Answers
Answer:
Step-by-step explanation:
Maybe
2x times 11x
Related Questions
A car can travel 28 miles per gallon of gas. How far can the car travel on 8 gallons of gas?
Answers
A car can travel 28 miles per gallon of gas. How far can the car travel on 8 gallons of gas?
Applying proportion
28/1=x/8
solve for x
x=(28)*8
x=224 miles
the answer is 224 milesIn a probability experiment, Craig rolled a six-sided die 62 times. The die landed on a number greater than three 36 times. What is the ratio of rolls greater than three to rolls less than or equal to three?
Answers
Answer:
31/55
Step-by-step explanation:
an equation that shows that two ratios are equal is a(n)
Answers
An equation that shows that two ratios are equal is referred to as a true proportion.
What is an Equation?This refers to as a mathematical term which is used to show or depict that two expressions are equal and is usually indicated by the sign = .
In the case in which the equation shows that two ratios are equal is referred to as a true proportion and an example is:
10/5 = 4/2 which when expressed will give the same value which is 2 as the value which makes them equal and is thereby the reason why it was chosen as the correct choice.
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Four points are labeled on the number line. M K L zo 0.5 1 Which point best represents 3? F. Point K G. H. Point 2 Point M Point N J.
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The point that best represents 1/3 is point M .
The number line ranges from 0 to 0.5 with 10 divi
Evaluate 2(x - 4) + 3x - x^2 for x = 2.O A. -6O B. -2O C. 6O D. 2
Answers
C. 6
Explanation
To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number.so
Step 1
given
[tex]2(x-4)+3x-x^2[/tex]a)let
[tex]x=2[/tex]b) now, replace and calculate
[tex]\begin{gathered} 2(x-4)+3x-x^2 \\ 2(2-4)+3(2)-(2^2) \\ 2(-2)+6-4 \\ -4+6-4 \\ -4+6-4=6 \end{gathered}[/tex]therefore, the answer is
C. 6
I hope this helps you
Find the output, f, when the input, t, is 7 f = 2t - 3 f = Stuck? Watch a video or use a hint.
Answers
Answer:
f=11
Explanation:
Given the function:
[tex]f=2t-3[/tex]When the input, t=7
The value of the output, f will be gotten by substituting 7 for t.
[tex]\begin{gathered} f=2t-3 \\ =2(7)-3 \\ =14-3 \\ f=11 \end{gathered}[/tex]The output, f is 11.
Aaquib can buy 25 liters of regular gasoline for $58.98 or 25 liters of permimum gasoline for 69.73. How much greater is the cost for 1 liter of premimum gasolinz? Round your quotient to nearest hundredth. show your work :)
Answers
The cost for 1 liter of premium gasoline is $0.43 greater than the regular gasoline.
What is Cost?This is referred to as the total amount of money and resources which are used by companies in other to produce a good or service.
In this scenario, we were given 25 liters of regular gasoline for $58.98 or 25 liters of premium gasoline for $69.73.
Cost per litre of premium gasoline is = $69.73 / 25 = $2.79.
Cost per litre of regular gasoline is = $58.98/ 25 = $2.36.
The difference is however $2.79 - $2.36 = $0.43.
Therefore the cost for 1 liter of premimum gasoline is $0.43 greater than the regular gasoline.
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find 2x:3y if x:y = 2:5
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4 : 15
Explanation:[tex]\begin{gathered} \text{x : y = 2: 5} \\ \frac{x}{y}\text{ = }\frac{2}{5} \\ \\ 2x\text{ : 3y = ?} \end{gathered}[/tex][tex]\begin{gathered} 2x\colon\text{ 3y = }\frac{2x}{3y} \\ 2x\colon3y\text{ = }\frac{2}{3}\times\frac{x}{y} \end{gathered}[/tex][tex]\begin{gathered} \text{substitute for x/y in 2x:3y} \\ \frac{2}{3}\times\frac{x}{y}\text{ =}\frac{2}{3}\times\frac{2}{5} \\ =\text{ }\frac{4}{15} \\ \\ \text{Hence, 2x:3y = }\frac{4}{15} \\ or \\ 4\colon15 \end{gathered}[/tex]212385758487✖️827648299199375
Answers
Answer:
1.7578071e+26
Step-by-step explanation:
Choose the algebraic description that maps ΔABC onto ΔA′B′C′ in the given figure.Question 7 options:A) (x, y) → (x + 4, y + 8)B) (x, y) → (x + 8, y + 4)C) (x, y) → (x – 4, y – 8)D) (x, y) → (x + – 8, y – 4)
Answers
Step 1
Given the triangle, ABC translated to A'B'C'
Required to find the algebraic description that maps triangle ABC and A'B'C'
Step 2
The coordinates of points A, B,C are in the form ( x,y)
Hence
[tex]\begin{gathered} A\text{ has a coordinate of ( -3,-2)} \\ B\text{ has a coordinate of (-6,-5)} \\ C\text{ has a coordinate of (-1,-4)} \end{gathered}[/tex]Step 3
Find the algebraic description that maps triangle ABS TO A'B'C'
[tex]\begin{gathered} A^{\prime}\text{ has a coordinate of (5,2)} \\ B^{\prime}\text{ has a coordinate of ( 2,-1)} \\ C^{\prime}\text{ has a coordinate of ( 7, 0)} \end{gathered}[/tex]The algebraic description is found using the following;
[tex]\begin{gathered} (A^{\prime}-A^{})=(x^{\prime}-x,\text{ y'-y)} \\ OR \\ (B^{\prime}-B)=(x^{\prime}-x,\text{ y'-y)} \\ OR \\ (C^{\prime}-C)=(x^{\prime}-x,\text{ y'-y)} \end{gathered}[/tex]Hence,
[tex]\begin{gathered} =\text{ ( 5-(-3)), (2-(-2))} \\ =(8,4) \\ \text{Hence the algebraic description from triangle ABC to A'B'C' will be } \\ =(x,y)\Rightarrow(x\text{ + 8, y+4)} \end{gathered}[/tex]Hence the answer is option B
what is the area if one of the triangular side of the figure?
Answers
Compound Shape
The shape of the figure attached consists on four triangles and one square.
The base of each triangle is B=12 cm and the height is H=10 cm, thus the area is:
[tex]A_t=\frac{BH}{2}[/tex]Calculating:
[tex]A_t=\frac{12\cdot10}{2}=60[/tex]The area of each triangle is 60 square cm.
Now for the square of a side length of L=12.
The area of a square of side length a, is:
[tex]A_s=a^2[/tex]Calculate the area of the square:
[tex]A_s=12^2=144[/tex]The total surface area is:
A = 60*4 + 144
A= 240 + 144
A = 384 square cm
If y = (x/x+1)5, then dy/dx
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The value of dy/dx is 5x^4 / (x + 1)^6.
What is the derivative?
A function's sensitivity to change with respect to a change in its argument is measured by the derivative of a function of a real variable.
The given function is y = (x / (x + 1))^5
Taking derivative on both sides,
dy/dx = d/dx (x / (x + 1))^5)
Using chain rule,
dy/dx = 5(x / x + 1)^4 x d/dx (x / x + 1)
Using the quotient rule of derivative,
d/dx (x / x + 1) = 1 / (x + 1)^2
So,
dy/dx = 5(x / x+1)^4 x (1 / (x + 1)^2)
dy/dx = 5x^4 / (x + 1)^6
Therefore, the derivative of the given function is, dy/dx = 5x^4 / (x + 1)^6.
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i will drop a picture
Answers
B) y= -1/2x -4
1) Let's start by picking two points from that line: (0,3) and (-2,-1). Now we can plug them into the slope formula and find out the slope of that line:
[tex]m=\frac{y_2-y_1}{x_2-x_1}\Rightarrow m=\frac{-1-3}{-2-0}=\frac{-4}{-2}=2[/tex]2) Examining that graph we can see that when x=0 y=3, so the linear coefficient b is 3. Therefore we can write the equation as y= 2x-3.
2.2) Since the question wants a perpendicular line, then the slope of this perpendicular line must be reciprocal and opposite to m=2, so:
[tex]m\perp=-\frac{1}{2}[/tex]So, plugging the given point (6,-7) we can find out the linear coefficient of that perpendicular line:
y=mx +b
-7 = 6(-1/2) +b
-7 =-3 +b
-7+3 = b
b=-4
3) Hence, the answer is y= -1/2x -4
A bus travels 8.4 miles eastand then 14.7 miles north.What is the angle of the bus'resultant vector?Hint: Draw a vector diagram.O[?]
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A bus travels 8.4 miles east and then 14.7 miles north.
What is the angle of the bus resultant vector?
see the figure below to better understand the problem
The angle of the bus resultant vector R is equal to
tan(x)=14.7/8.4
mm
In ∆PQR, p=13 inches, q=18 inches and r= 12 inches. Find the area of ∆PQR to the nearest square inch.
Answers
Given data:
The first side of the triangle is p=13 inches.
The second side of the triangle is q=18 inches.
The third side of the triangle is r= 12 inches.
The semi-perimeter is,
[tex]\begin{gathered} s=\frac{p+q+r}{2} \\ =\frac{13\text{ in+18 in+12 in}}{2} \\ =21.5\text{ in} \end{gathered}[/tex]The expression for the area of the triangle is,
[tex]\begin{gathered} A=\sqrt[]{s(s-p)(s-q)(s-r)_{}} \\ =\sqrt[]{21.5\text{ in(21.5 in-13 in)(21.5 in-18 in)(21.5 in-12 in)}} \\ =\sqrt[]{(21.5\text{ in)(8.5 in)(3.5 in)(9.5 in)}} \\ =77.95in^2 \end{gathered}[/tex]Thus, the area of the given triangle is 77.95 sq-inches.
In the diagram below, BS and ER intersect as show. Determine the measure of
Answers
Can you help me answer part A and part B?
Answers
Part A.
Given:
P = (5, 4), Q = (7, 3), R = (8, 6), S = (4, 1)
Let's find the component of the vector PQ + 5RS.
To find the component of the vector, we have:
[tex]=\lparen Q_1-P_1,Q_2-P_2)=<7-5,3-4>[/tex]For vector RS, we have:
[tex]=\lparen S_1-R_1,S_2-R_2)=<4-8,1-6>[/tex]Hence, to find the vector PQ+5RS, we have:
[tex]\begin{gathered} =<7-5,3-4>+5<4-8,1-6> \\ \\ =\left(2,-1\right)+5\left(-4,-5\right) \\ \\ =\left(2,-1\right)+\left(5\ast-4,5\ast-5\right) \\ \\ =\left(2,-1\right)+\left(-20,-25\right) \end{gathered}[/tex]Solving further:
[tex]\begin{gathered} =<2-20,-1-25> \\ \\ =<-18,-26> \end{gathered}[/tex]Therefoee, the component of the vector PQ+5RS is:
<-18, -26>
• Part B.
Let's find the magnitude of the vector PQ+5RS.
To find the magnitude, apply the formula:
[tex]m=\sqrt{\left(x^2+y^2\right?}[/tex]Thus, we have:
[tex]\begin{gathered} m=\sqrt{\left(-18^2+-26^2\right?} \\ \\ m=\sqrt{324+676} \\ \\ m=\sqrt{1000} \\ \\ m=\sqrt{10\ast10^2} \\ \\ m=10\sqrt{10} \end{gathered}[/tex]Therefore, the magnitude of the vector is:
[tex]10\sqrt{10}[/tex]ANSWER:
Part A. <-18, -26>
Part B. 10√10
The number of bottles a machine fills is proportional to the number of minutes the machine operates. The machine
fills 250 bottles every 20 minutes. Create a graph that shows the number of bottles, y, the machine fills in a minutes.
To graph a line, select the line tool. Click on a point on the coordinate plane that lies on the line. Drag your mouse to
another point on the coordinate plane and a line will be drawn through the two points
Answers
It is to be noted that the correct graph is graph A. This is because it shows the coordinates (2, 25). See the explanation below.
What is the calculation justifying the above answer?It is information given is the rate of change of the linear relationship between the stated variable variables:
Number of Bottles; andTime.The ratio given is depicted as:
r = [250 bottles]/ [20 mintures]
r = 25/2 bottles per min
By inference, we know that our starting point coordinates (0,0), because zero bottles were filled at zero minutes.
Thus, we must use the point-slope form to arrive at the equation that exhibits or represents the relationship of the linear graph.
The point-slope form is given as:
y-y₁ = m(x-x₁)
Recall that our initial coordinates are (0, 0,) where x₁ = 0 and y₁ = 0. Hence
⇒ y - 0 = 25/2(x-0)
= y = 25x/2
Hence, if x = 2, then y must = 25
Proof: y = 25(2)/2
y = 50/2
y = 25.
Hence, using the principle of linear relationships, the first graph is the right answer, because it shows the points (2,25) which are part of the relation.
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Elsie is moving to iowa city iowa, with her three-year-old daughter. The table shows the results of a family budget estimator for iowa City for Elsie and her daughter."If Elsie earns $45,000 per year at her new job, can she stay on budget in lowa City? A. Yes, because she can easily afford $4020 per month.B. Yes, because she will not actually need all the items that the family budget estimator includes. C. No, because she will only make $3750 per month before taxes are taken out. D.No, because she will not be able to find housing as low as $853 per month?
Answers
In order to determine what is the correct statement, calculate the amount of money Elsie can spend per month, based on her earnings per year.
Divide 45,000 by 12:
45,000/12 = 3,750
You can notice that the amount of money Elsie can spend per month is lower than the total expenses shown in the table.
Hence, the correct statement is:
C. No, because she will only make $3750 per month before taxes are taken out.
determine if each expression is equivalent to [tex] \frac{ {7}^{6} }{ {7}^{3} } [/tex]
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The question says we are to check the options that are equal
[tex]\frac{7^6}{7^3}[/tex]Using the law of indices
[tex]\frac{7^6}{7^3}=7^{6-3\text{ }}=7^3[/tex]So we will check all the options(applying the laws of indices)
The first option is
[tex]7^9(7^{-6})=7^{9-6}=7^3[/tex]yes, the first option is equivalent
We will move on and check the second option
[tex]\frac{7^{-8}}{7^{-11}}\text{ = }7^{-8+11}=7^3[/tex]Yes the second option is equivalent
We will move on to check the third option
[tex](7^5)(7^3)divideby7^{4\text{ }}=7^{5+3-4\text{ }}=7^4[/tex]No the third option is not eqquivalent to the question
We will move to tthe next option, fourth option
[tex]7^{-3\text{ }}\times7^{6\text{ }}=7^{-3+6}=7^3[/tex]yes this option is equivalent to the fraction
Moving on to the fifth option
[tex](7^3)^{0\text{ }}=7^{3\times0}=7^0=\text{ 1}[/tex]No the fifth option is not equivalent to the question
A cannery needs to know the volume-to-surface-area ratio of a can to find the size that will create the greatest profit. Find the volume-to-surface-area ratio of a can.Hint : For a cylinder, S = 2πr2 + 2πrh and V = πr2h.a. 1/2b. 2(r+h) / rhc. πr(2r + 2h − rh)d. rh / 2(r+h)
Answers
SOLUTION
[tex]Volume\text{ }of\text{ }can=\pi r^2h[/tex][tex]Surface\text{ }area\text{ }of\text{ }can=2\pi r^2+2\pi rh[/tex]The ratio can be established as shown below
[tex]\begin{gathered} \frac{\pi r^2h}{2\pi r^2+2\pi rh} \\ \frac{\pi r^2h}{2\pi r(r+h)} \\ \frac{rh}{2(r+h)} \end{gathered}[/tex]The correct answer is OPTION D
The admission fee at an amusement park is 1.5 dollars for children and 4 dollars for adults. On a certainday, 252 people entered the park, and the admission fees collected totaled 728 dollars. How many childrenand how many adults were admitted?Your answer isnumber of children equalsnumber of adults equalso
Answers
Answer: Number of children = 112, number of adult = 140
Let the number of children = x
Let the number of adult =
According to the question, 252 people entered the park
Mathematically, the number of adult and children that entered the park sum up to 252
x + y = 252 ------- equation 1
$1.5 is charged for children for the admission fee into the park
$4 is charged for adult for the admission fee into the park
A totaled of $728 was realized from both children and adult that were admitted into the park
This implies that the total amount realized is equal to the number of children and adults inside the park per amount charged respectively
1.5* x + 4 * y = 728
1.5x + 4y = 728 -------- equation 2
Equation 1 and 2 can be solve simultaneously using substitution method
x + y = 252 ----- 1
1.5x + 4y = 728 ------ 2
Make x the subject of the formula in equation 1
x + y = 252
x = 252 - y ----- equation 3
Substitute equation 3 into equation 2
1.5(252 - y ) + 4y = 728
Open the parenthesis
1.5 x 252 - 1.5 x y + 4y = 728
378 - 1.5y + 4y = 728
Collect the like terms
-1.5y + 4y = 728 - 378
2.5y = 350
Divide both sides by 2.5
y = 350/2.5
y = 140
To find x, put the value of y into equation 1
x + y = 252
x = 252 - y
x = 252 - 140
x = 112
The number of children = 112
The number of adults = 140
Julie wants to purchase a jacket that costs $125. So far she has saved $42 and plans tosave an additional $25 per week. She gets paid every Friday, so she only gets money toput aside once a week. How many weeks, x, will it take for her to save at least $125?
Answers
cost of the jacket = $125
money saved = $42
extra savings = $25/week
Ok
125 = 42 + 25w
w = number of weeks
Solve for w
125 - 42 = 25w
83 = 25w
w = 83/25
w = 3.3
She needs to save at least 3.3 weeks
What does the slower car travel at Then what does the faster car travel at
Answers
Given that two cars are 188 miles apart, travelling at different speeds, meet after two hours.
To Determine: The speed of both cars if the faster car is 8 miles per hour faster than the slower car
Solution:
Let the slower car has a speed of S₁ and the faster car has a speed of S₂. If the faster speed is 8 miles per hour faster than the slower car, then,
[tex]S_2=8+S_1====\text{equation 1}[/tex]It should be noted that the distance traveled is the product of speed and time. Then, the total distance traveled by each of the cars before they met after 2 hours would be
[tex]\begin{gathered} \text{distance}=\text{speed }\times time \\ \text{Distance traveled by the faster car after 2 hours is} \\ =S_2\times2=2S_2 \\ \text{Distance traveled by the slower car after 2 hours is} \\ =S_1\times2=2S_1 \end{gathered}[/tex]It was given that the distance between the faster and the slower cars is 188 miles. Then, the total distance traveled by the two cars when they meet is 188 miles.
Therefore:
[tex]\begin{gathered} \text{Total distance traveled by the two cars is} \\ 2S_1+2S_2=188====\text{equation 2} \end{gathered}[/tex]Combining equation 1 and equation 2
[tex]\begin{gathered} S_2=8+S_1====\text{equation 1} \\ 2S_1+2S_2=188====\text{equation 2} \end{gathered}[/tex]Substitute equation 1 into equation 2
[tex]\begin{gathered} 2S_1+2(8+S_1)=188 \\ 2S_1+16+2S_1=188 \\ 2S_1+2S_1=188-16 \\ 4S_1=172 \end{gathered}[/tex]Divide through by 4
[tex]\begin{gathered} \frac{4S_1}{4}=\frac{172}{4} \\ S_1=43 \end{gathered}[/tex]Substitute S₁ in equation 1
[tex]\begin{gathered} S_2=8+S_1 \\ S_2=8+43 \\ S_2=51 \end{gathered}[/tex]Hence,
The slower car travels at 43 miles per hour(mph), and
The faster car travels as 51 miles per hour(mph)
The equation of a line that is perpindicular to y=10x but passes through (1, -3)
Answers
The equation of line is y = -x/10 + -29/10.
Given,
The equation of a line that is perpendicular to y = 10x
and, passes through the (1, -3)
To find the equation of line.
Now, According to the question:
Find the slope of the line that is perpendicular to y = 10x;
m = - 1/10
We know that, Slope of line is ;
y = mx + c
m = -1/10
x = 1
y = -3
Substitute and calculate
- 3 = -1/10 + b
b = -29/10
Now, y = mx + b
Substitute all the values in above slope equation:
y = -x/10 + -29/10
Hence, The equation of line is y = -x/10 + -29/10.
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The question is which of these statements are true about radicals exponents and rational exponents
Answers
We have the following:
I)
[tex]\sqrt[n]{a}=a^{\frac{1}{n}}[/tex]It´s true
II)
[tex]a^{\frac{1}{2}}=\sqrt[]{a}[/tex]It´s true
III)
[tex]\begin{gathered} a^{\frac{p}{q}}=\sqrt[p]{a^q}=(\sqrt[p]{a})^q \\ (\sqrt[p]{a})^q=(a^{\frac{1}{p}})^q=a^{\frac{q}{p}} \end{gathered}[/tex]It´s false
IV)
[tex]\sqrt[]{a}[/tex]It´s true
V)
[tex]\begin{gathered} a^{\frac{1}{n}}=\sqrt[]{a^n} \\ \sqrt[]{a^n}=a^{\frac{n}{2}} \end{gathered}[/tex]It´s false
Special right trianglesFind the exact values of the side lengths c and a
Answers
Since it is a right triangle, we can use the trigonometric ratio cos(θ) to find the length c.
[tex]\cos(\theta)=\frac{\text{ Adjacent side}}{\text{ Hypotenuse}}[/tex]So, we have:
[tex]\begin{gathered} \cos(\theta)=\frac{\text{ Adjacent side}}{\text{ Hypotenuse}} \\ \cos(45°)=\frac{c}{7} \\ \text{ Multiply by 7 from both sides} \\ \cos(45\degree)\cdot7=\frac{c}{7}\cdot7 \\ 7\cos(45\degree)=c \\ \frac{7\sqrt{2}}{2}=c \end{gathered}[/tex]Second triangleSince it is a right triangle, we can use the trigonometric ratio cos(θ) to find the length a.
So, we have:
[tex]\begin{gathered} \cos(\theta)=\frac{\text{ Adjacent side}}{\text{ Hypotenuse}} \\ \cos(60°)=\frac{a}{2} \\ \text{ Multiply by 2 from both sides} \\ \cos(60°)\cdot2=\frac{a}{2}\cdot2 \\ 2\cos(60\degree)=a \\ 2\cdot\frac{1}{2}=a \\ 1=a \end{gathered}[/tex]Answer[tex]\begin{gathered} c=\frac{7\sqrt{2}}{2} \\ a=1 \end{gathered}[/tex]Write an equation of variation to represent the situation and solve for the missing information The time needed to travel a certain distance varies inversely with the rate of speed. If ittakes 8 hours to travel a certain distance at 36 miles per hour, how long will it take to travelthe same distance at 60 miles per hour?
Answers
The time needed to travel a certain distance varies inversely with the rate of speed, so:
[tex]\begin{gathered} let\colon \\ t=\text{time} \\ v=\text{rate of speed} \\ t\propto\frac{1}{v} \end{gathered}[/tex]8hours----------------------------->36mi/h
xhours----------------------------->60mi/h
[tex]\begin{gathered} \frac{8}{x}=\frac{36}{60} \\ \text{ Since the it varies inversely:} \\ \frac{8}{x}=(\frac{36}{60})^{-1} \\ \frac{8}{x}=\frac{5}{3} \\ \text{solve for x:} \\ x=\frac{3\cdot8}{5} \\ x=4.8h \end{gathered}[/tex]4.8 hours or 4 hours and 48 minutes
Triangle ABC is similar to triangle DEF. Find the measure of side DE. Round youranswer to the nearest tenth if necessary.C7BF27E15DAD
Answers
Given:
Triangle ABC is similar to triangle DEF.
[tex]\frac{DE}{AB}=\frac{EF}{BC}[/tex][tex]\begin{gathered} \frac{DE}{15}=\frac{27}{7} \\ DE=\frac{27}{7}\times15 \\ DE=57.9 \end{gathered}[/tex]Review: Solve for Area AND Circumference. A giant holiday cookie has a radius of 5 inches. What is the area of the cookie? What is the circumference of the cookie?
Answers
Remember that the formual for the area of a circle is:
[tex]A=\pi r^2[/tex]And the formula for the circumference is:
[tex]C=2\pi r[/tex]Using this formulas and the data given,
[tex]\begin{gathered} A=\pi(5^2)\Rightarrow A=78.54 \\ C=2\pi(5)\Rightarrow A=31.42 \end{gathered}[/tex]The cookie has an area of 78.54 square inches and a circumference of 31.42 inches
