)
Length: x + 8 (same reason; this is x + 4 + 4)
The area of the garden and the border combined is 320 sq. ft.
The dimensions of the garden with the border around it are (x + 4) and (x + 8).
A (rectangle) = lw
A (garden with border) = lw
320 sq. ft. = (x + 4) (x + 8)
320 sq. ft. = x2 + 12x + 32
Transpose 320 to the right side of the equation.
0 = x2 + 12x + 32 - 320
0 = x2 + 12x - 288
Factor out.
0 = (x + 24) (x - 12)
One or both of the amounts are equal to zero when the product of two values is zero.
Equate the factors to 0.
x + 24 = 0 x - 12 = 0
x = - 24 x = 12
Since we cannit have a negative measure of distance, x = 12.
Find the original dimensions of the garden.
The original dimensions of the garden (without the border) are x and x + 4.
Width = x = 12
Length = x + 4 = 12 + 4 = 16
The original dimensions of the garden are 12 ft by 16 ft.
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Help me to solve this question
The value of x is equal to 3 and the length of VS is 3.5 for the circle Z.
How to evaluate for the value of x and length VS in the circleSince ZU and ZV is equal to 8, then QR is equal to ST and the radii ZY and ZW bisect ST and QR respectively.
we shall solve for x in the circle as follows:
QR = ST
4x - 5 = 7
4x = 7 + 5 {add 5 to both sides}
4x = 12
x = 12/4 {divide through by 4}
x = 3
The length VS = 7/2
VS = 3.5
Therefore, the value of x is equal to 3 and the length of VS is 3.5 for the circle Z.
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19. What is the value of g(2) in the function below? g(x) = 4(3)*
The value of g(2) = 36 for the given function.
The given function g is defined by,
[tex]g(x) = 4(3)^{x}[/tex]
Now to find the value of g(2), put x = 2 in the given function we get,
g(2) = 4(3)²
g(2) = 4 × 3 × 3
g(2) = 36
Therefore, the value of g(2) = 36 for the given function.
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What are the four rules of multiplication?.
Four rules of multiplication are :
1. 0 × a = 0 , a ∈ R.
2. 1 × a = a , a ∈ R.
3. -a × -a = + a² , +a × +a = + a², , a ∈ R.
4. a × b = b × a, a and b ∈ R.
As given in the question,
Four rules of the multiplication are given by :
1. Zero × any number = 0
0 × a = 0 , a ∈ R.
Example : 0 × 5 = 0
2. One × any number = Number itself.
1 × a = a , a ∈ R.
Example : 1 × 5 = 5
3. Multiply two numbers with same sign gives positive negative.
-a × -a = + a , +a × +a = + a, , a ∈ R.
Example : -2× -2 = 4
3 × 3 = 9
4. Multiplication of two numbers in any order does not affect the result.
a × b = b × a, a and b ∈ R.
Example : 2 × 3 = 3 × 2
Therefore, the four rules of the multiplication are :
1. 0 × a = 0 , a ∈ R.
2. 1 × a = a , a ∈ R.
3. -a × -a = + a² , +a × +a = + a², , a ∈ R.
4. a × b = b × a, a and b ∈ R.
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Given f(x)=-x+3f solve for x when f(x)=4
The value of variable, x when f(x) = 4 according to the given function expression; f(x) = -x + 3 is; -1.
What is the value of x when f(x) = 4 according to the function?It follows from the task content that the value of x is to be determined according to the given function expression; f (x) = -x + 3.
Hence, when f (x) = 4, the resulting expression is;
4 = -x + 3
Hence, to determine the value of x, we must solve for x as follows;
4 - 3 = -x
1 = -x
x = -1.
Ultimately, the value of x for which the function instance f(x) = 4 is; x = -1.
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Show how to add the fractions 1/8 and 1/12 by using the LCM of 8 and 12 as the common denominator
(Quickly, and will give brainliest i to the best described one.)
Adding the fractions 1/8 and 1/12 by using the LCM of 8 and 12 as the common denominator exists 5/24.
What is meant by fractions?A fraction is a piece of the entire. In mathematics, the number is represented as a quotient, where the numerator and denominator are divided. Both are integers in a straightforward fraction. In the numerator or denominator of a complex fraction is a fraction. A correct fraction has a numerator that is lower than its denominator.
