First solution
[tex]\begin{gathered} \text{The first equation in the second system (Equation 2.1),} \\ \text{was formed by multiplying (Equation 1.1) by -3} \end{gathered}[/tex][tex]\begin{gathered} \text{proof:} \\ -3\text{ (3x - 4y= 10) = -9x + 12y = -30} \end{gathered}[/tex]Second solution
The second equation in the second system (Equation 2.2) was formed by adding both equations in the first system.
That is;
(Equation 2.2) = (Equation 1.1) + (Equation 1.2)
[tex]\begin{gathered} \text{proof:} \\ 3x\text{ -4y = 10 } \\ +\text{ 6x + y = 38} \\ (3x+6x)\text{ + (-4y+y) = 10+38} \\ 9x\text{ -3y = 48} \end{gathered}[/tex]The field inside a running track is made up of a rectangle that is 84.39 m long and 73 m wide, together with a half-circle at each end.
Answer:
Step-by-step explanation:
Find out the area of the running track that goes around the field .
To proof
Formula
Area of rectangle = length× breadth
area of running track = outside area - inside area
First case ( outside )
length = 73 + 2 × 9.76
= 92.52m
Breadth = 84.39 m
radius of outside semi circle
=46.26m
outside area = area of rectangle + 2× area of the semi- circle
= 92.52× 84.39 + 3.14× 46.26 ×46.26
= 7807.76+ 6719.56
= 14527.32 m² ( approx)
Second case
radius of the semi- circle
=36.5m
inside area = area of rectangle + 2× area of the semi- circle
= 73× 84.39 + 3.14× 36.5 ×36.5
= 6160.47 + 4183.27
= 10343.74m²
area of running track= 14527.32 m² - 10343.74m²
= 4183.58m²
Hence proved
Answer:
Find out the area of the running track that goes around the field .
Step-by-step explanation:
Suppose that among the 5000 students at a high school, 1200 are taking an online class and1700 prefer watching basketball to watching football. Taking an online class and preferringbasketball are independent. How many students are taking an online course and preferbasketball to football?
Solution:
Given:
[tex]\begin{gathered} total=5000 \\ n_{online\text{ class}}=1200 \\ n_{basketball}=1700 \end{gathered}[/tex]Since both events are independent, then;
[tex]P(A\cap B)=P(A)\times P(B)[/tex]Hence,
[tex]\begin{gathered} P(online)=\frac{1200}{5000} \\ P(basketball)=\frac{1700}{5000} \\ Hence,\text{ } \\ P(online\cap basketball)=\frac{1200}{5000}\times\frac{1700}{5000} \\ P(online\cap basketball)=\frac{51}{625} \\ P(online\cap basketball)=0.0816 \end{gathered}[/tex]The number of students taking an online course and prefer basketball to football is;
[tex]\begin{gathered} n(online\cap basketball)=0.0816\times5000 \\ n(online\cap basketball)=408 \end{gathered}[/tex]Therefore, the number of students taking an online course and prefer basketball to football is 408
In the diagram, transversal t cuts parallel lines a and b. Which equation is necessarily true?
Option-D is correct, m∠3 + m∠5 = 180°. This is accurate because according to the transversal theorem, the angles from the same side must sum up to 180°.
Given that,
This is about angle theorems.
Option A: m∠1 = m∠2. This is untrue since the sum of all angles on a straight line is 180° and the line that separates these two angles is not parallel to the horizontal straight line to evenly divide it.
Option B: m∠4 = m∠6; This statement is not true because though their sum is 180° but again they are transverse angles which are not equal from the line that forms them.
Option C: m∠1 + m∠5 = 90°; This is incorrect since the line that forms each of them is not at a 45° angle and m∠1 = m∠5
Option D; m∠3 + m∠5 = 180°. This is accurate because according to the transversal theorem, the angles from the same side must sum up to 180°.
Option E; m∠7 = m∠8. The assertion is false for the same reason as in option A.
That means only option D is true.
