∵ m< OZQ = m[tex]\because m\angle OZP=62[/tex]Substitute the measures of the given angles in the equation above
[tex]\therefore125=62+m\angle PZQ[/tex]Subtract 62 from both sides
[tex]\begin{gathered} \therefore125-62=62-62+m\angle PZQ \\ \therefore63=m\angle PZQ \end{gathered}[/tex]The measure of angle PZQ is 63 degrees
55mL of hardener to each container of resin. How much hardener should be added to 14 containers of resin?Write your answer in liters.
The amount of hardener added to 1 container of resin = 55mL.
The amount of hardener added to 14 containers is calculated as,
[tex]\begin{gathered} \text{Amount of hardener = 55 }\times\text{ 14 } \\ \text{Amount of hardener = 770 mL} \\ \text{Amount of hardener = 0.770 L} \end{gathered}[/tex]Thus 0.770 litres of hardener must be added to 14 containers of resin.
In parallelogram ABCD… Justify your answer with the applicable property.
Solution
For this case we have the following measures:
m <1= x+12
m < 2= 6x -18
We can set up both angles equal:
x +12 = 6x -18
Solving for x we have:
12+18 = 5x
5x = 30
x= 30/5= 6
Then the value of m< 2 is:
m< 2= 6*6 -18= 36-18= 18
the best second answer is:
If a quadrilateral is ||gram the opposite angles are congruent
O GRAPHS AND FUNCTIONSGraphically solving a system of linear equations
(-3,4)
Explanationhere we have a system of 2 linear functions, To solve a system of linear equations graphically we graph both equations in the same coordinate system. The solution to the system will be in the point where the two lines intersect.
so
Step 1
graph the function (1)
a)
[tex]y=-\frac{1}{3}x+3[/tex]to graph the line we need 2 poins, so
i) P1, when x=0
[tex]\begin{gathered} y=-\frac{1}{3}x+3 \\ y=-\frac{1}{3}(0)+3=3 \\ so \\ P1=(0,3) \end{gathered}[/tex]ii) P2; when x= 3
[tex]\begin{gathered} y=-\frac{1}{3}(3)+3=-1+3=2 \\ so \\ P2;\text{ \lparen3,2\rparen} \end{gathered}[/tex]iii) now, draw a line that passes trought P1 and P2
Step 2
now, graph line 2 ( function 2)
i) P3, when x= 0
[tex]\begin{gathered} 3x+y=-5 \\ replace\text{ and solve for y} \\ 3(0)+y=-5 \\ y=5 \\ so,P3=(0,-5) \end{gathered}[/tex]ii) P5, when x= 2
[tex]\begin{gathered} 3x+y=-5 \\ replace\text{ and solve for y} \\ 3(2)+y=-5 \\ 6+y=-5 \\ subtract\text{ 6 in both sides} \\ y=-6-5=-11 \\ y=-11 \\ so,\text{ P4=\lparen2,-11\rparen} \end{gathered}[/tex]iii) now, draw a line that passes trought P3 and P4
Step 3
finally, the solution is the orderede pair where the lines intersect each other
therefore, the solution is
(-3,4)
I hope this helps you
suppose there are two types of tickets to a show . advance and same day. advance tickets cost $15 and same day tickets cost 30. for one more performance there are 55 tickets sold in all and the total amount paid for them was 1275. how many tickets of each typer were sold?
Advanced tickets(x): $15
Same day tickets(y) : $30
For one more performance there are 55 tickets sold
x+ y= 55 (a)
The total amount paid for them was 1275
15x+30y= 1275 (b)
System of equations:
x+y= 55 (a)
15x+30y = 1275 (b)
Solve for x in (a)
x=55-y
Replace x on (b)
15(55-y)+30y = 1275
82
3/4 = m + 1/4
What is m? m = ?
Answer 3/4 = m + 1/4 is 2/4
Explanation.3/4 = m + 1/4
m = 3/4 - 1/4
m = (3 - 1)/4
m = [tex]\frac{2}{4}[/tex]
__________________
Class: Elementary School
Lesson: Fractions
[tex]\boxed{ \colorbox{lightblue}{ \sf{ \color{blue}{ Answer By\:Cyberpresents}}}}[/tex]
multiply mentally to find the product
8 * 404 = 8(----- + 4)
At first, we will split 404 into two numbers one of them is 4
To find the other number subtract 4 from 404
404 - 4 = 400
8 * 404 = 8(400 + 4)
Now we will multiply 8 by 40 and 8 by 4
8(400 + 4) = 8 * 400 + 8 * 4
It is easy to find the product of 8 and 4
8 * 4 = 32
8 * 400 = 3200
Let us add them
3200 + 32 = 3232
The answer is 3232
graph the inequality 3x+y<4
Subsituting (0,0) in the inequality,
[tex]\begin{gathered} 3\times0+0<4 \\ 0<4 \end{gathered}[/tex]Hence the line 3x+y=4, demarcating the plane contains the origin.
Thus, the above graph gives the required region of inequality.
Need help answering all these questions for the red bird.Quadratic equation of the red bird: h(x) = -x^2 + 10x - 9King Pig located at the point (11,9) Moustache Pig located at the point (10,4)
The maximum heigh is located at the vertex. The vertex is:
[tex]\begin{gathered} V=(h,k) \\ where: \\ h=-\frac{b}{2a}=-\frac{10}{2(-1)}=5 \\ k=h(h)=-(5^2)+10(5)+9=-25+50-9=16 \end{gathered}[/tex]Therefore, the maximum height is the y-coordinate of the vertex which is 16.
The axis of symetry is located at the x-coordinate of the vertex,so:
The axis of symetry is x = 5.
The distance traveled can be found using the roots:
The roots of the equation are:
[tex]\begin{gathered} -x^2+10x-9=x^2-10x+9=(x-9)(x-1) \\ so \\ x=1 \\ or \\ x=9 \end{gathered}[/tex]So, the distance traveld is:
[tex]\Delta x=x2-x1=9-1=8[/tex]---
The bird will hit the ground on the second root, so:
The point where it hits the grund is (9,0).
The starting point is located at the first root, so the starting point is:
(1,0)
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Which data sets should be displayed on a stem display instead of a dot plot? Select all that apply. A) 11, 23, 9, 24, 34, 18, 15, 11, 8, 14, 16B) -14, -15, -17, -15, -15, -15, -12, -14.-14C) 5,3, 8, 3, 7,5,6,3, 7, 3, 7, 6,5,6D) 1.1, 1.2, 1.1, 1.3, 1.4, 1.1, 1.2, 1.4, 1.2, 1.1E) 42.7, 39.8, 41.1, 39.7, 40.1, 39.8.42.3
In order to determine which data sets should be displayed on a stem display, you consider that the stem display is usefull in the cases in which you have data which can be grouped easily. For instance, for data set in which there are differents number with the same first digit(s).
According with the previous definition you can notice that the options E) and A) are the best options, because there are different number that can be grouped, for example, according to the first number.
For other options you have other situations, for option D) there is no way to group the data. For option C) there is only one number on each data, so, there wouldn't be leafs in the diagram, and the same applies to option B), the first number is the same in all data, then, there is no way to group.
Glenda borrowed $4,500 at a simple interest rate of 7% for 3 years to
buy a car. How much simple interest did Glenda pay?
Answer: I = $ 1,102.50
Step-by-step explanation: First, converting R percent to r a decimal
r = R/100 = 7%/100 = 0.07 per year,
then, solving our equation
I = 4500 × 0.07 × 3.5 = 1102.5
I = $ 1,102.50
The simple interest accumulated
on a principal of $ 4,500.00
at a rate of 7% per year
for 3.5 years is $ 1,102.50.
Bella drove her car 81 km and used 9 liters of fuel. She wants to know how many kilometers (x) she can drive on 22 liters of fuel. She assumes her car will continue consuming fuel at the same rate.
Find the proportion between liters of fuel
that is find 22/9 = 2.444
thats how much liters have more to consume
now multiply 2.444 by 81 , the kilometers she has drived
It gives as result 2.444 x 81 = 198 kilometers
Fill in the blank with the correct inequality symbol. State which property of inequalities is being utilized.If x-8>10, then x_18.
GIVEN
The inequality:
[tex]x-8>10[/tex]SOLUTION
The inequality is to be solved.
Add 8 to both sides of the inequality. This follows the Addition Property of Inequalities:
[tex]if\text{ }xTherefore:[tex]\begin{gathered} x-8+8>10+8 \\ x>18 \end{gathered}[/tex]ANSWER
[tex]x>18[/tex]A rectangular garden has a walkway around it. The area of the garden is 2(4.5x +1.5). Thecombined area of the garden and the walkway is 3.5(8x + 4). Find the area of the walkway aroundthe garden as the sum of two terms.The area of the walkway around the garden is(Simplify your answer. Use integers or decimals for any numbers in the expression.)
In this case, we'll have to carry out several steps to find the solution.
Step 01:
DataL
garden area = 2(4.5x +1.5)
garden + walkway area = 3.5(8x + 4)
walkway area = ?
Step 02:
walkway area:
walkway area = 3.5(8x + 4) - 2(4.5x +1.5)
= 28x + 14 - 9x - 3
= 19x + 11
The answer is:
The area of the walkway around the garden is 19x + 11
A local pizza parlor has the following list of toppings available for selection. The parlor is running a special to encourage patrons to try new combinations of toppings. They list all possible three topping pizzas (3 distinct toppings) on individual cards and give away a free pizza every hour to a lucky winner. Find the probability that the first winner randomly selects the card for the pizza topped with spicy italian sausage, banana peppers and beef. Express your answer as a fractionPizza toppings: Green peppers, onions, kalamata olives, sausage, mushrooms, black olives, pepperoni, spicy italian sausage, roma tomatoes, green olives, ham, grilled chicken, jalapeño peppers, banana peppers, beef, chicken fingers, red peppers
First, we need to find out how many possible combinations of pizza toppings there would be.
To do this, we will use the formula for Combination.
Combination is all the possible arrangements of things in which order does not matter. In our example, this would mean that a pizza topped with spicy Italian sausage, banana pepper, and beef is the same as a pizza topped with banana pepper, beef, and Italian sausage.
The formula for combination is
[tex]C(n,r)=^nC_r=_nC_r=\frac{n!}{r!(n-r)!}[/tex]From our given, n would be 17, since there are a total of 17 toppings (including spicy Italian sausage, banana peppers, and beef) and r would be 3 since there are three toppings that you chose.
Substituting it in the formula,
[tex]C(n,r)=\frac{n!}{r!(n-r)!}[/tex][tex]C(17,3)=\frac{17!}{3!(17-3)!}[/tex][tex]C(17,3)=680[/tex]Now, since we know that there are a total of 680 combinations of pizza toppings, we can now solve the probability of the first winner selecting a pizza topped with Italian sausage, banana peppers, and beef.
The length of a rectangle is given by a number, x (metres). The width is two metres longer than the length. The area of the rectangle is 120 m^2
metersGiven:
a.) The length of a rectangle is given by a number, x (meters).
b.) The width is two meters longer than the length.
c.) The area of the rectangle is 120 m^2.
Let's first recall the formula for getting the area of the triangle.
Area = L x W
Where,
L = Length
W = Width
The width is two meters longer than the length. Therefore, we can say that:
W = L + 2
Let's now determine the measure of the dimension of the rectangle:
Let,
x = length of the rectangle
We get,
[tex]\begin{gathered} \text{ A = L x W} \\ 120\text{ = L x (L + 2)} \\ 120=L^2\text{ + 2L} \\ L^2\text{ + 2L - 120 = 0} \\ (L\text{ - 10)(L + 12) = 0} \end{gathered}[/tex]Based on the relationships given, the Length of the rectangle has two possible measures.
L - 10 = 0
L = 10 m
L + 12 = 0
L = -12 m
Since a length must never be a negative value, the length of the rectangle must be 10 m.
For the width, we get:
W = L + 2 = 10 + 2 = 12 m
Summary:
Length = 10 m
Width = 12 m
a road is 4/7 of a mile long. a crew needs to replace 4/5 of the road. how long is the section that needs to be repaired
To solve this problem we need to find the fraction of a fraction, for that we just have to multiply them. This is done below:
[tex]\frac{4}{7}\cdot\frac{4}{5}=\frac{16}{35}\text{ of a mile}[/tex]The section is 16/35 of a mile long.
A third friend wants to offer Rebecca andSteve some of the animal models she hasalready made. The model she has of thegiant squid is 5 inches tall. Using thesame scale (2 in:5ft), how tall would thegiant squid be in real life?
From the present question, it is said that the scale of a model is equal to:
[tex]e=\frac{2in}{5ft}[/tex]It means that the ratio of the size of the model and the real size of the giant squid must be always this same value. It was given that the size of the model is 5 in. Because we don't know the size of the real-life giant squid, we will use it as x. From this, we can write the following relation:
[tex]\frac{5in}{x}=\frac{2in}{5ft}[/tex]Now, we just need to isolate x in the present relation to find how tall would be a giant squid in real life.
[tex]\begin{gathered} \to2in\times x=5in\times5ft \\ x=\frac{5in\times5ft}{2in}=\frac{25}{2}ft=12.5ft \end{gathered}[/tex]From the solution developed above, we conclude that the real-life giant squid would be 12.5 ft tall.
Can you help me with question number 4 and double check all my other work. (I don’t really understand functions.)
SOLUTION
The relation is a function because each x-value has a unique y-value. That is each domain has only one image. Therefore, the relation is a function
What is the position of see on the number line belowWrite your answer as a fraction or mixed number
Answer:
1/3
Explanation:
We can see that from 0 to 1 the number line is divided into 6 parts and the point is right after the second part. Therefore, the fraction that represents point C is 2/6
This fraction is also equal to 1/3 because we can divide the line from 0 to 1 into 3 parts and take the first. The point will be at the exact same position of C.
Therefore, the answer is:
1/3
Drag each number to the correct location on the table
Step-by-step explanation:
There is no table attached, please recheck and resend.
Frank makes 8 dollars for each hour of work. Write an equation to represent his total pay p after working h hours
The equation will be
P = 8h
here, P = total pay
h= working hours.
Solve T=C(8+AB) for A
In a right triangle, if the hypotenuse is equal to 16 feet and the side adjacent to ∠θ is equal to 5 feet, what is the approximate measurement of ∠θ?
We have the diagram:
We use the trigonometric identity cosine:
[tex]\cos\theta=\frac{adjacent}{hypotenuse}[/tex]Substitute the values:
[tex]\begin{gathered} \cos\theta=\frac{5}{16} \\ \theta=\cos^{-1}(\frac{5}{16})=71.79 \end{gathered}[/tex]Answer: 71.79°
Find the midpoint M of the line segment joining the points C=(6,2) and D=(2,8).
Given
[tex]point\text{ C \lparen6,2\rparen and Point \lparen2,8\rparen}[/tex]Solution
Formula
[tex]\begin{gathered} M=(\frac{x_1+x_2}{2},\text{ }\frac{y_1+y_2}{2}) \\ \end{gathered}[/tex][tex]\begin{gathered} x_1=6 \\ x_2=2 \\ y_1=2 \\ y_2=8 \end{gathered}[/tex]Now
[tex]\begin{gathered} M=(\frac{6+2}{2},\text{ }\frac{2+8}{2}) \\ \\ M=(\frac{8}{2},\frac{10}{\text{2}}) \\ \\ M=(4,5) \end{gathered}[/tex]The midpoint M of the line segment joining the points C=(6,2) and D=(2,8). is
[tex]M=(4,5)[/tex]For which value(s) of x will the rational expression below equal zero? Che all that apply. (x - 5)(x+2) x + 1 A.-5 B. 2 c. 1 1 D. -1 E. 5 F. -2
The rational expression we have is:
[tex]\frac{(x-5)(x+2)}{x+1}[/tex]For a rational expression to be equal to 0, the numerator of the expression has to be equal to 0.
The numerator is: (x-5)(x+2)
That has to be equal to 0:
[tex](x-5)(x+2)=0[/tex]Here, we apply the zero product property, which tells us that if a product is equal to 0, one of the two elements, or the two elements, are equal to 0:
[tex]\begin{gathered} x-5=0 \\ x+2=0 \end{gathered}[/tex]We solve the two equations, and get the two values that will make the rational equation equal to 0:
[tex]\begin{gathered} x=5 \\ x=-2 \end{gathered}[/tex]Answer:
E. 5
F. -2
If a price changes from $105,300 to $104,399 will that be a percentincrease or decrease?
If the price changes from $105,300 to $104,399, It means that there is a decrease in price.
Decrease = 105,300 - 104,399 = $901
The percentage decrease is gotten by dividing the decrease by the initial price and multiplying by 100. It becomes
[tex]\frac{901}{105300}\text{ }\times\text{ 100 = 0.8557\%}[/tex]By rounding up to the nearest whole number, it becomes 1%
The percent decrease is 1%
Write the standard form of the equation of the circle described below
Given:
Center ( 8, -4)
Radius (r) = 3
Find-:
Standard equation of a circle
Explanation-:
The standard equation of a circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex]Where,
[tex]\begin{gathered} (h,k)=\text{ Center} \\ \\ r=\text{ Radius} \end{gathered}[/tex]So equation of circle is:
[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ \\ (h,k)=(8,-4) \\ \\ r=3 \end{gathered}[/tex][tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ \\ (x-8)^2+(y-(-4))^2=3^2 \\ \\ (x-8)^2+(y+4)^2=9 \end{gathered}[/tex]A hummingbird's brain has a weight of approximately 2.94 x 10- ounces. An elephant's brain has a weight ofapproximately 1.76 x 102 ounces.Approximately how many times heavier is the elephant's brain than the hummingbird's brain?A) 60B) 600C) 6,000D) 60,000
Given the information on the problem,we have to divide the weight of the elephant's brain by the weight of the bird's brain, then, using the rules of exponents, we have the following:
[tex]undefined[/tex]Find the product.Simplify to lowest terms:[tex] \frac{9}{10} \times \frac{3}{8} [/tex]A. 5/18B. 1/3C. 2/3D. 27/80
Answer:
D. 27/80
Explanation:
Given the expression
[tex]\frac{9}{10}\times\frac{3}{8}[/tex]We can multiply the numerators together, (Do likewise for the denominators).
[tex]=\frac{27}{80}[/tex]We cannot simplify thi
I will send u a picture of my equation
Answer:
where is the picture????
