Answers
Given:
Two points (5, 5) and (-1, 3).
To find the midpoint and distance:
Using the midpoint formula,
[tex]\begin{gathered} m=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}) \\ =(\frac{5-1}{2},\frac{5+3}{2}) \\ =(\frac{4}{2},\frac{8}{2}) \\ =(2,4) \end{gathered}[/tex]Thus, the mid-point formula is (2, 4).
Using the distance formula,
[tex]\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2_{}} \\ =\sqrt[]{(-1-5)^2+(3-5)^2} \\ =\sqrt[]{(-6)^2+(-2)^2} \\ =\sqrt[]{36+4} \\ =\sqrt[]{40} \\ =2\sqrt[]{10}\text{ units} \end{gathered}[/tex]Thus, the distance between the two points is,
[tex]2\sqrt[]{10}units[/tex]Related Questions
Which expression is equivalent to 6x + 7- 12.2 - (32 + 2) - x?(A)7x - 28B7x - 21©5x - 28D5x - 21please hurry
Answers
Please help me with this question:Graph the function F(x) = x^2 + 4x - 12 on the coordinate plane by finding the important points below.Be sure to show all steps in your calculations.(a)What are the x-intercepts?(b)What is the y-intercept?(c)What is the maximum or minimum value?(d)Use the points to graph the function.
Answers
Given the function:
[tex]f(x)=x^2+4x-12[/tex]Let's graph the function.
Let's find the following:
• (a). x-intercepts:
The x-intercepts are the points the function crosses the x-axis.
To find the x-intercepts substitute 0 for f(x) and solve for x.
[tex]\begin{gathered} 0=x^2+4x-12 \\ \\ x^2+4x-12=0 \end{gathered}[/tex]Factor the left side using AC method.
Find a pair of numbers whose sum is 4 and product is -12.
We have:
6 and -2
Hence, we have
[tex]\begin{gathered} (x+6)(x-2)=0 \\ \\ \end{gathered}[/tex]Equate the individual factors to zero and solve for x.
[tex]\begin{gathered} x+6=0 \\ Subtract\text{ 6 frm both sides:} \\ x+6-6=0-6 \\ x=-6 \\ \\ \\ x-2=0 \\ Add\text{ 2 to both sides:} \\ x-2+2=0+2 \\ x=2 \end{gathered}[/tex]Therefore, the x-intercepts are:
x = -6 and 2
In point form, the x-intercepts are:
(x, y) ==> (-6, 0) and (2, 0)
• (b). The y-intercept.
The y-intercept is the point the function crosses the y-axis.
Substitute 0 for x and solve f(0) to find the y-intercept:
[tex]\begin{gathered} f(0)=0^2+4(0)-12 \\ \\ f(0)=-12 \end{gathered}[/tex]Therefore, the y-intercept is:
y = -12
In point form, the y-intercept is:
(x, y) ==> (0, -12)
• (c). What is the maximum or minimum value?
Since the leading coefficient is positive the graph will have a minimum value.
To find the point where it is minimum, apply the formula:
[tex]x=-\frac{b}{2a}[/tex]Where:
b = 4
a = 1
Thus, we have:
[tex]\begin{gathered} x=-\frac{4}{2(1)} \\ \\ x=-\frac{4}{2} \\ \\ x=-2 \end{gathered}[/tex]To find the minimum values, substitute -2 for x and solve for f(-2):
[tex]\begin{gathered} f(-2)=(-2)^2+4(-2)-12 \\ \\ f(-2)=4-8-12 \\ \\ f(-2)=-16 \end{gathered}[/tex]Therefore, the minimum value is at:
y = -16
Using the point form, we have the minimum point:
(x, y) ==> (-2, -16).
• (d). Use the points to plot the graph.
We have the points:
(x, y) ==> (-6, 0), (2, 0), (0, -12), (-2, -16)
Plotting the graph using the points, we have:
What is the area of the rectangle whose coordinates are at A(-1,4), B(3, 2), Clo,-4) and D(-4,-2) (Round to the nearest whole number.)
Answers
Answer:
Explanation:
The area of the rectangle with the given coordinates is:
[tex]undefined[/tex]Find value of x. Math 80 I know it’s something to do with sine right?
Answers
Given
To find the value of x.
Explanation:
It is given that,
[tex]\theta=34\degree[/tex]Then,
[tex]\begin{gathered} \sin34\degree=\frac{x}{29} \\ 0.55919\times29=x \\ x=16.21659 \\ x=16.22 \end{gathered}[/tex]Hence, the value of x is 16.22.
Choose the median for the set of data. 99 95 93 92 97 95 97 97 93 97 a. 7b. 95.5 c. 96d. 97
Answers
The median is the middle of a sorted list of number. So, we need to place the number in value order, that is,
[tex]92,93,93,95,95,97,97,97,97,99[/tex]then, the middle is between the 5th and 6th number:
then, we need to find the mean value of these numbers. So, the median is
[tex]\text{ median=}\frac{95+97}{2}=96[/tex]Therefore, the answer is option C.
looking to recieve help with finding the vertex of the parabola.
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
f(x) = - 2x² + 4x + 2
Step 02:
y = ax² + bx + c
a = -2
b= 4
c = 2
vertex of the parabola equation
[tex]yv\text{ =- }\frac{b^{2}-4ac}{4a}[/tex][tex]\begin{gathered} yv\text{ = -}\frac{4^2-4\cdot(-2)\cdot(2)}{4\cdot(-2)} \\ yv\text{ = -}\frac{(16+16)_{}}{-8} \end{gathered}[/tex]yv = (- 32) / (- 8)
yv = 4
[tex]xv\text{ = -}\frac{b}{2a}[/tex][tex]\begin{gathered} xv\text{ =- }\frac{4}{2(-2)} \\ xv\text{ = }\frac{-4}{-4} \end{gathered}[/tex]xv = 1
Vertex:
(xv , yv ) = (1 , 4 )
The answer is:
The vertex of the parabola is (1 , 4)
h(x) = 10x - x^2 find h(4)
Answers
We have the following expression
[tex]h(x)=10x-x^2[/tex]In our case x is equal to 4, then, we will evalute the given function h(x) when x is 4. It yields,
[tex]h(4)=10(4)-(4)^2[/tex]which gives
[tex]\begin{gathered} h(4)=40-16 \\ h(4)=24 \end{gathered}[/tex]Therefore, the asnswer is h(4)=24
find the inverse of each given function f(x)=4x-12f^-1(x)=______x+______
Answers
The original function is f(x) = 4x - 12...
to find the inverse function, we need to solve it for x:
f(x) = 4x - 12
f(x) + 12 = 4x
(f(x) + 12)/ 4 = x
f(x)/4 + 3 = x
if we change now f^-1(x) for x and x for f^-1(x):
x/4 + 3 = f^-1(x)
f^-1(x) = x/4 + 3
f^-1(x) = (1/4)x + 3
Answer:
Which trig equation should be used to solve for x?
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Solution:
To find the appropiate trigonometric formula.
we know that,
for the right angle triangle, we have that,
[tex]\sin \theta=\frac{opposite\text{ side}}{hypotenuse}[/tex]The side opposite to the right angle is hypotenuse, the side opposite to the angle theta is opposite side and the other side is adjacent side.
Also we have,
[tex]\cos \theta=\frac{adjacent\text{ side}}{hypotenuse}[/tex][tex]\tan \theta=\frac{opposite\text{ side}}{adjacent\text{ side}}[/tex]Using this we get,
[tex]\sin 37\degree=\frac{x}{12}[/tex]Answer is:
[tex]\sin 37\degree=\frac{x}{12}[/tex]Suppose a sample of 879 new car buyers is drawn. Of those sampled, 288 preferred foreign over domestic cars. Using the data construct a 95% confidence interval for the population proportion of new car buyers who prefer for foreign cars over domestic cars. Round your answers to three decimal places
Answers
To find the confidence interval for a proportion, we use the following formula:
[tex]Confidence\text{ }interval=p\pm z\cdot\sqrt{\frac{p(p-1)}{n}}[/tex]Where:
p is the sample proportion
z the chosen z-value
n sample size
Since we want to make a confidence interval of 95%, we need to use z = 1.96. The sample size is n = 879.
We can use cross multiplication to find p, which is the percentage of the total sample size that preferred foreign cars:
[tex]\begin{gathered} \frac{879}{288}=\frac{100\%}{x} \\ . \\ x=100\%\cdot\frac{288}{879} \\ . \\ x=32.765\% \end{gathered}[/tex]p is the proportion in decimal, we need to divide by 100:
[tex]p=\frac{32.765}{100}=0.32765[/tex]Now, we can use the formula:
[tex]Confidence\text{ }interval=0.32765\pm1.96\sqrt{\frac{0.32765(1-0.32765)}{879}}=0.32765\pm0.031028[/tex][tex]\begin{gathered} Lower\text{ }endpoint=0.32765-0.031028=0.296616 \\ Upper\text{ }endpoint=0.32765+0.031028=0.35867 \end{gathered}[/tex]Thus, the answer is:
Lower endpoint: 0.297
Upper endpoint: 0.359
Height: Suppose you are 5 feet 8 inches tall. Give your height in meters and centimeters.For example, "9'2" = 2.8 meters = 2 meters and 80 centimeters."You are meters andcentimeters.
Answers
Height is 5 feet 8 inches.
1 feet is 12 inches. So,
(5*12) + 8 = 68 inches
Now, let's convert to meters.
We know:
1 inch = 0.0254 meters
So, 68 inches would be:
68 * 0.0254 = 1.7272 meters
We would need to convert the fractional part (excess of 1, which is 0.7272) to cm.
We know:
1 m = 100 cm
So,
0.7272 m is:
0.7272 * 100 = 72.72 cm
Hence,
The answer is:
1 meters and 73 centimeters (rounded to neaerest cm)which statements and reason complete steps 3 , 4 and 6 of the proof ?
Answers
Statement 1:
ΔABC ≅ ΔCBD ≅ ΔACD
Reason: Given
_________________________________
Statement 2:
b/c = y/b; a/x = x/a
Reason: corresponding sides of similar triangles are proportional
(we want to have to have in the next statement that b² = cy; a² = cx
and proportionality is usually represented as fractions, if we observe the figure, the fractions of this statement correspond to the division of similar sides of the triangles)
________________________
Statement 3:
b² = cy; a² = cx
Reason: cross product property
(if we multiply both sides of b/c = y/b by b, we obtain b² = cy, and if we do the same for a/x = x/a we obtain a² = cx, since we are multiplying, it is called product, then, the option that best fit this field is cross product property)
_______________________________
Statement 4:
a² + b² = cx + cy
Reason: addition property of equality
(we want to prove that a² + b² = c², from the previous statement we can add both equalities so we obtain a² + b² , which is nearer to the conclusion we want to prove)
____________________
Statement 5:
a² + b² = c(x + y)
Reason: factor
(we find the common factor of cx and cy, it is c, then cx + cy = c(x + y))
___________________________
Statement 6:
c = x + y
Reason: Segment addition postulate
(we almost have the conclusion in the previous statement except for the (x + y) of the right part of the equality, since in the figure we observe that c = x + y, then we can use it to replace (x + y))
___________________________
Statement 7:
a² + b² = c²
Reason: substitution
(we substitute c by (x + y) of the statement 5)
⊕
A customer wants to leave a 15% tip. The bill was $35. How much should the customer leave as a tip?
Answers
The customer wants to leave 15% tip, if the bill is $35, then the tip is
[tex]=15\text{ \% of 35}[/tex][tex]=\frac{15}{100}\times\text{ \$35}[/tex][tex]=\text{ \$5.25}[/tex]Therefore, the customer should leave $5.25 as a tip.
what is 388 divided by 6
Answers
Answer:
64.666666666666666666666666... or 64 2/3 or sixty-four and two thirds
One number is 22 more than another. Their product is – 121.Step 1 of 2: Set up an equation to solve the given word problem. Let x be the smaller number.Answer# KeypadKeyboard ShortcutsO x + x + 22 = - 121O x(22x) = - 121O x(x + 22)- 121O x(x – 22)- 121
Answers
Let it be:
• x: The smaller number.
,• x + 22: The larger number.
The product of both numbers is:
[tex]x(x+22)[/tex]Since the product of both numbers is -121, we can write:
[tex]x(x+22)=-121[/tex]The word 'is' is represented by the symbol =.
Therefore, the equation to solve the given word problem is:
[tex]x(x+22)=-121[/tex]Step 2To find the numbers, we solve the previous equation.
[tex]\begin{gathered} x(x+22)=-121 \\ \text{ Apply the distributive property on the left side} \\ x\cdot x+22\cdot x=-121 \\ x^2+22x=-121 \\ \text{ Add }121\text{ from both sides} \\ x^2+22x+121=-121+121 \\ x^2+22x+121=0 \end{gathered}[/tex]Now, we can factor the expression on the left side using the perfect square trinomial rule.
[tex]a^2+2ab+b^2=(a+b)^2[/tex]Then, we have:
[tex]\begin{gathered} x^2+22x+121=0 \\ x^2+2\cdot11\cdot x+11^2=0 \\ (x+11)^2=0 \\ \text{ Apply square root to both sides of the equation} \\ \sqrt[]{(x+11)^2}=\sqrt[]{0} \\ x+11=0 \\ \text{ Subtract 11 from both sides} \\ x+11-11=0-11 \\ x=-11 \end{gathered}[/tex]Finally, we find the another number.
[tex]\begin{gathered} x+22=-11+22 \\ x+22=11 \end{gathered}[/tex]Therefore, the numbers are -11 and 11.
In this chart, can you please figure out how the Medians AY, BZ, and CX are created by? and can find out how the Altitudes AE, BF, and CD are created by as well?
Answers
$480 invested at 15% compounded quarterly after a period of six years
Answers
Answer: $1161
Step-by-step explanation: The equation for compound interest is A=P(1+r/n)^n*t. P is the principal, in this case, being $480 originally invested, r is the rate, in this case being 15% or 0.15, and n is 4 because it is compounded quarterly. t is 6 because the period invested is 6 years. A=480(1+0.15/4)^4*6. This can simplify to 480(1.0375)^24, which equals approximately $1161 dollars. If the question requires to the tenths, it is $1161.3, and for the hundredths, $1161.33.
A bookstore spent $241 to send a group of students to a readingcompetition. Each student who won was given a $5 gift certificate. Anda personalized bookmark that cost $2. Included in the $241 was $45 forthe salary of a staff member who accompanied the students to thecompetition. How many students won prizes?
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A bookstore spent $241 to send a group of students to a reading
competition. Each student who won was given a $5 gift certificate. And
a personalized bookmark that cost $2. Included in the $241 was $45 for
the salary of a staff member who accompanied the students to the
competition. How many students won prizes?
Let
x -----> number of students that won prizes
we have that
the equation that represents this situation is
241=(5+2)x+45
241=7x+45
solve for x
7x=241-45
7x=196
x=28
therefore
28 students won prizes14. In the isosceles trapezoid shown, GJ = 5, HI = 9, and GI = 8.6. Determine the length of HJ.O A. 4.3B. 5C. 8.6D. 9
Answers
In the isosceles trapezoid GJIH the length of HJ is 8.6
It is given that GJIH is the isosceles trapezoid
In an isosceles trapezoid the two non parallel sides are isosceles, that is the angle formed by them and the length of those two sides are equal.
The sides ,
GH = JI
GI and JH are the two diagonals of the trapezoid.
In any isosceles trapezium have equal opposite sides. Therefore diagonals of trapezium are equal.
The length of one of the diagonal GI is 8.6
So the length of another diagonal HJ is lenght of GI = 8.6
Therefore, in the isosceles trapezoid GJIH the length of HJ is 8.6
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help with this question
Answers
ok
When f(x) = 3, from the graph we obtain that x = 1 or only 1
Find the slope and the y-intercept of the line. 4x + 2y= -6 Write your answers in simplest form. Undefined 08 slope: . X ? y -intercept: 0
Answers
Transform equation form Ax + By = C
to y = ax + b
THen
4x + 2y = -6
A= 4. B= 2. C= -6
y = (-A/B)•x +(D/B)
y= (-4/2)•x + (-6/2)
y = -2x -3
Therefore in new equation
Slope a = -2
Y intercept b = -3
Use the given triangle to fill in the blank.bCasin BB
Answers
We can apply trigonometric ratios, on this case we ned to use sine
[tex]\sin (\alpha)=\frac{O}{H}[/tex]Where alpha is th reference angle, O the opposite side from the reference angles and H the hypotenuse of the triangle
On our case O is b and H is c, then replacing
[tex]\sin (B)=\frac{b}{c}[/tex]then sinB is b/c, then right option is first
At what point do they intersect Round to 2 decimal places.
Answers
Solution
See attached graph below
The intersection point of the graph is ( - 0.72 , 0.37 )
The expression 12x+6 can be used to describe a sequence algebraically. Which of the following could be the first five numbers in this sequence?A. 18, 36, 54, 72, 90B. 6, 12, 18, 24, 30C. 18, 30, 42, 54, 66D. 6, 18, 24, 36, 42
Answers
We need to find the first five numbers of a sequence determined by the expression:
[tex]12x+6[/tex]Notice that each time we increase the value of x by 1 unit, we add 12 to the previous result. Thus, subsequent terms in the sequnce differ by 12 units.
From the options, the only one with all the terms differing by 12 units is the beginning at x=1:
[tex]\begin{gathered} x=1:12(1)+6=18 \\ \\ x=2:12(2)+6=30 \\ \\ x=3:12(3)+6=42 \\ \\ x=4:12(4)+6=54 \\ \\ x=5:12(5)+6=66 \end{gathered}[/tex]Therefore, the answer is: C. 18, 30, 42, 54, 66
Find the area of the shape. 12 m 6 m 11 m 4 m 3. What is the perimeter of the above shape?
Answers
Area of the given shape is obtained as,
[tex]\begin{gathered} A=(12\times6)+(11-6)\times4 \\ A=72+(5\times4) \\ A=72+20 \\ A=92m^2 \end{gathered}[/tex]Perimeter of the shape is simply the addition of all the sides
i.e.
[tex]\begin{gathered} P=12+11+4+6 \\ P=23+10 \\ P=33m \end{gathered}[/tex]Use synthetic division to find the result when x³ + 3x² - 6x + 20 is divided by
x + 5.
Answers
Answer:
[tex]x^{2} + 8x + 34 + \frac{190}{x-5}[/tex]
Step-by-step explanation:
write the equation for this line in slope intercept form.y= ? × + __ a) -4 b) 2c) -2 d) -1/2
Answers
we know that
the equation in slope intercept form is equal to
y=mx+b
In this problem
we have
b=-4 ------> because the y-intercept is (0,-4)
Find the slope
we need two points
we take
(-2,0) and (0,-4)
so
m=(-4-0)/(0+2)
m=-4/2
m=-2
therefore
y=-2x-4PLSSS ANSWER ASAP PLS!!!! Solve y3 = 27.A. y = 9 B. y = 3 y= 3 C. y = 3 D. y = 5.2
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Work out the rage 51,38,48,36,39,40,39,47
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The range of the given data set will be 15.
What is the range?When the sample maximum and minimum are subtracted, the range of a collection of data is the difference between the greatest and lowest values. It uses the same units as the data to express itself.Find the biggest observed value of a variable (the maximum) and subtract the smallest observed value to determine the range (the minimum).The range is the range of values, from lowest to highest. Example: The lowest value in 4, 6, 9, 3, and 7 is 3, while the highest value is 9. The range is therefore 9 - 3 = 6.So, the range of the given data:
In increasing order: 36, 38, 39, 39, 40, 47, 48, 51The range will be:
51 - 3615
Therefore, the range of the given data set will be 15.
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Correct questions:
Work out the range 51,38,48,36,39,40,39,47
A chemist is using 383 milliliters of a solution of acid and water, If 17.3% of the solution is acid, how many milliliters of acid are there? Round your answer to the nearest tenth.
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A chemist is using 383 milliliters of a solution of acid and water.
If 17.3% of the solution is acid, how many milliliters of acid are there?
We basically need to calculate 17.3% of 383 milliliters.
[tex]\begin{gathered} acid=17.3\%\: of\: 383\: mL \\ acid=\frac{17.3}{100}\times383 \\ acid=0.173\times383 \\ acid=6.3\: mL \end{gathered}[/tex]Therefore, the solution has 6.3 milliliters of acid.