Diana made a recipe that yields 6 and 1 over 2 cups. If each serving is 1 over 4 cup, which expression will help Diana determine the number of servings her recipe will yield? 6 and 1 over 2 ⋅ 1 over 4 6 and 1 over 2 ÷ 1 over 4 6 and 1 over 2 + 1 over 4 6 and 1 over 2 − 1 over 4
Answer:
6 and 1 over 2 ÷ 1 over 4
Step-by-step explanation:
Given,
The total cups in a recipe = 6 and 1 over 2 cups
[tex]=6\frac{1}{2}\text{ cups}[/tex]
Also, the cups in each serving = 1 over 4 cup
[tex]=\frac{1}{4}\text{ cups}[/tex]
Hence, the number of servings = [tex]\frac{\text{total cups in a recipe}}{\text{cups in each serving}}[/tex]
[tex]=\frac{6\frac{1}{2}}{\frac{1}{4}}[/tex]
= 6 and 1 over 2 ÷ 1 over 4
Second option is correct.
PLEASE HELP ME!!!
What is the simplified form of the quantity 15 x y squared over x squared minus 5x plus 6 all over the quantity 5 x squared y over 2x squared minus 7x plus 3 ?
Answer: [tex]\frac{3y(2x-1)}{x(x-2)}[/tex]
Step-by-step explanation:
Given problem to simplify is [tex]\frac{\frac{15xy^2}{x^2-5x+6} }{\frac{5x^2y}{2x^2-7x+3} } \\\\=\frac{15xy^2}{x^2-5x+6}\cdot\ \frac{2x^2-7x+3} {5x^2y}............\text{(by fractional division property,the denominator invert and its reciprocal multiply to numerator)}\\\\=\frac{15xy^2}{(x-3)(x-2)}\cdot\frac{(x-3)(2x-1)} {5x^2y}.........\ \text{(factorizing quadratic equation)}[/tex]
[tex]=\frac{3y(2x-1)}{x(x-2)}........\text{(cancelling like terms with same degree and coefficients from numerator and denominator)}[/tex]
so the simplified form of the given problem is [tex]\frac{3y(2x-1)}{x(x-2)}[/tex]
what is the converse to the following conditional statement if x=12 then 2x-5=19
Final answer:
The converse of the given conditional statement 'if x=12 then 2x-5=19' is 'if 2x-5=19, then x=12'. To verify its truth, we solve for x when 2x-5 equals 19, resulting in x equaling 12, thus showing that in this instance, the converse is true.
Explanation:
The converse of a conditional statement is formed by swapping the hypothesis and the conclusion of the original statement. For the statement 'if x=12 then 2x-5=19', its converse would be 'if 2x-5=19, then x=12'. To test the validity of the converse, we substitute the value of x back into the equation 2x-5 and check if it equals 19 when x=12.
However, we need to be cautious because the converse of a true conditional statement is not always true. To determine the truth of the converse, one must check if every instance where 2x-5 equals 19 also means that x must be equal to 12. If there is even a single case where 2x-5 is 19 and x is not 12, then the converse is not true.
For instance, let's test the converse: If we solve the equation 2x-5=19 for x, we get:
x = (19+5)/2
x = 24/2
x = 12
Therefore, for this specific case, the original statement and the converse are both true.
what is the decimal representation of 27/100?
In a group of 60 students, 12 students take Algebra I, 18 students take Algebra II, and 8 students take both subjects. How many students don't take either of these subjects?
Suppose $16,537.50 in interest was earned after $75,000 was invested at a simple interest rate of 3.15%. How long (in years) was the money invested?
Answer:
7 Years
Step-by-step explanation:
M to the second power equals 49. Is it 7?
The map shows Santa Cruz Boulevard and the construction site for the new town hall. Find the equation of a “street” that passes through the building site and is parallel to Santa Cruz Boulevard.
Answer:
the equation of a “street” that passes through the building site and is parallel to Santa Cruz Boulevard[tex]y=\frac{x}{2}+4[/tex]
Step-by-step explanation:
The slope is find by 2 points on line [tex](x_1,y_1)\,\text{and}\,(y_2,y_2)[/tex] is calculated as; [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Equation of line is in slope-intercept form is written as;[tex](y-y_1)=m(x_2-x_1)[/tex]
We can easily take two points from given graphs are
(2,5) and (6,7)
The slope of line is;
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{7-5}{6-2}[/tex]
[tex]m=\frac{2}{4}[/tex]
[tex]m=\frac{1}{2}[/tex]
the slope of line is [tex]\frac{1}{2}[/tex]
Now, find the equation of line with the slope-intercept form
[tex](y-y_1)=m(x-x_1)[/tex]
[tex](y-5)=\frac{1}{2}(x-2)[/tex]
Add both the sides by 5 in above expression,
[tex]y=\frac{1}{2}(x-2)+5[/tex]
[tex]y=\frac{x}{2}-1+5[/tex]
[tex]y=\frac{x}{2}+4[/tex]
Therefore, the equation of a “street” that passes through the building site and is parallel to Santa Cruz Boulevard[tex]y=\frac{x}{2}+4[/tex]
Melanie has a piece of cloth 12 and 1/3 yards long. How many 3/4 yard-long pieces can be cut from the cloth?
Answer: 16 pieces
Step-by-step explanation:
To get the number of pieces, we simply divide 12 1/3 by 3/4
12 1/3 ÷ 3/4
but 12 1/3 = 37/ 4 ( converting to improper fraction)
12 1/3 ÷ 3/4
=37/ 3 ÷ 3/4
= 37/3 × 4/3
= 148/9
= 16. 44444
= 16 approximately
Therefore we can get 16 pieces of yard from the cloth
The probability of drawing a blue card is 5/11 what is the probability of NOT drawing a blue card?
A set of equations is given below: Equation E: c = 2d + 1 Equation F: c = 3d + 7 Which statement describes a step that can be used to find the solution to the set of equations? (1 point)
Equation F can be written as c = 3(c – 1) + 7.
Equation F can be written as c = 2(c – 7) + 1.
Equation F can be written as d + 1 = 3d + 7.
Equation F can be written as 2d + 1 = 3d + 7.
find the area of triangle qpm. round the answer to the nearest tenth. a. 5.2 square units b. 6.3 square units c. 6.5 square units d. 12.6 square units
We need to solve for the angles of the smaller triangle in order to solve for the angle of the larger triangle which would help us solve the missing measurement of a side.
Given:
51 degrees.
Cut the triangle into two equal sides and it forms a right triangle. All interior angles of a triangle sums up to 180 degrees.
180 – 51 – 90 = 39 degrees
39 degrees * 2 = 78 degrees.
Angle Q is 78 degrees.
In the bigger triangle, 4.3 is the hypotenuse. We need to solve for the measurement of the long leg which is the opposite of the 78 degree angle.
We will use the formula:
Sine theta = opposite / hypotenuse
Sin(78 deg) = opposite / 4.3
Sin(78 deg) * 4.3 = opposite
4.21 = opposite. This is also the height of the triangle.
Area of a triangle = ½ * base * height
A = ½ * 3units * 4.21units
A = 6.315 square units.
Which of the following best describes the expression 7(x + 9)?
A.) The product of a constant factor 7 and a 2-term factor x + 9
B.) the sum of a constant factor 7 and a 2-term factor x + 9
C.) the sum of a constant factors 7 and x + 9
D.) the product of a constant factors 7 and x + 9
A.
got it right on my test, flvs
A basketball team has eight boys and four girls on the roster. The boys average 12 points each. The team averages 136 points as a whole. How many points does each girl average?
8 x 12 = 96
136-96 =40
40/4 = 10
each girl averages 10 points
Which expression represents the composition [f o g](x) for the functions below? f(x) = 2x + 3 g(x) = x – 6
2x – 9
2x – 3
2x – 15
2x2 – 9x – 18
Answer:
Option A is correct
2x-9
Step-by-step explanation:
Given the functions:
f(x) = 2x + 3
g(x) = x -6
We have to find [f o g](x).
