The perimeter of a rectangle is 34 units. Its width W is 6.5 units.
Write an equation to represent the perimeter in terms of the length L, and find the value of L
Answer:The length of rectangle is 10.5 units
Solution:Given that,
Perimeter of rectangle = 34 units
Width of rectangle = 6.5 units
Let "L" be the length of rectangle
The perimeter of rectangle is given by formula:
Perimeter = 2(length + width)
Substituting the values we get,
[tex]34 = 2(L + 6.5)[/tex]
Thus the equation is found
Solve for "L"
[tex]L + 6.5 = \frac{34}{2}\\\\L + 6.5 = 17\\\\L = 17 - 6.5\\\\L =10.5[/tex]
Thus length of rectangle is 10.5 units
Teresa, Charlie, and Justin served a total of 153 orders Monday at the school cafeteria. Justin served 4 times as many orders as Charlie. Teresa served 9 more orders than Charlie. How many orders did they each serve?
Teresa served 33 orders and Charlie served 24 orders and Justin served 96 orders
Solution:
Let "a" be the orders served by Teresa
Let "b" be the orders served by Charlie
Let "c" be the orders served by Justin
Teresa, Charlie, and Justin served a total of 153 orders
Therefore,
a + b + c = 153 -------- eqn 1
Justin served 4 times as many orders as Charlie
Orders served by Justin = 4( orders served by Charlie )
c = 4b ---------- eqn 2
Teresa served 9 more orders than Charlie
orders served by Teresa = 9 + orders served by Charlie
a = 9 + b ----------- eqn 3
Let us solve eqn 1 and eqn 2 and eqn 3
Substitute eqn 2 and eqn 3 in eqn 1
9 + b + b + 4b = 153
9 + 6b = 153
6b = 153 - 9
6b = 144
b = 24
Substitute b = 24 in eqn 3
a = 9 + 24
a = 33
Substitute b = 24 in eqn 2
c = 4(24)
c = 96
Thus Teresa served 33 orders and Charlie served 24 orders and Justin served 96 orders
I need help -6(2x+6)=-132
Answer:
x=8
Step-by-step explanation:
First you want to distribute -6 to (2x+6) which you will then get -12x-36=-132. Now you want to get x by itself by getting rid of -36, so add 36 on both sides of the equation to get -12x=-96. Isolate x by dividing by -12 on both sides of the equation which will leave you with the equation x=8
BICYCLING The bicycle path at the
park is a loop that covers a distance
of m miles. Dot biked 2 loops each on
Monday and Wednesday and 3 loops
on Friday. On Sunday, Dot biked
10 miles. Write an expression in
simplest form that represents the
total distance that Dot biked this
week.
Dot bikes 7m+10 miles this week.
Step-by-step explanation:
Distance of one loop = m miles
Distance of 2 loops = 2m
Distance of 3 loops = 3m
Distance covered on Sunday = 10 miles
Total distance = Monday + Wednesday + Friday + Sunday
Total distance = 2 loops + 2 loops + 3 loops + 10 miles
Total distance = 2m + 2m + 3m + 10
Total distance = (7m+10) miles
Dot bikes 7m+10 miles this week.
Keywords: addition, distance
Learn more about distance at:
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What is the perimeter of this red polygon?
Answer:
Answer: The perimeter of the red polygon is 26 cm.
Step-by-step explanation:
Answer:
Tangents from an external point are equal. This can be used to find the perimeter
Perimeter = 22+22+22+22+27+27+98+98
= 338 in.
Hope this helps!
A man and his wife go shopping. They begin with $200 total. First, they stop for lunch, spending $15.00. Then, they buy three items at $20.00 each. Later, the wife spends twice what her husband spends. They return home with $20.00 cash. How much did the wife spend?
Amount spent by the wife is $70
Step-by-step explanation:
Given:
the total amount = $200
Amount spent on Lunch = $15.00
They buy three items at $20.00 each
The wife spends twice what her husband spends
They return home with $20.00 cash.
To Find:
Amount spent by the wife = ?
Solution:
Initially after spending $15.00 on lunch they balance cash with them will be
200 - 15.00 = $185
Then they are buy 3 items each of which costs $20.00
So the balance after buying the 3 items will be
= 200 - 3(20)
= 185- 60.00
= $125
Now the wife is spending twice what her husband spends
so let the amount spent be the husband be x then the amount spent by the wife will be 2x.
Now after spending 2x+x amount they are left with $20.00
that is
125 -2x+x = 20
125 -3x = 20
125 -20 = 3x
105 = 3x
[tex]x = \frac{105}{3}[/tex]
x = 35
So the wife will be spending 2(35) = $70
Graph the system of linear inequalities. y≥2/3 x-3 y<-4x+7
Answer:
The answer is given in the graph attached.
Step-by-step explanation:
i) The answer is given in the graph attached.
A math teacher wants to buy 25 new scientific calculators for the classroom. Acme and Zenith makes two different type of calculators. Acme calculators cost $15 each. Zenith calculators cost $12 each. The math teacher has $330 to spend. How many of each calculators can she buy?
Answer: 10 Acme and 15 Zenith.
She can buy 10 Acme and 15 Zenith calculators.
What is the system of equations?One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.
Given:
A math teacher wants to buy 25 new scientific calculators for the classroom.
Acme and Zenith makes two different type of calculators.
Acme calculators cost $15 each.
Zenith calculators cost $12 each.
The math teacher has $330 to spend.
Let x represents the number Acme calculators and y represents Zenith.
Now, we have the system of equations,
x + y = 25
So, y = 25 - x
And 15x + 12y = 330
Substituting the value of y,
15x + 300 - 12x = 330
3x = 330 - 300
3x = 30
x = 10
So, y = 15
Therefore, 10 Acme and 15 Zenith calculators.
To learn more about the system of equation;
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Eight less than 1/3 a number n is -13?
-4, -9, -14. What is a formula for the nth term if the given sequence in explicit formula
Answer: the formula is
(-4) + (-5) = -9
(-9) + (-5) = -14
Step-by-step explanation:
Answer:
an = 1 − 5n
Explanation:
a1 = 1 − 5 (1) = −4
a2 = 1 − 5 (2) = −9
a3 = 1 − 5 (3) = −14
Alegbra, K12 Question. Answer needed ASAP --- Brainliest to the correct answer!
Good evening ,
Answer:
-1Step-by-step explanation:
From the table :
f(x) = g(x) only when x = -1 then -1 is the only solution
f(-1) = 9 = g(-1)
note : the equation could have some other solutions not shown in the table
:)
ANSWER QUICK
What are the values of a, b, and c in the quadratic equation 0=1/2x^2-3x?
Answer:
[tex]a=\dfrac{1}{2}\\ \\b=-3\\ \\c=0[/tex]
Step-by-step explanation:
The general form of the quadratic equation is
[tex]ax^2+bx+c=0[/tex]
You are given the quadratic equation
[tex]0=\dfrac{1}{2}x^2-3x[/tex]
It can be rewritten in standard form as
[tex]\dfrac{1}{2}x^2-3x=0[/tex]
Hence,
[tex]a=\dfrac{1}{2}\\ \\b=-3\\ \\c=0[/tex]
Find the next two terms of this sequence
112, 28, 7, ...........
Answer:
1.75, 0.4375
Step-by-step explanation:
Note there is a common ratio between consecutive terms, that is
r = 28 ÷ 112 = 7 ÷ 28 = 0.25
Thus the sequence is geometric.
To obtain a term in the sequence multiply the previous term by 0.25
7 × 0.25 = 1.75
1.75 × 0.25 = 0.4375
The next 2 terms in the sequence are 1.75, 0.4375
How to solve 7(x+2y)=
Answer:
7x + 14y
Step-by-step explanation:
7(x + 2y)
Multiply 7 by the values inside the parenthesis (x + 2y)
7x + 14y
Hope this helps :)
Add the two expressions.
3z−4 and 2z + 5
Enter your answer in the box.
Answer:
5z+1
Step-by-step explanation:
(3z-4)+(2z+5)
3z-4+2z+5
3z+2z-4+5
5z-4+5
5z+1
Answer:
5z+1
Step-by-step explanation:
3z-4+2z+5
Group like terms
3z+2z+5-4
Simplify
5z+1
A gym instructor has a total of 60 hand weight in her studio. Some of the hand weights are 3 pound weights and the rest are 5 pound weights. If there are 10 more 5-lb weights than 3-lb weights, then how many of each kind does she have?
Answer:
35 5-lb weights25 3-lb weightsStep-by-step explanation:
Let t and f represent the numbers of three- and five-pound weights. The problem statement tells us ...
f + t = 60
f - t = 10
Adding these two equations, we get ...
(f +t) +(f -t) = (60) +(10)
2f = 70 . . . . . eliminate parentheses
f = 35 . . . . . . divide by 2
She has 35 5-lb weights, and 25 3-lb weights.
The equation of a given circle in. general form is x^2+y^2+12y+27=0. Write the equation in standard form, (x-h)^2+(y-k)^2=r^2, by completing the squares in the equation. Show your work in the table.
Answer:
Center (h, k) = (0, 6)
Radius, r = 3 units
Step-by-step explanation:
The given equation of the circle is: [tex]$ x^2 + y^2 + 12y + 27 = 0 $[/tex]
STEP I: Move the constant term to the right hand side.
To do that we subtract 27 on both the sides, we get:
[tex]$ x^2 + y^2 + 12y = -27 $[/tex]
STEP II: Divide the co - effecient of 'x' by 2 and square it.
Here there is no 'x' term. Its co-effecient is 0.
STEP III: Add the result on both sides.
Since, we got 0 in the previous step, there would no change in the equation
STEP IV: We repeat the process for 'y'.
Here, the co-effecient of 'y' is: 12.
Dividing by 2 and squaring it will yield:
[tex]$ \frac{12}{2} = 6; \hspace{5mm} 6^2 = 36 $[/tex]
STEP V: Adding 36 to both the sides of the equation, it becomes:
[tex]$ x^2 + y^2 + 12y + 36 = -27 + 36 $[/tex]
[tex]$ \implies x^2 + y^2 + 12y + 36 = 9 $[/tex]
We have arrived at perfect squares.
STEP VI: Write in the form of perfect squares.
[tex]$ (x - 0)^2 + (y - 6)^2 = 3^2 $[/tex]
STEP VII: Compare it with the standard form.
[tex]$ (x - h)^2 + (y - k)^2 = r^2 $[/tex]
We get: The centre of the circle: (h, k) = (0, 6) and
the radius of the circle, r = 3 units.
(-3,4) is one of many solutions to the inequality:
2x+y ≥ -2
True or false
Answer:
True
Step-by-step explanation:
Answer:
True
Step-by-step explanation:
(-3,4) it shows that -3 =x and 4 =y
2x + y ≥ -2
Inserting both values into the equation
2(-3) + 4
-6 +4
-2
Answer confirms equation
BRAINIEST RIGHT AWAY!! ANSWER NOW!
You take a pan of brownies out of the oven and set them on the counter in a room that is 70 degrees F, If the brownies start at 400 degrees F, approximately how long will it be before they are cool enough to eat at 160 degrees F? Use Newton's Law of Cooling with k = 0.035.
Answer:
i would say wait abought 50 mins
Step-by-step explanation:
i dont know whow to explain i might be wrong but its some whaere around 50 mins irl
Using Newton's Law of Cooling with a cooling constant of 0.035, it will take approximately 42.53 minutes for the brownies to cool from 400 degrees F to 160 degrees F.
To estimate the time it would take for brownies to cool from 400 degrees F to 160 degrees F using Newton's Law of Cooling, we can use the equation [tex]T(t) = T_s + (T_0 - T_s)e^{(-kt)[/tex], where T(t) is the temperature of the object at time t, T_s is the surrounding temperature, T_0 is the initial temperature of the object, and k is the cooling constant (0.035 in this case).
First, set T(t) = 160 degrees F (the desired temperature), T_s = 70 degrees F (room temperature), and T_0 = 400 degrees F (initial temperature of brownies). Plug in the values into the equation: 160 = 70 + (400 - 70)e^(-0.035t).
Simplify and solve for t. Subtract 70 from both sides: 90 = 330e^(-0.035t). Divide both sides by 330: 90/330 = e^(-0.035t), which simplifies to 0.2727 ≈ e^(-0.035t).
Take the natural logarithm of both sides to solve for t: ln(0.2727) = -0.035t. Solving for t gives t ≈ -ln(0.2727)/0.035, which calculates to approximately t ≈ 42.53 minutes.
Hence, the brownies should cool to 160 degrees F in about 42.53 minutes.
if anyone can answers these i will give them a brainlist.
1. A tree casts a shadow 21 m long. The angle of
elevation of the sun is 51°. What is the height of the
tree?
2.a helicopter is hovering over a landing pad 100m from where you are standing. the helicopter’s angle of elevation off the ground is 12 degrees. what is the altitude of the helicopter?
Answer:
1. X= 25.9 meters
2.X= 21.3 meters
Step-by-step explanation:
1. Tan 50°= X/21
2. Tan 12°= X/100
draw triangle abc where:
AB has the length 3.9cm (this is drawn for you)
angle CAB is 50
and
angle ABC is 63
Step-by-step explanation:
We are asked to draw a triangle.
The information we are given with is AB is a line segment with length 3.9 cm.
∠CAB = 50°.
∠ABC = 63°.
With the given details we need to draw triangle using given angles. We need protractor and ruler to draw the triangle.
Step 1: Draw the line segment of length 3.9 cm using ruler and mark as AB.
Step 2: Using protractor, we need to mark the angle. Keep the center of the protractor at the A and mark with a point at 50°.
Step 3: Draw a line from a passing through the marked point.
Step 4: Repeat step 2 with marking at 63° and step 3 on the other side.
Step 5: Mark the intersection point as C.
What is the algebraic expression to 6 less than twice a number
Answer:
it would be 2x-6
Step-by-step explanation:
since you don't know what the value of "the number" is you would put a variable, x. and there is 2 of this number.
then 6 less would be -6 of this variable.
Write the ratio in simplest form.
8 min : 12 min
Answer:
2:3
Step-by-step explanation:
Answer:
2min :3min
Step-by-step explanation:
8 min divided by 4 =2
12 min divided by 4 =3
If k(x) = 5x – 6, which expression is equivalent to (k + k)(4)?
HELP PLS
Answer:
The third dot
Step-by-step explanation:
I did this question before :)
Which best describes the complement of spinning any number less than 3?
Answer:
The complement of spinning any number less than 3, is spinning a number equal to or greater than 3.Explanation:
The complement of a subset is the subset of elements that are not in the given subset.
You must know which numbers the spinner has.
Assuming the spinner has the numbers 1, 2, 3, 4, the complement of spinning any number less than 3, is spinning a number that is not less than 3.
Then, that is spinning a number that is equal to or greater than 3.
The numbers that are equal to or greater than four, for a spinner that has the numbers 1, 2, 3, and 4 are 3 and 4.
Thus, the complement of spinning any number less than 3 is spinning a three or a four.
Answer:
C
Step-by-step explanation:
rearrange the equation so b is the independent variable a-7=3(b+2)
Answer:
Step-by-step explanation:
a - 7 = 3(b + 2)
a - 7 = 3b + 6
a - 7 - 6 = 3b
a - 13 = 3b
(a - 13) / 3 = b <====
Answer:
-13-1/4 b
Step-by-step explanation:
b is on the outside of the fraction not with the four.
-13-\frac{1}{4b}
3x = x+6 show the steps please
Answer:
x = 3
Step-by-step explanation:
Given
3x = x + 6 ( subtract x from both sides )
2x = 6 ( divide both sides by 2 )
x = 3
Answer:
Step-by-step explanation:
3x = x + 6.....subtract x from both sides
3x - x = x - x + 6
2x = 6 ...divide both sides by 2
(2/2)x = 6/2
1x = 6/2
x = 3 <=====
Ajar contains a mixture of 10 black balls, 8 red balls, and 2 white balls all the same size. What is the probability of
drawing either a red, black, or white ball in one draw?
Answer:
10 black- 10/20 - 50%
8 red- 8/20 - 40%
2 white - 2/20 -10%
Step-by-step explanation:
The total number of balls = 10 + 8 + 2 = 20 balls
probability of black balls = 10/20 = 50%
probability of red balls = 8/20 = 40%
probability of white balls = 2/20 = 10%
the three probabilities:
probability that the ball is one of the three colors = (10/20) + (8/20) + (2/20)
= 1 = 100%
PLS I NEED ASAP WILL GIVE BRAINLIEST
Which equation is linear?
y=2x+2
2
y=2x^+2
3
y=2x^+2
4
y=2x^+2
For this case we have that by definition, a linear equation is of the form:
[tex]ax + b = 0[/tex]
The variable (s) involved in the equation always have exponent 1.
Some examples of linear equations are:
[tex]x + 5 = 3y\\y + 6 = 3x\\y = 2x + 2[/tex]
Answer:
In a linear equation the variables have exponent 1.
[tex]y = 2x + 2[/tex]
Consider the transformation shown
Use the drop-down menus to complete the sentence.
The transformation is
because the
preserved
Image
Pre-image
Answer:
Nonrigid
Segment lents are not
Step-by-step explanation:
Answer:
answer in picture
Step-by-step explanation:
A gardener uses a wheelbarrow to move soil from a truck to his garden. On the first trip from the truck to the garden, the wheelbarrow
is half-full of soil and the gardener applies a certain force to cause it to accelerate. On the second trip, the wheelbarrow is full of soil.
Although the gardener applies the same amount of force to the wheelbarrow, he cannot move it with the same rate of acceleration.
What should the gardener do to move the wheelbarrow at the same rate of acceleration for the second trip?
A. reduce the amount of soil by one-half and apply the same amount of force
B. keep the amount of soil the same and apply less force
C. reduce the amount of soil by one-quarter and apply the same amount of force
D. double the amount of soil, and apply less force
Reset
Reset
Submit
1 of 10 Answered
Session Timer: 4:08
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Answer:
Step-by-step explanation:
it seems to me that if he wants the same rate of acceleration as the first trip, then he would need the same amount of soil as the first trip.
Therefore, he should reduce the amount of soil by one half and apply the same force. <====
Because the first time it was half full.....and since the second trip was all the way full, if he reduced it by one half, it would contain the same amount as the first trip....so he can then get the same rate of acceleration.
Answer:
A.
Step-by-step explanation:
According to Newton's second law of motion, an object with a larger mass requires more force to accelerate it at a certain rate than an object with less mass. This means that an object with a larger mass requires more force to accelerate.
To move the wheelbarrow at the same rate of acceleration for the second trip, the amount of soil must be the same as in the first trip. Since the gardener first filled only one-half of the wheelbarrow with soil, the gardener must reduce the amount of soil by one-half and apply the same amount of force.