Therefore, Option-D is correct, m∠3 + m∠5 = 180°. This is accurate because according to the transversal theorem, the angles from the same side must sum up to 180°.
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i dont know how to answer part b, but you need part a to answer it so that's at the top
GIVEN:
We are told that the original price of a sofa is $500 and rthen it has been reduced by 20%, leaving the new price at $400.
The company cant sell the sofa after 3 weeks so they reduce the price to $320.
Required;
To find the percentage decrease.
Step-by-step solution;
At the point of reducing the price further, the original price has now been put at $400 and the new price has been set at $320. We take note that in terms of percentage, the original price is 100% while the new price will be represented by x (that is, yet unknown).
With this information we can set up an equation based on the ratio of the two prices as compared to the two percentages.
This means;
[tex]\begin{gathered} Original\text{ }price=400(100\%) \\ \\ New\text{ }price=320(x\%) \end{gathered}[/tex]Therefore;
[tex]\frac{400}{320}=\frac{100}{x}[/tex]Now we cross multiply;
[tex]\begin{gathered} x=\frac{100\times320}{400} \\ \\ x=\frac{320}{4} \\ \\ x=80 \end{gathered}[/tex]The new price is now given as 80% which simply means 20% was deducted from the original price. In other words, there was a 20% price reduction.
ANSWER:
There was a 20% decrease.
What’s does “solve for x in terms of y” mean?
When you have a function written in explicit form with two variables(let's call them 'x' and 'y'), it is written as a combination of 'x' and 'y' equal to some constant.
[tex]\begin{gathered} F(x,y)=k \\ k\in\mathfrak{\Re } \end{gathered}[/tex]To "solve for x in terms of y", is the same as rewritting this function as an equality in the following form:
[tex]x=f(y)[/tex]Let's try an example to show how this works.
Given the following function:
[tex]y^2+x^{}=2[/tex]Now, solving for x in terms of y, is the same as rewriting x as a function of y.
[tex]x=2-y^2[/tex]The student Fun Club plans to go to the movies. At the matinee, tickets cost $6 and popcorn is $3. At evening shows, tickets cost $9 and popcorn is $4. The Fun Club attends a matinee and spends less than $60, and then attends an evening show and spends more than $36. If they purchased the same number of tickets and popcorns at each show, which of the following is a possible solution for the number of tickets and popcorns purchased?3 tickets and 2 popcorns7 tickets and 5 popcorns9 tickets and 3 popcorns8 tickets and 6 popcorns
MAtine:
each ticket = $6
Each popcorn = $3
Evening:
Each ticket = $9
Each popcorn = $4
Number of tickets = t
Number of popcorns = p
Fun club attends at matinee, spends less than $60
6t + 3p < 60
Then attends an evening show and spends more than $36
9t + 4p > 36
The system of inequations:
6t + 3p < 60
9t + 4p > 36
Graph each and find the solution
6x + 3y < 60
9x + 4y > 36
Where both areas overlap is the solution:
Answer: 7 tickets and 5 popcorns
An ice company charged $8.16 for 6 bags of ice. If a convenience store bought 7 bags ofice, how much would it have cost them?
In order to solve this problem, we need to use proportions.
We have:
cost in dollars number of bags of ice
8.16 6
x 7
We are assuming that the cost is proportional to the number of bags of ice. So, to find the value x that represents the cost for 7 bags of ice, we can cross multiply the proportions above:
x * 6 = 8.16 * 7
Now if we divide both sides by 6, we isolate the variable x on the left side of the equation, and find its value:
x * 6 = 8.16 * 7
x * 6/6 = 8.16 * 7/6
x = (8.16/6) * 7
x = 1.36 * 7
x = 9.52
Therefore, it would have cost them $9.52.
Use the distributive property to multiply (2w+ 7)(2w-7).
Here are the steps in multiplying binomials using the distributive property:
1. Multiply the first 2w and first 7 by the terms inside the second parenthesis/binomial. Add the products.
[tex](2w)(2w)+(2w)(-7)+(7)(2w)+(7)(-7)[/tex]2. Simplify.
