Let x be the amount of gallons of grape juice we are using to get the mixture we want. Let y be the amount of gallons of cranberry juice used to get the desired mixture.
Since we are told that we want a total of 200 gallons of the new mixture, this amount would be the sum of gallons of each liquid. So we have this equation
[tex]x+y=200[/tex]To find the values of x and y, we need another equation relating this variables. Note that since we have 200 gallons of the new mixture and the cost per gallon of the new mixture is 1.75, the total cost of the new mixture would be
[tex]1.75\cdot200=350[/tex]As with quantities, the total cost of the new mixture would be the cost of each liquid. In the case of the grape juice, since we have x gallons and a cost of 1.50 per gallon, the total cost of x gallons of grape juice is
[tex]1.50\cdot x[/tex]In the same manner, the total cost of the cranberry juice would be
[tex]2\cdot y[/tex]So, the sum of this two quantites should be the total cost of the new mixture. Then, we get the following equation
[tex]1.50x+2y=350[/tex]If we multiply this second equation by 2 on both sides, we get
[tex]3x+4y=700[/tex]Using the first equation, we get
[tex]x=200\text{ -y}[/tex]Replacing this value in the second equation, we get
[tex]3\cdot(200\text{ -y)+4y=700}[/tex]Distributing on the left side we get
[tex]600\text{ -3y+4y=700}[/tex]operating on the left side, we get
[tex]600+y=700[/tex]Subtracting 600 on both sides, we get
[tex]y=700\text{ -600=100}[/tex]Now, if we replace this value of y in the equation for x, we get
[tex]x=200\text{ -100=100}[/tex]Thus we need 100 gallons of each juice to produce the desired mixture.
Simplify the given expression into the form a+bi, where a and b are rational numbers?
Given:
2(-36- 3i )+ (5+2i)(12-2i)
Open the parenthesis
2(-36- 3i) + 5( 12 - 2i) + 2i ( 12 - 2i)
- 72 - 6i + 60 - 10i + 24i + 4 ( Note: i² = -1)
Re-arrange
-72+60 + 4 - 6i - 10i + 24i
= -8 + 8i
hello,Can you please help me with question # 25 in the picture?Thank you
To find the sum of an arithmetic sequence up to the nth term, we use the sum formula, which is
[tex]S_n=n(\frac{a_1+a_n}{2})[/tex]where a1 represents the first term, and an the nth term.
The general term of our sequence is
[tex]a_n=3n+2[/tex]We want to sum up to the 16th term. Evaluanting n = 16 and n = 1 on this expression, we get the terms to plug in our formula
[tex]\begin{gathered} a_1=3(1)+2=3+2=5 \\ a_{16}=3(16)+2=48+2=50 \end{gathered}[/tex]Then, the sum is equal to
[tex]\sum_{i\mathop{=}1}^{16}(3i+2)=16(\frac{50+5}{2})=8\cdot55=440[/tex]The result of this sum is 440.
Scientists are conducting an experiment with a gas in a sealed container. The mass of the gas is measured and the scientists realize that the gas is leaking over time in a linear way. Eight minutes since the experiment started the gas had a mass of 302.4 grams. Seventeen minutes since the experiment started the gas had a mass of 226.8 gramsLet x be the number of minutes that have passed since the experiment started and let y be the mass of the gas in grams at that moment. Use a linear equation to model the weight of the gas over time.a) This lines slope-intercept equation is [ ] b) 39 minutes after the experiment started, there would be [ ] grams of gas left. c) if a linear model continues to be accurate, [ ] minutes since the experiment started all gas in the container will be gone.
Here, we want to model an experiment linearlly
From the question, we have it that;
The coordinates are written as;
(number of minutes, mass of gas)
So, what we have to do know is to set up the two given points
These are the points;
(8,302.4) and (17,226.8)
Now, using these two points, we can model the equation
We start by getting the slope of the line that passes through these two points
To do this, we shall use the slope equation
We have this as;
[tex]\begin{gathered} \text{slope m = }\frac{y_2-y_1}{x_2-x_1} \\ \\ (x_1,y_1)\text{ = (8,302.4)} \\ (x_2,y_2)\text{ = (17,226.8)} \\ \text{substituting these values;} \\ m\text{ = }\frac{226.8-302.4}{17-8}\text{ = }\frac{-75.6}{9}\text{ = -8.4} \end{gathered}[/tex]The general equation representing a linear model is ;
[tex]\begin{gathered} y\text{ = mx + b} \\ m\text{ is slope} \\ b\text{ is y-intercept} \\ y\text{ = -8.4x + b} \end{gathered}[/tex]To get the y-intercept so as to write the complete equation, we use any of the two points and substitute its coordinates
Let us substitute the coordinates of the first point
[tex]\begin{gathered} 302.4\text{ = -8.4(8) + b} \\ 302.4\text{ = -67.2 + b} \\ b\text{ = 67.2 + 302.4} \\ b\text{ = 369.6 } \end{gathered}[/tex]a) Thus, we have the complete linear model as;
[tex]y\text{ = -8.4x + 369.6}[/tex]b) To get this, we simply substitute the value of x given into the linear model
[tex]\begin{gathered} y\text{ = -8.4(39) + 369.6} \\ y\text{ = -327.6 + 369.6} \\ y\text{ = 42} \end{gathered}[/tex]39 minutes after the experiment started, there would be 42 grams
c) If all the gas is gone, then the value of y will br zero at this point
To get the corresponding x-value which is the time, we have it that;
[tex]\begin{gathered} 0\text{ = -8.4x +369.6} \\ 8.4x=\text{ 369.6} \\ x\text{ = }\frac{369.6}{8.4} \\ x\text{ = 44} \end{gathered}[/tex]In 44 minutes, all the gas in the container will be gone
Find the exact values of the six trigonometric functions of the real number t
In a unit circle, given the (x,y) coordinate, x corresponds to cosine, and y corresponds to sine.
Then use the trigonometric identity to solve for tangent.
We therefore have the following ratios for sin, cos, and tan.
[tex]\begin{gathered} \sin t=\frac{15}{17} \\ \cos t=-\frac{8}{17} \\ \tan t=\frac{\sin t}{\cos t}=\frac{\frac{15}{17}}{-\frac{8}{17}}=-\frac{15}{8} \\ \\ \text{Therefore,} \\ \sin t=\frac{15}{17} \\ \cos t=-\frac{8}{17} \\ \tan t=-\frac{15}{8} \end{gathered}[/tex]Solving for the reciprocal of sin, cos, and tan we have
[tex]\begin{gathered} \csc t=\Big(\sin t\Big)^{-1}=\Big(\frac{15}{17}\Big)^{-1}=\frac{17}{15} \\ \sec t=\Big(\cos t\Big)^{-1}=\Big(-\frac{8}{17}\Big)^{-1}=-\frac{17}{8} \\ \cot t=\Big(\tan t\Big)^{-1}=\Big(-\frac{15}{8}\Big)^{-1}=-\frac{8}{15} \\ \\ \text{Therefore,} \\ \csc t=\frac{17}{15} \\ \sec t=-\frac{17}{8} \\ \cot t=-\frac{8}{15} \end{gathered}[/tex]Use the Pythagorean Theorem to find the missing side length. *A. 12B. 144C. 10D. 24
We use the Pythagorean theorem formula to find the missing side length.
[tex]\begin{gathered} a^2+b^2=c^2 \\ \text{ Where} \\ a\text{ and }b\text{ are the sides} \\ c\text{ is the hypotenuse} \end{gathered}[/tex]Then, we have:
[tex]\begin{gathered} a=x \\ b=16 \\ c=20 \end{gathered}[/tex][tex]\begin{gathered} a^{2}+b^{2}=c^{2} \\ x^2+16^2=20^2 \\ x^2+256=400 \\ \text{ Subtract 256 from both sides} \\ x^2+256-256=400-256 \\ x^2=144 \\ $$\text{ Apply square root to both sides of the equation}$$ \\ \sqrt{x^2}=\sqrt{144} \\ x=12 \end{gathered}[/tex]AnswerThe length of the missing side is 12.
Multiply the expressions.
-0.6y(4.5 - 2.8y) =
answer 1
-2.86
-2.7
1.68
3.9
--------- y² +
answer 2
-2.86
-2.7
1.68
3.9
Answer:
1.68y²+ 2.7y is the answer
hope it helps
Question 10 of 10
Question 10
▸
Find the Error One cleaning solution uses 1 part vinegar with 2 parts water. Another cleaning solution uses 2 parts vinegar with 3 parts water
A student says that these mixtures are equivalent because, in each solution, there is one more part of water than vinegar. Find the error and
correct it.
