Please help!! A fire hydrant 2.5 feet high casts a 5 foot shadow. How tall is a street light that casts a 26 foot shadow at the same time?
Answers
Related Questions
Erick, Mia, and Isabelle golfed 9 holes. Erick scored 10 more than Mia, and Isabelle scored 16 less than twice Mia's score. Use the drop-down menus to complete the statements about the expression that represents the scenario. What does the expression x + x + 10 + 2x – 16 represent from the given scenario? What does the variable in the expression represent? What is the expression in simplified form? What is the constant in the simplified expression?
Answers
Answer:
1. The total score of all three players.
2. Mia's score.
3. 4x-6\
4. -6
The mathematical expression from the scenario represents the total golf scores of Erick, Mia, and Isabelle. The variable represents Mia's score, and the simplified expression is 4x - 6, with -6 being the constant.
Explanation:From the given scenario, the expression x + x + 10 + 2x - 16 represents the total score of Erick, Mia, and Isabelle. The variable 'x' in this expression represents Mia's golf score, as other scores are dependent on it.
To simplify the expression, we group like terms: x (Mia's score) + x (Erick's score, which is 10 more than Mia's) + 2x (Isabelle's score, which is 16 less than twice Mia's) - 16. Simplifying this, we get 4x - 6. So, the simplified expression is 4x - 6.
The constant in the simplified expression is -6. This is the value that is added or subtracted to the variable's value, irrespective of its value.
Learn more about Algebraic Expressions here:https://brainly.com/question/953809
#SPJ2
Find the values of sand y
VR=y
TS=x+11
VT=y-3x
RS=x+2
Answers
therefore, y=x+11 and x+2=y-3x
y=x+11 , 2=y-4x
y=x+11 , y=4x+2
then use the process of elimination:
y=4x+2 then plug in: y=3+11
- y=x+11 y=14
0=3x-9 I think this is how you'd do it, tbh it's just an educated
3x=9 , x=3 guess. Btw, sorry if it looks weird
the radius of a circular park is 120 m. to nearest meter, what is the circumference of the park.
Answers
A=πr²
2 x 3.14 x 120 = 754
Chris wants to make an enclosed rectangular area for a mulch pile. She wants to make the enclosure in such a way as to use a corner of her back yard. She also wants it to be twice as long as it is wide. Since the yard is already fenced, she simply needs to construct two sides of the mulch pile enclosure. She has only 15 feet of material available. Find the dimensions of the enclosure that will produce the maximum area
Answers
The enclosure having the maximum area meeting Chris's requirement is 10 ft × 5 ft.
Chris should construct the enclosure with a width of 5 feet and a length of 10 feet, using her 15 feet of fencing material, which will result in a maximum enclosed area of 50 square feet.
Chris wants to construct an enclosed rectangular area for a mulch pile and use her backyard's corner fence effectively, thereby constructing only two sides of the mulch pile enclosure. She has 15 feet of fencing material to use and wants the length of the rectangular enclosure to be twice the width. To find the dimensions that will produce the maximum area, we can set up an equation.
Let x represent the width (in feet) and 2x represent the length (in feet), since the length is twice the width.
Since Chris is using the corner of the yard, she only needs to construct two sides of the fence.
Therefore, the amount of fencing material she will use (perimeter of two sides) is given by the equation x + 2x = 15, which simplifies to 3x = 15.
Solving for x, we find that x = 5 feet. Thus, the width of the enclosure is 5 feet, and the length is twice that, or 10 feet.
The maximum area that Chris can enclose is therefore 5 ft imes 10 ft = 50 square feet.
Which two equations would be most appropriately solved by using the zero product property? Select each correct answer. 4x² = 13 0.25x2+0.8x−8=0 −(x−1)(x+9)=0 3x2−6x=0
Answers
Answer:
−(x−1)(x+9)=0
And..
3x2−6x=0
Step-by-step explanation:
Final answer:
The two equations most appropriately solved by using the zero product property are −(x−1)(x+9)=0 and 3x²−6x=0, as they can be directly factored into a product of terms equaling zero.
Explanation:
The question involves finding which two equations would be most appropriately solved by using the zero product property. The zero product property states that if the product of two numbers is zero, then at least one of the multiplicands must be zero. Therefore, equations that can be factored into a product of terms equaling zero can be solved using this property.
