D 7.7
1) Rational numbers are numbers that can be written as a ratio like
1/2, 3/5, 5, and so on.
2) The rational numbers between 7 2/3 and the √60
At first 7 2/3 can be rewritten as 23/3 or 7.66
√60 it is not a rational number but it is approximately 7.74
3) So the only is 7.7
For each ordered pair, determine whether it is a solution to the system of equations.y=-3x+56x+2y=10Is it a solution?YesNo(x, y)(-2, 11)(4,-7)(0,4)(-3,-6)
Given: The system of equations:
[tex]\begin{gathered} y=-3x+5 \\ 6x+2y=10 \end{gathered}[/tex]Required: Check whether the given order pair are solution to the system of equation or not.
(-2, 11)
(4,-7)
(0,4)
(-3,-6)
Explanation:
The equations are
[tex]\begin{gathered} 3x+y=5 \\ 6x+2y=10 \end{gathered}[/tex]These are actually the same equations and solution to these two equations are infinite.
So we check solution for first equation only.
Any orderd pair is a solution, if it satisfies the equation.
(1) Put (-2,11) in equation 3x+y=5
[tex]\begin{gathered} 3(-2)+11=5 \\ -6+11=5 \end{gathered}[/tex]which is true. Hence, (-2,11) is a solution.
(2) Put (4,-7) in equation
[tex]3(4)-7=12-7=5[/tex]which is correct. Hence (4,-7) is a solution.
(3) Put (0,4) in the equation
[tex]3(0)+4=0+4=4\ne5[/tex]Hence, (0,4) is not a solution.
(4) Put (-3,-6) in the equation.
[tex]3(-3)-6=-9-6=-15\ne5[/tex]Hence, (-3,-6) is not a solution.
Final Answer: (-2,11) and (4,-7) are solution to system of equation, whereas (0,4) and (-3,-6) are not.
The net of the triangle prism is shown below. Each of the bases is shaped like a isosceles triangle. What is the total surface area of the triangular prism in square centimeters
Given:
Height, h = 4 cm
Base, = 6 cm
Length, L = 20 cm
To find the permieter of the base which is the is isosceles triangle, let's find the two equal sides using pythagorean theorem.
We have:
[tex]\begin{gathered} c=\sqrt[]{3^2+4^2} \\ \\ c=\sqrt[]{9+16} \\ \\ c=\sqrt[]{25} \\ \\ c=5 \end{gathered}[/tex]thus, perimeter of the base is:
P = 5 + 5 + 6 = 16 cm
Thus, we have:
TSA =
[tex]\begin{gathered} TSA=(\frac{1}{2}\times6\times4)+(\frac{1}{2}\times6\times4)+(20\times5)+(20\times5)+(20\times6) \\ \\ \text{TSA}=12+12+100+100+120 \\ \\ \text{TSA}=344cm^2 \end{gathered}[/tex]What is the y-intercept of the equation?y=4x+5O (0,3)0 (0,4)O (0,5)0 (0,6)
To find the y intercept of the equation
y=4x + 5
We will compare it with the equation of the straight line;
y=mx + b
The b represents the slope
Hence comparing the two b=5
Therefore, the y intercept is 5
Option C is the correct option which is 5
OR
we can set the x to zero in the given equation;
y=4x + 5
y = 4(0) + 5
y = 5
Hence 5 is the y intercept
Hence comparing the two b=5
Therefore, the y intercept is 5
Option C is the correct option which is (0,5)
Or we can set the x raight line;
y=mx + b
The b
5. Which expression has the GREATEST value? 1 point 49 x 2 V 49 V16 A B 125 + V16 (25 x 3
Let's calculate the value of each expression:
A)
[tex]\sqrt[]{49}\cdot2=7\cdot2=14[/tex]B)
[tex]\sqrt[]{49}-\sqrt[]{16}=7-4=3[/tex]C)
[tex]\sqrt[]{25}+\sqrt[]{16}=5+4=9[/tex]D)
[tex]\sqrt[]{25}\cdot3=5\cdot3=15[/tex]The greatest value from these 4 options is 15, so the correct option is D.
12^x = 94Solve the equations and check for extraneous solutions
Given
[tex]12^x=94[/tex]Solve for x as shown below
[tex]\begin{gathered} \Rightarrow ln(12^x)=ln(94) \\ \Rightarrow xln(12)=ln(94) \\ \Rightarrow x=\frac{ln(94)}{ln(12)}\approx1.8284 \end{gathered}[/tex]The exact answer is x=ln(94)/ln(12). There are no extraneous solutions.
An airplane is flying at an altitude of 11,000 feet. The pilot wants to make asmooth final descent to the runway at an angle of depression of 7º. Howfar from the runway should the pilot begin the descent? Round to thenearest tenth.
Given:
Altitude of plane = 11,000 feet
Angle of depression = 7 degrees
Let's find the how far away from the runway should the pilot begin to descend.
Let's first draw a figure that represents this situation:
Here, we are to solve for x.
Since the pilot is to make a descent to the runway, we are asked to find the horizontal distance fro
To solve for x, apply the trigonometric ratio formula for tan.
Thus, we have:
[tex]\tan \theta=\frac{\text{opposite}}{\text{adjacent}}[/tex]WHere:
Opposite side is the side opposite the given angle = x
Adjacent side is the side adjacent to the given angle = 11000
θ = 7 degrees
Thus, we have:
[tex]\tan 7=\frac{x}{11000}[/tex]Let's solve for x:
Multiply both sides by 11000
[tex]\begin{gathered} 11000\tan 7=\frac{x}{11000}\ast11000 \\ \\ 11000(0.1227845609)=x \\ \\ 1350.6=x \end{gathered}[/tex]x = 1350.6 ft
Therefore, the pilot should begin the descent at a distance of 1350.6 ft from the runway.
ANSWER:
711Suppose a point has polar coordinates 6,with the angle measured in radians.6Find two additional polar representations of the point.Write each coordinate in simplest form with the angle in (-21, 211].
The Solution.
The given polar coordinate is
[tex](6,\frac{7\pi}{6})[/tex]The additional polar representations of the given point are:
Moving clockwise, we get
[tex](6,-\frac{5\pi}{6})[/tex]Starting from the negative point and moving anticlockwise, we have;
[tex](-6,\frac{\pi}{6})[/tex]The correct answer are:
[tex](6,\frac{5\pi}{6})\text{ and (-6,}\frac{\pi}{6})[/tex]How does g(x)= 2.10 change over the interval from x2 to x - 37g(x) decreases by 10g(x) Increases by a factor of 10g(x) decreases by a factor of 10g(x) increases by 1,000%
we are given the function
[tex]g(x)=2\cdot10^x[/tex]we want to check how the function changes from x=2 to x=3. We will calculate
[tex]\frac{g(3)}{g(2)}[/tex]to check how it changed. So we have
[tex]\frac{g(3)}{g(2)}=\frac{2\cdot10^3}{2\cdot10^2}=10^{3\text{ -2}}=10[/tex]which means that g increases by a factor of 10
Last year, Tom opened an investment account with $6200. At the end of the year, the amount in the account had increased by 24.5%. How much is thisincrease in dollars? How much money was in his account at the end of last year?
The volume of the figure shown is 576 cubic in. How would the volume change if the height changed 6 in?
The given figure is a rectangular prism.
The volume of a rectangular prism is given by
[tex]V=l\cdot w\cdot h[/tex]Where l is the length, w is the width, and h is the height of the rectangular prism.
The volume of the figure shown is 576 cubic in for the following dimensions.
Length = 8 in
Width = 6 in
Height = 12 in
[tex]V=8\cdot6\cdot12=576\: in^3[/tex]If the height is changed to 6 in, then the volume is
[tex]V=8\cdot6\cdot6=288\: in^3[/tex]Therefore, the volume of the figure will be reduced to 288 cubic inches if the height is changed to 6 inches.
A serving of ice cream is 1/4 cup. How much ice cream is on 3 1/2 servings?
The number of cups of ice cream is:
[tex]\begin{gathered} 3\frac{1}{2}\div\frac{1}{4} \\ \frac{7}{2}\times\frac{4}{1} \\ \frac{28}{2}=14 \end{gathered}[/tex]Hence, there would be 14 cups of serving of the ice cream
Bobby measured the middle school and made a scale drawing. The gym is 135 inches wide in the drawing. The actual gym is 63 feet wide. What scale did Bobby use for the drawing?15 inches :
Answe
15 inches : 7 feet.
Explanation
The actual gym width = 63 feet
The gym width in the drawing = 135 inches
The required scale is 135 inches : 63 feet.
Divide all through by 9
135/9 : 63/9 = 15 inches : 7 feet.
Therefore, the scale Bobby use for the drawing is 15 inches : 7 feet.
y=2/3x+8 put in standard form
Standard Form of LIne:
[tex]Ax+By=C[/tex]So, that is basically putting x and y's to the left side and the constant to the right side.
We have:
[tex]y=\frac{2}{3}x+8[/tex]Let's get rid of the fraction by multiplying the whole equation by 3, to get:
[tex]\begin{gathered} 3\times(y=\frac{2}{3}x+8) \\ 3y=2x+24 \end{gathered}[/tex]Now re-arranging and putting in standard form:
[tex]-2x+3y=24[/tex]Can a triangle have two right angles? How can you justify your answer?
NO
The sum of all the angles of a triangle add up to 180°.
A triangle has 3 angles.
If a triangle has 2 right angles, each right angle measures 90°.
90°+90°= 180°
The third angle can't be zero.
Can you pls help me I don’t know how to do this
Answer:
a is 11
b is 6
c is 4
Explanation:
Here, we want to get the values of a, b and c
The general form of a quadratic equation is:
[tex]f(x)\text{ = ax}^2+bx\text{ + c}[/tex]where a is the coefficient of x^2
b is the coefficient of x
c is the last value
Looking at the equation given :
a is 11
b is 6
c is 4
The options for the first drop down menu is 2.5 3 5 or 6The options for the second drop down menu is 26.5 37 53 74
ANSWER:
DE = 2.5 units
EDF = 74°
STEP-BY-STEP EXPLANATION:
The first thing in this case is to calculate the ratio between both triangles with the known sides BC and EF:
[tex]r=\frac{6}{3}=2[/tex]Now, this ratio is conserved in all the triangles since they are similar, therefore, we calculate the DE value like this:
[tex]\begin{gathered} r=\frac{AB}{DE} \\ DE=\frac{AB}{r}=\frac{5}{2} \\ DE=2.5 \end{gathered}[/tex]Being similar triangles, the angles are equal, we know that an isoceles triangle, because it has two equal sides, therefore, it also has two equal angles and knowing that the sum of the internal angles in a triangle is equal to 180 degrees, we can calculate the value of the angle EDF, just like this:
[tex]\begin{gathered} 180=53+53+\text{EDF} \\ \text{ Solving for EDF} \\ \text{EDF}=180-53-53 \\ \text{EDF }=74\text{\degree} \end{gathered}[/tex]If length of EF is 3 units, then the length of DE is 2.5 units. If m
What is the measure of 21, 22 and 23?sр1 2/360°4 61°9mZ1 =mZ2 =mZ3 =
6In AABC, AB = x, BC = y, and CA = 2x. A similarity transformation with a scale factor of 0.5 maps AABC to AMNO, such that vertices M, N, and Ocorrespond to A B, and C, respectively. If OM=5, what is AB?OA AB=2.5OB. AB=10OC AB=5OD. AB=1.25OE AB=2
Triangle ABC is scaled to triangle MNO with a scale factor of 0.5.
The lengths of triangle ABC are:
AB = x
BC = y
CA = 2x
The corresponding lengths of triangle MNO are:
MN = 0.5 AB = 0.5x
NO = 0.5 BC = 0.5y
OM = 0.5 CA = 0.5 (2x) = x
We are given OM = 5, thus:
x = 5
Length of AB is x, thus:
AB = 5
Answer: C AB = 5
Use the value of the discriminant to determine the number and type of roots for each equation.X^2=4x-4
The first step we have to follow is to write the equation in standard form:
[tex]\begin{gathered} x{}^2=4x-4 \\ x^2-4x+4=0 \end{gathered}[/tex]The discriminant of a quadratic expression is given by:
[tex]D=b^2-4ac[/tex]If the discriminant is greater than 0 and has a rational square root, the equation has 2 real rational roots; if it is greater than 0 and does not have a rational square root, the equation has 2 real irrational roots; if it is equal to 0, the equation only has 1 real rational root; and if it is less than 0, the equation has no real roots.
Find the discriminant using the values of the equation:
[tex]\begin{gathered} D=(-4)^2-4(1)(4) \\ D=16-16 \\ D=0 \end{gathered}[/tex]It means that this equation has 1 real, rational root.
Use the unit circle to evaluate the followingHow do I solve this problem?
Notice that:
[tex]\cos (\frac{4\pi}{3})=\cos (\pi+\frac{\pi}{3})\text{.}[/tex]Recall that:
[tex]\cos (\pi+x)=-\cos (x)\text{.}[/tex]Therefore:
[tex]\cos (\frac{4\pi}{3})=-\cos (\frac{\pi}{3})=-\frac{1}{2}\text{.}[/tex]Answer:
[tex]cos(\frac{4\pi}{3})=-\frac{1}{2}\text{.}[/tex]Given the equation y= 4x + 1, what is the slope of the line represented by the equation?
Linear equations are in the form
[tex]y=mx+b[/tex]in which b represents the y intercept and m represents the slope of the line that will be graphed.
according to this the slope of the line represented by the equation given ill be 4.
Negative 4 times a number is no less than 5 A -4n < 5B -4n > 5C -4n <_ 5D -4n _> 5
Answer:
The correct inequality is;
[tex]-4n\ge5[/tex]Explanation:
Given that Negative 4 times a number is no less than 5.
Let n represent the number.
Negative 4 times a number is;
[tex]\begin{gathered} -4\times n \\ -4n \end{gathered}[/tex]Negative 4 times a number is no less than 5.
Since the statement says that it is no less than that implies that it is either greater than or equal to 5;
[tex]-4n\ge5[/tex]Therefore, the correct inequality is;
[tex]-4n\ge5[/tex]-2x-y=12y=-26-9xI need help with using elimination
Given the system of equations:
[tex]\begin{cases}-2x-y=12 \\ y=-26-9x\end{cases}[/tex]We can rewrite the second equation:
[tex]\begin{cases}-2x-y=12 \\ 9x+y=-26\end{cases}[/tex]Now, we can add these two equations, canceling the variable y:
[tex]\begin{gathered} -2x-y+9x+y=12-26 \\ 7x=-14 \\ \Rightarrow x=-2 \end{gathered}[/tex]Now, we can use this result to find the value of y. Using the second equation:
[tex]\begin{gathered} 9\cdot(-2)+y=-26 \\ -18+y=-26 \\ y=-26+18 \\ \Rightarrow y=-8 \end{gathered}[/tex]The solution is:
[tex]\begin{gathered} x=-2 \\ y=-8 \end{gathered}[/tex]It's possible to build a triangle with side lengths 3,3, and 3. A. True B. False
A triangle with three equal sides is called an equilateral triangle. So, a triangle with three equal sides 3 can be made. The answer is true.
A flight attendant surveyed passengers on a flight about where they would prefer to sit. The results are shown in the Aisle WindowTotal Front 4 8. 12 Back 10 14 24 Total 14 22 36 What is the probability that a passenger prefers to sit in the front of the plane and prefers a window seat?
The question of probabilities takes into account the number of required outcomes over the number of total outcomes.
A look at the table shows that the intersection of front and window seats is at 8. That is the first figure on the second column indicates those who would prefer a fron seat by the window. Note that there is a total of 36 passengers.
Hence the probability that a passenger prefers to sit in the front of the plane and prefers a window seat is shown as
[tex]\begin{gathered} P(\text{front and window)=}\frac{Number\text{ of required outcomes}}{Number\text{ of possible outcomes}} \\ P(\text{front and windows)=}\frac{8}{36} \\ P(\text{fron and window)=}\frac{2}{9} \end{gathered}[/tex]The correct answer is option D
George runs hurdles he clears the hurdles in 90% of the time which of the following statements apply9/9 times9/10 times90/10090/1000
Answer:
Jorge clears the hurdles in 90/100 times
Explanation:
Given that "Jorge runs hurdles he clears the hurdles in 90% of the time"
Then 90% can be written in fraction as;
[tex]90\text{\%=}\frac{90}{100}=\frac{900}{1000}=\frac{9}{10}[/tex]Any of the fractions above are correct.0
So, from the given options, Only option C is correct.
Jorge clears the hurdles in 90/100 times
which of the following statementsvmust bevtrue based on the diagram below
Given data:
The given triangles.
The GH is the segment bisector or G is the mid point of DE.
Thus, the options first and fifth are correct.
write a quadratic equation in the form x^2 + bc + c= 0 that has the following rootsroots {5,1}}
x² - 6x + 5 = 0
Explanation:The roots of the equation: (5, 1)
To get the equation we use the formula:
x² - (sum of roots)x + product of roots = 0
Sum of roots = 5 + 1
Sum of roots = 6
product of roots = 5 × 1
product of roots = 5
The equation becomes:
x² - 6x + 5 = 0
At a local restaurant, the amount of time that customers have to wait for their food isnormally distributed with a mean of 18 minutes and a standard deviation of 4minutes. Using the empirical rule, determine the interval of minutes that the middle68% of customers have to wait.Submit Answer
Answer:
(14, 22)
Explanation:
The amount of time that customers have to wait for their food is normally distributed with:
[tex]undefined[/tex]• Mean = 18 minutes
,• Standard deviation = 4 minutes.
The Empirical Rule
For normal distributions, the empirical rule states that:
• 68% of observed data points will lie inside one standard deviation of the mean.
,• 95% will fall within two standard deviations
,• 99.7% will occur within three standard deviations.
By the empirical rule, 68% of observed data points will lie inside one standard deviation of the mean.
Therefore, the interval of minutes that the middle 68% of customers have to wait is:
[tex](\mu-\sigma,\mu+\sigma)=(18-4,18+4)=(14,22)[/tex]The interval is (14, 22).
Given the following measurements, calculate the minimum and maximum possible areas of the object. Round your answer to the nearest whole square unit. The length and width of a book cover are 23.5 centimeters and 15 centimeters, respectively. The minimum possible area is about cm2. The maximum possible area is about cm2.
Find the area
The area of a rectangle is equal to
A