We have two types of textbooks. Let's use "x" to represent the number of math textbooks and "y" to represent the number of history textbooks.
Altogether, the bookseller sold 240 math and history textbooks. So:
x + y = 240
Now, the number of history textbooks sold was 72 less than the number of math books sold. So:
y = x - 72
Now we can substitute for y in the equation and solve:
x + y = 240
x + (x - 72) = 240
2x - 72 = 240
2x = 312
x = 156
The bookseller sold 156 math textbooks.
Since y = x - 72, he must have sold 84 history textbooks.
Let's check our answers:
x + y = 240
156 + 84 = 240
That is true, so we did get the correct answers.
The ___ is the ratio of a length of the new figure to the corresponding length on the original figure
What does please put it in simplest radical form and rationalize the denominators
N=
M=
Answer:
n = 6
m = 6√3
Step-by-step explanation:
Reference angle = 30°
Opposite = n
Adjacent = m
Hypotenuse = 12
✔️To find n, apply the trigonometric ratio, SOH:
Sin 30° = Opp/Hyp
Sin 30° = n/12
n = Sin 30° × 12
n = ½ × 12 = 6
✔️To find m, apply the trigonometric ratio, CAH:
Cos 30° = Adj/Hyp
Cos 30° = m/12
m = Cos 30° × 12
m = √3/2 × 12 (cos 30 = √3/2)
m = √3 × 6
m = 6√3
What is the range of the function on the graph?
Range is the output values which are the y values.
The dot is at y = 2 and the line moves upward to the right off the graph. This means the line will continue to infinity.
The range would be 2 to infinity.
(2, infinity)
Can someoneee please help me
9514 1404 393
Answer:
37°
Step-by-step explanation:
The diagonals of a rhombus are angle bisectors. Angle 1 matches the other half of angle L.
∠1 = 37°
__
Angle 2 is the complement, 53°, and angle 3 is the same as angle 2, 53°.
The diagonals of a rhombus are perpendicular bisectors of each other, so angle 4 is 90°.
INDEPENDENT PRACTICE 3. Teresa makes a circular pizza with a 14-inch diameter. Which is the approximate area of her pizza? A. 43.96 in? B. 87.92 in2 C. 153.86 in2 D. 615.44 in?
A. 43.96in?
Step_by_step explanationSolve for x.
3x - 4 = 2x - 10
O x = 6
OX= -6
OX= 14
O x=-14
Please help
Will give you brainly
Answer:
x = -6
Step-by-step explanation:
We have the equation 3x - 4 = 2x - 10 and are asked to find "x".
To solve , we need to get "x" alone entirely.
3x - 4 = 2x - 10
Subtract 2x from both sides :
x - 4 = -10
Add 4 to both sides to get our answer :
x = -6
Answer:
the answer is equal to-6
Bob took out a 5 year loan for $4000 and paid 3% annual simple interest
Bill took out a 4 year loan for $4000 and paid 5% annual simple interest
What is the sum of amounts of interest bob and bill paid for their loans
twenty subtract from 28
Answer:
8
Step-by-step explanation:
Answer:
-8
Step-by-step explanation:
20-28= -8
Express f(x) in the form f(x) = (x - k)q(x) +r for the given value of k.
f(x) = 4x^3+ x² + x-8, k= -1
Answer:
f(x) = (x + 1)*(4*x² - 3*x + 4) - 12
Step-by-step explanation:
We have:
f(x) = 4*x³ + x² + x - 8
We want to write this in:
f(x) = (x - k)*q(x) + r.
with k = -1
Then we want to write:
4*x³ + x² + x - 8 = (x - (-1))*q(x) + r
4*x³ + x² + x - 8 = (x + 1)*q(x) + r
Because f(x) is polynomial of degree 3, we know that q(x) must be a polynomial of degree 2.
then:
q(x) = a*x² + b*x + c
Then:
4*x³ + x² + x - 8 = (x + 1)*(a*x² + b*x + c) + r
4*x³ + x² + x - 8 = a*x³ + b*x² + c*x + a*x² + b*x + c + r
if we take common factors in the right side we get:
4*x³ + x² + x - 8 = a*x³ + (b + a)*x² + (c + b)*x + (c + r)
Now, we must have:
4*x³ = a*x³
then:
4 = a
We also must have:
x² = (b + a)*x²
1 = (b + 4)
1 - 4 = b
-3 = b
We also must have:
x = (c + b)*x
1 = (c + (-3))
1 + 3 = c
4 = c
And finally:
- 8 = (c + r)
-8 = 4 + r
-8 - 4 = r
-12 = r
Then:
f(x) = (x + 1)*(4*x² - 3*x + 4) - 12
Solve for
3+4 |x/2 + 3| = -11
9514 1404 393
Answer:
no solution
Step-by-step explanation:
The absolute value cannot be negative. Here, the absolute value expression must be -3.5 in order to satisfy the equation. It cannot have that value.
there is no solution
David invests $7000 in two different accounts. The first account paid 2 %, the second account paid 5
% in interest. At the end of the first year he had earned $182 in interest. How much was in each
account?
