Given:
An isosceles triangle has an angle that measures 40°.
To find:
The other possible angles of the triangle.
Solution:
Case 1: 40° is the measure of base angle of isosceles triangle.
Then, the other base angle is 40°.
Let x be the measure of third angle.
The sum of all interior angles of a triangle is 180 degrees. So,
[tex]x+40^\circ+40^\circ=180^\circ[/tex]
[tex]x=180^\circ-40^\circ-40^\circ[/tex]
[tex]x=100^\circ[/tex]
So, the possible angles are 40° and 100°.
Case 2: 40° is the measure of vertical angle of isosceles triangle.
Let y be the measure of base angles, then
[tex]y+y+40^\circ=180^\circ[/tex]
[tex]2y=180^\circ -40^\circ[/tex]
[tex]y=\dfrac{140^\circ}{2}[/tex]
[tex]y=70^\circ [/tex]
So, the possible angles are 40° and 70°.
Therefore, the correct options are A, B and D.
if x+y=12 and xy=27 . find x^3+y^3
pls help with steps
Answer:
Step-by-step explanation:
use formula
x^3+y^3=(x+y)^3-3*x*y(x+y)
=12^3-3*27(12)
=1728-972
=756
Answer:
x^3 + y^3 = 756
Step-by-step explanation:
Given that, x+y=12 and xy=27
We know that,
[tex]( x + y )^3 = x^3 + y^3 + 3xy(x + y)[/tex]
∴ [tex]12^3 = x^3 + y^3 + 3 * 27 * 12[/tex]
[tex]=> 1728 = x^3 + y^3 + 972[/tex]
[tex]x^3 + y^3 = 1728 - 972[/tex]
[tex]==> x^3 + y^3 = 756[/tex]
Given: AM = 8, AB = 5x +1 and M is the midpoint of AB, find x and AB
X=
AB=
Answer:
x = 3
AB = 16
Step-by-step explanation:
Given: AM = 8, AB = 5x +1 and M is the midpoint of AB, the AM = MB
AB = 2AM
5x+1 = 2(8)
5x + 1 = 16
x = 16 - 1
5x = 15
x = 15/5
x = 3
Hence the value of x is 3
Since AB = 5x+1
AB = 5(3) + 1
AB = 15 + 1
AB = 16
Help me with the question
Answer:
Step-by-step explanation:
When the sun is at a certain angle in the sky, a 50 foot building will cast a 20 foot shadow. What is the length of the shadow in feet cast by a 20 foot pole at the same time?
Answer:
Prepara a bar graph. (Mention the scale)
Potato= 25 per kg
Tomato= 40 per kg
Cauliflower= 10 per kg
Chilli= 15 per kg
Lemon= 30 per kg
Answer:
8 ft
Step-by-step explanation:
The height of the building/pole and shadow of each are in proportion.
let x be the length of shadow of the pole, then
[tex]\frac{50}{20}[/tex] = [tex]\frac{20}{x}[/tex] ( cross- multiply )
50x = 400 ( divide both sides by 50 )
x = 8
The shadow cast by the pole is 8 ft
Mathematics pls help me.
Answer:
I think the answer may be 465
Step-by-step explanation:
105+115=220
150+95=245
245+220=465
Geometry//// volume of a cylinder ✨✨✨✨
Answer:
595.82 cubic feet
Step-by-step explanation:
The formula for a cylinder is pi times radius squared times height. First, you take the diameter and divide it by two to get 4.25. Now do 4.25 times 4.25 and get 18.0625.
Now multiply 18.0625 by 10.5 to get 189.65625.
Now multiply that by pi (3.14) to get 595.82 (Rounded to the nearest hundreth)
John needs 6 cups of ice cream to make 4 servings of milkshake. How many servings can John make using 3 gallons of ice cream?
Answer:
24
Step-by-step explanation:
-------- 24 --------
Hope that helps
Gunther's starting weight is 248 pounds, and he plans to lose 2 pounds each week. Use a linear equation to determine Gunther's weight after 10 weeks
y = 248 - 2x
good luck :))))
Select the reason that the best supports statement 6 in the given proof
Answer: Substitution
I hope this helps!:)
Substitution is the reason that the best supports statement 6 in the given proof
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that ∠A=∠B, ∠A= 55 and ∠B=5x+10
We need to prove x=9
The given statements and reasons are given as below
∠A≅∠B (By given)
∠A=∠B (Congruency)
m∠A=55 (By given)
55=m∠B (Substitution)
m∠B=5x+10 (Given)
55=5x+10(Substitution)
45=5x
x=9 (Division property of equality)
Hence, substitution is the reason that the best supports statement 6 in the given proof
To learn more on Equation:
https://brainly.com/question/10413253
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21 POINTS HELPPPP
ASAP
Answer:
-3 1/4 + 4 3/4= 1 1/2
Step-by-step explanation:
I need help I’ll give brainlist answer.
