Answer:
x=-3
<ABD=88
<CBD=23
Step-by-step explanation:
We know that <ABC is made up of 2 angles: <ABD and <CBD.
We also know that the m<ABC is 111.
Therefore, <ABD and <CBD added together must equal 111.
<ABD+ <CBD =111
We know that <ABD is -10x+58 and <CBD is 6x+41, so we can substitute these in.
-10x+58+6x+41=111
Combine like terms
(-10x+6x)+(58+41)=111
-4x+99=111
Now we need to solve for x. First, move all the constants to the same side. Subtract 99 from both sides, since 99 is being added to -4x.
-4x+99-99=111-99
-4x=12
Next, divide both sides by -4, since -4 and x are being multiplied.
-4x/-4=12/-4
x=-3
Now we know x, and can substitute it in to find the angle measures.
<ABD
-10x+58
-10(-3)+58
30+58
88
<CBD
6x+41
6(-3)+41
-18+41
23
[tex]m \angle ABD = 88^{\circ}\\m \angle CBD = 23^{\circ}[/tex]
Given:
m∠ABC = 111∘
m∠ABD = (-10x+58)∘
m∠CBD = (6x+41)∘
First, find the value of x by creating an equation
Thus:
[tex]m\angle ABD + m \angle CBD = m \angle ABC[/tex] (angle addition postulate)
Substitute
[tex](-10x+58) + (6x+41) = 111[/tex]
Solve for x
[tex]-10x+58 + 6x+41 = 111[/tex]]
Add like terms
[tex]-10x+58 + 6x+41 = 111\\-4x + 99 = 111\\-4x = 111 - 99\\-4x = 12\\[/tex]
Divide both sides by -4
[tex]x = -3[/tex]
Find m∠ABD and m∠CBD by plugging in the value of x
[tex]m\angle ABD = -10x + 58 \\m\angle ABD = -10(-3) + 58 \\m\angle ABD = 88^{\circ}[/tex]
[tex]m \angle CBD = 6x + 41\\m \angle CBD = 6(-3) + 41\\m \angle CBD = 23^{\circ}\\[/tex]
Therefore:
[tex]m \angle ABD = 88^{\circ}\\m \angle CBD = 23^{\circ}[/tex]
Learn more here:
https://brainly.com/question/4208193
A stick 1 meter long casts a shadow 1.5 meters long. A building casts a shadow 17 meters long. How tall is the building (to 2 decimal places)
BC =
Round your answer to the nearest hundredth.
Answer:
Since its a right triangle you automatically know the C is 90 degrees. And since all triangle have to add up to 180 degrees, you know B has to equal 40 degrees.
A= 50
B= 40
C= 90
B + C
40 + 90
BC = 130 degrees
Answer:
2.3
Step-by-step explanation:
Khan
Kathy found the volume of the figure using the expression (4 * 3 * 8) + (10 * 3 * 4). Sandy found the volume of the figure using the expression (3 * 10 x 4) + (4 * 3 * 4). Use the drop-down menus to explain who is correct. 10 cm Click the arrows to choose an answer from each menu, The expression for the volume of the figure was correctly determined by Choose... because the figure was divided into two rectangular → prisms that Choose...
Answer:
The correct options are;
1) Sandy is correct
2) The figure was divided into two rectangular prisms that are calculated separately
Step-by-step explanation:
Here we have to divide the figure into two rectangular prisms so as not to calculate for a dimension twice
Therefore, the figure can be split into a horizontal prism at the top with dimensions and volume = 10 × 4 × 3 and the vertical prism below will now have a dimension and hence, volume of 4 × 4 × 3
Therefore the volume of the figure is the sum of the volumes of the two prisms found as follows;
Volume of the figure = 10 × 4 × 3 + 4 × 4 × 3 = 168
We can try the othe way to confirm as follows
Volume of the prism below = 4 × 3 × 8 = 96
Volume of the horizontal prism above is now = 4 × 3 × 6 = 72
Volumre of the figure = 96 + 72 = 168
Therefore, since the volume = (10 × 4 × 3) + (4 × 4 × 3), Sandy is correct
Because the figure was divided into two rectangular prisms that are calculated separately.
Answer:
1(sandy is correct)
2(do not overlap
Step-by-step explanation:
A bag contains 12 red, 30 blue, 20 green, 10 yellow, and 8 black marbles. Nancy chooses 1 marble from the bag. What is the probability that the marble is red, blue, or black?
A.18
B.38
C.58
D.78
Step-by-step explanation:
Total marbles = 12 + 30 + 20 + 10 + 8 = 80
Probability = 12 + 30 + 8 = 50
= 50 / 80 = 5 / 8
Someone please help me. I’m not good at mah but I would be thankful for ur help.
Answer:
1. 44 inches
hope this helps :)
Find the area of a circle whose circumference is 87 m.
A. 4 m 2
B. 8 m2
C. 16 m2
D. 64 m2
Answer:
None of those are right, the answer is about 602.32 m2
Step-by-step explanation:
Which has a value closest to 9?
✓99
V83
VIO
V63
Answer:
[tex]\sqrt{83\\}[/tex] has the closet value to 9 bc its 9.11
of the following numbers, which has the most factors of 3?
a) 81
b) 270
c) 999
d) 3333
Answer:
81 has the most factors of 3
Step-by-step explanation:
To conclude which of the following options has the most factors of 3, take each of the number's prime factorization, which will help us solve the problem.
( 1 ) 81 is a composite number and is 9 squared. Knowing that 3 squared = 9, we can say that the prime factorization of 81 = 3 [tex]*[/tex] 3 [tex]*[/tex] 3 [tex]*[/tex] 3, which can also be denoted as 3⁴.
( 2 ) 270 is a composite number. The exponents in the prime factorization are 1, 3, and 1, and therefore it's prime factorization is - 3 [tex]*[/tex] 5 [tex]*[/tex] 3 [tex]*[/tex] 2 [tex]*[/tex] 3, composed of 3 3s.
( 3 ) If we put all of it together we have the factors 3 x 3 x 3 x 37 = 999. It can also be written in exponential form, with 3 to the power of 3 - hence having 3 factors of 3.
And finally the value 3333 has the prime factorization of 3 [tex]*[/tex] 11 [tex]*[/tex] 101, and as you can see it has 1 factor of 3. 81, having 4 factors of 3, is present with the most factors, and therefore is our solution.
Number 81 has the most number of factor 3. Option A is correct.
A number from the options to be determined that has the most number of factor 3.
factors can be defined by splitting the value into multipliable values.
Here,
Factors of 81 = 3,3,3,3 Number of factor 3 = 4
Factors of 270 =2,3,3,3,5 Number of factor 3 = 3
Factors of 999 =3,3,11 Number of factor 3 = 2
Factors of 3333 = 3,11 Number of factor 3 = 1
As per the above comparison, 81 has the most number of factor 3.
Thus, Number 81 has the most number of factors 3.
Learn more about Factors here:
https://brainly.com/question/24182713
#SPJ2
Write a formula for quadratic function if its graph has the vertex at point (0,6) and passes through the point (−1,−2).
Answer:
y = - 8x² + 6
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k) = (0, 6), thus
y = a(x - 0)² + 6, that is
y = ax² + 6
To find a substitute (- 1, - 2) into the equation
- 2 = a(- 1)² + 6, that is
- 2 = a + 6 ( subtract 6 from both sides )
- 8 = a
y = - 8x² + 6
The formula of the quadratic function is [tex]y = -8x^2 + 6[/tex]
A quadratic function is represented as:
[tex]y = a(x - h)^2 + k[/tex]
The vertex of the quadratic function is given as:
[tex](h,k) = (0,6)[/tex]
So, we have:
[tex]y = a(x - 0)^2 + 6[/tex]
This gives:
[tex]y = ax^2 + 6[/tex]
The quadratic function passes through (-1,-2).
So, we have:
[tex]-2 = a(-1)^2 + 6[/tex]
[tex]-2 = a + 6[/tex]
Subtract 6 from both sides
[tex]a = -8[/tex]
Substitute -8 for a in [tex]y = ax^2 + 6[/tex]
[tex]y = -8x^2 + 6[/tex]
Hence, the formula of the quadratic function is [tex]y = -8x^2 + 6[/tex]
Read more about quadratic functions at:
https://brainly.com/question/11631534
Write a linear equation from a slope and a point
The volume of a rectangular prism is v = Lwh, where v is the volume, L is the length, w is the width, and h is the height. Rewrite this equation with w solved in terms of v, l, and h.
Answer:
w=v/lh
Step-by-step explanation:
lwh=v
To isolate w, we'd have to divide both sides by (lh)
Therefore, w = v/lh
Hope this helped and have a good rest of your day!
Which graph represents -x+ 8y > - 24
Kind of need a picture to help answer the question.
Ken baked a pan of brownies for a potluck. The number of squares he cuts the brownies into will depend on the number of people attending the potluck. s = the number of squares Ken cuts the brownies into. p = the number of people attending the potluck. Which of the variables is independent and which is dependent?
Answer:
P is the independent variable while S is the dependent variable
Hope this Helps :)
Stephanie and alejandro
were planning thier wedding.
Stephine saved up four times.
more money than alejandro
because he lost his job at walmart. Together $15,600 How much did each one save ?
steps ?
Answer:
Stephanie saved
Step-by-step explanation:
x+4x=15600
5x=15600
divide by 5 on both sides
you get 3120
since stephanie got 4 times more, you multiply 3120*4 and get 12480
therefore, Alejandro saved 3120
: )
Solve the following system of equations using any method you want.
y + 2x = 2
2x - 5y = 14 please help
Answer:
y = - 2, x = 2
Step-by-step explanation:
Remove x and solve for y
2x - 2x - 5y - y = 12
-6y = 12
y = - 2
Substitute y back into the equation
-2 + 2x = 2
2x = 4
x = 2
please help!!! i really need the answer to this question, ill mark you as brainleist
Hey there! I'm happy to help you! :)
We see that there are 160 songs in total. Let's split them up into groups of rock, country, and pop.
ROCK
Our problem says that 3/8 of the songs are rock songs. We know that we have 160 songs. We just need to multiply 3/8 by 160 and we will have the number of rock songs.
3/8*160=60
Therefore, we have 60 rock songs.
COUNTRY
We see that 25% of our songs are country songs. 25% is the same thing as 1/4, or 0.25. We can multiply this by our total number of songs to see how many are country.
0.25(160)= 40
We have 40 country songs.
POP
All we have in the problem is that the remaining songs are pop. The nice thing is is that we already know how many rock and country songs we have, so we can simply subtract those from 160 and we will then be able to tell how many pop songs there are.
160-60-40= 60
Therefore, there are 60 pop songs.
I hope that this helps you! Have a wonderful day!
Which of the following inequalities is correct?
Answer:
a < b < c
Step-by-step explanation:
a is -4, which is less than b, at 1, and c at 7.
If this answer is correct, please make me Brainliest!
Answer:
the answer is a it cant not be b,c
(x + m)(x + n) if m= 5 and n = -7
Answer:
[tex]x^2-2x-35[/tex]
Step-by-step explanation:
[tex](x+5)(x-7)=[/tex]
[tex]x^2+5x-7x-35=[/tex]
[tex]x^2-2x-35[/tex]
Hope this helps!
Answer:
X^2-2x-35
Step-by-step explanation:
(X)(x)+(x)(-7)+(5)(x)+(5)(-7)
X^2-7x+5x-35
X^2-2x-35
Hope that was the answer you were looking for
(9x2+3x-5) - (3x2+4x-10)
Answer:
39
Step-by-step explanation:
I'm assuming x is supposed to be a multiplication sign.