An element of a whole or, more broadly, any number of equal pieces, is represented by a fraction. When used in conversational English, a fraction indicates the number of components of a particular size, as in one-half, eight-fifths, and three-quarters.
Let the fractions be 1/8 and 1/12
8 = 2 × 4
12 = 3 × 4
By using LCM, we get
[tex]$2 \times 3 \times 4=24 \quad\{L C M\}$[/tex]
= 1/8 + 1/12
simplifying the equation, we get
[tex]$=\frac{1 \times 3}{8 \times 3}+\frac{1 \times 2}{12 \times 2}$[/tex]
= 3/24 + 2/24
= 5/24
Therefore, adding the fractions 1/8 and 1/12 by using the LCM of 8 and 12 as the common denominator exists 5/24.
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Classify this triangle by its sides and angles.
A.) right and scalene
B.) acute and scalene
C.) right and equilateral
D.) acute and equilateral
Answer:
acute and scalene, remember:
Isoceles: An isosceles triangle is a triangle with two sides of equal length. The two equal sides are called legs and the third side is called the base.
Scalene: A scalene triangle is a triangle with all sides of different lengths. None of its angles are congruent.
Equilateral: An equilateral triangle is a triangle with all three sides of equal length. All three angles are congruent and measure 60 degrees.
A cylinder has a height of 14 millimeters and a radius of 19 millimeters. What is its volume? Use 3.14 and round your answer to the nearest hundredth.
The volume of cylinder = 15,869.56 mm.
Why is the volume of a cylinder formula?The formula for determining a cylinder's volume is the base area times the height. Volume of a cylinder is r2h cubic units.
To calculate a box's volume, you need to know its height, width, and depth. The volume can be calculated by multiplying these three dimensions.
Assume for the moment that the spherical discs are stacked h levels high. The volume of the cylinder will now be calculated by multiplying the discs' base areas by their heights, "h". Therefore, r2h is used to represent the volume of a cylinder with base radius r and height h. The amount of material required to fill an object can be calculated using the volume of the object.
We know that the volume of cylinder = πr²h
Given,
height = 14 mm
radius = 19 mm
V = π × 19 × 19 × 14
⇒ V = 15,869.56 mm
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Check off all the characteristics that apply to a Rhombus.
1)Diagonals are perpendicular
2)2 pairs of consecutive sides are congruent
3) Diagonals are congruent
4) Diagonals bisect each other
5)Both pairs of opposite angles are congruent
6)4 right angles
7)Diagonals bisect opposite angles
8) Diagonals bisect angles formed by congruent sides
9)1 pair of opposite angles are congruent
10)Both pairs of opposite sides are congruent
11) Diagonals bisect opposite angles
12)Consecutive angles are supplementary
13) Both pairs of opposite sides are parallel
14)Exactly 1 pair of sides are parallel
15)4 sides are congruent
Estimate the slope of the curve at the designated point.
The required slope of the curve at the designated point P is 1/4.
What is the slope of the line?The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.
Here,
The slope of the curve at point p is given as
= rise/run
From the graph,
rise = 2 and run = 8
slope of the curve at point P = 2 / 8 = 1/4
Thus, the required slope of the curve at the designated point P is 1/4.
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Part B: if D(t)=1200, find the value of t and interpret its meaning in the context of the problem.
The Chang family has been traveling for 18 hours, thus, t-value is 18.
How should t-test results be interpreted?A significant t-score, also known as a t-value, implies that the groups are distinct, whereas a small t-score suggests that the groups are similar. Degrees of freedom are the values in a study that are open to change and are crucial for determining the significance and reliability of the null hypothesis.
D(t) = 2,280 - 60t
D(t) = 1,200; find t.
D(t) = 2,280 - 60t
1200 = 2280 - 60t
From both sides of the equation, deduct 2280.
1200 - 2,280 = 2280 - 60t - 2,280
- 1080 = - 60t
multiplied by -60 on both sides
- 1080 / -60 = - 60t / -60
18 = t
t = 18
The Chang family had travelled for 18 hours, according to this.
The Chang family has been traveling for 18 hours, t = 18.
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The complete question is,
Having just returned from a cross-country road vacation, the Chang family is traveling back home. They can visualize their distance from home in miles after t hours of travel by using the function D(t) = 2,280 - 60t during the journey. If D(t) = 1,200, what does t represent? That value stands for what?
A.t = 20; the Chang family has been traveling for 20 hours.
B. t = 20, meaning the Chang family will need to travel 20 more hours to reach home.
The Chang family has been traveling for 18 hours, thus c. t = 18.
The Chang family must go home for an additional 18 hours using the formula D. t = 18.
determine whether each pair of expressions are equivalent iready
The pair of expressions 4p + 3c and (c +2p)(2) are not equivalent because they aren't equal.
What is an Equivalent expression?This is referred to as the expressions that work the same even though they look different.
we were given: 4p + 3c and (c +2p)(2)
: 4p + 3c = (c +2p)(2)
: 4p + 3c = 2c + 4p
They are not equal thereby making them not to be equivalent.
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The full question:
determine whether each pair of expressions are equivalent 4p + 3c and (c +2p)(2)
Chad and Amy are married with no children, and they're filing their federal
income tax return. Chad had a gross income of $54,300 last year, while Amy had
a gross income of $50,900; they plan to use the standard deduction. They're
trying to decide whether to file their return jointly or separately, so they want to
calculate how much less they would pay in federal income taxes if they filed
jointly rather than separately.
Gross income means all income you receive in the form of money, goods, property, and services that isn't exempt from tax.
What is Gross Income?There are different components to gross income in respects to an individual and a company. An individual will easily be able to determine their gross income by consulting a recent pay stub or calculating their hours worked and wage. Alternatively, gross income of a company may require a bit more computation.An individual’s gross income is used by lenders or landlords to determine whether that person is a worthy borrower or renter. When filing federal and state income taxes, gross income is the starting point before subtracting deductions to determine the amount of tax owed.To learn more about tax refer to:
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4x 2 −3x−16, find f(−2)
Answer:
-26
Step-by-step explanation
1) substitute -2 for X
4(-2)(2)-3(-2)-16
2) solve
-8(2)+6-16
-16+6-16
-10-16
-26
The value of function at x= -2 is f(-2) is 54.
What is Function?In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
We have,
f(x) = 4x² - 3x - 16.
Now, to find the value of f(-2) put the value of x= -2.
so, f(-2)= 4(-2)² - 3(-2) - 16
= 4(16) + 6 - 16
= 64 -10
= 54
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A rocket is launched upwards by physics students record a tight as a function of the time since it was launched. The rocket reaches a peak height of 112 feet at a time of 2.48 seconds. The rocket then falls and hits the ground 5.12 seconds after it was launched. find a model for the height of the rocket h(t) in vertex form. Round your value of a to the nearest tenth.
The height of the rocket 45.161 km.
How is the height in vertex form determined?
By adding a and b to h=-b2a, you may determine h, the x-coordinate of the vertex.
Determine k, the vertex's y-coordinate, by calculating k=f(h)=f(b2a).
According to the graph, the velocity first increases for 20 seconds before declining for 120 seconds before changing course.
Thus, it was at its highest peak at t=120 seconds.
Therefore, all that is left to do is figure out the triangle OAB's area at its highest point. This is 2 base + perpendicular = 2 120 * 1000 * 60 km.
The rocket reaches a peak height of 112 feet at a time of 2.48 seconds. The rocket then falls and hits the ground 5.12 seconds after it was launched.
According to the graph, the velocity first increases for 20 seconds before declining for 112 seconds before changing course.
Thus, it was at its highest peak at t = 112
2.48 seconds.
Therefore, all that is left to do is figure out the triangle OAB's area at its highest point. This is 2 base + perpendicular = 112 * 1000 /2.48 = 45.161 km.
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What is the y intercept of y=mx+b
Answer:
the b part
Step-by-step explanation:
Answer: The y-intercept of y=mx+b is B
Step-by-step explanation:
1. Y is the y-variable
2. Mx is the slope
3. B is the y-intercept.
The outside temperature in a town is -20°F what change in temperature in degrees Fahrenheit what bring the outside temperature to 0°F
Answer:
An increase of 20
Step-by-step explanation:
-20 + 20 = 0
The change in temperature in degrees Fahrenheit required is A = 20°F
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
The current temperature is -20°F, and we want to know how much it needs to increase to reach 0°F.
On simplifying the equation , we get
We can calculate this by finding the difference between the two temperatures:
0°F - (-20°F) = 0°F + 20°F = 20°F
Hence , the temperature needs to increase by 20°F to reach 0°F
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solve for G.
-3g =57
Answer:
g = -19
Step-by-step explanation:
Given equation,
→ -3g = 57
Now the value of g will be,
→ -3g = 57
→ g = 57/-3
→ g = -(57/3)
→ [ g = -19 ]
Hence, the value of g is -19.
Answer:g=-19 I hope this helps
Step-by-step explanation:
-3g=57
Divide both sides of the equation by -3
-3g divide (-3)=57 divide (-3)
Any expression divided by itself equals 1
g=57 divide (-3) then you do
Dividing a positive and a negative equals a negative: (+) divide(-)=(-)
g=-57 divide 3
Next thing you do is
Calculate the quotient which something like this
g=-19
So you’re answer is g=-19
The diagram shows two parallel lines cut by a transversal. One angle measure is shown.
Find the values of and .
The measure of the angles are a = 54, b = 54, c = 126, d = 54, e = 126, f = 54, and g = 126 degrees.
What are vertically opposite angles?It is defined as the angles when two lines intersect each other and at the intersecting point, some pair of angles are formed which we call vertically opposite angles, as the name describes that they have vertically opposite angles.
here, we have,
It is given that:
The diagram shows two parallel lines cut by a transversal.
As we know from the definition of the vertically opposite angles:
b = 54 degrees
a + c = 54 + b (a = c)
2a = 54x2
a = 54 degrees
Since a and g are opposite interior angles, they are congruent, so you proceed with the process as you did for the first and check to see if the angles are acute or obtuse to ensure that the angle measurements are accurate.
Similarly:
b = 54
c = 126
d = 54
e = 126
f = 54
g = 126
Thus, the measure of the angles are a = 54, b = 54, c = 126, d = 54, e = 126, f = 54, and g = 126 degrees.
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Determine an expression that produces a given resultant vector. Write an expression that can be used to produce factor be from vector a, and explain how you determine the expression
Expression to produce vector b: b = d - c, where d and c add to a. Find d and c using a's components, b is inverse of a.
What is vector ?
Vector is a term that refers colloquially to some quantities that cannot be expressed by a single number, or to elements of some vector spaces.
Suppose vector "a" is given and we want to determine an expression to produce vector "b". To do this, we need to find two vectors, "c" and "d", such that:
a = c + d
where c and d are the vectors that when added together produce vector a. The expression to produce vector b can then be represented as:
b = d - c
The expression can be determined by first finding the components of vector a, and then using these components to determine the components of vectors c and d. For example, if vector a is represented as:
a = <a1, a2, a3>
We can set c and d equal to:
c = <a1/2, a2/2, a3/2>
d = <a1/2, a2/2, a3/2>
So, the expression to produce vector b can be represented as:
b = d - c = <a1/2, a2/2, a3/2> - <a1/2, a2/2, a3/2> = <0, 0, 0>
Expression to produce vector b: b = d - c, where d and c add to a. Find d and c using a's components, b is inverse of a.
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Let's say vector a is represented by the expression (a1, a2), and vector b is represented by the expression (b1, b2).
Then, the expression for the resultant vector (c1, c2) can be calculated as follows:
c1 = a1 + b1
c2 = a2 + b2
So the expression for the resultant vector is (a1 + b1, a2 + b2).
To determine an expression that produces vector b from vector a, you would need to know the relationship between the two vectors. If vector b is a scalar multiple of vector a, the expression for vector b can be represented as:
b = k * a
Where "k" is the scalar factor. If vector b is a vector that is in the opposite direction of vector a, the expression for vector b can be represented as:
b = -1 * a
In this case, the scalar factor is -1.
