The number of people who can still have a hot dog is 82 people
Given:
Total hot dogs bought = 8 dozens
1 dozen = 12Total hot dogs bought = 8 × 12
= 96
Number of hot dogs his pet ate = 14
Each guests eats one hot dogNumber of guests who are hotdog = Total hot dogs bought - Number of hot dogs his pet ate
= 96 - 14
= 82
Therefore, the number of people who can still have a hot dog is 82 people
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Which absolute value function, when graphed, represents
the parent function, f(x) = |xl, reflected over the x-axis and
translated 1 unit to the right?
5 -4 -3 -2 -1
1
2
3
4
5
f(x) = -1 | + 1
f(x) = -x-11
f(x) = |-*1 + 1
f(x) = |-* - 11
anche
Save and Exit
Answer:
f(x) = -|x| + 1
Step-by-step explanation:
f(x) = |xl when reflected over the x-axis is f(x) = -|x|.
When reflected over x-axis a graph becomes negative in y value.
f(x) = -|x| then translate 1 unit to the right is f(x) = -|x| + 1. Adding 1 translates the graph towards the right because the positive x-axis is on the right.
Solve the system by graphing. Write the solution as an ordered pair.
y = –3x + 3
y = 12x – 4
The solution on the graph is the coordinate of the point where both lines intersect
Given the equation of two lines expessed as;
y = -3x + 3 and y = 12 x - 4
Since both expressions ara y values, equating both will give;
-3x + 3 = 12x - 4
-3x - 12x = -4 - 3
-15x = -7
x = 7/15
Substitute x = 7/15 into any of the equatons;
y = -3x + 3
y = -3(7/15) + 3
y = -7/5 + 3
y = 8/5
Hence the solution as an ordered pair is (7/15, 8/15)
The solution on the graph is the coordinate of the point where both lines intersect as shown in the graph below;
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Solve linear equations :
Solve step by step for each one
7. 10n - 11 = 3 + 4n + 6n
8. -8(k + 4) = -96
9. -6(2k + 5) + 7k = -6 + 7k
Answer: 7.) Wrong Question
8.) 8
(9.) - 2
Step-by-step explanation:
7.) 10n - 11 = 3 + 4n + 6n
Collect like terms
10n - 4n - 6n = 3 + 11
10n - 10n = 14
It's not possible to have zero n = 14
8.) -8(k + 4) = - 96
Exland the bracket
-8k - 32 = - 96
Collect like terms
-8k = - 96 + 32
-8k = - 64
Divide through by -8
-8k/-8 = - 64/-8
k = 8
9.) -6(2k + 5) + 7k = -6 + 7k
Open the bracket
-12k - 30 +7k = -6 + 7k
Collect like terms
-12k + 7k - 7k = - 6 + 30
-12k = 24
Divide both sides by -12
-12k/-12 = 24/-12
k = -2
Solve using a suitable inverse operation:
A) a/5= -2
I just want to know what this means and how to do it.
Answer:
a = - 10
Step-by-step explanation:
Given
[tex]\frac{a}{5}[/tex] = - 2
a is divided by 2. The inverse operation to division is multiplication, thus
Multiply both sides by 5 to clear the fraction
a = 5 × - 2 = - 10
how do you write six times the quantity two x plus three y with numbers??
Answer:
12x + 18y
Step-by-step explanation:
Lets first write the quantity "two x plus three y", this means, that we have x and y as unknowns. x is 2 times, so we have 2x; and y is 3 times, so he have 3y:
2x + 3y
Additionally we have that this quantity is six times, what means that it is multiplied by a number 6:
6(2x +3y)
If you like, we can apply the distributive property that means that given any three numbers a, b, c we have that a(b+c)=ab + ac. In our case a is 6, b is 2x and c is 3y. Thus, operating:
6(2x +3y) = 6*2x + 6*3y = 12x + 18y
So, "six times the quantity two x plus three y" is 12x + 18y
The cost of having one pizza delivered is $14. Each additional pizza cost $9 more. Write the explicit and recursive formula to represent the situation.
Answer:
14 +(9×x) = y x being the number of pizzas that are not the first one and y is the amount it all cost
Answer:
See explanation below:
Step-by-step explanation:
Here we want to express the number of pizza delivered. Lets try to understand the case.
