First, write out the binomial expression.
[tex]x^2\text{ + 25}[/tex]The binomial expression is a prime mathematical express meaning it has two factors, 1 and x^2 + 25.
Therefore,
[tex]\begin{gathered} \text{The factors of x}^2+25 \\ \text{are 1 and (x}^2\text{ + 25).} \end{gathered}[/tex]Line Segment AC is 10 centimeters (cm) long, Point M is the midpoint of AC.What will happen to the length of AC if Point A is moved so that the length of AM is squared and the length of MC remains the same?The length of AC will triple.The length of AC will double.The length of AC will be squared.The length of AC will be five times as large.
We know that AC is 10 centimeters long, and M is the midpoint of AC.
If we move point A as the problem says, we have.
As you can observe, the length of AC is triple.
Hence, the right answer is the first option: The length of AC will triple.The figure below is composed of squares and semi-circles. Find the perimeter of this shape. Show your work.
Problem
Solution
For this case we can find the perimeter of the figure with the following operation
[tex]P=(2\cdot4)+\pi(4)+(2\cdot4)+\pi(4)=2\pi(4)+8+8[/tex]Then the final answer would be:
[tex]P=16+8\pi[/tex]Select all the statements below that are true for the following graph
From the graph given,
It is an absolute function
The following statements are true about the graph
i) The vertex is located at (2, -2)
ii) The graph has two zeros
ii) The range is [-2, ∞)
A giant pie is created in an attempt to break a world record for baking. The pie is shown below:What is the area of the slice of pie that was cut, rounded to the nearest hundredth? 78.13 ft2 82.43 ft2 86.31 ft2 91.98 ft2
step 1
Find out the area of the complete pie
[tex]A=pi*r^2[/tex]r=30/2=15 ft ----> the radius is half the diameter
substitute
[tex]\begin{gathered} A=pi*15^2 \\ A=225pi\text{ ft}^2 \end{gathered}[/tex]Remember that the area of a complete circle, subtends a central angle of 360 degrees
so
Applying proportion
Find out the area for a central angle of 42 degrees
[tex]\begin{gathered} \frac{225pi}{360^o}=\frac{x}{42^o} \\ \\ x=\frac{225p\imaginaryI}{360^{o}}*42^o \\ \\ x=26.25pi \\ x=26.25*3.14 \\ x=82.43\text{ ft}^2 \end{gathered}[/tex]The answer is 82.43 ft212. What is the equation of a circle with center (6,-4) and radius 6?(x - 6)2 + (y + 4)2 = 6(x + 6)2 + (y - 4)2 = 36(x + 6)2 + (y - 4)2 = 6(x - 6)2 + (y + 4)2 = 36
The equation of a circle with center (h, k) and radius r is given by the following expression:
[tex](x-h)^2+(y-k)^2=r^2[/tex]In this case, the center of the circle is located at (6, -4), and its radius equals 6, then by replacing 6 for h, -4 for k and 6 for r, we get:
[tex]\begin{gathered} (x-6)^2+(y-(-4))^2=6^2 \\ (x-6)^2+(y+4)^2=36 \end{gathered}[/tex]Then, the last option is the correct answer: (x - 6)^2 + (y + 4)^2 = 36
Which number line shows the solutions to n -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
The expression
[tex]n<-3[/tex]means "n takes values less than -3 but without taking the 3", for the symbol <.
Then, the number line that shows the solutions of the expression is
What is the vertex for the graph of y– 4 = - (x+1)^2??O A. (4,-1)O B. (1,-4)O c. (-1,4)O D. (-4,1)
The equiation of parabola in vertex form is:
[tex]y\text{ = a}\cdot(x-h)^2\text{ + k}[/tex]where (h, k) are the coordinates of the vertex and a is a constant. In our case we have:
[tex]y-4=-(x+1)^2[/tex]add 4 to both sides:
[tex]y\text{ -4 +4 = -}(x+1)^2\text{ + 4}[/tex]Resolving:
[tex]y=-(x+1)^2\text{ + 4}[/tex]Therefore we already have it in the vertex form and we have to:
[tex]\begin{gathered} h\text{ = -1 } \\ k\text{ = 4} \end{gathered}[/tex]Therefore the answer is c. (-1, 4)
Can you just tell me the answer to this problem I need to finish it quickly I don’t need to work lol sorry it’s #6 I need help in
The combined triangles will look as shown below:
It can be observed that the lengths of the three sides fit alongside one another perfectly. This means that the lengths are equal.
Also, the middle piece of the three triangles has no space when it aligns with the other two triangles. This means that all the angles add up to 180°.It would also be a safe assumption that the angles are equal to each other, therefore the measure of each angle will be:
[tex]\Rightarrow\frac{180}{3}=60\degree[/tex]Therefore, it can be observed that the sides and angles of the three triangles are equal.
Ezra has a square brick patio. He wants to reduce the width by 6 feet and increase the length by 6 feet.Let xrepresent the length of one side of the square patio Write expressions for the length and width of the new patio. Then find the area of the new patio if the original patio measures 13 feet by 13 feet.
Explanation:
Ezra has a square brick patio where x represents the length of one side of this square patio:
And hee wants to reduce the width by 6 feet, and increase the length by 6 feet.
The new width is x-6,
The new length is x+6.
[tex]\begin{gathered} Expressions\text{ for the length and the width of the new patio:} \\ l=x+6 \\ w=x-6 \end{gathered}[/tex]Then, we need to find the area of the new patio:
[tex]A=lw[/tex]We multiply the length by the width. The area is:
[tex]lw=(x+6)(x-6)[/tex]And finally, if the original measure of the sides is x=13 ft, the area of the new patio is:
[tex]\begin{gathered} (x+6)(x-6) \\ \downarrow \\ (13+6)(13-6) \\ \downarrow \\ (19)(7) \\ \downarrow \\ 133 \end{gathered}[/tex]Since it represents the area the units are square feet:
133 square feet.
These results are shown in option B.
Answer:
[tex]lw=(x+6)(x-6);133\text{ square feet}[/tex]Given: AB = CB, LABD= LABD= LCBD Prove: LA= LCStatement Reason
Explanation:
We know that AB = CD and that ∠ABD = CBD because it is given information.
Then, we have that BD = BD because a side is congruent to itself. It is called the reflexive property of congruence.
Now, we can say that ΔABD = ΔBDC by SAS (Side - Angle - Side) because we have two congruent sides and the angle between them is also congruent
Finally, ∠A = ∠C because the corresponding sides of congruent triangles are congruent
Answer:
Therefore, the answer is
I need to know the new equation, I’ve provided a picture
Hello there. To solve this question, we'll simply have to make x => x + 5 in the function.
Given the function:
[tex]f(x)=4x^2-3^{}[/tex]We have to determine f(x + 5)
By making x => x + 5 in this function, we get:
[tex]f(x+5)=4\cdot(x+5)^2-3[/tex]Now remember the binomial expansion of order 2:
[tex](a+b)^2=a^2+2ab+b^2[/tex]Therefore we have:
[tex]f(x+5)=4\cdot(x^2+2\cdot x\cdot5+5^2)-3[/tex]Multiply the terms inside parentheses and calculate the square.
[tex]f(x+5)=4\cdot(x^2_{}+10x+25)-3[/tex]Apply the distributive property
[tex]f(x+5)=4x^2+4\cdot10x+4\cdot25-3[/tex]Multiply and add the numbers
[tex]\begin{gathered} f(x+5)=4x^2+40x+100-3 \\ \boxed{f(x+5)=4x^2+40x+97} \end{gathered}[/tex]This is the answer we're looking for.
A way of showing this is the correct answer is to make x = 1 and x = 6 in the former function:
[tex]\begin{gathered} f(1)=4\cdot1^2-3=4\cdot1-3=4-3=1 \\ f(6)=4\cdot6^2-3=4\cdot36-3=144-3=141 \end{gathered}[/tex]Then making x = 1 in the expression we found after:
[tex]f(1+5)=f(6)=4\cdot1^2+40\cdot1+97=4+40+97=141[/tex]As expected.
Use the Distance and Slope Formulas to complete the tables below. Round to the nearest tenth,1. Find the length of MN, given the coordinates M (4,- 4) and N (2.0).imImMN:
Given the coordinates;
[tex]\begin{gathered} M(4,-4) \\ N(2,0) \end{gathered}[/tex]The slope m of the line MN is;
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \text{Where x}_1=4,y_1=-4,x_2=2,y_2=0 \end{gathered}[/tex][tex]\begin{gathered} m=\frac{0-(-4)}{2-4} \\ m=\frac{4}{-2} \\ m=-2 \end{gathered}[/tex]The slope of a line parallel to the line MN must have a slope equal to line MN, that is;
[tex]\mleft\Vert m=-2\mright?[/tex]The slope of a line perpendicular to line MN has a slope of negative reciprocal of line MN, that is;
[tex]\begin{gathered} \perp m=-\frac{1}{-2} \\ \perp m=\frac{1}{2} \end{gathered}[/tex]Using the distance formula to find the length of MN, the formula is given as;
[tex]D=\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2}[/tex][tex]\begin{gathered} \text{Where x}_1=4,y_1=-4,x_2=2,y_2=0 \\ |MN|=\sqrt[]{(0-(-4)^2+(2-4)^2} \\ |MN|=\sqrt[]{16+4} \\ |MN|=\sqrt[]{20} \\ |MN|=4.5 \end{gathered}[/tex]1. Find the domain and range of f(x) = sqrt(x)2. Find the domain and range of f(x) = 3x + 2
We have the function:
[tex]f(x)=\sqrt[]{x}[/tex]The domain is the set of values of x for which f(x) is defined. In this case, f(x) is defined only for non-negative values of x, so the domain is D:{x≥0}.
The range is the set of values that f(x) can take for the domain in which it is defined. In this case, f(x) will only take non-negative values, so the range can be defined as R: {y≥0}.
For the linear function f(x) = 3x+2, we don't have restrictions for the domain and the the range: both x and y can take any real value, so the domain and range are D: {x: all real numbers} and R: {y: all real numbers}.
Answer:
For the function f(x) = √x, the domain is D:{x≥0} and the range is R: {y≥0}.
For the function f(x) 3x+2, the domain is D: {x: all real numbers} and the range is R: {y: all real numbers}.
6x-4>23what two values solve for x
Given:
[tex]6x-4>23[/tex][tex]\begin{gathered} 6x-4+4>23+4 \\ 6x>27 \\ x>\frac{27}{6} \\ x>4.5 \end{gathered}[/tex]Dane is using two differently sized water pumps to clean up flooded water. The larger pump can
remove the water alone in 240 min. The smaller pump can remove the water alone in 400 min.
How long would it take the pumps to remove the water working together?
minutes
The rate of work obtained from the 240 and 400 minutes it takes for the large and small pumps to remove the water alone respectively, gives the duration it takes for the two pumps to remove the water working together as 150 minutes.
What is the rate of work formula?The rate of work in completing a project is given by the reciprocal of the time it takes to complete the project.
The given parameters are;
The time it takes the larger pump to remove the water, A = 240 minutes
The time it takes the smaller pump to remove the water, B = 400 minutes
The rate of doing work by the larger pump = [tex]\frac{1}{240}[/tex]
The work rate of the smaller pump = [tex]\frac{1}{400}[/tex]
The rate of work of the two pumps combined, [tex]\frac{1}{r}[/tex], is therefore;
[tex]\dfrac{1}{A} +\dfrac{1}{B} = \dfrac{1}{r}[/tex]
Where;
r = The time it takes for the two pumps to remove the water together
Which gives;
[tex]\dfrac{1}{240} +\dfrac{1}{400} = \dfrac{1}{150} = \dfrac{1}{r}[/tex]
∴ r = 150
The time it takes for the two pumps to remove the water together is 150 minutes
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Answer: 150 min
(I completed the question)
If Rolle's Theorem can be applied, find all values of c in the open interval (a, b) such that f '(c) = 0. (Enter your answers as a comma-separated list. If Rolle's Theorem cannot be applied, enter NA.)
