Yes, the pizza parlor charges a delivery fee and the equation describing the total amount Luke spends, d, to get p pizzas delivered is d = 10.60p.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
It is given that:
Luke gets pizza delivered from the same local pizza parlor every Thursday. This week, he ordered 3 pizzas for his family and spent $32.75.
Last week he ordered 4 pizzas and spent $41.50.
Each pizza costs when ordered 3 pizzas
= 32.75/3 = $10.91
Each pizza costs when ordered 4 pizzas
= 41.50/4 = $10.37
Yes, the pizza parlor charges a delivery fee.
= (41.50+32.75)/(3+4) = 10.60
d = 10.60p
Thus, yes, the pizza parlor charges a delivery fee and the equation describing the total amount Luke spends, d, to get p pizzas delivered is d = 10.60p.
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6. a right triangle has a line of symmetry. select all conclusions that must be true. a. all sides of the triangle have the same length. b. all angles of the triangle have the same measure. c. two sides of the triangle have the same length. d. two angles of the triangle have the same measure. e. no sides of the triangle have the same length. f. no angles of the triangle have the same measure.
Answer:
C.
D.
Step-by-step explanation:
For right triangle has a line of symmetry two sides of the triangle have the same length and two angles of the triangle have the same measure.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
A right angle triangle is a triangle in which one angle is a right angle, i.e., in which two sides are perpendicular.
If a right triangle has a line of symmetry then two sides of triangle will have same length and two angles are equal.
For a triangle to have a line of symmetry, it must be an isosceles triangle, meaning two of it’s sides and two of it’s angles must be the same.
From there it follows that for a right triangle to have a line of symmetry it must be an isosceles right triangle, meaning it must either have two 90-degree angles, or two identical non-90-degree angles.
Hence for right triangle has a line of symmetry two sides of the triangle have the same length and two angles of the triangle have the same measure.
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which option please help
Step-by-step explanation:
when lines are parallel gradiant should be the same in both equations
or m in y=mx+c
A)
1. y=-3x-6
2. y=-3x+6
therefore A is parallell
B)
1. y=44x+7/2
2.y=2/3x-17
therefore not parallel
c)
1. y=8x/7-17/7
2. y=-23x/21+30/21
therefore not parallel
d)
1. y=-8x/7+6
y=-7x/8-12
therefore not parallel
might have missed something-am tired. let me know if you have an issue.
a_1=4 and an=a_{n-1}+6
The value of the fifth term based on the expression a + (n - 1) + 6 is 14.
How to calculate the value?From the information, it should be noted that the first term has been given and the nth series has been given.
It should be noted that the fifth term will be:
= a + (n - 1) + 6
where
a = 4
n = 5
Therefore, a + (n - 1) + 6
= 4 + (5 - 1) + 6
= 4 + 4 + 6
= 14
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a_1=4 and an=a + {n-1}+6. Find the fifth term
Estimate each value to the nearest whole number.
5.4²
Hey there!
(5.4)^2
= 5.4^2
= 5.4 * 5.4
= 29.16
Therefore, your answer should be:
29.16
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
On a slow weekend, you spend at least two hours on homework. on a busyweekend, you spend as much as five hours on homework. write an ablosue value inequality that repersents the number of hours you spend doing homework on a typical week day. math problem
The absolute value inequality that represents the number of hours spent on doing homework is 2 ≤ x ≤ 5
Let us assume that one spends x hours doing homework on a typical weekday. Then we can write
The inequality expression for a slow weekend is given as;
X ≥ 2
In the same vein, the inequality expression for a busy weekend is given as;
X ≤ 5
Pooling the two inequalities expression we have;
2 ≤ x ≤ 5
Two inequality expression could be written simultaneously if they can be expressed individually. They are commonly referred to as a “double” inequality and is often written in the form a ≤ f (x) ≤ b
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Me ayudan? La necesito para mañana
Answer:
1. 9/10 x 3 = 93/10
2. 9/8
Espero que esto ayude a tener un buen día!
A teacher asked students why it is necessary to check for extraneous roots when squaring both sides of the equation. Which of the following answers is the best? Is this answer complete? Explain.
(A) Because the squared equation can have negative roots.
B) Because squaring is multiplication, and any multiplication is a potential source of extraneous roots.