If we buy one pizza (p1) the cost is 14 because of the delivery plus 9 for the cost of the pizza. So:
p1 = 14 + 9 = 23
If we buy 2 pizzas (p2) we have to pay 14 for the delivery and 9 for each pizza:
p2 = 14 + 9 + 9 = 14 + 2*9 = 32
If 3 pizzas are bought (p3) the reasoning is the same, 14 for the delivery and 9 for each pizza:
p3 = 14 + 9 + 9 + 9 = 14 + 3*9 = 41
Here we can see a pattern: for any amount of pizzas n the cost will be 14 plus n-times 9, the price of a pizza. It is:
pn = 14 + 9*n
But we can separate the last equation in such a way:
pn = 14 + 9*(n-1) + 9 , as 9*(n-1) + 9 = 9*n
But if our general formula it true, the first to terms on the right are the vost of buying n-1 pizzas, so:
pn = pn-1 + 9
We can keep on separating terms as we did to arrive to this form, this is, separating the 9n in 9*(n-2) + 9*2, 9*(n-3) + 9*3, ..., 9*(n-m) + 9*m for any m < n . Here I will keep pn = pn-1 + 9 as the Recursive Formula, but you could use other formulation with, e.g., pn-2, pn-3, etc, using the above recursion.
Now, the explicit formula is such that gives as the value of any amount, finding all the terms of the sequence with those not depending on previous terms (contrary to the recursive). This formula was showed above and is: pn = 14 + 9*n. This is, given any number of pizzas we can find the cost without knowing the cost of previous values.
So, we have:
Recursive: pn = pn-1 + 9
Explicit: pn = 14 + 9*n
The lengths of the sides of a triangle are6, 8, 10. Can the triangle be a right triangle?
Answer:
Yes
Step-by-step explanation:
Another way of stating the question: Does the Pythagorean Theorem apply here? Does 6^2 + 8^2 = 10^2?
Does 36 + 64 = 100? YES
Yes, this is a right triangle.
Answer: Yes. That is because it fits the requirements of the Pythagoream Therom:
6^2+8^2 10^2
36+64 100
100 = 100 :)
five numbers that have 3, 7, and 13 as prime factors
Step-by-step explanation:
(3)(7)(13) = 273
(3)(3)(7)(13) = 819
(3)(7)(7)(13) = 1911
(3)(7)(13)(13) = 3549
(3)(3)(3)(7)(13) = 2457
(3)(7)(7)(7)(13) = 13377
(3)(7)(13)(13)(13) = 46137
....
Which postulate proves these two triangles are congruent ?
Answer:
HL
Step-by-step explanation:
HL is used for right triangles that are congruent. These two triangles are congruent(the same) and they happen to be right triangles, therefore, HL.
The postulate that proves the triangle are congruent is hypotenuse-leg (HL) congruency theorem.
Here, we have,
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.
here, we have,
HL is used for right triangles that are congruent.
These two triangles are congruent(the same) and they happen to be right triangles, therefore, HL.
The postulate that proves the triangle are congruent is hypotenuse-leg (HL) congruency theorem.
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Maura runs 5 miles in 1.25 hours. Ava runs 3 miles in 0.83 hours. Who runs faster?
Answer:
Maura runs faster
Step-by-step explanation:
To avoid decimals ,multiply all by 100
Maura 500 mi/125h = 4 mi/h
Ava 300 mi /83 h =3.61445.....mi/h
Answer:
still from 2019
wsp my dude
Step-by-step explanation:
Grant has 2/3
of ice cream in a bowl. He then removes two 1/6
cups of ice cream to share with his little br
amount of ice cream left in Grant's bowl?
Answer: 2/6 or 1/3
Step-by-step explanation:
2/3 = 4/6. 1 /6 Two times is 2/6 so by subtracting you should get 2/6 or 1/3
find the value for x.
