∠2 and ∠3 form a linear pair. ∠3 and ∠1 are vertical angles. m∠1= 62 ∘ . What is m∠3?
In the sophomore class at Dixon high school the number of students taking French is 2/3 of the number taking Spanish. How many students are studying each language if the total number of students in French and Spanish is 310?
To find the number of students studying each language, assign variables, write equations based on the given information, and solve the system of equations.
Explanation:To solve this problem, let's assign variables. Let x represent the number of students taking Spanish, and y represent the number of students taking French.
According to the given information, the number of students taking French is 2/3 of the number taking Spanish. So, we can write this as an equation:
y = (2/3)x
The total number of students taking French and Spanish is 310. So, we can write another equation:
x + y = 310
Now, we can solve these two equations to find the values of x and y. Substituting the value of y from the first equation into the second equation, we get:
x + (2/3)x = 310
(5/3)x = 310
x = (3/5) * 310
x = 186
Substituting x = 186 back into the first equation, we find:
y = (2/3) * 186
y = 124
Therefore, there are 186 students taking Spanish and 124 students taking French.
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Find the unit rate. 6 2/5 revolutions in 2 2/3 seconds
Choose the fraction that goes in the blank 1/2< <4/5
Solve the systems of equations:
5x−2y−4=0
3x+16y−54=0
What is x?
What is y?
A nickel and a dime are flipped. What is the probability both coins will land tails up
What is the approximate circumference of a circle that has a diameter of 20 Centimeters
Find f(-5) if f(n) = n3 + 3n2
A) -50
B) -7
C) 0
D) 22
William saw painting in a museum, and later found a picture of the same painting in a book. The actual painting measures 36“ x 54“. The picture of the paining measured 4“ x 6“. What is the scale factor for the dilation?
The net of a square pyramid is shown below:
What is the surface area of the solid?
10 square inches
16 square inches
24 square inches
28 square inches
Answer: 28 square inches
Step-by-step explanation:
We know that the area of a triangle is given by :-
[tex]\text{A}=\dfrac{1}{2}*b*h[/tex], where b is base and h is the height of the triangle.
From the given picture, it cam be seen that alll the traingles area of same measure, the base of the triangle = 2 inches
The height of the triangle = 6 inches
Now, the area of a triangle is given by :-
[tex]\text{A}_1=\dfrac{1}{2}*6*2=6\ in^2[/tex]
Area of the square in the center =[tex](side)^2=(2)^2=4\ in^2[/tex]
Now, the total surface area of the pyramid is given by :-
[tex]\text{S.A.}=4+4(6)=28\ in^2[/tex]
what is the area in square centimeters of the trapezoid below the height is 6.4 and the base is 12.9 and 8.6
Answer:
The area of given trapezoid is 68.8 cm²
Step-by-step explanation:
Given: A trapezoid with height 6.4 cm and parallel base is 12.9 cm and 8.6 cm.
We have to find the area of area of this trapezoid.
Area of trapezoid = [tex]\frac{1}{2}\times \text{sum of parallel sides}\times height[/tex]
Given : Height = 6.4 cm
and parallel base is 12.9 cm and 8.6 cm.
Substitute, we have,
Area of trapezoid = [tex]\frac{1}{2}\times (12.9+8.6)\times 6.4[/tex]
Simplify, we have,
Area of trapezoid = [tex]\frac{1}{2}\times 21.5\times 6.4[/tex]
Area of trapezoid = 68.8 cm²
Thus, The area of given trapezoid is 68.8 cm²
At the school carnival, the sixth graders are making directional arrows, as shown below.
Each arrow is to be painted red. How much area needs to be painted for 1 arrow?
26 square inches
29 square inches
32 square inches
44 square inches
-3x+2(4x-8)-16
Help me solve this
Fair Race UNIT NAME: FUNCTIONS
Directions: Follow the instructions below to design a fair race for the new video game Animal Tracks. 1. Choose two animals with different speeds. You can choose from the chart that starts at the bottom of this page or do research to choose your own. 2. Design a fair race in which the two animals have an equal chance of winning if they race at their top speed. Here are a few tips for your design: a. The race is fair if the two animals could finish the race in the same amount of time. b. You can give the slower animal a shorter distance to race. c. Since this is a video game, the race does not need to be realistic—it can be any length, and the animals can run at a constant speed. 3. Write a system of two linear equations showing the distance each animal can travel to model the fair race. Be sure to define all variables. 4. Graph the system to prove that the two animals have an equal chance of winning the race. Explain how the graph proves the race is fair. Your equations, graph, and explanation for your race design will be submitted as your portfolio assessment.
Animal Speed (mph) cheetah 70 lion 50 coyote 43 rabbit 35 kangaroo 30 squirrel 12 chicken 9 antelope 61 elk 45 ostrich 40 giraffe 32
Animal Speed (mph) elephant 25 pig 11 mouse 8
I need help wiith 3. Write a system of two linear equations showing the distance each animal can travel to model the fair race. Be sure to define all variables. I choose The mouse and squirrel ....can i get help on the equuations? Can someone explain it to me?
The linear equation for squirrel y = 12x.
The linear equation for mouse y = 8x
The distance covered by the squirrel is 36km at time 3hours.
The distance covered by the squirrel is 24km at time 3hours.
What is linear equation?A linear equation is an "algebraic equation is of the form y=mx + b where 'm' is the slope of the line and 'b' is the y - intercept".
According to the question,
Animal Mouse Squirrel
Speed(mph) 8 12
"x" the time goes along with x-axis and "y" is the distance covered by the animal.
The mouse time and distance would plot the graph (1,8)(2,16)(3,24)....
The squirrel time and distance would plot the graph (1,12)(2,24)(3,36)....
Let us consider the track is straight line and shorter distance is 50 meters.
Formula for straight line equation y = mx + b where 'b' is the base value, 'x' is the time and 'y' is the distance.
The linear equation for squirrel y = 12x+b and the squirrel starts at 0 meters per hour. so the equation becomes y = 12x.
The linear equation for mouse y = 8x + b and the mouse starts at 0 meters. so the equation becomes y = 8x.
Distance covered by the mouse and the squirrel at time x = 3 we can find the distance covered by mouse and the squirrel.
y =12x
y = 12(3)
y = 36.
The distance covered by the squirrel is 36km at time 3hours.
For mouse, at time x = 3 hours.
y = 8(3)
y=24.
The distance covered by the squirrel is 24km at time 3hours.
Hence, The linear equation for squirrel y = 12x.
The linear equation for mouse y = 8x
The distance covered by the squirrel is 36km at time 3hours.
The distance covered by the squirrel is 24km at time 3hours.
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If x < 5 and x > c, give a value of c such that there are no solutions to the compound inequality. Explain why there are no solutions
Final answer:
To ensure there are no solutions to the compound inequality x < 5 and x > c, we can choose c to be 5 or larger, such as c = 6, making the inequality impossible.
Explanation:
To determine a value of c such that the compound inequality x < 5 and x > c has no solutions, we need to choose a value of c that makes the inequality impossible to satisfy.
One way to ensure there are no solutions is to choose c so that it is greater than or equal to 5.
If c is 5 or any number larger than 5, then there is no real number x that can be both greater than c and at the same time less than 5.
For example, if we choose c = 6, then the set of values greater than 6 (x > 6) does not intersect with the set of values less than 5 (x < 5).
Therefore, c = 6 would ensure that there are no solutions to the compound inequality.
CAN ANYONE HELP ME WITH THIS PLSSSSSSSSSSSSSSS
Jade is painting a rectangular wall. The wall is 414 yards long and 223 yards high. The formula for the area of a rectangle is A=bh. What is the area of the wall? Enter your answer as a mixed number in simplest form in the box. $$ yd2
Answer:
Its actually 11 1/3
Step-by-step explanation:
Show three ways to make $20 .Use tally marks to record the bills.
shane works at an electronics store. He earns 13% commission on his sales. Shane's commission this month is $780. What are his total sales for the month
Answer:
Shane's total sales is $6000.
Step-by-step explanation:
It is given that the Shane earns 13% commission on his sales and the Shane's commission this month is $780.
Let the Shane's total sales be x. So, 13% of x is $780.
[tex]x\times \frac{13}{100}=780[/tex]
Solve the above equation to find the value of x.
[tex]x=780\times \frac{100}{13}[/tex]
[tex]x=6000[/tex]
The value of x is 6000, therefore Shane's total sales is $6000.
1.01<0.99 true,4.5=4.50 true, 3.5<3.39 true?, lastly is 1.51>1.15 true?
