Answer:
Step-by-step explanation:
Equation of line: y = mx + c
y = x - 6
Slope m = 1
y-intercept c = -6
Answer:
m = 1
c = -6
Step-by-step explanation:
Formula for a line is y = mx+c
m = gradient
c = intercept.
Here:
m = 1
c = -6
Hope this helps
Good Luck
Line t is the perpendicular bisector of FG. If line t intersects FG at point H,
which of the following statements must be true?
Check all that apply.
A. Point His the midpoint of FG
B. Line tintersects FG at a right angle
C. FG = FH
D. Line tis perpendicular to FG
E. Line tis parallel to FG
A, B, D are your answers
AP E X
Point H is the midpoint of FG, Line t intersects FG at a right angle and Line t is perpendicular to FG are true statements.
What is Coordinate Geometry?A system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.
A. Point H is the midpoint of FG: This statement must be true because line t is the perpendicular bisector of FG, which means it passes through the midpoint of FG and intersects FG at a right angle.
Therefore, H is the midpoint of FG.
B. Line t intersects FG at a right angle: This statement must be true because line t is the perpendicular bisector of FG, which means it intersects FG at a right angle.
C. FG = FH: This statement is not necessarily true.
While H is the midpoint of FG, the length of FH depends on the position of point H along line t. It could be greater than, less than, or equal to half the length of FG.
D. Line t is perpendicular to FG
This statement must be true because line t is the perpendicular bisector of FG, which means it is perpendicular to FG.
E. Line t is parallel to FG: This statement is not true. If line t were parallel to FG, it would not intersect FG at all, let alone at a right angle as required for a perpendicular bisector.
Therefore, Point H is the midpoint of FG, Line t intersects FG at a right angle and Line t is perpendicular to FG are true statements.
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A company's total sales (in millions of dollars) t months from now are given by S(t) = sqrt t + 2. In your own words, find and interpret S(20) and S'(20). Use these results to estimate the total sales after 24 months and after 25 months.
Answer:
S(20) = [tex]\sqrt{20+2}[/tex] = 4.69 ; value of total sales after 20 months is 4.69 million dollars
S'(20) = [tex]\dfrac{1}{\sqrt{20+2} }[/tex] = 0.21 ; increase in the total sales after 20 months is 0.21 millions of dollars
S(24) = [tex]\sqrt{24+2}[/tex] = 5.10; 5.10 millions of dollars
S(25) = [tex]\sqrt{25+2}[/tex] = 5.20 ; 5.20 millions of dollars
Step-by-step explanation:
[tex]S(t) = \sqrt{t+2}[/tex]
[tex]S(t+h) = \sqrt{t+2+h}[/tex]
[tex]S(t+h) - S(t)= \sqrt{t+2+h }- \sqrt{t+2}[/tex]
[tex]\dfrac{S(t+h) - S(t)}{h}= \dfrac{\sqrt{t+2+h }- \sqrt{t+2}}{h}[/tex]
By rationalization:
[tex]\dfrac{\sqrt{t+2+h }- \sqrt{t+2}}{h} * \dfrac{ {\sqrt{t+2+h }- \sqrt{t+2}} }{ {\sqrt{t+2+h }- \sqrt{t+2}}}[/tex]
[tex]\\ \\ \dfrac{t+2+h-t-2}{h \sqrt{t+2+h }+ \sqrt{t+2} } = \dfrac {h}{\sqrt{t+2+h }+\sqrt{t+2} }[/tex]
= [tex]\dfrac {1}{\sqrt{t+2+h }+\sqrt{t+2} }[/tex]
[tex]\lim_{k \to \infty} \dfrac {1}{\sqrt{t+2+h }+\sqrt{t+2} } = \dfrac{1}{t+2}[/tex]
[tex]S' (t) = \dfrac{1}{\sqrt{t+2} }[/tex]
S(20) = [tex]\sqrt{20+2}[/tex] = 4.69 ; value of total sales after 20 months is 4.69 million dollars
S'(20) = [tex]\dfrac{1}{\sqrt{20+2} }[/tex] = 0.21 ; increase in the total sales after 20 months is 0.21 millions of dollars
S(24) = [tex]\sqrt{24+2}[/tex] = 5.10; 5.10 millions of dollars
S(25) = [tex]\sqrt{25+2}[/tex] = 5.20 ; 5.20 millions of dollars
The admission fee at an amusement park is $1.50 for children and $4 for adults. On a certain day, 250 people entered the park, and the admission fees collected totaled $750.00. How many children and how many adults were admitted?
Answer:
100 children
150 adults
Step-by-step explanation:
c- children
a- adults
---------------
we get equations as per question:
1.5c+4a= 750 c+a= 250 ⇒ a= 250- c1.5c +4(250-c)= 750 ⇒ 1.5c- 4c+1000=750 ⇒ 2.5 c= 250 ⇒ c= 100a= 250-100 ⇒ a= 150Children 100, adults 150
what type of solution does this equation have?
Answer:
Two real solutions
Step-by-step explanation:
We have the equation [tex]u^2=80[/tex]
To get a solution, we must solve for u.
When we solve for u, we need to square root each side, but when we do this, we must add a ± to the side that opposite to the u in order to compensate. This is because you could get 80 in two different ways:
[tex](\sqrt{80} )(\sqrt{80})=80 \\\\(-\sqrt{80} )(-\sqrt{80})=80[/tex]
This would mean that when we solve for u, we would get [tex]u=[/tex] ± [tex]\sqrt{80}[/tex]
Which is the same thing as [tex]u=\sqrt{80}[/tex] and [tex]u=-\sqrt{80}[/tex]
Which are two real solutions.
Answer:
2 real solutions
Step-by-step explanation:
u^2=80 is worked out as u as a variable times 2/u 2 times and when u do that you have to find the value of u and the result should be equal to 80. plz rate as the brainliest
Luisa had $29.90 in her piggy bank. She made $5.50 a week for 4 weeks by baby-sitting. Write a sequence to show how much money she had in her piggy bank after each week.
Answer:Week 1: $35.40
Week 2: $40.90
Week 3: $46.40
Week 4: $51.90
Step-by-step explanation:
29.90 + 5.50(x) = y
replace x with 1, 2, 3, or 4 for each week.
Bag A contains 3 white marbles and 2 red marbles. Bag B contains 6 white marbles and 3 red marbles.A person draws one marble from each bag.Find the probability that both marbles are white.
Answer:
There is a 9 out of 14 chance that the marble will be white or there is a 3 out of 5 chance along with a 6 out of 9 chance.
Step-by-step explanation:
Since there's a total of 14 marbles from both bags and there are a possible 9 white marbles, it would be a total of 9 out of 14, or it would be separate and be a 3 out of 5 chance with a 6 out of 9 chance.
i need help with 8-35 and 8-36
Answer:
8 - 35
a. 350 unit²
b. 81.23 unit²
c. 41.57 unit²
8 - 36
Beth should buy 3 bags of fertilizer
Step-by-step explanation:
8 - 35
a. The figure consists of 9 isosceles triangles of side lengths 11 and vertex angle = 360/9 = 40°
Hence base angles = (180 - 40)/2 = 70°
Therefore, the base of the triangles = sin(40) × 11/sin(70) = 7.52
Hence area of figure = 9 × 0.5 × 7.52 × √(11² - (7.52/2)²) =349.99 ≈ 350 unit²
b. Area of a decagon
We note that the vertex angle = 36°
∴ Half the base = tan(18) × 5 = 1.62
Area = 10 × 1.62 × 5 = 81.23 unit²
c. The area of a hexagon = [tex]s^2 \times \dfrac{3\sqrt{3} }{2}[/tex]
s = 4 therefore, the area = [tex]4^2 \times \dfrac{3\sqrt{3} }{2} = 41.57 \, unit^2[/tex]
8 - 36
Area, A of a regular pentagon = [tex]A = a^2 \times \dfrac{1}{4} \sqrt{5(5 + 2\sqrt{5} )}[/tex]
a = 15 ft., therefore, A = [tex]15^2 \times \dfrac{1}{4} \sqrt{5(5 + 2\sqrt{5} )}[/tex] = 387.11 ft.²
Therefore, since a bag of fertilizer can fertilize 150 ft.², the number of bags of fertilizer that will fertilize 387.11 ft.² will be 387.11/150 = 2.58 bags
Therefore, since 2 bags of fertilizers will not be enough, Beth should buy 3 bags of fertilizer.
