Given:
The ratio of the number of fiction books to the number of non-fiction books in a library is 5:2.
Total number of books = 1421
To find:
The number of books of each type.
Solution:
Let the number of fiction books be 5x and number of non-fiction books be 2x.
Total number of books = 1421
[tex]5x+2x=1421[/tex]
[tex]7x=1421[/tex]
[tex]x=\dfrac{1421}{7}[/tex]
[tex]x=203[/tex]
Now,
Number of fiction books : [tex]5(203)=1015[/tex]
Number of non-fiction books : [tex]2(203)=406[/tex]
Therefore, the number of fiction and non-fiction books are 1015 and 406 respectively.
The total cost of the skateboard is $ ?
The table below represents the number of hours a student worked and the amount of money the student earned. What is the initial amount this student is paid? (Base pay, when number of hours, h = 0) I’LL PAY YOU 30 DOLLARS IN CASHAPP RIGHT NOW WHEN YOU DO IT!
The initial amount this student is paid is 0 and this can be determined by using the two-point slope form of the line.
Given :
The given table represents the number of hours a student worked and the amount of money the student earned.
The following steps can be used in order to determine the initial amount this student is paid:
Step 1 - The two-point form of the line can be used in order to determine the initial amount this student is paid.
Step 2 - So, the linear equation that represents the given situation is:
[tex]\rm \dfrac{d-50}{h-8}=\dfrac{93.75-50}{15-8}[/tex]
Step 3 - Simplify the above expression.
[tex]\rm \dfrac{d-50}{h-8}=6.25[/tex]
d - 50 = 6.25h - 50
d = 6.25h
Step 4 - Now, substitute the value of (h = 0) in the above expression.
d = 0
Therefore, the correct option is D) There is no base pay.
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- klhat percentage of 40 is 8?
Step-by-step explanation:
8/40 x 100% = 20%
Topic: percentage
If you like to venture further, do check out my insta (learntionary) where I regularly post useful math tips! Thank you!
What is the quotient of x and three increased by 12 = 20
Answer:
x= 24
Step-by-step explanation:
Quotient means divide, increased means add
x/3 + 12 =20
Subtract 12 from each side
x/3 +12-12 = 20-12
x/3=8
Multiply each side by 3
x/3 * 3 =8*3
x= 24
Answer:700 / n, the quotient of 700 and a number. 2w, two times a ... h - 3, three less than a number ... 20 + m, 20 more than a number. x - 12, a number decreased by 12.
Step-by-step explanation:
What additional information could be used to prove that the triangles are congruent using AAS or ASA? Select three options. AngleB ≅ AngleP and BC ≅ PQ AngleA ≅ AngleT and AC = TQ = 3.2cm AngleA ≅ AngleT and AngleB ≅ AngleP AngleA ≅ AngleT and BC ≅ PQ AC = TQ = 3.2 cm and CB = QP = 2.2 cm
Answer:
a b d
Step-by-step explanation:
bigbrain
The additional information that could be used to prove that ΔABC ≅ ΔPTQ using AAS or ASA are:
1. ∠B ≅ ∠P and BC ≅ PQ
2. ∠A ≅ ∠T and AC = TQ = 3.2cm
4. ∠A ≅ ∠T and BC ≅ PQ
Recall:
For two triangles to be congruent by AAS Congruence Theorem, they must have two pairs of congruent angles and a pair of non-included congruent side.For two triangles to be congruent by ASA Congruence Theorem, they must have two pairs of congruent angles and a pair of included congruent side.We are given:
∠C ≅ ∠Q
To prove that ΔABC ≅ ΔPTQ by ASA, the additional information needed are:
∠B ≅ ∠PBC ≅ PQAlternatively, the ASA can be used if the following additional information is given:
∠A ≅ ∠TAC = TQ = 3.2cmUsing the AAS Congruence Theorem, the additional information needed would be:
∠A ≅ ∠TBC ≅ PQIn summary, the additional information that could be used to prove that ΔABC ≅ ΔPTQ using AAS or ASA are:
1. ∠B ≅ ∠P and BC ≅ PQ
2. ∠A ≅ ∠T and AC = TQ = 3.2cm
4. ∠A ≅ ∠T and BC ≅ PQ
Learn more about Congruence Theorem on:
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PLZZZZ HELP ME!!!!! factor 15x + 81
Answer: 3(5x+27)
Step-by-step explanation:
15 and 81 are both divisible by 3.
Answer:
-5.4
Step-by-step explanation:
x= -81/15= -5.4
If l is parallel to m, solve for x and y.
Answer:
x=17, y=9
Step-by-step explanation:
(5x - 38)° = (3x - 4)°
2x = 34
x=17
(5(17)-38))=47
90°+47°+(7y-20)=180°
7y-20=43°
y=9
The value of x is 17 and y is 9.
What are the properties of parallel lines?Following are the properties of parallel lines,
The pairs of vertically opposite angles are equal.The pairs of corresponding angles are equal.The pairs of alternate exterior angles are equal.The pairs of alternate interior angles are equal.Given:
<1 = 7y -20
<2 = 5x - 38
<3 = 90
exterior angle = 3x -4
Using alternate interior angle
5x - 38 = 3x-4
2x = 34
x=17
So, <2 = (5(17)-38))
<2 =47
Using angle sum property
90°+47°+(7y-20)=180°
7y-20=43°
y=9
Hence, the value of x is 17 and y is 9.
Learn more about parallel lines here:
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For a 4-unit class like Statistics, students should spend average of 12 hours studying for the class. A survey
was done on 23 students, and the distribution of total study hours per week is bell-shaped with a mean of
14 hours and a standard deviation of 2.9 hours.
Use the Empirical Rule to answer the following questions.
a) 68% of the students spend between
hours and
hours on Statistics each week.
b) 95% of the students spend between
hours and
hours on Statistics each week.
C) 99.7% of the students spend between
hours and
hours on Statistics each week.
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For the following scatter plot, interpret the type of trend the
data set will hold.
1.Positive
2.Negative
3.No trend
Find the derivative:
f(x)=tan[tex](x^{2} +5)[/tex]
Answer:
[tex] 2x \sec^2 (x^2 + 5) [/tex]
Step-by-step explanation:
[tex] f(x) = \tan (x^2 + 5) [/tex]
[tex] \dfrac{d}{dx} \tan u = \sec^2 u \dfrac{d}{dx} u [/tex]
[tex] \dfrac{d}{dx} \tan (x^2 + 5) = \sec^2 (x^2 + 5) \dfrac{d}{dx} (x^2 + 5) [/tex]
[tex] \dfrac{d}{dx} \tan (x^2 + 5) = [\sec^2 (x^2 + 5)]2x [/tex]
[tex] \dfrac{d}{dx} \tan (x^2 + 5) = 2x \sec^2 (x^2 + 5) [/tex]
Katie say whaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaatttttttttttttttttttt
Answer:
fr
Step-by-step explanation:
A squirrel jumps along the number line. Each of its jumps is 5 units long. The squirrel sometimes jumps to the right and sometimes to the left. It starts at point 6. Can it land at this point? (The point is 101)
9514 1404 393
Answer:
yes
Step-by-step explanation:
For some integer n, the squirrel lands on numbers that are ...
5n +6
We want to see if n is an integer when ...
5n +6 = 101
5n = 95
n = 19 . . . . yes, an integral number of jumps will get the squirrel to 101
identify an equation in slope-intercept form the line parallel to y=-3x+7that passes through (2,-4)
Answer:
y=-3x+2
Step-by-step explanation:
Same slope = parallel. You can aso double check this answer by either graphing using the desmos online graphing calculator or by plugging in the point into the equation y = -3(2) + 2 --> y = -6 + 2 --> y = -4, so we are correct.
Answer:
y=-3x+2
Step-by-step explanation:
In this equation the slope is the same as the original equation (-3), but has a different y-intercept meaning that this line is parallel. As for satisfying the requirement that the line is parallel and passes through (2,-4), I plugged the coordinates into the equation y=-3x+b to get -4=-3(2)+b, and then found what b would have to equal to make the equation true.
(plus I put my answer into a graphing calculator to check my work)
to decrease an amount 37% multiply by
Answer:
if x is the amount =100%
then to decrease the amount by 37% =(100-37)% = 63% of x =x*63/100 =x*0.63
multiply the amount by 0.63
Step-by-step explanation:
Answer:
0.63
Step-by-step explanation:
if x is the amount=100% then to decrease by 37% multiply by 0.63
A plumber charges $55 for a house visit plus $25 for every hour he spends working. Which equation could be used to find t, the total cost of a house visit that lasted h hours ?
Answer:
55+25h=t
Step-by-step explanation:
work out the size of angle x.
image included
Answer:
x = 105°
General Formulas and Concepts:
Geometry
Corresponding AnglesStep-by-step explanation:
If the 2 lines are parallel, which they are, we can use specific theorems to help us solve for different angles.
Here, we see that we will use the Corresponding Angles Theorem. According the the theorem, this will allow us to find our value for x.
Answer:
Step-by-step explanation:
x° = 105°
Angles are corresponding
A function f(x)is graphed on the coordinate plane.
What is the function rule in slope-intercept form?
Enter your answer in the box.
f(x)=
Answer:
[tex]f(x)=2x+1[/tex]
Step-by-step explanation:
At x=0, the y is at 1
at x=1, y went up to 3
the change between 3 and 1 is 2 therefore the equation is
[tex]f(x)=2x+1[/tex]
I hope this helps you and good luck!
1. What is the m value (slope) and the b value (y-intercept)
in the equation y = 4x - 2 (m=
b=
2. What is the formula for slope?
[tex]y=4x-2[/tex]
m = 4 and b = -2
Formula to find slope can be meant 2 ways.
( 1 ) m = rise/run
( 2 ) [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex] if it's a small text then it's m = y2-y1 / x2-x1
3 and 4 plz help me im nice
Answer:
3. 7.2
4. 20
Step-by-step explanation:
Evaluate the following expression:
3.65+(-8.2)=
MUST SHOW WORK!
Answer:
-4.55
Step-by-step explanation:
8.20
- 3.65
4.55
then just add a negative sign to it !
-4.55
hope this helps : )
have a good day
Which slope-intercept equation is parallel to the line y = 2x – 4 and goes through the point (0, 5).
a y=2x+5
b y=2x+1
c y=-1/2x-4
d y=-1/2x+5
Answer:
A.
Step-by-step explanation:
Sorry I can't really explain
A school survey asked 120 fifth-graders what they bought to give as gifts for Mothers Day. The results are shown in the circle graph.
How many more fifth-graders bought clothes than bought perfume
Answer:
40
Step-by-step explanation:
Find the ratio between 450 ml and 1l.
Answer:
450mL : 1L = 9 : 20
Step-by-step explanation:
recall that 1L = 1000 mL,
450 mL : 1L can be expressed as
450mL : 1000 mL (we can simplify this with the following steps)
450 : 1000 (divide both sides by 10)
45 : 100 (divide both sides by 5)
9 : 20 (answer)
Two people enter a whispering gallery and want to know where they should stand so they can hear the other person's whisper. The gallery is 100 feet wide and the vertical distance from their head to the peak of the ceiling is 30 ft.
Answer:
The two people should stand 40 feet from the center so that they can hear each other whisper
Step-by-step explanation:
From the question
Width of the gallery = 100 feet
Width = 2a
a = Width/2
a = 100/2 = 50 feet
Height of the gallery = b = 30 feet
Hence, the distance is
d² = a² - b²
d = √a² - b²
d = √50² - 30²
d = √2500 - 900
d = √1600
d = 40 feet
Hence, the two people should stand 40 feet from the center so that they can hear each other whisper.
i really need help i have 1 minute to complete!!!!!
Answer:
8 angles are formed, and if angle one is 105° then angles 4, 5, and 8 are also 105°. and angles 2, 3, 6, and 7 would be 75°
Pls help ASAP!
What postulate are the triangles congruent by?
Answer:
If two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle, the triangles are congruent.
You guys are life savers but does anyone know the answers to these questions? I’m so confused rn
Answer:
The third choice
Step-by-step explanation:
We need to find the slope and y-intercept of the line and then put it into y = mx = b form. To find the slope, pick a point on the line; I will use (-2, 5); count how many units up you need to go to get to the next point on the line, which in this case it would be 3. The count how many to the right or left you would need to go, which is 1 to the left. Moving left means a negative, so it is -1. Your slope fraction would be [tex]\frac{3}{-1}[/tex] , since slope is rise over run. You can sub this fraction in for m in y = mx + b, which will give you a revised equation of y = -3x = b. To find the y intercept, or b, just find the point where the line crosses the y-axis, which is -1. So, the equation is now y = -3x - 1.The correct answer is third choice.
Function A has
The equation of line Ais
Function B has
Two different linear functions are shown below with two
points given from each function Use slope intercept form
or point slope form to find the equation of each
Linear Function A
Points (-5,-2), (5,7)
Linear Function B
Points(7,5).(-2,5)
The equation of line Bis
Answer: 4,1,2,2
explanation: I did it on edge 2021
⚠️PLEASE HELP IT IS AN EMERGENCY⚠️
On the same set of axes, graph y - x= 4 and its inverse. Which statement is true about the two graphs?
A) They intersect at (0,4)
B) They intersect at (0,-4)
C) They are parallel
D) They are perpendicular
Do u think I should get a belly button piercing? I’m going to be 16 soon.. I already have a nose piercing tho so idk if that would be to much?
Answer:
no. i think that is weird-ish.
Step-by-step explanation: