Answer:
B. A = 14
C = 4
Explanation:
The system of equation is:
A + 10C = 54
A + 9C = 50
So, we can solve for A using the first equation:
A + 10C = 54
A + 10C - 10C = 54 - 10C
A = 54 - 10C
Now, we can replace A by (54 - 10C) on the second equation, so:
A + 9C = 50
(54 - 10C) + 9C = 50
54 - 10C + 9C = 50
54 - C = 50
54 - C + C = 50 + C
54 = 50 + C
54 - 50 = 50 + C - 50
4 = C
Then, we can replace C by 4 and calculate A, so:
A = 54 - 10C
A = 54 - 10(4)
A = 54 - 40
A = 14
Therefore, the solution of the system is:
A = 14
C = 4
Question 2 1 Simplify. DO NOT PUT ANY SPACES IN YOUR ANSWER. Keep you answer in fraction form. -2/5t - 6+ 2/3t + 15
-2/5t - 6 + 2/3t + 15
Combining similar terms
(-2/5t + 2/3t) + (-6 + 15)
4/15t + 9
IN Date OUT IN OUT Employee Time Card: 7:30 10/1 11:30 4:15 12:00 John Apple 10/2 8:15 11:00 5:15 11:45 10/3 11:15 3:55 7:00 12:10 Dept: Cust. Serv. 4:30 10:55 12:00 6:25 10/4 NOTE: NO OVERTIME 1:30 5:00 12:45 10/5 6:00 TOTAL HOURS RATE per hour: $13.75 What is John's total pay for the week? deneaker notes
I can see it now
thank you
11:30-7:30= 4h
11:00-8.15=2:45h
11:15-7:00=4:15h
10:55-6:25=4:30h
10:45-6:00=4:45h
Total = 4+2.75+4.25+4.5+4.75=20.25
4:15-12:00=4:15h
5:15-11:45=5:30h
3:55-12:10=3:45h
4:30-12:00=4:30h
5:00-1:30=3:30h
Total = 4.25+5.5+3.75+4.5+3.5=21.5
Total hours = 21.5+20.25=41.75
ok, the total pay would be:
Rate per hour * total hours:
[tex]13.75\times41.75=574.0625[/tex]Did you get the same value? hello? are you still with me? ok
do you have any question? oh, remember: After our session, the answer is saved in your profile . My pleasure
I need your help know
Given the following data
Base area of the cone = 6cm
Height of the cone = 9 cm
The volume of a cone is given as
[tex]\begin{gathered} V\text{ = }\frac{1}{3}\cdot\text{ }\pi\cdot r^2\cdot\text{ h} \\ \text{where }\pi\text{ = 3.14},\text{ r = 6cm , and h = 9cm} \\ V\text{ = }\frac{1}{3}\cdot\text{ 3.14 }\cdot6^2\cdot\text{ 9} \\ V\text{ = }\frac{1}{3}\text{ x 3.14 x 36 x 9} \\ V\text{ = }\frac{3.14\text{ x 36 x 9}}{3} \\ V\text{ = }\frac{1017.36}{3} \\ V=339.1cm^3 \end{gathered}[/tex]Convert 7 liters into gallons using measurement conversion 1 liter= 1.0567 quarts. Round to two decimals
Convert 7 liters into gallons
We have the measurement conversion 1 liter= 1.0567 quarts
and the gallons = 4 quarts
So, 7 liters = 7 * 1.0567 quarts = 7.3969 quarts
We will convert from the quarts to gallons as follows:
1 gallons = 4 quarts
x gallons = 7.3969 quarts
so, the value of x will be:
[tex]x=\frac{7.3969}{4}=1.849225[/tex]Round to two decimals
so, the answer will be 1.85 gallons
The half-life of radium is 1690 years. If 70 grams are present now, how much will be present in 570 years?
Solution
Given that
Half life is 1690 years.