(C) Because when you square both sides of the equation, you add to the solution set the roots of the equation a=-b .
(D) Because any operation with an equation may result in extraneous roots.
Because the squared equation can have negative roots.
If the equation you're given already includes the squared variable (and you don't multiply by the variable yourself), then you don't need to worry about the extraneous root. Both solutions will be correct because the variable was already squared.
You only need to worry about the extraneous root in the case of a quadratic equation if you made the equation quadratic by multiplying by a variable. Any time you square a negative number or a variable (which may be negative), you risk losing information by making it positive. That means that, if you square a variable (especially for variables on both sides of the equation, which can easily hide a negative) or a negative number, you should always do a quick plug-in and check.
Because the squared equation can have negative roots.
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Which postulate proves these two triangles are congruent
The postulate that proves the triangle are congruent is hypotenuse-leg (HL) congruency theorem.
What is a triangle?A triangle is a polygon that has three angles and three sides. The sum of angles in a triangle is 180 degrees.
Types of triangles are isosceles, scalene and equilateral triangles. Two angles are said to be complementary if their sum is 90 degrees.
Two triangles are said to be congruent if all their corresponding sides and angles are congruent. This means that the triangles have equal angles and equal sides.
The postulate that proves the triangle are congruent is hypotenuse-leg (HL) congruency theorem.
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Use the properties of exponential and logarithmic functions to solve each system. Check your answers.
log (2 x-y)=1
log (x+y)=3 log 2
The solved logarithmic function is 2x - y = e and x + y = 8 for log (2x - y) = 1 and log (x + y) = 3 log 2 respectively.
What is a logarithmic and exponential function?
Logarithmic functions and exponential functions are inverses of each other. The logarithmic function is denoted by using the word log while exponential by using the alphabet, e. For example log 10 = 1 and e^2.
Solving the given expressions: log (2x - y) = 1 and log (x + y) = 3 log 2
Applying given properties of logarithmic and exponential function;
log a + log b = log (ab)
4 log x = log x⁴
e^(log x) = 1
e^(x + y) = (e^x) × (e^y)
Take expression, log (2x - y) = 1
Applying exponential on both sides, we get,
e^(log 2x - y) = e^1
2x - y = e
To Check Results,
Taking logarithm both sides,
log (2x - y) = log e
log (2x - y) = 1
Thus, the answer is verified.
Take expression, log (x + y) = 3 log 2
Applying exponential on both sides, we get,
e^(log (x + y) = e^(3 log 2)
x + y = e^(log 8)
x + y = 8
To Check Results,
Taking logarithm both sides,
log (x + y) = log 8
log (x + y) = 3 log 2
Thus, the answer is verified.
Hence, the solved expression is 2x - y = e and x + y = 8 for log (2x - y) = 1 and log (x + y) = 3 log 2 respectively.
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Ms. Moya has received 13 Starbucks cards from students and generally gets 2 more
each year she teaches. Ms. Powers has only ever been given 1 Starbucks gift card but
plans to get 5 more each year she teaches. Which equation models the situation to find
the number of years before they have the same number of Starbucks cards?
Answer:
13+2=15+2=17+2=19+2=21
1+5=6+5=11+5=16+21
(The Pink Answer)
my non-blurry pic. Sorry, the other one was so blurry.
14. Constant of variation, k = 3/2
15. The graph does not represent a direct variation.
16. Constant of variation, k = 1/4
17. Constant of variation, k = 1
What is a Direct Variation?A direct variation is a proportional relationship where variable x varies directly with variable y. The equation of a direct variation is modelled by the equation below:
y = kx.
k is the constant of proportionality of the relationship between x and y. It is also referred as the unit rate. On a proportional or direct variation graph, it can be determined by using any point on the graph (x, y) to find k.
k = y/x.
How to Determine a Graph that Represents a Direct Variation?All graphs that represent direct variations passes through the origin (0, 0). The coordinate of the constant of proportionality of a direct variation graph is (1, k), where the constant of variation = k, and x = 1.
14. The graph passes through the origin (0, 0), so it represents a direct variation.
Constant of variation, k = 3/2
15. The graph does not pass through the origin (0, 0), so it does represent a direct variation.
16. The graph passes through the origin (0, 0), so it represents a direct variation.
Constant of variation, k = 1/4
17. The graph passes through the origin (0, 0), so it represents a direct variation.
Constant of variation, k = 1
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For a result to be considered _____, the chances of its occurring as a result of random error are often less than 5 percent.