In the first cleaning solution, the ratio of vinegar to water is
however, has a ratio of
Need help with this question?
Check Answer
The ratios
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The second solution.
equivalent
Done and
The error is that there is no proportional relationship between the ratios which is corrected and can be described as a linear relationship with the help of the equation y = m + 1.
What is the proportional relationship?Relationships between two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportional relationship, one variable is consistently equal to the other's constant value. The "constant of proportionality" is the name of this constant.So, the ratios we have:
1:2 and 2:3.Then, performing:
1/2 = 0.52/3 = 0.67Hence, ratios of 1:2 and 2:3 are not equal.
Therefore, the error is that the relationship between the given ratios is not proportional.
As can be seen, each ratio has a difference of 1, that is:
2 - 1 = 13 - 2 = 1Therefore, when one variable changes by 1, the other variable only changes by a constant value (y = x = c).
It can therefore be described as a linear relationship, and the constant is 1.The equation has the following form:
y = x + 1Where y stands for the water solution and x for the vinegar component.
Therefore, the error is that there is no proportional relationship between the ratios which is corrected and can be described as a linear relationship with the help of the equation y = m + 1.
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Select your answer to the question below: * AABC is shown below. Suppose the triangle is translated 5 units to the right and 7 units down. What are the coordinates of the image of vertex B after this transformation? : Y 6 B'C 2 A C. 8 G 2 4 A (8-6) B (2-6) c (-3.-6) D (2.0)
From the given graph,
The coordinates of point B are (-3, 7)
The triangle ABC has translated 5 units to the right and 7 units down
That means the x coordinate of B must add by 5 and the y-coordinate must subtract by 7
The rule is (x + 5, y - 7)
The image of point B is B'
B' = (-3 + 5, 7 - 7)
B' = (2, 0)
The image of point B is (2, 0)
Given slope of m=2/3 and y-intercept b=1 graph the line
ok! to graph your first point, you know the y-intercept is 1, so your point is (0,1)
graph that
because we knkow the slope is 2/3 and it's y change/x change, move up 2 and left 3 for your next point, which is (2,4)
we can graph a third point for accuracy, and move up 2 and left 3 again to get (4,7)
create a line connecting all the points
f(x)=-17x+2 and g(x)=x^2+1 find f(-7) + g(-7)
Answer:
171
Explanation:
Given f(x) and g(x) defined below:
[tex]\begin{gathered} f\mleft(x\mright)=-17x+2 \\ g\mleft(x\mright)=x^2+1 \end{gathered}[/tex]To find the value of f(-7) + g(-7), substitute -7 for x in both functions:
[tex]\begin{gathered} f\mleft(-7\mright)=-17(-7)+2=121 \\ g\mleft(-7\mright)=(-7)^2+1=50 \\ \implies f\mleft(-7\mright)+g\mleft(-7\mright) \\ =121+50 \\ =171 \end{gathered}[/tex]a point is chosen at random in the large square. find the probability that the point is in the smaller shaded square. each side of the large square: 16 cmeach side of the shaded square: 6 cm*round to the nearest hundredth
The Probability of the point being in the smaller shaded square is 0.79.
What is meant by probability?Probability equals possibility. It is a branch of mathematics concerned with the occurrence of a random event. The value ranges from 0 to 1. Probability has been introduced in mathematics to predict how likely events are to occur.Probability = the number of possible outcomes. the total number of possible outcomes For example, the probability of flipping a coin and getting heads is 12, because there is only one way to get a head and the total number of possible outcomes is two (a head or tail).The probability is a measure of the likelihood of an event occurring. It assesses the event's likelihood. P(E) = Number of Favorable Outcomes/Number of Total Outcomes is the probability formula.Therefore,
|Ω| = 6² = 36
< br / > |A| = 3.14.3² = 278.26
Then we get,
< br / > P |A| = 28.26/36 ≈ 0.79
∴ the probability that the point is in the smaller shaded square is 0.79
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Please ANSWER this
The table shows the parts of gelatin and water used to make a dessert.
Boxes of Gelatin Powder (oz) Water (cups)
3 9 6
7
At this rate, how much gelatin and water will Jeff use to make 7 boxes?
Jeff will use 14 oz of powder and 21 cups of water to make 7 boxes of gelatin.
Jeff will use 13 oz of powder and10 cups of water to make 7 boxes of gelatin.
Jeff will use 27 oz of powder and 18 cups of water to make 7 boxes of gelatin.
Jeff will use 21 oz of powder and 14 cups of water to make 7 boxes of gelatin.
Jeff needs 21 oz of gelatin and 14 cups of water to make 7 boxes
How to determine the amount of gelatin and water needed to make 7 boxes?The table of values is given as
Boxes Gelatin Powder (oz) Water (cups)
3 9 6
From the above table, we can see that
Gelatin Powder = 3 * Boxes
Water = 2 * Boxes
When there are 7 boxes, the equations become
Gelatin Powder = 3 * 7
Water = 2 * 7
Evaluate the products in the above equation
So, we have
Gelatin Powder = 21
Water = 14
Hence, the amount of gelatin and water needed to make 7 boxes are 21 oz and 14 cups respectively
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Answer: D: jeff will use 21 oz of powder and 14 cups of water
Step-by-step explanation:
the chart says there are
3 boxes of gelatin ) 9 oz of powder ) 6 cups of water
that equals the same as
1 box of gelatin ) 3 oz of power ) 2 cups of water
so for every box of gelatin, there is 3oz of powder and 2 cups of water
if he wants to make 7 boxes.....
7x3oz=21 oz
7x2cups=14 cups
so the Answer is D
GEOMETRY Draw the next two figures in the pattern shown below. OOO
Given , the pattern
O , OO , .....
so, the first term is 1 circle
The second is 2 circles
So, the next two figures are:
OOO , OOOO
a triangle with an area of 8 in^2 is dilated by a factor of 3. the area of the dilated triangle is ___ in^2(no image included)
we have:
[tex]A=\frac{1}{2}(b\times3)(h\times3)=\frac{1}{2}(9bh)=\frac{9}{2}bh[/tex]therefore:
[tex]A=72[/tex]answer: 72 in^2
Hi, can you help me to solve this problem please!
We have the following function
[tex]f(x)=7+6x[/tex]Now, we must replace the variable x by the given value, that is,
[tex]f(10)=7+6(10)[/tex]which gives
[tex]\begin{gathered} f(10)=7+60 \\ f(10)=67 \end{gathered}[/tex]Therefore, the answer is f(10)=67
Geo help please The price of an item has been reduced by 5% the original price was $60 what is the price of the item now
To answer this question, we can proceed as follows:
1. The original price of the item was $60.
2. If the price of this item has been reduced by 5%, we need to find the 5% of the original price as follows:
[tex]5\%=\frac{5}{100}\Rightarrow5\%(\$60)\Rightarrow\frac{5}{100}\cdot\$60=\frac{\$300}{100}=\$3[/tex]3. Therefore, the price of the item now is:
[tex]P_{\text{item}}=\$60-\$3=\$57[/tex]In summary, the price of the item now is $57.
[From the question, we have that the words "reduced by" imply a subtraction.]
Need help with my math yall please??
The value of the expression after simplification is found as -3.
What is termed as simplification?Simplify simply way of making something easier to understand. Simply or simplification in mathematics refers to reducing an expression/fraction/problem to a simpler form. It simplifies the problem by calculating and solving it. We can —Simplify fractions by removing all common factors from the numerator and denominator as well as composing the fraction in its simplest form.By grouping as well as combining similar terms, you can simplify mathematical expressions. This helps make the expression simple to understand and solve.For the given expression;
5x + 8 = 2x - 1
Subtract 8 from both side.
5x + 8 - 8 = 2x - 1 - 8
Simplify
5x = 2x - 9
Subtract both side by 2x.
5x - 2x = 2x - 9 - 2x
3x = -9
Divide both side by 3.
3x/3 = -9/3
x = -3
Thus, the value of the expression is found as -3.
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The Leaning Tower of Pisa
was completed in 1372 and
makes an 86* angle with
the ground. The tower is
about 57 meters tall, measured
vertically from the ground
to its highest point. If you
were to climb to the top and
then accidently drop your
keys, where would you
start looking for them?
How far from the base of.
the tower would they land?
The distance where the keys would drop from the base is 3.5m
Calculation far from the base of tower?Height of the tower = 57m
Angle it makes to the ground = 86°
To solve this question, you have to understand that the tower isn't vertically upright and the height of the tower is different from the distance from the top of the tower to the ground.
The tower makes an angle 86° to the ground and that makes it not vertically straight because a vertically straight building is at 90° to the ground.