Since we can apply Rolle's Theorem:
[tex]\begin{gathered} f^{\prime}(x)=-\sin (x) \\ so\colon \\ f^{\prime}(x)=0 \\ -\sin (x)=0 \end{gathered}[/tex]Take the inverse sine of both sides:
[tex]\begin{gathered} x=\sin ^{-1}(0) \\ x=\pi n \\ n\in\Z \end{gathered}[/tex]Since it is for the interval:
[tex]\lbrack\pi,3\pi\rbrack[/tex]The solutions are:
[tex]x=\frac{3\pi}{2},\frac{5\pi}{2}[/tex]Answer:
[tex]\begin{gathered} c=\frac{3\pi}{2},\frac{5\pi}{2} \\ or \\ c\approx4.71,7.85 \end{gathered}[/tex]ring×heart=hathat×2=heartheart-ring=1/4
Let's begin by identifying key information given to us:
[tex]undefined[/tex]which of the following describes the area of a circle?
The area of the circle is given by:
[tex]A=\pi r^2[/tex]So, the area of a circle is basically:
[tex]A=\frac{1}{2}\times2\pi r\times r[/tex]It can be seen as the number of squares inside of the circle
An open topped box can be created by cutting congruent squares from each of the four corners of a piece of cardboard that has dimensions of 30 cm by 40 cm and folding up the sides. Determine the dimensions of the squares that must be cut to create a box with volume of 2448cm^3.
Let's start by drawing the situation:
According to this, one of the dimensions of the box is 40-2x. The other one is 30-2x and the last one, that we could say it's the height, is x.
The volume of a box is given by the product of the three dimensions:
[tex]\begin{gathered} V=(40-2x)\cdot(30-2x)\cdot x \\ V=(1200-80x-60x+4x^2)\cdot x \\ V=1200x-140x^2+4x^3 \end{gathered}[/tex]Use the given value of the volume to find x:
[tex]\begin{gathered} 2448=1200x-140x^2+4x^3 \\ 4x^3-140x^2+1200x-2448=0 \end{gathered}[/tex]Factoring this expression we have that:
[tex]\begin{gathered} 4(x-3)(x^2-32x+204)=0 \\ x-3=0 \\ x=3 \end{gathered}[/tex]One of the possible dimensions of the square is 3. Now, solve the quadratic expression (third factor) to find the other 2 options:
[tex]\begin{gathered} x^2-32x+204=0 \\ x=\frac{-(-32)\pm\sqrt[]{(-32)^2-4(1\cdot204)}}{2\cdot1} \\ x=\frac{32\pm\sqrt[]{1024-816}}{2} \\ x=\frac{32\pm\sqrt[]{208}}{2} \\ x1=\frac{32+\sqrt[]{208}}{2} \\ x2=\frac{32-\sqrt[]{208}}{2} \end{gathered}[/tex]It means that the squares can have 3 different dimensions, which are:
[tex]3,\frac{32+\sqrt[]{208}}{2},\frac{32-\sqrt[]{208}}{2}[/tex]Nevertheless, the second possible option is not coherent since it's value is close to 23 and the dimensions of the cardboard are 30 and 40. It means that the possible dimensions are 3 and (32-sqrt(208))/2.
5 Ramon sched 13 -6 She said she thought about taking away and then 3 more from 13. CanRamon do this? Show a diagram and write an equation to show what this solution path would look like
we know that
14-7=7 --------> given problem
so
we have
14-8
Rewrite the expression
14-(7+1)
14-7-1
Remember that
14-7=7
substitute
7-1
6
we have
12-6=6
so
12-7
rewrite
12-(6+1)
12-6-1
substitute
6-1
5
we have
13-6
13-(3+3)
13-3-3
10-3
7
A cylindrical barrel has a radius of 1.2 feet and a height of 4 feet. Find the volume of the barrel.
ANSWER:
18.1 ft³
STEP-BY-STEP EXPLANATION:
Given:
Radius (r) = 1.2 ft
Height (h) = 4 ft
We can determine the volume of the cylindrical barrel using the following formula:
[tex]V=\pi\cdot r^2\cdot h[/tex]We substitute each value and calculate the volume, like this:
[tex]\begin{gathered} V=\left(3.14\right)\left(1.2^2\right)\left(4\right) \\ \\ V=18.1\text{ ft}^3 \end{gathered}[/tex]The volume of the barrel is 18.1 ft³
Art wants to calculate the diagonal distance across opposite corners of a rectangular parcel. The parcel is 161’ by 326’ . How long is the diagonal measurement?
Recall that the formula for the length of the diagonal of a rectangle is:
[tex]l=\sqrt[]{a^2+b^2}.[/tex]Where a, and b are the lengths of the sides of the rectangle.
Substituting a=161´, b=326´ in the above formula we get:
[tex]\begin{gathered} l=\sqrt[]{(161^{\prime})^2+(326^{\prime})^2}, \\ l=363.5890537^{\prime}\text{.} \end{gathered}[/tex]Answer: 363.5890537 ´.
Let's say you have a bag with 12 cherries, 4 of the cherries are sweet and 8 are sour. If you pick a cherry atrandom, what is the probability that it will be sweet? Write your answer as a reduced fraction.Pot)
1) A rolled die has just 6 outcomes; from 1 to 6
[tex]\text{Probability = }\frac{number\text{ of required events}}{nu\text{mber of total events}}[/tex]Number of total events for a die = 6
[tex]\begin{gathered} a)\text{ p(6) } \\ \text{for this the number of required events = 1 because there can and there is only one six showing at a time} \\ p(6)\text{ =}\frac{1}{6} \end{gathered}[/tex][tex]\begin{gathered} b)\text{ p(even)} \\ Here\text{ number of total events are 1,2,3,4,5 and 6} \\ \text{The number of even numbers = 3} \\ \\ p(\text{even) =}\frac{3}{6}=\frac{1}{2} \end{gathered}[/tex][tex]\begin{gathered} c)p(\text{greater than 1)} \\ \text{Here total number of outcomes are 1,2,3,4,5 and 6} \\ \text{numbers greater than 1 are 2,3,4,5 and 6}\ldots..\text{ Th}ere\text{ are 5 of them} \\ \text{Hence} \\ p(\text{greater than 1) =}\frac{5}{6} \end{gathered}[/tex][tex]\begin{gathered} 2)\text{ Total number of cherries = 12} \\ p(\text{sweet) =}\frac{number\text{ of sw}eet\text{ cherries}}{Total\text{number of cherries}} \\ \text{number of swe}et\text{ cherries= 4} \\ p(\text{sweet) =}\frac{4}{12}=\frac{1}{3} \end{gathered}[/tex]on a grid 2/3 of the squares are shaded with a color 1/4 of the squares on the grid is shaded blue what fraction of the Shaded squares are blue squares
Given:
a grid 2/3 of the squares are shaded with color.
And 1/4 of the squares on the grid is shaded blue
So, to Find the fraction of the Shaded squares are blue squares
Multiply both fractions
So,
[tex]\frac{2}{3}\times\frac{1}{4}=\frac{2}{12}=\frac{2}{2\cdot6}=\frac{1}{6}[/tex]so, the answer will be 1/6 of the Shaded squares are blue squares
Your friend subtracts to find
44 - 18 = 26. He uses 26+ 18 to check his work. Your
cousin tells him he should use 18 + 26. Who is correct?
Explain how you know.
Answer:
technically it's both
Step-by-step explanation:
because if you have the answer plus 18 and if it works and you get 44 that will be the answer
3
Type the correct answer in the box. Use numbers instead of words.
The number 392,000 is divided by 10.
What is the value of the digit 2 in the quotient?
Reset
Next
The value of the digit 2 in the quotient is 200
We know that,
Place value is the value of each digit in a number.
From the question, we have
392,000/10 = 39200
The value of the digit 2 in the quotient is 2 hundreds, or 200
Divide:
The simplest definition of split is to divide into two or more equally sized pieces, locations, groups, or divisions. Simply put, to divide something is to give it to a group in equal portions or to cut it into equal pieces. Consider a diagonal that creates two triangles with equal areas from a square. A division operation could result in an integer or it could not. Decimal numbers may be used to express the outcome occasionally.
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Solve 2sin (2x) + 2 = 0 on the interval [0, 27).π 3π 9π 11π8' 85π 7π4 4π 9π8' 85π 7π 13π 15π8' 8' 8' 8
I need help question
[tex]f(x)=x^2-4x-94[/tex]
The diffrentiated function will be
[tex]2x-4[/tex]RULES FOR DIFFERENTIATION
[tex]\begin{gathered} y=x^n \\ \frac{dy}{dx}=nx^{n-1} \end{gathered}[/tex]Also
[tex]\begin{gathered} y=kx \\ \frac{dy}{dx}=k \end{gathered}[/tex]Also
[tex]\begin{gathered} y=k \\ \frac{dy}{dx}=0 \end{gathered}[/tex]One bar of candy A and two bars of candy B have 782 calories. Two bars of candy A and one bar of candy B contain 787 calories. Find the caloric content of eachcandy barCandy bar A contains calories and candy bar B contains calories
ANSWER:
Candy bar A: 264 calories
Candy bar B: 259 calories
STEP-BY-STEP EXPLANATION:
Let x be the number of calories in candy bar A and y be the number of calories in candy bar B.
We can establish the following system of equations according to the data of the statement:
[tex]\begin{gathered} x+2y=782\rightarrow x=782-2y \\ \\ 2x+y=787 \end{gathered}[/tex]We substitute the first equation into the second and solve for y, just like this:
[tex]\begin{gathered} 2\cdot(782-2y)+y=787 \\ \\ 1564-4y+y=787 \\ \\ -3y=787-1564 \\ \\ y=\frac{-777}{-3} \\ \\ y=259 \\ \\ \text{ Now, for x:} \\ \\ x=782-2y \\ \\ x=782-2\cdot259 \\ \\ x=782-518 \\ \\ x=264 \end{gathered}[/tex]Therefore:
Candy bar A contains 264 calories and candy bar B contains 259 calories
grandma has $250000 to invest. she divides her money into two accounts. one account is in ultra-safe treasury bills paying 4% interest, and the other is in riskier corporate bonds paying 6%. if she needs $12,000 per year in income from her investments, how much should she invest in each account
for the ultra-safe treasury bills:
[tex]\begin{gathered} I_1=PV\cdot r\cdot t \\ I_1=x\cdot0.04\cdot1 \\ I_1=0.04x \\ \text{where:} \\ x=\text{amount 1} \end{gathered}[/tex]For riskier corporate bonds:
[tex]\begin{gathered} I_2=PV\cdot r\cdot t \\ I_2=y\cdot0.06\cdot1 \\ I_2=0.06y \\ \text{Where:} \\ y=\text{amount 2} \end{gathered}[/tex]she needs $12,000 per year, so:
[tex]\begin{gathered} I_1+I_2=12000 \\ 0.04x+0.06y=12000 \end{gathered}[/tex]grandma has $250000 to invest, therefore:
[tex]x+y=250000[/tex]Let:
[tex]\begin{gathered} x+y=250000\text{ (1)} \\ 0.04x+0.06y=12000\text{ (2)} \\ \text{From (1) solve for x:} \\ x=250000-y\text{ (3)} \\ \text{ Replace (3) into (2)} \\ 0.04(250000-y)+0.06y=12000 \\ 10000-0.04y+0.06y=12000 \\ 0.02y=12000-10000 \\ 0.02y=2000 \\ y=\frac{2000}{0.02} \\ y=100000 \end{gathered}[/tex]Replace y into (3):
[tex]\begin{gathered} x=250000-100000 \\ x=150000 \end{gathered}[/tex]Therefore, grandma needs to invest $150000 in ultra-safe treasury bills, and