Using a system of equations, it is found that she has 9 picture books.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
Variable x: Number of picture books.Variable y: Number of encyclopedias.Variable z: Number of fairy tale books.The ratio of the number of picture books encyclopedias, and fairy tale books Annette had is 3:4:5, hence:
[tex]\frac{x}{y} = \frac{3}[4}, \frac{x}{z} = \frac{3}{5}, \frac{y}{z} = \frac{4}[5}[/tex]
She gave half of her encyclopedias to her brother and he gave her 5 books of fairytales. Now she has 14 more books of fairy tales than encyclopedias, hence:
z + 5 - 0.5y = 14.
z - 0.5y = 9
From the ratios, we have that:
[tex]y = \frac{4}{3}x, z = \frac{5}{3}x[/tex]
Hence we solve for x to find the number of picture books:
[tex]z - \frac{y}{2} = 9[/tex]
[tex]\frac{5}{3}x - \frac{2}{3}x = 9[/tex]
x = 9.
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Describe how the graph of the function g(x) = -5x²-2 is related to the graph of
the function f(x) = 5x².
(A) reflection of f(x) = 5x² across the x-axis and translated left 2 units
(B) translation of f(x) = 5x² down 2 units
(C) reflection of f(x) = 5x² across the x-axis and translated down 2 units
(D) reflection of f(x) = 5x² right 2 units
Answer:
(C) reflection of f(x) = 5x² across the x-axis and translated down 2 units
C = 75h + 125
The equation above gives the amount C, in dollars, an electrician charges for a job that takes h hours. Ms. Sanchez and Mr. Roland each hired this electrician. The electrician worked 2 hours longer on Ms. Sanchez's job than on Mr. Roland's job. How much more did the electrician charge Ms. Sanchez than Mr. Roland?
Ms. Sanchez paid 150 dollars more than Mr. Roland.
How much more did the electrician charge Ms. Sanchez than Mr. Roland?Let's say that the electrician worked for x hours in Mr. Roland's home, then worked for (x + 2) hours in Ms. Sanchez home.
Then we need to find the difference between the linear equations:
C(x + 2) - C(x) = (75*(x + 2) + 125) - (75*x + 125)
If we simplify that, we get:
75*x + 75*2 + 125 - 75*x - 125
= 75*2 = 150
This means that Ms. Sanchez paid 150 dollars more than Mr. Roland.
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A friend asked lara to help her divide 456.3 by 100. what should lara tell her? a. move the decimal point three places to the right. b. move the decimal point two places to the right. c. move the decimal point three places to the left. d. move the decimal point two places to the left.
Answer:
Step-by-step explanation:
The correct answer is D. If we are multiplying by 10 we would move the decimal place one place to the right to show that the number is now 10 times bigger. If we multiply by one hundred. We are getting 100 times bigger, so we would move the decimal place 2 places to the right.
The opposite is true if we are dividing. Instead of moving the decimal to the right to show that the number is getting bigger, we move to the left to show that the number is getting smaller. If we are getting smaller by 10, we would move the decimal one place to the left. In this case, we are getting 100 times smaller so we move the decimal two places to the left.
Which of these statements is true for f(x) = 2.3*?
OA. The y-intercept is (0, 1).
OB. The domain is x > 0.
OC. The y-intercept is (0, 2).
OD. It is always decreasing.
The true statement for f(x) = 2(3)^x is the y-intercept is (0, 2).
How to determine the true statement?The function is given as:
f(x) = 2(3)^x
Set x = 0 to determine the y-intercept
f(0) = 2(3)^0
Evaluate
f(0) = 2
This means that the y-intercept of f(x) = 2(3)^x is (0,2)
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If a line that passes through the
points (8, 10) and (4, -6) also passes through the point (b, 2b), then find the value of b?
Find the missing value so that the two points have a slope of 1/2.
(9, 1) and (3, y)
Please explain
Answer: -2
Step-by-step explanation:
Substituting into the slope formula,
[tex]\frac{y-1}{3-9}=\frac{1}{2}\\\\y-1=-3\\\\y=-2[/tex]
Pls help me on 103 :((
Answer:
J) [tex]18cm^2[/tex]
Step-by-step explanation:
a square inscribed in a circle means that the radius of the circle is the same thing as a line drawn from the center of the square to a corner.
this will give you the side measurements for a triangle (look at the attached picture). now use the Pythagorean theorem to find the hypotenuse aka the side length of the square. then multiply it by itself.
Answer: H
Step-by-step explanation:
Finding the DiameterIf we draw a line through a diagonal of the square, two triangles are formed. The angle opposite the diagonal is 90°, as all angles are 90° in a square. One of the properties of a circle state that the angle in a semicircle is always 90°, which means that the diagonal formed a semi-circle.
A semi-circle only forms when a diameter is drawn in a circle, making the diagonal a diameter. This will be useful information, as we can calculate the side length of a square using the length of its diagonal.
A diameter is just twice the length of a radius, so the diagonal of the square would be 6 cm.
[tex]2*3=6[/tex]
Finding the Length of One SideThe diagonal also splits the square into two 45-45-90 triangles. These triangles have a special property that their hypotenuse is √2 times each leg, and all legs are the same length.
Therefore, we can calculate the length of a leg by dividing the hypotenuse by √2.
[tex]\frac{6}{\sqrt{3}}[/tex]
The length of one side of the square is [tex]\frac{6}{\sqrt{3}}[/tex]
Finding the AreaAs we already know the length of one side, we can just square it to get the area.
[tex](\frac{6}{\sqrt{3}})^2[/tex]
[tex]\frac{6^2}{(\sqrt{3})^2}[/tex] [Properties of Exponents]
[tex]\frac{36}{3}[/tex]
[tex]12[/tex]
Hence, the area of the square is 12 cm².
A shopkeeper has $680 in the denominations of $50, $20, $10 and $5 notes. The number of notes of each denomination is equal. What is the total number of notes?
The total number of notes is 32
The number of notes
Let the number of notes be x
$50 = x
$20 = x
$10 = x
$5 = x
Total number of notes = 4x
Let's find 'x'
50x + 20x + 10x + 5x = 680
85x = 680
x = 680/ 85
x = 8
We know that;
Total number of notes = 4x = 4 × 8 = 32 notes
Thus, the total number of notes is 32
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The planner needs a clearance of 9 feet under the arch has the planner met the minimum
Yes, the planner has met the minimum height, as the minimum height was 9 feet and the maximum height of the arc is 9.6 feet
How to explain the information?As we can see that at the mid value, for x=4, the value of f(x)=9.4
It means that the maximum height occurs at mid of the arc where it is height is 9.6 feet above the ground.
It means that the planner has met the minimum height, as the minimum height was 9 feet and the maximum height of arc is 9.6 feet
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find the area of the following
Answer:
24000 ft²
Step-by-step explanation:
Triangle PRS:b = base = PR = 240 ft
2AS = 240 ft
[tex]\sf AS = \dfrac{240}{2}\\\\ AS = 120 \ ft[/tex]
h = height = AS = 120 ft
[tex]\sf \boxed{\bf \ Area \ of \ triangle = \dfrac{1}{2}b*h}[/tex]
[tex]\sf =\dfrac{1}{2}*240*120\\\\ = 120 * 120\\\\ = 14400 \ ft^2[/tex]
Triangle PRQ:b = PR = 240 ft
3BQ = 240 ft
[tex]\sf BQ = \dfrac{240}{3}\\\\ BQ = 80 \ ft[/tex]
[tex]\sf Area \ of \ triangle \ PRQ = \dfrac{1}{2}*240*80[/tex]
= 120 * 80
= 9600 ft²
Area of the quadrilateral PQRS = area of ΔPRS + area of ΔPRQ
= 14400 + 9600
= 24000 ft²
help me please im in a rush
Answer:
The answers are in the image
Step-by-step explanation:
The solutions are in the image
4. The area of a rectangle is x² + 5x - 24. Which of the following could be one of the dimensions?
O(x-8)
O(x-6)
O(x+8)
O(x-4)
Answer:
the correct answer is c (x+8)
Step-by-step explanation:
x+8=0
=x= -8
put x= -8 in the given polynomial
(-8)²+5(-8)-24
= 64-40-24
=24-24= 0
omg please help me!!!
area = pi * r^2
here, the radius is 2 as its the diameter/2.
so the area is 4pi.
circumference = 2*pi*r.
so the circumference is 4pi as well.
Question 5 of 10
Suppose f(x) = x² and g(x)= (1x)
graph of g(x) with the graph of f(x)?
Which statement best compares the
A. The graph of g(x) is the graph of f(x) horizontally stretched by a
factor of 4.
B. The graph of g(x) is the graph of f(x) vertically stretched by a
factor of 4.
C. The graph of g(x) is the graph of f(x) shifted units right.
D. The graph of g(x) is the graph of f(x) horizontally compressed by a
factor of 4.
