Each face of a pyramid is an isosceles triangle with a 70 degree vertex angle. What are the measures of the base angles?
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We are given that each face of a pyramid is an isosceles triangle and that its vertex angle is 70 degrees. This problem can be exemplified in the following diagram:
Since the triangle is isosceles, its base angles are the same, and the sum of the interior angles must be equal to 180 degrees. Therefore, we have the following relationship:
[tex]70+x+x=180[/tex]Adding like terms, we get:
[tex]70+2x=180[/tex]Now we solve for "x", first by subtracting 70 on both sides:
[tex]\begin{gathered} 70-70+2x=180-70 \\ 2x=110 \end{gathered}[/tex]Now we divide both sides by 2
[tex]x=\frac{110}{2}=55[/tex]Therefore, the base angles of the pyramid are 55 degrees.
Related Questions
Michael withdraws $40 from his checking account each day how long will it take him to withdraw $680
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Solution
- The amount Michael withdraws every day is $40.
- The number of days it takes to withdraw $680 is given by:
[tex]\frac{\text{Total Amount Withdrawn}}{\text{Amount Withdrawn per day}}[/tex]- Using the formula above, we have:
[tex]\frac{\text{Total Amount Withdrawn}}{\text{Amount Withdrawn per day}}=\frac{680}{40}=17\text{ days}[/tex]Final Answer
The answer is 17 days
hello this the the problem Im stuck on. I need to know where to plot the point on the graph aswell. ty
Answers
Given:
The rent for trucks is $3750.
The additional charge per ton of sugar is $150.
To write: The equation relating the total cost C and amount of sugar S.
Explanation:
The equation represents the total cost C and the amount of sugar S is given by,
[tex]C=3750+150S[/tex]Let us find the three coordinates to plot the graph.
When
[tex]S=0[/tex]Then,
[tex]\begin{gathered} C=3750+150(0) \\ =3750 \end{gathered}[/tex]When
[tex]S=1[/tex]Then,
[tex]\begin{gathered} C=3750+150 \\ =3900 \end{gathered}[/tex]When
[tex]S=2[/tex]Then,
[tex]\begin{gathered} C=3750+150(2) \\ =3750+300 \\ =4050 \end{gathered}[/tex]So, the coordinates are,
[tex](0,3750),(1,3900),(2,4050)[/tex]The equation represents the total cost C and the amount of sugar S is given by,
[tex]C=3750+150S[/tex]The graph is,
Quadrilateral ABCD is a rhombus.DA АC СBMatch the reasons that justifies the given statements.
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A rhombus is a quadrilateral with 4 congruent sides.
For the Rhombus ABCD given
[tex]\begin{gathered} AB\mleft\Vert DC\text{ }\mright? \\ \\ \text{Opposite sides of a rho}mbus\text{ are parallel} \end{gathered}[/tex]Also,
[tex]\begin{gathered} DA\cong CB \\ \text{Opposite sides of a rhombus are congruent} \end{gathered}[/tex]Also,
[tex]\begin{gathered} <\text{ADC}\cong<\text{ABC} \\ \text{Opposite angles of a rhombus are congruent} \end{gathered}[/tex]Last year, Trey opened an investment account with $8800. At the end of the year, the amount in the account had decreased by 6.5%. How much is this decrease in dollars? How much money was in his account at the end of last year?Decrease in amount:$Year-end amount:$
Answers
ANSWER
[tex]\begin{gathered} decrease=572 \\ Year-end\text{ amount=8228} \end{gathered}[/tex]EXPLANATION
Initial amount is $8800
percentage decrease is 6.5%
Decrease amount (in dollars );
[tex]\begin{gathered} \frac{6.5}{100}\times8800 \\ =6.5\times88 \\ =572 \end{gathered}[/tex]The amount of money in the account at the end of last year= Initial amount - decrease
[tex]\begin{gathered} A=8800-572 \\ =8228 \end{gathered}[/tex]Decrease in amount: $572
Year-end amount: $8228
Gor trapezoid HJKL, T and S are midpoint of the legs. If HJ = 14 and LK = 42, find TS.
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First, we are going to divide the figure and named new points X and Y as:
Now, we know that TS is the sum of TX and XS.
