In this problem, we are applying function notation. When we see a function written as
[tex]f(x),[/tex]we read it as "f of x" or "f as a function of x."
We will take the value of x and substitute it into the quation.
The function rule states
[tex]f(x)=-2x+3[/tex]Since we are given f(-3), we will substitute each x-value (inside parentheses), and simplify:
[tex]f(-3)=-2(-3)+3=6+3=9[/tex]Therefore, f(-3) = 9.
find the length of the radius if the circumference is 13.2 round to one decimal place. use 3.14 for π
Given
[tex]\begin{gathered} \text{Circumference of Circle = 13.2 unit} \\ \pi\text{ = 3.14} \end{gathered}[/tex]Required :
[tex]\text{length of radius (r) = ?}[/tex]The formula for the circumference of a circle:
[tex]\text{Circumference of circle = 2}\pi r[/tex]When we substitute and simplify:
[tex]\begin{gathered} 13.2\text{ = 2 }\times\text{ }\pi\text{ }\times\text{ r} \\ \text{making r the subject of formula} \\ r\text{ = }\frac{13.2}{2\text{ }\times\text{ 3.14}} \\ r\text{ = 2.1019} \\ \approx\text{ 2.1 unit (1.d.p)} \end{gathered}[/tex]How much fencing does Susie need.Option d: x = 10 and 80 ft of fencing.
The area of a rectangle is given by the product of its dimensions.
If the rectangle area is 200 ft² and the dimensions are 2x and x, we have:
[tex]\begin{gathered} 200=2x\cdot x \\ 2x^2=200 \\ x^2=100 \\ x=10 \end{gathered}[/tex]The total fencing needed is (2x+2x+x+x) from the perimeter and (x+x) from the internal fencing, so:
[tex]\begin{gathered} (2x+2x+x+x)+(x+x) \\ =6x+2x \\ =8x \\ =8\cdot10 \\ =80\text{ ft} \end{gathered}[/tex]Therefore the correct option is d.
you roll a number cu
Question:
Solution:
A die has 6 faces with numbers 1 through 6. Three faces have even numbers, and 3 faces have odd numbers.
Each roll of the die can result in 6 different outcomes.
The total number of different outcomes of rolling a die 3 times are 6 * 6 * 6 = 216.
There are 3 possible even number outcomes on the first roll and another 3 possible even number outcomes on the second roll. The third roll needs to be a 3, so there is one single desired outcome of the third roll.
Total number of desired outcomes: 3 * 3 * 1 = 9
probability(even, even, 3) = 9/216 = 1/24
So the correct answer (there is an error in the typography) would be 124.
Find the difference, (12m+1) - (5m - 4) O A. 7m-3 O B. 17m-3 O C. 7m + 5 O D. 17m + 5
Given the expression
(12m+1) - (5m - 4)
First we need to expand the parenthesis
12m + 1 - 5m - (-4)
Note that product of two negative sign will result in a positive sign, so the expression becomes;
12m+1-5m+4
Collect like terms;
12m-5m+1+4
Evaluate the resulting expression:
12m-5m+1+4
7m + 5
Hence option C is correct
The transformation shown here maps each point on the preimage up 5 and right 4A) translation B) reflection C) rotation
Recall that, in geometry, a translation simply means moving without rotating, resizing, or anything else.
To translate a shape every point of the shape must move in the same direction and with the same distance.
Since the given transformations only move the shape 5 units up and 4 units right, then it is a translation.
Answer: Option A.
The posted speed limit is 45 miles per hour. Choose all the metric measures that are faster than 45 miles per hour. Customary and Metric Unit Equivalents DATA Length Weight/Mass Capacity 1 m - 3.28 ft 1 Oz - 28.35 g 1 gal - 3.79 L 1 m - 39.37 in. 1 kg - 2.20 lb 1 gt - 0.95 L 1 in. - 2.54 cm 1 metric ton (1) - 1.102 T 1 mi - 1.61 km A 45 km per hour B. 64.1 km per hour C. 86.4 km per hour D. 91 km per hour E. 112.3 km per hour
Converting 45 miles/hour to km/h, we have:
[tex]45\frac{miles}{h}\cdot(\frac{1.61\frac{\operatorname{km}}{h}}{1\frac{\text{miles}}{h}})=72.45\text{ km/h}[/tex]Metric measures that are faster than 45 miles/hour = C. 86.4 km per hour / D. 91 km per hour / E. 112.3 km per hour
i need to know everything i can be taught about Quadratic Relationships?
The line of symmetry is where one side of the graph is the same as the other side of the graph
Looking at the graph, the line at x = -1 , the left side is the same as the right side
The line of symmetry is x = -1
Where would the square root of 18 fall on the x-axis?
Answer:
4.24
Explanation:
Given the expression:
[tex]\sqrt[]{18}[/tex]If 18 falls on the x-axis, then the square root will be on the y-axis.
Using the coordinate grid:
Thus, the square root of 18 is approximately 4.24.
A and B are complementary angles. If A = (x + 6) andB = (7x + 30) then find the measure of A
Answer:
Concept:
Two angles are said to be complementary when they add up together to give 90 degrees
[tex]\begin{gathered} \angle A+\angle B=90^0 \\ \text{where,} \\ \angle A=(x+6) \\ \angle B=(7x+30)^0 \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} \angle A+\angle B=90^0 \\ x+6+7x+30=90^0 \\ \text{collect similar terms, we will have} \\ x+7x+6+30=90 \\ 8x+36=90 \\ \text{substract 36 from both sides} \\ 8x+36-36=90-36 \\ 8x=54 \\ \text{divide both sides by 8} \\ \frac{8x}{8}=\frac{54}{8} \\ x=6.75 \end{gathered}[/tex]To determine the value of angle A,
We will substitute the value of x= 6.75 below
[tex]\begin{gathered} A=x+6 \\ A=6.75+6 \\ A=12.75^0 \end{gathered}[/tex]Hence,
A= 12.75°
The sum of two numbers is -6 andtheir difference is 12. What is thevalue of the smallest of the twonumbers?
Formulating a system of equations, we have:
x+y=-6 Equation 1
x-y=12 Equation 2
Solving the system of equations, we have:
y = -6 - x (Subtracting x from both sides of the Equation 1)
x - (-6 - x)=12 (Replacing y=-6-x in the Equation 2)
x + 6 + x = 12 (Using the sign rules)
2x + 6 = 12 (Adding like terms)
2x = 6 (Subtracting 6 from both sides of the Equation)
x=3 (Dividing on both sides by 2)
Replacing x=3 in y=-6-x , we have:
y = -6 - 3
y= -9
Given that the numbers are 3 and -9, the smallest of them is -9.
The answer is -9.
a math teacher instructed students to create a diagram and use it to classify the numbers listed below Which diagram correctly classifies the numbers
Theconstant number π has the following value:
π = 3.15149...
That is, is a number with infinite decimals and without any periodicity. This type of numbers are known as irrational numbers. Hence, number π is an irrational number.
Find the surface area of a rectangle solid with edges of length 2cm,5cm, and 7cm
The surface area for a rectangular prism is given to be:
[tex]A=2(lw+lh+wh)[/tex]where l, w, and h are the lengths of the solid.
From the question, we have:
[tex]\begin{gathered} l=2\text{ cm} \\ w=5\text{ cm} \\ h=7\text{ cm} \end{gathered}[/tex]Therefore, the volume is calculated to be:
[tex]\begin{gathered} A=2((2\times5)+(2\times7)+(5\times7)) \\ A=2(10+14+35) \\ A=2(59) \\ A=118\text{ cm}^2 \end{gathered}[/tex]The surface area is 118 square centimeters.
the perimeter of a square newspaper add is 24 cm. how long is each side?
perimeter of the square newspaper = 24 cm
[tex]\begin{gathered} \text{perimeter of a square =4l} \\ \text{where} \\ l=\text{length} \\ 24=4l \\ l=\frac{24}{4} \\ l=6\text{ cm} \end{gathered}[/tex]Each side = 6 cm
Let f(x) = 4x + 7. Find f-1(15)
1. replace f(x) with y
[tex]y=4x+7[/tex]2. Replace every x with a y and replace every y with an x
[tex]x=4y+7[/tex]3. Solve for y:
[tex]\begin{gathered} 4y=x-7 \\ y=\frac{x-7}{4} \end{gathered}[/tex]4. Replace y with f−1(x):
[tex]f^{-1}(x)=\frac{x-7}{4}[/tex]Evaluate the inverse for x = 15:
[tex]f^{-1}(15)=\frac{15-7}{4}=\frac{8}{4}=2[/tex]When driving on a high way, noticed a sign saying exit to Johnstown is 1 3/4 miles away, while exit to Jerrystown is 4 1/2 miles away. How faris Johnstown from Jerrystown?
For this case we know that the exit to Johnstown is 1 3/4 miles away and the exit to Jerrystown is 4 1/2 miles away and we want to find the distance from Johnstown to Jerrystown. And in order to do this we just need to take the difference between the two fractions, but let's convert the values like this:
[tex]1\frac{3}{4}mi=\frac{7}{4}mi,4\frac{1}{2}mi=\frac{9}{2}mi[/tex]Then the distance between thw two cities is given by:
[tex]\frac{9}{2}mi-\frac{7}{4}mi=\frac{18-7}{4}=\frac{11}{4}mi[/tex]Final answer: 11/4 mi or 2.75 mi
Calculate the cone:1) the length of the base of the cone if its height is 12 cm and the radius of the base is 5 cm;2) the length of the apex if its base radius is 2 cm and its base radius is 10 cm;3) the length of the base radius if its height is 5 dm and its base radius is 15 dm.
Answer:
Explanation:
Here, we want to get the length of the base of the cone
The base of the cone, its height and the slant height forms a right triangle
Please help this is due in an hour. the equation is q+q+.3q=180 pls help.
q=45
Explanation
Step 1
the sum of the internal angles of a triangle must be 180 , then
[tex]\begin{gathered} 3q+q+q=180 \\ \\ \\ \end{gathered}[/tex]Step 2
add similar terms
[tex]\begin{gathered} 3q+q+q=180 \\ 4q=180 \end{gathered}[/tex]Step 3
divide both sides by 4
[tex]\begin{gathered} 4q=180 \\ \frac{4q}{4}=\frac{180}{4} \\ q=45 \end{gathered}[/tex]I hope this helps you.
200×200 divided by 20
The value of the numerical expression (200 × 200) / 20 will be 2,000.
Given that:
Expression, (200 × 200) / 20
When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.
Simplify the expression, then we have
⇒ (200 × 200) / 20
⇒ 200 × 10
⇒ 2,000
More about the value of the expression link is given below.
https://brainly.com/question/23671908
#SPJ6
simplify the factors of ratioa) 600g : 4kgb) 350 : 400
To simplify the given questions
Part A
[tex]600g\colon4Kg[/tex]
To find the ratio, we will first have to convert the factors into the same units
We will convert 4kg to grams
So that we will have
[tex]\begin{gathered} 1\operatorname{kg}=1000g \\ 4\operatorname{kg}=4000g \end{gathered}[/tex]Therefore
[tex]600g\colon4Kg=600g\colon4000g[/tex]Next, we will have to reduce the ratios to the lowest term
Thus, the answer is
[tex]3\colon20[/tex]Part B
[tex]350\colon400[/tex]Since they have the same units, we will reduce the ratio to its lowest term
Therefore, the answer will be
[tex]7\colon8[/tex]if u add the two equations 6x+4y=46 and -6x+9y=6 what do you get?
Combining like terms
[tex]\begin{gathered} 6x+4y-6x+9y=46+6 \\ 6x-6x+4y+9y=46+6 \\ (6-6)x+(4+9)y=52 \\ 0\cdot x+13y=52 \\ 13y=52 \\ y=\frac{52}{13}=4 \end{gathered}[/tex]Think of y = 4 as y=f(x)=4
This means that for any value of x you replace, you will always get y = 4
What is the area of this circle? (use 3.14 for 1)
Explanation
the area of a circle is given by:
[tex]\text{Area}_{circle}=\pi(\frac{diameter^2}{4})[/tex]then
let
diameter= 12 cm
replace.
[tex]\begin{gathered} \text{Area}_{circle}=\pi(\frac{diameter^2}{4}) \\ \text{Area}_{circle}=\pi(\frac{(12^2}{4}) \\ \text{Area}_{circle}=(3.14)\cdot(36) \\ \text{Area}_{circle}=113.04 \end{gathered}[/tex]so, the answer is
[tex]113.04[/tex]I hope this helps you
The equations of three lines are given below.Line 1: 4x - 6y = 2Line 2: y = 3/2 * x - 7Line 3: 2y = 3x + 5For each pair of lines, determine whether they are parallel, perpendicular, or neither.
Answer:
Explanation:
The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m represents slope
c represents y intercept
Considering equation 1,
4x - 6y = 2
By rearranging the equation,
4x - 2 = 6y
6y = 4x - 2
Dividing both sides of the equation by 6, we have
6y/6 = 4x/6 - 2/6
y = 2x/3 - 1/3
Thus, slope = 2/3
Considering equation 2,
y = 3x/2 - 7
slope = 3/2
Considering equation 3,
2y = 3x + 5
Dividing both sides by 2,
2y/2 = 3x/2 + 5/2
y = 3x/2 + 5/2
slope = 3/2
Recall, two lines are parallel if they have equal slope. the slopes of equation 2 and 3 is 3/2. Since it is equal,
Line 1 and line 2 : neither
Line 1 and Line 3: neither
line 2 and line 3 are parallel
play the phrase as an expression then evaluate the expression when x equals 4
The sum of a number x and 8: x+8
All divided by 3:
[tex]\frac{x+8}{3}[/tex]When x equals 4:
[tex]\frac{4+8}{3}=\frac{12}{3}=4[/tex]Then, the phrase evaluated when x is 4 is equal to 4. (Answer: 4)
State all integer values of x in the interval [-4,3] that satisfy the following inequality 5x-5> -20
Inequality:
[tex]5x-5>-20[/tex]The integer values included in [-4, 3] are: -4, -3, -2, -1, 0, 1, 2, and 3.
To know which are included, we have to solve the inequality as follows:
[tex]5x-5+5>-20+5[/tex][tex]5x>-15[/tex][tex]x>-\frac{15}{5}[/tex][tex]x>-3[/tex]Then, all the values greater than -3 are included, but not -3.
Answer: x = -2, -1, 0, 1, 2, and 3.
18. What is the value of x in the right triangle? 9 х A) 7 B) 777 C) 785 D) V7
Given a right-angled triangle
Where
[tex]\begin{gathered} \text{Hyp}=\text{Hypotenuse}=9\text{ units} \\ \text{Adj}=\text{Adjacent}=2\text{ units} \\ \text{Opp}=\text{Opposite}=x\text{ units} \end{gathered}[/tex]The value of x can be deduced by using the Pythagorean theorem
The formula of the Pythagorean theorem is
[tex]\text{Hyp}^2=\text{Opp}^2+\text{Adj}^2[/tex][tex]9^2=x^2+2^2[/tex]Solve for x
[tex]\begin{gathered} 9^2=x^2+2^2 \\ 81=x^2+4 \\ \text{Collect like terms} \\ x^2=81-4 \\ x^2=77 \\ \text{Square of both sides} \\ \sqrt[]{x^2}=\sqrt[]{77}^{} \\ x=\sqrt[]{77}\text{ units} \end{gathered}[/tex]Hence, the answer is option B
the tigers scored twice as many points as the buzzers .the tigers scored. poilnts did the buzzers score?
We know that
- the Tigers scored 8 points.
- this is twice as the score of the Buzzers.
Since
2 x 4 = 8
then, 8 is twice as 4.
Then the Buzzers scored 4.
Answer: 4
Statistics show that the fractional part of a battery, B, that is still good after 6 hours of use is given by B = 4-0.011 What fractional part of the battery is still operatingafter 300 hours of use?AnswerHow to enter your answer (opens in new window)Keypad
Answer
Explanation
Given:
[tex]B=4^{-0.01t}[/tex]where:
t=300 hours
To determine the fractional part of the battery after 300 hours of use, we plug in t=300 into B=4^-0.01t. So,
[tex]\begin{gathered} B=4^{-0.01t} \\ B=4^{-0.01(300)} \\ Simplify \\ B=4^{-3} \\ B=\frac{1}{64} \end{gathered}[/tex]Therefore, the answer is:
[tex]\frac{1}{64}[/tex]A bagel shop makes bagels that serve 1 person each. For a party, the baker is asked to make a large bagel in the same shape that will serve 25 people. The scale factor is 2.9. The bagels are topped with a thin layer of cream cheese . Assume the thickness of the cream cheese is the same on both bagels. How many times more cream cheese will be required for the dilated bagel as for the original ? Round your answer to the nearest tenth.
EXPLANATION
Let's see the facts:
Number of people: 25
Scale factor = 2.9
The shop would require:
[tex]\frac{25}{2.9}=8.62[/tex]Answer: the shop would requires 8.62 more times of cream cheese.
Use Example 1 as a model to evaluate the limitlim n→∞ nf(ci)Δxii = 1over the region bounded by the graphs of the equations. (Round your answer to three decimal places.)f(x) = x, y = 0, x = 0, x = 21Hint: Let ci = 21i2n2.
Answer:
Explanation:
ΔΔΔΔΔΔΔ Simplified = What is the ratio of A to * ? What is the ratio of * to (A ) ? = =