Let A(t) = amount remaining in t years
[tex]\begin{gathered} A(t)=A_0e^{kt} \\ \\ \text{ where }A_{0\text{ }}\text{ is the initial amount} \\ \\ k\text{ is a constant to be determined.} \\ \end{gathered}[/tex]SInce A(1690) = (1/2)A0 and A0 = 70
[tex]\begin{gathered} \Rightarrow35=70e^{1690k} \\ \\ \Rightarrow\frac{1}{2}=e^{1690k} \\ \\ \Rightarrow\ln(\frac{1}{2})=1690k \\ \\ \Rightarrow k=\frac{\ln(\frac{1}{2})}{1690} \\ \\ \Rightarrow k=-0.0004 \end{gathered}[/tex]So,
[tex]A(t)=70e^{-0.0004t}[/tex][tex]\Rightarrow A(570)=70e^{-0.0004(570)}\approx55.407\text{ g}[/tex]Therefore, the answer is 55.407 g
Determine the missing coordinates in the ordered pair (-1,?) so that it will satisfy the given equation
we have the equation
2x-3y=4
Remember that
if the ordered pair is a solution of the given equation, then the ordered pair must satisfy the given equation
we have the ordered pair (-1,a)
substitute the given coordinates in the equation
2(-1)-3(a)=4
-2-3a=4
solve for a
3a=-2-4
3a=-6
a=-2
therefore
the missing coordinate is -2
find the volume of a right circular cone that has a height of 4.3m and a base with a circumference of 17.6. round your answer to the nearest tenth
Answer:
Explanation:
The volume of a right circular cone can be found using the below formula;
[tex]V=\pi\times r^2\times\frac{h}{3}[/tex]where V = volume of the cone
r = radius of the base
h = height of the cone ne
Trini Cars break down on the highway.show me estimates that she is 20 to 30 miles from the nearest car repair shop she calls a towing company that charges a fee of $80 plus $3 per mile to tow a car.if training uses this towing company, which is the best estimate for the amount of money,m,she will pay for the company to tow her car.a .103 greater than sign and greater than sign 113 b.140 greater than sign M greater than sign 150 c.114 greater than 5 m greater than 170 d. 560 greater than 10 m > 70
We have that the cost is $80 plus $3 per mile, and also we now that the car is 20 to 30 miles from the car repair shop. So we have that Trini have to pay
[tex]\begin{gathered} 80\text{ + 3(20) }\leq\text{ M }\leq\text{ 80 + 3(30)} \\ 80\text{ + 60 }\leq\text{ M }\leq\text{ 80 + 90} \\ 140\text{ }\leq\text{ M }\leq170 \end{gathered}[/tex]So the answer is: b.140 greater than sign M greater than sign 150.
how many apples are in 4 dozen
There are 48 apples in 4 dozen
Explanations:1 dozen = 12
This means that:
1 dozen of apples = 12 apples
4 dozen = 12 x 4
4 dozen = 48 apples
See attachment for problem
The liters in the tank when it is filled to a height of 3.70 is 5,580 liters
The liters that needs to be added to 100% capacity is 480 liters
What is the volume?A right circular cone is a three dimensional object has a flat circular base that tapers to a vertex. The volume of a right circular cone is the amount of space in the right circular cone.
Volume of a cone = 1/3(πr²h)
Where:
π = pi = 3.14r = radius h = heightVolume of the right circular cone when its filled to a height of 3.70 = 1/3 x 3.14 x 3.70 x 1.20² = 5.58 m³
5.58 x 1000 = 5,580 liters
Volume of the right circular cone when it is full = 1/3 x 3.14 x 4 x 1.20² = 6.03 m³
6.03 x 1000 = 6030 liters
Liters that needs to be added to 100% capacity = 6030 liters - 5,580 liters = 480 liters
To learn more about the volume of a cone, please check: https://brainly.com/question/13705125
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I need help on answering 3. (d) I have two choices it can be which is false and sometimes true.
Question:
Solution:
If x represents a positive integer, then the point x is a natural number, that is, x is greater than zero, in particular, if x is a number greater than zero it can be a number greater than any number after zero. For example, it can be greater than 1.
Then the question d is ALWAYS TRUE.
The ship leaves at 18 40 to sail to the next port.
It sails 270 km at an average speed of 32.4 km/h
Find the time when the ship arrives.
Answer:
Step-by-step explanation:
Given:
t₁ = 18:40 or 18 h 40 min
S = 270 km
V = 32.4 km/h
____________
t₂ - ?
Ship movement time:
t = S / V = 270 / 32.4 ≈ 8.33 h = 8 h 20 min
t₂ = t₁ + t = 18 h 40 min + 8 h 20 min
40 min + 20 min = 60 min = 1 h
18 h +8 h = 26 h = 24 h + 2 h
2 h + 1 h = 3 h
t₂ = 3:00
The ship will arrive at the destination port at 3:00 the next day.
Answer:
32.4 - 27.0 = 5.4
18.40 + 54 =
7hrs:34mins
The ship arrived at
7:34pm
Which of these numbers is irrational?
✍️Record your work/explanation on your document or paper
Which of these numbers is irrational?
✍️Record your work/explanation on your document or paper
\sqrt{5}
5
\frac{3}{5}
5
3
-3.5
3.\overline{5}3.
5
The students of a school were asked to participate in a competition for making and decorating penholders in the shape of a cylinder with a base, using cardboard.Each penholder was to be radius of 3cm and height 10.5 cm. The school was to supply the competitors with cardboard. If there were 35 competitors, how much cardboard was required to be brought for the competition. Assume: pi = 22/7
Recall the surface area for the following figures.
[tex]\begin{gathered} \text{Cylinder}=2\pi rh+2\pi r^2 \\ \\ \text{The term }2\pi r^2\text{ includes a cover both the top and bottom of the cylinder} \\ \text{Since we will be using only the bottom modify the formula such that it only} \\ \text{includes the bottom part} \\ \\ \text{Pen Holder Surface Area}=2\pi rh+\pi r^2 \end{gathered}[/tex]Given that
height = h = 10.5 cm
radius = r = 3 cm
π = 22/7
Substitute the following given and we have the surface area for the pen holder
[tex]\begin{gathered} \text{Pen Holder Surface Area}=2\pi rh+\pi r^2 \\ \text{Pen Holder Surface Area}=2(\frac{22}{7})(3\operatorname{cm})(10.5\operatorname{cm})+(\frac{22}{7})(3\operatorname{cm})^2 \\ \text{Pen Holder Surface Area}=198\operatorname{cm}+(\frac{22}{7})(9\operatorname{cm}) \\ \text{Pen Holder Surface Area}=198\operatorname{cm}+\frac{198}{7}\operatorname{cm} \\ \text{Pen Holder Surface Area}=\frac{1584}{7}\operatorname{cm}^2 \end{gathered}[/tex]Now that we have the surface area, multiply it by 35 since there are 35 competitors in the competition
[tex]undefined[/tex]the ratio of red candies to Blue candies is 5:4 in the bag if there are 20 blue candies in the bag how many rare candies are there
The ratio of Red candies to Blue candies is 5:4 in the bag.
Sophia spent $40 on supplies to make 20 bracelets. She plans to sell them at a craft show for $5 each. Let y represent the amount of her profit. Is it discrete or continuous? And what are the domain and range?
we have that
y ------> the amount of her profit
x -----ghe number of bracelets
REmember that
Profit is equal to sell minus cost
so
y=5x-40
the domain is the interval (0,1,2,3,4,5) ------> is a discrete
the range is equal to
For x=
Solve this system of linear equations. Separatethe x- and y-values with a comma.18x - 10y = 749x - 9y = 45
Given,
[tex]\begin{gathered} \text{The system of pair of linear equation is,} \\ 18x-10y=74\ldots\ldots\ldots\ldots\ldots.\ldots.(i) \\ 9x-9y=45\ldots\ldots\ldots..\ldots\ldots\ldots.(ii) \end{gathered}[/tex]Multiplying equation (ii) by 2 as it make the coefficent of x in both equation equal.
[tex]\begin{gathered} 18x-10y=74\ldots\ldots\ldots\ldots\ldots.\ldots.(i) \\ 18x-18y=90\ldots\ldots\ldots..\ldots\ldots\ldots.(iii) \\ \end{gathered}[/tex]Substracting equation (i) from equation (iii) then we get,
[tex]\begin{gathered} 18x-18y-(18x-10y)=90-74 \\ 18x-18y-18x+10y=16 \\ -8y=16 \\ y=-2 \end{gathered}[/tex]The value of y is -2.
Substituting the value of y in equation (i) then,
[tex]\begin{gathered} 18x-10y=74 \\ 18x+20=74 \\ 18x=54 \\ x=3 \end{gathered}[/tex]Hence, the solution of the linear pair (x, y) is (3, -2).
Quadrilateral PQRS is plotted in the coordinate plane. The quadrilateral is dilated by a scale factor of 3/4. What are the new ordered pairs for P'Q'R'S'?
Explanation:
The first thing is to state the coordinates of Quadrilateral PQRS
P (5, 5), Q (3, 5), R (3, 1), S (5, 1)
Then we find the distance between two points using the distance formula
[tex]dis\tan ce\text{ = }\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2}[/tex][tex]\begin{gathered} P(5,5),Q(3,5)\text{ = (x1, y1) and (x2, y2)} \\ \text{distance PQ = }\sqrt[]{(5-5)^2+(3-5)^2}\text{ = }\sqrt[]{0+(-2)^2}\text{ =}\sqrt[]{4} \\ \text{distance PQ = }2 \end{gathered}[/tex][tex]\begin{gathered} Q(3,5),R(3,1)\text{= (x1, y1) and (x2, y2)} \\ \text{distance QR = }\sqrt[]{(1-5)^2+(3-3)^2}\text{ = }\sqrt[]{(-4)^2+0}\text{ = }\sqrt[]{16} \\ \text{distance QR = 4} \end{gathered}[/tex]It is a quadrilateral, meaning the two lengths are equal. Like wise the two widths are equal.
length PQ = length SR = 2
Length QR = length PS = 4
Scale factor = 3/4
Scale factor = corresponding side of new image/ corresponding side of original image
PQRS = original image, P'Q'R'S' = new image
3/4 = P'Q'/PQ
3/4 = P'Q'/2
P'Q' = 2(3/4) = 6/4 = 3/2
Since P'Q' = S'R'
S'R' = 3/2
3/4 = Q'R'/QR
3/4 = Q'R'/4
Q'R' = 3/4 (4) = 12/4 = 3
Since Q'R' = P'S
P (5, 5), Q (3, 5), R (3, 1), S (5, 1)
PQRS to P'Q'R'S' = 3/4(
P' = 3/4 (5, 5) = (15/4, 15/4)
Q' = 3/4 (3, 5) = (9/4, 15/4)
R' = 3/4 (3, 1) = (9/4, 3/4)
S' = 3/4 (5, 1)
2x + 4x = 3x + 3x Solve for x.
You have the following expression:
2x +4x = 3x + 3x
in order to solve for x, proceed as follow:
2x +4x = 3x + 3x simplify like terms both sides
6x = 6x
Due to the previous result is the trivial solution, it means that the equation has infinite solutions.
The path of the baseball follows the equation h= -4.9t^2 + 60t + 1.5 where h represents the height of the baseball, t seconds after the baseball was hit. How long will it take the baseball to return to the ground?
SOLUTION
Given the question in the question tab, the following are the steps to solve the problem:
Step 1: Write out the equation for the path of the baseball where h is height and t is time in seconds
[tex]h=-4.9t^2+60t+1.5[/tex]Step 2: Rewrite the new equation
The height of the baseball when it returns to the ground is zero(0). Therefore, at that point where the baseball returns to the ground, the function becomes:
[tex]0=-4.9t^2+60t+1.5[/tex]Step 3: We solve the quadratic equation to get the value of t:
[tex]\begin{gathered} 0=-4.9t^2+60t+1.5 \\ u\sin g\text{ quadratic formula which states that:} \\ x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ a=-4.9,b=60,c=1.5 \\ \text{Substituting the values, we have:} \\ \frac{-60\pm\sqrt[]{60^2-4(-4.9)(1.5)}}{2(-4.9)} \\ =\frac{-60\pm\sqrt[]{3600+29.4}}{-9.8} \\ =\frac{-60\pm60.2445}{-9.8} \\ =\frac{-60+60.2445}{-9.8}\text{ or }\frac{-60-_{}60.2445}{-9.8} \\ =\frac{0.2445}{-9.8}or\frac{-120.2445}{-9.8} \\ t=-0.024948979\text{ or }12.26984184 \\ t\approx-0.0249\text{ or 12.270} \end{gathered}[/tex]Since the value for time cannot be negative, hence the time it will it take the baseball to return to the ground is approximately 12.270 seconds
On its website a tv station displays temperature data for each hour during the past 24 hours. The data are displayed as using two different functions on a line graph. One function shows the current temperature and the other function shows the historical average. Which quantities are represented by the y-values on the line graph
, Given the question, we are asked to find which of the quantities are represented by the y-values on the line graph .