For a result to be considered significant, the chances of its occurring as a result of random error are often less than 5 percent.
What is Random error?A coincidental discrepancy between the observed and true values of anything is known as a random error (e.g., a researcher misreading a weighing scale records an incorrect measurement).
It's not always a mistake when there is random error; rather, it happens when measurements are made. Even when you measure the same item repeatedly, there will always be some variation in your results because to changes in the environment, the instrument, or your own perceptions.
Your measurements are equally likely to be greater or lower than the genuine values due to random error, which has unexpected effects.
According to the given data,
For a result to be considered significant, the chances of its occurring as a result of random error are often less than 5 percent.
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Suppose your teacher offers to give the whole class a bonus if everyone passes the next math test. The teacher says she will give everyone a 10-point bonus and increase everyone's grade by (9%) of their score.
a. You earned a 75 on the test. Would you rather have the 10 -point bonus first and then the \(9 \%\) increase, or the (9%) increase first and then the 10 -point bonus?
b. Is this the best plan for all students? Explain.
Function f(x) to represent the 10-point bonus. f(x) = x+10
Function g(x) to represent the 9% increase. g(x) = X +0.09x
g(x) = 1.09x
Use a composite function to find your grade if the 10-point bonus is applied before the 9% increase.
(g.f)x = g(f(x))
f(75) = 85
g(85) = 92.65
Use a composite function to find your grade if the 9% increase is applied before the 10-point bonus.
(f.g)(x) = f(g(x))
g(75) = 1.09(75) = 81.75
f(x) = 81.75+10 = 91.75
You would want 10 point bonus applied before percentage increase. the 10 point bonus is flat increase.
whereas the percentage increased larger if multiplying by a bigger number your grade would be almost 1% higher with is option
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Carol has a balance of $520 in her checking account. She writes three
checks each for $120 from the account. She also deposits 2 paychecks for
$240 each. What is her balance now?
w
dealer in
stail
Answer:
$640
Step-by-step explanation:
3 checks at $120 each = 3 x 120 = $360
This will reduce the balance so we should treat it as -360
2 paychecks at 240 = 2 x 240 = $480
This will increse the balance so we should treat it as +480
Net balance = 520 - 360+480=640
Balance = $640
Someone help with this question
The the simplified form of the given expression 12.5 - 31/2 + 1 1/4 is -7/4.
Hence, option D) -7/4 is the correct answer.
What is the simplified form of the given expression?
Given the expression in the question;
12.5 - 31/2 + 1 1/4
First, convert the mixed fraction into an improper fraction.
1 1/4 = ( 1×4 + 1 )/4 = ( 4 + 1 )/4 = 5/4
Now, rewrite the expression as;
12.5 - 31/2 + 5/4
Find the common denominator
( 12.5/1 × 4/4 ) - ( 31/2 × 2/2 ) + ( 5/4 × 1/1 )
( 12.5/1 × 4/4 ) - ( 31/2 × 2/2 ) + ( 5/4 × 1/1 )
Perform the multiplication operation
50/4 - 62/4 + 5/4
Now, combine the numerators over the common denominator.
( 50 - 62 + 5 )/4
( -12 + 5 )/4
( -7 )/4
-7/4
The the simplified form of the given expression 12.5 - 31/2 + 1 1/4 is -7/4.
Hence, option D) -7/4 is the correct answer.
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5. Table Item The table shows the time and
distance Hector walked in a 5-kilometer-long
walk for charity. The distance is proportional
to the time walked. Complete the table to
show the times of his last three walks.
(Lesson 3)
Distance (km) Time (min)
1.5
13.5
2010
4.5
5
The distance being proportional to the time Hector walked 2 km in 18 minutes.
Two variables are proportional if they can be written in the form ak=b where k is the proportionality constant.
Here the proportionality constant is speed.
Speed is defined as the distance covered in unit time. The unit of speed can be written as kilometer per hour, miles per hour or meters per second.
The distance is proportional to the time walked therefore:
1.5/2=13.5/T₁
or, T₁=18
Similarly:
1.5/4.5=13.5/T₂
or, T₂=40.5 minutes
again,
1.5/5=13.5/T₃
or, T₃=45 minutes.
