Answer:
The possible values of k are 3 and -3
Step-by-step explanation:
Given
Points: (-3,k) and (2,0)
Distance between them = √34
Required
Determine the value of k
The distance between two points is calculated as thus;
[tex]Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
Let
[tex](x_1,y_1) = (-3,k)[/tex]
[tex](x_2,y_2) = (2,0)[/tex]
Substitute these values in the given formula
[tex]Distance = \sqrt{(-3 - 2)^2 + (k - 0)^2}[/tex]
Evaluate the brackets
[tex]Distance = \sqrt{-5^2 + k^2}[/tex]
[tex]Distance = \sqrt{25 + k^2}[/tex]
Recall that Distance = √34
So; we have
[tex]\sqrt{34} = \sqrt{25 + k^2}[/tex]
Take square of both sides
[tex]34 = 25 + k^2[/tex]
Collect Like Terms
[tex]k^2 = 34 - 25[/tex]
[tex]k^2 = 9[/tex]
Take square root of both sides
[tex]k = \±3[/tex]
Hence, the possible values of k are 3 and -3
For the solution (2,2) , find the value of ‘c’ in the equation 2x + cy = 8
We have a solution (2,2) so x = 2 and y = 2. Then:
[tex]2x+cy=8\\\\2\cdot2+c\cdot2=8\\\\4+2c=8\\\\2c=8-4\\\\2c=4\quad|:2\\\\\boxed{c=2}[/tex]
What is 1/2 of a right angle called
Answer:
acute angle
Step-by-step explanation:
acute = less than 90 degrees
right = exactly 90 degrees
obtuse = more than 90 degrees
90 divided by 2 = 45
45 is less than 90 so acute angle
1/2 of a right angle is called an acute angle. The correct answer would be an option (D).
What are the vertical angles?When two lines intersect at a location, vertical angles are generated. They are always equal to each other.
An angle with a measure of 1/2(90°) : 45°
As per the given question, the required solution would be as:
Straight: An angle with a measure of exactly 180° is considered straight. 45° is not a straight angle.
Obtuse: An angle with a measure greater than 90° and less than 180° is considered obtuse. 45° is not an obtuse angle.
Acute: An angle with a measure less than 90° is considered acute. 45° is an acute angle.
Thus, 1/2 of a right angle is called an acute angle.
Learn more about the angled here.
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An ice cream shop is testing some new flavors of ice cream. They invent 252525 new flavors for customers to try, and throw out the 131313 least popular flavors. The shop makes 808080 cartons of each of the remaining flavors. It takes 222 cartons to get one liter (\text{L})(L)left parenthesis, start text, L, end text, right parenthesis of ice cream. How much total ice cream is in the cartons?
Answer:
480litres total ice creamStep-by-step explanation:
Total number of ice cream invented for customers to try = 25 new flavours
Amount of least popular flavors thrown out = 13 flavors
Remaining flavor nit thrown out = Total ice cream invented - amount thrown out = 25 - 13
= 12 flavors
The remaining number flavors that was produced is 12 flavors.
If 80 cartons of each of the remaining flavor was made, the total amount of cartons made = 12* 80 = 960 cartons.
Since 2 cartons contains 1 litre
960 cartons will contains (960*1/2) litres
Hence 960 cartons will contain 480litres of the ice cream.
This shows that there are total of 480 litres of ice cream in the cartons
0.1m + 8 - 12n when 30 and n = 1/4
0.1m + 8 - 12n when 30 and n = 1/4
= 3+8-3
= 3+8-3= 8
8
if AB ll CD , EF ll BC, angle bac = 65 and angle dhf = 35 find angle agh
Answer: 100
Step-by-step explanation:
You know that AB is || to CD, angle BAC ≅ ACD (this is the theorem where a line connecting the diagnose of two parallel line, the alternative interior angles are equal/ congruent)
You know that EF is || to BC, angle DHF ≅ GHC (these two are vertically opposite angle which are equal/ this is a theorem)
-------------------------------------------------------------------------
we now know the angles in ΔGHC where angle GHC=35, angle GCH=65, and angle CGH=80 (subtract other angles from 180)
angle AGH is supplementary w=angle with CGH, which means we subtract 80 from 180, we get 100 will be the angle of AGH
The hypotenuse of right triangle ABC, line segment AC, measures 13 cm. The length of line segment BC is 5 cm.
Answer:
Step-by-step explanation:
Pythagorean theorem: In a right angle triangle, the square of hypotenuse is equal to the sum of squares of other two sides
BC² + AB² = AC²
5² + AB² = 13²
25 + AB² = 169
AB² = 169 - 25
AB² = 144
AB = √144 = √12*12
AB = 12cm
VIOLI me eg 20(20-x) = 300 What is the value of x? Round to the units place.
Answer:
x=5
Step-by-step explanation:
20(20-x) = 300
Divide each side by 20
20/20(20-x) = 300/20
20-x = 15
Subtract 20 from each side
20-x-20 = 15-20
-x = -5
Multiply each side by -1
x = 5
Answer:
x = 5
Step-by-step explanation:
20(20-x) = 300
20( -x + 20) = 300
-20x + 20 * 20 = 300
-20x = 300 - 400
x = -100 / -20
x = 5
Find the common ratio of the geometric sequence: 8, -2, 1/2, -1/8
Answer:
-1/4
Step-by-step explanation:
You just need to see what number is being divided from each term
How do you find the answer for? 4(3x+7)=19
Answer:
3/4
Step-by-step explanation:
open the brackets by multiplication
12x+28= 19
12x= 19-28
12x= -9 (divide)
-9/12x
x= 3/4
Answer:
[tex]\boxed{x=-0.75 }[/tex]
Step-by-step explanation:
4 ( 3x + 7 ) = 19
→ Expand the brackets
12x + 28 = 19
→ Minus 28 from both sides to isolate 12x
12x = -9
→ Divide 12 from both sides to isolate x
[tex]x=-\frac{9}{12} =- \frac{3}{4} =-0.75[/tex]
Evaluate 19 - (-13). The solution is.
Answer:
32
Step-by-step explanation:
19-(-13)
=19+13 (after removing the brackets, the minus sign becomes positive)
=32
Answer:
32
Step-by-step explanation:
if there are two negative signs next to each other (they willl usually be separated by parenthesis) they would become an addition sign, so this question would actually be 19+13
cameras actual price was $ 400. after discount its price was $280. calculate the percentage reduction in the price of the camera.
Answer:
30% discount
Step-by-step explanation:
Let the percent reduction be x%
Actual price =$400
Discounted price=$280
Therefore, by the problem => [tex]400-x%400=280[/tex]%*400=280
=>[tex]400-\frac{x}{100} *400=280\\400-4x=280\\-4x=280-400\\-4x=-120\\4x=120\\x=120/40\\x=30[/tex]
There was 30% discount on the camera
What is the slope of the line that passes through the points (−6,−4) ) and (−12,−4)? Write your answer in simplest form.
Answer:
Slope: 0
Step-by-step explanation:
To find the slope use the expression y2 - y1/x2 - x1
Either of the coordinate can be y2 or y1 they just x1 and y1 have to be the same coordinate
Let's make (-12, -4) x2 and y2 & (-6, -4) x1 and y1
Next substitute the numbers into the expression
-4 +4/-12 + 6
This will equal 0/-6
The slope is only 0 because whenever you divide 0 by a number it will always be zero unless it is something like 14/0, this means it is undefined (only for slopes)
Answer:
0
Step-by-step explanation:
To find the gradient of a line, we take the change in the y value divided by the change in the x value.
In this instance, the line passes through (-6, -4) and (-12,-4) , that means the line has a constant y value.
Following the equation to find gradient, we take the difference in y divided by the difference in x
[tex]\frac{(-4) - (-4)}{(-6) - (-12)} = \frac{0}{6} = 0[/tex]
and we see that the gradient is 0, which means that it is a flat line
15 points :0) Thanks for the help (you'll get brainlisest)
Answer:
See below
Step-by-step explanation:
( a ) The value 1200 in this content represents the starting value, or the number of bacteria that was present in the beginning.
( b ) 1.8 represents the growth factor, or by how much more the bacteria increases, in multiples of the quantity.
( c ) As you can tell 1000 has a similar function as 1200, it models the number of bacteria present in the beginning. The difference between the studies is that the second study is present with a starting value of 1000 yet a similar growth factor, and hence will always have a smaller number of bacteria after t hours.
Z=8+6x-px
I need to solve the literal equation for x. Please help!!
Answer:
x = (z-8)/(6-p)
Step-by-step explanation:
Here in this question, we are to solve for x.
In quite more understandable words, we are trying to make x the subject of the formula.
To do this, we simply bring together, the terms that have x common to them.
Let’s proceed mathematically;
z = 8 + 6x - px
Let’s take 8 to z to make it negative and factor out x since it’s common to the two terms on the right hand side of the equation.
z - 8 = x(6-p)
The final thing to do here is to isolate x and this gives the below;
We can do this by dividing both sides by the coefficient of x which is 6-p in this case.
Thus;
x = (z-8)/(6-p)
3y when y=45 ........
Answer:
[tex]135[/tex]
Step-by-step explanation:
[tex]3y = 3 \times 45 = 135[/tex]
Hope this helps ;) ❤❤❤
A new youth center is being built in erie . The perimeter of the rectangular playing field is 296 yards. The length of the field is 2 yards less than double the width. What are the dimensions of the playing field?
Answer:
The dimensions are 50 yards by 98 yards
Step-by-step explanation:
If the width is w, then the length is 2w - 2. Perimeter can be expressed by 2 * (length + width), therefore:
2 * (2w - 2 + w) = 296
2 * (3w - 2) = 296
3w - 2 = 148
3w = 150
w = 50 so 2w - 2 = 2 * 50 - 2 = 98
Answer:
[tex]\Large \boxed{\mathrm{98 \ yards \cdot 50 \ yards}}[/tex]
Step-by-step explanation:
Let the length be l.
Let the width be w.
[tex]l = 2w - 2[/tex]
The perimeter of the rectangle is 296 yards.
[tex]P = 2l + 2w[/tex]
Plug in the value for l and P.
[tex]296 = 2(2w-2) + 2w[/tex]
Evaluate and solve for w.
[tex]296 = 4w - 4 + 2w \\\\296 = 6w - 4 \\\\300 = 6w \\\\50 = w[/tex]
The width is 50 yards.
Let w = 50 for l.
Evaluate and solve for l.
[tex]l = 2(50) - 2 \\ \\ l = 100 - 2 \\\\l = 98[/tex]
The length is 98 yards.
If sin²∅ + sin∅ = 1 , then what is the value of sin²∅ + sin⁴∅.
Answer:
Step-by-step explanation:
Given sin²∅ + sin∅ = 1, we are to find the value of sin²∅ + sin⁴∅. ... 2
From sin²∅ + sin∅. = 1; sin²∅ = 1 - sin∅. ... 3
Substitute equation 3 into 1
sin²∅ + sin⁴∅
= sin²∅ + (sin²∅)²
= (1 - sin∅)+( 1 - sin∅)²
open the parenthesis
= 1 - sin∅+ (1-2sin∅+ sin²∅)
= 1 - sin∅+ 1-2sin∅+ sin²∅
= 1+1-sin∅-2sin∅+sin²∅
= 2 - 3sin∅+sin²∅
Since sin²∅ = 1 - sin∅, the resulting equation becomes;
= 2 - 3sin∅+(1 - sin∅)
= 2 - 3sin∅+1-sin∅
= 3-4sin∅
Answer:
6/10
Step-by-step explanation:
The value of Sin(A) is 6/10
please help me on this
Converse of the corresponding angles postulate
============================================
Explanation:
The corresponding angles postulate says that if we have two parallel lines, then the corresponding angles are congruent.
The converse of this is where we go in reverse: if we know the corresponding angles are congruent, then the lines are parallel.
Corresponding angles are ones where they are on the same side of the transversal line, and also on the same side of each adjacent parallel line. In this case, the angles 52 are to the right of the tranversal, and each are above their neighboring parallel line. We could say the two corresponding angles are both in the upper right hand corner (think of the two lines crossing to form 4 corners or regions)
Find the value of the expression x/y for the given values of x and y. Write your answer in the simplest form.x-5/3,y= -1/7
Answer:
X/Y=-5/3/-17.
-5/3×-1/7=-35/3.
using the Pythagoras rule. A rectangular hockey field is 50m long and 35m wide calculate the length of it's diagonal
Answer:
[tex]\huge\boxed{The\ length\ of\ Diagonal = 61 \ m}[/tex]
Step-by-step explanation:
Length = 50 m
Width = 35 m
Using Pythagorean Theorem:
[tex]c^2 = a^2 + b^2[/tex]
Where c = diagonal , a = length (50 m) and b = width (35 m)
=> [tex]c^2 = 50^2+35^2[/tex]
=> [tex]c^2 = 2500 + 1225[/tex]
=> [tex]c^2 = 3725[/tex]
Taking sqrt on both sides
=> c = 61 m
The length of Diagonal = 61 m.
Step-by-step explanation:
a squared +b squared= c squared
where c is the hypotenuse
35^2+50^2=c^2
1225+2500=c^2
3725=c^2
c^2=61.0328
Answer in simplest form.
Chris spent 5/6 hour drawing and 2/6 hour reading. How much more time did he spend
drawing than reading?
Step-by-step explanation:
Time = 5/6 - 2/6 = 3/ 6 = 1/2
the expression 7x + 300 represents the amount of interest that is being paid for a new tv in dollars, where x is months. what does 7x represent, and is it a term, factor, or coefficient
Answer:
7x means that you are paying for 7 months. and 7x is a term.
Step-by-step explanation:
Rules for whether its a term, coefficient, or factor:
a TERM has a variable. 7x is a term.
a COEFFICIENT is the number part of a term. in 7x, the coefficient is 7.
a FACTOR is something which is multiplied by something else. A factor can be a number, variable, term, or a longer expression.
Translate the following phrase into an algebraic expression. Do not simplify. Use the variable names "x" or "y" to describe the unknowns.
the sum of two numbers multiplied by 7
Answer:
7x+7y=
Step-by-step explanation:
(x+y)7
used 7 to open the bracket.
7x+7y
what is all the real solution of the equation
Answer:I think its C
Step-by-step explanation:
Answer:
x=1, or 6, or 4 (D)
Step-by-step explanation:
x³-11x²+34x-24=0 solve by factorizing
(x-1)(x-6)(x-4)=0
x-1=0
x=1
if x-6=0
x=6
x-4=0
x=4
check : x³-11x²+34x-24=0
x=1 : (1)³-11(1)²+34(1)-24=0
1-11+34-24=-35+35=0 (correct)
x=6 : 6³-11(6)²+34(6)-24=0 (correct)
x=4 : 4³-11(4)²+34(4)-24=0 (correct)
Given: g(x) = x-4 and
h(x) = 2x-8.
What are the restrictions on the domain of gh?
Answer:
Step-by-step explanation:
6
2
mº + 7m-6
Evaluate the expression when m=-4
Step-by-step explanation:
m² + 7m - 6
(-4)² + 7(-4) - 6
16 - 28 - 6
- 18
When you use the midpoint formula can you take either points as x ,y? Why or why not ?
Answer:
Yes, we can take either points as x and y because addition is commutative
Step-by-step explanation:
First of all, the midpoint formula is given as;
(x, y) = [((x₁ + x₂)/2), ((y₁ + y₂)/2)]
For example, if we assume that we have two endpoints having coordinates as (2, 5) and (4, 7)
Now, let (2, 5) represent the first coordinate and (4, 7) represent the second coordinate.
Thus, Coordinates of midpoint = [((2 + 4)/2), ((5 + 7)/2)]
This gives;
(x, y) = (3, 6)
Now,if we change the order of the coordinates by making (4, 7) to be the first coordinate and (2, 5) to be the second coordinate. Thus;
Coordinates of midpoint = [((4 + 2)/2), ((7 + 5)/2)] = (3, 6)
We can see that the coordinates of the midpoint remains the same even after interchanging the coordinates as first and second.
This is because we are adding two numbers and addition is commutative (in commutative properties, changing the order of the operands will not change the result). Thus, it doesn't matter in which order we have the endpoints.
The sum of five consecutive even integers is 530 list integers from smallest to largest
Step-by-step explanation:
Let the 5 even integers be x-4,x-2,x,x+2,x+4
Hence, x-4+x-2+x+x+2+x+4=530
Hence, 5x=530
Hence, x=530/5
Hence,x=106
so.. the integers are 102,104,106,108,110
Larry runs 2.5 miles and sees a total of 12 dogs. If Larry runs for a total of 8 miles, approximately how many dogs will Larry see?
Answer:
38.4
Step-by-step explanation:
We have 8/2.5=3.2 What does this mean? Well, it means that (if the miles are porportional to the dogs) that means he will see 3.2 as many dogs. So, we have 12*3.2=38.4, or 38 if the homework is asking for a rounded number. Hope I helped!
Larry sees 12 dogs per 2.5 miles.
Your trying to find out how many dogs Larry sees in 8 miles.
[tex]\frac{2.5}{12} = \frac{8}{x}[/tex]
So you want to find x.
To go from 2.5 to 8, you have to multiply by 3.2
So do the same thing to the denominator; 12 × 3.2=38.4
Since there are 38.4 dogs, you have to round down because 0.4 dogs is no dog.
Larry sees 38 dogs in 8 miles.
♡ Hope this helped! ♡
❀ 0ranges ❀
Benjamin works at a printing company. He
is making T-shirts for a high school volleyball
team. The press he runs can imprint 3 T-shirts
per minute with the school's mascot.
Answer:
The independent quantity is time and the dependent quantity is T-shirt printed
Step-by-step explanation:
We are asked to determine the dependent and independent quantity.
An independent quantity is a quantity that is not dependent on other quantities while a dependent quantity is a quantity that depends on other quantity. In the the question, the number of T-shirts being made depends on the amount of time the machine works making 3 T shirts per minute, this means that the number of T-shirts made is dependent on the time.
The independent quantity is time and the dependent quantity is T-shirt