On a coordinate plane, a line goes through points (negative 3, negative 3) and (0, 3). What is the slope of the line on the graph? 1 1/2 2 3
Answer:
2
Step-by-step explanation:
We can find the slope between two points by using
m= (y2-y1)/(x2-x1)
= (3 - -3)/(0 - -3)
= (3+3)/(0+3)
= 6/3
=2
Answer:
The slope of the line is 2
Step-by-step explanation:
using rise/run will help you figure this out :)
I'm really confused about this. Probabilities have always been a pain for me and I really don't understand this
Answer:
A
Step-by-step explanation:
The first thing to notice is the question says it is given that the person is between the ages 23 and 60, so we only care about those people. So then we want to know how likely it would be to pick someone with over 50 messages a month. So what you would do is take the amount of people who are between 23 and 60 and send over 50 text messages, and divide that by the total amount of people 23-60 (since that is the pool of people we have). Doing so we find there is 229 people aged 23-60 which then makes the answer 157/229 or A.
Tam buying stationary. I buy 3 pens and 4 pencils costing 83p and Caroline
buys 2 pens and 7 pencils costing 90p.
How much is one pen?
Answer:
Step-by-step explanation:
Answer:
therefore one pen can cost approx 15.6 p
Can someone help me please ?!?!?
Answer:
13*12 is greater than 11*14 by 2 meters^2
Step-by-step explanation:
[tex]A=wl=13*12=156m^2\\A=wl=11*14=154m^2[/tex]
Goodluck
Answer:
Jenny's room has a great area.
Step-by-step explanation:
Jenny's room
[tex]area = l \times b \\ = 13 \times 12 \\ = 156 {ft}^{2} [/tex]
Ruth's room
[tex]area = l \times b \\ = 14 \times 11 \\ = 154 {ft}^{2} [/tex]
so,
[tex]156 > 154[/tex]
So ,Jenny's room has a great area than Ruth's room.
hope this helps
brainliest appreciated
good luck! have a nice day!
The density of a marble is 2.7g/cm3. What is the mass of th marble slab
Answer:
if the marble slab is 1 cm³ in volume the mass is 2.7 g but u did not put a volume
Una fabrica produce 132 litros de yogurt diarios .Con 49 litros se llenan botellas de 0,25litros xada una y con el resto que queda en el deposito se llenan botellas de 0,5 litros ¿cuantas botellas de yogurt se llenan ?
Answer:
[tex]z = 362\,botellas[/tex]
Step-by-step explanation:
(This exercise has been presented in Spanish and for that reason explanation will be held in Spanish)
La cantidad de botellas de 0,25 litros que se llenan con 49 litros de yogurt es:
[tex]x = \frac{49\,L}{0.25\,\frac{L}{botella} }[/tex]
[tex]x = 196\,botellas[/tex]
La cantidad remanente de yogurt es:
[tex]V_{r} = 132\,litros - 49\,litros[/tex]
[tex]V_{r} = 83\,litros[/tex]
Ahora, la cantidad de botellas de 0,5 litros que se llenan con el volumen remanente es:
[tex]y = \frac{83\,litros}{0.5\,\frac{litros}{botella} }[/tex]
[tex]y = 166\,botellas[/tex]
Finalmente, el total de botellas a llenar es:
[tex]z = 196\,botellas + 166\,botellas[/tex]
[tex]z = 362\,botellas[/tex]
Olives garden is only 10 yd and the watermelon plants she wants to grown requir 2.5yd each how many watermelon plants can she grows
Answer:
4
Step-by-step explanation:
10÷2.5
Answer:
4 plants
Step-by-step explanation:
She can grow 4 plants because 10/2.5 is equal to 4. So, the answer is 4 plants.
Evaluate the formula F = 1.8 C + 32 for C = -30
Answer:
F = -22
Step-by-step explanation:
F = 1.8 C + 32 for C = -30
F = 1.8 C + 32 = 1.8(-30) + 32 = -54 + 32 = -22
Answer:
The value of F is -22
Step-by-step explanation:
F=1.8 C+32
F=1.8*-30+32
F=-54+32
F=-22
What is 8064 minutes, in days remember there are 60 minutes in an hour and 24 hours in a day.
Answer:
B. 6 days
Step-by-step explanation:
60 minutes-->1 hour
8064 minutes--> ?
=8064 x (1/60)
=134.4 hours
24 hours-->1 day
134.4 hours-->?
