What is the surfacearea, in square inches,of the square pyramidbelow?
hi, for solve this question we need to use the formula below:
[tex]\text{Area of each triangle + area of the quadrangular base = Total area}[/tex]First, the area of the base:
[tex]\begin{gathered} \text{area base = side }\cdot\text{ side} \\ \text{area base = 4in }\cdot\text{ 4in} \\ \text{area base = 16in}^2 \end{gathered}[/tex]Now, the area of each triangular side:
we have the base as 4in, and the height as 9in.
So, using the formula:
[tex]\begin{gathered} \text{area = }\frac{\text{ base }\cdot\text{ height}}{2} \\ \text{area = }\frac{\text{ 4 }\cdot9}{2} \\ \text{area = }\frac{\text{3}6}{2}=18in^2\text{ each triangular side} \end{gathered}[/tex]Now, let's sum all of the values:
4 triangular sides + 1 quadrangular side
(4 * 18in) + (1 * 16in)
72in² + 16in² = 88in²
Answer: ALTERNATIVE NUMBER 2. 88in²
Choose the answer that represents the product below as an exponentialexpression(8.2). (8.2). (8.2)A. 3.8.2B. 8.2^4C. 3^8.2D. 8.2^3
We have
[tex]\mleft(8.2)\cdot(\mright?8.2)\cdot(8.2)[/tex]the base is 8.2 and the exponent is the number of times the number repeated in this case it is 3 therefore the answer is
[tex]8.2^3[/tex]ANSWER
D. 8.2^3
Which of the following systems of equations has the solution (1, 4)? y = –3x – 1y = –x + 5 y = 3x + 1y = x – 5y = –x – 5
Step 1
To find the systems of equations that has the solution (1,4). The value of x, 1 input into the equations must give 4 as the value of y. We will now test the options.
1) y=-3x-1
[tex]\begin{gathered} y=-3(1)-1 \\ y=-4 \\ False \end{gathered}[/tex]2) y=-x+5
[tex]\begin{gathered} y=-(1)+5=4 \\ True \end{gathered}[/tex]3) y=3x+1
[tex]\begin{gathered} y=3(1)+1=4 \\ True \end{gathered}[/tex]4) y=x-5
[tex]\begin{gathered} y=1-5=-4 \\ false \end{gathered}[/tex]5) y=-x-5
[tex]\begin{gathered} y=-(1)-5=-6 \\ False \end{gathered}[/tex]Answer;
[tex]\begin{gathered} y=-x+5 \\ y=3x+1 \\ \end{gathered}[/tex]A={1,2,3,4,5} and B={6,7,8,9}. Find A∪B
Answer:
{1, 2, 3, 4, 5, 6, 7, 8, 9}
Step-by-step explanation:
[tex]A \cup B[/tex] represents the set of all elements in [tex]A[/tex] or [tex]B[/tex].
According to the propertyWhich choice is equivalent to the quotient below!
Answer:
A
Step-by-step explanation:
Because square root of 30 is 5.4 rounded, and square root of 6 is 2.4 rounded, so 5.4 divided 2.4 is 2.25, and square root of 5 (Answer choice A) is 2.25 rounded as well. They are more accurate when not rounded btw u can check yourself:) HAVE A GREAT DAY/NIGHTT!
The sum of nine and a number is forty less than fifteen
Answer:
x = -34
Step-by-step explanation:
Lets use "x" as the missing number
9 + x = 15 - 40
9 + x = -25
x = -25 - 9
x = -34
How is 600:450 and 60:45 equivalent
How is 60:45 and 4:3 equivalent
How is 600:450 and 4:3 equivalent
Solve
-21 < 3x - 12 < 6
Answer:
-3 < x < 6
Step-by-step explanation:
-21 < 3x - 12 < 6
first lets add 12 to everything
-9 < 3x < 18
now lets divide everything by 3
-3 < x < 6
Using the prototype oblique triangle shown below and the information given, find the measure of the remaining sides and angles in the triangle.
find:
beta:
a:
b:
Using the law of sines, the remaining angles and sides of the triangle are given as follows:
[tex]\beta = 20^\circ[/tex]a = 8.2.b = 6.What is the law of sines?Suppose we have a triangle in which:
Side with a length of a is opposite to angle A.Side with a length of b is opposite to angle B.Side with a length of c is opposite to angle C.The lengths and the sine of the angles are related according to the equation presented as follows:
[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]
The remaining angle measure is given as follows:
[tex]\beta = 180 - (132 + 28) = 20^\circ[/tex]
(this is because the sum of the internal angles of a triangle is of 20º).
