Answer:
[tex]x_1=1+\sqrt{89}\\\\x_2=1-\sqrt{89}[/tex]
Step-by-step explanation:
Apply Distributive property:
[tex](x+7)(x-9)=25\\\\x^2-9x+7x-63=25[/tex]
Add like terms and then add 63 to both sides of the equation:
[tex]x^2-2x-63=25\\\\x^2-2x-63+63=25+63\\\\x^2-2x=88[/tex]
Pick the coefficient of the x term, divide it by 2 and square it:
[tex](\frac{2}{2})^2=1[/tex]
Add it to both sides of the equation:
[tex]x^2-2x+1=88+1[/tex]
Rewriting the left side as a squared binomial, we get:
[tex](x-1)^2=89[/tex]
Apply square root to both sides:
[tex]\sqrt{(x-1)^2}=\±\sqrt{89}\\\\x-1=\±\sqrt{89}[/tex]
And finally we need to add 1 to both sides of the equation. Then we get:
[tex]x-1+1=\±\sqrt{89}+1\\\\x=\±\sqrt{89}+1\\\\\\x_1=1+\sqrt{89}\\\\x_2=1-\sqrt{89}[/tex]
WILL MARK BRAINLIEST
the last two pics are for question two
Answer:
1. 702 square centimeters
2. m∠YWX = 63°
Step-by-step explanation:
1.
The total surface area is area of all the sides.
There are 2 triangles (slanted side) with base 14 and height 11. Thus area would be [tex]2(\frac{1}{2}*14*11)=154[/tex]There are 2 triangles (another slanted side) with base 10 and height 12. Thus area would be [tex]2(\frac{1}{2}*10*12)=120[/tex]There are two rectangles with base 10 and height 6. Thus area would be [tex]2(10*6)=120[/tex]There are two rectangles with base 14 and height 6. Thus area would be [tex]2(14*6)=168[/tex]The bottom is a rectangle with area 10 * 14 = 140Adding all these up 154 + 120 + 120 + 168 + 140 = 702 centimeters square.
2.
Angle WYX is equal to 46° (vertical angles are equal).
Now looking at triangle XWY, we know all three angles will add up to 180°. Given x =71° and Y = 46°, we can figure out W (Angle YWX)
71 + 46 + Angle YWX = 180
Angle YWX = 180 - 71 - 46 = 63°
Second answer choice is correct.
What is the simplified form of n^-6p^3
Answer:
p^3
--------
n^6
Answer: correct option is C
Step-by-step explanation:
Took test
From the top of a 100 foot high pole, an observer measures the angle of depression of a car on the road as 28 degrees. Find, to the nearest hundredth of a foot, the distance from the car to the base of the pole.
This is a quick sketch of the problem
the answer is about 235.31 ft
you have to use this equation to get the length of the other side, which is roughly 213 ft:
[tex]100 \div \sin(28) [/tex]
then it's just Pythagorean Theorem to get the end result:
[tex] {100}^{2} + {213}^{2} = {c}^{2} [/tex]
To find the distance from the car to the base of the pole, use the tangent function. Plug in the values and solve for the adjacent side.
Explanation:To find the distance from the car to the base of the pole, we can use trigonometry. Since the observer is looking down at an angle of depression, we can use the tangent function. Tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height of the pole (100 ft) and the adjacent side is the distance from the car to the base of the pole.
So, using the formula tan(angle) = opposite/adjacent, we can plug in the values and solve for the adjacent side:
tan(28 degrees) = 100 ft/adjacent
adjacent = 100 ft / tan(28 degrees)
Using a calculator, we find that the distance from the car to the base of the pole is approximately 169.38 ft.
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When constructing a perpendicular line through a point on a line, how can you verify that the lines constructed are perpendicular?
Answer:
The answer in the procedure
Step-by-step explanation:
Let
m1 and m2 ----> the slopes of the lines constructed
we know that
If two lines are perpendicular, then the product of their slopes is equal to -1
therefore
To verify if the lines constructed are perpendicular
Multiply their slopes
if m1*m2=-1 ------> the lines are perpendicular
Answer:
C. Check the intersecting lines with the corner of a piece of paper to ensure the lines create 90° angles. Took the test just now and got it right
Step-by-step explanation:
2. What is the formula for finding the horizontal distance between two points on a coordinate plane?
[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{a}~,~\stackrel{y_1}{b})\qquad (\stackrel{x_2}{c}~,~\stackrel{y_2}{d})\qquad \qquad d = \sqrt{\underset{\underset{\textit{horizontal distance}}{\uparrow }}{( x_2- x_1)^2} + ( y_2- y_1)^2} \\\\[-0.35em] ~\dotfill\\\\ \textit{so in short is just }x_2-x_1[/tex]
Find the missing factor.
8x2 - 15x + 7 = (8x - 7)(
)
Answer:
(x - 1)
Step-by-step explanation:
Given
8x² - 15x + 7
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 8 × 7 = 56 and sum = - 15
The factors are - 8 and - 7
Use these factors to split the x- term
8x² - 8x - 7x + 7 ( factor the first/second and third/fourth terms )
= 8x(x - 1) - 7(x - 1) ← factor out (x - 1) from each term
= (x - 1)(8x - 7) ← in factored form
The missing factor is (x - 1)
3x − y − 3z if x = −2, y = 1, and z = −2.
Answer: -1
Step-by-step explanation:
3x − y − 3z if x = −2 y = 1 z = −2
Step 1: 3(-2)-1-3(-2)
Step 2: -6-1+6
Step 3: -7+6
Step 4: -1
Fraction: 17/60 what is the decimal?
Fraction: 1/60 what is the decimal?
Fraction:5/60 what is the decimal?
Fraction: 4/60 what is the decimal?
Fraction:6/60what is the decimal?
Fraction:12/60 what is the decimal?
Fraction:3/60 what is the decimal?
Fraction:2/60 what is the decimal? I'm sorry if this is alot of work.i only have 12 points I would give more if I had the chance
Answer:
1. 0.283333333
2. 0.016666667
3. 0.0833333333333333
4.0.0666666666666667
5. 0.1
6. 0.2
7. 0.05
8.0.0333333333333333
Step-by-step explanation:
Simply divide the numerator by the denominator. ex. 17 divided by 60.
Hope this helps :)
What statements are true regarding given statement and diagram
Answer:
Statements 1, 2, 4, and 5.
Step-by-step explanation:
(Follow along with the diagram)
The first thing we should do is figure out the measure of every angle. We know immediantly that CED is 90 degrees, and consequently CEA is too. This verifies the first two statements. We are told that EB bisects AEC (AEC = CEA). This means that EB splits AEC into two congruect angles, BEA and CEB. If BEA = CEB, and BEA + CEB = CEA, then BEA and CEB both equal 45 degrees. This verfies statement 4, and helps us start statement 5. Statement 5 says that DEB = 135 degrees. We can see that the angle DEB is made up of angles CEB and CED. We already know that CEB = 45, and CED = 90. 90 + 45 = 135. So, statement 5 is true.
Regarding the incorrect statements, I will explain why they are false. We deduced that BEA = 45, so statement 6, stating that AEB (same as BEA) is 35, is not true. Statement 3 says that CEA = 1/2 of CEB. This equation regards the angles' measurements. If we plug in their known measurements, the equation reads 90 = 1/2 of 45. Through logic, we know this is not true. So, statement 3 is also false.
Statements are true regarding the given statement and diagram1, 2, 4, and 5.
1: ∠CED is a right angle.
2: ∠CEA is a right angle.
3: m∠CEB = m∠BEA
5 : m∠DEB = 135°
The first thing we should do is figure out the measure of every angle. We know immediately that CED is 90 degrees, and consequently, CEA is too. This verifies the first two statements. We are told that EB bisects AEC (AEC = CEA).
This means that EB splits AEC into two congruent angles, BEA and CEB. If BEA = CEB and BEA + CEB = CEA, then BEA and CEB both equal 45 degrees.
This verifies statement 4 and helps us start statement 5. Statement 5 says that DEB = 135 degrees. We can see that the angle DEB is made up of angles CEB and CED.
We know that CEB = 45, and CED = 90. 90 + 45 = 135. So, statement 5 is true.
What are congruent angles?Congruent angles are two or more angles that are identical to each other. Thus, the measure of these angles is equal to each other.
What is congruent angle example?Congruent angles have the same angle measure. For example, a regular pentagon has five sides and five angles, and each angle is 108 degrees. Regardless of the size or scale of a regular polygon, the angles will always be congruent.
Are congruent angles 180 or 90?In general, all congruent angles are not supplementary angles. For angles to add up to 180, they must be supplementary angles. So only right angles are congruent as well as supplementary angles because they have the same measure and they add up to 180.
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I leave my family's vacation cabin at 8 a.m. and start driving home at a nice, safe 45 mph. Two hours later, my husband, who always drives as fast as the law will allow, leaves the cabin and starts driving home 65 mph. When can I expect him to pass me?
Answer:
2:30 pm
Step-by-step explanation:
In two hours (from 10am), she is 45 * 2 = 90 miles from vacation cabin.
From then on her average is still 45 mph and her husband's is 65 mph. So, husband catches her 20 miles (65-45=20) in every hour.
The husband has to catch up 90 miles. How long would it take if he is catching up at 20 miles an hour?
90/20 = 4.5 hours
So husband starts at 10am and 4.5 hours form that time is 2.30pm
Help me pleaseeeeeeeeeeeeeeeeeeeeee
Answer:
base= 2 cm
Step-by-step explanation:
A=1/2bh
(1/2x)40=1/2b(10)x(1/2)
20=b(10)/10
2=b
Answer:
base = 8 cm
Step-by-step explanation:
A= 1/2bh
40=1/2*b*10
40/ 1/2= 80
80/10= 8
b=8
The Bishop family celebrated a birthday by dining out at a local restaurant. Their
18 percent tip at the table for the server. What is the total amount that the family v
if necessary.
O
$17.54
$107.20
$114.99
$116.94
Answer:
$114.99
Step-by-step explanation:
rt4by5by4by5v4fcefrcekjj3ivc24ino3rmf44g4g
gv5y43t4r3wgy54bt3bt 4hnht6bgrvf
sorry if there is random numbers and letters i am glitchy
Answer:
97.45 • 0.18 = 17.54. 97.45 + 17.54 = 114.99. I think this is right.
Step-by-step explanation:
Which system of equations is represented by the graph?
A) y = x
y = -x-10, over x-4
B) y = −x
y = x+10, over x-4
C) y = x
y = -x+10 divided by the quantity x-4
D) y = −x
y = -x+10 divided by the quantity x-4
Answer:
[tex]\large\boxed{C)\ \left\{\begin{array}{ccc}y=x\\\\y=\dfrac{-x+10}{x-4}\end{array}\right}[/tex]
Step-by-step explanation:
We have the points
(-2 , -2) → x = -2 and y = -2 → x = y
(5, 5) → x = 5 and y = 5 → x = y
The equation of a line is [tex]y=x[/tex]
The hyperbola has the vertical asymptote x = a and the horizontal asymptote y = -1.
Therefore the second equation is:
[tex]y=\dfrac{a}{x-4}-1=\dfrac{a}{x-4}-\dfrac{x-4}{x-4}=\dfrac{a-(x-4)}{x-4}=\dfrac{a-x+4}{x-4}[/tex]
Where a > 0.
The corresponding equation in the solutions to choose is:
[tex]y=\dfrac{-x+10}{x-4}[/tex]
7. A large wall map is drawn so that 1 inch equals
3 miles. On the map, the distance from Kansas
City to Denver is 192 inches. How far is the
round trip from Kansas City to Denver in
miles?
(A) 192- miles
(B) 577 miles
(C) 385 miles
(D) 1,155 miles
CHAPTI
The correct answer is (D) 1,155 miles (rounded to the nearest whole number).
To find the round trip distance from Kansas City to Denver, we need to calculate the actual distance in miles based on the scale given in the map.
On the map, 1 inch represents 3 miles. The distance from Kansas City to Denver on the map is given as 192 inches. To find the actual distance in miles:
Actual distance = (Distance on the map) × (Scale factor)
Actual distance = 192 inches × 3 miles/inch
Actual distance = 576 miles
Since the round trip distance includes going from Kansas City to Denver and back, we need to double the actual distance:
Round trip distance = 2 × 576 miles
Round trip distance = 1152 miles
So, the correct answer is (D) 1,155 miles (rounded to the nearest whole number).
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How many distinct zeroes does the function [tex]f(x)=(2x+1)(x+1)(5x-4)(2x+2)\\[/tex] have?
It has 3 zeroes which are
[tex]\frac{-1}{2}, -1, \frac{4}{5}[/tex]
Hope this helped!
~Just a girl in love with Shawn Mendes
The students in a class were asked how many siblings they have. The data obtained is represented in the dot plot. The number of students who have no siblings is . The number of students who have three or more siblings is .
Answer:
0 Siblings: 4 Students
3 or more siblings: 5 students
Step-by-step explanation:
The numbers at the bottom represents how many siblings they have and the dots represent the number of studens so using this we know:
0 Siblings: 4 Students
1 Sibling: 3 Students
2 Siblings: 3 Students
3 Siblings: 1 Student
4 Siblings: 0 Students
5 Siblings: 2 Students
6 Siblings: 1 Student
7 Siblings: 1 Student
3 or more: 1 + 0 + 2 + 1 + 1 = 5
3 or more siblings: 5 students
Answer:
0 Siblings: 4 Students3 or more siblings: 5 students
Step-by-step explanation:
Using the quadratic Formula to solve 2x^3=4x-7 what are the values of x
Answer:
[tex]x=1(+/-)0.5i\sqrt{10}[/tex]
Step-by-step explanation:
we know that
The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to
[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]2x^{2}=4x-7[/tex]
[tex]2x^{2}-4x+7=0[/tex]
so
[tex]a=2\\b=-4\\c=7[/tex]
substitute
[tex]x=\frac{4(+/-)\sqrt{(-4)^{2}-4(2)(7)}} {2(2)}[/tex]
[tex]x=\frac{4(+/-)\sqrt{-40}} {4}[/tex]
Remember that
[tex]i=\sqrt{-1}[/tex]
[tex]x=\frac{4(+/-)2i\sqrt{10}} {4}[/tex]
[tex]x=1(+/-)0.5i\sqrt{10}[/tex]
which polygons are similar??
Answer:
1 and 4 should be the answer since 1 is 4 just angled differently
^-^
A vegetable garden in the shape of a rectangle is to be divided up into 4 sections using the diagonals. A stake marks the intersection of the diagonals. What is the length of 1 diagonal if the distance from 1 vertex to the stake is 8.1 feet?
A. 24.3 ft
B. 16.2 ft
C. 4.05 ft
D 8.1 ft
Answer:
B. 16.2 ft
Step-by-step explanation:
one vertex to the stake is 8.1, and because the stake is the "halfway" point, the diagonal is twice that length.
8.1 * 2 = 16.2 ft
Answer:
The correct option is B.
Step-by-step explanation:
Given: Rectangle with the stake marking where diagonal intersect each other.
To find : The length of the one of the diagonal.
Solution:
Diagonals of rectangle bisect each other into two equal parts.
So, the distance of all vertices from the stake will be same as that of the 8.1 feet.
So the length of the diagonal will be:
[tex]2\times \text{Distance from 1 vertex to the stake}[/tex]
[tex]=2\times 8.1 feet=16.2 feet[/tex]
Hence, the length of the diagonal will be 16.2.
The image of a transformation is the original figure before the transformation is performed.
Please select the best answer from the choices provided
T
F
Answer:
F ................................
Are the graphs of the lines in the pair parallel? Explain.
y = 2/3x– 17
4x – 6y = –6
Answer:
Yes, they are parallel.
Step-by-step explanation:
Parallel lines have the same slope. We must find the slopes of the two lines.
When the equation of a line is written in the slope-intercept form,
y = mx + b,
the slope is m.
The first line has equation
[tex] y = \dfrac{2}{3}x - 17 [/tex]
It is already written in the slope-intercept form. Comparing y = 2/3x - 17 with y = mx + b, you see that m = 2/3. The slope of the first line is 2/3.
Now we solve the second equation for y to obtain the slope-intercept form of that equation.
4x - 6y = -6
Subtract 4x from both sides.
-6y = -4x - 6
Divide both sides by -6.
[tex] \dfrac{-6}{-6}y = \dfrac{-4}{-6}x + \dfrac{-6}{-6} [/tex]
[tex] y = \dfrac{2}{3}x + 1 [/tex]
We now compare this form of the second equation with y = mx + b, and we see that m = 2/3.
Both equations have the same slope, 2/3, so the lines are parallel.
An object in geometry with no width, length or height is a(n):
A. line
B. point
c. ray
D. angle
Answer:
The correct answer is B. point
Step-by-step explanation:
We know that a line has a length so option a cannot be correct.
A point is represented by a dot which has no length, width and height.
A ray is formed by a collection of points which altogether make its length.
Similarly an angle is formed by two rays.
So, angle, ray and line, all of them have length, width or height.
Hence, B. Point is the right answer ..
Find the area of the rhombus. d1 = 14 m; d2 = 18 m The area of the rhombus is ? m2.
Answer:
Area of rhombus = 126 m²
Explanation:
We are given that the two diagonals of the rhombus are:
D₁ = 14 meters and D₂ = 18 meters
The area of the rhombus using its diagonals can be calculated using the following rule:
[tex]Area = \frac{D_1 * D_2}{2}[/tex]
Substitute with the given values to get the area as follows:
[tex]Area = \frac{14*18}{2}=126 m^2[/tex]
Hope this helps :)
Answer:
2.16m2
Step-by-step explanation:
what is the factor xsquared plus 4x plus 4
Answer:
(x + 2)²
Step-by-step explanation:
x² + 4x + 4 ← is a perfect square of the form
(x + a)² = x² + 2ax + a²
Comparing coefficients of like terms
4 = 2² ⇒ a = 2 and 2ax = (2 × 2)x = 4x
Hence
x² + 4x + 4 = (x + 2)²
HELPP ME PLEASE ASPAAAAAAP PLEASEEEEE
Answer:
4Step-by-step explanation:
1, 2 and 3 are interior angles
4 is the exterior angle
Write the point-slope form of an equation of the line through the points (6, -1) and (5, -7).
A. y−5=6(x+7)
B. y+1=6(x−6)
C. y−6=6(x+1)
D. y+7=6(x+5)
Answer:
B. y + 1 = 6(x - 6)
Step-by-step explanation:
First, find the rate of change [slope], then insert the coordinates into the formula with their CORRECT signs. Remember, in the Point-Slope Formula, y - y₁ = m(x - x₁), all the negative symbols give the OPPOSITE term of what they really are.
If f(x) = 4x - 12, what is f(2)
Answer:
D
Step-by-step explanation:
f(2)=4(2)-12
=8-12
=-4
Answer:
D. -4
Step-by-step explanation:
We have the following function:
[tex]f(x)=4x-12[/tex]
and we are asked to find the value of the function [tex]f(x)[/tex] when the variable [tex]x[/tex] is equal to 2: [tex]f(2)[/tex].
This means that we must substitute the value of [tex]x = 2[/tex] wherever there is an [tex]x[/tex] in the function:
[tex]f(2)=4(2)-12[/tex]
[tex]f(2)=8-12[/tex]
[tex]f(2)=-4[/tex]
The answer is D. -4
Someone please help me out ?
If a seed is planted, it has a 85% chance of growing into a healthy plant.
If 6 seeds are planted, what is the probability that exactly 1 doesn't grow?
Deshawn won 95 pieces of gum playing hoops at the county fair. At school he gave four to every student in his math class. Write an expression for how many pieces of gum deshawn has now
Answer:
x = 95 - 4y
Step-by-step explanation:
Let the pieces he has now be a variable x and the no. of students in his class be y, So the pieces he gave to everyone become 4y (note that 4 here means he had given four to each) and as he had won 95 pieces at the fair in the starting,
therefore the equation becomes:-
x = 95 - 4y
The expression for how many pieces of gum Deshawn has now is 95 - (4 x number of students in his math class).
Explanation:To find out how many pieces of gum Deshawn has after giving four to every student in his math class, we need to subtract the number of pieces of gum he gave away from the total number he won at the county fair.
We can represent this situation using the expression: 95 - (4 x number of students in Deshawn's math class).
For example, if there were 20 students in Deshawn's math class, the expression would be: 95 - (4 x 20) = 95 - 80 = 15.
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