Answer:
Step-by-step explanation:
If the second angle's measure is based on the first angle's measure, and the third angle's measure is also based on the first angle's measure, then the first angle is the main angle. We will call that x.
1st angle: x
2nd angle: x + 20%
3rd angle: x - 20%
By the Triangle Angle-Sum Theorem, all those angles will add up to 180, so:
x + (x + 20%) + (x - 20%) = 180 and
3x = 180 so
x = 60. That means that
2nd angle: 60 + (.2*60) which is
60 + 12 = 72 and
3rd angle: 60 - (.2*60) which is
60 - 12 = 48. Let's check those angles. If
∠1 = 60
∠2 = 72
∠3 = 48,
then ∠1 + ∠2 + ∠3 = 180 and
60 + 72 + 48 does in fact equal 180, so you're done!
Use the elimination method to solve the system of equations. Choose the
correct ordered pair.
6x+2y = 8
12x + y = 22
O A. (-1,1)
O B. (4,-4)
O C. (2,-2)
O D. (-3,3)
Answer:
A. (-1,1)
Step-by-step explanation:
6x+2y = 8
-2y =-2
6x=6
6x=6
X=1
Select the correct answer.
What is the value of this expression when g= -3.5?
8-[2g-5]
OA.
20
OB.
10
OC. 6
OD.
-4
Answer:
A. 20
Step-by-step explanation:
We are given the expression:
8-(2g-5)
and asked to find the value of the expression when g=-3.5. Therefore, we must plug -3.5 in for g.
8- (2(-3.5)-5)
Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
First, solve inside the parentheses. Begin by multiplying 2 and -3.5
8-(-7-5)
Next, subtract 5 from -7
8-(-12)
Finally, subtract -12 from 8.
8+12
20
The value of the expression 8-(2g-5) when g=-3.5 is 20. Therefore A. 20 is correct.
For the rectangle with given area of 10x^2+11x+3 determine the binomial factors that describes the dimensions.
PLEASE HELP!!! WILL MARK BRAINLIEST!!!
=========================================
Explanation:
We could use the AC factoring method here. Multiply the first coefficient (10) with the last term (3) to get 10*3 = 30.
We need to find factors of 30 that add to 11
1+30 = 31
2+15 = 17
3+10 = 13
5+6 = 11
we have found the pair of factors that add to 11. So we'll break the 11x into 5x+6x and then use factor by grouping method
10x^2 + 11x + 3
10x^2 + 5x + 6x + 3
(10x^2 + 5x) + (6x + 3)
5x(2x + 1) + 3(2x + 1)
(5x+3)(2x+1)
We see the two factors are 5x+3 and 2x+1.
To check the answer, use either the box method, distribution, or FOIL rule to expand out (5x+3)(2x+1) and you should get 10x^2+11x+3 again.
--------------------------------
As an alternative, you can solve 10x^2+11x+3 = 0 through any method you prefer (graphing, completing the square, quadratic formula). The quadratic formula is the best option as it works for any quadratic. The two solutions you should get are x = -3/5 and x = -1/2
Using x = -3/5 and x = -1/2, we can do the following
x = -3/5 becomes 5x = -3 after multiplying both sides by 5, then you add 3 to both sides to get 5x+3 = 0x = -1/2 becomes 2x = -1 after multiplying both sides by 2, and then turns into 2x+1 = 0 after adding 1 to both sidesNote how we have the 5x+3 and 2x+1 as found in the section above. At this point we can stop as we found the factors needed. I'm using the zero product property which says that if A*B = 0, then either A = 0 or B = 0.
Find the area of the shaded region
Answer:
[tex] \mathsf{ {5x}^{2} + 28x + 21}[/tex]
Option A is the right option.
Step-by-step explanation:
Let's find the area of large rectangle:
[tex] \mathsf{(3x + 6)(2x + 4)}[/tex]
Multiply each term in the first parentheses by each term in the second parentheses
[tex] \mathsf{ = 3x(2x + 4) + 6(2x + 4)}[/tex]
Calculate the product
[tex] \mathsf{ = 6 {x}^{2} + 12x + 12x + 6 \times 4}[/tex]
Multiply the numbers
[tex] \mathsf{ = 6 {x}^{2} + 12x + 12x + 24}[/tex]
Collect like terms
[tex] \mathsf{ = {6x}^{2} + 24x + 24}[/tex]
Let's find the area of small rectangle
[tex] \mathsf{(x - 3)(x - 1)}[/tex]
Multiply each term in the first parentheses by each term in the second parentheses
[tex] \mathsf{ = x( x - 1) - 3(x - 1)}[/tex]
Calculate the product
[tex] \mathsf{ = {x}^{2} - x - 3x - 3 \times ( - 1)}[/tex]
Multiply the numbers
[tex] \mathsf{ = {x}^{2} - x - 3x + 3}[/tex]
Collect like terms
[tex] \mathsf{ = {x}^{2} - 4x + 3}[/tex]
Now, let's find the area of shaded region:
Area of large rectangle - Area of smaller rectangle
[tex] \mathsf{6 {x}^{2} + 24x + 24 - ( {x}^{2} - 4x + 3)}[/tex]
When there is a ( - ) in front of an expression in parentheses, change the sign of each term in the expression
[tex] \mathsf{ = {6x}^{2} + 24x + 24 - {x}^{2} + 4x - 3}[/tex]
Collect like terms
[tex] \mathsf{ = {5x}^{2} + 28x + 21}[/tex]
Hope I helped!
Best regards!
what is 2-3+5÷16?
please give the answer by solving it
Answer:
HOPE IT HELPS. PLEASE MARK IT AS BRAINLIEST
Answer:
Step-by-step explanation:
2-3+5/16 = -1+5/16 = 4/16 = 1/4 = 0.25
hope it helps
find the slope of this line.
Answer:
slope = [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 2) and (x₂, y₂ ) = (3, 3) ← 2 points on the line
m = [tex]\frac{3-2}{3-0}[/tex] = [tex]\frac{1}{3}[/tex]
Answer:
Slope=1/3
Step-by-step explanation:
we kown,
m=y2-y1/x2-x1
then you should take two point where line should be passing through these two pionts.
In graph you can see that (0,2) and(-3,1) are passing points of the line.
Here, x1=0
x2= -3
y1=2
y2=1
Now,
m= 1-2/ -3-0
= -1/ -3
=1/3
So, The slope of the line is 1/3.
I hope this will be helpful for you.
trigonometry plz... helllppp thx
Answer:
90°
I think.
Step-by-step explanation:
Cause... As you see it's a right angle triangle... And also when you ad 6+15 u get 90...
I
Question in screenshot answer must be in cm
Answer:
30.5 cm
Step-by-step explanation:
0 < h ≤ 10 ⇔ Midpoint = 5
10 < h ≤ 20 ⇔ Midpoint = 15
20 < h ≤ 30 ⇔ Midpoint = 25
30 < h ≤ 40 ⇔ Midpoint = 35
40 < h ≤ 50 ⇔ Midpoint = 45
50 < h ≤ 60 ⇔ Midpoint = 55
⇒ Multiply each corresponding midpoint with it's frequency
(5 × 1) + (15 × 4) + (25 × 7) + (35 × 2) + (45 × 3) + (55 × 3) = 610
⇒ Divide the total of 610 by the frequencies added together
610 ÷ (1 + 4 + 7 + 2 + 3 + 3) = 610 ÷ 20 = 30.5
Suppose we have four integers, no two of which are congruent $\pmod 6$. Let $N$ be the product of the four integers. If $N$ is not a multiple of $6$, then what is the remainder of $N$ when $N$ is divided by $6$?
Answer:
4
Step-by-step explanation:
Given:
A, B, C, D have distinct positive values for mod 6
A (mod 6) = 1
B (mod 6) = 2
C (mod 6) = 4
D (mod 6) = 5
Each mod 6 value cannot be a zero since the product ABCD is not a multiple of 6.
Furthermore, in order that ABCD mod 6 > 0, we cannot have a residue equal to 3, else the product with a residue 2 or 4 will make the product a multiple of 6.
Thus the only positive residues can only be 1,2,4,5
A*B*C*D (mod 6) > 0 = 1*2*4*5 (mod 6) = 4
What is the simplified form of this expression?
(-3x2 + 2x − 4) + (4x2 + 5x + 9)
Answer:
[tex]\large \boxed{\sf \ \ x^2 + 7x + 5 \ \ }[/tex]
Step-by-step explanation:
[tex]\mathrm{\sf (-3x^2 + 2x -4) + (4x^2 + 5x + 9)}[/tex]
Remove brackets.
[tex]\large{\sf -3x^2 + 2x -4 + 4x^2 + 5x + 9}[/tex]
Group like terms.
[tex]\large{\sf -3x^2 + 4x^2 + 2x + 5x + 9 -4}[/tex]
Combine like terms.
[tex]\large{\sf x^2 + 7x + 5}[/tex]
The simplified form of this expression (-3x² + 2x − 4) + (4x² + 5x + 9) is determined as x² + 7x + 5.
What is the simplified form of this expression?To simplify the given expression, we need to combine like terms.
The given expression;
(-3x² + 2x − 4) + (4x² + 5x + 9)
Let's start by combining the terms with the same degree of x:
Combine the x² terms:
(-3x² + 4x²) + 2x - 4 + 5x + 9
Simplify further;
x² + 7x + 5
Thus, the simplified form of this expression (-3x² + 2x − 4) + (4x² + 5x + 9) is determined as x² + 7x + 5.
Learn more about simplification here: https://brainly.com/question/28008382
#SPJ2
What is the determinant of the coefficient matrix of the system –7 –2 –1 0
Answer:
0
Step-by-step explanation:
Please check attachment for complete solution
Answer:
D. 0
Step-by-step explanation:
last option
Please answer this ASAP. The question is down below. Thank you!
Answer:
[tex]y = .5x^2 -2x -5[/tex]
Step-by-step explanation:
Well we can start by seeing if the parabola is the same width by comparing it to its parent function ( y = x^2 )
In y = x^2 the 2nd lowest point is just up 1 and right 1 away from the vertex.
This is not true for our parabola.
So we can widen it by to the desidered width by making the x^2 into a .5x^2.
So far we’ve got y = .5x^2
Now the parabola y intercept is at -5.
So we can add a -5 into the equation making it.
y = .5x^2 - 5
Now for the x value.
So we can find the x value by seeing how far away the parabola is from from the y axis.
So the x value is -2x.
So the full equation is [tex]y = .5x^2 -2x -5[/tex]
Look at the image below to compare.
Answer: [tex]Vertex: y=\dfrac{1}{2}(x-2)^2-7[/tex]
[tex]Standard: y=\dfrac{1}{2}x^2-2x-5[/tex]
Transformations: vertical shrink by a factor of 1/2,
horizontal shift 2 units to the right,
vertical shift 7 units down.
Step-by-step explanation:
Vertex form: y = a(x - h)² + k
Standard form: y = ax² + bx + c
Given: Vertex (h, k) = (2, -7), the y-intercept (0, c) = (0, -5)
Input those values into the Vertex form to solve for the a-value
-5=a(0 - 2)² - 7
2 = a(- 2)²
2 = 4a
[tex]\dfrac{1}{2}=a[/tex]
a) Input a = 1/2 and (h, k) = (2, -7) into the Vertex form
[tex]\large\boxed{y=\dfrac{1}{2}(x-2)^2-7}[/tex]
b) You can plug in a = 1/2, c = -5, (x, y) = (2, -7) to solve for "b"
or
You can expand the Vertex form (which is what I am going to do):
[tex]y=\dfrac{1}{2}(x-2)^2-7\\\\\\y=\dfrac{1}{2}(x^2-4x+4)-7\\\\\\y=\dfrac{1}{2}x^2-2x+2-7\\\\\\\large\boxed{y=\dfrac{1}{2}x^2-2x-5}[/tex]
c) Use the Vertex form to describe the transformations as follows:
a is the vertical stretch (if |a| > 1) or shrink (if |a| < 1)h is the horizontal shift (positive is to the right, negative is to the left)k is the vertical shift (positive is up, negative is down)[tex]y=\dfrac{1}{2}(x-2)^2-7[/tex]
a = 1/2 --> vertical shrink by a factor of 1/2
h = 2 --> horizontal shift 2 units to the right
k = -7 --> vertical shift 7 units down
if amir joins indian army, he is courageous.
convert this into contrapositive statement
If Amir is not courageous, then he will not join the indian army.
Find the coordinates for the equation.
{y=-x^2+5
{-x+y=3
Answer:
I hope you will get help from these...
Question 1
52 + 2 × (9) + 6 =
Answer:
76Step-by-step explanation:
Use BODMAS rule:
B = Bracket
O = Of
D = Division
M = Multiplication
A = Addition
S = Subtraction
Now, let's Solve,
[tex]52 + 2 \times (9) + 6[/tex]
First, we have to multiply the numbers:
[tex] = 52 + 18 + 6[/tex]
Add the numbers:
[tex] = 76[/tex]
Hope this helps...
Good luck on your assignment...
Tucker was asked to solve the equation 5x + 3 = 6x + 1. He did not know if his first step should be to add 5 negative x-tiles, or 1 negative unit tile, to both sides. What advice would you give Tucker to help him decide on his first step?
Answer:
He should use the negative 1 unit tile.
Step-by-step explanation:
He should do this because in this equation you wish to isolate the variable on one side, and it would be better to first take away any constants. Afterwards, the variable would be next.
Answer: It does not matter which he does first. Either way, zero pairs will be created on both sides, which will isolate the variable to determine x. Adding the x-tiles and then the unit tile, or visa versa, will give the same solution.\
Explanation: that's what i put and i got it right
PLZZZZZ MARK ME BRAINIEST
can ya'll help me find x and y and how to do it. Thanks
Answer:
x = 904 and y = 18
Step-by-step explanation:
Let's start by calculating x
tan 32° =[tex]\frac{x}{15}[/tex] x = 15*tan 32° x =9.37 x≈ 9.4Let's use the pythagorian theorem to find y
x²+15² =y² 9.4²+15² = y² y = [tex]\sqrt{9.4^{2}+15^{2} }[/tex] y = 17.7 y ≈ 18Which transformation does not preserve orientation? A. rotation B. reflection across the y-axis C. dilation D. translation
-5x-2y=-6
Slope:
y-intercept:
Answer:
Slope = m = -5/2
Y-intercept = b = -3
Step-by-step explanation:
[tex]-5x-2y = -6[/tex]
Getting it in a slope - intercept form:
[tex]-2y = 5x+6\\Dividing \ both \ sides \ by \ -2\\y = \frac{-5x}{2} + (-3)\\y = \frac{-5x}{2} -3\\[/tex]
Comparing it wit the slope intercept equation [tex]y = mx+b[/tex] we get
Slope = m = -5/2
Y-intercept = b = -3
in a certain game, points you win are positive numbers and points you lose are negative numbers. What is the value of the series plays: win 8, lose 7, will 11, lose 2?
a -15
B -4
C 4
d 12
Answer:
4
Step-by-step explanation
+8 + (-7) + (+11) + (-2)= 4
The value of the series plays is 10.
--------------------------
In this question, we have to find the total amount of points, considering the number of points on each series.
Win 8: Add 8 points.Lose 7: Subtract 7 points.Win 11: Add 11 points.Lose 2: Subtract 2 points.--------------------------
The total is:
[tex]T = 8 - 7 + 11 - 2 = 1 + 9 = 10[/tex]
10 points.
A similar question is given at https://brainly.com/question/14350453
7
A section of a rectangle is shaded.
The area of the shaded section is 63 square units. What
is the value of x?
7
х
9 units
11 units
O 18 units
21 units
This question is incomplete. Please find attached to this solved question, the diagram required to solve this question.
Answer:
11 units
Step-by-step explanation:
The shaded portion of the rectangle forms the shape of a trapezium
The area of a trapezium = 1/2(a + b)h
From the diagram, we can see than x = b
a = 7 units
b = 7 units
Area of the trapezium = Area of the shaded portion = 63 square units
A = 1/2(a + b)h
63 = 1/2(7 + b)7
63 = 1/2(49 + 7b)
63 × 2 = 49 + 7b
126 - 49 = 7b
7b = 77
b = 77/7
b = 11 units
Since x = b, x = 11 units
The value of x is 11
Start by calculating the area (A) of the trapezoid using
[tex]A= 0.5 * (a + b)h[/tex]
Using the parameters from the complete question, we have:
[tex]63 = 0.5 * (7 + x) * 7[/tex]
Multiply both sides by 2
[tex]126 = (7 + x) * 7[/tex]
Divide both sides by 7
[tex]18 = 7 + x[/tex]
Subtract 7 from both sides
[tex]x = 11[/tex]
Hence, the value of x is 11
Read more about shaded areas at:
https://brainly.com/question/24579466
Danny drove to Yosemite Park from his home at 60 mph. on his trip home, his rate was 10 mph less and ...?
Answer: 300 mi.
Step-by-step explanation:
Let t be the time taken to drive to the park (at 60 mph)
Let t + 1 be the time taken to drive home from the part (at 50 mph)
Distance to the park = 60t
Distance from the park = 50(t + 1)
Obviously the distances should be the same so equate them.
60t = 50(t + 1)
60t = 50t + 50
10t = 50
t = 50/10
t = 5 hours
Now figure the distance. You can use either equation for the distance to or from the park:
60t = 60(5) = 300 miles
or
50(t+1) = 50(6) = 300 miles
The distance to or from the park will be 300 miles.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
Let assume t be the time taken to drive to the park (at 60 mph).
Let assume t + 1 be the time taken to drive home from the part (at 50 mph)
The Distance to the park = 60t
The Distance from the park = 50(t + 1)
Obviously the distances should be the same, so equate them;
60t = 50(t + 1)
60t = 50t + 50
10t = 50
t = 50/10
t = 5 hours
Now figure the distance. We can use either equation for the distance to or from the park:
60t = 60(5) = 300 miles
50(t+1) = 50(6) = 300 miles
Therefore, the distance to or from the park will be 300 miles.
Learn more about equations here;
https://brainly.com/question/10413253
#SPJ2
Please help fast! Brainliest will be given if correct :) Divide 32x3 + 48x2 − 40x by 8x
Answer:
4[tex]x^{2}[/tex]+6x-5
Step-by-step explanation:
Factor out 8x from the numerator.
Answer:38.4
Step-by-step explanation:
(32x3)+(48x2)-40x/8x
96+96-40x/8x
192-5x=0
192=5x
192/5=38.4
would someone please help me thank you very much * no fake answer *
Answer:
a = 1500
b = 0.97
Step-by-step explanation:
The equation we are modeling is ;
F(x) = ab^x
Now we have two parameters to fix.
These are the density and the annual percentage increase
We can substitute the value of 1500 for a and also make a corresponding substitution for b.
Now for b, the value to substitute is quite dicey.
3% = 3/100 = 0.03
To make any substitution, we need to subtract this value from 1 and that would be 0.97
So it is this 0.97 that we now raise x to for each of the number of years
PLS HELP ASAP Event A and event B are independent events. Given that P(B)=13 and P(A∩B)=16, what is P(A)?
Answer:
The probability of event A happening which is P(A) = 1/2
Step-by-step explanation:
To answer this question, we will have to make use of the mathematical formula for independent events.
Firstly, what do we mean by independent events?
Independent events are events that occur freely of each other. What this means is that the occurrence or non-occurrence of one of the events does not disturb the occurrence or non-occurrence of the other event.
Given that A and B are independent events, then mathematically;
P(A ∩ B) = P(A) P(B)
Now from the question, we know that We are to find P(A), inputing the values we have;
1/6 = P(A) * 1/3
P(A) = 1/6/1/3
P(A) = 1/2
If one plane is flying at 40mph. While another is flying at 100mph. They are 200 miles apart, how long will it take them to collide if they are going in the same direction
Answer:
1 and 3/7 hour
Step-by-step explanation:
Every hour they get 140 miles closer (100 + 40). So you divide 200 by 140 which gets you 1.42... or 1 and 3/7 of an hour.
Find the value of x.
x = 64°
Step-by-step Explanation
x = 1/2[(360° - 2*58°)-2*58°]
x = 1/2[(360° - 2*58°) - 2*58°]
x = 1/2[(360° - 116°) - 116°]
x = 1/2[244° - 116°]
x = 1/2[128°]
x = 64°
A man has 3 different suits, 4 different shirts and 5 different pairs of shoes. In how many different ways can this man wear a suit a shirt and a pair of shoes?
Answer:
60
Step-by-step explanation:
We want to find the number of ways to wear a suit, shirt, and pair of shoes.
Therefore, we can use the fundamental counting principal, which is: If there is x ways to do one thing, y ways to do another and z ways for another, then there are x * y * z ways to do all things.
Therefore, we must multiply the suits, shirts and shoes.
suits * shirts * shoes
The man has 3 different suits, 4 different shirts and 5 different pairs of shoes.
3 * 4 * 5
12 * 5
60
There are 60 different ways to wear a suit, shirt and pair of shoes.
the dimensions of a block of stamps are 30 cm wide by 20 cm high. the same number of stamps could also have been arranged in a block 24 cm wide. How high would this second block be?
Answer:The hight of such a stamp block would have to be 26 cm high by 24 cm wide
Step-by-step explanation: The way that i got my answer was by using this equation A+B=C
1.) 30cm+20cm=50cm
2.) 24cm+x=50cm
3.)50cm-24cm=x
4.)26cm=x
Simplify the following:
1.√7 × √7
2.√18 × √2
3.√45
4.√50/5
5.2√2 × 4√5
6.√48 - √12
7.(2-√3) (1+√3))
Answer:
1. 7
2. 6
[tex]3. 3\sqrt{5}[/tex]
4?
5. [tex]8\sqrt{10}[/tex]
6.[tex]5\sqrt{3}[/tex]
7. [tex]-1+\sqrt{3}[/tex]
Step-by-step explanation:
1. [tex]\sqrt{7} *\sqrt{7} =\sqrt{49}=7[/tex]
2. [tex]\sqrt{18}*\sqrt{2} =\sqrt{36}=6[/tex]
3.[tex]\sqrt{45}=\sqrt{9^{2}*5 }=3\sqrt{5}[/tex]
4. here there are two cases
[tex]\sqrt{\frac{50}{5} }=\sqrt{10}[/tex]
[tex]\frac{\sqrt{50} }{5} =\frac{5\sqrt{2} }{5} =\sqrt{2}[/tex]
5. [tex]2\sqrt{2} *4\sqrt{5} =8\sqrt{10}[/tex]
6. [tex]\sqrt{48}- \sqrt{12} =4\sqrt{3} -2\sqrt{3} =2\sqrt{3}[/tex]
7. [tex](2-\sqrt{3} )(1+\sqrt{3} )=2+2\sqrt{3}-\sqrt{3} -3=-1+\sqrt{3}[/tex]