Answer: x = -13
=========================
Work Shown:
19 = 38/2
19 & 1/2 = 19 + 1/2
19 & 1/2 = 38/2 + 1/2
19 & 1/2 = (38+1)/2
19 & 1/2 = 39/2
-------
In the original equation, replace the "19 & 1/2" with "39/2" to get
(5/2)x + (1/2)x = 39/2 + (9/2)x
Each term involves a fraction with a denominator of 2. If we multiply both sides by the common denominator, then the fractions will cancel out
For example: 2*(5/2)x = (10/2)x = 5x
So after multiplying both sides by 2, you should have this new equation
5x + 1x = 39 + 9x
--------
Let's solve that latest equation for x
5x + 1x = 39 + 9x
6x = 39 + 9x
6x-9x = 39 + 9x-9x ... subtract 9x from both sides
-3x = 39
-3x/(-3) = 39/(-3) .... divide both sides by -3
x = -13
10. Estimate by rounding -5 2/5+9 8/11-3 5/6
Answer:
0.5
Step-by-step explanation:
-5 2/5=-27/5
9 8/11=107/11
-3 5/6=-23/6
--------------------
-27/5+107/11-23/6
-27/5-23/6+107/11
-162/30-115/30+107/11
-277/30+107/11
-3047/330+3210/330=163/330=0.493=0.5
What should the following rate be divided by to convert it to a unit rate?
6 inches
12 hours
Answer:
so if all of the awnsers are whole numbers it is going to be 12/12
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
Unit rate is a rate that has 1 as denominator.
Given the rate: 6 inches / 12 hours, we have to divide numerator and denominator by 12 to transform the denominator in 1, as follows:
[tex]\frac{6}{12} = \frac{6/12}{12/12} =[/tex] 0.5 inches/hour
what is the answer because am stuck
Answer:
30 Oranges!
Step-by-step explanation:
Given that for every 2 apples there are 3 oranges.
How many oranges would be there in a basket of 20 apples?
Since for every couple of apples we have 3 oranges we will calculate how many couples of apples are there in the basket.
Given there are 20 apples. This means that there are [tex]$ \frac{20}{2} $[/tex] = 10 pairs of apples.
Since for one pair we have three oranges, for 10 pairs we would have 3 X 10 = 30 oranges.
Therefore, we can conclude that the number of oranges in the bigger basket would be 30.
Bills annual salary is 2/3 of Jen's annual salary.if bills salary is$64,000, what is Jen's salary?
Answer:
$96,000
Step-by-step explanation:
To find Jen's annual salary, divide Bill's annual salary of $64,000 by 2/3, resulting in Jen's salary being $96,000.
Explanation:To calculate Jen's annual salary based on the information that Bill's annual salary is 2/3 of Jen's, first express Bill's salary as a fraction of Jen's:
Let J represent Jen's annual salary.According to the problem, we have that Bill's salary equals 2/3 of Jen's, so (2/3)*J = $64,000.To find Jen's salary J, divide Bill's salary by 2/3, so J = $64,000 / (2/3).After calculation, J = $64,000 * (3/2), which simplifies to J = $96,000.Therefore, Jen's annual salary is $96,000.
What is the equation of the line that is perpendicular to the y-axis and contains the point (-2,7)
A: y=-x+5
B: x=-2
C: y=x+9
D: y=7
Answer:
y = 7
Step-by-step explanation:
The straight line which is perpendicular to the y-axis will be either x-axis or parallel to the x-axis.
Now, the general equation for all straight line which is either x-axis or parallel to x-axis are given by y = c ........... (1), where c is any constant.
For c = 0 the line will be x -axis. therefore, y = 0, is the equation of x-axis.
Now, if the line (1) passes through the point (-2, 7), then the equation will be y = 7. (Answer)
{Since, the point (-2,7) will satisfy the equation (1) and then c will be equal to 7.}
h/2 + 3 = 3(h/4 - 1)
Answer:
h=24
Step-by-step explanation:
h/2+3=3(h/4-1)
h/2+3=3h/4-3
h/2-3h/4=-3-3
2h/4-3h/4=-6
-h/4=-6
-h=-6*4
-h=-24
h=24
A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 350 cubic
centimeters of soup. The sides and bottom of the container will be made of styrofoam costing 0.03 cents per square
centimeter. The top will be made of glued paper, costing 0.08 cents per square centimeter. Find the dimensions for
the package that will minimize production cost.
