Answer with Step-by-step explanation:
Complete question:
The coordinates of the vertices of the triangle are (-8,8),(-8,-4), and. Consider QR the base of the triangle. The measure of the base is b = 18 units, and the measure of the height is h = units. The area of triangle PQR is square units.
Let
P=(-8,8)
Q=(-8,-4)
QR=b=18 units
Height of triangle, h=Length of PQ
Distance formula
[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Using the formula
Height of triangle, h=[tex]\sqrt{(-8+8)^2+(-4-8)^2}=12units[/tex]
Area of triangle PQR=[tex]\frac{1}{2}\times base\times height[/tex]
Area of triangle PQR=[tex]\frac{1}{2}\times 18\times 12[/tex]
Area of triangle PQR=108 square units
Length of QR=18units
Let the coordinates of R(x,y)
[tex]\sqrt{(x+8)^2+(y+4)^2}=18[/tex]
[tex](x+8)^2+(y+4)^2=324[/tex]
[tex]x^2+64+16x+y^2+8y+16=324[/tex]
[tex]x^2+y^2+16x+8y=324-64-16[/tex]
[tex]x^2+y^2+16x+8y=244[/tex] ......(1)
Using Pythagoras theorem
[tex]H=\sqrt{P^2+B^2}[/tex]
[tex]H=\sqrt{(18)^2+(12)^2}[/tex]
[tex]H=6\sqrt{13}[/tex]units
[tex](6\sqrt{13})^2=(x+8)^2+(y-8)^2[/tex]
[tex]x^2+64+16x+y^2+64-16y=468[/tex]
[tex]x^2+y^2+16x-16y=468-64-64=340[/tex]
[tex]x^2+y^2+16x-16y=340[/tex] .....(2)
Subtract equation (2) from (1) we get
[tex]24y=-96[/tex]
[tex]y=-96/24=-4[/tex]
Using the value of y in equation (1)
[tex]x^2+16x+16-32=244[/tex]
[tex]x^2+16x=244-16+32[/tex]
[tex]x^2+16x=260[/tex]
[tex]x^2+16x-260=0[/tex]
[tex]x^2+26x-10x-260=0[/tex]
[tex]x(x+26)-10(x+26)=0[/tex]
[tex](x+26)(x-10)=0[/tex]
[tex]x=-26, x=10[/tex]
Hence, the coordinate of R (10,-4) or (-26,-4).
Sofia bought a clothes iron that was discounted 15% off of the original price of $35. What was the sale price of the clothes iron?
Answer:
35 - 0.15 * 35 so it is $29.75
Step-by-step explanation:
I got u
Answer:
$29.75
Step-by-step explanation:
15% = .15
.15 x 35 = 5.25
35 - 5.25 = 29.75
A study is done to determine the average salary for all Santa Clara County teachers. If we were to randomly pick 15 schools in Santa Clara County and average together the salaries of all teachers, would this be a good sampling technique or a bad sampling technique
Answer:
Good sampling technique
Step-by-step explanation:
In other to determine the mean value for a population, it may be necessary to make inference from the a small subset of the population, called the sample, if it is impossible, difficult or inefficient to get all population data. Hence, in other to select a subset of the population, then the sample must be selected at random, such that all elements of the population have equal chances of being selected and hence, be representative of the population. Since, the sampling technique adopted above is done at random, hence, it is a good sampling technique.
Use Cramer's Rule to solve (if possible) the system of linear equations.
x1 + 2x2 =8
- x1 + x2 = 1
Required:
Find the coefficient matrix.
Answer:
x1 = 2
x2 = 3
Step-by-step explanation:
[tex]x_1=\frac{D_{x1}}{D}\\\\x_2=\frac{D_{x2}}{D}[/tex]
Here D is the coefficient matrix.
Hence
[tex]x_1=\frac{6}{3}\\x_1=2[/tex]
&
[tex]x_2=\frac{9}{3}\\x_2=3[/tex]
the Barnes family drove 140 miles the first day and 220 miles on the second day. If they drove about 60 miles per hour, approximately how many hours did they drive?
What is the range of g?
y
--
.
9
7.
6+
5+
4+
3+
2+
1+
.
3
{4}}
-7 -6 -5 -4 -3 -2
+++
2 3 4 5 6 7
-2
-3
-4+
-5
-6+
7
7
Answer:
y 9 5 473648
Step-by-step explanation:
Why is the number of operators per shift multiplied by approximately 4.5 to obtain the total number of operators required to run the plant
I believe you meant "why is the number of shifts multiplied by approximately 4.5 to obtain the total number of operators required to run the plant"
Answer and Explanation:
There are 3 shifts per day, 49 weeks per year and 5 shifts per operator per week
To get total number of operators required to run the plant, we multiply number of shifts in a year by number if operators per shift.
49 weeks×5 shifts= 245 shifts per operator per year
365×3 shifts= 1095 shifts per year
1095/245=4.5 operators per shift
total number of operators required to run the plant(per day) = 4.5×3= 13.5 approximately 14
total number of operators required to run the plant(per year) =4.5×1095=4927.5 approximately 4928
Find the probability of selecting 3 cards from a standard deck without
replacing them and all 3 are hearts.
Answer:
B
Step-by-step explanation:
THere are 52/4= 13 hearts we can draw
The number of ways to draw 3 hearts from 13 is
13C3= 286
The number of ways to draw 3 cards from 52 is
52C3= 22100
divide these
286/22100= 11/850
This is answer B
A family eats out at a restaurant and the total for their meals is $73.89. They also pay sales tax of 5.8% and leave a tip for their server. If the family leaves a total of $93, which of the following might be a description of the service they received?
a.
They left a 10% tip, so the service was probably below average.
b.
They left a 15% tip, so the service was probably average.
c.
They left a 20% tip, so the service was probably above average.
d.
They left a 25% tip, so the service was probably outstanding.
The answer is They left a 20% tip, so the service was probably above average.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
here, we have,
First step is to the amount of the sales tax.
If 100% is $73.89,
5.8% will be x (tax):
100% : $73.89 = 5.8% : x.
x = $73.89 * 5.8% : 100%.
x = $4.28.
Now, we have the price for meals, sales tax, and the total amount of money left, so we can calculate how much the tip is:
$93.00 - $73.89 - $4.28 = $14.83.
So, the tip is $14.83.
Let represent it as percent.
If $73.89 is 100%, $14.83 will be x.
$73.89 : 100% = $14.83 : x.
x = $14.83 * 100% : $73.89.
x = 20%.
So, they left a 20% tip, so the service was probably above average.
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11 Emilio makes metal fences.
He is making a fence using this design.
1.44 m
DO NOT WRITE IN THIS AREA
1.8 m
.
The fence will need
3 horizontal metal pieces of length 1.8m
2 tall metal pieces of length 1.44 m
5 medium metal pieces
6 short metal pieces as shown on the diagram.
The heights of the tall, medium and short metal pieces are in the ratio 9:8:7
.
How many metres of metal in total does Emilio need to make the fence?
Answer:
Step-by-step explanation: 7 3 13 31
3 × 1.8 long pieces Calculate the ratios
2 × 1.44 9 tall vertical piece 1.44 / 9 = x / 9 x = 1.44
5 × ___ 8 medium vertical pieces 1.44 / 9 = x / 8 x = 1.28
6 × ___ 7 short vertical pieces 1.44 / 9 = x / 7 x = 1.12
3 × 1.8 long pieces
2 × 1.44 9 tall vertical piece 1.44 / 9 = x / 9 x = 1.44
5 × 1.28 8 medium vertical pieces 1.44 / 9 = x / 8 x = 1.28
6 × 1.12 7 short vertical pieces 1.44 / 9 = x / 7 x = 1.12
3 × 1.8 long pieces = 5.4 m
2 × 1.44 9 tall vertical piece = 2.88 m
5 × 1.28 8 medium vertical pieces = 6.4 m
6 × 1.12 7 short vertical pieces = 6.72 m
Total = 21.4 m
Consider a relation on the set of all states in the United States given by: two states are related if they have a border in common. Is it an equivalence relation
Answer:
Yes it is an equivalence relation
Explanation:
An equivalence relation is a binary relation between two values that are symmetric, transitive and reflexive. In other words, when we say a value x is equal(using "=") to a value y, there is an equivalence relation between them.
Example, given set {x, y, z} where ~ means equivalence:
x ~ y if y ~ z means symmetric
since x ~ y and y ~ z, then x ~ z means transitive
x ~ x means reflexive
Equivalence relations share a common attribute or attributes(example, a satisfying condition)
The above condition that two states are related from the set of all US states if they have a border in common satisfies the condition of equivalence listed hence it is an equivalence relation.
Find the domain and range of the function graphed below, in interval notation.
Answer:
Domain: [-2,1)
Range: [0,4]
Step-by-step explanation:
The required domain and range of the function graphed are -2 ≤ x < 1 and 0 ≤ y ≤ 4.
Given that,
To determine the domain and range of the function graphed below, in interval notation.
Range, it is the set of the values that come out to an outcome for a certain mathematical operations.
Here,
The projected line of the curve on the horizontal axis is from greater and equal to -2 to less than 1,
Domain = -2 ≤ x < 1
The projected line of the curve on the vertical axis is from greater or equal to 0 to less than or equal to 4,
Range = 0 ≤ y ≤ 4.
Thus, the required domain and range of the function graphed are -2 ≤ x < 1 and 0 ≤ y ≤ 4.
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Get brainly if right!! Plsss help
The 8t h term in the arithmetic sequence is 17, and 12t h term is 25. Find the first
term, and the sum of the first 20 terms.
Step-by-step explanation:
t8 = a1 + (n - 1)*d
t8 = 17
17 = a1 + 7*d
t12 = 25
25 = a1 + 11d
17 = a1 + 7d Subtract
8 = 4d Divide by 4
8/4 = 4d/4
2 = d
17 = a1 + 7d
17 = a1 + 7*2
17 = a1 + 14 Subtract 14
3 = a1
Sum 20 terms
The 20 term = a1 + 19*2
The 20 term = 3 + 38
= 41
Sum = (a1 + a20) * 20 / 2
Sum = (3 + 41)* 20/2
Sum = 44 * 10
Sum = 440
An RLC series circuit has an applied voltage of 240 volts. R = 48 ohm, XL = 100 ohm, and XC = 36 ohm. What is the circuit impedance (Z)?
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Answer:
48 +j64 ohms
Step-by-step explanation:
The impedance of a series circuit is the sum ...
R + jXl -jXc
= 48 +j100 -j36
= 48 +j64 . . . . ohms
_____
Additional comment
"j" is the electrical engineer's name for √-1, because "i" is used to represent current.
the sum of the square of the number and a second number is 42
Step-by-step explanation:
x+x squared =42. The square of the number is the number square. By my incredibly accurate guess and check strategy (works most of the time )6*6 = 36+6=42
Long division: 2/ 2769
Answer:
1384.5
Step-by-step explanation
Diviseion is just the oppisite of multiplication so you can think to yourself that what times two equals 2769. If you multiply 1384.5 on a calculater you get 2769.
If a+bi, where b is not equal to 0, is a complex zero of a polynomial with real coefficients, then so is its _____ , a-bi.
a.) linear factorization
b.) irreducible factor
c.) reducible factor
d.) complex factor
e.) fundamental theorem
f.) conjugate
Hello,
answer f: conjugate
if all coefficients are real and a+ib a zero, its conjgate a-ib is also a zero.
Which of the following statements must be true about this diagram? Check all
that apply.
4 3
1
1
N
A. The degree measure of 23 equals the sum of the degree
measures of 21 and 22.
B. m23 is greater than m 2
C. The degree measure of 24 equals the sum of the degree
measures of 22 and 23.
D. m 4 is greater than m_2.
E. m24 is greater than m 1.
F. The degree measure of 24 equals the sum of the degree measures
of 21 and 22.
Answer:
D, E, and F
Step-by-step explanation:
✔️Statement D is true:
Rationale: m<4 is more than 90°, while m<2 is less than 90°. Therefore m<4 is greater than m<2
✔️Statement E is true:
Rationale: m<4 is more than 90°, while m<1 is less than 90°. Therefore m<4 is greater than m<1
✔️Statement F is true:
Rationale:
m<4 is an external angle of the triangle.
m<1 and m<2 are interior angles that are opposite to m<4. Therefore, based on the external angle theorem of a triangle,
m<4 = m<1 + m<2
Jessica purchases a kayak in Florida, where the state sales taxes are 6%. She paid $72 in sales tax. What was the retail price of the kayak?
Answer:
72 is 6% of 1200.
Step-by-step explanation:
Multiply 72 by 100.
72*100
Then divide the number by 6
(72*100)/6
You should get 1200.
If 6 playes cost 54$ how much do 30 plates cost
Answer:
270 plates
Step-by-step explanation:
First, you need to find how much one plate costs.
6x = 54
---- ----
6 6
x = 9
Now, multiply 30 plates with x, which is 9.
30(9) = 270
The answer is 270.
Answer:
270
Step-by-step explanation:
54($)÷6= 9 then 9×30=270
I WILL MARK THE ANSWER AS BRAINLIEST IF RIGHT
PLEASE HELP ME BE CORRECT BEFORE ANSWERING PLEASE
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Answer:
D neither
Step-by-step explanation:
Reflection across a vertical line is required to change the figure left-to-right without changing it top-to-bottom. Translation along a directed line segment must then map corresponding points.
Sequence A involves reflection over a horizontal line, so can be rejected immediately. Sequence B does the translation so that point N gets moved to the location of point B. However, point N corresponds to point D (see the similarity statement), so that translation is inappropriate.
Neither sequence will map KLMN to ABCD.
Multiply the polynomial 4x(2x+3) (show work pls)
Answer:
8^2+12x
Step-by-step explanation:
4x(2x+3)
=4x times 2x+4x times 3
=4 times 2xx+4 times 3x
Answer:
8x^2 +12x
Step-by-step explanation:
Step 1) Multiply each term in the parentheses by 4x
4xx2x+4xx3
Step 2) Calcuate the product
8x^2 +12x
Congruent sides???????????
Answer:
the second option : ST and WX
Step-by-step explanation:
congruent means they would completely cover each other when oriented in the same direction and positioned at the same location.
after dying the two mirroring actions we get
VS correlates to ZW
ST correlates to WX
TU correlates to XY
UV correlates to ZY
Please help me out with these questions :
Answer:
Step-by-step explanation:
1. 3/7 x = 12
3x = 84
x = 28
2. 3x+ 6 = 39
3x = 33
x = 11
3. 1/3 x - 3/4 x = 15
9x - 4x = 180
x = 36
4. 1/4 x = x -21
3/4 x = 21
3x = 84
x=28
5. 86-36 = 50
50/2
25
You return from a trip with 480 Canadian dollars. How much are your Canadian dollars worth in U.S. dollars? Use the exchange rate shown below. Currency U.S. dollars per Canadian dollar Canadian dollars per U.S. dollar Canadian dollar 0.5823 1.717 The 480 Canadian dollars are equivalent to about $ (Round to the nearest cent as needed.)
591 Dollars 42 Cents (591 Dollars when rounded)
The following is a scatterplot of the percent of children under age 18 who are not in school or in the labor force vs. the number of juvenile violent crime arrests for each of the 50 states. The least-squares regression line has been drawn in on the plot. We would like to predict what the number of juvenile violent crime arrests would be in a state if 25% of children are not in school or in the labor force. This is called
Answer:
Extrapolation
Step-by-step explanation:
From the linear regression plot created in the picture given, se could see that Tha percentage of student covered by the the plot is just above 16%. Therefore, to predict the percentage of the number of juvenile violent crime arrests would be in a state if 25% of children are not in school or in the labor force will require us to assume that the current trend continues into the future. Hence, we use the information and indications we have at present to make prediction into the future based on the assumption that we the current trend will remain relevant and applicable. This assumption into the future based on current trend is called EXTRAPOLATION.
Need help with this math
Answer:
Step-by-step explanation:
office at point A =(-7,-5) ........................in the form (x1,y1)
supermarket and point B = (-2,-6)........in the form (x2,y2)
home Home at point C = (4,-6).............in the from (x3,y3)
find the total distance from A to B + B to C
ABdist= sqrt[ (x2-x1)^2 + (y2-y1)^2 ]
ABdist = sqrt[ (-2-(-7))^2 + (-6-(-5))^2 ]
ABdist = sqrt[ (-2 + 7)^2 + (-6 +5)^2]
ABdist = sqrt[ [tex]5^{2}[/tex] + [tex](-1)^{2}[/tex]]
ABdist = sqrt[ 25 + 1 }
ABdist = [tex]\sqrt{26}[/tex]
BCdist= sqrt[ (x3-x2)^2 + (y3-y2)^2 ]
BCdist = sqrt[ (4-(-2))^2 + (-6-(-6))^2]
BCdist = sqrt[ 4+2)^2 + -6+6)^2 ]
BCdist = sqrt [ [tex]6^{2}[/tex] + [tex]0^{2}[/tex] ]
BCdist = [tex]\sqrt{36}[/tex]
BCdist = 6
total distance = [tex]\sqrt{26}[/tex] +6
The first answer looks good
Badluckville had been expecting a $50 million investment for a new golf resort, but the contract was cancelled.
Badluckville's mayor estimates that this will cost the city $300 million in total economic activity. What is the mayor's
estimate of the multiplier and marginal propensity to consume?
Answer:
multiplier = 6
marginal propensity to consume = .83
Step-by-step explanation:
/ means divided by
1 .
300,000,000 / 50,000,000 =
multiplier =
6
2.
300,000,000 - 50,000,000 =
250,000,000
250,000,000/300,000,000 =
marginal propensity to consume =
0.83333333333
or
.83
quizlet
marginal propensity to consume is equal to ΔC / ΔY, where ΔC is the change in consumption, and ΔY is the change in income
investopedia
The of the matrix whose columns are vectors which define the sides of a parallelogram one another is the area of the parallelogram?
Answer:
absolute value of the determinant, adjacent to, equal to
Step-by-step explanation:
The absolute value of a determinant of the [tex]\text{matrix whose}[/tex] columns are the vectors and they define the [tex]\text{sides}[/tex] of a [tex]\text{parallelogram}[/tex] which is adjacent to one another and is equal to the [tex]\text{area}[/tex] of the [tex]\text{parallelogram}[/tex].
The determinant is a real number. They are like matrices, but we use absolute value bars to show determinants whereas to represent a matric, we use square brackets.
Please help! Rewrite the function
Answer:
The answer is below
Step-by-step explanation:
A function is used to show the relationship between two or more variables. This variables are known as the input variables and output variables.
The input variables are variables which do not depend on other variables while the output variables are variables that depends on other variables.
Given that g(x) = 12x / (x-5); rewriting in the form g(x) = [a/(x-h)] + k, gives:
[tex]g(x)=\frac{60}{x-5}+12[/tex]
The graph of g(x) was plotted using online geogebra graphing calculator. The graph is attached.
Zach read a book for 10 minutes every weekend in the first month, 20 minutes in the second month, 40 minutes in the third month, and 80 minutes in the fourth month.
Victoria read a book for 35 minutes every weekend in the first month, 50 minutes in the second month, 65 minutes in the third month, and 80 minutes in the fourth month.
Which statement best describes the methods used by Zach and Victoria to increase the time they spent reading a book? (1 point)
Select one:
a. Zach's method is linear because the number of minutes increased by an equal factor every month.
b. Victoria's method is linear because the number of minutes increased by an equal number every month.
c. Both Victoria's and Zach's methods are exponential because the number of minutes increased by an equal factor every month.
d. Both Victoria's and Zach's methods are exponential because the number of minutes increased by an equal number every month.
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Answer:
b. Victoria's method is linear because the number of minutes increased by an equal number every month
Step-by-step explanation:
Zach's reading doubled each month, a characteristic of an exponential function.
Victoria's reading increased by 15 minutes each month, characteristic of a linear function.
The only reasonable description among those offered is the one shown above: choice B.