What is the gcf of 18 and 14
multiply the number of legs on a snake by the number of hours in day .What's the product
A sporting goods store sells right-handed baseball gloves and left handed baseball gloves. In 1 month 12 gloves were sold for a total revenue of $561. Right-handed gloves cost $45 and left-handed gloves cost $52. How many of each type of gloves did they sell?
They sold 3 left handed gloves and 9 right handed gloves.
To solve this problem, we have to write a system of equations.
Data given;
total number of gloves = 12revenue for 12 gloves = $561right handed gloves (x) = 45left handed gloves (y) = 52Equations[tex]x + y = 12...equation (i)\\ 45x + 52y = 561 equation (ii)[/tex]
From equation (i)
[tex]x + y = 12\\ x = 12 - y...equation (iii)[/tex]
Substitute equation (iii) into equation (ii)
[tex]45x + 52y = 561\\ x = 12 - y\\ 45(12- y) + 52y = 561\\ 540 - 45y +52y = 561\\ 540 + 7y = 561\\ 7y = 21\\ y = 3[/tex]
Put y = 3 in equation (i)
[tex]x + y = 12\\ x + 3 = 12\\ x = 9[/tex]
From the calculations above, they sold 9 right handed gloves and 3 left handed gloves
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Using front end estimation find a reasonable estimate of: 719 · 26
Answer:
C
Step-by-step explanation:
A campground consists of 9 square campsites arranged in a line along a beach. The distance from the edge of a campsite to the water at the end of the beach is 5 yd. The area of the campground, including the beach, is 1115 sq yd. What is the width of one campsite?
Answer:
i think it is 54
Step-by-step explanation:
what is 7.5% greater than 840.76
At silver Gym, membership is $45 per month, and personal training sessions are $25 each. At fit factor, membership is $75 per month, and personal training sessions are $15 each. In one month, how many personal training sessions would Sarah have to buy to make the total cost at the two gyms equal?
Final answer:
By setting up and solving an equation based on the monthly membership and per-session training costs at both Silver Gym and Fit Factor, it's determined that Sarah would need to buy 3 personal training sessions for the total cost at the two gyms to be equal.
Explanation:
To find how many personal training sessions Sarah would have to buy to make the total cost at Silver Gym and Fit Factor equal, we'll set up an equation. Let x be the number of personal training sessions.
At Silver Gym, the total cost is $45 (membership) + $25x (personal training sessions).
At Fit Factor, the total cost is $75 (membership) + $15x (personal training sessions).
Setting these two expressions equal to each other gives us the equation:
45 + 25x = 75 + 15x.
To solve for x, first subtract 15x from both sides, giving: 10x = 30. Then divide both sides by 10 to isolate x, resulting in x = 3.
Therefore, Sarah would have to buy 3 personal training sessions in one month for the total costs at both gyms to be equal.
Answer:
3 sessions
Step-by-step explanation:
You want to know the number of personal training sessions Sarah would have to buy to make the total costs the same at Silver Gym and Fit Factor. Silver Gym costs $45 per month and $25 per session, while Fit Factor costs $75 per month and $15 per session.
DifferencesSilver Gym costs $25 -15 = $10 more per personal training session, but $75 -45 = $30 less for the monthly fee. This means it takes $30/$10 = 3 sessions for the difference in fees to be made up by the difference in session costs.
Sarah would have to buy 3 sessions for the total cost to be the same.
EquationsIf you need to see this using equations, we can write the cost equations as ...
S = 45 +25x . . . . . . . . cost for x sessions at Silver Gym
F = 75 +15x . . . . . . . . . cost for x sessions at Fit Factor
Setting these equal, we have ...
S = F
45 +25x = 75 +15x
25x -15x = 75 -45 . . . . . . . subtract 45+15x from both sides
10x = 30
x = 30/10 = 3 . . . . sessions for equal cost
Sarah would have to buy 3 sessions for the total cost to be the same.
__
Additional comment
These "break even" problems usually have a higher fixed cost associated with a lower per use cost, and vice versa. The costs are the same when the number of uses, multiplied by the difference in use cost, comes to the same amount as the difference in fixed costs. Here, the $10 difference in session cost, times 3 sessions, is equal to the $30 difference in monthly membership fee.
Bens mom wants to buy carpet for the family room the measures 12 feet by 11 feet she can purchase the carpet on sale for $6 how much will bens mom spend to carpet the family room
re are 5 short rows of chairs, each with an equal number of chairs. On a crowded day, the ushers added 2 chairs to each long row and 3 chairs to each short row.