Solution.
Length of the Baseplate = 12inches
Width of the Baseplate = 10inches
[tex]\begin{gathered} \text{Area = Length }\times\text{ Breadth(Width)} \\ \text{ = 12 }\times10 \\ \text{ = 120 in}^2 \\ \end{gathered}[/tex]Final Answer = 120
1 block: 11 houses = 2 blocks : ??? houses
How to do 2 step equations Can you solve 2x + 5=21?
Given
The equation,
[tex]2x+5=21[/tex]To find the value of x or to solve for x.
Explanation:
It is given that,
The equation is,
[tex]2x+5=21[/tex]That implies,
[tex]\begin{gathered} 2x+5=21 \\ 2x=21-5 \\ 2x=16 \\ x=\frac{16}{2} \\ x=8 \end{gathered}[/tex]Hence, the value of x is 8.
A circle has area 36 cm². What is the diameter?
Answer:
6.77 cm
Explanation:
Given that the area of a circle = 36 cm²
We want to find the diameter of the circle.
The area of a circle of radius r is calculated using the formula:
[tex]A=\pi r^2[/tex]Substitute A=36 and π=3.14:
[tex]\begin{gathered} 36=3.14r^2 \\ \text{ Divide both sides by 3.14} \\ \frac{36}{3.14}=\frac{3.14r^2}{3.14} \\ r^2=\frac{36}{3.14} \\ \text{ Take the square root of both sides} \\ r=\sqrt{\frac{36}{3.14}} \\ r=3.3845 \end{gathered}[/tex]Finally, to get the diameter, multiply the radius by 2.
[tex]\begin{gathered} Diameter=Radius\times2 \\ =3.3845\times2 \\ =6.769 \\ Diameter\approx6.77\;cm \end{gathered}[/tex]The diameter of the circle is approximately 6.77 cm.
A. Step 1B. Step 2C. Priya did not make a mistake
We will have the following:
[tex]\frac{f}{0.25}=16\Rightarrow f=16\cdot0.25[/tex][tex]\Rightarrow f=4[/tex]From this we can see that there was no mistaky on Priya's side. [Option 3]
True or false the function f(x) = -3(x+10)^2 has a minimum
Notice that:
[tex]\begin{gathered} f^{\prime}(x)=-6(x+10), \\ f^{\prime\prime}(x)=-6. \end{gathered}[/tex]Since for all x, f''(x)<0, by the second derivative criteria we get that f(x) reaches a maximum.
Answer: False.
Determine the independent and dependent quantities in each scenario include when possible Part A: A lamp manufacturing company produces 750 lamps per shift Part B:a grocery store sells pears by the pound. A customer purchases 3 pounds by $5.07
Here, we want to establish the independent and independent quantities in each of the parts
The independent quantities are simply the quantities that do not depend on the dependent quantity. The dependent quantity are the quantities that depend on the independent quantity
a) Here, we have 750 lamps produced per shift
This is obtained by dividing the number of lamps produced by the number of shifts it took to produce them
In this case, the number of lamps produced is dependent on the number of shifts'
Number of shifts is the independent variable while the number of lamps is the dependent variable
b) Here, the cost per pair is 5.07/3 = 1.69
So here, the cost is dependent on the number of pears
The number of pears is the independent variable while the cost of the pears is the dependent variable
Dante is saving money to buy a game. So far he has saved $20, which is four-fiths of the total cost of the game. How much does the game cosх$?
Money saved = $20
According to the statement we can establish the following equation
[tex]20=\frac{4}{5}X[/tex]where X is the total cost of the game
now let's find X
[tex]\begin{gathered} \frac{4}{5}X=20 \\ 5\cdot\frac{4}{5}X=20\cdot\: 5 \\ 4X=100 \\ \frac{4X}{4}=\frac{100}{4} \\ X=25 \end{gathered}[/tex]Therefore the total cost of the videogame is $25
find all real solutions[tex](2x + 17) \div (x + 1) = x + 5[/tex]
We have the next equation
[tex]\frac{2x+17}{x+1}=x+5[/tex][tex]2x+17=(x+5)(x+1)[/tex][tex]\begin{gathered} 2x+17=x^2+x+5x+5 \\ 2x+17=x^2+6x+5 \end{gathered}[/tex]Then we sum similar terms
[tex]\begin{gathered} x^2+(6x-2x)+(5-17)=0 \\ x^2+4x-12=0 \end{gathered}[/tex]then we solve the quadratic equation
We can factorize the equation
[tex](x+6)(x-2)=0[/tex]so the solutions are
x=-6
x=2
write a polynomial function in standard form with the given zeros x= -1,-2,-3,-4
Explanation: For this question we have 4 zeros so x can be as follows
x = -1 or x = -2 or x = -3 or x = -4
We can turn the equalities above into factors as follows
[tex]\begin{gathered} x=-1\rightarrow x+1=0 \\ x=-2\rightarrow x+2=0 \\ x=-3\rightarrow x+3=0 \\ x=-4\rightarrow x+4=0 \end{gathered}[/tex]Step 1: Now that we have the factors we can build a function and simplify it as follows
[tex]\begin{gathered} y=(x+1)(x+2)(x+3)(x+4) \\ y=(x^2+2x+x+2)(x^2+4x+3x+12) \\ y=(x^2+3x+2)(x^2+7x+12) \\ y=x^4+7x^3+12x^2+3x^3+21x^2+36x+2x^2+14x+24 \\ y=x^4+7x^3+3x^3+12x^2+21x^2+2x^2+36x+14x+24 \\ y=x^4+10x^3+35x^2+50x+24 \end{gathered}[/tex]Final answer: So the final answer is
[tex]y=x^4+10x^3+35x^2+50x+24[/tex].
Find the general solution to dy/dx = 2y passing through the point (5, 1)
We will have the following:
[tex]\frac{\partial y}{\partial x}=2y\Rightarrow\frac{1}{2y}\partial y=\partial x[/tex][tex]\Rightarrow\int (\frac{1}{2y})\partial y=\int \partial x\Rightarrow\frac{\log (y)}{2}=x+c[/tex]Then we find "c":
[tex]\frac{\log(1)}{2}=5+c\Rightarrow c=-5[/tex]Thus, the general solution passing through (5, 1) is:
[tex]\frac{\log(y)}{2}=x-5[/tex]The line M is parallel to the line y=-2x+2 and goes through the origin. Which of these points is on the line M? (-2,-4)(1,1)(2,-2)(-2,4)
Answer:
(-2,4)
Explanation:
Two lines are said to be parallel if their slopes are the same.
Comparing the line y =-2x+2 to the slope-intercept form y=mx+b, the slope of the line is -2.
Therefore, the slope of line M that is parallel to it is also - 2.
Since the line M goes through the origin, the y-intercept of line M is 0.
Therefore, the equation of line M is:
[tex]y=-2x[/tex]Therefore, the point which is on line M is the point that satisfies the equation above.
This point is (-2,4).
Check
[tex]\begin{gathered} \text{When }x=-2,y=4 \\ y=-2x \\ 4=-2(-2) \\ 4=4 \end{gathered}[/tex]The minimum diameter for a hyperbolic cooling tower is 76 feet, which occurs at a height of 173 feet. The top of the cooling tower has a diameter of 93 feet, and the total height of the tower is 250 feet. Write the equation for the hyperbola that models the sides of the cooling tower assuming that the center of the hyperbola occurs at the height for which the diameter is least.Round your a and b values to the nearest hundredth if necessary.
STEP - BY - STEP EXPLANATION
What to find?
The equation for the hyperbola that models the sides of the cooling tower assuming that the center of the hyperbola occurs at the height for which the diameter is least.
Given:
Minimum diameter = 76 feet
Height = 173 feet
Diameter of the top of cooling tower = 93 feet
Total height of tower = 250 feet
Consider the general hyperbolic formula below:
[tex]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1[/tex]But;
2a = 76
⇒ a = 38
x=93/2 =46.5
y=250 - 173 =77
Substitute the values into the formula above and determine the value of b.
[tex]\frac{(46.5)^2}{38^2}-\frac{77^2}{b^2}=1[/tex][tex]b=109.18[/tex]Now substitute the values a= 38 and b=109.18 into the general formula
[tex]\frac{x^2}{38^2}-\frac{y^2}{109.18^2}=1[/tex]ANSWER
[tex]\frac{x^2}{38^2}-\frac{y^2}{109.18^2}=1[/tex]What is the y-intercept of the graph of y = 2.5x?a. 2.5b. 0c. 1d. -1
Solution
- We are asked to find the y-intercept of the graph of:
[tex]y=2.5x[/tex]- In order to find the y-intercept, we need to know the definition of the y-intercept.
- The y-intercept is the y-value where the graph crosses the y-axis.
- An implication of this definition is that whenever the graph crosses the y-axis, the x-value at that point is zero. This means that we simply need to substitute x = 0 into the equation given to us to find the y-intercept of the graph.
- The y-intercept can thus is gotten as follows:
[tex]\begin{gathered} y=2.5x \\ \text{put }x=0 \\ y=2.5(0) \\ \\ \therefore y=0 \end{gathered}[/tex]Final Answer
The y-intercept of the graph is y = 0 (OPTION B)
In the diagram of \bigtriangleup△GKJ below, LH KJ, GL=6, LK=30, and GH=3. What is the length of GJ?
From the given figures
Since LH // KJ, then
[tex]\frac{GL}{LK}=\frac{GH}{HJ}[/tex]GL = 6, LK = 30
GH = 3, HJ = y
Substitute them in the ratio above
[tex]\frac{6}{30}=\frac{3}{y}[/tex]By using cross multiplication
[tex]\begin{gathered} 6\times y=30\times3 \\ 6y=90 \end{gathered}[/tex]Divide both sides by 6
[tex]\begin{gathered} \frac{6y}{6}=\frac{90}{6} \\ y=15 \end{gathered}[/tex]Since GJ = GH + HJ
[tex]\begin{gathered} GJ=3+15 \\ GJ=18 \end{gathered}[/tex]The answer is 36
l A golf ball is hit in the air. The table shown describes y, the height of the ball, in feet, given the time elapsed, x, in seconds, since the time the ball was hit.Based on the information in the table, which statements are true? Select each correct statement.
Given:
y is the height of the ball in feet
x is the time in seconds
In the given table you can identify the next maximum:
x=3
y=30
The ball has height 0 when it is in the earth so it is hit at second 0 and will be back in the earth at second 6
Then, from the given statements the next are true:
The maximum height of the ball was 30 feetThe ball was in the air for only 6 secondshow do you write out this number in word 506,341,209.54
You write this number in word this way:
Five hundred six million three hundred fourty one thousand two hundred nine point fifty four.
Write the expression that can be used tofind the height of the Eiffel Tower.
First, let's picture the problem:
I have represented the height of the Effiel tower as H
Using the trigonometric ratios:
[tex]\begin{gathered} \tan 53^0\text{ = }\frac{H}{225} \\ H=225\times\tan 53^0^{} \end{gathered}[/tex]Hence the required expression is :
[tex]\begin{gathered} \text{Height of tower = d }\times\text{ tan}\phi \\ \text{if d is the distance of the base} \end{gathered}[/tex]find the value of the term in the arithmetic sequence 1,6,11,16...(8th term)
We need to find the 8th term of the following arithmetic sequence:
[tex]1,6,11,16,...[/tex]The formula to find the n-th term an of aₙ arithmetic sequence is:
[tex]a_n=a_1+(n-1)d[/tex]where a₁ is the first term and d is the difference between two consecutive terms.
The first term of this sequence is a₁ = 1, and d is given by:
[tex]\begin{gathered} d=a_2-a_1 \\ \\ d=6-1 \\ \\ d=5 \end{gathered}[/tex]Then, for n = 8, we obtain:
[tex]\begin{gathered} a_8=1+(8-1)5 \\ \\ a_8=1+7(5) \\ \\ a_8=1+35 \\ \\ a_8=36 \end{gathered}[/tex]Answer:
The 8th term is 36.
A rectangular play area has an area of 7,497 square meters. If the width of the rectangle is 49 meters, find the length.
If a rectangular play area has an area of 7,497 square meters. and the width of the rectangle is 49 meters, then the length is 153 meters
A rectangular play area has an area of 7,497 square meters
If the width of the rectangle is 49 meters
Let the length of the rectangular play be l
Area of a rectangle can be given by
area = length x width
7497 = l x 49
l = 7497 / 49
l = 153
Therefore, if a rectangular play area has an area of 7,497 square meters. and the width of the rectangle is 49 meters, then the length is 153 meters
To learn more about rectangle refer here
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which number is four units away from -1a) -3b) - 4 c) 3d) 4
3 (option c)
Explanation:Four units away from -1 could be towards the negative number line or positive number line
Towards the negative number from -1 = -2, -3, -4, -5
4th number = -5
Towards the positive number from -1 = 0, 1, 2, 3
4th number = 3
From the above, the number that could be found in the option is 3
Hence, four units away from -1 is 3 (option c)
Solve for v. v + 4/5 = 1/3. Simplify your answer as much as possible.
Answer:
v = -7/15.
Explanation:
Given the equation:
[tex]v+\frac{4}{5}=\frac{1}{3}[/tex]To solve for v, first, subtract 4/5 from both sides of the equation:
[tex]\begin{gathered} v+\frac{4}{5}-\frac{4}{5}=\frac{1}{3}-\frac{4}{5} \\ \implies v=\frac{1}{3}-\frac{4}{5} \end{gathered}[/tex]Next, simplify the right-hand side by taking the lowest common multiple of the denominators:
[tex]\begin{gathered} v=\frac{5-3(4)}{15}=\frac{5-12}{15} \\ \implies v=-\frac{7}{15} \end{gathered}[/tex]The value of v is -7/15.
Determine the probability of being dealt 4 Aecs of cards, from a deck of 52 playing cards, with a replacement.
Given:
4 Aces of cards from a deck of 5 playing cards.
[tex]\begin{gathered} \text{Probability of drawing 4 Aces }=\frac{4}{52}\times\frac{4}{52}\times\frac{4}{52}\times\frac{4}{52}\times4! \\ \text{Probability of drawing 4 Aces }=\frac{1}{13}\times\frac{1}{13}\times\frac{1}{13}\times\frac{1}{13}\times24 \\ \text{Probability of drawing 4 Aces }=\frac{24}{28561} \end{gathered}[/tex]suppose we spin the following spinner with the first spin giving us the numerator and the second spin giving the denominator of a fraction. What is the probability that the fraction will be less than or equal to 5/6?
numerator = top number
denominator = bottom number
numerator less than or equal to 5
total numbers = 4
numbers less than or equal to 5 = 2 ( 5 and 4)
Denominator
5, 6 or 7 = 3
Possible fractions = 4/5, 4/6, 4/7, 5/6 and 5/7
5 out of 16 possible fractions
probability = 5/16
Determine the equation of the line that passes through the point (1/8,2) and is perpendicular to the line 5y+2x=2.
Step 1
Given;
Determine the equation of the line that passes through the point (1/8,2) and is perpendicular to the line 5y+2x=2.
Step 2
Find the slope of the new line based on a perpendicular relationship
[tex]\begin{gathered} m_1=-\frac{1}{m_2} \\ \end{gathered}[/tex][tex]\begin{gathered} 5y=2-2x \\ y=\frac{2-2x}{5} \\ y=\frac{2}{5}-\frac{2}{5}x \\ -\frac{2}{5}=-\frac{1}{m_2} \\ 2m_2=5 \\ m_2=\frac{5}{2} \end{gathered}[/tex]Thus the equation will be;
[tex]\begin{gathered} (\frac{1}{8},2) \\ y=\frac{5}{2}x+b \\ b=y-intercept \\ 2=\frac{5}{2}(\frac{1}{8})+b \\ 2=\frac{5}{16}+b \\ b=2-\frac{5}{16} \\ b=\frac{27}{16} \end{gathered}[/tex][tex]y=\frac{5}{2}x+\frac{27}{16}[/tex]Answer;
[tex]y=\frac{5}{2}x+\frac{27}{16}[/tex]An expression is shown.2 3/4÷4 1/2What is the value of the expression, in simplest form?
ANSWER
[tex]\frac{11}{18}[/tex]EXPLANATION
Given:
[tex]2\frac{3}{4}\div4\frac{1}{2}[/tex]
Which of the following statements is NOT true about the data above?
Explanation
A matrix is a rectangular array of numbers arranged into columns and rows
[tex]\begin{bmatrix}{a_{11}} & {a_{21}} & {.} & {a_{1n}} \\ {a_{21}} & {.\text{.}} & {.} & {\square} \\ {a_{31}} & {.\text{.}} & {.\text{.}} & {\square} \\ {a_{41}} & {.\text{.}} & {.\text{.}} & {a_{mn}}\end{bmatrix}[/tex]where m is the number of rows and n is the number of columns
The dimensions of a matrix tells its size: the number of rows and columns of the matrix, in that order.
Step 1
check the dimension of the given functino
rows:5
columns: 4
therefore the matrix is a 5 *4 matrix: true
Step 2
the matrix shows the number of medalls for 5 countries,
we can see that the total for USA is 7, so USA has won the most overall medals in Olumpic soccer :true
Step 3
[tex]C_{3,1}[/tex]
it is
rows:3
column 1
we can see the entry for C(3,1) is
3
hence
C) false
Step 4
[tex]C_{4,1}[/tex]
it is
rows:4
column 1
it indicates Nigeria has won 1 medal in Olympic soccer
threfo
Find each unit price and decide which is the better buy. Assume that we are comparing sizes of the same breadFrozen orange juice $1.51 for 14 ounces $0.51 for 4 ounces Find the unit price if a frozen orange juice which cost $1.51 for 14 ounces
Unit price of a frozen orange juice which costs $1.51 for 14 ounces = $0.108 per ounce
Unit price of a frozen orange juice which costs $0.51 for 4 ounces = $0.128
The better buy is the frozen orange juice which costs $1.51 for 14 ounces
Option B
Explanations:Cost of 14 ounces of orange juice = $1.51
Cost od 4 ounces of orange juice = $0.51
Unit price of a frozen orange juice which costs $1.51 for 14 ounces
Unit price = $1.51 / 14
Unit price of a frozen orange juice which costs $1.51 for 14 ounces = $0.108 per ounce
Unit price of a frozen orange juice which costs $0.51 for 4 ounces
Unit price = $0.51 / 4
Unit price of a frozen orange juice which costs $0.51 for 4 ounces = $0.128
The better buy is the one with the lower unit price
Since the frozen orange juice which costs $1.51 for 14 ounces has the lower unit price, it is the better buy
1. Sue uses 2.59 pounds ofstrawberries and 0.65 poundof blueberries to make fruitsalad. She serves the sameamount of salad in each of 9bowls. What is the weight,in pounds, of each serving tothe nearest tenth?
Problem:
Sue uses 2.59 pounds of strawberries and 0.65 pounds of blueberries to make a fruit salad. She serves the same amount of salad in each of 9
bowls. What is the weight, in pounds, of each serving to
the nearest tenth?
Solution:
The total weight of the fruit salad is:
2.59 pounds + 0.65 pounds = 3.24 pounds.
Now, if she serves the same amount of salad in each of 9 bowls, we have that the weight in each serving is:
[tex]\frac{3.24}{9}=\text{ 0.36 pounds}[/tex]Then, we can conclude that the correct answer is:
0.36 pounds.
You are going to paint your door on the outside. Your door is 7 feet 2 inches tall and 32inches wide. You need to know the surface area of the front of your door to determine howmuch paint to buy. The hardware store sells paint by how much covers a square foot. What isthe surface area you should report to the hardware store?
Data
height = 7 ft 2 in
width = 32 in
1.- Convert height into inches
1 ft ------------ 12 in
7 ft ------------ x
x = 84 in
total height = 84 + 2
= 86 in
2.- Calculate the area
Area = height x width
Area = 84 x 32
Area = 2688 in 2
The coordinates of the vertices of triangle RST are R(-2, -3), S(4,5), and T (8,2). List the angles of triangle RST in order from smallest to largest.
The first step is to plot the triangle RST with the given coordinates. The diagram of the triangle RST is shown below. We can see that the smallest angle is angle R, The larger angle is angle T while the largest angle is angle S
Listing the angles in order from smallest to largest., it becomes
angle R, angle T and angle S