Answer:
3,990
Step-by-step explanation:
y=((3x+1)³)-², find dy/dx
please help with this problem
Answer:
choice 1) 0, -4/5
Step-by-step explanation:
1/(t² + t) = 1/t - 5
multiply both sides of the equation by (t² + t):
1 = (t² + t)/t - 5t² - 5t
1 = t + 1 - 5t² -5t
-5t² - 4t = 0
t(-5t - 4) = 0
t = 0
-5t = 4
divide both sides by -5:
t = -4/5
Carl paid $40 for 12.5 gallons of gas.After calculating,he said that the cost per gallon was about 31 cents per gallon.Is there anything wrong with Carl's thinking?.
Answer:
Well yes, because it should have cost $3.2 PER gallon
Step-by-step explanation:
Divide 40 by 12.5 to find out how much of a per gallon costs! Hope it helps.
a publisher for a promising new novel figures fixed costs overhead, advances, promotion, copy editing, type setting and so on at $57,000 and variable costs printing, paper, binding, shipping at $2.90 for each book produced. If the book is sold to distributors for $10 each, how many must be sold to break even?
Answer:
$2.90 for each book produced. If the book is sold to distributors for $10 each, how many must be sold to break even?
Step-by-step explanation:
. citizen of the represented state
What type of polynomial is 14x2 + 3x – 15?
Answer:
Step-by-step explanation:
There are three terms. So, 14x² + 3x -15 is a trinomial
PLEASE HURRY! FIRST PERSON GETS BRAINLIST!!!!!!
Hank is throwing a surprise party. The party costs $20 per person. Create an equation and graph to represent the relationship between the cost of the party and the number of friends attending.
The independent variable is ____.
A. Number of friends (f)
B. Cost of party (c)
Answer:
B
Step-by-step explanation:
A small pond contains 8 catfish and two bluegill. If eight fish are caught at random what is the probability that all of them are catfish
Drag each tile to the table to multiply
(6x – y)(2x – y + 2).
fill the table
2x -y 2
6x 12^2 -6xy 12x
-y -2xy y^2 -2y
Which temperature is warmer: -3 or -4 degrees Celsius?
Answer:
-3
Step-by-step explanation:
Chuck put new wallpaper in his bathroom. The pattern of the wallpaper
used 3 triangles to make a straight angle. The measures of the angles
are (9x - 72). (73x + ) and 11) What is the measure of the
obtuse angle? 7.3.5
ext
Tota
Answer:
x = 2.93
Step-by-step explanation:
The sum of angles of the triangle is 180degrees, hence;
9x - 72 + 73x + 11 = 180
82x - 61 = 180
82x = 180 + 61
82x = 241
Divide both sides by 82
82x/82 = 241/82
x = 2.93
Note that the functions might not be accurate but the same methos should be employed for any function given
Please help asap!!!!
Answer:
[tex] m\widehat {MP} =46\degree [/tex]
Step-by-step explanation:
By inscribed angle theorem:
[tex] m\angle MQP=\frac{1}{2} \times \widehat {MP} [/tex]
[tex] 23\degree =\frac{1}{2} \times m\widehat {MP} [/tex]
[tex] 23\degree \times 2= m\widehat {MP} [/tex]
[tex] m\widehat {MP} =46\degree [/tex]
Find the conjugate and product of
i2 + 9
Answer:
i2 - 9
-85
Step-by-step explanation:
Conjugate of an expression is gotten by simply changing the sign to the opposite sign. For example, the conjugate of 5 is -5, the conjugate of x+2 is x-2. Given the complex value 2i+9, the conjugate will be -85
Taking their product
(2i+9)(2i-9)
Expand
2i(2i)-9(2i)+9(2i)+9(-9)
= 4i²-18-+18i-81
= 4i² - 81
Since i² = -1
= 4(-1) - 81
= -4-81
= -85
Hence the product will give -85
Question 11. What is the product of 1.6 x 10- and 3.2 x 10' A. 5.12 x 10-4 B. 5.12 x 10 C.5.12 x 10 D. 5.12 x 104 please help will mark as brallinat
Answer:
A- [tex]5.12*10^{-4}[/tex]
Step-by-step explanation:
1.6* 3.2
add the exponents so 10 to the -4
The double box plot shows the cost of the top-selling lunch menu items at two local restaurants. Determine which inference is true about the two populations.
Answer:
The spread of the data for The Red Brick Grill is greater than that for Sophie's Cafe.
Step-by-step explanation:
In the picture
Geometry Question!!!
9514 1404 393
Answer:
12.5 cm
Step-by-step explanation:
Triangle IDA is a 3-4-5 right triangle with a scale factor of 5. That is, segment AI is 25 cm long. Since IS is half the length of the diagonal, it is ...
IS = (25 cm)/2
IS = 12.5 cm
__
If you like, you can work out the length of AI using the Pythagorean theorem:
AI² = DI² +DA²
AI = √(15² +20²) = √(225 +400) = √625 = 25
A triangle has side lengths of 12 centimeters, 12 centimeters, and 18 centimeters. What kind of triangle is it?
Answer:
isosceles triangle
Step-by-step explanation:
2 sides the same
A plumber charges a customer a one-time service fee of $79, $62 per hour for labor, and a surcharge of $15 per hour due to the call being an emergency.
Write an expression to represent the total charges for the plumber in two different ways. Let h represent the number of hours the job takes.
Answer:
As a plumber charges a customer a one-time service fee of $ 79, $ 62 per hour for labor, and a surcharge of $ 15 per hour due to the call being an emergency, to write an expression to represent the total charges for the plumber in two different ways, with H representing the number of hours the job takes, the following equations should be formulated:
Option 1:
Fixed amount + amount per hour multiplied by the number of hours + emergency amount multiplied by the number of hours = X
79 + 62H + 15H = X
Option 2:
Fixed amount + sum of emergency amount and the amount per hour multiplied by the number of hours = X
79 + ((62 + 15) x H) = X
Find the limit when X approaches zero
2xsinx/1-cosx
Answer:
4
Step-by-step explanation:
[tex] Lim_{x \to 0}\frac{2 x\sin x}{1-\cos x} [/tex]
[tex] =Lim_{x \to 0}\frac{2 x\sin x}{1-\cos x}\times \frac{1+\cos x}{1+\cos x} [/tex]
[tex] =Lim_{x \to 0}\frac{2 x\sin x(1+\cos x) }{1^2 -\cos^2 x} [/tex]
[tex] =Lim_{x \to 0}\frac{2 x\sin x(1+\cos x) }{1 -\cos^2 x} [/tex]
[tex] =Lim_{x \to 0}\frac{2 x\sin x(1+\cos x) }{sin^2 x} [/tex]
[tex] =Lim_{x \to 0}\frac{2x(1+\cos x) }{sin x} [/tex]
[tex] =Lim_{x \to 0} 2(1+\cos x) \times \frac{1}{Lim_{x \to 0}\frac{sin x}{x}} [/tex]
[tex] =2(1+\cos 0) \times 1 [/tex]
[tex] = 2(1+1) [/tex]
[tex] = 2(2) [/tex]
[tex] \therefore Lim_{x \to 0}\frac{2 x\sin x}{1-\cos x}= 4 [/tex]
how to get the answer.
how to get the 1.2762815625?
I know it says to multiple, but how to multiple to get that number?
thanks
9514 1404 393
Answer:
1.05 × 1.05 × 1.05 × 1.05 × 1.05 = 1.2762815625
Step-by-step explanation:
An exponent indicates how many times the base is a factor in the product. That is, 1.05 to the 5th power means ...
1.05⁵ = 1.05 × 1.05 × 1.05 × 1.05 × 1.05
This multiplication expression is evaluated in the usual way.
= 1.1025 × 1.05 × 1.05 × 1.05
= 1.157625 × 1.05 × 1.05
= 1.21550625 × 1.05
= 1.2762815625
__
All scientific and graphing calculators have a button for computing the power of a number. On my calculator its label is [tex]\displaystyle \boxed{y^x}[/tex]. The particulars of the function of this button can be found in the manual for your calculator.
For on-line calculators, such as the go.ogle calculator, or the Desmos graphing calculator, the caret (^) is used to signify an exponent. (See the input line in the first attachment for an example.)