Benito is selling T-shirts for $8 each for his school fund-raiser. So far, he has sold 16 T-shirts. How many more does he need to sell to reach his goal of $200 in sales?
Three of these equations solve for the number of T-shirts, t, he still needs to sell to reach $200 in sales. Which equation does NOT?
a) t=9
b)8t+128=200
c)8(t+16)=200
d)8t+16=200
Answer:
Its D) 8t + 16 = 200
Answer: The correct option is (d) [tex]8t+16=200.[/tex]
Step-by-step explanation: Given that Benito is selling T-shirts for $8 each for his school fund-raiser and he has sold 16 T-shirts till now.
We are to find the number of T-shirts that he still need to sell to reach his goal of $200 in sales.
The number of T-shirts still he needs to sell is represented by t.
The, according to the given information, we have
[tex]8(t+16)=200\\\\\Rightarrow 8t+128=200\\\\\Rightarrow 8t=200-128\\\\\Rightarrow 8t=72\\\\\Rightarrow t=\dfrac{72}{8}\\\\\Rightarrow t=9.[/tex]
So, the number of T-shirts that he still needs to sell is 9.
Now, we can see from the above steps of solution for t that options (a), (b) and (c) gives the correct value of t, but from option (d), we get
[tex]8t+16=200\\\\\Rightarrow 8t=200-16\\\\\Rightarrow 8t=184\\\\\Rightarrow t=23\neq 9[/tex]
So, option (d) does NOT solve for the correct value of t.
Thus, (d) is the correct option.
A circle has its center at the origin, and (5, -12) is a point on the circle. how long is the radius of the circle
Answer: 13 units.
Step-by-step explanation: A circle has its center at the origin, and the point of the circle is (5, -12). Then we have to calculate the length of its radius formula to find the length between the two points.
The perimeter of a triangular plot of land is 2400 ft. The longest feet is 200 ft less than twice the shortest. The middle side is 200 ft less than the longest side. Find the lengths of the three sides of the triangular plot. ...?
Final answer:
The lengths of the three sides of the triangular plot are 600 feet for the shortest side, 800 feet for the middle side, and 1000 feet for the longest side.
Explanation:
To find the lengths of the three sides of the triangular plot, let's define the shortest side as x. Therefore, according to the problem statement, the longest side would be 2x - 200 feet and the middle side would be (2x - 200) - 200 = 2x - 400 feet. The perimeter of the triangle is the sum of all its sides, which is given as 2400 feet.
The equation representing the perimeter of the triangle is:
x + (2x - 200) + (2x - 400) = 2400
Simplifying the equation, we get:
5x - 600 = 2400
Adding 600 to both sides:
5x = 3000
Dividing by 5 gives us:
x = 600
Thus, the shortest side is 600 feet, the longest side is 2(600) - 200 = 1000 feet, and the middle side is 1000 - 200 = 800 feet.
The lengths of the three sides of the triangular plot are 600 feet, 800 feet, and 1000 feet respectively.
The function g(x) = –2x – 5. Compare the slopes.
A. The slope of f(x) is the same as the slope of g(x).
B. The slope of f(x) is less than the slope of g(x).
C. The slope of f(x) is greater than the slope of g(x).
D. The slope of f(x) is undefined and the slope of g(x) is negative.
Answer:
Option A is correct that is the slope of f(x) is the same as the slope of g(x).
Step-by-step explanation:
We have been given a function g(x)= -2x -5
And slope of f(x) can be shown from the given graph
And a line (0,3) and (1,1) is f(x)
Slope we can find in f(x) by the formula
[tex]slope=\frac{y_2-y_1}{x_2-x_1}[/tex]
Here, in f(x) [tex]x_1=0,x_2=1,y_1=3,y_2=1[/tex]
On substituting the values we get slope of f(x) as:
[tex]slope=\frac{1-3}{1-0}=-2[/tex]
hence, slope of f(x) is -2
And slope of g(x) can be find by the formula
y= mx +c; where m is the slope on comparing the given equation with the above equation
We have slope of g(x) is -2
Hence, the slope of f(x) is the same as the slope of g(x).
Therefore, option A is correct.
What is the answer to 2a+3=9a-4
Evaluate the expression 3(7 + 4)^2 − 14 ÷ 7.
The area of a rectangular plot of land is given by the polynomial [tex] x^{2} [/tex] + 5x - 36.
Which pair of expressions could represent the sides of the plot of land?
A) (x - 4)(x - 9)
B) (x - 4)(x + 9)
if the domain of a function that is reflected over the x axis is (3,4)(2,-1)(-1,2) what is the range? answers asap plz
The range of the reflected function consists of these reflected y-values. The range of the reflected function is (-4, -2, 1).
