Answer: ab + bc + ac = 155
Step-by-step explanation:
Given: a² + b² + c² = 90 and a + b + c = 20
Square the second equation, subtract it from the first equation, then simplify.
Square the second equation:
(a + b + c)² = 20²
a² + b² + c² + 2ab + 2bc + 2ac = 400
Subtract the equations:
a² + b² + c² + 2ab + 2bc + 2ac = 400
- (a² + b² + c² = 90)
2ab + 2bc + 2ac = 310
Simplify:
2(ab + bc + ac) = 310
÷2 ÷2
ab + bc + ac = 155
Solve the following equation 3x-1=2x -2/3
Answer:
1/3
Step-by-step explanation:
3x-1 = 2x -2/3
Collect like terms.
3x -2x = 1 - 2/3
x=1/3
How many solutions does the equation 8x-4=10 have ? PLEASE HELP QUICK
Answer:
one solution
Step-by-step explanation:
8x-4=10
Add 4 to each side
8x - 4+4 = 10+4
8x = 12
Divide by 8
8x/8 = 12/8x
x = 3/2
Answer:
one solution
Step-by-step explanation:
[tex]8x - 4 = 10 \\ 8x = 10 + 4 \\ 8x = 14 \\ \frac{8x}{8} = \frac{14}{8} \\ x = \frac{7}{4} [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
HELPZZZZ PLEZZZZZZZ
The height of a pyramid is doubled, but its length and width are cut in half. What is true about the volume of the new pyramid?
A) The new pyramid has a volume that is One-fourth the volume of the original pyramid.
B) The new pyramid has a volume that is One-half the volume of the original pyramid.
C) The new pyramid has the same volume as the volume of the original pyramid.
D) The new pyramid has a volume that is 2 times the volume of the original pyramid.
It's only one answer!!!
Answer:it is B
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
I got it correct
Which polyhedron has more faces than a tetrahedron but fewer faces than an
octahedron?
A. Dodecahedron
B. Hexahedron
c. lcosahedron
D. Pyramid
Answer:
B. Hexahedron
Step-by-step explanation:
It helps to know the number faces in the named solids.
tetrahedron: 4 faces
octahedron: 8 faces
A. Dodecahedron : 12 faces
B. Hexahedron : 6 faces
D. lcosahedron : 20 faces
D. Pyramid: 4 for a triangular pyramid; more for other pyramids
Which polyhedron has more than 4 faces and less than 8 faces?
Answer: B. Hexahedron
The reason the answer is not a pyramid is that a pyramid may have exactly 4 faces or more than 7 faces.
Answer:
B
Step-by-step explanation:
Cube or Hexahedron ( 6 faces) has more faces than tetrahedron ( 4 faces), but fewer than octahedron ( 8 faces)
what do 10n represent in p (n)=10n-1200
Step-by-step explanation:
The term 1200 represents the 11
How many meters are in a kilometre
Answer:
3000meter
Step-by-step explanation:
[tex] \frac{300000}{100} = 3000[/tex]
Can someone answer this question please please help me I really need it if it’s correct I will mark you brainliest .
Answer:
We divided the figure into 1 triangle and 2 rectangles.
Adding up the area of them, we get the total area:
A = 14 x (10 + 8 + 12 - 16)/2 + 8 x 5 + 6 x (12 + 8)
= 258 (yd2)
Hope this helps!
:)
Evaluate the finite geometric series for the specified number of terms. 1 + 2 + 4 + 8 + 16 + ...; n = 27
What is the greatest common factor of 8m^{2}8m
2
8, m, squared, 4m4m4, m, and 10m^410m
4
10, m, start superscript, 4, end superscript?
Answer:
2mStep-by-step explanation:
Given the functions 8m², 4m and 10m⁴, in order to find the greatest common factor, we will find a factor common to all the functions as shown;
8m² = 2*2*(2*m)*m
4m = 2*(2*m)
10m⁴ = (2*m)*5*m³
from the three expansion, it ca be seen that only 2 and m are common to all the function as shown in parentheses.
The greatest common factor factor will be the product of 2 and m i.e 2*m = 2m
PLZ HELP MEH!! it would mean a lot! :) thx
Which of the following equations are equivalent to -2m - 5m - 8 = 3 + (-7) + m?
-15m = -4m
-7m - 8 = m - 4
-3m - 8 = 4 - m
m - 4 = -7m - 8
-8 - 7m = -4 + m
-8 - 3m = 4 - m
Step-by-step explanation:
-2m - 5m - 8 = 3 - 7 + m
Solving like terms
-7m - 8 = - 4 + m
Rearranging
-7m - 8 = m - 4
If using the method of completing the square to solve the quadratic equation x^2+15x+25=0x
2
+15x+25=0, which number would have to be added to "complete the square"?
Answer:
x = -15/2 ± (1/2)*5√5
Step-by-step explanation:
I will assume that you meant x^2+15x+25=0.
To complete the square, take half of the coefficient of x, square the result, add this square into the equation after '15x,' and then subtract the square from the result:
x^2+15x+25=0 => x^2 + 15x + (15/2)^2 - (15/2)^2 + 25 = 0.
Rewrite the first two terms as (x + 15/2)^2 - 225/4 + 100/4 = 0, or
(x + 15/2)^2 - 125/4 = 0
Taking the square root of both sides, we obtain the solutions:
x + 15/2 ±√[125/4], or
x = -15/2 ± (1/2)*5√5
The quadratic equation x²+15x+25=0, (15/2)² is a number to be added to "complete the square"
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .
The quadratic equation x²+15x+25=0
x²+15x+(15/2)²+25-(15/2)²=0
(x+15/2)²+25-225/4
(x+15/2)²+(100-225)/4
(x+15/2)²+(-125/4)
(x+15/2)²-(√125/√4)²
(x+15/2+√125/√4)(x+15/2-√125/√4)
(x+15/2+√125/2)(x-15/2-√125/2)
(x+(15+√125)/2)(x-(15+√125)/2)
Hence (15/2)² is a number to be added to "complete the square"
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Doroteo determined that the correlation coefficient for a set of data was -.9 what percent of the total variation in the Y values is not explained by the regression line
Answer: 10%
Step-by-step explanation:
(1 - 0.9) × 100 = 10%
With a correlation Coefficient of -0.9. This signifies a strong negative correlation between the x and y variables. That is an increase in the x variable leads to a corresponding decrease in the y variable and vice versa. The correlation Coefficient could also be interpreted to mean that about 90% of the variation in the y variable is explained by the regression line or equation. With the the remaining 10% being unexplained. This is why a correlation Coefficient of 1 or - 1 refers to a perfect relationship, meaning 100% variation in y is explained by the regression line.
. Find the range of the data.
7,4, 12, 1, 8, 8, 4, 14, 13, 9, 11, 10, 2,7,5, 3, 1, 8,5,3
Answer:
Range: 13
Step-by-step explanation:
Population size:20
Lowest value: 1
Highest value: 14
Answer: 13
Hope this helps.
Ross drives 280 miles in 4 hours. If Ross continues to drive at the same rate, how many miles can he drive in 12 hours?
Answer:
Step-by-step explanation:3,360
plz help me I can't do anything and I have to pass this assignment for online School
Answer:
It will take 8
Step-by-step explanation:
2 cubic units we take 1 / 4 which four equals one and eight equals 2, so it will take a eight 1/4 to fill the prism.
$1500.00 in a simple interest savings account. Two years later, the total account balance is $1665.00.
What is the interest rate of the savings account?
What will be the total amount of money in the account after 8 years? $
please answer
Answer:
interest rate=45.04
I after 8 years=5994
step on step explainaton:
I=PRT
1500=1665×r/100×2
r=45.04
I after 8 years= I=PRT
=1665×45/100×8=5994
The table shows the height in feet, y, of a pebble dropped from a tall bridge after x seconds.
Which descriptions are true of the function shown in the table? Check all that apply.
quadratic
linear
rational
y = –16x + 150
y = –16x2 + 150
y = + 150
nvm . jus got it wrong and it's A and E
Answer:
The answer is A & E
Step-by-step explanation:
quadratic
y=-16x^2 + 150
Answer: A and E
Step-by-step explanation:
edge 2023
In a class full of men and woman 4/7 are woman what is the ratio of men and woman in the simplist form ?
Answer:
4:7
Step-by-step explanation:
i don't think that you can simplify it any further so you just change the / to a :
Shantanu bought more apples than bananas, and he bought more bananas than cantaloupes. Let a represent the number of apples Shantanu bought, let b represent the number of bananas, and let c represent the number of cantaloupes. Let's compare the expressions b+c and a. Which statement is correct?
Answer:
There is not enough information to tell
Step-by-step explanation:
We are given that:
a>b
b>c
Therefore:
a>c
However, we are not given enough information to draw a relationship between b+c and a.
In order to better understand this situation, try applying values. Let a=4, b=2, and c=1.
In this case, a > b+c. However if a = 9, b=8 and c=7, then a < b+c.
In both stipulated cases, the given conditions are met, but no conclusion can be reached regarding the relationship between b+c and a.
Please help me with this question is hard and i will give you a Brainiest
Answer:
0
Step-by-step explanation:
10(x-2)=-20
10x-20=-20
10x=0
x=0
Can somebody help me on this one?
Answer:
I pretty sure the answer is Nervous
nervous, because it sends signals to your brain and it’s basically the main thing that makes you move.
for example, when the oven is hot you can feel the heat and notice how you don’t touch it, that’s because your brain knows that if you touch the oven you’re going to burn yourself and your brain stops you from touching the surface of the oven.
Rewrite the equation by completing the square.
x^2+ 12x + 36 = 0
Answer:
(x+6)^2 =0
Step-by-step explanation:
x^2+ 12x + 36 = 0
Subtract 36 from each side
x^2+ 12x + 36-36 = 0-36
x^2 +12x = -36
Take the coefficient of x
12
Divide by 2
12/2 =6
Square it
6^2 =36
Add this to each side
x^2+ 12x + 36 = -36+36
(x+12/2)^2 = 0
(x+6)^2 =0
The given quadratic equation [tex]x^2+ 12x + 36 = 0[/tex] is written in squaring form as [tex](x + 6)^2 = 0[/tex].
Used the concept of a quadratic equation that states,
An algebraic equation with the second degree of the variable is called a Quadratic equation.
Given that the equation is,
[tex]x^2+ 12x + 36 = 0[/tex]
Now completing the square as
[tex]x^2+ 12x + 36 = 0[/tex]
It can be written as,
[tex]x^2+ 12x + 6^2 = 0[/tex]
[tex]x^2+ 2\times 6\times x + 6^2 = 0[/tex]
[tex](x + 6)^2 = 0[/tex]
Therefore, the equation is written as [tex](x + 6)^2 = 0[/tex].
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In a study done in Miami's economically disadvantaged community, it was determined that 38 out of 62 children who attended preschool needed social services later in life compared to 49 out 61 children who did not attend preschool. Test the claim that the proportion of children who need social services later in life is greater amongst the children who did not attend preschool compare to the ones who did attend preschool. Use a 0.05 level of significance.
Answer:
Step-by-step explanation:
This is a test of 2 population proportions. Let 1 and 2 be the subscript for the children who attended preschool and need social services later in life and children who did not attend preschool and need social services later in life. The population proportion for the children who attended preschool and children who did not attend preschool would be p1 and p2 respectively.
p1 - p2 = difference in the proportion of proportion of the children who attended preschool and children who did not attend preschool .
The null hypothesis is
H0 : p1 = p2
p1 - p2 = 0
The alternative hypothesis is
Ha : p1 < p2
p1 - p2 < 0
it is a left tailed test
Sample proportion = x/n
Where
x represents number of success(number of complaints)
n represents number of samples
For children who attended preschool,
x1 = 38
n1 = 62
p1 = 38/62 = 0.61
For children who did not attend preschool,
x2 = 49
n2 = 61
p2 = 49/61 = 0.8
The pooled proportion, pc is
pc = (x1 + x2)/(n1 + n2)
pc = (38 + 49)/(62 + 61) = 0.71
1 - pc = 1 - 0.71 = 0.29
z = (p1 - p2)/√pc(1 - pc)(1/n1 + 1/n2)
z = (0.61 - 0.8)/√(0.71)(0.29)(1/62 + 1/61) = - 0.19/0.08183139728
z = - 2.32
Since it is a left tailed test, we would determine the probability for the area below the z score from the normal distribution table. Therefore,
p = 0.01
Since alpha, 0.05 > than the p value, 0.01, then we would reject the null hypothesis. Therefore, At a 5% level of significance, the the proportion of children who need social services later in life is greater amongst the children who did not attend preschool compare to the ones who did attend preschool.
WORTH 60 POINTS AND BRAINLIEST. DO NOT PLAGIARIZE OR WRITE FAKE ANSWERS I WILL REPORT THANK YOU!!
A. David notices that the shape of the Ligersville toxic dump site is somewhat like a triangle. He claims that he can approximate the perimeter of the dump site without doing any extra measurements. What assumption about side AB of the dump site would David need to make in order to justify his claim?
B. Based on the assumption in part A, determine the approximate length of side AB of the dump site. Explain your reasoning in at least two sentences.
C. Determine the approximate perimeter of the Ligersville toxic dump site. Explain your reasoning.
Answers and Step-by-step explanations:
A. David would need to assume that side AB is the hypotenuse of the almost-right triangle that A, B, and C make. That way, he can use the Pythagorean Theorem to solve for AB.
B. AB² = 24² + 32² = 1600 ⇒ AB = √1600 = 40 yards
We can use the Pythagorean Theorem because we assume that ABC is in the form of a right triangle, with AB as the hypotenuse. Then since whenever we have a right triangle, we can use the Pythagorean Theorem to solve for an unknown side, that applies here as well.
C. The approximate perimeter is 24 + 32 + 40 = 96 yards. Using the approximation of AB from part B, we simply add up all the side lengths of this "triangle", as that is the definition of "perimeter". Thus, when we add them all together, we get a total of 96 yards.
Answer:
A. Assumption: length of the curve AB is equal to the hypotenuse of the triangle formed AB was a straight line.
B. 40 yards
C. 96 yards
Step-by-step explanation:
A. Assumption: length of the curve AB is equal to the hypotenuse of the triangle formed AB was a straight line.
B. AB² = 32² + 24²
AB² = 1600
AB = 40
Since we have assumed that AB is equal to the hypotenuse, we can use pythagoras theorem to find an approximate length of AB
C. Perimeter is the sum of all lengths:
32 + 24 + 40 = 96
Antonio has a kite, in the directions on how to put the kite together it says that the drawing is to scale where 10 cm = 1 meter. If the kite when put together is 1.5 m. Tall, how tall is it in the drawing?
Answer: 15cm.
Step-by-step explanation:
Hi, to answer this question we have to multiply the real height of the kite (1.5m) by the scale factor of the drawing (10):
Mathematically speaking:
Since 1 m = 10 cm
So:
1.5 m x 10 cm/m = 15 cm
The kite is 15 centimeters tall in the drawing.
Feel free to ask for more if needed or if you did not understand something.
Mr. Maxwell White bought a house at the cost of GHȼ250,000,000.00. He paid 20% of the cost out of his own resources an took a loan for the remaining amount at 2 1/2 % simple interest per annum. Calculate the total amount Mr. Maxwell White paid for the house, if he paid the loan 8 years later.
Answer:GHȼ290,000,000
Step-by-step explanation:
Given the following :
Cost of house = 250,000,000
Amount paid out of his own resources = 20% of house cost
Amount loaned = 250,000,000 - (20% of 250,000,000)
Rate = 2 1/2% = 5/2% = 0.025
Period or time = 8 years
Therefore,
Amount paid out of his own resources :
0.2 × 250,000,000 = 50,000,000
Amount loaned = (250,000,000 - 50,000,000) = 200,000,000 = principal
Simple Interest on loan = (principal × rate × time)
200,000,000 × 0.025 × 8 = 40,000,000
Total amount paid back= (200,000,000 + 40,000,000) = 240,000,000
Total amount paid for the house :
Total loan paid + amount paid from own resource:
240,000,000 + 50,000,000 = 290,000,000
Aprivate high school charges $57,000 for tuition, but this figure is expected to rise 10% per
year. What will the tuition be in 3 years?
Answer:
$75,867
Step-by-step explanation:
that will be the answer
Please help! Correct answers only please!
You roll a 6-sided die two times.
What is the probability of rolling an odd number and then rolling a 3?
Simplify your answer and write it as a fraction or whole number.
Answer:
1/12
Step-by-step explanation:
to get a odd number is a 1/2 chance. to roll a 3 is a 1/6 chance. multiply those together to get 1/12.
if the radius of a circle 3 meters. what is the circles diameter?
Answer:
6 m
Step-by-step explanation:
the radius is half of the diameter
A quadrilateral is circumscribed around a circle. The sum of the lengths of two of its opposite sides is 15 cm. Find the perimeter of the quadrilateral.
Answer:
The perimeter of the quadrilateral is 30 cm.
Step-by-step explanation:
To circumscribe implies drawing a required figure around a given figure, while to inscribe means drawing a required figure inside a given figure. From the question, the quadrilateral is circumscribed around the circle.
And given that the sum of the lengths of its two opposite sides is 15 cm.
The perimeter of a figure is the sum of the length of the sides of the figure. For this quadrilateral, the sum of opposite sides are equal.Thus;
Perimeter of the quadrilateral = 2(l+b)
= (l + b) + (l + b)
= 15 + 15
= 30
The perimeter of the quadrilateral is 30 cm.