Helpful information:
To minimize the cost of the package:
Radius:
Height:
Minimum
To minimize production cost, we need to find the dimensions of the package that will satisfy the volume equation and minimize the cost equation. Taking the partial derivatives of the cost equation with respect to the variables 'r' and 'h', and setting them equal to zero, we can find the critical points. Solving these equations, we find that the dimensions for the package that will minimize production cost are a height of 7 cm and a radius of 2.5 cm.
Explanation:To find the dimensions of the package that will minimize production cost, we need to consider the cost of the sides and bottom made of styrofoam and the cost of the top made of glued paper. Let's denote the radius of the base of the cylinder as 'r' and the height of the cylinder as 'h'.
The volume of a cylinder is given by the formula V = πr²h. We know that the volume of the package needs to be 350 cubic centimeters, so we can write the equation as πr²h = 350.
The cost of the sides and bottom of the container is given by the formula C1 = 0.03 * (2πrh + πr²), and the cost of the top is given by the formula C2 = 0.08 * πr².
To minimize the cost, we need to find the values of 'r' and 'h' that satisfy the volume equation and minimize the cost equation.
Since this is a calculus problem, we will differentiate the cost equation with respect to 'r' and 'h', and set the derivatives equal to zero to find the critical points.
Taking the partial derivatives of C1 and C2 with respect to 'r' and 'h', we get:
∂C1/∂r = 0.03 * (2πh + 2πr) = 0∂C1/∂h = 0.03 * (2πr) = 0∂C2/∂r = 0.08 * (2πr) = 0∂C2/∂h = 0Solving these equations, we find that h = 7 cm and r = 2.5 cm. Therefore, the dimensions for the package that will minimize production cost are a height of 7 cm and a radius of 2.5 cm.
There are 70 students attending summer camp, 21 girls and 49 boys. What is
the ratio of girls to boys at summer camp?
O A. 7:3
O B. 3:7
O 6. 2:1
SUBMIT
The height of a skydiver jumping out of an airplane is given by h=16t +3200
Answer:
The answer is yes :)
Step-by-step explanation:
Brenda recorded a temperature of 19°C, and Cooper recorded a temperature 17°C higher. What temperature did Cooper record?
Answer:
Cooper recorded a temperature of 36° C.Step-by-step explanation: If you add 19 and 17 together you get 36.
Hope this helps! :)
A scientist measured the wavelength of an X-ray as 0.0000000065 meters. Write the number in scientific notation.
Answer:
[tex]6.5 \times 10^{-9}[/tex]
Step-by-step explanation:
The scientific notation of a number is to express the number in the form [tex]x\times 10^{y}[/tex] where x is the base of ten.
So, if we want to express the number 0.0000000065, then we can write it as
[tex]\frac{6.5}{1000000000} = 6.5 \times 10^{-9}[/tex].
So, we can write 0.0000000065 as [tex]65\times 10^{-10}[/tex] or [tex]0.65 \times 10^{-8}[/tex] but those are not the scientific notation.
Therefore, [tex]6.5 \times 10^{-9}[/tex] is the scientific notation of 0.0000000065. (Answer)
Urgent!!! Triangle ABC has angles the following angle measures. m<A=2x+7 , m<B=10x+10 and m<C=8x+23. what is the value of x and what is the measure of each angle?
x=
m<A=
m<B=
m<C=
Answer:
The Value of x= 7.
m∠A= 21°
m∠B= 80°
m∠C= 79°
Step-by-step explanation:
Given:
m∠A = 2x+7
m∠B = 10x+10
m∠C = 8x+23
We need to find the value of x and measures of each angle.
Now by angle sum property which states that sum of all angles of a triangle are 180°.
Hence from above statement we can say in ΔABC;
m∠A+m∠B+m∠C=180
Now substituting the given values in above equation we get;
[tex]2x+7+10x+10+8x+23=180\\2x+10x+8x+7+10+23=180\\20x+40=180\\20x=180-40\\20x=140\\\\x=\frac{140}{20} =7[/tex]
Hence value of x is 7.
