The given quadratic equation is:
[tex]x^2+2=0[/tex]Subtract 2 from both sides
[tex]\begin{gathered} x^2+2-2=0-2 \\ x^2=\text{ -2} \end{gathered}[/tex]Find the square root of both sides
[tex]\begin{gathered} \sqrt[]{x^2}=\text{ }\sqrt[]{-2} \\ x=\sqrt[]{-2} \\ x=\pm\sqrt[]{2}\times\sqrt[]{-1} \\ x\text{ =}\pm\text{ }\sqrt[]{2}i \\ x\text{ = }\pm i\sqrt[]{2} \end{gathered}[/tex][tex]\begin{gathered} x\text{ = }-i\sqrt[]{2}\text{ or i}\sqrt[]{2} \\ \end{gathered}[/tex]Write this ratio as a fraction in simplest form without any units. 25 days to 5 weeks
Given:
There are given the statement:
25 days to 5 weeks.
Explanation:
To find the ratio, first, we need to convert the value of days into the week.
So,
To convert days into the week, we need to divide by 7.
So,
[tex]\frac{25}{7}week[/tex]Now,
The ratio as a fraction is:
[tex]\frac{25}{\frac{7}{5}}=\frac{25}{7\times5}[/tex]Then,
[tex]\begin{gathered} \frac{25}{\frac{7}{5}}=\frac{25}{7\times5} \\ =\frac{5}{7} \end{gathered}[/tex]Final answer:
Hence, the ratio as a fraction is shown below:
[tex]\frac{5}{7}[/tex]A U.S. dime has a diameter of about millimeters. What is the area of one side of a dime to the nearest square millimeter? Use as an approximation for .The area of one side of a U.S. dime is approximately blank square millimeters.The solution is
A US dime has a diameter of 18 millimeters. That makes the radius 9 millimeters, because
[tex]\begin{gathered} \text{radius}=\frac{\text{diameter}}{2} \\ \text{radius}=\frac{18}{2} \\ radius=9 \end{gathered}[/tex]The area of the dime (which is circular in shape) is given by the formula;
[tex]\begin{gathered} \text{Area of a circle} \\ A=\pi\times r^2 \\ r=9,\pi=3.14 \\ A=3.14\times9^2 \\ A=254.34mm^2 \end{gathered}[/tex]The area of one side of the dime is 254 square millimeters (approximated to the nearest square millimeter)
A chemistry student needs 80.0 mL of ethanolamine for an experiment. By consulting the CRC Handbook of Chemistry and Physics, the student discovers thatthe density of ethanolamine is 1.02 g.cm. Calculate the mass of ethanolamine the student should welgh out.Be sure your answer has the correct number of significant digits.
STEP 1: Identify and Set Up
We are given a question that requires us to find mass when given volume and density.
It is common knowledge that these parameters are related by the formulae:
[tex]\begin{gathered} \text{density = }\frac{\text{mass}}{\text{volume}} \\ \text{This gives mass = volume }\times\text{ density} \end{gathered}[/tex]We use this relation to find mass
STEP 2: Execute
Density = 1.02 g/cc
Volume = 80ml = 80 cc
Mass is therefore:
[tex]\text{mass = 1.02}\times80=81.6g[/tex]Mass = 81.6g
Consider the function f(x)= log5 xComplete the following and then graphx= 1/5 f(x)?x=1 f(x)? x=5 f(x)?x=25 f(x)?
Given:
[tex]f(x)=\log_5x[/tex]Required: Function values at x = 1/5, 1, 5, and 25.
Explanation:
Use the logarithmic properties
[tex]\log_b1=0,\log_b\frac{A}{B}=\log_bA-\log_bB,\log_bb=1,\log_bb^n=n[/tex]To find f(1/5), substitute 1/5 for x into f(x).
[tex]\begin{gathered} f(\frac{1}{5})=\log_5(\frac{1}{5}) \\ =\log_51-\log_55 \\ =0-1 \\ =-1 \end{gathered}[/tex]To find f(1), substitute 1 for x into f(x).
