If the statement is true, type true in the space provided. If it is false, replace the underlined word(s) with the word(s) that will make the statement true.
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The sum and difference of two simple quadratic surds are said to be conjugate surds to each other.
In general, the following surds are conjugate to each other:
[tex](x\sqrt{a}+y\sqrt{b})\text{ and \lparen}x\sqrt{a}-y\sqrt{b})[/tex]Therefore, the conjugate of the surd:
[tex](5-\sqrt{7})[/tex]will be:
[tex](5+\sqrt{7})[/tex]The statement is true.
Related Questions
Use the graph to answer the question.Which statement matches the vector operation shown on the coordinate grid?
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We have the correct statement about the vectors in the graph.
We can already see that it is a sum of vectors like:
[tex]v+w=u[/tex]As v has starting point at (-1,0) and ending point at (3,3), we can describe the vector as:
[tex]v=(3-(-1))\hat{i}+(3-0)\hat{j}=4\hat{i}+3\hat{j}[/tex]As w starts at (3, 3) and ends on (5, 2), we can describe it as:w
[tex]w=(5-3)\hat{i}+(2-3)\hat{j}=2\hat{i}-1\hat{j}[/tex]Finally, u starts at (-1,0) and ends at (5,2), so it can be described as:
[tex]u=(5-(-1))\hat{i}+(2-0)\hat{j}=6\hat{i}+2\hat{j}[/tex]Answer: v + w = u for v = 4i + 3j, u = 2i - j and u = 6i + 2j [Option C].
Please help me with the question below(also please answer the question in a maximum of 5-10 minutes).
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Given that Tom's yard is in the shape of a trapezoid, you know that the formula for calculating the area of a trapezoid is:
[tex]A=\frac{(b_1+b_2)}{2}\cdot h[/tex]Where "h" is the height of the trapezoid and these are the bases:
[tex]\begin{gathered} b_1 \\ b_2 \end{gathered}[/tex]In this case, you can identify that:
[tex]\begin{gathered} b_1=65\text{ }ft \\ b_2=50\text{ }ft \\ h=30\text{ }ft \end{gathered}[/tex]Then, you can substitute values into the formula and evaluate:
[tex]A=\frac{(65\text{ }ft+50\text{ }ft)}{2}\cdot30\text{ }ft[/tex][tex]A=\frac{115\text{ }ft}{2}\cdot30\text{ }ft[/tex][tex]A=\frac{3450\text{ }ft^2}{2}[/tex][tex]A=\frac{3450\text{ }ft^2}{2}[/tex][tex]A=1725\text{ }ft^2[/tex]Hence, the answer is:
[tex]1725\text{ }ft^2[/tex]3-35. Fisher thinks that any two lines must have a point of intersection. Is he correct? If so, explain how youknow. If not, produce a counterexample. That is, find two lines that do not have a point of intersection and explainhow you know
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Any two lines must have a point of intersection, with ONLY ONE exception : when the lines are parallel. That means they have exactly the same inclination or Slope.
As an example of two lines that hasnt point of intersection they are
y = 5x + 16
y = 5x + 11
We know both lines have no point of intersection because
both have the same slope or inclination m. By comparation with slope intercept equation
y = mx + b
then we see both have same inclination, and b is 11 in one line and 16 in the other line. This means both lines are parallel with one line going over the other line, without touching it in any point.
J(-6-2)3-*NWMark this and return2--9-8-7-6-5-4-3-2-3₁ 1 2 3 4 5 61-5737-2-cd-6--7--8-2 do-9--10--11--12--13-8 9 10 11 xK(8,-9)What is the x-coordinate of the point that divides thedirected line segment from J to K into a ratio of 2:5?X == (m²²7 m )(x₂ − ×₁) + X₁m+n0 000-22Save and ExitNextSubmit
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Use the given formula:
[tex]x=(\frac{m}{m+n})(x_2-x_1)+x_1[/tex]Being m: 2 and n: 5
x1: -6
x2: 8
[tex]\begin{gathered} x=(\frac{2}{2+5})(8-(-6))+(-6) \\ \\ x=\frac{2}{7}*(14)-6 \\ \\ x=4-6 \\ \\ x=-2 \end{gathered}[/tex]Then, the x-coordinate of th point that divides the directed line segment from J to K into a ratio 2:5 is -2Answer: -2Polynomial Functions:Find P(-1) and p(2) for each function.“P(x) = 4-3x”
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P(-1):
[tex]\begin{gathered} P(-1)=4-3(-1) \\ P(-1)=4+3 \\ P(x)=7 \end{gathered}[/tex]P(2):
[tex]\begin{gathered} P(2)=4-3(2) \\ P(2)=4-6 \\ P(2)=-2 \end{gathered}[/tex]At a school on Monday, 3 out of every 4 students were wearing shirts. There were 600 students present in school on Monday. How many of the students were wearing shirts? A. 599, because 600 - (4 - 3) = 599 B. 450, because C. 50, because 600 - (4 x 3) = 50 600 - Student D. 800, because 450 4= Students 3=sludents 4 600 600 800 so
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3 out of 4 students mean
3/4th students were wearing shirts.
Total students = 600
So,
3/4th of 600 students were wearing shirt.
Let us calcualte (3/4)th of 600:
[tex]\begin{gathered} \frac{3}{4}\times600 \\ =\frac{3\times600}{4} \\ =\frac{1800}{4} \\ =450 \end{gathered}[/tex]Answer450 students
write an equation of each parabola in vertex form. Vertex (3,-2) Point (2,3)
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The equation of Parabola in the vertex form with vertex (3,-2) and point(2,3) is y = 5(x-3)² - 2 .
The equation of parabola with vertex (h,k) is denoted by the equation
y = a(x-h)² + k
In the question ,
it is given that
the vertex of the Parabola is (3,-2) and the point is (2,3)
So, the equation of the parabola with vertex (3,-2) will be
y = a(x-3)² - 2
Since the point (2,3) lies on the parabola ,
So, 3 = a(2-3)² - 2
3 + 2 = a*(-1)²
5 = a
Substituting a in the equation y = a(x-3)² - 2 ,
we get
y = 5(x-3)² - 2
Therefore , The equation of Parabola in the vertex form with vertex (3,-2) and point(2,3) is y = 5(x-3)² - 2 .
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Send me Answers for Questions A, B, and C
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Answer: A) 4 B) 30 C) 6
Step-by-step explanation:
For question A, you subtract the highest number and the lowest number (10-6)
For question B, you add all the frequency numbers together
For question C, you use your answer on B and divide it by 5
Which formula can be used to find the sum of the mesures of all the interior angles of a regular polygon with n sides?
A. S = (n-2)180 degrees
B. S = (n+2)180 degrees
C. S = (n-2)90 degrees
D. S = (n+2)90 degrees
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Answer:180(n – 2),
Step-by-step explanation:
Can someone show me how to do this one correctly?
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ANSWER:
Juwan has 19 dimes and 6 quarters in his pocket.
STEP-BY-STEP EXPLANATION:
From the statement we can establish the following system of equations:
Taking into account that one dime is 10 cents and a quarter is 25 cents.
Let x be the number of dimes
Let y be the number of quarters
[tex]\begin{gathered} x+y=25\rightarrow x=25-y\text{ (1)} \\ 10x+25y=340\text{ (2)} \end{gathered}[/tex]We solve the system of equations by means of the substitution method, we substitute equation (1) in (2):
[tex]\begin{gathered} 10\cdot(25-y)+25y=340 \\ 250-10y+25y=340 \\ 15y=340-250 \\ y=\frac{90}{15} \\ y=6 \\ \\ \text{therefore, for x:} \\ x=25-6 \\ x=19 \end{gathered}[/tex]Therefore they are 19 dimes and 6 quarters
Find the solutions to the following quadratic equation negative 3X squared plus 4X plus one equals zero (-3x^2 + 4x + 1 = 0)
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Answer:
Explanation:
Given:
[tex]-3x^2+4x+1=0[/tex]To find:
the value of x using the quadratic formula
The quadratic formula is given as:
[tex]$$x\text{ = }\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}$$[/tex]where a = -3, b = 4, c = 1
[tex]\begin{gathered} x\text{ = }\frac{-4\pm\sqrt{(4)^2-4(-3)(1)}}{2(-3)} \\ \\ x\text{ = }\frac{-4\pm\sqrt{16+12}}{-6} \\ \\ x\text{ = }\frac{-4\pm\sqrt{28}}{-6} \end{gathered}[/tex][tex]undefined[/tex]Write an expression to show how much Gretchen paid for drama,action, and comedy videos if she paid $4 for each at a sale. Evaluate the expressionGretchen’s video purchasesMystery 6Action 3Comedy 5Drama 2Romance 2
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Let d the number of drama videos, c the number of comedy videos and a the number of action videos.
If the cost per video (independently of the genre) is $4, then, for the total cost of the videos Gretchen payed, you can write:
total = 4d + 4c + 4a
Now, based on the given table, you have:
d = 2
c = 5
a = 3
By replacing the previous values into the expression for total, and by simplifying, you obtain:
total = 4(2) + 4(5) + 4(3)
total = 8 + 20 + 12
total = 40
Hence, Gretchen payed $40 for the videos
Graph the line y = 5x – 1, then name the slope and y-intercept by looking at the graph.
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Answer:
m = 5
y-intercept = (0, -1)
Step-by-step explanation:
y = mx + b
y = 5x - 1
m = 5
y-intercept = b = (0, -1)
Point 1: (0, -1)
Point 2: (1, 4)
Point 3: (-1, -6)
I hope this helps!
State if the given binomial is a factor of the given polynomial.Question #9
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We can use the Factor Theorem to state if the given binomial is a factor of the given polynomial.
The factor theorem states that when f(c)=0 that means the remainder is zero and (x-c) must be a factor of the polynomial.
The given polynomial is:
[tex]k^3+8k^2+6k-12[/tex]Then if (k+2) is a factor of the polynomial, k+2=0, k=-2, f(-2) must be equal to 0.
Let's check:
[tex]\begin{gathered} f(k)=k^3+8k^2+6k-12 \\ f(-2)=(-2)^3+8(-2)^2+6(-2)-12 \\ f(-2)=-8+8\cdot4-12-12 \\ f(-2)=-8+32-24 \\ f(-2)=32-32 \\ f(-2)=0 \end{gathered}[/tex]Thus, (k+2) is a factor of the given polynomial.
Compare the triangles and determjne whether they can be proven congruent, if possible by SSS, SAS, ASA, AAS or HL
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Since the triangles has a pair of congruent (equal) angles , and an equal side between the angles. It is congruent by ASA ( angle -side -angle)
Which values are solutions to the inequality below?Check all that apply.√x ≤ 5A. 1B. 18C. -5D. 25E. 24F. 625
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Given the inequality:
[tex]\sqrt[]{x}<5[/tex]We need to solve the inequality to get a range of values for x.
This we can do by finding the square of both sides:
[tex]\begin{gathered} (\sqrt[]{x})^2<5^2 \\ x<25 \end{gathered}[/tex]On checking the options given, we will pick the numbers that are strictly less than 25.
Therefore, the correct options are:
OPTION A
OPTION B
OPTION C
OPTION F
On a particular day, the amount of untreated water coming into the plant can be modeled by f(t) = 100 + 30cos(t/6) where t is in hours since midnight and f(t) represents thousands of gallons of water. The amount of treated water at any given time, t, can be modeled by g(t) = 30e^cos(t/2)a) Define a new function, a′(t), that would represent the amount of untreated water inside the plant, at any given time, t.b) Find a′ (t).c) Determine the critical values of this function over the interval [0, 24).
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a)The amount of untreated water inside the plant will be the difference between the difference f(t) - g(t), then, a(t) can be defined as follows:
[tex]a(t)=100+30cos(\frac{t}{6})-30e^{cos(\frac{t}{2})}[/tex]b) the derivative of a(t) is the following:
[tex]a^{\prime}(t)=-5sin(\frac{t}{6})+15sin(\frac{t}{2})e^{cos(\frac{t}{2})}[/tex]c) the critical values of a(t) over the interval [0, 24) are:
[tex]\begin{gathered} t=0 \\ t=6\pi \end{gathered}[/tex]I need your help know
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Given the following data
Base area of the cone = 6cm
Height of the cone = 9 cm
The volume of a cone is given as
[tex]\begin{gathered} V\text{ = }\frac{1}{3}\cdot\text{ }\pi\cdot r^2\cdot\text{ h} \\ \text{where }\pi\text{ = 3.14},\text{ r = 6cm , and h = 9cm} \\ V\text{ = }\frac{1}{3}\cdot\text{ 3.14 }\cdot6^2\cdot\text{ 9} \\ V\text{ = }\frac{1}{3}\text{ x 3.14 x 36 x 9} \\ V\text{ = }\frac{3.14\text{ x 36 x 9}}{3} \\ V\text{ = }\frac{1017.36}{3} \\ V=339.1cm^3 \end{gathered}[/tex]8. Anna withdrew $50 from her checking account. She spent $28 on a pair of shoes. What fraction of her money does Anna have left?
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Explanation:
If she spent $28 of the $50 she withdrew, she now has:
[tex]50-28=22[/tex]$22
The fraction is:
[tex]\frac{22}{50}=\frac{11}{25}[/tex]Answer:
Anna has 11/25 of her money left.
Given ΔABC with m∠B = 62°, a = 14, and c = 16, what is the measure of A?
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1) Let's sketch this out to better grasp it
2) We can see that there are two legs and two angles (one of them is missing) so let's solve it using the Law of Sines:
[tex]undefined[/tex]The fraction models below represent two fractions of the same whole: How much of the8음을16
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So 4/5 times 5/8 is 1/2.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.Solve the inequality and describe the solution set.y-6 > 1232, Math symbolsRelations► Geometry► Groups► Trgonometry3 of 3 AnsweredType here to searcho66F Mosty clou
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The problem gives the inequality:
[tex]y-6\ge12[/tex]solving for y we get:
[tex]\begin{gathered} y\ge12+6 \\ y\ge18 \end{gathered}[/tex]The solution set is all real numbers equal or greater than 18, i.e.,
[tex]\lbrack18,+\infty)[/tex]What is the remainder when 5x3 + 2x2 - 7 is divided by x + 9?-93,7503,800-3,490
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Explanation
Given the expression
[tex]5x^3+2x^2-7[/tex]The remainder when it is divided by x+9 can be seen below;
[tex]r=5(-9)^3+2(-9)^2-7=-3645+162-7=-3490[/tex]Answer: -3490
Which expression demonstrates how the Distributive Property could be used to find the product of 5 and 48?
A. 50 − 5 (2)
B. 5 (50) − 2
C. 5 (50) + 5 (2)
D. 5 (50 − 2) + 5 (2)
E. None of these
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Answer:
Step-by-step explanation:
C
An envelope is 15 centimeters wide, and it measures 17 centimeters along the diagonal. The envelope is __ centimeters tall.
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An envelope is rectangular in shape.
Given the width = 15cm, and diagonal = 17cm
Let h represent the tall length of the envelope
Applying Pythagoras theorem, we have
[tex]\begin{gathered} 17^2=15^2+h^2 \\ 289=225+h^2 \\ h^2=289-225 \\ h^2=64 \\ h=\sqrt[]{64} \\ h=8\operatorname{cm} \end{gathered}[/tex]The envelope is 8cm tall
What is a stem and leaf plot? How is it used and how exactly do i solve one? (an example would be great)
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A stem and leaf plot is a table where each of the data is divided into two parts. The stem, that is the first digit and the leaf is the last digits. Let's say that we have the following set of data.
[tex]10,\text{ 12, 25, 28, 29, 35, 38, 40, 44}[/tex]If we want to make a stem and leaf plot of that data, we first write a column where we place the first digit of each number without repetition, like this:
[tex]\begin{gathered} 1 \\ 2 \\ 3 \\ 4 \end{gathered}[/tex]These are the stems. Now the leaves are the last digit of each number put in order next to the corresponding first digit, like this:
[tex]\begin{gathered} 1\parallel\text{ 0 2} \\ 2\parallel\text{ 5 8 9} \\ 3\text{ }\parallel\text{5 8} \\ 4\text{ }\parallel\text{0 4} \end{gathered}[/tex]In an arithmetic sequence with a1=-5 and d=-3, which term is -24?The term -24 is the ___th term of the sequence
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Given:
[tex]\begin{gathered} a_1=-15 \\ d=-3 \\ a_n=-24 \end{gathered}[/tex]To find:
The value of n.
Explanation:
The nth term formula for the arithmetic sequence is,
[tex]a_n=a_1+(n-1)d[/tex]Substituting the given values we get,
[tex]\begin{gathered} -24=-15+(n-1)(-3) \\ -24=-15-3n+3 \\ -24=-3n-12 \\ -3n=-24+12 \\ -3n=-12 \\ n=4 \end{gathered}[/tex]Thus, -24 is the 4th term of the sequence.
Final answer:
The term -24 is the 4th term of the sequence.
Hello! I need a little bit of help with this question please. (This information is not from an open test, it is a book as I'm studying for the ASVAB I am going to take later on.)
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Given:
[tex]\sqrt{100}-\sqrt{64}[/tex]To find:
We need to solve this sum and find the final answer
Step-by-step solution:
To solve this problem, we need to know the square root of 100 and 64.
√100 = 10
√64 = 8
[tex]\begin{gathered} =\sqrt{100}-\sqrt{64} \\ \\ =10\text{ - 8} \\ \\ =2 \end{gathered}[/tex]Final answer:
Thus 2 (Option A) is the correct answer.
what is the y intercept of y = 250 + 15x
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The y-intercept of y = 250 + 15x is (0,250)
What is y-intercept?A line's y-intercept is the distance in y coordinates from the line's intersection with the y-axis at its origin. A location on the graph where x is 0 is known as the y-intercept. The y-intercept of a line that is perpendicular to the x-axis is undefined.
This is an illustration of a y-intercept. Think about the line y = x + 3. The point where this graph crosses the y-axis is (0,3). Therefore, the y-intercept of the line y = x+ 3 is (0,3).
Here to determine the y-intercept put x=0,
Given, y = 250 + 15x
Replacing x by 0 in the above equation we get,
y = 250 + 15×0
y=250 +0
y=250
Therefore, the y-intercept of y = 250 + 15x is (0,250)
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22The value of the hypotenuse in the right triangle shown isinches.14 in48 inFigure not drawn to scale
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SOL
Step 1 :
In this question, we are meant to find the value of
the hypotenuse in the right angle below:
Before, we proceed, we still need to remind ourselves of Pythagoras' theorem,
Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.
Step 2 :
From the above theorem, we can see that that the two adjacent sides are :
14 inches and 48 inches.
From the principle of Pythagoras' Theorem,
[tex]\begin{gathered} c^2=a^2+b^2 \\ \text{where a = 14 inches} \\ b\text{ = 48 inches} \\ c^2=14^2+48^2 \\ c^2\text{ = ( 14 x 14 ) + ( 48 x 48 )} \\ c^2\text{ = 196 + 2304} \\ c^2\text{ = 2500} \\ \text{square root both sides, we have that :} \\ c\text{ = 50 inches} \end{gathered}[/tex]
CONCLUSION :
The value of the hypotenuse in the Right angle, c = 50 inches.