[tex][fog](x) = f[g(x)][/tex]
Substitute the function g(x),
[tex][fog](x) = f[x-6][/tex]
Replace the value of x with x-6 in f(x) we have;
[tex][fog](x) =2(x-6)+3[/tex]
⇒[tex][fog](x) =2x-12+3[/tex]
⇒[tex][fog](x) =2x-9[/tex]
Therefore, the value of [tex][fog](x)[/tex] is, 2x-9
Cual es el minimo comu multiplo de 81,27,9
Help me please asap :(
A ship traveled for 4 hours heading east and for 3 hours heading north. If the total distance traveled was 149 miles, and the ship traveled 3 miles per hour faster heading north, at what speed was the ship traveling east?
Solve 5^x=81. 2
Round to the nearest ten-thousandth.
X≈????
What is the solution to the equation x + 8.5 = 64.5? 7.6 48 56 73
In a line of students, Jenna is number 8. The teacher says that a rule for a number pattern is add 4. The first student in line says the first term, 7. What number should Jenna say?
Jaime drew a square that has sides that are whole numbers of centimeters. Which could not be the area of Jaime's square? A. 25cm2 B. 36cm2 C. 50cm2 D. 64cm2
Final answer:
To find the area of a square, we use the formula A = s², where A represents the area and s represents the length of a side. Evaluating the options, the area that could not be Jaime's square is C. 50cm².
Explanation:
To find the area of a square, we need to multiply the length of one side by itself. So, the formula for the area of a square is A = s², where A represents the area and s represents the length of a side. We can evaluate the given options using this formula:
A. 25cm²: This could be the area of Jaime's square since 5² = 25.B. 36cm²: This could be the area of Jaime's square since 6² = 36.C. 50cm²: This could not be the area of Jaime's square since there is no whole number that can be squared to give 50.D. 64cm²: This could be the area of Jaime's square since 8² = 64.Therefore, the answer is C. 50cm².
What process can you use to help you write a system of linear equations when dealing with mixture problems
a washer and dryer cost $978 combined the washer cost $78 more than the dryer what is the cost of the dryer
Answer:
$450
Step-by-step explanation:
2x+78=978
2x=900 [subtract 78 from both sides]
x=450 [divide both sides by 2]
PLEASE HELP!! ISSA DUMB KID!
The table shows the ratio of caramel corn to hot pepper corn in a bag. What is the constant of proportionality?
Hot Pepper Corn | Caramel Corn
5_______________8
10 _____________ 16
15______________ 24
Which of the binomials below is a factor of this trinomial? x2 - 5x - 36 A. x + 4 B. x - 4 C. x2 + 7 D. x - 7
Option A is correct, x+4 is the binomial factor of the given trinomial x² - 5x - 36
What is Polynomial?
Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables
The given trinomial is x² - 5x - 36
Now we have to factorize the given polynomial.
x² - 9x +4x - 36
x(x-9)+4(x-9)
(x+4)(x-9)
The factorial form of the trinomial x² - 5x - 36 is (x+4)(x-9)
So x+4 is the binomial factor of the given trinomial.
Hence, Option A is correct, x+4 is the binomial factor of the given trinomial x² - 5x - 36
To learn more on Polynomials click:
https://brainly.com/question/11536910
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In three more years Miguel's grandfather will be six times as old as Miguel was last year. When Miguel's grandfather present age is added to his grandfathers age is added to his grandfathers present age the total is 68. How old is his grandfather now ?
Harvey the wonder hamster can run 3 1/6 km in 1/4 hour find his average speed in kilometers pe hour
there are 4 quarters to 1 hour
3 1/6 x 4 =
19/6 * 4 = 76/6 = 12 4/6, reduces to 12 2/3 km per hour
Answer:- The average speed of Harvey the wonder hamster is[tex]12\frac{2}{3}\ km/hour[/tex].
Explanation:-
Given: Distance traveled by Harvey [tex]=3\frac{1}{6}\ km=\frac{19}{6}\ km[/tex]
Time taken[tex]=\frac{1}{4}\ hour[/tex]
[tex]Speed=\frac{Distance}{Time}\\\Rightarrow\ Speed=\frac{\frac{19}{6}}{\frac{1}{4}}\\\\=\frac{19\times4}{6}\\\\=\frac{38}{ 3}\\\\=12\frac{2}{3}\ km/hour[/tex]
Therefore, the average speed of Harvey the wonder hamster is[tex]12\frac{2}{3}\ km/hour[/tex].
convert 72832 ounces' to tons?