in rectangle QRST , QS = 3x+7 and RT = 5X-3.find the lengths of the diagonals of QRSTeach diagonal has a length of ....... units.
Answers
Consider the rectangle drawn below,
Consider the properties of rectangle that the opposite sides are equal, and both the diagonals are also equal in length.
[tex]QS=RT\Rightarrow3x+7=5x-3\Rightarrow5x-3x=7+3\Rightarrow2x=10\Rightarrow x=5[/tex]Thus, the value of 'x' is 5.
Substitute the value to obtain the diagonal QS as,
[tex]QS=3(5)+7=15+7=22[/tex]Similarly solve for the diagonal RT as,
[tex]RT=5(5)-3=25-3=22[/tex]Already we knew that the diagonal will be equal with the length 22 units.
Related Questions
Two chords intersect with the measures shown in the drawing. What is the value of x? 0 4 -2 2
Answers
it is given that
the length of cords segments are
8 , 2x , 5x , 5
we know that when two chords intersect
the multiplication of the segments of the one chord will be equal the other chord
so,
[tex]8\times5=2x\times5x[/tex][tex]\begin{gathered} 40=10x^2 \\ x^2=4 \\ x=2 \end{gathered}[/tex]thus, the answer is x = 2
Use inverse trig ratios to find the angle measures sinX = 0,259 [ Choose ] Cosx = 0,743 [ Choose ] < tanX = 4 [Choose < sinX = 4/7 [ Choose
Answers
ANSWER:
[tex]\begin{gathered} x=15.01\text{\degree} \\ x=42.01\text{\degree} \\ x=75.96\text{\degree} \\ x=34.85\text{\degree} \end{gathered}[/tex]STEP-BY-STEP EXPLANATION:
We calculate the value of the angles for each point as follows:
[tex]\begin{gathered} \sin x=0.259\rightarrow x=\arcsin 0.259\rightarrow x=15.01\text{\degree} \\ \cos x=0.743\rightarrow x=\arccos 0.753\rightarrow x=42.01\text{\degree} \\ \tan x=4\rightarrow x=\arctan 4\rightarrow x=75.96\text{\degree} \\ \sin x=\frac{4}{7}\rightarrow x=\arcsin \frac{4}{7}\rightarrow x=34.85\text{\degree} \end{gathered}[/tex]what is the probability of a student owning a car that is not blue or green round to two decimal places
Answers
0.83
Explanation
The probability of an event is the number of favorable outcomes divided by the total number of outcomes possible
[tex]P=\frac{favorable\text{ ourcomes}}{\text{total possible outcomes}}[/tex]Step |
Let
[tex]\begin{gathered} \text{favorable outcomes=car that is not blue or gre}en,\text{ so} \\ \text{favorable outcomes=}red\text{ cars+yellow cars+white cars+other} \\ \text{favorable outcomes=}40+29+26+14 \\ \text{favorable outcomes=}109 \end{gathered}[/tex]now, the total outcomes is the total of cars
[tex]\text{total outcomes=40+13+29+26+10+14=132}[/tex]Finally, replace in the equation
[tex]\begin{gathered} P=\frac{favorable\text{ ourcomes}}{\text{total possible outcomes}} \\ p=\frac{109}{132} \\ P=0.83 \end{gathered}[/tex]so, the answer is 0.83
I hope this helps you
The dash in-front of the whole number is a negative sign, Just a little heads up :)
Answers
Okay, here we have this:
We need to solve the following expression:
[tex]\begin{gathered} -5\cdot2\text{ }\frac{1}{4} \\ =-5\cdot\frac{8+1}{4} \\ =-5\cdot\frac{9}{4} \\ =-\frac{45}{4} \\ =-11.25 \end{gathered}[/tex]Finally we obtain that the result is -11.25.
The local water slides have 40 employees,of which 95% are temporary.How many temporary employees are there?
Answers
Mul,tiply the number of employees by the percentage in decimal form (divided by 100)
40 x (95/100) = 40 x 0.95 = 38 employees
Find the slope of the line that passes through (4, 3) and (9, 10). Simplify your answer and write it as a proper fraction, improper fraction
Answers
Answer:
Slope = 7/5
Explanation:
The slope of a line that passes through the points (x1, y1) and (x2, y2) can be calculated as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]So, replacing (x1, y1) by (4, 3) and (x2, y2) by (9, 10), we get that the slope of the line is equal to:
[tex]m=\frac{10-3}{9-4}=\frac{7}{5}[/tex]Therefore, the slope is equal to 7/5
Poss Combine like terms to create an equivalent expression. Skill 4 3 2 m 5 m т 5 5 Over Introl Subs Quiz 80% Take Com
Answers
Collecting like terms =>
[tex]\begin{gathered} (\frac{2m}{5}-\frac{3m}{5})\text{- }\frac{4}{5} \\ we\text{ can simplify the terms with m coefficient} \\ \frac{2}{5}m\text{ -}\frac{3}{5}m \\ =\text{ find the lowest common multiple of the denominator} \\ =\text{ lowest common multiple of 5 and 5 is 5} \\ =\text{ }\frac{2m\text{ - 3m}}{5} \\ \Rightarrow\text{ }\frac{-m}{5} \\ \\ \\ \end{gathered}[/tex][tex]\begin{gathered} \text{Then we will obtain} \\ \frac{-m}{5}\text{ -}\frac{4}{5} \end{gathered}[/tex]We may decide to further simplify the expression or leave the answer as it is shown above,
On simplification we will need to get the lowest common multiple of the denominator which is 5
[tex]\frac{-m}{5}\text{ -}\frac{4}{5}\Rightarrow\text{ }\frac{-m\text{ - 4}}{5}[/tex]Find the inverse function of F(x)=2 arccos xF^-1(x)=
Answers
Given the inverse function
[tex]f(x)\text{ = 2arccosx}[/tex]A function g is the inverse of f if for y = f(x) , x = g(y)
[tex]\begin{gathered} y\text{ = 2arccosx} \\ \arccos x\text{ = }\frac{y}{2} \\ \arccos a\text{ = b} \\ a=\cos (b) \end{gathered}[/tex][tex]\begin{gathered} x=\text{ cos(}\frac{y}{2}) \\ \text{substitute y = x} \\ y=\cos (\frac{x}{2}) \end{gathered}[/tex]Hence the correct answer is Option B
Determine whether each parabola has a horizontal directrix or vertical directrix 1. (y-3)²= 1/8 (x+1) horizontal or vertical directrix2. (x-2)²=6(y-3) horizontal or vertical directrix 3. (y+4)²=-12(x+2)horizontal or vertical directrix4. (x+3)²= -8(y+2) horizontal or vertical directrix
Answers
Answer
1) Horizontal directrix.
2) Vertical directix.
3) Horizontal directix.
4) Vertical directrix.
Explanation
A parabola with a vertical axis will have a horizontal directrix.
A parabola with a horizontal axis will have a vertical directrix.
A parabola with a vertical axis will have a standard equation of the parabola as
(x - h)² = 4p (y - k),
where p ≠ 0.
The vertex of this parabola is at (h, k). The focus is at (h, k + p).
The directrix is the line y = k - p and it is a vertical directrix.
A parabola with a horizontal axis will have a standard equation of the parabola as
(y - k)² = 4p (x - h),
where p ≠ 0.
The vertex of this parabola is at (h, k). The focus is at (h + p, k).
The directrix is the line x = h - p and it is a horizontal directrix.
So, for this questions,
1.) (y - 3)² = 1/8 (x + 1)
This is of the form (y - k)² = 4p (x - h), so, we can easily see that this parabola has a horizontal directrix.
2.) (x - 2)²= 6 (y - 3)
This is of the form (x - h)² = 4p (y - k), so, we can easily see that this parabola has a vertical directrix.
3.) (y + 4)² = -12 (x + 2)
This is of the form (y - k)² = 4p (x - h), so, we can easily see that this parabola has a horizontal directrix.
4.) (x+3)²= -8(y+2)
This is of the form (x - h)² = 4p (y - k), so, we can easily see that this parabola has a vertical directrix.
Hope this Helps!!!
The function f is defined by the following rule.f(x) = 3x-3Complete the function table.хf(x)- 4-30145
Answers
Use a calculator and inverse functions to find the radian measures of a given angle around your answer to the nearest hundredth.angles whose sign is -0.26
Answers
Answer
Option C is correct.
x = -0.26 + 2pn
OR
x = -2.88 + 2pn
Explanation
Using the calculator and inverse functions
Let the unknown angle be x
Sin x = -0.26
x = Sin⁻¹ (-0.26)
x = -0.26 or -2.88 (From the calculator)
In order to generalize it, we add 2pi to both of them.
x = -0.26 + 2pn
OR
x = -2.88 + 2pn
Hope this Helps!!!
Sam wants to cover a gift box with paper the top of the box is 8in wide and 15in long the box is 12in tall what is the minimum amount of paper Sam will need to cover the entire box?
Answers
In order to find the amount of paper that will be needed, we need to calculate the surface area of this rectangular prism.
The faces of this figure are:
- 2 rectangles with dimensions 8 in and 15 in,
- 2 rectangles with dimensions 15 in and 12 in,
- 2 rectangles with dimensions 12 in and 8 in.
Calculating the area of each rectangle, we have:
[tex]\begin{gathered} A_1=8\cdot15=120 \\ A_2=15\cdot12=180 \\ A_3=12\cdot8=96 \end{gathered}[/tex]Now, the surface area is:
[tex]\begin{gathered} S=2A_1+2A_2+2A_3 \\ S=240+360+192 \\ S=792\text{ in}^2 \end{gathered}[/tex]So the amount of paper needed is 792 in².
Amber has a job babysitting. She makes 7.50 per hour. What is the constant rate of change?
Answers
Remember that the constant rate of change refers to the change between the variable.
In this case, the constant rate of change is $7.50 per hour, in other words, it's 7.50. As an equation would be
[tex]y=\frac{15}{2}x[/tex]I need help with this please thank you number 14
Answers
Answer:
The question is given below as
Concept:
The question will be solved using the linear pair theorem below
The Linear Pair Theorem states that two angles that form a linear pair are supplementary; that is, their measures add up to 180 degrees.
By applying the principle, we will have that
[tex]\begin{gathered} \angle x+88^0=180^0 \\ collect\text{ similar terms,} \\ subtract\text{ 88 from both sides} \\ \operatorname{\angle}x+88^0-88^0=180^0-88^0 \\ \angle x=92^0 \end{gathered}[/tex]Hence,
The value of x= 92°
Step 2:
By applying the linear pair theorem, we will also have that
[tex]\begin{gathered} \angle z+88^0=180^0 \\ collect\text{ similar terms, } \\ subtract\text{ 88 from both sides} \\ \operatorname{\angle}z+88^0-88=180^0-88 \\ \angle z=92^0 \end{gathered}[/tex]Hence,
The value of z= 92°
Step 3:
By applying the linear pair theorem also, we will have that
[tex]\begin{gathered} \angle x+\angle y=180^0 \\ 92^0+\angle y=180^0 \\ collect\text{ similar terms,} \\ substract\text{ 92 from both sides} \\ 92^0-92^0+\operatorname{\angle}y=180^0-92^0 \\ \angle y=88^0 \end{gathered}[/tex]Hence,
The value of y= 88°
What is 3[cos(60)+isin60]*1/2[cos(15)+isin(15)]
Answers
1) Let's simplify this expression considering the trigonometric ratios and the complex numbers as well.
[tex]\begin{gathered} 3\left[\cos \left(60^{\circ \:}\right)+i\sin \left(60^{\circ \:}\right)\right]\frac{1}{2}\left[\cos \left(15^{\circ \:}\right)+i\sin \left(15^{\circ \:}\right)\right] \\ Convert\:to\:radians: \\ 3\left[\cos \left(\frac{\pi }{3}\right)+i\sin \left(\frac{\pi }{3}\right)\right]\frac{1}{2}\left[\cos \left(\frac{\pi }{12}\right)+i\sin \left(\frac{\pi }{12}\right)\right] \\ \quad \cos \left(x\right)+i\sin \left(x\right)=e^{ix} \\ 3\times\frac{1}{2}\lbrack\left[e^{i\frac{\pi}{3}}\right]\left[e^{i\frac{\pi}{12}}\right] \\ \frac{3\left(-1\right)^{\frac{5}{12}}}{2} \\ \end{gathered}[/tex]We have transitioned that to work with radians for convenience and used one identity. Note that we could have written our final answer in a radical form.
Solve x2 + 12x + 25Hias17 by completing the square. Select all the possible solutions.-6 + 70-6 + 2.7–6 – 276-606-270-6-77
Answers
we are given the following expression:
[tex]x^2+12x+25=17[/tex]First, we will subtract 17 to both sides:
[tex]\begin{gathered} x^2+12x+25-17=17-17 \\ x^2+12x+8=0 \end{gathered}[/tex]We get an expression of the form:
[tex]ax^2+bx+c=0[/tex]To complete the square we will add and subtract the following term:
[tex]\frac{b^2}{4a}[/tex]Replacing the values:
[tex]\frac{12^2}{4(1)}=36[/tex]Therefore, we will add and subtract 36:
[tex]x^2+12x+36-36+8=0[/tex]Now we associate the first three terms:
[tex](x^2+12x+36)-36+8=0[/tex]Now we factor in the associated terms:
[tex](x+6)^2-36+8=0[/tex]Solving the operations:
[tex](x+6)^2-28=0[/tex]Now we solve for "x", first by adding 28 to both sides:
[tex](x+6)^2=28[/tex]Now we take square root to both sides:
[tex](x+6)=\sqrt[]{28}[/tex]Now we subtract 6 to both sides:
[tex]x=-6\pm\sqrt[]{28}[/tex]Now we factor 28 as 7*4:
[tex]undefined[/tex]I need help with question 3, the model is above it.
Answers
we have Pattern A
0,4,8,12,
In this problem we have an arithmetic sequence
the common factor d=4
therefore
in step 4
there are 12+4=16 dots
answer is 16 dotsYasmin has some identical rectangular tiles.
Each tile is L’cm by W'cm.
Using 9 of her tiles, Yasmin makes rectangle ABCD, shown in the diagram below.
Diagram NOT
accurately drawn
The area of ABCD is 1620 cm²
Work out the value of L and the value of W.
B
Diagram NOT
accurately drawn
Answers
The dimensions L and W, considering the area of the rectangle, are given as follows:
L = 6.1 cm.W = 4.9 cm.How to obtain the area of a rectangle?The area of a rectangle of dimensions L and W is given by the multiplication of these dimensions, as follows:
Considering the image shown at the end of the answer, with the composition of the smaller rectangles, the dimensions of the large rectangle are given as follows:
Width: 5W = 4L.Length: L + W.Hence the expression for the area of the rectangle is given as follows:
5W(L + W) = 1620.
From the width relation, we have that:
5W = 4L
W = 0.8L.
Hence the length is obtained as follows:
5W(L + W) = 1620.
5 x 0.8L(L + 0.8L) = 1620
7.2L³ = 1620
L = (1620/7.2)^(1/3) -> cubic root
L = 6.1 cm.
W = 0.8L = 0.8 x 6.1 = 4.9 cm.
Missing InformationThe problem is given by the image shown at the end of the answer.
More can be learned about the area of a rectangle at
https://brainly.com/question/25292087
#SPJ1
On your fifteenth birthday you discover you have a rich aunt sally aunt sally is a very generous women and wants to provide for your future she has decided that she will initially give you $1 then $2 the next year and so on doubling the amount each year until your 30. Use a chart to keep track how much money she will give you each year for the first 5 years.
Answers
Let's fill a table with the first two years, we already know those
So, we need to complete the chart for years 3,4, and 5. We know that in year 3, will receive double the money than we get in year 2, this is 2*$2=$4. Now we write that result on our table.
In year 4 we'll get double the money than in year 3, this is 2*$4=$8
Similarly, in year 5 we get double the money than what we got in year 4: 2*$8=$16
And we have filled in the table!
Now, a bonus, the pattern here seems to be an equation, notice this:
year 1 -> $1 = $2^0
year 2 ->$2 = $2^1
year 3 -> $4 = $2^2
year 4 -> $8 = $2^3
year 5 -> $16 = $2^4
This means that the amount of money we'll receive each year is given by
[tex]2^{t-1}[/tex]Where t is the year! (year 1, year 2, etc)
Find the value of b.a=5 and c = 10A.9.5B.10C.9D.8.7Please can you explain.
Answers
1) Assuming this is a right triangle, we can find the missing leg by making use of the Pythagorean Theorem.
2) Thus, we can write out this:
[tex]\begin{gathered} c^2=a^2+b^2 \\ \\ (10)^2=5^2+b^2 \\ \\ 100=25+b^2 \\ \\ b^2=100-25 \\ \\ b=\sqrt{75} \\ \\ b\approx8.7 \end{gathered}[/tex]Note that the hypotenuse (the largest side) is always on the left side. And that this is an approximation rounded off to the nearest tenth.
3) Thus, the answer is:
[tex]D.\:8.7[/tex]Simplify the inequality. Graph it, write it in interval notation, and then inequality notation. Write your answer in interval notation.3x+2<−4 or 3x+3>27Clear All Draw: Line segments interval inequality
Answers
given the inequality
[tex]3x+2<−4\text{ }or\text{ }3x+3>27[/tex]then
[tex]3x<−4-2\text{ }or\text{ }3x>27-3[/tex][tex]3x<−6\text{ }or\text{ }3x>24[/tex][tex]x<−2\text{ }or\text{ }x>8[/tex]Graph:
notice the empty circle because the ineqaulity does not have equal symbol
interval:
[tex]\left(-\infty \:,\:-2\right)\cup \left(8,\:\infty \:\right)[/tex]inequality:
[tex]x<-2\text{ }or\text{ }x>8[/tex]need help with math
Answers
Here, we want to get the solution to the inequality
To do this, we simply move on to collect like terms
We simply have to bring -4 to the other side
Mathematically, we have this as;
[tex]\begin{gathered} 2x\text{ -4 }\leq\text{ 12} \\ 2x\leq\text{ 12 + 4} \\ 2x\leq\text{ 16} \\ \text{ x }\leq\frac{16}{2} \\ x\leq8 \end{gathered}[/tex]Three people share 4/5 of a lasagna. What fraction of the lasagna does each person eat?
Answers
4/15
1) Since 3 people share 4/5 of a lasagna we can write:
[tex]\frac{\frac{4}{5}}{3}=\frac{4}{5}\times\frac{1}{3}=\frac{4}{15}[/tex]Remember that when dividing a fraction we must multiply the dividend (4/5) by the reciprocate of the divisor (3).
2) So each one ate 4/15 of a whole lasagna.
Reduce to the lowest terms by canceling -14/9 times -3/7
Answers
Answer:
2/3
Explanation:
Given the below;
[tex]\frac{-14}{9}\times\frac{(-3)}{7}[/tex]We can see from the above that 9 is divisible by 3 and that 14 is divisible by 7, let's go ahead and reduce to the lowest term as shown below;
[tex]\frac{-14}{9}\times\frac{(-3)}{7}=\frac{-2}{3}\times\frac{(-1)}{1}=\frac{2}{3}[/tex]identify the terms, like terms, coefficients and constants 2c - 2b + c + 3 + b - 4
Answers
1) In this expression, we have
1.1 ) Terms: We have 6 terms in total.
2c -2b +c +3 + b -4 Combining like terms we can rewrite them as
c -b -1
1.2) Like terms are the ones that share the same variable
2c, c
-2b, b
1.3) Coefficients the numbers that multiply the variables
2c - 2b + c + 3 + b - 4
So we have:
2, -2, 1
1.4) The constants. Simply put in this case, the numbers that do not vary
-4 and 3
using the digits -9 to 9, without repeating any numbers, place a number in each box to create a system of equations that has a solution in quadrant 2. Tip: in quadrant 2, the x - coordinate is negative and the y-coordinate is positive.
Answers
Okay, here we have this:
Considering the provided information and options, we are going to find the requested numbers, so we obtain the following:
So first we will choose two values for x and y that meet the given tip: in quadrant 2, the x - coordinate is negative and the y-coordinate is positive.
For our case we will take x=-1 and y=1, then we can write the following two equations:
1x+3y=2 -> 1(-1)+3(1)=2 -> -1+3=2 -> 2=2
y=7x+8 -> 1=7(-1)+8 -> 1=-7+8 -> 1=1
find a set of parametric equations for the rectangular equation
Answers
We have for the fisrt equation that
[tex]\begin{gathered} t\text{ = 2 -x } \\ x\text{ = 2 - t = -t + 2} \end{gathered}[/tex]Now knowing this we are going to replace in the second equation
[tex]\begin{gathered} y\text{ = 8x - 6} \\ y\text{ = 8(-t + 2) - 6 = -8t +16 -6} \\ y\text{ = -8t +10} \end{gathered}[/tex]So the answer is the fourth option.
kris is buying 165 square feet to turf to put on the floor of his square garage. which measurement is closest to the side length of each side of the garage?A 83 ftB 41 ftC 13 ftD 12ft
Answers
SOLUTION
Kris is buying 165 square feet to turf to put on the floor of his square garage.
which measurement is closest to the side length of each side of the garage?
Area of the square = Length x Length
165 = L X L
L^2 = 165
square root both sides, we have :
L = 12. 845
L = 13 feet ............... OPTION C
Solve for y. y - 10 = 7 - X
Answers
We are given the following expression:
[tex]y-10=7-x[/tex]To solve for "y" we will add 10 to both sides:
[tex]y-10+10=7-x+10[/tex]Adding like terms:
[tex]y=17-x[/tex]Which expression would be easier to simplify if you used the associative property to change the grouping? OA. 6+ 1; +3) OB. I(-0.2) +(-0.6)] +1.7 O c.(2+)+-) O D. (60+ 40) +-27)
Answers
A.
[tex]6+\lbrack\frac{4}{9}+(-\frac{2}{9})\rbrack[/tex]Since both fractions have the same numerator, you can factorize 1/9 aout of the parentheses, because:
[tex]\begin{gathered} \frac{1}{9}\cdot4=\frac{4}{9} \\ \text{and} \\ \frac{1}{9}\cdot2=\frac{2}{9} \end{gathered}[/tex]Then you can simplify the expression as:
[tex]6+\frac{1}{9}\lbrack4+(-2)\rbrack=6+\frac{1}{9}\lbrack4-2\rbrack[/tex]