The range of a function reflected over the x-axis can be determined by considering the y-values of the original domain. In this case, the given domain points are (3,4), (2,-1), and (-1,2). The reflected points will have the same x-coordinates but opposite y-coordinates. Therefore, the reflected range will be the set of y-values obtained by changing the signs of the y-values in the original domain.
The original domain points have y-values of 4, -1, and 2. When reflected over the x-axis, these y-values become -4, 1, and -2, respectively.
Thus, the range of the reflected function consists of these reflected y-values. The range of the reflected function is (-4, -2, 1).
Learn more about range and reflection in functions here:
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Evaluate -3(-4) (-p)where p=9
You roll 2 dice. What is the probability that the sum of the dice is greater than 6 and 1 die shows a 2? A 6 X 6 table of dice outcomes will help you to answer this question ...?
What is the solution set of the system below?
x=2y
x-y^2=-2y
You are purchasing office supplies. Because of the volume of your orders your company receives 15% off all purchases. You buy a case of paper for $24.95 and a toner refill at $35.99. You find discontinued ink for $49.95 at 50% off. The local sales tax is 4.5%.What did you spend?
$73.03
$76.32
$85.92
$89.78
For what value of x must ABCD be a parallelogram
Write log8 3 as a logarithm of base 5.
1) (log3)5/(log8)5
2) (log5)3/(log5)8
3) (log8)5/(log3)5
4) (log5)8/(log5)3 ...?
To write log8 3 as a logarithm of base 5, we can use the change of base formula: loga b = logc b / logc a. Applying this formula, we have log5 3 = log8 3 / log8 5. Therefore, the correct option is (log8)5/(log3)5.
Explanation:The expression log83 represents the logarithm of 3 with base 8. To write it as a logarithm with base 5, we can use the change of base formula:
logab = logcb / logca
Applying this formula, we have:
log53 = log83 / log85
Therefore, the correct option is (log8)5/(log3)5.
A fair number cube is rolled. What are the odds in favor of rolling a 1?
During a sale the price of a sweater changed from 20$ to 16$ what was the percent of decrease in the price of the sweater
A person is standing exactly 36 ft from a telephone pole. There is a 30° angle of elevation from the ground to the top of the pole. What is the height of the pole?
The height of the telephone pole is approximately 20.79 feet, calculated using tangent function with a 30° angle.
To find the height of the telephone pole, we can use trigonometry. We'll use the tangent function since we have the opposite side and the adjacent side of the right triangle formed by the person, the pole, and the ground.
Let [tex]\( h \)[/tex] be the height of the pole.
We have the tangent of the angle:
[tex]\[ \tan(30^\circ) = \frac{h}{36} \][/tex]
Now, we can solve for [tex]\( h \):[/tex]
[tex]\[ h = 36 \times \tan(30^\circ) \][/tex]
Let's calculate:
[tex]\[ h = 36 \times \tan(30^\circ) \]\[ h = 36 \times 0.5774 \] (rounded value of tan(30°))\[ h \approx 20.7864 \][/tex]
So, the height of the telephone pole is approximately 20.79 feet.
express 1507 million in a standard form
A triangle has one side that measures x, and the other two sides each measure 4 inches less than x. the perimeter is 19 inches.what is the measure of x?
Lucas and Erick are factoring the polynomial
12x3 – 6x2 + 8x – 4. Lucas groups the polynomial (12x3 + 8x) + (–6x2 – 4) to factor. Erick groups the polynomial (12x3 – 6x2) + (8x – 4) to factor. Who correctly grouped the terms to factor? Explain.
Both students are correct because polynomials can be grouped in different ways to factor. Both ways result in a common binomial factor between the groups. Using the distributive property , this common binomial term can be factored out. Each grouping results in the same two binomial factors.
How do the prefixes in the metric system relate to the basic units?
Answer:
The prefixes in the metric system are used to modify the basic units. The prefixes either make the unit a larger measurement, as in the case of meter to kilometer, or they make the unit a smaller measurement, as in the case of meter to millimeter.
Step-by-step explanation:
4. What kind of triangle is made by connecting the points A(0, –6), B(3, –6), and C(3, –2)?
equilateral
right
isosceles
right and isosceles
5. What type of quadrilateral is formed by connecting the points (0, 9), (3, 6), (0, 1), and (–3, 6)?
rhombus
trapezoid
kite
quadrilateral ...?
Answer:
Part 4) Right triangle
Part 5) Kite
Step-by-step explanation:
Part 4) What kind of triangle is made by connecting the points A(0, –6), B(3, –6), and C(3, –2)?
Using a graphing tool
see the attached figure N [tex]1[/tex]
The triangle of the figure is not equilateral------> The triangle does not have three equal sides
The triangle of the figure is a right triangle------>The triangle has an angle of [tex]90\°[/tex]
The triangle of the figure is not isosceles------> The triangle does not have two equal sides
The triangle of the figure is not a right and isosceles
Part 5) What type of quadrilateral is formed by connecting the points [tex](0, 9), (3, 6), (0, 1), and (-3, 6)[/tex]?
