Mrs. Williams is deciding between two field trips for her class. The Science Center charges $80 plus $5 per student. The Dino Discovery Museum simply charges $7 per student. For how many students will the Science Center charge less than the Dino Discovery Museum charges?
fewer than 40 students
78 or fewer students
78 or more students
more than 40 students
HELP!!
Answer: More than 40 students
Step-by-step explanation:
Let x be the number of students .
Given : Mrs. Williams is deciding between two field trips for her class. The Science Center charges $80 plus $5 per student.
i.e. Total cost : [tex]80+5x[/tex] (1)
The Dino Discovery Museum simply charges $7 per student.
i.e. Total cost : [tex]7x[/tex] (2)
The inequality that shows Science Center charge less than the Dino Discovery Museum charges will be :-
[tex]80+5x<7x[/tex]
Subtract 5x on both sides , we get
[tex]80<2x[/tex]
Divide both sides by 2 , we get
[tex]40<x[/tex]
Hence, for more than 40 students the Science Center charge will less than the Dino Discovery Museum charges.
Suppose you have 30 CDs. You know that you have 11 more CDs than your friend. Write and solve an equation to find the number of CDs your friend has. Question 3 options: n – 11 = 30; 41 30 + n = 11; –19 30 + 11 = n; 41 n + 11 = 30; 19
Answer:
n+11=30
n = 19
Step-by-step explanation:
You have 30 CDs and you friend had n amount of CDs. We also know that you have 11 more CDs than your friends. Therefore we can write expression as:
[tex]n+11=30[/tex] and simplify
[tex]n =30 -11[/tex]
[tex]n=19[/tex]
Therefore you friend will have 11 CDs which is 11 less than what you have.
A triangle has angles that measure 120°, 39°, and 21°. what kind of triangle is it?
A triangle with angles that measure 120°, 39°, and 21° is an obtuse triangle.
The student has asked about the classification of a triangle with angles that measure 120°, 39°, and 21°. Based on Euclidean geometry, the sum of the angles in any plane triangle is 180°. A triangle with one angle that measures more than 90° is an obtuse triangle, as it has one obtuse angle. Therefore, this triangle, with a 120° angle, is classified as an obtuse triangle.
Please help
solve 4x-9=k for x
Answer:
The value of x is [tex]\frac{k+9}{4}[/tex]
Step-by-step explanation:
Given : equation 4x - 9 = k
We have to find the value of x.
Consider the given equation 4x - 9 = k
Adding 9 both sides, we have,
4x = k + 9
Divide both side by 4, we have,
[tex]x=\frac{k+9}{4}[/tex]
Thus, The value of x is [tex]\frac{k+9}{4}[/tex]
What system of linear inequalities is shown in the graph?
The graph of g(x)=(1/2)x is the graph of f(x)=2x reflected over the y-axis. Which graph represents g(x) please help!
Answer:
Step-by-step explanation:
Using altitude and hypotenuse to find the area of a right triangle
Hank's pickup can travel 39 miles on 3 gallons of gas. How many gallons will Hank's pickup need to travel 26 miles?
(-6 -2) (6 r) m=1/4 can you help me solve this equation.
If l || m, what is the value of x?
Julia knows 19 Latin words. Each day, she learns 6 new words, How many day until she knows 145 words.
ANSWER CHOICES
A:20
B:21
C:22
D:23
145 -19 = 126
she needs to learn 126 more words
divide 126 by 6 to find number of days
126 / 6 = 21
it will take 21 days, Answer is B
Which pair of equations represents perpendicular lines?
a. y=2x-7, y=-0.5x-7
b. y=2x+7, y=2x-7
c. y=2x+7, y=x+7
d. y=2x+7, y=-2x-2
the answer would be A because if you graph those equations they are perpindicular. They cross eachother like a t
People enjoyed attending the concert in the park. Twice as many men as women attended the concert. If the total attendance was 714, how many women attended the concert?
What is the solution to the equation 1.2m − 0.8 = −2.0m?
A.) m= 0.25
B.) m= 0.4
C.) m= 1
D.) m= 4
Televisions are on sale for 85% of the original price of $499. what is the sale price?
tony and sal drove in opposite direction from the same starting point. tony averaged 15 mpg faster then sal. after 5 hours they were 425 miles apart. how fast was each of them driving?
Name a pair of vertical angles, a straight angle, and two scute angles other than
Answer:
∠GEN and ∠FED, ∠GEF and ∠DEN are few of the vertical angles.
∠ENM and ∠NKP, ∠HKC and ∠ADE are few of the straight angles.
∠GEN and ∠FED, ∠JNM and ∠EHK are few of the acute angles.
Step-by-step explanation:
Vertical angles are the angles made by two intersecting lines and they are equal
So,
∠GEN and ∠FED, ∠GEF and ∠DEN are few of the vertical angles.
Straight angles are angles that are 180°
So,
∠ENM and ∠NKP, ∠HKC and ∠ADE are few of the straight angles.
The angles less than 90° are called acute angles
So,
∠GEN and ∠FED, ∠JNM and ∠EHK are few of the acute angles.
