Answer:
Step-by-step explanation:
Let the line to be found be Line 2
Given:
Line 1 :
y = 4x + 6
Since y = mx + b
We can substitute and find that the slope of Line 1 is 4
Therefore slope of Line 2 = (4)
Line 2:
Point - (1,6)
Slope - 4
Therefore: 6 = (4)(1) + b
So equating it we get : b = 2
Answer = 2The area of triangle QTU is 6 square units, and the area of triangle RSU is 6 square units. The dimensions in the figure below are labeled in units. What is the area of triangle STU in square units
Answer:
The area of a triangle is 1/2BH, or 1/2 times the base times the height.
If the area = 6, and B and H must both be whole numbers.
The area of the triangle ΔSTU is given by A = 12 units²
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
Given data ,
Let the area of the triangle ΔSTU be represented as A
Now , the area of triangle ΔQTU is 6 square units, and the area of triangle ΔRSU is 6 square units
So , the base of the triangle ΔSTU = 6 units
The height of the triangle ΔSTU = 4 units
So , area of the triangle = ( 1/2 ) x Length x Base
On simplifying , we get
The area of triangle ΔSTU = ( 1/2 ) x 4 x 6
The area of triangle ΔSTU = 12 units²
Therefore , the value of A is 12 units²
Hence , the area of the triangle is 12 units²
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The complete question is attached below :
The area of triangle QTU is 6 square units, and the area of triangle RSU is 6 square units. The dimensions in the figure below are labeled in units. What is the area of triangle STU in square units?
A boat covers 25 km upstream and 44 km downstream in t hours. Also, it covers 15 km upstream and 22 km downstream in 5 hours. Find the speed of the boat in still water and that of the stream.
9514 1404 393
Answer:
boat speed: (7t -95)/(6t² -110t +500)
stream speed: (37t -345)/(6t² -110t +500)
Step-by-step explanation:
The relation between time, speed, and distance is ...
time = distance/speed
The boat speed (b) is added to the stream speed (s) going downstream. The stream speed is subtracted going upstream. The given relations tell us ...
25/(b-s) +44/(b+s) = t
15/(b-s) +22/(b+s) = 5
This gives us 2 equations in 3 unknowns, so we can only provide a solution in terms of one of the unknowns. Since we are asked for the speeds, they will be provided in terms of t.
Subtracting the first equation from 2 times the second gives ...
2(15/(b-s) +22/(b+s)) -(25/(b-s) +44/(b+s)) = 2(5) -(t)
5/(b-s) = 10 -t
5/(10 -t) = b -s
Substituting for b-s in the second equation gives ...
15/(5/(10-t)) +22/(b+s) = 5
30 -3t +22/(b+s) = 5
22/(b+s) = 3t -25
22/(3t -25) = b+s
Adding the equations for the sum and difference of speeds, we get ...
(b-s) +(b+s) = 5/(10-t) +22/(3t -25)
2b = (5(3t -25) +22(10 -t))/((10-t)(3t-25)) = (95 -7t)/((10-t)(3t-25))
b = (7t -95)/(6t² -110t +500)
Subtracting the equations for sum and difference of speeds, we get ...
(b+s) -(b-s) = 22/(3t -25) -5/(10 -t)
2s = (22(10-t) -5(3t -25))/((10-t)(3t-25))
s = (37t -345)/(6t² -110t +500)
__
The speed of the boat in still water is (7t -95)/(6t² -110t +500) km/h.
The speed of the stream is (37t -345)/(6t² -110t +500) km/h.
__
Note that these solutions only make sense for values of t between 25/3 and 345/37, approximately 8.33 < t < 9.32. For t=9 hours, the boat speed is 8 km/h and the stream speed is 3 km/h.
plz help which one has a total of 40 square units
Answer:
The First One
Step-by-step explanation:
Because its dimensions are 5 by 8
In ΔIJK, k = 81 inches, i = 65 inches and ∠J=28°. Find the area of ΔIJK, to the nearest square inch.
Answer: 1236
its the answer from deltamath
Work out the value of x when
2^30 / 8^9 =2^x
I need help wit math
Answer:
1/2
Step-by-step explanation:
Even numbers on the dice:
2, 4, 6
Probability of getting even:
3/6
1/2
6. Monique is making an ottoman for her living room. She covers the top of the ottoman with fabric. How much surface would she need to stain, if she stains the sides of the ottoman (excluding the bottom)?
4.2
The solid was created by connecting two congruent square pyramids to a rectangular prism.
18 in
x
15
1
15 in.
What is the surface area of this solid?
square inches
Answer:
The answer is "[tex]\bold{1920 \ in^2}[/tex]".
Step-by-step explanation:
Please find the graph file.
Rectangular solid area:
Its region comprises four rectangles, each 15 for each case 14 in each.
The rectangle field is the formula [tex]A = lw[/tex]
The four rectangles are therefore covered by a zone: [tex]\to A = 4lw = 4 \times 15 \ in \times 14 \ in = 840 \ in^2.[/tex]
square Pyramids area:
The pyramids in both squares have 8 triangular facets.
Each triangle has a 15-inch basis with a 14-inch base.
The triangle zone formulation is [tex]A = \frac{1}{2}bh[/tex]
That's it. The 8 triangles area is [tex]\to A = 8 \times \frac{1}{2}bh = 4bh = 4 \times 15 \ in \times 18 \ in = 1080 \ in^2[/tex]
Total field surface:
Strong rectangular[tex]= 840 \ in^2[/tex]
Pyramids in the Square[tex]= 1080[/tex]
Overall area [tex]= 1920 \ in^2[/tex]
The number is [tex]1920\ in^2[/tex] for a total area.
Can someone help me out with this? I'm trying to hustle.
Answer:
decay factor i think
Step-by-step explanation:
Gina subtracted 6 8 from 1 and found a difference of 2 8 . Which statement best describes the difference of 6 8 from 1 is 2 8 ? F The difference of 2 8 is not reasonable because 1 – 3 4 = 1 4 . G The difference of 2 8 is reasonable because 3 4 – 1 4 _ = 1 2 . H The difference of 2 8 is reasonable because 1 – 3 4 = 1 4 . J The difference of 2 8 is not reasonable because 3 4 – 1 4 = 1 2 .
Answer:
Statement H : The difference of 2/8 is reasonable because 1 – 3/4 = 1/4 .
Step-by-step explanation:
Given - Gina subtracted 6/8 from 1 and found a difference of 2/8 .
To find - Which statement best describes the difference of 6/8 from 1 is 2/8 ? Statement F : The difference of 2/8 is not reasonable because 1 – 3/4 = 1/4 .
Statement G : The difference of 2/8 is reasonable because 3/4 – 1/4 = 1/2 .
Statement H : The difference of 2/8 is reasonable because 1 – 3/4 = 1/4 .
Statement J : The difference of 2/8 is not reasonable because 3/4 – 1/4 = 1/2 .
Proof -
If we subtract 6/8 from 1 , we get
[tex]1 - \frac{6}{8} = \frac{8 - 6}{8} = \frac{2}{8}[/tex]
So, the difference is 2/8
It is reasonable.
So,
The correct statement is - Statement H : The difference of 2/8 is reasonable because 1 – 3/4 = 1/4 .
Reason -
As we can write
[tex]\frac{6}{8} = \frac{3}{4}[/tex] and [tex]\frac{2}{8} = \frac{1}{4}[/tex]
So,
either we subtract 6/8 from 1 or 3/4 from 1 , we get the same result because both the values are equal
So the correct statement is - H : The difference of 2/8 is reasonable because 1 – 3/4 = 1/4 .
Which is the most accurate way to estimate 34% of 85?
A: 1/3 x 81
B: 1/2 x 81
C: 1/2 x 84
D: 1/3 x 84
10. A basketball court is being painted. Everything shown below will be painted blue. How any square feet will be painted blue?
