We have two points and we need to calculate the distance between them.
The points are P1(-4,3) and P2(3,2).
We can apply the following formula for the distance between points:
[tex]D=\sqrt{(x_2-x_1)^2}+(y_2-y_1)^2[/tex][tex]\begin{gathered} D=\sqrt{(3-(-4))^2}+(3-2)^2 \\ D=\sqrt{7^2+1^2}=\sqrt{49+1}=\sqrt{50}=\sqrt{(25\cdot2})=5\sqrt{2} \end{gathered}[/tex]The answe is 5 times the square root of 2:
[tex]D=5\sqrt{2}[/tex]For the rotation -1046°, find the coterminal angle from 0° < O < 360°, the quadrant and the reference angle.
Solution
Step 1
In order to find a coterminal angle, or angles of the given angle, simply add or subtract 360 degrees of the terminal angle as many times as possible.
Step 2
The reference angle is the smallest possible angle made by the terminal side of the given angle with the x-axis. It is always an acute angle (except when it is exactly 90 degrees). A reference angle is always positive irrespective of which side of the axis it is falling.
Coterminal angle
[tex]\begin{gathered} Coterminal\text{ angle = -1046 + 3}\times360 \\ Coterminal\text{ angle = -1046 + 1080} \\ Coterminal\text{ angle = 34} \end{gathered}[/tex]Quadrant = 1st quadrant
Reference angle
0° to 90°: reference angle = angle
Reference angle = 34
Final answer
Solve one-fourth + two-sixths = ___.
Answer:
7/12
Step-by-step explanation:
base: 4 in. area: 22 in
Area of a triangle
The area of a triangle of base length b and height h is:
[tex]A=\frac{b\cdot h}{2}[/tex]We are given the area as A=22 square inches and the base length b=4 inches. We are required to find the height.
Solving for h:
[tex]h=\frac{2\cdot A}{b}[/tex]Substituting:
[tex]h=\frac{2\cdot22in^2}{4in}=\frac{44in^2}{4in}=11in[/tex]The height is 11 inches
Can you please help me
The area for a trapezoid can be found through the fromula
[tex]A=\frac{1}{2}(B+b)\cdot h[/tex]in which B represents the major base, b the minor base and h the height of the trapezoid.
According to this the area of the trapezoid is going to be:
[tex]\begin{gathered} A=\frac{1}{2}(37+22)\cdot23 \\ A=\frac{1}{2}(59)23 \\ A=\frac{1357}{2}cm^2 \\ A=678.5cm^2 \end{gathered}[/tex]According to the complex conjugates theorem, if -3+i is a root of a function what else is a root?
To have an understanding of the question, we need to understand what the complex conjugates theorem is.
In a simpler form, what the complex conjugate theorem is saying is that perhaps, we have a Polynomial N with a complex root x + yi, then the complex conjugate of x + yi which in this case is x -yi is also a root of the polynomial N
Applying this to the question at hand;
x = -3 and y = 1
We find the conjugate of the above by negating y( turning it to a negative number)
So its conjugate will be -3 -i
Summarily; According to the complex conjugates theorem, if -3+i is a root of a function , -3 - i is also a root of the function
Solve the proportions 28/35=8/r
ANSWER
r = 10
EXPLANATION
To solve for r first we have to put r in the numerator. To do that, we have to multiply both sides of the proportion by r:
[tex]\begin{gathered} \frac{28}{35}\cdot r=\frac{8}{r}\cdot r \\ \frac{28}{35}r=8 \end{gathered}[/tex]Now, we have to multiply both sides by 35:
[tex]\begin{gathered} \frac{28}{35}r\cdot35=8\cdot35 \\ 28r=280 \end{gathered}[/tex]And finally divide both sides by 28:
[tex]\begin{gathered} \frac{28r}{28}=\frac{280}{28} \\ r=10 \end{gathered}[/tex]Simplify Remove all perfectsquares from inside the square root. v52
The square root we need to simplify is:
[tex]\sqrt[]{52}[/tex]We need to find an expression equivalent to 54 which includes a perfect square number (4, 16, 25, etc,...)
In this case, we note that:
[tex]52=4\times13[/tex]We substitute this in the square root:
[tex]\sqrt[]{4\times13}[/tex]And we calculate the square root of 4 which is 2, and that goes outside the square root:
[tex]2\sqrt[]{13}[/tex]we left the number 13 inside the square root because the square root of 13 is not exact.
Answer:
[tex]2\sqrt[]{13}[/tex]How many different ID cards can be made if there are four digits can be used more than once? What if digits can be repeated?
ANSWERS
1) 5,040
2) 10,000
EXPLANATION
1) If we have 10 numbers (from 0 to 9), the ID cards have 4 of them and the digits do not repeat, we have 10 numbers to choose from for the first digit, 9 numbers for the second digit, 8 numbers for the third digit, and 7 numbers for the fourth digit. So,
[tex]10\cdot9\cdot8\cdot7=5,040[/tex]Hence, there are 5,040 different ID cards that can be made if no digit can be used more than once.
2) In this case, the numbers can be repeated, so for each of the four digits we have 10 options to choose from,
[tex]10\cdot10\cdot10\cdot10=10^4=10,000[/tex]Hence, there are 10,000 different ID cards that can be made if digits can be repeated.
12. The PRODUCT of six and a number increased by 2, translates to ? *6 +x+26x + 2O 6-8-2
Call the unknown number x.
The product of six and a number, would be written as 6x.
The product of six and a number increased by 2, would be written as 6x+2.
Find the area of this figure.Triangle: Rectangle: Half circle: Total area:
To determine the area of the figure given we need to divide the composite figure into figures in which we know how to find the area. We divide the figure into a triangle, a rectangle and a circle.
The area of a triangle is given by:
[tex]A=\frac{1}{2}bh[/tex]where b is the base and h is the height. For the triangle shown the base is 6 and its height is 6, therefore:
[tex]A=\frac{1}{2}(6)(6)=\frac{36}{2}=18[/tex]The area of the rectangle is given by:
[tex]A=lw[/tex]where l is the length and w is the width. For this triangle the length is 9 and the width is 6 then we have:
[tex]A=(9)(6)=54[/tex]The area of a circle is given by:
[tex]A=\pi r^2[/tex]where r is the radius of the circle. The circle shown has a diameter of 6; we know that the radius is half the diameter, then the radius is 3. Plugging the radius, we have:
[tex]A=(3.14)(3)^2=28.26[/tex]Now we add the areas of each figure, therefore we have:
[tex]18+54+28.26=100.26[/tex]Find area under standard normal curve between -1.69 and 0.84
Required:
We need to find the area under the standard normal curve between -1.69 and 0.84
Explanation:
We need to find P(-1.69
P-value form z-table is
[tex]P(x<-1.69)=0.045514[/tex][tex]P(x<0.84)=0.79955[/tex]We know that
[tex]P(-1.69Substitute know values.[tex]P(-1.69Final answer:0.7540 is the area under the standard normal curve between -1.69 and 0.84.
A 1. Which of the following is equivalent to 37g - 11g? a. (37 - 11)g b. (37 - 11) +g c.(37 - 11) + g2 d. (37 - 11)9
From 37g - 11g we can factorize g. It yields
[tex]37g-11g=(37-11)g[/tex]Hence, the aswer is a.
Estimate a 15% tip on a dinner bill of $89.14 by first rounding the bill amount to the nearest ten dollars. 1
Let:
C = Cost of the dinner
T = Tip
r = Percentage of the tip
[tex]\begin{gathered} C=89 \\ r=0.15 \\ T=C\cdot r \\ T=89\cdot0.15 \\ T=13.35 \end{gathered}[/tex]Answer:
$13.35
A car rental company charges a $85 initial fee and $45 dollars a day to rent a car. Write an equation representing the cost, y, of renting the car for x days. (y= mx + b)
The given equation, y = mx + b is the slope intercept form of a linear equation where
m represents slope
b represents y intercept
The slope represents the rate of change of the values of y with respect to x. The values of y in this case represents the cost of renting the car while x represents the number of days for which the car is rented. Therefore,
slope, m = $45
The y intercept is the value of y when x is zero. We can see that the initial fee is $85. This means that even if the car is rented for zero days, the initial fee of $85 must be charged, Thus, y intercept is 85
Therefore, the equation representing the cost, y, of renting the car for x days is
y = 45x + 85
Directons: Write each equation in slope-intercept form. Identify the slope and y-intercept.
Given:
The equation is x - y = -8.
Explanation:
The slope intercept form of linear equation is,
[tex]y=mx+c[/tex]Here, m is slope and c is y-intercept.
Simplify the given equation to obtain in slope-intercept form.
[tex]\begin{gathered} x-y=-8 \\ y=x+8 \\ y=1\cdot x+8 \end{gathered}[/tex]So slope of line is m = 1 and y-intercept is 8.
Answer:
Equation in slope ntercept form: y = x + 8
Slope: 1
Y-intercept: 8 OR (0,8)
Determine if the expression -w is a polynomial or not. If it is a polynomial, state thetype and degree of the polynomial.The given expression representsJa polynomial. The polynomial is aand has a degree of
SOLUTION
We want to show if the expression -w is a polynomial or not
-w can also be written as
[tex]-1(w^1)[/tex]Since it has one term, and the power or exponent is not negative number or fraction, it is a polynomial.
Since it has one term, it is a monomial
So it is a polynomial called a monomial.
Since it has an exponent or power of 1
It is a polynomial of degree 1
Would to ask question about composite shape perimeter. Having trouble sending drawing
First let's split the shape in two, like this:
As you can see, now we have a triangle on the right, the length of the base of this triangle is the length of the bottom side of the original figure minus the lenght of the top side of the original figure, we can find it like this:
b = 100 ft - 70 ft = 30 ft
The height of the triangle "h" equals the height of the rectangle, which is 50 ft, then we can find the length of the missing side a (the hypotenuse of the triangle) by means of the Pythagorean theorem, like this:
[tex]\begin{gathered} a^2=h^2+b^2 \\ a=\sqrt[]{h^2+b^2} \end{gathered}[/tex]Where "a" is the length of the hypotenuse, "h" is the height and "b" is the base. By replacing 30 for b and 50 for h, we get:
[tex]a=\sqrt[]{50^2+30^2}=\sqrt[]{2500+900}=10\sqrt[]{34}=58.3[/tex]Then the length of the missing side of the composite shape is around 58.3 ft:
Now that we know the lengths of the sides of this figure we can calculate its perimeter by summing them up, like this:
Perimeter = 70 + 50 + 100 + 58.3 = 278.3
The perimeter of this plot of land equals 278.3 ft
Solve this equation.
2/3x−1/5x=x−1
A. 1 13/15
B. 1 7/8
C. 1 7/15
D. 7/8
Answer:
your answer would be c 1 7/15 tell me if I'm wrong
Step-by-step explanation:
Answer:
B 1 7/8
Step-by-step explanation:
2/3x−1/5x=x−1
1. multiply both sides by 15
10x-3x=15x-15
2. collect like terms
7x = 15x -15
3. move the variable to the left
7x-15x=-15
4. collect like terms
-8x = -15
5. divide both sides by -8
x=15/8
or
1 7/8
Need answer to pictured problem! The answer should be in reference to trig identities
Step 1. The expression that we have is:
[tex]cos^2(5x)[/tex]and we need to find the equivalent expression.
Step 2. The trigonometric identity we will use to solve this problem is:
[tex]cos^2A=1-sin^2A[/tex]In this case:
[tex]A=5x[/tex]Step 3. Applying the trigonometric identity to our expression, substituting 5x in the place of A:
[tex]cos^2(5x)=\boxed{1-sin^2(5x)}[/tex]This is shown in option d).
Answer:
[tex]\boxed{d)\text{ }1-s\imaginaryI n^2(5x)}[/tex]how would I simplify 3x^3-12x÷3x^3+6x^2-24x?
To simplify:
[tex]3x^3-12x\div3x^3+6x^2-24x[/tex]On division we get,
[tex]\begin{gathered} \frac{3x^3-12x}{3x^3+6x^2-24x}=\frac{3x(x^2-4)}{3x(x^2+2x-8)} \\ =\frac{(x^2-4)}{(x^2+2x-8)} \\ =\frac{(x+2)(x-2)}{(x-2)(x+4)_{}} \\ =\frac{x+2}{x+4} \end{gathered}[/tex]Hence, the simplest form is,
[tex]\frac{x+2}{x+4}[/tex]Please help me help help me please help help me out
1) We can find the inverse function, by following some steps. So let's start with swapping the variables this way:
[tex]\begin{gathered} f(x)=\sqrt[3]{x-1}+4 \\ y=\sqrt[3]{x-1}+4 \end{gathered}[/tex]2) Now let's isolate that x variable getting rid of that cubic root:
[tex]\begin{gathered} x=\sqrt[3]{y-1}+4 \\ x-4=\sqrt[3]{y-1} \\ (x-4)^3=(\sqrt[3]{y-1})^3 \\ (x-4)^3=y-1 \\ y=(x-4)^3+1 \end{gathered}[/tex]Note that when we isolate the y on the left we had to adjust the sign dividing it by -1, to get y, not -y.
Admission to the fair costs $6.00. Each ride costs you$0.50. You have $22.00 to spend at the fair on rides and admission. Express the number of tickets you can buy as an inequality.
Let:
x = Number of rides
Total money spent = $6.00 + $0.50x
Since you have $22.00 to spend at the fair on rides and admission:
[tex]\begin{gathered} 6+0.5x\leq22 \\ \text{solving for x:} \\ 0.5x\leq22-6 \\ 0.5x\leq16 \\ x\leq\frac{16}{0.5} \\ x=32 \end{gathered}[/tex]a financial advisor estimates that a company's profits follow the equation.
The equation that represent the profit is given by:
[tex]y=1000\cdot2^x[/tex]So in 3 years there are 36 months so the equation will be:
[tex]\begin{gathered} y=1000\cdot2^{36} \\ y=68^{},719,476,736,000 \end{gathered}[/tex]So is option A) it don't have sence because the profits are to great.
The boxplot below shows salaries for Construction workers and Teachers.ConstructionTeacher2025465030 35 40Salan (thousands of S)If a person is making the median salary for a construction worker, they are making more than what percentage ofTeachers?They are making more than% of Teachers.Check Answer
Const Workers , Teachers
Median salary of const Worker =45
Median salary of teacher = 40
Then, they are making more than 100% of teachers
Answer is
100%
The organizer of a conference is selecting workshops to include. She will select from 5 workshops about genetics and 8 workshops about ethics. In how many ways can she select 6 workshops if fewer than 3 must be about genetics?
We have the following:
- 5 possible about genetics and need fewer than 3 (so it can be 0, 1 or 2).
- 8 about ethics
- want to select 6 in total.
We can calculate all the possible ways by doing it in three situations:
1 - From the 6, 0 will be genetics and 6 will be ethics
2 - From the 6, 1 will be genetics and 5 will be ethics
3 - From the 6, 2 will be genetics and 4 will be ethics
All of these will have to add up to find the total number of ways.
1 - 0 genetics, 6 ethics:
Since no genetics will be chosen, we can choose any 6 from the 8 possible about ethics, that is, we have a situation of "8 choose 6"
The equation for a situation "n choose k" and the number of ways in it is:
[tex]n=\frac{n!}{k!(n-k)!}[/tex]So, if we have "8 choose 6":
[tex]n_1=\frac{8!}{6!(8-6)!}=\frac{8\cdot7\cdot6!}{6!2!}=\frac{8\cdot7}{2}=4\cdot7=28[/tex]So, in this first we have 28 ways.
2 - 1 genetics, 5 ethics:
Here, we will have one equation for each and the total number of ways will be the multiplication of both.
For genetics, we have to pick 1 from 5, so "5 choose 1":
[tex]\frac{5!}{1!(5-1)!}=\frac{5\cdot4!}{4!}=5_{}[/tex]For ethics, we have to pick 5 from 8, so "8 choose 5":
[tex]\frac{8!}{5!(8-5)!}=\frac{8\cdot7\cdot6\cdot5!}{5!3!}=\frac{8\cdot7\cdot6}{3\cdot2}=8\cdot7=56[/tex]So, the total number of ways is the multiplicatinos of them:
[tex]n_2=5\cdot56=280[/tex]3 - 2 genetics, 4 ethics:
Similar to the last one.
For genetics, we have to pick 2 from 5, so "5 choose 2":
[tex]\frac{5!}{2!(5-2)!}=\frac{5\cdot4\cdot3!}{2\cdot3!}=\frac{5_{}\cdot4}{2}=5\cdot2=10[/tex]For ethics, we have to pick 4 from 8, so "8 choose 4":
[tex]\frac{8!}{4!(8-4)!}=\frac{8\cdot7\cdot6\cdot5\cdot4!}{4!4!}=\frac{8\cdot7\cdot6\cdot5}{4\cdot3\cdot2}=2\cdot7\cdot5=70[/tex]So, the total number of ways is the multiplicatinos of them:
[tex]n_3=10\cdot70=700[/tex]Now, the total number of ways is the sum of all these possibilities, so:
[tex]\begin{gathered} n=n_1+n_2+n_3 \\ n=28+280+700 \\ n=1008 \end{gathered}[/tex]So, the total number of ways is 1008.
Translate the following into algebraic equation and solve: Twice the sum of a number and five is equal to 40.
Let:
x = Unknown number
Twice the sum of a number and five:
[tex]2(x+5)[/tex]Is equal to 40:
[tex]2(x+5)=40[/tex]Solve for x:
Expand the left hand side using distributive property:
[tex]2x+10=40[/tex]Subtract 10 from both sides:
[tex]2x=30[/tex]Divide both sides by 2:
[tex]x=15[/tex]T x 3/4 for t = 8/9
repalce t=8/9
[tex]\begin{gathered} \frac{8}{9}\times\frac{3}{4} \\ \\ \frac{24}{36}=\frac{2}{3} \end{gathered}[/tex]the result is 2/3
If lines l, m, and n are parallel,AE is perpendicular to l, AC = 10, CD = 14, andAF = 6, what is the length of DG ? Give your answer as a decimal.
Using the properties of parallel line and similar triangle we calculate the length of the side DG to be 19.4 units .
In triangle ACF by using the properties of Pythagoras Theorem we can say that
AC² = FA² + CF²
Given:
AC = 10 , FA = 6
∴10² = 6² + CF²
or, CF = 8 units.
Now in triangles ΔACF and triangle ΔADG
CF is parallel to DG , therefore the two triangles are similar.
therefore we can say that using the properties of similar triangle we will use the ratio of the sides to find the given side.
AC/AD=CF/DG
or, 10/24 = 8 / DG
or, DG = 192 /10
or, DG = 19.2 units
Triangles that share the same form but differ in size are said to be similar. All equilateral triangles and squares with equal sides serve as examples of related items.
In other words, two similar triangles have similar sides that are proportionately equal and similar angles that are congruent.
Hence the length of the side is 19.2 units.
To learn more about parallel lines visit:
https://brainly.com/question/29042593
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A rectangular garden covers 690 square meters. The length of the garden is 1 meter more than three times its width. Find the dimensions of the gardenThe length isand the width is01(Type whole numbers.)
Ok, so
We got the situation here below:
We know that the area of the garden is 690 m².
So, we got that the height (1+3x) multiplied by the width (x), should be equal to 690.
[tex]\begin{gathered} (1+3x)(x)=690 \\ x+3x^2=690 \end{gathered}[/tex]We have to solve:
[tex]3x^2+x-690=0[/tex]If we solve this quadratic equation, we obtain two solutions.
One of both solutions is negative, so we will not use it.
The second one is positive and equals to 15. So, x=15.
Now that we know that x=15, we replace:
x, (Width) is equal to 15 meters.
1+3x (Length), is equal to 46 meters.
Therefore, these are the dimensions of the garden.
Width: 15 meters
Lenght: 46 meters.
I need help with my math. I am working on linear equations. I don’t understand what I am doing and I am struggling on my homework. C/-9 + 6 = 14
Given:
[tex]\frac{C}{-9}+6=14[/tex]Solve this equation to find the value of C,
[tex]\begin{gathered} \frac{C}{-9}+6=14 \\ \text{Subtract 6 from both sides} \\ \frac{C}{-9}+6-6=14-6 \\ \frac{C}{-9}=8 \\ Multiply\text{ both sides by -9} \\ \frac{C}{-9}(-9)=8(-9) \\ C=-72 \end{gathered}[/tex]Answer: C= -72