Given:
Triangle ABC is right angled at A.
[tex]m\angle B=(5x+7)^\circ[/tex]
[tex]m\angle C=(4x+29)^\circ[/tex]
To find:
The degree measure of each angle in the triangle.
Solution:
According to the given information,
[tex]m\angle A=90^\circ[/tex]
[tex]m\angle B=(5x+7)^\circ[/tex]
[tex]m\angle C=(4x+29)^\circ[/tex]
Now,
[tex]m\angle A+m\angle B+m\angle C=180^\circ[/tex] (Angle sum property)
[tex]90^\circ+(5x+7)^\circ+(4x+29)^\circ=180^\circ[/tex]
[tex](9x+126)^\circ=180^\circ[/tex]
[tex]9x+126=180[/tex]
[tex]9x=180-126[/tex]
[tex]9x=54[/tex]
Divide both sides by 9.
[tex]x=\dfrac{54}{9}[/tex]
[tex]x=6[/tex]
Now,
[tex]m\angle A=90^\circ[/tex]
[tex]m\angle B=(5(6)+7)^\circ[/tex]
[tex]m\angle B=37^\circ[/tex]
[tex]m\angle C=(4(6)+29)^\circ[/tex]
[tex]m\angle C=53^\circ[/tex]
Therefore, the measures of ∠A, ∠B, ∠C are 90°, 37°, 53° respectively.
Answer:
(6×-5)°× (×+9)°w(4×)°y
A square target is shown. A dart is dropped randomly onto the target. The dart is equally kely to hit any spot on the target
18 cm
3 cm
18 cm
3 cm
not drawn to scale
What is the probability that the dart will hit a spot in the shaded square?
och
D
Probability helps us to know the chances of an event occurring. The probability that the dart will hit a spot in the shaded square is 0.028.
What is Probability?Probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
The area of the dark area = 3cm × 3cm = 9cm²
The area of the white area = (18cm×18cm)-(3cm×3cm) = 315cm²
Now, the probability that the dart will hit a spot in the shaded square will be,
Probability = 9 / 315 = 0.028
Hence, the probability that the dart will hit a spot in the shaded square is 0.028.
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answer these 2 questions if ur smart?!?!?
1. (4x+5y)(2x-3y)+3xy= 4x*2x-4x*3y+5y*2x-5y*3y+3xy=8x^2-12xy+10xy-15y^2+3xy= 8x^2+xy-15y^2
2. (2x^2+3)(4x+5)-8x(x^2-2)=2x^2*4x+2x^2*5+3*4x+3*5-8x*x^2+8x*2=
=8x^3+10x^2+12x+15-8x^3+16x=
=10x^2+28x+15
Answer:
1. [tex]8x^2+xy-15y^2[/tex] 2. [tex]10x^2 + 28x + 15[/tex]
Step-by-step explanation:
For Question 1:
[tex](4x + 5y) (2x - 3y) + 3xy[/tex]
= [tex]8x^2 - 12xy + 10xy - 15y^2 + 3xy[/tex]
[tex]=8x^2+xy-15y^2[/tex] (cannot simplify any further)
For Question 2:
[tex](2x^2 + 3)(4x +5) - 8x(x^2 -2)[/tex]
[tex]=8x^3 + 10x^2 + 12x + 15 - 8x^3 + 16x[/tex]
[tex]=10x^2 + 28x + 15[/tex] (cannot simplify any further)
Simplify: -x - 4x + 2
Answer:
5x+2
Step-by-step explanation:
:)
Answer:
16x little 2 on top - 40xy + 25y little 2 on top
Step-by-step explanation:
Please help!!!