[tex]\begin{gathered} f(1)=\log_51 \\ =0 \end{gathered}[/tex]To find f(5), substitute 5 for x into f(x).
[tex]\begin{gathered} f(5)=\log_55 \\ =1 \end{gathered}[/tex]To find f(25), substitute 25 for x into f(x).
[tex]\begin{gathered} f(25)=\log_525 \\ =\log_55^2 \\ =2\log_55 \\ =2 \end{gathered}[/tex]
A small restaurant was purchased for 316000 with no down payment and a 6.6% loan for 10 year. Find the monthly payment
We will have the following:
First, we calculate the total payment per year:
[tex]p_y=316000\cdot0.066\Rightarrow p_y=20856[/tex]Now, we calculate the monthly payment:
[tex]316000=\frac{p}{0.0055}(1-\frac{1}{(1+0.066)^{120}})\Rightarrow1738=p(0.9995331951\ldots)[/tex][tex]\Rightarrow p=\frac{1738}{(1-\frac{1}{(1+0.066)^{120}})}\Rightarrow p=1738.811686[/tex]So, the monthly payment will be approximately $1738.811686.
In the parallelogram ABCD, MLA = 2x + 50 and m C = 3x + 40. The measure of LA is
The measure of angle m∠A will be 70°,for the parallelogram ABCD
Parallelogram and its Properties:
Parallelogram is a special kind of quadrilateral, in which opposite sides are equal and parallel to each other.
Properties:
1. Opposite sides are parallel to each other.
2. Length of opposite sides are equal.
3.Diagonally opposite angles are equal.
4. Diagonals bisects each other.
5. Sum of any two adjacent angle is 180°
From figure,
ABCD is a parallelogram
m∠A = 2x + 50
m∠ C = 3x + 40
In a parallelogram ABCD we know opposite angles are equal to each other,
m∠A = m∠C
2x + 50 = 3x + 40
3x - 2x = 50 - 40
x = 10
Hence,
m∠A = 2x + 50
put the value of x we get,
m∠A = 2 * 10 + 50
= 20 + 50
= 70°
m∠A = 70°
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how do I write 1 9/10 as dollars and cent
Please help me help help me please help help me
When we are given a polynomial of the form:
[tex]ax^n+bx^{n-1}+cx^{n-2}+..+d^{}[/tex]Then the number that is multiplied by no variable or contains no variables is called the constant of the polynomial. In the above example, it would be "d".
Therefore, in the given polynomial we have:
[tex]3x^9+4x+129[/tex]Therefore, the constant of the polynomial is 129.
Simplify the following expression. Leave your answer in the form a^b.3^19/3^13= ___
Given the expression:
[tex]\frac{3^{19}}{3^{13}}[/tex]To simplify the expression, we will use the following rule of the exponents:
[tex]\frac{a^m}{a^n}=a^{m-n}[/tex]The answer will be:
[tex]\begin{gathered} \frac{3^{19}}{3^{13}}=3^{19-13}^{} \\ \\ =3^6 \end{gathered}[/tex]you will write the answer as 3^6
I think I have the right answer but I would still like to be 100% sure that I understand i also have to show my work
To solve this inequality, we can proceed as follows:
First: multiply both sides of the inequality by 9:
[tex]9\cdot\frac{x}{9}\leq9\cdot1\Rightarrow x\leq9[/tex]Then, the answer is x <= 9. In interval notation, we have that the answer is:
(-infinity, 9 ]. Or graphically:
in 2 years steve wants to buy a bicycle that 800.00. if he opens a savings account that earns 3 % interest compounded monthly how much will he have to despoit as principal to have enough money in 2 years to buy the bike
Answer
393.55
Explanation
The amount that results after an amount P is invested at compound interest at rate r% and time period t is given as
A = P (1 + r)ᵗ
For this question,
A = 800
r = 3% = 0.03
t = 2 (12) = 24 (Since the interest is compounded monthly, over 2 years)
P = ?
800 = P (1 + 0.03)²⁴
800 = P (1.03)²⁴
800 = P (2.0328)
2.0328P = 800
Divide both sides by 2.0328
(2.0328P/2.0328) = (800/2.0328)
P = 393.55
Hope this Helps!!!
