given (10,5) and (x,-10), find all x such that the distance between these two points is 17. separate multiple answers with a comma.
Answers
x = (2, 18)
Explanation:Given the points (10, 5) and (x, -10)
The distance between these points is:
[tex]\begin{gathered} D=\sqrt[]{(x-10)^2+(-10-5)^2} \\ \\ =\sqrt[]{(x-10)^2+(-15)^2} \\ \\ =\sqrt[]{(x-10)^2+225} \end{gathered}[/tex]The distance is given to be 17, so
[tex]\begin{gathered} \sqrt[]{(x-10)^2+225}=17 \\ \\ (x-10)^2+225=17^2 \\ (x-10)^2=17^2-225 \\ (x-10)^2=289-225 \\ (x-10)^2=64 \\ x-10=\pm\sqrt[]{64}=8 \\ x=\pm8+10 \\ x=8+10=18 \\ OR \\ x=-8+10=2 \end{gathered}[/tex]x = 2 or x = 18
Related Questions
Use a net to find the surface area of the rectangular prism the height of the rectangular prism meets the base at a 90° angle
Answers
Answer:
406 square inches
Explanation:
The net of a rectangular prism has 6 rectangular faces.
In this prism, the dimensions of the faces are:
• 2 rectangles with length 7 in. and width 5 in.
,• 2 rectangles with length 7 in. and width 14 in.
,• 2 rectangles with length 14 in. and width 5 in.
Next, we find the surface area of the prism:
[tex]\begin{gathered} \text{Surface Area}=2(7\times5)+2(7\times14)+2(14\times5) \\ =2(35)+2(98)+2(70) \\ =70+196+140 \\ =406in^2 \end{gathered}[/tex]The surface area of the rectangular prism is 406 in².
Anton counted 36 dogs and cats at the animal shelter. He noticed that there are 18 fewer cats than dogs. If c= the number of cats and d= the number of dogs, then which system of equations represents the situation?
Answers
Answer: 2d + 18 = 36
Step-by-step explanation:
c = number of cats, d = number of dogs
1. d + c = 36 because there are 36 cats and dogs combined
2. c = d - 18 because there are 18 fewer cats than dogs
3. d + d - 18 = 36 because we inserted the equation of step 2 in the equation of step 1
4. 2d + 18 = 36 is the simplified equation of step 3
Solve for the unknown: K/2+3=5
Answers
Solve for K:
[tex]\frac{K}{2}+3=5[/tex]Subtracting 3 to each member of the equation:
[tex]\frac{K}{2}+3-3=5-3[/tex]Operating:
[tex]\frac{K}{2}=2[/tex]Now we multiply by 2:
[tex]2\cdot\frac{K}{2}=2\cdot2[/tex]Simplifying and operating:
[tex]K=4[/tex]Answer: K = 4
Please explain how you got the question because i have no idea how to plug in the numbers
Answers
Given sequence:
[tex]\frac{1}{2},\text{ }1,\text{ }\frac{3}{2},2[/tex]To find the 109th term, we need to first determine whether the sequence follows an arithmetic progression or a geometric progression.
Check
The sequence is arithmetic if the successive terms of the sequence are formed by adding or subtracting a value.
The sequence is geometric if the successive terms of the sequence are formed by multiplying or dividing by a value.
We have that:
first term = 1/2
second term = 1
third term = 3/2
Taking the difference of the second term from the first term:
[tex]\begin{gathered} =\text{ 1-}\frac{1}{2} \\ \text{ = }\frac{1}{2} \end{gathered}[/tex]Taking the difference of the third term from the second term:
[tex]undefined[/tex]Graph f(x)=-2x + 4. What is x when f(x)=-8? Complete the explanation on how you found x.
Answers
f(x) = - 2x + 4
To find the value of x at f(x) = -8
Substitute f(x) in the equation above by -8
-8 = -2x + 4
Subtract 4 from both sides to move 4 from the right side to the left side
-8 - 4 = -2x + 4 - 4
-12 = -2x
Divide both sides by -2 to find x
[tex]-\frac{12}{-2}=-\frac{2x}{-2}[/tex]6 = x
The value of x at f(x) = -8 is 6
The first point x = 0
f(0) = -2(0) + 4
f(0) = 0 + 4
f(0) = 4
The point is (0, 4)
The second point y = 0
f(x) = 0
0 = -2x + 4
Add 2x to both sides
0 + 2x = -2x + 2x + 4
2x = 4
Divide both sides by 2
x = 2
The point is (2, 0)
at y = -8 x = 6
I tried to solve this but I immediately got confused.
Answers
Firstly, let us find the perimeter.
Perimeter P is;
[tex]P=AB+BC+AC[/tex]The length of AB and AC can be calculated using the formula for distance between two points.
[tex]\begin{gathered} AB=\sqrt[]{4^2+2^2} \\ AB=\sqrt[]{16+4} \\ AB=\sqrt[]{20} \\ AB=4.47\operatorname{cm} \end{gathered}[/tex][tex]\begin{gathered} AC=\sqrt[]{4^2+4^2} \\ AC=\sqrt[]{16+16} \\ AC=\sqrt[]{32} \\ AC=5.66\operatorname{cm} \end{gathered}[/tex][tex]BC=6\operatorname{cm}[/tex]substituting we have;
[tex]\begin{gathered} P=AB+BC+AC \\ P=4.47\operatorname{cm}+6\operatorname{cm}+5.66\operatorname{cm} \\ P=16.13\operatorname{cm} \end{gathered}[/tex]The perimeter is 16.13 cm.
Secondly, The Area A.
[tex]A=\frac{1}{2}bh[/tex][tex]undefined[/tex].shvsguvsguvsguvsguss
Answers
Answer:
what is that ? What do you mean
Answer:
m
Step-by-step explanation:
Hii i forgot how to multiply fractions and I'm a bit rusty since the pandemic
Answers
Solution
The area of a rectangle is given as length(l) x width(w)
length = 2 1/4
width = 1 1/2
Hence substituting these values into the formula
[tex]\begin{gathered} \text{Area = 2}\frac{1}{4}\times1\frac{1}{2} \\ \text{Area = }\frac{(4\times2)+1}{4}\times\frac{(2\times1)+1}{2} \\ \text{Area = }\frac{9}{4}\times\frac{3}{2} \\ \text{Area = }\frac{27}{8}in^2 \\ \text{Area = 3}\frac{3}{8}in^2 \end{gathered}[/tex]Use a suitable half-angle formula to find the exact value of cos(15°).
Answers
Remember that
[tex]\cos (\frac{x}{2})=\pm\sqrt[]{\frac{1_{}+\cos x}{2}}[/tex]For x=30 degrees
[tex]\cos (\frac{30^o}{2})=\cos (15^o)=\sqrt[]{\frac{1+\cos 30^o}{2}}[/tex]we know that
[tex]\cos 30^o=\frac{\sqrt[]{3}}{2}[/tex]substitute
[tex]\cos (15^o)=\sqrt[]{\frac{1+\frac{\sqrt[]{3}}{2}}{2}}[/tex][tex]\cos (15^o)=\sqrt[]{\frac{2+\sqrt[]{3}}{4}}[/tex][tex]\cos (15^o)=\frac{\sqrt[]{2+\sqrt[]{3}}}{2}[/tex]Pluto has a diameter of 1,413 miles. What does this distance equal in kilometers?
(1 mile = 1.6 kilometers)
A. 12,761 km
B. 2,275 km
C. 3,476 km
D. 143,042 km
Answers
Therefore, B (2,275 km) is correct.
Use a graph in a [-2π, 2π, π/2] by [-3, 3, 1] viewing rectangle to complete the identity
Answers
We have the expression:
[tex]\frac{1-2\cos 2x}{2\sin x-1}[/tex]Let's work first with the numerator. We have that we can write cos2x like this:
[tex]\cos 2x=1-\sin ^2x[/tex]doing this substitution we get the following:
[tex]\begin{gathered} 1-2\cos 2x=1-2\cdot(1-\sin ^2x)=1-2+4\sin ^2x=4\sin ^2x-1 \\ =(2\sin x+1)(2\sin x-1) \end{gathered}[/tex]Now that we have these two factors, we can use them on the original identity to get:
[tex]\frac{1-2\cos2x}{2\sin x-1}=\frac{(2\sin x+1)(2\sin x-1)}{2\sin x-1}=2\sin x+1[/tex]therefore, the resulting identity is 2sinx+1
Andre used 1/2 of a stick of butter to make multiple batches of brownies. The recipe calls 1/8 for of a stick of butter for each batch. How many batches did he make?
Please help!! Will give brainlest
Answers
1/8 + 1/8 + 1/8 + 1/8 = 4/8
4/8 = 1/2
First six non zero multiples of 21
Answers
Answer:
21, 42, 63, 84, 105, 126
Step-by-step explanation:
The maximum grade allowed between two stations in a rapid transit rail system is 3.6% between station A and station , which are 300 feet apart, the tracks rise 7ft. What is the grade of the tracks between these stations? round the answer to the nearest tenth of a percent. Does this grade meet the rapid-transit rail standards
Answers
To determine the grade we first need to find the slope of the track, the slope is given by:
[tex]slope=\frac{rise}{run}[/tex]In this case, we know that the track rise 7 ft in a 300 ft run, then we have:
[tex]slope=\frac{7}{300}=0.023[/tex]Now that we know the slope we just multiply it by 100 to find the grade:
[tex]\begin{gathered} grade=100*(0.023) \\ grade=2.3 \end{gathered}[/tex]Hence the grade of the track is 2.3% and since this is less than 3.6% we conclude that this track meets the rapid-transit rail standards
Kylie has an idea for how to calculate 23 23. She says,
"Twenty times 20 is 400, and 3 times 3 is 9;, so 23 23 should be 400 plus 9, which is 409."
What is wrong with Kylie's method? Don't just start over in a different way and don't compute 23-23
directly and compare the answer with Kylie's, work with Kylie's idea. Shade the large square below,
which consists of 23 rows with 23 small squares in each row, to help you explain your answer.
Answers
Answer:
Don't just start over in a different way, work with Kylie's idea. Use the large square below, which consists of 23 rows with 23; Question: 1. Kylie has an idea for how to calculate 23-23. She says, Twenty times 20 is 400, and 3 times 3 is 9, so 23-23 should be 400 plus 9, which is 409.
Step-by-step explanation:
What are the solutions to the equation 3|x + 5| - 2 = 13 ?
Answers
To solve the absolute value equation;
[tex]3|x+5|-2=13[/tex]Note that the left side of the equation is an absolute value. The first step is to remove the absolute value sign, and then the next step is to solve while using the positive and negative value of the number on the right side of the equation.
This is shown below;
[tex]\begin{gathered} 3|x+5|-2=13 \\ \text{remove the absolute value sign;} \\ We\text{ now have;} \\ 3(x+5)-2=13 \\ 3(x+5)=13+2 \\ 3x+15=15 \\ \text{Subtract 15 from both sides;} \\ 3x+15-15=15-15 \\ 3x=0 \\ \text{Divide both sides by 3} \\ \frac{3x}{3}=\frac{0}{3} \\ x=0 \end{gathered}[/tex]Let us now solve for the equation when the right side is -13.
[tex]\begin{gathered} 3(x+5)-2=-13 \\ 3(x+5)=-13+2 \\ 3x+15=-11 \\ \text{Subtract 15 from both sides;} \\ 3x+15-15=-11-15 \\ 3x=-26 \\ \text{Divide both sides by 3;} \\ \frac{3x}{3}=-\frac{26}{3} \end{gathered}[/tex]ANSWER:
[tex]\begin{gathered} x=0, \\ OR \\ x=-\frac{26}{3} \end{gathered}[/tex]The last option is the correct answer
Liam is comparing the costs of phone plans at two different companies to determine which plan to buy. Company A charges $50 each month plus an additional $10 per gigabyte of data used. Company B charges $60 each month plus an additional $8 per gigabyte of data used. The following equation represents the cost of the phone plans for the two companies when they are equal, where g represents the amount of gigabytes of data used. 50+10g+60+8g Complete each of the statements below with the correct answer choice.
The cost of the phone plans will be the same for company A and company B when
5?10?15?18? gigabytes of data are used.
If company A changes the cost of data per gigabyte to
20?24?50?8? , then the two phone plans will never have the same cost.
If company B's initial monthly cost Increases by $10?Decreases by $10
and the cost of data per gigabyte Remains the same? Decreases by $2? Increases by $2, then the cost of the two phone plans will always be the same.
Answers
1. Using equations, the cost of the phone plans will be the same for company A and company B when A. 5 gigabytes of data are used.
2. If company A changes the cost of data per gigabyte to D. 8, then the two phone plans will never have the same cost.
3. If company B's initial monthly cost B. Decreases by $10 and the cost of data per gigabyte B. Decreases by $2, then the cost of the two phone plans will always be the same.
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal or equivalent in value.
Equations are represented using the equation sign (=) to establish the equality of two numerical values or mathematical expressions.
Company A Company B
Fixed charge $50 $60
Variable charge per gigabyte $10 $8
The equation to represent when the two plans are equal:
50 + 10g = 60 + 8g
10g - 8g = 60 - 50
2g = 10
g = 5
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The radius of a circular pond is increasing at a constant rate, which can be modeled by the function r(t) = 5t, where tis time in months. Thearea of the pond is modeled by the function A(1) = 1+?. The area of the pond with respect to time can be modeled by the compositionA(r(t).Which function represents the area with respect to time?OAA(r(t) = 5x52OBA(r(t) = 25m€2O cA(r(E) = 10x92O D.A(-(t)) = 51t?
Answers
Explanation
We are asked to find the function that represents the area with respect to time A(r(t))
Given that
[tex]\begin{gathered} r(t)=5t \\ \\ A(r)=\pi r^2 \end{gathered}[/tex]what we will simply do will be to put in the value of r(t) into the equation of A(r)
Thus
[tex]\begin{gathered} A(r)=[\pi\times(5t)^2] \\ \\ A(r)=\pi\times25t^2 \\ \\ A(r)=25\pi t^2 \end{gathered}[/tex]Thus, the answer is option B
Solve for u.
(u-1)²=2u²+8u+25
Answers
Answer:
u = -4 or -6
Step-by-step explanation:
We know that,
( a + b ) = a² + 2ab + b²
Accordingly, let us solve the given equation.
( u - 1 )² = 2u² + 8u + 25
First, solve the brackets.
u² - 2u + 1 = 2u² + 8u + 25
Subtract u² by both sides.
-2u + 1 = 2u² - u² + 8u + 25
-2u + 1 = u² + 8u + 25
Now, add 2u by both sides.
1 = u² + 8u + 2u + 25
Subtract 1 by both sides.
0 = u² + 10u + 25 -1
0 = u² + 10u + 24
And solve the quadratic equation and solve for u.
0 = u² + 6u + 4u + 24
0 = u ( u + 6 ) + 4 ( u + 6 )
0 = ( u + 4 ) ( u + 6 )
Therefore,
u + 4 = 0
u = -4
or
u + 6 = 0
u = -6
Expand the sum: 3(2y-5)
Answers
The sum of the given expression is found as 6y - 15.
What is termed as the distributive property?To "distribute" something means to divide it or give a share or portion of it. The distributive property refers to the distributive law of multiplication placed above a white basic arithmetic operations such as addition and subtraction. This property states that multiplying the sum of two or even more addends by a number produces the same outcome as multiplying each addend separately by the number and afterwards adding this same products together.In other words, a combination of the type A (B+ C) can be solved using the distributive property as A (B + C) = A B +AC.For the given question,
The equation is stated as;
sum: 3(2y-5)
Using distributive property.
= 3×2y - 3×5
On simplification;
= 6y - 15
Thus the sum of the given expression is found as 6y - 15.
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What is inverse of square root? How could the inverse be used to solve an equation that included a square root?
Answers
The power 2 (or exponent 2) is the inverse of the square root:
√x*√x = (√x)² = x
What is the inverse of the square root?
The square root of a number X, gives a number Y such that the product between Y and itself is equal to X, this means that:
if:
√x = y
Then:
y*y = x
So we could write:
√x*√x = (√x)² = x
So the exponent 2 is the inverse of the square root.
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a rectangle has a lenght of 33 yard less than 6 times it's width. if the area of the rectangle is 6195 square yards, find the length of the rectangle
Answers
Answer
The length of the Rectangle is 177 yards
SOLUTION
Problem Statement
The question tells us that the rectangle has a length of 33 yards less than 6 times its width. We are asked to find the length of the rectangle given that the area of the rectangle is 6195 square yards.
Solution
To solve the question, we simply need to interpret each sentence of the question
Let us go through each portion and come up with equations.
[tex]\begin{gathered} Let\text{ the length of the rectangle be }l \\ \text{Let the width of the rectangle be }w \\ \\ \text{ We are told the length is 33 yards times less than 6 times its width: } \\ l=6w-33\text{ (Equation 1)} \\ \\ \text{ We are told that the Area of the rectangle is 6196} \\ \therefore l\times w=6195\text{ (Equation 2)} \end{gathered}[/tex]Now that we have the equations, we can solve them simultaneously. We shall use the substitution method.
[tex]\begin{gathered} l=6w-33\text{ (Equation 1)} \\ lw=6195\text{ (Equation 2)} \\ \text{From Equation 2, we have that:} \\ w=\frac{6195}{l} \\ \text{ Substituting the expression for w into Equation 1.} \\ \\ l=6w-33\text{ becomes,} \\ l=6(\frac{6195}{l})-33 \\ \text{ Multiply both sides by l} \\ l\times l=l(\frac{6\mleft(6195\mright)}{l}-33) \\ \\ l^2=37,170-33l \\ \text{ rewrite the equation, we have:} \\ l^2+33l-37170=0 \end{gathered}[/tex]
We have obtained a quadratic equation in terms of the length of the rectangle. After solving the equation, we can find the length of the rectangle.
To solve, we shall apply the Quadratic Formula. The Quadratic Formula is given by:
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \text{Given the Quadratic equation,} \\ ax^2+bx+c=0 \\ (In\text{ our case, x is }l) \end{gathered}[/tex]Let us apply the formula to our equation as follows:
[tex]\begin{gathered} Given\text{ the equation: } \\ l^2+33l-37170=0 \\ a=1,b=33,c=-37170 \\ \\ \therefore l=\frac{-33\pm\sqrt[]{33^2-4(-37170)(1)}}{2(1)} \\ \\ l=\frac{-33\pm\sqrt[]{1089+148,680}}{2} \\ \\ l=\frac{-33\pm\sqrt[]{149,769}}{2} \\ \\ l=\frac{-33\pm387}{2} \\ \\ l=177\text{ or -210} \\ \\ \text{ Since we are dealing with lengths and lengths cannot be negative, } \\ \text{Length of the Rectangle is 177 yards} \end{gathered}[/tex]Final Answer
The length of the Rectangle is 177 yards
4 x 107 is
?
times as much as 4 x 10³.
Answers
Step-by-step explanation:
I think thats 10 times
Answer: 4 x 10^4
Step-by-step explanation:
4 x 10^7= 40,000,000
4 x 10^3 = 4,000
Now 40,000,000 - 4,000 = 40,000
40,000 converts to 4 x 10^4
The average speed, s, in miles per hour that a student walks the 3 miles from home to school varies inversely as the number of hours, h that the student walks.The formula is given by s = 3/hAs the number of hours it takes the student to walk from home to school increases, what happens to the speed?
Answers
If the number of hours it takes the student to walk home increases, then the speed decreases
Let us see an example
if h = 1
and we increase h to be = 3
[tex]\begin{gathered} \text{when h =1} \\ \text{The sp}eed,\text{ s =}\frac{3}{1}=3milesperhour \end{gathered}[/tex][tex]\begin{gathered} \text{When h increases to 3} \\ s\text{ =}\frac{3}{3}=1mileper\text{ hour} \end{gathered}[/tex]3miles/hour is more than 1 mile/hour so hence the speed will decrease when the time increases
The answer is option A, the speed decreases
Complete the order pairs below so they satisfy the equation Y=-3x+2Complete the order pairs (0,__) (7,__) (__,17)
Help!!
Answers
The ordered pairs which satisfy the equation are (0,2) , (7,19) (-5,17) .
Finding the values of the variables that result in equality is the first step in solving a variable equation.
The values of the unknown variables that fulfil the equality are the equation's solutions, also known as the variables for which the equation must be solved. The two forms of equations are identity equations and conditional equations. All feasible values of the variables share the same identity. Only specific instances where the values of the variables coincide can result in the truth of a conditional equation. Two phrases are combined into one by using the equals sign ("="). The "left hand side" and "right hand side" of the equation refer to the expressions on each side of the equals sign. It's typical.At x = 0 the value of y from the equation is :
y = 2
At x = 7 , y =-19
at y=17 , x= -5
Therefore the ordered pairs are :(0,2) , (7,19) (-5,17) .
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Function or not function (3,7), (3,6), (5,4), (4,7)
Answers
Express y in terms of x. Then find the value of y when x= -15 - y = 3xY in terms of x:Y=
Answers
first solve y
[tex]\begin{gathered} 5-y=3x \\ 5-y-5=3x-5 \\ -y=3x-5 \\ (-1)\times-y=(-1)\times(3x-5) \\ y=-3x+5 \end{gathered}[/tex]now replace x=-1
[tex]\begin{gathered} y=-3(-1)+5 \\ y=3+5 \\ y=8 \end{gathered}[/tex]Kayla's class went on a field trip to an aquarium. One tank had 30 clown fish. She miscounted the total number of clown fish in the tank and recorded it as 24 fish. What is Kayla's percent error?a 6%b 25%c 30%d 30%
Answers
Error = Value with error - Correct value
Error = 24-30 = -6
(Note tha the minus sign means the value is less than the correct value)
[tex]\text{ \%error = }\frac{\text{error}}{\text{True value}}\text{ x 100\%}[/tex][tex]=\frac{6}{30}\text{ x 100\% = 20\%}[/tex]find the slope x intercept and y intercept of the standard form equation below 7x + 3y equals 42
Answers
Given the equation of the line :
[tex]7x+3y=42[/tex]To find the slope, we will write the equation of the line in slope- intercept form
So, it will be as following :
[tex]\begin{gathered} 7x+3y=42 \\ 3y=-7x+42 \end{gathered}[/tex]Divide all terms by 3
[tex]\begin{gathered} \frac{3y}{3}=-\frac{7x}{3}+\frac{42}{3} \\ \\ y=-\frac{7}{3}x+14 \end{gathered}[/tex]Which will be similar to the general form: y = m * x + b
Where m is the slope
So, the slope of the given equation = -7/3
To find y- intercept, substitute with x = 0
[tex]\begin{gathered} 7\cdot0+3y=42 \\ 3y=42 \\ \\ y=\frac{42}{3}=14 \end{gathered}[/tex]To find x- intercept , substitute with y = 0
[tex]\begin{gathered} 7x+3\cdot0=42 \\ 7x=42 \\ \\ x=\frac{42}{7}=6 \end{gathered}[/tex]so, the answer is :
[tex]\begin{gathered} x-\text{intercept}=6 \\ y-\text{inercept}=14 \\ \text{slope}=-\frac{7}{3} \end{gathered}[/tex]Donovan walked a total of 5 3/8 miles on Sunday and Saturday if he walked 2 and 1/4 Mile on Saturday how many did he walk on Sunday
Answers
The total miles Donovan walked were 5 3/8, we know that he walked 2 1/4 saturday then:
[tex]\begin{gathered} 5\frac{3}{8}-2\frac{1}{4}=\frac{43}{8}-\frac{9}{4} \\ =\frac{43}{8}-\frac{18}{8} \\ =\frac{25}{8} \\ =3\frac{1}{8} \end{gathered}[/tex]He walked 3 1/8 miles on sunday.