Substituting the value of x in all angles we get;
m∠A=[tex]2x+7=2\times7+7=14+7=21\°[/tex]
m∠B=[tex]10x+10=10\times7+10=70+10=80\°[/tex]
m∠C=[tex]8x+23= 8\times7 +23 = 56+23=79\°[/tex]
Final answer:
To find the value of x and the measure of each angle in triangle ABC, set up an equation using the given angle measures. Solve for x and substitute it back in to find the measures of each angle. Then : m<A = 2(7) + 7 = 21 degrees
m<B = 10(7) + 10 = 80 degrees
m<C = 8(7) + 23 = 79 degrees
Explanation:
To find the value of x and the measure of each angle in triangle ABC, we need to set up an equation using the given angle measures. Since the sum of the angles in a triangle is 180 degrees, we can write the equation as:
m<A + m<B + m<C = 180
Substituting the given angle measures, we have:
(2x + 7) + (10x + 10) + (8x + 23) = 180
Simplifying the equation:
20x + 40 = 180
Subtracting 40 from both sides:
20x = 140
Dividing both sides by 20:
x = 7
Now that we know the value of x, we can find the measure of each angle by substituting x into the respective expressions:
m<A = 2(7) + 7 = 21 degrees
m<B = 10(7) + 10 = 80 degrees
m<C = 8(7) + 23 = 79 degrees
no one helped me with the last question but i got it can someone help me with this
y = 2x
Step-by-step explanation:
The linear functions are given by:
y = mx+b
To find the slope, we have to find the change in x and y
The change in x is:
[tex]-14-(42) =-14+42 =28\\14+14= 28[/tex]
The change in y is:
[tex]-28-(-84) = -28+84 = 56\\28-(-28) = 28+28 = 56[/tex]
The slope is:
[tex]Slope = \frac{change\ in\ y}{Change\ in\ x}\\=\frac{56}{28}\\= 2[/tex]
Putting slope in equation of linear function
[tex]y =2x+b[/tex]
To find the value of b, we will put any pair of input and output in the slope-intercept form
So, putting (14,28)
[tex]28 = 2(14) + b\\28 = 28+b\\b = 28-28\\b = 0[/tex]
Hence,
the linear equation for function is:
y = 2x
Keywords: Linear function, slope intercept form
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How can I factor 24 + 32x
Answer:
8(3+4x)
Step-by-step explanation:
it it can be pulled out of both 24 and 32.
When the solution of x2 + 9x − 9 is expressed as 9 plus or minus the square root of r, all over 2, what is the value of r? x equals negative b plus or minus the square root of b squared minus 4 times a times c, all over 2 times a
A: 117
B: 54
C:45
D: 9
Answer:
The answer is option A. 117
Step-by-step explanation:
The general solution of the quadratic equation is:
[tex]x=\frac{-b \pm \sqrt{b^2-4ac} }{2a}[/tex]
The given equation is x2 + 9x − 9 is expressed as minus 9 plus or minus the square root of r, all over 2
Comparing to the general solution
∴ r = determinant = b² - 4 a c
From the given equation: a = 1 , b = 9 and c = -9
∴ r = 9² - 4 * 1 * (-9) = 81 + 36 = 117
The answer is option A. 117
Answer:
117
Step-by-step explanation:
how do i solve this
Answer:
y = -2x + 3
Step-by-step explanation:
Slope-intercept equation of a line is:
y = mx + b
where m is the slope and b is the y intercept.
Here, m = -2 and b = 3.
y = -2x + 3
Franklin Construction Company build a sidewalk around two sides of a new library, as shown in the figure. what is the area of the sidewalk.
please help
Answer:
[tex]630.36\ ft^2[/tex]
Step-by-step explanation:
we know that
To find out the area of the sidewalk, multiply the length by the width of the sidewalk
The width of the sidewalk is equal to
[tex]113.4\ ft-110\ ft=3.4\ ft[/tex]
or
[tex]75.4\ ft-72\ ft=3.4\ ft[/tex]
The area is equal to
[tex]113.4(3.4)+72(3.4)\\385.56+244.8\\630.36\ ft^2[/tex]
20 pts! A line passes through (3, 7) and (6, 9). Which equation best represents the line?
y = 3 over 2 x + 5
y = 2 over 3 x + 5
y = 3x + 2
y = 2 over 3 x + 2
Answer:
y = 2 over 3 x + 5
Step-by-step explanation:
m= y2-y1/x2-x1
m= (9-7)/(6-3)
m=2/3
y=mx+b
y= 2/3x+b
(3,7)
7=2/3(3)+b
7=6/3+b
7=2+b
5=b
b=5
y=2/3x+5