=134.4 × (1/24)
=5.6 days
≈6 days
You come home from Brian’s Orchard with a big brown bag of apples: 23 Granny Smiths, 14 Honey Crisp and 31 Red Delicious. What is the probability you reach in and pull out: a. one of each? b. 4 Honey Crisps c. 2 G. Smiths & 1 R. Delicious
Answer:
A.) 4991/157216
B.) 2401/1336336
C.) 16399/314432
Step-by-step explanation:
Given the following :
Granny Smith = 23
Honey crisp = 14
Red delicious = 31
Probability = (number of required outcome / number of possible outcomes)
Number of possible outcomes = 23 + 14 + 31 = 68
With replacement :
A.) one of each :
P(granny Smith) × P(Honey crisp) × P(Red delicious)
P(granny Smith) = 23/68
P(Honey crisp) = 14/68 = 7/34
P(red delicious) = 31/68
(23/68 × 7/34 × 31/68) = 4991/157216
B) 4 honey crisp:
P(4 Honey crisp) = P(honey crisp) × P(honey crisp) × P(honey crisp) × P(honey crisp)
7/34 × 7/34 × 7/34 × 7/34 = 2401/1336336
C.) 2 granny Smith and 1 red delicious
P(granny Smith) × P(granny Smith) × P(red delicious)
23/68 × 23/68 × 31/68 = 16399/314432
I am having real trouble with this equation
7 - 12
how can you go lower then zero?
Answer:
Subtract 12 from 7 = -5
A prism is a three dimentional shape with the same ________ all the way through
Can anybody fill in the blank?
A prism is a three-dimensional shape with the same cross-section all the way through.
What is prism?A prism is a solid shape that is bound on all its sides by plane faces.
A prism is a type of three-dimensional (3D) shape with flat sides. It has two ends that are the same shape and size (and look like a 2D shape).It has the same cross-section all along the shape from end to end; that means if you cut through it you would see the same 2D shape as on either end.
Hence, a prism is a three-dimensional shape with the same cross-section all the way through.
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Somebody please help me!! I will mark the brainlest
Answer:
96
Step-by-step explanation:
Triangles (front and back)
There are two right triangles -- front and back.
One triangle = 1/2*h*b
h = 3
b = 4
One triangle = 1/2 * 3 * 4
One triangle = 6
two triangles = 2*6 =12
Rectangle using the Net
Area = L * W
L = 3 + 4 + 5 = 12
W = 7
Area = 12 * 7 = 84
Total Area
Area = 12 + 84
Area = 96
Luca decides to play Wheel of Letters. To play the game, contestants spin a wheel with 26 equal sections, lettered A through Z. If the pointer lands on any letter in the phrase "County Fair," the contestant wins a prize. What is the probability that Luca will win Wheel of Letters? Your answer must be simplified
Answer:
wouldnt it be 10 out of 26 percent chance or 2.6
Step-by-step explanation:
there are 10 letters in county fair and 26 letters so you divide 26 by 10
The probability that Luca will win Wheel of Letters is [tex]\frac{5}{13}[/tex] given there are 26 equal sections lettered A to Z and the contestant win if the pointer lands on any letter in the phrase "COUNTY FAIR". This is obtained by using probability concept.
What is probability ?Probability of an event to occur is the ratio number of favourable outcomes to total number of outcomes.For example, probability of getting head while tossing a coin is 1/2. ⇒P(getting head)=1/2 Find the probability that Luca will win:
Given total number of outcomes are 26
Since "COUNTY FAIR" has 10 letters, number of favourable outcomes are 10.
According to definition of probability we get ,
P(winning) =[tex]\frac{10}{26}[/tex] =[tex]\frac{5}{13}[/tex]
Hence the probability that Luca will win Wheel of Letters is [tex]\frac{5}{13}[/tex] given there are 26 equal sections lettered A to Z and the contestant win if the pointer lands on any letter in the phrase "COUNTY FAIR".
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Light bulbs cost £2.30 each. Yasmin buys as many as she can with £20. How much change should she get? Give your answer in pounds, £.
Answer:
£1.6
Step-by-step explanation:
£20 ÷ £2.3= 8 remainder 1.6
change= £1.6
Answer:
1.60 euros
Step-by-step explanation:
2.30 times 8 = 18.40
20-18.40 = 1.60
Find the volume of a triangular prism that has a triangle base of14 and height of 17 with a prism height of 5
What is the slope of the line x=3
Answer: The slope is infinite
Step-by-step explanation:
An infinite slope is simply a vertical line. When you plot it on a line graph, an infinite slope is any line which runs parallel to the y-axis. You can also describe this as any line that doesn't move along the x-axis but stays fixed at one constant x-axis coordinate, making the change along the x-axis.
A number cube (dice) is rolled and a letter is selected from the word GIRAFFE. What is the compound probability of P ( 4 and F) P(EVEN NUMBER AND VOWEL)
Answer:
P (4 and F) = 1 in 21 or 4.76%
P(EVEN NUMBER AND VOWEL) = 3 in 14 or 21.43%
Step-by-step explanation:
The probability of rolling a four on a die is 1 in 6.
The probability of picking the letter F in the word GIRAFFE is 2 in 7.
Therefore:
[tex]P (4\ and\ F)=P(4)*P(F)\\ P (4\ and\ F)=\frac{1}{6}*\frac{2}{7}\\ P (4\ and\ F)=\frac{1}{21}= 4.76\%[/tex]
The probability of rolling an even number (2, 4 or 6) on a die is 3 in 6.
The probability of picking a vowel (A, E, I) in the word GIRAFFE is 3 in 7.
Therefore:
[tex]P (Even\ and\ Vowel)=P(Even)*P(Vowel)\\ P (Even\ and\ Vowel)=\frac{3}{6}*\frac{3}{7}\\ P (Even\ and\ Vowel)=\frac{3}{14}= 21.43\%[/tex]
Calculate the angle to the nearest degree: csc (x) = 1.0353
Answer:
[tex]75^{\circ}[/tex]
Step-by-step explanation:
Given: [tex]\csc (x) = 1.0353[/tex]
To find: angle to the nearest degree
Solution:
A triangle is a polygon that has three sides, three angles ,and three vertices.
Trigonometry explains the relationship between the sides and angles of the triangle.
The angle can be expressed in two forms: degrees or radians.
[tex]\csc (x) = 1.0353\\x=74.995\approx 75^{\circ}[/tex]
The sum of three numbers is 54 . The third number is 2 times the second. The second number is 10 more than the first. What are the numbers?
first number:
second number:
third number:
Answer:
First number: 6
Second number: 16
Third number: 32
Step-by-step explanation:
x + y + z = 54
z = 2y
y = x + 10
Now you can substitute y = x + 10 into z = 2y
The equation becomes z = 2x + 20
Now plug it into the main equation.
x + x + 10 + 2x + 20 = 54
4x + 30 = 54
4x = 24
x = 6
y = 16
z = 32
x^2+{a/a+b + a+b/a}x+1=0 solve for x please solve and i will mark you as the brainliest..its urgent i need to confirm my answer...
Answer:
x^2 + {a/(a + b) + (a + b)/a}x + 1 = 0
Delta = {a/(a + b) + (a + b)/a}^2 - 4
= {a/(a + b)}^2 + {(a + b)/a}^2 + 2 - 4
= {a/(a + b)}^2 + {(a + b)/a}^2 - 2
= {a/(a + b) - (a + b)/a}^2
If a is not equal to zero and a is not equal to -b => delta is always larger than 0
=> Solution 1 = - [ {a/(a + b) + (a + b)/a} + |{a/(a + b) - (a + b)/a}| ]/2
=> Solution 2 = - [ {a/(a + b) + (a + b)/a} - |{a/(a + b) - (a + b)/a}| ]/2
Hope this helps!
:)
State the steps on how to solve 5x2 – 18 = 27 using Square root Property in solving Quadratic Equation.
Answer: x = 3
Step-by-step explanation:
From the question,
5x² – 18 = 27
Collect the like terms
5x² = 27 + 18
5x² = 45
We can th n divide both side by 5 which is the coefficient of x²
5x²/5 = 45/5
x² = 9
To get the value of x, we find the square root of 9
x² = 9
x =✓9
x = 3
The value of x is 3
√2 (√45 + √80) can be written in the form a√10 where a is an integer. Find the value of a.
Answer:
a = 7
Step-by-step explanation:
Using the rule of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]
Given
[tex]\sqrt{2}[/tex] ([tex]\sqrt{45}[/tex] + [tex]\sqrt{80}[/tex] ) ← distribute parenthesis by [tex]\sqrt{2}[/tex]
= [tex]\sqrt{90}[/tex] + [tex]\sqrt{160}[/tex]
= [tex]\sqrt{9(10)}[/tex] + [tex]\sqrt{16(10)}[/tex]
= [tex]\sqrt{9}[/tex] × [tex]\sqrt{10}[/tex] + ([tex]\sqrt{16}[/tex] × [tex]\sqrt{10}[/tex] )
= 3[tex]\sqrt{10}[/tex] + 4[tex]\sqrt{10}[/tex]
= 7[tex]\sqrt{10}[/tex] → in the form a[tex]\sqrt{10}[/tex]
with a = 7
Answer:
7
Step-by-step explanation:
√2 (√45 + √80) = √90+√160= 3√10+4√10= 7√10
7√10= a√10
a=7