[tex]4w^2-14w+14w-49[/tex]3. Combine similar terms like -14w and 14w and the result is 0.
[tex]4w^2+0-49[/tex][tex]4w^2-49[/tex]Hence, the product of the two binomials is 4w² - 49.
John needs to wrap the edge of his rectangular desk with duct tape He knows the width is 10/8 of a meter and the length of a meter How much duct tape does he need to wrap the desks perimeter
13/4 m or 3.25 meters
1) Given the width is 10/8 meter
The length is 3/8 meter
2) To wrap the rectangular desk let's use this formula, for the Perimeter (2p):
2p= 2(w+l) Plug into w and l the measures
2p = 2(3/8 +10/8) Proceed with the sum within the parentheses
2p = 2(13/8) Distribute the factor
2p =13/4
3) Hence, the perimeter is 13/4 or 3.25 meters
1. What value of x=? makes therelation not a function?2 12HRUL00-A) -5B) 0C) 4D) 6(MGSE9-12.F.IF.1) Understand Functions
In functions, for any value of x, there's a unique value for y.
On the table, in the x column, having 6 yielding two different values of y in rows 2 and 3 will mean that it's not a function because the y values must be unique.
Therefore, the answer is 6
the product in simplest form.
5/6 2/5
Answer:
1/3
Step-by-step explanation:
[tex]\frac{5}{6}*\frac{2}{5} = \frac{5*2}{6*5} =\frac{10}{30} = \frac{1}{3}[/tex]
5 and 5 cancel out, 2 becomes 1, and 6 simplifies to 3.
A value and a sequence is times the previous value like this 8 16 32 64. How would the sequence be represented as a recursive equation?
Given:
The sequence is 8, 16, 32, 64.
The first term is 8.
[tex]undefined[/tex]A new video game has been released. The table shows the proportional relationship between the number of levels completed and the time it should take to complete them. Number of Levels 4 5 Time (hours) ? 2.5 How many minutes should it take to complete 4 levels? 180 minutes 120 minutes 60 minutes 50 minutes
Proportionately, the number of minutes it should take to complete 4 levels is B. 120 minutes.
What is the proportion?Proportion is the ratio between one value and another.
Proportions show the relative amount of a variable or value contained in the whole or another variable.
Proportions as fractional values are depicted using fractions, decimals, or percentages.
Number Time
of Levels (hours)
4 ?
5 2.5
The proportion of hours for level 5 = 0.5 (2.5/5) for each level.
If every level takes 0.5 hours or 30 minutes, level 4 will take 2 hours (0.5 x 4).
Or:
If level 5 takes 2.5 hours, level 4 will take 2 hours (2.5/5 x 4).
Thus, proportionately, to complete level 4 will take Option B.
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Convert to find the equivalent rate. 300 fluid ounces minute fluid ounces second
Answer
Explanation
We want to convert 300 fluid ounces per minute into fluid ounces per second.
Note that
1 minute = 60 seconds
We then do the conversion thus
[tex]undefined[/tex]10. Sarah wants to buy a blouse that costs $28. Her mom said she can buy this when it goes on sale for of the original price. What will the sale price be? 18 11. A class has eighteen students. The teacher asks how many students in the class have pets and finds of 18 the students have pets. How many students do not have pets? 12. Mrs. Bennett asked each of her 30 math students to select their favorite type of pizza. 30 of the students chose cheese pizza of the students chose pepperoni pizza 3 The remaining chose sausage pizza, How many students chose sausage pizza?
Sarah wants to buy a blouse that costs $28. Her mom said she can buy this when it goes on sale for 2/7 of the original price.
2/7 part of 28 is
[tex]28\times\frac{2}{7}=8[/tex]So, the selling price will be $8.
Please do it in such a way where you draw a line from A to C to use in your explanation. Also please draw the diagram so I can visualize.
We have to prove that triangles ABC and ADC are congruents.
