Answer:
The water she need is [tex]7\frac{7}{8} \ cups.[/tex] and strawberry syrup [tex]11\frac{13}{16}\ cups[/tex].
Step-by-step explanation:
Given:
Dina wants to make 15 3/4 cups of strawberry drink by mixing water and strawberry syrup with a ratio of 2 1/4 cup of water for every 3/4 cup of syrup.
Now, to find the quantity of water and syrup she need to use.
As given in question ratio so:
Strawberry syrup = 2 1/4 = 9/4.
Water = 3/4.
Total cups of strawberry drink = 15 3/4 = 63/4.
Let the strawberry syrup be [tex]\frac{9}{4} x[/tex].
And let the water be [tex]\frac{3}{4} x[/tex].
According to question:
[tex]\frac{9x}{4} + \frac{3x}{4}=\frac{63}{4}[/tex].
On adding the fractions:
⇒[tex]\frac{9x+3x}{4} =\frac{63}{4}[/tex]
⇒[tex]\frac{12x}{4} =\frac{63}{4}[/tex]
Multiplying both sides by 4 we get:
⇒[tex]12x=63[/tex]
Dividing both sides by 12 we get:
⇒[tex]x=\frac{63}{12}[/tex]
Dividing numerator and denominator by 3 on R.H.S we get:
⇒[tex]x=\frac{21}{4}[/tex]
Now, putting the value of [tex]x[/tex] on ratios:
Strawberry syrup = [tex]\frac{9}{4}\times x=\frac{9}{4}\times\frac{21}{4}[/tex]
= [tex]\frac{189}{16}[/tex]
= [tex]11\frac{13}{16}\ cups[/tex]
Water = [tex]\frac{3}{4}\times x =\frac{3}{4} \times\frac{21}{4}[/tex]
= [tex]\frac{63}{8}[/tex]
= [tex]7\frac{7}{8} \ cups.[/tex]
Therefore, the water she need is [tex]7\frac{7}{8} \ cups.[/tex] and strawberry syrup [tex]11\frac{13}{16}\ cups[/tex].
x+ 1/8 =1.375 what is the anser
Answer:
1.25
Step-by-step explanation:
x+1/8=1.375
x=1.375-0.125
x=1.25
Answer: 1.25
Move all terms not containing x to the right side of the equation.
Exact Form:
x = 54
Decimal Form:
x = 1.25
Mixed Number Form:
x = 1 1/4
Hope this helps
The area of a triangle is 80in^2. The ratio of the length of its base to its height is 5:2. What are the base and height of the triangle? ..... show work
Answer: base = 20 inches , height = 8 inches
Step-by-step explanation:
The formula fro calculating the area of a triangle , given the base and the height is given as ;
A = [tex]\frac{1}{2}[/tex]bh
The ratio of its base to the height is given as 5: 2 , this means that
2b = 5h , that is
b = [tex]\frac{5h}{2}[/tex]
Substitute this into the formula for finding area , that is
80 = [tex]\frac{1}{2}[/tex] X [tex]\frac{5h}{2}[/tex] X h
80 = [tex]\frac{5h^{2}}{4}[/tex]
Therefore :
[tex]5h^{2}[/tex] = 80 x 4
[tex]5h^{2}[/tex] = 320
[tex]h^{2}[/tex] = 320 / 5
[tex]5h^{2}[/tex] = 64
h = 8 inches
Substitute h = 8 into b = [tex]\frac{5h}{2}[/tex] , then
b = 20 inches
Therefore , the base of the triangle is 20 inches and the height is 8 inches
on average, Shawnte drinks 1/2 of a 6 ounce glass of water in 2/3 hour. How much water does she drink in an hour?
Answer:
3 ounces every 40 minutes
60 divided by 40= 1.5
3x1.5= 4.5 ounces
A line passes through point A(10,15). A second point on the line has an x-value that is 125% of the x-value of point A and a y-value that is 75% of the y-value of point A. Use point A to write an equation of the line in point-slope form.
