Answer:
ab² - 9
Step-by-step explanation:
Given in the question an expression
(ab + 3)(ab - 3)
To product mentally we will use polynomial identity called
Difference of squares
a² - b² = (a+b)(a-b)here a = ab
b = 3
(ab + 3)(ab - 3) = ab² - 3² = ab² - 9
Answer:
[tex]a^2b^2 - 9[/tex]
Step-by-step explanation:
We are given the following expression and we are to determine its product mentally:
[tex] ( a b + 3 ) ( a b - 3 ) [/tex]
For this, we can use the FOIL method, which stands for First, Outer, Inner, Last.
First means multiply the terms which come first in each of the binomial, Outer means multiply the outermost terms in the product. Inner means multiply the innermost two terms. Last means multiply the terms which occur last in each binomial.
So we get:
[tex]ab*ab +3*(-3)=a^2b^2 - 9[/tex]
The following figure is a trapezoid. The top base is 18 inches, and the bottom base is 22 inches. The height of the trapezoid is 8.5 inches. Find the area of the trapezoid. Explain or show how you got your answer.
Answer:
The area would be 170 cubic inches.
Step-by-step explanation:
To find the area, use the area of a trapezoid formula.
A = (a + b)/2*h
Now input the values
A = (18 + 22)/2 * 8.5
A = 40/2 * 8.5
A = 20 * 8.5
A = 170
How many thirds are in 1/3
?
I believe that the answer is there is 1 thirds in 1/3 I hope this helps
Answer:
one
Step-by-step explanation:
There is only one third is 1/3.
If you enjoy baking, think of it in the sense of a recipe calling for 4/3 cups of sugar. You grab a 1/3 cup and you would scoop four times in order to have 4/3 cups of sugar.
however since your recipe only calls for 1/3, you will only need one scoop.
for f(x)=3x+1 and g(x)=x^2-6, fine (f-g)(x)
Answer:
= -x^2 +3x+7
Step-by-step explanation:
f-g(x)
means to subtract g(x) from f(x)
f(x)- g(x)=3x+1 -(x^2-6)
Distribute the minus sign
f(x)-g(x)= 3x+1 -x^2 +6
= 3x+7-x^2
= -x^2 +3x+7
Answer:
[tex]\large\boxed{(f-g)(x)=-x^2+3x+7}[/tex]
Step-by-step explanation:
[tex](f-g)(x)=f(x)-g(x)\\\\f(x)=3x+1,\ g(x)=x^2-6\\\\\text{Substitute:}\\\\(f-g)(x)=(3x+1)-(x^2-6)\\\\(f-g)(x)=3x+1-x^2-(-6)\\\\(f-g)(x)=3x+1-x^2+6\\\\(f-g)(x)=-x^2+3x+(1+6)\\\\(f-g)(x)=-x^2+3x+7[/tex]
If the sum of two congruent lengths equal the length of a third side,then the triangle created is isosceles. Is this a true statement?
Answer:
False
Step-by-step explanation:
To form a triangle, the sum of any two sides must be LARGER than the length of the third side.
This question says the sum of two sides are equal to the length of the third side. This wouldn't form a triangle.
Final answer:
Yes, the statement is true. If the sum of two congruent lengths is equal to the length of a third side in a triangle, then the triangle is isosceles.
Explanation:
Yes, the statement is true. If the sum of two congruent lengths is equal to the length of a third side in a triangle, then the triangle is isosceles.
In an isosceles triangle, two sides have the same length (congruent sides) and the remaining side is different (non-congruent side).
For example, if we have a triangle ABC where AB = BC (congruent sides) and AC is a different length (non-congruent side), then the triangle ABC is isosceles.
There are 18 black-and-white photos in the album if there are 90 photos in the album with fraction of the photos are black and white
Answer:
18/90 or you can say 18 over 90.
Step-by-step explanation:
So we have 18 out of the total of 90 photos.
So we know automatically the fraction is 18/90, we have 18 out of the rest of the 90 photos.
The fraction of photos in the album that are black and white is calculated by dividing the number of black and white photos (18) by the total number of photos (90) which results in a fraction of 0.2 or 1/5.
Explanation:To find what fraction of the photos are black and white, you'll start by considering all of the photos in the album. This is your total and it's 90 photos. Then, focus on the specific type of photos you're interested in, which are the black and white ones. There are 18 black and white photos. So to find the fraction of photos that are black and white, you would divide the number of black and white photos (18) by the total number of photos (90). This calculation would look something like this: 18 ÷ 90 = 0.2
So, the fraction of black-and-white photographs is 0.2 or, expressed as a common fraction, 1/5. This means that out of every 5 photos in the album, 1 of them is black and white.
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Given a=-3 and b=4 and c=-5, evaluate |c-a-b|.
Answer:
2
4
6
answer should be 6
explanation: -5-(-3)-4 = -5 + 3 - 4 = -2 - 4 = -6 and the absolute value of -6 is 6
Can you please help me with this?
Answer:
A
Step-by-step explanation:
The volume of a prism can be found by multiplying the area of the base by the height. It is the formula V = B*h. Here B = 108. Substitute and solve.
V = 108*8 = 864
This is answer A.
What’s the answer to this question
Answer:
The length is 65 cm and the width is 12 cm
Step-by-step explanation:
A = lw = 780
P = 2 (l+w) = 154
The length is 5 more than 5 times the width
l=5w+5
P = 2 (l+w) = 154
Divide each side by 2
2 /2 (l+w) = 154/2
l+w = 77
Substituting l = 5w+5
5w+5 +w = 77
6w+5 = 77
Subtract 5 from each side
6w +5-5 = 77-5
6w = 72
Divide each side by 6
6w/6 = 72/6
w = 12
Now lets find l
l = 5w+5
l = 5(12)+5
l = 60+5
l = 65
which describes the type of sequence in 99, 89.9, 78.8, 68.7, . . . . . ?
a) neither geometric nor arithmetic
b) geometric
c) arithmetic
d) both arithmetic and geometric
(pLeAsE TelL mE wHY yOu PIcKeD YoUr AnSwER)
Answer:
Step-by-step explanation:
The is neither geometric nor arithmetic. The differences have to be the same.
99 - 89.9 = 9.1
89.9 - 78.8 = 11.1
78.8 - 68.7 = 10.1
==========
Find the area of the shaded region
write an expression for the calculation the difference of the products 5 and 2 and 5 and 1
Answer: 5
Step-by-step explanation: The first piece of information that you need to know is that the product is the answer when two numbers are multiplied. Therefore, you need to multiply the two sets of numbers, and then subtract.
The formula will be:
(5 x 2) - (5 x 1)=
First, do what is inside the parentheses:
10 - 5=
And solve...
5
The expression for the calculation the difference of the products 5 and 2 and 5 and 1 is (5 x 2) - (5 x 1).
What are arithmetic Operation?Addition (Finding the Sum; '+') Subtraction (Finding the difference; '-') Multiplication (Finding the product; '×' ) Division (Finding the quotient; '÷')
The first thing you should be aware of is that the result of multiplying two integers is the product.
The two sets of numbers must therefore be multiplied before being subtracted.
The Expression will be:
(5 x 2) - (5 x 1)
First, work on the brackets separately
(5 x 2) = 10
(5 x 1)= 5
So, (5 x 2) - (5 x 1)
= 10 - 5
=5
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Which expression is a factor of 9r^2-4r+1?
A)3r-1
B)r-1
C)9r-1
D)There are no real factors
Answer:
Step-by-step explanation:
We could answer this either by checking each listed expression to see whether it is a factor of 9r^2-4r+1, or
We could take the coefficients of 9r^2-4r+1, determine the quantity b²-4ac (called the 'discriminant') and draw a conclusion based upon whether the discriminant is -, + or 0.
Let's use the 2nd approach.
Here, a = 9, b = -4 and c = 1.
Then the discriminant is b²2 - 4ac, or (-4)² - 4(9)(1), or 16 - 36.
Since 16 - 36 is negative, we conclude that this 9r^2 - 4r + 1 has NO REAL FACTORS.
Answer: is C
Step-by-step explanation:
Complete each of the following statements with the letter that represents the expression
The equivalent expressions are:
(3x² - 7x + 14) + (5x² + 4x - 6) = B. 8x² - 3x + 8
(2x² - 5x - 3) + (-10x² + 2x + 7) = A. -8x² - 3x + 4
(12x² - 2x - 13) + (-4x² + 5x + 9) = C. 8x² + 3x - 4
We have,
Expression:
(3x² - 7x + 14) + (5x² + 4x - 6)
Combine like terms.