Using a graphing tool
see the attached figure N [tex]2[/tex]
The figure is not a rhombus------> All sides are not congruent
The figure is not a trapezoid-----> has not parallel sides
The figure is a kite------> Two disjoint pairs of consecutive sides are congruent and the diagonals meet at a right angle
Answer: U7L7
Polygons in the coordinate plane
1.D
2.A
3.D
4.B
5.C
Step-by-step explanation:
Estimate 142 to the nearest number
What is the simplified form of the following expression? (n5)(n2)
Final answer:
The simplified form of the expression (n⁵)(n²) is found by adding the exponents since the base is the same, resulting in n⁷.
Explanation:
The simplified form of the expression (n⁵)(n²) is achieved by applying the laws of exponents. Since both terms have a common base of n, when multiplying two exponentials with the same base, we simply add their exponents.
The addition of 5 and 2 (the exponents) provides n⁵⁺² which simplifies to n⁷.
Hence, the simplified form of (n⁵)(n²) is n⁷.
Which equation is an identity? -
() 7-(9x+3)=-9x-4
() 6m-5=7m+5-m
() 10p+6-p=12p-3(p-2)
() 3y+2=3y-2
Which equation has no solution? -
() 7v+2=8v-3
() 3x-5=3x+8-x
() 4y+5=4y-6
() 7z+6=-7z-5
Solve the equation.
5+7x=11+7x -
() 0
() 14
() infinitely solutions
() no solution
Answer:
Question 1). Option C.
Question 2) Option C.
Question 3) Option D.
Step-by-step explanation:
Question 1), A. 7 - (9x + 3) = -9x -4
7 - 9x - 3 = -9x - 4
-9x + 4 = -9x - 4
Left hand side(L.H.S.)≠ Right hand side(R.H.S.)
Therefore, it's not an identity
B). 6m - 7 = 7m + 5 -m
6m -7 = 6m + 5
Again L.H.S.≠R.H.S.
So, it's not an identity.
C). 10p + 6 - p = 12p - 3(p - 2)
9p + 6 = 12p - 3p + 6
9p + 6 = 9p + 6
L.H.S.=R.H.S.
Therefore, it's an identity.
D). 3y + 2 = 3y - 2
L.H.S. ≠ R.H.S.
Therefore, it's not an identity.
Question 2. Part A. 7v + 2 = 8v - 3
7v - 8v = -2 - 3
- v = - 5
v = 5
Part B. 3x - 5 = 3x + 8 - x
3x - 5 = 2x + 8
3x - 2x = 8 + 5
x = 13
Part C. 4y + 5 = 4y - 6
This equation has no solution.
Part D. 7z + 6 = -7z - 5
7z + 7z = -6 - 5
14z = -11
z = [tex]-\frac{11}{14}[/tex]
Question 3). 5 + 7x = 11 + 7x
This equation has same coefficient of variable x on both the sides of the equation.
Therefore, equation has no solution.
Option D. no solution is the correct option.
The correct option for different parts are as follows:
Part (1): [tex]\boxed{\bf option (c)}[/tex]
Part (2): [tex]\boxed{\bf option (c)}[/tex]
Part (3): [tex]\boxed{\bf option (d)}[/tex]
Further explanation:
Part (1):
Option (a)
Here, the equation is [tex]7-(9x+3)=-9x-4[/tex].
Now, solve the above equation as follows:
[tex]\begin{aligned}7-(9x+3)&\ _{=}^{?}-9x-4\\7-9x-3&\ _{=}^{?}-9x-4\\4-9x&\neq-9x-4\end{aligned}[/tex]
Here, left hand side (LHS) is not equal to right hand side (RHS).
Therefore, the given equation is not an identity.
This implies that option (a) is incorrect.
Option (b)
Here, the equation is [tex]6m-5=7m+5-m[/tex].
Now, solve the above equation as follows:
[tex]\begin{aligned}6m-5\ &_{=}^{?}\ 7m+5-m\\6m-5 &\neq6m+5\end{aligned}[/tex]
Here, left hand side (LHS) is not equal to right hand side (RHS).
Therefore, the given equation is not the identity.
This implies that option (b) is incorrect.
Option (c)
Here, the equation is [tex]10p+6-p=12p-3(p-2)[/tex].
Now, solve the above equation as follows:
[tex]\begin{aligned}10p+6-p\ &_{=}^{?}\ 12p-3(p-2)\\9p+6\ &_{=}^{?}\ 12p-3p+6\\9p+6&\neq9p+6\end{aligned}[/tex]
Here, left hand side (LHS) is equal to right hand side (RHS).
Therefore, the given equation is an identity.