The distance from where the keys drop to the base of the tower can be calculated using
We have to use cosθ = adjacent / hypothenus
θ = 86°
Adjacent = ? = x
Hypothenus = 57m
Cos θ = x / hyp
Cos 86 = x / 57
X = 57 × cos 86
X = 57× 0.06976
X = 3.97 = 4m
The keys would fall from the tower's base at a distance of about 4 meters.
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[tex]5x + 17 = 82[/tex]simplify as much as possible
To answer this question, we can follow the next steps:
1. Subtract 17 to both sides of the equation (we apply here the subtraction property of equality):
[tex]5x+17-17=82-17\Rightarrow5x+0=65\Rightarrow5x=65[/tex]2. To isolate the variable, x, in the equation, we need to divide by 5 to both sides of the equation, as follows:
[tex]\frac{5x}{5}=\frac{65}{5}\Rightarrow\frac{5}{5}=1\Rightarrow x=\frac{65}{5}\Rightarrow x=13[/tex]We can check this result if we substitute this last value into the original equation:
[tex]5x+17=82\Rightarrow5(13)+17=82\Rightarrow65+17=82\Rightarrow82=82[/tex]The result is always TRUE.
Therefore, the value for the unknown value of x is x = 13.
A play court on the school playground is shaped like a square joined by a semicircle. The perimeteraround the entire play court is 182.8 ft., and 62.8 ft. of the total perimeter comes from the semicircle.aWhat is the radius of the semicircle? Use 3.14 for atb.The school wants to cover the play court with sports court flooring. Using 3.14 for, how manysquare feet of flooring does the school need to purchase to cover the play court?
The total perimeter of the court is 182.8 ft, of this, 62.8ft represents the perimeter of the semicircle.
a)
The perimeter of the semicircle is calculated as the circumference of half the circle:
[tex]P=r(\pi+2)[/tex]Now write it for r
[tex]\begin{gathered} \frac{P}{r}=\pi \\ r=\frac{P}{\pi} \end{gathered}[/tex]Knowing that P=62.8 and for pi we have to use 3.14
[tex]\begin{gathered} r=\frac{62.8}{3.14} \\ r=20ft \end{gathered}[/tex]The radius of the semicircle is r=20 ft
b.
To solve this exercise you have to calculate the area of the whole figure.
The figure can be decomposed in a rectangle and a semicircle, calculate the area of both figures and add them to have the total area of the ground.
Semicircle
The area of the semicircle (SC) can be calculated as
[tex]A_{SC}=\frac{\pi r^2}{2}[/tex]We already know that our semicircla has a radius of 10ft so its area is:
[tex]A_{SC}=\frac{3.14\cdot20^2}{2}=628ft^2[/tex]Rectangle
To calculate the area of the rectangle (R) you have to calculate its lenght first.
We know that the total perimeter of the court is 182.8ft, from this 62.8ft corresponds to the semicircle, and the rest corresponds to the rectangle, so that:
[tex]\begin{gathered} P_T=P_R+P_{SC} \\ P_R=P_T-P_{SC} \\ P_R=182.8-62.8=120ft \end{gathered}[/tex]The perimeter of the rectangle can be calculated as
[tex]P_R=2w+2l[/tex]The width of the rectangle has the same length as the diameter of the circle.
So it is
[tex]w=2r=2\cdot20=40ft[/tex]Now we can calculate the length of the rectangle
[tex]\begin{gathered} P_R=2w+2l \\ P_R-2w=2l \\ l=\frac{P_R-2w}{2} \end{gathered}[/tex]For P=120ft and w=40ft
[tex]\begin{gathered} l=\frac{120-2\cdot40}{2} \\ l=20ft \end{gathered}[/tex]Now calculate the area of the rectangle
[tex]\begin{gathered} A_R=w\cdot l \\ A_R=40\cdot20 \\ A_R=800ft^2 \end{gathered}[/tex]Finally add the areas to determine the total area of the court
[tex]\begin{gathered} A_T=A_{SC}+A_R=628ft^2+800ft^2 \\ A_T=1428ft^2 \end{gathered}[/tex]The Hughes family and the Gonzalez family each used their sprinklers last summer. The Hughes family's sprinkler was used for 15 hours. The Gonzalez family's sprinkler was used for 35 hours. There was a combined total output of 1475 L of water. What was the water output rate for each sprinkler if the sum of the two rates was 65 L per hour?
Answer:
Hughes Family: 40 L/ hour
Gonzalez family: 25L/hour
Step-by-step explanation:
Let us use the following variables to denote the output rates for each sprinkler.
Let H = water output rate for the Hughes family
Let G = water output rate for the Gonzalez family
(I am using H ang G rather than the traditionally used X and Y to easily identify which rate belongs to which family)
The general equation for the volume of water outputted, V, in time h hours at a rate of r per hour is
V = r x h
Given r
Using this fact
Water Output for Hughes family at rate H for 15 hours = 15H
Water Output for Gonzalez family at rate G for 35 hours = 35 G
The total of both outputs = 1475
That gives us one equation
15H + 35G = 1475 [1]
We are given the combined rate as 65 L per hour
Sum of the two rates = combined rate
H + G = 65 [2]
Let's write down these two equations and solve for H and GA $40,000 is placed in a scholarship fund that earns an annual interest rate of 4.25% compounded daily find the value in dollars of the account after 2 years assume years have 365 days round your answer to the nearest cent
SOLUTION
From the question, we want to find the value in dollars of the account after 2 years.
We will usethe formula
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ Where\text{ A = value of the account, amount in dollars = ?} \\ P=principal\text{ money invested = 40,000 dollars } \\ r=annual\text{ interest rate = 4.25\% = }\frac{4.25}{100}=0.0425 \\ n=number\text{ of times compounded = daily = 365} \\ t=time\text{ in years = 2 years } \end{gathered}[/tex]Applying this, we have
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ A=40,000(1+\frac{0.0425}{365})^{365\times2} \\ A=40,000(1.000116438)^{730} \\ A=40,000\times1.0887116 \\ A=43,548.467179 \\ A=43,548.47\text{ dollars } \end{gathered}[/tex]Hence the answer is 43,548.47 to the nearest cent
Classwork Area of Algebra Tiles 1 An If the side lengths of a tile can be measured exactly, then the area of the tile can be calculated by multiplying these two lengths together. The area is measured in square units. For example, the tile at right measures 1 unit by 5 units, so it has an area of 5 square units. 1 The next tile at right has one side length that is exactly one unit long. If the other side length cannot have a numerical value, what can it be called? ?
The other side of a tile can be called as width of hte tile
Simplify by writing the expression with positive exponents. Assume that all variables represent nonzero real numbers
Explanation
Let's remember some properties ofthe fractions ans exponents,
[tex]\begin{gathered} a^{-n}=\frac{1}{a^n} \\ (\frac{a}{b})^n=\frac{a^n}{b^n} \\ (ab)^n=a^nb^n \\ (a^n)^m=a^{m\cdot n} \end{gathered}[/tex]so
Step 1
[tex]\lbrack\frac{4p^{-2}q}{3^{-1}m^3}\rbrack^2[/tex]reduce by using the properties
[tex]\begin{gathered} \lbrack\frac{4p^{-2}q}{3^{-1}m^3}\rbrack^2 \\ \lbrack\frac{4q}{3^{-1}m^3p^2}\rbrack^2 \\ \lbrack\frac{3^1\cdot4q}{m^3p^2}\rbrack^2 \\ \lbrack\frac{12q}{m^3p^2}\rbrack^2 \\ \lbrack\frac{144q^2}{m^{3\cdot2}p^{2\cdot2}}\rbrack^{} \\ \lbrack\frac{144q^2}{m^6p^4}\rbrack^{} \end{gathered}[/tex]therefore, the answer is
[tex]\lbrack\frac{144q^2}{m^6p^4}\rbrack^{}[/tex]I hope this helps you
Drag and drop the correct value next to its equivalent expression number maybe use ones are not at all.
Solution:
Expression:
[tex]\begin{gathered} \frac{2}{3}\times42=2\times14 \\ \frac{2}{3}\times42=28 \end{gathered}[/tex]Expression:
[tex]\begin{gathered} \frac{5}{12}\times26=\frac{5}{6}\times13 \\ \\ \frac{5}{12}\times26=\frac{65}{6} \\ \\ \frac{5}{12}\times26=10\frac{5}{6} \end{gathered}[/tex]ANSWER:
[tex]\frac{5}{12}\times26=10\frac{5}{6}[/tex]Expression:
[tex]\begin{gathered} \frac{11}{15}\times20=\frac{11}{3}\times4 \\ \\ \frac{11}{15}\times20=\frac{44}{3} \\ \\ \frac{11}{15}\times20=14\frac{2}{3} \end{gathered}[/tex]ANSWER:
[tex]\frac{11}{15}\times20=14\frac{2}{3}[/tex]Expresion:
[tex]\begin{gathered} \frac{3}{8}\times54=\frac{3}{4}\times27 \\ \\ \frac{3}{8}\times54=\frac{81}{4} \\ \\ \frac{3}{8}\times54=20\frac{1}{4} \end{gathered}[/tex]ANSWER:
[tex]\frac{3}{8}\times54=20\frac{1}{4}[/tex]Geometric mean of36 and 21
The Geometric Mean is:
[tex]6\sqrt[]{21}[/tex]Explanation:Given 36 and 21, the Geometric Mean is given as:
[tex]\begin{gathered} m=\sqrt[]{36\times21} \\ =\sqrt[]{6^2\times21} \\ =6\sqrt[]{21} \end{gathered}[/tex]These figures are similar. Thearea of one is given. Find thearea of the other.area=32 in?9 in12 in[ ? Jina
To find the area of similar figures whe you know the area of one of the figures and the length of corresponding sides:
1. Find the scale factor: in this case as you have the area of the largest figure find the scale factor for a reduction:
[tex]SF=\frac{small}{\text{big}}=\frac{9}{12}=\frac{3}{4}[/tex]2. Find the missing area: the area in similar figures is equal to the scale factor squared multiplied by the given area.
[tex]\begin{gathered} A=(\frac{3}{4})^2\cdot32in^2 \\ \\ A=(\frac{9}{16})\cdot32in^2 \\ \\ A=\frac{288}{16}in^2 \\ \\ A=18in^2 \end{gathered}[/tex]Then, the missing area is 18 square inchesA media company wants to track the results of its new marketing plan, so the video production manager recorded the number of views for one of the company's online videos. The results of the first 5 weeks are shown in this table. Write an equation to model the relationship between the number of weeks, x, and the number of views, f(x). Enter the correct answer in the box by replacing the values of a and b.
ANSWER
[tex]f(x)=5120\cdot1.25^x[/tex]EXPLANATION
We want to write an equation that models the relationship between the number of weeks (x) and the number of views, f(x).
From the table, we see that the relationship of the two terms (number of views and number of weeks) is exponential.
The general form of an exponential function is given as:
[tex]f(x)=a\cdot b^x[/tex]where a = initial value
b = exponential factor
We have to find a and b.
We do this by replacing x and f(x) in the function with values from the table.
Let us use the first set of values:
[tex]\begin{gathered} 5120=a\cdot b^0 \\ \Rightarrow5120=a\cdot1 \\ \Rightarrow a=5120 \end{gathered}[/tex]We have found the value of a, now we can find the value of b by using another set of values from the table.
That is:
[tex]\begin{gathered} 6400=5120\cdot b^1 \\ 6400=5120\cdot b \\ \text{Divide both sides by 5120:} \\ b=\frac{6400}{5120} \\ b=1.25 \end{gathered}[/tex]Now, we have found a and b.
Therefore, the equation that models the relationship between number of views and number of weeks is:
[tex]f(x)=5120\cdot1.25^x[/tex]The circumference of a circle is 18pi meters. What is the radius?Give the exact answer in simplest form. ____ meters. (pi, fraction)
Given:
The circumference of a circle, C=18π m.
The expression for the circumference of a circle is given by,
[tex]C=2\pi r[/tex]Put the value of C in the above equation to find the radius.
[tex]\begin{gathered} 18\pi=2\pi r \\ r=\frac{18\pi}{2\pi} \\ r=9\text{ m} \end{gathered}[/tex]Therefore, the radius of the circle is 9 m.
If triangle JKL = triangle TUV , which of the following can you NOT conclude as being true? __ ___JK = TU
If two triangles are said to be congruent, then they must have equal side lengths and equal angle measures.
See a sketch of triangles JKL and TUV below:
As shown in the sketch above:
- The side JK is equal in length as with the side TU
- The angle L is equal in measure as with the angle V
- The side LJ is equal in length as with the side VT
- The angle K is equal in measure as with the angle U
Therefore, we can NOT conclude that the angle J is equal in measure as with the angle V: Option B