Then side a is calculated from the law of sines as follows:
sin(28º)/a = sin(132º)/13
a = 13sin(28º)/sin(132º)
a = 8.2.
Side b is also calculated from the law of sines, as follows:
sin(20º)/b = sin(132º)/13
b = 13sin(20º)/sin(132º)
b = 6.
A similar problem, also about the law of sines, is given at https://brainly.com/question/4372174
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what is the range of the relation[(-5,0),(-4,-3),(-3,4),(-1,0),(-4,-1)]
The range is the set of values that the relation takes for the domain for which it is defined.
Is the set of values of the dependent variable.
In this case, we have the relation [(-5,0),(-4,-3),(-3,4),(-1,0),(-4,-1)].
The dependant variable takes the values: 0, -3, 4, 0 and -1. Some values are repeated.
We put the repeated values only once and sort to write the range.
Then, the range is R = {-3, -1, 0, 4}.
Answer: Range = {-3, -1, 0, 4}
Dakota fills a measuring cup 5/8 cup of sugar 2 times to make a cake. Which multiplication equation shows the total amount of sugar Dakota uses?
We have that Dakota fills a measuring cup 5/8 cup of sugar two times. The multiplication equation that shows the total amount of sugar is:
[tex]2\cdot\frac{5}{8}=\frac{10}{8}=\frac{8}{8}+\frac{2}{8}=1+\frac{2}{8}=1\frac{2}{8}[/tex]We needed to multiply the fraction 5/8 by 2, and then solve for the given operations.
Therefore, the answer is the last option:
2 x 5/8 = 10/8 = 1 2/8 cups of sugar
Perform the indicated operation.Subtract (4x^2-5) from the sum of (x^2 - 5x + 1) and (3x^2 – 3x+4)The answer is
We have the sum of
[tex]\mleft(x^2-5x+1\mright)+(3x^2-3x+4)[/tex]we sum similar terms
[tex]4x^2-8x+5[/tex]then we subtract (4x^2-5) from the result of the sum above
[tex](4x^2-8x+5)-\mleft(4x^2-5\mright)=4x^2-8x+5-4x^2+10[/tex]then we sum similar terms, and we find the answer
[tex]-8x+10[/tex]help me please
thank you
In interval notation, the inequality is [tex](-\infty, -4][/tex].
indicate the equation of the given line in standard form show all your work for full creditthe line containing the diagonal ,BD,of a square whose vertices areA(-3,3) B(3,3) C (3,-3) and D (-3,-3)find two equations one for each diagonal
ANSWER:
x + y = 0
x - y = 0
EXPLANATION:
Given the coordinates:
A(-3,3)
B(3,3)
C(3,-3) and
D (-3,-3)
One diagonal is line AC.
Find the slope of AC:
[tex]m\text{ = }\frac{y2-y1}{x2-x1}=\text{ }\frac{-3-3}{3-(-3)}=\frac{-6}{6}=\text{ -1}[/tex]Solpe of AC = -1
Using the slope intercept form, y = mx+b, we have:
y = -1x + b
y = -x + b
The equation for AC:
y = -x
The other diagonal is BD.
find the slope of BD:
[tex]m\text{ = }\frac{y2-y1}{x2-x1}=\text{ }\frac{-3-3}{-3-3}=\frac{-6}{-6}=\text{ 1}[/tex]Slope of BD = 1
The equation of BD:
y = 1x
y = x
Therefore the equation of both lines in standard form will be:
AC ==> x + y = 0
BD ==> x - y = 0
use a calculator.15. Select all the numbers that are solutions to the equation x2 = 15. (2 pt)A. 225B. 225C. 7.5D. 715E. -V15
√15, and -√15
1) Considering the equation below, let's solve it:
[tex]\begin{gathered} x^2=15 \\ \sqrt[]{x^2}=\sqrt[]{15} \\ x=\sqrt[]{15},\text{ -}\sqrt[]{15} \end{gathered}[/tex]2) So the answer is √15, and -√15
Since (√15)² = 15 and (-√15)²=15
3.168×10 9 and 4.8 \times 10^24.8×10 2 expressed in scientific notation?