We can draw a driagram of the triangles as:
As AB and AD are radius of the same circle, we have:
[tex]AB\cong AD[/tex]The same can be said for CB and CD, so:
[tex]CD\cong CD[/tex]Then, we have a shared side between the two triangle. Then, given the reflexive property we have:
[tex]AC\cong AC[/tex]Then, as we have 3 pair of congruent sides, by the SSS postulate, we can conclude that the triangles ABC and ADC are congruent. Then, all three pair of angles are also congruent.
NOTE:
If we just want to prove that the angles Then, we four right triangles (or a rhombus). Then, each angle of the erhombus is bisected.
The left angle at vertex D is complementary to the lower angle at A. The left angle at vertex B is complementary to the upper angle at A. As both angles at A are equal, The left angle at D and the left angle at B are complementary to the same angle.
Then, they have the same measure.
The same analysis can be done for the right angles.
Then, as both halves of the angles are equal, then the total angle
Find the opposite of the given number 18/19
The opposite of a number is the same distance from 0 on a number line as the original number, but on the other side of 0, then we have to invert the sign of the original number, if we have a positive one and we are told to find its opposite we just put it a negative sign, if the original number is negative then we rewrite it as a positive number.
In this case, we have 18/19, then the opposite number of it is -18/19
which of the following is not a way to represent the solution of the inequality 2(x+1) >or equal to 20?
The only incorrect choice in the options is B.
A number line with a closed circle on 9 and shading to the left
Explanations:The given inequality is expressed as:
[tex]2\text{ (x + 1) }\ge\text{ 20}[/tex]Step 1: Open up the brackets[tex]2x\text{ + 2 }\ge\text{ 20}[/tex]Step 2: Collect like terms[tex]\begin{gathered} 2x\text{ }\ge\text{ 20 - 2} \\ 2x\text{ }\ge\text{ 18} \end{gathered}[/tex]Step 3: Divide both sides by 2[tex]\begin{gathered} \frac{2x}{2}\ge\frac{18}{2} \\ x\text{ }\ge\text{ 9} \end{gathered}[/tex]This can also be written as:[tex]9\text{ }\leq\text{ x}[/tex]Drawing this on a number line:This means that x is includes 9 and all the numbers above 9.
From the number line drawn above. A number line with a close circle on 9 and shading to the right is drawn.
Which graph correctly shows the solution to the inequality
explain your reasoning.
The solution for the given inequality is x≥3. Therefore, option C is the correct answer.
The given inequality is (7x-3)/9 ≥ 8-2x.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
Inequality can be solved as follows:
(7x-3)/9 ≥ 8-2x
Multiply 9 on both the sides of an inequality, we get
7x-3 ≥ 9(8-2x)
⇒ 7x-3≥72-18x
Add 3 on both the sides of an inequality, we get
7x≥75-18x
Add 18x on both the sides of an inequality, we get
25x≥75
⇒ x≥3
The solution for the given inequality is x≥3. Therefore, option C is the correct answer.
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7) The diameter on a scale drawing of a circular clock is 11 inches. Find the area, in square inches, of theactual clock if the scale on the drawing is -inches represents inches of the actual clock. Round to thenearest tenth.1lin
we know that
3/4 inches represents 3 inches of actual clock ----> given
so
Applying proportion
Find out how much represents 11 inches in the actual
3/0.75=x/11
solve for x
x=(3/0.75)*11
x=44 in
that means
The diameter of the actual clock is 44 inches
so
the radius of the actual clock is
r=44/2=22 in
Find out the area
[tex]\begin{gathered} A=pi*r^2 \\ A=pi*22^2 \\ A=1,520.5\text{ in}^2 \end{gathered}[/tex]The area is 1,520.5 square inchesSelect the correct answer from each drop-down menu.Veronica wants to cut a sheet of paper into squares with an area of 12 square inches. For the best approximation, the length of each sideof the square pleces of paper must be approximately equal to 3.46 v Inches. If each side were exactly this length, the area of eachsquare would bev square Inches.1. 11.97162. 12.04093. 16
Note that the area of a square is the square of its side.