TS = TX + XS
Adittionally, TX has the same length of HJ, so:
TX = HJ = 14
Now, we want to know the length of YK, and we can calculate it using the following equation:
LK = LY + YK LY is also equal to HJ, so LY = 14
42 = 14 + YK
42 - 14 = YK
28 = YK
Finally, since T and S are midpoints, the length of XS is the half of the length of YK. It means that XS is:
XS = YK/2
XS = 28/2
XS = 14
Therefore, TS is equal to:
TS = TX + XS
TS = 14 + 14
TS = 28
Answer: TS = 28
What is 1/3 of the sum of 45 and a number is 16 Translated to algebraic equation
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the statement given 1/3 of the sum of 45 and a number is 16
[tex]\frac{1}{3}(45+x)=16[/tex]In order to find the value of x, w
help me please. using the axis of symmetry find the vertex for the follow quadratic function. f (x)=3x^2-6x+8
Answers
Answer:
[tex]P(1,5)[/tex]
Explanation: Axis of symmetry is a vertical line that makes function symmetrical along either side:
In case of parabla function or:
[tex]y(x)=3x^2-6x+8[/tex]We get axial symmetry where the first derivate is zero, and in fact, that is the x value for vertex:
Therefore:
[tex]\begin{gathered} f^{\prime}(x)=(3x^2-6x+8)^{\prime}=6x-6=0 \\ \therefore\rightarrow \\ x=\frac{6}{6}=1 \end{gathered}[/tex]And the corresponding y-value is:
[tex]f(1)=3(1)^2-6(1)+8=5[/tex]Therefore vertex is at the point:
[tex]P(1,5)[/tex]One package of markers has dimensions 6"×8"×1"what are the dimensions of the box that will hold 30 packages of markers and use the LEAST amount of cardboard? A. 6"×8"×30" B. 6"×16"×15" C. 10"×10"×10"D. 12"×8"×15" E. 18"×8"×10
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The required Dimensions are 6'' x 8'' x 30'' , That is option A
Given that the shape below is a rectangle, we know that the diagonals, lines AD and CB, are ____.
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The given information is the shape is a rectangle.
About the diagonals of rectangles, there are two known properties:
- The diagonals of a rectangle bisect each other
- Both diagonals have the same length
Then, the answer is option C. They have the same length
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
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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.
Find the area of this parallelogram. Be sure to include the correct unit in your answer.19 yd12 yd11 yd
Answers
Given a parallelogram as shown below:
The formula to calculate the area of the parallelogram is given to be:
[tex]A=b\times h[/tex]From the question provided, we have the following parameters:
[tex]\begin{gathered} a=12\text{ yd} \\ b=11\text{ yd} \\ h=9\text{ yd} \end{gathered}[/tex]Therefore, we can use the formula to calculate the area as shown below:
[tex]\begin{gathered} A=b\times h \\ A=11\times9 \\ A=99yd^2 \end{gathered}[/tex]The area of the parallelogram is 99 squared yards (99 yd²).
Given the recursive formula for an arithmetic sequence,An = an-1 - Tt, where the first term of the sequence is 7. Which of the following could be explicitformulas for the sequence? Select all that apply.
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From the recursive formula:
[tex]a_n=a_{n-1}-\pi[/tex]we notice that the common difference of the sequence is -pi. Now we know that the first term is 7, then the explicit formula is:
[tex]a_n=7-\pi(n-1)[/tex]when
[tex]n>0[/tex]We can relabel this sequence if we assume we start at zero, in this case the sequence will be:
[tex]a_n=7-\pi n[/tex]when:
[tex]n\ge0[/tex]Last year, Bob had $10,000 to invest. He invested some of it in an account that paid 10% simple interest per year, and he invested the rest in an account that paid 8% simple interest per year. After one year, he received a total of $820 in interest. How much did he invest in each account?
Answers
Given:
The total amount is P = $10,000.
The rate of interest is r(1) = 10% 0.10.
The other rate of interest is r(2) = 8%=0.08.
The number of years for both accounts is n = 1 year.
The total interest earned is A = $820.
The objective is to find the amount invested in each account.
Explanation:
Consider the amount invested for r(1) as P(1), and the interest earned as A(1).
The equation for the amount obtained for r(1) can be calculated as,
[tex]\begin{gathered} A_1=P_1\times n\times r_1 \\ A_1=P_1\times1\times0.1 \\ A_1=0.1P_1\text{ . . . . .(1)} \end{gathered}[/tex]Consider the amount invested for r(2) as P(2), and the interest earned as A(2).
The equation for the amount obtained for r(2) can be calculated as,
[tex]\begin{gathered} A_2=P_2\times n\times r_2 \\ A_2=P_2\times1\times0.08 \\ A_2=0.08P_2\text{ . . . . . (2)} \end{gathered}[/tex]Since, it is given that the total interest earned is A=$820. Then, it can be represented as,
[tex]A=A_1+A_2\text{ . . . . . (3)}[/tex]On plugging the obtained values in equation (3),
[tex]820=0.1P_1+0.08P_2\text{ . . . . .(4)}[/tex]Also, it is given that the total amount is P = $10,000. Then, it can be represented as,
[tex]\begin{gathered} P=P_1+P_2 \\ 10000=P_1+P_2 \\ P_1=10000-P_2\text{ . }\ldots\ldots.\text{. .(3)} \end{gathered}[/tex]Substitute the equation (3) in equation (4).
[tex]undefined[/tex]Find the volume of the figure. 6 cm. 6 cm. 1 8 cm. 10 cm. Volume of the prism cm3
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The volume of the pyramid is 144 cm³
Explanations:The volume of a prism is given by the formula:
V = BH
where B is the base area
and H is the height
The base of the the pyramid is the lateral triangle, and the area is given by the formula:
B = 0.5 x b x h
b = 8 cm
h = 6 cm
B = 0.5 x 8 x 6
B = 24 cm²
The volume is then:
V = BH, where H = 6 cm
V = 24 x 6
V = 144 cm³
2×+22=2(x+11)whats the property
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Distributive property
In this property, multiplying the sum of two or more terms in that add up in a bracket by a number outside the bracket will be equal to multiplying each term in the bracket individually and then followed by sum of the product. In this question:
2x + 22 = 2(x + 11 ) in that when you perform product on the right side of the equation, the result is the same i.e 2x + 2*11 = 2x + 22
13. (08.05 MC)What is the shape of the cross section taken perpendicular to the base of a cylinder? (1 point)CircleRectangleSquareTriangle
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ANSWER
Rectangle
EXPLANATION
If we take a cross-section perpendicular to the base of a cylinder,
We get a rectangle.
The base of the cylinder is circular and the
Answer: Rectangle
Step-by-step explanation:
I got it right on the test
geometry special parallelogramsSide GH =Side JG =Side FH =
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we have that
In a rhombus the length sides are congruent
the diagonals bisect each other and are perpendicular
so
If mmIn the right triangle IFJ
mtan(30)=FJ/IJ
Remember that
[tex]\tan (30^o)=\frac{\sqrt[]{3}}{3}[/tex]FJ=4
substitute the given values
[tex]\begin{gathered} \frac{\sqrt[]{3}}{3}=\frac{4}{IJ} \\ \\ IJ=\frac{12}{\sqrt[]{3}}\cdot\frac{\sqrt[]{3}}{\sqrt[]{3}}=4\sqrt[]{3} \end{gathered}[/tex]Find the length side IF
Applying Pythagorean Theorem
IF^2=4^2+IJ^2
IJ^2=48
IF^2=16+48
IF^2=64
IF=8 units
that means
side GH=8 units
side JG=side IJ=4√3 units
side FH=2*side FJ=2*4=8 units
I need help with this practice from my ACT prep guide Having trouble
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Given:
[tex]f(x)=-4\cos (\frac{2}{3}x+\frac{\pi}{3})-3[/tex]Can you please answer this question for me. I don’t want full explanation I just want the answers
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we have the fractions
1/4 and 3/4
Remember that
If the denominators are the same, then the fraction with the greater numerator is the greater fraction
3/4 > 1/4
use the number line
Divide number 1 into 4 parts
I need help with finding the output y when x is -4 it's on a graph
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As observed from the graph, the curve is a straight line from point (-2,-1) to (-5,2).
Consider that the equation of a straight line passing through two points is given by,
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}\times(x-x_1)[/tex]So the equation of the line passing through (-2,-1) and (-5,2) is given by,
[tex]\begin{gathered} y-(-1)=\frac{2-(-1)}{-5-(-2)}\times(x-(-2)) \\ y+1=\frac{3}{-3}\times(x+2) \\ y+1=-x-2 \\ y=-x-3 \end{gathered}[/tex]Note that this function is only for the interval [-2, -5].
Now, the value of 'y' corresponding to the input x=-4 is calculated as,
[tex]\begin{gathered} y=-(-4)-3 \\ y=4-3 \\ y=1 \end{gathered}[/tex]Thus, the required output is y = 1 .
Puppets made by each puppeteer43ASCNumber of puppetsAsMYCol?0AlexKalinBruceMarcoMYPuppeteerProIf the mean of the data set is 3 puppets, find the number of puppets Marco made.ProTeapuppets
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Remember that we can get the mean of a dataset by adding up each datum and dividing such sum by the number of data.
Now, let's call the number of puppets Marco made M
This way, we would have that:
[tex]\frac{1+4+3+M}{4}=3[/tex]Solving for M :
[tex]\begin{gathered} \frac{1+4+3+M}{4}=3 \\ \\ \rightarrow\frac{8+M}{4}=3 \\ \\ \rightarrow8+M=12\rightarrow M=12-8 \\ \Rightarrow M=4 \end{gathered}[/tex]Therefore, we can conclude that Marco made 4 puppets.
Hi, can you help me answer this question please, thank you!
Answers
Let x be a random variable representing the blood pressures of adults in the USA. Since it is normally distributed, we would apply the formula for determining z score which is expressed as
z = (mean - population mean)/standard deviation
From the information given,
population mean = 121
Standard deviation = 16
For stage 2 high blood pressure, the probability is
P(x greater than or equal to 160). It is also equal to 1 - P(x < 160)
Thus, for x = 160, we have
z = (160 - 121)/16 = 2.4375
From the standard normal distribution table, the probability value corresponding to a z score of 2.4375 is 0.9927
P(x < 160) = 0.9927
P(x greater than or equal to 160) = 1 - 0.9927 = 0.0073
Converting to percentage, it is 0.0073 * 100 = 0.73%
b) If 2000 peaople were sampled, the number of people with stage 2 high blood pressure would be
0.73/100 * 2000 14.6
To the nearest person, it is 15 people
c) For stage 1, the probability is
P(140 < x < 160)
For x = 140,
z = (140 - 121)/16 = 1.1875
From the standard normal distribution table, the probability value corresponding to a z score of 1.1875 is 0.883
Recall, for x = 160, the probaility is 0.9927
Thus,
P(140 < x < 160) = 0.9927 - 0.883 = 0.1097
Converting to percentage, it is
0.1097 * 100 = 10.97%
d) The 30th percentile refers to all values of blood pressure below k, where k is the 30th percentile. This means that we would find
P(x < k) = 0.3
The z score corresponding to a probability value of 0.3 is - 0.52
Thus,
(k - 121)/16 = - 0.52
k - 121 = - 0.52 * 16 = - 8.32
k = - 8.32 + 121
k = 112.68
The pressure for the 30th percentile is 112.68
i need help with this question
Answers
The side AB = BD
7x + 10 = 9x - 2
SImplify for x :
Subtract 7x from both side :
7x + 10 - 7x = 9x - 7x - 2
10 = 2x - 2
Add 2 on both side :
10 + 2 = 2x - 2 + 2
12 = 2x
divide both side by 2 :
2x/2 = 12/2
x = 6
Julie can run 3 laps in 9 minutes. At this rate, how many laps can she run in 24 minutes?
Answers
Answer:
Julie can run 12 laps
Step-by-step explanation:
9 min = 3 laps
9 x 2 = 18 = 6 laps
9 cant fit into 24 again
24 - 18 = 6
6 + 6 = 12 laps
Which of the following are greater than 1/443% 5/90.151/121.4
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To solve this, we will need to convert all values to decimal.
First convert 1/4 to decimal:
[tex]\frac{1}{4}\text{ = 0.25}[/tex]Now convert 43% to decimal:
[tex]43\text{percent = }\frac{43}{100}\text{ = 0.43}[/tex]Simplify 5/9:
[tex]\frac{5}{9}\text{ = }0.56[/tex]0.15 is already a decimal value.
Simplify 1/12:
[tex]\frac{1}{12}\text{ = 0.083}[/tex]1.4 is already a decimal.
After simplifying, we have the following values:
0.25
0.43
0.56
0.15
0.083
1.4
We can see the values greater than 0.25 are:
0
15. [-/1 Points]DETAILSCURRENMEDMATH11 2.9.027.Divide the fraction. Express your answer to the nearest tenth. A calculator may be used.180,000120,000eBook16. [-/1 Points]DETAILSCURRENMEDMATH11 2.3.028.Divide the fraction. Express your answer to the nearest tenth. A calculator may be used.0.110.08eBook
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You have the following fraction:
180000/120000
First of all you cancel zeros:
180000/120000 = 18/12
next, you can simplify
18/12 = 9/6 = 3/2
finally 3/2 is:
3/2 = 1.5
Hence: 180000/120000 = 1.5
Furthermore, for the following fraction:
0.11/0.08
Here, you can use a calculator. The result is:
0.11/0.08 = 1.375
that is approximately
1.375 ≈ 1.4
For other fractions:
350/10,000 = 35/1,000 = 0.035
which is approximately
0.035 ≈ 0.04
6.01/7.2 = 0.834 ≈ 0.83
Really need help with this math assignment please help no
Answers
In a linear relationship, each step of x modifies the y value in the same way.
In the first table, when x = 1, y = 3 and when x = 2, y = 6. This is an increment of 3. If this is a linear relationship, we expect the next value of y to be the previous value plus 3, thus y = 9. But in the table shows x =3 and y = 12. We can rule out the first table.
With similar reasoning, in the second table, we see (1, 2) and (2, 5). This is an increase of the y value of 3. We expect the next value to be y = 8, but we see (3, 9). The second table is not a linear relationship.
In the third table, we see (1, -3) and (2, -5). This is a decrease of -2. We expect the next value of y to be y = -7, and we do see (3, -7). The next value should be y = -9, and the table shows (4, -9). Table 3 shows a linear relationship.
To be sure, let's see the 4th table. We see (1, -2) and (2, -4). This is a decrease of -2. The expected next value is y = -6, but the next point is (3, -2). Fourth table is not a linear relationship.
Thus, the correct answer is the top-right table.
Step by step solution thank you much appreciated
Answers
Answer:
11.796
Step-by-step explanation:
2nd term
[tex] {1.3}^{2} = 1.3 + \frac{1.3}{ \frac{10}{3} } [/tex]
[tex] {1.3}^{2} = 1.69[/tex]
add first term
[tex]27.8 + 1.69 = 29.49[/tex]
times by 0.4 or ×2/5
[tex]29.49 \times \frac{2}{5} = \frac{58.98}{5} [/tex]
[tex] = 11.796[/tex]
The Hornet's soccer team scored 5 goals in their last match.The other team, the Panthers, won by 3 goals. Which integerrepresents the number of goals that the Panthers won by?
Answers
The match was Hornet's vs Panthers
Hornets's scored 5 goals
Panthers won by 3 goals, this means that the panters scored 3 more goals than the Hornets.
That would be +3 goals.
Adina sets up a taste test of 3 different waters: tap, bottled in glass, and bottled in plastic. She puts these waters in identical cups and has a friend taste them one by one. The friend then tries to identify which water was in each cup. Assume that Adina's friend can't taste any difference and is randomly guessing. What is the probability that Adina's friend correctly identifies each of the 3 cups of water
Answers
Given
3 different waters: tap, bottled in glass, and bottled in plastic.
Find
probability that Adina's friend correctly identifies each of the 3 cups of water
Explanation
As we have given three different waters : tap , bottled in glass and bottled in plastic.
number of ways in which the person can make guesses about the 3 cups of water =
[tex]\begin{gathered} ^3P_3 \\ \frac{3!}{0!} \\ 6 \end{gathered}[/tex]number of ways in which person identifies correctly the 3 cups of water = 1
so , probability that Adina's friend correctly identifies each of the 3 cups of water =
[tex]P\text{ = }\frac{number\text{ of ways in which person identifies correctly the 3 cups of water}}{number\text{ of ways in which the person can make guesses about the 3 cups of water }}[/tex]so , P = 1/6
Final Answer
Therefore , the probability that adina's friend correctly identifies each of the cup of water = 1/6