The value of 3.168 × 10^9 × 4.8 × 10^2 in scientific notation is 15.2064 × 10^11.
What is scientific notation?It should be noted that scientific notation is used to express the numbers that are either too large or too small.
The expression is illustrated as:
= 3.168 × 10^9 × 4.8 × 10^2
= 15.2064 × 10^11
It should be noted that the exponent is that we add the powers.
Learn more about scientific notation on:
brainly.com/question/1767229
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An inverse variation includes the points (-4, 3) and (-1, n). Find n.
In a inverse variation you have two variables, in this case (x,y) x and y, and a constant value k in the form:
[tex]y=\frac{k}{x}[/tex]When x increase y decreases and when x decreases y increases (inverse variation)
As you have two (x,y) data;
(-4, 3 ) and (-1 , n)
And both have the same constant k.
[tex]\begin{gathered} 3=\frac{k}{-4} \\ \\ n=\frac{k}{-1} \end{gathered}[/tex]Solve in the first equation the k:
[tex]\begin{gathered} k=-4\cdot3 \\ k=-12 \end{gathered}[/tex]Use the value of k= -12 to find n in the second equation:
[tex]n=\frac{-12}{-1}=12[/tex]Then , the value of n is 12slove equations with variables on both sides-4 + 9z = 10z
What is X for
3(2x + 11) + 4(2x + 3) = 9(2x + 13) - 3x
Answer:
x = -72
Step-by-step explanation:
3(2x + 11) + 4(2x + 3) = 9(2x + 13) - 3x
(6x + 33) + (8x + 12) = (18x + 117 ) - 3x
14x + 45 = (18x + 117) - 3x
14x + 45 = 15x + 117
-45
14x = 15x + 72
-15x
-1x = 72
/-1
x = -72
I am stuck on trying to solve these two problems can someone please help me with themWrite an equivalent fraction for each problem below. 24/42 and 16/20
ANSWER :
The equivalent fractions are :
24/42 = 4/7
16/20 = 4/5
EXPLANATION :
From the problem, we have the fractions 24/42 and 16/20
For 24/42
We need to think of a number that the numerator and the denominator will be divisible of.
24 and 42 are both divisible by 6.
That will be :
[tex]\frac{24}{42}\rightarrow\frac{24\div6}{42\div6}=\frac{4}{7}[/tex]Therefore, the equivalent fraction for 24/42 is 4/7
For 16/20
We will do the same procedure, 16 and 20 are divisible by 4.
That will be :
[tex]\frac{16}{20}\rightarrow\frac{16\div4}{20\div4}=\frac{4}{5}[/tex]The equivalent fraction for 16/20 is 4/5
This hutch is made up of two rectangular prisms. 1 7 ft 2 ft 2 127 ft 22 ft 4 ft What is the total volume of this hutch, in cubic feet?
Answer
40 cubic feet
Step-by-step explanation
The volume of a rectangular prism is calculated as follows:
[tex]V=whl[/tex]where w is the width, h is the height and l is the length of the prism.
The hutch is made up of two rectangular prisms, one with a width of 1 1/3 ft, a height of 2 1/2 ft, and a length of 4 ft. The other one has a width of 2 2/3 ft, a height of 2 1/2 ft, and a length of 4 ft.
To calculate the volume of the hutch, first, we need to calculate the volume of each prism, and then add them.
The volume of the smaller prism is:
[tex]\begin{gathered} V_1=1\frac{1}{3}\cdot2\frac{1}{2}\cdot4 \\ V_1=13\frac{1}{3}\text{ cubic feet} \end{gathered}[/tex]The volume of the bigger prism is:
[tex]\begin{gathered} V_2=2\frac{2}{3}\cdot2\frac{1}{2}\cdot4 \\ V_2=26\frac{2}{3}\text{ cubic feet} \end{gathered}[/tex]Finally, the volume of the hutch is:
[tex]V_1+V_2=13\frac{1}{3}+26\frac{2}{3}=40\text{ cubic feet}[/tex]Instructions: State the domain and range of the given function.
In this problem, we are going to state the domain (x-values)of the given scatter plot.
Notice that we are given individual points. That means the domain will also have individual values, or the x-vaues of the points.