Answer:
All beside D
Step-by-step explanation:
help me out a little
PLEASE ANSWER QUICK. I AM SO CONFUSED. HELP.
Answer:
Slope: 2
This is because it is going up two blocks within one block space.
Feel free to mark it as branliest :D
gradient = 2
Rise over Run = 5 / 2.5 = 2
Please help me thanks :))
Answer:
What do you need help with?
The sum of two numbers is 58. The smaller number is 20 less than the larger number. What are the numbers?
Answer:
x=38 Larger number
y=20 Smaller number
Step-by-step explanation:
38+20=58
If the board length of an average log is 8.25 and the price per board foot is 7.95. What is the value of the timber if there are 100 logs?
Answer:
6558.75
Step-by-step explanation:
total value of 100 logs = total value of an average log x 100 total value of an average log = length of an average log x price per board foot
8.25 x 7.95 = 65.5875
65.5875 x 100 = 6558.75
which shows the numbers in order from least to greatest?
3.93,3.51,3.72,3.19
3.19,3.51,3.72,3.93
Step-by-step explanation:
3.19=3.2
3.51=3.5
3.72=3.7
3.93=3.9
you take over the number kn the tenth .... if its 1 234 you round down and if its 5 or more you round up... simple
The number of apple slices placed in 5 different pies is listed below. 94, 90, 82, 94, 85 What is the difference between the mean and the mode of these numbers?
Answer:
Mode: 94
Mean: 89
Difference between them: 5
Step-by-step explanation:
A) En cada caja hay 5 caramelos. Si tengo 8 cajas ¿cuántos caramelos tengo? b) Romina tiene 9 pelotas y Lidia 4 veces más que ella. ¿Cuántas pelotas tiene Lidia?
Answer:
a) 40 caramelos
b) 13 bolas
Step-by-step explanation:
A) En cada caja hay 5 caramelos. Si tengo 8 cajas, ¿cuántos caramelos tengo?
1 caja = 5 caramelos
8 cajas = x
Multiplicar cruzada
x × 1 caja = 8 cajas × 5 caramelos
x = 8 cajas × 5 caramelos / 1 caja
x = 40 caramelos
b) Romina tiene 9 bolas y Lidia 4 veces más que ella. ¿Cuántas bolas tiene Lidia?
Romina = 9 bolas
Lidia = 4 bolas más que ella
Lidia = 9 bolas + 4 bolas
= 13 bolas
48% as its simplest fraction
Answer:
12/25
Step-by-step explanation:
Percent means out of 100
48% means 48/100
Divide top and bottom by 4
12/25
How do I solve this?
Answer:
25
Step-by-step explanation:
C = √a^2+b^2
√7^2+24^2
√49+576
√625
C=25
How to graph y= 2x -2
Answer:
start at the y coordinate -2 then go up 2 and right 1
Step-by-step explanation:
The volume of a cylinder measures 2,797.74 in. The radius of the cylinder is 9 in. Determine the height.
Answer:
11 inches
Step-by-step explanation:
V(cylinder) = πr²·h
2797.74 = 81π·h
h = 2797.74 ÷ 81π
h ≈11
Please help out I can’t really love this
========================================================
Explanation:
When we divide two fractions like this, we flip the second fraction and multiply like so...
[tex]\frac{5}{7} \div \frac{8}{9}\\\\\frac{5}{7} \times \frac{9}{8}\\\\\frac{5 \times 9}{7 \times 8}\\\\\frac{45}{56}\\\\[/tex]
which points us to choice B as the answer.
The fraction 45/56 cannot be reduced further because 45 and 56 do not have any factors in common other than 1.
Answer:
45/56
Step-by-step explanation:
5/7 ÷ 8/9
Copy dot flip
5/7 * 9/8
5*9 =45
7*8 = 56
45/56
Find the slope of the line.
(-2, 1)
)
(2, 1)
3-2-1
Answer:
(0-2)
Step-by-step explanation:
Answer:
0
Step-by-step explanation:
A horizontal line has a slope of zero
Using the formula
m = (y2-y1)/(x2-x1)
= (1-1)/(2 - -2)
= 0/(2+2)
= 0/4
Sammy has 21 books on his shelf. Two-thirds of the books are mysteries. How many books are mysteries?
Answer:
14 books my good sir
Step-by-step explanation:
Triangle XY Z has vertices X = (5, -1), Y = (1, 4), and Z=
(-8,0). Triangle X'Y'Z' is formed when triangle XYZ is
reflected over the y-axis. What are the coordinates of
triangle X'Y'Z'?
Answer:
see explanation
Step-by-step explanation:
Under a reflection in the y- axis
a point (x, y ) → (- x, y ) , then
X (5, - 1 ) → X' (- 5, - 1 )
Y (1, 4 ) → Y' (- 1, 4 )
Z (- 8, 0 ) → Z' (8, 0 )
Let e be the line through A (-4,5) and B (3. t) that is perpendicular to the line through
P (1, 3) and Q(-4, 2). Find the value of t.
Let l be the line through A (4, -3) and B (t, -2) that is parallel to the line through
P(-2, 4) and Q (4, -1). Find the value of t.
Determine the signs of sino coso and tane if O is an angle in standard position and
P (2,-5) is a point on its terminal side.
Answer:
Step-by-step explanation:
product of slopes of perpendicular lines=-1
(t-5)/(3+4)×(2-3)/(-4-1)=-1
(t-5)/7×(-1/-5)=-1
(t-5)/35=-1
t-5=-1×35=-35
t=-35+5
t=-30
2.
slopes of parallel lines are equal.
(-2+3)/(t-4)=(-1-4)/(4+2)
1/(t-4)=-5/6
t-4=-6/5
t=4-6/5=(20-6)/5=14/5
3.
x>0,y<0
so P lies in4th quadrant.
except cos and sec all are negative.
so only cos and sec are positive.
5/6 x 3/4 as an array is?
Question:
5/6 x 3/4 as an array is?
Answer:
0.625 or 5/8
Step-by-step explanation:
Using Arrays to Explore Numbers
Arrays are useful models for multiplication which can be used in a variety of ways, ranging from highly structured lessons to games and open investigations.
An array is formed by arranging a set of objects into rows and columns. Each column must contain the same number of objects as the other columns, and each row must have the same number as the other rows.
The following array, consisting of four columns and three rows, could be used to represent the number sentence 3 x 4 = 12, 4 x 3 =12, 3 + 3 + 3 + 3 = 12 and 4 + 4 + 4 =12.
Building Multiplication Facts and Tables
Arrays can be used for building multiplication facts in a meaningful way. Before drilling and memorising tables, children must understand how these facts are derived. For example, by progressively adding another column of three objects, children can build the three-times tables for themselves. This representation not only assists in understanding the process, but provides a visual image for children to draw upon as they begin to use and memorise the basic number facts.
Using arrays to explore larger numbers
Arrays can be helpfully used to explore calculations such as 13 x 5 where the array can be split into useful chunks such as 10 and 3. This means that children can use their known number facts to work out calculations.
Here 13 x 5 = (10 x 5) + (3 x 5).
After a while drawing all the dots can get very tedious! The blank array then becomes a very useful tool for helping children model their thinking and work out how to do more complex multiplications in an informal way.
Here's a child using the blank array, as a thinking tool, to help them work out 15 x 14.
The blank array helps children to use other strategies, such as compensating, when carrying out multiplication. Here, to work out 34 x 9, the child has decided to do 34 x 10 and then take off the 34 x 1.
Beyond the blank array this 'dividing the multiplication into easy parts' strategy can be formalised into the grid method. The children can see how the 'abstract' grid method overlays the array and formalises the blank array into a standard form.
Division as the Inverse Operation of Multiplication
Of the four operations, division is the most troublesome for young students. Full understanding of division tends to lag well behind the other operations. For many children opportunities to explore the concept with concrete materials are curtailed well before they perceive the relationships between division and the other three operations. One such relationship, the inverse relationship between division and multiplication, can be effectively illustrated using arrays.
For example; 3×5=15 or 3 rows of 5 make 15, can be represented by the following array.
Looking at the array differently reveals the inverse, that is
15÷3=5 or 15 put into 3 rows makes 5 columns - or 5 in each row.
Language clearly plays an important role in being able to express the mathematical relationships and the physical array supports this aspect of understanding by giving the children a concrete image to talk about.
Placing the mathematics into a real-life context through word problems can facilitate both understanding of the relationship and its expression through words.
For example, "The gardener planted 3 rows of 5 seeds. How many seeds did she plant?" poses quite a different problem to "The gardener planted 15 seeds in 3 equal rows. How many seeds in each row?" yet both these word problems can be modelled using the same array.
Further exploration of the array reveals two more ways of expressing inverse relationships: 5×3=15 and 15÷3=5 .
The word problems can be adapted to describe these operations and highlight the similarities and differences between the four expressions modelled by the one array.
Using the blank array
Suppose you want to figure out 176 ÷ 8. We can set this up as an array with the value of one side missing.
Using known multiplication facts the value of the missing side can be built up.
So the child can see that 22 lots of 8 is the same as 176.
The array is a very powerful tool for supporting the development of children's thinking around both multiplication and division.
please help!!!! due soon!!