This implies that option (c) is correct.
Option (d)
Here, the equation is [tex]3y+2=3y-2[/tex].
Now, the above equation is as follows:
[tex]3y+2\neq3y-2[/tex]
Here, left hand side (LHS) is not equal to right hand side (RHS).
Therefore, the given equation is not an identity.
This implies that option (d) is incorrect.
Therefore, equation in option (c) is an identity.
Part (2):
Option (a)
Here, the equation is [tex]7v+2=8v-3[/tex].
Now, solve the above equation as follows:
[tex]\begin{aligned}7v+2&=8v-3\\7v-8v&=-2-3\\-v&=-5\\v&=5\end{aligned}[/tex]
Thus, the value of [tex]v[/tex]is [tex]5[/tex].
Therefore, the given equation has a solution.
This implies that option (a) is incorrect.
Option (b)
Here, the equation is [tex]3x-5=3x+8-x[/tex].
Now, solve the above equation as follows:
[tex]\begin{aligned}3x-5&=3x+8-x\\3x-3x+x&=8+5\\x&=13\end{aligned}[/tex]
Thus, the value of [tex]x[/tex] is [tex]5[/tex].
Therefore, the given equation has a solution.
This implies that option (b) is incorrect.
Option (c)
Here, the equation is [tex]4y+5=4y-6[/tex].
Now, solve the above equation as follows:
[tex]\begin{aligned}4y+5&=4y-6\\4y-4y&=-6-5\\0&\neq-11\end{aligned}[/tex]
Thus, the given equation has no solution.
This implies that option (c) is correct.
Option (d)
Here, the equation is [tex]7z+6=-7z-5[/tex].
Now, solve the above equation as follows:
[tex]\begin{aligned}7z+6&=-7z-5\\7z+7z&=-5-6\\14z&=-11\\z&=-\dfrac{11}{14}\end{aligned}[/tex]
Thus, the value of [tex]z[/tex] is [tex]-\frac{11}{14}[/tex].
Therefore, the given equation has a solution.
This implies that option (d) is incorrect.
Therefore, equation in option (c) does not have solution.
Part (3):
The equation is [tex]5+7x=11+7x[/tex].
Solve the above equation as follows:
[tex]\begin{aligned}5+7x&=11+7x\\7x-7x&=11-5\\0&\neq6\end{aligned}[/tex]
Therefore, the given equation has no solution.
Option (a)
Here, the value of [tex]x[/tex] is [tex]0[/tex].
But the equation [tex]5+7x=11+7x[/tex] has no solution.
So, option (a) is incorrect.
Option (b)
Here, the value of [tex]x[/tex] is [tex]14[/tex].
But the equation [tex]5+7x=11+7x[/tex] has no solution.
So, option (b) is incorrect.
Option (c)
In option (c) it is given that there are infinite number of solutions.
But the equation [tex]5+7x=11+7x[/tex] has no solution.
So, option (c) is incorrect.
Option (d)
In option (d) it is given that the solution does not exist.
As per our calculation the equation [tex]5+7x=11+7x[/tex] does not have any solution.
So, option (d) is correct.
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Answer details:
Grade: Middle school
Subject: Mathematics
Chapter: Linear equations
Keywords: Linear equations, linear equation in one variable, linear equation in two variable, slope of a line, equation of the line, function, real numbers, ordinates, abscissa, interval, open interval, closed intervals, semi-closed intervals, semi-open intervals, sets, range domain, codomain.
Simplify
-(2/3)(-9y)(3/2)(8x)(0)
A.
72xy
B.
–72xy
C.
72
D.
0
What is the rounded number for 0.6?
Answer:
1
Step-by-step explanation:
6 Is rounded to 10 like 0.6 is rounded to 1
The x-intercept of the line x = 3.5 is...?
Which is the converse of this conditional?
If it is appropriate, then I play golf.
A.
If it is appropriate, then I do not play golf.
B.
If I play golf, then it is appropriate.
C.
If I do not play golf, then it is appropriate.
D.
If it is not appropriate, then I play golf.
Which description represents the expression 3x + 4 ?
the sum of 3 times a number and 4
4 added to 3 plus a number
4 divided by the product of 3 and a number
4 less than 3 times a number
Answer:
first option
Step-by-step explanation:
To know this, let's begin with discarting options.
The expression is 3x + 4
This expression means that you have 3 times a number and then you add 4 to that number.
According to this, the second option states that to the number 4 you add the 3, in other words 4 + 3 and then a number. This cannot be the correct option.
The third option states a division, but we don't have in the expression any division, so, this is not the option.
The fourth option is the same as the second option with the difference that instead of adding you do a substract, which is not the case.
So with this we can conclude that the correct option is the first one, sum 3 times a number with 4.
the answer is (A) the sum of 3 times a number and 4