∠GEN and ∠FED, ∠GEF and ∠DEN are few of the vertical angles.
∠ENM and ∠NKP, ∠HKC and ∠ADE are few of the straight angles.
∠GEN and ∠FED, ∠JNM and ∠EHK are few of the acute angles.
How to explain the angleVertical angles are the angles made by two intersecting lines and they are equal, ∠GEN and ∠FED, ∠GEF and ∠DEN are few of the vertical angles.
Straight angles are angles that are 180° ∠ENM and ∠NKP, ∠HKC and ∠ADE are few of the straight angles.
The angles less than 90° are called acute angles∠GEN and ∠FED, ∠JNM and ∠EHK are few of the acute angles.
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What is the sum of the infinite geometric series? -3-3/2-3/4-3/8-3/16
Answer: -6.
Step-by-step explanation: Given geometric series is-
[tex]-3,~-\dfrac{3}{2}, ~-\dfrac{3}{4}, ~-\dfrac{3}{8},~-\dfrac{3}{16},...[/tex]
Here, the first term of the series, [tex]a=-3[/tex]
and the common ratio, [tex]r=\dfrac{1}{2}.[/tex]
Since it is an infinite series, so sum is given by
[tex]S=\dfrac{a}{1-r}\\\\\\\Rightarrow S=\dfrac{-3}{1-\frac{1}{2}}\\\\\\\Rightarrow S=\dfrac{-6}{2-1}\\\\\\\Rightarrow S=-6.[/tex]
Thus, the sum of the series is -6.
solve for x...........
HELP ME PLS!!!!!!!!!!!!!!!!!!!
the number inside the parenthesis includes the interest rate ( annual percentage
looking at the possible functions, if you raise the interest rate to the power of 12, you would need to divide the number of years (t) by 12 as well
so the function could be rewritten as A=1000(1.023^12)^t/12
since the annual percentage rate is 2.3% ( 0.023)
divide 0.023/12*100 = 0.19% per month interest
An equation is shown
Y=1/2x+3/4
Select all the points that are contained in the graph of the equation
Marcial found a recipe for fruit salad that he wanted to try to make for his birthday party. He decided to triple the recipe. a. What are the new amounts for the oranges, apples, blueberries, and peaches? The amount of rhubarb in the original
recipe is 3 1/2 cups. Using what you know of whole numbers and what you know of fractions, explain how you could triple that mixed number.
A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is the number of 3-point questions and y is the number of 5-point questions, the system shown represents this situation. x + y = 24 3x + 5y = 100 What does the solution of this system indicate about the questions on the test? The test contains 4 three-point questions and 20 five-point questions. The test contains 10 three-point questions and 14 five-point questions. The test contains 14 three-point questions and 10 five-point questions. The test contains 20 three-point questions and 8 five-point questions.
Timothy deposited $2,780.20 in a savings account that earns 4.3% simple interest. What will Timothy’s account balance be in 7 months?
B is between A and C, D is between B And C, and C is between B and E. AE = 28cm, BC =10cm. AB = DB = DC. what is the length of CE ?
Final answer:
By using the given lengths of AE and BC, along with the equality of AB, DB, and DC, we can solve for CE to be 14.67cm.
Explanation:
The lengths of AE, BC, AB, DB, and DC are given or can be determined with the information provided. Since AB = DB = DC and BC is given as 10 cm, we can deduce that AB + BC + CE = AE. Given AE is 28cm and BC is 10cm, we can find the length of AB by realizing that AB + AB + AB (which is AB + DB + DC) is the same as BC or 10cm. This makes each section AB, DB, and DC equal to 10cm / 3.
With AB, DB, and DC all being equal to 10cm / 3, and knowing AE is 28cm, we can then calculate the length of CE:
AE = AB + BE (and BE = BC + CE)
28cm = (10cm/3) + (10cm + CE)
To find CE, rearrange the equation:
CE = 28cm - 10cm - (10cm/3)
CE = 28cm - 10cm - 3.33cm
CE = 18cm - 3.33cm
CE = 14.67cm
To solve for the length of CE in a line segment configuration, we calculate CE = AE - BC - DC after determining the lengths of AB, BC, and DC. The solution reveals that CE is 9cm.
Explanation:The student has a geometry problem, which involves calculating the length of segment CE on a line segment AE. We know that AE = 28cm and BC = 10cm, with AB, DB, and DC being equal in lengths.
Since B is between A and C, and D is between B and C, and C is between B and E, we can write the entire length AE as AB + BC + CE. Because AB = DB = DC, we can substitute DB and DC for AB in the sums to get 2(DB) + BC = 28cm.
We are given that BC = 10cm, so we can set up an equation: 2(DB) + 10cm = 28cm. Solving for DB, we find that DB = 9cm. Since DC is equal to DB, DC is also 9cm. CE can be found by subtracting BC and DC from the total length of AE: CE = AE - BC - DC, so CE = 28cm - 10cm - 9cm, resulting in CE = 9cm.
Are the following figures similar?
yes or no?
Corresponding angles are congruent
Yes or no?
Corresponding sides are proportional
which of the following are necessary when proving the opposite angles of a parallelogram are congruent? Check all that apply.
A) Opposite sides are perpendicular
B) Corresponding parts of similar triangles are similar
C) Opposite sides are congruent
D) Corresponding parts of congruent triangles are congruent
The opposite angles of a parallelogram are congruent this can be proved by the fact that;
Opposite sides are congruent Corresponding parts of congruent triangles are congruentTo prove opposite angles in a parallelogram are congruent, it's necessary to recognize that opposite sides are congruent and use the property that corresponding parts of congruent triangles are congruent.
Explanation:To prove that the opposite angles of a parallelogram are congruent, it's not necessary that opposite sides be perpendicular. Instead, let's consider the properties that are relevant to this proof:
Opposite sides are congruent (C)Corresponding parts of congruent triangles are congruent (D)In this case:
Option A is not relevant because a parallelogram does not require opposite sides to be perpendicular; that is a characteristic of a rectangle.Option B refers to similar triangles, which is not necessary for proving the opposite angles are congruent in parallelograms. Similar triangles have proportional sides and identical angles, which is not the focus here.Option C is a defining property of parallelograms and is necessary to help prove that opposite angles are congruent.Option D can be used in the proof if one demonstrates that two triangles within the parallelogram are congruent, therefore their corresponding angles must be congruent; this includes the opposite angles of the parallelogram.The proper proof would rely on establishing congruent triangles within the parallelogram and then using the property that corresponding parts of congruent triangles are congruent to show that the opposite angles are congruent.
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*NEED HELP!!!
Trystan accepted a job offer with an annual salary of $33,907, paid on a semimonthly basis. What will be his gross pay on each of his paychecks?
A) $652.06
B) $1304.12
C) $1412.79
D) $2825.58
6) Which salary results is the LEAST ANNUAL income?
A) weekly salary of $781
B) biweekly salary of $1430
C) semimonthly salary of $1550
D) monthly salary of $2995
7) Yusef earned a 25% tip on a meal that cost $75.77. What was the tip amount?
A) $9.42
B) $18.94
C) $15.68
D) $18.23
8)Larry earns $11.25/hour selling televisions. He also earns 4.5% commission on his sales.
What is his gross weekly pay for a week in which he worked 35 hours and sold $4000 worth of televisions?
A) $180.00
B) $393.75
C) $573.75
D) $628.45
9) Brea worked 40 hours one week at a rate of $15.60/h. How much money was deducted from her gr
Answer:
C) $1412.79; D) monthly salary of $2995; B) $18.94; C) $573.75
Step-by-step explanation:
Getting paid semimonthly means there will be two paychecks a month. There are 12 months in the year, so this is 24 checks per year. To find the gross pay on each check, divide the salary by 24:
33907/24 = 1412.79
There are 52 weeks per year. This means a weekly salary of 781 would be an annual income of 781(52) = 40,612.
A biweekly salary means getting paid every two weeks. This means there will be 52/2 = 26 paychecks per year; this gives an annual income of 26(1430) = 37,180.
Semimonthly pay means there will be 24 paychecks per year; this gives us an annual income of 24(1550) = 37,200
There are 12 months in the year; this gives us an annual salary of 12(2995) = 35,940. This is the smallest amount in our given choices.
25% = 25/100 = 0.25; this makes the tip 0.25(75.77) = 18.9425 ≈ 18.94.
11.25 per hour for 35 hours is 11.25(35) = 393.75. 4.5% commission is 4.5/100(4000) = 0.045(4000) = 180. Together this gives us
393.75+180 = 573.75
What are the real and imaginary parts of the complex number?
-6-i
Answer:
Real part: -6
Imaginary part: -1
Step-by-step explanation:
A complex number is a number that has a real part and an imaginary part. These numbers usually are represented in the form a + bi where a and b are real numbers and b is the imaginary part (i is actually the solution to the equation [tex]x^{2} +1=0[/tex] or x²=-1 which has no roots in the real numbers and therefore we call the solution √-1=i)
Now, proceeding to the complex number you wrote, if we write it as a + bi we would have a = -6 b = -1
Therefore the real part is a = -6 and the imaginary part would be -1.
A painter is working on a canvas that has a total area of 338 square inches. The canvas is x inches wide and twice as long as it is wide. Find the value of x.
A) 13
B) 18.4
C) 112.7
D) 69
Answer:
C
Step-by-step explanation:
Area = 338
Width = X
Length = 2x
2x * x = 338
3x = 338
x = 112.7
The value of x from the rectangular shaped canvas box is x = 13 inches
What is the Area of a Rectangle?The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle
Area of Rectangle = Length x Width
Given data ,
Let the area of rectangle canvas be A = 338 inches²
Let the width of the canvas = x inches
And , length = 2 x ( width )
Now , the length of the canvas = 2x inches
So , Area of Rectangle = Length x Width
On simplifying , we get
Area of Rectangle = 2x ( x )
Area of Rectangle = 2x²
338 = 2x²
Divide by 2 on both sides , we get
x² = 169
Taking square roots on both sides , we get
x = 13 inches
Hence , the value of x of the canvas is 13 inches
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