In your graph, we are given th following points:
(2,2)
(2,10)
(3,7)
(5,5)
(8,5)
So, the domain for the graph will have the values 2, 3, 5, 8, or the first option on your dropdown menu.
this one is way to hard
f(5) = -4(5 - 1)
f(5) = -4(4)
f(5) = - 16
Find the exact value of sin 120° in simplest form with a rationaldenominator.
Use this description to write the quadratic function in vertex form:The parent function f(x)=x^2 is vertically stretched by a factor of 2 and translated 14 units right and 6 units up.
The vertex form is given by:
[tex]y=a(x-h)^2+k[/tex]The parent function is:
[tex]f(x)=x^2[/tex]The function is vertically stretched by a factor of 2 :
[tex]2f(x)=2x^2[/tex]and translated 14 units right:
[tex]2f(x-14)=2(x-14)^2[/tex]and 6 units up:
[tex]2f(x-14)+6=2(x-14)^2+6[/tex]Answer:
[tex]g(x)=2(x-14)^2+6[/tex]A set of data has a normal distribution with a mean of 56 and a standard deviation of 9. Find the percent of data within the following interval. from 29 to 83 The percent of data within the given interval is ____%.
Solution
We are given
[tex]\begin{gathered} \mu=56 \\ \sigma=9 \end{gathered}[/tex]First, we will find the probability p(29 < x-bar < 83)
Note: z score formula
[tex]z=\frac{\bar{x}-\mu}{\sigma}[/tex]To find the probability
[tex]\begin{gathered} p(29<\bar{x}<83)=p(\bar{x}<83)-p(\bar{x}<29) \\ p(29<\bar{x}<83)=p(z<\frac{83-56}{9})-p(z<\frac{29-56}{9}) \\ p(29<\bar{x}<83)=p(z<3)-p(z<-3) \\ p(29<\bar{x}<83)=0.99865-0.0013499 \\ p(29<\bar{x}<83)=0.9973001 \\ p(29<\bar{x}<83)=0.9973\text{ \lparen to four decimal places\rparen} \end{gathered}[/tex]Therefore, the percentage within the given interval will be
[tex]0.9973\times100=99.73\%[/tex]The answer is
[tex]\begin{equation*} 99.73\% \end{equation*}[/tex]Solve for x
23x-5
21x+5
B.__ angles form a straight line.
Complete the sentences
A. All right angles are 90 degrees (by definition)
B. supplemenatry angles form straight line (by definition)
C. If two angles form a linear pair, then the are supplementary (by definition)
D. When two lines intersect, the inverse angles are congruent.
In the given image of two intersecting lines, you have m∠1 = 67°
E. angle 2 and angle 1 are supplementary, then;
m∠2 + m∠1 = 180°
m∠2 = 180° - m∠1
m∠2 = 180° - 67°
m∠2 = 113°
F. angle 3 and angle 1 are congruent, then:
m∠3 = m∠1 = 67°
Due to the given image, you have the following expressions:
2x + x + 60° = 180° supplementary angles
3x + 60° = 180° subtract 60 both sides
3x = 180° - 60°
3x = 120° divide both sides by 3
x = 120/3
x = 40°
Furthermore, for y, you have:
x + y + y + 20° = 180° supplementary angles
x + 2y + 20° = 180° replace x = 40
40 + 2y + 20° = 180°
2y + 60° = 180° subtract 60 both sides
2y = 180° - 60°
2y = 120°
y = 120/2 divide by 2 both sides
y = 60°
Answer: 180 degree's make up a straight line.
Step-by-step explanation:
Four friends are playing a game. 36 cards are dealt out between the friends. Which equation can be used to find how many cards each person receives
Given
Four friends are playing a game.
36 cards are dealt out between the friends.
To find: Which equation can be used to find how many cards each person receives.
Explanation:
It is given that,
Four friends are playing a game.
36 cards are dealt out between the friends.
Let x be the number of cards received by each person.
Then,
[tex]\begin{gathered} 4x=36 \\ x=\frac{36}{4} \\ x=9 \end{gathered}[/tex]Hence, each person receives 9 cards.
Thus,
[tex]undefined[/tex]16. What is the average of the following numbers? 7, 4, 6, 11, 10, 17, 15? (a) 14 (b) 9 (c) 10 (d) 12 (e) 20
Answer:
C: 10
Step-by-step explanation:
