Answer:
[tex] {7}^{ - 8} [/tex]
Step-by-step explanation:
[tex] {7}^{ - 1} \times {7}^{ - 7} \\ {7}^{ - 1 + - 7} \\ {7}^{ - 8} [/tex]
Hope this helps you.
John turned in the following solution to an inequality and his teacher marked it wrong. What mistake did John make?
A. incorrectly reversed the inequality symbol
B. Failure to combine like terms
C. Incorrect division
D. Incorrect addition
In the figure, .
∠AEB and ∠CED are congruent
.
∠AEC and ∠
are congruent by the Vertical Angles Theorem.
Answer:
∠AEC ≅ ∠BED by vertical angles theorem
Answer:
Answer:
∠AEC ≅ ∠BED by vertical angles theorem
Step-by-step explanation:
Use a substitution strategy to solve the following problem.
Two isosceles triangles have the same base length. The equal sides of one of the triangles
are 3 times as long as the equal sides of the other. Find the lengths of the sides of the triangles when
their perimeters are 34 cm and 82 cm.
Answer:
The length of the equal sides of the isosceles triangle with a perimeter of 34 cm perimeter is 12 cm
The length of the equal sides of the isosceles triangle with a perimeter of 82 cm perimeter is 36 cm
The base length of both triangles is 10 cm
Step-by-step explanation:
The given parameters are;
The base length of the triangles are equal
The base length of one of the triangle = The base length of the other triangle
The equal sides of one of the triangles = 3 × The length of the equal sides of the other
The perimeter of the triangles are; 34 cm and 82 cm
Let 'b' represent the base length of each triangle, let 'a' represent the length of an equal side of the smaller triangle with a perimeter of 34 cm and let 'c' represent the length of an equal side of the larger triangle with a perimeter of 82 cm
For the smaller triangle, we have;
b + 2·a = 34..(1)
For the other triangle;
b + 2·c = 82...(2)
Given that the side length of the larger triangle are larger than those of the smaller triangle, and that the side length of the larger triangle is 3 times the side length of the smaller triangle, we get;
c = 3·a
By the substitution method, from equation (2) we get;
b + 2·c = b + 2 × 3·a = b + 6·a = 82
∴ b + 6·a = 82...(3)
Subtracting equation (1) from equation (3) gives;
b + 6·a - (b + 2·a) = 82 - 34 = 48
b - b + 6·a - 2·a = 48
4·a = 48
a = 48/4 = 12
The length of the equal sides of the 34 cm perimeter (smaller) isosceles triangle, a = 12 cm
From c = 3·a, and a = 12, we get;
c = 3 × 12 = 36
The length of the equal sides of the 82 cm perimeter (larger) isosceles triangle, c = 36 cm
From equation (1), we get;
b + 2·a = 34
∴ b + 2 × 12 = 34
b = 34 - 2 × 12 = 10
The base length of both triangles, b = 10 cm
Find the value of the variable that results in congruent triangles. Explain. SAS (Side, Angle, Side) or ASA (Angle, Side, Angle)
well, let's keep in mind that the SAS postulate, so if one Side and the Angle next to it and the following Side after the angle are equal on both triangles, both triangles are congruent. Now, we have the angle 30° with sides and 9 and 2x and sides 9 and x + 4, well, the 9's are equal, dohh, you know, if only the 2x = x + 4, we'd be golden
[tex]2x = x + 4\implies 2x - x = 4\implies \boxed{x = 4}[/tex]
Find the area of this prism.
Sally plots (−4,π)on the polar plane.
How does she proceed?
Drag a phrase to each box to correctly complete the statements.
Solution :
As Sally determines the angle of rotation, since it is π, she lies on the negative x-axis. The first block then should be negative x-axis if r is positive and in the positive x-axis if r is negative.
My other reason for changing the dragged phase would be as they used the word, therefore, in the last sentence, which would mean an interference from the above statements, from the drag phase you have given the interference would be positive x-axis.
Given three points A(-7, 1), B(m, 6) and P(-1, n). If the point P divides AB internally in the ratio of 3: 2, find the values of m and n.
Answer:
m = 3 , n = 4
Step-by-step explanation:
Using Section Formula.
[tex]If \ the \ line \ segment \ AB \ where \ A = (x _1, y_1) \ and \ B = (x_2, y_2) \ divided \ by \ P =(x , y) \ in \ the \ ratio \ a : b,\\\\Then \ the \ points \ of \ P \ \\\\x = \frac{ax_2 + bx_1}{a+b} \ and \ y = \frac{ay_2 + by_1}{a+b}[/tex]
[tex]Here (x_1 , y_ 1 ) = ( -7 , 1 ) \ and \ (x_ 2 , y _ 2 ) = (m , 6)\\\\ratio\ a:b = 3 : 2\\\\Therefore, P (x, y) \\\\x = \frac{3m + (2\times -7)}{5} \ \ \ \ \ \ \ \ \ \ \ [ \ x = -1 \ ] \\\\-1 = \frac{3m - 14}{5}\\\\- 5 = 3m - 14\\\\-5 + 14 = 3m\\\\9 = 3m \\\\m = 3[/tex]
[tex]y =\frac{3\times 6 + 2 \times 1}{5}\\\\n = \frac{18 + 2}{5} = \frac{20}{5} = 4[/tex]
It doesn’t give options so I can’t guess
Answer:
x = 135
Step-by-step explanation:
The angles are vertical angles and vertical angles are equal
125 = x-10
Add 10 to each side
125+10 = x
135 =x
don't mind the purple dot
Answer:
option A
Step-by-step explanation:
22 : 15 + 10hours = 8 : 15
8 : 15 + 35 minutes = 8 : 50
Therefore the difference = 10 hours 35 minutes
In a school 640 teachers like either milk or curd or both . The ratio of number of twacher who like milk to the number pf teachers who like curd is 3:2 and 160 teachers like both milk and curd . Find: How many teachers like milk?& How many teachers like curd only.
3+2=5
Milk =3/5×640 = 384
Curd 2/5×640 = 256
If U={1,2,3,.............,10} A={2,4,6,8,10} and B= {1,3,5,7,9); then
find(A-B)?
Answer:
{2, 4, 6, 8,10}
Step-by-step explanation:
GIven U={1,2,3,.............,10} A={2,4,6,8,10} and B= {1,3,5,7,9);
Required
A-B = AnB'
B' = {2, 4, 6, 8,10}
AnB' are elements common to both A and B'.Hence;
AnB' = A- B = {2, 4, 6, 8,10}
Irene faced north. She turned 270 ° to the left and then 90 ° more to the left.
In what direction is Irene now facing?
Solve this please!!,!,!
Answer:
z = -74
Step-by-step explanation:
12 = (2+z) / -6
Multiply each side by -6
-6 * 12 = (2+z)/ -6 * -6
-72 = 2+z
Subtract 2 from each side
-72-2 = 2+z-2
-74 =z
PLEASE HELP WILL MARK BRAINLIEST
Hannah lost four points on a test and earned four points on an extra credit question what does the sum of 0 mean in the description of this situation?
Answer:
Is that it's not about the answers and the questions
AC = 16, AB = x + 1, and BC = x + 7. What is the measure of the length of AB? HELP
Answer:
5
Step-by-step explanation:
AC=AB+BC
so 16=x+1+x+7
which simplifies to 16=2x+8
subtract eight from both sides to get 8=2x
then divide by 2 to get that x=4
AB=x+1, which substitutes into 4+1=5
A 6) Set both given equations equal to zero, then combine them into one standard form
equation. Simplify if possible.
7x + 3 = 5 and y-1 = 6
Answer:
The standard equation is 7x + y = 9
Step-by-step explanation:
Equations given are:
7x + 3 = 5 and y - 1 = 6
Set both given equations equal to zero, then combine them into one standard form equation
Set the equations to zero by moving the constant from R.H.S to L.H.S
7x + 3 - 5 = 0
7x - 2 = 0 ---- eq 1
y - 1 = 6
y - 1 - 6 = 0
y - 7 = 0 ----- eq 2
We have to combine eq 1 and eq 2
7x - 2 + y - 7 = 0
7x + y - 9 = 0
The standard form of an equation is Ax + By = C
In this kind of equation, x and y are variables and A, B, and C are integers
Thus the standard equation is:
7x + y - 9 = 0
7x + y = 9
Thus the standard equation is 7x + y = 9
By the definition of a ▱, AD∥BC and AB∥DC. Using, AD as a transversal, ∠A and ∠ are same-side interior angles, so they are . Using side as a transversal, ∠B and ∠C are same-side interior angles, so they are supplementary. Using AB as a transversal, ∠A and ∠B are same-side interior angles, so they are supplementary. Therefore, ∠A is congruent to ∠C because they are supplements of the same angle. Similarly, ∠B is congruent to ∠.
Step-by-step explanation:
is it a question ? please check.
Answer:
Step-by-step explanation:
D.
supplementary.
BC.
D.
25 points!!! I will give brainliest to the first CORRECT answer!!
Answer:
It's well be 2 cause that is the only one thag makes sense
After reading The Lord of the Rings, Francesca signs up for archery lessons. At her first lesson, she sets up her target 5 feet away from her. After lots of practice, she now sets up her target 15 yards away. How many times farther away does Francesca set up her target now?
Answer:
[tex]3[/tex] times
Step-by-step explanation:
[tex]5x=15[/tex]
Divide both sides by 5
[tex]x=3[/tex]
Hope this helps
Answer:
9 Times
Step-by-step explanation:
You need to find how many times farther away Amy sets up her target. She used to set it up 5 feet away. Start by finding how many feet away she sets up her target now.
There are 3 feet in a yard, so multiply 15 yards by 3.
15×3=45
Now, Amy sets up her target 45 feet away. She used to set it up 5 feet away. You can use a multiplication fact to find how many times farther away she sets up her target now.
5×9=45
Amy sets up her target 9 times farther away now.
1) The population of Leafy Lake starts at 3,000 and grows by 25% every year. What will the population be in 6 years?
how do I solve it
Answer:
Step-by-step explanation:
Rate of increase = r = 25%
n = number of years = 6
P = Current population = 3000
Population after n years = [tex]P*(1 + \frac{r}{100})^{n}[/tex]
[tex]= 3000 * (1 +0.25)^{6}\\\\= 3000 * (1.25)^{6}\\\\= 3000 * 3.8\\\\= 11400=[/tex]
2. A company manufactures fuses. The percentage of non-defective fuses is 95.4%. A sample of 9 fuse was selected. Calculate the probability of selecting at least 3 defective fuses.
Answer:
0.0067 = 0.67% probability of selecting at least 3 defective fuses.
Step-by-step explanation:
For each fuse, there are only two possible outcomes. Either it is defective, or it is not. The probability of a fuse being defective is independent of any other fuse, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
A company manufactures fuses. The percentage of non-defective fuses is 95.4%.
This means that 100 - 95.4 = 4.6% = 0.046 are defective, which means that [tex]p = 0.046[/tex]
A sample of 9 fuse was selected.
This means that [tex]n = 9[/tex]
Calculate the probability of selecting at least 3 defective fuses.
This is:
[tex]P(X \geq 3) = 1 - P(X < 3)[/tex]
In which
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{9,0}.(0.046)^{0}.(0.954)^{9} = 0.6545[/tex]
[tex]P(X = 1) = C_{9,1}.(0.046)^{1}.(0.954)^{8} = 0.2840[/tex]
[tex]P(X = 2) = C_{9,2}.(0.046)^{2}.(0.954)^{7} = 0.0548[/tex]
Then
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.6545 + 0.2840 + 0.0548 = 0.9933[/tex]
[tex]P(X \geq 3) = 1 - P(X < 3) = 1 - 0.9933 = 0.0067[/tex]
0.0067 = 0.67% probability of selecting at least 3 defective fuses.
Proportions in similar triangles
Answer:
x = 4
Step-by-step explanation:
Given that DE is parallel to AC then DE divides the sides proportionally, so
[tex]\frac{BD}{DA}[/tex] = [tex]\frac{BE}{EC}[/tex] , substitute values
[tex]\frac{x+2}{x}[/tex] = [tex]\frac{3}{2}[/tex] ( cross- multiply )
3x = 2(x + 2) ← distribute
3x = 2x + 4 ( subtract 2x from both sides )
x = 4
HELP
Find the circumference of this circle
using 3 for T.
C [?]
Answer:
3
Step-by-step explanation:
3
Find the set of the possible values of p for which the equation 3x² + px + 3 = 0 has no real roots.
*Using graphical method or comparing the signs.
Answer:
[tex]delta = {b}^{2} - 4ac = {p}^{2} - 4 \times 3 \times 3 = {p}^{2} - 36[/tex]
The equation has no real roots if delta <0
that is -6<p<6
An angle is bisected, forming two new angels. If the original angle had a measure of 14 degree, what is the measure of each new angle
Answer:
The measure of each angle will be 7 degrees. It is because a bisector divides an angle in two equal halves. 14 / 2 = 7
If using the method of completing the square to solve the quadratic equation
22 + 2x + 16 = 0, which number would have to be added to "complete the
square"?
Answer:
complete the square 2 x + 38 = 0
Step-by-step explanation:
Subtract the sum of 12ab –10bc –18ac and 9ab +12bc + 14ac from the sum of ab + 2bc and 3bc –ac.
Answer:
this is the answers
Find f(x+2) of the function f(x)= 4x^2+2x-4 HELP ASAP PLEASE WORTH 40 POINTS
Answer:
Given
f(x)= 4x²+2x-4To find f(x + 2) substitute x with x + 2 in the given function:
f(x+2)= 4(x + 2)² + 2(x + 2) - 4
= 4(x² + 4x + 4) + 2x + 4 - 4
= 4x² + 16x + 16 + 2x
= 4x² + 18x + 16
f(x+2)
4(x+2)²+2(x+2)-44(x²+4x+4)+2x-4-44x²+16x+16+2x4x²+18x+16someone help me with this
Answer:
stars: triangles
3 : 1
Step-by-step explanation:
There are 3 starts and 1 triangle
stars: triangles
3 : 1
Answer:
3:1
Step-by-step explanation:
3 Stars and 1 Triangle