You need to use PEMDAS for this:
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
(9x2+3x-5)-(3x2+4x-10)=
(18-15)-(6-40)=
3-(-36)=
3+36=
39
Please Help Now Running out of time! In Sal’s sock drawer, there are 2 red, 2 blue, 2 yellow, 2 black, and 2 green socks. If he randomly picks one sock from the drawer, and then another, which fractions should Sal multiply to find the probability of choosing a pair of green socks?
Answer:
Step-by-step explanation:
C
Answer:
C
Step-by-step explanation:
2/10 1/9
The value of x 3y, for x = -2 and y = 3, is -24. True False
Answer:
true
Step-by-step explanation:
x^3 y when x = -2 and y = 3
(-2)^3 * 3
-8 *3
-24
This is true
George still has 40 percent of his book to read. If George has read 180 pages, how many pages does he still have to read? How do you know?
Answer: 72
Step-by-step explanation: so you do a line = line method the lines should look like they are fractions.
you do it for the both numbers the percent is always out of 100.
it should look like this
40% ?
--------- = -----------
100% 180
then you cross multiply 40 and 180 and than divide it by 100. your answer should be 72. you later replace the ? with 72
you know this because It is smaller than 180 and its bigger than the number 40.
The number pages left to read is 12 pages.
Given that, George still has 40 percent of his book to read.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Let the total number of pages be x.
Now, x-40% of x=180
⇒ x-0.4x=180
⇒ 0.6x=180
⇒ x=180/0.6
⇒ x=300
So, remaining pages = 300-180=120
Therefore, the number pages left to read is 12 pages.
To learn more about the percentage visit:
brainly.com/question/24159063.
#SPJ2
What is the area of one of the triangular faces?
4 in
3 in
7 in
7 in
5 in
4 in
5 in
Answer:6
Step-by-step explanation:
I got it corrected on the assignment
Answer:
it is 6
Step-by-step explanation:
the person above me is right :) have a nice day
(◍•ᴗ•◍)✧*。
Please please please please please please please pppppppllllllllllleeeeeeeaaaaasssseeehelp
Answer:
70
Step-by-step explanation:
its in the tens value
Answer:
70
Step-by-step explanation:
The number is in the tenths place.
Use the formula to help you answer the question below. Do not include units
in your answer.
Rate . Time = Distance
How many hours will it take to complete a 45-km bike ride if you go 12 km per
hour the whole time?
It will take about 3.75 hours to complete.
!!!!!!NEED HELP !!!!!! y=-50x + 750 which of the following does NOT match the equation shown.
Answer:
I think its B
Hope it helps :/
Answer:
y=10x-50
Step-by-step explanation:
A circle has a radius of 5/3 units and is centered at (9.2 -7.4)
Write the equation of the Circle.
Answer:
(x - 9.2)^2 + (y + 7.4)^2 = (5/3)^2
Step-by-step explanation:
We start with (x - h)^2 + (y - k)^2 = r^2. The center is (h, k) and the radius is r.
Then we have:
(x - 9.2)^2 + (y + 7.4)^2 = (5/3)^2
What is the area of the triangle shown below?
Answer:
48
Step-by-step explanation:
Split it into 2 right triangles flip one around and you have a rectangle who's area is equal to 10x6.
a=6
c=2
b=?
Solve for b:
Determine whether each statement is true or false.
(FINALEXAM)
Answer:
1. False
2. True
Step-by-step explanation:
How do you know when expression are equivalent
Answer:
If two things are equivalent, they are the same. Equivalent expressions are expressions that are the same, even though they may look a little different. If you plug in the same variable value into equivalent expressions, they will each give you the same value when you simplify.
Step-by-step explanation:
Answer: Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(
Step-by-step explanation: