Given:
seven less than the product of four and a number is equal to 3
Let the number = x
So, the product of four and a number = 4x
seven less than the product of four and a number will be 4x - 7
so, the expression will be:
4x - 7 = 3
1. Graph each of the following equations below using a tale of values or by another method. Fill in theInformation for each graph.X-intercept:a) y = x2 + 4x - 5y-intercept:хуVertex:Max/MinAxis of SymmetryDomain:Range:
The equation is
[tex]y=x^2+4x-5[/tex]We can already find the vertex using the vertex formulas
[tex]\begin{gathered} x_V=-\frac{b}{2a}=\frac{-4}{2}=-2 \\ \\ \\ y_V=-\frac{\Delta}{4a}=-\frac{b^2-4ac}{4a}=-\frac{16+20}{4}=-\frac{36}{4}=-9 \end{gathered}[/tex]Therefore the vertex is
[tex](x_V,y_V)=(-2,-9)[/tex]Now we have the vertex we also have the axis of symmetry and the max/min of the function, in that case, it's a minimum because a > 0. Therefore
[tex]\begin{gathered} \text{ axis of symmetry = }x_V=-2 \\ \\ \min\lbrace y\rbrace=y_V=-9 \end{gathered}[/tex]We can find the x-intercept easily
[tex]\begin{gathered} x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ \\ x=\frac{-4\pm\sqrt{4^2+4\cdot5}}{2} \\ \\ x=\frac{-4\pm\sqrt{16+20}}{2} \\ \\ x=\frac{-4\pm\sqrt{36}}{2} \\ \\ x=\frac{-4\pm6}{2} \\ \\ \end{gathered}[/tex]Hence
[tex]\begin{gathered} x=\frac{-4\pm6}{2}=-2\pm3 \\ \\ x_1=-1 \\ x_2=-5 \end{gathered}[/tex]The y-intercept is just the c value, then it's -5.
Now we can do the domain, there's no restriction for parabolas in the domain, then
[tex]\text{ domain = }\mathbb{R}[/tex]And the range is
[tex]\text{ range = \lbrack}y_V,+\infty)=[-9,+\infty)[/tex]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
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]
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.
Point C is between A and B on AB. Use the given information to write an equation in terms of x. Then solve the equation to find x, AC, BC, and AB.
We have the following:
[tex]\begin{gathered} AB=AC+CB \\ AC=2x+5 \\ AB=27x \\ CB=5x+15 \end{gathered}[/tex]replacing:
[tex]\begin{gathered} 27x=2x+5+5x+15 \\ 27x-2x-5x=20 \\ 20x=20 \\ x=\frac{20}{20} \\ x=1 \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} AC=2\cdot1+5=7 \\ AB=27\cdot1=27 \\ CB=5\cdot1+15=20 \end{gathered}[/tex]x = 1
AC = 7
AB = 27
CB = 20
Need help finding the x-intercepts for equation in picture. I can see them on the graph but I need to work it out by solving.
Answer:
The x-intercepts of the function are;
[tex]\begin{gathered} x=-2 \\ \text{and} \\ x=-4 \end{gathered}[/tex]Explanation:
Given the function;
[tex]f(x)=-2(x+3)^2+2[/tex]We want to derive the x-intercepts of the function.
The x-intercept is at f(x)=0;
[tex]\begin{gathered} f(x)=-2(x+3)^2+2=0 \\ -2(x+3)^2+2=0 \\ -2(x^2+6x+9)^{}+2=0 \\ -2x^2-12x-18^{}+2=0 \\ -2x^2-12x-16=0 \\ -x^2-6x-8=0 \\ x^2+6x+8=0 \end{gathered}[/tex]solving for x;
[tex]\begin{gathered} x^2+6x+8=0 \\ x^2+2x+4x+8=0 \\ (x+2)(x+4)=0 \\ x+2=0 \\ x=-2 \\ \text{and} \\ x+4=0 \\ x=-4 \end{gathered}[/tex]Therefore, the x-intercepts of the function are;
[tex]\begin{gathered} x=-2 \\ \text{and} \\ x=-4 \end{gathered}[/tex]Method 2: quadratic root property;
[tex]\begin{gathered} f(x)=-2(x+3)^2+2=0 \\ -2(x+3)^2+2=0 \\ -2(x+3)^2=-2 \\ \text{divide both sides by -2;} \\ (x+3)^2=1 \\ \text{square root both sides;} \\ \sqrt{(x+3)^2}=\sqrt{1} \\ x+3=\pm1 \\ x=-3\pm1 \\ so\text{ the values of x are;} \\ x=-3+1=-2 \\ \text{and} \\ x=-3-1=-4 \end{gathered}[/tex]Therefore, the x-intercepts are;
[tex]\begin{gathered} x=-2 \\ \text{and } \\ x=-4 \end{gathered}[/tex]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
Lamar has $80,000 in a savings account. the interest rate is 1% per year and is not compounded. to the nearest cent how much will he have in 3 years?
Simple Interest
The interest rate for Lamar's savings account is 1% per year. This means his money earns 1% at the end of each year.
The formula to calculate the interest is:
I = P.r.t
Where P is the principal or initial saved amount, r is the interest rate, and t is the time.
P = $80,000
r = 1%. This must be converted to decimal
r = 1 / 100 = 0.01
t = 3 years
Calculate the interest:
I = 80,000*0.01*3
I = $2,400
That amount is added to the principal:
A = P + I
A = $80,000 + $2,400
A = $82,400
He will have $82,400 in 3 years
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.
Stuck on this question, any help greatly appreciated.Don't understand the concept of what the question is asking
You have the line segment PQ shown in the exercise. Notice that you must copy the length of that line using the compass. Notice that one of the endpoints of the new line is R.
In order to copy it, you can follow these steps:
1. You need to place the compass on one of the endpoints of the line PQ.
2. Open the compass to the length of the segment PQ (one leg of the compass must be on the endpoint P and the other one on the endpoint Q).
3. Using the amount of opening found in the previous step, place the compass on the point R and make a mark with the other leg of the compass.
Notice that by applying these steps, you get a segment with the same length of PQ.
Therefore, the answer is:
If y=-4 when x = 10, find y when x = 2.
With the help of the cross-multiplication method, we know that the value y is -4/5 when x is 2.
What do we mean by the cross-multiplication method?In mathematics, more specifically in elementary arithmetic and elementary algebra, one could cross-multiply an equation between two fractions or rational expressions to make the equation easier or to determine the value of a variable.
To cross-multiply two fractions, multiply the numerator of the first fraction by the denominator of the second, and the numerator of the second fraction by the denominator of the first.
So, the value of y when x = 2 is:
We know that when y = -4, then x = 10.
Now, calculate y when x = 2.
y/x = y/x
-4/10 = y/2
10y = -8
y = -8/10
y = -4/5
Therefore, with the help of the cross-multiplication method, we know that the value y is -4/5 when x is 2.
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(08.01 MC)Find the height of a square pyramid that has a volume of 12 cubic feetand a base length of 3 feet. (1 point)
Recall that we can do the following picture
We want to find the height of this pyramid and are told the volume of the pyramid. Recall that the volume of a square pyramid of height h and base length b is given by the formula
[tex]V=\frac{1}{3}b^2\cdot h[/tex]In our case, we have V=12, and b=3. So we have the following equation
[tex]12=\frac{1}{3}\cdot3^2\cdot h=3\cdot h[/tex]So, we should find the value of h from this equation. To do, we simply divide both sides by 3, so we get
[tex]h=\frac{12}{3}=4[/tex]so the height of the pyramid is 4 feet.