Explanation
In the question, we are told that the tv station displays temperature data using two different functions on a line graph. One of the functions shows the current temperature and the other function shows the historical average.
A function, by definition, can only have one output value(y) for any input value. In this case the input values are the time the temperature which we result in the output value of the historical average and temperature.
Therefore,
Answer
Option D
There are 6 dogs and 2 mice. Write a ratio for the number of ears to th number of paws. * 6:2 3 people are in a room. Write a ratio to represent the number of finger
each dog has 4 paws, then 6 dogs have 6*4 = 24 paws
each mouse has 4 paws, then 2 mice have 2*4 = 8 paws
Total number of paws: 24 + 8 = 32 paws
each dog has 2 ears, then 6 dogs have 6*2 = 12 ears
each mouse has 2 ears, then 2 mice have 2*2 = 4 ears
total number of ears: 12 + 4 = 16 ears
The ratio for the number of ears to the number of paws: 16/32 = 1/2 or 1:2
2) Add or subtract the following polynomials: (5pts each) 1) (98-7x' +5x-3)+(2x* +4x'-6x-8) = ii) (8x* +6x - 4x2 -2)-(3x* – 5x – 7x+9)=
When we are adding/subtracting polynomials, we add or subtract like terms.
For example,
x^2 added with x^2 terms
x^4 added with x^4 terms
numbers (constants) added with numbers etc.
2 i)[tex](9x^5-7x^2+5x-3)+(2x^4+4x^3-6x-8)[/tex]Since we are "adding" the 2nd parenthesis polynomial, we can take out the parenthesis and put them in order and them simply add/subtract(!) The steps are shown below:
[tex]\begin{gathered} (9x^5-7x^2+5x-3)+(2x^4+4x^3-6x-8) \\ =9x^5-7x^2+5x-3+2x^4+4x^3-6x-8 \\ =9x^5+2x^4+4x^3-7x^2+5x-6x-3-8 \\ =9x^5+2x^4+4x^3-7x^2-x-11 \end{gathered}[/tex]Note: there were like terms with "x's" and "constants". We added/subtracted them only.
the probability he chooses orange fruit
Consider that the total number of fruits are 10. The probability to get some fruit is given by the quotient in between the number of suc a fruit and the total number of fruits.
Then, at the first time, the probability of getting a kiwi is:
p1 = 1/10 = 0.1 (becasue there is one kiwi)
After the kiwi is taken out, the number of fruits are 9. In this case, the probability of getting one orange is:
p2 = 3/9 = 0.33 (because there are three oranges)
THe probability of the two previous events, that is, to obtain one kwi and then one orange is the product of the probabilities p1 and p2:
P = p1*p2 = (0.1)(0.33) = 0.03
Hence, the probabilty is approximately 0.03
Find F as a function of x and evaluate it at x = 2, x = 5 and x = 8.
Given:
[tex]F(x)=\int_2^x(t^3+6t-4)dt[/tex]Find-:
[tex]F(x),F(2),F(5),F(8)[/tex]Sol:
[tex]\begin{gathered} F(x)=\int_2^x(t^3+6t-4)dt \\ \\ \end{gathered}[/tex]Use integration then:
[tex]\begin{gathered} F(x)=\int_2^x(t^3+6t-4)dt \\ \\ F(x)=[\frac{t^4}{4}+\frac{6t^2}{2}-4t]_2^x^ \\ \\ \\ F(x)=\frac{x^4}{4}+3x^2-4x-\frac{2^4}{4}-3(2)^2+4(2) \\ \\ F(x)=\frac{x}{4}^4+3x^2-4x-8 \end{gathered}[/tex]The function value at x = 2 is:
[tex]\begin{gathered} F(x)=\frac{x^4}{4}+3x^2-4x-8 \\ \\ F(2)=\frac{2^4}{4}+3(2)^2-4(2)-8 \\ \\ F(2)=4+12-8-8 \\ \\ F(2)=16-16 \\ \\ F(2)=0 \end{gathered}[/tex]The function value at x = 5
[tex]\begin{gathered} F(x)=\frac{x^4}{4}+3x^2-4x-8 \\ \\ F(5)=\frac{5^4}{4}+3(5)^2-4(5)-8 \\ \\ F(5)=156.25+75-20-8 \\ \\ F(5)=203.25 \end{gathered}[/tex]Function value at x = 8
[tex]\begin{gathered} F(x)=\frac{x^4}{4}+3x^2-4x-8 \\ \\ F(8)=\frac{8^4}{4}+3(8)^2-4(8)-8 \\ \\ F(8)=1024+192-32-8 \\ \\ F(8)=1216-40 \\ \\ F(8)=1176 \end{gathered}[/tex]Explaining the Converse of the Pythagorean TheoremThe converse of the Pythagorean Theorem states that if the three sides of a triangle work for the equation a^2 + b^2 = c^2, then the triangle is a right triangle. To prove this, you can use what’s called a proof by contradiction. That is, you can prove something is true because it cannot be false.Start by assuming a triangle is not a right triangle and the sides work for the equation a^2 + b^2 = c^2. Here is a diagram of the triangle. Keep this diagram window open as you work on the tasks in this section.Now, create a right triangle with legs a and b. Call the hypotenuse n. Here is a diagram of the triangle. Keep this diagram window open as you work on the tasks in this section.questionsPart ASince triangle 2 is a right triangle, write an equation applying the Pythagorean Theorem to the triangle.Part BSince the equations for both triangles have a^2 + b^2, you can think of the two equations for c^2 and n^2 as a system of equations. Substitute what a^2 + b^2 equals in the first equation for a^2 + b^2 in the second equation. After you substitute, what equation do you get?Part CNow, take the square root of both sides of the equation from part B and write the resulting equation.Part DIs there any way for this equation to be true? How?Part EWhat does this show about the relationship between the two triangles?Part FDoes this mean that triangle 1 is a right triangle? Why or why not?
Part A: Since triangle 2 is a right triangle, write an equation applying the Pythagorean Theorem to the triangle.
Triangle 2 has the following sides: a, b and n
Writing it into an equation will be:
[tex]\text{ a}^2\text{ + b}^2\text{ = n}^2[/tex]The answer is a² + b² = n²
Part B: Since the equations for both triangles have a^2 + b^2, you can think of the two equations for c^2 and n^2 as a system of equations. Substitute what a^2 + b^2 equals in the first equation for a^2 + b^2 in the second equation. After you substitute, what equation do you get?
Equation 1 (Triangle 1): a² + b² = c²
Equation 2 (Triangle 2): a² + b² = n²
Substitute what a^2 + b^2 equals in the first equation for a^2 + b^2 in the second equation, it will be:
[tex]\text{ a}^2\text{ + b}^2\text{ = n}^2[/tex][tex]\text{ c}^2\text{ = n}^2[/tex]The answer is c² = n²
Part C : Now, take the square root of both sides of the equation from part B and write the resulting equation.
[tex]\text{ c}^2\text{ = n}^2[/tex][tex]\text{ }\sqrt{c^2}\text{ = }\sqrt{n^2}[/tex][tex]\text{ c = n}[/tex]The answer is c = n
Peri earned $55 for 5 dog walks. If Peri earned $22, how many times did she walk her neighbor's dog?
Answer:
2
Step-by-step explanation:
55÷5=11
22÷11=2
5. Joseph Cheyenne is earning an annual salary of $24,895. He has been offered the job in the ad. How much more would he earn per month if he is paid: a. the minimum? b. the maximum
Joseph has an annual salary of $24895 dollars and she get the new job that is between 28000-36000 dollars so:
the minimum will be:
[tex]24895+28000=52000[/tex]and the maximun will be:
[tex]24895+36000=60895[/tex]4y+3+6xWhat is the numerical coefficient of the first term?What is the constant term?
We are given the following expression:
[tex]4y+3+6x[/tex]The numerical coefficient is the number that multiplies a variable, in this case, the first variable is "y" and the numerical coefficient is 4.
The constant in an expression is the number that does not multiply any variable, in this case, the constant is 3.
Solve the inequality and write the solution using:
the inequality
