The formula to calculate the volume of a prism is given as
[tex]V=\text{Base Area }\times Height[/tex]The volume is given as 45 and the height is 9.
Hence, we can get the base area as
[tex]\begin{gathered} A=\frac{V}{h} \\ A=\frac{45}{9} \\ A=5 \end{gathered}[/tex]Therefore, the area of the base is 5 ft².
The correct option is OPTION B.
Consider parallelogram QRST below.Use the information given in the figure to find m ZR, x, and m ZROS.R.4x1275040°7S
The opposite angles of a parallelogram are equal, therefore:
[tex]\begin{gathered} m\angle R=m\angle T \\ so\colon \\ m\angle R=75 \end{gathered}[/tex]Opposite sides of a parallelogram are parallel and equal so:
[tex]\begin{gathered} QT=RS \\ 4x=12 \\ x=\frac{12}{4} \\ x=3 \end{gathered}[/tex]∠TSQ and ∠RQS are alternate interior angles, therefore:
[tex]\begin{gathered} m\angle RQS=m\angle TSQ \\ so_{}\colon \\ m\angle RQS=40 \end{gathered}[/tex]Find sectheta costheta, and cottheta where theta is the angle show in the figure
We will have the following:
We first determine the missing side of the triangle:
[tex]x=\sqrt{17^2-8{}^2}\Rightarrow x=15[/tex]Now, we determine the expressions:
[tex]\begin{gathered} sec(\theta)=\frac{17}{8} \\ \\ \\ cos(\theta)=\frac{8}{17} \\ \\ \\ cot(\theta)=\frac{8}{15} \end{gathered}[/tex]Part 1: Person A has a car with the average fuel consumption of 20 miles per gallon. Person B has an average fuel consumption of 30 miles per gallon. Person C has an average fuel consumption of 40 miles per gallon. they are trying to work out how much fuel they will each save if they change cars. Person A, " I am going to buy Person B's car." Person B says, " I am going to buy Person C's car." Person C says that each week they will both save the same amount of fuel.Is person C correct? Part 2: Person C wants to buy a new car. Each week, he wants to save the same amount of fuel as person A saved. What average fuel consumption should person C look for in a new car?
Let's assum that each person drives 120 miles per week.
Then for person A we have:
[tex]\begin{gathered} 20mi\rightarrow1\text{gal} \\ 120mi\rightarrow xgal \\ \Rightarrow x=\frac{120}{20}=6gal \\ x=6\text{gal} \end{gathered}[/tex]for person B we have:
[tex]\begin{gathered} 30mi\rightarrow1gal \\ 120mi\rightarrow xgal \\ \Rightarrow x=\frac{120}{30}=4gal \\ x=4\text{gal} \end{gathered}[/tex]finally, for person C:
[tex]\begin{gathered} 40mi\rightarrow1gal \\ 120mi\rightarrow xgal \\ \Rightarrow x=\frac{120}{40}=3gal \\ x=3\text{gal} \end{gathered}[/tex]Then, if person A changes to person B's car, we have that the save is:
[tex]6-4=2[/tex]if person B buys person C's car, then the save is:
[tex]4-3=1[/tex]therefore, the savings on gas will be different for both of them and person C is incorrect.
2)Since person A saved 2 gallons, then the new car for Person C must save 2 gallons for each mile traveled.
Then we have the following equation:
[tex]3-x=2[/tex]where 'x' represents the number of gallons consumed in 120 miles. then, solving for x we have:
[tex]\begin{gathered} 3-x=2 \\ \Rightarrow-x=2-3=-1 \\ \Rightarrow-x=-1 \\ x=1 \end{gathered}[/tex]therefore, person C will need to buy a car that uses 1 gallon for eah 120 miles traveled
133/ 12 i need the answer
We will have:
[tex]\frac{133}{12}=11.08333\ldots\approx11[/tex]The fraction is approximately 11.
. Which of the following points are solutions of 5y – 2x ≤ 9?A. both (–3, 1/5), and (5, –17.6)B. (5, –17.6) onlyC. (–3, 1/5) onlyD. both (0, 2) and (5, –17.6)
we have the inequality
5y – 2x ≤ 9
Remember that
If an ordered pair is a solution to the inequality, then the ordered pair must satisfy the inequality
so
Verify each ordered pair
1) (–3, 1/5)
substitute in the given inequality
5(1/5) – 2(-3)x ≤ 9
1+6 ≤ 9
7 ≤ 9 -----> is true
that means ----> the ordered pair is a solution
2) (5, –17.6)
5(-17.6) – 2(5) ≤ 9
-88-10 ≤ 9 ------> is true
that means ----> the ordered pair is a solution
3) (0, 2)
5(2) – 2(0) ≤ 9
10 ≤ 9 -----> is not true
The ordered pair is not a solution
therefore
The answer is
A. both (–3, 1/5), and (5, –17.6)Completing a race) Ned spent 63 minutes walking 11 while If the ratio of time walking to jogging was 9:1, race? 2 minutes did he spend completing the
While completing the race, Ned spent 63 min walking if the ratio of time walking to jogging was 9:1, how many minutes did he spend completing the race?
Let
x-----> time spent walking
y -----> tiime spent jogging
we have
x/y=9/1
x=9y -----> equation A
we have
x=63 min
substitute in the equation A
63=9y
solve for y
y=7 minutes
therefore
teh answer is
7 minutesGiven the right triangle find the value of sec(90 degree - theta) when a= 12, b= 5, c= 13
Use the next trigonometric identities:
[tex]\begin{gathered} \sec (90º-\theta)=\frac{1}{\cos (90º-\theta)} \\ \\ \cos (90º-\theta)=\sin \theta \end{gathered}[/tex]Then, the sec(90º - θ) is:
[tex]\sec (90º-\theta)=\frac{1}{\sin \theta}[/tex]The sin(θ) is:
[tex]\sin \theta=\frac{opposite}{hypotenuse}=\frac{5}{13}[/tex]Then:
[tex]\sec (90º-\theta)=\frac{1}{\frac{5}{13}}=\frac{13}{5}[/tex]Then, the sec(90º - θ) is 13/5.a. Triangle ABC with coordinates A (3, 4), B (7,7), and C (8, 1) is translated 6 units left and 7 units down.
Triangle ABC with coordinates A (3, 4), B (7,7), and C (8, 1) is translated 6 units left and 7 units down.
we have that
the rule of the translation is
(x,y) -------> (x-6, y-7)
Applying the rule to the coordinates of triangle ABC
A(3,4) ------> A'(3-6,4-7)
A'(-3,-3)
B(7,7) ------> B'(7-6, 7-7)
B'(1,0)
C(8,1) --------> C'(8-6,1-7)
C'(2,-6)
Line Segment WV has an endpoint at (5, -7) and the midpoint is at (-3, 2). What are the coordinates of the other endpoint? Write your answer as an ordered pair: (x, y)
Answer:
Step-by-step explanation: it is that
4. A farmhouse shelters no more than 12 animals. Some are goats and some are ducks.Altogether there are more than 34 legs. How many of each animal could there be?What are you being asked to find?What are you given?Define your variables.Create & solve a system.Explain your solution(s).
• What are you being asked to find? define your variables
We are being asked to find the number of goats and ducks that there might be in the farmhouse.
• What are you given?
,•
From the information given by the question, we know that there are as many as 12 animals and that they have as many as 34 legs.
• Create & solve a system
from the given information we can write two expressions, one for the total number of animals, which equals 12, and another for the number of legs, let's call x to the number of goats and y to the number of ducks.
We know that there are a total of 12 animals, this is the number of goats plus the number of ducks, then we can write the expression:
goats + ducks = 12
x + y = 12
0.
And we know that there are 34 legs since a duck has 2 legs and a goat has 4, the number of legs of all the ducks would be the number of ducks times 2 and the number of legs of all the goats is 4 times the number of goats, then we can express the equation:
goat's legs + duck's legs = 34
4x + 2y = 34
Then, the system of equations that we have to solve is:
1. x + y = 12
2. 4x + 2y = 34
Now let's solve the system of equations, by following these steps:
Solve for y from the first equation:
x+y=12
x-x+y=12-x
y=12-x
Replace the expression y=12-x into the second equation and find the value of x.
4x + 2y = 34
4x+2(12-x)=34
4x+2*12-2x=34
4x+24-2x=34
2x+24=34
2x+24-24=34-24
2x=10
2x/2=10/2
x=5
Now that we know that x equals 5, let's replace it into the expression y=12-x, to find the value of y:
y=12-x
y=12-5=7
Then, x equals 5 and y equals 7
• Explain your solution
,•
In the farmhouse could there be a total of 5 ducks and 7 goats
Is my answer correct? 3/4 + 9/16 = 3/16
Answer:
is not correct because the lcm will be 16 and u will get 21/16
i added the choices for the first box as well.
Looking at the triangles, we see that they have two congruent sides, and the angles between them are congruent too.
Then, the two triangles are related by side-angle-side (SAS), so the triangles are congruent (SAS theorem).
Question 5 of 10According to this diagram, what is cos 16°?
Explanation
We are given the following:
We are required to determine the value of cos 16° from the diagram given.
We know that according to the trigonometry ratio rules:
[tex]\cos\theta=\frac{adjacent}{hypotenuse}[/tex]So, we have:
[tex]\cos16\degree=\frac{24}{25}[/tex]Hence, the answer is:
[tex]\cos16\operatorname{\degree}=\frac{24}{25}[/tex]Solve the Equation: -6x=12Your answer
Answer:
x = -2
Step-by-step explanation:
Divide both sides by the coefficient of x, which is -6
= -6x/-6 = 12/-6
x = -2
A car travels 120 miles on 10 gallons of gas. At this rate, how many gallons will it need to travel 312 miles?
26 gallons
1) We can write this information setting up a proportion
miles gallons
120 10
312 x
2) Assuming the pace hasn't changed, then we can consider that as proportional:
120x = 312 * 10
120x= 3120
x = 3120/120
x =26
3) So 26 gallons are going to be needed for those 312 miles.
Simplify the Expression [tex]12g + 3 - g {}^{2} + 2[/tex] g=4
done
Find the geographic mean between each pair of numbers. A. 28 and 14. B. 7 and 36
In order to find the geographic mean between each of this pair of numbers, first we would have to define what is the geographic mean.
The geographic mean is the average of a set of numbers.
Therefore, the geographic mean for A. 28 and 14 would be:
Geographic mean (28,14)= (28*14)^0.5
=(392)^0.5=19.798990
The geographic mean for B. 7 and 36 would be:
Geographic mean (7,36)=(7*36)^0.5
=(252)^0.5=15.874508
So, Geographic mean for (28,14) would be 19.798990 and for (7,36) would be 15.874508
What is the slope-intercept form of the line with the point (0, 3) and a slope = -2?O A. y = 2x + 3O C. y = -2x + 3D. y = -2x - 3B. y = 2x - 3
The form of the linear equation is
[tex]y=mx+b[/tex]m is the slope
b is the y-intercept
The given equation is
[tex]y=-2x+3[/tex]Compare it with the form above to find m and b
Since the coefficient of x is -2, then
m = -2
Since m is the slope of the line, then
The slope of the line is -2
The answer is B
Item Price (dollars) $1,400 $2,400 $3,000 $4,400 Sales Tax (dollars) $112 $192 $240 $352 Based on the table, what is the rate of change? O The rate of change for the sales tax is $0.07 per dollar. O The rate of change for the sales tax is $0.08 per dollar. O The rate of change for the sales tax is $0.06 per dollar. The rate of change for the sales tax is $0.125 per dollar.
We know that the rate of change is a rate that describes how one quantity changes in relation to another quantity. If x is the independent variable and y is the dependent variable, then
[tex]r\text{ = }\frac{Change\text{ in y}}{\text{Change in x}}\text{ = }\frac{Y2-Y1}{X2-X1}[/tex]where (X1,Y1) and (X2,Y2) are points of our model.
So, in this case we have that:
[tex]r\text{ = }\frac{Y2-Y1}{X2-X1_{}}\text{ = }\frac{112-352}{1400-4400}\text{ = }\frac{240}{3000}\text{ = 0.08}[/tex]So, the correct answer is: the rate of change for the sales tax is $0.08 per dollar.
Linus leaves his house and walks 7 blocks West to avoid Lucy. He then walks 3 blocks North to visit Charlie Brown. What is the shortest distance between the houses? Round to the nearest tenth.
First, draw a schematic representation of that situation:
The shortest distance between the starting point (Linus's house) and the endpoint (Charlie's house) is a straight line. Since a right triangle is formed with the sides of length 7 blocks and 3 blocks, we can use the Pyhtagorean Theorem to find the length of the hypotenuse:
[tex]\begin{gathered} ?=\sqrt[]{3^2+7^2} \\ =\sqrt[]{9+49} \\ =\sqrt[]{58} \\ \approx7.6 \end{gathered}[/tex]Therefore, the shortest distance between those two points would be 7.6 blocks.
logitechExample 6:Triangle XYZ is graphed below. Draw and label Triangle X'Y'Z' after a dilation using a scale factor oftwo.I.113XWhat will be the coordinates of point Y" after a reflection of polygon X'Y'Z' over the x-axis?Answer
First answer:
Second Answer:
The coordinates of the Y'' after reflection of poligon X'Y'Z' over the x axis: (-2, -4)
John has 44 quarters.Jan has 100 dimes. Whohas more money?
Note that 10 dimes = $1
Also 4 quarters = $1
That means, 100 dimes equals $10
Also, 44 quarters =
3. The height of a projectile object fired into the air can be modeled by h(t) = -16t² + 48t + 3, where his
height, in feet, and t is time, in seconds. What is the maximum height the projectile will reach?
A. 3 feet
B. 35 feet
C. 39 feet
D. 105 feet
Answer:
C. 39 feet
Step-by-step explanation:
[tex]{ \tt{h(t) = - 16 {t}^{2} + 48t + 3 }}[/tex]
- Let us find the limits of the function
[tex] { \tt{ \frac{d \{h(t) \}}{dt} = - 32t + 48 }} \\ [/tex]
- So, let us differentiate for the second time;
[tex]{ \tt{ \frac{d {}^{2} \{h(t) \} }{dt {}^{2} } = - 32}} \\ [/tex]
- So, at maximum height; d{h(t)}/dt is 0;
[tex]{ \tt{ - 32t + 48 = 0}} \\ { \tt{ - 32t = - 48}} \\ { \tt{t = 1.5 \: seconds}}[/tex]
- Therefore; maximum height is;
[tex]{ \tt{h(t) = - {16t}^{2} + 48t + 3}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ { \tt{h(1.5) = - 16(1.5) {}^{2} + 48(1.5) + 3}} \\ { \tt{h(1.5) = - 36 + 72 + 3}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ { \tt{h(1.5) = 39 \: feet}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
i need help with math
Answer:
x = 33
Step-by-step explanation:
Creating an equation
The angles shown are corresponding angles
Corresponding angles are angles that occupy the same position and are on the same side of the transversal. For a better sense of this, kindly review the attached image.
Corresponding angles are congruent ( equal to each other )
This means that 124 = 4x - 8
Solving for x
124 = 4x - 8
==> add 8 to both sides
132 = 4x
==> divide both sides by 4
33 = x
1. If a line AB is translated in a plane to form A'B', what is true?AB = BBAA = BBA'A' = B'BAA' = BB'
ANSWER
[tex]AA\text{'}=BB\text{'}[/tex]EXPLANATION
We have that line AB is translated in a plane to form line A'B'.
When a line/figure is translated, its shape and size do not change, which means that the distance between corresponding points on the pre-image and image must remain the same.
In other words, the distance between A and A' must be equal to the distance between B and B'.
Therefore, the correct answer is:
[tex]AA\text{'}=BB\text{'}[/tex]What is the the quotient of 23.7 and 0.8?
A quotient is the result of the division of two numbers. The given numbers are 23.7 and 0.8. Thus,
Quotient = 23.7/0.8
Quotient = 29.625
3. Find the median, range, and interquartile range for this data set. 21, 31, 26, 24, 28. 26 Median: Range: IQR:
The given data set is 21,31,26,24,28,26.
Arranging the data set in the ascending order,
21,24,26,26,28,31.
The data set contains 6 numbers,
The median can be determined by taking the average of 3rd and 4th term of the data set,
[tex]\begin{gathered} \text{Median}=\frac{26+26}{2} \\ =26 \end{gathered}[/tex]Thus, the required median is 26.
The range can be determined by taking the difference between the highest and the lowest value of the data set,
[tex]\begin{gathered} \text{Range}=31-21 \\ =10 \end{gathered}[/tex]Thus, the range of the data set is 10.
The interquartile range of the data set can be determined by taking the difference of quartile 1 and quartile 3.
[tex]\begin{gathered} \text{IQR}=Q_3-Q_1 \\ =28-24 \\ =4 \end{gathered}[/tex]Thus, the required interquartile range is 4.
The function h is defined by h (x)=3x² - 4.Find h (3x).
When we have a function f(x) we can evaluate it for different arguments (the value of x) by replacing the argument in the definition of the function.
In this case, we know h(x) and we have to express h(3x). To do this, we replace x in the original function with 3x:
[tex]\begin{gathered} h(x)=3x^2-4 \\ h(3x)=3(3x)^2-4=3\cdot(3^2x^2)-4=3\cdot9x^2-4=27x^2-4 \end{gathered}[/tex]Answer: h(3x) = 27x²-4
This pentagonal prism is cut by the plane shown. The plane is parallel to the base of the pentagonal prism. What is the shape of the cross-section?
If the plane is parallel to the base, then the cross section has the same shape of the base: a penthagon.
Find the circumference of a circle with a Diameter = 12 m. Use 3.14 for π and round to 2 decimal places. ANS. C= B_____________. m
The circumference of a circle is given by the formula
[tex]s=2\cdot\pi\cdot r[/tex]however we also knos that the diameter can be written as
[tex]D=2\cdot r[/tex]meaning that the formula for the circumference can also be written as
[tex]s=D\cdot\pi[/tex]then the circumference for the given information is:
[tex]\begin{gathered} s=12\cdot3.14 \\ s=37.68 \end{gathered}[/tex]