An equation is y− = (x− )
The equation of the line in the point-slope form is y - 15 = [tex]-\frac{3}{2}[/tex] (x - 10)
Step-by-step explanation:
The point-slope form of a linear equation is [tex]y-y_{1}=m(x-x_{1})[/tex] , where
m is the slope of the line, where [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] , [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] are two points on the line[tex](x_{1},y_{1})[/tex] is a point on the line∵ Point A = (10 , 15)
∵ The x-coordinate of the second point is 125% of x-coordinate
of point A
∴ x-coordinate of second point = [tex]\frac{125}{100}[/tex] × 10
∴ x-coordinate of second point = 12.5
∵ The y-coordinate of the second point is 75% of y-coordinate
of point A
∴ y-coordinate of second point = [tex]\frac{75}{100}[/tex] × 15
∴ y-coordinate of second point = 11.25
∴ The coordinates of the second point are (12.5 , 11.25)
Let us find the slope of the line by using the rule of it above
∵ [tex](x_{1},y_{1})[/tex] = (10 , 15)
∵ [tex](x_{2},y_{2})[/tex] = (12.5 , 11.25)
∴ [tex]m=\frac{11.25-15}{12.5-10}=\frac{-3.75}{2.5}=-\frac{3}{2}[/tex]
Now we can write the equation
∵ The point-slope form is [tex]y-y_{1}=m(x-x_{1})[/tex]
∵ [tex]m=-\frac{3}{2}[/tex]
∵ [tex](x_{1},y_{1})[/tex] = (10 , 15)
- Substitute these values in the form of the equation
∴ y - 15 = [tex]-\frac{3}{2}[/tex] (x - 10)
The equation of the line in the point-slope form is y - 15 = [tex]-\frac{3}{2}[/tex] (x - 10)
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A construction crew has just finished building a road. The road is 10 5/6 kilometers long. If the crew worked for 5 days, how many kilometers of road did they build each day? (Assume they built the same amount each day.)
Write your answer as a mixed number in simplest form.
Answer:
Step-by-step explanation:
10 5/6 km...in 5 days
(10 5/6) / 5 =
(65/6) / 5 =
65/6 * 1/5 =
65/30 =
2 1/6 kilometers per day <===
Which input value produces the same output value for the
two functions on the graph?
O
O x=-1
Ox= 0
O
Ox=4
Answer: [tex]d)x=4[/tex]
Step-by-step explanation:
The missing graph is attached. And the options are:[tex]a)x=-1\\b)x=0\\c)x=3\\d)x=4[/tex]
By definition, a relation is a function if and only if each input value has one and only one output value.
It is important to remember that the input values are the values of "x" and the output values are the values of "y".
Observe the graph attached.
You can identify in the graph that the function f(x) and the function g(x) intersect each other at the following point:
[tex](4,3)[/tex]
Where the x-coordinate (input value) is:
[tex]x=4[/tex]
And the y-coordinate (output value) is:
[tex]y=3[/tex]
Therefore, you can conclude that the input value that produces the same output value for the two functions on the graph, is:
[tex]x=4[/tex]
The similarity ratio of two similar polygons is 2:3. Compare
the smaller polygon to the larger polygon. Find the ratio
of their areas.
Answer:
The ratio of their areas is 4:9
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
Let
z ---> the scale factor
x ---> the area of the smaller polygon
y ---> the area of the larger polygon
[tex]z^2=\frac{x}{y}[/tex]
we have
[tex]z=\frac{2}{3}[/tex] ---> the scale factor is given
substitute
[tex](\frac{2}{3})^2=\frac{x}{y}[/tex]
[tex]\frac{4}{9}=\frac{x}{y}[/tex]
Rewrite
[tex]\frac{x}{y}=\frac{4}{9}[/tex]
therefore
The ratio of their areas is 4:9
What is the first step to solve this equation 11 minus 3x equals 44
Answer:
x=-11
Step-by-step explanation:
11-3x=44
3x=11-44
3x=-33
x=-33/3
x=-11
which equation is the slope intercept form of this equation?
y-4=-2(x-5)
A) y=-2x+14
B)2x+y=6
C)y-4=-2x+10
D)x=-1/2y+3
Please help me!!!!!!!!!!! ☆I will give brainliest if right☆
Answer:
A) y = -2x + 14Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
We have the equation i point-slope form.
Convert to the slope-intercept form:
[tex]y-4=-2(x-5)[/tex] use the distributive property
[tex]y-4=-2x+(-2)(-5)[/tex]
[tex]y-4=-2x+10[/tex] add 4 t oboth sides
[tex]y-4+4=-2x+10+4\\\\y=-2x+14[/tex]
PLZZZ HURRYYYY ITS TIMEDDDDD
Daniel expanded the expression as shown. What errors did he make? Select three options.
-2(-8x-4y+3/4)=-10x-8y-1 1/4
A. The first term should be positive.
B. The second term should be positive.
C.The last term should be -1 1/2, not -1 1/4.
D. He divided -8 by -2 instead of multiplying -8 by -2.
E. He did not simplify the expression completely.
Answer:
Step-by-step explanation:
-2(-8x - 4y + 3/4) =
16x + 8y - 3/2 ....(-3/2 is the same as - 1 1/2)
errors.....
A. the first term should be positive
B. the second term should be positive
C. the last term should be - 1 1/2
Daniel expanded the expression . The errors made by Daniel are
A. The first term should be positive.
B. The second term should be positive.
C. The last term should be -1 1/2, not -1 1/4.
Given :
Daniel expanded the expression as shown
[tex]-2(-8x-4y+3/4)\\-10x-8y-1 1/4[/tex]
Lets multiply -2 inside the parenthesis and see what happens
[tex]-2(-8x-4y+3/4) \\-2 (-8x)-2(-4y)-2(\frac{3}{4} )[/tex]
we know that negative times negative is positive
Also to simplify the fraction ,we can cancel out 2 and 4
[tex]-2 (-8x)-2(-4y)-2(\frac{3}{4} )\\+16x+8y-\frac{3}{2} \\+16x+8y-1\frac{1}{2} \\[/tex]
So the first and second terms are positive
Also the constant term is -1 1/2
So the errors he make are
A. The first term should be positive.
B. The second term should be positive.
C.The last term should be -1 1/2, not -1 1/4.
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Graph a line with a slope of
that contains the point (6,3).
Guy wants to swim 500 meters. After 75 meters, he takes a break. What percent of his goal has he already met?
Answer:
15%
Step-by-step explanation:
75/500=0.15=15%
Answer:
15%
Step-by-step explanation:
divide 75/500 by 25/25= 3/20
3/20 x 5/5= 15/100
Which ordered pair is a solution to the system of inequalities?
y> 2x
y> 7
A. (4,8)
B. (0,0)
c. (3,7)
D. (1,9)
Answer:
D
Step-by-step explanation:
To determine which ordered pair is a solution.
Substitute the x and y values into the inequalities.
Note that both must be true for the pair to be a solution of the system.
(4, 8)
8 > 2(4) → 8 > 8 ← False
8 > 7 ← True
(0, 0)
0 > 2(0) → 0 > 0 ← False
0 > 7 ← False
(3, 7)
7 > 2(3) → 7 > 6 ← True
7 > 7 ← False
(1, 9)
9 > 2(1) → 9 > 2 ← True
9 > 7 ← True
Thus (1, 9) is a solution to the system of equations. → D
The ordered pair (1,9) is the solution to the system of inequalities.
Explanation:To determine which ordered pair is a solution to the system of inequalities, we need to check if each pair satisfies both inequalities. Let's check:
A. (4,8): For y > 2x, 8 > 2(4) = 8 > 8, which is false. For y > 7, 8 > 7, which is true. Therefore, (4,8) is NOT a solution to the system.
B. (0,0): For y > 2x, 0 > 2(0) = 0 > 0, which is false. For y > 7, 0 > 7, which is false. Therefore, (0,0) is NOT a solution to the system.
C. (3,7): For y > 2x, 7 > 2(3) = 7 > 6, which is true. For y > 7, 7 > 7, which is false. Therefore, (3,7) is NOT a solution to the system.
D. (1,9): For y > 2x, 9 > 2(1) = 9 > 2, which is true. For y > 7, 9 > 7, which is true. Therefore, (1,9) is a solution to the system.
Thus, the ordered pair (1,9) is the solution to the system of inequalities.
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Use a matrix to solve the system.
8.
2x + 6y = 38
(5x - y = 15
Answer:
x=4 and y=5
Step-by-step explanation:
The given system of equations are
[tex]2x+6y=38[/tex]
[tex]5x-y=15[/tex]
The matrix form is
[tex]\begin{bmatrix}2&6\\ \:5&-1\end{bmatrix}\begin{bmatrix}x\\ \:y\end{bmatrix}=\begin{bmatrix}38\\ \:15\end{bmatrix}[/tex]
Let as assume
[tex]A=\begin{bmatrix}2&6\\ \:5&-1\end{bmatrix}[/tex]
[tex]X=\begin{bmatrix}x\\ \:y\end{bmatrix}[/tex]
[tex]B=\begin{bmatrix}38\\ \:15\end{bmatrix}[/tex]
then,
[tex]AX=B[/tex]
[tex]X=A^{-1}B[/tex]
We know that,
[tex]\begin{bmatrix}a\:&\:b\:\\ c\:&\:d\:\end{bmatrix}^{-1}=\frac{1}{\det \begin{bmatrix}a\:&\:b\:\\ c\:&\:d\:\end{bmatrix}}\begin{bmatrix}d\:&\:-b\:\\ -c\:&\:a\:\end{bmatrix}[/tex]
[tex]A^{-1}=\frac{1}{\det \begin{bmatrix}2&6\\ 5&-1\end{bmatrix}}\begin{bmatrix}-1&-6\\ -5&2\end{bmatrix}[/tex]
[tex]A^{-1}=\frac{1}{-32}\begin{bmatrix}-1&-6\\ -5&2\end{bmatrix}[/tex]
[tex]X=\frac{1}{-32}\begin{bmatrix}-1&-6\\ -5&2\end{bmatrix}\begin{bmatrix}38\\ \:15\end{bmatrix}[/tex]
[tex]X=\frac{1}{-32}\begin{bmatrix}\left(-1\right)\cdot \:38+\left(-6\right)\cdot \:15\\ \left(-5\right)\cdot \:38+2\cdot \:15\end{bmatrix}[/tex]
[tex]X=\frac{1}{-32}\begin{bmatrix}-128\\ -160\end{bmatrix}[/tex]
[tex]\begin{bmatrix}x\\ \:y\end{bmatrix}=\begin{bmatrix}4\\ 5\end{bmatrix}[/tex]
Therefore, the value of x is 4 and value of y is 5.
Oceanside bike rental charges 11 dollars plus 8 hours for renting. Tom paid 51 dollars to rent a bike . How many hrs did he pay to have the bike checked out
Answer:
Tom paid $51 renting the bike for 5 hours
Step-by-step explanation:
Given:
Oceanside bike rental charges $11 plus $8 per hour for renting.
Tom paid $51 to rent a bike.
To find the number of hours Tom rented the bike for.
Solution:
Let Tom rent the bike for =[tex]x[/tex] hours.
Hourly rate of renting = $8 per hour
Using unitary method find cost of renting for [tex]x[/tex] hours.
If renting for 1 hour costs = $8
Then for [tex]x[/tex] hours, the cost in dollars will be = [tex]8x[/tex]
Fixed charges = $11
∴ Total cost of renting a bike in dollars for [tex]x[/tex] hours will be given as:
[tex]8x+11[/tex]
Tom paid a total charge of = $51.
So, we have:
[tex]8x+11=51[/tex]
Subtracting both sides by 11.
[tex]8x+11-11=51-11[/tex]
[tex]8x=40[/tex]
Dividing both sides by 8.
[tex]\frac{8x}{8}=\frac{40}{8}[/tex]
∴ [tex]x=5[/tex]
Thus, Tom rents the bike for 5 hours.
A rectangular field is 400 meters long and 350 M wide what is the area of the field in square kilometers do not round the answer and be sure to include the correct unit in the answer
Final answer:
The area of a rectangular field that is 400 meters long and 350 meters wide is calculated by multiplying the length and width in meters to get square meters and then converting to square kilometers. The field's area is 0.14 square kilometers.
Explanation:
To calculate the area of a rectangular field, you multiply the length by the width. The area is usually given in square units.
In this case, the field is 400 meters long and 350 meters wide. To find the area in square meters, we do the following calculation:
Area = Length × Width
Area = 400 m × 350 m
Area = 140,000 m2
To convert square meters to square kilometers, you need to remember that 1 square kilometer equals 1,000,000 square meters. Therefore, you divide the area in square meters by 1,000,000 to get the area in square kilometers:
Area in square kilometers = Area in square meters / 1,000,000
Area in square kilometers = 140,000 m2 / 1,000,000
Area in square kilometers = 0.14 km2
The area of the field is 0.14 square kilometers.
To find the area of the rectangular field in square kilometers, the measurements of 400 meters and 350 meters must first be converted to kilometers, resulting in an area of 0.14 square kilometers.
Explanation:To calculate the area of a rectangular field in square kilometers, we can use the formula for the area of a rectangle which is length × width. First, we need to convert the measurements into the same unit, so we will convert meters to kilometers. We know that 1 kilometer is equivalent to 1000 meters. Therefore, a field that is 400 meters long is 0.4 kilometers long (400 ÷ 1000 = 0.4 km), and a field that is 350 meters wide is 0.35 kilometers wide (350 ÷ 1000 = 0.35 km).
Now, with both measurements in kilometers, we can find the area:
To find the area of a rectangular field, you need to multiply its length by its width. In this case, the length is 400 meters and the width is 350 meters. So, the area of the field is 400 * 350 = 140,000 square meters.To convert this to square kilometers, we need to divide the area by 1,000,000 (since there are 1,000,000 square meters in a square kilometer). So, the area of the field in square kilometers is 140,000 / 1,000,000 = 0.14 square kilometers.Therefore, the area of the rectangular field is 0.14 square kilometers.the temperature is -4 it increases to 8 how many degrees did the temperature increase
Answer:
12 degrees.
Step-by-step explanation:
8 - (-4) = 12. So, the temperature increased by 12 degrees.
The temperature increased by 12 degrees from -4 to 8.
Explanation:The question is asking for the temperature change from -4 to 8 degrees. To find the increase in temperature, you subtract the initial temperature from the final temperature. In this case, 8 (final temperature) minus (-4) (initial temperature), equals 12°C. Hence, the temperature increased by 12 degrees.
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all uses the expression 4.2 * 12.3 * 14.6 to determine the cost of tile in the Floor of a room that measures 12.3 ft by 14.6 feet each square foot of tile cost 4.20 dollars how many decimal places will be in Polish final answer
one
three
five
eight
Answer:
There are three decimal places in the final answer.
Step-by-step explanation:
We have to calculate the expression 4.2 × 12.3 × 14.6, in which the floor dimensions are 12.3 ft by 14.6 ft. which I have to cover with tiles and each square foot of tile costs $4.20.
So, the area of the floor is (12.3 × 14.6) sq. ft. = 179.58 square feet.
Now, the cost of covering the floor with tiles will be = $(179.58 × 4.2) = $754.236.
Therefore, there are three decimal places in the final answer. (Answer)
Find the coordinates of the center of the given circle
(x - 5)2 + (y + 3)2 = 25
(5,-3)
(5.3)
(-5,3)
Answer:
The coordinates are (5.3)
Step-by-step explanation:
15-0 = 0-15. True or False. Justify your statement.
Answer:
False
Step-by-step explanation:
15-0=0
0-15=-15
Find the midpoint of the segment with the endpoints (9,8) and (3,5)
Answer:
The midpoints are ( 6, 6.5 ).
Step-by-step explanation:
Given that the endpoints are A ( 9, 8) and B (3,5)-
As we know that-
If a line segment AB is with endpoints ([tex]x_{1}, y_{1}[/tex]) and ([tex]x_{2}, y_{2}[/tex] then the mid points C are-
C = ([tex]\frac{x_{1} + x_{2} }{2}[/tex] , [tex]\frac{y_{1} + y_{2} }{2}[/tex] )
Here,
A ( [tex]x_{1} = 9, y_{1} = 8[/tex] and B ( [tex]x_{2} = 3, y_{2} =5[/tex]
then the midpoints C are-
C = ( [tex]\frac{9 + 3 }{2}[/tex], [tex]\frac{8 + 5 }{2}[/tex]
C= ( 12/2 , 13/2 )
C = ( 6, 6.5 )
Hence the midpoints are (6, 6.5).
What is the Square root of -1
Answer:
the square root of -1 is i
Step-by-step explanation:
Answer:
[tex]\large\boxed{\sqrt{-1}=i}[/tex]
Step-by-step explanation:
[tex]\sqrt{-1}=i\\\\i-\text{immaginary unit}\ \left(i^2=-1\right)\\\\\text{It's a complex number.}[/tex]
What is the equation for the line?
Answer:
y=4x
Step-by-step explanation:
The line goes through the points (0, 0) and (2, 8).
You can plug these in to the slope formula, and the slope is 4
Since the line intersects the y-axis at 0, the y-intersect is 0.
Using these two pieces of information, you now know that the equation is
y=4x+0, or y=4x.
Hope this helps!
Answer:
Y = mx + c
Step-by-step explanation:
Where
m = gradient or slope
c = intercept (value of y when x=0)
Y = how far up
x = how far along
is (2,4), (-5,2), (7,1), (-6,2) a relation or function
Answer: Function
Step-by-step explanation: A function is a special type of relation and for a relation to be a function, each x-term must correspond with exactly 1 y-term.
The easiest way to determine whether a relation is a function is to look at the x-coordinate of each ordered pair. If any of our ordered pairs have the same x-coordinate with a different y-coordinate, then our relation is no a function.
Since none of our x-terms repeat with different y-terms, this is a function.
Use the following figure to answer the question
∠ 1 and ∠ 2 are verical angles.
True
False
Answer:
False
Step-by-step explanation:
The only vertical angles shown are 1 and 3. The other pair is 2 and 4
change the subject of the formula to w help
[tex]d = w - r { }^{2} [/tex]
Answer:
w = d + r²
Step-by-step explanation:
Given
d = w - r² ( isolate w by adding r² to both sides )
d + r² = w
If every 3 hours John walked 8 miles. How many miles did John walk in 1 hour
8 ÷ 3 = 2 2/3 miles
yeeeeeeeee
Answer:
2.66 miles every hour
Step-by-step explanation:
8/3
help me in math tasks please
Answer:
1. 3/5 c
2. 7 c
3. 2/5 b
4. $3.24 c
5. -3.2 b
Step-by-step explanation:
1.
2/5 + 1/5 = 3/5
2.
a negative + a negative = a positive
2+5 = 7
3.
terminating means the decimal ends. When u divide a & c they keep on going but 2/5 ends
4.
divide 16.8 by 5.19 = 3.23 round up so 3.24
5.
multiply the two together to get the answer
Use natural logarithms to solve the equation. Round to the nearest thousandth.
3e^2x+2=28
A. 1.0797
B. 0.4689
C. 0.9261
D. 2.1595
Answer:
A. 1.0797
Step-by-step explanation:
Given the equation,
3e^2x+2=28
To solve for x, first we move 2 to the other side of the equation.
3e^2x = 28-2
3e^2x = 26
Dividing both sides by 3
e^2x = 26/3
e^2x = 8.67
Taking the natural logarithm if both sides
ln(e^2x) = ln8.67
2x = ln8.667
2x = 2.1595
x = 2.1595/2
x = 1.0797
Use the rule 6x to write a sequence. Start your sequence with x = 0. Be sure to write a sequence of at least six numbers, each separated by commas: 0, ___, ___, ___, ___, ___
Sequence by the given rule will be 0, 6, 12, 18, 24, 30, 36.
Given rule for the sequence to be formed,
Terms = 6xHere, x = 0, 1, 2, 3, 4, 5
To write the sequence, substitute the values of x in the rule given,
1st term → 6 × 0 = 0
2nd term → 6 × 1 = 6
3rd term → 6 × 2 = 12
4th term → 6 × 3 = 18
5th term → 6 × 4 = 24
6th term → 6 × 5 = 30
Therefore, sequence will be → 0, 6, 12, 18, 24, 30, 36.
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