[tex]A=s^2[/tex]If the area is 12 square inches, the side is approximately :
[tex]\begin{gathered} 12=s^2 \\ s=\sqrt[]{12} \\ s=3.46 \end{gathered}[/tex]And the area will be :
[tex]\begin{gathered} A=3.46^2 \\ A=11.9716 \end{gathered}[/tex]The answers are :
3.46 inches
and
11.9716 square inches
Rhombus STAR has vertices S(-1,2), T(2,3), A(3,0), and R(0,-1).What is the perimeter of rhombus STAR?ABCD√344√34√104√10
INFORMATION:
We know that:
- Rhombus STAR has vertices S(-1,2), T(2,3), A(3,0), and R(0,-1)
And we must calculate the perimeter of the rhombus
STEP BY STEP EXPLANATION:
To calculate it, we must find first the measure of one of the sides.
We can find one of the sides calculating the distance between two consecutive vertices.
So, calculating the distance between vertices S and T
[tex]\begin{gathered} d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ d=\sqrt{(2-(-1))^2+(3-2)^2} \\ d=\sqrt{3^2+1^2} \\ d=\sqrt{10} \end{gathered}[/tex]Finally, to find the perimeter, we need to use that the rhombus has 4 equal sides. So, we the perimeter would be
[tex]\begin{gathered} perimeter=4\times\sqrt{10} \\ perimeter=4\sqrt{10} \end{gathered}[/tex]ANSWER:
D. 4√10
I need help. I have no idea on this question
ANSWER:
The total surface area is 450 mm^2
STEP-BY-STEP EXPLANATION:
We have a pyramid with a triangular base, which the formula to calculate the total surface area is the following
[tex]\begin{gathered} A_T=A_B+A_L \\ A_B=\frac{b\cdot h}{2} \\ A_L=3\cdot\frac{b\cdot l}{2} \end{gathered}[/tex]Replacing:
[tex]\begin{gathered} A_T=\frac{20\cdot15}{2}+3\cdot\frac{20\cdot10}{2} \\ A_T=150+300 \\ A_T=450 \end{gathered}[/tex]Hello could you please help me with this problem. Write and equation in standard form of the line that passes through (2,-3) and (-3,7).
Given:
point (2,-3) and (-3,7)
First, solve for the slope of the line
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \text{substitute} \\ (x_1,y_1)=(2,-3) \\ (x_2,y_2)=(-3,7) \\ \\ m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{7-(-3)}{-3-2} \\ m=\frac{7+3}{-5} \\ m=\frac{10}{-5} \\ m=-2 \end{gathered}[/tex]Now that we have solved for the slope, substitute it to the slope-intercept form y = mx + b to find the y-intercept. Use the point (2,-3) but using (-3,7) works just as well.
[tex]\begin{gathered} y=mx+b \\ -3=(-2)(2)+b \\ -3=-4+b \\ -3+4=b \\ b=1 \end{gathered}[/tex]The slope intercept form of the line is
[tex]y=-2x+1[/tex]Rearrange it to follow the standard form Ax + By = C, and we have
[tex]\begin{gathered} y=-2x+1 \\ y+2x=-2x+2x+1 \\ 2x+y=\cancel{-2x+2x}+1 \\ \\ \text{The equation of the line that passes through (2,-3) and (-3,7) in standard form is} \\ 2x+y=1 \end{gathered}[/tex]Nigel and Phyllis train for a marathon. The equation y = 1.25z + 4 represents that Nigel currently runs 4 miles per week and increases his total miles per week, y, by 1.25 for a numberof weeks. The graph represents Phyllis's running mileage.