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John needs to paint one wall in his school. He knows that 11 can of paint covers an area of 22 square meters. John uses a meter stick to measure the dimensions of the wall as shown
The number of cans required for John to paint the wall is given by the equation A = 3.375 cans ≈ 4 cans
What is the Area of a Rectangle?The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle
Area of Rectangle = Length x Width
Given data ,
Let the area of the wall be A
Now , the area of wall A = area of rectangle + area of triangle
The side length of the rectangle = 3m
The width of the rectangle = 2 m
The height of the triangle = 1 m
The base of the triangle = 1.5 m
So , the area of the triangle = ( 1/2 ) x 1.5 x 1 = 0.75 m²
Now , the area of the rectangle = length x width
Area of the rectangle = 3 x 2 = 6 m²
So , the area of the figure = 6.75 m²
Now , 11 can of paint covers an area of 22 square meters
So , 1 square meters = 11/22 cans
1 square meters = 1/2 cans
And , the number of cans required for 6.75 m² of area = 6.75 ( 1/2 ) cans
The number of cans required for 6.75 m² of area = 3.375 cans
The number of cans required for 6.75 m² of area = 4 cans
Hence , the number of cans is 4 cans
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Math pls help I don’t want to fail
Step-by-step explanation:
x1, y1 = (-5,-2)
slope,m = -6/5
general equation, y= MX + C
(y-y1)/(x-x1)=m
(y+2)/(x+5)=-6/5
5y+10=-6x-30
5y=-6x-40
y=-(6x/5) - 8
solve (x+1)(5x+6)=0
x=
or
x=
Answer:
x = - [tex]\frac{6}{5}[/tex] , x = - 1
Step-by-step explanation:
(x + 1)(5x + 6) = 0 ← in standard form
equate each factor to zero and solve for x
5x + 6 = 0 ( subtract 6 from both sides )
5x = - 6 ( divide both sides by 5 )
x = - [tex]\frac{6}{5}[/tex]
or
x + 1 = 0 ( subtract 1 from both sides )
x = - 1
Pls help! I need to get this done in 10 minutes!
Answer:
$41.04
Step-by-step explanation:
set up a proportions equation:
[tex]\frac{18.20}{2\frac{1}{3}} =\frac{x}{5\frac{1}{4}}[/tex]
cross multiply and solve for x. this gives you:
x = 41.04
hope this helped, good luck!
HELP PLEASE
Sandi made cookies for the teachers at her daughter's school. She made 20 sugar cookies and 18 chocolate cookies and put them in a box for the teacher's lounge. If one cookie broke, what is the probability it was a chocolate cookie?
A. 9/19
B. 1/18
C. 1/20
D. 19/21
Answer: A. 9/19
Step-by-step explanation:
20 + 18(amount of cookies) = 38
there are 18 chocolate chip cookies, so it's an 18/38 chance it's a chocolate chip cookie that broke, but 18/38 can be simplified.
18 divided by 2 is 9 and 38 divided by 2 is 19
so 9/19
Adam ran 21.5 miles less than Jacob. If Adam ran 17.5 miles. How many miles did Jacob run? Write an equation and solve.
Answer:
39 miles
Step-by-step explanation:
We can start by using algebra to represent the problem in equation form. Let j be the number of miles Jacob ran.
From the information given, we know that:
Adam ran 21.5 miles less than Jacob.
Adam ran 17.5 miles.
We can use these two pieces of information to set up the following equation:
j = 17.5 + 21.5
Now we can solve for j by adding 21.5 to both sides:
j = 39
So Jacob ran 39 miles.
Solve for u in terms of q, r, s, and t. sr=qut u=
Answer: u = sr/qut
Step-by-step explanation:
Given the equation sr = qut, we can solve for u by isolating it on one side of the equation. To do this, we divide both sides by qut. This gives us sr/qut = u. This means that u can be represented in terms of q, r, s, and t as sr/qut. This is the final result.
.........
Given the equation sr = qut, we can solve for u in terms of q, r, s, and t by isolating u on one side of the equation.
To do this, we can divide both sides of the equation by (qut)
sr/qut = u
Then we have u = sr/qut
So, u is expressed in terms of q, r, s, and t as u = sr/qut
Solve for x. Leave your answer in simplest radical form.
The value of x using Pythagoras theorem is x = √30.
The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
Using Pythagoras theorem,
⇒ 5² + base² = 8²
⇒ 25 + base² = 64
⇒ base = √64 - 25
⇒ base = √39
In the other triangle,
x² + 3² = 39
⇒ x² = 39 - 9
⇒ x = √30
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