Luke opened a savings account 3 years ago. the account earns 6%interest compounded quarterly if the current balance is 300.00 how much did he deposit initially
Answer
This is similar to the first one too.
A = P (1 + r)ᵗ
For this question,
A = 300
r = 6% = 0.06
t = 3 (4) = 12 (Since the interest is compounded quarterly, over 3 years; there are 4 quarters per year)
300 = P (1 + 0.06)¹²
300 = P (1.06)¹²
300 = P (2.0122)
2.0122P = 300
Divide both sides by 2.0122
(2.0122P/2.0122) = (300/2.0122)
P = 149.09
Hope this Helps!!!
Enter the value of the expression using the Order of Operations. (4 x 3) + 23 x 4-3
Starting with the expression:
[tex](4\times3)+23\times4-3[/tex]Solve parenthesis first. Since 4 times 3 equals 12, then the expression is equal to:
[tex]12+23\times4-3[/tex]Next, solve for multiplications. In this case, solve 23 times 4:
[tex]12+92-3[/tex]Finally, solve additions and substractions from left to right:
[tex]\begin{gathered} 12+92-3=104-3 \\ =101 \end{gathered}[/tex]Therefore:
[tex](4\times3)+23\times4-3=101[/tex]Blank 1: 2/5Question 8 (1 point)Point - (4-7)Point B - (B. 1)mBlank 1:
We have to use the slope formula.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Let's replace the given points.
[tex]m=\frac{1-(-7)}{8-4}=\frac{1+7}{4}=\frac{8}{4}=2[/tex]Hence, the slope is 2.$75.00 is shared among 3 people in the ratio 2:4:9 how much is the largest share?
The ratio is 2:4:9, so we can consider the total parts we are dividing the total as 2+4+9 = 15.
Then, the first person receives 2/15, the second receives 4/15 and the third receives 9/15.
As the total is 75, we can calculate each part as:
[tex]\begin{gathered} p_1=75*\frac{2}{15}=10 \\ \\ p_2=75*\frac{4}{15}=20 \\ \\ p_3=75*\frac{9}{15}=45 \end{gathered}[/tex]Then, the largest share correspond to the third person and is $45.00.
Answer: $45.00
if a pound of almonds cost eight dollars how many ounces can be bought for $3.80
Proportions
A pound of almonds is said to cost 8 dollars.
But one pound is equivalent to 16 ounces, therefore:
16 ounces cost 8 dollars
Dividing by 8 we get that
2 ounces of almonds cost 1 dollar
Thus, for $3.80 we can buy 2*3.80 = 7.60 ounces of almonds
1. What is the solution of the matrix equation?L-02(-2, 1)(10, 6)(-4, 3)O(-3, 4)
Solving Matrix Equation.
[tex]\begin{gathered} \begin{bmatrix}{8} & {5} & {} \\ {\square} & {\square} & {} \\ {5} & {4} & {}\end{bmatrix}\begin{bmatrix}{x} & {} & {} \\ {\square} & {} & {} \\ {y} & {} & {}\end{bmatrix}=\text{ }\begin{bmatrix}{2} & {} & {} \\ {} & {} & {} \\ {1} & {} & {}\end{bmatrix} \\ \end{gathered}[/tex]Thus, the correct answer is;
x = 3/7 and y = -2/7
I was on vacation for this unit and having a hard time
1.a
We can rewrite the given information in an algebraic expression as follows:
[tex]\frac{3}{8}x=6[/tex]where x represents the number of 3/8-inch thick books. Solving for x:
[tex]x=\frac{6}{\frac{3}{8}}[/tex]We can rearrange the operation:
[tex]x=\frac{6}{3}\cdot8[/tex][tex]x=\frac{48}{3}[/tex][tex]x=16[/tex]Then, we need 16 3/8-inch books to make a stack 6 inches tall.
1.b
To solve this exercise, we can use the same procedure as in 1.a.
0. Writing the information in an algebraic expression.
[tex]\frac{1}{2}x=2\cdot\frac{3}{4}[/tex]where x represents the groups of 1/2 pound.
We can convert the mixed number into an improper fraction:
[tex]2\cdot\frac{3}{4}=\frac{2\cdot4+3}{4}=\frac{8+3}{4}=\frac{11}{4}[/tex]2. Rewriting the operation:
[tex]\frac{1}{2}x=\frac{11}{4}[/tex][tex]x=\frac{\frac{11}{4}}{\frac{1}{2}}[/tex][tex]x=\frac{11\cdot2}{4\cdot1}[/tex][tex]x=\frac{22}{4}[/tex][tex]x=5.5[/tex]We have 5.5 groups of 1/2 pounds in 2 (3/4) pounds.
Answer:
• 1.a 16
,• 2.b 5.5
In parallelogram ABCD, which angle is congruent to
In parallelogram ABCD, which angle is congruent to ?
Let us draw the parallelogram to better understand the problem.
As you can see from the above figure,
∠ABC and ∠CDA are congruent. (drawn in black color)
Also, ∠BCD and ∠DAB are congurent. (drawn in red color)
This means that the opposite angles are congruent in a parallelogram.
Therefore, the correct answer is option C
∠ABC and ∠CDA are congruent.
Below is a pattern that can be used to cut out and fold to make a cube. If each edge is 5 inches, what will be the surface area of the cube? A 30 in? B 120 in С 150 in? D 3,125 in
In words, the surface area of a cube is the area of the six squares that cover it. The area of one of them is a*a, or a^2
[tex]A=6a^2[/tex]Here, a = 5 inches
[tex]\begin{gathered} A=6\cdot(5^2) \\ A=6\cdot25 \\ A=150 \end{gathered}[/tex]The answer would be 150 in^2
Write the STANDARD FORM of the equation through the point (4,-4) witha slope of -2.
The general equation of line with the slope "m" and passing points (a,b) is :
y - b = m (x -a)
In the given question:
Slope m = -2, passing points (a,b) = (4,-4)
Substitute the value of a = 4, b = -4 in the general equation of line
[tex]\begin{gathered} y-b=m(x-a) \\ y-(-4)=(-2)(x-4) \\ y+4=-2(x-4) \\ y+4=-2x+8 \\ y+2x=8-4 \\ 2x+y=4 \end{gathered}[/tex]The equation with the slope -2 and passing points (4,-4) is 2x + y = 4
Answer : 2x + y = 4
solve each inequality graph and check the solution (JUST NUMBER 8)
ANSWER
p ≤ -3
EXPLANATION
To solve this inequality first we have to subtract 5 from both sides:
[tex]\begin{gathered} 2-5\ge5-5+p \\ -3\ge p \end{gathered}[/tex]That's the solution, but we can flip it to see it more clearly:
[tex]p\le-3[/tex]To graph this, we have to draw a line from -3 to the left. Usually we have to draw a filled circle on -3, to indicate that that value is included in the solution.
Sam used his calculator to multiply two large numbers. His calculator gave the result 6E7. Which numbers are equal to the result his calculatorshowed? Select all that apply.0.00000066x 1076 x 1076,000,00060,000,000
The expression: 6E7, is a way of writing a number in scientific notation and it is equivalent to:
[tex]6\cdot10^7[/tex]Since 10^7=10,000,000, then:
[tex]6\cdot10^7=60,000,000[/tex]A standard die is rolled. Find the probability that the number rolled is less than 3. Express your answer as a fraction
Once a die has the numbers 1,2,3,4,5 and 6, it means the numbers that are less than 3 are just the numbers 1 and 2. Now the probability can be built as follows:
As we can see above, once there are just two possibilities of numbers that are less than 3, the probability that the number rolled is less than 3 is equal to 2/6.
HURRRYYY Given that AD is congruent to DC , find the length of XC.
The length of XC is 20
What does congruence of triangle mean?Triangles are said to be congruent if the three angles and three sides of a triangle are equal to the corresponding angles and sides of another triangle.
To be congruent, two triangles must have the same size and shape. The two triangles under consideration must overlap. If you rotate, flip, and/or move the triangle, its position and appearance will look different. In this case, we need to identify the six parts of one triangle and the corresponding parts of the other triangle.
For the triangles ΔAXD and ΔCXD
AD = DC ( congruent sides)
∠XDA = ∠XDC = 90° ( XD is perpendicular to AC)
XD is the common side.
This proves that triangles ΔAXD and ΔCXD are congruent
So it concludes, that XD = XC
2m + 10 = 4m
10 = 4m - 2m
10 = 2m
m = [tex]\frac{10}{2}[/tex]
m = 5
XC = 4m
XC = 4 × 5 = 20
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How would I solve this and what would be the answer?
Solution
(1). Domain
Since the graph is a polynomial, thus
The domain is all the elements of the set of Real Number
[tex]DOMAIN=(-\infty,\infty)[/tex](2) . Range
Notice that the graph is on the x - axis and above the x - axis throughout
The range will be
[tex]Range=\lbrack0,\infty)[/tex](3). x - intercept
We check where the graph touch the x - axis ( we have two)
That is at
[tex]\begin{gathered} x=-1 \\ \text{and} \\ x=2 \end{gathered}[/tex](4). y - intercept
We also check where the graph touch the y - axis
That is at
[tex]y=4[/tex](5). End Behaviour
First from the graph
[tex]x\rightarrow\infty,f(x)\rightarrow\infty[/tex]Second from the graph
[tex]x\rightarrow-\infty,f(x)\rightarrow\infty[/tex]The slope of the line is 2 and goes through the point (-8,6)
Given:
Slope m=2
The point,
[tex](x_1,y_1_{})=(-8,-6)[/tex]Using point-slope formula,
[tex]y-y_1=m(x-x_1)[/tex]Therefore, we get the equation,
[tex]y-(-6)=2(x-(-8)_{})[/tex]OWhat is the image point of (-4, 6) after the transformation r y=x 0 Rotation of 180 degrees
Given the point (-4,6).
So, The rule for a rotation by 180° about the origin is (x,y)→(−x,−y). Therefore, the new point is:
(-4,6) --> ( - ( - 4), - (6) ) --> (4, - 6)
Answer: ( 4, - 6 )
Pls helpppp I don't know what 2×2 IS plsss
we have
2*2=2+2=4
5*5=5+5+5+5+.5=25
5 times 5
example
2*3
its 2 times 3
3+3=6
4*3
4 times 3
3+3+3+3=12
Answer:
2 x 2 = 4.
two multiplied by two equals four.
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The equation of the parabola in the vertex form with vertex (6,-6) and passing through (8,6) is y = 3(x - 6)² - 6 , the correct option is (b) .
In the question ,
it is given that ,
the parabola passes through the point (8,6) .
the vertex of the parabola = (6,-6) .
We know that the equation of parabola in the vertex form with vertex (h,k) is
(y - k) = C.(x - h)²
we substitute the vertex and the point passing ,
we get ,
6 - (-6) = C.(8 - 6)²
6 + 6 = C(2)²
12 = 4C
C = 12/4
C = 3
So , the equation is (y - (-6)) = 3.(x - 6)²
y + 6 = 3(x - 6)²
y = 3(x - 6)² - 6
Therefore , The equation of the parabola in the vertex form with vertex (6,-6) and passing through (8,6) is y = 3(x - 6)² - 6 , the correct option is (b) .
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If the radius of circle M is 7, and LK = 18, find JK
Answer:
JK = 24
Explanation:
If the radius of circle M is 7, we can say that MJ = 7 and ML = 7
So, the length of MK will be equal to:
MK = ML + LK
MK = 7 + 18
MK = 25
Now, we have a right triangle JMK, and we know the length of one leg MJ = 7 and the length of the hypotenuse MK = 25. Using the Pythagorean theorem, we can find the length of the other side JK, so
[tex]\begin{gathered} JK=\sqrt[]{MK^2-MJ^2^{}} \\ JK=\sqrt[]{25^2-7^2} \\ JK=\sqrt[]{625-49} \\ JK=\sqrt[]{576} \\ JK=24 \end{gathered}[/tex]Therefore, the value of JK is 24.