Hence the total time taken to complete the distances 2,4.5 and 5 is given by 18,40.5 and 45 minutes.
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4x - 11x + 32 = 4 if the value for x is 5
Answer:
no solution or -3=4
Step-by-step explanation:
Solve for t -7/4= 5/2t
Solve for T
Answer:
t=−7/6
I hope this helps.
Find the equation of the straight line passing through the point (3, 3)
which is perpendicular to the line
y=-1/2x-4
The equation of the straight line passing through the point (3, 3)
which is perpendicular to the line y=-1/2x-4 is y= 2x-3
What is the equation of line?A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept.
The equation for a straight line is y = mx + c. (1)
The line is parallel to the equation y=-1/2 x-4 ....(2),
meaning that the value of m in equation (1) is 2 y = 2x + c
The needed line has the equation y= 2x-3 since it goes through the point (3,3) where 3=2(3)+c provides c=-3.
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Ifa box of apples is distributed among 28 children , each gets 3 . iF 7 children were not present , their share would also ne distriibuted among the others How many apples would each children get
Answer:
First subtract 28 by 7.
28 - 7 = 21
Then multiply 28 times 3
28 times 3 is 84
Then finally divide 84 by 21
84/21 = 4
Each of the children would get 4 apples
Step-by-step explanation:
AB= 6 cm, AC = 12 cm
Calculate the length of CD.
Give your answer to 3 significant figures.
C
D
55°
12 cm
B 6 cm
Applying the sine ratio, the length of CD is calculated as: 12.687 cm.
How to Apply the Sine Ratio?The sine ratio is stated as:
sin ∅ = opposite length / hypotenuse length of a right triangle.
Use the Pythagorean theorem to find BC:
BC = √(AC² - AB²)
AC = 12 cm
AB = 6 cm
Plug in the values
BC = √(12² - 6²)
BC = √(144 - 36)
BC = √108
Find the length of CD using the sine ratio:
∅ = 55
Opposite length = BC = √108
Hypotenuse length = CD
Substitute
sin 55 = √108/CD
(CD)(sin 55) = √108
CD = √108/sin 55
CD ≈ 12.687.
Therefore, applying the sine ratio, the length of CD is calculated as: 12.687 cm.
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The price of an item plus 6% sales tax
The expression of the statement is 1.06x
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to determine the expression of the statement?The statement is given as
The price of an item plus 6% sales tax
Let the price of the item be x
So, we have the sales tax amount to be
Sales tax amount = x * 6%
Evaluate the product
So, we have
Sales tax amount = 0.06x
So, the total amount is
Total = x + 0.06x
Evaluate the sum
So, we have
Total = 1.06x
Hence, the expression of the statement is 1.06x
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Can someone help me with this please? I need the answers and the work shown please... thank you!
Answer:
Below
Step-by-step explanation:
Ok, there is a few ways to slove this problem. You could just try to plug in both xs and see which is true, or you could actually do the math. I will do the math.
Alright, the first question is a corrseponding angle, so they are equal to each other. Set it up like this:
3x-1=x+5
Now, you need to get the variable by itself, so do that.
3x-1=x+5
+1 +1
3x=x+6
-x -x
2x=6
/2 /2
x=3
The arrow will go to the right.
Now, you have a same side exterior angle. When you add these together, they will equal 180 degrees, so set up the equation like this.
8x+10+6x+2=180
Now, solve
8x+10+6x+2=180
Combine like terms (8x+6x)+(10+2)
14x+12=180
-12 -12
14x=168
/14 /14
x=12
Your arrow will go down.
Same side interior angles is your next problem, and it is like same side exterior angles as it equal 180. Set up your equation accordingly
10x-8+5x+8=180
Combine like terms (10x+5x)+(8-8)
15x=180
/15 /15
x=12
Your arrow will go down.
These are opposite side exterior angles, so they will equal each other. Set up the equation accordingly.
9x+18=10x-8
Get the variable on one side and by themselves
9x+18=10x-8
+8 +8
9x+26=10x
-9x -9x
26=x
Your arrow will go upper corner right
This problem is opposite side exterior angles, so they will equal each other. Set up the equation accordingly.