−(x−1)(x+9)=0: This equation is already in a factored form and directly applies the zero product property. Set each factor equal to zero and solve for x: x−1=0 or x+9=0, which gives x = 1 or x = −9.3x²−6x=0: This equation can be factored as 3x(x−2)=0. By applying the zero product property, set 3x=0 and x−2=0, solving for x gives x = 0 or x = 2.The other options, 4x² = 13 and 0.25x²+0.8x−8=0, are not immediately in a form that uses the zero product property without further manipulation or do not directly apply to this property.
Compute the requested value to hundredths of a percent. Choose the correct answer. You see a used car you wish to buy. The dealer quotes you a price of $1,595. You have a Blue Book quotation of $1,435 for the same model and year. How much greater (%) is the dealer's price from the Blue Book? It is _____%.
Answers
$ 1,435 ---> 100%
$ 1,595 ---> x
Clearing x we have:
x = ((1595) / (1435)) * (100)
x = 111.1498258
Then, the difference is:
111.1498258 - 100 = 11.14982578%
hundredths of a percent:
11.15%
Answer:
the dealer's price from the Blue Book: It is 11.15%
Answer:
11.15
Step-by-step explanation:
Which of the following best describes the intersection of two planes? (Points : 5)
line
line segment
point <
ray
I think its Point?
Answers
A car travels 200 miles in the same time that a train travels 300 miles. The speed of the train is 20 miles per hour more than the speed of the car. Which equation could be used to determine the speed of the car, r, in miles per hour?
Answers
time= distance/rate
and the train is going 300 miles
the car is going 200 miles
the train goes 20 miles faster than the car
fitting the numbers into the equation
200/r=300/(r+20)
cross multiply
200/r = 300/(r+20)
200(r+20) = 300r
distributive property
4000+200r=300r
subtract 200r from both sides to add like terms
4000=100r
divide 100 from each side to get r by itself
40 = rate of car
60 = rate of train
The ratio of the segments into which the altitude to the hypotenuse of a right triangle divides the hypotenuse is 9 : 4. what is the length of the altitude? 6 36 3 cannot be determined
Answers
√(4*9) : 4 : 9 = 6 : 4 : 9
Since these are ratios, not measures, the actual length of the altitude cannot be determined. (4th selection)
If you add 0.43 to a certain number then subtract 0.58 from the result and then another 4.04, you’ll get 30.3. What is the certain number?
Please show how you did it.
Answers
(((0.43+x)-.58)-4.04) = 30.3
(0.43+x)-4.64 = 30.3
x-4.21 = 30.3
x = 30.3 + 4.21
x = 34.51
The answer is 34.51 and there's the work for you. Have a great day!
Answer:
34.49
Step-by-step explanation:
You do it reverse
30.3+4.04=34.34
34.34+0.58=34.92
34.92-0.43=34.49
WILL GIVE BRAINLIEST!!!!!
1. Use the parabola tool to graph the quadratic function f(x)=x2+10x+16 . Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.
2. Use the parabola tool to graph the quadratic function f(x)=−(x−3)(x+1) .
Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.
3. Use the parabola tool to graph the quadratic function f(x)=−x2+4.
Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.
4. Use the parabola tool to graph the quadratic function f(x)=2x2+16x+30 .
Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.
5. Select ALL the statements that are true for the graph of y=(x+2)2+4 .
The graph has a maximum.
The graph has a minimum.
The vertex is (2, 4) .
The vertex is (−2, 4) .
Answers
1. f(x)=x²+10x+16
Use the formula to find the vertex = (-b/2a, f(-b/2a)) , here in the above equation a=1(As, a>0 the parabola is open upward), b=10. by putting the values.
-b/2a = -10/2(1) = -5
f(-b/2a)= f(-5)= (-5)²+10(-5)+16= -9
So, Vertex = (-5, -9)
Now, find y- intercept put x=0 in the above equation. f(0)= 0+0+16, we get point (0,16).
Now find x-intercept put y=0 in the above equation. 0= x²+10x+16
x²+10x+16=0 ⇒x²+8x+2x+16=0 ⇒x(x+8)+2(x+8)=0 ⇒(x+8)(x+2)=0 ⇒x=-8 , x=-2
From vertex, y-intercept and x-intercept you can easily plot the graph of given parabolic equation. The graph is attached below.
2. f(x)=−(x−3)(x+1)
By multiplying the factors, the general form is f(x)= -x²+2x+3.
Use the formula to find the vertex = (-b/2a, f(-b/2a)) , here in the above equation a=-1(As, a<0 the parabola is open downward), b=2. by putting the values.