composition of functions
g(x)=2x-5 h(x)=x^2-2
find g(h(-8))
Answer:
g(h(-8)) = 119
Step-by-step explanation:
Given
g(x)=2x-5h(x)=x²-2To determine
g(h(-8)) = ?In order to determine g(h(-8)), we need to determine h(-8) first
substituting x = -8 in h(x)=x²-2
h(-8) = (-8)² - 2
h(-8) = 64 - 2
h(-8) = 62
so
g(h(-8)) = g(62)
now substituting x = 62 in g(x)=2x-5
g(62)=2(62)-5
g(62) = 124 - 5
g(62) = 119
so
g(h(-8)) = g(62) = 119
Therefore,
g(h(-8)) = 119HELPP ME I JUST HAVE A 67 IF I GET THIS ONE WORN GI HAVE A 50 AS A GRADE PLEASEE
Answer:
4,000 cm
Step-by-step explanation:
10,000 x 0.4
just do 10,000 x 4
(40,000)
and then move the decimal point one space to the left
(4,000)
The sum of four consecutive integers is -26. What are the integers? A book has pases.
Answer:
In the same manner, the third integer can be represented as n + 2 {n + 2} n+2 and the fourth integer as n + 3 {n + 3} n+3. We can then translate “the sum of four consecutive integers is 238” into an equation.
Step-by-step explanation:
Jake said he can find 630 ÷ 10 by taking the 0 off of 630 to get 63. Jake finds 35.270 ÷ 10 using the same method and gets 35.27. Use the drop-down menus to complete the statement about why Jake is correct or incorrect.
Answer:
Jake is incorrect with his methodology for solving these problems
Step-by-step explanation:
Jake is incorrect with his methodology for solving these problems. This is because dividing a number by 10 requires moving the decimal point one digit to the left. When dividing 630 by 10, removing the zero works because by moving the decimal one digit to the left we would simply drop the zero and the decimal would not be needed leaving the answer as 63. However, this does not work on numbers that already have a decimal such as 35.270. This number divided by 10 would be 3.527 but simply removing the 0 like Jake states would give us the incorrect answer of 35.27
Answer:
Step-by-step explanation:
tamara has completed 60% of her practice time for the track meet. If she is expected to practice for 18h, how long has she already practiced?
Answer:
10h and 48min
Step-by-step explanation:
60*18=1080
1080/100=10.8
so 10.8h which means 10 hours and 48 min
Members of a softball team raised $1648.50 to go to a tournament. They rented a bus for $896.50 and budgeted $47 per player for meals. Write and solve an equation which can be used to determine xx, the number of players the team can bring to the tournament.
Answer:
The number of players the team can bring to the tournament is 16.
Step-by-step explanation:
With the information provided, the equation would express that the total cost to go to the tournament is equal to the price to rent a bus plus the result of multiplying the amount per player for meals for the number of players.
Total cost=896.50+47x, where:
x is the number of players
Now, as you know that the softball team raised $1,648.50 to go to a tournament, you can replace the total cost with this number and solve for x:
1,648.50=896.50+47x
1,648.50-896.50=47x
752=47x
x=752/47
x=16
According to this, the answer is that the number of players the team can bring to the tournament is 16.
Answer:
Equation: 47x + 896.5 = 1648.5
X= 16
Step-by-step explanation:
Delta Math
the graph of y=f(x) is shown below. what are all of the real solutions of f(x)=0
All real solutions of the function y=f(x) are x = -4 and x = 4
What is a solution ?Suppose that we've a function y = f(x) such that f(x) is quadratic.
When y = 0, then the values of x for which f(x) = 0 is called solution of quadratic equation f(x) = 0. These solution gives values of x, and when we plot x and f(x), we'd see that the graph intersects the x-axis at its solution points.
we are Given graph in the attachment represents the function y = f(x)
Since Real solutions of the function shows all the points where the curve of the graph either touches or crosses the x-axis.
Thus the graph of the function touches and crosses at x = -4 and x = 4
Therefore, all real solutions of the function y=f(x) are x = -4 and x = 4
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what is the explicit rule for 64,67,70,73,76
Answer: The answer is 3.
Step-by-step explanation:
64+3=67 67+3=70 Etc.
Given the equation log2x + log2(x – 7) = 3, solve for x.
Answer:
x∈{-1, 8}Step-by-step explanation:
[tex]\log_2x +\log_2(x-7) = 3\\\\\log_2[x\cdot(x-7)]= 3\log_22\\\\\log_2(x^2-7x)= \log_22^3\\\\x^2-7x=2^3\\\\x^2-7x-8=0\quad\implies \quad a=1\,,\ \ b=-7\,,\ \ c=-8 \\\\x=\dfrac{-(-7)\pm\sqrt{(-7)^2-4\cdot1\cdot(-8)}}{2\cdot1}= \dfrac{7\pm\sqrt{49+32}}{2} =\dfrac{7\pm\sqrt{81}}{2}\\\\x=\dfrac{7+9}2=8\qquad\vee\qquad x=\dfrac{7-9}2=-1[/tex]
If he starts at 1 and jumps 3 units to the left, then where is he on the number line? How far away from zero is he? (explain how you got your answer )
Answer:
he is at -3
Step-by-step explanation:
On a number chart, If he goes 3 left hes going 3 negative. So it would be -3
I hope this helps!
Answer:
-2
Step-by-step explanation:
You subtract 3 from one
First jump 0
Second jump -1
Third Jump -2
Need help on this asap please
Answer:
the second one
so B
Step-by-step explanation:
Answer:
3.15=315% is true
Step-by-step explanation:
The last one D is true
I hope this helps. Best of luck
Solve; 2304 divided by 6
Answer:
your answer is going to be 384
factor x^3 +7x^2−5x−35
Answer:
(x^2-5)(x + 7)
Step-by-step explanation:
Here, we want to factorize the given expression
That would be;
x^2(x + 7) - 5(x + 7)
= (x^2-5)(x+ 7)
Answer:
(x+7) (x^2 - 5)
Step-by-step explanation:
x
3
+7x
2
−5x−35
=x
2
(x)+x
2
(7)−5(x)−5(7)
=x
2
(x+7)−5(x+7)
Now we are left with a common factor of (x+7)(x+7)left parenthesis, x, plus, 7, right parenthesis, so we can factor it out:
\begin{aligned} &\phantom{=}x^2\purpleC{(x+7)}-5\purpleC{(x+7)} \\\\ &=\purpleC{(x+7)}(x^2-5) \end{aligned}
=x
2
(x+7)−5(x+7)
=(x+7)(x
2
−5)
. _ .
................
Hey there!
I believe the answer to your question is 24.
If it's being reduced by 1/3, you are being left with 2/3, so we can take 2/3 of 9 and you get 6. Perimeter is adding up all the side lengths. Thus, we do 6 + 6 + 6 + 6, and that is 24.
Sorry for any confusion before, I didn't understand the problem before. Hope it helps! Have a great day, and sorry if it's late.
The aquarium where Evan works has a special tank for the baby sharks. The tank is shaped like a rectangular prism and is 18 meters long by 15 meters wide. It is 8 meters from the bottom of the tank to the top. What is the volume of the shark tank?
Answer:
The volume of the shark tank is [tex]2160 m^3[/tex]
Step-by-step explanation:
The tank is in the shape of a rectangular prism.
The length of the tank, [tex]l=18[/tex] m.
The width of the tank, [tex]w=15[/tex] m.
The height of the tank, [tex]h=8[/tex] m.
We know that, volume of a rectangular prism [tex]=l\times w \times h[/tex].
So, the volume of the tank [tex]=18\times 15\times 8=2160 m^3[/tex]
Hence, the volume of the shark tank is [tex]2160 m^3[/tex].
How many super saiyans does it take to screw in a light bulb?
Answer:
bro just use ur hand
Step-by-step explanation:
Answer:
Probably a lot considering Vegeta couldn't safely break an egg :)
Step-by-step explanation:
Which is an equivalent equation solved for t?
O te fry
O tufa
O t= a(f - V)
O t = v(f – a)
Answer:
[tex]\dfrac{v-u}{a}[/tex]
Step-by-step explanation:
The given equation should be:
v = u +at ...(1)
Where
u is initial velocity, v is final velocity, a is acceleration and t is time
We need to solve the above equation for t.
Subtract u from both sides.
v-u= u +at -u
v-u=at
Dividing both sides by a.
[tex]\dfrac{v-u}{a}=\dfrac{at}{a}\\\\t=\dfrac{v-u}{a}[/tex]
So, the expression for t is equal to [tex]\dfrac{v-u}{a}[/tex].
Is Figure B a scaled copy of Figure A? Explain how you know.
Answer:
yes
Step-by-step explanation:
Which has the greatest variance?
{5,5,5,5,5)
{1, 1, 1, 1, 21)
{1,3,5,7,9)
{3,4,5,6,7)
Answer
1,3,5,7,9
Step-by-step explanation:
Denver, Colorado is called " The Mile High City" because of it's elevation is 5280 feet above sea level. Someone tells you that the elevation of Death Valley, California is- 282 feet.
Answer:
A. 5,562 feet higher
B. 0 feet
Step-by-step explanation:
A. Calculation for how many feet higher is denver than death valley
Numbers of feet=5,280 feet-(- 282 feet)
Numbers of feet=5,280 feet+282 feet
Numbers of feet=5,562 feet higher
Therefore the numbers of feet higher is denver than death valley will be 5,562 feet higher
B. Since ocean level tend to have 0 feet which means that in a situation where you were standing close to the ocean what the elevation would be is 0 feet.
y=−34x 2 +1542x−10037
Answer:
10105
1542
Step-by-step explanation:
Solve equation 3x^2-4x=7 by completing square
Step-by-step explanation:
3x2-4x-7=0(3x-7)(x+1)=03x-7=0 and x+1=0x=7/3 and x=-1The difference between 31 and a number is 7
Answer:
thirty-eight
Step-by-step explanation:
31+7= answer
Answer:
i think its either 38 or 24
Step-by-step explanation:
i dont really understand this :(
Calvin takes piano lessons at a community music school located 3.7 miles directly north of the sports complex. What is the length of a straight line between Calvin's house and the music school? Round to the nearest tenth.
Answer:
The answer is below
Step-by-step explanation:
Calvin school is 2.3 miles directly south of his house. After school, he takes a bus 1.8 miles west of his school to the sport complex.
a) What is the length of a straight line between calvins house and the sports complex? Round to the nearest tenth.
b) Calvin takes piano lessons at a community music school located 3.7 miles directly north of the sports complex. What is the length of a straight line between Calvin's house and the music school? Round to the nearest tenth.
Solution:
a) Calvin school, his house and the sport complex form a right angled triangle. The hypotenuse of the right angled triangle is the length of the line between Calvin's house and the sport complex. Let the length of the line between Calvin's house and the sport complex be x.
Using Pythagoras law for right angled triangle, we get that:
x² = 2.3² + 1.8²
x² = 8.53
x = √8.53
x = 2.9 miles to the nearest tenth
b) This forms a right angled triangle with the hypotenuse = length of a straight line between Calvin's house and the music school. one side of the triangle = 1.8 miles and the other side = 3.7 - 2.3 = 1.4 miles.
Let x = length of a straight line between Calvin's house and the music school. Hence:
x² = 1.8² + 1.4²
x² = 5.2
x = √5.2
x = 2.3 miles to the nearest tenth
help pleseeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee i think i spelled that wrong
but stillplese help
What is the measure of angle RST?
a. 87
b. 131
c. 93
d. 90
Option c. 93°.
Alright, so in this one um the angle um so uh this angle right here, let's see right here, right which these two angles these angles are going to be equal because those are vertical angles. So these this angle is equal to um So angle P. S. T. Is equal to one half the sum of those two arcs added together, so 43 plus 1 31 So one half of Uh was that 1 74, So 1 74, divide by two 87. So this is 87 and then you take 18687 And you get 93.
What is the measure of ∠ RST?Triangle RST is isosceles means that two of its angles are equal. (1) The measure of angle T is 100 degrees --> since no other angle can be equal to 100 degrees (because in this case, the sum of the angles will be more than 180 degrees) than the other two angles, R and S, are equal: R=(180-100)/2=40.
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