2x+5=3x-7
+7 +7
2x+12=3x
-2x -2x
12=x
Your arrow will go up
Now, you have a same side exterior angle. When you add these together, they will equal 180 degrees, so set up the equation like this.
8x+5+2x-15=180
Combine like terms (8x+2x)+(5-15)
10x-10=180
+10 +10
10x=190
/10 /10
x=19
Arrow goes diagonal right down
The angles are opposite side interior angles, so they are equal to each other. Set up your equation like this:
4x-4=-3x+52
+4 +4
4x=-3x+56
+3x +3x
7x=56
/7 /7
x=8
That is your finish!
What is the solution of (x+2)³/₄=27 ?
(A) x=27 (B) x=79 (C) x=81 (D) x=83
The solution (B) x=79.
Rewriting the equation to find the solution -
(x+2)³/₄=27
Raising both sides of the equation with exponent ⁴/₃
((x+2)³/₄)⁴/₃ = 27⁴/₃
Cancelling the exponents on Left Hand Side of the equation. Writing the value on Right Hand Side of the equation in exponent form
x + 2 = (3³)⁴/₃
Cancelling 3 on Right Hand Side of the equation
x + 2 = 3⁴
Solving Right Hand Side of the equation
x + 2 = 81
Shifting 2 to Right Hand Side of the equation
x = 81 - 2
Performing subtraction on Right Hand Side of the equation
x = 79
Hence, the solution is (B) x=79.
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Solve each equation.
2⁵x⁺¹=32
After solving the equation, x = 4/5 is the value of x in [tex]2^{5x+1} = 32[/tex]
⇒ [tex]2^{5x+1} = 32[/tex]
⇒ [tex]2^{5x+1} = 2^5[/tex]
⇒ 5x + 1 = 5
⇒ 5x = 5 - 1
⇒ 5x = 4
⇒ x = 4/5
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
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Eight times a number plus 5 times another number is -13. The sum of the two numbers is 1. What are the numbers?
Answer:
One number is -6 and the other number is 7.
Step-by-step explanation:
Let x be one of the numbers and y be the other number.
So 8x + 5y = -13.
Also, x + y = 1
These two equations are the algebraic version of the words in the problem.
We need to solve this system of equations. You may be studying solving systems of equations using substitution or elimination method or even matrices. I will show you here using elimination method, sometimes called addition or subtraction method.
We need to multiply x+y=1 by -5.
-5(x + y = 1)
-5x - 5y = -5
We can stack the two equation and add them together to eliminate one of the variables.
8x + 5y = -13
-5x - 5y = -5
___________ Add.
3x = -18
3x = -18 Now divide by 3.
x = -6
Put thus value back into one of the original equations.
x = -6
x + y = 1
Substitute.
-6 + y = 1
Add 6.
y = 7
When one number is -6 and the other number is 7, then both equations will be true.
help
Which expression is equivalent to 5(2.47y − 2.03)?
12.35y + 10.15
12.35y − 10.15
12.35y + 2.03
12.35y − 2.03
Step-by-step explanation:
I will first expand. Whatever is in the brackets will be multiplied by 5=5(2,47y)+5(-2,03)
=12.35y-10,15
Please help!!
Find the values of x and y that make k || j and
m || n.
x= ?
y= ?
For x = 80 and y = 130, l and m will be parallel to j and n respectively.
If two lines are parallel, then the sum of the interior angles is supplementary.
Thus, if m || n, then (x - 30) and (x + 50) will be supplementary
⇒ (x - 30) + (x + 50) = 180
x - 30 + x + 50 = 180
2x + 20 = 180
2x = 180 - 20
2x = 160
x = 80
Thus, if x = 80, then k will be parallel to l
Now, if m || n, then y and (x - 30) must be supplementary
⇒ (x - 30) + y = 180
x - 30 + y = 180
we found that x = 80
⇒ 80 - 30 + y = 180
50 + y = 180
y = 180 - 50
y = 130
Thus, if y = 130 then, k will be parallel to l.
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If y varies directly as x and y= 64 when x=4 find x when y=48
Answer:
If y varies directly as x and y= 64 when x=4 find x when y=48
x=3
Write the phrase as an expression. Twice a number w
Answer: w2
Step-by-step explanation:
It is just w2, or w*2, or w x 2. You just have the number w twice.