-b/2a = -2/2(-1) = 1
f(-b/2a)= f(1)=-(1)²+2(1)+3= 4
So, Vertex = (1, 4)
Now, find y- intercept put x=0 in the above equation. f(0)= 0+0+3, we get point (0, 3).
Now find x-intercept put y=0 in the above equation. 0= -x²+2x+3.
-x²+2x+3=0 the factor form is already given in the question so, ⇒-(x-3)(x+1)=0 ⇒x=3 , x=-1
From vertex, y-intercept and x-intercept you can easily plot the graph of given parabolic equation. The graph is attached below.
3. f(x)= −x²+4
Use the formula to find the vertex = (-b/2a, f(-b/2a)) , here in the above equation a=-1(As, a<0 the parabola is open downward), b=0. by putting the values.
-b/2a = -0/2(-1) = 0
f(-b/2a)= f(0)= −(0)²+4 =4
So, Vertex = (0, 4)
Now, find y- intercept put x=0 in the above equation. f(0)= −(0)²+4, we get point (0, 4).
Now find x-intercept put y=0 in the above equation. 0= −x²+4
−x²+4=0 ⇒-(x²-4)=0 ⇒ -(x-2)(x+2)=0 ⇒x=2 , x=-2
From vertex, y-intercept and x-intercept you can easily plot the graph of given parabolic equation. The graph is attached below.
4. f(x)=2x²+16x+30
Use the formula to find the vertex = (-b/2a, f(-b/2a)) , here in the above equation a=2(As, a>0 the parabola is open upward), b=16. by putting the values.
-b/2a = -16/2(2) = -4
f(-b/2a)= f(-4)= 2(-4)²+16(-4)+30 = -2
So, Vertex = (-4, -2)
Now, find y- intercept put x=0 in the above equation. f(0)= 0+0+30, we get point (0, 30).
Now find x-intercept put y=0 in the above equation. 0=2x²+16x+30
2x²+16x+30=0 ⇒2(x²+8x+15)=0 ⇒x²+8x+15=0 ⇒x²+5x+3x+15=0 ⇒x(x+5)+3(x+5)=0 ⇒(x+5)(x+3)=0 ⇒x=-5 , x= -3
From vertex, y-intercept and x-intercept you can easily plot the graph of given parabolic equation. The graph is attached below.
5. y=(x+2)²+4
The general form of parabola is y=a(x-h)²+k , where vertex = (h,k)
if a>0 parabola is opened upward.
if a<0 parabola is opened downward.
Compare the given equation with general form of parabola.
-h=2 ⇒h=-2
k=4
so, vertex= (-2, 4)
As, a=1 which is greater than 0 so parabola is opened upward and the graph has minimum.
The graph is attached below.
Here are a bunch of CORRECT answers, your answer is somewhere in there. For the first CORRECT answer the second point is -5,-9. Don't make the same mistake I did on question 3, but it still shows the correct answer. I love to help.
in a pile of coins there are 7 more quarters than nickels if there is a total of $2.65 in coins how many quarters are there guess check and revise to solve
Answers
A quarter is worth $0.25 and a nickle is worth $0.05. Suppose the number of quarters is represented by q and the number of nickels is represented by n.
First Equation
"There are 7 more quarters than nickels" could be written as
⇒ q = n + 7
Second Equation
"There is a total of $2.65" could be written as
⇒ 0.25q + 0.05n = 2.65 (change to whole number, multiply both side by 100)
⇒ 25q + 5n = 265
Work on the system of equation
Substitute q = n + 7 to the second equation
25q + 5n = 265
25(n + 7) + 5n = 265
25n + 175 + 5n = 265
30n + 175 = 265
30n = 265 - 175
30n = 90
n = 90/30
n = 3
The number of nickels is 3
Substitute n = 3 to the first equation
q = n + 7
q = 3 + 7
q = 10
The number of quarters is 10
Bianca planted seeds to grow zinnias, sunflowers, and marigolds. After several weeks, 18 out of 50 zinnia seeds, 12 out of 30 sunflower seeds, and 14 out of 40 marigold seeds grew into plants. Drag the names of the plants in order from the least percentage of plants that grew to the greatest percentage of plants that grew.
Answers
% of sunflower seeds that grew = 12/30(100)= 40%
% of marigold seeds that grew = 14/40(100) = 31.8 %
Therefore, in order of the percentage that grew;
Sunflower has the highest %, followed by zinnia seeds and lastly the marigold seed
Given that z20 = –2 and z50= – 1, which of the following do you know?
1.) The variance is 10.
2.) The standard deviation is 30.
3.) The mean is 80.
4.) The median is 40.
5.) The data point x=20 is 2 standard deviations form the mean
6.) The data point x=50 is 1 standard deviation from the mean
7.) The data point x=45 has a z-valued of 1.5
Answers
Answer:
it is 2;3;5;6
Step-by-step explanation:
Given that z20 = –2 and z 50= –1, which of the following do you know?
The variance is 10.
The standard deviation is 30.
The mean is 80.
The median is 40.
The data point x = 20 is 2 standard deviations from the mean.
The data point x = 50 is 1 standard deviation from the mean.
The data point x = 45 has a z-value of 1.5.
answer2356 on edge
The solution is, it is 2;3;5;6.
What is standard deviation?A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
here, we have,
Given that z20 = –2 and z 50= –1, which of the following do you know?
The variance is 10.
The standard deviation is 30.
The mean is 80.
The median is 40.
The data point x = 20 is 2 standard deviations from the mean.
The data point x = 50 is 1 standard deviation from the mean.
The data point x = 45 has a z-value of 1.5.
so, we get,
answer2, 3, 5, 6 on edge.
Learn more about standard deviation here:
brainly.com/question/23907081
#SPJ3
Find the balance in the account after the given period. $3500 deposit 6.75% compounded monthly, after 6 months
Answers
[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to &\$3500\\ r=rate\to 6.75\%\to \frac{6.75}{100}\to &0.0675\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\to &12\\ t=years\to \frac{6}{12}\to &\frac{1}{2} \end{cases} \\\\\\ A=3500\left(1+\frac{0.0675}{12}\right)^{12\cdot \frac{1}{2}}\implies A=3500(1.005625)^6[/tex]
What is the area of a triangle that has a base of 3 feet and a height of 6 feet?
A: 18 ft^2
B: 18 ft C: 9 ft^ 2 D: 4.5 ft^2
Answers
The formula of area of triangle is given by
[tex] A= \frac{1}{2} b*h [/tex]
Where b is the base and h is the height .
In the given question, base ,b = 3 feet
Height, h= 6 feet
Substituting the values of b and h in the formula, we will get
[tex] A = \frac{1}{2}*3*6 = 9 ft^2 [/tex]
Correct option is C .
Answer:
9 ft^ 2
Step-by-step explanation:
What transformation has changed the parent function f(x) = 3(2)x to its new appearance shown in the graph below?
exponential graph passing through point 0, 5.
f(x) + 2
f(x) + 4
f(x + 2)
f(x + 4)
Answers
f (x) = 3 * (2) ^ x
Then, we have the following fact that is a fact of the problem:
"exponential graph passing through point 0, 5"
Thus,
Original graphic:
f (x) = 3 * (2) ^ x
f (0) = 3 * (2) ^ 0
f (0) = 3
Graph with transformation:
g (x) = 3 * (2) ^ x + 2
g (0) = 3 * (2) ^ 0 + 2
g (0) = 3 + 2
g (0) = 5
Go through the point (0, 5)
Therefore the graph is:
g (x) = 3 * (2) ^ x + 2
g (x) = f (x) + 2
answer:
f (x) + 2
Leyla drops a penny from a height of 150 m.
How long will it take the penny to hit the ground?
Use the formula h(t)=−4.9t2+vot+h o, where vo is the initial velocity and h o is the initial height. Round to the nearest tenth of a second.
Answers
Answer:
I believe its 5.5
Step-by-step explanation:
Which values are solutions to the inequality below? Check all that apply [tex] \sqrt{x} [/tex]>13
a) 26
b) 28560
c) 15
d) 170
e)1
f)251
Answers
question 1
Solve the system of equations and choose the correct answer from the list of options.
d + e = 15
−d + e = −5
Label the ordered pair as (d, e).
A (0, 0)
B (10, −5)
C (5, 10)
D (10, 5)
question2
A set of equations is given below:
Equation S: y = x + 9
Equation T: y = 2x + 1
Which of the following steps can be used to find the solution to the set of equations?
A x = 2x + 1
B x + 9 = 2x
C x + 1 = 2x + 9
D x + 9 = 2x + 1
Question 3
A set of equations is given below:
Equation C: y = 6x + 9
Equation D: y = 6x + 2
Which of the following options is true about the solution to the given set of equations?
A One solution
B No solution
C Two solutions
D Infinite solutions
question 4
Solve the system of equations and choose the correct answer from the list of options.
2x + y = −4
y = 3x + 2
A negative 6 over five comma negative 8 over 5
B negative 8 over 5 comma negative 6 over 5
C negative 5 over 6 comma negative 11 over 5
D negative 11 over 5 comma negative 6 over 5
question 5
A system of equations is given below:
y = –2x + 1
6x + 2y = 22
Which of the following steps could be used to solve by substitution?
A 6x + 2(−2x + 1) = 22
B −2x + 1 = 6x + 2y
C 6(−2x + 1) + 2y = 22
D 6(y = −2x + 1)
Answers
2. d
3. b
4. a
5. a
those are the answers to the questions
Answer:
1.D
2.D
3.B
4.A
5.A
Step-by-step explanation:
1.We are given that two equations
[tex]d+e=15[/tex]
[tex]-d+e=-5[/tex]
Adding two equations then we get
[tex]2 e=10[/tex]
[tex]e=\frac{10}{2}=5[/tex]
Substitute e=5 in equation one then we get
[tex]5+e=15[/tex]
[tex] d=15-5[/tex]
[tex]d=10[/tex]
Hence, the ordered pair as (10, 5).
Therefore,Option D is true.
2.We are given that two equations
Equation S:[tex]y=x+9[/tex]
Equatin T:[tex]y=2x+1[/tex]
Using substitution method
Substitute the value of y from equation one in equation second then we get
[tex]x+9=2x+1[/tex]
Therefore, option D is true.
3.We are given that two equations
Equation C :[tex]y=6x+9[/tex]
Equation D[tex]:y=6x+2[/tex]
The two equations can be written as
[tex]6x-y+9=0[/tex]
[tex]6x-y+2=0[/tex]
[tex]a_1=6,b_1=-1,c_1=9[/tex]
[tex]a_2=6,b_2=-1,c_2=2[/tex]
[tex]\frac{a_1}{a_2}=\frac{6}{6}=1:1[/tex]
[tex]\frac{b_1}{b_2}=\frac{-1}{-1}=1:1[/tex]
[tex]\frac{c_1}{c_2}=\frac{9}{2}[/tex]
[tex]\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2}[/tex]
Therefore, system of equations have no solution
Hence, option B is true.
4.We are given that two equations
[tex]2x+y=-4[/tex]
[tex]y=3x+2[/tex]
Using substitution method
Substitute value of y from equation second in equation one
Then we get
[tex]2x+3x=2=-4[/tex]
[tex]5 x=-4-2[/tex]
[tex]5 x=-6[/tex]
[tex]x=-\frac{6}{5}[/tex]
Substitute the value of x in equation second then we get
[tex]y=3\times( -\frac{6}{5})+2[/tex]
[tex]y=\frac{-18+10}{5}[/tex]
[tex]y=-\frac{8}{5}[/tex]
Hence, option A is true.
5.We are given that two equations
[tex]y=-2x+1[/tex]
[tex]6x+2y=22[/tex]
Using substitution method
Substitute value of y from equation one in second equation then we get
[tex]6x+2(-2x+1)=22[/tex]
Hence, option A is true.
A pool in the shape of s rectangle has a perimeter 80 feet. The pool is 8 feet less wide than it is long
Answers
44 for length and 36 for width
what expression represents a number t increased by 10
Answers
t+10
Find the area of the triangle. Round the answer to the nearest tenth.
A.
27.1 square units
B.
29.0 square units
C.
178.3 square units
D.
356.6 square units
Answers
Answer:
The correct option is C.
Step-by-step explanation:
Given information: AB=20.4, BC=17.7 and ∠ B = 99 °.
It two sides and their inclined angle is given then the area of the triangle is
[tex]A=\frac{1}{2}ab\sin C[/tex]
Where, a and b are two sides of a triangle and C is their inclined angle.
The area of given triangle is
[tex]A=\frac{1}{2}\times 20.4\times 17.7 \sin 99^{\circ}[/tex]
[tex]A=178.317253[/tex]
[tex]A\approx 178.3[/tex]
The area of the triangle ABC is 178.3 square units. Therefore the correct option is C.
Find X. This is Big Ideas Geometry Chapter 9.3
Answers
You can set up a ratio with the largest triangle to the second largest.
30/50=x/40
50x=1200 x=24 units
The value of x of the triangle is: x = 24 units
How to find the length of similar triangles?Pythagoras Theorem is defined as the way in which you can find the missing length of a right angled triangle.
The triangle has three sides, the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).
Pythagoras is in the form of;
a² + b² = c²
Thus, the length of the base is:
c² = 30² + 40²
c² = 2500
c = √2500
c = 50 units
Using the concept of similarity ratio, we have:
30/50 = x/40
Cross multiply to get:
50x = 1200
x = 24 units
Read more about similar triangle ratio at: https://brainly.com/question/31009546
#SPJ3
Jane plans to invest $500 at 8.25% interest, compounded continuously. After 14 years, how much money has she accumulated? Has her money doubled or tripled?
Answers
After 14 years, Jane has accumulated approximately $1587.45, which means her initial investment of $500 has more than tripled due to the power of compound interest at a rate of 8.25%, compounded continuously.
Jane plans to invest $500 at 8.25% interest, compounded continuously. To find out how much money she has accumulated after 14 years, we use the formula for continuous compounding: [tex]A = Pe^{rt}[/tex], where:
For Jane's investment:
P = $500
r = 8.25% or 0.0825 (as a decimal)
t = 14 years
Plugging these values into the formula gets us:
[tex]A = 500e^{0.0825*14}[/tex]
Calculating this gives us:
[tex]A \approx 500e^{1.155} \approx 500 * 3.1749 \approx $1587.45[/tex]
Jane's money has more than tripled in 14 years. It has not quadrupled, but it has significantly grown beyond double the original investment.
helpppppppppppppppppppppppppppppppp
Answers
(1 / x) = ((x + 3) / (2x ^ 2))
(2x) = (x + 3)
Then we clear x:
(2x) = (x + 3)
2x-x = 3
x = 3
Answer:
x = 3
option 4
10 Michael has a drawer with 8 pairs of black socks and 12 pairs of white socks. Without looking he takes a white pair of socks out of the drawer. What is the probability that the next pair he takes out is black?
Answers
8:19 is the ratio from black pair of socks to the total pairs of socks
You can also say 8/19 or 42% chance
Therefore the propability of choosing a pair of black socks:
[tex]\frac{8}{19} [/tex]
Write the equation of the line passing through point (4, -1) and perpendicular to the line whose equation is 2x - y - 7 = 0.
Answers
x + 2y + 4 =0
Explanation:
1) You know a point (4 - 1) and that the line is perpendicular to a given line.
2) From the equation of the perpendicular line whose equation was given, you determine the slope, for which you can use the slope-intercept form of the equation:
2x - y - 7 = 0 => y = 2x + 7.
The slope is the coeffiicient of x, which is 2.
Therefore, slope = 2.
3) The slope of the other line is the negative inverse of the slope of the perpedicular line:
slope = - 1/2
4) Now that you have the slope of your line and the point (4, - 1) you determine the equation with this procedure:
y - b
------- = slope
x - a
where a y b are the coordinates of the point (4, - 1) and the slope is -1/2
=>
y - (-1)
---------- = - 1/2
x - 4
5) Simplify
2(y + 1) = - (x - 4)
2y + 1 = - x + 4
2y + x +1 + 4 = 0
x + 2y + 4 =0 <---------- this is the equation searched.
Given: a quadrilateral with sides of 12 yards, 14 yards, 16 yards, and 18 yards. On a drawing, 1 inch = 2 yards, how long are the sides of the quadrilateral on the drawing?
A. 6,7,8 and 9 inches
B. 24,28,32 and 36 inches
C. 60, 70, 80 and 90 inches
Answers
[tex] \frac{12}{2} \: \: \: \frac{14}{2} \: \: \: \frac{16}{2} \: \: \: \frac{18}{2} \: \: \: \\ 6 \: \: \: \: \: 7 \: \: \: \: \: 8 \: \: \: \: \: 9[/tex]
so A is true
Answer:
The correct answer is option A, 6 , 7, 8, 9 inches
Step-by-step explanation:
Given the scale of drawing ,
[tex]1 inch = 2 yards\\[/tex]
The size of each side of a quadrilateral when converted as per the scale pf map
[tex]= \frac{12}{2} , \frac{14}{2} , \frac{16}{2} , \frac{18}{2} \\= 6, 7, 8 , 9 inches\\[/tex]
How many distinct pairs of perfect squares differ by 35? (the pair $a, b$ is the same as the pair $b, a$.)?
Answers
One pair is ((35±1)/2)^2 = {17^2, 18^2} = {289, 324}
The other is ((7±5)/2)^2 = {1^2, 6^2} = {1, 36}
Answer:
2
Step-by-step explanation: