Answer:
(-3, -5)
Step-by-step explanation:
By using the distance formula, we see that the length of RT is [tex]\sqrt{(6+9)^2+(-2+7)^2}[/tex] which equals [tex]5\sqrt{10}[/tex].
The ratio of RS to ST is 3:2, so we can write the distance of RS as [tex](5\sqrt{10} / 5) * 3[/tex] which equals [tex]3\sqrt{10}[/tex]. The distance of ST is then [tex]2\sqrt{10}[/tex].
Since we know the distance of RS and ST, we can find the coordinates of point S by using the distance formula again:
[tex]\sqrt{(6-x)^2+(-2-y)^2} = 3\sqrt{10}[/tex] and [tex]\sqrt{(-9-x)^2+(-7-y)^2} = 2\sqrt{10}[/tex]
We solve for x and y, getting (-3, -5).
The required coordinate point s is (-3, -5).
Given that,
The points R (6,-2) and T (-9,- 7).
To find the coordinates of point S on line RT such that the ratio of RS to ST is 3: 2
Coordinate, is represented as the values on the x-axis and y-axis of the graph
Here,
Let the coordinates of s be (x, y)
Applying the section formula,
x = [mx₂ + nx₁]/ m+n ; y = [my₂ + ny₁]/ m+n
Since, m = 3 n = 2,
x = [3*-9 + 6*2] / 3 + 2 ; y = [-7*3 + -2*2] / 3 + 2
x = [-27 + 12] / 5 ; y = [-21 - 4]/ 5
x = [-15] / 5 ; y = -25 / 5
x = -3 ; y = -5
Thus, the required coordinate point s is (-3, -5)
Learn more about coordinate here:
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can anybody please solve it
Answer:
98.25
Step-by-step explanation:
Order of Operations: BPEMDAS
Step 1: Convert [tex]27^{\frac{4}{3} }[/tex]
[tex]27^{\frac{4}{3} }[/tex] = ∛(27⁴) = 81
Step 2: Convert [tex]32^{0.8}[/tex]
[tex]32^{0.8}[/tex] = 16
Step 3: Convert [tex]0.8^{-1}[/tex]
[tex]0.8^{-1}[/tex] = 1.25
Step 4: Combine
81 + 16 + 1.25
97 + 1.25
98.25
X + 9 < 4x
What does the X, stand for??
answers:
1. 4
2. 2
3. 3
4. 1
Pls hurry .
Answer:
Option a
4 is correct answer
hope it helped you:)
Answer:
1
Step-by-step explanation:
Change 95.61º to degrees, minutes, and seconds.
a. 95° 43' 44"
b. 95° 41' 43"
c. 950 36' 36'
d. 95° 44' 60"
Please select the best answer from the choices provided
Answer:
In my opnion, i think that the answer to your question is D. 95° 44' 60"
Step-by-step explanation:
if you were to break up each of these into segments, A, and B, would not add additionally to 95.61 degrees, minutes, and seconds. C is most definitly wrong because the inch mark, and foot" marks are wrong, and there is no degree mark. Espiecailly since its not possible to be 950 degree. Therefore, I would say option D is correct.
I hope this helps good luck
PLZ HELP ASAP !!!!!!
Answer:
4.57°
Step-by-step explanation:
tan ∅ = ∆y / ∆x
tan ∅ = 8/100 = 2/25
∅= 4.57°
"I think of a number multiply if by itself and add 4 to the result"
Answer:
Step-by-step explanation:
let the number be x
x multiplied by x = [tex]x^{2}[/tex]
Adding 4 to the result
= [tex]x^{2}[/tex] + 4
Hope this helps
plz mark as brainliest!!!!!
Help ASAP! Find x: 4−x/5 + x+2/3 =6 Thank you!
Answer:
x=44
Step-by-step explanation:
Pretty straightforward!
4-x/5 +x+2/3=6
3(4-x) + 5(x+2) = 90 (Multiply both sides of the equation by 15, a multiple of both 5 and 3)
12-3x+5x+10=90 (Use Distributive property to multiply across parentheses)
-3x+5x=90-12+10 (Bring like terms together/Signs change when moved to the other side)
2x=88
x=44
Thank you for your time!
Answer: x=44
Step-by-step explanation: Pretty straightforward!
4-x/5 +x+2/3=6
3(4-x) + 5(x+2) = 90 (Multiply both sides of the equation by 15, a multiple of both 5 and 3)
12-3x+5x+10=90 (Use Distributive property to multiply across parentheses)
-3x+5x=90-12+10 (Bring like terms together/Signs change when moved to the other side)
2x=88
x=44
Thank you for your time!
What is the value of x?
Answer: x=24
Step-by-step explanation:
The four angles form a linear pair and a linear pair is basically a line which means it forms 180°.
(x-5)+(3x-1)+(2x-6)+(2x)=180
Take off parentheses
x-5+3x-1+2x-6+2x=180
Move like terms together
x+3x+2x+2x-5-1-6=180
Combine like terms
8x-12=180
Add 12 on both sides
8x-12+12=180+12
8x=192
Divide 8 on both sides
8/8 x=192/8
x=24
Hope this helps!! :)
Please let me know if you have any question
Find the angles of the rhombus if the ratio of the angles formed by diagonals and the sides of the rhombus is 6:5
Answer:
Which Angles are you talking about?
Angles A and B?
Step-by-step explanation:
Let f(x) = 3x2 + x − 3 and g(x) = x2 − 5x + 1. Find f(x) − g(x)
Answer:
Step-by-step explanation:
3[tex]x^{2}[/tex]+x-3= [tex]x^{2}[/tex] - 5x
combine like terms
3[tex]x^{2}[/tex] +[tex]x^{2}[/tex]= 4[tex]x^{2}[/tex]
x -5x = -4x
then combine 4[tex]x^{2}[/tex] and -4x
How can understanding decimals and fractions help you in real, everyday life? What can
you use them for?
Step-by-step explanation:
Decimals are great for when you are dealing with money and want to round up, and fractions are used when baking (such as need 1/4 or a half cup of something)
if k is -3 and m is 6 then what is the length of km?
Answer:
-18
Step-by-step explanation:
km
k= -3
m= 6
km = -3*6
km = -18
Answer:
The answer is -18.
Step-by-step explanation:
k×m
-3×6
-18
Sally begins hiking at an elevation of 224 feet. Then, she descends 131 feet
and climbs 67 feet higher than her current position. She then descends
163 feet. Write an addition sentence to describe the situation. Then determine
and interpret the sum.
Answer:
The sum −3 is an indication that Sally is 3 feet below her initial position.
Step-by-step explanation:
Represent the distances going up (ascend) as positive and distances going down (descend) as negative so that the sum is:
224 + (-131) + 67+ (-163)
Add by using the commutative property:
224 + 67 + (-131) + (-163) = 291
The sum −3 is an indication that Sally is 3 feet below her initial position.
Please help ASAP! Find y: 1/6 y− 1/2 =3− 1/2 y Thank you!
Answer:
y = [tex]\frac{21}{4}[/tex]
Step-by-step explanation:
Given
[tex]\frac{1}{6}[/tex] y - [tex]\frac{1}{2}[/tex] = 3 - [tex]\frac{1}{2}[/tex] y
Multiply through by 6 to clear the fractions
y - 3 = 18 - 3y ( add 3y to both sides )
4y - 3 = 18 ( add 3 to both sides )
4y = 21 ( divide both sides by 4 )
y = [tex]\frac{21}{4}[/tex] = 5.25
I'll give 15 points if your answer is the best and give u brainiest
Answer:
B; C; A; B
Step-by-step explanation:
So, let's go through each of the choices.
So we know that one of the angles is 60 degrees.
I) The triangle is scalene.
This might be true. Since there are 180 degrees in a triangle, and we know 60, that leaves 120 degrees. Anything two combinations of different values that add up to 120 will make the triangle scalene. However, if the two values are the same (e.g. 60;60), they it's not scalene. Thus, this might be true.
II) The other two angles add up to 120.
This must be true. The interior angles sum of a triangle is 180. Since we already know one is 60, then the other two must add up to be 180-60 or 120.
III) The other two angles are obtuse.
This cannot be true. We know that there is only 120 degrees left in the triangle. Obtuse angles are greater than 90 degrees.
Therefore, if we subtract the minimum: 120-90, we will get at most 30 left. This is not enough for another obtuse angle. The most we can have is one obtuse angle and two acute angles.
IV) The triangle is right-angled.
This might be true. Since there are 120 degrees left, the other two degrees may be 90 and 30, given us 30-60-90. This, however, doesn't have to be it. So, this statement may be true.
f x is a prime number, then x + 1 is not a prime number.
A counterexample is x =
Answer:
x=2
Step-by-step explanation:
x=2
x+1=3
and 3 is a prime
Answer:
A counterexample is x = 3
Step-by-step explanation:
We are given that x is a prime number, and x + 1 is not a prime number. However consider the number 3. We know that 3 is a prime number, as it is present as factors of 1 and itself. However 3 + 1 = 4 - which falls into the category of a composite number, as it can divide into 2 * 2. Therefore your counterexample could be x = 3.
Find a linear inequality with the following solution set. Each grid line represents one unit.(Give your answer in the form $ax+by+c>0$ or $ax+by+c\geq0$ where $a,$ $b,$ and $c$ are integers with no common factor greater than 1.)
Answer:
-x + 2y + 1 > 0
Step-by-step explanation:
Let's find the equation of the dashed line first. From the graph, we can see that it has a slope of 1/2 and a y-intercept of -1/2 so using slope-intercept form, the equation of the line is y = 1/2x - 1/2. Since the line is dashed and not solid, we know that we will use either < or > instead of ≤ or ≥, and because we can see that the shaded region is above the dashed line, we know that the linear equation is y > 1/2x - 1/2. However, we want the answer to be in the form ax + by + c > 0 where a, b, and c are integers so therefore:
y > 1/2x - 1/2
= 2y > x - 1
= -x + 2y + 1 > 0
A linear inequality is an expression which make comparison between linear expressions using inequalities. The linear inequality of the graph is: [tex]-x + 2y +1 > 0[/tex]
First, we calculate the slope of the dashed line using:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Two points on the graph will be:
[tex](x_1,y_1) = (1,0)[/tex]
[tex](x_2,y_2) = (3,1)[/tex]
The slope (m) is:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{1-0}{3-1}[/tex]
[tex]m = \frac{1}{2}[/tex]
The equation of the line is calculated as:
[tex]y = m(x - x_1) + y_1[/tex]
So, we have;
[tex]y = \frac12(x - 1) + 0[/tex]
[tex]y = \frac12(x - 1)[/tex]
Multiply through by 2
[tex]2y= x - 1[/tex]
Now, we convert the equation to an inequality.
The line on the graph is a dashed line. This means that the inequality is either > or <. Also, the upper region of the graph that is shaded means that the inequality is >.
So, the equation becomes
[tex]2y > x-1[/tex]
Rewrite as:
[tex]-x + 2y +1 > 0[/tex]
So, the linear inequality is: [tex]-x + 2y +1 > 0[/tex]
Learn more about linear inequality at:
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Construct a 90% confidence interval, using the inequality . To test the effectiveness of a new drug that is reported to increase the number of hours of sleep patients get during the night, researchers randomly select 13 patients and record the number of hours of sleep each gets with and without the new drug.
Answer:
The 90% confidence interval is (-1.987, -1.320).
Step-by-step explanation:
The data provided is:
Sleep without Sleep using
the drug the drug d=without-with
2.5 4.3 -1.8
2.7 4.2 -1.5
3.8 5.0 -1.2
3.8 6.2 -2.4
1.8 2.5 -0.7
4.7 7.1 -2.4
4.8 7.1 -2.3
2.7 3.3 -0.6
1.8 3.5 -1.7
2.2 4.3 -2.1
3.6 4.3 -0.7
5.3 7.0 -1.7
5.2 7.6 -2.4
Compute the sample mean and sample standard deviation:
[tex]\bar d=\frac{1}{n}\sum d=\frac{1}{13}\times [(-1.8)+(-1.5)+(-1.2)+...+(-2.4)]=-1.654\\\\S_{d}=\sqrt{\frac{1}{n-1}\sum [d-\bar d]^{2}}=0.6753[/tex]
The degrees of freedom of the test is:
df = n - 1 = 13 - 1 = 12
Compute the critical value of t for 90% confidence level and 12 degrees of freedom as follows:
[tex]t_{\alpha/2, (n-1)}=t_{0.10/2, 12}=1.782[/tex]
Compute the 90% confidence interval as follows:
[tex]\bar d-t_{\alpha/2, (n-1)}\cdot\frac{S_{d}}{\sqrt{n}}<\mu_{d}<\bar d+t_{\alpha/2, (n-1)}\cdot\frac{S_{d}}{\sqrt{n}}[/tex]
[tex]-1.645-[1.782\cdot\frac{0.6753}{\sqrt{13}}]<\mu_{d}<-1.645+[1.782\cdot\frac{0.6753}{\sqrt{13}}]\\\\-1.645-0.334<\mu_{d}<-1.654+0.334\\\\-1.988<\mu_{d}<-1.320[/tex]
Thus, the 90% confidence interval is (-1.987, -1.320).
Comparing rational numbers
Which statements are true? Check all that apply.
-8(2x +x )/-2y , if x=-5, y=2 and z=0
Answer:
-8(2x +x )/-2y = - 30Step-by-step explanation:
x=-5, y=2 and z=0
-8(2x +x )/-2y =(-8•3x)/-2y = [-8•3(-5)] / (-2•2) = 120/(-4) =-30
simplify each expression 4a + 5a^2 + 2a^2 + a^2
Answer:
a(4+5a+2a+a) or
a(5a+2a+a+4)
Step-by-step explanation:
You could take out one A from each number since they all have an A in them. You could reorganize it and put it in numerical order. Hope this helped :)
Answer:
4a + 8a^2Step-by-step explanation:
4a + 5a^2 + 2a^2 + a^2= 4a + 8 a^2[tex]good \: luck[/tex]PLS ANSWER ASAP PLEAAAAAAASE I HAVE LIKE 10 MINUTES
Three equal-sized cardboard boxes are stacked on top of each other. Each box is 56.4 cm in height. What is the combined height of the 3 stacked boxes? 18.8 cm 59.4 cm 112.8 cm 169.2 cm
Answer: 169.2cm
Step-by-step explanation:
From the question, we are informed that three equal-sized cardboard boxes are stacked on top of each other and that each box is 56.4 cm in height.
To get the combined height of the 3 stacked boxes, we multiply 56.4cm by 3. This will be:
= 56.4cm × 3
= 169.2cm
Katie wants to collect over 100100100 seashells. She already has 343434 seashells in her collection. Each day, she finds 121212 more seashells on the beach. Katie can use fractions of days to find seashells.
Answer:
Step-by-step explanation:
which of the following lists the fractions 4/7,5/9, and 2/3 in order of least to greatest
Answer:
[tex]E. \frac{5}{9} < \frac{4}{7} < \frac{2}{3}[/tex]
1. a set within a set; all the elements of one set are also contained in another set
Answer:
"subset"
Step-by-step explanation:
The "set within a set" is called a "subset."
I don't understand this. Can someone help me out?
Answer:
A
Step-by-step explanation:
The range is the y-values, so it’s all numbers less than or equal to 4.
The domain is the x-values, so it’s all real numbers.
Una compañía encuentra que su utilidad esta dada por R=2pe^-0.1p cuando au producto esta cotizado en p dolares por unidad. Encuentre la utilidad marginal con respecto al precio cuando p es a.) $5 b.) $10 c.) $15
a) La utilidad marginal al precio de $ 5 es 1.091.
b) La utilidad marginal al precio de $ 10 es 0.662.
c) La utilidad marginal al precio de $ 15 es 0.402.
La utilidad marginal es la derivada de la función utilidad. Si [tex]r(p) = 2\cdot p\cdot e^{-0.1\cdot p}[/tex], entonces la función de utilidad marginal es la siguiente:
[tex]r'(p) = \frac{dr}{dp}[/tex]
[tex]r'(p) = 2\cdot e^{-0.1\cdot p}-0.2\cdot e^{-0.1\cdot p}[/tex] (1)
Ahora procedemos a evaluar (1) para cada valor citado en el enunciado:
a) $ 5
[tex]r'(5) = 2\cdot e^{-0.1\cdot 5}-0.2\cdot e^{-0.1\cdot 5}[/tex]
[tex]r'(5) = 1.091[/tex]
La utilidad marginal al precio de $ 5 es 1.091.
b) $ 10
[tex]r'(10) = 2\cdot e^{-0.1\cdot 10}-0.2\cdot e^{-0.1\cdot 10}[/tex]
[tex]r'(10) = 0.662[/tex]
La utilidad marginal al precio de $ 10 es 0.662.
c) $ 15
[tex]r'(15) = 2\cdot e^{-0.1\cdot 15}-0.2\cdot e^{-0.1\cdot 15}[/tex]
[tex]r'(15) = 0.402[/tex]
La utilidad marginal al precio de $ 15 es 0.402.
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Help, Answer ASAP will give brainliest
Answer:
x = 5 and x = 11
Step-by-step explanation:
The segment through the center is a perpendicular bisector of the chord, thus
5x - 6 = 2x + 9 ( subtract 2x from both sides )
3x - 6 = 9 ( add 6 to both sides )
3x = 15 ( divide both sides by 3 )
x = 5
-------------------------------------------------------
Tangents to a circle from an external point are congruent, thus
4x - 1 = 3x + 10 ( subtract 3x from both sides )
x - 1 = 10 ( add 1 to both side
Answer:
x = 5 and x = 11
Step-by-step explanation:
The segment through the centre is a perpendicular bisector of the chord, thus
5x - 6 = 2x + 9 ( subtract 2x from both sides )
3x - 6 = 9 ( add 6 to both sides )
3x = 15 ( divide both sides by 3 )
x = 5
-------------------------------------------------------
Tangents to a circle from an external point are congruent, thus
4x - 1 = 3x + 10 ( subtract 3x from both sides )
x - 1 = 10 ( add 1 to both sides )
x = 11
solve by square roots 4x^2+11= 59
Answer:
x= ±2 sqrt(3)
Step-by-step explanation:
4x^2+11= 59
Subtract 11 from each side
4x^2+11-11= 59-11
4x^2 = 48
Divide by 4
4/4x^2 = 48/4
x^2 = 12
Take the square root of each side
sqrt(x^2) = sqrt(12)
x = ±sqrt(4*3)
x= ±2 sqrt(3)
Subtract 11 from each side
4x^2+11-11= 59-11
4x^2 = 48
Divide by 4
4/4x^2 = 48/4
x^2 = 12
Take the square root of each side
sqrt(x^2) = sqrt(12)
x = ±sqrt(4 x 3)
A local service organization is wrapping gifts at the mall to raise money for charity. Yesterday, they wrapped 14 small gifts and 15 large gifts, earning a total of $205. Today, they wrapped 47 small gifts and 45 large gifts, and earned $640. How much did they charge to wrap the gifts?
Answer:
The answer is below
Step-by-step explanation:
Let the money charged to wrap a small gift be $x and the money charged to wrap a large gift be $y. The cost of wrapping 14 small gifts and 15 large gifts is $205, It can be represented by the equation:
14x + 15y = 205 (1)
Also, the cost of wrapping 47 small gifts and 45 large gifts is $640. It can be represented by the equation:
47x + 45y = 640 (2)
Solving equation 1 and equation 2 simultaneously. Multiply equation 1 by 3 and subtract from equation 2:
5x = 25
x = 25/5 = 5
x = 5
Put x = 5, in equation 1 and solve:
14(5) + 15y = 205
15y + 70 = 205
15y = 205 - 70
15y = 135
y = 135 / 15
y = 9
This means that the money charged to wrap the small gift is $5 and to wrap the large gifts is $9