Answer:
The answer is "148 ft".
Step-by-step explanation:
Using formula:
Calculating rectangle area:
[tex]A=lw[/tex]
[tex]=15 \times 8\\\\=120[/tex]
Calculating semicircle area:
[tex]A=\frac{1}{2} \pi r^2\\\\[/tex]
[tex]=\frac{1}{2} \times \pi \times 7.5^2\\\\=\frac{1}{2} \times \pi \times 56.25\\\\=28.125\ \pi \\\\=28 \ \pi[/tex]
Total area:
[tex]=120+28\\\\=148[/tex]
there are 12 girls in Chloe's first grade class. The ration of girls to boys is 6:5. How many boys are in Chloe's class?
to
Which of the following expressions is equivalent
(x + 7)(x2 – 3x + 2)?
A. 3 - 3x2 + 2x + 14
B. x3 + 4x2 - 19x + 14
C. x°- 3x + 14
D. 2 - 2x + 9
Answer: B.x^3+4x^2-19x+14 is correct
Step-by-step explanation:
(x + 7)(x2 – 3x + 2)
Multiplying both
x^3-3x^2+2x+7x^2-21x+14
x^3+4x^2-19x+14
After expanding the given equation, the equivalent expression is found to be [tex]x^3 + 4x^2 -19x +14[/tex]
The correct answer is B
Given expression:
[tex](x + 7)(x^2 - 3x + 2)[/tex]
To find:
the equivalent expression in expanded formThe given expression can be expanded as follows;
[tex](x + 7)(x^2 - 3x + 2)\\\\remove \ the \ bracket \ by \ multiplying \ through \ with \ "x" \ and \ "7"\\\\x(x^2 - 3x + 2) + 7(x^2 - 3x + 2)\\\\x^3 - 3x^2 + 2x + 7x^2 - 21x+ 14\\\\simplify \ further \ by \ collecting \ similar \ terms \ together\\\\x^3 + (-3x^2 + 7x^2)+ (2x-21x) + 14\\\\x^3 + 4x^2 - 19x+ 14[/tex]
Thus, the equivalent expression of the given equation is [tex]x^3 + 4x^2 -19x +14[/tex]
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Please help Tameca already has $55 dollars in her savings account. If she puts $5 per week in her account, write and solve an inequality to find out how many weeks she must save to have at least $100 in her account.
Answer:
x=9
Step-by-step explanation:
55+5x=100. -subtract 55 from 100
5x=45. - divide 45 by 5
x=9
the topic is piecewise functions, can someone help? i’m a little confused :)
Given:
The piecewise function is:
[tex]f(x)=\begin{cases}x+5&x<-2\\x^2+2x+3&x\geq -2\end{cases}[/tex]
To find:
The values of [tex]f(-4),f(-2),f(0),f(3)[/tex].
Solution:
For [tex]x<-2[/tex], the function is
[tex]f(x)=x+5[/tex]
For [tex]x\geq -2[/tex], the function is
[tex]f(x)=x^2+2x+3[/tex]
a) The value of [tex]f(-4)[/tex] is:
[tex]f(-4)=-4+5[/tex]
[tex]f(-4)=1[/tex]
b) The value of [tex]f(-2)[/tex] is:
[tex]f(-2)=(-2)^2+2(-2)+3[/tex]
[tex]f(-2)=4-4+3[/tex]
[tex]f(-2)=3[/tex]
c) The value of [tex]f(0)[/tex] is:
[tex]f(0)=(0)^2+2(0)+3[/tex]
[tex]f(0)=0-0+3[/tex]
[tex]f(0)=3[/tex]
d) The value of [tex]f(3)[/tex] is:
[tex]f(3)=(3)^2+2(3)+3[/tex]
[tex]f(3)=9+6+3[/tex]
[tex]f(3)=18[/tex]
Therefore, the required values are [tex]f(-4)=1,f(-2)=3,f(0)=3,f(3)=18[/tex].
What are the TWO ways you chose to display the data?
Olivia runs 4 miles per day. She ran 5 days during the first week of the month. She ran only 3 days each week for the next 3 weeks. Simplify the expression (5 + 3 * 3) * 4 to find how many miles Olivia ran last month.
Answer:
(5+3^2)*4
Step-by-step explanation:
i belive im correct
Olivia ran 56 miles last month.
What is the expression?
Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.
Given,
She ran 5 days during the first week of the month
She ran only 3 days each week for the next 3 weeks.
Number of mile she ran given by expression (5 + 3 * 3) * 4
= (5 + 9) * 4
= 1 4 *4
= 56
Therefore, Olivia ran 56 miles last month.
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To win at LOTTO in one state, one must correctly select 6 numbers from a collection of 65 numbers (1
through 65). The order in which the selection is made does not matter. How many different selections
are possible?
The average mass of 5 man basketball team is 70Kg. Four of team members have a mass of 50kg, 62kg, 81kg, and 84kg What is the mass of the fifth player???? 15 POINTS!!!
Answer:
The mass of the fifth player is 73 kg
Step-by-step explanation:
Since the average mass of the 5 players is 70kg
what this mean is that the total sum of all the masses of the players is equal to the product of 5 and 70 kg
we have this as 5 * 70kg = 350 kg
So, by adding the masses of all the players, we get 350kg
Thus, for us to get the mass of the 5th player, we have to subtract the sum of the remaining 4 from the total 350kg
Mathematically, we have this as;
350 - ( 50 + 62+ 81 + 84) = 73 kg
3). Find the area of a circle with a radius of
3 ft.
Answer:
Step-by-step explanation:
1.5
Answer:
A=πr2=π·32≈28.27433ft²
Step-by-step explanation:
what is the area of this figure
Answer:
141
Step-by-step explanation:
2*3=6
5*9=45
6*15=90
141
Answer:
add all the sides I guess...
Step-by-step explanation:
or you can break that figure into rectangles. then find their areas and later sum up all the areas and you'll have your area of this shape
A+6,when a=2?
Pls answer
Answer:
8
Step-by-step explanation:
a + 6; a = 2
2 + 6 = 8
Thus, The answer is 8
-TheUnknownScientist
Please help me with this.
Answer:
B
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
please please answer and dont put any links :)
Find the distance between points.
Answer:
3 units
Step-by-step explanation:
Here, The distance between two points is 3 units
-TheUnknownScientist
HELP ME PLEASE
Find the Volume of each cylinder. Round to the nearest tenth
471.2
The 10 is the diameter and you need the radius to do it so you do diameter dived by 2 which gives you the radius then you the radius to the power of 2
so the formula would be (3.14)(5)²(6)
Combine like terms.
4n + 11 − 2n − 5
Hey there!
4n + 11 - 2n - 5
COMBINE the LIKE TERMS
= (4n - 2n) + (11 - 5)
= 4n - 2n + 11 - 5
= 2n + 6
Therefore, your answer should be:
2n + 6
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Answer:
[tex] \sf \: 2n + 6[/tex]
Step-by-step explanation:
Now we have to,
→ Simplify the given expression.
Main steps included in solving,
→ Rearranging the expression.
→ Combining the like terms.
The expression is,
→ 4n + 11 - 2n - 5
Let's simplify the expression,
→ 4n + 11 - 2n - 5
→ (4n - 2n) + (11 - 5)
→ (2n) + (6)
→ 2n + 6
Hence, the answer is 2n + 6.
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP HELP I NEED HELP ASAP
HELP I NEED HELP ASAP HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
9514 1404 393
Answer:
B. (2, 1)
Step-by-step explanation:
As a first guess you might say the right angle will be at the point that has the x-coordinate of A (2) and the y-coordinate of B (1).
You notice that the point (2, 1) is on the list of answer choices, so that is a good choice.
The coordinates of C could be (2, 1).
__
Or, you can plot the points and see what forms a right triangle.
Pythagorean Thereom