Answer:
Is an acute triangle
Step-by-step explanation:
we know that
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we have
G(7,3), H(9, 0), I(5, -1)
step 1
Find the distance GH
substitute in the formula
[tex]d=\sqrt{(0-3)^{2}+(9-7)^{2}}[/tex]
[tex]d=\sqrt{(-3)^{2}+(2)^{2}}[/tex]
[tex]GH=\sqrt{13}\ units[/tex]
step 2
Find the distance IH
substitute in the formula
[tex]d=\sqrt{(0+1)^{2}+(9-5)^{2}}[/tex]
[tex]d=\sqrt{(1)^{2}+(4)^{2}}[/tex]
[tex]IH=\sqrt{17}\ units[/tex]
step 3
Find the distance GI
substitute in the formula
[tex]d=\sqrt{(-1-3)^{2}+(5-7)^{2}}[/tex]
[tex]d=\sqrt{(-4)^{2}+(-2)^{2}}[/tex]
[tex]GI=\sqrt{20}\ units[/tex]
step 4
Verify what type of triangle is the polygon
we know that
If applying the Pythagoras Theorem
[tex]c^{2}=a^{2}+b^{2}[/tex] ----> is a right triangle
[tex]c^{2}> a^{2}+b^{2}[/tex] ----> is an obtuse triangle
[tex]c^{2}< a^{2}+b^{2}[/tex] ----> is an acute triangle
where
c is the greater side
we have
[tex]c=\sqrt{20}\ units[/tex]
[tex]a=\sqrt{17}\ units[/tex]
[tex]b=\sqrt{13}\ units[/tex]
substitute
[tex]c^{2}= (\sqrt{20})^{2}=20[/tex]
[tex]a^{2}+b^{2}=(\sqrt{17})^{2}+(\sqrt{13})^{2}=30[/tex]
therefore
[tex]c^{2}< a^{2}+b^{2}[/tex]
Is an acute triangle
Answer:
ACUTE !!!!!!!!
Step-by-step explanation:
What is the solution to this Logarithmic Equation?
(Those are L's infront of the N)
ln x + ln x = 0
Answer:
x = 1
Step-by-step explanation:
ln x + ln x = 0
2ln x = 0
ln x = 0
recall ln x = [tex]log_{e}[/tex]x
so equation becomes
[tex]log_{e}[/tex]x = 0
or [tex]e^{0}[/tex]=x
since anything raised to the power of zero = 1
x = 1
Answer:
x = 1
Step-by-step explanation:
We are to find the solution of the following logarithmic equation:
[tex] ln ( x ) + l n ( x ) = 0 [/tex]
We will add the similar elements to get:
[tex] 2 l n ( x ) = 0 [/tex]
Dividing both sides by 2 and simplify to get:
[tex] \frac { 2 l n ( x ) } { 2 } = \frac { 0 } { 2 } [/tex]
[tex]ln(x)=0[/tex]
Applying the rule [tex]a=log_b(b^a)[/tex] to get:
[tex]0=ln(e^0)=ln(1)[/tex]
[tex]ln(x)=ln(1)[/tex]
Here the logs have the same base, so:
x = 1
prove that (x-2)is factor of p (x)=2x³-3x²-17x+30
Answer:
P(2)=0 then x-2 is a factor of P(x)
Step-by-step explanation:
To see if (x-2) is a factor just plug in 2 for x into the polynomial expression.
2(2)^3-3(2)^2-17(2)+30
2(8)-3(4)-34+30
16-12-34+30
4-34+30
-30+30
0
Since P(2)=0 then x-2 is a factor
The circle below is centered at the point (8, 4) and has a radius of length 4.
What is its equation?
Answer:
(x - 8)^2 + (y - 4)^2 = 16.
Step-by-step explanation:
The standard form can be written as:
(x - a)^2 + (y - b)^2 = r^2 where (a, b) is the center and r = the radius.
So here we have a = 8, b = 4 and r = 4.
(x - 8)^2 + (y - 4)^2 = 4^2
(x - 8)^2 + (y - 4)^2 = 16.
What is the approximate area of a circle with a radius of 11 m?
Answer:
380.13
Step-by-step explanation:
area= (pi)x(r^2)
pi times r squared
Answer:
380 m^2 to the nearest whole number.
Step-by-step explanation:
That would be 3.14 * 11^2
= 380 .
The equation y2/100+x2/4 =1 represents an ellipse. Which points are the vertices of the ellipse? (−10, 0) and (10, 0) (−2, 0) and (2, 0) (0, −10) and (0, 10) (0, −2) and (0, 2)
The vertices of the ellipse (10, 0), (-10, 0), (0, 10), and (0, -10) can be determined using the center and major axes of the ellipse.
Explanation:The vertices of the ellipse are at (10, 0), (-10, 0), (0, 10), and (0, -10). To find the vertices of an ellipse, you use the major and minor axes that pass through the center of the ellipse. In this case, the center is (4.619, 5.425), and the major axes are inclined at an angle of 128° 51' to the x-axis.
What is the product of (3a + 2)(4a2 - 2a + 9)?
12a3 - 2a + 18
12a + 6a +9
1203 - 6a2 + 23a + 18
12a3 + 2a + 23a + 18
To find the product of two expressions, we use the distributive property and multiply each term from the first expression with each term from the second expression, then combine the like terms.
The product of[tex](3a + 2)(4a^2 - 2a + 9) is 12a^3 - 6a^2 + 23a + 18.[/tex]
To find the product of two binomials, you can use the distributive property. In this case, you multiply each term in the first binomial, 3a and 2, by each term in the second binomial, 4a^2, -2a, and 9, and then combine like terms.
[tex](3a + 2)(4a^2 - 2a + 9) = 3a * 4a^2 + 3a * (-2a) + 3a * 9 + 2 * 4a^2 + 2 * (-2a) + 2 * 9[/tex]
Now, perform the multiplications:
[tex]12a^3 - 6a^2 + 27a + 8a^2 - 4a + 18[/tex]
Combine like terms:
[tex](12a^3 - 6a^2) + (27a - 4a) + 1812a^3 - 6a^2 + 23a + 18[/tex]
So, the product of[tex](3a + 2)(4a^2 - 2a + 9)[/tex]is indeed[tex]12a^3 - 6a^2 + 23a + 18.[/tex]
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Find the x-intercepts of the parabola with
vertex (-3,-14) and y-intercept (0,13).
Write your answer in this form: (x1,y1),(X2,y2).
If necessary, round to the nearest hundredth.
Answer:
(-0.84, 0) and (-5.16, 0).
Step-by-step explanation:
Two cylinders with different radii have the same
volume.
Which statement is true?
A.
The bases of the two cylinders must have the
same areas.
B.
The cylinder with the smaller radius must be
taller.
C.
The cylinder with the larger radius must be
taller.
D.
The heights of the two cylinders must be
equal.
A triangle ABC has two side lengths of 28 ft. and 24 ft. If angle C is 91°, what's the measurement of angle B?
Answer:
B = 58.9
Step-by-step explanation:
We are given that a triangle ABC has two side lengths of 28 ft. and 24 ft. with angle C measuring 91°. We are to find the measure of angle B.
AB = 28 ft
AC = 24 ft
For this, we will use the sine formula:
[tex]\frac{sin B}{24} = \frac{sin91}{28}[/tex]
[tex]sin B = \frac{sin91 \times 24}{28}[/tex]
[tex] sin B = 0 . 8 5 7 [/tex]
[tex] B = sin' 0 . 8 5 7 [/tex]
B = 58.9
Help me I need to pass so I can go on to the next thing plz someone help me
Answer:
i cant see the picture
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
The scale factor is the ratio of the corresponding sides of the image to the original, that is
scale factor = [tex]\frac{CA'}{CA}[/tex] = [tex]\frac{4+16}{4}[/tex] = [tex]\frac{20}{4}[/tex] = 5
What is -a^-2 if a = -5? (PLEASE HELP WILL MARK BRAINLIEST!!!)
Answer:
-1/25
Step-by-step explanation:
-a^-2
-(-5)^-2
=-1/25
Solve: In 2x + In 2 =0
Answer:
x = [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
Using the rules of logarithms
• log x + log y ⇔ log(xy)
• [tex]log_{b}[/tex] = n ⇔ x = [tex]b^{n}[/tex]
Given
ln 2x + ln 2 = 0
ln(2x × 2) = 0
ln 4x = 0
4x = [tex]e^{0}[/tex] = 1 ( divide both sides by 4 )
x = [tex]\frac{1}{4}[/tex]
A hockey goalie blocks 75% of shots at the goal. How many shots can the goalie predict she or he will block in 75 tries
Answer:
56
Step-by-step explanation:
75% of 75 tries = 0.75×75 = 56.25
Rounding, he can expect to block 56 shots.
Use the property of exponents to rewrite the expression
(-4qr)(-4qr)(-4qr)(-4qr)
Answer:
(-4qr)^4
Step-by-step explanation:
(-4qr)(-4qr)(-4qr)(-4qr)
There are 4 sets of -4qr being multiplied together
(-4qr)^4
7. If the value of x varies directly with the value of y, and x = 3 when y = 21. What is the valu
y, and x = 3 when y = 21. What is the value of x when y =
105?
Answer:
15
Step-by-step explanation:
Because x=y÷7
i.e,105÷7=15
Rebecca has 45 coins, all nickels and dimes. The total value of the coins is $3.60. How many
of each type of coin does Rebecca have?
Answer:
Rebecca has 18 nickels and 27 dimes
Step-by-step explanation:
Let x be the number of nickels Rebecca has, then 45-x is the number of dimes she has.
The total value of Rebecca's coins is $3.60.
1 nickel - 5 cents
x nickels - 5x cents
1 dime - 10 cents
45-x dimes - 10(45-x) cents
Total x nickels and 45-x dimes is 5x+10(45-x) cents that is $3.60=360 cents. So,
5x+10(45-x)=360
5x+450-10x=360
5x-10x=360-450
-5x=-90
5x=90
x=18
45-x=45-18=27
Which value of x is a solution of the inequality?
4x+7≥35
x = 6
x = 7
x = 3
x = 0
Answer:
x = 7
Step-by-step explanation:
Just try all the choices and see which one gives a valid answer
4x+7≥35
x = 6 : 4 (6) + 7 = 31 is NOT ≥35 (not valid)
x = 7 : 4 (7) + 7 = 35 IS ≥35 (valid) (ANSWER)
x = 3 : 4 (3) + 7 = 19 is NOT ≥35 (not valid)
x = 0 : 4 (0) + 7 = 7 is NOT ≥35 (not valid)
Answer:
x = 7
Step-by-step explanation:
Just try all the choices and see which one gives a valid answer
4x+7≥35
x = 6 : 4 (6) + 7 = 31 is NOT ≥35 (not valid)
x = 7 : 4 (7) + 7 = 35 IS ≥35 (valid) (ANSWER)
x = 3 : 4 (3) + 7 = 19 is NOT ≥35 (not valid)
x = 0 : 4 (0) + 7 = 7 is NOT ≥35 (not valid)
Find measure of angle A
Round to the nearest degree
To solve this question, we must use the cosine rule:
cos(A) = (b^2 + c^2 - a^2)/2bc, where A is the angle you want to find, a is the side opposite that angle, and b and c are the other two sides of the triangle.
Given that we know that a = 6, b = 12, c = 14, we can substitute these values into the formula to get:
cos(A) = (12^2 + 14^2 - 6^2)/2(12)(14)
cos(A) = (144 + 196 - 36)/336
cos(A) = 304/336
cos(A) = 19/21
A = cos-1(19/21)
A = 25° (to the nearest degree)
The teacher tells the class the highest marks obtained by a student in her class is twice the lowest marks plus 7 . the highest score is 87. what is the lowest score? (pls tell with example and formula) thanks! (i am in grade 7)!
Answer:
40
Step-by-step explanation:
highest=2(lowest)+7
Replace the variables here:
87=2(lowest)+7
minus 7 on both sides
80=2(lowest)
divide both sides by 2
40=lowest
eh best describes the range of the function
Which best describes the range of the function f(x)=2(1/4)x
after it has been reflected over the y-axis?
Answer:
(0,∞)
Step-by-step explanation:
The problems tells us to find the range of the function
f(x)=2*(1/4)^x
after it has been reflected over the y-axis
This means
g(x) = 2*(1/4)^(-x)
To quickly find the answer, we can plot the equation and examine the range in the graph.
The range of both functions is the same
(0,∞)
See attached picture
Which statement best describes a square?
A. A special rectangle that has four right angles
B. A special trapezoid that has four sides of equal length
C. A special rectangle that has four sides of equal length
D. A special trapezoid that has four right angles
Answer:
I believe its B
I hope this helped :)
option C.
The statement that best describes a square is: A special rectangle that has four sides of equal length. This statement aligns with the definition of a square within the field of geometry, where a square is understood as a type of rectangle with all sides being the same length. Therefore, the correct answer is C. A special rectangle that has four sides of equal length.
A square indeed has four right angles, similar to a rectangle. By extension, it has congruent opposite sides and equal angles, but the defining feature that differentiates a square from other rectangles is the fact that all four sides are of equal length. The concept of rectangles forming squares can be seen in the given reference, implying that equal rectangles can be arranged to form a square - a concept important in understanding how a square is a special case of a rectangle.
Question 6 (5 points)
What is the slope of the line through (–4, 3) and (5, 3)?
Question 6 options:
a)
undefined
b)
0
c)
1
d)
9
[tex]\bf (\stackrel{x_1}{-4}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{3}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{3-3}{5-(-4)}\implies \cfrac{0}{5+4}\implies \cfrac{0}{9}\implies 0[/tex]
Answer:
b 0
Step-by-step explanation:
To find the slope between 2 points
m= (y2-y1)/(x2-x1)
= (3-3)/(5--4)
= (3-3)/(5+4)
= 0/9
=0
The slope is 0
What will be the coordinates of vertex A of the image?
Answer:
(1.0)
Step-by-step explanation:
we know that
The scale factor of the dilation is 0.25 ----> given problem
The coordinates of point A(-5,-3) and F(3,1)
step 1
Find the x-coordinate of point A'
The horizontal distance between A and F is equal to
AFx=3-(-5)=8
The horizontal distance after dilation between A'F is equal to
A'F=0.25*8=2
so
the x-coordinate of vertex A' is equal to the x-coordinate of F minus the horizontal distance after dilation A'F
A'x=3-2=1
step 2
Find the y-coordinate of point A'
The vertical distance between A and F is equal to
AFy=1-(-3)=4
The vertical distance after dilation between A'F is equal to
A'Fy=0.25*4=1
so
the y-coordinate of vertex A' is equal to the y-coordinate of F minus the vertical distance after dilation A'F
A'y=1-1=0
therefore
The coordinates of vertex A of the image is (1.0)
Find the area of this figure
Answer:
22.34 km²
Step-by-step explanation:
Here we have a circle whose diameter is 5 1/3 km. As an improper fraction, that's 16/3 km. Half that, or 8/3 km, is the radius.
The area of a circle is A = πr², where r is the radius.
In this case, the area is A = π(8/3 km)², or (64/9)π km², or 22.34 km² (same as first answer choice).
Which functions could represent a reflection over the y axis of the given function
Answer:
g(x) = 1/2*(4)^(–x) and
g(x) =1/2*(1/4)^(x)
Please, see attached picture.
Step-by-step explanation:
Your full question is attached in the picture below
To easily solve this problem, we can graph each equation and see, which one represents a reflection of the function over the y axis.
See, second image.
The answers are
g(x) = 1/2*(4)^(–x) and
g(x) =1/2*(1/4)^(x)
What is the measure of angle D?
52o
54o
57o
126o
For a given trapezium ABCD, measure of angle [tex]D = 52\°[/tex].
What is an angle?" An angle is defined as when two rays meet at a common point known as vertex."
According to the question,
Given trapezium ABCD,
Measure of angle [tex]BAD= 128\°[/tex]
Measure of angle [tex]ABC= 126\°[/tex]
Measure of angle [tex]BCD= 54\°[/tex]
Sum of all the interior angles in a trapezium is equal to [tex]360\°[/tex].
Therefore,
[tex]\angle ABC + \angle BCD +\angle CDA + \angle DAB = 360\°\\\\\implies 126\°+54\°+ \angle CDA + 128\°=360\°\\\\\implies \angle CDA = 360\° - 308\°\\\\\implies \angle CDA = 52\°[/tex]
Hence, Option (A) is the correct answer.
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Factor the polynomial expression x6 – x3 – 20
Answer:
x6 − x3 − 20 = (x3)2 − x3 − 20 = (x3 + 4)(x3 − 5)
Step-by-step explanation:
In this trinomial, the exponent of the first term, 6, is double the exponent in the second term, 3. And, the third term contains no variables. So, we can factor the expression as we would a quadratic, but treating x3 as if it were x:
Answer:
(x³ - 5)(x³ + 4)
Step-by-step explanation:
Consider the factors of the constant term (- 20) which sum to give the coefficient of the x³ term (- 1)
The factors are - 5 and + 4, since
- 5 × 4 = - 20 and - 5 + 4 = - 1, hence
[tex]x^{6}[/tex] - x³ - 20 = (x³ - 5)(x³ + 4)
Please please help me
Answer:
multiply 2/5 by 4
Step-by-step explanation:
When we divide fractions, we use copy dot flip
2/5 ÷ 1/4
Copy dot flip
2/5 * 4/1
For this case we must find the quotient of the following expression:
[tex]\frac {\frac {2} {5}} {\frac {1} {4}} =[/tex]
Applying double C we have:
[tex]\frac {2 * 4} {5 * 1} = \frac {8} {5}[/tex]
This is equivalent to multiplying the following: [tex]\frac {2} {5} * 4 = \frac {8} {5}[/tex]
Answer:
OPTION A
Substitute t=3 and t=5 to determine if the two expressions are equivalent. 4(t+3) 4t+12 Which statements are true? Check all that apply. The value of both expressions when t=3 is 32. The two expressions are not equivalent. The value of both expressions when t=5 is 15. The value of both expressions when t=5 is 23. The two expressions are equivalent. The value of both expressions when t=3 is 24.
Answer:
Answers are:
The value of both expressions when t=3 is 32.
The the value of both expressions when t=3 is 24.
The two expressions are equivalent.
Step-by-step explanation:
These answers are 100% correct. I just finished my quiz. I hope this helps
Please mark me brainlyest :)
The correct statements are that, both the equations are equivalent when the value of t is taken 3 and The value of both the equations is 24 when t is taken as 3.
So, the correct options that match the statement above are E and F.
Simplification of expressions. Taking the value of t as 3 in both the equations, we get,[tex]4(t+3)\\\\4(3+3)\\\\\\4\ \rm x\ 6=24[/tex]Now, in the second expression, [tex]4t+12\\\\4\ \rm x\ 3+12\\\\12+12=24[/tex] Whereas, when the value of t is taken as 5 the values obtained are as 23 and 32 respectively.Hence, the correct options are E and F that the equations are of both the values when t is 3 is obtained as 24. And both the expressions are equivalent when t is taken as 3.
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What’s 0.85 in simplest form
Answer:
17/20
Step-by-step explanation:
To find the simplest form of 0.85 you need to turn it into a fraction.
To turn it into a fraction you put 85 over 100 since 0.85 is in the hundredths place.
85/100 can be simplified to 17/20 because 85/5 is 17 and 100/5 is 20
Answer:
17/20
Step-by-step explanation:
The simplest form of a number is a fraction. .85 as a fraction is 85/100. Simplifying this into 17/20 puts it into its simplest form.