3x² - 7x + 14 + 5x² + 4x - 6
8x² - 3x + 8
Expression:
(2x² - 5x - 3) + (-10x² + 2x + 7)
Combine like terms.
2x² - 5x - 3 - 10x² + 2x + 7
-8x² - 3x + 4
Expression:
(12x² - 2x - 13) + (-4x² + 5x + 9)
Combine like terms.
12x² - 4x² - 2x + 5x - 13 + 9
8x² + 3x - 4
Thus,
(3x² - 7x + 14) + (5x² + 4x - 6) = B. 8x² - 3x + 8
(2x² - 5x - 3) + (-10x² + 2x + 7) = A. -8x² - 3x + 4
(12x² - 2x - 13) + (-4x² + 5x + 9) = C. 8x² + 3x - 4
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Question
I need to know what this is please help me
the answer is D. Multiply by 2 to get the next term
Answer:
It is D, multiply by 2 to get the next term.
Step-by-step explanation:
1 x 2 = 2
2 x 2 = 4
4 x 2 = 8
and so on.....
Plzzzzzzzzz Help meeeee
Answer:
circumference so with all the diameters and stuff it would be 4[tex]\pi[/tex] or 12.56
Jamal is making a scale drawing of his property. The drawing is 15 inches long and 12 inches wide. How long and wide is the property if one-inch equals 5 feet?
Answer:
75ft long 60 ft wide
Step-by-step explanation:
one inch is 5 feet so for every foot you would x 5
15x5=75
12x5=60
The actual dimensions of Jamal's property are 75 feet long and 60 feet wide.
How to solve for the dimensionsIf Jamal's scale drawing is 15 inches long and 12 inches wide, and one inch on the drawing represents 5 feet in real life, we can calculate the actual dimensions of the property.
Length of the property:
15 inches on the drawing represents 15 * 5 = 75 feet in real life.
Width of the property:
12 inches on the drawing represents 12 * 5 = 60 feet in real life.
Therefore, the actual dimensions of Jamal's property are 75 feet long and 60 feet wide.
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A cube had a volume of 1/512 cubic meter. What is the length of each side of the cube using the formula "volume=Length×Width×Hight." Please explain your thinking.
Answer:
The length of each side of the cube is [tex]\frac{1}{8}\ m[/tex]
Step-by-step explanation:
we know that
The volume of a cube is equal to
[tex]V=LWH[/tex]
but remember that in a cube
Length, width and height have the same value
so
Let
b-----> the length side of the cube
[tex]L=W=H=b[/tex]
substitute in the formula
[tex]V=(b)(b)(b)=b^{3}[/tex]
In this problem we have
[tex]V=\frac{1}{512}\ m^{3}[/tex]
substitute and solve for b
[tex]b^{3}=\frac{1}{512}[/tex]
[tex]b=\sqrt[3]{\frac{1}{512}}\\ \\b=\frac{1}{8}\ m[/tex]
therefore
The length of each side of the cube is [tex]\frac{1}{8}\ m[/tex]
See an algebraic equation to solve the problem. The sides of a triangle are in the ratio 3 : 4 : 5. What is the length of each side if that perimeter of the triangle is 90 cm?
Answer:
22.5
30
37.5
Step-by-step explanation:
You have to multiply each ratio part by x to get them properly set up to add to 90.
3x + 4x + 5x = 90 Combine the left side
12x = 90 Divide by 12
12x/12 =90/12 Do the division
x = 7.5
3x = 3*7.5 = 22.5
4x = 4*7.5 = 30
5x = 5*7.5 = 37.5
Total 90
Final answer:
The lengths of the sides of the triangle with a perimeter of 90 cm and sides in the ratio 3:4:5 are 22.5 cm, 30 cm, and 37.5 cm. This is found by setting up an equation with variable x representing the common multiplier for the ratio, solving for x, and then calculating each side's length.
Explanation:
To solve the problem of finding the length of each side of a triangle with sides in the ratio 3:4:5 and a perimeter of 90 cm, we first set up an algebraic equation. Let the sides of the triangle be 3x, 4x, and 5x, respectively. The perimeter is the sum of these sides, so we have the equation 3x + 4x + 5x = 90 cm. Simplifying this gives us 12x = 90 cm. To find the value of x, we divide both sides of the equation by 12, resulting in x = 90 cm / 12, which simplifies to x = 7.5 cm. Subsequently, the lengths of the sides are 3x = 22.5 cm, 4x = 30 cm, and 5x = 37.5 cm.
a biologist wants to estimate the median with of over two hundred oak trees in a forest
Answer:
47 cm
Step-by-step explanation:
its really simple just put them in from least to greatest then cross one off from each side until you get your middle number.
what are the trig ratios for a right triangle?
Sintheta=[tex]\frac{Perpendicular}{Hypotenuse}[/tex]
Costheta=[tex]\frac{Base}{Hypotenuse}[/tex]
Tantheta=[tex]\frac{Perpendicular}{Base}[/tex]
Easy way to remember this ' Some People Have Curly Brown Hair Through Proper Brushing'
Hope this helps :)
The trigonometric ratios for a right triangle are sine, cosine, and tangent, which relate the sides of the triangle.
Explanation:The trigonometric ratios for a right triangle are sine, cosine, and tangent. Each ratio is defined in terms of the sides of the triangle.
The sine (sin) ratio is defined as the ratio of the opposite side to the hypotenuse. It is calculated as sin(A) = y/h, where y is the length of the opposite side and h is the length of the hypotenuse.
The cosine (cos) ratio is defined as the ratio of the adjacent side to the hypotenuse. It is calculated as cos(A) = x/h, where x is the length of the adjacent side and h is the length of the hypotenuse.
The tangent (tan) ratio is defined as the ratio of the opposite side to the adjacent side. It is calculated as tan(A) = y/x, where y is the length of the opposite side and x is the length of the adjacent side.
Felipe transferred a balance of $3700 to a new credit...
Answer:
(3700)(1+.059/12)^4(1+.172/12)^8 is the corect answer -Apex
Step-by-step explanation:
Answer:
Option C is correct.
Step-by-step explanation:
Felipe transferred a balance of $3700 to a new credit.
The card had an introductory offer of 5.9% APR for the first 4 months and after that 17.2 % APR.
The card compounds interest monthly, that gives n = 12
So, the equation that represents Felipe's balance at the end of the year will be:
[tex]p(1+\frac{r}{n})^{a}\times (1+\frac{r}{n})^{b}[/tex]
Here a is the introductory rate number of months that is 4
And b is the rest of the standard months that is 8
So, the expression becomes:
[tex]3700(1+\frac{0.059}{12})^{4}\times (1+\frac{0.172}{12})^{8}[/tex]
PLEASE HELP FAST!!!
Simplify the expression.
(x + 6)^2
Please don’t guess I really need to get this problem correct. My grade depends on it!
(a+b)²=a²+2ab+b²
(x+6)²=x²+2× x × 6+6²=x²+12x+36
hope this helps :)
Answer:
[tex]\large\boxed{(x+6)^2=x^2+12x+36}[/tex]
Step-by-step explanation:
[tex](x+6)^2\\\\\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\=x^2+2(x)(6)+6^2=x^2+12x+36\\\\\text{Other method}\\\\(x+6)^2=(x+6)(x+6)\\\\\text{use FOIL:}\ (a+b)(c+d)=ac+ad+bc+bd\\\\=(x)(x)+(x)(6)+(6)(x)+(6)(6)=x^2+6x+6x+36\\\\=x&^2+12x+36[/tex]
Can i get help on 80 and 90 please
Answer:
vvv
Step-by-step explanation:
80: The answer is .1675 or .17 (rounded)
Explanation: 1/4 = .25 and 2/3 = .66 repeated/ .67
.25x.67=.1675
90: B baskets in a attempts. There is 12 baskets in 25 attempts. 12/25 = .48
The field goal average is .48
Hope this helps xoxo
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Solve. 90^x = 27. Explain every step.
Answer:
The answer is ⇒ x = 0.73244
Step-by-step explanation:
∵ 90^x = 27 ⇒ insert log in both sides
∴ [tex]log(90)^{x}=log(27)[/tex]
∵ 90 = 9 × 10 , 27 = 3³
∵ log(a)^b = b log(a)
∴ log(9 × 10)^x = x log(9 × 10)
∴ [tex]xlog(9*10)=log(3^{3})[/tex]
∵ log(a × b) = log(a) + log(b)⇒log(9 × 10) = log(9) + log(10)
∴ [tex]x[log(9)+log(10)]=3log(3)[/tex]
∵ log(10) = 1 , 9 = 3²
∴ [tex]x[log(3)^{2}+1]=3log(3)[/tex]
∴ [tex]x[2log(3)+1] = 3log(3)[/tex]
∴ x = (3log3)/[2log(3)+1]
∴ x = 0.73244
ANSWER
[tex]x \approx0.732[/tex]
EXPLANATION
The given exponential equation is
[tex] {90}^{x} = 27[/tex]
We take natural log of both sides
[tex] ln( {90}^{x} ) = ln(27) [/tex]
Recall and the following property of logarithms.
[tex] ln( {a}^{n} ) = n \: ln(a) [/tex]
This implies that;
[tex]x ln(90) = ln(27) [/tex]
Solve for x.
[tex]x = \frac{ ln(27) }{ ln(90) } [/tex]
[tex]x \approx0.732[/tex]
sara works at a local hotdog stand. she makes $5.00 per hour (h) and $1 per hot dog (d) that she sells. write an equation that sara could use to determine her pay check.
Answer: 5h + d
Step-by-step explanation: The equation that Sara could use to determine her pay check is 5h + d = amount she will earn.
Help need ASAP!! Thanks!! Length of a rectangle is 5 cm longer than the width. Four squares are constructed outside the rectangle such that each of the squares share one side with the rectangle. The total area of the constructed figure is 120 cm2. What is the perimeter of the rectangle?
Answer:
The perimeter of rectangle is [tex]18\ cm[/tex]
Step-by-step explanation:
Let
x-----> the length of the rectangle
y----> the width of the rectangle
we know that
[tex]x=y+5[/tex] ----> equation A
[tex]120=xy+2x^{2}+2y^{2}[/tex] ---> equation B (area of the constructed figure)
substitute the equation A in equation B
[tex]120=(y+5)y+2(y+5)^{2}+2y^{2}[/tex]
[tex]120=y^{2}+5y+2(y^{2}+10y+25)+2y^{2}\\ 120=y^{2}+5y+2y^{2}+20y+50+2y^{2}\\120=5y^{2}+25y+50\\5y^{2}+25y-70=0[/tex]
using a graphing tool -----> solve the quadratic equation
see the attached figure
The solution is
[tex]y=2\ cm[/tex]
Find the value of x
[tex]x=y+5[/tex] ----> [tex]x=2+5=7\ cm[/tex]
Find the perimeter of rectangle
[tex]P=2(x+y)=2(7+2)=18\ cm[/tex]
The graph models which linear equation?
3x + 5y = 10
v-2x-2
3x - 5y = 10
Answer:
a
Step-by-step explanation:
Based on the slope and y-intercept, the graph most closely models the linear equation 3x + 5y = 10.
Out of the three choices you provided, the graph most closely resembles the equation 3x + 5y = 10. Here's why:
Slope: The slope of the line in the graph is positive. This means that as x increases, y also increases. The equation 3x + 5y = 10 has a positive slope of [tex]$\dfrac{3}{5}$[/tex], which matches the slope of the line in the graph.Y-intercept: The y-intercept of the line in the graph is 2. This means that the line passes through the point (0, 2). When you plug x = 0 into the equation 3x + 5y = 10, you get 5y = 10, which means y = 2.So, the equation 3x + 5y = 10 also has a y-intercept of 2.
The other two equations do not match the graph as well:
The equation v - 2x - 2 does not have a positive slope.The equation 3x - 5y = 10 has a negative slope and a different y-intercept.What is the answer to this question?
Answer:
80 HOPE THIS HELPED
Step-by-step explanation:
20+20+20+20=80
20 X 4 = 80
what is the volume of a cylinder with a radius of 6 cm and height of 13
Answer:
V≈1470.27cm³
Hope this helps :D
What is the solution to the equation 1 over 2 multiplied by n equals 8 ? (5 points) n = 10 n = 6 n = 4 n = 16
Answer: n=16
Step-by-step explanation:
The solution to the equation is n = 16.
The equation 1/2 * n = 8 can be solved by multiplying both sides by 2 to find n = 16.
To solve the equation 1/2 * n = 8:
Multiply both sides by 2 to isolate n: n = 8 * 2 = 16.
Therefore, the solution to the equation is n = 16.