Answer:
100
Step-by-step explanation:
You are given the equation
[tex]4x-4.5=10.73+5.7+7x[/tex]
There are 5 coefficients:
[tex]4, \ -4.5,\ 10.73,\ 5.7,\ 7[/tex]
Two of them are integers
[tex]4,\ 7[/tex]
two of them are decimals with one digit after point
[tex]-4.5,\ 5.7[/tex]
and one is a decimal with two digits after point
[tex]10.73[/tex]
To get rid of fractions, we have to get rid of digits after point. The maximum number of digits after point is 2, then we have to multiply the equation by 100:
[tex]400x-450=1,073x+570+700x[/tex]
Final answer:
To eliminate decimals in an equation, multiply all terms by a power of 10 to shift the decimals to whole numbers, simplifying the calculation process.
Explanation:
To get rid of decimals in the equation 4x - 4.5 = 10.73x + 5.7 + 7x, you would multiply each term by a power of 10 that shifts the decimals to whole numbers. By determining the highest number of decimal places in the terms, you can multiply all terms by a suitable power of 10.
For example, if the highest number of decimal places is 2, you would multiply all terms by 100. This action shifts the decimals two places to the right, converting them into whole numbers and simplifying the equation.
By multiplying all terms by the appropriate power of 10, you eliminate decimals and work with whole numbers, making it easier to solve the equation.
What is the fewest number of full weeks Briyana would have to work to have enough money?
8 weeks
9 weeks
10 weeks
11 weeks
Answer:
10 weeks
Step-by-step explanation:
The number of weeks will be 10. Then the correct option is C.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
Briyana has $150, and she needs to save at least $560 is the fewest number of full weeks Briyana for a spring break trip.
If she can save $45 would have to work to have enough money per week.
Let w be the number of weeks.
Then the inequality will be
45w + 150 ≥ 560
Simplify the inequality, then the number of week will be
45w + 150 ≥ 560
45w ≥ 560 – 150
45w ≥ 410
w ≥ 410 / 45
w ≥ 9.11
Then the number of weeks will be 10.
Then the correct option is C.
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Reduce the following fractions to lowest terms:
6/9
In order to get the answer to this question you must find the number that the numerator and the denominator is dividable by (common factor) then divide.
[tex]\frac{6}{9}[/tex]
[tex]CF=3[/tex]
[tex]6\div3=2[/tex]
[tex]9\div3=3[/tex]
[tex]= \frac{2}{3}[/tex]
Therefore your answer is "2/3."
Hope this helps.
The sum of two numbers is 100 and the difference is 80
Answer:
10 and 90 are the numbers
10+90=100
90-10=80
The larger number is 90 and the smaller number is 10.
What are the equations that reperesent the question?
a + b = 100 equation 1
a - b = 80 equation 2
Where:
a = larger number b = smaller number What is the larger number ?In order to determine the value of a, add equation 2 and equation 1
2a = 180
Divide both sides by 2
a = 90
What is the smaller number?
Subtract 90 from 100,
b = 100 - 90
b = 10
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Stella graphed y = 100 - 25/3 * x to represent the percentage of battery life remaining on her phone after x hours. What is a reasonable domain for this situation ?
Answer:
from 0 to 12 hours, that is [tex]0\leq x\leq 12[/tex]
Step-by-step explanation:
Notice that the x represents the number of phone hours used, therefore it has to be a number larger or equal zero, but NOT a negative number.
So on one end we have that the number of phone hours used (x) must be larger or equal zero: [tex]x\geq 0[/tex]
On the other hand, when the battery goes to zero, there are no more phone hours to use. We can find what is that other limit by making the battery percent (y variable) equal to zero, and solve the equation for x, thus giving us the upper limit of usable phone hours:
[tex]y=0=100-\frac{25}{3} x\\\frac{25}{3} x=100\\25 x = 100*3 = 300\\x = \frac{300}{25} = 12[/tex]
Therefore, the upper limit for the number of usable phone hours is 12 hours.
Then we write:
[tex]0\leq x\leq 12[/tex] hours
Look around you to find something in the U.S. that is measured in metrics.
Final answer:
In the U.S., the metric system is used in scientific, medical, and nutritional contexts, with units like liters for beverages, grams for food nutrition labels, and millimeters or centimeters for scientific measurements.
Explanation:
To find something in the U.S. that is measured in metric units, one needs to look no further than scientific or medical fields. For example, beverages such as soda are commonly sold in liters, which is a metric unit of volume. Moreover, medications are often measured in milligrams or grams. If we explore other common usages, we find that the nutrition facts on food products provide information in grams and milliliters.
In academics, specifically in science classes, the metric system is the standard for measuring length, with units like millimeters, centimeters, meters, and kilometers. The metric system's fundamental units include the meter (m) for length, the kilogram (kg) for mass, and the second (s) for time. When estimating conversion to metric units, it's also important to choose the appropriate measurement tool based on the size of the object being measured.
Final answer:
In the U.S., the metric system is often used in science, medicine, and industries involving international standards. Common examples include nutritional information on food labels and the labeling of bottled beverages. It is also used for some athletic event distances like 5K and 10K races.
Explanation:
When trying to find something in the U.S. that is measured in metric units, one can look at scientific settings. In the United States, the metric system is primarily used in science, medicine, and in industries where international standards are important. For example, scientists usually use the International System of Units (SI), which includes meters to measure length and kilograms to measure mass. Although the U.S. commonly uses the customary system with units such as inches and pounds, metric units are often found on nutrition labels, where calories, sugar content, and other nutritional information are listed in grams or milliliters.
Some everyday items that might be measured using the metric system include bottled beverages (usually listed in liters or milliliters), medications (measured in milligrams or grams), and distances in some athletic events, such as 5K and 10K races (measured in kilometers)
An atom has 10 positive electric charges known as protons and 10 negative electric charges known as electrons.A proton is +1, and an electron is -1. What is the net charge of this atom
Answer:
0
Step-by-step explanation:
10 protons and 0 electrons gives the atom a positive charge. 10 electrons and 0 protons gives the atom a negative charge. Therefore 10 protons and 10 electrons gives the atom a net charge of 0 and the charge of the atom is neutral. HOPE THIS HELPS! PLEASE VOTE THIS BRAINLIEST!!!!!!!!!!!!!!
The atom is neutral, with 10 protons (+1 each) and 10 electrons (-1 each), resulting in a net charge of 0 due to equal positive and negative charges.
The net charge of an atom is determined by the balance between its protons and electrons.
Protons carry a positive charge of +1, while electrons carry a negative charge of -1.
In a neutral atom, the number of protons is equal to the number of electrons, resulting in a net charge of 0.
This implies, the atom has 10 protons (positive charges) and 10 electrons (negative charges).
Since the number of protons is equal to the number of electrons, the net charge of this atom is 0. It is a neutral atom.
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Which functions are equivalent to f (x) = RootIndex 4 StartRoot 162 EndRoot Superscript x? Check all that apply.
Answer:
[tex]f(x)=162^\frac{x}{4}[/tex]
[tex]f(x)=[3\sqrt[4]{2}]^{x}[/tex]
[tex]f(x)=[3(2^{\frac{1}{4}})]^{x}[/tex]
Step-by-step explanation:
we have
[tex]f(x)=\sqrt[4]{162^{x}}[/tex]
Remember that
[tex]\sqrt[n]{a^{m}}=a^{m/n}[/tex]
[tex](a^{m})^{n}=a^{m*n}[/tex]
so
1) [tex]\sqrt[4]{162^{x}}=162^\frac{x}{4}[/tex]
2) The number 162 decompose in prime factors is
[tex]162=(2)(3^4)[/tex]
substitute
[tex]f(x)=\sqrt[4]{[(2)(3^4)]^{x}}={[(2)(3^4)]^{x/4}={{[(2)(3^4)]^{(1/4)}}^x=[3\sqrt[4]{2}]^{x}[/tex]
3) [tex]f(x)=[3\sqrt[4]{2}]^{x}=[3(2^{\frac{1}{4}})]^{x}[/tex]
therefore
[tex]f(x)=162^\frac{x}{4}[/tex]
[tex]f(x)=[3\sqrt[4]{2}]^{x}[/tex]
[tex]f(x)=[3(2^{\frac{1}{4}})]^{x}[/tex]
Answer:
A.B. E.
Step-by-step explanation:
Kevin can ride his bike 2 miles in 12 minutes. At this rate, how many miles can he ride in 60 minutes?
Answer:
At this rate he can ride his bike 10 miles in 60 minutes.
Step-by-step explanation:
I divided 60 by 12 which is 5.
Then I multiplied 2 by 5 which is 10. So, this was the simplest way of getting to 10 miles in 60 minutes from 2 miles in 12 minutes.
Yours truly,
Que.
Answer:
At this rate he can ride his bike 10 miles in 60 minutes.
Step-by-step explanation:
I divided 60 by 12 which is 5.
Then I multiplied 2 by 5 which is 10. So, this was the simplest way of getting to 10 miles in 60 minutes from 2 miles in 12 minutes.
The icy one,
Que.
Solve for x.
12x + 14
1 + 5x
76
Answer:
12x +14
1.) divide both sides but 12 to get the variable alone
12x becomes just the variable x
14 is now 1.16 with the 6 having a line above it showing its repeating.
x = 1.16 repeated
a single layer of gold atoms form a surface whose dimensions are 1.0x10^3 angstroms by 1.0x10^3 angstroms. 1 angstrom=10^-10 meter.
A)what is the area of this surface in square angstroms? [ ]
B) What is the surface area in square centimeters? [ ]
Answer:
Part A) [tex]1*10^{6}\ angstroms^{2}[/tex]
Part B) [tex]1*10^{-10}\ cm^{2}[/tex]
Step-by-step explanation:
Remember that
When multiply numbers in scientific notation, multiply the coefficients and then add the exponents
Part A) what is the area of this surface in square angstroms?
The area is equal to
[tex]A=(1*10^{3})( (1*10^{3})=(1)*(10^{3+3})=1*10^{6}\ angstroms^{2}[/tex]
Part B) What is the surface area in square centimeters
we know that
1 angstrom=10^-10 m
so
1 angstrom=10^-8 cm
Convert angstroms to cm
[tex](1*10^{3})\ angstroms=(1*10^{3})*(10^{-8})=(1*10^{-5})\ cm[/tex]
The area is equal to
[tex]A=(1*10^{-5})(1*10^{-5})=(1)*(10^{-5-5})=1*10^{-10}\ cm^{2}[/tex]
What is 79800/50 in simplest form
Answer:
1,596
Step-by-step explanation:
79800 is divisible by 50
A bedroom is shaped like a rectangular prism. The floor has a length of 4.57 meters and a width of 4.04 meters. The height of the room is 2.3 meters
Answer:42.46444
Step-by-step explanation: 4.57×4.04x2.3
I think 42.46444 is the answer
The percentage uncertainty for each measurement, sum them, and apply this to the area, resulting in an uncertainty of approximately 0.0350 m².
To calculate the area of a rectangular room, you multiply the length by the width. In this case, we have been provided with the measurements for the length (3.955 "+/-" 0.005 m) and the width (3.050 "+/-" 0.005 m). Multiplying these measurements gives us the area of the room, albeit with some uncertainty due to measurement errors.
First, calculate the area using nominal values:
Area = Length x Width = 3.955 m x 3.050 m = 12.07275 m²
To compute the uncertainty in the area, apply the rule for the multiplication of quantities with uncertainties:
The percentage uncertainty for both the length and the width is:
Length: 0.005 / 3.955 = 0.001264 (about 0.1264%)
Width: 0.005 / 3.050 = 0.001639 (about 0.1639%)
Add the percentage uncertainties:
Total percentage uncertainty = 0.1264% + 0.1639% = 0.2903%
Apply this to the area:
Uncertainty in area = 0.2903% of 12.07275 m² ≈ 0.0350 m²
Therefore, the area of the room with its uncertainty is:
12.07275 m² "+/-" 0.0350 m² (approximately, we could round the nominal area to 12.073 m² and the uncertainty to 0.035 m² due to significant figures)
Stefanie spends entire allowance one month she spends 1/2 of a on new clothes 1/4 on food 1/6 on movies and 1/12 on Music how much more does she spend on clothes that he does on movies
A: 1/4
B: 1/2
C: 1/6
D: 1/3
Answer:
Option D: 1/3
Step-by-step explanation:
Let
x ------> the entire Stefanie's allowance
we know that
She spends on clothes (1/2)x
She spends on movies (1/6)x
To find out how much more does she spend on clothes that he does on movies, subtract the amount she spends on movies from the amount she spend on clothes
[tex]\frac{1}{2}x-\frac{1}{6}x=\frac{2}{6}x[/tex]
Simplify
[tex]\frac{1}{3}x[/tex]
therefore
She spends 1/3 more on clothes that he does on movies
What is the slope of the line passing through the points (2, −5) and (4, 1)?
54
2
3
−45
Answer:
3
its formula is y2-y1(/x2-x1)
Hey!
-----------------------------------------------
Formula: [tex]m = \frac{y2 - y1}{x2 - x1}[/tex]
-----------------------------------------------
Steps To Solve:
~Substitute
[tex]m = \frac{1 - (-5)}{4 - 2}[/tex]
~Simplify
[tex]m = \frac{6}{2}~or~3[/tex]
-----------------------------------------------
Answer:
[tex]\large\boxed{C)~3}[/tex]
-----------------------------------------------
Hope This Helped! Good Luck!
BRAINLIEST ASAP
solve for y
-140=18+4(5y-2)
Answer:
Variable Y is equal to 7.5.
Step-by-step explanation:
First, open the brackets:
18 + 20y - 8 = -140
Second, subtract 18 and add 8 from/to both sides.
20y = -140 - 18 + 8
20y = -150
Third, divide by 20.
y = 7.5
NEED HELP ASP plz
What is the value of x?
Enter your answer in the box. x =
Answer:
Okay they're going to be the same answer so solve like this
Step-by-step explanation:
2x+20=3x-30
Escribe el número 317 en forma expandida?
Answer:300+10+7=317
Step-by-step explanation:
Tienes que expandir el número en las partes de 100 las de 10 y láser de 1 como las de 100 es 300 la de 10 es 10 y la de 1 es 7
Write the equation of the line that passes through (-7,-4) and (-6,-2) in slope-intercept form.
A.) y=2x-4
B.) y=-2x-14
C.) y=2x+10
D.) y=1/2x+1
Option C) [tex]y=2x+10[/tex] is correct
Equation of a line passing through points [tex]\boldsymbol{\left ( x_1,y_1 \right ),\left ( x_2,y_2 \right )}[/tex] is given by [tex]\boldsymbol{y-y_1=\left ( \frac{y_2-y_1}{x_2-x_1} \right )\left ( x-x_1 \right )}[/tex]
Given points are as follows:
[tex]\left ( x_1,y_1 \right )=\left ( -7,-4 \right )\\\left ( x_2,y_2 \right )=\left ( -6,-2 \right )[/tex]
Equation of a line is [tex]y+4=\left ( \frac{-2+4}{-6+7} \right )\left (x+7\right )[/tex]
[tex]y+4=2\left ( x+7 \right )[/tex]
[tex]y+4=2x+14[/tex]
[tex]\boldsymbol{y=2x+10}[/tex]
So, option C) is correct.
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Final answer:
To find the equation of a line in slope-intercept form, we need to determine the slope and the y-intercept of the line. Using the formula for slope, we find that the slope is 2. Then, using one of the points and the slope, we find the y-intercept to be 10. Therefore, the equation of the line is y = 2x + 10.
Explanation:
To find the equation of a line in slope-intercept form, we need to determine the slope and the y-intercept of the line. The slope can be found using the formula:
slope = (y2 - y1) / (x2 - x1)
Given the points (-7, -4) and (-6, -2), the slope is:
slope = (-2 - (-4)) / (-6 - (-7))
slope = 2 / 1
slope = 2
Now that we have the slope, we can use one of the points and the slope to find the y-intercept. Let's use the point (-7, -4) and the slope of 2:
y = mx + b
-4 = 2(-7) + b
-4 = -14 + b
b = -4 + 14
b = 10
Therefore, the equation of the line in slope-intercept form is y = 2x + 10.
Trapezoid ABCD was dilated to create trapezoid A'B'C'D'. On a coordinate plane, 2 trapezoids are shown. Trapezoid A B C D has points (negative 4, 0), (negative 2, 4), (2, 4) and (4, 0). Trapezoid A prime B prime C prime D prime has points (negative 2, 0), (negative 1, 2), (1, 2), and (2, 0). Which statements are true about the trapezoids? Select three options. The length of side AD is 8 units. The length of side A'D' is 4 units. The image is larger than the pre-image. Sides CD and C'D' both have the same slope, 2. The scale factor is 1/2.
For trapezoids ABCD and A'B'C'D' on a coordinate plane, side AD's length is 8 units, A'D's length is 4 units and also the scale factor is 1/2.
The question asks for facts about the dilation of trapezoid ABCD to create trapezoid A'B'C'D' on a coordinate plane. First, we are to compare the length of side AD with side A'D'. The coordinates of AD are (-4, 0) and (4, 0), so the length is 4 - (-4) = 8 units. For A'D', using coordinates (-2, 0) and (2, 0), the length is 2 - (-2) = 4 units. This confirms that:
The length of side AD is 8 units.
The length of side A'D' is 4 units.
Next, to determine whether the image is larger than the pre-image, we examine the scale factor. As the original trapezoid has been halved in size, the scale factor is indeed 1/2. Therefore, the image is not larger; it is smaller. Hence, this option is not true.
Examining the slopes of sides CD and C'D', we can use the coordinates (2, 4) to (4, 0) and (1, 2) to (2, 0) respectively to calculate the slope. The slope of CD is (0-4)/(4-2) = -4/2 = -2, and for C'D' it is (0-2)/(2-1) = -2/1 = -2. Both slopes are indeed the same, and thus, we confirm:
Sides CD and C'D' both have the same slope, -2 not 2 as stated in the options.
The final option about the scale factor being 1/2 is true and confirms:
The scale factor is 1/2.
The true statements are:
- The length of side AD is 8 units.
- The length of side A'D' is 4 units.
- The scale factor is 1/2.
To determine which statements are true about the trapezoids, let's analyze the given information:
1. The length of side AD is 8 units.
- To find the length of side AD, we can use the distance formula between points A and D.
- Distance formula: [tex]\(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)[/tex]
- [tex]\(AD = \sqrt{(4 - (-4))^2 + (0 - 0)^2} = \sqrt{8^2} = 8\)[/tex]
- This statement is true.
2. The length of side A'D' is 4 units.
- To find the length of side A'D', we can use the distance formula between points A' and D'.
- Distance formula: [tex]\(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)[/tex]
-[tex]\(A'D' = \sqrt{(2 - (-2))^2 + (0 - 0)^2} = \sqrt{4^2} = 4\)[/tex]
- This statement is true.
3. The image is larger than the pre-image.
- We can compare the lengths of corresponding sides.
- The length of side AD is 8 units, while the length of side A'D' is 4 units.
- Since the lengths of corresponding sides are not proportional, the image is not larger than the pre-image.
- This statement is false.
4. Sides CD and C'D' both have the same slope, 2.
- The slopes of sides CD and C'D' can be calculated using the coordinates of the points.
- Slope formula:[tex]\(m = \frac{y_2 - y_1}{x_2 - x_1}\)[/tex]
- For side CD: [tex]\(m_{CD} = \frac{4 - 4}{2 - (-2)} = \frac{0}{4} = 0\)[/tex]
- For side C'D':[tex]\(m_{C'D'} = \frac{2 - 0}{1 - (-1)} = \frac{2}{2} = 1\)[/tex]
- Since the slopes are not the same, this statement is false.
5. The scale factor is 1/2.
- To find the scale factor, we can compare the corresponding side lengths of the pre-image and the image.
- The length of side AD is 8 units, and the length of side A'D' is 4 units.
- The scale factor is the ratio of corresponding side lengths: [tex]\(\frac{4}{8} = \frac{1}{2}\)[/tex]
- This statement is true.
Twenty-one crackers contain 147 Calories. Find the unit rate in Calories per cracker.
The unit rate in Calories per cracker is
Answer The unit rate in calories per cracker is 7.
(I'll add explanation if needed)
I hope this helped! :)
Please help I don’t understand
Answer:
i think its the first one
Step-by-step explanation:
How are integers and their opposites related
Answer: Whole numbers less than zero are called negative integers. The integer zero is neither positive nor negative, and has no sign. Two integers are opposites if they are each the same distance away from zero, but on opposite sides of the number line. Positive integers can be written with or without a sign.
Step-by-step explanation:
If AC = 18 and CD = 5, AD = [?]
8
Enter
The length of segment AD is found by subtracting the length of CD from that of AC, which gives AD = 18 - 5 = 13.
Explanation:In this problem, you are given the lengths of segments AC and CD. The question is asking you to find the length of segment AD. This looks like a problem of segment addition in geometry. Segment addition postulate states that if a point B lies on a line segment AC, then the whole length of the segment AC equals the addition of AB + BC. In this case, however, we are given that the whole length AC equals 18, and a part of it, CD equals 5. To find the length of the unknown segment AD, we now need to subtract CD from AC. Therefore, using the segment addition postulate, we can solve this problem as follows:
AD = AC - CD
AD = 18 - 5
AD = 13
So, the length of segment AD equals 13.
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The perimeter of an isosceles triangle less than 20 inches. If the base is 5 inches, what is the maximum length of each of the legs?
Answer:
7.5 inches
Step-by-step explanation:
take the 5 away from the 20, you have 15 inches left. Isosceles triangles have two equal sides; 15 divided into two equally is 7.5
Which of the following fractions is equivalent to 15/35
Answer:3/7 is the equivalent fraction of 15/35.
Step-by-step explanation:
Divide both by 5. Hope this helped you.
Answer:
Equivalent fraction to 15/35 is 3/7 .
since 5 has common factor of both numerator and denominator so divide both by 5. hence we get the values which is equivalent to 15/35.
Lani's mother gave her and her two sisters $21 to spend at the movies. If each girl gets the same amount, how much do they each have to spend?
each sister gets 21 dollars, so there are three sisters there fore 21*3 equals 63
Answer:
$7.
Step-by-step explanation:
We have been given that Lani's mother gave her and her two sisters $21 to spend at the movies.
We are asked to find the amount each girl have to spend.
To solve our given problem, we will divide $21 with 3 as Lani and her two sisters would be 3 persons.
[tex]\text{Amount that each girl have to spend}=\frac{\$21}{1+2}[/tex]
[tex]\text{Amount that each girl have to spend}=\frac{\$21}{3}[/tex]
[tex]\text{Amount that each girl have to spend}=\$7[/tex]
Therefore, each girl gets $7 to spend.
Answer quick
The diagram shows a quadrilateral ABCD.
AE is parallel to BC.
EF is the angle bisector of angle AED.
Answer:
y = 25
Step-by-step explanation:
Since AE and BC are parallel, then
∠AED = ∠BCE = 110° ( corresponding angles )
Since EF is the angle bisector of ∠AED, then
∠AEF = ∠FED = 55°
∠AFE and ∠DFE form a straight angle, thus
∠AFE = 180° - 80° = 100°
The sum of the angles in ΔAEF = 180°, thus
y = 180 - (55 + 100) = 180 - 155 = 25
the value of the angle EAF will be 15 degrees.
What are complementary angles?When the sum of two angles is equal to 90 degrees, they are called complementary angles. For example, 30 degrees and 60 degrees are complementary angles.
Given a figure:
The diagram shows a quadrilateral ABCD.
AE is parallel to BC.
EF is the angle bisector of angle AED
Since ∠AFE and ∠EFD are supplementary angles.
And ∠EFD = 80 degrees
Thus,
∠AFE +∠EFD = 180
∠AFE = 100
Since AE is parallel to BC.
∠BCE and ∠AED will be the same
Thus, ∠AED = 110°
Since EF is the angle bisector of angle AED.
∠AEF will be 55°
So in ΔAEF
∠AED = 110°
∠AEF = 55°
From the property of the triangle
The sum of All angles is 180°.
Thus
∠A + ∠E + F = 180°
y + 110 +55 = 180
y = 15
therefore, the value of ∠EAF will be 15 degrees.
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What is 47 rounded to he nearest 10
Answer:
EXAMPLE I Round 47 to the nearest ten. Here is a part of a number line; 47 is between 40 and 50. Since 47 is closer to 50, we round up to 50. 42 is between 40 and 50.;it5
Can you explain step by step for #15 and #16 I have a test on this tomorrow
Answer:
15.
[tex]\left\{\begin{array}{l}x+y=50\\0.2x+0.1y=6\end{array}\right.[/tex]
16. 10 ml of 20% saline and 40 ml of 10% saline
Step-by-step explanation:
A chemist takes x ml of 20% saline and y ml of 10% saline. In total, he takes
x + y ml that is 50 ml, so
[tex]x + y = 50.[/tex]
There are [tex]0.2x[/tex] ml of salt in x ml of 20% saline and [tex]0.1y[/tex] ml of salt in 10% saline. There are [tex]0.12\cdot 50=6[/tex] ml of salt in 50 ml of 12% saline. Thus,
[tex]0.2x+0.1y=6[/tex]
15. We get the system of two equations:
[tex]\left\{\begin{array}{l}x+y=50\\0.2x+0.1y=6\end{array}\right.[/tex]
16. Solve this system. From the first equation:
[tex]x=50-y[/tex]
Substitute it into the second equation:
[tex]0.2(50-y)+0.1y=6\\ \\10-0.2y+0.1y=6\\ \\-0.1y=6-10\\ \\-0.1y=-4\\ \\y=40\\ \\x=50-y=50-40=10[/tex]
Solve for f
2f = -12
f=?
Answer:
f = -6
Step-by-step explanation:
2 it's multiplying the f, so in order to get only f, you need to divide both sides by 2
2f / 2 = -12 / 2
f = -6