From Phyllis's graph:
[tex]\begin{gathered} (x1,y1)=(0,6) \\ (x2,y2)=(4,9) \\ m=\frac{y2-y1}{x2-x1}=\frac{9-6}{4-0}=\frac{3}{4} \\ \text{ Using the point slope equation:} \\ y-y1=m(x-x1) \\ y-6=\frac{3}{4}(x-0) \\ y=\frac{3}{4}x+6 \\ y=0.75x+6 \end{gathered}[/tex]At the start of training, Phyllis runs more miles per week than Nigel because Phyllis runs 6 miles per week, while Nigel runs 4 miles per week
Juan made a scale drawing of his garden below. The scale of his drawing is 1 cm = 5 ft. What is the perimeter of his garden in feet
First let's find the perimeter of the scale drawing. The perimeter is the sum of all sides of the figure.
Looking at the figure, there are two sides without the length. The length of the vertical missing side can be calculated as 8 - 2 = 6 cm, and the length of the horizontal missing side can be calculated as 20 - 9 = 11 cm.
So the perimeter of the scale drawing is:
[tex]20+8+9+2+11+6=56[/tex]Now, to find the perimeter of the garden, we can use a rule of three:
[tex]\begin{gathered} 1\text{ cm}\to5\text{ ft} \\ 56\text{ cm}\to x\text{ ft} \\ \\ \frac{1}{56}=\frac{5}{x} \\ x=56\cdot5 \\ x=280 \end{gathered}[/tex]So the perimeter of the garden is 280 ft.
Find the area of the shape shown below. 7TH As 6 Asy TATUS 2 Col units? Stuck? Watch a video or use a hint. Pro Raport a problem
Answer:
Step-by-step explanation:
The equation 4.05p + 14.40 = 4.50(p +3) represents the number p of pounds of peanuts you need to make trail mix. How many pounds of peanuts do you need for the trail mix?
The equation given is a one variable equation, "p".
The question asks to find the value of "p", which is the pounds of peanuts.
So, we need to solve the euqation for "p".
[tex]4.05p+14.40=4.50(p+3)[/tex]First, we need to put all the terms that have "p" in one side. For this, we will have to use the distributive property in the parenthesys first:
[tex]\begin{gathered} 4.05p+14.40=4.50p+4.50\cdot3 \\ 4.05p+14.40=4.50p+13.50 \end{gathered}[/tex]Now, we can substract 4.05p in both sides to get the "p" term of the left to the right:
[tex]\begin{gathered} -4.05p+4.05p+14.40=-4.05p+4.50p+13.50 \\ 14.40=(4.50-4.05)p+13.50 \\ 14.40=0.45p+13.50 \end{gathered}[/tex]Now, we do the same for the 13.50, substract it in both sides:
[tex]\begin{gathered} 14.40-13.50=0.45p+13.50-13.50 \\ 0.9=0.45p \\ 0.45p=0.9 \end{gathered}[/tex]Now, we can divide both sides by 0.45:
[tex]\begin{gathered} \frac{0.45p}{0.45}=\frac{0.9}{0.45} \\ p=2 \end{gathered}[/tex]So, the answer is p = 2, thus, you need 2 pounds of peanuts for the trail mix.
f(x) = x + 6f(x) = x - 6What’s the answers
Question:
Solution:
Consider the following function:
[tex]f(x)\text{ = x+6}[/tex]this is equivalent to:
[tex]y\text{ = x+6}[/tex]solving for x, we get:
[tex]x\text{ = y - 6}[/tex]exchanging the notation we get:
[tex]f(x)\text{ = x- 6}[/tex]The same procedure is applied analogously for the function f(x) = x-6.
We can conclude that the correct answer is:
YES
You have a bank account in which your balance increases annually at a rate of 4%. If your initial investment was $100. Write an equation that represents your balance.
Initial investment = $100
The balance increases annually at a rate = 4%
The increased amount = 4% of $100
This gives
[tex]\frac{4}{100}\times\text{\$}100=\text{\$}4[/tex]Hence the investment increase annually by $4 yearly
In the second year the investment will increase by 2 x $4 = $8
In the third year the investment will increase by 3 x $4 = $$12
This implies that
In n years
The investment will increase by n × $4 = $4n
The balance at n years is given as
Balance = Investment + year increment
This is as shown below
[tex]\text{Balnace }=\text{ \$100 }+\text{ \$4n}[/tex]