Answer: A
Step-by-step explanation:
See attached image.
(06.04 MC)
Find the perimeter of the image below:
Answer: 39 units
Step-by-step explanation:
Using the distance formula, we get that:
[tex]PT=\sqrt{10^2 + 4^2}=\sqrt{116}\\\\TS=\sqrt{7^2 + 0^2}=7\\\\SR=\sqrt{7^2 + 1^2}=\sqrt{50}\\\\RQ=\sqrt{6^2 + 5^2}=\sqrt{61}\\\\PQ=\sqrt{2^2 + 6^2}=\sqrt{40}[/tex]
So, the perimeter is
[tex]\sqrt{116}+7+\sqrt{50}+\sqrt{61}+\sqrt{40} \approx 39[/tex]
Manufacturers were subdivided into groups by volume of sales. Those with more than $100 million in sales were classified as large; those from $50 to $100 million as medium size; and those between $25 and $50 million, and so on. Samples were then selected from each of these groups. What is this type of sampling called
Stratified random sampling is used to subdivided into groups by volume of sales.
According to the statements
Manufacturers are subdivided into groups by volume of sales. and for this Stratified random sampling is used.
Stratified random sampling is the technique used divide the population can be partitioned into subpopulations.
Thus, Stratified random sampling is used to subdivided into groups by volume of sales.
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20 PIONTSSS TO WHOEVER ANDWER THIS QUESTION !!!
Answer:
The answer would be 36cm².
Step-by-step explanation:
⇒ Two prisms are similar.
⇒ Scale factor = 3:8
⇒ The ratio of the surface area is 9:64.
⇒ So S₁ : S₂ = 9:64
⇒ S₁ : 256 = 9:64
⇒ S₁ = 36cm²
This would mean that the answer is 36 centimeters ² (squared).
find the value in the figure
 i need help putting it in expanded form and solving it
Answer:
4x^04x^04x^04x^1 which equals 256
Step-by-step explanation:
The 4 outside of the parentheses says take what you have outside of the parentheses and multiply it by itself that may times.
x raised to the zero is 1, so you are just left with 4x4x4x4 or 256
Full factor of 32a^3+ 12a^2
Answer:
4a²*(9a + 3)
Step-by-step explanation:
Factorize:Prime factorize 32 and 12. Then find GCF.
32a³ = 2 * 2 * 2 * 2 * 2 * a³
12a² = 2 * 2 * 3 * a²
GCF = 2 * 2 * a² = 4a²
32a³ + 12a² = (4a²*9a) + (4a²*3)
=4a²*(9a + 3)
Next, you will make a scatterplot. Name a point that will be on your scatterplot and describe what it represents.
The point (12, 190) means that the temperature after 12 hours is 190 degrees Celsius
How to make a scatter plot?To do this, we make use of the following points
(12, 190), (14, 201), (15, 301), (16, 305), (18, 350), (20, 40), (25, 450)
Where x represents the number of hours and y represents temperature
See attachment for the scatter plot.
The description of a pointTo do this, we make use of the point (12, 190)
This means that the temperature after 12 hours is 190 degrees Celsius
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Please help me solve this random answers will be removed
Answer:
AB-46 cm
Step-by-step explanation:
Use law of cosines
AB^2 = 24^2 + 26^2 - 2 (24)(26)cos 134
AB= 46 cm
Solve for x in the equation: 8a = 2xy + b.
Step-by-step explanation:
Simplifying 8a = 2xy + b
Reorder the terms: 8a = b + 2xy
Solving 8a = b + 2xy
Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right.
Divide each side by '8'. a = 0.125b + 0.25xy
Simplifying a = 0.125b + 0.25xy
i need help with this page
9a). The measure of segment GH from the given information can be evaluated as one-fourth of the perimeter; 48/4 = 12 cm.
9b). The measure of <EJF is 90° as the angle EJF is a right angle made at the intersection of the rhombus diagonals.
9c). The measure of <EHG is 60° as the opposite angles in a rhombus are congruent and <EHG = 2 × <EHJ = 2 × 30 = 60°.
10a). The sides labelled in the rectangle are congruent by the rectangle diagonal congruence concept; it therefore follows that the required value of x is; 9x+ 20 = 10x +8; and x = 12.
10b). The angle measures as labelled in the rhombus are congruent as this follows from the fact that the diagonal is an angle bisector. Hence, 2x +15 = 5x +3; and x = 4.
What is congruence?The concept of congruence describes a similarly between 2 or more geometric figures or elements.
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If the original recipe made 14 pancakes and the cafeteria plans to charge $.50 per pancake, how much money will they make if they sell all of the
If they sell all the pancakes, they will win $7
how much money will they make if they sell all of the pancackes?
We know that they can make a batch of 14 pancakes, such that each one can be sold for $0.50
Then the total amount that they get if they sell all the pancakes is given by the product:
P = 14*$0.50 = $7
If they sell all the pancakes, they will win $7
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A school system is reducing the amount of dumpster loads of trash removed each week. in week 5, there were 60 dumpster loads of waste removed. in week 10, there were 40 dumpster loads removed. assume that the reduction in the amount of waste each week is linear. write an equation in function form to show the amount of trash removed each week. f(x) = −4x 60 f(x) = 4x 60 f(x) = −4x 80 f(x) = 4x 80
The equation in function form is f(x)=-4x+80.
What is linear function?
A linear function is a function which forms a straight line in a graph. It is generally a polynomial function whose degree is utmost 1 or 0.
We can find the equation in function form as shown below:
We have given two points (5,60) and (10,40)
Slope of line
m = (40-60)/ (10-5)
m=-20/5
m=-4
Equation in slope intercept form
(y-y1) =m(x-x1)
(y-60) =-4(x-5)
y-60=-4x+20
y=-4x+20+60
y=-4x+80
y=f(x)
f(x)=-4x+80
Hence, the equation in function form is f(x)=-4x+80.
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Solve the equation
3(2x + 2) = 3x - 15
• Using distributive property
[tex]6x + 6 = 3x - 15[/tex]
• Solving the like terms
[tex]6x - 3x = - 15 - 6[/tex]
[tex]3x = - 2 1[/tex]
[tex]x = - \dfrac{21}{3} [/tex]
[tex]x = - 7[/tex]
Hope it helps you any confusions you may ask!
there are five chemistry instructors and six physics instructors at a college. if a committee of four instructors is selected,
The probability of at least one of them being a physics instructor is 120 ways to form the committee.
Probability of Independent Events: The 'At Least One' Rule?Sometimes, simply the occurrence of the event at least once matters when computing independent events. The "At Least One" Rule is used to describe this. The complement of the probability of the event never occurring will be used to calculate the probability of the event occurring at least once.
There are five chemistry instructors and six physics instructors at a college. If a committee of four instructors is selected.
Starting with 6, choose two because we require at least two professors. Let's move on to the remaining 8 individuals (there were initially 10, but now there are just 8): and select 3.
6 select 2; 8 select 3
15×56 =840
We then chose 5 individuals from a group of 10, at least 2 of whom were lecturers.
(9) = 20 options for selecting the professors. 3
(3) = 6 options for selecting the professors.
(9) (¹) = 20 × 6 = 120 ways.
Therefore, 120 ways to form the committee.
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Complete question:
There are five chemistry instructors and six physics instructors at a college. If a committee of four instructors is selected, find the probability of at least one of them being a physics instructor?
i don’t know this answer help pls
Answer:
c
Step-by-step explanation:
Starting price is $5.50. And for every mile it costs $1.50.
Which explains how to show that
X=-8/3
is a root of
9×^2+48×+64=0?
a. Graph
9x^2 + 48x + 64 = 0
to show that
x=-8/3
is where the parabola crosses the y axis.
b. Graph
9x^2 + 48x +64 = 0
to show that the parabola's vertex is just above the value
x=-8/3
c. Substitute
x=-8/3
back into
9x^2 + 48x + 64 =0
and simplify to show that a true statement
results.
d. Substitute
x=-8/3
back into
9x^2 + 48x + 64 = 0
and simplify to show the values of
a
c
remain perfect squares.
Answer:
c. Substitute
Step-by-step explanation:
A graph of the function on the left shows the parabola touches the x-axis at x = -8/3. That is, the vertex is on the x-axis. It crosses the y-axis at y = 64.
Show a value is a rootA given solution to an equation can be verified by substituting that value into the equation an showing the result is a true statement. Here, the value x=-8/3 is a root of the given equation because that value makes the equation true.
[tex]9\left(-\dfrac{8}{3}\right)^2+48\left(-\dfrac{8}{3}\right)+64=0\\\\9\left(\dfrac{64}{9}\right)-\left(\dfrac{48\cdot8}{3}\right)+64=0\\\\64-\dfrac{3\cdot2\cdot8\cdot8}{3}+64=0\\\\64-2\cdot64+64=0\\\\0=0\qquad\text{True}[/tex]