I need help with my pre-calc work! The question image is attached.Which of the functions are bounded below? Check the two that apply.g(x) = -4xg(x) = xˆ2g(x) = xˆ3g(x) = | x + 4 | - 1
using a graphing tool
graph the functions
see the attached figure to better understand the problem
Remember that
A function f is bounded below if there is some number b that is less than or equal to every number in the range of f.
therefore
in this problem
g(x)=x^2 and g(x)=x^3 are bounded below
Question 8 of 10The table below shows the number of e-mails received each day by acompany employee for two separate weeks. If the data were represented witha comparative dot plot, which day would have more dots for week 2 than forweek 1?Week 1 Week 2Monday74.Tuesday83Wednesday52Thursday97Friday69
Solution
It's Friday
Because, the number of dots for week 2 is 9, while the number of dots for week 1 is 6.
Hence, the correct option is A.
Michael and Karim are eating buffalo wings at a constant rate. Michael can eat 5.5 wings per minute. Karim's eating information is shown in the table below. Time (minutes) Wings eaten 1 6 2 12 18 3if they both ate 6 min how many wings would each person eat
a) Karim eats faster
b) Number of wings Micheal will eat = 33 wings
Number of wings Karim will eat = 36 wings
Explanation:a) Michael eat 5.5 wings per minute
we need to find the constant rate Karim eats from the table
The constant rate = change in wings eaten/ change in time
The constant rate = (12 - 6)/(2-1) = (18-12)/(3-2)
= 6/1 = 6/1
The constant rate Karim eats = 6 wings per minute
Rate of Mcheal eating = 5.5
Rate of Karim eating = 6
Karim eats faster
Reason: Because Karim consumes more wings than Micheal when they are given same time, he will eat faster.
6 > 5.5
b) If they both ate 6 min:
Number of wings = rate × time
Number of wings Micheal will eat = 5.5 × 6 = 33 wings
Number of wings Karim will eat = 6 × 6 = 36 wings
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
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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
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]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
The scatterplot shows the average number of hours each of 13 people spends at work every week and the average number of hours each of them spends recreational activities every week.Based on the scatterplot,what is the best prediction of the average number of hours a person spends at work every week if that person spends an average of 10 hours on recreational activities every week?A.33 hB.95 hC.50 hD.65 h
We want to find the best prediction of the average number of hours a person spends at work every week if that person spends an average of 10 hours on recreational activities every week.
We will construct a line that adapts to the system by simple linear regression, and then we will find the x-value that makes the line take y=10.
First, we have the data:
We remember that in a simple regression model, we want to write an equation of the form:
[tex]y=\hat{\alpha}+\hat{\beta}x[/tex]where:
[tex]\begin{gathered} \hat{\alpha}=\bar{y}-\hat{\beta}\bar{x} \\ \hat{\beta}=\frac{nS_{xy}-S_xS_y}{nS_{xx}-S^2_x}_{} \end{gathered}[/tex]And the Sx, Sy and Sxx are the sums over all the x-values, the y-values and the multiplication of the x-values and y-values (respectively).
We will find those values:
[tex]\begin{gathered} S_x=\sum ^{13}_{i=1}x_i=370 \\ S_y=\sum ^{13}_{i=1}y_i=336.5 \end{gathered}[/tex]Also, we have:
[tex]\begin{gathered} S_{xx}=\sum ^{13}_{i=1}x^2_i=12600 \\ S_{xy}=\sum ^{13}_{i=1}x_iy_i=8680_{}_{} \end{gathered}[/tex]And applying the formula, having in mind that n=13, we get:
[tex]\begin{gathered} \hat{\beta}=\frac{nS_{xy}-S_xS_y}{nS_{xx}-S^2_x}_{} \\ =\frac{13(8680)-(370)(336.5)}{13(12600)-(370^2)} \\ =\frac{-11665}{26900} \\ \approx-0.4336 \end{gathered}[/tex]And, for alpha:
[tex]\begin{gathered} \hat{\alpha}=\frac{1}{n}S_y-\hat{\beta}\frac{1}{n}S_x \\ =\frac{1}{13}(336.5)-(-0.4336)\frac{1}{13}(370) \\ \approx38.2255 \end{gathered}[/tex]This means that the linear regression equation will be:
[tex]y=38.2255-0.4336x[/tex]For finding the x-value that will have 10 hours of recreational activities, we replace the 10 value on y, and clear out the variable x:
[tex]10=38.2255-0.4336x[/tex]And thus,
[tex]\begin{gathered} 10-38.2255=-0.4336x \\ \frac{-28.2255}{-0.4336}=x \\ 65.09=x \end{gathered}[/tex]This means that when a person works 65 hours approximately, he will have 10 hours of recreational activities every week.
Which car gets better mileage: a car that gets 23 miles per gallon or a car that gets 45 kilometers per gallon?
A car that gets 45 kilometers per gallon has better mileage than a car that gets 23 miles per gallon
What is mileage of a car?
The mileage of a car is the number of miles that it can travel using one gallon or litre of fuel.
The first car that gets a mileage of 23 miles per gallon
The second car gets 45 kilometers per gallon
1 mile = 1.6 km
1 km = 1/1.6 mile
45 km = (1/1.6) 45
45 km = 28.125 miles
28.125 miles > 23 miles
Therefore, a car that gets 45 kilometers per gallon has better milegae than a car that gets 23 miles per gallon
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how do i get 24 using numbers 5,8,0.3,5 once
The given numbers are 5, 8, 0.3, 5. To get 24 from these numbers, we form the following expression
[tex](5+5)\cdot8\cdot0.3[/tex]Let's solve it to see if it gives 24 at the end.
[tex](5+5)\cdot8\cdot0.3=(10)\cdot8\cdot0.3=10\cdot0.24=24[/tex]Therefore, the answer is
[tex](5+5)\cdot8\cdot0.3[/tex]What is the value of cos(150°)?
Given that cos(150°).
[tex]\cos (150^o)=\cos (180^o-30^o)[/tex][tex]\text{Use }\cos (180^o-30^o)=-\cos 30^o[/tex][tex]\cos (150^o)=-\cos (30^o)[/tex][tex]\text{Use }\cos (30^o)=\frac{\sqrt[]{3}}{2}\text{.}[/tex][tex]\cos (150^o)=-\frac{\sqrt[]{3}}{2}[/tex]Hence the required value is
[tex]\cos (150^o)=-\frac{\sqrt[]{3}}{2}[/tex]Factor completely.28 – 7x2Show Calculator
A map is created on a coordinate plane . Typ's house is located at (7,8) and the library is located at (7,-6) Each unit on the coordinate plane represents 1 block. How many blocks is it from Ty's house to the library? explain
We will have to calculate the distance between the two points ( that is between Ty's house to library
[tex]\text{distance betw}en\text{ two points = }\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex][tex](x_1,y_1)=(7,8)and(x_2,y_2)=(7,-6)_{}[/tex][tex]\begin{gathered} d=\text{ }\sqrt[]{(7-7)^2+(-6-8)^2}\text{ =}\sqrt{\text{ }0^2+(-14)^2}\text{ =}\sqrt[]{14^2\text{ }} \\ d=\text{ 14} \end{gathered}[/tex]There are 14 blocks between Ty's house to the library
how 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.
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]Is this correct? If not can you show me how to do it?
D. The rental cost in dollars, for each paddleboard.
Explanation:
You were in the right track with linking 40 to the paddleboards.
But remember that t represent the total cost and not the total number of paddleboards and kayak, and also since p represent the number of paddleboards (while k represent the number of kayak)
To find t, you need to sum the cost of all the kayaks and the sum of all the paddleboards.
=> t = 25k + 40p
with 25k = total cost of all the kayaks
and
with 40p = total cost of all the paddleboards => in others words the total number of paddleboards (p) * the cost of each paddleboards (40)
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)
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